Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, 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("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.39396\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39396 | −1.69279 | −0.846394 | − | 0.532558i | \(-0.821231\pi\) | ||||
−0.846394 | + | 0.532558i | \(0.821231\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.73106 | 1.86553 | ||||||||
\(5\) | −3.93829 | −1.76126 | −0.880629 | − | 0.473807i | \(-0.842879\pi\) | ||||
−0.880629 | + | 0.473807i | \(0.842879\pi\) | |||||||
\(6\) | −2.39396 | −0.977331 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.14409 | −1.46516 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.42812 | 2.98143 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.73106 | 1.07706 | ||||||||
\(13\) | −2.99890 | −0.831744 | −0.415872 | − | 0.909423i | \(-0.636524\pi\) | ||||
−0.415872 | + | 0.909423i | \(0.636524\pi\) | |||||||
\(14\) | 2.39396 | 0.639813 | ||||||||
\(15\) | −3.93829 | −1.01686 | ||||||||
\(16\) | 2.45868 | 0.614669 | ||||||||
\(17\) | −6.60457 | −1.60184 | −0.800922 | − | 0.598769i | \(-0.795657\pi\) | ||||
−0.800922 | + | 0.598769i | \(0.795657\pi\) | |||||||
\(18\) | −2.39396 | −0.564262 | ||||||||
\(19\) | −5.90310 | −1.35426 | −0.677132 | − | 0.735861i | \(-0.736778\pi\) | ||||
−0.677132 | + | 0.735861i | \(0.736778\pi\) | |||||||
\(20\) | −14.6940 | −3.28568 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.02551 | −1.25641 | −0.628203 | − | 0.778049i | \(-0.716209\pi\) | ||||
−0.628203 | + | 0.778049i | \(0.716209\pi\) | |||||||
\(24\) | −4.14409 | −0.845908 | ||||||||
\(25\) | 10.5101 | 2.10203 | ||||||||
\(26\) | 7.17925 | 1.40797 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.73106 | −0.705104 | ||||||||
\(29\) | −1.52075 | −0.282397 | −0.141198 | − | 0.989981i | \(-0.545096\pi\) | ||||
−0.141198 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(30\) | 9.42812 | 1.72133 | ||||||||
\(31\) | 8.46902 | 1.52108 | 0.760541 | − | 0.649290i | \(-0.224934\pi\) | ||||
0.760541 | + | 0.649290i | \(0.224934\pi\) | |||||||
\(32\) | 2.40219 | 0.424652 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.8111 | 2.71158 | ||||||||
\(35\) | 3.93829 | 0.665693 | ||||||||
\(36\) | 3.73106 | 0.621843 | ||||||||
\(37\) | −0.607840 | −0.0999283 | −0.0499641 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499641 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(38\) | 14.1318 | 2.29248 | ||||||||
\(39\) | −2.99890 | −0.480208 | ||||||||
\(40\) | 16.3206 | 2.58052 | ||||||||
\(41\) | −1.70333 | −0.266015 | −0.133007 | − | 0.991115i | \(-0.542463\pi\) | ||||
−0.133007 | + | 0.991115i | \(0.542463\pi\) | |||||||
\(42\) | 2.39396 | 0.369396 | ||||||||
\(43\) | −3.23364 | −0.493125 | −0.246562 | − | 0.969127i | \(-0.579301\pi\) | ||||
−0.246562 | + | 0.969127i | \(0.579301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.93829 | −0.587086 | ||||||||
\(46\) | 14.4249 | 2.12683 | ||||||||
\(47\) | −4.80237 | −0.700498 | −0.350249 | − | 0.936657i | \(-0.613903\pi\) | ||||
−0.350249 | + | 0.936657i | \(0.613903\pi\) | |||||||
\(48\) | 2.45868 | 0.354879 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −25.1609 | −3.55829 | ||||||||
\(51\) | −6.60457 | −0.924825 | ||||||||
\(52\) | −11.1891 | −1.55164 | ||||||||
\(53\) | −6.12834 | −0.841793 | −0.420896 | − | 0.907109i | \(-0.638284\pi\) | ||||
−0.420896 | + | 0.907109i | \(0.638284\pi\) | |||||||
\(54\) | −2.39396 | −0.325777 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.14409 | 0.553777 | ||||||||
\(57\) | −5.90310 | −0.781885 | ||||||||
\(58\) | 3.64062 | 0.478037 | ||||||||
\(59\) | 6.23883 | 0.812227 | 0.406113 | − | 0.913823i | \(-0.366884\pi\) | ||||
0.406113 | + | 0.913823i | \(0.366884\pi\) | |||||||
\(60\) | −14.6940 | −1.89699 | ||||||||
\(61\) | −2.08899 | −0.267467 | −0.133734 | − | 0.991017i | \(-0.542697\pi\) | ||||
−0.133734 | + | 0.991017i | \(0.542697\pi\) | |||||||
\(62\) | −20.2745 | −2.57487 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −10.6681 | −1.33351 | ||||||||
\(65\) | 11.8105 | 1.46492 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.599719 | −0.0732673 | −0.0366337 | − | 0.999329i | \(-0.511663\pi\) | ||||
−0.0366337 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(68\) | −24.6420 | −2.98829 | ||||||||
\(69\) | −6.02551 | −0.725386 | ||||||||
\(70\) | −9.42812 | −1.12688 | ||||||||
\(71\) | 1.40968 | 0.167298 | 0.0836489 | − | 0.996495i | \(-0.473343\pi\) | ||||
0.0836489 | + | 0.996495i | \(0.473343\pi\) | |||||||
\(72\) | −4.14409 | −0.488385 | ||||||||
\(73\) | 7.08851 | 0.829648 | 0.414824 | − | 0.909902i | \(-0.363843\pi\) | ||||
0.414824 | + | 0.909902i | \(0.363843\pi\) | |||||||
\(74\) | 1.45515 | 0.169157 | ||||||||
\(75\) | 10.5101 | 1.21361 | ||||||||
\(76\) | −22.0248 | −2.52642 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.17925 | 0.812890 | ||||||||
\(79\) | −1.02327 | −0.115126 | −0.0575632 | − | 0.998342i | \(-0.518333\pi\) | ||||
−0.0575632 | + | 0.998342i | \(0.518333\pi\) | |||||||
\(80\) | −9.68299 | −1.08259 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.07770 | 0.450307 | ||||||||
\(83\) | 3.08729 | 0.338874 | 0.169437 | − | 0.985541i | \(-0.445805\pi\) | ||||
0.169437 | + | 0.985541i | \(0.445805\pi\) | |||||||
\(84\) | −3.73106 | −0.407092 | ||||||||
\(85\) | 26.0107 | 2.82126 | ||||||||
\(86\) | 7.74120 | 0.834755 | ||||||||
\(87\) | −1.52075 | −0.163042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.48531 | −0.263442 | −0.131721 | − | 0.991287i | \(-0.542050\pi\) | ||||
−0.131721 | + | 0.991287i | \(0.542050\pi\) | |||||||
\(90\) | 9.42812 | 0.993811 | ||||||||
\(91\) | 2.99890 | 0.314370 | ||||||||
\(92\) | −22.4815 | −2.34386 | ||||||||
\(93\) | 8.46902 | 0.878197 | ||||||||
\(94\) | 11.4967 | 1.18579 | ||||||||
\(95\) | 23.2481 | 2.38521 | ||||||||
\(96\) | 2.40219 | 0.245173 | ||||||||
\(97\) | 2.55296 | 0.259214 | 0.129607 | − | 0.991565i | \(-0.458628\pi\) | ||||
0.129607 | + | 0.991565i | \(0.458628\pi\) | |||||||
\(98\) | −2.39396 | −0.241827 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 39.2139 | 3.92139 | ||||||||
\(101\) | −15.1573 | −1.50821 | −0.754106 | − | 0.656753i | \(-0.771929\pi\) | ||||
−0.754106 | + | 0.656753i | \(0.771929\pi\) | |||||||
\(102\) | 15.8111 | 1.56553 | ||||||||
\(103\) | −13.8364 | −1.36334 | −0.681670 | − | 0.731660i | \(-0.738746\pi\) | ||||
−0.681670 | + | 0.731660i | \(0.738746\pi\) | |||||||
\(104\) | 12.4277 | 1.21864 | ||||||||
\(105\) | 3.93829 | 0.384338 | ||||||||
\(106\) | 14.6710 | 1.42498 | ||||||||
\(107\) | 0.445651 | 0.0430827 | 0.0215413 | − | 0.999768i | \(-0.493143\pi\) | ||||
0.0215413 | + | 0.999768i | \(0.493143\pi\) | |||||||
\(108\) | 3.73106 | 0.359021 | ||||||||
\(109\) | 11.0988 | 1.06307 | 0.531536 | − | 0.847036i | \(-0.321615\pi\) | ||||
0.531536 | + | 0.847036i | \(0.321615\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.607840 | −0.0576936 | ||||||||
\(112\) | −2.45868 | −0.232323 | ||||||||
\(113\) | −8.08938 | −0.760985 | −0.380492 | − | 0.924784i | \(-0.624245\pi\) | ||||
