Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6015,2,Mod(1,6015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6015 = 3 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6015.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: | \(48.0300168158\) |
Analytic rank: | \(0\) |
Dimension: | \(43\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.07772 | −1.46917 | −0.734585 | − | 0.678517i | \(-0.762623\pi\) | ||||
−0.734585 | + | 0.678517i | \(0.762623\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.31692 | 1.15846 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.07772 | −0.848225 | ||||||||
\(7\) | −4.42665 | −1.67312 | −0.836558 | − | 0.547878i | \(-0.815436\pi\) | ||||
−0.836558 | + | 0.547878i | \(0.815436\pi\) | |||||||
\(8\) | −0.658463 | −0.232802 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.07772 | −0.657032 | ||||||||
\(11\) | −1.48363 | −0.447331 | −0.223665 | − | 0.974666i | \(-0.571802\pi\) | ||||
−0.223665 | + | 0.974666i | \(0.571802\pi\) | |||||||
\(12\) | 2.31692 | 0.668836 | ||||||||
\(13\) | 6.43697 | 1.78529 | 0.892647 | − | 0.450757i | \(-0.148846\pi\) | ||||
0.892647 | + | 0.450757i | \(0.148846\pi\) | |||||||
\(14\) | 9.19733 | 2.45809 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −3.26573 | −0.816433 | ||||||||
\(17\) | −0.558508 | −0.135458 | −0.0677290 | − | 0.997704i | \(-0.521575\pi\) | ||||
−0.0677290 | + | 0.997704i | \(0.521575\pi\) | |||||||
\(18\) | −2.07772 | −0.489723 | ||||||||
\(19\) | 2.52484 | 0.579239 | 0.289619 | − | 0.957142i | \(-0.406471\pi\) | ||||
0.289619 | + | 0.957142i | \(0.406471\pi\) | |||||||
\(20\) | 2.31692 | 0.518078 | ||||||||
\(21\) | −4.42665 | −0.965974 | ||||||||
\(22\) | 3.08256 | 0.657205 | ||||||||
\(23\) | 7.03342 | 1.46657 | 0.733285 | − | 0.679921i | \(-0.237986\pi\) | ||||
0.733285 | + | 0.679921i | \(0.237986\pi\) | |||||||
\(24\) | −0.658463 | −0.134408 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.3742 | −2.62290 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −10.2562 | −1.93824 | ||||||||
\(29\) | −1.58577 | −0.294469 | −0.147235 | − | 0.989102i | \(-0.547037\pi\) | ||||
−0.147235 | + | 0.989102i | \(0.547037\pi\) | |||||||
\(30\) | −2.07772 | −0.379338 | ||||||||
\(31\) | 1.47401 | 0.264741 | 0.132370 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132370 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(32\) | 8.10220 | 1.43228 | ||||||||
\(33\) | −1.48363 | −0.258267 | ||||||||
\(34\) | 1.16042 | 0.199011 | ||||||||
\(35\) | −4.42665 | −0.748240 | ||||||||
\(36\) | 2.31692 | 0.386153 | ||||||||
\(37\) | −4.72112 | −0.776147 | −0.388074 | − | 0.921628i | \(-0.626859\pi\) | ||||
−0.388074 | + | 0.921628i | \(0.626859\pi\) | |||||||
\(38\) | −5.24591 | −0.851000 | ||||||||
\(39\) | 6.43697 | 1.03074 | ||||||||
\(40\) | −0.658463 | −0.104112 | ||||||||
\(41\) | 1.86270 | 0.290904 | 0.145452 | − | 0.989365i | \(-0.453536\pi\) | ||||
0.145452 | + | 0.989365i | \(0.453536\pi\) | |||||||
\(42\) | 9.19733 | 1.41918 | ||||||||
\(43\) | 2.32977 | 0.355287 | 0.177644 | − | 0.984095i | \(-0.443153\pi\) | ||||
0.177644 | + | 0.984095i | \(0.443153\pi\) | |||||||
\(44\) | −3.43744 | −0.518214 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −14.6135 | −2.15464 | ||||||||
\(47\) | −2.29045 | −0.334096 | −0.167048 | − | 0.985949i | \(-0.553424\pi\) | ||||
−0.167048 | + | 0.985949i | \(0.553424\pi\) | |||||||
\(48\) | −3.26573 | −0.471368 | ||||||||
\(49\) | 12.5952 | 1.79932 | ||||||||
\(50\) | −2.07772 | −0.293834 | ||||||||
\(51\) | −0.558508 | −0.0782068 | ||||||||
\(52\) | 14.9139 | 2.06819 | ||||||||
\(53\) | 7.52558 | 1.03372 | 0.516859 | − | 0.856070i | \(-0.327101\pi\) | ||||
0.516859 | + | 0.856070i | \(0.327101\pi\) | |||||||
\(54\) | −2.07772 | −0.282742 | ||||||||
\(55\) | −1.48363 | −0.200052 | ||||||||
\(56\) | 2.91479 | 0.389505 | ||||||||
\(57\) | 2.52484 | 0.334424 | ||||||||
\(58\) | 3.29478 | 0.432625 | ||||||||
\(59\) | −0.844805 | −0.109984 | −0.0549921 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549921 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(60\) | 2.31692 | 0.299113 | ||||||||
\(61\) | 12.7934 | 1.63803 | 0.819013 | − | 0.573775i | \(-0.194522\pi\) | ||||
0.819013 | + | 0.573775i | \(0.194522\pi\) | |||||||
\(62\) | −3.06259 | −0.388949 | ||||||||
\(63\) | −4.42665 | −0.557705 | ||||||||
\(64\) | −10.3026 | −1.28783 | ||||||||
\(65\) | 6.43697 | 0.798407 | ||||||||
\(66\) | 3.08256 | 0.379437 | ||||||||
