Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8014,2,Mod(1,8014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8014 = 2 \cdot 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8014.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9921121799\) |
Analytic rank: | \(0\) |
Dimension: | \(91\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.66657 | −1.53954 | −0.769772 | − | 0.638319i | \(-0.779630\pi\) | ||||
−0.769772 | + | 0.638319i | \(0.779630\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.59792 | 1.60904 | 0.804519 | − | 0.593927i | \(-0.202423\pi\) | ||||
0.804519 | + | 0.593927i | \(0.202423\pi\) | |||||||
\(6\) | 2.66657 | 1.08862 | ||||||||
\(7\) | 3.19859 | 1.20895 | 0.604476 | − | 0.796623i | \(-0.293383\pi\) | ||||
0.604476 | + | 0.796623i | \(0.293383\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.11059 | 1.37020 | ||||||||
\(10\) | −3.59792 | −1.13776 | ||||||||
\(11\) | −1.32899 | −0.400706 | −0.200353 | − | 0.979724i | \(-0.564209\pi\) | ||||
−0.200353 | + | 0.979724i | \(0.564209\pi\) | |||||||
\(12\) | −2.66657 | −0.769772 | ||||||||
\(13\) | 2.26975 | 0.629514 | 0.314757 | − | 0.949172i | \(-0.398077\pi\) | ||||
0.314757 | + | 0.949172i | \(0.398077\pi\) | |||||||
\(14\) | −3.19859 | −0.854858 | ||||||||
\(15\) | −9.59410 | −2.47719 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.09379 | 1.47796 | 0.738980 | − | 0.673727i | \(-0.235308\pi\) | ||||
0.738980 | + | 0.673727i | \(0.235308\pi\) | |||||||
\(18\) | −4.11059 | −0.968876 | ||||||||
\(19\) | 4.87657 | 1.11876 | 0.559381 | − | 0.828910i | \(-0.311039\pi\) | ||||
0.559381 | + | 0.828910i | \(0.311039\pi\) | |||||||
\(20\) | 3.59792 | 0.804519 | ||||||||
\(21\) | −8.52925 | −1.86123 | ||||||||
\(22\) | 1.32899 | 0.283342 | ||||||||
\(23\) | 7.31948 | 1.52622 | 0.763109 | − | 0.646270i | \(-0.223672\pi\) | ||||
0.763109 | + | 0.646270i | \(0.223672\pi\) | |||||||
\(24\) | 2.66657 | 0.544311 | ||||||||
\(25\) | 7.94502 | 1.58900 | ||||||||
\(26\) | −2.26975 | −0.445134 | ||||||||
\(27\) | −2.96147 | −0.569935 | ||||||||
\(28\) | 3.19859 | 0.604476 | ||||||||
\(29\) | −5.39268 | −1.00139 | −0.500697 | − | 0.865622i | \(-0.666923\pi\) | ||||
−0.500697 | + | 0.865622i | \(0.666923\pi\) | |||||||
\(30\) | 9.59410 | 1.75163 | ||||||||
\(31\) | −2.70729 | −0.486244 | −0.243122 | − | 0.969996i | \(-0.578172\pi\) | ||||
−0.243122 | + | 0.969996i | \(0.578172\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.54385 | 0.616905 | ||||||||
\(34\) | −6.09379 | −1.04508 | ||||||||
\(35\) | 11.5083 | 1.94525 | ||||||||
\(36\) | 4.11059 | 0.685099 | ||||||||
\(37\) | 2.13851 | 0.351568 | 0.175784 | − | 0.984429i | \(-0.443754\pi\) | ||||
0.175784 | + | 0.984429i | \(0.443754\pi\) | |||||||
\(38\) | −4.87657 | −0.791085 | ||||||||
\(39\) | −6.05244 | −0.969165 | ||||||||
\(40\) | −3.59792 | −0.568881 | ||||||||
\(41\) | 4.41143 | 0.688950 | 0.344475 | − | 0.938796i | \(-0.388057\pi\) | ||||
0.344475 | + | 0.938796i | \(0.388057\pi\) | |||||||
\(42\) | 8.52925 | 1.31609 | ||||||||
\(43\) | 1.02970 | 0.157027 | 0.0785136 | − | 0.996913i | \(-0.474983\pi\) | ||||
0.0785136 | + | 0.996913i | \(0.474983\pi\) | |||||||
\(44\) | −1.32899 | −0.200353 | ||||||||
\(45\) | 14.7896 | 2.20470 | ||||||||
\(46\) | −7.31948 | −1.07920 | ||||||||
\(47\) | 6.69810 | 0.977018 | 0.488509 | − | 0.872559i | \(-0.337541\pi\) | ||||
0.488509 | + | 0.872559i | \(0.337541\pi\) | |||||||
\(48\) | −2.66657 | −0.384886 | ||||||||
\(49\) | 3.23095 | 0.461564 | ||||||||
\(50\) | −7.94502 | −1.12360 | ||||||||
\(51\) | −16.2495 | −2.27539 | ||||||||
\(52\) | 2.26975 | 0.314757 | ||||||||
\(53\) | 6.02243 | 0.827244 | 0.413622 | − | 0.910449i | \(-0.364264\pi\) | ||||
0.413622 | + | 0.910449i | \(0.364264\pi\) | |||||||
\(54\) | 2.96147 | 0.403005 | ||||||||
\(55\) | −4.78161 | −0.644752 | ||||||||
\(56\) | −3.19859 | −0.427429 | ||||||||
\(57\) | −13.0037 | −1.72239 | ||||||||
\(58\) | 5.39268 | 0.708093 | ||||||||
\(59\) | −4.11176 | −0.535306 | −0.267653 | − | 0.963515i | \(-0.586248\pi\) | ||||
−0.267653 | + | 0.963515i | \(0.586248\pi\) | |||||||
\(60\) | −9.59410 | −1.23859 | ||||||||
\(61\) | −4.38096 | −0.560924 | −0.280462 | − | 0.959865i | \(-0.590488\pi\) | ||||
−0.280462 | + | 0.959865i | \(0.590488\pi\) | |||||||
\(62\) | 2.70729 | 0.343826 | ||||||||
\(63\) | 13.1481 | 1.65650 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.16636 | 1.01291 | ||||||||
\(66\) | −3.54385 | −0.436218 | ||||||||
\(67\) | −6.73124 | −0.822352 | −0.411176 | − | 0.911556i | \(-0.634882\pi\) | ||||
−0.411176 | + | 0.911556i | \(0.634882\pi\) | |||||||
\(68\) | 6.09379 | 0.738980 | ||||||||
\(69\) | −19.5179 | −2.34968 | ||||||||
\(70\) | −11.5083 | −1.37550 | ||||||||
\(71\) | −4.54564 | −0.539468 | −0.269734 | − | 0.962935i | \(-0.586936\pi\) | ||||
−0.269734 | + | 0.962935i | \(0.586936\pi\) | |||||||
\(72\) | −4.11059 | −0.484438 | ||||||||
\(73\) | 10.2577 | 1.20057 | 0.600286 | − | 0.799785i | \(-0.295053\pi\) | ||||
0.600286 | + | 0.799785i | \(0.295053\pi\) | |||||||
\(74\) | −2.13851 | −0.248596 | ||||||||
\(75\) | −21.1859 | −2.44634 | ||||||||
\(76\) | 4.87657 | 0.559381 | ||||||||
\(77\) | −4.25090 | −0.484435 | ||||||||
\(78\) | 6.05244 | 0.685303 | ||||||||
\(79\) | 5.60002 | 0.630051 | 0.315026 | − | 0.949083i | \(-0.397987\pi\) | ||||
0.315026 | + | 0.949083i | \(0.397987\pi\) | |||||||
\(80\) | 3.59792 | 0.402260 | ||||||||
\(81\) | −4.43481 | −0.492757 | ||||||||
\(82\) | −4.41143 | −0.487161 | ||||||||
\(83\) | −0.675599 | −0.0741566 | −0.0370783 | − | 0.999312i | \(-0.511805\pi\) | ||||
−0.0370783 | + | 0.999312i | \(0.511805\pi\) | |||||||
\(84\) | −8.52925 | −0.930617 | ||||||||
\(85\) | 21.9249 | 2.37809 | ||||||||
\(86\) | −1.02970 | −0.111035 | ||||||||
\(87\) | 14.3799 | 1.54169 | ||||||||
\(88\) | 1.32899 | 0.141671 | ||||||||
\(89\) | −1.83218 | −0.194211 | −0.0971054 | − | 0.995274i | \(-0.530958\pi\) | ||||
−0.0971054 | + | 0.995274i | \(0.530958\pi\) | |||||||
\(90\) | −14.7896 | −1.55896 | ||||||||
\(91\) | 7.25998 | 0.761052 | ||||||||
\(92\) | 7.31948 | 0.763109 | ||||||||
\(93\) | 7.21918 | 0.748594 | ||||||||
\(94\) | −6.69810 | −0.690856 | ||||||||
\(95\) | 17.5455 | 1.80013 | ||||||||
\(96\) | 2.66657 | 0.272156 | ||||||||
\(97\) | 13.9690 | 1.41834 | 0.709170 | − | 0.705038i | \(-0.249070\pi\) | ||||
0.709170 | + | 0.705038i | \(0.249070\pi\) | |||||||
\(98\) | −3.23095 | −0.326375 | ||||||||
\(99\) | −5.46295 | −0.549047 | ||||||||
\(100\) | 7.94502 | 0.794502 | ||||||||
\(101\) | 10.6892 | 1.06361 | 0.531806 | − | 0.846866i | \(-0.321514\pi\) | ||||
0.531806 | + | 0.846866i | \(0.321514\pi\) | |||||||
\(102\) | 16.2495 | 1.60894 | ||||||||
\(103\) | 9.90004 | 0.975480 | 0.487740 | − | 0.872989i | \(-0.337821\pi\) | ||||
0.487740 | + | 0.872989i | \(0.337821\pi\) | |||||||
\(104\) | −2.26975 | −0.222567 | ||||||||
\(105\) | −30.6875 | −2.99480 | ||||||||
\(106\) | −6.02243 | −0.584950 | ||||||||
\(107\) | −5.86232 | −0.566732 | −0.283366 | − | 0.959012i | \(-0.591451\pi\) | ||||
−0.283366 | + | 0.959012i | \(0.591451\pi\) | |||||||
\(108\) | −2.96147 | −0.284968 | ||||||||
