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: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.697.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 7x - 5 \) |
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 | 1.2 | ||
Root | \(2.94883\) 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 | ||||||||
\(7\) | −14.4806 | −0.781877 | −0.390938 | − | 0.920417i | \(-0.627849\pi\) | ||||
−0.390938 | + | 0.920417i | \(0.627849\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.9443 | 0.382214 | 0.191107 | − | 0.981569i | \(-0.438792\pi\) | ||||
0.191107 | + | 0.981569i | \(0.438792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.8276 | −0.828373 | −0.414186 | − | 0.910192i | \(-0.635934\pi\) | ||||
−0.414186 | + | 0.910192i | \(0.635934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −126.063 | −1.79852 | −0.899259 | − | 0.437416i | \(-0.855894\pi\) | ||||
−0.899259 | + | 0.437416i | \(0.855894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 60.5995 | 0.731709 | 0.365855 | − | 0.930672i | \(-0.380777\pi\) | ||||
0.365855 | + | 0.930672i | \(0.380777\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 50.3522 | 0.456485 | 0.228243 | − | 0.973604i | \(-0.426702\pi\) | ||||
0.228243 | + | 0.973604i | \(0.426702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −71.3302 | −0.456748 | −0.228374 | − | 0.973574i | \(-0.573341\pi\) | ||||
−0.228374 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.7087 | −0.166330 | −0.0831650 | − | 0.996536i | \(-0.526503\pi\) | ||||
−0.0831650 | + | 0.996536i | \(0.526503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 72.4028 | 0.349666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 76.6164 | 0.340423 | 0.170212 | − | 0.985408i | \(-0.445555\pi\) | ||||
0.170212 | + | 0.985408i | \(0.445555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 396.151 | 1.50898 | 0.754492 | − | 0.656309i | \(-0.227883\pi\) | ||||
0.754492 | + | 0.656309i | \(0.227883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −351.146 | −1.24533 | −0.622665 | − | 0.782488i | \(-0.713950\pi\) | ||||
−0.622665 | + | 0.782488i | \(0.713950\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.16809 | −0.0129357 | −0.00646786 | − | 0.999979i | \(-0.502059\pi\) | ||||
−0.00646786 | + | 0.999979i | \(0.502059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −133.313 | −0.388669 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 171.983 | 0.445730 | 0.222865 | − | 0.974849i | \(-0.428459\pi\) | ||||
0.222865 | + | 0.974849i | \(0.428459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −69.7213 | −0.170931 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 116.634 | 0.257363 | 0.128682 | − | 0.991686i | \(-0.458926\pi\) | ||||
0.128682 | + | 0.991686i | \(0.458926\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 523.955 | 1.09976 | 0.549882 | − | 0.835242i | \(-0.314673\pi\) | ||||
0.549882 | + | 0.835242i | \(0.314673\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 194.138 | 0.370460 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −872.421 | −1.59079 | −0.795397 | − | 0.606088i | \(-0.792738\pi\) | ||||
−0.795397 | + | 0.606088i | \(0.792738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 802.371 | 1.34118 | 0.670591 | − | 0.741827i | \(-0.266040\pi\) | ||||
0.670591 | + | 0.741827i | \(0.266040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.5264 | −0.0216869 | −0.0108435 | − | 0.999941i | \(-0.503452\pi\) | ||||
−0.0108435 | + | 0.999941i | \(0.503452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −201.921 | −0.298844 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 597.959 | 0.851590 | 0.425795 | − | 0.904820i | \(-0.359994\pi\) | ||||
0.425795 | + | 0.904820i | \(0.359994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 75.9439 | 0.100433 | 0.0502164 | − | 0.998738i | \(-0.484009\pi\) | ||||
0.0502164 | + | 0.998738i | \(0.484009\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 630.316 | 0.804322 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 799.744 | 0.952502 | 0.476251 | − | 0.879309i | \(-0.341995\pi\) | ||||
0.476251 | + | 0.879309i | \(0.341995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 562.246 | 0.647685 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −302.998 | −0.327230 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 445.123 | 0.465932 | 0.232966 | − | 0.972485i | \(-0.425157\pi\) | ||||
0.232966 | + | 0.972485i | \(0.425157\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −202.087 | −0.199093 | −0.0995466 | − | 0.995033i | \(-0.531739\pi\) | ||||
−0.0995466 | + | 0.995033i | \(0.531739\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 782.676 | 0.748732 | 0.374366 | − | 0.927281i | \(-0.377860\pi\) | ||||
0.374366 | + | 0.927281i | \(0.377860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1886.42 | 1.70437 | 0.852184 | − | 0.523242i | \(-0.175278\pi\) | ||||
