Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, 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("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.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: | \(76.4664753674\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{201}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 648) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.58872\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-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 | ||||||||
\(5\) | −18.1774 | −1.62584 | −0.812920 | − | 0.582375i | \(-0.802123\pi\) | ||||
−0.812920 | + | 0.582375i | \(0.802123\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.822553 | 0.0444137 | 0.0222068 | − | 0.999753i | \(-0.492931\pi\) | ||||
0.0222068 | + | 0.999753i | \(0.492931\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −65.5323 | −1.79625 | −0.898125 | − | 0.439741i | \(-0.855070\pi\) | ||||
−0.898125 | + | 0.439741i | \(0.855070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31.8226 | 0.678922 | 0.339461 | − | 0.940620i | \(-0.389755\pi\) | ||||
0.339461 | + | 0.940620i | \(0.389755\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −124.420 | −1.77507 | −0.887535 | − | 0.460741i | \(-0.847584\pi\) | ||||
−0.887535 | + | 0.460741i | \(0.847584\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −27.8872 | −0.336725 | −0.168362 | − | 0.985725i | \(-0.553848\pi\) | ||||
−0.168362 | + | 0.985725i | \(0.553848\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −43.1774 | −0.391440 | −0.195720 | − | 0.980660i | \(-0.562704\pi\) | ||||
−0.195720 | + | 0.980660i | \(0.562704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 205.420 | 1.64336 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −39.8226 | −0.254995 | −0.127498 | − | 0.991839i | \(-0.540695\pi\) | ||||
−0.127498 | + | 0.991839i | \(0.540695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −294.839 | −1.70822 | −0.854108 | − | 0.520096i | \(-0.825896\pi\) | ||||
−0.854108 | + | 0.520096i | \(0.825896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.9519 | −0.0722096 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −104.177 | −0.462883 | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231441 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −307.645 | −1.17186 | −0.585928 | − | 0.810363i | \(-0.699270\pi\) | ||||
−0.585928 | + | 0.810363i | \(0.699270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 361.081 | 1.28057 | 0.640283 | − | 0.768139i | \(-0.278817\pi\) | ||||
0.640283 | + | 0.768139i | \(0.278817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 397.645 | 1.23410 | 0.617048 | − | 0.786926i | \(-0.288328\pi\) | ||||
0.617048 | + | 0.786926i | \(0.288328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.323 | −0.998027 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −107.161 | −0.277730 | −0.138865 | − | 0.990311i | \(-0.544345\pi\) | ||||
−0.138865 | + | 0.990311i | \(0.544345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1191.21 | 2.92041 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 188.935 | 0.416903 | 0.208452 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208452 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −99.0166 | −0.207832 | −0.103916 | − | 0.994586i | \(-0.533137\pi\) | ||||
−0.103916 | + | 0.994586i | \(0.533137\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −578.453 | −1.10382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −425.048 | −0.775043 | −0.387522 | − | 0.921861i | \(-0.626669\pi\) | ||||
−0.387522 | + | 0.921861i | \(0.626669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −445.532 | −0.744718 | −0.372359 | − | 0.928089i | \(-0.621451\pi\) | ||||
−0.372359 | + | 0.928089i | \(0.621451\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −499.806 | −0.801341 | −0.400670 | − | 0.916222i | \(-0.631223\pi\) | ||||
−0.400670 | + | 0.916222i | \(0.631223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −53.9038 | −0.0797781 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −570.275 | −0.812164 | −0.406082 | − | 0.913837i | \(-0.633105\pi\) | ||||
−0.406082 | + | 0.913837i | \(0.633105\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1308.74 | 1.73076 | 0.865381 | − | 0.501115i | \(-0.167077\pi\) | ||||
0.865381 | + | 0.501115i | \(0.167077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2261.63 | 2.88598 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1323.00 | −1.57570 | −0.787852 | − | 0.615864i | \(-0.788807\pi\) | ||||
−0.787852 | + | 0.615864i | \(0.788807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.1757 | 0.0301534 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 506.919 | 0.547461 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 944.872 | 0.989044 | 0.494522 | − | 0.869165i | \(-0.335343\pi\) | ||||
0.494522 | + | 0.869165i | \(0.335343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1398.10 | 1.37739 | 0.688694 | − | 0.725052i | \(-0.258185\pi\) | ||||
