Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,4,Mod(1,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, 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("2304.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.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: | \(135.940400653\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 2x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 384) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.06909\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1 |
$q$-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 | ||||||||
\(5\) | −17.4288 | −1.55888 | −0.779441 | − | 0.626475i | \(-0.784497\pi\) | ||||
−0.779441 | + | 0.626475i | \(0.784497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.99032 | 0.161462 | 0.0807310 | − | 0.996736i | \(-0.474275\pi\) | ||||
0.0807310 | + | 0.996736i | \(0.474275\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.6274 | 0.291299 | 0.145649 | − | 0.989336i | \(-0.453473\pi\) | ||||
0.145649 | + | 0.989336i | \(0.453473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −43.3156 | −0.924121 | −0.462061 | − | 0.886848i | \(-0.652890\pi\) | ||||
−0.462061 | + | 0.886848i | \(0.652890\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 37.8823 | 0.540459 | 0.270229 | − | 0.962796i | \(-0.412900\pi\) | ||||
0.270229 | + | 0.962796i | \(0.412900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.8823 | 0.964539 | 0.482270 | − | 0.876023i | \(-0.339813\pi\) | ||||
0.482270 | + | 0.876023i | \(0.339813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −191.204 | −1.73343 | −0.866714 | − | 0.498806i | \(-0.833772\pi\) | ||||
−0.866714 | + | 0.498806i | \(0.833772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 178.765 | 1.43012 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −138.918 | −0.889530 | −0.444765 | − | 0.895647i | \(-0.646713\pi\) | ||||
−0.444765 | + | 0.895647i | \(0.646713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 212.136 | 1.22906 | 0.614529 | − | 0.788894i | \(-0.289346\pi\) | ||||
0.614529 | + | 0.788894i | \(0.289346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −52.1177 | −0.251700 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −270.404 | −1.20146 | −0.600731 | − | 0.799451i | \(-0.705124\pi\) | ||||
−0.600731 | + | 0.799451i | \(0.705124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −441.411 | −1.68139 | −0.840693 | − | 0.541511i | \(-0.817852\pi\) | ||||
−0.840693 | + | 0.541511i | \(0.817852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.1177 | 0.227392 | 0.113696 | − | 0.993516i | \(-0.463731\pi\) | ||||
0.113696 | + | 0.993516i | \(0.463731\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 436.234 | 1.35386 | 0.676929 | − | 0.736049i | \(-0.263311\pi\) | ||||
0.676929 | + | 0.736049i | \(0.263311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.058 | −0.973930 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −278.348 | −0.721398 | −0.360699 | − | 0.932682i | \(-0.617462\pi\) | ||||
−0.360699 | + | 0.932682i | \(0.617462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.224 | −0.454101 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −830.039 | −1.83156 | −0.915778 | − | 0.401684i | \(-0.868425\pi\) | ||||
−0.915778 | + | 0.401684i | \(0.868425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −724.580 | −1.52087 | −0.760434 | − | 0.649416i | \(-0.775014\pi\) | ||||
−0.760434 | + | 0.649416i | \(0.775014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 754.940 | 1.44060 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 859.529 | 1.56729 | 0.783643 | − | 0.621211i | \(-0.213359\pi\) | ||||
0.783643 | + | 0.621211i | \(0.213359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 681.264 | 1.13875 | 0.569374 | − | 0.822078i | \(-0.307186\pi\) | ||||
0.569374 | + | 0.822078i | \(0.307186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 785.058 | 1.25869 | 0.629343 | − | 0.777128i | \(-0.283324\pi\) | ||||
0.629343 | + | 0.777128i | \(0.283324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31.7793 | 0.0470337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1018.82 | −1.45096 | −0.725481 | − | 0.688243i | \(-0.758382\pi\) | ||||
−0.725481 | + | 0.688243i | \(0.758382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −467.334 | −0.618031 | −0.309015 | − | 0.951057i | \(-0.599999\pi\) | ||||
−0.309015 | + | 0.951057i | \(0.599999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −660.244 | −0.842512 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 510.706 | 0.608256 | 0.304128 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304128 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −129.527 | −0.149210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1392.26 | −1.50360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −234.235 | −0.245186 | −0.122593 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122593 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 205.555 | 0.202509 | 0.101255 | − | 0.994861i | \(-0.467714\pi\) | ||||
