Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1815) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.456850 | −0.323042 | −0.161521 | − | 0.986869i | \(-0.551640\pi\) | ||||
−0.161521 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.79129 | −0.895644 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.37780 | 1.65465 | 0.827327 | − | 0.561721i | \(-0.189860\pi\) | ||||
0.827327 | + | 0.561721i | \(0.189860\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.456850 | −0.144469 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.913701 | 0.253415 | 0.126707 | − | 0.991940i | \(-0.459559\pi\) | ||||
0.126707 | + | 0.991940i | \(0.459559\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46410 | −0.794719 | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | −1.79129 | −0.400544 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.582576 | 0.121475 | 0.0607377 | − | 0.998154i | \(-0.480655\pi\) | ||||
0.0607377 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.417424 | −0.0818636 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.84190 | −1.48198 | ||||||||
\(29\) | −9.66930 | −1.79554 | −0.897772 | − | 0.440460i | \(-0.854815\pi\) | ||||
−0.897772 | + | 0.440460i | \(0.854815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.58258 | −1.54148 | −0.770738 | − | 0.637152i | \(-0.780112\pi\) | ||||
−0.770738 | + | 0.637152i | \(0.780112\pi\) | |||||||
\(32\) | −4.73930 | −0.837798 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.791288 | 0.135705 | ||||||||
\(35\) | 4.37780 | 0.739984 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.58258 | 1.24657 | 0.623284 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623284 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(38\) | 1.58258 | 0.256728 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205 | 0.273861 | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.66930 | −1.47456 | −0.737278 | − | 0.675590i | \(-0.763889\pi\) | ||||
−0.737278 | + | 0.675590i | \(0.763889\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.266150 | −0.0392417 | ||||||||
\(47\) | −3.41742 | −0.498483 | −0.249241 | − | 0.968441i | \(-0.580181\pi\) | ||||
−0.249241 | + | 0.968441i | \(0.580181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.1652 | 1.73788 | ||||||||
\(50\) | −0.456850 | −0.0646084 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.63670 | −0.226970 | ||||||||
\(53\) | −12.1652 | −1.67101 | −0.835506 | − | 0.549481i | \(-0.814825\pi\) | ||||
−0.835506 | + | 0.549481i | \(0.814825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.58258 | 1.01326 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.41742 | 0.580036 | ||||||||
\(59\) | −13.5826 | −1.76830 | −0.884150 | − | 0.467202i | \(-0.845262\pi\) | ||||
−0.884150 | + | 0.467202i | \(0.845262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.55945 | −0.455741 | −0.227871 | − | 0.973691i | \(-0.573176\pi\) | ||||
−0.227871 | + | 0.973691i | \(0.573176\pi\) | |||||||
\(62\) | 3.92095 | 0.497961 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.41742 | −0.427178 | ||||||||
\(65\) | 0.913701 | 0.113331 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.41742 | −0.539674 | −0.269837 | − | 0.962906i | \(-0.586970\pi\) | ||||
−0.269837 | + | 0.962906i | \(0.586970\pi\) | |||||||
\(68\) | 3.10260 | 0.376246 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.10080 | 0.597004 | 0.298502 | − | 0.954409i | \(-0.403513\pi\) | ||||
0.298502 | + | 0.954409i | \(0.403513\pi\) | |||||||
\(74\) | −3.46410 | −0.402694 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.20520 | 0.711786 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.818350 | 0.0920716 | 0.0460358 | − | 0.998940i | \(-0.485341\pi\) | ||||
0.0460358 | + | 0.998940i | \(0.485341\pi\) | |||||||
\(80\) | 2.79129 | 0.312075 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.58258 | 0.174766 | ||||||||
\(83\) | 15.8745 | 1.74245 | 0.871227 | − | 0.490881i | \(-0.163325\pi\) | ||||
0.871227 | + | 0.490881i | \(0.163325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.73205 | −0.187867 | ||||||||
\(86\) | 4.41742 | 0.476343 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7477 | −1.56326 | −0.781628 | − | 0.623745i | \(-0.785610\pi\) | ||||
−0.781628 | + | 0.623745i | \(0.785610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | −1.04356 | −0.108799 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.56125 | 0.161031 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.41742 | 0.448521 | 0.224261 | − | 0.974529i | \(-0.428003\pi\) | ||||
0.224261 | + | 0.974529i | \(0.428003\pi\) | |||||||
\(98\) | −5.55765 | −0.561408 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.79129 | −0.179129 | ||||||||
\(101\) | −1.82740 | −0.181833 | −0.0909166 | − | 0.995859i | \(-0.528980\pi\) | ||||
−0.0909166 | + | 0.995859i | \(0.528980\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.16515 | 0.706003 | 0.353002 | − | 0.935623i | \(-0.385161\pi\) | ||||
0.353002 | + | 0.935623i | \(0.385161\pi\) | |||||||
\(104\) | 1.58258 | 0.155184 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.55765 | 0.539807 | ||||||||
\(107\) | 13.0381 | 1.26044 | 0.630218 | − | 0.776418i | \(-0.282965\pi\) | ||||
0.630218 | + | 0.776418i | \(0.282965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.92820 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.2197 | 1.15465 | ||||||||
\(113\) | −9.00000 | −0.846649 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.582576 | 0.0543255 | ||||||||
\(116\) | 17.3205 | 1.60817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.20520 | 0.571235 | ||||||||
\(119\) | −7.58258 | −0.695094 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.62614 | 0.147223 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.3739 | 1.38061 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.84190 | 0.695856 | 0.347928 | − | 0.937521i | \(-0.386885\pi\) | ||||
0.347928 | + | 0.937521i | \(0.386885\pi\) | |||||||
\(128\) | 11.0399 | 0.975795 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.417424 | −0.0366105 | ||||||||