0.852184 | + | 0.523242i | \(0.175278\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 604.673 | 0.531351 | 0.265675 | − | 0.964063i | \(-0.414405\pi\) | ||||
0.265675 | + | 0.964063i | \(0.414405\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1585.09 | 1.31958 | 0.659792 | − | 0.751448i | \(-0.270644\pi\) | ||||
0.659792 | + | 0.751448i | \(0.270644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −251.761 | −0.204146 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1825.47 | 1.40622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1136.56 | −0.853913 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1464.36 | −1.02316 | −0.511579 | − | 0.859236i | \(-0.670939\pi\) | ||||
−0.511579 | + | 0.859236i | \(0.670939\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −420.667 | −0.280564 | −0.140282 | − | 0.990112i | \(-0.544801\pi\) | ||||
−0.140282 | + | 0.990112i | \(0.544801\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −877.515 | −0.572107 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −154.631 | −0.0964305 | −0.0482152 | − | 0.998837i | \(-0.515353\pi\) | ||||
−0.0482152 | + | 0.998837i | \(0.515353\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1838.83 | −1.12207 | −0.561033 | − | 0.827793i | \(-0.689596\pi\) | ||||
−0.561033 | + | 0.827793i | \(0.689596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −541.422 | −0.316615 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 356.651 | 0.204264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1647.61 | 0.905887 | 0.452943 | − | 0.891539i | \(-0.350374\pi\) | ||||
0.452943 | + | 0.891539i | \(0.350374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1023.34 | 0.551509 | 0.275754 | − | 0.961228i | \(-0.411072\pi\) | ||||
0.275754 | + | 0.961228i | \(0.411072\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 143.543 | 0.0743851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −880.210 | −0.447442 | −0.223721 | − | 0.974653i | \(-0.571820\pi\) | ||||
−0.223721 | + | 0.974653i | \(0.571820\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −729.128 | −0.356915 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1346.77 | 0.647159 | 0.323580 | − | 0.946201i | \(-0.395114\pi\) | ||||
0.323580 | + | 0.946201i | \(0.395114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2579.87 | 1.19543 | 0.597714 | − | 0.801709i | \(-0.296076\pi\) | ||||
0.597714 | + | 0.801709i | \(0.296076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −689.415 | −0.313799 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2877.71 | 1.26467 | 0.632337 | − | 0.774694i | \(-0.282096\pi\) | ||||
0.632337 | + | 0.774694i | \(0.282096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −362.014 | −0.156375 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1906.79 | −0.796204 | −0.398102 | − | 0.917341i | \(-0.630331\pi\) | ||||
−0.398102 | + | 0.917341i | \(0.630331\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4841.10 | 1.98805 | 0.994023 | − | 0.109173i | \(-0.0348201\pi\) | ||||
0.994023 | + | 0.109173i | \(0.0348201\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −383.082 | −0.152242 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1757.86 | −0.687418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 104.064 | 0.0394230 | 0.0197115 | − | 0.999806i | \(-0.493725\pi\) | ||||
0.0197115 | + | 0.999806i | \(0.493725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3903.96 | 1.45603 | 0.728013 | − | 0.685563i | \(-0.240444\pi\) | ||||
0.728013 | + | 0.685563i | \(0.240444\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4844.92 | 1.75222 | 0.876108 | − | 0.482115i | \(-0.160131\pi\) | ||||
0.876108 | + | 0.482115i | \(0.160131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −947.744 | −0.337607 | −0.168803 | − | 0.985650i | \(-0.553990\pi\) | ||||
−0.168803 | + | 0.985650i | \(0.553990\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1032.90 | 0.357120 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1980.75 | −0.674838 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 845.015 | 0.279669 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3869.01 | −1.26234 | −0.631169 | − | 0.775645i | \(-0.717425\pi\) | ||||
−0.631169 | + | 0.775645i | \(0.717425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1755.73 | 0.556929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 415.718 | 0.130050 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4894.73 | 1.48984 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3123.95 | −0.938094 | −0.469047 | − | 0.883173i | \(-0.655403\pi\) | ||||
−0.469047 | + | 0.883173i | \(0.655403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1436.53 | 0.420025 | 0.210013 | − | 0.977699i | \(-0.432649\pi\) | ||||
0.210013 | + | 0.977699i | \(0.432649\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3375.00 | 0.973913 | 0.486956 | − | 0.873426i | \(-0.338107\pi\) | ||||