0.101255 | + | 0.994861i | \(0.467714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 391.379 | 0.374405 | 0.187203 | − | 0.982321i | \(-0.440058\pi\) | ||||
0.187203 | + | 0.982321i | \(0.440058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −934.274 | −0.844109 | −0.422055 | − | 0.906570i | \(-0.638691\pi\) | ||||
−0.422055 | + | 0.906570i | \(0.638691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 584.123 | 0.513292 | 0.256646 | − | 0.966505i | \(-0.417383\pi\) | ||||
0.256646 | + | 0.966505i | \(0.417383\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 582.706 | 0.485101 | 0.242551 | − | 0.970139i | \(-0.422016\pi\) | ||||
0.242551 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3332.47 | 2.70221 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 113.280 | 0.0872635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1218.06 | −0.915145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −937.053 | −0.670501 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1461.03 | 1.02083 | 0.510416 | − | 0.859928i | \(-0.329491\pi\) | ||||
0.510416 | + | 0.859928i | \(0.329491\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −98.4323 | −0.0656494 | −0.0328247 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328247 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 238.873 | 0.155736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2171.06 | 1.35391 | 0.676956 | − | 0.736024i | \(-0.263299\pi\) | ||||
0.676956 | + | 0.736024i | \(0.263299\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1624.70 | −0.991407 | −0.495703 | − | 0.868492i | \(-0.665090\pi\) | ||||
−0.495703 | + | 0.868492i | \(0.665090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −460.333 | −0.269195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2421.17 | 1.38667 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −636.658 | −0.350047 | −0.175024 | − | 0.984564i | \(-0.556000\pi\) | ||||
−0.175024 | + | 0.984564i | \(0.556000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1819.34 | 0.980503 | 0.490252 | − | 0.871581i | \(-0.336905\pi\) | ||||
0.490252 | + | 0.871581i | \(0.336905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3697.29 | −1.91596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1656.50 | −0.842059 | −0.421029 | − | 0.907047i | \(-0.638331\pi\) | ||||
−0.421029 | + | 0.907047i | \(0.638331\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −571.761 | −0.279882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.82 | 1.07101 | 0.535505 | − | 0.844532i | \(-0.320121\pi\) | ||||
0.535505 | + | 0.844532i | \(0.320121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1667.01 | −0.772439 | −0.386219 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386219 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −320.761 | −0.146000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2500.53 | 1.09891 | 0.549457 | − | 0.835522i | \(-0.314835\pi\) | ||||
0.549457 | + | 0.835522i | \(0.314835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 534.562 | 0.230909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 378.742 | 0.158148 | 0.0790740 | − | 0.996869i | \(-0.474804\pi\) | ||||
0.0790740 | + | 0.996869i | \(0.474804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3093.88 | 1.27053 | 0.635265 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635265 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4712.82 | 1.87294 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 402.590 | 0.157435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3656.98 | 1.38539 | 0.692695 | − | 0.721230i | \(-0.256423\pi\) | ||||
0.692695 | + | 0.721230i | \(0.256423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2788.12 | 1.03986 | 0.519930 | − | 0.854209i | \(-0.325958\pi\) | ||||
0.519930 | + | 0.854209i | \(0.325958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1147.74 | 0.415091 | 0.207546 | − | 0.978225i | \(-0.433452\pi\) | ||||
0.207546 | + | 0.978225i | \(0.433452\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4842.73 | −1.72508 | −0.862542 | − | 0.505986i | \(-0.831129\pi\) | ||||
−0.862542 | + | 0.505986i | \(0.831129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −415.408 | −0.143625 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7693.29 | 2.62109 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 848.942 | 0.280969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3222.35 | 1.05135 | 0.525677 | − | 0.850684i | \(-0.323812\pi\) | ||||
0.525677 | + | 0.850684i | \(0.323812\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1117.50 | −0.354478 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 634.355 | 0.198446 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1640.89 | −0.499449 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4932.61 | −1.48122 | −0.740610 | − | 0.671935i | \(-0.765463\pi\) | ||||
−0.740610 | + | 0.671935i | \(0.765463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3619.49 | 1.05830 | 0.529150 | − | 0.848529i | \(-0.322511\pi\) | ||||