\(67\) | −2.81592 | −0.344019 | −0.172010 | − | 0.985095i | \(-0.555026\pi\) | ||||
−0.172010 | + | 0.985095i | \(0.555026\pi\) | |||||||
\(68\) | −1.29402 | −0.156923 | ||||||||
\(69\) | 7.03342 | 0.846725 | ||||||||
\(70\) | 9.19733 | 1.09929 | ||||||||
\(71\) | −6.45925 | −0.766572 | −0.383286 | − | 0.923630i | \(-0.625208\pi\) | ||||
−0.383286 | + | 0.923630i | \(0.625208\pi\) | |||||||
\(72\) | −0.658463 | −0.0776007 | ||||||||
\(73\) | −14.8625 | −1.73952 | −0.869761 | − | 0.493474i | \(-0.835727\pi\) | ||||
−0.869761 | + | 0.493474i | \(0.835727\pi\) | |||||||
\(74\) | 9.80916 | 1.14029 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 5.84985 | 0.671024 | ||||||||
\(77\) | 6.56750 | 0.748436 | ||||||||
\(78\) | −13.3742 | −1.51433 | ||||||||
\(79\) | −12.2729 | −1.38081 | −0.690405 | − | 0.723423i | \(-0.742568\pi\) | ||||
−0.690405 | + | 0.723423i | \(0.742568\pi\) | |||||||
\(80\) | −3.26573 | −0.365120 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.87016 | −0.427387 | ||||||||
\(83\) | −15.5654 | −1.70853 | −0.854264 | − | 0.519839i | \(-0.825992\pi\) | ||||
−0.854264 | + | 0.519839i | \(0.825992\pi\) | |||||||
\(84\) | −10.2562 | −1.11904 | ||||||||
\(85\) | −0.558508 | −0.0605787 | ||||||||
\(86\) | −4.84062 | −0.521977 | ||||||||
\(87\) | −1.58577 | −0.170012 | ||||||||
\(88\) | 0.976915 | 0.104139 | ||||||||
\(89\) | 3.07441 | 0.325887 | 0.162943 | − | 0.986635i | \(-0.447901\pi\) | ||||
0.162943 | + | 0.986635i | \(0.447901\pi\) | |||||||
\(90\) | −2.07772 | −0.219011 | ||||||||
\(91\) | −28.4942 | −2.98700 | ||||||||
\(92\) | 16.2959 | 1.69896 | ||||||||
\(93\) | 1.47401 | 0.152848 | ||||||||
\(94\) | 4.75891 | 0.490844 | ||||||||
\(95\) | 2.52484 | 0.259043 | ||||||||
\(96\) | 8.10220 | 0.826927 | ||||||||
\(97\) | 1.79405 | 0.182158 | 0.0910791 | − | 0.995844i | \(-0.470968\pi\) | ||||
0.0910791 | + | 0.995844i | \(0.470968\pi\) | |||||||
\(98\) | −26.1693 | −2.64350 | ||||||||
\(99\) | −1.48363 | −0.149110 | ||||||||
\(100\) | 2.31692 | 0.231692 | ||||||||
\(101\) | 1.53032 | 0.152272 | 0.0761362 | − | 0.997097i | \(-0.475742\pi\) | ||||
0.0761362 | + | 0.997097i | \(0.475742\pi\) | |||||||
\(102\) | 1.16042 | 0.114899 | ||||||||
\(103\) | −5.23053 | −0.515380 | −0.257690 | − | 0.966228i | \(-0.582961\pi\) | ||||
−0.257690 | + | 0.966228i | \(0.582961\pi\) | |||||||
\(104\) | −4.23851 | −0.415620 | ||||||||
\(105\) | −4.42665 | −0.431997 | ||||||||
\(106\) | −15.6360 | −1.51871 | ||||||||
\(107\) | 4.59052 | 0.443783 | 0.221891 | − | 0.975071i | \(-0.428777\pi\) | ||||
0.221891 | + | 0.975071i | \(0.428777\pi\) | |||||||
\(108\) | 2.31692 | 0.222945 | ||||||||
\(109\) | 15.6570 | 1.49966 | 0.749832 | − | 0.661628i | \(-0.230134\pi\) | ||||
0.749832 | + | 0.661628i | \(0.230134\pi\) | |||||||
\(110\) | 3.08256 | 0.293911 | ||||||||
\(111\) | −4.72112 | −0.448109 | ||||||||
\(112\) | 14.4562 | 1.36599 | ||||||||
\(113\) | −2.49926 | −0.235111 | −0.117555 | − | 0.993066i | \(-0.537506\pi\) | ||||
−0.117555 | + | 0.993066i | \(0.537506\pi\) | |||||||
\(114\) | −5.24591 | −0.491325 | ||||||||
\(115\) | 7.03342 | 0.655870 | ||||||||
\(116\) | −3.67409 | −0.341131 | ||||||||
\(117\) | 6.43697 | 0.595098 | ||||||||
\(118\) | 1.75527 | 0.161585 | ||||||||
\(119\) | 2.47232 | 0.226637 | ||||||||
\(120\) | −0.658463 | −0.0601092 | ||||||||
\(121\) | −8.79885 | −0.799895 | ||||||||
\(122\) | −26.5811 | −2.40654 | ||||||||
\(123\) | 1.86270 | 0.167954 | ||||||||
\(124\) | 3.41517 | 0.306691 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 9.19733 | 0.819364 | ||||||||
\(127\) | 4.38227 | 0.388864 | 0.194432 | − | 0.980916i | \(-0.437714\pi\) | ||||
0.194432 | + | 0.980916i | \(0.437714\pi\) | |||||||
\(128\) | 5.20157 | 0.459759 | ||||||||
\(129\) | 2.32977 | 0.205125 | ||||||||
\(130\) | −13.3742 | −1.17300 | ||||||||
\(131\) | −2.38767 | −0.208612 | −0.104306 | − | 0.994545i | \(-0.533262\pi\) | ||||
−0.104306 | + | 0.994545i | \(0.533262\pi\) | |||||||
\(132\) | −3.43744 | −0.299191 | ||||||||
\(133\) | −11.1766 | −0.969134 | ||||||||
\(134\) | 5.85069 | 0.505423 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0.367757 | 0.0315349 | ||||||||
\(137\) | −3.86352 | −0.330082 | −0.165041 | − | 0.986287i | \(-0.552776\pi\) | ||||
−0.165041 | + | 0.986287i | \(0.552776\pi\) | |||||||
\(138\) | −14.6135 | −1.24398 | ||||||||
\(139\) | 21.5796 | 1.83036 | 0.915178 | − | 0.403050i | \(-0.132050\pi\) | ||||