\(131\) | −20.9753 | −1.83262 | −0.916311 | − | 0.400468i | \(-0.868848\pi\) | ||||
−0.916311 | + | 0.400468i | \(0.868848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1652 | −1.31499 | ||||||||
\(134\) | 2.01810 | 0.174337 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 19.3303 | 1.65150 | 0.825750 | − | 0.564037i | \(-0.190752\pi\) | ||||
0.825750 | + | 0.564037i | \(0.190752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.74655 | 0.657054 | 0.328527 | − | 0.944495i | \(-0.393448\pi\) | ||||
0.328527 | + | 0.944495i | \(0.393448\pi\) | |||||||
\(140\) | −7.84190 | −0.662762 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.65480 | 0.306704 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.66930 | −0.802992 | ||||||||
\(146\) | −2.33030 | −0.192857 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.5826 | −1.11648 | ||||||||
\(149\) | 2.74110 | 0.224560 | 0.112280 | − | 0.993677i | \(-0.464185\pi\) | ||||
0.112280 | + | 0.993677i | \(0.464185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.74655 | 0.630406 | 0.315203 | − | 0.949024i | \(-0.397927\pi\) | ||||
0.315203 | + | 0.949024i | \(0.397927\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.58258 | −0.689369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7477 | 0.857762 | 0.428881 | − | 0.903361i | \(-0.358908\pi\) | ||||
0.428881 | + | 0.903361i | \(0.358908\pi\) | |||||||
\(158\) | −0.373864 | −0.0297430 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.73930 | −0.374675 | ||||||||
\(161\) | 2.55040 | 0.201000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.7477 | −1.62509 | −0.812544 | − | 0.582900i | \(-0.801918\pi\) | ||||
−0.812544 | + | 0.582900i | \(0.801918\pi\) | |||||||
\(164\) | 6.20520 | 0.484545 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.25227 | −0.562886 | ||||||||
\(167\) | −4.47315 | −0.346143 | −0.173071 | − | 0.984909i | \(-0.555369\pi\) | ||||
−0.173071 | + | 0.984909i | \(0.555369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.1652 | −0.935781 | ||||||||
\(170\) | 0.791288 | 0.0606890 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.3205 | 1.32068 | ||||||||
\(173\) | 6.92820 | 0.526742 | 0.263371 | − | 0.964695i | \(-0.415166\pi\) | ||||
0.263371 | + | 0.964695i | \(0.415166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.37780 | 0.330931 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.73750 | 0.504997 | ||||||||
\(179\) | −7.58258 | −0.566748 | −0.283374 | − | 0.959009i | \(-0.591454\pi\) | ||||
−0.283374 | + | 0.959009i | \(0.591454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.16515 | −0.383923 | −0.191961 | − | 0.981402i | \(-0.561485\pi\) | ||||
−0.191961 | + | 0.981402i | \(0.561485\pi\) | |||||||
\(182\) | −1.82740 | −0.135456 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00905 | 0.0743882 | ||||||||
\(185\) | 7.58258 | 0.557482 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.12159 | 0.446463 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.58258 | 0.114812 | ||||||||
\(191\) | 22.7477 | 1.64597 | 0.822984 | − | 0.568065i | \(-0.192308\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.4068 | 1.18099 | 0.590494 | − | 0.807042i | \(-0.298933\pi\) | ||||
0.590494 | + | 0.807042i | \(0.298933\pi\) | |||||||
\(194\) | −2.01810 | −0.144891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.7913 | −1.55652 | ||||||||
\(197\) | 12.4104 | 0.884205 | 0.442102 | − | 0.896965i | \(-0.354233\pi\) | ||||
0.442102 | + | 0.896965i | \(0.354233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7477 | −1.11633 | −0.558163 | − | 0.829731i | \(-0.688494\pi\) | ||||
−0.558163 | + | 0.829731i | \(0.688494\pi\) | |||||||
\(200\) | 1.73205 | 0.122474 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.834849 | 0.0587397 | ||||||||
\(203\) | −42.3303 | −2.97100 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.46410 | −0.241943 | ||||||||
\(206\) | −3.27340 | −0.228069 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.55040 | 0.176838 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4304 | −1.61301 | −0.806506 | − | 0.591226i | \(-0.798644\pi\) | ||||
−0.806506 | + | 0.591226i | \(0.798644\pi\) | |||||||
\(212\) | 21.7913 | 1.49663 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.95644 | −0.407174 | ||||||||
\(215\) | −9.66930 | −0.659441 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.5728 | −2.55061 | ||||||||
\(218\) | 3.16515 | 0.214371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.58258 | −0.106456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.3303 | −1.09356 | −0.546779 | − | 0.837277i | \(-0.684146\pi\) | ||||
−0.546779 | + | 0.837277i | \(0.684146\pi\) | |||||||
\(224\) | −20.7477 | −1.38627 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.11165 | 0.273503 | ||||||||
\(227\) | 20.1570 | 1.33786 | 0.668932 | − | 0.743323i | \(-0.266752\pi\) | ||||
0.668932 | + | 0.743323i | \(0.266752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0000 | 1.12339 | 0.561696 | − | 0.827344i | \(-0.310149\pi\) | ||||
0.561696 | + | 0.827344i | \(0.310149\pi\) | |||||||
\(230\) | −0.266150 | −0.0175494 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.7477 | −1.09954 | ||||||||
\(233\) | 14.1425 | 0.926503 | 0.463252 | − | 0.886227i | \(-0.346683\pi\) | ||||
0.463252 | + | 0.886227i | \(0.346683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.41742 | −0.222928 | ||||||||
\(236\) | 24.3303 | 1.58377 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.46410 | 0.224544 | ||||||||
\(239\) | −11.1153 | −0.718989 | −0.359495 | − | 0.933147i | \(-0.617051\pi\) | ||||
−0.359495 | + | 0.933147i | \(0.617051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1715 | −1.68585 | −0.842926 | − | 0.538029i | \(-0.819169\pi\) | ||||
−0.842926 | + | 0.538029i | \(0.819169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.37600 | 0.408182 | ||||||||
\(245\) | 12.1652 | 0.777203 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.16515 | −0.201394 | ||||||||
