Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.18756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | 2.18756 | 1.26299 | 0.631493 | − | 0.775382i | \(-0.282442\pi\) | ||||
0.631493 | + | 0.775382i | \(0.282442\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.616139 | −0.275546 | −0.137773 | − | 0.990464i | \(-0.543994\pi\) | ||||
−0.137773 | + | 0.990464i | \(0.543994\pi\) | |||||||
\(6\) | 2.18756 | 0.893066 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.78540 | 0.595133 | ||||||||
\(10\) | −0.616139 | −0.194840 | ||||||||
\(11\) | 3.42998 | 1.03418 | 0.517089 | − | 0.855931i | \(-0.327015\pi\) | ||||
0.517089 | + | 0.855931i | \(0.327015\pi\) | |||||||
\(12\) | 2.18756 | 0.631493 | ||||||||
\(13\) | 6.38112 | 1.76980 | 0.884902 | − | 0.465776i | \(-0.154225\pi\) | ||||
0.884902 | + | 0.465776i | \(0.154225\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.34784 | −0.348010 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.47999 | 0.601486 | 0.300743 | − | 0.953705i | \(-0.402765\pi\) | ||||
0.300743 | + | 0.953705i | \(0.402765\pi\) | |||||||
\(18\) | 1.78540 | 0.420823 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.616139 | −0.137773 | ||||||||
\(21\) | −2.18756 | −0.477364 | ||||||||
\(22\) | 3.42998 | 0.731275 | ||||||||
\(23\) | 2.70527 | 0.564088 | 0.282044 | − | 0.959401i | \(-0.408988\pi\) | ||||
0.282044 | + | 0.959401i | \(0.408988\pi\) | |||||||
\(24\) | 2.18756 | 0.446533 | ||||||||
\(25\) | −4.62037 | −0.924074 | ||||||||
\(26\) | 6.38112 | 1.25144 | ||||||||
\(27\) | −2.65701 | −0.511341 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 6.00017 | 1.11420 | 0.557101 | − | 0.830444i | \(-0.311913\pi\) | ||||
0.557101 | + | 0.830444i | \(0.311913\pi\) | |||||||
\(30\) | −1.34784 | −0.246081 | ||||||||
\(31\) | −7.72644 | −1.38771 | −0.693855 | − | 0.720115i | \(-0.744089\pi\) | ||||
−0.693855 | + | 0.720115i | \(0.744089\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.50328 | 1.30615 | ||||||||
\(34\) | 2.47999 | 0.425315 | ||||||||
\(35\) | 0.616139 | 0.104147 | ||||||||
\(36\) | 1.78540 | 0.297567 | ||||||||
\(37\) | 4.26808 | 0.701669 | 0.350834 | − | 0.936438i | \(-0.385898\pi\) | ||||
0.350834 | + | 0.936438i | \(0.385898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.9591 | 2.23524 | ||||||||
\(40\) | −0.616139 | −0.0974202 | ||||||||
\(41\) | −1.28851 | −0.201232 | −0.100616 | − | 0.994925i | \(-0.532081\pi\) | ||||
−0.100616 | + | 0.994925i | \(0.532081\pi\) | |||||||
\(42\) | −2.18756 | −0.337547 | ||||||||
\(43\) | −10.3584 | −1.57964 | −0.789819 | − | 0.613340i | \(-0.789826\pi\) | ||||
−0.789819 | + | 0.613340i | \(0.789826\pi\) | |||||||
\(44\) | 3.42998 | 0.517089 | ||||||||
\(45\) | −1.10005 | −0.163986 | ||||||||
\(46\) | 2.70527 | 0.398871 | ||||||||
\(47\) | 1.53750 | 0.224267 | 0.112134 | − | 0.993693i | \(-0.464232\pi\) | ||||
0.112134 | + | 0.993693i | \(0.464232\pi\) | |||||||
\(48\) | 2.18756 | 0.315746 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.62037 | −0.653419 | ||||||||
\(51\) | 5.42512 | 0.759669 | ||||||||
\(52\) | 6.38112 | 0.884902 | ||||||||
\(53\) | −5.11208 | −0.702198 | −0.351099 | − | 0.936338i | \(-0.614192\pi\) | ||||
−0.351099 | + | 0.936338i | \(0.614192\pi\) | |||||||
\(54\) | −2.65701 | −0.361573 | ||||||||
\(55\) | −2.11335 | −0.284964 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00017 | 0.787860 | ||||||||
\(59\) | 12.7768 | 1.66339 | 0.831696 | − | 0.555232i | \(-0.187370\pi\) | ||||
0.831696 | + | 0.555232i | \(0.187370\pi\) | |||||||
\(60\) | −1.34784 | −0.174005 | ||||||||
\(61\) | −5.54592 | −0.710082 | −0.355041 | − | 0.934851i | \(-0.615533\pi\) | ||||
−0.355041 | + | 0.934851i | \(0.615533\pi\) | |||||||
\(62\) | −7.72644 | −0.981259 | ||||||||
\(63\) | −1.78540 | −0.224939 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.93166 | −0.487662 | ||||||||
\(66\) | 7.50328 | 0.923590 | ||||||||
\(67\) | 4.16481 | 0.508813 | 0.254406 | − | 0.967097i | \(-0.418120\pi\) | ||||
0.254406 | + | 0.967097i | \(0.418120\pi\) | |||||||
\(68\) | 2.47999 | 0.300743 | ||||||||
\(69\) | 5.91793 | 0.712435 | ||||||||
\(70\) | 0.616139 | 0.0736427 | ||||||||
\(71\) | 0.0244707 | 0.00290414 | 0.00145207 | − | 0.999999i | \(-0.499538\pi\) | ||||
0.00145207 | + | 0.999999i | \(0.499538\pi\) | |||||||
\(72\) | 1.78540 | 0.210411 | ||||||||
\(73\) | 13.0675 | 1.52943 | 0.764715 | − | 0.644368i | \(-0.222880\pi\) | ||||
0.764715 | + | 0.644368i | \(0.222880\pi\) | |||||||
\(74\) | 4.26808 | 0.496155 | ||||||||
\(75\) | −10.1073 | −1.16709 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.42998 | −0.390883 | ||||||||
\(78\) | 13.9591 | 1.58055 | ||||||||
\(79\) | 2.96283 | 0.333344 | 0.166672 | − | 0.986012i | \(-0.446698\pi\) | ||||
0.166672 | + | 0.986012i | \(0.446698\pi\) | |||||||
\(80\) | −0.616139 | −0.0688865 | ||||||||
\(81\) | −11.1685 | −1.24095 | ||||||||
\(82\) | −1.28851 | −0.142292 | ||||||||
\(83\) | 12.9425 | 1.42062 | 0.710312 | − | 0.703887i | \(-0.248554\pi\) | ||||
0.710312 | + | 0.703887i | \(0.248554\pi\) | |||||||
\(84\) | −2.18756 | −0.238682 | ||||||||
\(85\) | −1.52802 | −0.165737 | ||||||||
\(86\) | −10.3584 | −1.11697 | ||||||||
\(87\) | 13.1257 | 1.40722 | ||||||||
\(88\) | 3.42998 | 0.365637 | ||||||||
\(89\) | −12.4510 | −1.31980 | −0.659899 | − | 0.751354i | \(-0.729401\pi\) | ||||
−0.659899 | + | 0.751354i | \(0.729401\pi\) | |||||||
\(90\) | −1.10005 | −0.115956 | ||||||||
\(91\) | −6.38112 | −0.668923 | ||||||||
\(92\) | 2.70527 | 0.282044 | ||||||||
\(93\) | −16.9020 | −1.75266 | ||||||||
\(94\) | 1.53750 | 0.158581 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.18756 | 0.223266 | ||||||||
\(97\) | −1.51714 | −0.154042 | −0.0770211 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770211 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 6.12389 | 0.615474 | ||||||||
\(100\) | −4.62037 | −0.462037 | ||||||||
\(101\) | −9.92823 | −0.987896 | −0.493948 | − | 0.869491i | \(-0.664447\pi\) | ||||
−0.493948 | + | 0.869491i | \(0.664447\pi\) | |||||||
\(102\) | 5.42512 | 0.537167 | ||||||||
\(103\) | 8.34988 | 0.822738 | 0.411369 | − | 0.911469i | \(-0.365051\pi\) | ||||
0.411369 | + | 0.911469i | \(0.365051\pi\) | |||||||
\(104\) | 6.38112 | 0.625720 | ||||||||
\(105\) | 1.34784 | 0.131536 | ||||||||
\(106\) | −5.11208 | −0.496529 | ||||||||
\(107\) | 13.5562 | 1.31053 | 0.655264 | − | 0.755400i | \(-0.272557\pi\) | ||||
0.655264 | + | 0.755400i | \(0.272557\pi\) | |||||||
\(108\) | −2.65701 | −0.255671 | ||||||||
\(109\) | 0.558302 | 0.0534756 | 0.0267378 | − | 0.999642i | \(-0.491488\pi\) | ||||
0.0267378 | + | 0.999642i | \(0.491488\pi\) | |||||||
\(110\) | −2.11335 | −0.201500 | ||||||||
\(111\) | 9.33667 | 0.886197 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.0986 | 0.949999 | 0.474999 | − | 0.879986i | \(-0.342448\pi\) | ||||
0.474999 | + | 0.879986i | \(0.342448\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.66682 | −0.155432 | ||||||||
\(116\) | 6.00017 | 0.557101 | ||||||||
\(117\) | 11.3929 | 1.05327 | ||||||||