0.529150 | + | 0.848529i | \(0.322511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −305.759 | −0.0882320 | −0.0441160 | − | 0.999026i | \(-0.514047\pi\) | ||||
−0.0441160 | + | 0.999026i | \(0.514047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 639.648 | 0.179849 | 0.0899244 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899244 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7603.05 | −2.11050 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1744.94 | 0.472262 | 0.236131 | − | 0.971721i | \(-0.424121\pi\) | ||||
0.236131 | + | 0.971721i | \(0.424121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3357.29 | 0.897354 | 0.448677 | − | 0.893694i | \(-0.351895\pi\) | ||||
0.448677 | + | 0.893694i | \(0.351895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5822.24 | 1.51824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3460.15 | −0.891351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1317.45 | 0.331301 | 0.165650 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165650 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2032.01 | −0.504945 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3036.12 | 0.736917 | 0.368459 | − | 0.929644i | \(-0.379886\pi\) | ||||
0.368459 | + | 0.929644i | \(0.379886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −808.592 | −0.193990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1655.76 | 0.388206 | 0.194103 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194103 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4851.29 | 1.12458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5292.72 | 1.19964 | 0.599820 | − | 0.800135i | \(-0.295239\pi\) | ||||
0.599820 | + | 0.800135i | \(0.295239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8010.52 | 1.79559 | 0.897795 | − | 0.440414i | \(-0.145168\pi\) | ||||
0.897795 | + | 0.440414i | \(0.145168\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1899.80 | 0.416591 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5692.81 | 1.23483 | 0.617415 | − | 0.786638i | \(-0.288180\pi\) | ||||
0.617415 | + | 0.786638i | \(0.288180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2024.83 | 0.429861 | 0.214931 | − | 0.976629i | \(-0.431047\pi\) | ||||
0.214931 | + | 0.976629i | \(0.431047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −247.761 | −0.0520419 | −0.0260210 | − | 0.999661i | \(-0.508284\pi\) | ||||
−0.0260210 | + | 0.999661i | \(0.508284\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1319.96 | −0.271480 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3477.94 | −0.707905 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8133.61 | −1.62174 | −0.810871 | − | 0.585225i | \(-0.801006\pi\) | ||||
−0.810871 | + | 0.585225i | \(0.801006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14466.6 | 2.85518 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8282.12 | 1.60190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 191.732 | 0.0367152 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12628.6 | 2.37085 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2974.82 | −0.553035 | −0.276518 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276518 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4451.52 | 0.811648 | 0.405824 | − | 0.913951i | \(-0.366985\pi\) | ||||
0.405824 | + | 0.913951i | \(0.366985\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8273.75 | 1.49412 | 0.747061 | − | 0.664755i | \(-0.231464\pi\) | ||||
0.747061 | + | 0.664755i | \(0.231464\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −429.036 | −0.0760160 | −0.0380080 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380080 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1476.34 | −0.259119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3026.12 | 0.521293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7743.29 | −1.32160 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1304.48 | 0.218596 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8196.71 | −1.36112 | −0.680562 | − | 0.732691i | \(-0.738264\pi\) | ||||
−0.680562 | + | 0.732691i | \(0.738264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14980.6 | −2.44322 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2000.35 | −0.323341 | −0.161670 | − | 0.986845i | \(-0.551688\pi\) | ||||
−0.161670 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2254.46 | 0.358023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2024.62 | −0.318715 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7707.48 | −1.19239 | −0.596195 | − | 0.802840i | \(-0.703321\pi\) | ||||
−0.596195 | + | 0.802840i | \(0.703321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9681.98 | −1.48500 | −0.742499 | − | 0.669847i | \(-0.766360\pi\) | ||||
−0.742499 | + | 0.669847i | \(0.766360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10540.3 | 1.58925 | 0.794626 | − | 0.607099i | \(-0.207667\pi\) | ||||
0.794626 | + | 0.607099i | \(0.207667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11873.6 | −1.77518 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −514.158 | −0.0755884 | −0.0377942 | − | 0.999286i | \(-0.512033\pi\) | ||||