−0.380492 | + | 0.924784i | \(0.624245\pi\) | |||||||
\(114\) | 14.1318 | 1.32357 | ||||||||
\(115\) | 23.7302 | 2.21285 | ||||||||
\(116\) | −5.67401 | −0.526819 | ||||||||
\(117\) | −2.99890 | −0.277248 | ||||||||
\(118\) | −14.9355 | −1.37493 | ||||||||
\(119\) | 6.60457 | 0.605440 | ||||||||
\(120\) | 16.3206 | 1.48986 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.00096 | 0.452765 | ||||||||
\(123\) | −1.70333 | −0.153584 | ||||||||
\(124\) | 31.5984 | 2.83762 | ||||||||
\(125\) | −21.7005 | −1.94095 | ||||||||
\(126\) | 2.39396 | 0.213271 | ||||||||
\(127\) | 0.179659 | 0.0159422 | 0.00797109 | − | 0.999968i | \(-0.497463\pi\) | ||||
0.00797109 | + | 0.999968i | \(0.497463\pi\) | |||||||
\(128\) | 20.7347 | 1.83271 | ||||||||
\(129\) | −3.23364 | −0.284706 | ||||||||
\(130\) | −28.2740 | −2.47979 | ||||||||
\(131\) | 9.38232 | 0.819737 | 0.409868 | − | 0.912145i | \(-0.365575\pi\) | ||||
0.409868 | + | 0.912145i | \(0.365575\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.90310 | 0.511864 | ||||||||
\(134\) | 1.43570 | 0.124026 | ||||||||
\(135\) | −3.93829 | −0.338954 | ||||||||
\(136\) | 27.3699 | 2.34695 | ||||||||
\(137\) | 0.893617 | 0.0763468 | 0.0381734 | − | 0.999271i | \(-0.487846\pi\) | ||||
0.0381734 | + | 0.999271i | \(0.487846\pi\) | |||||||
\(138\) | 14.4249 | 1.22792 | ||||||||
\(139\) | 2.12281 | 0.180054 | 0.0900271 | − | 0.995939i | \(-0.471305\pi\) | ||||
0.0900271 | + | 0.995939i | \(0.471305\pi\) | |||||||
\(140\) | 14.6940 | 1.24187 | ||||||||
\(141\) | −4.80237 | −0.404433 | ||||||||
\(142\) | −3.37471 | −0.283199 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.45868 | 0.204890 | ||||||||
\(145\) | 5.98916 | 0.497373 | ||||||||
\(146\) | −16.9696 | −1.40442 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −2.26789 | −0.186419 | ||||||||
\(149\) | 14.3220 | 1.17331 | 0.586653 | − | 0.809838i | \(-0.300445\pi\) | ||||
0.586653 | + | 0.809838i | \(0.300445\pi\) | |||||||
\(150\) | −25.1609 | −2.05438 | ||||||||
\(151\) | −13.7837 | −1.12170 | −0.560850 | − | 0.827918i | \(-0.689525\pi\) | ||||
−0.560850 | + | 0.827918i | \(0.689525\pi\) | |||||||
\(152\) | 24.4630 | 1.98421 | ||||||||
\(153\) | −6.60457 | −0.533948 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.3535 | −2.67902 | ||||||||
\(156\) | −11.1891 | −0.895842 | ||||||||
\(157\) | −11.4608 | −0.914668 | −0.457334 | − | 0.889295i | \(-0.651196\pi\) | ||||
−0.457334 | + | 0.889295i | \(0.651196\pi\) | |||||||
\(158\) | 2.44966 | 0.194884 | ||||||||
\(159\) | −6.12834 | −0.486009 | ||||||||
\(160\) | −9.46054 | −0.747922 | ||||||||
\(161\) | 6.02551 | 0.474877 | ||||||||
\(162\) | −2.39396 | −0.188087 | ||||||||
\(163\) | 4.94262 | 0.387136 | 0.193568 | − | 0.981087i | \(-0.437994\pi\) | ||||
0.193568 | + | 0.981087i | \(0.437994\pi\) | |||||||
\(164\) | −6.35521 | −0.496258 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.39086 | −0.573642 | ||||||||
\(167\) | 8.53421 | 0.660397 | 0.330198 | − | 0.943912i | \(-0.392884\pi\) | ||||
0.330198 | + | 0.943912i | \(0.392884\pi\) | |||||||
\(168\) | 4.14409 | 0.319723 | ||||||||
\(169\) | −4.00662 | −0.308201 | ||||||||
\(170\) | −62.2687 | −4.77579 | ||||||||
\(171\) | −5.90310 | −0.451422 | ||||||||
\(172\) | −12.0649 | −0.919939 | ||||||||
\(173\) | 13.0876 | 0.995031 | 0.497515 | − | 0.867455i | \(-0.334246\pi\) | ||||
0.497515 | + | 0.867455i | \(0.334246\pi\) | |||||||
\(174\) | 3.64062 | 0.275995 | ||||||||
\(175\) | −10.5101 | −0.794492 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.23883 | 0.468939 | ||||||||
\(178\) | 5.94973 | 0.445951 | ||||||||
\(179\) | 25.8622 | 1.93303 | 0.966514 | − | 0.256612i | \(-0.0826063\pi\) | ||||
0.966514 | + | 0.256612i | \(0.0826063\pi\) | |||||||
\(180\) | −14.6940 | −1.09523 | ||||||||
\(181\) | 21.4202 | 1.59215 | 0.796077 | − | 0.605195i | \(-0.206905\pi\) | ||||
0.796077 | + | 0.605195i | \(0.206905\pi\) | |||||||
\(182\) | −7.17925 | −0.532161 | ||||||||
\(183\) | −2.08899 | −0.154422 | ||||||||
\(184\) | 24.9703 | 1.84083 | ||||||||
\(185\) | 2.39385 | 0.175999 | ||||||||
\(186\) | −20.2745 | −1.48660 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.9179 | −1.30680 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −55.6552 | −4.03765 | ||||||||
\(191\) | −3.73988 | −0.270608 | −0.135304 | − | 0.990804i | \(-0.543201\pi\) | ||||
−0.135304 | + | 0.990804i | \(0.543201\pi\) | |||||||
\(192\) | −10.6681 | −0.769905 | ||||||||
\(193\) | 6.07932 | 0.437599 | 0.218799 | − | 0.975770i | \(-0.429786\pi\) | ||||
0.218799 | + | 0.975770i | \(0.429786\pi\) | |||||||
\(194\) | −6.11169 | −0.438794 | ||||||||
\(195\) | 11.8105 | 0.845770 | ||||||||
\(196\) | 3.73106 | 0.266504 | ||||||||
\(197\) | 21.5458 | 1.53508 | 0.767538 | − | 0.641003i | \(-0.221482\pi\) | ||||
0.767538 | + | 0.641003i | \(0.221482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8965 | −1.05598 | −0.527992 | − | 0.849249i | \(-0.677055\pi\) | ||||
−0.527992 | + | 0.849249i | \(0.677055\pi\) | |||||||
\(200\) | −43.5549 | −3.07980 | ||||||||
\(201\) | −0.599719 | −0.0423009 | ||||||||
\(202\) | 36.2861 | 2.55308 | ||||||||
\(203\) | 1.52075 | 0.106736 | ||||||||
\(204\) | −24.6420 | −1.72529 | ||||||||
\(205\) | 6.70819 | 0.468521 | ||||||||
\(206\) | 33.1238 | 2.30784 | ||||||||
\(207\) | −6.02551 | −0.418802 | ||||||||
\(208\) | −7.37332 | −0.511248 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −9.42812 | −0.650602 | ||||||||
\(211\) | 16.9594 | 1.16753 | 0.583766 | − | 0.811922i | \(-0.301579\pi\) | ||||
0.583766 | + | 0.811922i | \(0.301579\pi\) | |||||||
\(212\) | −22.8652 | −1.57039 | ||||||||
\(213\) | 1.40968 | 0.0965894 | ||||||||
\(214\) | −1.06687 | −0.0729298 | ||||||||
\(215\) | 12.7350 | 0.868520 | ||||||||
\(216\) | −4.14409 | −0.281969 | ||||||||
\(217\) | −8.46902 | −0.574915 | ||||||||
\(218\) | −26.5701 | −1.79955 | ||||||||
\(219\) | 7.08851 | 0.478997 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8064 | 1.33232 | ||||||||
\(222\) | 1.45515 | 0.0976630 | ||||||||
\(223\) | −13.8125 | −0.924954 | −0.462477 | − | 0.886631i | \(-0.653039\pi\) | ||||
−0.462477 | + | 0.886631i | \(0.653039\pi\) | |||||||
\(224\) | −2.40219 | −0.160503 | ||||||||
\(225\) | 10.5101 | 0.700676 | ||||||||
\(226\) | 19.3657 | 1.28819 | ||||||||
\(227\) | −7.25345 | −0.481428 | −0.240714 | − | 0.970596i | \(-0.577382\pi\) | ||||
−0.240714 | + | 0.970596i | \(0.577382\pi\) | |||||||
\(228\) | −22.0248 | −1.45863 | ||||||||
\(229\) | −0.327136 | −0.0216178 | −0.0108089 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108089 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(230\) | −56.8093 | −3.74589 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.30213 | 0.413755 | ||||||||
\(233\) | 16.2452 | 1.06426 | 0.532128 | − | 0.846664i | \(-0.321393\pi\) | ||||
0.532128 | + | 0.846664i | \(0.321393\pi\) | |||||||
\(234\) | 7.17925 | 0.469322 | ||||||||
\(235\) | 18.9131 | 1.23376 | ||||||||
\(236\) | 23.2774 | 1.51523 | ||||||||
\(237\) | −1.02327 | −0.0664683 | ||||||||
\(238\) | −15.8111 | −1.02488 | ||||||||