\(109\) | 18.2037 | 1.74360 | 0.871799 | − | 0.489863i | \(-0.162953\pi\) | ||||
0.871799 | + | 0.489863i | \(0.162953\pi\) | |||||||
\(110\) | 4.78161 | 0.455908 | ||||||||
\(111\) | −5.70248 | −0.541255 | ||||||||
\(112\) | 3.19859 | 0.302238 | ||||||||
\(113\) | 10.4459 | 0.982670 | 0.491335 | − | 0.870971i | \(-0.336509\pi\) | ||||
0.491335 | + | 0.870971i | \(0.336509\pi\) | |||||||
\(114\) | 13.0037 | 1.21791 | ||||||||
\(115\) | 26.3349 | 2.45574 | ||||||||
\(116\) | −5.39268 | −0.500697 | ||||||||
\(117\) | 9.33000 | 0.862559 | ||||||||
\(118\) | 4.11176 | 0.378518 | ||||||||
\(119\) | 19.4915 | 1.78678 | ||||||||
\(120\) | 9.59410 | 0.875817 | ||||||||
\(121\) | −9.23378 | −0.839434 | ||||||||
\(122\) | 4.38096 | 0.396633 | ||||||||
\(123\) | −11.7634 | −1.06067 | ||||||||
\(124\) | −2.70729 | −0.243122 | ||||||||
\(125\) | 10.5959 | 0.947729 | ||||||||
\(126\) | −13.1481 | −1.17132 | ||||||||
\(127\) | −11.4991 | −1.02038 | −0.510189 | − | 0.860063i | \(-0.670424\pi\) | ||||
−0.510189 | + | 0.860063i | \(0.670424\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.74576 | −0.241750 | ||||||||
\(130\) | −8.16636 | −0.716237 | ||||||||
\(131\) | −9.49369 | −0.829467 | −0.414734 | − | 0.909943i | \(-0.636125\pi\) | ||||
−0.414734 | + | 0.909943i | \(0.636125\pi\) | |||||||
\(132\) | 3.54385 | 0.308453 | ||||||||
\(133\) | 15.5981 | 1.35253 | ||||||||
\(134\) | 6.73124 | 0.581491 | ||||||||
\(135\) | −10.6551 | −0.917047 | ||||||||
\(136\) | −6.09379 | −0.522538 | ||||||||
\(137\) | 11.5333 | 0.985358 | 0.492679 | − | 0.870211i | \(-0.336018\pi\) | ||||
0.492679 | + | 0.870211i | \(0.336018\pi\) | |||||||
\(138\) | 19.5179 | 1.66147 | ||||||||
\(139\) | 19.6241 | 1.66449 | 0.832246 | − | 0.554407i | \(-0.187055\pi\) | ||||
0.832246 | + | 0.554407i | \(0.187055\pi\) | |||||||
\(140\) | 11.5083 | 0.972625 | ||||||||
\(141\) | −17.8609 | −1.50416 | ||||||||
\(142\) | 4.54564 | 0.381462 | ||||||||
\(143\) | −3.01648 | −0.252250 | ||||||||
\(144\) | 4.11059 | 0.342549 | ||||||||
\(145\) | −19.4024 | −1.61128 | ||||||||
\(146\) | −10.2577 | −0.848933 | ||||||||
\(147\) | −8.61555 | −0.710599 | ||||||||
\(148\) | 2.13851 | 0.175784 | ||||||||
\(149\) | 6.55575 | 0.537068 | 0.268534 | − | 0.963270i | \(-0.413461\pi\) | ||||
0.268534 | + | 0.963270i | \(0.413461\pi\) | |||||||
\(150\) | 21.1859 | 1.72982 | ||||||||
\(151\) | −18.7026 | −1.52200 | −0.760998 | − | 0.648754i | \(-0.775290\pi\) | ||||
−0.760998 | + | 0.648754i | \(0.775290\pi\) | |||||||
\(152\) | −4.87657 | −0.395542 | ||||||||
\(153\) | 25.0491 | 2.02510 | ||||||||
\(154\) | 4.25090 | 0.342547 | ||||||||
\(155\) | −9.74061 | −0.782385 | ||||||||
\(156\) | −6.05244 | −0.484583 | ||||||||
\(157\) | −16.5108 | −1.31771 | −0.658854 | − | 0.752271i | \(-0.728958\pi\) | ||||
−0.658854 | + | 0.752271i | \(0.728958\pi\) | |||||||
\(158\) | −5.60002 | −0.445514 | ||||||||
\(159\) | −16.0592 | −1.27358 | ||||||||
\(160\) | −3.59792 | −0.284440 | ||||||||
\(161\) | 23.4120 | 1.84512 | ||||||||
\(162\) | 4.43481 | 0.348432 | ||||||||
\(163\) | −15.7314 | −1.23218 | −0.616089 | − | 0.787677i | \(-0.711284\pi\) | ||||
−0.616089 | + | 0.787677i | \(0.711284\pi\) | |||||||
\(164\) | 4.41143 | 0.344475 | ||||||||
\(165\) | 12.7505 | 0.992624 | ||||||||
\(166\) | 0.675599 | 0.0524367 | ||||||||
\(167\) | −19.1834 | −1.48446 | −0.742229 | − | 0.670146i | \(-0.766231\pi\) | ||||
−0.742229 | + | 0.670146i | \(0.766231\pi\) | |||||||
\(168\) | 8.52925 | 0.658046 | ||||||||
\(169\) | −7.84825 | −0.603712 | ||||||||
\(170\) | −21.9249 | −1.68157 | ||||||||
\(171\) | 20.0456 | 1.53293 | ||||||||
\(172\) | 1.02970 | 0.0785136 | ||||||||
\(173\) | −7.94282 | −0.603882 | −0.301941 | − | 0.953327i | \(-0.597635\pi\) | ||||
−0.301941 | + | 0.953327i | \(0.597635\pi\) | |||||||
\(174\) | −14.3799 | −1.09014 | ||||||||
\(175\) | 25.4128 | 1.92103 | ||||||||
\(176\) | −1.32899 | −0.100177 | ||||||||
\(177\) | 10.9643 | 0.824127 | ||||||||
\(178\) | 1.83218 | 0.137328 | ||||||||
\(179\) | −22.1103 | −1.65260 | −0.826302 | − | 0.563227i | \(-0.809560\pi\) | ||||
−0.826302 | + | 0.563227i | \(0.809560\pi\) | |||||||
\(180\) | 14.7896 | 1.10235 | ||||||||
\(181\) | −13.1737 | −0.979191 | −0.489595 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489595 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(182\) | −7.25998 | −0.538145 | ||||||||
\(183\) | 11.6821 | 0.863568 | ||||||||
\(184\) | −7.31948 | −0.539599 | ||||||||
\(185\) | 7.69417 | 0.565687 | ||||||||
\(186\) | −7.21918 | −0.529336 | ||||||||
\(187\) | −8.09860 | −0.592228 | ||||||||
\(188\) | 6.69810 | 0.488509 | ||||||||
\(189\) | −9.47251 | −0.689024 | ||||||||
\(190\) | −17.5455 | −1.27289 | ||||||||
\(191\) | 3.67683 | 0.266046 | 0.133023 | − | 0.991113i | \(-0.457532\pi\) | ||||
0.133023 | + | 0.991113i | \(0.457532\pi\) | |||||||
\(192\) | −2.66657 | −0.192443 | ||||||||
\(193\) | −6.87538 | −0.494901 | −0.247450 | − | 0.968901i | \(-0.579593\pi\) | ||||
−0.247450 | + | 0.968901i | \(0.579593\pi\) | |||||||
\(194\) | −13.9690 | −1.00292 | ||||||||
\(195\) | −21.7762 | −1.55942 | ||||||||
\(196\) | 3.23095 | 0.230782 | ||||||||
\(197\) | 1.60178 | 0.114122 | 0.0570612 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570612 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(198\) | 5.46295 | 0.388235 | ||||||||
\(199\) | 1.18019 | 0.0836611 | 0.0418306 | − | 0.999125i | \(-0.486681\pi\) | ||||
0.0418306 | + | 0.999125i | \(0.486681\pi\) | |||||||
\(200\) | −7.94502 | −0.561798 | ||||||||
\(201\) | 17.9493 | 1.26605 | ||||||||
\(202\) | −10.6892 | −0.752087 | ||||||||
\(203\) | −17.2489 | −1.21064 | ||||||||
\(204\) | −16.2495 | −1.13769 | ||||||||
\(205\) | 15.8720 | 1.10855 | ||||||||
\(206\) | −9.90004 | −0.689769 | ||||||||
\(207\) | 30.0874 | 2.09122 | ||||||||
\(208\) | 2.26975 | 0.157379 | ||||||||
\(209\) | −6.48093 | −0.448295 | ||||||||
\(210\) | 30.6875 | 2.11764 | ||||||||
\(211\) | −21.3981 | −1.47311 | −0.736553 | − | 0.676379i | \(-0.763548\pi\) | ||||
−0.736553 | + | 0.676379i | \(0.763548\pi\) | |||||||
\(212\) | 6.02243 | 0.413622 | ||||||||
\(213\) | 12.1213 | 0.830535 | ||||||||
\(214\) | 5.86232 | 0.400740 | ||||||||
\(215\) | 3.70476 | 0.252663 | ||||||||
\(216\) | 2.96147 | 0.201502 | ||||||||
\(217\) | −8.65950 | −0.587845 | ||||||||
\(218\) | −18.2037 | −1.23291 | ||||||||
\(219\) | −27.3528 | −1.84833 | ||||||||
\(220\) | −4.78161 | −0.322376 | ||||||||
\(221\) | 13.8313 | 0.930397 | ||||||||
\(222\) | 5.70248 | 0.382725 | ||||||||
\(223\) | −23.5596 | −1.57767 | −0.788834 | − | 0.614606i | \(-0.789315\pi\) | ||||
−0.788834 | + | 0.614606i | \(0.789315\pi\) | |||||||
\(224\) | −3.19859 | −0.213714 | ||||||||
\(225\) | 32.6587 | 2.17725 | ||||||||
\(226\) | −10.4459 | −0.694852 | ||||||||
\(227\) | −14.6906 | −0.975051 | −0.487526 | − | 0.873109i | \(-0.662100\pi\) | ||||
−0.487526 | + | 0.873109i | \(0.662100\pi\) | |||||||
\(228\) | −13.0037 | −0.861193 | ||||||||
\(229\) | −14.2127 | −0.939201 | −0.469600 | − | 0.882879i | \(-0.655602\pi\) | ||||
−0.469600 | + | 0.882879i | \(0.655602\pi\) | |||||||
\(230\) | −26.3349 | −1.73647 | ||||||||
\(231\) | 11.3353 | 0.745809 | ||||||||
\(232\) | 5.39268 | 0.354046 | ||||||||