0.688694 | + | 0.725052i | \(0.258185\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 960.551 | 0.918892 | 0.459446 | − | 0.888206i | \(-0.348048\pi\) | ||||
0.459446 | + | 0.888206i | \(0.348048\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1935.87 | 1.74905 | 0.874523 | − | 0.484983i | \(-0.161174\pi\) | ||||
0.874523 | + | 0.484983i | \(0.161174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1305.40 | −1.14711 | −0.573555 | − | 0.819167i | \(-0.694436\pi\) | ||||
−0.573555 | + | 0.819167i | \(0.694436\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1094.03 | −0.910777 | −0.455389 | − | 0.890293i | \(-0.650500\pi\) | ||||
−0.455389 | + | 0.890293i | \(0.650500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 784.856 | 0.636419 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −102.342 | −0.0788374 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2963.49 | 2.22651 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1461.82 | −1.04600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1301.05 | 0.909050 | 0.454525 | − | 0.890734i | \(-0.349809\pi\) | ||||
0.454525 | + | 0.890734i | \(0.349809\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1957.67 | 1.30566 | 0.652832 | − | 0.757503i | \(-0.273581\pi\) | ||||
0.652832 | + | 0.757503i | \(0.273581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.9387 | −0.0149552 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2553.97 | 1.59270 | 0.796351 | − | 0.604834i | \(-0.206761\pi\) | ||||
0.796351 | + | 0.604834i | \(0.206761\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −205.260 | −0.125252 | −0.0626258 | − | 0.998037i | \(-0.519947\pi\) | ||||
−0.0626258 | + | 0.998037i | \(0.519947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2085.41 | −1.21951 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 723.872 | 0.414582 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −164.240 | −0.0903027 | −0.0451513 | − | 0.998980i | \(-0.514377\pi\) | ||||
−0.0451513 | + | 0.998980i | \(0.514377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3427.71 | −1.84731 | −0.923654 | − | 0.383228i | \(-0.874812\pi\) | ||||
−0.923654 | + | 0.383228i | \(0.874812\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5359.42 | 2.77729 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −988.085 | −0.502279 | −0.251139 | − | 0.967951i | \(-0.580805\pi\) | ||||
−0.251139 | + | 0.967951i | \(0.580805\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −35.5157 | −0.0173853 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2845.45 | 1.36732 | 0.683660 | − | 0.729801i | \(-0.260387\pi\) | ||||
0.683660 | + | 0.729801i | \(0.260387\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3205.89 | −1.48550 | −0.742752 | − | 0.669566i | \(-0.766480\pi\) | ||||
−0.742752 | + | 0.669566i | \(0.766480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1184.33 | −0.539065 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1785.63 | −0.784735 | −0.392368 | − | 0.919808i | \(-0.628344\pi\) | ||||
−0.392368 | + | 0.919808i | \(0.628344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 168.969 | 0.0729875 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1318.84 | −0.550696 | −0.275348 | − | 0.961345i | \(-0.588793\pi\) | ||||
−0.275348 | + | 0.961345i | \(0.588793\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3462.97 | 1.42210 | 0.711051 | − | 0.703141i | \(-0.248220\pi\) | ||||
0.711051 | + | 0.703141i | \(0.248220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1893.68 | 0.752574 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8153.51 | 3.18847 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1591.31 | 0.602844 | 0.301422 | − | 0.953491i | \(-0.402539\pi\) | ||||
0.301422 | + | 0.953491i | \(0.402539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −764.456 | −0.285113 | −0.142556 | − | 0.989787i | \(-0.545532\pi\) | ||||
−0.142556 | + | 0.989787i | \(0.545532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1191.63 | −0.430965 | −0.215483 | − | 0.976508i | \(-0.569132\pi\) | ||||
−0.215483 | + | 0.976508i | \(0.569132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2708.20 | 0.964719 | 0.482360 | − | 0.875973i | \(-0.339780\pi\) | ||||
0.482360 | + | 0.875973i | \(0.339780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −32.7562 | −0.0113253 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5592.20 | 1.90525 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1827.52 | 0.604842 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3298.95 | 1.07635 | 0.538173 | − | 0.842834i | \(-0.319115\pi\) | ||||
0.538173 | + | 0.842834i | \(0.319115\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6563.54 | −2.08200 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −242.521 | −0.0758682 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3959.35 | −1.20513 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2521.67 | 0.757234 | 0.378617 | − | 0.925553i | \(-0.376400\pi\) | ||||