0.486956 | + | 0.873426i | \(0.338107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −396.743 | −0.111552 | −0.0557758 | − | 0.998443i | \(-0.517763\pi\) | ||||
−0.0557758 | + | 0.998443i | \(0.517763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.8405 | 0.00578503 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 394.888 | 0.106875 | 0.0534376 | − | 0.998571i | \(-0.482982\pi\) | ||||
0.0534376 | + | 0.998571i | \(0.482982\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1003.83 | −0.268309 | −0.134154 | − | 0.990960i | \(-0.542832\pi\) | ||||
−0.134154 | + | 0.990960i | \(0.542832\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 666.567 | 0.173818 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2352.93 | −0.606128 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6616.38 | 1.66383 | 0.831916 | − | 0.554901i | \(-0.187244\pi\) | ||||
0.831916 | + | 0.554901i | \(0.187244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 702.124 | 0.174475 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5198.46 | −1.26175 | −0.630877 | − | 0.775883i | \(-0.717305\pi\) | ||||
−0.630877 | + | 0.775883i | \(0.717305\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1109.45 | −0.266169 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2229.79 | 0.522793 | 0.261396 | − | 0.965232i | \(-0.415817\pi\) | ||||
0.261396 | + | 0.965232i | \(0.415817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −859.916 | −0.199337 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1227.05 | 0.278121 | 0.139060 | − | 0.990284i | \(-0.455592\pi\) | ||||
0.139060 | + | 0.990284i | \(0.455592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −271.993 | −0.0609683 | −0.0304842 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304842 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 348.606 | 0.0764427 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1373.62 | 0.297952 | 0.148976 | − | 0.988841i | \(-0.452402\pi\) | ||||
0.148976 | + | 0.988841i | \(0.452402\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 583.170 | 0.123804 | 0.0619022 | − | 0.998082i | \(-0.480283\pi\) | ||||
0.0619022 | + | 0.998082i | \(0.480283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7637.81 | −1.60431 | −0.802157 | − | 0.597113i | \(-0.796314\pi\) | ||||
−0.802157 | + | 0.597113i | \(0.796314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5736.49 | −1.17984 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10978.9 | 2.23467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1859.74 | −0.370810 | −0.185405 | − | 0.982662i | \(-0.559360\pi\) | ||||
−0.185405 | + | 0.982662i | \(0.559360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −583.169 | −0.115096 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1955.06 | −0.378140 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5084.79 | 0.973695 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2619.78 | −0.491830 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3932.33 | 0.731042 | 0.365521 | − | 0.930803i | \(-0.380891\pi\) | ||||
0.365521 | + | 0.930803i | \(0.380891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4756.90 | −0.867328 | −0.433664 | − | 0.901075i | \(-0.642780\pi\) | ||||
−0.433664 | + | 0.901075i | \(0.642780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9621.84 | 1.73757 | 0.868784 | − | 0.495192i | \(-0.164902\pi\) | ||||
0.868784 | + | 0.495192i | \(0.164902\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5132.07 | −0.909293 | −0.454647 | − | 0.890672i | \(-0.650234\pi\) | ||||
−0.454647 | + | 0.890672i | \(0.650234\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −994.646 | −0.174575 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7639.37 | −1.31599 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −970.691 | −0.165675 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 60.3564 | 0.0101141 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7436.78 | −1.23493 | −0.617466 | − | 0.786598i | \(-0.711841\pi\) | ||||
−0.617466 | + | 0.786598i | \(0.711841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4362.11 | 0.711425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10303.6 | −1.66549 | −0.832745 | − | 0.553656i | \(-0.813232\pi\) | ||||
−0.832745 | + | 0.553656i | \(0.813232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −400.321 | −0.0635736 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6897.28 | 1.08577 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3021.04 | 0.467371 | 0.233685 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233685 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10116.8 | 1.55169 | 0.775845 | − | 0.630923i | \(-0.217324\pi\) | ||||
0.775845 | + | 0.630923i | \(0.217324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2056.72 | 0.310108 | 0.155054 | − | 0.987906i | \(-0.450445\pi\) | ||||