\(239\) | −29.0009 | −1.87591 | −0.937955 | − | 0.346756i | \(-0.887283\pi\) | ||||
−0.937955 | + | 0.346756i | \(0.887283\pi\) | |||||||
\(240\) | −9.68299 | −0.625034 | ||||||||
\(241\) | −29.3358 | −1.88968 | −0.944841 | − | 0.327530i | \(-0.893784\pi\) | ||||
−0.944841 | + | 0.327530i | \(0.893784\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.79413 | −0.498968 | ||||||||
\(245\) | −3.93829 | −0.251608 | ||||||||
\(246\) | 4.07770 | 0.259985 | ||||||||
\(247\) | 17.7028 | 1.12640 | ||||||||
\(248\) | −35.0964 | −2.22862 | ||||||||
\(249\) | 3.08729 | 0.195649 | ||||||||
\(250\) | 51.9502 | 3.28562 | ||||||||
\(251\) | 12.8316 | 0.809925 | 0.404963 | − | 0.914333i | \(-0.367285\pi\) | ||||
0.404963 | + | 0.914333i | \(0.367285\pi\) | |||||||
\(252\) | −3.73106 | −0.235035 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.430097 | −0.0269867 | ||||||||
\(255\) | 26.0107 | 1.62885 | ||||||||
\(256\) | −28.3018 | −1.76887 | ||||||||
\(257\) | 19.5210 | 1.21769 | 0.608844 | − | 0.793290i | \(-0.291633\pi\) | ||||
0.608844 | + | 0.793290i | \(0.291633\pi\) | |||||||
\(258\) | 7.74120 | 0.481946 | ||||||||
\(259\) | 0.607840 | 0.0377693 | ||||||||
\(260\) | 44.0658 | 2.73284 | ||||||||
\(261\) | −1.52075 | −0.0941322 | ||||||||
\(262\) | −22.4609 | −1.38764 | ||||||||
\(263\) | 23.9606 | 1.47747 | 0.738736 | − | 0.673995i | \(-0.235423\pi\) | ||||
0.738736 | + | 0.673995i | \(0.235423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.1352 | 1.48261 | ||||||||
\(266\) | −14.1318 | −0.866477 | ||||||||
\(267\) | −2.48531 | −0.152098 | ||||||||
\(268\) | −2.23759 | −0.136682 | ||||||||
\(269\) | 11.3260 | 0.690558 | 0.345279 | − | 0.938500i | \(-0.387784\pi\) | ||||
0.345279 | + | 0.938500i | \(0.387784\pi\) | |||||||
\(270\) | 9.42812 | 0.573777 | ||||||||
\(271\) | 6.12278 | 0.371932 | 0.185966 | − | 0.982556i | \(-0.440459\pi\) | ||||
0.185966 | + | 0.982556i | \(0.440459\pi\) | |||||||
\(272\) | −16.2385 | −0.984604 | ||||||||
\(273\) | 2.99890 | 0.181502 | ||||||||
\(274\) | −2.13929 | −0.129239 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −22.4815 | −1.35323 | ||||||||
\(277\) | 0.600165 | 0.0360604 | 0.0180302 | − | 0.999837i | \(-0.494260\pi\) | ||||
0.0180302 | + | 0.999837i | \(0.494260\pi\) | |||||||
\(278\) | −5.08192 | −0.304793 | ||||||||
\(279\) | 8.46902 | 0.507027 | ||||||||
\(280\) | −16.3206 | −0.975344 | ||||||||
\(281\) | 23.8022 | 1.41992 | 0.709960 | − | 0.704242i | \(-0.248713\pi\) | ||||
0.709960 | + | 0.704242i | \(0.248713\pi\) | |||||||
\(282\) | 11.4967 | 0.684618 | ||||||||
\(283\) | −17.3400 | −1.03076 | −0.515379 | − | 0.856962i | \(-0.672349\pi\) | ||||
−0.515379 | + | 0.856962i | \(0.672349\pi\) | |||||||
\(284\) | 5.25958 | 0.312099 | ||||||||
\(285\) | 23.2481 | 1.37710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.70333 | 0.100544 | ||||||||
\(288\) | 2.40219 | 0.141551 | ||||||||
\(289\) | 26.6204 | 1.56590 | ||||||||
\(290\) | −14.3378 | −0.841947 | ||||||||
\(291\) | 2.55296 | 0.149657 | ||||||||
\(292\) | 26.4477 | 1.54773 | ||||||||
\(293\) | −14.9122 | −0.871179 | −0.435589 | − | 0.900145i | \(-0.643460\pi\) | ||||
−0.435589 | + | 0.900145i | \(0.643460\pi\) | |||||||
\(294\) | −2.39396 | −0.139619 | ||||||||
\(295\) | −24.5703 | −1.43054 | ||||||||
\(296\) | 2.51894 | 0.146411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −34.2864 | −1.98616 | ||||||||
\(299\) | 18.0699 | 1.04501 | ||||||||
\(300\) | 39.2139 | 2.26402 | ||||||||
\(301\) | 3.23364 | 0.186384 | ||||||||
\(302\) | 32.9976 | 1.89880 | ||||||||
\(303\) | −15.1573 | −0.870766 | ||||||||
\(304\) | −14.5138 | −0.832425 | ||||||||
\(305\) | 8.22704 | 0.471079 | ||||||||
\(306\) | 15.8111 | 0.903860 | ||||||||
\(307\) | 29.0453 | 1.65771 | 0.828853 | − | 0.559467i | \(-0.188994\pi\) | ||||
0.828853 | + | 0.559467i | \(0.188994\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8364 | −0.787124 | ||||||||
\(310\) | 79.8470 | 4.53500 | ||||||||
\(311\) | −20.3651 | −1.15480 | −0.577399 | − | 0.816462i | \(-0.695932\pi\) | ||||
−0.577399 | + | 0.816462i | \(0.695932\pi\) | |||||||
\(312\) | 12.4277 | 0.703580 | ||||||||
\(313\) | −29.4807 | −1.66635 | −0.833174 | − | 0.553010i | \(-0.813479\pi\) | ||||
−0.833174 | + | 0.553010i | \(0.813479\pi\) | |||||||
\(314\) | 27.4366 | 1.54834 | ||||||||
\(315\) | 3.93829 | 0.221898 | ||||||||
\(316\) | −3.81786 | −0.214772 | ||||||||
\(317\) | 7.62530 | 0.428280 | 0.214140 | − | 0.976803i | \(-0.431305\pi\) | ||||
0.214140 | + | 0.976803i | \(0.431305\pi\) | |||||||
\(318\) | 14.6710 | 0.822710 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 42.0142 | 2.34866 | ||||||||
\(321\) | 0.445651 | 0.0248738 | ||||||||
\(322\) | −14.4249 | −0.803865 | ||||||||
\(323\) | 38.9875 | 2.16932 | ||||||||
\(324\) | 3.73106 | 0.207281 | ||||||||
\(325\) | −31.5188 | −1.74835 | ||||||||
\(326\) | −11.8324 | −0.655338 | ||||||||
\(327\) | 11.0988 | 0.613764 | ||||||||
\(328\) | 7.05873 | 0.389753 | ||||||||
\(329\) | 4.80237 | 0.264763 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.6731 | 1.13630 | 0.568148 | − | 0.822926i | \(-0.307660\pi\) | ||||
0.568148 | + | 0.822926i | \(0.307660\pi\) | |||||||
\(332\) | 11.5189 | 0.632180 | ||||||||
\(333\) | −0.607840 | −0.0333094 | ||||||||
\(334\) | −20.4306 | −1.11791 | ||||||||
\(335\) | 2.36187 | 0.129043 | ||||||||
\(336\) | −2.45868 | −0.134132 | ||||||||
\(337\) | −5.46255 | −0.297564 | −0.148782 | − | 0.988870i | \(-0.547535\pi\) | ||||
−0.148782 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(338\) | 9.59169 | 0.521719 | ||||||||
\(339\) | −8.08938 | −0.439355 | ||||||||
\(340\) | 97.0475 | 5.26314 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 14.1318 | 0.764161 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 13.4005 | 0.722505 | ||||||||
\(345\) | 23.7302 | 1.27759 | ||||||||
\(346\) | −31.3312 | −1.68438 | ||||||||
\(347\) | 9.58110 | 0.514341 | 0.257170 | − | 0.966366i | \(-0.417210\pi\) | ||||
0.257170 | + | 0.966366i | \(0.417210\pi\) | |||||||
\(348\) | −5.67401 | −0.304159 | ||||||||
\(349\) | 9.36045 | 0.501054 | 0.250527 | − | 0.968110i | \(-0.419396\pi\) | ||||
0.250527 | + | 0.968110i | \(0.419396\pi\) | |||||||
\(350\) | 25.1609 | 1.34491 | ||||||||
\(351\) | −2.99890 | −0.160069 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.6629 | −1.47235 | −0.736173 | − | 0.676794i | \(-0.763369\pi\) | ||||
−0.736173 | + | 0.676794i | \(0.763369\pi\) | |||||||
\(354\) | −14.9355 | −0.793815 | ||||||||
\(355\) | −5.55171 | −0.294654 | ||||||||
\(356\) | −9.27282 | −0.491459 | ||||||||
\(357\) | 6.60457 | 0.349551 | ||||||||
\(358\) | −61.9131 | −3.27221 | ||||||||
\(359\) | −2.60258 | −0.137359 | −0.0686796 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686796 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(360\) | 16.3206 | 0.860172 | ||||||||
\(361\) | 15.8466 | 0.834033 | ||||||||
\(362\) | −51.2793 | −2.69518 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.1891 | 0.586466 | ||||||||
\(365\) | −27.9166 | −1.46122 | ||||||||
\(366\) | 5.00096 | 0.261404 | ||||||||
