Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.4281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.29027\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.4120 | 0.886166 | 0.443083 | − | 0.896481i | \(-0.353885\pi\) | ||||
0.443083 | + | 0.896481i | \(0.353885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −57.6104 | −1.57911 | −0.789554 | − | 0.613681i | \(-0.789688\pi\) | ||||
−0.789554 | + | 0.613681i | \(0.789688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.7864 | 0.827492 | 0.413746 | − | 0.910392i | \(-0.364220\pi\) | ||||
0.413746 | + | 0.910392i | \(0.364220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.4120 | −0.448149 | −0.224075 | − | 0.974572i | \(-0.571936\pi\) | ||||
−0.224075 | + | 0.974572i | \(0.571936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 70.6104 | 0.852586 | 0.426293 | − | 0.904585i | \(-0.359819\pi\) | ||||
0.426293 | + | 0.904585i | \(0.359819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.37433 | 0.0668545 | 0.0334273 | − | 0.999441i | \(-0.489358\pi\) | ||||
0.0334273 | + | 0.999441i | \(0.489358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.1607 | 0.109885 | 0.0549424 | − | 0.998490i | \(-0.482502\pi\) | ||||
0.0549424 | + | 0.998490i | \(0.482502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −50.9847 | −0.295391 | −0.147696 | − | 0.989033i | \(-0.547186\pi\) | ||||
−0.147696 | + | 0.989033i | \(0.547186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −82.0601 | −0.396306 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −159.693 | −0.709550 | −0.354775 | − | 0.934952i | \(-0.615443\pi\) | ||||
−0.354775 | + | 0.934952i | \(0.615443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.2056 | 0.240757 | 0.120379 | − | 0.992728i | \(-0.461589\pi\) | ||||
0.120379 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −84.6580 | −0.300238 | −0.150119 | − | 0.988668i | \(-0.547966\pi\) | ||||
−0.150119 | + | 0.988668i | \(0.547966\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −434.434 | −1.34827 | −0.674135 | − | 0.738609i | \(-0.735483\pi\) | ||||
−0.674135 | + | 0.738609i | \(0.735483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −73.6454 | −0.214710 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −138.490 | −0.358926 | −0.179463 | − | 0.983765i | \(-0.557436\pi\) | ||||
−0.179463 | + | 0.983765i | \(0.557436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 288.052 | 0.706199 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 631.011 | 1.39238 | 0.696192 | − | 0.717856i | \(-0.254876\pi\) | ||||
0.696192 | + | 0.717856i | \(0.254876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 82.8743 | 0.173950 | 0.0869751 | − | 0.996210i | \(-0.472280\pi\) | ||||
0.0869751 | + | 0.996210i | \(0.472280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −193.932 | −0.370066 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −431.813 | −0.787379 | −0.393689 | − | 0.919244i | \(-0.628801\pi\) | ||||
−0.393689 | + | 0.919244i | \(0.628801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −450.284 | −0.752660 | −0.376330 | − | 0.926486i | \(-0.622814\pi\) | ||||
−0.376330 | + | 0.926486i | \(0.622814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −33.5655 | −0.0538157 | −0.0269079 | − | 0.999638i | \(-0.508566\pi\) | ||||
−0.0269079 | + | 0.999638i | \(0.508566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −945.504 | −1.39935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 509.312 | 0.725343 | 0.362672 | − | 0.931917i | \(-0.381865\pi\) | ||||
0.362672 | + | 0.931917i | \(0.381865\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 811.292 | 1.07290 | 0.536451 | − | 0.843932i | \(-0.319765\pi\) | ||||
0.536451 | + | 0.843932i | \(0.319765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 157.060 | 0.200418 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −499.820 | −0.595290 | −0.297645 | − | 0.954677i | \(-0.596201\pi\) | ||||
−0.297645 | + | 0.954677i | \(0.596201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 636.563 | 0.733296 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −353.052 | −0.381288 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 625.481 | 0.654722 | 0.327361 | − | 0.944899i | \(-0.393841\pi\) | ||||
0.327361 | + | 0.944899i | \(0.393841\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −241.156 | −0.237583 | −0.118792 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118792 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1436.46 | −1.37417 | −0.687083 | − | 0.726579i | \(-0.741109\pi\) | ||||
−0.687083 | + | 0.726579i | \(0.741109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −801.329 | −0.723995 | −0.361997 | − | 0.932179i | \(-0.617905\pi\) | ||||
−0.361997 | + | 0.932179i | \(0.617905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1573.48 | −1.38268 | −0.691338 | − | 0.722531i | \(-0.742979\pi\) | ||||