\(248\) | −14.8655 | −0.943957 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.456850 | −0.0288937 | ||||||||
\(251\) | 5.58258 | 0.352369 | 0.176185 | − | 0.984357i | \(-0.443624\pi\) | ||||
0.176185 | + | 0.984357i | \(0.443624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.58258 | −0.224791 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | −5.83485 | −0.363968 | −0.181984 | − | 0.983302i | \(-0.558252\pi\) | ||||
−0.181984 | + | 0.983302i | \(0.558252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.1950 | 2.06264 | ||||||||
\(260\) | −1.63670 | −0.101504 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.58258 | 0.592014 | ||||||||
\(263\) | 11.4014 | 0.703038 | 0.351519 | − | 0.936181i | \(-0.385665\pi\) | ||||
0.351519 | + | 0.936181i | \(0.385665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.1652 | −0.747299 | ||||||||
\(266\) | 6.92820 | 0.424795 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.91288 | 0.483356 | ||||||||
\(269\) | 8.83485 | 0.538670 | 0.269335 | − | 0.963047i | \(-0.413196\pi\) | ||||
0.269335 | + | 0.963047i | \(0.413196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.6929 | 1.01402 | 0.507009 | − | 0.861940i | \(-0.330751\pi\) | ||||
0.507009 | + | 0.861940i | \(0.330751\pi\) | |||||||
\(272\) | −4.83465 | −0.293144 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.83105 | −0.533503 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.82740 | −0.109798 | −0.0548989 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0548989 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(278\) | −3.53901 | −0.212256 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.58258 | 0.453146 | ||||||||
\(281\) | 23.7164 | 1.41480 | 0.707401 | − | 0.706812i | \(-0.249867\pi\) | ||||
0.707401 | + | 0.706812i | \(0.249867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7737 | −0.640430 | −0.320215 | − | 0.947345i | \(-0.603755\pi\) | ||||
−0.320215 | + | 0.947345i | \(0.603755\pi\) | |||||||
\(284\) | 14.3303 | 0.850347 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.1652 | −0.895171 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 4.41742 | 0.259400 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.13701 | −0.534703 | ||||||||
\(293\) | −1.73205 | −0.101187 | −0.0505937 | − | 0.998719i | \(-0.516111\pi\) | ||||
−0.0505937 | + | 0.998719i | \(0.516111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.5826 | −0.790808 | ||||||||
\(296\) | 13.1334 | 0.763364 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.25227 | −0.0725422 | ||||||||
\(299\) | 0.532300 | 0.0307837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.3303 | −2.43988 | ||||||||
\(302\) | −3.53901 | −0.203647 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.66930 | −0.554573 | ||||||||
\(305\) | −3.55945 | −0.203814 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.4931 | −0.884238 | −0.442119 | − | 0.896956i | \(-0.645773\pi\) | ||||
−0.442119 | + | 0.896956i | \(0.645773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.92095 | 0.222695 | ||||||||
\(311\) | 11.5826 | 0.656788 | 0.328394 | − | 0.944541i | \(-0.393493\pi\) | ||||
0.328394 | + | 0.944541i | \(0.393493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.58258 | 0.315546 | 0.157773 | − | 0.987475i | \(-0.449569\pi\) | ||||
0.157773 | + | 0.987475i | \(0.449569\pi\) | |||||||
\(314\) | −4.91010 | −0.277093 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.46590 | −0.0824634 | ||||||||
\(317\) | −30.1652 | −1.69424 | −0.847122 | − | 0.531399i | \(-0.821667\pi\) | ||||
−0.847122 | + | 0.531399i | \(0.821667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.41742 | −0.191040 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.16515 | −0.0649313 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.913701 | 0.0506830 | ||||||||
\(326\) | 9.47860 | 0.524971 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | −14.9608 | −0.824816 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7477 | 1.52515 | 0.762577 | − | 0.646898i | \(-0.223934\pi\) | ||||
0.762577 | + | 0.646898i | \(0.223934\pi\) | |||||||
\(332\) | −28.4358 | −1.56062 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.04356 | 0.111819 | ||||||||
\(335\) | −4.41742 | −0.241350 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.190700 | 0.0103881 | 0.00519406 | − | 0.999987i | \(-0.498347\pi\) | ||||
0.00519406 | + | 0.999987i | \(0.498347\pi\) | |||||||
\(338\) | 5.55765 | 0.302296 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.10260 | 0.168262 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.6120 | 1.22093 | ||||||||
\(344\) | −16.7477 | −0.902977 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.16515 | −0.170160 | ||||||||
\(347\) | −21.9844 | −1.18018 | −0.590091 | − | 0.807337i | \(-0.700908\pi\) | ||||
−0.590091 | + | 0.807337i | \(0.700908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.9808 | −1.39072 | −0.695359 | − | 0.718662i | \(-0.744755\pi\) | ||||
−0.695359 | + | 0.718662i | \(0.744755\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.8348 | −0.949253 | −0.474627 | − | 0.880187i | \(-0.657417\pi\) | ||||
−0.474627 | + | 0.880187i | \(0.657417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 26.4174 | 1.40012 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.46410 | 0.183083 | ||||||||
\(359\) | −8.75560 | −0.462103 | −0.231052 | − | 0.972942i | \(-0.574217\pi\) | ||||
−0.231052 | + | 0.972942i | \(0.574217\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 2.35970 | 0.124023 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.16515 | −0.375556 | ||||||||
\(365\) | 5.10080 | 0.266988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.25227 | −0.0653681 | −0.0326841 | − | 0.999466i | \(-0.510406\pi\) | ||||
−0.0326841 | + | 0.999466i | \(0.510406\pi\) | |||||||
\(368\) | 1.62614 | 0.0847682 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.46410 | −0.180090 | ||||||||
\(371\) | −53.2566 | −2.76495 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8564 | −0.717458 | −0.358729 | − | 0.933442i | \(-0.616790\pi\) | ||||
