Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(1,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(106.203438010\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
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 | \(\chi\) | \(=\) | 1800.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.1918 | 0.526051 | 0.263025 | − | 0.964789i | \(-0.415280\pi\) | ||||
0.263025 | + | 0.964789i | \(0.415280\pi\) | |||||||
\(12\) | 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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 205.687 | 1.86472 | 0.932362 | − | 0.361526i | \(-0.117744\pi\) | ||||
0.932362 | + | 0.361526i | \(0.117744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 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 | \(-0.0911291\pi\) | ||||
0.959298 | + | 0.282396i | \(0.0911291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 320.788 | 1.22192 | 0.610959 | − | 0.791662i | \(-0.290784\pi\) | ||||
0.610959 | + | 0.791662i | \(0.290784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −83.1214 | −0.294788 | −0.147394 | − | 0.989078i | \(-0.547089\pi\) | ||||
−0.147394 | + | 0.989078i | \(0.547089\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −276.434 | −0.857915 | −0.428957 | − | 0.903325i | \(-0.641119\pi\) | ||||
−0.428957 | + | 0.903325i | \(0.641119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −64.2122 | −0.187208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 390.888 | 1.01307 | 0.506534 | − | 0.862220i | \(-0.330927\pi\) | ||||
0.506534 | + | 0.862220i | \(0.330927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −779.110 | −1.71918 | −0.859589 | − | 0.510986i | \(-0.829280\pi\) | ||||
−0.859589 | + | 0.510986i | \(0.829280\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −483.171 | −1.01416 | −0.507080 | − | 0.861899i | \(-0.669275\pi\) | ||||
−0.507080 | + | 0.861899i | \(0.669275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −123.707 | −0.225571 | −0.112785 | − | 0.993619i | \(-0.535977\pi\) | ||||
−0.112785 | + | 0.993619i | \(0.535977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | \(-0.285404\pi\) | ||||
0.624251 | + | 0.781224i | \(0.285404\pi\) | |||||||
\(74\) | 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 | \(-0.602965\pi\) | ||||
−0.317861 | + | 0.948137i | \(0.602965\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 94.8490 | 0.112966 | 0.0564830 | − | 0.998404i | \(-0.482011\pi\) | ||||
0.0564830 | + | 0.998404i | \(0.482011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1031.84 | 1.18864 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −252.041 | −0.263823 | −0.131912 | − | 0.991261i | \(-0.542112\pi\) | ||||
−0.131912 | + | 0.991261i | \(0.542112\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 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 | \(-0.286315\pi\) | ||||
0.622013 | + | 0.783007i | \(0.286315\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 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 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 507.314 | 0.390802 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −962.673 | −0.723271 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −334.343 | −0.222990 | −0.111495 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111495 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(132\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1186.02 | −0.693564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | \(-0.788915\pi\) | ||||
−0.788060 | + | 0.615598i | \(0.788915\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3434.34 | −1.68114 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2816.33 | −1.35333 | −0.676663 | − | 0.736292i | \(-0.736575\pi\) | ||||
−0.676663 | + | 0.736292i | \(0.736575\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1836.41 | 0.850933 | 0.425466 | − | 0.904974i | \(-0.360110\pi\) | ||||
0.425466 | + | 0.904974i | \(0.360110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1621.99 | 0.738274 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1224.22 | 0.538011 | 0.269006 | − | 0.963139i | \(-0.413305\pi\) | ||||
0.269006 | + | 0.963139i | \(0.413305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2729.58 | −1.13977 | −0.569883 | − | 0.821726i | \(-0.693011\pi\) | ||||
−0.569883 | + | 0.821726i | \(0.693011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2642.36 | 1.08511 | 0.542555 | − | 0.840020i | \(-0.317457\pi\) | ||||
0.542555 | + | 0.840020i | \(0.317457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −583.118 | −0.228031 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | \(-0.828362\pi\) | ||||
−0.858111 | + | 0.513464i | \(0.828362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −823.941 | −0.297987 | −0.148993 | − | 0.988838i | \(-0.547603\pi\) | ||||
−0.148993 | + | 0.988838i | \(0.547603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3329.70 | −1.18611 | −0.593055 | − | 0.805162i | \(-0.702078\pi\) | ||||