\(233\) | −23.9962 | −1.57204 | −0.786020 | − | 0.618201i | \(-0.787862\pi\) | ||||
−0.786020 | + | 0.618201i | \(0.787862\pi\) | |||||||
\(234\) | −9.33000 | −0.609921 | ||||||||
\(235\) | 24.0992 | 1.57206 | ||||||||
\(236\) | −4.11176 | −0.267653 | ||||||||
\(237\) | −14.9328 | −0.969992 | ||||||||
\(238\) | −19.4915 | −1.26345 | ||||||||
\(239\) | 24.6830 | 1.59661 | 0.798306 | − | 0.602252i | \(-0.205730\pi\) | ||||
0.798306 | + | 0.602252i | \(0.205730\pi\) | |||||||
\(240\) | −9.59410 | −0.619296 | ||||||||
\(241\) | 16.5929 | 1.06884 | 0.534421 | − | 0.845218i | \(-0.320530\pi\) | ||||
0.534421 | + | 0.845218i | \(0.320530\pi\) | |||||||
\(242\) | 9.23378 | 0.593570 | ||||||||
\(243\) | 20.7101 | 1.32856 | ||||||||
\(244\) | −4.38096 | −0.280462 | ||||||||
\(245\) | 11.6247 | 0.742674 | ||||||||
\(246\) | 11.7634 | 0.750006 | ||||||||
\(247\) | 11.0686 | 0.704277 | ||||||||
\(248\) | 2.70729 | 0.171913 | ||||||||
\(249\) | 1.80153 | 0.114167 | ||||||||
\(250\) | −10.5959 | −0.670146 | ||||||||
\(251\) | 11.8700 | 0.749225 | 0.374612 | − | 0.927182i | \(-0.377776\pi\) | ||||
0.374612 | + | 0.927182i | \(0.377776\pi\) | |||||||
\(252\) | 13.1481 | 0.828251 | ||||||||
\(253\) | −9.72753 | −0.611565 | ||||||||
\(254\) | 11.4991 | 0.721516 | ||||||||
\(255\) | −58.4644 | −3.66118 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.8871 | 1.49003 | 0.745017 | − | 0.667046i | \(-0.232442\pi\) | ||||
0.745017 | + | 0.667046i | \(0.232442\pi\) | |||||||
\(258\) | 2.74576 | 0.170943 | ||||||||
\(259\) | 6.84020 | 0.425029 | ||||||||
\(260\) | 8.16636 | 0.506456 | ||||||||
\(261\) | −22.1671 | −1.37211 | ||||||||
\(262\) | 9.49369 | 0.586522 | ||||||||
\(263\) | 6.35171 | 0.391663 | 0.195832 | − | 0.980638i | \(-0.437259\pi\) | ||||
0.195832 | + | 0.980638i | \(0.437259\pi\) | |||||||
\(264\) | −3.54385 | −0.218109 | ||||||||
\(265\) | 21.6682 | 1.33107 | ||||||||
\(266\) | −15.5981 | −0.956383 | ||||||||
\(267\) | 4.88564 | 0.298996 | ||||||||
\(268\) | −6.73124 | −0.411176 | ||||||||
\(269\) | 21.2676 | 1.29671 | 0.648354 | − | 0.761339i | \(-0.275458\pi\) | ||||
0.648354 | + | 0.761339i | \(0.275458\pi\) | |||||||
\(270\) | 10.6551 | 0.648450 | ||||||||
\(271\) | −25.0598 | −1.52227 | −0.761136 | − | 0.648592i | \(-0.775358\pi\) | ||||
−0.761136 | + | 0.648592i | \(0.775358\pi\) | |||||||
\(272\) | 6.09379 | 0.369490 | ||||||||
\(273\) | −19.3592 | −1.17167 | ||||||||
\(274\) | −11.5333 | −0.696753 | ||||||||
\(275\) | −10.5589 | −0.636724 | ||||||||
\(276\) | −19.5179 | −1.17484 | ||||||||
\(277\) | 1.28916 | 0.0774578 | 0.0387289 | − | 0.999250i | \(-0.487669\pi\) | ||||
0.0387289 | + | 0.999250i | \(0.487669\pi\) | |||||||
\(278\) | −19.6241 | −1.17697 | ||||||||
\(279\) | −11.1286 | −0.666250 | ||||||||
\(280\) | −11.5083 | −0.687749 | ||||||||
\(281\) | −11.5384 | −0.688321 | −0.344160 | − | 0.938911i | \(-0.611836\pi\) | ||||
−0.344160 | + | 0.938911i | \(0.611836\pi\) | |||||||
\(282\) | 17.8609 | 1.06360 | ||||||||
\(283\) | −10.5119 | −0.624870 | −0.312435 | − | 0.949939i | \(-0.601145\pi\) | ||||
−0.312435 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(284\) | −4.54564 | −0.269734 | ||||||||
\(285\) | −46.7863 | −2.77138 | ||||||||
\(286\) | 3.01648 | 0.178368 | ||||||||
\(287\) | 14.1103 | 0.832907 | ||||||||
\(288\) | −4.11059 | −0.242219 | ||||||||
\(289\) | 20.1342 | 1.18437 | ||||||||
\(290\) | 19.4024 | 1.13935 | ||||||||
\(291\) | −37.2494 | −2.18360 | ||||||||
\(292\) | 10.2577 | 0.600286 | ||||||||
\(293\) | −17.8079 | −1.04035 | −0.520175 | − | 0.854059i | \(-0.674133\pi\) | ||||
−0.520175 | + | 0.854059i | \(0.674133\pi\) | |||||||
\(294\) | 8.61555 | 0.502469 | ||||||||
\(295\) | −14.7938 | −0.861327 | ||||||||
\(296\) | −2.13851 | −0.124298 | ||||||||
\(297\) | 3.93577 | 0.228377 | ||||||||
\(298\) | −6.55575 | −0.379764 | ||||||||
\(299\) | 16.6134 | 0.960776 | ||||||||
\(300\) | −21.1859 | −1.22317 | ||||||||
\(301\) | 3.29357 | 0.189838 | ||||||||
\(302\) | 18.7026 | 1.07621 | ||||||||
\(303\) | −28.5034 | −1.63748 | ||||||||
\(304\) | 4.87657 | 0.279691 | ||||||||
\(305\) | −15.7623 | −0.902549 | ||||||||
\(306\) | −25.0491 | −1.43196 | ||||||||
\(307\) | −20.8759 | −1.19145 | −0.595724 | − | 0.803189i | \(-0.703135\pi\) | ||||
−0.595724 | + | 0.803189i | \(0.703135\pi\) | |||||||
\(308\) | −4.25090 | −0.242217 | ||||||||
\(309\) | −26.3991 | −1.50179 | ||||||||
\(310\) | 9.74061 | 0.553230 | ||||||||
\(311\) | 20.5052 | 1.16274 | 0.581371 | − | 0.813639i | \(-0.302517\pi\) | ||||
0.581371 | + | 0.813639i | \(0.302517\pi\) | |||||||
\(312\) | 6.05244 | 0.342652 | ||||||||
\(313\) | −9.60209 | −0.542742 | −0.271371 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271371 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(314\) | 16.5108 | 0.931760 | ||||||||
\(315\) | 47.3057 | 2.66538 | ||||||||
\(316\) | 5.60002 | 0.315026 | ||||||||
\(317\) | −22.4659 | −1.26181 | −0.630905 | − | 0.775860i | \(-0.717316\pi\) | ||||
−0.630905 | + | 0.775860i | \(0.717316\pi\) | |||||||
\(318\) | 16.0592 | 0.900556 | ||||||||
\(319\) | 7.16683 | 0.401265 | ||||||||
\(320\) | 3.59792 | 0.201130 | ||||||||
\(321\) | 15.6323 | 0.872510 | ||||||||
\(322\) | −23.4120 | −1.30470 | ||||||||
\(323\) | 29.7168 | 1.65349 | ||||||||
\(324\) | −4.43481 | −0.246378 | ||||||||
\(325\) | 18.0332 | 1.00030 | ||||||||
\(326\) | 15.7314 | 0.871281 | ||||||||
\(327\) | −48.5414 | −2.68435 | ||||||||
\(328\) | −4.41143 | −0.243581 | ||||||||
\(329\) | 21.4244 | 1.18117 | ||||||||
\(330\) | −12.7505 | −0.701891 | ||||||||
\(331\) | 12.3144 | 0.676863 | 0.338432 | − | 0.940991i | \(-0.390104\pi\) | ||||
0.338432 | + | 0.940991i | \(0.390104\pi\) | |||||||
\(332\) | −0.675599 | −0.0370783 | ||||||||
\(333\) | 8.79053 | 0.481718 | ||||||||
\(334\) | 19.1834 | 1.04967 | ||||||||
\(335\) | −24.2185 | −1.32320 | ||||||||
\(336\) | −8.52925 | −0.465309 | ||||||||
\(337\) | −11.1065 | −0.605007 | −0.302503 | − | 0.953148i | \(-0.597822\pi\) | ||||
−0.302503 | + | 0.953148i | \(0.597822\pi\) | |||||||
\(338\) | 7.84825 | 0.426889 | ||||||||
\(339\) | −27.8548 | −1.51286 | ||||||||
\(340\) | 21.9249 | 1.18905 | ||||||||
\(341\) | 3.59797 | 0.194841 | ||||||||
\(342\) | −20.0456 | −1.08394 | ||||||||
\(343\) | −12.0556 | −0.650943 | ||||||||
\(344\) | −1.02970 | −0.0555175 | ||||||||
\(345\) | −70.2238 | −3.78072 | ||||||||
\(346\) | 7.94282 | 0.427009 | ||||||||
\(347\) | −28.1726 | −1.51239 | −0.756194 | − | 0.654348i | \(-0.772943\pi\) | ||||
−0.756194 | + | 0.654348i | \(0.772943\pi\) | |||||||
\(348\) | 14.3799 | 0.770846 | ||||||||
\(349\) | 22.7155 | 1.21593 | 0.607967 | − | 0.793962i | \(-0.291985\pi\) | ||||
0.607967 | + | 0.793962i | \(0.291985\pi\) | |||||||
\(350\) | −25.4128 | −1.35837 | ||||||||
\(351\) | −6.72178 | −0.358782 | ||||||||
\(352\) | 1.32899 | 0.0708355 | ||||||||
\(353\) | 20.2776 | 1.07927 | 0.539634 | − | 0.841900i | \(-0.318563\pi\) | ||||
0.539634 | + | 0.841900i | \(0.318563\pi\) | |||||||
\(354\) | −10.9643 | −0.582746 | ||||||||
\(355\) | −16.3548 | −0.868025 | ||||||||
\(356\) | −1.83218 | −0.0971054 | ||||||||
\(357\) | −51.9754 | −2.75083 | ||||||||