−0.358729 | + | 0.933442i | \(0.616790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.91915 | −0.305257 | ||||||||
\(377\) | −8.83485 | −0.455018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7477 | −0.808906 | −0.404453 | − | 0.914559i | \(-0.632538\pi\) | ||||
−0.404453 | + | 0.914559i | \(0.632538\pi\) | |||||||
\(380\) | 6.20520 | 0.318320 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.3923 | −0.531717 | ||||||||
\(383\) | −6.33030 | −0.323463 | −0.161732 | − | 0.986835i | \(-0.551708\pi\) | ||||
−0.161732 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.49545 | −0.381509 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.91288 | −0.401716 | ||||||||
\(389\) | −4.74773 | −0.240719 | −0.120360 | − | 0.992730i | \(-0.538405\pi\) | ||||
−0.120360 | + | 0.992730i | \(0.538405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00905 | −0.0510299 | ||||||||
\(392\) | 21.0707 | 1.06423 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.66970 | −0.285635 | ||||||||
\(395\) | 0.818350 | 0.0411757 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.3303 | 1.62261 | 0.811306 | − | 0.584622i | \(-0.198757\pi\) | ||||
0.811306 | + | 0.584622i | \(0.198757\pi\) | |||||||
\(398\) | 7.19435 | 0.360620 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.79129 | 0.139564 | ||||||||
\(401\) | −14.3303 | −0.715621 | −0.357811 | − | 0.933794i | \(-0.616477\pi\) | ||||
−0.357811 | + | 0.933794i | \(0.616477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.84190 | −0.390633 | ||||||||
\(404\) | 3.27340 | 0.162858 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.3386 | 0.959759 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.4340 | 0.960947 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(410\) | 1.58258 | 0.0781578 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.8348 | −0.632328 | ||||||||
\(413\) | −59.4618 | −2.92593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8745 | 0.779249 | ||||||||
\(416\) | −4.33030 | −0.212311 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.33030 | 0.211549 | 0.105775 | − | 0.994390i | \(-0.466268\pi\) | ||||
0.105775 | + | 0.994390i | \(0.466268\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.3303 | −1.91684 | −0.958421 | − | 0.285359i | \(-0.907887\pi\) | ||||
−0.958421 | + | 0.285359i | \(0.907887\pi\) | |||||||
\(422\) | 10.7042 | 0.521071 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.0707 | −1.02328 | ||||||||
\(425\) | −1.73205 | −0.0840168 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5826 | −0.754094 | ||||||||
\(428\) | −23.3549 | −1.12890 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.41742 | 0.213027 | ||||||||
\(431\) | 4.18710 | 0.201686 | 0.100843 | − | 0.994902i | \(-0.467846\pi\) | ||||
0.100843 | + | 0.994902i | \(0.467846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.5826 | −0.652737 | −0.326368 | − | 0.945243i | \(-0.605825\pi\) | ||||
−0.326368 | + | 0.945243i | \(0.605825\pi\) | |||||||
\(434\) | 17.1652 | 0.823954 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.4104 | 0.594351 | ||||||||
\(437\) | −2.01810 | −0.0965389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.28245 | −0.204390 | −0.102195 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.723000 | 0.0343896 | ||||||||
\(443\) | 11.1652 | 0.530472 | 0.265236 | − | 0.964183i | \(-0.414550\pi\) | ||||
0.265236 | + | 0.964183i | \(0.414550\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.7477 | −0.699109 | ||||||||
\(446\) | 7.46050 | 0.353265 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.9608 | −0.706832 | ||||||||
\(449\) | −21.1652 | −0.998845 | −0.499423 | − | 0.866358i | \(-0.666454\pi\) | ||||
−0.499423 | + | 0.866358i | \(0.666454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.1216 | 0.758296 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.20871 | −0.432186 | ||||||||
\(455\) | 4.00000 | 0.187523 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.0043 | 1.54388 | 0.771938 | − | 0.635697i | \(-0.219287\pi\) | ||||
0.771938 | + | 0.635697i | \(0.219287\pi\) | |||||||
\(458\) | −7.76645 | −0.362903 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.04356 | −0.0486563 | ||||||||
\(461\) | −18.4249 | −0.858134 | −0.429067 | − | 0.903273i | \(-0.641158\pi\) | ||||
−0.429067 | + | 0.903273i | \(0.641158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.4955 | 0.906031 | 0.453015 | − | 0.891503i | \(-0.350348\pi\) | ||||
0.453015 | + | 0.891503i | \(0.350348\pi\) | |||||||
\(464\) | −26.9898 | −1.25297 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.46099 | −0.299299 | ||||||||
\(467\) | 12.5826 | 0.582252 | 0.291126 | − | 0.956685i | \(-0.405970\pi\) | ||||
0.291126 | + | 0.956685i | \(0.405970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.3386 | −0.892974 | ||||||||
\(470\) | 1.56125 | 0.0720151 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.5257 | −1.08286 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.46410 | −0.158944 | ||||||||
\(476\) | 13.5826 | 0.622556 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.07803 | 0.232264 | ||||||||
\(479\) | 30.8353 | 1.40890 | 0.704451 | − | 0.709753i | \(-0.251193\pi\) | ||||
0.704451 | + | 0.709753i | \(0.251193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820 | 0.315899 | ||||||||
\(482\) | 11.9564 | 0.544601 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.41742 | 0.200585 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.58258 | −0.252971 | −0.126485 | − | 0.991968i | \(-0.540370\pi\) | ||||
−0.126485 | + | 0.991968i | \(0.540370\pi\) | |||||||
\(488\) | −6.16515 | −0.279083 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.55765 | −0.251069 | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.7477 | 0.754280 | ||||||||
\(494\) | 1.44600 | 0.0650586 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.9564 | −1.07568 | ||||||||
\(497\) | −35.0224 | −1.57097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3303 | −0.462448 | −0.231224 | − | 0.972901i | \(-0.574273\pi\) | ||||