−0.691338 | + | 0.722531i | \(0.742979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1777.62 | −1.47986 | −0.739930 | − | 0.672683i | \(-0.765142\pi\) | ||||
−0.739930 | + | 0.672683i | \(0.765142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.8717 | −0.0298983 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −515.535 | −0.397135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1987.96 | 1.49358 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2006.78 | −1.40215 | −0.701075 | − | 0.713088i | \(-0.747296\pi\) | ||||
−0.701075 | + | 0.713088i | \(0.747296\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1262.69 | −0.842149 | −0.421075 | − | 0.907026i | \(-0.638347\pi\) | ||||
−0.421075 | + | 0.907026i | \(0.638347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1158.86 | 0.755533 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −678.275 | −0.422985 | −0.211492 | − | 0.977380i | \(-0.567832\pi\) | ||||
−0.211492 | + | 0.977380i | \(0.567832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −136.614 | −0.0833630 | −0.0416815 | − | 0.999131i | \(-0.513271\pi\) | ||||
−0.0416815 | + | 0.999131i | \(0.513271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2234.50 | −1.30670 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −85.8034 | −0.0491420 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1445.14 | −0.794569 | −0.397285 | − | 0.917695i | \(-0.630047\pi\) | ||||
−0.397285 | + | 0.917695i | \(0.630047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2635.74 | −1.42048 | −0.710242 | − | 0.703958i | \(-0.751414\pi\) | ||||
−0.710242 | + | 0.703958i | \(0.751414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 254.924 | 0.132103 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1523.92 | 0.774662 | 0.387331 | − | 0.921941i | \(-0.373397\pi\) | ||||
0.387331 | + | 0.921941i | \(0.373397\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 121.028 | 0.0592442 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2382.91 | −1.14506 | −0.572528 | − | 0.819885i | \(-0.694037\pi\) | ||||
−0.572528 | + | 0.819885i | \(0.694037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3380.54 | −1.56643 | −0.783215 | − | 0.621751i | \(-0.786422\pi\) | ||||
−0.783215 | + | 0.621751i | \(0.786422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −692.618 | −0.315256 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −99.6851 | −0.0438088 | −0.0219044 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219044 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 410.301 | 0.177233 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3412.90 | −1.42510 | −0.712549 | − | 0.701622i | \(-0.752459\pi\) | ||||
−0.712549 | + | 0.701622i | \(0.752459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4063.94 | 1.66890 | 0.834448 | − | 0.551087i | \(-0.185787\pi\) | ||||
0.834448 | + | 0.551087i | \(0.185787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 798.465 | 0.317321 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1809.66 | 0.707676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2163.72 | −0.819693 | −0.409847 | − | 0.912154i | \(-0.634418\pi\) | ||||
−0.409847 | + | 0.912154i | \(0.634418\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4432.06 | 1.65299 | 0.826493 | − | 0.562946i | \(-0.190332\pi\) | ||||
0.826493 | + | 0.562946i | \(0.190332\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4233.88 | 1.53122 | 0.765612 | − | 0.643302i | \(-0.222436\pi\) | ||||
0.765612 | + | 0.643302i | \(0.222436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2833.94 | −1.00951 | −0.504755 | − | 0.863263i | \(-0.668417\pi\) | ||||
−0.504755 | + | 0.863263i | \(0.668417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 281.642 | 0.0973762 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −316.028 | −0.107670 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4067.89 | −1.34633 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2775.59 | 0.905589 | 0.452794 | − | 0.891615i | \(-0.350427\pi\) | ||||
0.452794 | + | 0.891615i | \(0.350427\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 423.290 | 0.134270 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −836.763 | −0.261766 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1218.36 | −0.370840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 317.706 | 0.0954043 | 0.0477021 | − | 0.998862i | \(-0.484810\pi\) | ||||
0.0477021 | + | 0.998862i | \(0.484810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 855.603 | 0.250169 | 0.125085 | − | 0.992146i | \(-0.460080\pi\) | ||||
0.125085 | + | 0.992146i | \(0.460080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 687.782 | 0.198471 | 0.0992356 | − | 0.995064i | \(-0.468360\pi\) | ||||
0.0992356 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4228.01 | −1.18878 | −0.594390 | − | 0.804177i | \(-0.702607\pi\) | ||||