\(367\) | −10.3394 | −0.539710 | −0.269855 | − | 0.962901i | \(-0.586976\pi\) | ||||
−0.269855 | + | 0.962901i | \(0.586976\pi\) | |||||||
\(368\) | −14.8148 | −0.772274 | ||||||||
\(369\) | −1.70333 | −0.0886716 | ||||||||
\(370\) | −5.73079 | −0.297930 | ||||||||
\(371\) | 6.12834 | 0.318168 | ||||||||
\(372\) | 31.5984 | 1.63830 | ||||||||
\(373\) | −5.15587 | −0.266961 | −0.133480 | − | 0.991051i | \(-0.542615\pi\) | ||||
−0.133480 | + | 0.991051i | \(0.542615\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21.7005 | −1.12061 | ||||||||
\(376\) | 19.9015 | 1.02634 | ||||||||
\(377\) | 4.56058 | 0.234882 | ||||||||
\(378\) | 2.39396 | 0.123132 | ||||||||
\(379\) | −35.4223 | −1.81952 | −0.909761 | − | 0.415133i | \(-0.863735\pi\) | ||||
−0.909761 | + | 0.415133i | \(0.863735\pi\) | |||||||
\(380\) | 86.7401 | 4.44968 | ||||||||
\(381\) | 0.179659 | 0.00920422 | ||||||||
\(382\) | 8.95313 | 0.458082 | ||||||||
\(383\) | −31.4076 | −1.60486 | −0.802428 | − | 0.596750i | \(-0.796459\pi\) | ||||
−0.802428 | + | 0.596750i | \(0.796459\pi\) | |||||||
\(384\) | 20.7347 | 1.05811 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.5537 | −0.740762 | ||||||||
\(387\) | −3.23364 | −0.164375 | ||||||||
\(388\) | 9.52524 | 0.483571 | ||||||||
\(389\) | 20.0789 | 1.01804 | 0.509020 | − | 0.860755i | \(-0.330008\pi\) | ||||
0.509020 | + | 0.860755i | \(0.330008\pi\) | |||||||
\(390\) | −28.2740 | −1.43171 | ||||||||
\(391\) | 39.7959 | 2.01257 | ||||||||
\(392\) | −4.14409 | −0.209308 | ||||||||
\(393\) | 9.38232 | 0.473275 | ||||||||
\(394\) | −51.5799 | −2.59856 | ||||||||
\(395\) | 4.02992 | 0.202767 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.63351 | 0.182361 | 0.0911804 | − | 0.995834i | \(-0.470936\pi\) | ||||
0.0911804 | + | 0.995834i | \(0.470936\pi\) | |||||||
\(398\) | 35.6616 | 1.78756 | ||||||||
\(399\) | 5.90310 | 0.295525 | ||||||||
\(400\) | 25.8410 | 1.29205 | ||||||||
\(401\) | 37.6309 | 1.87920 | 0.939598 | − | 0.342279i | \(-0.111199\pi\) | ||||
0.939598 | + | 0.342279i | \(0.111199\pi\) | |||||||
\(402\) | 1.43570 | 0.0716064 | ||||||||
\(403\) | −25.3977 | −1.26515 | ||||||||
\(404\) | −56.5529 | −2.81361 | ||||||||
\(405\) | −3.93829 | −0.195695 | ||||||||
\(406\) | −3.64062 | −0.180681 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 27.3699 | 1.35501 | ||||||||
\(409\) | 16.1059 | 0.796386 | 0.398193 | − | 0.917302i | \(-0.369637\pi\) | ||||
0.398193 | + | 0.917302i | \(0.369637\pi\) | |||||||
\(410\) | −16.0592 | −0.793106 | ||||||||
\(411\) | 0.893617 | 0.0440789 | ||||||||
\(412\) | −51.6243 | −2.54335 | ||||||||
\(413\) | −6.23883 | −0.306993 | ||||||||
\(414\) | 14.4249 | 0.708943 | ||||||||
\(415\) | −12.1587 | −0.596845 | ||||||||
\(416\) | −7.20393 | −0.353202 | ||||||||
\(417\) | 2.12281 | 0.103954 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.7128 | −0.865325 | −0.432662 | − | 0.901556i | \(-0.642426\pi\) | ||||
−0.432662 | + | 0.901556i | \(0.642426\pi\) | |||||||
\(420\) | 14.6940 | 0.716993 | ||||||||
\(421\) | 30.2721 | 1.47537 | 0.737686 | − | 0.675144i | \(-0.235919\pi\) | ||||
0.737686 | + | 0.675144i | \(0.235919\pi\) | |||||||
\(422\) | −40.6001 | −1.97638 | ||||||||
\(423\) | −4.80237 | −0.233499 | ||||||||
\(424\) | 25.3964 | 1.23336 | ||||||||
\(425\) | −69.4149 | −3.36712 | ||||||||
\(426\) | −3.37471 | −0.163505 | ||||||||
\(427\) | 2.08899 | 0.101093 | ||||||||
\(428\) | 1.66275 | 0.0803720 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.4871 | −1.47022 | ||||||||
\(431\) | 19.1918 | 0.924438 | 0.462219 | − | 0.886766i | \(-0.347053\pi\) | ||||
0.462219 | + | 0.886766i | \(0.347053\pi\) | |||||||
\(432\) | 2.45868 | 0.118293 | ||||||||
\(433\) | 21.7538 | 1.04542 | 0.522711 | − | 0.852510i | \(-0.324921\pi\) | ||||
0.522711 | + | 0.852510i | \(0.324921\pi\) | |||||||
\(434\) | 20.2745 | 0.973208 | ||||||||
\(435\) | 5.98916 | 0.287158 | ||||||||
\(436\) | 41.4102 | 1.98319 | ||||||||
\(437\) | 35.5692 | 1.70151 | ||||||||
\(438\) | −16.9696 | −0.810841 | ||||||||
\(439\) | 2.70519 | 0.129112 | 0.0645558 | − | 0.997914i | \(-0.479437\pi\) | ||||
0.0645558 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −47.4159 | −2.25534 | ||||||||
\(443\) | 38.2274 | 1.81624 | 0.908118 | − | 0.418713i | \(-0.137519\pi\) | ||||
0.908118 | + | 0.418713i | \(0.137519\pi\) | |||||||
\(444\) | −2.26789 | −0.107629 | ||||||||
\(445\) | 9.78786 | 0.463989 | ||||||||
\(446\) | 33.0666 | 1.56575 | ||||||||
\(447\) | 14.3220 | 0.677409 | ||||||||
\(448\) | 10.6681 | 0.504021 | ||||||||
\(449\) | 22.7112 | 1.07181 | 0.535904 | − | 0.844279i | \(-0.319971\pi\) | ||||
0.535904 | + | 0.844279i | \(0.319971\pi\) | |||||||
\(450\) | −25.1609 | −1.18610 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −30.1819 | −1.41964 | ||||||||
\(453\) | −13.7837 | −0.647614 | ||||||||
\(454\) | 17.3645 | 0.814956 | ||||||||
\(455\) | −11.8105 | −0.553686 | ||||||||
\(456\) | 24.4630 | 1.14558 | ||||||||
\(457\) | −1.57183 | −0.0735271 | −0.0367636 | − | 0.999324i | \(-0.511705\pi\) | ||||
−0.0367636 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(458\) | 0.783152 | 0.0365943 | ||||||||
\(459\) | −6.60457 | −0.308275 | ||||||||
\(460\) | 88.5388 | 4.12814 | ||||||||
\(461\) | −28.1276 | −1.31003 | −0.655017 | − | 0.755614i | \(-0.727339\pi\) | ||||
−0.655017 | + | 0.755614i | \(0.727339\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.69202 | −0.218057 | −0.109028 | − | 0.994039i | \(-0.534774\pi\) | ||||
−0.109028 | + | 0.994039i | \(0.534774\pi\) | |||||||
\(464\) | −3.73904 | −0.173580 | ||||||||
\(465\) | −33.3535 | −1.54673 | ||||||||
\(466\) | −38.8903 | −1.80156 | ||||||||
\(467\) | −17.6135 | −0.815054 | −0.407527 | − | 0.913193i | \(-0.633609\pi\) | ||||
−0.407527 | + | 0.913193i | \(0.633609\pi\) | |||||||
\(468\) | −11.1891 | −0.517214 | ||||||||
\(469\) | 0.599719 | 0.0276924 | ||||||||
\(470\) | −45.2773 | −2.08849 | ||||||||
\(471\) | −11.4608 | −0.528084 | ||||||||
\(472\) | −25.8543 | −1.19004 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.44966 | 0.112517 | ||||||||
\(475\) | −62.0424 | −2.84670 | ||||||||
\(476\) | 24.6420 | 1.12947 | ||||||||
\(477\) | −6.12834 | −0.280598 | ||||||||
\(478\) | 69.4270 | 3.17552 | ||||||||
\(479\) | −10.7070 | −0.489215 | −0.244608 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244608 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(480\) | −9.46054 | −0.431813 | ||||||||
\(481\) | 1.82285 | 0.0831148 | ||||||||
\(482\) | 70.2287 | 3.19883 | ||||||||
\(483\) | 6.02551 | 0.274170 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.0543 | −0.456542 | ||||||||
\(486\) | −2.39396 | −0.108592 | ||||||||
\(487\) | 38.7602 | 1.75639 | 0.878197 | − | 0.478299i | \(-0.158746\pi\) | ||||
0.878197 | + | 0.478299i | \(0.158746\pi\) | |||||||
\(488\) | 8.65695 | 0.391882 | ||||||||
\(489\) | 4.94262 | 0.223513 | ||||||||
\(490\) | 9.42812 | 0.425919 | ||||||||
\(491\) | −6.00061 | −0.270804 | −0.135402 | − | 0.990791i | \(-0.543233\pi\) | ||||
−0.135402 | + | 0.990791i | \(0.543233\pi\) | |||||||
\(492\) | −6.35521 | −0.286515 | ||||||||