−0.0377942 | + | 0.999286i | \(0.512033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −477.826 | −0.0696641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13682.7 | −1.96214 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11272.4 | −1.60331 | −0.801657 | − | 0.597785i | \(-0.796048\pi\) | ||||
−0.801657 | + | 0.597785i | \(0.796048\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −832.350 | −0.116478 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6956.92 | −0.965726 | −0.482863 | − | 0.875696i | \(-0.660403\pi\) | ||||
−0.482863 | + | 0.875696i | \(0.660403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6017.30 | 0.822034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10201.3 | 1.38260 | 0.691299 | − | 0.722569i | \(-0.257039\pi\) | ||||
0.691299 | + | 0.722569i | \(0.257039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2461.56 | 0.328406 | 0.164203 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164203 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −553.877 | −0.0733200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 546.451 | 0.0712240 | 0.0356120 | − | 0.999366i | \(-0.488662\pi\) | ||||
0.0356120 | + | 0.999366i | \(0.488662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7243.25 | −0.936846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17756.8 | 2.26188 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2084.56 | 0.263529 | 0.131764 | − | 0.991281i | \(-0.457936\pi\) | ||||
0.131764 | + | 0.991281i | \(0.457936\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9710.59 | 1.20929 | 0.604643 | − | 0.796497i | \(-0.293316\pi\) | ||||
0.604643 | + | 0.796497i | \(0.293316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9188.81 | −1.13580 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2873.69 | −0.349984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6659.89 | 0.805160 | 0.402580 | − | 0.915385i | \(-0.368114\pi\) | ||||
0.402580 | + | 0.915385i | \(0.368114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2482.08 | −0.295727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8145.09 | 0.963438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10576.7 | 1.23318 | 0.616592 | − | 0.787283i | \(-0.288513\pi\) | ||||
0.616592 | + | 0.787283i | \(0.288513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4871.09 | −0.563901 | −0.281951 | − | 0.959429i | \(-0.590981\pi\) | ||||
−0.281951 | + | 0.959429i | \(0.590981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6772.00 | 0.772918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2166.72 | −0.245562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16916.7 | 1.89060 | 0.945302 | − | 0.326196i | \(-0.105767\pi\) | ||||
0.945302 | + | 0.326196i | \(0.105767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1163.88 | −0.129174 | −0.0645870 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645870 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15273.8 | −1.67196 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1856.28 | −0.201812 | −0.100906 | − | 0.994896i | \(-0.532174\pi\) | ||||
−0.100906 | + | 0.994896i | \(0.532174\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1472.21 | −0.157893 | −0.0789465 | − | 0.996879i | \(-0.525156\pi\) | ||||
−0.0789465 | + | 0.996879i | \(0.525156\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8901.02 | −0.948200 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9620.94 | −1.01123 | −0.505613 | − | 0.862761i | \(-0.668733\pi\) | ||||
−0.505613 | + | 0.862761i | \(0.668733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4691.06 | −0.489786 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2257.51 | 0.232602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3613.53 | −0.369877 | −0.184938 | − | 0.982750i | \(-0.559209\pi\) | ||||
−0.184938 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17710.7 | 1.78931 | 0.894654 | − | 0.446759i | \(-0.147422\pi\) | ||||
0.894654 | + | 0.446759i | \(0.147422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1674.57 | 0.168087 | 0.0840433 | − | 0.996462i | \(-0.473217\pi\) | ||||
0.0840433 | + | 0.996462i | \(0.473217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15208.3 | −1.50697 | −0.753484 | − | 0.657466i | \(-0.771628\pi\) | ||||
−0.753484 | + | 0.657466i | \(0.771628\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2570.26 | 0.253057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 681.406 | 0.0662391 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14280.1 | 1.37940 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6458.37 | 0.616056 | 0.308028 | − | 0.951377i | \(-0.400331\pi\) | ||||
0.308028 | + | 0.951377i | \(0.400331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11712.7 | 1.11030 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4082.45 | 0.382216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11337.7 | −1.05495 | −0.527474 | − | 0.849571i | \(-0.676861\pi\) | ||||
−0.527474 | + | 0.849571i | \(0.676861\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14946.7 | 1.37380 | 0.686898 | − | 0.726754i | \(-0.258972\pi\) | ||||