−0.593055 | + | 0.805162i | \(0.702078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 139.982 | 0.0483980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5529.21 | −1.72971 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(-0.520847\pi\) | ||||
−0.0654458 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3657.93 | −0.942303 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1149.46 | −0.289057 | −0.144529 | − | 0.989501i | \(-0.546167\pi\) | ||||
−0.144529 | + | 0.989501i | \(0.546167\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2067.34 | 0.484705 | 0.242352 | − | 0.970188i | \(-0.422081\pi\) | ||||
0.242352 | + | 0.970188i | \(0.422081\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.593497\pi\) | ||||
−0.289524 | + | 0.957171i | \(0.593497\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6280.54 | 1.33333 | 0.666665 | − | 0.745357i | \(-0.267721\pi\) | ||||
0.666665 | + | 0.745357i | \(0.267721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5233.40 | 1.09927 | 0.549635 | − | 0.835405i | \(-0.314767\pi\) | ||||
0.549635 | + | 0.835405i | \(0.314767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5356.17 | −1.10162 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3989.83 | −0.812097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2438.21 | −0.486149 | −0.243074 | − | 0.970008i | \(-0.578156\pi\) | ||||
−0.243074 | + | 0.970008i | \(0.578156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12711.0 | −2.45852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1387.87 | 0.265766 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7910.44 | −1.47060 | −0.735298 | − | 0.677744i | \(-0.762958\pi\) | ||||
−0.735298 | + | 0.677744i | \(0.762958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | \(-0.667774\pi\) | ||||
−0.503009 | + | 0.864281i | \(0.667774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3724.09 | −0.659829 | −0.329915 | − | 0.944011i | \(-0.607020\pi\) | ||||
−0.329915 | + | 0.944011i | \(0.607020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −160.898 | −0.0282400 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1798.47 | −0.309812 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9524.43 | −1.53955 | −0.769776 | − | 0.638314i | \(-0.779632\pi\) | ||||
−0.769776 | + | 0.638314i | \(0.779632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | \(-0.539800\pi\) | ||||
−0.124711 | + | 0.992193i | \(0.539800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 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 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4069.23 | 0.542893 | 0.271447 | − | 0.962453i | \(-0.412498\pi\) | ||||
0.271447 | + | 0.962453i | \(0.412498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8608.89 | 1.07209 | 0.536044 | − | 0.844190i | \(-0.319918\pi\) | ||||
0.536044 | + | 0.844190i | \(0.319918\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13008.8 | 1.54992 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3738.23 | −0.435858 | −0.217929 | − | 0.975965i | \(-0.569930\pi\) | ||||
−0.217929 | + | 0.975965i | \(0.569930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8993.95 | −1.04118 | −0.520592 | − | 0.853806i | \(-0.674289\pi\) | ||||
−0.520592 | + | 0.853806i | \(0.674289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8067.48 | 0.914316 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | \(-0.406235\pi\) | ||||
0.290329 | + | 0.956927i | \(0.406235\pi\) | |||||||
\(434\) | 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 | \(-0.337361\pi\) | ||||
0.489003 | + | 0.872282i | \(0.337361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5951.29 | 0.625521 | 0.312760 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312760 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6156.51 | 0.642791 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13912.7 | 1.42409 | 0.712047 | − | 0.702132i | \(-0.247768\pi\) | ||||
0.712047 | + | 0.702132i | \(0.247768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1595.25 | −0.155074 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2566.49 | −0.235894 | −0.117947 | − | 0.993020i | \(-0.537631\pi\) | ||||
−0.117947 | + | 0.993020i | \(0.537631\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5222.51 | −0.462943 | −0.231471 | − | 0.972842i | \(-0.574354\pi\) | ||||
−0.231471 | + | 0.972842i | \(0.574354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5305.27 | −0.451307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2456.04 | −0.206528 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −634.460 | −0.0530459 | −0.0265229 | − | 0.999648i | \(-0.508444\pi\) | ||||
−0.0265229 | + | 0.999648i | \(0.508444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10061.6 | −0.831669 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30140.0 | 2.47720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19824.0 | −1.61102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1232.35 | −0.0984807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18078.4 | 1.43669 | 0.718347 | − | 0.695685i | \(-0.244899\pi\) | ||||