0.915178 | + | 0.403050i | \(0.132050\pi\) | |||||||
\(140\) | −10.2562 | −0.866805 | ||||||||
\(141\) | −2.29045 | −0.192891 | ||||||||
\(142\) | 13.4205 | 1.12622 | ||||||||
\(143\) | −9.55007 | −0.798617 | ||||||||
\(144\) | −3.26573 | −0.272144 | ||||||||
\(145\) | −1.58577 | −0.131691 | ||||||||
\(146\) | 30.8801 | 2.55565 | ||||||||
\(147\) | 12.5952 | 1.03884 | ||||||||
\(148\) | −10.9384 | −0.899134 | ||||||||
\(149\) | 14.5330 | 1.19059 | 0.595296 | − | 0.803507i | \(-0.297035\pi\) | ||||
0.595296 | + | 0.803507i | \(0.297035\pi\) | |||||||
\(150\) | −2.07772 | −0.169645 | ||||||||
\(151\) | 14.8051 | 1.20482 | 0.602411 | − | 0.798186i | \(-0.294207\pi\) | ||||
0.602411 | + | 0.798186i | \(0.294207\pi\) | |||||||
\(152\) | −1.66252 | −0.134848 | ||||||||
\(153\) | −0.558508 | −0.0451527 | ||||||||
\(154\) | −13.6454 | −1.09958 | ||||||||
\(155\) | 1.47401 | 0.118396 | ||||||||
\(156\) | 14.9139 | 1.19407 | ||||||||
\(157\) | 12.3905 | 0.988866 | 0.494433 | − | 0.869216i | \(-0.335376\pi\) | ||||
0.494433 | + | 0.869216i | \(0.335376\pi\) | |||||||
\(158\) | 25.4997 | 2.02864 | ||||||||
\(159\) | 7.52558 | 0.596817 | ||||||||
\(160\) | 8.10220 | 0.640535 | ||||||||
\(161\) | −31.1345 | −2.45374 | ||||||||
\(162\) | −2.07772 | −0.163241 | ||||||||
\(163\) | −8.50867 | −0.666450 | −0.333225 | − | 0.942847i | \(-0.608137\pi\) | ||||
−0.333225 | + | 0.942847i | \(0.608137\pi\) | |||||||
\(164\) | 4.31571 | 0.337000 | ||||||||
\(165\) | −1.48363 | −0.115500 | ||||||||
\(166\) | 32.3406 | 2.51012 | ||||||||
\(167\) | −9.85827 | −0.762856 | −0.381428 | − | 0.924399i | \(-0.624568\pi\) | ||||
−0.381428 | + | 0.924399i | \(0.624568\pi\) | |||||||
\(168\) | 2.91479 | 0.224881 | ||||||||
\(169\) | 28.4345 | 2.18727 | ||||||||
\(170\) | 1.16042 | 0.0890004 | ||||||||
\(171\) | 2.52484 | 0.193080 | ||||||||
\(172\) | 5.39789 | 0.411585 | ||||||||
\(173\) | −4.62289 | −0.351472 | −0.175736 | − | 0.984437i | \(-0.556230\pi\) | ||||
−0.175736 | + | 0.984437i | \(0.556230\pi\) | |||||||
\(174\) | 3.29478 | 0.249776 | ||||||||
\(175\) | −4.42665 | −0.334623 | ||||||||
\(176\) | 4.84513 | 0.365216 | ||||||||
\(177\) | −0.844805 | −0.0634994 | ||||||||
\(178\) | −6.38776 | −0.478783 | ||||||||
\(179\) | −1.34249 | −0.100343 | −0.0501713 | − | 0.998741i | \(-0.515977\pi\) | ||||
−0.0501713 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(180\) | 2.31692 | 0.172693 | ||||||||
\(181\) | 9.38498 | 0.697580 | 0.348790 | − | 0.937201i | \(-0.386593\pi\) | ||||
0.348790 | + | 0.937201i | \(0.386593\pi\) | |||||||
\(182\) | 59.2029 | 4.38841 | ||||||||
\(183\) | 12.7934 | 0.945714 | ||||||||
\(184\) | −4.63125 | −0.341420 | ||||||||
\(185\) | −4.72112 | −0.347104 | ||||||||
\(186\) | −3.06259 | −0.224560 | ||||||||
\(187\) | 0.828618 | 0.0605946 | ||||||||
\(188\) | −5.30678 | −0.387037 | ||||||||
\(189\) | −4.42665 | −0.321991 | ||||||||
\(190\) | −5.24591 | −0.380579 | ||||||||
\(191\) | −15.6325 | −1.13113 | −0.565563 | − | 0.824705i | \(-0.691341\pi\) | ||||
−0.565563 | + | 0.824705i | \(0.691341\pi\) | |||||||
\(192\) | −10.3026 | −0.743528 | ||||||||
\(193\) | −1.12574 | −0.0810323 | −0.0405161 | − | 0.999179i | \(-0.512900\pi\) | ||||
−0.0405161 | + | 0.999179i | \(0.512900\pi\) | |||||||
\(194\) | −3.72753 | −0.267621 | ||||||||
\(195\) | 6.43697 | 0.460961 | ||||||||
\(196\) | 29.1821 | 2.08443 | ||||||||
\(197\) | −20.7500 | −1.47838 | −0.739189 | − | 0.673498i | \(-0.764791\pi\) | ||||
−0.739189 | + | 0.673498i | \(0.764791\pi\) | |||||||
\(198\) | 3.08256 | 0.219068 | ||||||||
\(199\) | 15.8179 | 1.12130 | 0.560649 | − | 0.828054i | \(-0.310552\pi\) | ||||
0.560649 | + | 0.828054i | \(0.310552\pi\) | |||||||
\(200\) | −0.658463 | −0.0465604 | ||||||||
\(201\) | −2.81592 | −0.198620 | ||||||||
\(202\) | −3.17957 | −0.223714 | ||||||||
\(203\) | 7.01963 | 0.492682 | ||||||||
\(204\) | −1.29402 | −0.0905993 | ||||||||
\(205\) | 1.86270 | 0.130096 | ||||||||
\(206\) | 10.8676 | 0.757180 | ||||||||
\(207\) | 7.03342 | 0.488857 | ||||||||
\(208\) | −21.0214 | −1.45757 | ||||||||
\(209\) | −3.74593 | −0.259111 | ||||||||
\(210\) | 9.19733 | 0.634676 | ||||||||
\(211\) | 26.4561 | 1.82131 | 0.910656 | − | 0.413166i | \(-0.135577\pi\) | ||||
0.910656 | + | 0.413166i | \(0.135577\pi\) | |||||||
\(212\) | 17.4361 | 1.19752 | ||||||||
\(213\) | −6.45925 | −0.442580 | ||||||||
\(214\) | −9.53782 | −0.651992 | ||||||||
\(215\) | 2.32977 | 0.158889 | ||||||||
\(216\) | −0.658463 | −0.0448028 | ||||||||