\(493\) | 10.0439 | 0.452355 | ||||||||
\(494\) | −42.3798 | −1.90676 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.8226 | 0.934962 | ||||||||
\(497\) | −1.40968 | −0.0632326 | ||||||||
\(498\) | −7.39086 | −0.331193 | ||||||||
\(499\) | −28.9776 | −1.29722 | −0.648608 | − | 0.761123i | \(-0.724648\pi\) | ||||
−0.648608 | + | 0.761123i | \(0.724648\pi\) | |||||||
\(500\) | −80.9659 | −3.62091 | ||||||||
\(501\) | 8.53421 | 0.381280 | ||||||||
\(502\) | −30.7184 | −1.37103 | ||||||||
\(503\) | −12.8657 | −0.573653 | −0.286827 | − | 0.957982i | \(-0.592600\pi\) | ||||
−0.286827 | + | 0.957982i | \(0.592600\pi\) | |||||||
\(504\) | 4.14409 | 0.184592 | ||||||||
\(505\) | 59.6940 | 2.65635 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.00662 | −0.177940 | ||||||||
\(508\) | 0.670319 | 0.0297406 | ||||||||
\(509\) | 19.7361 | 0.874788 | 0.437394 | − | 0.899270i | \(-0.355902\pi\) | ||||
0.437394 | + | 0.899270i | \(0.355902\pi\) | |||||||
\(510\) | −62.2687 | −2.75730 | ||||||||
\(511\) | −7.08851 | −0.313577 | ||||||||
\(512\) | 26.2842 | 1.16161 | ||||||||
\(513\) | −5.90310 | −0.260628 | ||||||||
\(514\) | −46.7326 | −2.06129 | ||||||||
\(515\) | 54.4917 | 2.40119 | ||||||||
\(516\) | −12.0649 | −0.531127 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.45515 | −0.0639355 | ||||||||
\(519\) | 13.0876 | 0.574481 | ||||||||
\(520\) | −48.9439 | −2.14633 | ||||||||
\(521\) | −23.3926 | −1.02485 | −0.512423 | − | 0.858733i | \(-0.671252\pi\) | ||||
−0.512423 | + | 0.858733i | \(0.671252\pi\) | |||||||
\(522\) | 3.64062 | 0.159346 | ||||||||
\(523\) | −10.7796 | −0.471361 | −0.235680 | − | 0.971831i | \(-0.575732\pi\) | ||||
−0.235680 | + | 0.971831i | \(0.575732\pi\) | |||||||
\(524\) | 35.0060 | 1.52924 | ||||||||
\(525\) | −10.5101 | −0.458700 | ||||||||
\(526\) | −57.3607 | −2.50105 | ||||||||
\(527\) | −55.9343 | −2.43653 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.3068 | 0.578556 | ||||||||
\(530\) | −57.7788 | −2.50975 | ||||||||
\(531\) | 6.23883 | 0.270742 | ||||||||
\(532\) | 22.0248 | 0.954897 | ||||||||
\(533\) | 5.10810 | 0.221256 | ||||||||
\(534\) | 5.94973 | 0.257470 | ||||||||
\(535\) | −1.75510 | −0.0758797 | ||||||||
\(536\) | 2.48529 | 0.107348 | ||||||||
\(537\) | 25.8622 | 1.11603 | ||||||||
\(538\) | −27.1140 | −1.16897 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.6940 | −0.632329 | ||||||||
\(541\) | −6.42155 | −0.276084 | −0.138042 | − | 0.990426i | \(-0.544081\pi\) | ||||
−0.138042 | + | 0.990426i | \(0.544081\pi\) | |||||||
\(542\) | −14.6577 | −0.629602 | ||||||||
\(543\) | 21.4202 | 0.919231 | ||||||||
\(544\) | −15.8655 | −0.680226 | ||||||||
\(545\) | −43.7103 | −1.87234 | ||||||||
\(546\) | −7.17925 | −0.307243 | ||||||||
\(547\) | −28.0529 | −1.19946 | −0.599728 | − | 0.800204i | \(-0.704724\pi\) | ||||
−0.599728 | + | 0.800204i | \(0.704724\pi\) | |||||||
\(548\) | 3.33414 | 0.142427 | ||||||||
\(549\) | −2.08899 | −0.0891558 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.97715 | 0.382440 | ||||||||
\(552\) | 24.9703 | 1.06280 | ||||||||
\(553\) | 1.02327 | 0.0435137 | ||||||||
\(554\) | −1.43677 | −0.0610427 | ||||||||
\(555\) | 2.39385 | 0.101613 | ||||||||
\(556\) | 7.92031 | 0.335896 | ||||||||
\(557\) | 23.1102 | 0.979211 | 0.489606 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489606 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(558\) | −20.2745 | −0.858289 | ||||||||
\(559\) | 9.69734 | 0.410154 | ||||||||
\(560\) | 9.68299 | 0.409181 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −56.9815 | −2.40362 | ||||||||
\(563\) | −28.8436 | −1.21561 | −0.607806 | − | 0.794086i | \(-0.707950\pi\) | ||||
−0.607806 | + | 0.794086i | \(0.707950\pi\) | |||||||
\(564\) | −17.9179 | −0.754481 | ||||||||
\(565\) | 31.8583 | 1.34029 | ||||||||
\(566\) | 41.5114 | 1.74485 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −5.84182 | −0.245117 | ||||||||
\(569\) | −17.7760 | −0.745208 | −0.372604 | − | 0.927991i | \(-0.621535\pi\) | ||||
−0.372604 | + | 0.927991i | \(0.621535\pi\) | |||||||
\(570\) | −55.6552 | −2.33114 | ||||||||
\(571\) | 17.8981 | 0.749012 | 0.374506 | − | 0.927225i | \(-0.377812\pi\) | ||||
0.374506 | + | 0.927225i | \(0.377812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.73988 | −0.156236 | ||||||||
\(574\) | −4.07770 | −0.170200 | ||||||||
\(575\) | −63.3289 | −2.64100 | ||||||||
\(576\) | −10.6681 | −0.444505 | ||||||||
\(577\) | 21.0769 | 0.877441 | 0.438721 | − | 0.898624i | \(-0.355432\pi\) | ||||
0.438721 | + | 0.898624i | \(0.355432\pi\) | |||||||
\(578\) | −63.7281 | −2.65074 | ||||||||
\(579\) | 6.07932 | 0.252648 | ||||||||
\(580\) | 22.3459 | 0.927864 | ||||||||
\(581\) | −3.08729 | −0.128083 | ||||||||
\(582\) | −6.11169 | −0.253338 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −29.3754 | −1.21556 | ||||||||
\(585\) | 11.8105 | 0.488305 | ||||||||
\(586\) | 35.6992 | 1.47472 | ||||||||
\(587\) | 17.3136 | 0.714609 | 0.357305 | − | 0.933988i | \(-0.383696\pi\) | ||||
0.357305 | + | 0.933988i | \(0.383696\pi\) | |||||||
\(588\) | 3.73106 | 0.153866 | ||||||||
\(589\) | −49.9935 | −2.05995 | ||||||||
\(590\) | 58.8205 | 2.42160 | ||||||||
\(591\) | 21.5458 | 0.886277 | ||||||||
\(592\) | −1.49448 | −0.0614228 | ||||||||
\(593\) | −26.3881 | −1.08363 | −0.541814 | − | 0.840498i | \(-0.682262\pi\) | ||||
−0.541814 | + | 0.840498i | \(0.682262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.0107 | −1.06634 | ||||||||
\(596\) | 53.4363 | 2.18884 | ||||||||
\(597\) | −14.8965 | −0.609673 | ||||||||
\(598\) | −43.2586 | −1.76898 | ||||||||
\(599\) | −28.2593 | −1.15465 | −0.577323 | − | 0.816516i | \(-0.695903\pi\) | ||||
−0.577323 | + | 0.816516i | \(0.695903\pi\) | |||||||
\(600\) | −43.5549 | −1.77812 | ||||||||
\(601\) | −0.440908 | −0.0179850 | −0.00899251 | − | 0.999960i | \(-0.502862\pi\) | ||||
−0.00899251 | + | 0.999960i | \(0.502862\pi\) | |||||||
\(602\) | −7.74120 | −0.315508 | ||||||||
\(603\) | −0.599719 | −0.0244224 | ||||||||
\(604\) | −51.4277 | −2.09256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 36.2861 | 1.47402 | ||||||||
\(607\) | 0.559085 | 0.0226925 | 0.0113463 | − | 0.999936i | \(-0.496388\pi\) | ||||
0.0113463 | + | 0.999936i | \(0.496388\pi\) | |||||||
\(608\) | −14.1804 | −0.575091 | ||||||||
\(609\) | 1.52075 | 0.0616240 | ||||||||
\(610\) | −19.6952 | −0.797436 | ||||||||
\(611\) | 14.4018 | 0.582635 | ||||||||
\(612\) | −24.6420 | −0.996095 | ||||||||
\(613\) | 30.3820 | 1.22712 | 0.613559 | − | 0.789649i | \(-0.289737\pi\) | ||||
0.613559 | + | 0.789649i | \(0.289737\pi\) | |||||||
\(614\) | −69.5335 | −2.80614 | ||||||||
\(615\) | 6.70819 | 0.270500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.35080 | 0.0946395 | 0.0473198 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473198 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(618\) | 33.1238 | 1.33243 | ||||||||
\(619\) | 6.11038 | 0.245597 | 0.122798 | − | 0.992432i | \(-0.460813\pi\) | ||||
0.122798 | + | 0.992432i | \(0.460813\pi\) | |||||||
\(620\) | −124.444 | −4.99778 | ||||||||