0.718347 | + | 0.695685i | \(0.244899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24815.3 | 1.93972 | 0.969860 | − | 0.243661i | \(-0.0783486\pi\) | ||||
0.969860 | + | 0.243661i | \(0.0783486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | \(-0.625162\pi\) | ||||
−0.383155 | + | 0.923684i | \(0.625162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5136.73 | 0.388660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15251.4 | 1.12368 | 0.561838 | − | 0.827247i | \(-0.310094\pi\) | ||||
0.561838 | + | 0.827247i | \(0.310094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2683.78 | −0.196695 | −0.0983474 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983474 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7369.88 | 0.531737 | 0.265868 | − | 0.964009i | \(-0.414341\pi\) | ||||
0.265868 | + | 0.964009i | \(0.414341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 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 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1583.69 | −0.101844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8099.23 | 0.513414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18711.0 | 1.18046 | 0.590232 | − | 0.807233i | \(-0.299036\pi\) | ||||
0.590232 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3968.19 | 0.246821 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25792.2 | −1.58929 | −0.794643 | − | 0.607077i | \(-0.792342\pi\) | ||||
−0.794643 | + | 0.607077i | \(0.792342\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20256.7 | 1.24237 | 0.621186 | − | 0.783663i | \(-0.286651\pi\) | ||||
0.621186 | + | 0.783663i | \(0.286651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6655.43 | −0.404408 | −0.202204 | − | 0.979343i | \(-0.564810\pi\) | ||||
−0.202204 | + | 0.979343i | \(0.564810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14952.6 | −0.904375 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8490.91 | 0.508844 | 0.254422 | − | 0.967093i | \(-0.418115\pi\) | ||||
0.254422 | + | 0.967093i | \(0.418115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15543.8 | −0.918816 | −0.459408 | − | 0.888225i | \(-0.651938\pi\) | ||||
−0.459408 | + | 0.888225i | \(0.651938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13519.8 | −0.795553 | −0.397777 | − | 0.917482i | \(-0.630218\pi\) | ||||
−0.397777 | + | 0.917482i | \(0.630218\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1724.41 | −0.100104 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9272.95 | −0.533499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11565.3 | −0.662421 | −0.331211 | − | 0.943557i | \(-0.607457\pi\) | ||||
−0.331211 | + | 0.943557i | \(0.607457\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28227.5 | −1.60247 | −0.801235 | − | 0.598350i | \(-0.795823\pi\) | ||||
−0.801235 | + | 0.598350i | \(0.795823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4208.31 | 0.237850 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9746.71 | −0.529674 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | \(-0.583622\pi\) | ||||
−0.259695 | + | 0.965691i | \(0.583622\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 68113.4 | 3.57765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26201.8 | 1.29374 | 0.646871 | − | 0.762600i | \(-0.276077\pi\) | ||||
0.646871 | + | 0.762600i | \(0.276077\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15051.7 | 0.734282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24451.7 | 1.18809 | 0.594045 | − | 0.804432i | \(-0.297530\pi\) | ||||
0.594045 | + | 0.804432i | \(0.297530\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28935.9 | 1.37835 | 0.689176 | − | 0.724594i | \(-0.257973\pi\) | ||||
0.689176 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2512.27 | −0.116895 | −0.0584477 | − | 0.998290i | \(-0.518615\pi\) | ||||
−0.0584477 | + | 0.998290i | \(0.518615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18988.0 | 0.873320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3593.34 | −0.164635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2650.18 | 0.120036 | 0.0600182 | − | 0.998197i | \(-0.480884\pi\) | ||||
0.0600182 | + | 0.998197i | \(0.480884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | \(-0.316602\pi\) | ||||
0.544810 | + | 0.838560i | \(0.316602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8399.07 | 0.371887 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14944.8 | 0.656775 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29725.5 | 1.29183 | 0.645917 | − | 0.763408i | \(-0.276475\pi\) | ||||
0.645917 | + | 0.763408i | \(0.276475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2050.38 | −0.0887773 | −0.0443887 | − | 0.999014i | \(-0.514134\pi\) | ||||