\(217\) | −6.52494 | −0.442942 | ||||||||
\(218\) | −32.5307 | −2.20326 | ||||||||
\(219\) | −14.8625 | −1.00431 | ||||||||
\(220\) | −3.43744 | −0.231752 | ||||||||
\(221\) | −3.59510 | −0.241832 | ||||||||
\(222\) | 9.80916 | 0.658348 | ||||||||
\(223\) | 24.2406 | 1.62327 | 0.811634 | − | 0.584167i | \(-0.198579\pi\) | ||||
0.811634 | + | 0.584167i | \(0.198579\pi\) | |||||||
\(224\) | −35.8656 | −2.39637 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 5.19276 | 0.345417 | ||||||||
\(227\) | −11.6881 | −0.775766 | −0.387883 | − | 0.921709i | \(-0.626794\pi\) | ||||
−0.387883 | + | 0.921709i | \(0.626794\pi\) | |||||||
\(228\) | 5.84985 | 0.387416 | ||||||||
\(229\) | 17.6754 | 1.16802 | 0.584012 | − | 0.811745i | \(-0.301482\pi\) | ||||
0.584012 | + | 0.811745i | \(0.301482\pi\) | |||||||
\(230\) | −14.6135 | −0.963584 | ||||||||
\(231\) | 6.56750 | 0.432110 | ||||||||
\(232\) | 1.04417 | 0.0685531 | ||||||||
\(233\) | 22.3503 | 1.46422 | 0.732108 | − | 0.681189i | \(-0.238537\pi\) | ||||
0.732108 | + | 0.681189i | \(0.238537\pi\) | |||||||
\(234\) | −13.3742 | −0.874299 | ||||||||
\(235\) | −2.29045 | −0.149412 | ||||||||
\(236\) | −1.95734 | −0.127412 | ||||||||
\(237\) | −12.2729 | −0.797211 | ||||||||
\(238\) | −5.13678 | −0.332968 | ||||||||
\(239\) | −3.42123 | −0.221301 | −0.110651 | − | 0.993859i | \(-0.535293\pi\) | ||||
−0.110651 | + | 0.993859i | \(0.535293\pi\) | |||||||
\(240\) | −3.26573 | −0.210802 | ||||||||
\(241\) | 24.3443 | 1.56815 | 0.784077 | − | 0.620664i | \(-0.213137\pi\) | ||||
0.784077 | + | 0.620664i | \(0.213137\pi\) | |||||||
\(242\) | 18.2815 | 1.17518 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 29.6412 | 1.89758 | ||||||||
\(245\) | 12.5952 | 0.804680 | ||||||||
\(246\) | −3.87016 | −0.246752 | ||||||||
\(247\) | 16.2523 | 1.03411 | ||||||||
\(248\) | −0.970584 | −0.0616321 | ||||||||
\(249\) | −15.5654 | −0.986420 | ||||||||
\(250\) | −2.07772 | −0.131406 | ||||||||
\(251\) | −28.3171 | −1.78736 | −0.893678 | − | 0.448708i | \(-0.851884\pi\) | ||||
−0.893678 | + | 0.448708i | \(0.851884\pi\) | |||||||
\(252\) | −10.2562 | −0.646078 | ||||||||
\(253\) | −10.4350 | −0.656042 | ||||||||
\(254\) | −9.10513 | −0.571307 | ||||||||
\(255\) | −0.558508 | −0.0349751 | ||||||||
\(256\) | 9.79785 | 0.612366 | ||||||||
\(257\) | −23.2754 | −1.45188 | −0.725941 | − | 0.687757i | \(-0.758596\pi\) | ||||
−0.725941 | + | 0.687757i | \(0.758596\pi\) | |||||||
\(258\) | −4.84062 | −0.301364 | ||||||||
\(259\) | 20.8987 | 1.29858 | ||||||||
\(260\) | 14.9139 | 0.924922 | ||||||||
\(261\) | −1.58577 | −0.0981565 | ||||||||
\(262\) | 4.96091 | 0.306486 | ||||||||
\(263\) | 21.2062 | 1.30763 | 0.653815 | − | 0.756654i | \(-0.273167\pi\) | ||||
0.653815 | + | 0.756654i | \(0.273167\pi\) | |||||||
\(264\) | 0.976915 | 0.0601250 | ||||||||
\(265\) | 7.52558 | 0.462293 | ||||||||
\(266\) | 23.2218 | 1.42382 | ||||||||
\(267\) | 3.07441 | 0.188151 | ||||||||
\(268\) | −6.52425 | −0.398532 | ||||||||
\(269\) | 29.1884 | 1.77965 | 0.889824 | − | 0.456304i | \(-0.150827\pi\) | ||||
0.889824 | + | 0.456304i | \(0.150827\pi\) | |||||||
\(270\) | −2.07772 | −0.126446 | ||||||||
\(271\) | 25.6360 | 1.55728 | 0.778638 | − | 0.627474i | \(-0.215911\pi\) | ||||
0.778638 | + | 0.627474i | \(0.215911\pi\) | |||||||
\(272\) | 1.82394 | 0.110592 | ||||||||
\(273\) | −28.4942 | −1.72455 | ||||||||
\(274\) | 8.02730 | 0.484947 | ||||||||
\(275\) | −1.48363 | −0.0894662 | ||||||||
\(276\) | 16.2959 | 0.980895 | ||||||||
\(277\) | −10.7203 | −0.644118 | −0.322059 | − | 0.946720i | \(-0.604375\pi\) | ||||
−0.322059 | + | 0.946720i | \(0.604375\pi\) | |||||||
\(278\) | −44.8363 | −2.68910 | ||||||||
\(279\) | 1.47401 | 0.0882469 | ||||||||
\(280\) | 2.91479 | 0.174192 | ||||||||
\(281\) | 27.2623 | 1.62633 | 0.813166 | − | 0.582032i | \(-0.197742\pi\) | ||||
0.813166 | + | 0.582032i | \(0.197742\pi\) | |||||||
\(282\) | 4.75891 | 0.283389 | ||||||||
\(283\) | 5.89342 | 0.350327 | 0.175164 | − | 0.984539i | \(-0.443955\pi\) | ||||
0.175164 | + | 0.984539i | \(0.443955\pi\) | |||||||
\(284\) | −14.9655 | −0.888041 | ||||||||
\(285\) | 2.52484 | 0.149559 | ||||||||
\(286\) | 19.8424 | 1.17330 | ||||||||
\(287\) | −8.24550 | −0.486717 | ||||||||
\(288\) | 8.10220 | 0.477427 | ||||||||
\(289\) | −16.6881 | −0.981651 | ||||||||
\(290\) | 3.29478 | 0.193476 | ||||||||
\(291\) | 1.79405 | 0.105169 | ||||||||
\(292\) | −34.4351 | −2.01516 | ||||||||