−0.231224 | + | 0.972901i | \(0.574273\pi\) | |||||||
\(500\) | −1.79129 | −0.0801088 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.55040 | −0.113830 | ||||||||
\(503\) | 6.10985 | 0.272425 | 0.136212 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136212 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.82740 | −0.0813183 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.0471 | −0.623240 | ||||||||
\(509\) | 26.7477 | 1.18557 | 0.592786 | − | 0.805360i | \(-0.298028\pi\) | ||||
0.592786 | + | 0.805360i | \(0.298028\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3303 | 0.987834 | ||||||||
\(512\) | −22.8981 | −1.01196 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.66565 | 0.117577 | ||||||||
\(515\) | 7.16515 | 0.315734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −15.1652 | −0.666318 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.58258 | 0.0694005 | ||||||||
\(521\) | −36.7477 | −1.60995 | −0.804974 | − | 0.593311i | \(-0.797821\pi\) | ||||
−0.804974 | + | 0.593311i | \(0.797821\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8890 | −0.957140 | −0.478570 | − | 0.878050i | \(-0.658845\pi\) | ||||
−0.478570 | + | 0.878050i | \(0.658845\pi\) | |||||||
\(524\) | 37.5728 | 1.64138 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.20871 | −0.227111 | ||||||||
\(527\) | 14.8655 | 0.647549 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6606 | −0.985244 | ||||||||
\(530\) | 5.55765 | 0.241409 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.1652 | 1.17776 | ||||||||
\(533\) | −3.16515 | −0.137098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.0381 | 0.563684 | ||||||||
\(536\) | −7.65120 | −0.330482 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.03620 | −0.174013 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9934 | −0.988564 | −0.494282 | − | 0.869302i | \(-0.664569\pi\) | ||||
−0.494282 | + | 0.869302i | \(0.664569\pi\) | |||||||
\(542\) | −7.62614 | −0.327571 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.20871 | 0.351946 | ||||||||
\(545\) | −6.92820 | −0.296772 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0369 | 1.75461 | 0.877306 | − | 0.479931i | \(-0.159338\pi\) | ||||
0.877306 | + | 0.479931i | \(0.159338\pi\) | |||||||
\(548\) | −34.6261 | −1.47916 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.4955 | 1.42695 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.58258 | 0.152347 | ||||||||
\(554\) | 0.834849 | 0.0354693 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.8763 | −0.588487 | ||||||||
\(557\) | 8.46955 | 0.358867 | 0.179433 | − | 0.983770i | \(-0.442574\pi\) | ||||
0.179433 | + | 0.983770i | \(0.442574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.83485 | −0.373674 | ||||||||
\(560\) | 12.2197 | 0.516377 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.8348 | −0.457041 | ||||||||
\(563\) | 43.5873 | 1.83699 | 0.918493 | − | 0.395437i | \(-0.129407\pi\) | ||||
0.918493 | + | 0.395437i | \(0.129407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | −0.378633 | ||||||||
\(566\) | 4.92197 | 0.206886 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.8564 | −0.581402 | ||||||||
\(569\) | 37.3821 | 1.56714 | 0.783570 | − | 0.621304i | \(-0.213397\pi\) | ||||
0.783570 | + | 0.621304i | \(0.213397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.627650 | 0.0262663 | 0.0131332 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131332 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.92820 | 0.289178 | ||||||||
\(575\) | 0.582576 | 0.0242951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.0000 | 0.832611 | 0.416305 | − | 0.909225i | \(-0.363325\pi\) | ||||
0.416305 | + | 0.909225i | \(0.363325\pi\) | |||||||
\(578\) | 6.39590 | 0.266035 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.3205 | 0.719195 | ||||||||
\(581\) | 69.4955 | 2.88316 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.83485 | 0.365589 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.791288 | 0.0326878 | ||||||||
\(587\) | −7.74773 | −0.319783 | −0.159891 | − | 0.987135i | \(-0.551114\pi\) | ||||
−0.159891 | + | 0.987135i | \(0.551114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.7309 | 1.22504 | ||||||||
\(590\) | 6.20520 | 0.255464 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.1652 | 0.869882 | ||||||||
\(593\) | 27.7128 | 1.13803 | 0.569014 | − | 0.822328i | \(-0.307325\pi\) | ||||
0.569014 | + | 0.822328i | \(0.307325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.58258 | −0.310855 | ||||||||
\(596\) | −4.91010 | −0.201126 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.243181 | −0.00994442 | ||||||||
\(599\) | −6.74773 | −0.275705 | −0.137852 | − | 0.990453i | \(-0.544020\pi\) | ||||
−0.137852 | + | 0.990453i | \(0.544020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.44600 | 0.0589836 | 0.0294918 | − | 0.999565i | \(-0.490611\pi\) | ||||
0.0294918 | + | 0.999565i | \(0.490611\pi\) | |||||||
\(602\) | 19.3386 | 0.788183 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.8763 | −0.564619 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5438 | 1.03679 | 0.518396 | − | 0.855141i | \(-0.326529\pi\) | ||||
0.518396 | + | 0.855141i | \(0.326529\pi\) | |||||||
\(608\) | 16.4174 | 0.665814 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.62614 | 0.0658403 | ||||||||
\(611\) | −3.12250 | −0.126323 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.82740 | 0.0738080 | 0.0369040 | − | 0.999319i | \(-0.488250\pi\) | ||||
0.0369040 | + | 0.999319i | \(0.488250\pi\) | |||||||
\(614\) | 7.07803 | 0.285646 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.4955 | 0.542428 | 0.271214 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271214 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(620\) | 15.3739 | 0.617429 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.29150 | −0.212170 | ||||||||
\(623\) | −64.5626 | −2.58665 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.55040 | −0.101935 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.2523 | −0.768249 | ||||||||