\(118\) | 12.7768 | 1.17620 | ||||||||
\(119\) | −2.47999 | −0.227340 | ||||||||
\(120\) | −1.34784 | −0.123040 | ||||||||
\(121\) | 0.764783 | 0.0695257 | ||||||||
\(122\) | −5.54592 | −0.502104 | ||||||||
\(123\) | −2.81869 | −0.254153 | ||||||||
\(124\) | −7.72644 | −0.693855 | ||||||||
\(125\) | 5.92749 | 0.530171 | ||||||||
\(126\) | −1.78540 | −0.159056 | ||||||||
\(127\) | 4.44613 | 0.394530 | 0.197265 | − | 0.980350i | \(-0.436794\pi\) | ||||
0.197265 | + | 0.980350i | \(0.436794\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −22.6595 | −1.99506 | ||||||||
\(130\) | −3.93166 | −0.344829 | ||||||||
\(131\) | 7.17183 | 0.626606 | 0.313303 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313303 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(132\) | 7.50328 | 0.653077 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.16481 | 0.359785 | ||||||||
\(135\) | 1.63709 | 0.140898 | ||||||||
\(136\) | 2.47999 | 0.212658 | ||||||||
\(137\) | −16.8073 | −1.43594 | −0.717971 | − | 0.696073i | \(-0.754929\pi\) | ||||
−0.717971 | + | 0.696073i | \(0.754929\pi\) | |||||||
\(138\) | 5.91793 | 0.503768 | ||||||||
\(139\) | −13.5566 | −1.14986 | −0.574929 | − | 0.818203i | \(-0.694970\pi\) | ||||
−0.574929 | + | 0.818203i | \(0.694970\pi\) | |||||||
\(140\) | 0.616139 | 0.0520733 | ||||||||
\(141\) | 3.36336 | 0.283246 | ||||||||
\(142\) | 0.0244707 | 0.00205353 | ||||||||
\(143\) | 21.8871 | 1.83029 | ||||||||
\(144\) | 1.78540 | 0.148783 | ||||||||
\(145\) | −3.69694 | −0.307014 | ||||||||
\(146\) | 13.0675 | 1.08147 | ||||||||
\(147\) | 2.18756 | 0.180427 | ||||||||
\(148\) | 4.26808 | 0.350834 | ||||||||
\(149\) | 13.5990 | 1.11408 | 0.557038 | − | 0.830487i | \(-0.311938\pi\) | ||||
0.557038 | + | 0.830487i | \(0.311938\pi\) | |||||||
\(150\) | −10.1073 | −0.825259 | ||||||||
\(151\) | −20.2325 | −1.64650 | −0.823250 | − | 0.567679i | \(-0.807841\pi\) | ||||
−0.823250 | + | 0.567679i | \(0.807841\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.42778 | 0.357964 | ||||||||
\(154\) | −3.42998 | −0.276396 | ||||||||
\(155\) | 4.76056 | 0.382378 | ||||||||
\(156\) | 13.9591 | 1.11762 | ||||||||
\(157\) | −11.1097 | −0.886648 | −0.443324 | − | 0.896361i | \(-0.646201\pi\) | ||||
−0.443324 | + | 0.896361i | \(0.646201\pi\) | |||||||
\(158\) | 2.96283 | 0.235710 | ||||||||
\(159\) | −11.1830 | −0.886866 | ||||||||
\(160\) | −0.616139 | −0.0487101 | ||||||||
\(161\) | −2.70527 | −0.213205 | ||||||||
\(162\) | −11.1685 | −0.877484 | ||||||||
\(163\) | −10.2803 | −0.805215 | −0.402608 | − | 0.915373i | \(-0.631896\pi\) | ||||
−0.402608 | + | 0.915373i | \(0.631896\pi\) | |||||||
\(164\) | −1.28851 | −0.100616 | ||||||||
\(165\) | −4.62306 | −0.359905 | ||||||||
\(166\) | 12.9425 | 1.00453 | ||||||||
\(167\) | −12.6748 | −0.980806 | −0.490403 | − | 0.871496i | \(-0.663150\pi\) | ||||
−0.490403 | + | 0.871496i | \(0.663150\pi\) | |||||||
\(168\) | −2.18756 | −0.168774 | ||||||||
\(169\) | 27.7187 | 2.13221 | ||||||||
\(170\) | −1.52802 | −0.117194 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.3584 | −0.789819 | ||||||||
\(173\) | 6.24437 | 0.474751 | 0.237376 | − | 0.971418i | \(-0.423713\pi\) | ||||
0.237376 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(174\) | 13.1257 | 0.995057 | ||||||||
\(175\) | 4.62037 | 0.349267 | ||||||||
\(176\) | 3.42998 | 0.258545 | ||||||||
\(177\) | 27.9499 | 2.10084 | ||||||||
\(178\) | −12.4510 | −0.933238 | ||||||||
\(179\) | 17.7976 | 1.33026 | 0.665128 | − | 0.746729i | \(-0.268377\pi\) | ||||
0.665128 | + | 0.746729i | \(0.268377\pi\) | |||||||
\(180\) | −1.10005 | −0.0819932 | ||||||||
\(181\) | −5.92757 | −0.440593 | −0.220296 | − | 0.975433i | \(-0.570702\pi\) | ||||
−0.220296 | + | 0.975433i | \(0.570702\pi\) | |||||||
\(182\) | −6.38112 | −0.473000 | ||||||||
\(183\) | −12.1320 | −0.896823 | ||||||||
\(184\) | 2.70527 | 0.199435 | ||||||||
\(185\) | −2.62973 | −0.193342 | ||||||||
\(186\) | −16.9020 | −1.23932 | ||||||||
\(187\) | 8.50633 | 0.622044 | ||||||||
\(188\) | 1.53750 | 0.112134 | ||||||||
\(189\) | 2.65701 | 0.193269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3567 | 1.18353 | 0.591764 | − | 0.806111i | \(-0.298432\pi\) | ||||
0.591764 | + | 0.806111i | \(0.298432\pi\) | |||||||
\(192\) | 2.18756 | 0.157873 | ||||||||
\(193\) | 19.9885 | 1.43881 | 0.719403 | − | 0.694593i | \(-0.244416\pi\) | ||||
0.719403 | + | 0.694593i | \(0.244416\pi\) | |||||||
\(194\) | −1.51714 | −0.108924 | ||||||||
\(195\) | −8.60072 | −0.615911 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.44430 | −0.245396 | −0.122698 | − | 0.992444i | \(-0.539155\pi\) | ||||
−0.122698 | + | 0.992444i | \(0.539155\pi\) | |||||||
\(198\) | 6.12389 | 0.435206 | ||||||||
\(199\) | 3.13027 | 0.221899 | 0.110949 | − | 0.993826i | \(-0.464611\pi\) | ||||
0.110949 | + | 0.993826i | \(0.464611\pi\) | |||||||
\(200\) | −4.62037 | −0.326710 | ||||||||
\(201\) | 9.11076 | 0.642623 | ||||||||
\(202\) | −9.92823 | −0.698548 | ||||||||
\(203\) | −6.00017 | −0.421129 | ||||||||
\(204\) | 5.42512 | 0.379834 | ||||||||
\(205\) | 0.793902 | 0.0554485 | ||||||||
\(206\) | 8.34988 | 0.581764 | ||||||||
\(207\) | 4.82999 | 0.335708 | ||||||||
\(208\) | 6.38112 | 0.442451 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.34784 | 0.0930097 | ||||||||
\(211\) | −16.6987 | −1.14959 | −0.574793 | − | 0.818299i | \(-0.694917\pi\) | ||||
−0.574793 | + | 0.818299i | \(0.694917\pi\) | |||||||
\(212\) | −5.11208 | −0.351099 | ||||||||
\(213\) | 0.0535310 | 0.00366788 | ||||||||
\(214\) | 13.5562 | 0.926684 | ||||||||
\(215\) | 6.38221 | 0.435263 | ||||||||
\(216\) | −2.65701 | −0.180786 | ||||||||
\(217\) | 7.72644 | 0.524505 | ||||||||
\(218\) | 0.558302 | 0.0378130 | ||||||||
\(219\) | 28.5858 | 1.93165 | ||||||||
\(220\) | −2.11335 | −0.142482 | ||||||||
\(221\) | 15.8251 | 1.06451 | ||||||||
\(222\) | 9.33667 | 0.626636 | ||||||||
\(223\) | 14.5844 | 0.976641 | 0.488320 | − | 0.872664i | \(-0.337610\pi\) | ||||
0.488320 | + | 0.872664i | \(0.337610\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −8.24921 | −0.549947 | ||||||||
\(226\) | 10.0986 | 0.671750 | ||||||||
\(227\) | −4.73333 | −0.314162 | −0.157081 | − | 0.987586i | \(-0.550208\pi\) | ||||
−0.157081 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8611 | 0.982051 | 0.491026 | − | 0.871145i | \(-0.336622\pi\) | ||||
0.491026 | + | 0.871145i | \(0.336622\pi\) | |||||||
\(230\) | −1.66682 | −0.109907 | ||||||||
\(231\) | −7.50328 | −0.493679 | ||||||||
\(232\) | 6.00017 | 0.393930 | ||||||||
\(233\) | −4.36751 | −0.286125 | −0.143062 | − | 0.989714i | \(-0.545695\pi\) | ||||
−0.143062 | + | 0.989714i | \(0.545695\pi\) | |||||||
\(234\) | 11.3929 | 0.744774 | ||||||||
\(235\) | −0.947313 | −0.0617959 | ||||||||
\(236\) | 12.7768 | 0.831696 | ||||||||
\(237\) | 6.48135 | 0.421009 | ||||||||
\(238\) | −2.47999 | −0.160754 | ||||||||
\(239\) | −24.2217 | −1.56677 | −0.783385 | − | 0.621537i | \(-0.786509\pi\) | ||||
−0.783385 | + | 0.621537i | \(0.786509\pi\) | |||||||
\(240\) | −1.34784 | −0.0870026 | ||||||||