\(358\) | 22.1103 | 1.16857 | ||||||||
\(359\) | 9.80334 | 0.517401 | 0.258700 | − | 0.965958i | \(-0.416706\pi\) | ||||
0.258700 | + | 0.965958i | \(0.416706\pi\) | |||||||
\(360\) | −14.7896 | −0.779479 | ||||||||
\(361\) | 4.78098 | 0.251630 | ||||||||
\(362\) | 13.1737 | 0.692392 | ||||||||
\(363\) | 24.6225 | 1.29235 | ||||||||
\(364\) | 7.25998 | 0.380526 | ||||||||
\(365\) | 36.9063 | 1.93177 | ||||||||
\(366\) | −11.6821 | −0.610635 | ||||||||
\(367\) | −24.6913 | −1.28888 | −0.644438 | − | 0.764656i | \(-0.722909\pi\) | ||||
−0.644438 | + | 0.764656i | \(0.722909\pi\) | |||||||
\(368\) | 7.31948 | 0.381554 | ||||||||
\(369\) | 18.1336 | 0.943997 | ||||||||
\(370\) | −7.69417 | −0.400001 | ||||||||
\(371\) | 19.2632 | 1.00010 | ||||||||
\(372\) | 7.21918 | 0.374297 | ||||||||
\(373\) | −30.8849 | −1.59916 | −0.799580 | − | 0.600560i | \(-0.794944\pi\) | ||||
−0.799580 | + | 0.600560i | \(0.794944\pi\) | |||||||
\(374\) | 8.09860 | 0.418768 | ||||||||
\(375\) | −28.2548 | −1.45907 | ||||||||
\(376\) | −6.69810 | −0.345428 | ||||||||
\(377\) | −12.2400 | −0.630392 | ||||||||
\(378\) | 9.47251 | 0.487214 | ||||||||
\(379\) | −0.433900 | −0.0222879 | −0.0111440 | − | 0.999938i | \(-0.503547\pi\) | ||||
−0.0111440 | + | 0.999938i | \(0.503547\pi\) | |||||||
\(380\) | 17.5455 | 0.900066 | ||||||||
\(381\) | 30.6631 | 1.57092 | ||||||||
\(382\) | −3.67683 | −0.188123 | ||||||||
\(383\) | −11.0133 | −0.562752 | −0.281376 | − | 0.959598i | \(-0.590791\pi\) | ||||
−0.281376 | + | 0.959598i | \(0.590791\pi\) | |||||||
\(384\) | 2.66657 | 0.136078 | ||||||||
\(385\) | −15.2944 | −0.779474 | ||||||||
\(386\) | 6.87538 | 0.349948 | ||||||||
\(387\) | 4.23266 | 0.215158 | ||||||||
\(388\) | 13.9690 | 0.709170 | ||||||||
\(389\) | −29.4374 | −1.49254 | −0.746269 | − | 0.665645i | \(-0.768157\pi\) | ||||
−0.746269 | + | 0.665645i | \(0.768157\pi\) | |||||||
\(390\) | 21.7762 | 1.10268 | ||||||||
\(391\) | 44.6033 | 2.25569 | ||||||||
\(392\) | −3.23095 | −0.163188 | ||||||||
\(393\) | 25.3156 | 1.27700 | ||||||||
\(394\) | −1.60178 | −0.0806967 | ||||||||
\(395\) | 20.1484 | 1.01378 | ||||||||
\(396\) | −5.46295 | −0.274523 | ||||||||
\(397\) | 21.5567 | 1.08190 | 0.540950 | − | 0.841054i | \(-0.318065\pi\) | ||||
0.540950 | + | 0.841054i | \(0.318065\pi\) | |||||||
\(398\) | −1.18019 | −0.0591574 | ||||||||
\(399\) | −41.5935 | −2.08228 | ||||||||
\(400\) | 7.94502 | 0.397251 | ||||||||
\(401\) | −29.9435 | −1.49531 | −0.747654 | − | 0.664088i | \(-0.768820\pi\) | ||||
−0.747654 | + | 0.664088i | \(0.768820\pi\) | |||||||
\(402\) | −17.9493 | −0.895231 | ||||||||
\(403\) | −6.14487 | −0.306098 | ||||||||
\(404\) | 10.6892 | 0.531806 | ||||||||
\(405\) | −15.9561 | −0.792864 | ||||||||
\(406\) | 17.2489 | 0.856050 | ||||||||
\(407\) | −2.84206 | −0.140876 | ||||||||
\(408\) | 16.2495 | 0.804470 | ||||||||
\(409\) | 16.2936 | 0.805667 | 0.402834 | − | 0.915273i | \(-0.368025\pi\) | ||||
0.402834 | + | 0.915273i | \(0.368025\pi\) | |||||||
\(410\) | −15.8720 | −0.783861 | ||||||||
\(411\) | −30.7544 | −1.51700 | ||||||||
\(412\) | 9.90004 | 0.487740 | ||||||||
\(413\) | −13.1518 | −0.647159 | ||||||||
\(414\) | −30.0874 | −1.47871 | ||||||||
\(415\) | −2.43075 | −0.119321 | ||||||||
\(416\) | −2.26975 | −0.111283 | ||||||||
\(417\) | −52.3289 | −2.56256 | ||||||||
\(418\) | 6.48093 | 0.316993 | ||||||||
\(419\) | −5.26824 | −0.257371 | −0.128685 | − | 0.991685i | \(-0.541076\pi\) | ||||
−0.128685 | + | 0.991685i | \(0.541076\pi\) | |||||||
\(420\) | −30.6875 | −1.49740 | ||||||||
\(421\) | 3.59050 | 0.174990 | 0.0874952 | − | 0.996165i | \(-0.472114\pi\) | ||||
0.0874952 | + | 0.996165i | \(0.472114\pi\) | |||||||
\(422\) | 21.3981 | 1.04164 | ||||||||
\(423\) | 27.5331 | 1.33871 | ||||||||
\(424\) | −6.02243 | −0.292475 | ||||||||
\(425\) | 48.4152 | 2.34848 | ||||||||
\(426\) | −12.1213 | −0.587277 | ||||||||
\(427\) | −14.0129 | −0.678131 | ||||||||
\(428\) | −5.86232 | −0.283366 | ||||||||
\(429\) | 8.04364 | 0.388351 | ||||||||
\(430\) | −3.70476 | −0.178660 | ||||||||
\(431\) | −1.15129 | −0.0554559 | −0.0277279 | − | 0.999616i | \(-0.508827\pi\) | ||||
−0.0277279 | + | 0.999616i | \(0.508827\pi\) | |||||||
\(432\) | −2.96147 | −0.142484 | ||||||||
\(433\) | 16.7962 | 0.807174 | 0.403587 | − | 0.914941i | \(-0.367763\pi\) | ||||
0.403587 | + | 0.914941i | \(0.367763\pi\) | |||||||
\(434\) | 8.65950 | 0.415669 | ||||||||
\(435\) | 51.7379 | 2.48064 | ||||||||
\(436\) | 18.2037 | 0.871799 | ||||||||
\(437\) | 35.6940 | 1.70747 | ||||||||
\(438\) | 27.3528 | 1.30697 | ||||||||
\(439\) | −34.9034 | −1.66585 | −0.832923 | − | 0.553388i | \(-0.813335\pi\) | ||||
−0.832923 | + | 0.553388i | \(0.813335\pi\) | |||||||
\(440\) | 4.78161 | 0.227954 | ||||||||
\(441\) | 13.2811 | 0.632434 | ||||||||
\(442\) | −13.8313 | −0.657890 | ||||||||
\(443\) | −0.622830 | −0.0295916 | −0.0147958 | − | 0.999891i | \(-0.504710\pi\) | ||||
−0.0147958 | + | 0.999891i | \(0.504710\pi\) | |||||||
\(444\) | −5.70248 | −0.270627 | ||||||||
\(445\) | −6.59204 | −0.312492 | ||||||||
\(446\) | 23.5596 | 1.11558 | ||||||||
\(447\) | −17.4813 | −0.826839 | ||||||||
\(448\) | 3.19859 | 0.151119 | ||||||||
\(449\) | −1.56565 | −0.0738878 | −0.0369439 | − | 0.999317i | \(-0.511762\pi\) | ||||
−0.0369439 | + | 0.999317i | \(0.511762\pi\) | |||||||
\(450\) | −32.6587 | −1.53955 | ||||||||
\(451\) | −5.86276 | −0.276067 | ||||||||
\(452\) | 10.4459 | 0.491335 | ||||||||
\(453\) | 49.8718 | 2.34318 | ||||||||
\(454\) | 14.6906 | 0.689465 | ||||||||
\(455\) | 26.1208 | 1.22456 | ||||||||
\(456\) | 13.0037 | 0.608955 | ||||||||
\(457\) | −7.80596 | −0.365147 | −0.182574 | − | 0.983192i | \(-0.558443\pi\) | ||||
−0.182574 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(458\) | 14.2127 | 0.664115 | ||||||||
\(459\) | −18.0466 | −0.842341 | ||||||||
\(460\) | 26.3349 | 1.22787 | ||||||||
\(461\) | 32.5904 | 1.51789 | 0.758944 | − | 0.651156i | \(-0.225716\pi\) | ||||
0.758944 | + | 0.651156i | \(0.225716\pi\) | |||||||
\(462\) | −11.3353 | −0.527366 | ||||||||
\(463\) | 1.65032 | 0.0766971 | 0.0383485 | − | 0.999264i | \(-0.487790\pi\) | ||||
0.0383485 | + | 0.999264i | \(0.487790\pi\) | |||||||
\(464\) | −5.39268 | −0.250349 | ||||||||
\(465\) | 25.9740 | 1.20452 | ||||||||
\(466\) | 23.9962 | 1.11160 | ||||||||
\(467\) | −21.9615 | −1.01626 | −0.508128 | − | 0.861281i | \(-0.669662\pi\) | ||||
−0.508128 | + | 0.861281i | \(0.669662\pi\) | |||||||
\(468\) | 9.33000 | 0.431279 | ||||||||
\(469\) | −21.5305 | −0.994184 | ||||||||
\(470\) | −24.0992 | −1.11161 | ||||||||
\(471\) | 44.0273 | 2.02867 | ||||||||
\(472\) | 4.11176 | 0.189259 | ||||||||
\(473\) | −1.36846 | −0.0629218 | ||||||||
\(474\) | 14.9328 | 0.685888 | ||||||||
\(475\) | 38.7445 | 1.77772 | ||||||||
\(476\) | 19.4915 | 0.893391 | ||||||||
\(477\) | 24.7557 | 1.13349 | ||||||||
\(478\) | −24.6830 | −1.12898 | ||||||||
\(479\) | −8.67908 | −0.396557 | −0.198279 | − | 0.980146i | \(-0.563535\pi\) | ||||
−0.198279 | + | 0.980146i | \(0.563535\pi\) | |||||||
\(480\) | 9.59410 | 0.437909 | ||||||||
\(481\) | 4.85387 | 0.221317 | ||||||||
\(482\) | −16.5929 | −0.755786 | ||||||||