0.155054 | + | 0.987906i | \(0.450445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4011.86 | −0.599795 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2034.25 | −0.299062 | −0.149531 | − | 0.988757i | \(-0.547776\pi\) | ||||
−0.149531 | + | 0.988757i | \(0.547776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3186.70 | −0.464601 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 67.6319 | 0.00969868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5846.96 | −0.831631 | −0.415816 | − | 0.909449i | \(-0.636504\pi\) | ||||
−0.415816 | + | 0.909449i | \(0.636504\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2490.41 | −0.348506 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6479.76 | −0.899489 | −0.449744 | − | 0.893157i | \(-0.648485\pi\) | ||||
−0.449744 | + | 0.893157i | \(0.648485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2769.58 | 0.378357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4930.57 | 0.668249 | 0.334124 | − | 0.942529i | \(-0.391559\pi\) | ||||
0.334124 | + | 0.942529i | \(0.391559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4843.57 | −0.646200 | −0.323100 | − | 0.946365i | \(-0.604725\pi\) | ||||
−0.323100 | + | 0.946365i | \(0.604725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1009.60 | 0.133647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11498.9 | −1.49875 | −0.749377 | − | 0.662144i | \(-0.769647\pi\) | ||||
−0.749377 | + | 0.662144i | \(0.769647\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6347.56 | −0.820997 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2989.79 | −0.380843 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8087.11 | 1.02237 | 0.511185 | − | 0.859471i | \(-0.329207\pi\) | ||||
0.511185 | + | 0.859471i | \(0.329207\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4956.24 | −0.617214 | −0.308607 | − | 0.951190i | \(-0.599863\pi\) | ||||
−0.308607 | + | 0.951190i | \(0.599863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1114.69 | 0.137783 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1068.36 | 0.130114 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4001.74 | −0.483798 | −0.241899 | − | 0.970301i | \(-0.577770\pi\) | ||||
−0.241899 | + | 0.970301i | \(0.577770\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1688.92 | −0.201226 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −379.720 | −0.0449149 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6684.47 | 0.779374 | 0.389687 | − | 0.920947i | \(-0.372583\pi\) | ||||
0.389687 | + | 0.920947i | \(0.372583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3614.61 | −0.418445 | −0.209223 | − | 0.977868i | \(-0.567093\pi\) | ||||
−0.209223 | + | 0.977868i | \(0.567093\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3151.58 | −0.359704 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7587.17 | −0.859880 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11100.0 | −1.24053 | −0.620263 | − | 0.784394i | \(-0.712974\pi\) | ||||
−0.620263 | + | 0.784394i | \(0.712974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11212.5 | 1.24443 | 0.622216 | − | 0.782846i | \(-0.286233\pi\) | ||||
0.622216 | + | 0.782846i | \(0.286233\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3051.32 | 0.334015 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7039.25 | 0.765297 | 0.382648 | − | 0.923894i | \(-0.375012\pi\) | ||||
0.382648 | + | 0.923894i | \(0.375012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11542.1 | 1.23788 | 0.618942 | − | 0.785437i | \(-0.287562\pi\) | ||||
0.618942 | + | 0.785437i | \(0.287562\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3998.72 | −0.425972 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2433.58 | 0.255785 | 0.127893 | − | 0.991788i | \(-0.459179\pi\) | ||||
0.127893 | + | 0.991788i | \(0.459179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5524.03 | 0.576754 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2811.23 | −0.289654 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11241.9 | −1.15071 | −0.575354 | − | 0.817904i | \(-0.695136\pi\) | ||||
−0.575354 | + | 0.817904i | \(0.695136\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9356.41 | −0.945275 | −0.472637 | − | 0.881257i | \(-0.656698\pi\) | ||||
−0.472637 | + | 0.881257i | \(0.656698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10726.8 | −1.07671 | −0.538356 | − | 0.842717i | \(-0.680955\pi\) | ||||
−0.538356 | + | 0.842717i | \(0.680955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10271.5 | −1.01780 | −0.508898 | − | 0.860827i | \(-0.669947\pi\) | ||||
−0.508898 | + | 0.860827i | \(0.669947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12633.2 | 1.24381 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4896.46 | −0.475982 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1514.99 | 0.146342 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7530.03 | 0.718280 | 0.359140 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359140 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2974.83 | −0.281997 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2225.61 | −0.208371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17882.0 | −1.66388 | −0.831942 | − | 0.554862i | \(-0.812771\pi\) | ||||