\(241\) | −17.1009 | −1.10157 | −0.550784 | − | 0.834648i | \(-0.685671\pi\) | ||||
−0.550784 | + | 0.834648i | \(0.685671\pi\) | |||||||
\(242\) | 0.764783 | 0.0491621 | ||||||||
\(243\) | −16.4608 | −1.05596 | ||||||||
\(244\) | −5.54592 | −0.355041 | ||||||||
\(245\) | −0.616139 | −0.0393637 | ||||||||
\(246\) | −2.81869 | −0.179713 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.72644 | −0.490629 | ||||||||
\(249\) | 28.3125 | 1.79423 | ||||||||
\(250\) | 5.92749 | 0.374887 | ||||||||
\(251\) | 27.3096 | 1.72377 | 0.861883 | − | 0.507107i | \(-0.169285\pi\) | ||||
0.861883 | + | 0.507107i | \(0.169285\pi\) | |||||||
\(252\) | −1.78540 | −0.112470 | ||||||||
\(253\) | 9.27904 | 0.583368 | ||||||||
\(254\) | 4.44613 | 0.278975 | ||||||||
\(255\) | −3.34263 | −0.209324 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.96817 | −0.621797 | −0.310899 | − | 0.950443i | \(-0.600630\pi\) | ||||
−0.310899 | + | 0.950443i | \(0.600630\pi\) | |||||||
\(258\) | −22.6595 | −1.41072 | ||||||||
\(259\) | −4.26808 | −0.265206 | ||||||||
\(260\) | −3.93166 | −0.243831 | ||||||||
\(261\) | 10.7127 | 0.663099 | ||||||||
\(262\) | 7.17183 | 0.443077 | ||||||||
\(263\) | −24.9314 | −1.53734 | −0.768669 | − | 0.639647i | \(-0.779080\pi\) | ||||
−0.768669 | + | 0.639647i | \(0.779080\pi\) | |||||||
\(264\) | 7.50328 | 0.461795 | ||||||||
\(265\) | 3.14975 | 0.193488 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.2371 | −1.66689 | ||||||||
\(268\) | 4.16481 | 0.254406 | ||||||||
\(269\) | −25.6665 | −1.56491 | −0.782456 | − | 0.622706i | \(-0.786033\pi\) | ||||
−0.782456 | + | 0.622706i | \(0.786033\pi\) | |||||||
\(270\) | 1.63709 | 0.0996299 | ||||||||
\(271\) | 18.7964 | 1.14180 | 0.570900 | − | 0.821020i | \(-0.306595\pi\) | ||||
0.570900 | + | 0.821020i | \(0.306595\pi\) | |||||||
\(272\) | 2.47999 | 0.150372 | ||||||||
\(273\) | −13.9591 | −0.844841 | ||||||||
\(274\) | −16.8073 | −1.01536 | ||||||||
\(275\) | −15.8478 | −0.955658 | ||||||||
\(276\) | 5.91793 | 0.356218 | ||||||||
\(277\) | 19.8745 | 1.19414 | 0.597071 | − | 0.802188i | \(-0.296331\pi\) | ||||
0.597071 | + | 0.802188i | \(0.296331\pi\) | |||||||
\(278\) | −13.5566 | −0.813073 | ||||||||
\(279\) | −13.7948 | −0.825872 | ||||||||
\(280\) | 0.616139 | 0.0368214 | ||||||||
\(281\) | −21.2943 | −1.27031 | −0.635156 | − | 0.772384i | \(-0.719064\pi\) | ||||
−0.635156 | + | 0.772384i | \(0.719064\pi\) | |||||||
\(282\) | 3.36336 | 0.200285 | ||||||||
\(283\) | −3.77466 | −0.224380 | −0.112190 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112190 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(284\) | 0.0244707 | 0.00145207 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.8871 | 1.29421 | ||||||||
\(287\) | 1.28851 | 0.0760584 | ||||||||
\(288\) | 1.78540 | 0.105206 | ||||||||
\(289\) | −10.8496 | −0.638214 | ||||||||
\(290\) | −3.69694 | −0.217092 | ||||||||
\(291\) | −3.31883 | −0.194553 | ||||||||
\(292\) | 13.0675 | 0.764715 | ||||||||
\(293\) | −16.9584 | −0.990721 | −0.495360 | − | 0.868688i | \(-0.664964\pi\) | ||||
−0.495360 | + | 0.868688i | \(0.664964\pi\) | |||||||
\(294\) | 2.18756 | 0.127581 | ||||||||
\(295\) | −7.87226 | −0.458341 | ||||||||
\(296\) | 4.26808 | 0.248077 | ||||||||
\(297\) | −9.11349 | −0.528818 | ||||||||
\(298\) | 13.5990 | 0.787770 | ||||||||
\(299\) | 17.2627 | 0.998326 | ||||||||
\(300\) | −10.1073 | −0.583546 | ||||||||
\(301\) | 10.3584 | 0.597047 | ||||||||
\(302\) | −20.2325 | −1.16425 | ||||||||
\(303\) | −21.7186 | −1.24770 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.41706 | 0.195660 | ||||||||
\(306\) | 4.42778 | 0.253119 | ||||||||
\(307\) | −2.68585 | −0.153289 | −0.0766447 | − | 0.997058i | \(-0.524421\pi\) | ||||
−0.0766447 | + | 0.997058i | \(0.524421\pi\) | |||||||
\(308\) | −3.42998 | −0.195441 | ||||||||
\(309\) | 18.2658 | 1.03911 | ||||||||
\(310\) | 4.76056 | 0.270382 | ||||||||
\(311\) | 1.77079 | 0.100412 | 0.0502062 | − | 0.998739i | \(-0.484012\pi\) | ||||
0.0502062 | + | 0.998739i | \(0.484012\pi\) | |||||||
\(312\) | 13.9591 | 0.790276 | ||||||||
\(313\) | 7.89729 | 0.446381 | 0.223191 | − | 0.974775i | \(-0.428353\pi\) | ||||
0.223191 | + | 0.974775i | \(0.428353\pi\) | |||||||
\(314\) | −11.1097 | −0.626955 | ||||||||
\(315\) | 1.10005 | 0.0619811 | ||||||||
\(316\) | 2.96283 | 0.166672 | ||||||||
\(317\) | −11.6202 | −0.652656 | −0.326328 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326328 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(318\) | −11.1830 | −0.627109 | ||||||||
\(319\) | 20.5805 | 1.15229 | ||||||||
\(320\) | −0.616139 | −0.0344432 | ||||||||
\(321\) | 29.6550 | 1.65518 | ||||||||
\(322\) | −2.70527 | −0.150759 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.1685 | −0.620475 | ||||||||
\(325\) | −29.4832 | −1.63543 | ||||||||
\(326\) | −10.2803 | −0.569373 | ||||||||
\(327\) | 1.22132 | 0.0675389 | ||||||||
\(328\) | −1.28851 | −0.0711461 | ||||||||
\(329\) | −1.53750 | −0.0847650 | ||||||||
\(330\) | −4.62306 | −0.254491 | ||||||||
\(331\) | −1.15352 | −0.0634032 | −0.0317016 | − | 0.999497i | \(-0.510093\pi\) | ||||
−0.0317016 | + | 0.999497i | \(0.510093\pi\) | |||||||
\(332\) | 12.9425 | 0.710312 | ||||||||
\(333\) | 7.62023 | 0.417586 | ||||||||
\(334\) | −12.6748 | −0.693534 | ||||||||
\(335\) | −2.56610 | −0.140201 | ||||||||
\(336\) | −2.18756 | −0.119341 | ||||||||
\(337\) | −7.31544 | −0.398497 | −0.199249 | − | 0.979949i | \(-0.563850\pi\) | ||||
−0.199249 | + | 0.979949i | \(0.563850\pi\) | |||||||
\(338\) | 27.7187 | 1.50770 | ||||||||
\(339\) | 22.0913 | 1.19983 | ||||||||
\(340\) | −1.52802 | −0.0828685 | ||||||||
\(341\) | −26.5016 | −1.43514 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.3584 | −0.558486 | ||||||||
\(345\) | −3.64627 | −0.196309 | ||||||||
\(346\) | 6.24437 | 0.335700 | ||||||||
\(347\) | −31.3704 | −1.68405 | −0.842025 | − | 0.539439i | \(-0.818636\pi\) | ||||
−0.842025 | + | 0.539439i | \(0.818636\pi\) | |||||||
\(348\) | 13.1257 | 0.703611 | ||||||||
\(349\) | −2.33966 | −0.125239 | −0.0626197 | − | 0.998037i | \(-0.519946\pi\) | ||||
−0.0626197 | + | 0.998037i | \(0.519946\pi\) | |||||||
\(350\) | 4.62037 | 0.246969 | ||||||||
\(351\) | −16.9547 | −0.904974 | ||||||||
\(352\) | 3.42998 | 0.182819 | ||||||||
\(353\) | −6.64960 | −0.353923 | −0.176961 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176961 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(354\) | 27.9499 | 1.48552 | ||||||||
\(355\) | −0.0150774 | −0.000800223 0 | ||||||||
\(356\) | −12.4510 | −0.659899 | ||||||||
\(357\) | −5.42512 | −0.287128 | ||||||||
\(358\) | 17.7976 | 0.940633 | ||||||||
\(359\) | 23.2605 | 1.22764 | 0.613821 | − | 0.789445i | \(-0.289631\pi\) | ||||
0.613821 | + | 0.789445i | \(0.289631\pi\) | |||||||
\(360\) | −1.10005 | −0.0579780 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.92757 | −0.311546 | ||||||||
\(363\) | 1.67301 | 0.0878100 | ||||||||
\(364\) | −6.38112 | −0.334462 | ||||||||
\(365\) | −8.05138 | −0.421428 | ||||||||
\(366\) | −12.1320 | −0.634150 | ||||||||