\(483\) | −62.4297 | −2.84065 | ||||||||
\(484\) | −9.23378 | −0.419717 | ||||||||
\(485\) | 50.2594 | 2.28216 | ||||||||
\(486\) | −20.7101 | −0.939431 | ||||||||
\(487\) | −21.4000 | −0.969728 | −0.484864 | − | 0.874590i | \(-0.661131\pi\) | ||||
−0.484864 | + | 0.874590i | \(0.661131\pi\) | |||||||
\(488\) | 4.38096 | 0.198317 | ||||||||
\(489\) | 41.9488 | 1.89699 | ||||||||
\(490\) | −11.6247 | −0.525150 | ||||||||
\(491\) | 5.96869 | 0.269363 | 0.134682 | − | 0.990889i | \(-0.456999\pi\) | ||||
0.134682 | + | 0.990889i | \(0.456999\pi\) | |||||||
\(492\) | −11.7634 | −0.530334 | ||||||||
\(493\) | −32.8618 | −1.48002 | ||||||||
\(494\) | −11.0686 | −0.497999 | ||||||||
\(495\) | −19.6552 | −0.883437 | ||||||||
\(496\) | −2.70729 | −0.121561 | ||||||||
\(497\) | −14.5396 | −0.652191 | ||||||||
\(498\) | −1.80153 | −0.0807286 | ||||||||
\(499\) | −16.9220 | −0.757531 | −0.378765 | − | 0.925493i | \(-0.623651\pi\) | ||||
−0.378765 | + | 0.925493i | \(0.623651\pi\) | |||||||
\(500\) | 10.5959 | 0.473865 | ||||||||
\(501\) | 51.1540 | 2.28539 | ||||||||
\(502\) | −11.8700 | −0.529782 | ||||||||
\(503\) | 3.44928 | 0.153796 | 0.0768980 | − | 0.997039i | \(-0.475498\pi\) | ||||
0.0768980 | + | 0.997039i | \(0.475498\pi\) | |||||||
\(504\) | −13.1481 | −0.585662 | ||||||||
\(505\) | 38.4587 | 1.71139 | ||||||||
\(506\) | 9.72753 | 0.432442 | ||||||||
\(507\) | 20.9279 | 0.929441 | ||||||||
\(508\) | −11.4991 | −0.510189 | ||||||||
\(509\) | −28.5841 | −1.26697 | −0.633485 | − | 0.773755i | \(-0.718376\pi\) | ||||
−0.633485 | + | 0.773755i | \(0.718376\pi\) | |||||||
\(510\) | 58.4644 | 2.58885 | ||||||||
\(511\) | 32.8101 | 1.45143 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −14.4418 | −0.637622 | ||||||||
\(514\) | −23.8871 | −1.05361 | ||||||||
\(515\) | 35.6195 | 1.56958 | ||||||||
\(516\) | −2.74576 | −0.120875 | ||||||||
\(517\) | −8.90172 | −0.391497 | ||||||||
\(518\) | −6.84020 | −0.300541 | ||||||||
\(519\) | 21.1801 | 0.929703 | ||||||||
\(520\) | −8.16636 | −0.358119 | ||||||||
\(521\) | 34.4759 | 1.51042 | 0.755208 | − | 0.655485i | \(-0.227536\pi\) | ||||
0.755208 | + | 0.655485i | \(0.227536\pi\) | |||||||
\(522\) | 22.1671 | 0.970227 | ||||||||
\(523\) | 12.0464 | 0.526754 | 0.263377 | − | 0.964693i | \(-0.415164\pi\) | ||||
0.263377 | + | 0.964693i | \(0.415164\pi\) | |||||||
\(524\) | −9.49369 | −0.414734 | ||||||||
\(525\) | −67.7650 | −2.95751 | ||||||||
\(526\) | −6.35171 | −0.276948 | ||||||||
\(527\) | −16.4977 | −0.718649 | ||||||||
\(528\) | 3.54385 | 0.154226 | ||||||||
\(529\) | 30.5748 | 1.32934 | ||||||||
\(530\) | −21.6682 | −0.941206 | ||||||||
\(531\) | −16.9018 | −0.733475 | ||||||||
\(532\) | 15.5981 | 0.676265 | ||||||||
\(533\) | 10.0128 | 0.433704 | ||||||||
\(534\) | −4.88564 | −0.211422 | ||||||||
\(535\) | −21.0922 | −0.911894 | ||||||||
\(536\) | 6.73124 | 0.290745 | ||||||||
\(537\) | 58.9587 | 2.54426 | ||||||||
\(538\) | −21.2676 | −0.916911 | ||||||||
\(539\) | −4.29391 | −0.184952 | ||||||||
\(540\) | −10.6551 | −0.458524 | ||||||||
\(541\) | −11.7617 | −0.505676 | −0.252838 | − | 0.967509i | \(-0.581364\pi\) | ||||
−0.252838 | + | 0.967509i | \(0.581364\pi\) | |||||||
\(542\) | 25.0598 | 1.07641 | ||||||||
\(543\) | 35.1285 | 1.50751 | ||||||||
\(544\) | −6.09379 | −0.261269 | ||||||||
\(545\) | 65.4954 | 2.80552 | ||||||||
\(546\) | 19.3592 | 0.828499 | ||||||||
\(547\) | 36.6164 | 1.56560 | 0.782802 | − | 0.622270i | \(-0.213790\pi\) | ||||
0.782802 | + | 0.622270i | \(0.213790\pi\) | |||||||
\(548\) | 11.5333 | 0.492679 | ||||||||
\(549\) | −18.0083 | −0.768577 | ||||||||
\(550\) | 10.5589 | 0.450232 | ||||||||
\(551\) | −26.2978 | −1.12032 | ||||||||
\(552\) | 19.5179 | 0.830737 | ||||||||
\(553\) | 17.9121 | 0.761702 | ||||||||
\(554\) | −1.28916 | −0.0547710 | ||||||||
\(555\) | −20.5170 | −0.870900 | ||||||||
\(556\) | 19.6241 | 0.832246 | ||||||||
\(557\) | −39.4054 | −1.66966 | −0.834830 | − | 0.550509i | \(-0.814434\pi\) | ||||
−0.834830 | + | 0.550509i | \(0.814434\pi\) | |||||||
\(558\) | 11.1286 | 0.471110 | ||||||||
\(559\) | 2.33715 | 0.0988509 | ||||||||
\(560\) | 11.5083 | 0.486312 | ||||||||
\(561\) | 21.5955 | 0.911761 | ||||||||
\(562\) | 11.5384 | 0.486716 | ||||||||
\(563\) | 36.6532 | 1.54475 | 0.772375 | − | 0.635167i | \(-0.219069\pi\) | ||||
0.772375 | + | 0.635167i | \(0.219069\pi\) | |||||||
\(564\) | −17.8609 | −0.752081 | ||||||||
\(565\) | 37.5836 | 1.58115 | ||||||||
\(566\) | 10.5119 | 0.441850 | ||||||||
\(567\) | −14.1851 | −0.595719 | ||||||||
\(568\) | 4.54564 | 0.190731 | ||||||||
\(569\) | −21.0877 | −0.884044 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(570\) | 46.7863 | 1.95966 | ||||||||
\(571\) | −16.8959 | −0.707072 | −0.353536 | − | 0.935421i | \(-0.615021\pi\) | ||||
−0.353536 | + | 0.935421i | \(0.615021\pi\) | |||||||
\(572\) | −3.01648 | −0.126125 | ||||||||
\(573\) | −9.80453 | −0.409590 | ||||||||
\(574\) | −14.1103 | −0.588954 | ||||||||
\(575\) | 58.1534 | 2.42516 | ||||||||
\(576\) | 4.11059 | 0.171275 | ||||||||
\(577\) | 25.2493 | 1.05114 | 0.525571 | − | 0.850750i | \(-0.323852\pi\) | ||||
0.525571 | + | 0.850750i | \(0.323852\pi\) | |||||||
\(578\) | −20.1342 | −0.837474 | ||||||||
\(579\) | 18.3337 | 0.761922 | ||||||||
\(580\) | −19.4024 | −0.805641 | ||||||||
\(581\) | −2.16096 | −0.0896518 | ||||||||
\(582\) | 37.2494 | 1.54404 | ||||||||
\(583\) | −8.00376 | −0.331482 | ||||||||
\(584\) | −10.2577 | −0.424466 | ||||||||
\(585\) | 33.5686 | 1.38789 | ||||||||
\(586\) | 17.8079 | 0.735639 | ||||||||
\(587\) | 15.1066 | 0.623516 | 0.311758 | − | 0.950161i | \(-0.399082\pi\) | ||||
0.311758 | + | 0.950161i | \(0.399082\pi\) | |||||||
\(588\) | −8.61555 | −0.355299 | ||||||||
\(589\) | −13.2023 | −0.543992 | ||||||||
\(590\) | 14.7938 | 0.609050 | ||||||||
\(591\) | −4.27127 | −0.175696 | ||||||||
\(592\) | 2.13851 | 0.0878921 | ||||||||
\(593\) | −8.33602 | −0.342319 | −0.171160 | − | 0.985243i | \(-0.554751\pi\) | ||||
−0.171160 | + | 0.985243i | \(0.554751\pi\) | |||||||
\(594\) | −3.93577 | −0.161487 | ||||||||
\(595\) | 70.1288 | 2.87500 | ||||||||
\(596\) | 6.55575 | 0.268534 | ||||||||
\(597\) | −3.14705 | −0.128800 | ||||||||
\(598\) | −16.6134 | −0.679371 | ||||||||
\(599\) | −3.67650 | −0.150218 | −0.0751088 | − | 0.997175i | \(-0.523930\pi\) | ||||
−0.0751088 | + | 0.997175i | \(0.523930\pi\) | |||||||
\(600\) | 21.1859 | 0.864912 | ||||||||
\(601\) | 33.5749 | 1.36955 | 0.684775 | − | 0.728755i | \(-0.259901\pi\) | ||||
0.684775 | + | 0.728755i | \(0.259901\pi\) | |||||||
\(602\) | −3.29357 | −0.134236 | ||||||||
\(603\) | −27.6694 | −1.12678 | ||||||||
\(604\) | −18.7026 | −0.760998 | ||||||||
\(605\) | −33.2224 | −1.35068 | ||||||||
\(606\) | 28.5034 | 1.15787 | ||||||||
\(607\) | 29.7699 | 1.20832 | 0.604162 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604162 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(608\) | −4.87657 | −0.197771 | ||||||||
\(609\) | 45.9955 | 1.86383 | ||||||||
\(610\) | 15.7623 | 0.638198 | ||||||||
\(611\) | 15.2030 | 0.615047 | ||||||||
\(612\) | 25.0491 | 1.01255 | ||||||||
\(613\) | −13.2420 | −0.534839 | −0.267420 | − | 0.963580i | \(-0.586171\pi\) | ||||