0.686898 | + | 0.726754i | \(0.258972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5262.51 | −0.480754 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2037.19 | 0.183865 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2631.77 | 0.236101 | 0.118051 | − | 0.993008i | \(-0.462336\pi\) | ||||
0.118051 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6907.45 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3582.58 | −0.315689 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12020.3 | −1.04674 | −0.523368 | − | 0.852107i | \(-0.675325\pi\) | ||||
−0.523368 | + | 0.852107i | \(0.675325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2347.57 | 0.203230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6821.29 | −0.583654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4636.04 | 0.394377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15846.1 | 1.33249 | 0.666247 | − | 0.745731i | \(-0.267899\pi\) | ||||
0.666247 | + | 0.745731i | \(0.267899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8891.64 | 0.743411 | 0.371706 | − | 0.928351i | \(-0.378773\pi\) | ||||
0.371706 | + | 0.928351i | \(0.378773\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8036.20 | 0.664255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24392.0 | 2.00477 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19120.0 | 1.55381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16283.3 | 1.31587 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3550.17 | −0.283705 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12833.5 | 1.01988 | 0.509940 | − | 0.860210i | \(-0.329667\pi\) | ||||
0.509940 | + | 0.860210i | \(0.329667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10180.6 | −0.800162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16257.0 | −1.27075 | −0.635375 | − | 0.772204i | \(-0.719155\pi\) | ||||
−0.635375 | + | 0.772204i | \(0.719155\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11097.1 | −0.857986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3046.59 | −0.234275 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1558.32 | −0.118542 | −0.0592712 | − | 0.998242i | \(-0.518878\pi\) | ||||
−0.0592712 | + | 0.998242i | \(0.518878\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2777.30 | −0.210138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9782.16 | −0.732272 | −0.366136 | − | 0.930561i | \(-0.619319\pi\) | ||||
−0.366136 | + | 0.930561i | \(0.619319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10155.9 | −0.756216 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7887.05 | 0.581094 | 0.290547 | − | 0.956861i | \(-0.406163\pi\) | ||||
0.290547 | + | 0.956861i | \(0.406163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21819.3 | 1.59914 | 0.799570 | − | 0.600573i | \(-0.205061\pi\) | ||||
0.799570 | + | 0.600573i | \(0.205061\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34180.5 | −2.47900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7190.22 | 0.518774 | 0.259387 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259387 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1397.48 | −0.0997884 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2958.12 | −0.210142 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13305.6 | −0.935569 | −0.467785 | − | 0.883843i | \(-0.654948\pi\) | ||||
−0.467785 | + | 0.883843i | \(0.654948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16945.9 | 1.18548 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8062.23 | 0.558307 | 0.279153 | − | 0.960246i | \(-0.409946\pi\) | ||||
0.279153 | + | 0.960246i | \(0.409946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1974.34 | −0.136034 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2185.21 | −0.149058 | −0.0745288 | − | 0.997219i | \(-0.523745\pi\) | ||||
−0.0745288 | + | 0.997219i | \(0.523745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3542.25 | 0.240418 | 0.120209 | − | 0.992749i | \(-0.461643\pi\) | ||||
0.120209 | + | 0.992749i | \(0.461643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21229.3 | 1.42660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6050.64 | 0.404593 | 0.202296 | − | 0.979324i | \(-0.435160\pi\) | ||||
0.202296 | + | 0.979324i | \(0.435160\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18895.7 | −1.25113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22514.2 | 1.48343 | 0.741713 | − | 0.670717i | \(-0.234014\pi\) | ||||
0.741713 | + | 0.670717i | \(0.234014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4255.88 | 0.277691 | 0.138845 | − | 0.990314i | \(-0.455661\pi\) | ||||
0.138845 | + | 0.990314i | \(0.455661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −228.949 | −0.0148663 | −0.00743315 | − | 0.999972i | \(-0.502366\pi\) | ||||
−0.00743315 | + | 0.999972i | \(0.502366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1527.17 | 0.0982102 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6013.82 | −0.384884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10243.5 | −0.649340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11429.2 | 0.721058 | 0.360529 | − | 0.932748i | \(-0.382596\pi\) | ||||