\(367\) | 10.6463 | 0.555733 | 0.277866 | − | 0.960620i | \(-0.410373\pi\) | ||||
0.277866 | + | 0.960620i | \(0.410373\pi\) | |||||||
\(368\) | 2.70527 | 0.141022 | ||||||||
\(369\) | −2.30051 | −0.119760 | ||||||||
\(370\) | −2.62973 | −0.136713 | ||||||||
\(371\) | 5.11208 | 0.265406 | ||||||||
\(372\) | −16.9020 | −0.876329 | ||||||||
\(373\) | −28.8794 | −1.49532 | −0.747659 | − | 0.664083i | \(-0.768822\pi\) | ||||
−0.747659 | + | 0.664083i | \(0.768822\pi\) | |||||||
\(374\) | 8.50633 | 0.439852 | ||||||||
\(375\) | 12.9667 | 0.669598 | ||||||||
\(376\) | 1.53750 | 0.0792904 | ||||||||
\(377\) | 38.2878 | 1.97192 | ||||||||
\(378\) | 2.65701 | 0.136662 | ||||||||
\(379\) | −33.1311 | −1.70183 | −0.850916 | − | 0.525302i | \(-0.823952\pi\) | ||||
−0.850916 | + | 0.525302i | \(0.823952\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.72616 | 0.498286 | ||||||||
\(382\) | 16.3567 | 0.836880 | ||||||||
\(383\) | −3.65421 | −0.186722 | −0.0933608 | − | 0.995632i | \(-0.529761\pi\) | ||||
−0.0933608 | + | 0.995632i | \(0.529761\pi\) | |||||||
\(384\) | 2.18756 | 0.111633 | ||||||||
\(385\) | 2.11335 | 0.107706 | ||||||||
\(386\) | 19.9885 | 1.01739 | ||||||||
\(387\) | −18.4938 | −0.940095 | ||||||||
\(388\) | −1.51714 | −0.0770211 | ||||||||
\(389\) | −9.25078 | −0.469033 | −0.234517 | − | 0.972112i | \(-0.575351\pi\) | ||||
−0.234517 | + | 0.972112i | \(0.575351\pi\) | |||||||
\(390\) | −8.60072 | −0.435515 | ||||||||
\(391\) | 6.70905 | 0.339291 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 15.6888 | 0.791395 | ||||||||
\(394\) | −3.44430 | −0.173521 | ||||||||
\(395\) | −1.82552 | −0.0918517 | ||||||||
\(396\) | 6.12389 | 0.307737 | ||||||||
\(397\) | 19.2309 | 0.965172 | 0.482586 | − | 0.875849i | \(-0.339698\pi\) | ||||
0.482586 | + | 0.875849i | \(0.339698\pi\) | |||||||
\(398\) | 3.13027 | 0.156906 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.62037 | −0.231019 | ||||||||
\(401\) | −29.5430 | −1.47531 | −0.737654 | − | 0.675179i | \(-0.764067\pi\) | ||||
−0.737654 | + | 0.675179i | \(0.764067\pi\) | |||||||
\(402\) | 9.11076 | 0.454403 | ||||||||
\(403\) | −49.3034 | −2.45597 | ||||||||
\(404\) | −9.92823 | −0.493948 | ||||||||
\(405\) | 6.88138 | 0.341939 | ||||||||
\(406\) | −6.00017 | −0.297783 | ||||||||
\(407\) | 14.6395 | 0.725651 | ||||||||
\(408\) | 5.42512 | 0.268583 | ||||||||
\(409\) | −39.8965 | −1.97276 | −0.986378 | − | 0.164494i | \(-0.947401\pi\) | ||||
−0.986378 | + | 0.164494i | \(0.947401\pi\) | |||||||
\(410\) | 0.793902 | 0.0392080 | ||||||||
\(411\) | −36.7668 | −1.81357 | ||||||||
\(412\) | 8.34988 | 0.411369 | ||||||||
\(413\) | −12.7768 | −0.628703 | ||||||||
\(414\) | 4.82999 | 0.237381 | ||||||||
\(415\) | −7.97439 | −0.391447 | ||||||||
\(416\) | 6.38112 | 0.312860 | ||||||||
\(417\) | −29.6559 | −1.45225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.5562 | −1.68818 | −0.844090 | − | 0.536201i | \(-0.819859\pi\) | ||||
−0.844090 | + | 0.536201i | \(0.819859\pi\) | |||||||
\(420\) | 1.34784 | 0.0657678 | ||||||||
\(421\) | −28.8651 | −1.40680 | −0.703399 | − | 0.710795i | \(-0.748335\pi\) | ||||
−0.703399 | + | 0.710795i | \(0.748335\pi\) | |||||||
\(422\) | −16.6987 | −0.812880 | ||||||||
\(423\) | 2.74505 | 0.133469 | ||||||||
\(424\) | −5.11208 | −0.248265 | ||||||||
\(425\) | −11.4585 | −0.555818 | ||||||||
\(426\) | 0.0535310 | 0.00259358 | ||||||||
\(427\) | 5.54592 | 0.268386 | ||||||||
\(428\) | 13.5562 | 0.655264 | ||||||||
\(429\) | 47.8793 | 2.31164 | ||||||||
\(430\) | 6.38221 | 0.307777 | ||||||||
\(431\) | −19.4879 | −0.938699 | −0.469350 | − | 0.883012i | \(-0.655512\pi\) | ||||
−0.469350 | + | 0.883012i | \(0.655512\pi\) | |||||||
\(432\) | −2.65701 | −0.127835 | ||||||||
\(433\) | −1.44225 | −0.0693102 | −0.0346551 | − | 0.999399i | \(-0.511033\pi\) | ||||
−0.0346551 | + | 0.999399i | \(0.511033\pi\) | |||||||
\(434\) | 7.72644 | 0.370881 | ||||||||
\(435\) | −8.08726 | −0.387754 | ||||||||
\(436\) | 0.558302 | 0.0267378 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 28.5858 | 1.36588 | ||||||||
\(439\) | 16.5525 | 0.790006 | 0.395003 | − | 0.918680i | \(-0.370744\pi\) | ||||
0.395003 | + | 0.918680i | \(0.370744\pi\) | |||||||
\(440\) | −2.11335 | −0.100750 | ||||||||
\(441\) | 1.78540 | 0.0850190 | ||||||||
\(442\) | 15.8251 | 0.752725 | ||||||||
\(443\) | 3.08768 | 0.146700 | 0.0733500 | − | 0.997306i | \(-0.476631\pi\) | ||||
0.0733500 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(444\) | 9.33667 | 0.443099 | ||||||||
\(445\) | 7.67152 | 0.363665 | ||||||||
\(446\) | 14.5844 | 0.690589 | ||||||||
\(447\) | 29.7486 | 1.40706 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −17.9081 | −0.845135 | −0.422568 | − | 0.906331i | \(-0.638871\pi\) | ||||
−0.422568 | + | 0.906331i | \(0.638871\pi\) | |||||||
\(450\) | −8.24921 | −0.388871 | ||||||||
\(451\) | −4.41957 | −0.208109 | ||||||||
\(452\) | 10.0986 | 0.474999 | ||||||||
\(453\) | −44.2598 | −2.07951 | ||||||||
\(454\) | −4.73333 | −0.222146 | ||||||||
\(455\) | 3.93166 | 0.184319 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.2954 | 1.46394 | 0.731970 | − | 0.681337i | \(-0.238601\pi\) | ||||
0.731970 | + | 0.681337i | \(0.238601\pi\) | |||||||
\(458\) | 14.8611 | 0.694415 | ||||||||
\(459\) | −6.58936 | −0.307565 | ||||||||
\(460\) | −1.66682 | −0.0777161 | ||||||||
\(461\) | −11.6085 | −0.540660 | −0.270330 | − | 0.962768i | \(-0.587133\pi\) | ||||
−0.270330 | + | 0.962768i | \(0.587133\pi\) | |||||||
\(462\) | −7.50328 | −0.349084 | ||||||||
\(463\) | 4.15132 | 0.192928 | 0.0964640 | − | 0.995336i | \(-0.469247\pi\) | ||||
0.0964640 | + | 0.995336i | \(0.469247\pi\) | |||||||
\(464\) | 6.00017 | 0.278551 | ||||||||
\(465\) | 10.4140 | 0.482937 | ||||||||
\(466\) | −4.36751 | −0.202321 | ||||||||
\(467\) | −24.9196 | −1.15314 | −0.576570 | − | 0.817047i | \(-0.695609\pi\) | ||||
−0.576570 | + | 0.817047i | \(0.695609\pi\) | |||||||
\(468\) | 11.3929 | 0.526635 | ||||||||
\(469\) | −4.16481 | −0.192313 | ||||||||
\(470\) | −0.947313 | −0.0436963 | ||||||||
\(471\) | −24.3030 | −1.11982 | ||||||||
\(472\) | 12.7768 | 0.588098 | ||||||||
\(473\) | −35.5291 | −1.63363 | ||||||||
\(474\) | 6.48135 | 0.297698 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.47999 | −0.113670 | ||||||||
\(477\) | −9.12710 | −0.417901 | ||||||||
\(478\) | −24.2217 | −1.10787 | ||||||||
\(479\) | −18.9778 | −0.867117 | −0.433559 | − | 0.901125i | \(-0.642742\pi\) | ||||
−0.433559 | + | 0.901125i | \(0.642742\pi\) | |||||||
\(480\) | −1.34784 | −0.0615201 | ||||||||
\(481\) | 27.2352 | 1.24182 | ||||||||
\(482\) | −17.1009 | −0.778926 | ||||||||
\(483\) | −5.91793 | −0.269275 | ||||||||
\(484\) | 0.764783 | 0.0347629 | ||||||||
\(485\) | 0.934769 | 0.0424457 | ||||||||
\(486\) | −16.4608 | −0.746677 | ||||||||
\(487\) | 36.1508 | 1.63815 | 0.819074 | − | 0.573687i | \(-0.194488\pi\) | ||||
0.819074 | + | 0.573687i | \(0.194488\pi\) | |||||||
\(488\) | −5.54592 | −0.251052 | ||||||||
\(489\) | −22.4887 | −1.01698 | ||||||||
\(490\) | −0.616139 | −0.0278343 | ||||||||
\(491\) | 3.08754 | 0.139339 | 0.0696693 | − | 0.997570i | \(-0.477806\pi\) | ||||