−0.267420 | + | 0.963580i | \(0.586171\pi\) | |||||||
\(614\) | 20.8759 | 0.842481 | ||||||||
\(615\) | −42.3237 | −1.70666 | ||||||||
\(616\) | 4.25090 | 0.171273 | ||||||||
\(617\) | −0.201658 | −0.00811845 | −0.00405923 | − | 0.999992i | \(-0.501292\pi\) | ||||
−0.00405923 | + | 0.999992i | \(0.501292\pi\) | |||||||
\(618\) | 26.3991 | 1.06193 | ||||||||
\(619\) | −20.3442 | −0.817702 | −0.408851 | − | 0.912601i | \(-0.634070\pi\) | ||||
−0.408851 | + | 0.912601i | \(0.634070\pi\) | |||||||
\(620\) | −9.74061 | −0.391193 | ||||||||
\(621\) | −21.6764 | −0.869845 | ||||||||
\(622\) | −20.5052 | −0.822182 | ||||||||
\(623\) | −5.86039 | −0.234791 | ||||||||
\(624\) | −6.05244 | −0.242291 | ||||||||
\(625\) | −1.60178 | −0.0640712 | ||||||||
\(626\) | 9.60209 | 0.383777 | ||||||||
\(627\) | 17.2819 | 0.690171 | ||||||||
\(628\) | −16.5108 | −0.658854 | ||||||||
\(629\) | 13.0316 | 0.519604 | ||||||||
\(630\) | −47.3057 | −1.88470 | ||||||||
\(631\) | −34.8064 | −1.38562 | −0.692811 | − | 0.721119i | \(-0.743628\pi\) | ||||
−0.692811 | + | 0.721119i | \(0.743628\pi\) | |||||||
\(632\) | −5.60002 | −0.222757 | ||||||||
\(633\) | 57.0595 | 2.26791 | ||||||||
\(634\) | 22.4659 | 0.892234 | ||||||||
\(635\) | −41.3727 | −1.64183 | ||||||||
\(636\) | −16.0592 | −0.636789 | ||||||||
\(637\) | 7.33344 | 0.290561 | ||||||||
\(638\) | −7.16683 | −0.283737 | ||||||||
\(639\) | −18.6853 | −0.739178 | ||||||||
\(640\) | −3.59792 | −0.142220 | ||||||||
\(641\) | 31.0353 | 1.22582 | 0.612910 | − | 0.790153i | \(-0.289999\pi\) | ||||
0.612910 | + | 0.790153i | \(0.289999\pi\) | |||||||
\(642\) | −15.6323 | −0.616957 | ||||||||
\(643\) | 19.7146 | 0.777470 | 0.388735 | − | 0.921350i | \(-0.372912\pi\) | ||||
0.388735 | + | 0.921350i | \(0.372912\pi\) | |||||||
\(644\) | 23.4120 | 0.922561 | ||||||||
\(645\) | −9.87901 | −0.388986 | ||||||||
\(646\) | −29.7168 | −1.16919 | ||||||||
\(647\) | 14.3874 | 0.565629 | 0.282814 | − | 0.959175i | \(-0.408732\pi\) | ||||
0.282814 | + | 0.959175i | \(0.408732\pi\) | |||||||
\(648\) | 4.43481 | 0.174216 | ||||||||
\(649\) | 5.46450 | 0.214500 | ||||||||
\(650\) | −18.0332 | −0.707319 | ||||||||
\(651\) | 23.0912 | 0.905014 | ||||||||
\(652\) | −15.7314 | −0.616089 | ||||||||
\(653\) | 5.24123 | 0.205105 | 0.102553 | − | 0.994728i | \(-0.467299\pi\) | ||||
0.102553 | + | 0.994728i | \(0.467299\pi\) | |||||||
\(654\) | 48.5414 | 1.89812 | ||||||||
\(655\) | −34.1575 | −1.33464 | ||||||||
\(656\) | 4.41143 | 0.172237 | ||||||||
\(657\) | 42.1652 | 1.64502 | ||||||||
\(658\) | −21.4244 | −0.835211 | ||||||||
\(659\) | −32.5676 | −1.26865 | −0.634327 | − | 0.773065i | \(-0.718723\pi\) | ||||
−0.634327 | + | 0.773065i | \(0.718723\pi\) | |||||||
\(660\) | 12.7505 | 0.496312 | ||||||||
\(661\) | 0.377381 | 0.0146784 | 0.00733922 | − | 0.999973i | \(-0.497664\pi\) | ||||
0.00733922 | + | 0.999973i | \(0.497664\pi\) | |||||||
\(662\) | −12.3144 | −0.478614 | ||||||||
\(663\) | −36.8823 | −1.43239 | ||||||||
\(664\) | 0.675599 | 0.0262183 | ||||||||
\(665\) | 56.1208 | 2.17627 | ||||||||
\(666\) | −8.79053 | −0.340626 | ||||||||
\(667\) | −39.4716 | −1.52835 | ||||||||
\(668\) | −19.1834 | −0.742229 | ||||||||
\(669\) | 62.8233 | 2.42889 | ||||||||
\(670\) | 24.2185 | 0.935641 | ||||||||
\(671\) | 5.82226 | 0.224766 | ||||||||
\(672\) | 8.52925 | 0.329023 | ||||||||
\(673\) | 28.3516 | 1.09287 | 0.546437 | − | 0.837500i | \(-0.315984\pi\) | ||||
0.546437 | + | 0.837500i | \(0.315984\pi\) | |||||||
\(674\) | 11.1065 | 0.427805 | ||||||||
\(675\) | −23.5289 | −0.905629 | ||||||||
\(676\) | −7.84825 | −0.301856 | ||||||||
\(677\) | −5.49077 | −0.211027 | −0.105514 | − | 0.994418i | \(-0.533649\pi\) | ||||
−0.105514 | + | 0.994418i | \(0.533649\pi\) | |||||||
\(678\) | 27.8548 | 1.06976 | ||||||||
\(679\) | 44.6811 | 1.71470 | ||||||||
\(680\) | −21.9249 | −0.840783 | ||||||||
\(681\) | 39.1736 | 1.50113 | ||||||||
\(682\) | −3.59797 | −0.137773 | ||||||||
\(683\) | −21.3734 | −0.817830 | −0.408915 | − | 0.912573i | \(-0.634093\pi\) | ||||
−0.408915 | + | 0.912573i | \(0.634093\pi\) | |||||||
\(684\) | 20.0456 | 0.766463 | ||||||||
\(685\) | 41.4959 | 1.58548 | ||||||||
\(686\) | 12.0556 | 0.460286 | ||||||||
\(687\) | 37.8991 | 1.44594 | ||||||||
\(688\) | 1.02970 | 0.0392568 | ||||||||
\(689\) | 13.6694 | 0.520762 | ||||||||
\(690\) | 70.2238 | 2.67337 | ||||||||
\(691\) | −26.3952 | −1.00412 | −0.502061 | − | 0.864832i | \(-0.667425\pi\) | ||||
−0.502061 | + | 0.864832i | \(0.667425\pi\) | |||||||
\(692\) | −7.94282 | −0.301941 | ||||||||
\(693\) | −17.4737 | −0.663771 | ||||||||
\(694\) | 28.1726 | 1.06942 | ||||||||
\(695\) | 70.6058 | 2.67823 | ||||||||
\(696\) | −14.3799 | −0.545070 | ||||||||
\(697\) | 26.8823 | 1.01824 | ||||||||
\(698\) | −22.7155 | −0.859795 | ||||||||
\(699\) | 63.9874 | 2.42023 | ||||||||
\(700\) | 25.4128 | 0.960514 | ||||||||
\(701\) | 32.9856 | 1.24585 | 0.622925 | − | 0.782282i | \(-0.285944\pi\) | ||||
0.622925 | + | 0.782282i | \(0.285944\pi\) | |||||||
\(702\) | 6.72178 | 0.253697 | ||||||||
\(703\) | 10.4286 | 0.393322 | ||||||||
\(704\) | −1.32899 | −0.0500883 | ||||||||
\(705\) | −64.2622 | −2.42025 | ||||||||
\(706\) | −20.2776 | −0.763157 | ||||||||
\(707\) | 34.1902 | 1.28585 | ||||||||
\(708\) | 10.9643 | 0.412064 | ||||||||
\(709\) | 7.39923 | 0.277884 | 0.138942 | − | 0.990301i | \(-0.455630\pi\) | ||||
0.138942 | + | 0.990301i | \(0.455630\pi\) | |||||||
\(710\) | 16.3548 | 0.613786 | ||||||||
\(711\) | 23.0194 | 0.863295 | ||||||||
\(712\) | 1.83218 | 0.0686639 | ||||||||
\(713\) | −19.8160 | −0.742114 | ||||||||
\(714\) | 51.9754 | 1.94513 | ||||||||
\(715\) | −10.8530 | −0.405880 | ||||||||
\(716\) | −22.1103 | −0.826302 | ||||||||
\(717\) | −65.8190 | −2.45806 | ||||||||
\(718\) | −9.80334 | −0.365858 | ||||||||
\(719\) | −10.3170 | −0.384761 | −0.192380 | − | 0.981320i | \(-0.561621\pi\) | ||||
−0.192380 | + | 0.981320i | \(0.561621\pi\) | |||||||
\(720\) | 14.7896 | 0.551175 | ||||||||
\(721\) | 31.6661 | 1.17931 | ||||||||
\(722\) | −4.78098 | −0.177930 | ||||||||
\(723\) | −44.2461 | −1.64553 | ||||||||
\(724\) | −13.1737 | −0.489595 | ||||||||
\(725\) | −42.8449 | −1.59122 | ||||||||
\(726\) | −24.6225 | −0.913827 | ||||||||
\(727\) | −18.4038 | −0.682560 | −0.341280 | − | 0.939962i | \(-0.610860\pi\) | ||||
−0.341280 | + | 0.939962i | \(0.610860\pi\) | |||||||
\(728\) | −7.25998 | −0.269073 | ||||||||
\(729\) | −41.9206 | −1.55261 | ||||||||
\(730\) | −36.9063 | −1.36596 | ||||||||
\(731\) | 6.27475 | 0.232080 | ||||||||
\(732\) | 11.6821 | 0.431784 | ||||||||
\(733\) | 41.4006 | 1.52917 | 0.764583 | − | 0.644526i | \(-0.222945\pi\) | ||||
0.764583 | + | 0.644526i | \(0.222945\pi\) | |||||||
\(734\) | 24.6913 | 0.911373 | ||||||||
\(735\) | −30.9980 | −1.14338 | ||||||||
\(736\) | −7.31948 | −0.269800 | ||||||||
\(737\) | 8.94577 | 0.329522 | ||||||||
\(738\) | −18.1336 | −0.667507 | ||||||||
\(739\) | 51.3016 | 1.88716 | 0.943580 | − | 0.331146i | \(-0.107435\pi\) | ||||
0.943580 | + | 0.331146i | \(0.107435\pi\) | |||||||
\(740\) | 7.69417 | 0.282843 | ||||||||
\(741\) | −29.5152 | −1.08427 | ||||||||