0.360529 | + | 0.932748i | \(0.382596\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25464.1 | −1.59136 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14469.9 | 0.900030 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29381.4 | −1.81045 | −0.905223 | − | 0.424938i | \(-0.860296\pi\) | ||||
−0.905223 | + | 0.424938i | \(0.860296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 249.316 | 0.0152909 | 0.00764546 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764546 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16025.8 | 0.973785 | 0.486893 | − | 0.873462i | \(-0.338130\pi\) | ||||
0.486893 | + | 0.873462i | \(0.338130\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8821.17 | −0.533530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14008.6 | −0.839511 | −0.419755 | − | 0.907637i | \(-0.637884\pi\) | ||||
−0.419755 | + | 0.907637i | \(0.637884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1715.56 | 0.102340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1011.91 | 0.0598152 | 0.0299076 | − | 0.999553i | \(-0.490479\pi\) | ||||
0.0299076 | + | 0.999553i | \(0.490479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23619.4 | 1.38985 | 0.694923 | − | 0.719084i | \(-0.255439\pi\) | ||||
0.694923 | + | 0.719084i | \(0.255439\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4163.28 | −0.242775 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26561.6 | 1.54194 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7700.41 | −0.443027 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25811.9 | −1.47842 | −0.739208 | − | 0.673477i | \(-0.764800\pi\) | ||||
−0.739208 | + | 0.673477i | \(0.764800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18255.2 | 1.03634 | 0.518172 | − | 0.855277i | \(-0.326613\pi\) | ||||
0.518172 | + | 0.855277i | \(0.326613\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −700.438 | −0.0395881 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20090.4 | 1.12553 | 0.562765 | − | 0.826617i | \(-0.309738\pi\) | ||||
0.562765 | + | 0.826617i | \(0.309738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37839.0 | −2.11059 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12056.8 | 0.666659 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16521.5 | 0.909563 | 0.454782 | − | 0.890603i | \(-0.349717\pi\) | ||||
0.454782 | + | 0.890603i | \(0.349717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28316.7 | 1.54549 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16721.7 | −0.908720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12431.4 | 0.669795 | 0.334897 | − | 0.942255i | \(-0.391298\pi\) | ||||
0.334897 | + | 0.942255i | \(0.391298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21600.4 | −1.15886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 614.674 | 0.0326976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 980.957 | 0.0519614 | 0.0259807 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259807 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40561.4 | −2.13048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8023.06 | 0.419644 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4115.73 | 0.213478 | 0.106739 | − | 0.994287i | \(-0.465959\pi\) | ||||
0.106739 | + | 0.994287i | \(0.465959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1170.35 | 0.0604522 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24833.5 | −1.27213 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20850.1 | −1.06367 | −0.531833 | − | 0.846849i | \(-0.678497\pi\) | ||||
−0.531833 | + | 0.846849i | \(0.678497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2428.92 | 0.122896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31517.2 | 1.58815 | 0.794074 | − | 0.607821i | \(-0.207956\pi\) | ||||
0.794074 | + | 0.607821i | \(0.207956\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9134.57 | 0.456549 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11415.0 | 0.568213 | 0.284106 | − | 0.958793i | \(-0.408303\pi\) | ||||
0.284106 | + | 0.958793i | \(0.408303\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5732.08 | 0.283028 | 0.141514 | − | 0.989936i | \(-0.454803\pi\) | ||||
0.141514 | + | 0.989936i | \(0.454803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11096.2 | 0.545683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2793.78 | −0.136291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7843.07 | −0.381089 | −0.190544 | − | 0.981679i | \(-0.561025\pi\) | ||||
−0.190544 | + | 0.981679i | \(0.561025\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31709.0 | −1.52849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29125.9 | −1.39841 | −0.699206 | − | 0.714920i | \(-0.746463\pi\) | ||||
−0.699206 | + | 0.714920i | \(0.746463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14228.5 | 0.677768 | 0.338884 | − | 0.940828i | \(-0.389951\pi\) | ||||
