Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.22168\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.80044 | 1.69961 | 0.849805 | − | 0.527098i | \(-0.176720\pi\) | ||||
0.849805 | + | 0.527098i | \(0.176720\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.80044 | 1.20181 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.44335 | −1.78707 | −0.893533 | − | 0.448998i | \(-0.851781\pi\) | ||||
−0.893533 | + | 0.448998i | \(0.851781\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.80044 | 0.921742 | 0.460871 | − | 0.887467i | \(-0.347537\pi\) | ||||
0.460871 | + | 0.887467i | \(0.347537\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.64291 | 1.52399 | 0.761994 | − | 0.647584i | \(-0.224220\pi\) | ||||
0.761994 | + | 0.647584i | \(0.224220\pi\) | |||||||
\(20\) | 3.80044 | 0.849805 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.842472 | 0.175668 | 0.0878338 | − | 0.996135i | \(-0.472006\pi\) | ||||
0.0878338 | + | 0.996135i | \(0.472006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.44335 | 1.88867 | ||||||||
\(26\) | −6.44335 | −1.26365 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −8.44335 | −1.56789 | −0.783946 | − | 0.620829i | \(-0.786796\pi\) | ||||
−0.783946 | + | 0.620829i | \(0.786796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.40132 | −1.68853 | −0.844264 | − | 0.535928i | \(-0.819962\pi\) | ||||
−0.844264 | + | 0.535928i | \(0.819962\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.80044 | 0.651770 | ||||||||
\(35\) | 3.80044 | 0.642392 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.60088 | 1.57838 | 0.789188 | − | 0.614152i | \(-0.210502\pi\) | ||||
0.789188 | + | 0.614152i | \(0.210502\pi\) | |||||||
\(38\) | 6.64291 | 1.07762 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.80044 | 0.600903 | ||||||||
\(41\) | −3.80044 | −0.593529 | −0.296765 | − | 0.954951i | \(-0.595908\pi\) | ||||
−0.296765 | + | 0.954951i | \(0.595908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.04424 | −1.22673 | −0.613367 | − | 0.789798i | \(-0.710185\pi\) | ||||
−0.613367 | + | 0.789798i | \(0.710185\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.842472 | 0.124216 | ||||||||
\(47\) | 6.24380 | 0.910751 | 0.455376 | − | 0.890299i | \(-0.349505\pi\) | ||||
0.455376 | + | 0.890299i | \(0.349505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 9.44335 | 1.33549 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.44335 | −0.893533 | ||||||||
\(53\) | −1.60088 | −0.219898 | −0.109949 | − | 0.993937i | \(-0.535069\pi\) | ||||
−0.109949 | + | 0.993937i | \(0.535069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.80044 | 0.512451 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.44335 | −1.10867 | ||||||||
\(59\) | −9.28583 | −1.20891 | −0.604456 | − | 0.796639i | \(-0.706609\pi\) | ||||
−0.604456 | + | 0.796639i | \(0.706609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.75841 | 1.12140 | 0.560700 | − | 0.828019i | \(-0.310532\pi\) | ||||
0.560700 | + | 0.828019i | \(0.310532\pi\) | |||||||
\(62\) | −9.40132 | −1.19397 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −24.4876 | −3.03731 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.15753 | 0.141415 | 0.0707073 | − | 0.997497i | \(-0.477474\pi\) | ||||
0.0707073 | + | 0.997497i | \(0.477474\pi\) | |||||||
\(68\) | 3.80044 | 0.460871 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.80044 | 0.454240 | ||||||||
\(71\) | −6.75841 | −0.802076 | −0.401038 | − | 0.916061i | \(-0.631350\pi\) | ||||
−0.401038 | + | 0.916061i | \(0.631350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.80044 | −0.912973 | −0.456486 | − | 0.889730i | \(-0.650892\pi\) | ||||
−0.456486 | + | 0.889730i | \(0.650892\pi\) | |||||||
\(74\) | 9.60088 | 1.11608 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.64291 | 0.761994 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.84247 | 0.319803 | 0.159902 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159902 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(80\) | 3.80044 | 0.424902 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.80044 | −0.419689 | ||||||||
\(83\) | −9.80044 | −1.07574 | −0.537869 | − | 0.843028i | \(-0.680771\pi\) | ||||
−0.537869 | + | 0.843028i | \(0.680771\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4434 | 1.56660 | ||||||||
\(86\) | −8.04424 | −0.867432 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −5.15753 | −0.546697 | −0.273348 | − | 0.961915i | \(-0.588131\pi\) | ||||
−0.273348 | + | 0.961915i | \(0.588131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.44335 | −0.675447 | ||||||||
\(92\) | 0.842472 | 0.0878338 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.24380 | 0.643998 | ||||||||
\(95\) | 25.2460 | 2.59019 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8867 | 1.91765 | 0.958827 | − | 0.283989i | \(-0.0916581\pi\) | ||||
0.958827 | + | 0.283989i | \(0.0916581\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.44335 | 0.944335 | ||||||||
\(101\) | 10.8867 | 1.08327 | 0.541634 | − | 0.840614i | \(-0.317806\pi\) | ||||
0.541634 | + | 0.840614i | \(0.317806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.80044 | 0.571534 | 0.285767 | − | 0.958299i | \(-0.407752\pi\) | ||||
0.285767 | + | 0.958299i | \(0.407752\pi\) | |||||||
\(104\) | −6.44335 | −0.631823 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.60088 | −0.155491 | ||||||||
\(107\) | −7.60088 | −0.734805 | −0.367403 | − | 0.930062i | \(-0.619753\pi\) | ||||
−0.367403 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 3.80044 | 0.362358 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 0.758411 | 0.0713453 | 0.0356726 | − | 0.999364i | \(-0.488643\pi\) | ||||
0.0356726 | + | 0.999364i | \(0.488643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.20177 | 0.298566 | ||||||||
\(116\) | −8.44335 | −0.783946 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.28583 | −0.854830 | ||||||||
\(119\) | 3.80044 | 0.348386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.75841 | 0.792949 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.40132 | −0.844264 | ||||||||
\(125\) | 16.8867 | 1.51039 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.84247 | 0.252229 | 0.126114 | − | 0.992016i | \(-0.459749\pi\) | ||||
0.126114 | + | 0.992016i | \(0.459749\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.4876 | −2.14770 | ||||||||