\(293\) | 4.62191 | 0.270015 | 0.135008 | − | 0.990845i | \(-0.456894\pi\) | ||||
0.135008 | + | 0.990845i | \(0.456894\pi\) | |||||||
\(294\) | −26.1693 | −1.52623 | ||||||||
\(295\) | −0.844805 | −0.0491864 | ||||||||
\(296\) | 3.10868 | 0.180689 | ||||||||
\(297\) | −1.48363 | −0.0860888 | ||||||||
\(298\) | −30.1955 | −1.74918 | ||||||||
\(299\) | 45.2739 | 2.61826 | ||||||||
\(300\) | 2.31692 | 0.133767 | ||||||||
\(301\) | −10.3131 | −0.594437 | ||||||||
\(302\) | −30.7608 | −1.77009 | ||||||||
\(303\) | 1.53032 | 0.0879145 | ||||||||
\(304\) | −8.24546 | −0.472909 | ||||||||
\(305\) | 12.7934 | 0.732547 | ||||||||
\(306\) | 1.16042 | 0.0663370 | ||||||||
\(307\) | 10.9881 | 0.627123 | 0.313561 | − | 0.949568i | \(-0.398478\pi\) | ||||
0.313561 | + | 0.949568i | \(0.398478\pi\) | |||||||
\(308\) | 15.2164 | 0.867032 | ||||||||
\(309\) | −5.23053 | −0.297555 | ||||||||
\(310\) | −3.06259 | −0.173943 | ||||||||
\(311\) | −0.114314 | −0.00648215 | −0.00324108 | − | 0.999995i | \(-0.501032\pi\) | ||||
−0.00324108 | + | 0.999995i | \(0.501032\pi\) | |||||||
\(312\) | −4.23851 | −0.239958 | ||||||||
\(313\) | −5.70116 | −0.322249 | −0.161124 | − | 0.986934i | \(-0.551512\pi\) | ||||
−0.161124 | + | 0.986934i | \(0.551512\pi\) | |||||||
\(314\) | −25.7439 | −1.45281 | ||||||||
\(315\) | −4.42665 | −0.249413 | ||||||||
\(316\) | −28.4353 | −1.59961 | ||||||||
\(317\) | 1.13763 | 0.0638958 | 0.0319479 | − | 0.999490i | \(-0.489829\pi\) | ||||
0.0319479 | + | 0.999490i | \(0.489829\pi\) | |||||||
\(318\) | −15.6360 | −0.876826 | ||||||||
\(319\) | 2.35269 | 0.131725 | ||||||||
\(320\) | −10.3026 | −0.575935 | ||||||||
\(321\) | 4.59052 | 0.256218 | ||||||||
\(322\) | 64.6887 | 3.60496 | ||||||||
\(323\) | −1.41015 | −0.0784626 | ||||||||
\(324\) | 2.31692 | 0.128718 | ||||||||
\(325\) | 6.43697 | 0.357059 | ||||||||
\(326\) | 17.6786 | 0.979128 | ||||||||
\(327\) | 15.6570 | 0.865831 | ||||||||
\(328\) | −1.22652 | −0.0677231 | ||||||||
\(329\) | 10.1390 | 0.558982 | ||||||||
\(330\) | 3.08256 | 0.169690 | ||||||||
\(331\) | −2.00858 | −0.110402 | −0.0552008 | − | 0.998475i | \(-0.517580\pi\) | ||||
−0.0552008 | + | 0.998475i | \(0.517580\pi\) | |||||||
\(332\) | −36.0638 | −1.97926 | ||||||||
\(333\) | −4.72112 | −0.258716 | ||||||||
\(334\) | 20.4827 | 1.12076 | ||||||||
\(335\) | −2.81592 | −0.153850 | ||||||||
\(336\) | 14.4562 | 0.788653 | ||||||||
\(337\) | −17.3508 | −0.945160 | −0.472580 | − | 0.881288i | \(-0.656677\pi\) | ||||
−0.472580 | + | 0.881288i | \(0.656677\pi\) | |||||||
\(338\) | −59.0790 | −3.21347 | ||||||||
\(339\) | −2.49926 | −0.135741 | ||||||||
\(340\) | −1.29402 | −0.0701779 | ||||||||
\(341\) | −2.18689 | −0.118427 | ||||||||
\(342\) | −5.24591 | −0.283667 | ||||||||
\(343\) | −24.7681 | −1.33735 | ||||||||
\(344\) | −1.53407 | −0.0827116 | ||||||||
\(345\) | 7.03342 | 0.378667 | ||||||||
\(346\) | 9.60507 | 0.516372 | ||||||||
\(347\) | 15.4484 | 0.829313 | 0.414657 | − | 0.909978i | \(-0.363902\pi\) | ||||
0.414657 | + | 0.909978i | \(0.363902\pi\) | |||||||
\(348\) | −3.67409 | −0.196952 | ||||||||
\(349\) | −26.3636 | −1.41121 | −0.705607 | − | 0.708604i | \(-0.749325\pi\) | ||||
−0.705607 | + | 0.708604i | \(0.749325\pi\) | |||||||
\(350\) | 9.19733 | 0.491618 | ||||||||
\(351\) | 6.43697 | 0.343580 | ||||||||
\(352\) | −12.0207 | −0.640703 | ||||||||
\(353\) | 4.81739 | 0.256404 | 0.128202 | − | 0.991748i | \(-0.459079\pi\) | ||||
0.128202 | + | 0.991748i | \(0.459079\pi\) | |||||||
\(354\) | 1.75527 | 0.0932914 | ||||||||
\(355\) | −6.45925 | −0.342821 | ||||||||
\(356\) | 7.12315 | 0.377526 | ||||||||
\(357\) | 2.47232 | 0.130849 | ||||||||
\(358\) | 2.78932 | 0.147420 | ||||||||
\(359\) | −30.8062 | −1.62589 | −0.812943 | − | 0.582343i | \(-0.802136\pi\) | ||||
−0.812943 | + | 0.582343i | \(0.802136\pi\) | |||||||
\(360\) | −0.658463 | −0.0347041 | ||||||||
\(361\) | −12.6252 | −0.664483 | ||||||||
\(362\) | −19.4994 | −1.02486 | ||||||||
\(363\) | −8.79885 | −0.461820 | ||||||||
\(364\) | −66.0187 | −3.46032 | ||||||||
\(365\) | −14.8625 | −0.777938 | ||||||||
\(366\) | −26.5811 | −1.38941 | ||||||||
\(367\) | −2.06412 | −0.107746 | −0.0538732 | − | 0.998548i | \(-0.517157\pi\) | ||||
−0.0538732 | + | 0.998548i | \(0.517157\pi\) | |||||||
\(368\) | −22.9693 | −1.19736 | ||||||||
\(369\) | 1.86270 | 0.0969681 | ||||||||
\(370\) | 9.80916 | 0.509954 | ||||||||
\(371\) | −33.3131 | −1.72953 | ||||||||