−0.594390 | + | 0.804177i | \(0.702607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2172.17 | 0.602964 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3113.46 | 0.842648 | 0.421324 | − | 0.906910i | \(-0.361565\pi\) | ||||
0.421324 | + | 0.906910i | \(0.361565\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4185.57 | −1.11874 | −0.559370 | − | 0.828918i | \(-0.688957\pi\) | ||||
−0.559370 | + | 0.828918i | \(0.688957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 368.227 | 0.0960210 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2738.72 | 0.705509 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1137.16 | 0.285963 | 0.142981 | − | 0.989725i | \(-0.454331\pi\) | ||||
0.142981 | + | 0.989725i | \(0.454331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −424.838 | −0.105571 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6957.03 | 1.68859 | 0.844295 | − | 0.535878i | \(-0.180019\pi\) | ||||
0.844295 | + | 0.535878i | \(0.180019\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2620.89 | −0.628780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1187.16 | −0.278339 | −0.139169 | − | 0.990269i | \(-0.544443\pi\) | ||||
−0.139169 | + | 0.990269i | \(0.544443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 692.451 | 0.160517 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1879.17 | −0.425929 | −0.212965 | − | 0.977060i | \(-0.568312\pi\) | ||||
−0.212965 | + | 0.977060i | \(0.568312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8561.28 | −1.91904 | −0.959522 | − | 0.281635i | \(-0.909123\pi\) | ||||
−0.959522 | + | 0.281635i | \(0.909123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1440.26 | −0.315822 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7204.78 | 1.56279 | 0.781396 | − | 0.624036i | \(-0.214508\pi\) | ||||
0.781396 | + | 0.624036i | \(0.214508\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7115.84 | −1.51066 | −0.755329 | − | 0.655345i | \(-0.772523\pi\) | ||||
−0.755329 | + | 0.655345i | \(0.772523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1361.24 | −0.285926 | −0.142963 | − | 0.989728i | \(-0.545663\pi\) | ||||
−0.142963 | + | 0.989728i | \(0.545663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1037.33 | 0.213351 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3926.28 | −0.799162 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1323.60 | 0.263910 | 0.131955 | − | 0.991256i | \(-0.457875\pi\) | ||||
0.131955 | + | 0.991256i | \(0.457875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3155.05 | −0.622693 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 286.023 | 0.0553216 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1389.41 | −0.266061 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −414.371 | −0.0777929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5864.61 | −1.09026 | −0.545132 | − | 0.838350i | \(-0.683521\pi\) | ||||
−0.545132 | + | 0.838350i | \(0.683521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5084.53 | 0.927065 | 0.463533 | − | 0.886080i | \(-0.346582\pi\) | ||||
0.463533 | + | 0.886080i | \(0.346582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2964.66 | −0.535375 | −0.267687 | − | 0.963506i | \(-0.586259\pi\) | ||||
−0.267687 | + | 0.963506i | \(0.586259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7443.17 | −1.31877 | −0.659385 | − | 0.751806i | \(-0.729183\pi\) | ||||
−0.659385 | + | 0.751806i | \(0.729183\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −988.634 | −0.173520 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2218.02 | −0.382086 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 969.659 | 0.165498 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7129.94 | −1.19479 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3965.35 | −0.658475 | −0.329238 | − | 0.944247i | \(-0.606792\pi\) | ||||
−0.329238 | + | 0.944247i | \(0.606792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2159.07 | 0.352127 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10319.1 | 1.66800 | 0.834000 | − | 0.551765i | \(-0.186045\pi\) | ||||
0.834000 | + | 0.551765i | \(0.186045\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2937.25 | 0.466455 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6838.00 | −1.07643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7755.95 | −1.19989 | −0.599944 | − | 0.800042i | \(-0.704811\pi\) | ||||
−0.599944 | + | 0.800042i | \(0.704811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11579.1 | 1.77597 | 0.887987 | − | 0.459869i | \(-0.152104\pi\) | ||||
0.887987 | + | 0.459869i | \(0.152104\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8495.91 | 1.28100 | 0.640498 | − | 0.767960i | \(-0.278728\pi\) | ||||
0.640498 | + | 0.767960i | \(0.278728\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2251.42 | 0.336600 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8260.19 | 1.21436 | 0.607181 | − | 0.794563i | \(-0.292300\pi\) | ||||