\(131\) | −14.1996 | −1.24062 | −0.620311 | − | 0.784356i | \(-0.712993\pi\) | ||||
−0.620311 | + | 0.784356i | \(0.712993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.64291 | 0.576014 | ||||||||
\(134\) | 1.15753 | 0.0999952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.80044 | 0.325885 | ||||||||
\(137\) | 12.7584 | 1.09002 | 0.545012 | − | 0.838428i | \(-0.316525\pi\) | ||||
0.545012 | + | 0.838428i | \(0.316525\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.55885 | −0.725952 | −0.362976 | − | 0.931798i | \(-0.618239\pi\) | ||||
−0.362976 | + | 0.931798i | \(0.618239\pi\) | |||||||
\(140\) | 3.80044 | 0.321196 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.75841 | −0.567153 | ||||||||
\(143\) | −6.44335 | −0.538820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32.0885 | −2.66480 | ||||||||
\(146\) | −7.80044 | −0.645569 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.60088 | 0.789188 | ||||||||
\(149\) | 10.8867 | 0.891874 | 0.445937 | − | 0.895064i | \(-0.352871\pi\) | ||||
0.445937 | + | 0.895064i | \(0.352871\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.31506 | 0.513912 | 0.256956 | − | 0.966423i | \(-0.417280\pi\) | ||||
0.256956 | + | 0.966423i | \(0.417280\pi\) | |||||||
\(152\) | 6.64291 | 0.538811 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −35.7292 | −2.86984 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1996 | −0.973631 | −0.486815 | − | 0.873505i | \(-0.661842\pi\) | ||||
−0.486815 | + | 0.873505i | \(0.661842\pi\) | |||||||
\(158\) | 2.84247 | 0.226135 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.80044 | 0.300451 | ||||||||
\(161\) | 0.842472 | 0.0663961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.68494 | −0.445279 | −0.222640 | − | 0.974901i | \(-0.571467\pi\) | ||||
−0.222640 | + | 0.974901i | \(0.571467\pi\) | |||||||
\(164\) | −3.80044 | −0.296765 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.80044 | −0.760662 | ||||||||
\(167\) | −24.4876 | −1.89491 | −0.947453 | − | 0.319894i | \(-0.896353\pi\) | ||||
−0.947453 | + | 0.319894i | \(0.896353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.5168 | 2.19360 | ||||||||
\(170\) | 14.4434 | 1.10775 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.04424 | −0.613367 | ||||||||
\(173\) | −15.2858 | −1.16216 | −0.581080 | − | 0.813846i | \(-0.697370\pi\) | ||||
−0.581080 | + | 0.813846i | \(0.697370\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.44335 | 0.713851 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.15753 | −0.386573 | ||||||||
\(179\) | −25.2460 | −1.88697 | −0.943487 | − | 0.331408i | \(-0.892476\pi\) | ||||
−0.943487 | + | 0.331408i | \(0.892476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.80044 | −0.579802 | −0.289901 | − | 0.957057i | \(-0.593622\pi\) | ||||
−0.289901 | + | 0.957057i | \(0.593622\pi\) | |||||||
\(182\) | −6.44335 | −0.477613 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.842472 | 0.0621079 | ||||||||
\(185\) | 36.4876 | 2.68262 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.80044 | 0.277916 | ||||||||
\(188\) | 6.24380 | 0.455376 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.2460 | 1.83154 | ||||||||
\(191\) | 20.9309 | 1.51451 | 0.757255 | − | 0.653119i | \(-0.226540\pi\) | ||||
0.757255 | + | 0.653119i | \(0.226540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.20177 | 0.374431 | 0.187216 | − | 0.982319i | \(-0.440054\pi\) | ||||
0.187216 | + | 0.982319i | \(0.440054\pi\) | |||||||
\(194\) | 18.8867 | 1.35599 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.3301 | 0.949728 | 0.474864 | − | 0.880059i | \(-0.342497\pi\) | ||||
0.474864 | + | 0.880059i | \(0.342497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8004 | −0.978287 | −0.489144 | − | 0.872203i | \(-0.662691\pi\) | ||||
−0.489144 | + | 0.872203i | \(0.662691\pi\) | |||||||
\(200\) | 9.44335 | 0.667746 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.8867 | 0.765986 | ||||||||
\(203\) | −8.44335 | −0.592607 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.4434 | −1.00877 | ||||||||
\(206\) | 5.80044 | 0.404136 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.44335 | −0.446766 | ||||||||
\(209\) | 6.64291 | 0.459500 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7292 | 0.945156 | 0.472578 | − | 0.881289i | \(-0.343324\pi\) | ||||
0.472578 | + | 0.881289i | \(0.343324\pi\) | |||||||
\(212\) | −1.60088 | −0.109949 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.60088 | −0.519586 | ||||||||
\(215\) | −30.5717 | −2.08497 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.40132 | −0.638203 | ||||||||
\(218\) | 8.00000 | 0.541828 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.80044 | 0.256226 | ||||||||
\(221\) | −24.4876 | −1.64721 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6031 | −1.64754 | −0.823772 | − | 0.566921i | \(-0.808135\pi\) | ||||
−0.823772 | + | 0.566921i | \(0.808135\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.758411 | 0.0504487 | ||||||||
\(227\) | −25.0022 | −1.65945 | −0.829727 | − | 0.558169i | \(-0.811504\pi\) | ||||
−0.829727 | + | 0.558169i | \(0.811504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6872 | 1.10272 | 0.551359 | − | 0.834268i | \(-0.314109\pi\) | ||||
0.551359 | + | 0.834268i | \(0.314109\pi\) | |||||||
\(230\) | 3.20177 | 0.211118 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.44335 | −0.554333 | ||||||||
\(233\) | −27.7734 | −1.81950 | −0.909749 | − | 0.415160i | \(-0.863726\pi\) | ||||
−0.909749 | + | 0.415160i | \(0.863726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.7292 | 1.54792 | ||||||||
\(236\) | −9.28583 | −0.604456 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.80044 | 0.246346 | ||||||||
\(239\) | 1.68494 | 0.108990 | 0.0544950 | − | 0.998514i | \(-0.482645\pi\) | ||||
0.0544950 | + | 0.998514i | \(0.482645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.4013 | −0.992087 | −0.496043 | − | 0.868298i | \(-0.665214\pi\) | ||||
−0.496043 | + | 0.868298i | \(0.665214\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.75841 | 0.560700 | ||||||||
\(245\) | 3.80044 | 0.242801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.8026 | −2.72347 | ||||||||
\(248\) | −9.40132 | −0.596985 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.8867 | 1.06801 | ||||||||