−0.831942 | + | 0.554862i | \(0.812771\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13309.9 | −1.22336 | −0.611679 | − | 0.791106i | \(-0.709506\pi\) | ||||
−0.611679 | + | 0.791106i | \(0.709506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8992.11 | 0.821469 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11618.8 | −1.04864 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9876.59 | 0.886046 | 0.443023 | − | 0.896510i | \(-0.353906\pi\) | ||||
0.443023 | + | 0.896510i | \(0.353906\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1983.95 | −0.175864 | −0.0879321 | − | 0.996126i | \(-0.528026\pi\) | ||||
−0.0879321 | + | 0.996126i | \(0.528026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1010.44 | 0.0890372 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9423.36 | −0.820595 | −0.410298 | − | 0.911952i | \(-0.634575\pi\) | ||||
−0.410298 | + | 0.911952i | \(0.634575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 195.870 | 0.0169565 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3913.38 | −0.334843 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.1210 | −0.00494421 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12938.3 | 1.08798 | 0.543988 | − | 0.839093i | \(-0.316914\pi\) | ||||
0.543988 | + | 0.839093i | \(0.316914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9800.41 | 0.819392 | 0.409696 | − | 0.912222i | \(-0.365635\pi\) | ||||
0.409696 | + | 0.912222i | \(0.365635\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3619.11 | 0.299148 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9631.66 | −0.791621 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15381.6 | −1.25000 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9432.11 | −0.762217 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1858.95 | −0.148554 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19852.4 | 1.57767 | 0.788836 | − | 0.614604i | \(-0.210684\pi\) | ||||
0.788836 | + | 0.614604i | \(0.210684\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3023.37 | −0.237627 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23140.5 | −1.80880 | −0.904402 | − | 0.426681i | \(-0.859683\pi\) | ||||
−0.904402 | + | 0.426681i | \(0.859683\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4322.57 | −0.334207 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8658.78 | −0.665838 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2127.55 | 0.161844 | 0.0809222 | − | 0.996720i | \(-0.474213\pi\) | ||||
0.0809222 | + | 0.996720i | \(0.474213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13634.1 | 1.03160 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17206.7 | −1.28806 | −0.644028 | − | 0.765002i | \(-0.722738\pi\) | ||||
−0.644028 | + | 0.765002i | \(0.722738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7925.47 | −0.590136 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13928.6 | −1.02622 | −0.513108 | − | 0.858324i | \(-0.671506\pi\) | ||||
−0.513108 | + | 0.858324i | \(0.671506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −201.457 | −0.0147648 | −0.00738239 | − | 0.999973i | \(-0.502350\pi\) | ||||
−0.00738239 | + | 0.999973i | \(0.502350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1258.81 | 0.0912970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 164.727 | 0.0118851 | 0.00594253 | − | 0.999982i | \(-0.498108\pi\) | ||||
0.00594253 | + | 0.999982i | \(0.498108\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1099.71 | −0.0785261 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2398.18 | 0.170364 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14327.9 | −1.00746 | −0.503728 | − | 0.863862i | \(-0.668039\pi\) | ||||
−0.503728 | + | 0.863862i | \(0.668039\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1739.73 | −0.121705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13213.8 | 0.915049 | 0.457525 | − | 0.889197i | \(-0.348736\pi\) | ||||
0.457525 | + | 0.889197i | \(0.348736\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9127.33 | −0.628881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13780.3 | −0.939979 | −0.469990 | − | 0.882672i | \(-0.655742\pi\) | ||||
−0.469990 | + | 0.882672i | \(0.655742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1473.27 | 0.0999933 | 0.0499966 | − | 0.998749i | \(-0.484079\pi\) | ||||
0.0499966 | + | 0.998749i | \(0.484079\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5682.79 | 0.381881 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9450.54 | −0.631937 | −0.315968 | − | 0.948770i | \(-0.602329\pi\) | ||||