\(629\) | −13.1334 | −0.523663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.4174 | −0.852614 | −0.426307 | − | 0.904578i | \(-0.640186\pi\) | ||||
−0.426307 | + | 0.904578i | \(0.640186\pi\) | |||||||
\(632\) | 1.41742 | 0.0563821 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.7810 | 0.547312 | ||||||||
\(635\) | 7.84190 | 0.311196 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.1153 | 0.440404 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.0399 | 0.436389 | ||||||||
\(641\) | 6.74773 | 0.266519 | 0.133260 | − | 0.991081i | \(-0.457456\pi\) | ||||
0.133260 | + | 0.991081i | \(0.457456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.4955 | −1.55755 | −0.778774 | − | 0.627304i | \(-0.784158\pi\) | ||||
−0.778774 | + | 0.627304i | \(0.784158\pi\) | |||||||
\(644\) | −4.56850 | −0.180024 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.74110 | −0.107847 | ||||||||
\(647\) | −29.7477 | −1.16950 | −0.584752 | − | 0.811212i | \(-0.698808\pi\) | ||||
−0.584752 | + | 0.811212i | \(0.698808\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.417424 | −0.0163727 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37.1652 | 1.45550 | ||||||||
\(653\) | 10.0000 | 0.391330 | 0.195665 | − | 0.980671i | \(-0.437313\pi\) | ||||
0.195665 | + | 0.980671i | \(0.437313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9753 | −0.819573 | ||||||||
\(656\) | −9.66930 | −0.377523 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.83485 | 0.266450 | ||||||||
\(659\) | −18.2342 | −0.710304 | −0.355152 | − | 0.934809i | \(-0.615571\pi\) | ||||
−0.355152 | + | 0.934809i | \(0.615571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | −12.6766 | −0.492688 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27.4955 | 1.06703 | ||||||||
\(665\) | −15.1652 | −0.588079 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.63310 | −0.218115 | ||||||||
\(668\) | 8.01270 | 0.310021 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.01810 | 0.0779661 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.3060 | 0.435814 | 0.217907 | − | 0.975969i | \(-0.430077\pi\) | ||||
0.217907 | + | 0.975969i | \(0.430077\pi\) | |||||||
\(674\) | −0.0871215 | −0.00335580 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.7913 | 0.838126 | ||||||||
\(677\) | 12.0290 | 0.462312 | 0.231156 | − | 0.972917i | \(-0.425749\pi\) | ||||
0.231156 | + | 0.972917i | \(0.425749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.3386 | 0.742148 | ||||||||
\(680\) | −3.00000 | −0.115045 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −46.3303 | −1.77278 | −0.886390 | − | 0.462939i | \(-0.846795\pi\) | ||||
−0.886390 | + | 0.462939i | \(0.846795\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3303 | 0.738573 | ||||||||
\(686\) | −10.3303 | −0.394413 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.9898 | −1.02898 | ||||||||
\(689\) | −11.1153 | −0.423459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.582576 | −0.0221622 | −0.0110811 | − | 0.999939i | \(-0.503527\pi\) | ||||
−0.0110811 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(692\) | −12.4104 | −0.471773 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.0436 | 0.381248 | ||||||||
\(695\) | 7.74655 | 0.293844 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | 0.227266 | ||||||||
\(698\) | 11.8693 | 0.449260 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.84190 | −0.296396 | ||||||||
\(701\) | 21.8890 | 0.826737 | 0.413368 | − | 0.910564i | \(-0.364352\pi\) | ||||
0.413368 | + | 0.910564i | \(0.364352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.2668 | −0.990672 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.14786 | 0.306649 | ||||||||
\(707\) | −8.00000 | −0.300871 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.0000 | −1.69001 | −0.845005 | − | 0.534758i | \(-0.820403\pi\) | ||||
−0.845005 | + | 0.534758i | \(0.820403\pi\) | |||||||
\(710\) | 3.65480 | 0.137162 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.5438 | −0.957295 | ||||||||
\(713\) | −5.00000 | −0.187251 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.5826 | 0.507605 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.00000 | 0.149279 | ||||||||
\(719\) | 16.3303 | 0.609018 | 0.304509 | − | 0.952510i | \(-0.401508\pi\) | ||||
0.304509 | + | 0.952510i | \(0.401508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.3676 | 1.16819 | ||||||||
\(722\) | 3.19795 | 0.119015 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.25227 | 0.343858 | ||||||||
\(725\) | −9.66930 | −0.359109 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.16515 | −0.191565 | −0.0957824 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957824 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(728\) | 6.92820 | 0.256776 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.33030 | −0.0862484 | ||||||||
\(731\) | 16.7477 | 0.619437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.6657 | −0.504754 | −0.252377 | − | 0.967629i | \(-0.581212\pi\) | ||||
−0.252377 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(734\) | 0.572101 | 0.0211166 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.76100 | −0.101772 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9844 | −0.808708 | −0.404354 | − | 0.914603i | \(-0.632504\pi\) | ||||
−0.404354 | + | 0.914603i | \(0.632504\pi\) | |||||||
\(740\) | −13.5826 | −0.499305 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.3303 | 0.893194 | ||||||||
\(743\) | 12.6567 | 0.464328 | 0.232164 | − | 0.972677i | \(-0.425419\pi\) | ||||
0.232164 | + | 0.972677i | \(0.425419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.74110 | 0.100426 | ||||||||
\(746\) | 6.33030 | 0.231769 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57.0780 | 2.08559 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0780 | 0.732658 | 0.366329 | − | 0.930485i | \(-0.380615\pi\) | ||||
0.366329 | + | 0.930485i | \(0.380615\pi\) | |||||||
\(752\) | −9.53901 | −0.347852 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.03620 | 0.146990 | ||||||||