0.0696693 | + | 0.997570i | \(0.477806\pi\) | |||||||
\(492\) | −2.81869 | −0.127076 | ||||||||
\(493\) | 14.8804 | 0.670178 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.77317 | −0.169591 | ||||||||
\(496\) | −7.72644 | −0.346927 | ||||||||
\(497\) | −0.0244707 | −0.00109766 | ||||||||
\(498\) | 28.3125 | 1.26871 | ||||||||
\(499\) | 30.9593 | 1.38593 | 0.692964 | − | 0.720972i | \(-0.256304\pi\) | ||||
0.692964 | + | 0.720972i | \(0.256304\pi\) | |||||||
\(500\) | 5.92749 | 0.265085 | ||||||||
\(501\) | −27.7268 | −1.23874 | ||||||||
\(502\) | 27.3096 | 1.21889 | ||||||||
\(503\) | 3.79268 | 0.169107 | 0.0845536 | − | 0.996419i | \(-0.473054\pi\) | ||||
0.0845536 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(504\) | −1.78540 | −0.0795280 | ||||||||
\(505\) | 6.11717 | 0.272211 | ||||||||
\(506\) | 9.27904 | 0.412504 | ||||||||
\(507\) | 60.6362 | 2.69295 | ||||||||
\(508\) | 4.44613 | 0.197265 | ||||||||
\(509\) | 36.0268 | 1.59686 | 0.798430 | − | 0.602087i | \(-0.205664\pi\) | ||||
0.798430 | + | 0.602087i | \(0.205664\pi\) | |||||||
\(510\) | −3.34263 | −0.148014 | ||||||||
\(511\) | −13.0675 | −0.578071 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.96817 | −0.439677 | ||||||||
\(515\) | −5.14469 | −0.226702 | ||||||||
\(516\) | −22.6595 | −0.997530 | ||||||||
\(517\) | 5.27359 | 0.231932 | ||||||||
\(518\) | −4.26808 | −0.187529 | ||||||||
\(519\) | 13.6599 | 0.599604 | ||||||||
\(520\) | −3.93166 | −0.172415 | ||||||||
\(521\) | 7.91028 | 0.346555 | 0.173278 | − | 0.984873i | \(-0.444564\pi\) | ||||
0.173278 | + | 0.984873i | \(0.444564\pi\) | |||||||
\(522\) | 10.7127 | 0.468882 | ||||||||
\(523\) | −33.0876 | −1.44682 | −0.723409 | − | 0.690420i | \(-0.757426\pi\) | ||||
−0.723409 | + | 0.690420i | \(0.757426\pi\) | |||||||
\(524\) | 7.17183 | 0.313303 | ||||||||
\(525\) | 10.1073 | 0.441120 | ||||||||
\(526\) | −24.9314 | −1.08706 | ||||||||
\(527\) | −19.1615 | −0.834688 | ||||||||
\(528\) | 7.50328 | 0.326538 | ||||||||
\(529\) | −15.6815 | −0.681804 | ||||||||
\(530\) | 3.14975 | 0.136817 | ||||||||
\(531\) | 22.8116 | 0.989939 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.22215 | −0.356141 | ||||||||
\(534\) | −27.2371 | −1.17867 | ||||||||
\(535\) | −8.35251 | −0.361111 | ||||||||
\(536\) | 4.16481 | 0.179892 | ||||||||
\(537\) | 38.9333 | 1.68009 | ||||||||
\(538\) | −25.6665 | −1.10656 | ||||||||
\(539\) | 3.42998 | 0.147740 | ||||||||
\(540\) | 1.63709 | 0.0704490 | ||||||||
\(541\) | 9.32192 | 0.400781 | 0.200390 | − | 0.979716i | \(-0.435779\pi\) | ||||
0.200390 | + | 0.979716i | \(0.435779\pi\) | |||||||
\(542\) | 18.7964 | 0.807374 | ||||||||
\(543\) | −12.9669 | −0.556462 | ||||||||
\(544\) | 2.47999 | 0.106329 | ||||||||
\(545\) | −0.343992 | −0.0147350 | ||||||||
\(546\) | −13.9591 | −0.597393 | ||||||||
\(547\) | −27.3456 | −1.16921 | −0.584607 | − | 0.811317i | \(-0.698751\pi\) | ||||
−0.584607 | + | 0.811317i | \(0.698751\pi\) | |||||||
\(548\) | −16.8073 | −0.717971 | ||||||||
\(549\) | −9.90167 | −0.422593 | ||||||||
\(550\) | −15.8478 | −0.675752 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.91793 | 0.251884 | ||||||||
\(553\) | −2.96283 | −0.125992 | ||||||||
\(554\) | 19.8745 | 0.844386 | ||||||||
\(555\) | −5.75269 | −0.244188 | ||||||||
\(556\) | −13.5566 | −0.574929 | ||||||||
\(557\) | −16.4963 | −0.698970 | −0.349485 | − | 0.936942i | \(-0.613643\pi\) | ||||
−0.349485 | + | 0.936942i | \(0.613643\pi\) | |||||||
\(558\) | −13.7948 | −0.583980 | ||||||||
\(559\) | −66.0981 | −2.79565 | ||||||||
\(560\) | 0.616139 | 0.0260366 | ||||||||
\(561\) | 18.6081 | 0.785633 | ||||||||
\(562\) | −21.2943 | −0.898246 | ||||||||
\(563\) | −35.4681 | −1.49480 | −0.747401 | − | 0.664373i | \(-0.768699\pi\) | ||||
−0.747401 | + | 0.664373i | \(0.768699\pi\) | |||||||
\(564\) | 3.36336 | 0.141623 | ||||||||
\(565\) | −6.22216 | −0.261768 | ||||||||
\(566\) | −3.77466 | −0.158661 | ||||||||
\(567\) | 11.1685 | 0.469035 | ||||||||
\(568\) | 0.0244707 | 0.00102677 | ||||||||
\(569\) | −43.3131 | −1.81578 | −0.907889 | − | 0.419210i | \(-0.862307\pi\) | ||||
−0.907889 | + | 0.419210i | \(0.862307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.18471 | 0.0495787 | 0.0247893 | − | 0.999693i | \(-0.492108\pi\) | ||||
0.0247893 | + | 0.999693i | \(0.492108\pi\) | |||||||
\(572\) | 21.8871 | 0.915147 | ||||||||
\(573\) | 35.7811 | 1.49478 | ||||||||
\(574\) | 1.28851 | 0.0537814 | ||||||||
\(575\) | −12.4994 | −0.521260 | ||||||||
\(576\) | 1.78540 | 0.0743916 | ||||||||
\(577\) | 12.9555 | 0.539343 | 0.269671 | − | 0.962952i | \(-0.413085\pi\) | ||||
0.269671 | + | 0.962952i | \(0.413085\pi\) | |||||||
\(578\) | −10.8496 | −0.451286 | ||||||||
\(579\) | 43.7260 | 1.81719 | ||||||||
\(580\) | −3.69694 | −0.153507 | ||||||||
\(581\) | −12.9425 | −0.536946 | ||||||||
\(582\) | −3.31883 | −0.137570 | ||||||||
\(583\) | −17.5343 | −0.726198 | ||||||||
\(584\) | 13.0675 | 0.540735 | ||||||||
\(585\) | −7.01958 | −0.290224 | ||||||||
\(586\) | −16.9584 | −0.700545 | ||||||||
\(587\) | 36.4405 | 1.50406 | 0.752030 | − | 0.659129i | \(-0.229075\pi\) | ||||
0.752030 | + | 0.659129i | \(0.229075\pi\) | |||||||
\(588\) | 2.18756 | 0.0902133 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −7.87226 | −0.324096 | ||||||||
\(591\) | −7.53460 | −0.309932 | ||||||||
\(592\) | 4.26808 | 0.175417 | ||||||||
\(593\) | 31.6814 | 1.30100 | 0.650500 | − | 0.759506i | \(-0.274559\pi\) | ||||
0.650500 | + | 0.759506i | \(0.274559\pi\) | |||||||
\(594\) | −9.11349 | −0.373931 | ||||||||
\(595\) | 1.52802 | 0.0626427 | ||||||||
\(596\) | 13.5990 | 0.557038 | ||||||||
\(597\) | 6.84763 | 0.280255 | ||||||||
\(598\) | 17.2627 | 0.705923 | ||||||||
\(599\) | 5.21417 | 0.213045 | 0.106523 | − | 0.994310i | \(-0.466028\pi\) | ||||
0.106523 | + | 0.994310i | \(0.466028\pi\) | |||||||
\(600\) | −10.1073 | −0.412630 | ||||||||
\(601\) | −8.43231 | −0.343961 | −0.171981 | − | 0.985100i | \(-0.555017\pi\) | ||||
−0.171981 | + | 0.985100i | \(0.555017\pi\) | |||||||
\(602\) | 10.3584 | 0.422176 | ||||||||
\(603\) | 7.43585 | 0.302811 | ||||||||
\(604\) | −20.2325 | −0.823250 | ||||||||
\(605\) | −0.471213 | −0.0191575 | ||||||||
\(606\) | −21.7186 | −0.882256 | ||||||||
\(607\) | 18.8481 | 0.765022 | 0.382511 | − | 0.923951i | \(-0.375059\pi\) | ||||
0.382511 | + | 0.923951i | \(0.375059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.1257 | −0.531880 | ||||||||
\(610\) | 3.41706 | 0.138353 | ||||||||
\(611\) | 9.81096 | 0.396909 | ||||||||
\(612\) | 4.42778 | 0.178982 | ||||||||
\(613\) | 14.8192 | 0.598542 | 0.299271 | − | 0.954168i | \(-0.403256\pi\) | ||||
0.299271 | + | 0.954168i | \(0.403256\pi\) | |||||||
\(614\) | −2.68585 | −0.108392 | ||||||||
\(615\) | 1.73671 | 0.0700307 | ||||||||
\(616\) | −3.42998 | −0.138198 | ||||||||
\(617\) | 14.2858 | 0.575123 | 0.287562 | − | 0.957762i | \(-0.407155\pi\) | ||||
0.287562 | + | 0.957762i | \(0.407155\pi\) | |||||||
\(618\) | 18.2658 | 0.734760 | ||||||||
\(619\) | −27.8881 | −1.12092 | −0.560459 | − | 0.828182i | \(-0.689375\pi\) | ||||