0.607181 | + | 0.794563i | \(0.292300\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1873.17 | −0.273097 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 167.828 | 0.0240671 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13765.5 | 1.95791 | 0.978953 | − | 0.204085i | \(-0.0654219\pi\) | ||||
0.978953 | + | 0.204085i | \(0.0654219\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2272.90 | −0.318068 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1048.30 | 0.145520 | 0.0727602 | − | 0.997349i | \(-0.476819\pi\) | ||||
0.0727602 | + | 0.997349i | \(0.476819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 665.601 | 0.0909289 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10636.6 | −1.44160 | −0.720799 | − | 0.693144i | \(-0.756225\pi\) | ||||
−0.720799 | + | 0.693144i | \(0.756225\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1505.81 | −0.200896 | −0.100448 | − | 0.994942i | \(-0.532028\pi\) | ||||
−0.100448 | + | 0.994942i | \(0.532028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4727.52 | 0.625809 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12411.4 | 1.61769 | 0.808846 | − | 0.588020i | \(-0.200092\pi\) | ||||
0.808846 | + | 0.588020i | \(0.200092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −231.643 | −0.0299608 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2546.56 | −0.324383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4807.65 | 0.607781 | 0.303891 | − | 0.952707i | \(-0.401714\pi\) | ||||
0.303891 | + | 0.952707i | \(0.401714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8688.87 | 1.08205 | 0.541024 | − | 0.841007i | \(-0.318037\pi\) | ||||
0.541024 | + | 0.841007i | \(0.318037\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1977.51 | −0.244434 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9199.98 | 1.12046 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10056.9 | 1.21584 | 0.607921 | − | 0.793997i | \(-0.292004\pi\) | ||||
0.607921 | + | 0.793997i | \(0.292004\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10356.2 | 1.23388 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4056.46 | −0.479816 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6643.15 | 0.774556 | 0.387278 | − | 0.921963i | \(-0.373415\pi\) | ||||
0.387278 | + | 0.921963i | \(0.373415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9771.06 | 1.13115 | 0.565573 | − | 0.824698i | \(-0.308655\pi\) | ||||
0.565573 | + | 0.824698i | \(0.308655\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −785.301 | −0.0896298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1360.13 | 0.154149 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7498.22 | 0.837997 | 0.418998 | − | 0.907987i | \(-0.362381\pi\) | ||||
0.418998 | + | 0.907987i | \(0.362381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12325.1 | −1.36792 | −0.683959 | − | 0.729521i | \(-0.739743\pi\) | ||||
−0.683959 | + | 0.729521i | \(0.739743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 520.705 | 0.0569993 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11635.6 | −1.26500 | −0.632500 | − | 0.774560i | \(-0.717971\pi\) | ||||
−0.632500 | + | 0.774560i | \(0.717971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12038.6 | 1.29113 | 0.645567 | − | 0.763703i | \(-0.276621\pi\) | ||||
0.645567 | + | 0.763703i | \(0.276621\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2499.10 | 0.266222 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10905.2 | 1.14621 | 0.573103 | − | 0.819483i | \(-0.305739\pi\) | ||||
0.573103 | + | 0.819483i | \(0.305739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3641.30 | −0.380182 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3182.81 | −0.327940 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 831.136 | 0.0850742 | 0.0425371 | − | 0.999095i | \(-0.486456\pi\) | ||||
0.0425371 | + | 0.999095i | \(0.486456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3846.15 | 0.388575 | 0.194288 | − | 0.980945i | \(-0.437760\pi\) | ||||
0.194288 | + | 0.980945i | \(0.437760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2127.77 | 0.213576 | 0.106788 | − | 0.994282i | \(-0.465943\pi\) | ||||
0.106788 | + | 0.994282i | \(0.465943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1169.95 | −0.115929 | −0.0579647 | − | 0.998319i | \(-0.518461\pi\) | ||||
−0.0579647 | + | 0.998319i | \(0.518461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7086.93 | −0.697749 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4877.18 | 0.474108 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1765.26 | 0.170517 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11243.2 | 1.07247 | 0.536236 | − | 0.844068i | \(-0.319846\pi\) | ||||
0.536236 | + | 0.844068i | \(0.319846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6193.91 | −0.587148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3127.41 | −0.292800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12169.5 | 1.13234 | 0.566172 | − | 0.824287i | \(-0.308424\pi\) | ||||