\(621\) | −6.02551 | −0.241795 | ||||||||
\(622\) | 48.7532 | 1.95483 | ||||||||
\(623\) | 2.48531 | 0.0995717 | ||||||||
\(624\) | −7.37332 | −0.295169 | ||||||||
\(625\) | 32.9123 | 1.31649 | ||||||||
\(626\) | 70.5757 | 2.82077 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42.7608 | −1.70634 | ||||||||
\(629\) | 4.01452 | 0.160069 | ||||||||
\(630\) | −9.42812 | −0.375625 | ||||||||
\(631\) | −28.8822 | −1.14978 | −0.574891 | − | 0.818230i | \(-0.694955\pi\) | ||||
−0.574891 | + | 0.818230i | \(0.694955\pi\) | |||||||
\(632\) | 4.24050 | 0.168678 | ||||||||
\(633\) | 16.9594 | 0.674075 | ||||||||
\(634\) | −18.2547 | −0.724987 | ||||||||
\(635\) | −0.707550 | −0.0280783 | ||||||||
\(636\) | −22.8652 | −0.906664 | ||||||||
\(637\) | −2.99890 | −0.118821 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.40968 | 0.0557659 | ||||||||
\(640\) | −81.6592 | −3.22787 | ||||||||
\(641\) | −39.8256 | −1.57302 | −0.786508 | − | 0.617579i | \(-0.788113\pi\) | ||||
−0.786508 | + | 0.617579i | \(0.788113\pi\) | |||||||
\(642\) | −1.06687 | −0.0421060 | ||||||||
\(643\) | 5.85723 | 0.230987 | 0.115493 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115493 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(644\) | 22.4815 | 0.885896 | ||||||||
\(645\) | 12.7350 | 0.501440 | ||||||||
\(646\) | −93.3345 | −3.67220 | ||||||||
\(647\) | 22.5855 | 0.887926 | 0.443963 | − | 0.896045i | \(-0.353572\pi\) | ||||
0.443963 | + | 0.896045i | \(0.353572\pi\) | |||||||
\(648\) | −4.14409 | −0.162795 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 75.4549 | 2.95958 | ||||||||
\(651\) | −8.46902 | −0.331927 | ||||||||
\(652\) | 18.4412 | 0.722213 | ||||||||
\(653\) | −40.8369 | −1.59807 | −0.799035 | − | 0.601284i | \(-0.794656\pi\) | ||||
−0.799035 | + | 0.601284i | \(0.794656\pi\) | |||||||
\(654\) | −26.5701 | −1.03897 | ||||||||
\(655\) | −36.9503 | −1.44377 | ||||||||
\(656\) | −4.18793 | −0.163511 | ||||||||
\(657\) | 7.08851 | 0.276549 | ||||||||
\(658\) | −11.4967 | −0.448188 | ||||||||
\(659\) | 32.5869 | 1.26941 | 0.634703 | − | 0.772756i | \(-0.281122\pi\) | ||||
0.634703 | + | 0.772756i | \(0.281122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6393 | 1.69737 | 0.848686 | − | 0.528898i | \(-0.177395\pi\) | ||||
0.848686 | + | 0.528898i | \(0.177395\pi\) | |||||||
\(662\) | −49.4906 | −1.92351 | ||||||||
\(663\) | 19.8064 | 0.769218 | ||||||||
\(664\) | −12.7940 | −0.496504 | ||||||||
\(665\) | −23.2481 | −0.901524 | ||||||||
\(666\) | 1.45515 | 0.0563858 | ||||||||
\(667\) | 9.16331 | 0.354805 | ||||||||
\(668\) | 31.8416 | 1.23199 | ||||||||
\(669\) | −13.8125 | −0.534023 | ||||||||
\(670\) | −5.65422 | −0.218442 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −2.40219 | −0.0926667 | ||||||||
\(673\) | −23.8718 | −0.920190 | −0.460095 | − | 0.887870i | \(-0.652185\pi\) | ||||
−0.460095 | + | 0.887870i | \(0.652185\pi\) | |||||||
\(674\) | 13.0771 | 0.503712 | ||||||||
\(675\) | 10.5101 | 0.404535 | ||||||||
\(676\) | −14.9489 | −0.574958 | ||||||||
\(677\) | −4.26651 | −0.163975 | −0.0819877 | − | 0.996633i | \(-0.526127\pi\) | ||||
−0.0819877 | + | 0.996633i | \(0.526127\pi\) | |||||||
\(678\) | 19.3657 | 0.743734 | ||||||||
\(679\) | −2.55296 | −0.0979736 | ||||||||
\(680\) | −107.791 | −4.13359 | ||||||||
\(681\) | −7.25345 | −0.277953 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.88217 | 0.225075 | 0.112537 | − | 0.993647i | \(-0.464102\pi\) | ||||
0.112537 | + | 0.993647i | \(0.464102\pi\) | |||||||
\(684\) | −22.0248 | −0.842140 | ||||||||
\(685\) | −3.51932 | −0.134466 | ||||||||
\(686\) | 2.39396 | 0.0914019 | ||||||||
\(687\) | −0.327136 | −0.0124810 | ||||||||
\(688\) | −7.95047 | −0.303109 | ||||||||
\(689\) | 18.3783 | 0.700156 | ||||||||
\(690\) | −56.8093 | −2.16269 | ||||||||
\(691\) | −0.237559 | −0.00903716 | −0.00451858 | − | 0.999990i | \(-0.501438\pi\) | ||||
−0.00451858 | + | 0.999990i | \(0.501438\pi\) | |||||||
\(692\) | 48.8305 | 1.85626 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.9368 | −0.870669 | ||||||||
\(695\) | −8.36023 | −0.317122 | ||||||||
\(696\) | 6.30213 | 0.238882 | ||||||||
\(697\) | 11.2497 | 0.426114 | ||||||||
\(698\) | −22.4086 | −0.848177 | ||||||||
\(699\) | 16.2452 | 0.614448 | ||||||||
\(700\) | −39.2139 | −1.48215 | ||||||||
\(701\) | −10.6036 | −0.400494 | −0.200247 | − | 0.979745i | \(-0.564174\pi\) | ||||
−0.200247 | + | 0.979745i | \(0.564174\pi\) | |||||||
\(702\) | 7.17925 | 0.270963 | ||||||||
\(703\) | 3.58814 | 0.135329 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.9131 | 0.712310 | ||||||||
\(706\) | 66.2239 | 2.49237 | ||||||||
\(707\) | 15.1573 | 0.570050 | ||||||||
\(708\) | 23.2774 | 0.874820 | ||||||||
\(709\) | −48.3236 | −1.81483 | −0.907415 | − | 0.420235i | \(-0.861947\pi\) | ||||
−0.907415 | + | 0.420235i | \(0.861947\pi\) | |||||||
\(710\) | 13.2906 | 0.498787 | ||||||||
\(711\) | −1.02327 | −0.0383755 | ||||||||
\(712\) | 10.2993 | 0.385984 | ||||||||
\(713\) | −51.0302 | −1.91110 | ||||||||
\(714\) | −15.8111 | −0.591715 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 96.4932 | 3.60612 | ||||||||
\(717\) | −29.0009 | −1.08306 | ||||||||
\(718\) | 6.23049 | 0.232520 | ||||||||
\(719\) | −36.2637 | −1.35241 | −0.676203 | − | 0.736715i | \(-0.736376\pi\) | ||||
−0.676203 | + | 0.736715i | \(0.736376\pi\) | |||||||
\(720\) | −9.68299 | −0.360864 | ||||||||
\(721\) | 13.8364 | 0.515294 | ||||||||
\(722\) | −37.9362 | −1.41184 | ||||||||
\(723\) | −29.3358 | −1.09101 | ||||||||
\(724\) | 79.9202 | 2.97021 | ||||||||
\(725\) | −15.9833 | −0.593605 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.15184 | 0.0427195 | 0.0213597 | − | 0.999772i | \(-0.493200\pi\) | ||||
0.0213597 | + | 0.999772i | \(0.493200\pi\) | |||||||
\(728\) | −12.4277 | −0.460601 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 66.8314 | 2.47354 | ||||||||
\(731\) | 21.3568 | 0.789909 | ||||||||
\(732\) | −7.79413 | −0.288079 | ||||||||
\(733\) | −27.1042 | −1.00111 | −0.500557 | − | 0.865703i | \(-0.666872\pi\) | ||||
−0.500557 | + | 0.865703i | \(0.666872\pi\) | |||||||
\(734\) | 24.7520 | 0.913614 | ||||||||
\(735\) | −3.93829 | −0.145266 | ||||||||
\(736\) | −14.4745 | −0.533535 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.07770 | 0.150102 | ||||||||
\(739\) | −23.8018 | −0.875563 | −0.437782 | − | 0.899081i | \(-0.644236\pi\) | ||||
−0.437782 | + | 0.899081i | \(0.644236\pi\) | |||||||
\(740\) | 8.93160 | 0.328332 | ||||||||
\(741\) | 17.7028 | 0.650328 | ||||||||
\(742\) | −14.6710 | −0.538590 | ||||||||
\(743\) | 15.0656 | 0.552704 | 0.276352 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276352 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(744\) | −35.0964 | −1.28670 | ||||||||
\(745\) | −56.4043 | −2.06650 | ||||||||
\(746\) | 12.3430 | 0.451908 | ||||||||
\(747\) | 3.08729 | 0.112958 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.445651 | −0.0162837 | ||||||||
\(750\) | 51.9502 | 1.89695 | ||||||||
\(751\) | 10.6107 | 0.387191 | 0.193596 | − | 0.981081i | \(-0.437985\pi\) | ||||