0.378617 | + | 0.925553i | \(0.376400\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3314.67 | −0.969173 | −0.484586 | − | 0.874743i | \(-0.661030\pi\) | ||||
−0.484586 | + | 0.874743i | \(0.661030\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4129.66 | −1.19168 | −0.595842 | − | 0.803101i | \(-0.703182\pi\) | ||||
−0.595842 | + | 0.803101i | \(0.703182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −986.257 | −0.277304 | −0.138652 | − | 0.990341i | \(-0.544277\pi\) | ||||
−0.138652 | + | 0.990341i | \(0.544277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7228.17 | −2.00644 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 358.998 | 0.0971618 | 0.0485809 | − | 0.998819i | \(-0.484530\pi\) | ||||
0.0485809 | + | 0.998819i | \(0.484530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2042.03 | 0.545804 | 0.272902 | − | 0.962042i | \(-0.412016\pi\) | ||||
0.272902 | + | 0.962042i | \(0.412016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6222.57 | 1.62263 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −887.443 | −0.228610 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2609.69 | −0.656264 | −0.328132 | − | 0.944632i | \(-0.606419\pi\) | ||||
−0.328132 | + | 0.944632i | \(0.606419\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2829.52 | 0.703124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 878.837 | 0.213309 | 0.106654 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106654 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −85.6915 | −0.0205583 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3217.33 | −0.754332 | −0.377166 | − | 0.926146i | \(-0.623101\pi\) | ||||
−0.377166 | + | 0.926146i | \(0.623101\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1947.91 | 0.451544 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7978.38 | −1.80837 | −0.904183 | − | 0.427146i | \(-0.859519\pi\) | ||||
−0.904183 | + | 0.427146i | \(0.859519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4248.21 | −0.952251 | −0.476126 | − | 0.879377i | \(-0.657959\pi\) | ||||
−0.476126 | + | 0.879377i | \(0.657959\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13461.6 | −2.95188 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 831.035 | 0.180260 | 0.0901301 | − | 0.995930i | \(-0.471272\pi\) | ||||
0.0901301 | + | 0.995930i | \(0.471272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2962.00 | 0.628819 | 0.314410 | − | 0.949287i | \(-0.398193\pi\) | ||||
0.314410 | + | 0.949287i | \(0.398193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4430.84 | 0.930693 | 0.465346 | − | 0.885129i | \(-0.345930\pi\) | ||||
0.465346 | + | 0.885129i | \(0.345930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −253.054 | −0.0520465 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10567.2 | 2.15087 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3422.86 | 0.682477 | 0.341239 | − | 0.939977i | \(-0.389154\pi\) | ||||
0.341239 | + | 0.939977i | \(0.389154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3434.36 | −0.677818 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1374.02 | −0.265757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 297.009 | 0.0568747 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1799.87 | 0.337902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −139.734 | −0.0259774 | −0.0129887 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129887 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7599.88 | 1.38569 | 0.692845 | − | 0.721086i | \(-0.256357\pi\) | ||||
0.692845 | + | 0.721086i | \(0.256357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3017.52 | −0.544921 | −0.272460 | − | 0.962167i | \(-0.587837\pi\) | ||||
−0.272460 | + | 0.962167i | \(0.587837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1921.21 | 0.340396 | 0.170198 | − | 0.985410i | \(-0.445559\pi\) | ||||
0.170198 | + | 0.985410i | \(0.445559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2609.67 | 0.458035 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3469.72 | 0.597710 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6536.98 | 1.11571 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 327.084 | 0.0548108 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −912.412 | −0.151513 | −0.0757563 | − | 0.997126i | \(-0.524137\pi\) | ||||
−0.0757563 | + | 0.997126i | \(0.524137\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7726.29 | 1.26010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6014.62 | −0.972218 | −0.486109 | − | 0.873898i | \(-0.661584\pi\) | ||||
−0.486109 | + | 0.873898i | \(0.661584\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19321.5 | 3.06838 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −563.715 | −0.0887398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2739.83 | 0.423867 | 0.211934 | − | 0.977284i | \(-0.432024\pi\) | ||||
0.211934 | + | 0.977284i | \(0.432024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7608.69 | −1.16700 | −0.583501 | − | 0.812112i | \(-0.698318\pi\) | ||||