0.566172 | + | 0.824287i | \(0.308424\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1702.75 | 0.156505 | 0.0782524 | − | 0.996934i | \(-0.475066\pi\) | ||||
0.0782524 | + | 0.996934i | \(0.475066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −539.052 | −0.0492448 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7390.07 | −0.666982 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16867.1 | −1.51318 | −0.756590 | − | 0.653890i | \(-0.773136\pi\) | ||||
−0.756590 | + | 0.653890i | \(0.773136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10396.8 | −0.921608 | −0.460804 | − | 0.887502i | \(-0.652439\pi\) | ||||
−0.460804 | + | 0.887502i | \(0.652439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1205.78 | 0.106251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5656.96 | −0.492614 | −0.246307 | − | 0.969192i | \(-0.579217\pi\) | ||||
−0.246307 | + | 0.969192i | \(0.579217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −550.878 | −0.0476897 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7182.32 | 0.614546 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25027.9 | 2.12906 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8808.99 | 0.740747 | 0.370373 | − | 0.928883i | \(-0.379230\pi\) | ||||
0.370373 | + | 0.928883i | \(0.379230\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6509.27 | −0.544227 | −0.272113 | − | 0.962265i | \(-0.587723\pi\) | ||||
−0.272113 | + | 0.962265i | \(0.587723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1601.53 | 0.132379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12112.6 | −0.995530 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2451.51 | 0.199225 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4006.65 | 0.323780 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4242.74 | 0.339050 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14119.6 | −1.12208 | −0.561042 | − | 0.827787i | \(-0.689600\pi\) | ||||
−0.561042 | + | 0.827787i | \(0.689600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7867.38 | 0.618352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7536.09 | −0.589068 | −0.294534 | − | 0.955641i | \(-0.595164\pi\) | ||||
−0.294534 | + | 0.955641i | \(0.595164\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1211.72 | 0.0936863 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8358.85 | 0.642775 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7113.19 | −0.541105 | −0.270553 | − | 0.962705i | \(-0.587206\pi\) | ||||
−0.270553 | + | 0.962705i | \(0.587206\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3283.58 | −0.248444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8995.70 | 0.673399 | 0.336700 | − | 0.941612i | \(-0.390689\pi\) | ||||
0.336700 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8888.09 | 0.661814 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12326.8 | −0.908202 | −0.454101 | − | 0.890950i | \(-0.650040\pi\) | ||||
−0.454101 | + | 0.890950i | \(0.650040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20671.0 | 1.51498 | 0.757492 | − | 0.652844i | \(-0.226424\pi\) | ||||
0.757492 | + | 0.652844i | \(0.226424\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 184.358 | 0.0133709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4732.48 | 0.341448 | 0.170724 | − | 0.985319i | \(-0.445389\pi\) | ||||
0.170724 | + | 0.985319i | \(0.445389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13314.9 | 0.950769 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7978.47 | 0.566783 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22571.9 | 1.58713 | 0.793564 | − | 0.608487i | \(-0.208223\pi\) | ||||
0.793564 | + | 0.608487i | \(0.208223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3600.05 | −0.251847 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8442.07 | 0.584611 | 0.292306 | − | 0.956325i | \(-0.405578\pi\) | ||||
0.292306 | + | 0.956325i | \(0.405578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2577.68 | 0.177604 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1168.01 | 0.0796722 | 0.0398361 | − | 0.999206i | \(-0.487316\pi\) | ||||
0.0398361 | + | 0.999206i | \(0.487316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14952.9 | 1.01488 | 0.507439 | − | 0.861687i | \(-0.330592\pi\) | ||||
0.507439 | + | 0.861687i | \(0.330592\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9939.80 | −0.667951 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15021.3 | 1.00444 | 0.502221 | − | 0.864739i | \(-0.332516\pi\) | ||||
0.502221 | + | 0.864739i | \(0.332516\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16850.1 | −1.11568 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3705.74 | −0.244165 | −0.122083 | − | 0.992520i | \(-0.538957\pi\) | ||||