0.193596 | + | 0.981081i | \(0.437985\pi\) | |||||||
\(752\) | −11.8075 | −0.430575 | ||||||||
\(753\) | 12.8316 | 0.467611 | ||||||||
\(754\) | −10.9179 | −0.397605 | ||||||||
\(755\) | 54.2841 | 1.97560 | ||||||||
\(756\) | −3.73106 | −0.135697 | ||||||||
\(757\) | −35.0862 | −1.27523 | −0.637615 | − | 0.770355i | \(-0.720079\pi\) | ||||
−0.637615 | + | 0.770355i | \(0.720079\pi\) | |||||||
\(758\) | 84.7997 | 3.08006 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −96.3423 | −3.49470 | ||||||||
\(761\) | 37.2895 | 1.35174 | 0.675872 | − | 0.737019i | \(-0.263767\pi\) | ||||
0.675872 | + | 0.737019i | \(0.263767\pi\) | |||||||
\(762\) | −0.430097 | −0.0155808 | ||||||||
\(763\) | −11.0988 | −0.401803 | ||||||||
\(764\) | −13.9537 | −0.504827 | ||||||||
\(765\) | 26.0107 | 0.940420 | ||||||||
\(766\) | 75.1887 | 2.71668 | ||||||||
\(767\) | −18.7096 | −0.675565 | ||||||||
\(768\) | −28.3018 | −1.02125 | ||||||||
\(769\) | 21.8827 | 0.789110 | 0.394555 | − | 0.918872i | \(-0.370899\pi\) | ||||
0.394555 | + | 0.918872i | \(0.370899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5210 | 0.703033 | ||||||||
\(772\) | 22.6823 | 0.816353 | ||||||||
\(773\) | −34.4742 | −1.23995 | −0.619975 | − | 0.784622i | \(-0.712857\pi\) | ||||
−0.619975 | + | 0.784622i | \(0.712857\pi\) | |||||||
\(774\) | 7.74120 | 0.278252 | ||||||||
\(775\) | 89.0106 | 3.19735 | ||||||||
\(776\) | −10.5797 | −0.379789 | ||||||||
\(777\) | 0.607840 | 0.0218061 | ||||||||
\(778\) | −48.0681 | −1.72332 | ||||||||
\(779\) | 10.0549 | 0.360254 | ||||||||
\(780\) | 44.0658 | 1.57781 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −95.2699 | −3.40685 | ||||||||
\(783\) | −1.52075 | −0.0543472 | ||||||||
\(784\) | 2.45868 | 0.0878099 | ||||||||
\(785\) | 45.1358 | 1.61097 | ||||||||
\(786\) | −22.4609 | −0.801154 | ||||||||
\(787\) | 11.6668 | 0.415878 | 0.207939 | − | 0.978142i | \(-0.433324\pi\) | ||||
0.207939 | + | 0.978142i | \(0.433324\pi\) | |||||||
\(788\) | 80.3887 | 2.86373 | ||||||||
\(789\) | 23.9606 | 0.853019 | ||||||||
\(790\) | −9.64747 | −0.343242 | ||||||||
\(791\) | 8.08938 | 0.287625 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.26466 | 0.222464 | ||||||||
\(794\) | −8.69849 | −0.308698 | ||||||||
\(795\) | 24.1352 | 0.855987 | ||||||||
\(796\) | −55.5797 | −1.96997 | ||||||||
\(797\) | −35.1322 | −1.24445 | −0.622223 | − | 0.782840i | \(-0.713770\pi\) | ||||
−0.622223 | + | 0.782840i | \(0.713770\pi\) | |||||||
\(798\) | −14.1318 | −0.500261 | ||||||||
\(799\) | 31.7176 | 1.12209 | ||||||||
\(800\) | 25.2474 | 0.892630 | ||||||||
\(801\) | −2.48531 | −0.0878140 | ||||||||
\(802\) | −90.0869 | −3.18108 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.23759 | −0.0789136 | ||||||||
\(805\) | −23.7302 | −0.836380 | ||||||||
\(806\) | 60.8012 | 2.14163 | ||||||||
\(807\) | 11.3260 | 0.398694 | ||||||||
\(808\) | 62.8133 | 2.20977 | ||||||||
\(809\) | −14.5235 | −0.510620 | −0.255310 | − | 0.966859i | \(-0.582178\pi\) | ||||
−0.255310 | + | 0.966859i | \(0.582178\pi\) | |||||||
\(810\) | 9.42812 | 0.331270 | ||||||||
\(811\) | 1.76417 | 0.0619483 | 0.0309741 | − | 0.999520i | \(-0.490139\pi\) | ||||
0.0309741 | + | 0.999520i | \(0.490139\pi\) | |||||||
\(812\) | 5.67401 | 0.199119 | ||||||||
\(813\) | 6.12278 | 0.214735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4655 | −0.681846 | ||||||||
\(816\) | −16.2385 | −0.568461 | ||||||||
\(817\) | 19.0885 | 0.667821 | ||||||||
\(818\) | −38.5570 | −1.34811 | ||||||||
\(819\) | 2.99890 | 0.104790 | ||||||||
\(820\) | 25.0287 | 0.874039 | ||||||||
\(821\) | −9.76074 | −0.340652 | −0.170326 | − | 0.985388i | \(-0.554482\pi\) | ||||
−0.170326 | + | 0.985388i | \(0.554482\pi\) | |||||||
\(822\) | −2.13929 | −0.0746162 | ||||||||
\(823\) | −45.6322 | −1.59064 | −0.795319 | − | 0.606191i | \(-0.792697\pi\) | ||||
−0.795319 | + | 0.606191i | \(0.792697\pi\) | |||||||
\(824\) | 57.3392 | 1.99750 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.9355 | 0.519674 | ||||||||
\(827\) | 20.7517 | 0.721608 | 0.360804 | − | 0.932642i | \(-0.382502\pi\) | ||||
0.360804 | + | 0.932642i | \(0.382502\pi\) | |||||||
\(828\) | −22.4815 | −0.781287 | ||||||||
\(829\) | 16.3868 | 0.569137 | 0.284568 | − | 0.958656i | \(-0.408150\pi\) | ||||
0.284568 | + | 0.958656i | \(0.408150\pi\) | |||||||
\(830\) | 29.1074 | 1.01033 | ||||||||
\(831\) | 0.600165 | 0.0208195 | ||||||||
\(832\) | 31.9926 | 1.10914 | ||||||||
\(833\) | −6.60457 | −0.228835 | ||||||||
\(834\) | −5.08192 | −0.175973 | ||||||||
\(835\) | −33.6102 | −1.16313 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.46902 | 0.292732 | ||||||||
\(838\) | 42.4037 | 1.46481 | ||||||||
\(839\) | 35.0935 | 1.21156 | 0.605782 | − | 0.795631i | \(-0.292860\pi\) | ||||
0.605782 | + | 0.795631i | \(0.292860\pi\) | |||||||
\(840\) | −16.3206 | −0.563115 | ||||||||
\(841\) | −26.6873 | −0.920252 | ||||||||
\(842\) | −72.4703 | −2.49749 | ||||||||
\(843\) | 23.8022 | 0.819791 | ||||||||
\(844\) | 63.2764 | 2.17806 | ||||||||
\(845\) | 15.7792 | 0.542822 | ||||||||
\(846\) | 11.4967 | 0.395265 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15.0676 | −0.517424 | ||||||||
\(849\) | −17.3400 | −0.595108 | ||||||||
\(850\) | 166.177 | 5.69982 | ||||||||
\(851\) | 3.66255 | 0.125550 | ||||||||
\(852\) | 5.25958 | 0.180190 | ||||||||
\(853\) | −11.3030 | −0.387007 | −0.193504 | − | 0.981100i | \(-0.561985\pi\) | ||||
−0.193504 | + | 0.981100i | \(0.561985\pi\) | |||||||
\(854\) | −5.00096 | −0.171129 | ||||||||
\(855\) | 23.2481 | 0.795069 | ||||||||
\(856\) | −1.84682 | −0.0631229 | ||||||||
\(857\) | 13.8531 | 0.473214 | 0.236607 | − | 0.971605i | \(-0.423965\pi\) | ||||
0.236607 | + | 0.971605i | \(0.423965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.23831 | −0.178729 | −0.0893645 | − | 0.995999i | \(-0.528484\pi\) | ||||
−0.0893645 | + | 0.995999i | \(0.528484\pi\) | |||||||
\(860\) | 47.5150 | 1.62025 | ||||||||
\(861\) | 1.70333 | 0.0580492 | ||||||||
\(862\) | −45.9445 | −1.56488 | ||||||||
\(863\) | −41.1289 | −1.40004 | −0.700022 | − | 0.714121i | \(-0.746826\pi\) | ||||
−0.700022 | + | 0.714121i | \(0.746826\pi\) | |||||||
\(864\) | 2.40219 | 0.0817243 | ||||||||
\(865\) | −51.5427 | −1.75250 | ||||||||
\(866\) | −52.0779 | −1.76968 | ||||||||
\(867\) | 26.6204 | 0.904075 | ||||||||
\(868\) | −31.5984 | −1.07252 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −14.3378 | −0.486098 | ||||||||
\(871\) | 1.79849 | 0.0609397 | ||||||||
\(872\) | −45.9944 | −1.55757 | ||||||||
\(873\) | 2.55296 | 0.0864046 | ||||||||
\(874\) | −85.1514 | −2.88029 | ||||||||
\(875\) | 21.7005 | 0.733612 | ||||||||
\(876\) | 26.4477 | 0.893584 | ||||||||
\(877\) | −5.41488 | −0.182848 | −0.0914238 | − | 0.995812i | \(-0.529142\pi\) | ||||
−0.0914238 | + | 0.995812i | \(0.529142\pi\) | |||||||
\(878\) | −6.47612 | −0.218558 | ||||||||
\(879\) | −14.9122 | −0.502975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.0961 | 0.373837 | 0.186918 | − | 0.982375i | \(-0.440150\pi\) | ||||
0.186918 | + | 0.982375i | \(0.440150\pi\) | |||||||