\(251\) | 17.9159 | 1.13084 | 0.565422 | − | 0.824802i | \(-0.308713\pi\) | ||||
0.565422 | + | 0.824802i | \(0.308713\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.842472 | 0.0529658 | ||||||||
\(254\) | 2.84247 | 0.178353 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.0442 | −0.626542 | −0.313271 | − | 0.949664i | \(-0.601425\pi\) | ||||
−0.313271 | + | 0.949664i | \(0.601425\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.60088 | 0.596570 | ||||||||
\(260\) | −24.4876 | −1.51866 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.1996 | −0.877252 | ||||||||
\(263\) | 11.7292 | 0.723252 | 0.361626 | − | 0.932323i | \(-0.382222\pi\) | ||||
0.361626 | + | 0.932323i | \(0.382222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.08406 | −0.373741 | ||||||||
\(266\) | 6.64291 | 0.407303 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.15753 | 0.0707073 | ||||||||
\(269\) | 20.1996 | 1.23159 | 0.615794 | − | 0.787907i | \(-0.288835\pi\) | ||||
0.615794 | + | 0.787907i | \(0.288835\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.39912 | −0.510210 | −0.255105 | − | 0.966913i | \(-0.582110\pi\) | ||||
−0.255105 | + | 0.966913i | \(0.582110\pi\) | |||||||
\(272\) | 3.80044 | 0.230436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7584 | 0.770764 | ||||||||
\(275\) | 9.44335 | 0.569456 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.88671 | −0.533951 | −0.266975 | − | 0.963703i | \(-0.586024\pi\) | ||||
−0.266975 | + | 0.963703i | \(0.586024\pi\) | |||||||
\(278\) | −8.55885 | −0.513326 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.80044 | 0.227120 | ||||||||
\(281\) | −4.31506 | −0.257415 | −0.128707 | − | 0.991683i | \(-0.541083\pi\) | ||||
−0.128707 | + | 0.991683i | \(0.541083\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.15532 | −0.128121 | −0.0640603 | − | 0.997946i | \(-0.520405\pi\) | ||||
−0.0640603 | + | 0.997946i | \(0.520405\pi\) | |||||||
\(284\) | −6.75841 | −0.401038 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.44335 | −0.381004 | ||||||||
\(287\) | −3.80044 | −0.224333 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.55665 | −0.150391 | ||||||||
\(290\) | −32.0885 | −1.88430 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.80044 | −0.456486 | ||||||||
\(293\) | −1.60088 | −0.0935246 | −0.0467623 | − | 0.998906i | \(-0.514890\pi\) | ||||
−0.0467623 | + | 0.998906i | \(0.514890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35.2902 | −2.05468 | ||||||||
\(296\) | 9.60088 | 0.558040 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.8867 | 0.630650 | ||||||||
\(299\) | −5.42835 | −0.313929 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.04424 | −0.463662 | ||||||||
\(302\) | 6.31506 | 0.363391 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.64291 | 0.380997 | ||||||||
\(305\) | 33.2858 | 1.90594 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.52962 | −0.429738 | −0.214869 | − | 0.976643i | \(-0.568933\pi\) | ||||
−0.214869 | + | 0.976643i | \(0.568933\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.7292 | −2.02928 | ||||||||
\(311\) | 6.24380 | 0.354053 | 0.177027 | − | 0.984206i | \(-0.443352\pi\) | ||||
0.177027 | + | 0.984206i | \(0.443352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.714173 | −0.0403675 | −0.0201837 | − | 0.999796i | \(-0.506425\pi\) | ||||
−0.0201837 | + | 0.999796i | \(0.506425\pi\) | |||||||
\(314\) | −12.1996 | −0.688461 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.84247 | 0.159902 | ||||||||
\(317\) | 8.71417 | 0.489437 | 0.244718 | − | 0.969594i | \(-0.421304\pi\) | ||||
0.244718 | + | 0.969594i | \(0.421304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.44335 | −0.472737 | ||||||||
\(320\) | 3.80044 | 0.212451 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.842472 | 0.0469491 | ||||||||
\(323\) | 25.2460 | 1.40473 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −60.8469 | −3.37518 | ||||||||
\(326\) | −5.68494 | −0.314860 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.80044 | −0.209844 | ||||||||
\(329\) | 6.24380 | 0.344232 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.04424 | 0.332221 | 0.166111 | − | 0.986107i | \(-0.446879\pi\) | ||||
0.166111 | + | 0.986107i | \(0.446879\pi\) | |||||||
\(332\) | −9.80044 | −0.537869 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.4876 | −1.33990 | ||||||||
\(335\) | 4.39912 | 0.240349 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.4876 | −1.87866 | −0.939329 | − | 0.343016i | \(-0.888551\pi\) | ||||
−0.939329 | + | 0.343016i | \(0.888551\pi\) | |||||||
\(338\) | 28.5168 | 1.55111 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.4434 | 0.783301 | ||||||||
\(341\) | −9.40132 | −0.509110 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.04424 | −0.433716 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.2858 | −0.821771 | ||||||||
\(347\) | −7.60088 | −0.408037 | −0.204018 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204018 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8425 | 0.794499 | 0.397250 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397250 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(350\) | 9.44335 | 0.504769 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −10.0442 | −0.534601 | −0.267300 | − | 0.963613i | \(-0.586132\pi\) | ||||
−0.267300 | + | 0.963613i | \(0.586132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.6849 | −1.36322 | ||||||||
\(356\) | −5.15753 | −0.273348 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −25.2460 | −1.33429 | ||||||||
\(359\) | 3.47258 | 0.183276 | 0.0916380 | − | 0.995792i | \(-0.470790\pi\) | ||||
0.0916380 | + | 0.995792i | \(0.470790\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.1283 | 1.32254 | ||||||||
\(362\) | −7.80044 | −0.409982 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.44335 | −0.337724 | ||||||||
\(365\) | −29.6451 | −1.55170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.40132 | 0.0731485 | 0.0365743 | − | 0.999331i | \(-0.488355\pi\) | ||||
0.0365743 | + | 0.999331i | \(0.488355\pi\) | |||||||
\(368\) | 0.842472 | 0.0439169 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.4876 | 1.89690 | ||||||||
\(371\) | −1.60088 | −0.0831137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.6451 | 0.706518 | 0.353259 | − | 0.935526i | \(-0.385074\pi\) | ||||