−0.122083 | + | 0.992520i | \(0.538957\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19883.5 | 1.29737 | 0.648685 | − | 0.761057i | \(-0.275319\pi\) | ||||
0.648685 | + | 0.761057i | \(0.275319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18451.8 | −1.19813 | −0.599064 | − | 0.800701i | \(-0.704461\pi\) | ||||
−0.599064 | + | 0.800701i | \(0.704461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8203.05 | −0.527525 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5016.28 | 0.317984 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24501.2 | −1.54576 | −0.772882 | − | 0.634549i | \(-0.781186\pi\) | ||||
−0.772882 | + | 0.634549i | \(0.781186\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10033.9 | 0.627060 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2856.44 | −0.177671 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12596.9 | −0.776205 | −0.388102 | − | 0.921616i | \(-0.626869\pi\) | ||||
−0.388102 | + | 0.921616i | \(0.626869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11302.8 | 0.693220 | 0.346610 | − | 0.938009i | \(-0.387333\pi\) | ||||
0.346610 | + | 0.938009i | \(0.387333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1011.85 | 0.0614839 | 0.0307419 | − | 0.999527i | \(-0.490213\pi\) | ||||
0.0307419 | + | 0.999527i | \(0.490213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36352.8 | −2.19872 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4763.76 | −0.285483 | −0.142741 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142741 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6313.44 | 0.376621 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3887.39 | −0.229789 | −0.114895 | − | 0.993378i | \(-0.536653\pi\) | ||||
−0.114895 | + | 0.993378i | \(0.536653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13798.4 | 0.811943 | 0.405972 | − | 0.913886i | \(-0.366933\pi\) | ||||
0.405972 | + | 0.913886i | \(0.366933\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5794.30 | −0.337885 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 126.549 | 0.00734630 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4774.42 | −0.274686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22080.3 | −1.26469 | −0.632343 | − | 0.774688i | \(-0.717907\pi\) | ||||
−0.632343 | + | 0.774688i | \(0.717907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8197.20 | 0.465353 | 0.232677 | − | 0.972554i | \(-0.425252\pi\) | ||||
0.232677 | + | 0.972554i | \(0.425252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10265.4 | 0.580192 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6789.28 | −0.380358 | −0.190179 | − | 0.981749i | \(-0.560907\pi\) | ||||
−0.190179 | + | 0.981749i | \(0.560907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3391.37 | 0.189165 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5371.53 | −0.297009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19512.4 | 1.07422 | 0.537109 | − | 0.843513i | \(-0.319516\pi\) | ||||
0.537109 | + | 0.843513i | \(0.319516\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 683.070 | 0.0372810 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1985.41 | −0.107895 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10670.1 | 0.574898 | 0.287449 | − | 0.957796i | \(-0.407193\pi\) | ||||
0.287449 | + | 0.957796i | \(0.407193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11276.0 | −0.604953 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3957.86 | −0.210538 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27297.4 | −1.44595 | −0.722973 | − | 0.690876i | \(-0.757225\pi\) | ||||
−0.722973 | + | 0.690876i | \(0.757225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −375.978 | −0.0197482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11172.5 | 0.584374 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23257.1 | −1.20632 | −0.603159 | − | 0.797621i | \(-0.706092\pi\) | ||||
−0.603159 | + | 0.797621i | \(0.706092\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23575.3 | −1.21774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 429.017 | 0.0219770 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18331.1 | 0.935163 | 0.467582 | − | 0.883950i | \(-0.345125\pi\) | ||||
0.467582 | + | 0.883950i | \(0.345125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2659.28 | 0.134551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13078.2 | −0.659011 | −0.329505 | − | 0.944154i | \(-0.606882\pi\) | ||||
−0.329505 | + | 0.944154i | \(0.606882\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24876.9 | 1.24336 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12129.6 | −0.603782 | −0.301891 | − | 0.953342i | \(-0.597618\pi\) | ||||
−0.301891 | + | 0.953342i | \(0.597618\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33145.5 | −1.63660 | −0.818298 | − | 0.574794i | \(-0.805082\pi\) | ||||