\(372\) | 3.41517 | 0.177068 | ||||||||
\(373\) | 22.1308 | 1.14589 | 0.572945 | − | 0.819594i | \(-0.305801\pi\) | ||||
0.572945 | + | 0.819594i | \(0.305801\pi\) | |||||||
\(374\) | −1.72164 | −0.0890237 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 1.50818 | 0.0777783 | ||||||||
\(377\) | −10.2075 | −0.525714 | ||||||||
\(378\) | 9.19733 | 0.473060 | ||||||||
\(379\) | 21.3004 | 1.09413 | 0.547063 | − | 0.837092i | \(-0.315746\pi\) | ||||
0.547063 | + | 0.837092i | \(0.315746\pi\) | |||||||
\(380\) | 5.84985 | 0.300091 | ||||||||
\(381\) | 4.38227 | 0.224511 | ||||||||
\(382\) | 32.4799 | 1.66181 | ||||||||
\(383\) | −16.4144 | −0.838735 | −0.419368 | − | 0.907816i | \(-0.637748\pi\) | ||||
−0.419368 | + | 0.907816i | \(0.637748\pi\) | |||||||
\(384\) | 5.20157 | 0.265442 | ||||||||
\(385\) | 6.56750 | 0.334711 | ||||||||
\(386\) | 2.33896 | 0.119050 | ||||||||
\(387\) | 2.32977 | 0.118429 | ||||||||
\(388\) | 4.15666 | 0.211023 | ||||||||
\(389\) | 15.1829 | 0.769805 | 0.384903 | − | 0.922957i | \(-0.374235\pi\) | ||||
0.384903 | + | 0.922957i | \(0.374235\pi\) | |||||||
\(390\) | −13.3742 | −0.677229 | ||||||||
\(391\) | −3.92822 | −0.198659 | ||||||||
\(392\) | −8.29350 | −0.418885 | ||||||||
\(393\) | −2.38767 | −0.120442 | ||||||||
\(394\) | 43.1127 | 2.17199 | ||||||||
\(395\) | −12.2729 | −0.617517 | ||||||||
\(396\) | −3.43744 | −0.172738 | ||||||||
\(397\) | 7.22477 | 0.362601 | 0.181301 | − | 0.983428i | \(-0.441969\pi\) | ||||
0.181301 | + | 0.983428i | \(0.441969\pi\) | |||||||
\(398\) | −32.8651 | −1.64738 | ||||||||
\(399\) | −11.1766 | −0.559530 | ||||||||
\(400\) | −3.26573 | −0.163287 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 5.85069 | 0.291806 | ||||||||
\(403\) | 9.48817 | 0.472640 | ||||||||
\(404\) | 3.54562 | 0.176401 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −14.5848 | −0.723833 | ||||||||
\(407\) | 7.00439 | 0.347195 | ||||||||
\(408\) | 0.367757 | 0.0182067 | ||||||||
\(409\) | 6.69677 | 0.331134 | 0.165567 | − | 0.986199i | \(-0.447055\pi\) | ||||
0.165567 | + | 0.986199i | \(0.447055\pi\) | |||||||
\(410\) | −3.87016 | −0.191133 | ||||||||
\(411\) | −3.86352 | −0.190573 | ||||||||
\(412\) | −12.1187 | −0.597046 | ||||||||
\(413\) | 3.73965 | 0.184016 | ||||||||
\(414\) | −14.6135 | −0.718213 | ||||||||
\(415\) | −15.5654 | −0.764077 | ||||||||
\(416\) | 52.1536 | 2.55704 | ||||||||
\(417\) | 21.5796 | 1.05676 | ||||||||
\(418\) | 7.78299 | 0.380678 | ||||||||
\(419\) | −3.57582 | −0.174690 | −0.0873451 | − | 0.996178i | \(-0.527838\pi\) | ||||
−0.0873451 | + | 0.996178i | \(0.527838\pi\) | |||||||
\(420\) | −10.2562 | −0.500450 | ||||||||
\(421\) | −2.99153 | −0.145798 | −0.0728991 | − | 0.997339i | \(-0.523225\pi\) | ||||
−0.0728991 | + | 0.997339i | \(0.523225\pi\) | |||||||
\(422\) | −54.9683 | −2.67581 | ||||||||
\(423\) | −2.29045 | −0.111365 | ||||||||
\(424\) | −4.95532 | −0.240652 | ||||||||
\(425\) | −0.558508 | −0.0270916 | ||||||||
\(426\) | 13.4205 | 0.650225 | ||||||||
\(427\) | −56.6318 | −2.74061 | ||||||||
\(428\) | 10.6359 | 0.514104 | ||||||||
\(429\) | −9.55007 | −0.461082 | ||||||||
\(430\) | −4.84062 | −0.233435 | ||||||||
\(431\) | 5.97384 | 0.287750 | 0.143875 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143875 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(432\) | −3.26573 | −0.157123 | ||||||||
\(433\) | 16.2663 | 0.781711 | 0.390855 | − | 0.920452i | \(-0.372179\pi\) | ||||
0.390855 | + | 0.920452i | \(0.372179\pi\) | |||||||
\(434\) | 13.5570 | 0.650756 | ||||||||
\(435\) | −1.58577 | −0.0760317 | ||||||||
\(436\) | 36.2758 | 1.73730 | ||||||||
\(437\) | 17.7583 | 0.849494 | ||||||||
\(438\) | 30.8801 | 1.47551 | ||||||||
\(439\) | −36.4207 | −1.73827 | −0.869134 | − | 0.494577i | \(-0.835323\pi\) | ||||
−0.869134 | + | 0.494577i | \(0.835323\pi\) | |||||||
\(440\) | 0.976915 | 0.0465726 | ||||||||
\(441\) | 12.5952 | 0.599773 | ||||||||
\(442\) | 7.46960 | 0.355293 | ||||||||
\(443\) | 8.11596 | 0.385601 | 0.192801 | − | 0.981238i | \(-0.438243\pi\) | ||||
0.192801 | + | 0.981238i | \(0.438243\pi\) | |||||||
\(444\) | −10.9384 | −0.519115 | ||||||||
\(445\) | 3.07441 | 0.145741 | ||||||||
\(446\) | −50.3651 | −2.38485 | ||||||||
\(447\) | 14.5330 | 0.687388 | ||||||||
\(448\) | 45.6061 | 2.15469 | ||||||||
\(449\) | −18.8078 | −0.887597 | −0.443799 | − | 0.896127i | \(-0.646369\pi\) | ||||
−0.443799 | + | 0.896127i | \(0.646369\pi\) | |||||||
\(450\) | −2.07772 | −0.0979446 | ||||||||