0.353259 | + | 0.935526i | \(0.385074\pi\) | |||||||
\(374\) | 3.80044 | 0.196516 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.24380 | 0.321999 | ||||||||
\(377\) | 54.4035 | 2.80192 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.51682 | 0.488846 | 0.244423 | − | 0.969669i | \(-0.421401\pi\) | ||||
0.244423 | + | 0.969669i | \(0.421401\pi\) | |||||||
\(380\) | 25.2460 | 1.29509 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.9309 | 1.07092 | ||||||||
\(383\) | 15.0420 | 0.768612 | 0.384306 | − | 0.923206i | \(-0.374441\pi\) | ||||
0.384306 | + | 0.923206i | \(0.374441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.80044 | 0.193688 | ||||||||
\(386\) | 5.20177 | 0.264763 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.8867 | 0.958827 | ||||||||
\(389\) | 2.63011 | 0.133352 | 0.0666760 | − | 0.997775i | \(-0.478761\pi\) | ||||
0.0666760 | + | 0.997775i | \(0.478761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.20177 | 0.161920 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.3301 | 0.671559 | ||||||||
\(395\) | 10.8026 | 0.543540 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.91373 | −0.146236 | −0.0731180 | − | 0.997323i | \(-0.523295\pi\) | ||||
−0.0731180 | + | 0.997323i | \(0.523295\pi\) | |||||||
\(398\) | −13.8004 | −0.691754 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.44335 | 0.472168 | ||||||||
\(401\) | 12.7584 | 0.637125 | 0.318562 | − | 0.947902i | \(-0.396800\pi\) | ||||
0.318562 | + | 0.947902i | \(0.396800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 60.5761 | 3.01751 | ||||||||
\(404\) | 10.8867 | 0.541634 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.44335 | −0.419037 | ||||||||
\(407\) | 9.60088 | 0.475898 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59868 | −0.227390 | −0.113695 | − | 0.993516i | \(-0.536269\pi\) | ||||
−0.113695 | + | 0.993516i | \(0.536269\pi\) | |||||||
\(410\) | −14.4434 | −0.713306 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.80044 | 0.285767 | ||||||||
\(413\) | −9.28583 | −0.456926 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.2460 | −1.82833 | ||||||||
\(416\) | −6.44335 | −0.315911 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.64291 | 0.324916 | ||||||||
\(419\) | 21.7734 | 1.06370 | 0.531851 | − | 0.846838i | \(-0.321497\pi\) | ||||
0.531851 | + | 0.846838i | \(0.321497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2018 | 1.42321 | 0.711603 | − | 0.702581i | \(-0.247969\pi\) | ||||
0.711603 | + | 0.702581i | \(0.247969\pi\) | |||||||
\(422\) | 13.7292 | 0.668326 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.60088 | −0.0777457 | ||||||||
\(425\) | 35.8889 | 1.74087 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.75841 | 0.423849 | ||||||||
\(428\) | −7.60088 | −0.367403 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.5717 | −1.47430 | ||||||||
\(431\) | 22.0442 | 1.06183 | 0.530917 | − | 0.847424i | \(-0.321848\pi\) | ||||
0.530917 | + | 0.847424i | \(0.321848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4035 | −0.788303 | −0.394152 | − | 0.919045i | \(-0.628962\pi\) | ||||
−0.394152 | + | 0.919045i | \(0.628962\pi\) | |||||||
\(434\) | −9.40132 | −0.451278 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 5.59647 | 0.267715 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.2858 | 0.825008 | 0.412504 | − | 0.910956i | \(-0.364654\pi\) | ||||
0.412504 | + | 0.910956i | \(0.364654\pi\) | |||||||
\(440\) | 3.80044 | 0.181179 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.4876 | −1.16476 | ||||||||
\(443\) | −1.95576 | −0.0929211 | −0.0464605 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464605 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6009 | −0.929171 | ||||||||
\(446\) | −24.6031 | −1.16499 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 24.7584 | 1.16842 | 0.584211 | − | 0.811602i | \(-0.301404\pi\) | ||||
0.584211 | + | 0.811602i | \(0.301404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.80044 | −0.178956 | ||||||||
\(452\) | 0.758411 | 0.0356726 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −25.0022 | −1.17341 | ||||||||
\(455\) | −24.4876 | −1.14800 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0885 | 1.03326 | 0.516628 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516628 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(458\) | 16.6872 | 0.779739 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.20177 | 0.149283 | ||||||||
\(461\) | −39.7734 | −1.85243 | −0.926216 | − | 0.376992i | \(-0.876958\pi\) | ||||
−0.926216 | + | 0.376992i | \(0.876958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.20177 | −0.334694 | −0.167347 | − | 0.985898i | \(-0.553520\pi\) | ||||
−0.167347 | + | 0.985898i | \(0.553520\pi\) | |||||||
\(464\) | −8.44335 | −0.391973 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.7734 | −1.28658 | ||||||||
\(467\) | 1.68494 | 0.0779699 | 0.0389850 | − | 0.999240i | \(-0.487588\pi\) | ||||
0.0389850 | + | 0.999240i | \(0.487588\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.15753 | 0.0534497 | ||||||||
\(470\) | 23.7292 | 1.09455 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.28583 | −0.427415 | ||||||||
\(473\) | −8.04424 | −0.369874 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 62.7314 | 2.87831 | ||||||||
\(476\) | 3.80044 | 0.174193 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.68494 | 0.0770675 | ||||||||
\(479\) | −27.2018 | −1.24288 | −0.621440 | − | 0.783462i | \(-0.713452\pi\) | ||||
−0.621440 | + | 0.783462i | \(0.713452\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −61.8619 | −2.82066 | ||||||||
\(482\) | −15.4013 | −0.701511 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 71.7778 | 3.25926 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9159 | 0.630591 | 0.315296 | − | 0.948993i | \(-0.397896\pi\) | ||||
0.315296 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(488\) | 8.75841 | 0.396475 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.80044 | 0.171686 | ||||||||
\(491\) | 3.20177 | 0.144494 | 0.0722468 | − | 0.997387i | \(-0.476983\pi\) | ||||
0.0722468 | + | 0.997387i | \(0.476983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.0885 | −1.44519 | ||||||||
\(494\) | −42.8026 | −1.92578 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.40132 | −0.422132 | ||||||||