−0.315968 | + | 0.948770i | \(0.602329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 161.837 | 0.0107156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17768.1 | 1.17071 | 0.585356 | − | 0.810777i | \(-0.300955\pi\) | ||||
0.585356 | + | 0.810777i | \(0.300955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5429.29 | 0.354255 | 0.177127 | − | 0.984188i | \(-0.443320\pi\) | ||||
0.177127 | + | 0.984188i | \(0.443320\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6441.62 | 0.418273 | 0.209136 | − | 0.977886i | \(-0.432935\pi\) | ||||
0.209136 | + | 0.977886i | \(0.432935\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11580.7 | −0.744740 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9658.51 | −0.612257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21418.5 | 1.35128 | 0.675639 | − | 0.737232i | \(-0.263868\pi\) | ||||
0.675639 | + | 0.737232i | \(0.263868\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7321.81 | 0.457570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5176.24 | 0.321962 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1413.11 | 0.0870740 | 0.0435370 | − | 0.999052i | \(-0.486137\pi\) | ||||
0.0435370 | + | 0.999052i | \(0.486137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23835.3 | 1.46185 | 0.730926 | − | 0.682456i | \(-0.239088\pi\) | ||||
0.730926 | + | 0.682456i | \(0.239088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13237.4 | −0.804350 | −0.402175 | − | 0.915563i | \(-0.631746\pi\) | ||||
−0.402175 | + | 0.915563i | \(0.631746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1626.37 | 0.0983677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23830.7 | 1.42813 | 0.714064 | − | 0.700081i | \(-0.246853\pi\) | ||||
0.714064 | + | 0.700081i | \(0.246853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2103.33 | 0.125472 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8249.82 | 0.487659 | 0.243830 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243830 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13951.8 | 0.820970 | 0.410485 | − | 0.911867i | \(-0.365359\pi\) | ||||
0.410485 | + | 0.911867i | \(0.365359\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4387.57 | 0.255854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3591.63 | −0.208499 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7306.17 | 0.420345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11395.9 | −0.652717 | −0.326358 | − | 0.945246i | \(-0.605822\pi\) | ||||
−0.326358 | + | 0.945246i | \(0.605822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3944.88 | 0.223950 | 0.111975 | − | 0.993711i | \(-0.464282\pi\) | ||||
0.111975 | + | 0.993711i | \(0.464282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6445.63 | −0.364301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30972.3 | −1.73517 | −0.867584 | − | 0.497290i | \(-0.834328\pi\) | ||||
−0.867584 | + | 0.497290i | \(0.834328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 773.153 | 0.0431250 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6677.70 | −0.369231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21561.2 | 1.18701 | 0.593506 | − | 0.804830i | \(-0.297743\pi\) | ||||
0.593506 | + | 0.804830i | \(0.297743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9194.13 | 0.501803 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49940.0 | −2.71394 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10381.1 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4642.91 | 0.249091 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2926.33 | 0.155666 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15336.2 | 0.812357 | 0.406179 | − | 0.913794i | \(-0.366861\pi\) | ||||
0.406179 | + | 0.913794i | \(0.366861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1445.55 | −0.0759272 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2707.11 | 0.141595 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26655.6 | 1.38260 | 0.691298 | − | 0.722570i | \(-0.257039\pi\) | ||||
0.691298 | + | 0.722570i | \(0.257039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11333.6 | −0.585416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1783.25 | −0.0913495 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31166.6 | −1.58997 | −0.794983 | − | 0.606631i | \(-0.792520\pi\) | ||||
−0.794983 | + | 0.606631i | \(0.792520\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44266.5 | 2.23975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5735.03 | 0.288988 | 0.144494 | − | 0.989506i | \(-0.453845\pi\) | ||||
0.144494 | + | 0.989506i | \(0.453845\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12165.3 | −0.608024 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28634.6 | 1.42536 | 0.712680 | − | 0.701489i | \(-0.247481\pi\) | ||||
0.712680 | + | 0.701489i | \(0.247481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14988.8 | 0.740086 | 0.370043 | − | 0.929015i | \(-0.379343\pi\) | ||||