\(755\) | 7.74655 | 0.281926 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.83485 | 0.248417 | 0.124208 | − | 0.992256i | \(-0.460361\pi\) | ||||
0.124208 | + | 0.992256i | \(0.460361\pi\) | |||||||
\(758\) | 7.19435 | 0.261311 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | −14.7701 | −0.535416 | −0.267708 | − | 0.963500i | \(-0.586266\pi\) | ||||
−0.267708 | + | 0.963500i | \(0.586266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.3303 | −1.09803 | ||||||||
\(764\) | −40.7477 | −1.47420 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.89200 | 0.104492 | ||||||||
\(767\) | −12.4104 | −0.448114 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.5101 | 1.64114 | 0.820568 | − | 0.571550i | \(-0.193657\pi\) | ||||
0.820568 | + | 0.571550i | \(0.193657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −29.3893 | −1.05774 | ||||||||
\(773\) | −48.4955 | −1.74426 | −0.872130 | − | 0.489274i | \(-0.837262\pi\) | ||||
−0.872130 | + | 0.489274i | \(0.837262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.58258 | −0.308295 | ||||||||
\(776\) | 7.65120 | 0.274662 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.16900 | 0.0777624 | ||||||||
\(779\) | 12.0000 | 0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.460985 | 0.0164848 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 33.9564 | 1.21273 | ||||||||
\(785\) | 10.7477 | 0.383603 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.2378 | 0.507523 | 0.253762 | − | 0.967267i | \(-0.418332\pi\) | ||||
0.253762 | + | 0.967267i | \(0.418332\pi\) | |||||||
\(788\) | −22.2306 | −0.791933 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.373864 | −0.0133015 | ||||||||
\(791\) | −39.4002 | −1.40091 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.25227 | −0.115492 | ||||||||
\(794\) | −14.7701 | −0.524171 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.2087 | 0.999831 | ||||||||
\(797\) | 4.33030 | 0.153387 | 0.0766936 | − | 0.997055i | \(-0.475564\pi\) | ||||
0.0766936 | + | 0.997055i | \(0.475564\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.91915 | 0.209405 | ||||||||
\(800\) | −4.73930 | −0.167560 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.54680 | 0.231176 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.55040 | 0.0898898 | ||||||||
\(806\) | 3.58258 | 0.126191 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.16515 | −0.111350 | ||||||||
\(809\) | 8.75560 | 0.307831 | 0.153915 | − | 0.988084i | \(-0.450812\pi\) | ||||
0.153915 | + | 0.988084i | \(0.450812\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.7980 | 1.92422 | 0.962109 | − | 0.272667i | \(-0.0879056\pi\) | ||||
0.962109 | + | 0.272667i | \(0.0879056\pi\) | |||||||
\(812\) | 75.8258 | 2.66096 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7477 | −0.726761 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.4955 | 1.17186 | ||||||||
\(818\) | −8.87841 | −0.310426 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.20520 | 0.216695 | ||||||||
\(821\) | −18.7665 | −0.654956 | −0.327478 | − | 0.944859i | \(-0.606199\pi\) | ||||
−0.327478 | + | 0.944859i | \(0.606199\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1652 | −0.668055 | −0.334028 | − | 0.942563i | \(-0.608408\pi\) | ||||
−0.334028 | + | 0.942563i | \(0.608408\pi\) | |||||||
\(824\) | 12.4104 | 0.432337 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.1652 | 0.945197 | ||||||||
\(827\) | 5.67290 | 0.197266 | 0.0986331 | − | 0.995124i | \(-0.468553\pi\) | ||||
0.0986331 | + | 0.995124i | \(0.468553\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000 | 0.659897 | 0.329949 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329949 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(830\) | −7.25227 | −0.251730 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.12250 | −0.108253 | ||||||||
\(833\) | −21.0707 | −0.730055 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.47315 | −0.154800 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.97830 | −0.0683392 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.4955 | 2.22398 | ||||||||
\(842\) | 17.9681 | 0.619220 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 41.9705 | 1.44468 | ||||||||
\(845\) | −12.1652 | −0.418494 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −33.9564 | −1.16607 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.791288 | 0.0271409 | ||||||||
\(851\) | 4.41742 | 0.151427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3567 | −0.731240 | −0.365620 | − | 0.930764i | \(-0.619143\pi\) | ||||
−0.365620 | + | 0.930764i | \(0.619143\pi\) | |||||||
\(854\) | 7.11890 | 0.243604 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.5826 | 0.771857 | ||||||||
\(857\) | 6.83285 | 0.233406 | 0.116703 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116703 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.6606 | 1.66028 | 0.830139 | − | 0.557556i | \(-0.188261\pi\) | ||||
0.830139 | + | 0.557556i | \(0.188261\pi\) | |||||||
\(860\) | 17.3205 | 0.590624 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.91288 | −0.0651529 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.92820 | 0.235566 | ||||||||
\(866\) | 6.20520 | 0.210861 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 67.3037 | 2.28444 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.03620 | −0.136762 | ||||||||
\(872\) | −12.0000 | −0.406371 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.921970 | 0.0311861 | ||||||||
\(875\) | 4.37780 | 0.147997 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5939 | −0.695407 | −0.347703 | − | 0.937605i | \(-0.613038\pi\) | ||||
−0.347703 | + | 0.937605i | \(0.613038\pi\) | |||||||
\(878\) | 1.95644 | 0.0660266 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4955 | 0.993727 | 0.496864 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496864 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.2432 | 1.15237 | 0.576187 | − | 0.817318i | \(-0.304540\pi\) | ||||
0.576187 | + | 0.817318i | \(0.304540\pi\) | |||||||