−0.560459 | + | 0.828182i | \(0.689375\pi\) | |||||||
\(620\) | 4.76056 | 0.191189 | ||||||||
\(621\) | −7.18793 | −0.288442 | ||||||||
\(622\) | 1.77079 | 0.0710023 | ||||||||
\(623\) | 12.4510 | 0.498837 | ||||||||
\(624\) | 13.9591 | 0.558810 | ||||||||
\(625\) | 19.4497 | 0.777988 | ||||||||
\(626\) | 7.89729 | 0.315639 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.1097 | −0.443324 | ||||||||
\(629\) | 10.5848 | 0.422044 | ||||||||
\(630\) | 1.10005 | 0.0438272 | ||||||||
\(631\) | 26.3781 | 1.05010 | 0.525048 | − | 0.851073i | \(-0.324047\pi\) | ||||
0.525048 | + | 0.851073i | \(0.324047\pi\) | |||||||
\(632\) | 2.96283 | 0.117855 | ||||||||
\(633\) | −36.5293 | −1.45191 | ||||||||
\(634\) | −11.6202 | −0.461498 | ||||||||
\(635\) | −2.73944 | −0.108711 | ||||||||
\(636\) | −11.1830 | −0.443433 | ||||||||
\(637\) | 6.38112 | 0.252829 | ||||||||
\(638\) | 20.5805 | 0.814789 | ||||||||
\(639\) | 0.0436899 | 0.00172835 | ||||||||
\(640\) | −0.616139 | −0.0243550 | ||||||||
\(641\) | 39.1472 | 1.54622 | 0.773110 | − | 0.634272i | \(-0.218700\pi\) | ||||
0.773110 | + | 0.634272i | \(0.218700\pi\) | |||||||
\(642\) | 29.6550 | 1.17039 | ||||||||
\(643\) | −6.20232 | −0.244596 | −0.122298 | − | 0.992493i | \(-0.539026\pi\) | ||||
−0.122298 | + | 0.992493i | \(0.539026\pi\) | |||||||
\(644\) | −2.70527 | −0.106603 | ||||||||
\(645\) | 13.9614 | 0.549731 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.11530 | −0.0831610 | −0.0415805 | − | 0.999135i | \(-0.513239\pi\) | ||||
−0.0415805 | + | 0.999135i | \(0.513239\pi\) | |||||||
\(648\) | −11.1685 | −0.438742 | ||||||||
\(649\) | 43.8240 | 1.72024 | ||||||||
\(650\) | −29.4832 | −1.15642 | ||||||||
\(651\) | 16.9020 | 0.662442 | ||||||||
\(652\) | −10.2803 | −0.402608 | ||||||||
\(653\) | −20.2029 | −0.790602 | −0.395301 | − | 0.918552i | \(-0.629360\pi\) | ||||
−0.395301 | + | 0.918552i | \(0.629360\pi\) | |||||||
\(654\) | 1.22132 | 0.0477572 | ||||||||
\(655\) | −4.41885 | −0.172659 | ||||||||
\(656\) | −1.28851 | −0.0503079 | ||||||||
\(657\) | 23.3306 | 0.910215 | ||||||||
\(658\) | −1.53750 | −0.0599379 | ||||||||
\(659\) | −23.3082 | −0.907958 | −0.453979 | − | 0.891012i | \(-0.649996\pi\) | ||||
−0.453979 | + | 0.891012i | \(0.649996\pi\) | |||||||
\(660\) | −4.62306 | −0.179953 | ||||||||
\(661\) | −28.4307 | −1.10583 | −0.552914 | − | 0.833238i | \(-0.686484\pi\) | ||||
−0.552914 | + | 0.833238i | \(0.686484\pi\) | |||||||
\(662\) | −1.15352 | −0.0448329 | ||||||||
\(663\) | 34.6184 | 1.34447 | ||||||||
\(664\) | 12.9425 | 0.502267 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.62023 | 0.295278 | ||||||||
\(667\) | 16.2321 | 0.628509 | ||||||||
\(668\) | −12.6748 | −0.490403 | ||||||||
\(669\) | 31.9041 | 1.23348 | ||||||||
\(670\) | −2.56610 | −0.0991372 | ||||||||
\(671\) | −19.0224 | −0.734351 | ||||||||
\(672\) | −2.18756 | −0.0843868 | ||||||||
\(673\) | −9.48697 | −0.365696 | −0.182848 | − | 0.983141i | \(-0.558532\pi\) | ||||
−0.182848 | + | 0.983141i | \(0.558532\pi\) | |||||||
\(674\) | −7.31544 | −0.281780 | ||||||||
\(675\) | 12.2764 | 0.472517 | ||||||||
\(676\) | 27.7187 | 1.06610 | ||||||||
\(677\) | 43.2866 | 1.66364 | 0.831820 | − | 0.555045i | \(-0.187299\pi\) | ||||
0.831820 | + | 0.555045i | \(0.187299\pi\) | |||||||
\(678\) | 22.0913 | 0.848411 | ||||||||
\(679\) | 1.51714 | 0.0582225 | ||||||||
\(680\) | −1.52802 | −0.0585969 | ||||||||
\(681\) | −10.3544 | −0.396782 | ||||||||
\(682\) | −26.5016 | −1.01480 | ||||||||
\(683\) | −16.3891 | −0.627110 | −0.313555 | − | 0.949570i | \(-0.601520\pi\) | ||||
−0.313555 | + | 0.949570i | \(0.601520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.3556 | 0.395668 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 32.5096 | 1.24032 | ||||||||
\(688\) | −10.3584 | −0.394910 | ||||||||
\(689\) | −32.6208 | −1.24275 | ||||||||
\(690\) | −3.64627 | −0.138811 | ||||||||
\(691\) | 41.4257 | 1.57591 | 0.787953 | − | 0.615735i | \(-0.211141\pi\) | ||||
0.787953 | + | 0.615735i | \(0.211141\pi\) | |||||||
\(692\) | 6.24437 | 0.237376 | ||||||||
\(693\) | −6.12389 | −0.232627 | ||||||||
\(694\) | −31.3704 | −1.19080 | ||||||||
\(695\) | 8.35277 | 0.316839 | ||||||||
\(696\) | 13.1257 | 0.497528 | ||||||||
\(697\) | −3.19550 | −0.121038 | ||||||||
\(698\) | −2.33966 | −0.0885576 | ||||||||
\(699\) | −9.55416 | −0.361372 | ||||||||
\(700\) | 4.62037 | 0.174634 | ||||||||
\(701\) | 46.1088 | 1.74150 | 0.870752 | − | 0.491722i | \(-0.163632\pi\) | ||||
0.870752 | + | 0.491722i | \(0.163632\pi\) | |||||||
\(702\) | −16.9547 | −0.639913 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.42998 | 0.129272 | ||||||||
\(705\) | −2.07230 | −0.0780473 | ||||||||
\(706\) | −6.64960 | −0.250261 | ||||||||
\(707\) | 9.92823 | 0.373390 | ||||||||
\(708\) | 27.9499 | 1.05042 | ||||||||
\(709\) | −27.0329 | −1.01524 | −0.507622 | − | 0.861580i | \(-0.669475\pi\) | ||||
−0.507622 | + | 0.861580i | \(0.669475\pi\) | |||||||
\(710\) | −0.0150774 | −0.000565843 0 | ||||||||
\(711\) | 5.28983 | 0.198384 | ||||||||
\(712\) | −12.4510 | −0.466619 | ||||||||
\(713\) | −20.9021 | −0.782791 | ||||||||
\(714\) | −5.42512 | −0.203030 | ||||||||
\(715\) | −13.4855 | −0.504330 | ||||||||
\(716\) | 17.7976 | 0.665128 | ||||||||
\(717\) | −52.9862 | −1.97881 | ||||||||
\(718\) | 23.2605 | 0.868075 | ||||||||
\(719\) | −47.8432 | −1.78425 | −0.892125 | − | 0.451789i | \(-0.850786\pi\) | ||||
−0.892125 | + | 0.451789i | \(0.850786\pi\) | |||||||
\(720\) | −1.10005 | −0.0409966 | ||||||||
\(721\) | −8.34988 | −0.310966 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.4092 | −1.39126 | ||||||||
\(724\) | −5.92757 | −0.220296 | ||||||||
\(725\) | −27.7230 | −1.02961 | ||||||||
\(726\) | 1.67301 | 0.0620911 | ||||||||
\(727\) | 4.90682 | 0.181984 | 0.0909919 | − | 0.995852i | \(-0.470996\pi\) | ||||
0.0909919 | + | 0.995852i | \(0.470996\pi\) | |||||||
\(728\) | −6.38112 | −0.236500 | ||||||||
\(729\) | −2.50327 | −0.0927136 | ||||||||
\(730\) | −8.05138 | −0.297995 | ||||||||
\(731\) | −25.6887 | −0.950131 | ||||||||
\(732\) | −12.1320 | −0.448412 | ||||||||
\(733\) | 52.5699 | 1.94172 | 0.970858 | − | 0.239657i | \(-0.0770349\pi\) | ||||
0.970858 | + | 0.239657i | \(0.0770349\pi\) | |||||||
\(734\) | 10.6463 | 0.392962 | ||||||||
\(735\) | −1.34784 | −0.0497158 | ||||||||
\(736\) | 2.70527 | 0.0997177 | ||||||||
\(737\) | 14.2852 | 0.526203 | ||||||||
\(738\) | −2.30051 | −0.0846828 | ||||||||
\(739\) | 25.2192 | 0.927702 | 0.463851 | − | 0.885913i | \(-0.346467\pi\) | ||||
0.463851 | + | 0.885913i | \(0.346467\pi\) | |||||||
\(740\) | −2.62973 | −0.0966709 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.11208 | 0.187670 | ||||||||
\(743\) | 5.58183 | 0.204777 | 0.102389 | − | 0.994744i | \(-0.467351\pi\) | ||||
0.102389 | + | 0.994744i | \(0.467351\pi\) | |||||||
\(744\) | −16.9020 | −0.619658 | ||||||||
\(745\) | −8.37889 | −0.306979 | ||||||||
\(746\) | −28.8794 | −1.05735 | ||||||||
\(747\) | 23.1075 | 0.845461 | ||||||||
\(748\) | 8.50633 | 0.311022 | ||||||||