−0.0443887 | + | 0.999014i | \(0.514134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4920.11 | −0.210689 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | \(-0.328106\pi\) | ||||
0.514154 | + | 0.857698i | \(0.328106\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1951.00 | 0.0811504 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16073.7 | 0.652065 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7706.51 | −0.303978 | −0.151989 | − | 0.988382i | \(-0.548568\pi\) | ||||
−0.151989 | + | 0.988382i | \(0.548568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8566.92 | −0.334422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7644.85 | 0.297400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13416.4 | 0.513066 | 0.256533 | − | 0.966536i | \(-0.417420\pi\) | ||||
0.256533 | + | 0.966536i | \(0.417420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29538.2 | 1.12575 | 0.562875 | − | 0.826542i | \(-0.309695\pi\) | ||||
0.562875 | + | 0.826542i | \(0.309695\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1950.88 | 0.0738490 | 0.0369245 | − | 0.999318i | \(-0.488244\pi\) | ||||
0.0369245 | + | 0.999318i | \(0.488244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12935.4 | 0.488009 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16362.6 | −0.613162 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2776.26 | −0.102996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11876.6 | −0.439142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3507.55 | 0.128408 | 0.0642042 | − | 0.997937i | \(-0.479549\pi\) | ||||
0.0642042 | + | 0.997937i | \(0.479549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | \(-0.349071\pi\) | ||||
0.456589 | + | 0.889678i | \(0.349071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11570.6 | 0.412623 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26416.7 | 0.932941 | 0.466471 | − | 0.884537i | \(-0.345525\pi\) | ||||
0.466471 | + | 0.884537i | \(0.345525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3800.84 | −0.133800 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1936.70 | −0.0675231 | −0.0337616 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337616 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5401.70 | −0.181887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79870.0 | 2.68101 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36159.0 | −1.19506 | −0.597528 | − | 0.801848i | \(-0.703850\pi\) | ||||
−0.597528 | + | 0.801848i | \(0.703850\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53046.3 | −1.72117 | −0.860587 | − | 0.509303i | \(-0.829903\pi\) | ||||
−0.860587 | + | 0.509303i | \(0.829903\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17097.0 | −0.549699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16425.7 | −0.526517 | −0.263259 | − | 0.964725i | \(-0.584797\pi\) | ||||
−0.263259 | + | 0.964725i | \(0.584797\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 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 | 1800.4.a.bk.1.1 | 2 | ||
3.2 | odd | 2 | 200.4.a.k.1.2 | 2 | |||
5.2 | odd | 4 | 360.4.f.e.289.2 | 4 | |||
5.3 | odd | 4 | 360.4.f.e.289.1 | 4 | |||
5.4 | even | 2 | 1800.4.a.bp.1.2 | 2 | |||
12.11 | even | 2 | 400.4.a.x.1.1 | 2 | |||
15.2 | even | 4 | 40.4.c.a.9.2 | ✓ | 4 | ||
15.8 | even | 4 | 40.4.c.a.9.3 | yes | 4 | ||
15.14 | odd | 2 | 200.4.a.l.1.1 | 2 | |||
20.3 | even | 4 | 720.4.f.m.289.1 | 4 | |||
20.7 | even | 4 | 720.4.f.m.289.2 | 4 | |||
24.5 | odd | 2 | 1600.4.a.cl.1.1 | 2 | |||
24.11 | even | 2 | 1600.4.a.cf.1.2 | 2 | |||
60.23 | odd | 4 | 80.4.c.c.49.2 | 4 | |||
60.47 | odd | 4 | 80.4.c.c.49.3 | 4 | |||
60.59 | even | 2 | 400.4.a.v.1.2 | 2 | |||
120.29 | odd | 2 | 1600.4.a.ce.1.2 | 2 | |||
120.53 | even | 4 | 320.4.c.g.129.2 | 4 | |||
120.59 | even | 2 | 1600.4.a.cm.1.1 | 2 | |||
120.77 | even | 4 | 320.4.c.g.129.3 | 4 | |||
120.83 | odd | 4 | 320.4.c.h.129.3 | 4 | |||
120.107 | odd | 4 | 320.4.c.h.129.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.c.a.9.2 | ✓ | 4 | 15.2 | even | 4 | ||
40.4.c.a.9.3 | yes | 4 | 15.8 | even | 4 | ||
80.4.c.c.49.2 | 4 | 60.23 | odd | 4 | |||
80.4.c.c.49.3 | 4 | 60.47 | odd | 4 | |||
200.4.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
200.4.a.l.1.1 | 2 | 15.14 | odd | 2 | |||
320.4.c.g.129.2 | 4 | 120.53 | even | 4 | |||
320.4.c.g.129.3 | 4 | 120.77 | even | 4 | |||
320.4.c.h.129.2 | 4 | 120.107 | odd | 4 | |||
320.4.c.h.129.3 | 4 | 120.83 | odd | 4 | |||
360.4.f.e.289.1 | 4 | 5.3 | odd | 4 | |||
360.4.f.e.289.2 | 4 | 5.2 | odd | 4 | |||
400.4.a.v.1.2 | 2 | 60.59 | even | 2 | |||
400.4.a.x.1.1 | 2 | 12.11 | even | 2 | |||
720.4.f.m.289.1 | 4 | 20.3 | even | 4 | |||
720.4.f.m.289.2 | 4 | 20.7 | even | 4 | |||
1600.4.a.ce.1.2 | 2 | 120.29 | odd | 2 | |||
1600.4.a.cf.1.2 | 2 | 24.11 | even | 2 | |||
1600.4.a.cl.1.1 | 2 | 24.5 | odd | 2 | |||
1600.4.a.cm.1.1 | 2 | 120.59 | even | 2 | |||
1800.4.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.bp.1.2 | 2 | 5.4 | even | 2 |