\(884\) | 2.83485 | 0.0953463 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.10080 | −0.171365 | ||||||||
\(887\) | −29.7309 | −0.998266 | −0.499133 | − | 0.866525i | \(-0.666348\pi\) | ||||
−0.499133 | + | 0.866525i | \(0.666348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.3303 | 1.15140 | ||||||||
\(890\) | 6.73750 | 0.225842 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.2523 | 0.979439 | ||||||||
\(893\) | 11.8383 | 0.396154 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.58258 | −0.253458 | ||||||||
\(896\) | 48.3303 | 1.61460 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.66930 | 0.322669 | ||||||||
\(899\) | 82.9875 | 2.76779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0707 | 0.701965 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.5885 | −0.518464 | ||||||||
\(905\) | −5.16515 | −0.171695 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8348 | 0.359765 | 0.179883 | − | 0.983688i | \(-0.442428\pi\) | ||||
0.179883 | + | 0.983688i | \(0.442428\pi\) | |||||||
\(908\) | −36.1069 | −1.19825 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.82740 | −0.0605778 | ||||||||
\(911\) | 17.2523 | 0.571593 | 0.285797 | − | 0.958290i | \(-0.407742\pi\) | ||||
0.285797 | + | 0.958290i | \(0.407742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −15.0780 | −0.498737 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.4519 | −1.00616 | ||||||||
\(917\) | −91.8258 | −3.03235 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.73750 | −0.222250 | −0.111125 | − | 0.993806i | \(-0.535445\pi\) | ||||
−0.111125 | + | 0.993806i | \(0.535445\pi\) | |||||||
\(920\) | 1.00905 | 0.0332674 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.41742 | 0.277213 | ||||||||
\(923\) | −7.30960 | −0.240599 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.58258 | 0.249314 | ||||||||
\(926\) | −8.90650 | −0.292686 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 45.8258 | 1.50430 | ||||||||
\(929\) | −20.3303 | −0.667016 | −0.333508 | − | 0.942747i | \(-0.608232\pi\) | ||||
−0.333508 | + | 0.942747i | \(0.608232\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.1413 | −1.38113 | ||||||||
\(932\) | −25.3332 | −0.829817 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.74835 | −0.188092 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.86001 | 0.322112 | 0.161056 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161056 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(938\) | 8.83485 | 0.288468 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.12159 | 0.199664 | ||||||||
\(941\) | 41.0369 | 1.33777 | 0.668883 | − | 0.743368i | \(-0.266773\pi\) | ||||
0.668883 | + | 0.743368i | \(0.266773\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.01810 | −0.0657184 | ||||||||
\(944\) | −37.9129 | −1.23396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.9129 | 0.809560 | 0.404780 | − | 0.914414i | \(-0.367348\pi\) | ||||
0.404780 | + | 0.914414i | \(0.367348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.66061 | 0.151290 | ||||||||
\(950\) | 1.58258 | 0.0513455 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.1334 | −0.425656 | ||||||||
\(953\) | −20.7846 | −0.673280 | −0.336640 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336640 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.7477 | 0.736099 | ||||||||
\(956\) | 19.9107 | 0.643958 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.0871 | −0.455134 | ||||||||
\(959\) | 84.6242 | 2.73266 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 42.6606 | 1.37615 | ||||||||
\(962\) | −3.16515 | −0.102049 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46.8806 | 1.50992 | ||||||||
\(965\) | 16.4068 | 0.528154 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.71940 | −0.151766 | −0.0758829 | − | 0.997117i | \(-0.524178\pi\) | ||||
−0.0758829 | + | 0.997117i | \(0.524178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.01810 | −0.0647973 | ||||||||
\(971\) | −25.5826 | −0.820984 | −0.410492 | − | 0.911864i | \(-0.634643\pi\) | ||||
−0.410492 | + | 0.911864i | \(0.634643\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.9129 | 1.08720 | ||||||||
\(974\) | 2.55040 | 0.0817201 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.93545 | −0.318026 | ||||||||
\(977\) | −12.1652 | −0.389198 | −0.194599 | − | 0.980883i | \(-0.562340\pi\) | ||||
−0.194599 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −21.7913 | −0.696097 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.6606 | −0.404016 | ||||||||
\(983\) | −21.4174 | −0.683110 | −0.341555 | − | 0.939862i | \(-0.610954\pi\) | ||||
−0.341555 | + | 0.939862i | \(0.610954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4104 | 0.395428 | ||||||||
\(986\) | −7.65120 | −0.243664 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.66970 | 0.180377 | ||||||||
\(989\) | −5.63310 | −0.179122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.2432 | −1.18307 | −0.591534 | − | 0.806280i | \(-0.701478\pi\) | ||||
−0.591534 | + | 0.806280i | \(0.701478\pi\) | |||||||
\(992\) | 40.6754 | 1.29145 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.0000 | 0.507489 | ||||||||
\(995\) | −15.7477 | −0.499237 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.4183 | −1.31173 | −0.655866 | − | 0.754878i | \(-0.727696\pi\) | ||||
−0.655866 | + | 0.754878i | \(0.727696\pi\) | |||||||
\(998\) | 4.71940 | 0.149390 | ||||||||
\(999\) | 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 | 5445.2.a.bl.1.2 | 4 | ||
3.2 | odd | 2 | 1815.2.a.t.1.3 | yes | 4 | ||
11.10 | odd | 2 | inner | 5445.2.a.bl.1.3 | 4 | ||
15.14 | odd | 2 | 9075.2.a.cu.1.2 | 4 | |||
33.32 | even | 2 | 1815.2.a.t.1.2 | ✓ | 4 | ||
165.164 | even | 2 | 9075.2.a.cu.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.t.1.2 | ✓ | 4 | 33.32 | even | 2 | ||
1815.2.a.t.1.3 | yes | 4 | 3.2 | odd | 2 | ||
5445.2.a.bl.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bl.1.3 | 4 | 11.10 | odd | 2 | inner | ||
9075.2.a.cu.1.2 | 4 | 15.14 | odd | 2 | |||
9075.2.a.cu.1.3 | 4 | 165.164 | even | 2 |