\(497\) | −6.75841 | −0.303156 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.2460 | −0.772037 | −0.386019 | − | 0.922491i | \(-0.626150\pi\) | ||||
−0.386019 | + | 0.922491i | \(0.626150\pi\) | |||||||
\(500\) | 16.8867 | 0.755197 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 17.9159 | 0.799627 | ||||||||
\(503\) | −0.487592 | −0.0217407 | −0.0108703 | − | 0.999941i | \(-0.503460\pi\) | ||||
−0.0108703 | + | 0.999941i | \(0.503460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.3743 | 1.84113 | ||||||||
\(506\) | 0.842472 | 0.0374525 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.84247 | 0.126114 | ||||||||
\(509\) | −28.7756 | −1.27546 | −0.637729 | − | 0.770261i | \(-0.720126\pi\) | ||||
−0.637729 | + | 0.770261i | \(0.720126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.80044 | −0.345071 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.0442 | −0.443032 | ||||||||
\(515\) | 22.0442 | 0.971385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.24380 | 0.274602 | ||||||||
\(518\) | 9.60088 | 0.421839 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.4876 | −1.07385 | ||||||||
\(521\) | −25.2460 | −1.10605 | −0.553024 | − | 0.833165i | \(-0.686526\pi\) | ||||
−0.553024 | + | 0.833165i | \(0.686526\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.0464 | 1.61993 | 0.809964 | − | 0.586480i | \(-0.199487\pi\) | ||||
0.809964 | + | 0.586480i | \(0.199487\pi\) | |||||||
\(524\) | −14.1996 | −0.620311 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.7292 | 0.511417 | ||||||||
\(527\) | −35.7292 | −1.55639 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2902 | −0.969141 | ||||||||
\(530\) | −6.08406 | −0.264275 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.64291 | 0.288007 | ||||||||
\(533\) | 24.4876 | 1.06068 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.8867 | −1.24888 | ||||||||
\(536\) | 1.15753 | 0.0499976 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.1996 | 0.870865 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.5318 | 1.31267 | 0.656333 | − | 0.754471i | \(-0.272107\pi\) | ||||
0.656333 | + | 0.754471i | \(0.272107\pi\) | |||||||
\(542\) | −8.39912 | −0.360773 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.80044 | 0.162943 | ||||||||
\(545\) | 30.4035 | 1.30234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.1619 | 1.93099 | 0.965493 | − | 0.260430i | \(-0.0838645\pi\) | ||||
0.965493 | + | 0.260430i | \(0.0838645\pi\) | |||||||
\(548\) | 12.7584 | 0.545012 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.44335 | 0.402666 | ||||||||
\(551\) | −56.0885 | −2.38945 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.84247 | 0.120874 | ||||||||
\(554\) | −8.88671 | −0.377560 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.55885 | −0.362976 | ||||||||
\(557\) | −9.96018 | −0.422026 | −0.211013 | − | 0.977483i | \(-0.567676\pi\) | ||||
−0.211013 | + | 0.977483i | \(0.567676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.8319 | 2.19225 | ||||||||
\(560\) | 3.80044 | 0.160598 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.31506 | −0.182020 | ||||||||
\(563\) | −33.8004 | −1.42452 | −0.712259 | − | 0.701916i | \(-0.752328\pi\) | ||||
−0.712259 | + | 0.701916i | \(0.752328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.88230 | 0.121259 | ||||||||
\(566\) | −2.15532 | −0.0905949 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.75841 | −0.283577 | ||||||||
\(569\) | 31.6849 | 1.32830 | 0.664151 | − | 0.747598i | \(-0.268793\pi\) | ||||
0.664151 | + | 0.747598i | \(0.268793\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.443355 | −0.0185538 | −0.00927691 | − | 0.999957i | \(-0.502953\pi\) | ||||
−0.00927691 | + | 0.999957i | \(0.502953\pi\) | |||||||
\(572\) | −6.44335 | −0.269410 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.80044 | −0.158627 | ||||||||
\(575\) | 7.95576 | 0.331778 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.714173 | −0.0297314 | −0.0148657 | − | 0.999889i | \(-0.504732\pi\) | ||||
−0.0148657 | + | 0.999889i | \(0.504732\pi\) | |||||||
\(578\) | −2.55665 | −0.106342 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −32.0885 | −1.33240 | ||||||||
\(581\) | −9.80044 | −0.406591 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.60088 | −0.0663018 | ||||||||
\(584\) | −7.80044 | −0.322785 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.60088 | −0.0661319 | ||||||||
\(587\) | 4.39912 | 0.181571 | 0.0907855 | − | 0.995870i | \(-0.471062\pi\) | ||||
0.0907855 | + | 0.995870i | \(0.471062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −62.4522 | −2.57330 | ||||||||
\(590\) | −35.2902 | −1.45288 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.60088 | 0.394594 | ||||||||
\(593\) | −34.2040 | −1.40459 | −0.702294 | − | 0.711887i | \(-0.747841\pi\) | ||||
−0.702294 | + | 0.711887i | \(0.747841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.4434 | 0.592120 | ||||||||
\(596\) | 10.8867 | 0.445937 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.42835 | −0.221982 | ||||||||
\(599\) | 5.24159 | 0.214166 | 0.107083 | − | 0.994250i | \(-0.465849\pi\) | ||||
0.107083 | + | 0.994250i | \(0.465849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0314 | 0.653936 | 0.326968 | − | 0.945035i | \(-0.393973\pi\) | ||||
0.326968 | + | 0.945035i | \(0.393973\pi\) | |||||||
\(602\) | −8.04424 | −0.327859 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.31506 | 0.256956 | ||||||||
\(605\) | 3.80044 | 0.154510 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.2902 | 1.27003 | 0.635016 | − | 0.772499i | \(-0.280994\pi\) | ||||
0.635016 | + | 0.772499i | \(0.280994\pi\) | |||||||
\(608\) | 6.64291 | 0.269406 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 33.2858 | 1.34770 | ||||||||
\(611\) | −40.2310 | −1.62757 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8717 | 0.641052 | 0.320526 | − | 0.947240i | \(-0.396140\pi\) | ||||
0.320526 | + | 0.947240i | \(0.396140\pi\) | |||||||
\(614\) | −7.52962 | −0.303871 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −22.3151 | −0.898370 | −0.449185 | − | 0.893439i | \(-0.648286\pi\) | ||||
−0.449185 | + | 0.893439i | \(0.648286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.68494 | −0.228497 | −0.114249 | − | 0.993452i | \(-0.536446\pi\) | ||||