−0.818298 | + | 0.574794i | \(0.805082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7225.72 | 0.355342 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13151.4 | −0.641580 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2612.04 | 0.126917 | 0.0634585 | − | 0.997984i | \(-0.479787\pi\) | ||||
0.0634585 | + | 0.997984i | \(0.479787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13178.7 | 0.635260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15839.7 | 0.760506 | 0.380253 | − | 0.924883i | \(-0.375837\pi\) | ||||
0.380253 | + | 0.924883i | \(0.375837\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 742.568 | 0.0353720 | 0.0176860 | − | 0.999844i | \(-0.494370\pi\) | ||||
0.0176860 | + | 0.999844i | \(0.494370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −25823.9 | −1.22528 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24474.6 | 1.15219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22719.0 | −1.06537 | −0.532683 | − | 0.846315i | \(-0.678816\pi\) | ||||
−0.532683 | + | 0.846315i | \(0.678816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23215.6 | 1.08022 | 0.540108 | − | 0.841596i | \(-0.318383\pi\) | ||||
0.540108 | + | 0.841596i | \(0.318383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1274.62 | −0.0590783 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4462.97 | 0.205266 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25941.0 | 1.18853 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7619.60 | −0.346440 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25481.4 | 1.15415 | 0.577073 | − | 0.816692i | \(-0.304195\pi\) | ||||
0.577073 | + | 0.816692i | \(0.304195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29174.3 | −1.31140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3214.39 | 0.143942 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22375.2 | −0.994440 | −0.497220 | − | 0.867624i | \(-0.665646\pi\) | ||||
−0.497220 | + | 0.867624i | \(0.665646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13646.4 | 0.604226 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1933.72 | 0.0849809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −605.139 | −0.0264948 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9293.69 | −0.403892 | −0.201946 | − | 0.979397i | \(-0.564727\pi\) | ||||
−0.201946 | + | 0.979397i | \(0.564727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26415.5 | 1.14374 | 0.571871 | − | 0.820344i | \(-0.306218\pi\) | ||||
0.571871 | + | 0.820344i | \(0.306218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11914.6 | 0.512084 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5977.74 | −0.255979 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18148.6 | −0.771486 | −0.385743 | − | 0.922606i | \(-0.626055\pi\) | ||||
−0.385743 | + | 0.922606i | \(0.626055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10438.4 | −0.442115 | −0.221058 | − | 0.975261i | \(-0.570951\pi\) | ||||
−0.221058 | + | 0.975261i | \(0.570951\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18909.8 | −0.795112 | −0.397556 | − | 0.917578i | \(-0.630142\pi\) | ||||
−0.397556 | + | 0.917578i | \(0.630142\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10162.8 | 0.425777 | 0.212888 | − | 0.977077i | \(-0.431713\pi\) | ||||
0.212888 | + | 0.977077i | \(0.431713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2313.35 | 0.0962219 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16902.7 | 0.700529 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16310.9 | 0.671174 | 0.335587 | − | 0.942009i | \(-0.391065\pi\) | ||||
0.335587 | + | 0.942009i | \(0.391065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24094.5 | −0.987925 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3463.09 | 0.140987 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32626.4 | 1.32356 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1177.63 | −0.0474367 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26423.7 | 1.06064 | 0.530322 | − | 0.847796i | \(-0.322071\pi\) | ||||
0.530322 | + | 0.847796i | \(0.322071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19242.4 | −0.766985 | −0.383493 | − | 0.923544i | \(-0.625279\pi\) | ||||
−0.383493 | + | 0.923544i | \(0.625279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3598.56 | 0.142935 | 0.0714677 | − | 0.997443i | \(-0.477232\pi\) | ||||
0.0714677 | + | 0.997443i | \(0.477232\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13195.7 | −0.520496 | −0.260248 | − | 0.965542i | \(-0.583804\pi\) | ||||
−0.260248 | + | 0.965542i | \(0.583804\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 498.425 | 0.0195919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29341.7 | −1.14540 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16748.5 | −0.651550 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2051.50 | −0.0792611 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40460.0 | 1.55785 | 0.778926 | − | 0.627116i | \(-0.215765\pi\) | ||||