0.370043 | + | 0.929015i | \(0.379343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8238.03 | −0.405125 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27316.5 | −1.33261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19998.2 | −0.971696 | −0.485848 | − | 0.874043i | \(-0.661489\pi\) | ||||
−0.485848 | + | 0.874043i | \(0.661489\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5116.68 | −0.246642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31663.4 | −1.52025 | −0.760123 | − | 0.649779i | \(-0.774861\pi\) | ||||
−0.760123 | + | 0.649779i | \(0.774861\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21227.4 | −1.01116 | −0.505581 | − | 0.862779i | \(-0.668722\pi\) | ||||
−0.505581 | + | 0.862779i | \(0.668722\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8756.01 | −0.415451 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4528.61 | −0.213193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21304.5 | 0.999037 | 0.499518 | − | 0.866303i | \(-0.333510\pi\) | ||||
0.499518 | + | 0.866303i | \(0.333510\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16993.1 | 0.790686 | 0.395343 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395343 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −717.717 | −0.0332660 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24006.5 | 1.10414 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11188.5 | 0.512618 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4401.05 | 0.200102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4191.03 | −0.189827 | −0.0949137 | − | 0.995486i | \(-0.530258\pi\) | ||||
−0.0949137 | + | 0.995486i | \(0.530258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22953.0 | −1.03175 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20343.9 | −0.911015 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34926.1 | 1.55225 | 0.776126 | − | 0.630578i | \(-0.217182\pi\) | ||||
0.776126 | + | 0.630578i | \(0.217182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 525.443 | 0.0232651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −188.615 | −0.00828903 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3645.64 | 0.159617 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1388.34 | −0.0603355 | −0.0301677 | − | 0.999545i | \(-0.509604\pi\) | ||||
−0.0301677 | + | 0.999545i | \(0.509604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11611.7 | −0.502766 | −0.251383 | − | 0.967888i | \(-0.580885\pi\) | ||||
−0.251383 | + | 0.967888i | \(0.580885\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6733.84 | −0.289418 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21279.2 | −0.911220 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5754.09 | 0.244603 | 0.122302 | − | 0.992493i | \(-0.460973\pi\) | ||||
0.122302 | + | 0.992493i | \(0.460973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31328.1 | 1.32689 | 0.663443 | − | 0.748227i | \(-0.269094\pi\) | ||||
0.663443 | + | 0.748227i | \(0.269094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22192.5 | 0.933143 | 0.466572 | − | 0.884483i | \(-0.345489\pi\) | ||||
0.466572 | + | 0.884483i | \(0.345489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26744.5 | 1.12048 | 0.560238 | − | 0.828331i | \(-0.310710\pi\) | ||||
0.560238 | + | 0.828331i | \(0.310710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16805.9 | 0.699028 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12899.4 | −0.534612 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40896.3 | 1.68283 | 0.841416 | − | 0.540388i | \(-0.181723\pi\) | ||||
0.841416 | + | 0.540388i | \(0.181723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19301.0 | −0.791381 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3447.08 | 0.140335 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16458.0 | 0.667655 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3857.80 | 0.155398 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2596.52 | 0.104224 | 0.0521120 | − | 0.998641i | \(-0.483405\pi\) | ||||
0.0521120 | + | 0.998641i | \(0.483405\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19284.5 | 0.768665 | 0.384332 | − | 0.923195i | \(-0.374432\pi\) | ||||
0.384332 | + | 0.923195i | \(0.374432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12590.5 | 0.500098 | 0.250049 | − | 0.968233i | \(-0.419553\pi\) | ||||
0.250049 | + | 0.968233i | \(0.419553\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28897.6 | 1.13984 | 0.569921 | − | 0.821699i | \(-0.306974\pi\) | ||||
0.569921 | + | 0.821699i | \(0.306974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14388.6 | −0.565579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8338.09 | 0.325489 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33874.1 | 1.31777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1810.07 | 0.0699332 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38957.0 | −1.49998 | −0.749991 | − | 0.661448i | \(-0.769942\pi\) | ||||