−0.583501 | + | 0.812112i | \(0.698318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8725.11 | 1.31555 | 0.657777 | − | 0.753212i | \(-0.271497\pi\) | ||||
0.657777 | + | 0.753212i | \(0.271497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8098.64 | 1.21079 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10470.0 | −1.53923 | −0.769614 | − | 0.638509i | \(-0.779551\pi\) | ||||
−0.769614 | + | 0.638509i | \(0.779551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6081.30 | −0.886616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9085.20 | 1.30285 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7894.14 | 1.12281 | 0.561405 | − | 0.827542i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827542i | \(0.310261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −88.1455 | −0.0123350 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −269.940 | −0.0374718 | −0.0187359 | − | 0.999824i | \(-0.505964\pi\) | ||||
−0.0187359 | + | 0.999824i | \(0.505964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1267.26 | −0.173122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8580.72 | 1.16296 | 0.581480 | − | 0.813561i | \(-0.302474\pi\) | ||||
0.581480 | + | 0.813561i | \(0.302474\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3414.93 | 0.455599 | 0.227800 | − | 0.973708i | \(-0.426847\pi\) | ||||
0.227800 | + | 0.973708i | \(0.426847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 979.834 | 0.129706 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3304.00 | −0.430642 | −0.215321 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215321 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5372.12 | 0.694833 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10366.1 | 1.32045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12756.1 | −1.61262 | −0.806311 | − | 0.591492i | \(-0.798539\pi\) | ||||
−0.806311 | + | 0.591492i | \(0.798539\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4628.52 | 0.576402 | 0.288201 | − | 0.957570i | \(-0.406943\pi\) | ||||
0.288201 | + | 0.957570i | \(0.406943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9382.53 | −1.15975 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6826.99 | 0.831453 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2965.55 | −0.358526 | −0.179263 | − | 0.983801i | \(-0.557371\pi\) | ||||
−0.179263 | + | 0.983801i | \(0.557371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 155.409 | 0.0185162 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23789.6 | −2.81394 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1870.26 | −0.218063 | −0.109031 | − | 0.994038i | \(-0.534775\pi\) | ||||
−0.109031 | + | 0.994038i | \(0.534775\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12650.6 | −1.46450 | −0.732248 | − | 0.681038i | \(-0.761529\pi\) | ||||
−0.732248 | + | 0.681038i | \(0.761529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25558.2 | −2.91707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −81.4464 | −0.00923060 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3266.47 | 0.365059 | 0.182530 | − | 0.983200i | \(-0.441571\pi\) | ||||
0.182530 | + | 0.983200i | \(0.441571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6788.95 | 0.753478 | 0.376739 | − | 0.926319i | \(-0.377045\pi\) | ||||
0.376739 | + | 0.926319i | \(0.377045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1204.10 | 0.131808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4918.55 | −0.534737 | −0.267368 | − | 0.963594i | \(-0.586154\pi\) | ||||
−0.267368 | + | 0.963594i | \(0.586154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14033.5 | −1.50508 | −0.752540 | − | 0.658546i | \(-0.771172\pi\) | ||||
−0.752540 | + | 0.658546i | \(0.771172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24048.8 | 2.56184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5374.04 | 0.564848 | 0.282424 | − | 0.959290i | \(-0.408862\pi\) | ||||
0.282424 | + | 0.959290i | \(0.408862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20160.7 | 2.10495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −475.808 | −0.0490247 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12169.2 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6186.08 | 0.624977 | 0.312489 | − | 0.949922i | \(-0.398837\pi\) | ||||
0.312489 | + | 0.949922i | \(0.398837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15197.8 | −1.52549 | −0.762743 | − | 0.646701i | \(-0.776148\pi\) | ||||
−0.762743 | + | 0.646701i | \(0.776148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1981.82 | 0.196377 | 0.0981883 | − | 0.995168i | \(-0.468695\pi\) | ||||
0.0981883 | + | 0.995168i | \(0.468695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −349.625 | −0.0344225 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23662.5 | −2.30022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5728.58 | −0.553359 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9779.52 | −0.932855 | −0.466427 | − | 0.884559i | \(-0.654459\pi\) | ||||