0.338884 | + | 0.940828i | \(0.389951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1746.71 | 0.0828771 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35953.6 | 1.69258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28133.7 | −1.31928 | −0.659641 | − | 0.751581i | \(-0.729292\pi\) | ||||
−0.659641 | + | 0.751581i | \(0.729292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14686.9 | 0.683377 | 0.341689 | − | 0.939813i | \(-0.389001\pi\) | ||||
0.341689 | + | 0.939813i | \(0.389001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37922.5 | 1.75770 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35260.9 | −1.62176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7240.08 | 0.331716 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28870.9 | 1.31267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21001.0 | 0.951214 | 0.475607 | − | 0.879658i | \(-0.342228\pi\) | ||||
0.475607 | + | 0.879658i | \(0.342228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1742.48 | 0.0783253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31385.6 | 1.40547 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13362.7 | −0.593892 | −0.296946 | − | 0.954894i | \(-0.595968\pi\) | ||||
−0.296946 | + | 0.954894i | \(0.595968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16525.5 | 0.731704 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8343.14 | 0.366654 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9965.13 | 0.436304 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39481.6 | −1.71582 | −0.857911 | − | 0.513798i | \(-0.828238\pi\) | ||||
−0.857911 | + | 0.513798i | \(0.828238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31157.5 | −1.34906 | −0.674531 | − | 0.738247i | \(-0.735654\pi\) | ||||
−0.674531 | + | 0.738247i | \(0.735654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38845.8 | −1.66958 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5121.87 | 0.219329 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21229.9 | 0.902470 | 0.451235 | − | 0.892405i | \(-0.350984\pi\) | ||||
0.451235 | + | 0.892405i | \(0.350984\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24603.8 | −1.04208 | −0.521041 | − | 0.853532i | \(-0.674456\pi\) | ||||
−0.521041 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13668.1 | 0.574710 | 0.287355 | − | 0.957824i | \(-0.407224\pi\) | ||||
0.287355 | + | 0.957824i | \(0.407224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27518.8 | 1.15291 | 0.576457 | − | 0.817127i | \(-0.304435\pi\) | ||||
0.576457 | + | 0.817127i | \(0.304435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12654.9 | −0.526369 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29054.1 | 1.20414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29951.5 | −1.23247 | −0.616234 | − | 0.787563i | \(-0.711343\pi\) | ||||
−0.616234 | + | 0.787563i | \(0.711343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5090.88 | −0.208737 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5590.49 | 0.227596 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3642.38 | −0.147761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51702.3 | 2.08265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5174.61 | 0.207708 | 0.103854 | − | 0.994593i | \(-0.466882\pi\) | ||||
0.103854 | + | 0.994593i | \(0.466882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9258.34 | 0.369030 | 0.184515 | − | 0.982830i | \(-0.440929\pi\) | ||||
0.184515 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24353.0 | −0.967304 | −0.483652 | − | 0.875260i | \(-0.660690\pi\) | ||||
−0.483652 | + | 0.875260i | \(0.660690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42283.4 | 1.66784 | 0.833919 | − | 0.551887i | \(-0.186092\pi\) | ||||
0.833919 | + | 0.551887i | \(0.186092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43581.4 | −1.71308 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10827.4 | −0.422663 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37231.0 | −1.44836 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2802.08 | −0.108260 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49843.1 | −1.91914 | −0.959568 | − | 0.281476i | \(-0.909176\pi\) | ||||
−0.959568 | + | 0.281476i | \(0.909176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8986.94 | −0.343675 | −0.171837 | − | 0.985125i | \(-0.554970\pi\) | ||||
−0.171837 | + | 0.985125i | \(0.554970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3693.99 | −0.140784 | −0.0703922 | − | 0.997519i | \(-0.522425\pi\) | ||||
−0.0703922 | + | 0.997519i | \(0.522425\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51613.0 | −1.95377 | −0.976886 | − | 0.213763i | \(-0.931428\pi\) | ||||
−0.976886 | + | 0.213763i | \(0.931428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4368.95 | 0.164825 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34847.4 | 1.30585 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6601.03 | −0.246534 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29469.5 | −1.09328 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10544.5 | −0.389886 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −53922.7 | −1.98061 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17016.8 | 0.622971 | 0.311486 | − | 0.950251i | \(-0.399173\pi\) | ||||