−0.749991 | + | 0.661448i | \(0.769942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21416.2 | 0.818989 | 0.409495 | − | 0.912313i | \(-0.365705\pi\) | ||||
0.409495 | + | 0.912313i | \(0.365705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12270.0 | 0.467631 | 0.233816 | − | 0.972281i | \(-0.424879\pi\) | ||||
0.233816 | + | 0.972281i | \(0.424879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23430.6 | −0.886947 | −0.443473 | − | 0.896288i | \(-0.646254\pi\) | ||||
−0.443473 | + | 0.896288i | \(0.646254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21204.8 | 0.799984 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −252.584 | −0.00946519 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9533.97 | 0.356073 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2047.80 | 0.0759709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21680.7 | −0.801654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24205.5 | −0.889081 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14548.3 | 0.532599 | 0.266300 | − | 0.963890i | \(-0.414199\pi\) | ||||
0.266300 | + | 0.963890i | \(0.414199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19448.2 | 0.707297 | 0.353649 | − | 0.935378i | \(-0.384941\pi\) | ||||
0.353649 | + | 0.935378i | \(0.384941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1058.98 | 0.0383868 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6091.49 | 0.219366 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23106.0 | 0.829376 | 0.414688 | − | 0.909964i | \(-0.363891\pi\) | ||||
0.414688 | + | 0.909964i | \(0.363891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31154.2 | −1.11100 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1915.41 | 0.0680846 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −687.069 | −0.0242648 | −0.0121324 | − | 0.999926i | \(-0.503862\pi\) | ||||
−0.0121324 | + | 0.999926i | \(0.503862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8078.72 | −0.284392 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8789.29 | 0.307423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17926.3 | −0.625003 | −0.312502 | − | 0.949917i | \(-0.601167\pi\) | ||||
−0.312502 | + | 0.949917i | \(0.601167\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11253.2 | −0.389843 | −0.194921 | − | 0.980819i | \(-0.562445\pi\) | ||||
−0.194921 | + | 0.980819i | \(0.562445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19947.1 | 0.688829 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43243.3 | 1.48386 | 0.741931 | − | 0.670476i | \(-0.233910\pi\) | ||||
0.741931 | + | 0.670476i | \(0.233910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 525.198 | 0.0179648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44192.2 | 1.50213 | 0.751063 | − | 0.660230i | \(-0.229541\pi\) | ||||
0.751063 | + | 0.660230i | \(0.229541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −520.319 | −0.0176305 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2239.14 | 0.0753968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28966.8 | −0.972334 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19519.8 | −0.651155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2689.33 | 0.0894345 | 0.0447172 | − | 0.999000i | \(-0.485761\pi\) | ||||
0.0447172 | + | 0.999000i | \(0.485761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49178.9 | −1.62536 | −0.812680 | − | 0.582710i | \(-0.801992\pi\) | ||||
−0.812680 | + | 0.582710i | \(0.801992\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26627.2 | 0.877318 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60933.9 | 1.99534 | 0.997670 | − | 0.0682270i | \(-0.0217342\pi\) | ||||
0.997670 | + | 0.0682270i | \(0.0217342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11151.8 | 0.364059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 255.703 | 0.00829672 | 0.00414836 | − | 0.999991i | \(-0.498680\pi\) | ||||
0.00414836 | + | 0.999991i | \(0.498680\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24224.6 | −0.783615 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17681.0 | −0.568475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33864.4 | 1.08551 | 0.542754 | − | 0.839892i | \(-0.317382\pi\) | ||||
0.542754 | + | 0.839892i | \(0.317382\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4738.72 | 0.150982 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52881.3 | −1.67981 | −0.839904 | − | 0.542735i | \(-0.817389\pi\) | ||||
−0.839904 | + | 0.542735i | \(0.817389\pi\) | |||||||
\(998\) | 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.c.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.i.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bl.1.2 | 3 | |||
12.11 | even | 2 | 2160.4.a.bt.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.i.1.2 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bl.1.2 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bt.1.2 | 3 | 12.11 | even | 2 |