−0.114249 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(620\) | −35.7292 | −1.43492 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.24380 | 0.250353 | ||||||||
\(623\) | −5.15753 | −0.206632 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.9602 | 0.678407 | ||||||||
\(626\) | −0.714173 | −0.0285441 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.1996 | −0.486815 | ||||||||
\(629\) | 36.4876 | 1.45486 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1725 | 1.83810 | 0.919050 | − | 0.394141i | \(-0.128958\pi\) | ||||
0.919050 | + | 0.394141i | \(0.128958\pi\) | |||||||
\(632\) | 2.84247 | 0.113067 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.71417 | 0.346084 | ||||||||
\(635\) | 10.8026 | 0.428690 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.44335 | −0.255295 | ||||||||
\(638\) | −8.44335 | −0.334276 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.80044 | 0.150226 | ||||||||
\(641\) | 35.4584 | 1.40052 | 0.700261 | − | 0.713887i | \(-0.253067\pi\) | ||||
0.700261 | + | 0.713887i | \(0.253067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.71417 | −0.264781 | −0.132391 | − | 0.991198i | \(-0.542265\pi\) | ||||
−0.132391 | + | 0.991198i | \(0.542265\pi\) | |||||||
\(644\) | 0.842472 | 0.0331980 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.2460 | 0.993291 | ||||||||
\(647\) | 30.2438 | 1.18901 | 0.594503 | − | 0.804093i | \(-0.297349\pi\) | ||||
0.594503 | + | 0.804093i | \(0.297349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.28583 | −0.364501 | ||||||||
\(650\) | −60.8469 | −2.38661 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.68494 | −0.222640 | ||||||||
\(653\) | 15.7734 | 0.617262 | 0.308631 | − | 0.951182i | \(-0.400129\pi\) | ||||
0.308631 | + | 0.951182i | \(0.400129\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −53.9646 | −2.10857 | ||||||||
\(656\) | −3.80044 | −0.148382 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.24380 | 0.243409 | ||||||||
\(659\) | −39.8575 | −1.55263 | −0.776314 | − | 0.630347i | \(-0.782913\pi\) | ||||
−0.776314 | + | 0.630347i | \(0.782913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.2588 | 1.37141 | 0.685704 | − | 0.727880i | \(-0.259494\pi\) | ||||
0.685704 | + | 0.727880i | \(0.259494\pi\) | |||||||
\(662\) | 6.04424 | 0.234916 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.80044 | −0.380331 | ||||||||
\(665\) | 25.2460 | 0.978998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.11329 | −0.275428 | ||||||||
\(668\) | −24.4876 | −0.947453 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.39912 | 0.169953 | ||||||||
\(671\) | 8.75841 | 0.338115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.9159 | 0.767703 | 0.383852 | − | 0.923395i | \(-0.374597\pi\) | ||||
0.383852 | + | 0.923395i | \(0.374597\pi\) | |||||||
\(674\) | −34.4876 | −1.32841 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.5168 | 1.09680 | ||||||||
\(677\) | 45.6894 | 1.75598 | 0.877992 | − | 0.478675i | \(-0.158883\pi\) | ||||
0.877992 | + | 0.478675i | \(0.158883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8867 | 0.724805 | ||||||||
\(680\) | 14.4434 | 0.553877 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.40132 | −0.359995 | ||||||||
\(683\) | −20.3593 | −0.779027 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.4876 | 1.85262 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.04424 | −0.306684 | ||||||||
\(689\) | 10.3151 | 0.392972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.2310 | 0.921790 | 0.460895 | − | 0.887455i | \(-0.347528\pi\) | ||||
0.460895 | + | 0.887455i | \(0.347528\pi\) | |||||||
\(692\) | −15.2858 | −0.581080 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.60088 | −0.288526 | ||||||||
\(695\) | −32.5274 | −1.23384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.4434 | −0.547081 | ||||||||
\(698\) | 14.8425 | 0.561796 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.44335 | 0.356925 | ||||||||
\(701\) | −14.2566 | −0.538464 | −0.269232 | − | 0.963075i | \(-0.586770\pi\) | ||||
−0.269232 | + | 0.963075i | \(0.586770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.7778 | 2.40543 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.0442 | −0.378020 | ||||||||
\(707\) | 10.8867 | 0.409437 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6557 | −0.400184 | −0.200092 | − | 0.979777i | \(-0.564124\pi\) | ||||
−0.200092 | + | 0.979777i | \(0.564124\pi\) | |||||||
\(710\) | −25.6849 | −0.963939 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.15753 | −0.193287 | ||||||||
\(713\) | −7.92035 | −0.296620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.4876 | −0.915784 | ||||||||
\(716\) | −25.2460 | −0.943487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.47258 | 0.129596 | ||||||||
\(719\) | 28.5589 | 1.06507 | 0.532533 | − | 0.846409i | \(-0.321240\pi\) | ||||
0.532533 | + | 0.846409i | \(0.321240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.80044 | 0.216020 | ||||||||
\(722\) | 25.1283 | 0.935178 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.80044 | −0.289901 | ||||||||
\(725\) | −79.7336 | −2.96123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.03144 | −0.223694 | −0.111847 | − | 0.993725i | \(-0.535677\pi\) | ||||
−0.111847 | + | 0.993725i | \(0.535677\pi\) | |||||||
\(728\) | −6.44335 | −0.238807 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.6451 | −1.09722 | ||||||||
\(731\) | −30.5717 | −1.13073 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.33006 | 0.122999 | 0.0614994 | − | 0.998107i | \(-0.480412\pi\) | ||||
0.0614994 | + | 0.998107i | \(0.480412\pi\) | |||||||
\(734\) | 1.40132 | 0.0517238 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.842472 | 0.0310539 | ||||||||
\(737\) | 1.15753 | 0.0426381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.66994 | 0.245358 | 0.122679 | − | 0.992446i | \(-0.460852\pi\) | ||||
0.122679 | + | 0.992446i | \(0.460852\pi\) | |||||||
\(740\) | 36.4876 | 1.34131 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.60088 | −0.0587703 | ||||||||
\(743\) | 15.2018 | 0.557699 | 0.278849 | − | 0.960335i | \(-0.410047\pi\) | ||||
0.278849 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.3743 | 1.51584 | ||||||||
\(746\) | 13.6451 | 0.499583 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.80044 | 0.138958 | ||||||||