\(742\) | −19.2632 | −0.707176 | ||||||||
\(743\) | −14.1002 | −0.517285 | −0.258642 | − | 0.965973i | \(-0.583275\pi\) | ||||
−0.258642 | + | 0.965973i | \(0.583275\pi\) | |||||||
\(744\) | −7.21918 | −0.264668 | ||||||||
\(745\) | 23.5870 | 0.864162 | ||||||||
\(746\) | 30.8849 | 1.13078 | ||||||||
\(747\) | −2.77711 | −0.101609 | ||||||||
\(748\) | −8.09860 | −0.296114 | ||||||||
\(749\) | −18.7511 | −0.685152 | ||||||||
\(750\) | 28.2548 | 1.03172 | ||||||||
\(751\) | −29.0479 | −1.05997 | −0.529986 | − | 0.848006i | \(-0.677803\pi\) | ||||
−0.529986 | + | 0.848006i | \(0.677803\pi\) | |||||||
\(752\) | 6.69810 | 0.244254 | ||||||||
\(753\) | −31.6520 | −1.15346 | ||||||||
\(754\) | 12.2400 | 0.445755 | ||||||||
\(755\) | −67.2905 | −2.44895 | ||||||||
\(756\) | −9.47251 | −0.344512 | ||||||||
\(757\) | −32.0960 | −1.16655 | −0.583275 | − | 0.812275i | \(-0.698229\pi\) | ||||
−0.583275 | + | 0.812275i | \(0.698229\pi\) | |||||||
\(758\) | 0.433900 | 0.0157600 | ||||||||
\(759\) | 25.9391 | 0.941531 | ||||||||
\(760\) | −17.5455 | −0.636443 | ||||||||
\(761\) | 12.0267 | 0.435966 | 0.217983 | − | 0.975953i | \(-0.430052\pi\) | ||||
0.217983 | + | 0.975953i | \(0.430052\pi\) | |||||||
\(762\) | −30.6631 | −1.11081 | ||||||||
\(763\) | 58.2261 | 2.10793 | ||||||||
\(764\) | 3.67683 | 0.133023 | ||||||||
\(765\) | 90.1245 | 3.25846 | ||||||||
\(766\) | 11.0133 | 0.397926 | ||||||||
\(767\) | −9.33266 | −0.336983 | ||||||||
\(768\) | −2.66657 | −0.0962215 | ||||||||
\(769\) | 1.27561 | 0.0459996 | 0.0229998 | − | 0.999735i | \(-0.492678\pi\) | ||||
0.0229998 | + | 0.999735i | \(0.492678\pi\) | |||||||
\(770\) | 15.2944 | 0.551171 | ||||||||
\(771\) | −63.6965 | −2.29397 | ||||||||
\(772\) | −6.87538 | −0.247450 | ||||||||
\(773\) | −19.8733 | −0.714791 | −0.357396 | − | 0.933953i | \(-0.616335\pi\) | ||||
−0.357396 | + | 0.933953i | \(0.616335\pi\) | |||||||
\(774\) | −4.23266 | −0.152140 | ||||||||
\(775\) | −21.5095 | −0.772643 | ||||||||
\(776\) | −13.9690 | −0.501459 | ||||||||
\(777\) | −18.2399 | −0.654351 | ||||||||
\(778\) | 29.4374 | 1.05538 | ||||||||
\(779\) | 21.5127 | 0.770772 | ||||||||
\(780\) | −21.7762 | −0.779712 | ||||||||
\(781\) | 6.04112 | 0.216168 | ||||||||
\(782\) | −44.6033 | −1.59501 | ||||||||
\(783\) | 15.9702 | 0.570730 | ||||||||
\(784\) | 3.23095 | 0.115391 | ||||||||
\(785\) | −59.4046 | −2.12024 | ||||||||
\(786\) | −25.3156 | −0.902977 | ||||||||
\(787\) | 19.6093 | 0.698995 | 0.349498 | − | 0.936937i | \(-0.386352\pi\) | ||||
0.349498 | + | 0.936937i | \(0.386352\pi\) | |||||||
\(788\) | 1.60178 | 0.0570612 | ||||||||
\(789\) | −16.9373 | −0.602983 | ||||||||
\(790\) | −20.1484 | −0.716848 | ||||||||
\(791\) | 33.4122 | 1.18800 | ||||||||
\(792\) | 5.46295 | 0.194117 | ||||||||
\(793\) | −9.94367 | −0.353110 | ||||||||
\(794\) | −21.5567 | −0.765019 | ||||||||
\(795\) | −57.7797 | −2.04924 | ||||||||
\(796\) | 1.18019 | 0.0418306 | ||||||||
\(797\) | −38.1433 | −1.35110 | −0.675552 | − | 0.737312i | \(-0.736095\pi\) | ||||
−0.675552 | + | 0.737312i | \(0.736095\pi\) | |||||||
\(798\) | 41.5935 | 1.47239 | ||||||||
\(799\) | 40.8168 | 1.44399 | ||||||||
\(800\) | −7.94502 | −0.280899 | ||||||||
\(801\) | −7.53134 | −0.266107 | ||||||||
\(802\) | 29.9435 | 1.05734 | ||||||||
\(803\) | −13.6324 | −0.481077 | ||||||||
\(804\) | 17.9493 | 0.633024 | ||||||||
\(805\) | 84.2344 | 2.96887 | ||||||||
\(806\) | 6.14487 | 0.216444 | ||||||||
\(807\) | −56.7115 | −1.99634 | ||||||||
\(808\) | −10.6892 | −0.376043 | ||||||||
\(809\) | 7.33870 | 0.258015 | 0.129007 | − | 0.991644i | \(-0.458821\pi\) | ||||
0.129007 | + | 0.991644i | \(0.458821\pi\) | |||||||
\(810\) | 15.9561 | 0.560640 | ||||||||
\(811\) | 36.8868 | 1.29527 | 0.647636 | − | 0.761950i | \(-0.275758\pi\) | ||||
0.647636 | + | 0.761950i | \(0.275758\pi\) | |||||||
\(812\) | −17.2489 | −0.605319 | ||||||||
\(813\) | 66.8236 | 2.34361 | ||||||||
\(814\) | 2.84206 | 0.0996141 | ||||||||
\(815\) | −56.6003 | −1.98262 | ||||||||
\(816\) | −16.2495 | −0.568846 | ||||||||
\(817\) | 5.02139 | 0.175676 | ||||||||
\(818\) | −16.2936 | −0.569693 | ||||||||
\(819\) | 29.8428 | 1.04279 | ||||||||
\(820\) | 15.8720 | 0.554273 | ||||||||
\(821\) | 4.01688 | 0.140190 | 0.0700950 | − | 0.997540i | \(-0.477670\pi\) | ||||
0.0700950 | + | 0.997540i | \(0.477670\pi\) | |||||||
\(822\) | 30.7544 | 1.07268 | ||||||||
\(823\) | 16.2283 | 0.565685 | 0.282842 | − | 0.959166i | \(-0.408723\pi\) | ||||
0.282842 | + | 0.959166i | \(0.408723\pi\) | |||||||
\(824\) | −9.90004 | −0.344884 | ||||||||
\(825\) | 28.1560 | 0.980265 | ||||||||
\(826\) | 13.1518 | 0.457610 | ||||||||
\(827\) | 26.6985 | 0.928399 | 0.464199 | − | 0.885731i | \(-0.346342\pi\) | ||||
0.464199 | + | 0.885731i | \(0.346342\pi\) | |||||||
\(828\) | 30.0874 | 1.04561 | ||||||||
\(829\) | 10.3889 | 0.360822 | 0.180411 | − | 0.983591i | \(-0.442257\pi\) | ||||
0.180411 | + | 0.983591i | \(0.442257\pi\) | |||||||
\(830\) | 2.43075 | 0.0843726 | ||||||||
\(831\) | −3.43762 | −0.119250 | ||||||||
\(832\) | 2.26975 | 0.0786893 | ||||||||
\(833\) | 19.6887 | 0.682174 | ||||||||
\(834\) | 52.3289 | 1.81200 | ||||||||
\(835\) | −69.0204 | −2.38855 | ||||||||
\(836\) | −6.48093 | −0.224148 | ||||||||
\(837\) | 8.01756 | 0.277127 | ||||||||
\(838\) | 5.26824 | 0.181988 | ||||||||
\(839\) | −49.2725 | −1.70108 | −0.850538 | − | 0.525913i | \(-0.823724\pi\) | ||||
−0.850538 | + | 0.525913i | \(0.823724\pi\) | |||||||
\(840\) | 30.6875 | 1.05882 | ||||||||
\(841\) | 0.0809489 | 0.00279134 | ||||||||
\(842\) | −3.59050 | −0.123737 | ||||||||
\(843\) | 30.7678 | 1.05970 | ||||||||
\(844\) | −21.3981 | −0.736553 | ||||||||
\(845\) | −28.2374 | −0.971395 | ||||||||
\(846\) | −27.5331 | −0.946609 | ||||||||
\(847\) | −29.5350 | −1.01484 | ||||||||
\(848\) | 6.02243 | 0.206811 | ||||||||
\(849\) | 28.0308 | 0.962015 | ||||||||
\(850\) | −48.4152 | −1.66063 | ||||||||
\(851\) | 15.6528 | 0.536569 | ||||||||
\(852\) | 12.1213 | 0.415268 | ||||||||
\(853\) | −44.4165 | −1.52079 | −0.760397 | − | 0.649459i | \(-0.774995\pi\) | ||||
−0.760397 | + | 0.649459i | \(0.774995\pi\) | |||||||
\(854\) | 14.0129 | 0.479511 | ||||||||
\(855\) | 72.1225 | 2.46654 | ||||||||
\(856\) | 5.86232 | 0.200370 | ||||||||
\(857\) | −9.19397 | −0.314060 | −0.157030 | − | 0.987594i | \(-0.550192\pi\) | ||||
−0.157030 | + | 0.987594i | \(0.550192\pi\) | |||||||
\(858\) | −8.04364 | −0.274605 | ||||||||
\(859\) | 0.626342 | 0.0213705 | 0.0106853 | − | 0.999943i | \(-0.496599\pi\) | ||||
0.0106853 | + | 0.999943i | \(0.496599\pi\) | |||||||
\(860\) | 3.70476 | 0.126331 | ||||||||
\(861\) | −37.6262 | −1.28230 | ||||||||
\(862\) | 1.15129 | 0.0392132 | ||||||||
\(863\) | 5.33294 | 0.181535 | 0.0907677 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907677 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(864\) | 2.96147 | 0.100751 | ||||||||
\(865\) | −28.5776 | −0.971669 | ||||||||
\(866\) | −16.7962 | −0.570758 | ||||||||
\(867\) | −53.6893 | −1.82339 | ||||||||
\(868\) | −8.65950 | −0.293923 | ||||||||
\(869\) | −7.44238 | −0.252466 | ||||||||
\(870\) | −51.7379 | −1.75408 | ||||||||
\(871\) | −15.2782 | −0.517682 | ||||||||