\(749\) | −13.5562 | −0.495333 | ||||||||
\(750\) | 12.9667 | 0.473477 | ||||||||
\(751\) | 25.7524 | 0.939718 | 0.469859 | − | 0.882742i | \(-0.344305\pi\) | ||||
0.469859 | + | 0.882742i | \(0.344305\pi\) | |||||||
\(752\) | 1.53750 | 0.0560668 | ||||||||
\(753\) | 59.7413 | 2.17709 | ||||||||
\(754\) | 38.2878 | 1.39436 | ||||||||
\(755\) | 12.4661 | 0.453686 | ||||||||
\(756\) | 2.65701 | 0.0966344 | ||||||||
\(757\) | −45.3483 | −1.64821 | −0.824106 | − | 0.566435i | \(-0.808322\pi\) | ||||
−0.824106 | + | 0.566435i | \(0.808322\pi\) | |||||||
\(758\) | −33.1311 | −1.20338 | ||||||||
\(759\) | 20.2984 | 0.736786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9534 | −0.904560 | −0.452280 | − | 0.891876i | \(-0.649389\pi\) | ||||
−0.452280 | + | 0.891876i | \(0.649389\pi\) | |||||||
\(762\) | 9.72616 | 0.352342 | ||||||||
\(763\) | −0.558302 | −0.0202119 | ||||||||
\(764\) | 16.3567 | 0.591764 | ||||||||
\(765\) | −2.72813 | −0.0986356 | ||||||||
\(766\) | −3.65421 | −0.132032 | ||||||||
\(767\) | 81.5300 | 2.94388 | ||||||||
\(768\) | 2.18756 | 0.0789366 | ||||||||
\(769\) | 12.9261 | 0.466126 | 0.233063 | − | 0.972462i | \(-0.425125\pi\) | ||||
0.233063 | + | 0.972462i | \(0.425125\pi\) | |||||||
\(770\) | 2.11335 | 0.0761597 | ||||||||
\(771\) | −21.8059 | −0.785321 | ||||||||
\(772\) | 19.9885 | 0.719403 | ||||||||
\(773\) | 14.0205 | 0.504281 | 0.252141 | − | 0.967691i | \(-0.418865\pi\) | ||||
0.252141 | + | 0.967691i | \(0.418865\pi\) | |||||||
\(774\) | −18.4938 | −0.664748 | ||||||||
\(775\) | 35.6990 | 1.28235 | ||||||||
\(776\) | −1.51714 | −0.0544621 | ||||||||
\(777\) | −9.33667 | −0.334951 | ||||||||
\(778\) | −9.25078 | −0.331657 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −8.60072 | −0.307955 | ||||||||
\(781\) | 0.0839340 | 0.00300340 | ||||||||
\(782\) | 6.70905 | 0.239915 | ||||||||
\(783\) | −15.9425 | −0.569738 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 6.84511 | 0.244312 | ||||||||
\(786\) | 15.6888 | 0.559600 | ||||||||
\(787\) | −4.13771 | −0.147494 | −0.0737468 | − | 0.997277i | \(-0.523496\pi\) | ||||
−0.0737468 | + | 0.997277i | \(0.523496\pi\) | |||||||
\(788\) | −3.44430 | −0.122698 | ||||||||
\(789\) | −54.5389 | −1.94164 | ||||||||
\(790\) | −1.82552 | −0.0649489 | ||||||||
\(791\) | −10.0986 | −0.359066 | ||||||||
\(792\) | 6.12389 | 0.217603 | ||||||||
\(793\) | −35.3892 | −1.25671 | ||||||||
\(794\) | 19.2309 | 0.682480 | ||||||||
\(795\) | 6.89026 | 0.244372 | ||||||||
\(796\) | 3.13027 | 0.110949 | ||||||||
\(797\) | 53.5733 | 1.89767 | 0.948833 | − | 0.315780i | \(-0.102266\pi\) | ||||
0.948833 | + | 0.315780i | \(0.102266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.81298 | 0.134894 | ||||||||
\(800\) | −4.62037 | −0.163355 | ||||||||
\(801\) | −22.2299 | −0.785456 | ||||||||
\(802\) | −29.5430 | −1.04320 | ||||||||
\(803\) | 44.8212 | 1.58170 | ||||||||
\(804\) | 9.11076 | 0.321312 | ||||||||
\(805\) | 1.66682 | 0.0587478 | ||||||||
\(806\) | −49.3034 | −1.73664 | ||||||||
\(807\) | −56.1468 | −1.97646 | ||||||||
\(808\) | −9.92823 | −0.349274 | ||||||||
\(809\) | 30.7139 | 1.07984 | 0.539922 | − | 0.841715i | \(-0.318454\pi\) | ||||
0.539922 | + | 0.841715i | \(0.318454\pi\) | |||||||
\(810\) | 6.88138 | 0.241787 | ||||||||
\(811\) | −43.6163 | −1.53158 | −0.765788 | − | 0.643093i | \(-0.777651\pi\) | ||||
−0.765788 | + | 0.643093i | \(0.777651\pi\) | |||||||
\(812\) | −6.00017 | −0.210565 | ||||||||
\(813\) | 41.1181 | 1.44208 | ||||||||
\(814\) | 14.6395 | 0.513113 | ||||||||
\(815\) | 6.33410 | 0.221874 | ||||||||
\(816\) | 5.42512 | 0.189917 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −39.8965 | −1.39495 | ||||||||
\(819\) | −11.3929 | −0.398098 | ||||||||
\(820\) | 0.793902 | 0.0277243 | ||||||||
\(821\) | −43.0095 | −1.50104 | −0.750521 | − | 0.660847i | \(-0.770197\pi\) | ||||
−0.750521 | + | 0.660847i | \(0.770197\pi\) | |||||||
\(822\) | −36.7668 | −1.28239 | ||||||||
\(823\) | −3.41982 | −0.119207 | −0.0596037 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596037 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(824\) | 8.34988 | 0.290882 | ||||||||
\(825\) | −34.6679 | −1.20698 | ||||||||
\(826\) | −12.7768 | −0.444560 | ||||||||
\(827\) | −27.6387 | −0.961093 | −0.480547 | − | 0.876969i | \(-0.659562\pi\) | ||||
−0.480547 | + | 0.876969i | \(0.659562\pi\) | |||||||
\(828\) | 4.82999 | 0.167854 | ||||||||
\(829\) | 25.7042 | 0.892745 | 0.446373 | − | 0.894847i | \(-0.352716\pi\) | ||||
0.446373 | + | 0.894847i | \(0.352716\pi\) | |||||||
\(830\) | −7.97439 | −0.276795 | ||||||||
\(831\) | 43.4765 | 1.50818 | ||||||||
\(832\) | 6.38112 | 0.221226 | ||||||||
\(833\) | 2.47999 | 0.0859266 | ||||||||
\(834\) | −29.6559 | −1.02690 | ||||||||
\(835\) | 7.80944 | 0.270257 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.5292 | 0.709593 | ||||||||
\(838\) | −34.5562 | −1.19372 | ||||||||
\(839\) | 36.9844 | 1.27684 | 0.638422 | − | 0.769686i | \(-0.279587\pi\) | ||||
0.638422 | + | 0.769686i | \(0.279587\pi\) | |||||||
\(840\) | 1.34784 | 0.0465049 | ||||||||
\(841\) | 7.00200 | 0.241448 | ||||||||
\(842\) | −28.8651 | −0.994757 | ||||||||
\(843\) | −46.5825 | −1.60439 | ||||||||
\(844\) | −16.6987 | −0.574793 | ||||||||
\(845\) | −17.0786 | −0.587521 | ||||||||
\(846\) | 2.74505 | 0.0943766 | ||||||||
\(847\) | −0.764783 | −0.0262783 | ||||||||
\(848\) | −5.11208 | −0.175550 | ||||||||
\(849\) | −8.25727 | −0.283389 | ||||||||
\(850\) | −11.4585 | −0.393023 | ||||||||
\(851\) | 11.5463 | 0.395803 | ||||||||
\(852\) | 0.0535310 | 0.00183394 | ||||||||
\(853\) | −39.1925 | −1.34193 | −0.670963 | − | 0.741491i | \(-0.734119\pi\) | ||||
−0.670963 | + | 0.741491i | \(0.734119\pi\) | |||||||
\(854\) | 5.54592 | 0.189777 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.5562 | 0.463342 | ||||||||
\(857\) | −5.62471 | −0.192136 | −0.0960682 | − | 0.995375i | \(-0.530627\pi\) | ||||
−0.0960682 | + | 0.995375i | \(0.530627\pi\) | |||||||
\(858\) | 47.8793 | 1.63457 | ||||||||
\(859\) | −23.0096 | −0.785076 | −0.392538 | − | 0.919736i | \(-0.628403\pi\) | ||||
−0.392538 | + | 0.919736i | \(0.628403\pi\) | |||||||
\(860\) | 6.38221 | 0.217631 | ||||||||
\(861\) | 2.81869 | 0.0960607 | ||||||||
\(862\) | −19.4879 | −0.663760 | ||||||||
\(863\) | 10.3667 | 0.352888 | 0.176444 | − | 0.984311i | \(-0.443541\pi\) | ||||
0.176444 | + | 0.984311i | \(0.443541\pi\) | |||||||
\(864\) | −2.65701 | −0.0903932 | ||||||||
\(865\) | −3.84740 | −0.130816 | ||||||||
\(866\) | −1.44225 | −0.0490097 | ||||||||
\(867\) | −23.7342 | −0.806055 | ||||||||
\(868\) | 7.72644 | 0.262252 | ||||||||
\(869\) | 10.1625 | 0.344738 | ||||||||
\(870\) | −8.08726 | −0.274184 | ||||||||
\(871\) | 26.5762 | 0.900499 | ||||||||
\(872\) | 0.558302 | 0.0189065 | ||||||||
\(873\) | −2.70870 | −0.0916756 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.92749 | −0.200386 | ||||||||
\(876\) | 28.5858 | 0.965825 | ||||||||
\(877\) | −37.9086 | −1.28008 | −0.640040 | − | 0.768341i | \(-0.721082\pi\) | ||||
−0.640040 | + | 0.768341i | \(0.721082\pi\) | |||||||