0.311486 | + | 0.950251i | \(0.399173\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2991.72 | −0.108804 | −0.0544019 | − | 0.998519i | \(-0.517325\pi\) | ||||
−0.0544019 | + | 0.998519i | \(0.517325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4966.55 | −0.180032 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −294.344 | −0.0105999 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5174.82 | 0.185747 | 0.0928736 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928736 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29509.3 | −1.05234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48338.6 | −1.71823 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49256.5 | −1.73956 | −0.869780 | − | 0.493439i | \(-0.835740\pi\) | ||||
−0.869780 | + | 0.493439i | \(0.835740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26685.3 | −0.939394 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7016.69 | −0.245423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31566.5 | −1.10057 | −0.550283 | − | 0.834978i | \(-0.685480\pi\) | ||||
−0.550283 | + | 0.834978i | \(0.685480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37575.6 | −1.30173 | −0.650866 | − | 0.759193i | \(-0.725594\pi\) | ||||
−0.650866 | + | 0.759193i | \(0.725594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84399.7 | 2.91456 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10289.3 | 0.353070 | 0.176535 | − | 0.984294i | \(-0.443511\pi\) | ||||
0.176535 | + | 0.984294i | \(0.443511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34005.2 | −1.16318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36779.7 | −1.25017 | −0.625085 | − | 0.780557i | \(-0.714936\pi\) | ||||
−0.625085 | + | 0.780557i | \(0.714936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63736.9 | −2.15966 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6492.15 | 0.218605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15210.9 | 0.510586 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48593.6 | −1.62102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35228.9 | 1.17155 | 0.585773 | − | 0.810475i | \(-0.300791\pi\) | ||||
0.585773 | + | 0.810475i | \(0.300791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15314.8 | 0.506155 | 0.253077 | − | 0.967446i | \(-0.418557\pi\) | ||||
0.253077 | + | 0.967446i | \(0.418557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4858.38 | −0.160074 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24074.3 | −0.788337 | −0.394168 | − | 0.919038i | \(-0.628967\pi\) | ||||
−0.394168 | + | 0.919038i | \(0.628967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5427.49 | 0.177184 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15244.1 | 0.494620 | 0.247310 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247310 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20003.7 | −0.647079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12259.6 | −0.394168 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37518.6 | −1.20264 | −0.601321 | − | 0.799008i | \(-0.705359\pi\) | ||||
−0.601321 | + | 0.799008i | \(0.705359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 84403.1 | 2.68920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1717.01 | −0.0545420 | −0.0272710 | − | 0.999628i | \(-0.508682\pi\) | ||||
−0.0272710 | + | 0.999628i | \(0.508682\pi\) | |||||||
\(998\) | 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 | 2304.4.a.by.1.1 | 4 | ||
3.2 | odd | 2 | 768.4.a.v.1.4 | 4 | |||
4.3 | odd | 2 | 2304.4.a.cb.1.1 | 4 | |||
8.3 | odd | 2 | inner | 2304.4.a.by.1.4 | 4 | ||
8.5 | even | 2 | 2304.4.a.cb.1.4 | 4 | |||
12.11 | even | 2 | 768.4.a.u.1.4 | 4 | |||
16.3 | odd | 4 | 1152.4.d.p.577.8 | 8 | |||
16.5 | even | 4 | 1152.4.d.p.577.1 | 8 | |||
16.11 | odd | 4 | 1152.4.d.p.577.2 | 8 | |||
16.13 | even | 4 | 1152.4.d.p.577.7 | 8 | |||
24.5 | odd | 2 | 768.4.a.u.1.1 | 4 | |||
24.11 | even | 2 | 768.4.a.v.1.1 | 4 | |||
48.5 | odd | 4 | 384.4.d.f.193.4 | yes | 8 | ||
48.11 | even | 4 | 384.4.d.f.193.8 | yes | 8 | ||
48.29 | odd | 4 | 384.4.d.f.193.5 | yes | 8 | ||
48.35 | even | 4 | 384.4.d.f.193.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.f.193.1 | ✓ | 8 | 48.35 | even | 4 | ||
384.4.d.f.193.4 | yes | 8 | 48.5 | odd | 4 | ||
384.4.d.f.193.5 | yes | 8 | 48.29 | odd | 4 | ||
384.4.d.f.193.8 | yes | 8 | 48.11 | even | 4 | ||
768.4.a.u.1.1 | 4 | 24.5 | odd | 2 | |||
768.4.a.u.1.4 | 4 | 12.11 | even | 2 | |||
768.4.a.v.1.1 | 4 | 24.11 | even | 2 | |||
768.4.a.v.1.4 | 4 | 3.2 | odd | 2 | |||
1152.4.d.p.577.1 | 8 | 16.5 | even | 4 | |||
1152.4.d.p.577.2 | 8 | 16.11 | odd | 4 | |||
1152.4.d.p.577.7 | 8 | 16.13 | even | 4 | |||
1152.4.d.p.577.8 | 8 | 16.3 | odd | 4 | |||
2304.4.a.by.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2304.4.a.by.1.4 | 4 | 8.3 | odd | 2 | inner | ||
2304.4.a.cb.1.1 | 4 | 4.3 | odd | 2 | |||
2304.4.a.cb.1.4 | 4 | 8.5 | even | 2 |