\(872\) | −18.2037 | −0.616455 | ||||||||
\(873\) | 57.4209 | 1.94340 | ||||||||
\(874\) | −35.6940 | −1.20737 | ||||||||
\(875\) | 33.8920 | 1.14576 | ||||||||
\(876\) | −27.3528 | −0.924167 | ||||||||
\(877\) | 33.6104 | 1.13494 | 0.567472 | − | 0.823393i | \(-0.307922\pi\) | ||||
0.567472 | + | 0.823393i | \(0.307922\pi\) | |||||||
\(878\) | 34.9034 | 1.17793 | ||||||||
\(879\) | 47.4861 | 1.60167 | ||||||||
\(880\) | −4.78161 | −0.161188 | ||||||||
\(881\) | 14.0574 | 0.473607 | 0.236803 | − | 0.971558i | \(-0.423900\pi\) | ||||
0.236803 | + | 0.971558i | \(0.423900\pi\) | |||||||
\(882\) | −13.2811 | −0.447198 | ||||||||
\(883\) | 0.648007 | 0.0218072 | 0.0109036 | − | 0.999941i | \(-0.496529\pi\) | ||||
0.0109036 | + | 0.999941i | \(0.496529\pi\) | |||||||
\(884\) | 13.8313 | 0.465199 | ||||||||
\(885\) | 39.4487 | 1.32605 | ||||||||
\(886\) | 0.622830 | 0.0209244 | ||||||||
\(887\) | 45.0985 | 1.51426 | 0.757129 | − | 0.653265i | \(-0.226601\pi\) | ||||
0.757129 | + | 0.653265i | \(0.226601\pi\) | |||||||
\(888\) | 5.70248 | 0.191363 | ||||||||
\(889\) | −36.7808 | −1.23359 | ||||||||
\(890\) | 6.59204 | 0.220966 | ||||||||
\(891\) | 5.89383 | 0.197451 | ||||||||
\(892\) | −23.5596 | −0.788834 | ||||||||
\(893\) | 32.6638 | 1.09305 | ||||||||
\(894\) | 17.4813 | 0.584664 | ||||||||
\(895\) | −79.5512 | −2.65910 | ||||||||
\(896\) | −3.19859 | −0.106857 | ||||||||
\(897\) | −44.3007 | −1.47916 | ||||||||
\(898\) | 1.56565 | 0.0522466 | ||||||||
\(899\) | 14.5995 | 0.486922 | ||||||||
\(900\) | 32.6587 | 1.08862 | ||||||||
\(901\) | 36.6994 | 1.22263 | ||||||||
\(902\) | 5.86276 | 0.195209 | ||||||||
\(903\) | −8.78254 | −0.292265 | ||||||||
\(904\) | −10.4459 | −0.347426 | ||||||||
\(905\) | −47.3978 | −1.57555 | ||||||||
\(906\) | −49.8718 | −1.65688 | ||||||||
\(907\) | 40.0990 | 1.33147 | 0.665733 | − | 0.746190i | \(-0.268119\pi\) | ||||
0.665733 | + | 0.746190i | \(0.268119\pi\) | |||||||
\(908\) | −14.6906 | −0.487526 | ||||||||
\(909\) | 43.9388 | 1.45736 | ||||||||
\(910\) | −26.1208 | −0.865896 | ||||||||
\(911\) | 43.0149 | 1.42515 | 0.712574 | − | 0.701597i | \(-0.247529\pi\) | ||||
0.712574 | + | 0.701597i | \(0.247529\pi\) | |||||||
\(912\) | −13.0037 | −0.430596 | ||||||||
\(913\) | 0.897866 | 0.0297150 | ||||||||
\(914\) | 7.80596 | 0.258198 | ||||||||
\(915\) | 42.0314 | 1.38951 | ||||||||
\(916\) | −14.2127 | −0.469600 | ||||||||
\(917\) | −30.3664 | −1.00279 | ||||||||
\(918\) | 18.0466 | 0.595625 | ||||||||
\(919\) | 29.5540 | 0.974895 | 0.487448 | − | 0.873152i | \(-0.337928\pi\) | ||||
0.487448 | + | 0.873152i | \(0.337928\pi\) | |||||||
\(920\) | −26.3349 | −0.868236 | ||||||||
\(921\) | 55.6669 | 1.83429 | ||||||||
\(922\) | −32.5904 | −1.07331 | ||||||||
\(923\) | −10.3174 | −0.339603 | ||||||||
\(924\) | 11.3353 | 0.372904 | ||||||||
\(925\) | 16.9905 | 0.558643 | ||||||||
\(926\) | −1.65032 | −0.0542330 | ||||||||
\(927\) | 40.6950 | 1.33660 | ||||||||
\(928\) | 5.39268 | 0.177023 | ||||||||
\(929\) | 0.891824 | 0.0292598 | 0.0146299 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146299 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(930\) | −25.9740 | −0.851722 | ||||||||
\(931\) | 15.7560 | 0.516381 | ||||||||
\(932\) | −23.9962 | −0.786020 | ||||||||
\(933\) | −54.6785 | −1.79009 | ||||||||
\(934\) | 21.9615 | 0.718602 | ||||||||
\(935\) | −29.1381 | −0.952917 | ||||||||
\(936\) | −9.33000 | −0.304961 | ||||||||
\(937\) | −23.3613 | −0.763180 | −0.381590 | − | 0.924332i | \(-0.624623\pi\) | ||||
−0.381590 | + | 0.924332i | \(0.624623\pi\) | |||||||
\(938\) | 21.5305 | 0.702994 | ||||||||
\(939\) | 25.6046 | 0.835576 | ||||||||
\(940\) | 24.0992 | 0.786029 | ||||||||
\(941\) | −4.93692 | −0.160939 | −0.0804695 | − | 0.996757i | \(-0.525642\pi\) | ||||
−0.0804695 | + | 0.996757i | \(0.525642\pi\) | |||||||
\(942\) | −44.0273 | −1.43449 | ||||||||
\(943\) | 32.2894 | 1.05149 | ||||||||
\(944\) | −4.11176 | −0.133826 | ||||||||
\(945\) | −34.0813 | −1.10867 | ||||||||
\(946\) | 1.36846 | 0.0444924 | ||||||||
\(947\) | 5.24835 | 0.170549 | 0.0852743 | − | 0.996358i | \(-0.472823\pi\) | ||||
0.0852743 | + | 0.996358i | \(0.472823\pi\) | |||||||
\(948\) | −14.9328 | −0.484996 | ||||||||
\(949\) | 23.2824 | 0.755777 | ||||||||
\(950\) | −38.7445 | −1.25704 | ||||||||
\(951\) | 59.9068 | 1.94261 | ||||||||
\(952\) | −19.4915 | −0.631723 | ||||||||
\(953\) | −6.68845 | −0.216660 | −0.108330 | − | 0.994115i | \(-0.534550\pi\) | ||||
−0.108330 | + | 0.994115i | \(0.534550\pi\) | |||||||
\(954\) | −24.7557 | −0.801496 | ||||||||
\(955\) | 13.2290 | 0.428079 | ||||||||
\(956\) | 24.6830 | 0.798306 | ||||||||
\(957\) | −19.1108 | −0.617766 | ||||||||
\(958\) | 8.67908 | 0.280408 | ||||||||
\(959\) | 36.8903 | 1.19125 | ||||||||
\(960\) | −9.59410 | −0.309648 | ||||||||
\(961\) | −23.6706 | −0.763567 | ||||||||
\(962\) | −4.85387 | −0.156495 | ||||||||
\(963\) | −24.0976 | −0.776535 | ||||||||
\(964\) | 16.5929 | 0.534421 | ||||||||
\(965\) | −24.7371 | −0.796314 | ||||||||
\(966\) | 62.4297 | 2.00864 | ||||||||
\(967\) | −14.3457 | −0.461327 | −0.230663 | − | 0.973034i | \(-0.574090\pi\) | ||||
−0.230663 | + | 0.973034i | \(0.574090\pi\) | |||||||
\(968\) | 9.23378 | 0.296785 | ||||||||
\(969\) | −79.2419 | −2.54562 | ||||||||
\(970\) | −50.2594 | −1.61373 | ||||||||
\(971\) | 47.4118 | 1.52152 | 0.760758 | − | 0.649035i | \(-0.224827\pi\) | ||||
0.760758 | + | 0.649035i | \(0.224827\pi\) | |||||||
\(972\) | 20.7101 | 0.664278 | ||||||||
\(973\) | 62.7692 | 2.01229 | ||||||||
\(974\) | 21.4000 | 0.685701 | ||||||||
\(975\) | −48.0867 | −1.54001 | ||||||||
\(976\) | −4.38096 | −0.140231 | ||||||||
\(977\) | 59.5117 | 1.90395 | 0.951974 | − | 0.306180i | \(-0.0990511\pi\) | ||||
0.951974 | + | 0.306180i | \(0.0990511\pi\) | |||||||
\(978\) | −41.9488 | −1.34138 | ||||||||
\(979\) | 2.43495 | 0.0778215 | ||||||||
\(980\) | 11.6247 | 0.371337 | ||||||||
\(981\) | 74.8280 | 2.38907 | ||||||||
\(982\) | −5.96869 | −0.190469 | ||||||||
\(983\) | 23.1944 | 0.739788 | 0.369894 | − | 0.929074i | \(-0.379394\pi\) | ||||
0.369894 | + | 0.929074i | \(0.379394\pi\) | |||||||
\(984\) | 11.7634 | 0.375003 | ||||||||
\(985\) | 5.76309 | 0.183627 | ||||||||
\(986\) | 32.8618 | 1.04653 | ||||||||
\(987\) | −57.1297 | −1.81846 | ||||||||
\(988\) | 11.0686 | 0.352139 | ||||||||
\(989\) | 7.53684 | 0.239658 | ||||||||
\(990\) | 19.6552 | 0.624684 | ||||||||
\(991\) | −19.6101 | −0.622936 | −0.311468 | − | 0.950257i | \(-0.600821\pi\) | ||||
−0.311468 | + | 0.950257i | \(0.600821\pi\) | |||||||
\(992\) | 2.70729 | 0.0859566 | ||||||||
\(993\) | −32.8373 | −1.04206 | ||||||||
\(994\) | 14.5396 | 0.461169 | ||||||||
\(995\) | 4.24621 | 0.134614 | ||||||||
\(996\) | 1.80153 | 0.0570837 | ||||||||
\(997\) | −13.7603 | −0.435794 | −0.217897 | − | 0.975972i | \(-0.569920\pi\) | ||||
−0.217897 | + | 0.975972i | \(0.569920\pi\) | |||||||
\(998\) | 16.9220 | 0.535655 | ||||||||
\(999\) | −6.33312 | −0.200371 |
(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 | 8014.2.a.e.1.13 | ✓ | 91 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8014.2.a.e.1.13 | ✓ | 91 | 1.1 | even | 1 | trivial |