0.778926 | + | 0.627116i | \(0.215765\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23036.5 | 0.880955 | 0.440477 | − | 0.897764i | \(-0.354809\pi\) | ||||
0.440477 | + | 0.897764i | \(0.354809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24591.6 | −0.937228 | −0.468614 | − | 0.883403i | \(-0.655246\pi\) | ||||
−0.468614 | + | 0.883403i | \(0.655246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31117.5 | −1.17793 | −0.588966 | − | 0.808158i | \(-0.700465\pi\) | ||||
−0.588966 | + | 0.808158i | \(0.700465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32935.3 | −1.24254 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30675.5 | −1.14952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17064.5 | 0.637323 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −874.933 | −0.0324590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4350.26 | 0.160852 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20319.7 | −0.746353 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25694.5 | 0.940651 | 0.470326 | − | 0.882493i | \(-0.344136\pi\) | ||||
0.470326 | + | 0.882493i | \(0.344136\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19061.3 | 0.693225 | 0.346612 | − | 0.938008i | \(-0.387332\pi\) | ||||
0.346612 | + | 0.938008i | \(0.387332\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46738.8 | −1.69423 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20723.3 | −0.746284 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2322.58 | 0.0833675 | 0.0416838 | − | 0.999131i | \(-0.486728\pi\) | ||||
0.0416838 | + | 0.999131i | \(0.486728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17464.9 | −0.622820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3992.32 | −0.141910 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25814.2 | −0.911664 | −0.455832 | − | 0.890066i | \(-0.650658\pi\) | ||||
−0.455832 | + | 0.890066i | \(0.650658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5200.13 | −0.183058 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9048.30 | −0.316482 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17757.8 | 0.619128 | 0.309564 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309564 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1857.32 | −0.0643431 | −0.0321715 | − | 0.999482i | \(-0.510242\pi\) | ||||
−0.0321715 | + | 0.999482i | \(0.510242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 466.099 | 0.0160957 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10837.6 | −0.371885 | −0.185943 | − | 0.982561i | \(-0.559534\pi\) | ||||
−0.185943 | + | 0.982561i | \(0.559534\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1301.88 | −0.0445321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2386.31 | 0.0811125 | 0.0405562 | − | 0.999177i | \(-0.487087\pi\) | ||||
0.0405562 | + | 0.999177i | \(0.487087\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10818.6 | 0.366578 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11131.9 | −0.374835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27191.6 | −0.912744 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22160.3 | −0.739238 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12418.4 | 0.412977 | 0.206489 | − | 0.978449i | \(-0.433796\pi\) | ||||
0.206489 | + | 0.978449i | \(0.433796\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50399.5 | −1.66570 | −0.832851 | − | 0.553498i | \(-0.813293\pi\) | ||||
−0.832851 | + | 0.553498i | \(0.813293\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2242.11 | −0.0738734 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56849.3 | −1.86159 | −0.930793 | − | 0.365547i | \(-0.880882\pi\) | ||||
−0.930793 | + | 0.365547i | \(0.880882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28794.8 | 0.940027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13309.5 | −0.431850 | −0.215925 | − | 0.976410i | \(-0.569277\pi\) | ||||
−0.215925 | + | 0.976410i | \(0.569277\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21169.4 | −0.684785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −624.296 | −0.0200723 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19322.3 | −0.619369 | −0.309684 | − | 0.950839i | \(-0.600223\pi\) | ||||
−0.309684 | + | 0.950839i | \(0.600223\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14169.7 | 0.451466 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8263.31 | 0.262489 | 0.131245 | − | 0.991350i | \(-0.458103\pi\) | ||||
0.131245 | + | 0.991350i | \(0.458103\pi\) | |||||||
\(998\) | 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 | 1080.4.a.e.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.k.1.3 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bj.1.1 | 3 | |||
12.11 | even | 2 | 2160.4.a.br.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.e.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.k.1.3 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bj.1.1 | 3 | 4.3 | odd | 2 | |||
2160.4.a.br.1.1 | 3 | 12.11 | even | 2 |