−0.466427 | + | 0.884559i | \(0.654459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3315.19 | −0.314261 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17175.4 | −1.60803 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18668.9 | −1.73710 | −0.868549 | − | 0.495603i | \(-0.834947\pi\) | ||||
−0.868549 | + | 0.495603i | \(0.834947\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16006.2 | −1.47118 | −0.735591 | − | 0.677426i | \(-0.763095\pi\) | ||||
−0.735591 | + | 0.677426i | \(0.763095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4954.71 | 0.452634 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −366.474 | −0.0330757 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9860.57 | −0.884609 | −0.442304 | − | 0.896865i | \(-0.645839\pi\) | ||||
−0.442304 | + | 0.896865i | \(0.645839\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10512.0 | 0.931825 | 0.465913 | − | 0.884831i | \(-0.345726\pi\) | ||||
0.465913 | + | 0.884831i | \(0.345726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25413.9 | −2.23941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16667.3 | −1.45140 | −0.725700 | − | 0.688011i | \(-0.758484\pi\) | ||||
−0.725700 | + | 0.688011i | \(0.758484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −411.117 | −0.0355905 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17460.4 | −1.49397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26058.6 | −2.21674 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10923.9 | −0.918586 | −0.459293 | − | 0.888285i | \(-0.651897\pi\) | ||||
−0.459293 | + | 0.888285i | \(0.651897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17488.0 | 1.46213 | 0.731067 | − | 0.682305i | \(-0.239022\pi\) | ||||
0.731067 | + | 0.682305i | \(0.239022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 36683.8 | 3.03220 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10302.7 | −0.846775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9790.05 | −0.795599 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35189.2 | −2.84367 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22433.3 | 1.79271 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8724.14 | −0.693309 | −0.346655 | − | 0.937993i | \(-0.612682\pi\) | ||||
−0.346655 | + | 0.937993i | \(0.612682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23728.9 | 1.86502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 959.834 | 0.0750266 | 0.0375133 | − | 0.999296i | \(-0.488056\pi\) | ||||
0.0375133 | + | 0.999296i | \(0.488056\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1110.54 | 0.0858632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −469.082 | −0.0360712 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14212.0 | 1.08112 | 0.540558 | − | 0.841307i | \(-0.318213\pi\) | ||||
0.540558 | + | 0.841307i | \(0.318213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11490.5 | 0.869405 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7110.56 | −0.532281 | −0.266141 | − | 0.963934i | \(-0.585749\pi\) | ||||
−0.266141 | + | 0.963934i | \(0.585749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19886.7 | 1.48078 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4859.18 | −0.358010 | −0.179005 | − | 0.983848i | \(-0.557288\pi\) | ||||
−0.179005 | + | 0.983848i | \(0.557288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8580.29 | −0.628851 | −0.314425 | − | 0.949282i | \(-0.601812\pi\) | ||||
−0.314425 | + | 0.949282i | \(0.601812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8869.49 | −0.643276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1029.99 | −0.0743136 | −0.0371568 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371568 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1076.51 | 0.0768695 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7022.50 | 0.498872 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15541.4 | 1.09278 | 0.546391 | − | 0.837530i | \(-0.316001\pi\) | ||||
0.546391 | + | 0.837530i | \(0.316001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8222.25 | 0.575198 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12643.5 | 0.875562 | 0.437781 | − | 0.899082i | \(-0.355765\pi\) | ||||
0.437781 | + | 0.899082i | \(0.355765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1860.31 | 0.128177 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17162.9 | 1.17071 | 0.585357 | − | 0.810776i | \(-0.300954\pi\) | ||||
0.585357 | + | 0.810776i | \(0.300954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4010.19 | −0.272178 | −0.136089 | − | 0.990697i | \(-0.543453\pi\) | ||||
−0.136089 | + | 0.990697i | \(0.543453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −53868.6 | −3.61995 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17321.2 | −1.15823 | −0.579114 | − | 0.815247i | \(-0.696601\pi\) | ||||
−0.579114 | + | 0.815247i | \(0.696601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12654.1 | 0.837855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2474.79 | 0.163060 | 0.0815300 | − | 0.996671i | \(-0.474019\pi\) | ||||