\(878\) | 16.5525 | 0.558619 | ||||||||
\(879\) | −37.0975 | −1.25127 | ||||||||
\(880\) | −2.11335 | −0.0712409 | ||||||||
\(881\) | 26.1648 | 0.881514 | 0.440757 | − | 0.897626i | \(-0.354710\pi\) | ||||
0.440757 | + | 0.897626i | \(0.354710\pi\) | |||||||
\(882\) | 1.78540 | 0.0601175 | ||||||||
\(883\) | −9.63158 | −0.324128 | −0.162064 | − | 0.986780i | \(-0.551815\pi\) | ||||
−0.162064 | + | 0.986780i | \(0.551815\pi\) | |||||||
\(884\) | 15.8251 | 0.532257 | ||||||||
\(885\) | −17.2210 | −0.578878 | ||||||||
\(886\) | 3.08768 | 0.103733 | ||||||||
\(887\) | 1.96127 | 0.0658531 | 0.0329266 | − | 0.999458i | \(-0.489517\pi\) | ||||
0.0329266 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(888\) | 9.33667 | 0.313318 | ||||||||
\(889\) | −4.44613 | −0.149119 | ||||||||
\(890\) | 7.67152 | 0.257150 | ||||||||
\(891\) | −38.3079 | −1.28336 | ||||||||
\(892\) | 14.5844 | 0.488320 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 29.7486 | 0.994942 | ||||||||
\(895\) | −10.9658 | −0.366546 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 37.7631 | 1.26087 | ||||||||
\(898\) | −17.9081 | −0.597601 | ||||||||
\(899\) | −46.3599 | −1.54619 | ||||||||
\(900\) | −8.24921 | −0.274974 | ||||||||
\(901\) | −12.6779 | −0.422363 | ||||||||
\(902\) | −4.41957 | −0.147156 | ||||||||
\(903\) | 22.6595 | 0.754062 | ||||||||
\(904\) | 10.0986 | 0.335875 | ||||||||
\(905\) | 3.65221 | 0.121403 | ||||||||
\(906\) | −44.2598 | −1.47043 | ||||||||
\(907\) | −43.4844 | −1.44387 | −0.721937 | − | 0.691958i | \(-0.756748\pi\) | ||||
−0.721937 | + | 0.691958i | \(0.756748\pi\) | |||||||
\(908\) | −4.73333 | −0.157081 | ||||||||
\(909\) | −17.7259 | −0.587930 | ||||||||
\(910\) | 3.93166 | 0.130333 | ||||||||
\(911\) | −4.93846 | −0.163618 | −0.0818092 | − | 0.996648i | \(-0.526070\pi\) | ||||
−0.0818092 | + | 0.996648i | \(0.526070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.3926 | 1.46918 | ||||||||
\(914\) | 31.2954 | 1.03516 | ||||||||
\(915\) | 7.47500 | 0.247116 | ||||||||
\(916\) | 14.8611 | 0.491026 | ||||||||
\(917\) | −7.17183 | −0.236835 | ||||||||
\(918\) | −6.58936 | −0.217481 | ||||||||
\(919\) | 1.25165 | 0.0412883 | 0.0206441 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206441 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(920\) | −1.66682 | −0.0549536 | ||||||||
\(921\) | −5.87544 | −0.193602 | ||||||||
\(922\) | −11.6085 | −0.382304 | ||||||||
\(923\) | 0.156150 | 0.00513975 | ||||||||
\(924\) | −7.50328 | −0.246840 | ||||||||
\(925\) | −19.7201 | −0.648394 | ||||||||
\(926\) | 4.15132 | 0.136421 | ||||||||
\(927\) | 14.9079 | 0.489639 | ||||||||
\(928\) | 6.00017 | 0.196965 | ||||||||
\(929\) | −38.7110 | −1.27007 | −0.635034 | − | 0.772484i | \(-0.719014\pi\) | ||||
−0.635034 | + | 0.772484i | \(0.719014\pi\) | |||||||
\(930\) | 10.4140 | 0.341488 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.36751 | −0.143062 | ||||||||
\(933\) | 3.87371 | 0.126819 | ||||||||
\(934\) | −24.9196 | −0.815394 | ||||||||
\(935\) | −5.24108 | −0.171402 | ||||||||
\(936\) | 11.3929 | 0.372387 | ||||||||
\(937\) | 18.5473 | 0.605913 | 0.302957 | − | 0.953004i | \(-0.402026\pi\) | ||||
0.302957 | + | 0.953004i | \(0.402026\pi\) | |||||||
\(938\) | −4.16481 | −0.135986 | ||||||||
\(939\) | 17.2758 | 0.563773 | ||||||||
\(940\) | −0.947313 | −0.0308979 | ||||||||
\(941\) | 24.6283 | 0.802859 | 0.401429 | − | 0.915890i | \(-0.368513\pi\) | ||||
0.401429 | + | 0.915890i | \(0.368513\pi\) | |||||||
\(942\) | −24.3030 | −0.791835 | ||||||||
\(943\) | −3.48577 | −0.113512 | ||||||||
\(944\) | 12.7768 | 0.415848 | ||||||||
\(945\) | −1.63709 | −0.0532544 | ||||||||
\(946\) | −35.5291 | −1.15515 | ||||||||
\(947\) | 20.7160 | 0.673178 | 0.336589 | − | 0.941652i | \(-0.390727\pi\) | ||||
0.336589 | + | 0.941652i | \(0.390727\pi\) | |||||||
\(948\) | 6.48135 | 0.210505 | ||||||||
\(949\) | 83.3851 | 2.70679 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.4199 | −0.824296 | ||||||||
\(952\) | −2.47999 | −0.0803770 | ||||||||
\(953\) | −42.6761 | −1.38242 | −0.691208 | − | 0.722656i | \(-0.742921\pi\) | ||||
−0.691208 | + | 0.722656i | \(0.742921\pi\) | |||||||
\(954\) | −9.12710 | −0.295501 | ||||||||
\(955\) | −10.0780 | −0.326116 | ||||||||
\(956\) | −24.2217 | −0.783385 | ||||||||
\(957\) | 45.0209 | 1.45532 | ||||||||
\(958\) | −18.9778 | −0.613144 | ||||||||
\(959\) | 16.8073 | 0.542735 | ||||||||
\(960\) | −1.34784 | −0.0435013 | ||||||||
\(961\) | 28.6979 | 0.925738 | ||||||||
\(962\) | 27.2352 | 0.878097 | ||||||||
\(963\) | 24.2033 | 0.779939 | ||||||||
\(964\) | −17.1009 | −0.550784 | ||||||||
\(965\) | −12.3157 | −0.396457 | ||||||||
\(966\) | −5.91793 | −0.190406 | ||||||||
\(967\) | 46.5740 | 1.49772 | 0.748860 | − | 0.662728i | \(-0.230602\pi\) | ||||
0.748860 | + | 0.662728i | \(0.230602\pi\) | |||||||
\(968\) | 0.764783 | 0.0245811 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.934769 | 0.0300136 | ||||||||
\(971\) | 16.9447 | 0.543782 | 0.271891 | − | 0.962328i | \(-0.412351\pi\) | ||||
0.271891 | + | 0.962328i | \(0.412351\pi\) | |||||||
\(972\) | −16.4608 | −0.527980 | ||||||||
\(973\) | 13.5566 | 0.434606 | ||||||||
\(974\) | 36.1508 | 1.15835 | ||||||||
\(975\) | −64.4960 | −2.06553 | ||||||||
\(976\) | −5.54592 | −0.177520 | ||||||||
\(977\) | 10.1186 | 0.323723 | 0.161862 | − | 0.986813i | \(-0.448250\pi\) | ||||
0.161862 | + | 0.986813i | \(0.448250\pi\) | |||||||
\(978\) | −22.4887 | −0.719110 | ||||||||
\(979\) | −42.7066 | −1.36491 | ||||||||
\(980\) | −0.616139 | −0.0196818 | ||||||||
\(981\) | 0.996792 | 0.0318251 | ||||||||
\(982\) | 3.08754 | 0.0985273 | ||||||||
\(983\) | 36.8594 | 1.17563 | 0.587816 | − | 0.808995i | \(-0.299988\pi\) | ||||
0.587816 | + | 0.808995i | \(0.299988\pi\) | |||||||
\(984\) | −2.81869 | −0.0898565 | ||||||||
\(985\) | 2.12217 | 0.0676179 | ||||||||
\(986\) | 14.8804 | 0.473887 | ||||||||
\(987\) | −3.36336 | −0.107057 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0222 | −0.891055 | ||||||||
\(990\) | −3.77317 | −0.119919 | ||||||||
\(991\) | 50.6580 | 1.60921 | 0.804603 | − | 0.593813i | \(-0.202378\pi\) | ||||
0.804603 | + | 0.593813i | \(0.202378\pi\) | |||||||
\(992\) | −7.72644 | −0.245315 | ||||||||
\(993\) | −2.52339 | −0.0800774 | ||||||||
\(994\) | −0.0244707 | −0.000776163 0 | ||||||||
\(995\) | −1.92868 | −0.0611432 | ||||||||
\(996\) | 28.3125 | 0.897114 | ||||||||
\(997\) | −19.9246 | −0.631019 | −0.315510 | − | 0.948922i | \(-0.602175\pi\) | ||||
−0.315510 | + | 0.948922i | \(0.602175\pi\) | |||||||
\(998\) | 30.9593 | 0.979999 | ||||||||
\(999\) | −11.3403 | −0.358792 |
(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 | 5054.2.a.bk.1.7 | 9 | ||
19.4 | even | 9 | 266.2.u.c.225.1 | ✓ | 18 | ||
19.5 | even | 9 | 266.2.u.c.253.1 | yes | 18 | ||
19.18 | odd | 2 | 5054.2.a.bj.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.u.c.225.1 | ✓ | 18 | 19.4 | even | 9 | ||
266.2.u.c.253.1 | yes | 18 | 19.5 | even | 9 | ||
5054.2.a.bj.1.3 | 9 | 19.18 | odd | 2 | |||
5054.2.a.bk.1.7 | 9 | 1.1 | even | 1 | trivial |