\(451\) | −2.76355 | −0.130130 | ||||||||
\(452\) | −5.79058 | −0.272366 | ||||||||
\(453\) | 14.8051 | 0.695604 | ||||||||
\(454\) | 24.2846 | 1.13973 | ||||||||
\(455\) | −28.4942 | −1.33583 | ||||||||
\(456\) | −1.66252 | −0.0778545 | ||||||||
\(457\) | 28.8194 | 1.34811 | 0.674057 | − | 0.738680i | \(-0.264550\pi\) | ||||
0.674057 | + | 0.738680i | \(0.264550\pi\) | |||||||
\(458\) | −36.7246 | −1.71603 | ||||||||
\(459\) | −0.558508 | −0.0260689 | ||||||||
\(460\) | 16.2959 | 0.759798 | ||||||||
\(461\) | −42.2802 | −1.96919 | −0.984593 | − | 0.174864i | \(-0.944051\pi\) | ||||
−0.984593 | + | 0.174864i | \(0.944051\pi\) | |||||||
\(462\) | −13.6454 | −0.634843 | ||||||||
\(463\) | −20.6245 | −0.958503 | −0.479252 | − | 0.877678i | \(-0.659092\pi\) | ||||
−0.479252 | + | 0.877678i | \(0.659092\pi\) | |||||||
\(464\) | 5.17869 | 0.240414 | ||||||||
\(465\) | 1.47401 | 0.0683557 | ||||||||
\(466\) | −46.4376 | −2.15118 | ||||||||
\(467\) | 3.42075 | 0.158294 | 0.0791468 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791468 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(468\) | 14.9139 | 0.689396 | ||||||||
\(469\) | 12.4651 | 0.575585 | ||||||||
\(470\) | 4.75891 | 0.219512 | ||||||||
\(471\) | 12.3905 | 0.570922 | ||||||||
\(472\) | 0.556273 | 0.0256045 | ||||||||
\(473\) | −3.45652 | −0.158931 | ||||||||
\(474\) | 25.4997 | 1.17124 | ||||||||
\(475\) | 2.52484 | 0.115848 | ||||||||
\(476\) | 5.72816 | 0.262550 | ||||||||
\(477\) | 7.52558 | 0.344573 | ||||||||
\(478\) | 7.10836 | 0.325129 | ||||||||
\(479\) | 30.4454 | 1.39109 | 0.695543 | − | 0.718485i | \(-0.255164\pi\) | ||||
0.695543 | + | 0.718485i | \(0.255164\pi\) | |||||||
\(480\) | 8.10220 | 0.369813 | ||||||||
\(481\) | −30.3897 | −1.38565 | ||||||||
\(482\) | −50.5806 | −2.30388 | ||||||||
\(483\) | −31.1345 | −1.41667 | ||||||||
\(484\) | −20.3862 | −0.926645 | ||||||||
\(485\) | 1.79405 | 0.0814636 | ||||||||
\(486\) | −2.07772 | −0.0942473 | ||||||||
\(487\) | −16.9043 | −0.766008 | −0.383004 | − | 0.923747i | \(-0.625110\pi\) | ||||
−0.383004 | + | 0.923747i | \(0.625110\pi\) | |||||||
\(488\) | −8.42398 | −0.381336 | ||||||||
\(489\) | −8.50867 | −0.384775 | ||||||||
\(490\) | −26.1693 | −1.18221 | ||||||||
\(491\) | 36.1062 | 1.62945 | 0.814724 | − | 0.579848i | \(-0.196888\pi\) | ||||
0.814724 | + | 0.579848i | \(0.196888\pi\) | |||||||
\(492\) | 4.31571 | 0.194567 | ||||||||
\(493\) | 0.885663 | 0.0398883 | ||||||||
\(494\) | −33.7678 | −1.51928 | ||||||||
\(495\) | −1.48363 | −0.0666841 | ||||||||
\(496\) | −4.81373 | −0.216143 | ||||||||
\(497\) | 28.5928 | 1.28256 | ||||||||
\(498\) | 32.3406 | 1.44922 | ||||||||
\(499\) | 2.69002 | 0.120422 | 0.0602110 | − | 0.998186i | \(-0.480823\pi\) | ||||
0.0602110 | + | 0.998186i | \(0.480823\pi\) | |||||||
\(500\) | 2.31692 | 0.103616 | ||||||||
\(501\) | −9.85827 | −0.440435 | ||||||||
\(502\) | 58.8349 | 2.62593 | ||||||||
\(503\) | 21.4498 | 0.956399 | 0.478199 | − | 0.878251i | \(-0.341290\pi\) | ||||
0.478199 | + | 0.878251i | \(0.341290\pi\) | |||||||
\(504\) | 2.91479 | 0.129835 | ||||||||
\(505\) | 1.53032 | 0.0680983 | ||||||||
\(506\) | 21.6810 | 0.963837 | ||||||||
\(507\) | 28.4345 | 1.26282 | ||||||||
\(508\) | 10.1534 | 0.450482 | ||||||||
\(509\) | −8.21098 | −0.363945 | −0.181973 | − | 0.983304i | \(-0.558248\pi\) | ||||
−0.181973 | + | 0.983304i | \(0.558248\pi\) | |||||||
\(510\) | 1.16042 | 0.0513844 | ||||||||
\(511\) | 65.7910 | 2.91042 | ||||||||
\(512\) | −30.7603 | −1.35943 | ||||||||
\(513\) | 2.52484 | 0.111475 | ||||||||
\(514\) | 48.3598 | 2.13306 | ||||||||
\(515\) | −5.23053 | −0.230485 | ||||||||
\(516\) | 5.39789 | 0.237629 | ||||||||
\(517\) | 3.39817 | 0.149452 | ||||||||
\(518\) | −43.4217 | −1.90784 | ||||||||
\(519\) | −4.62289 | −0.202922 | ||||||||
\(520\) | −4.23851 | −0.185871 | ||||||||
\(521\) | 10.3035 | 0.451405 | 0.225703 | − | 0.974196i | \(-0.427532\pi\) | ||||
0.225703 | + | 0.974196i | \(0.427532\pi\) | |||||||
\(522\) | 3.29478 | 0.144208 | ||||||||
\(523\) | 27.9991 | 1.22432 | 0.612158 | − | 0.790736i | \(-0.290302\pi\) | ||||
0.612158 | + | 0.790736i | \(0.290302\pi\) | |||||||
\(524\) | −5.53204 | −0.241668 | ||||||||
\(525\) | −4.42665 | −0.193195 | ||||||||
\(526\) | −44.0605 | −1.92113 | ||||||||
\(527\) | −0.823248 | −0.0358613 | ||||||||
\(528\) | 4.84513 | 0.210857 | ||||||||
\(529\) | 26.4690 | 1.15083 | ||||||||
\(530\) | −15.6360 | −0.679186 | ||||||||