\(882\) | −2.39396 | −0.0806089 | ||||||||
\(883\) | −51.4596 | −1.73175 | −0.865877 | − | 0.500256i | \(-0.833239\pi\) | ||||
−0.865877 | + | 0.500256i | \(0.833239\pi\) | |||||||
\(884\) | 73.8989 | 2.48549 | ||||||||
\(885\) | −24.5703 | −0.825923 | ||||||||
\(886\) | −91.5149 | −3.07450 | ||||||||
\(887\) | −19.9938 | −0.671325 | −0.335662 | − | 0.941982i | \(-0.608960\pi\) | ||||
−0.335662 | + | 0.941982i | \(0.608960\pi\) | |||||||
\(888\) | 2.51894 | 0.0845302 | ||||||||
\(889\) | −0.179659 | −0.00602558 | ||||||||
\(890\) | −23.4318 | −0.785435 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −51.5353 | −1.72553 | ||||||||
\(893\) | 28.3489 | 0.948659 | ||||||||
\(894\) | −34.2864 | −1.14671 | ||||||||
\(895\) | −101.853 | −3.40456 | ||||||||
\(896\) | −20.7347 | −0.692697 | ||||||||
\(897\) | 18.0699 | 0.603336 | ||||||||
\(898\) | −54.3697 | −1.81434 | ||||||||
\(899\) | −12.8793 | −0.429548 | ||||||||
\(900\) | 39.2139 | 1.30713 | ||||||||
\(901\) | 40.4751 | 1.34842 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.23364 | 0.107609 | ||||||||
\(904\) | 33.5231 | 1.11496 | ||||||||
\(905\) | −84.3591 | −2.80419 | ||||||||
\(906\) | 32.9976 | 1.09627 | ||||||||
\(907\) | −5.23855 | −0.173943 | −0.0869716 | − | 0.996211i | \(-0.527719\pi\) | ||||
−0.0869716 | + | 0.996211i | \(0.527719\pi\) | |||||||
\(908\) | −27.0630 | −0.898119 | ||||||||
\(909\) | −15.1573 | −0.502737 | ||||||||
\(910\) | 28.2740 | 0.937273 | ||||||||
\(911\) | −11.0131 | −0.364882 | −0.182441 | − | 0.983217i | \(-0.558400\pi\) | ||||
−0.182441 | + | 0.983217i | \(0.558400\pi\) | |||||||
\(912\) | −14.5138 | −0.480601 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.76290 | 0.124466 | ||||||||
\(915\) | 8.22704 | 0.271978 | ||||||||
\(916\) | −1.22056 | −0.0403286 | ||||||||
\(917\) | −9.38232 | −0.309831 | ||||||||
\(918\) | 15.8111 | 0.521844 | ||||||||
\(919\) | −28.8457 | −0.951533 | −0.475767 | − | 0.879572i | \(-0.657829\pi\) | ||||
−0.475767 | + | 0.879572i | \(0.657829\pi\) | |||||||
\(920\) | −98.3401 | −3.24218 | ||||||||
\(921\) | 29.0453 | 0.957077 | ||||||||
\(922\) | 67.3365 | 2.21761 | ||||||||
\(923\) | −4.22747 | −0.139149 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.38848 | −0.210052 | ||||||||
\(926\) | 11.2325 | 0.369123 | ||||||||
\(927\) | −13.8364 | −0.454446 | ||||||||
\(928\) | −3.65314 | −0.119920 | ||||||||
\(929\) | 16.2208 | 0.532186 | 0.266093 | − | 0.963947i | \(-0.414267\pi\) | ||||
0.266093 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(930\) | 79.8470 | 2.61829 | ||||||||
\(931\) | −5.90310 | −0.193466 | ||||||||
\(932\) | 60.6116 | 1.98540 | ||||||||
\(933\) | −20.3651 | −0.666723 | ||||||||
\(934\) | 42.1660 | 1.37971 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.4277 | 0.406212 | ||||||||
\(937\) | −27.4672 | −0.897315 | −0.448657 | − | 0.893704i | \(-0.648098\pi\) | ||||
−0.448657 | + | 0.893704i | \(0.648098\pi\) | |||||||
\(938\) | −1.43570 | −0.0468774 | ||||||||
\(939\) | −29.4807 | −0.962067 | ||||||||
\(940\) | 70.5660 | 2.30161 | ||||||||
\(941\) | 48.7222 | 1.58830 | 0.794150 | − | 0.607722i | \(-0.207916\pi\) | ||||
0.794150 | + | 0.607722i | \(0.207916\pi\) | |||||||
\(942\) | 27.4366 | 0.893934 | ||||||||
\(943\) | 10.2634 | 0.334223 | ||||||||
\(944\) | 15.3393 | 0.499251 | ||||||||
\(945\) | 3.93829 | 0.128113 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.1998 | 0.688902 | 0.344451 | − | 0.938804i | \(-0.388065\pi\) | ||||
0.344451 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(948\) | −3.81786 | −0.123998 | ||||||||
\(949\) | −21.2577 | −0.690055 | ||||||||
\(950\) | 148.527 | 4.81886 | ||||||||
\(951\) | 7.62530 | 0.247267 | ||||||||
\(952\) | −27.3699 | −0.887064 | ||||||||
\(953\) | 34.1228 | 1.10535 | 0.552673 | − | 0.833398i | \(-0.313608\pi\) | ||||
0.552673 | + | 0.833398i | \(0.313608\pi\) | |||||||
\(954\) | 14.6710 | 0.474992 | ||||||||
\(955\) | 14.7287 | 0.476610 | ||||||||
\(956\) | −108.204 | −3.49957 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.6322 | 0.828138 | ||||||||
\(959\) | −0.893617 | −0.0288564 | ||||||||
\(960\) | 42.0142 | 1.35600 | ||||||||
\(961\) | 40.7243 | 1.31369 | ||||||||
\(962\) | −4.36383 | −0.140696 | ||||||||
\(963\) | 0.445651 | 0.0143609 | ||||||||
\(964\) | −109.453 | −3.52526 | ||||||||
\(965\) | −23.9421 | −0.770724 | ||||||||
\(966\) | −14.4249 | −0.464112 | ||||||||
\(967\) | −18.8881 | −0.607400 | −0.303700 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303700 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 38.9875 | 1.25246 | ||||||||
\(970\) | 24.0696 | 0.772829 | ||||||||
\(971\) | 12.4847 | 0.400652 | 0.200326 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200326 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(972\) | 3.73106 | 0.119674 | ||||||||
\(973\) | −2.12281 | −0.0680541 | ||||||||
\(974\) | −92.7906 | −2.97320 | ||||||||
\(975\) | −31.5188 | −1.00941 | ||||||||
\(976\) | −5.13614 | −0.164404 | ||||||||
\(977\) | −13.8747 | −0.443890 | −0.221945 | − | 0.975059i | \(-0.571241\pi\) | ||||
−0.221945 | + | 0.975059i | \(0.571241\pi\) | |||||||
\(978\) | −11.8324 | −0.378360 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −14.6940 | −0.469382 | ||||||||
\(981\) | 11.0988 | 0.354357 | ||||||||
\(982\) | 14.3652 | 0.458413 | ||||||||
\(983\) | 43.8326 | 1.39804 | 0.699021 | − | 0.715101i | \(-0.253619\pi\) | ||||
0.699021 | + | 0.715101i | \(0.253619\pi\) | |||||||
\(984\) | 7.05873 | 0.225024 | ||||||||
\(985\) | −84.8537 | −2.70366 | ||||||||
\(986\) | −24.0448 | −0.765741 | ||||||||
\(987\) | 4.80237 | 0.152861 | ||||||||
\(988\) | 66.0502 | 2.10134 | ||||||||
\(989\) | 19.4843 | 0.619565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.8926 | 1.36253 | 0.681264 | − | 0.732037i | \(-0.261430\pi\) | ||||
0.681264 | + | 0.732037i | \(0.261430\pi\) | |||||||
\(992\) | 20.3442 | 0.645930 | ||||||||
\(993\) | 20.6731 | 0.656041 | ||||||||
\(994\) | 3.37471 | 0.107039 | ||||||||
\(995\) | 58.6667 | 1.85986 | ||||||||
\(996\) | 11.5189 | 0.364989 | ||||||||
\(997\) | −28.2985 | −0.896224 | −0.448112 | − | 0.893977i | \(-0.647903\pi\) | ||||
−0.448112 | + | 0.893977i | \(0.647903\pi\) | |||||||
\(998\) | 69.3713 | 2.19591 | ||||||||
\(999\) | −0.607840 | −0.0192312 |
(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 | 2541.2.a.bq.1.2 | 10 | ||
3.2 | odd | 2 | 7623.2.a.cx.1.9 | 10 | |||
11.3 | even | 5 | 231.2.j.g.64.1 | ✓ | 20 | ||
11.4 | even | 5 | 231.2.j.g.148.1 | yes | 20 | ||
11.10 | odd | 2 | 2541.2.a.br.1.9 | 10 | |||
33.14 | odd | 10 | 693.2.m.j.64.5 | 20 | |||
33.26 | odd | 10 | 693.2.m.j.379.5 | 20 | |||
33.32 | even | 2 | 7623.2.a.cy.1.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.g.64.1 | ✓ | 20 | 11.3 | even | 5 | ||
231.2.j.g.148.1 | yes | 20 | 11.4 | even | 5 | ||
693.2.m.j.64.5 | 20 | 33.14 | odd | 10 | |||
693.2.m.j.379.5 | 20 | 33.26 | odd | 10 | |||
2541.2.a.bq.1.2 | 10 | 1.1 | even | 1 | trivial | ||
2541.2.a.br.1.9 | 10 | 11.10 | odd | 2 | |||
7623.2.a.cx.1.9 | 10 | 3.2 | odd | 2 | |||
7623.2.a.cy.1.2 | 10 | 33.32 | even | 2 |