0.0815300 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11844.4 | −0.772831 | −0.386416 | − | 0.922325i | \(-0.626287\pi\) | ||||
−0.386416 | + | 0.922325i | \(0.626287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7848.64 | 0.509634 | 0.254817 | − | 0.966989i | \(-0.417985\pi\) | ||||
0.254817 | + | 0.966989i | \(0.417985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1088.24 | −0.0699829 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 894.755 | 0.0572643 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12961.7 | 0.821649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11346.0 | 0.715811 | 0.357906 | − | 0.933758i | \(-0.383491\pi\) | ||||
0.357906 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23649.7 | −1.47797 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10893.6 | −0.677583 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17585.2 | −1.08358 | −0.541791 | − | 0.840513i | \(-0.682253\pi\) | ||||
−0.541791 | + | 0.840513i | \(0.682253\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10644.9 | 0.652866 | 0.326433 | − | 0.945220i | \(-0.394153\pi\) | ||||
0.326433 | + | 0.945220i | \(0.394153\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7872.89 | 0.478385 | 0.239193 | − | 0.970972i | \(-0.423117\pi\) | ||||
0.239193 | + | 0.970972i | \(0.423117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12381.4 | −0.748862 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2721.08 | 0.163069 | 0.0815347 | − | 0.996671i | \(-0.474018\pi\) | ||||
0.0815347 | + | 0.996671i | \(0.474018\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35585.4 | −2.12280 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2000.76 | −0.118268 | −0.0591338 | − | 0.998250i | \(-0.518834\pi\) | ||||
−0.0591338 | + | 0.998250i | \(0.518834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27738.0 | −1.63220 | −0.816100 | − | 0.577911i | \(-0.803868\pi\) | ||||
−0.816100 | + | 0.577911i | \(0.803868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 416.968 | 0.0243148 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1719.44 | 0.0998153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6488.79 | 0.373319 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24693.0 | −1.41433 | −0.707166 | − | 0.707047i | \(-0.750027\pi\) | ||||
−0.707166 | + | 0.707047i | \(0.750027\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14764.7 | 0.838189 | 0.419095 | − | 0.907943i | \(-0.362348\pi\) | ||||
0.419095 | + | 0.907943i | \(0.362348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 777.208 | 0.0439271 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 571.548 | 0.0320200 | 0.0160100 | − | 0.999872i | \(-0.494904\pi\) | ||||
0.0160100 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46424.6 | −2.58948 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3410.13 | −0.188557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3507.58 | 0.193104 | 0.0965519 | − | 0.995328i | \(-0.469219\pi\) | ||||
0.0965519 | + | 0.995328i | \(0.469219\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3731.11 | 0.203639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38277.1 | 2.08013 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21145.2 | −1.13929 | −0.569644 | − | 0.821891i | \(-0.692919\pi\) | ||||
−0.569644 | + | 0.821891i | \(0.692919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2905.22 | 0.155864 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1150.01 | 0.0611749 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15815.2 | −0.837734 | −0.418867 | − | 0.908048i | \(-0.637573\pi\) | ||||
−0.418867 | + | 0.908048i | \(0.637573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12730.4 | 0.668664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37907.4 | 1.98273 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33309.8 | −1.72774 | −0.863871 | − | 0.503713i | \(-0.831967\pi\) | ||||
−0.863871 | + | 0.503713i | \(0.831967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 790.104 | 0.0408114 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8180.33 | −0.419048 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7037.29 | −0.359008 | −0.179504 | − | 0.983757i | \(-0.557449\pi\) | ||||
−0.179504 | + | 0.983757i | \(0.557449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44925.6 | −2.27310 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12661.3 | 0.638000 | 0.319000 | − | 0.947755i | \(-0.396653\pi\) | ||||
0.319000 | + | 0.947755i | \(0.396653\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27854.4 | 1.39217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32709.4 | −1.62819 | −0.814096 | − | 0.580730i | \(-0.802767\pi\) | ||||
−0.814096 | + | 0.580730i | \(0.802767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29381.2 | 1.45073 | 0.725364 | − | 0.688365i | \(-0.241671\pi\) | ||||