\(749\) | −7.60088 | −0.277730 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.23099 | −0.300353 | −0.150177 | − | 0.988659i | \(-0.547984\pi\) | ||||
−0.150177 | + | 0.988659i | \(0.547984\pi\) | |||||||
\(752\) | 6.24380 | 0.227688 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 54.4035 | 1.98126 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.6894 | −1.80599 | −0.902995 | − | 0.429651i | \(-0.858637\pi\) | ||||
−0.902995 | + | 0.429651i | \(0.858637\pi\) | |||||||
\(758\) | 9.51682 | 0.345667 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.2460 | 0.915769 | ||||||||
\(761\) | −0.111083 | −0.00402677 | −0.00201338 | − | 0.999998i | \(-0.500641\pi\) | ||||
−0.00201338 | + | 0.999998i | \(0.500641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | 20.9309 | 0.757255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0420 | 0.543491 | ||||||||
\(767\) | 59.8319 | 2.16040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.5739 | 1.64344 | 0.821718 | − | 0.569895i | \(-0.193016\pi\) | ||||
0.821718 | + | 0.569895i | \(0.193016\pi\) | |||||||
\(770\) | 3.80044 | 0.136958 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.20177 | 0.187216 | ||||||||
\(773\) | 22.2040 | 0.798621 | 0.399311 | − | 0.916816i | \(-0.369249\pi\) | ||||
0.399311 | + | 0.916816i | \(0.369249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −88.7800 | −3.18907 | ||||||||
\(776\) | 18.8867 | 0.677993 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.63011 | 0.0942941 | ||||||||
\(779\) | −25.2460 | −0.904532 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.75841 | −0.241835 | ||||||||
\(782\) | 3.20177 | 0.114495 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −46.3637 | −1.65479 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.1305 | −1.82261 | −0.911303 | − | 0.411737i | \(-0.864922\pi\) | ||||
−0.911303 | + | 0.411737i | \(0.864922\pi\) | |||||||
\(788\) | 13.3301 | 0.474864 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.8026 | 0.384341 | ||||||||
\(791\) | 0.758411 | 0.0269660 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.4335 | −2.00401 | ||||||||
\(794\) | −2.91373 | −0.103404 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.8004 | −0.489144 | ||||||||
\(797\) | 32.6872 | 1.15784 | 0.578919 | − | 0.815385i | \(-0.303475\pi\) | ||||
0.578919 | + | 0.815385i | \(0.303475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7292 | 0.839478 | ||||||||
\(800\) | 9.44335 | 0.333873 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.7584 | 0.450515 | ||||||||
\(803\) | −7.80044 | −0.275272 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.20177 | 0.112847 | ||||||||
\(806\) | 60.5761 | 2.13370 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.8867 | 0.382993 | ||||||||
\(809\) | −0.0840613 | −0.00295544 | −0.00147772 | − | 0.999999i | \(-0.500470\pi\) | ||||
−0.00147772 | + | 0.999999i | \(0.500470\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.6977 | 0.410763 | 0.205382 | − | 0.978682i | \(-0.434156\pi\) | ||||
0.205382 | + | 0.978682i | \(0.434156\pi\) | |||||||
\(812\) | −8.44335 | −0.296304 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.60088 | 0.336511 | ||||||||
\(815\) | −21.6053 | −0.756801 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −53.4372 | −1.86953 | ||||||||
\(818\) | −4.59868 | −0.160789 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.4434 | −0.504384 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.1725 | 1.60947 | 0.804737 | − | 0.593632i | \(-0.202306\pi\) | ||||
0.804737 | + | 0.593632i | \(0.202306\pi\) | |||||||
\(824\) | 5.80044 | 0.202068 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.28583 | −0.323095 | ||||||||
\(827\) | −27.2018 | −0.945898 | −0.472949 | − | 0.881090i | \(-0.656811\pi\) | ||||
−0.472949 | + | 0.881090i | \(0.656811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.2588 | −0.668886 | −0.334443 | − | 0.942416i | \(-0.608548\pi\) | ||||
−0.334443 | + | 0.942416i | \(0.608548\pi\) | |||||||
\(830\) | −37.2460 | −1.29283 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.44335 | −0.223383 | ||||||||
\(833\) | 3.80044 | 0.131677 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −93.0637 | −3.22060 | ||||||||
\(836\) | 6.64291 | 0.229750 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.7734 | 0.752150 | ||||||||
\(839\) | 28.5589 | 0.985961 | 0.492981 | − | 0.870040i | \(-0.335907\pi\) | ||||
0.492981 | + | 0.870040i | \(0.335907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.2902 | 1.45828 | ||||||||
\(842\) | 29.2018 | 1.00636 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.7292 | 0.472578 | ||||||||
\(845\) | 108.377 | 3.72827 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | −1.60088 | −0.0549745 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35.8889 | 1.23098 | ||||||||
\(851\) | 8.08848 | 0.277269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.2752 | 0.351817 | 0.175909 | − | 0.984406i | \(-0.443714\pi\) | ||||
0.175909 | + | 0.984406i | \(0.443714\pi\) | |||||||
\(854\) | 8.75841 | 0.299707 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.60088 | −0.259793 | ||||||||
\(857\) | 57.1747 | 1.95305 | 0.976526 | − | 0.215399i | \(-0.0691054\pi\) | ||||
0.976526 | + | 0.215399i | \(0.0691054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.82746 | 0.198830 | 0.0994152 | − | 0.995046i | \(-0.468303\pi\) | ||||
0.0994152 | + | 0.995046i | \(0.468303\pi\) | |||||||
\(860\) | −30.5717 | −1.04248 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.0442 | 0.750830 | ||||||||
\(863\) | −46.4478 | −1.58110 | −0.790550 | − | 0.612397i | \(-0.790205\pi\) | ||||
−0.790550 | + | 0.612397i | \(0.790205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −58.0929 | −1.97522 | ||||||||
\(866\) | −16.4035 | −0.557415 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.40132 | −0.319102 | ||||||||
\(869\) | 2.84247 | 0.0964243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.45836 | −0.252717 | ||||||||
\(872\) | 8.00000 | 0.270914 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.59647 | 0.189303 | ||||||||
\(875\) | 16.8867 | 0.570875 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2018 | 0.378257 | 0.189128 | − | 0.981952i | \(-0.439434\pi\) | ||||
0.189128 | + | 0.981952i | \(0.439434\pi\) | |||||||
\(878\) | 17.2858 | 0.583368 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.80044 | 0.128113 | ||||||||