0.725364 | + | 0.688365i | \(0.241671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2985.47 | 0.146818 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1592.36 | 0.0776816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2225.64 | −0.108142 | −0.0540712 | − | 0.998537i | \(-0.517220\pi\) | ||||
−0.0540712 | + | 0.998537i | \(0.517220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 62307.1 | 3.00343 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32628.1 | 1.56656 | 0.783281 | − | 0.621668i | \(-0.213545\pi\) | ||||
0.783281 | + | 0.621668i | \(0.213545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18690.6 | 0.890322 | 0.445161 | − | 0.895451i | \(-0.353146\pi\) | ||||
0.445161 | + | 0.895451i | \(0.353146\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1073.76 | −0.0509474 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6012.40 | 0.283045 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6845.67 | 0.321016 | 0.160508 | − | 0.987035i | \(-0.448687\pi\) | ||||
0.160508 | + | 0.987035i | \(0.448687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −161.873 | −0.00753190 | −0.00376595 | − | 0.999993i | \(-0.501199\pi\) | ||||
−0.00376595 | + | 0.999993i | \(0.501199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −60565.7 | −2.80721 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8579.37 | 0.394593 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29196.8 | 1.33770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17960.9 | 0.816625 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9959.12 | −0.451085 | −0.225543 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225543 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −899.899 | −0.0404510 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3150.96 | −0.141102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4656.36 | −0.206947 | −0.103473 | − | 0.994632i | \(-0.532996\pi\) | ||||
−0.103473 | + | 0.994632i | \(0.532996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49474.8 | −2.19061 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32753.5 | 1.43941 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 645.586 | 0.0282657 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 173.564 | 0.00754289 | 0.00377144 | − | 0.999993i | \(-0.498800\pi\) | ||||
0.00377144 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22674.1 | 0.981744 | 0.490872 | − | 0.871232i | \(-0.336678\pi\) | ||||
0.490872 | + | 0.871232i | \(0.336678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51723.1 | −2.22304 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10069.6 | −0.431199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40832.2 | 1.73575 | 0.867877 | − | 0.496779i | \(-0.165484\pi\) | ||||
0.867877 | + | 0.496779i | \(0.165484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4881.01 | 0.206733 | 0.103367 | − | 0.994643i | \(-0.467039\pi\) | ||||
0.103367 | + | 0.994643i | \(0.467039\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22213.4 | 0.934022 | 0.467011 | − | 0.884251i | \(-0.345331\pi\) | ||||
0.467011 | + | 0.884251i | \(0.345331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35477.2 | 1.48634 | 0.743168 | − | 0.669104i | \(-0.233322\pi\) | ||||
0.743168 | + | 0.669104i | \(0.233322\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42591.7 | 1.77157 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58274.9 | 2.41519 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23505.3 | −0.967213 | −0.483607 | − | 0.875285i | \(-0.660673\pi\) | ||||
−0.483607 | + | 0.875285i | \(0.660673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22803.2 | −0.934977 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21528.0 | 0.876433 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2437.63 | 0.0988876 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4498.12 | 0.181191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12434.1 | −0.499103 | −0.249551 | − | 0.968362i | \(-0.580283\pi\) | ||||
−0.249551 | + | 0.968362i | \(0.580283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 795.866 | 0.0317226 | 0.0158613 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158613 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8583.95 | 0.340955 | 0.170478 | − | 0.985362i | \(-0.445469\pi\) | ||||
0.170478 | + | 0.985362i | \(0.445469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37865.4 | −1.49357 | −0.746787 | − | 0.665063i | \(-0.768405\pi\) | ||||
−0.746787 | + | 0.665063i | \(0.768405\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32458.3 | 1.27585 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37371.5 | 1.45885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13526.1 | −0.526194 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1202.43 | −0.0464565 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4604.56 | 0.177292 | 0.0886459 | − | 0.996063i | \(-0.471746\pi\) | ||||