\(881\) | −34.7000 | −1.16907 | −0.584536 | − | 0.811368i | \(-0.698723\pi\) | ||||
−0.584536 | + | 0.811368i | \(0.698723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9204 | 1.34343 | 0.671713 | − | 0.740811i | \(-0.265559\pi\) | ||||
0.671713 | + | 0.740811i | \(0.265559\pi\) | |||||||
\(884\) | −24.4876 | −0.823607 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.95576 | −0.0657051 | ||||||||
\(887\) | −8.08848 | −0.271584 | −0.135792 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135792 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.84247 | 0.0953335 | ||||||||
\(890\) | −19.6009 | −0.657023 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.6031 | −0.823772 | ||||||||
\(893\) | 41.4770 | 1.38797 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −95.9460 | −3.20712 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.7584 | 0.826199 | ||||||||
\(899\) | 79.3787 | 2.64743 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.08406 | −0.202689 | ||||||||
\(902\) | −3.80044 | −0.126541 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.758411 | 0.0252244 | ||||||||
\(905\) | −29.6451 | −0.985437 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.95576 | −0.197758 | −0.0988789 | − | 0.995099i | \(-0.531526\pi\) | ||||
−0.0988789 | + | 0.995099i | \(0.531526\pi\) | |||||||
\(908\) | −25.0022 | −0.829727 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.4876 | −0.811756 | ||||||||
\(911\) | −22.4478 | −0.743728 | −0.371864 | − | 0.928287i | \(-0.621281\pi\) | ||||
−0.371864 | + | 0.928287i | \(0.621281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.80044 | −0.324347 | ||||||||
\(914\) | 22.0885 | 0.730622 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.6872 | 0.551359 | ||||||||
\(917\) | −14.1996 | −0.468911 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8867 | 0.820937 | 0.410468 | − | 0.911875i | \(-0.365365\pi\) | ||||
0.410468 | + | 0.911875i | \(0.365365\pi\) | |||||||
\(920\) | 3.20177 | 0.105559 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.7734 | −1.30987 | ||||||||
\(923\) | 43.5468 | 1.43336 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 90.6645 | 2.98103 | ||||||||
\(926\) | −7.20177 | −0.236665 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.44335 | −0.277167 | ||||||||
\(929\) | 15.4726 | 0.507639 | 0.253820 | − | 0.967252i | \(-0.418313\pi\) | ||||
0.253820 | + | 0.967252i | \(0.418313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.64291 | 0.217713 | ||||||||
\(932\) | −27.7734 | −0.909749 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.68494 | 0.0551331 | ||||||||
\(935\) | 14.4434 | 0.472348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8845 | 0.584261 | 0.292131 | − | 0.956378i | \(-0.405636\pi\) | ||||
0.292131 | + | 0.956378i | \(0.405636\pi\) | |||||||
\(938\) | 1.15753 | 0.0377946 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.7292 | 0.773961 | ||||||||
\(941\) | −6.65572 | −0.216970 | −0.108485 | − | 0.994098i | \(-0.534600\pi\) | ||||
−0.108485 | + | 0.994098i | \(0.534600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.20177 | −0.104264 | ||||||||
\(944\) | −9.28583 | −0.302228 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.04424 | −0.261541 | ||||||||
\(947\) | −32.2566 | −1.04820 | −0.524099 | − | 0.851657i | \(-0.675598\pi\) | ||||
−0.524099 | + | 0.851657i | \(0.675598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.2610 | 1.63154 | ||||||||
\(950\) | 62.7314 | 2.03528 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.80044 | 0.123173 | ||||||||
\(953\) | 37.6009 | 1.21801 | 0.609006 | − | 0.793166i | \(-0.291569\pi\) | ||||
0.609006 | + | 0.793166i | \(0.291569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 79.5468 | 2.57408 | ||||||||
\(956\) | 1.68494 | 0.0544950 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.2018 | −0.878849 | ||||||||
\(959\) | 12.7584 | 0.411991 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.3849 | 1.85113 | ||||||||
\(962\) | −61.8619 | −1.99451 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.4013 | −0.496043 | ||||||||
\(965\) | 19.7690 | 0.636387 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.48318 | −0.0798536 | −0.0399268 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399268 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 71.7778 | 2.30465 | ||||||||
\(971\) | 13.6849 | 0.439171 | 0.219585 | − | 0.975593i | \(-0.429530\pi\) | ||||
0.219585 | + | 0.975593i | \(0.429530\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.55885 | −0.274384 | ||||||||
\(974\) | 13.9159 | 0.445895 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.75841 | 0.280350 | ||||||||
\(977\) | −13.6849 | −0.437820 | −0.218910 | − | 0.975745i | \(-0.570250\pi\) | ||||
−0.218910 | + | 0.975745i | \(0.570250\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.15753 | −0.164835 | ||||||||
\(980\) | 3.80044 | 0.121401 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.20177 | 0.102172 | ||||||||
\(983\) | 31.2190 | 0.995731 | 0.497865 | − | 0.867254i | \(-0.334117\pi\) | ||||
0.497865 | + | 0.867254i | \(0.334117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.6601 | 1.61417 | ||||||||
\(986\) | −32.0885 | −1.02191 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −42.8026 | −1.36173 | ||||||||
\(989\) | −6.77705 | −0.215498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.51682 | 0.302312 | 0.151156 | − | 0.988510i | \(-0.451700\pi\) | ||||
0.151156 | + | 0.988510i | \(0.451700\pi\) | |||||||
\(992\) | −9.40132 | −0.298492 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.75841 | −0.214364 | ||||||||
\(995\) | −52.4478 | −1.66271 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9558 | −0.568665 | −0.284332 | − | 0.958726i | \(-0.591772\pi\) | ||||
−0.284332 | + | 0.958726i | \(0.591772\pi\) | |||||||
\(998\) | −17.2460 | −0.545913 | ||||||||
\(999\) | 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 | 1386.2.a.r.1.3 | yes | 3 | |
3.2 | odd | 2 | 1386.2.a.q.1.1 | ✓ | 3 | ||
7.6 | odd | 2 | 9702.2.a.dy.1.1 | 3 | |||
21.20 | even | 2 | 9702.2.a.dx.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.a.q.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1386.2.a.r.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
9702.2.a.dx.1.3 | 3 | 21.20 | even | 2 | |||
9702.2.a.dy.1.1 | 3 | 7.6 | odd | 2 |