0.0886459 | + | 0.996063i | \(0.471746\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13021.9 | −0.497979 | −0.248990 | − | 0.968506i | \(-0.580099\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4301.10 | 0.163923 | 0.0819613 | − | 0.996636i | \(-0.473882\pi\) | ||||
0.0819613 | + | 0.996636i | \(0.473882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15195.8 | 0.575225 | 0.287613 | − | 0.957747i | \(-0.407138\pi\) | ||||
0.287613 | + | 0.957747i | \(0.407138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1070.18 | 0.0403743 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11089.2 | −0.415551 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23973.1 | 0.895344 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11741.2 | 0.435587 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13332.9 | 0.492990 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −62947.9 | −2.31211 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4657.99 | 0.170525 | 0.0852624 | − | 0.996359i | \(-0.472827\pi\) | ||||
0.0852624 | + | 0.996359i | \(0.472827\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12892.8 | −0.468889 | −0.234444 | − | 0.972130i | \(-0.575327\pi\) | ||||
−0.234444 | + | 0.972130i | \(0.575327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −85765.0 | −3.10888 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1610.28 | 0.0579894 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36405.3 | 1.30675 | 0.653373 | − | 0.757036i | \(-0.273353\pi\) | ||||
0.653373 | + | 0.757036i | \(0.273353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14178.0 | −0.505605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21400.1 | −0.760682 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4279.70 | −0.151143 | −0.0755717 | − | 0.997140i | \(-0.524078\pi\) | ||||
−0.0755717 | + | 0.997140i | \(0.524078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9546.45 | 0.336061 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −148210. | −5.18394 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21006.6 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13529.1 | 0.468688 | 0.234344 | − | 0.972154i | \(-0.424706\pi\) | ||||
0.234344 | + | 0.972154i | \(0.424706\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13283.3 | 0.458711 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4153.14 | −0.142512 | −0.0712561 | − | 0.997458i | \(-0.522701\pi\) | ||||
−0.0712561 | + | 0.997458i | \(0.522701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15905.1 | −0.544048 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18387.5 | 0.625005 | 0.312503 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312503 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28926.0 | −0.980128 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2100.77 | 0.0707378 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57139.1 | 1.91800 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13895.9 | 0.463548 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34454.1 | 1.14578 | 0.572889 | − | 0.819633i | \(-0.305822\pi\) | ||||
0.572889 | + | 0.819633i | \(0.305822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2689.17 | −0.0888770 | −0.0444385 | − | 0.999012i | \(-0.514150\pi\) | ||||
−0.0444385 | + | 0.999012i | \(0.514150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −168.838 | −0.00556288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −148.959 | −0.00487782 | −0.00243891 | − | 0.999997i | \(-0.500776\pi\) | ||||
−0.00243891 | + | 0.999997i | \(0.500776\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 86699.3 | 2.83036 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32221.8 | 1.04549 | 0.522744 | − | 0.852490i | \(-0.324908\pi\) | ||||
0.522744 | + | 0.852490i | \(0.324908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21660.8 | 0.700681 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15590.6 | −0.501265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2979.37 | −0.0955023 | −0.0477512 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477512 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49228.1 | −1.56848 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32093.8 | −1.01948 | −0.509740 | − | 0.860328i | \(-0.670258\pi\) | ||||
−0.509740 | + | 0.860328i | \(0.670258\pi\) | |||||||
\(998\) | 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 | 1296.4.a.m.1.1 | 2 | ||
3.2 | odd | 2 | 1296.4.a.q.1.2 | 2 | |||
4.3 | odd | 2 | 648.4.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 648.4.a.f.1.2 | yes | 2 | ||
36.7 | odd | 6 | 648.4.i.t.433.2 | 4 | |||
36.11 | even | 6 | 648.4.i.n.433.1 | 4 | |||
36.23 | even | 6 | 648.4.i.n.217.1 | 4 | |||
36.31 | odd | 6 | 648.4.i.t.217.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
648.4.a.f.1.2 | yes | 2 | 12.11 | even | 2 | ||
648.4.i.n.217.1 | 4 | 36.23 | even | 6 | |||
648.4.i.n.433.1 | 4 | 36.11 | even | 6 | |||
648.4.i.t.217.2 | 4 | 36.31 | odd | 6 | |||
648.4.i.t.433.2 | 4 | 36.7 | odd | 6 | |||
1296.4.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1296.4.a.q.1.2 | 2 | 3.2 | odd | 2 |