\(531\) | −0.844805 | −0.0366614 | ||||||||
\(532\) | −25.8952 | −1.12270 | ||||||||
\(533\) | 11.9901 | 0.519349 | ||||||||
\(534\) | −6.38776 | −0.276426 | ||||||||
\(535\) | 4.59052 | 0.198466 | ||||||||
\(536\) | 1.85418 | 0.0800884 | ||||||||
\(537\) | −1.34249 | −0.0579328 | ||||||||
\(538\) | −60.6453 | −2.61460 | ||||||||
\(539\) | −18.6866 | −0.804890 | ||||||||
\(540\) | 2.31692 | 0.0997042 | ||||||||
\(541\) | 33.0225 | 1.41975 | 0.709874 | − | 0.704329i | \(-0.248752\pi\) | ||||
0.709874 | + | 0.704329i | \(0.248752\pi\) | |||||||
\(542\) | −53.2644 | −2.28790 | ||||||||
\(543\) | 9.38498 | 0.402748 | ||||||||
\(544\) | −4.52514 | −0.194014 | ||||||||
\(545\) | 15.6570 | 0.670670 | ||||||||
\(546\) | 59.2029 | 2.53365 | ||||||||
\(547\) | 4.82015 | 0.206095 | 0.103047 | − | 0.994676i | \(-0.467141\pi\) | ||||
0.103047 | + | 0.994676i | \(0.467141\pi\) | |||||||
\(548\) | −8.95144 | −0.382387 | ||||||||
\(549\) | 12.7934 | 0.546008 | ||||||||
\(550\) | 3.08256 | 0.131441 | ||||||||
\(551\) | −4.00381 | −0.170568 | ||||||||
\(552\) | −4.63125 | −0.197119 | ||||||||
\(553\) | 54.3279 | 2.31026 | ||||||||
\(554\) | 22.2737 | 0.946319 | ||||||||
\(555\) | −4.72112 | −0.200400 | ||||||||
\(556\) | 49.9981 | 2.12039 | ||||||||
\(557\) | −29.0822 | −1.23225 | −0.616127 | − | 0.787647i | \(-0.711299\pi\) | ||||
−0.616127 | + | 0.787647i | \(0.711299\pi\) | |||||||
\(558\) | −3.06259 | −0.129650 | ||||||||
\(559\) | 14.9967 | 0.634292 | ||||||||
\(560\) | 14.4562 | 0.610888 | ||||||||
\(561\) | 0.828618 | 0.0349843 | ||||||||
\(562\) | −56.6434 | −2.38936 | ||||||||
\(563\) | −26.7323 | −1.12663 | −0.563315 | − | 0.826242i | \(-0.690474\pi\) | ||||
−0.563315 | + | 0.826242i | \(0.690474\pi\) | |||||||
\(564\) | −5.30678 | −0.223456 | ||||||||
\(565\) | −2.49926 | −0.105145 | ||||||||
\(566\) | −12.2449 | −0.514690 | ||||||||
\(567\) | −4.42665 | −0.185902 | ||||||||
\(568\) | 4.25318 | 0.178459 | ||||||||
\(569\) | −19.0470 | −0.798491 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(570\) | −5.24591 | −0.219727 | ||||||||
\(571\) | −9.76891 | −0.408816 | −0.204408 | − | 0.978886i | \(-0.565527\pi\) | ||||
−0.204408 | + | 0.978886i | \(0.565527\pi\) | |||||||
\(572\) | −22.1267 | −0.925164 | ||||||||
\(573\) | −15.6325 | −0.653055 | ||||||||
\(574\) | 17.1318 | 0.715069 | ||||||||
\(575\) | 7.03342 | 0.293314 | ||||||||
\(576\) | −10.3026 | −0.429276 | ||||||||
\(577\) | 23.3735 | 0.973050 | 0.486525 | − | 0.873667i | \(-0.338264\pi\) | ||||
0.486525 | + | 0.873667i | \(0.338264\pi\) | |||||||
\(578\) | 34.6731 | 1.44221 | ||||||||
\(579\) | −1.12574 | −0.0467840 | ||||||||
\(580\) | −3.67409 | −0.152558 | ||||||||
\(581\) | 68.9027 | 2.85857 | ||||||||
\(582\) | −3.72753 | −0.154511 | ||||||||
\(583\) | −11.1652 | −0.462414 | ||||||||
\(584\) | 9.78640 | 0.404964 | ||||||||
\(585\) | 6.43697 | 0.266136 | ||||||||
\(586\) | −9.60304 | −0.396698 | ||||||||
\(587\) | −5.74205 | −0.237000 | −0.118500 | − | 0.992954i | \(-0.537809\pi\) | ||||
−0.118500 | + | 0.992954i | \(0.537809\pi\) | |||||||
\(588\) | 29.1821 | 1.20345 | ||||||||
\(589\) | 3.72165 | 0.153348 | ||||||||
\(590\) | 1.75527 | 0.0722632 | ||||||||
\(591\) | −20.7500 | −0.853542 | ||||||||
\(592\) | 15.4179 | 0.633672 | ||||||||
\(593\) | 30.6567 | 1.25892 | 0.629459 | − | 0.777033i | \(-0.283276\pi\) | ||||
0.629459 | + | 0.777033i | \(0.283276\pi\) | |||||||
\(594\) | 3.08256 | 0.126479 | ||||||||
\(595\) | 2.47232 | 0.101355 | ||||||||
\(596\) | 33.6718 | 1.37925 | ||||||||
\(597\) | 15.8179 | 0.647382 | ||||||||
\(598\) | −94.0665 | −3.84666 | ||||||||
\(599\) | 8.95067 | 0.365715 | 0.182857 | − | 0.983139i | \(-0.441465\pi\) | ||||
0.182857 | + | 0.983139i | \(0.441465\pi\) | |||||||
\(600\) | −0.658463 | −0.0268817 | ||||||||
\(601\) | 23.5695 | 0.961419 | 0.480710 | − | 0.876880i | \(-0.340379\pi\) | ||||
0.480710 | + | 0.876880i | \(0.340379\pi\) | |||||||
\(602\) | 21.4277 | 0.873328 | ||||||||
\(603\) | −2.81592 | −0.114673 | ||||||||
\(604\) | 34.3022 | 1.39574 | ||||||||
\(605\) | −8.79885 | −0.357724 | ||||||||
\(606\) | −3.17957 | −0.129161 | ||||||||
\(607\) | 17.9509 | 0.728604 | 0.364302 | − | 0.931281i | \(-0.381308\pi\) | ||||
0.364302 | + | 0.931281i | \(0.381308\pi\) | |||||||
\(608\) | 20.4568 | 0.829632 | ||||||||
\(609\) | 7.01963 | 0.284450 | ||||||||
\(610\) | −26.5811 | −1.07624 | ||||||||
\(611\) | −14.7435 | −0.596460 | ||||||||
\(612\) | −1.29402 | −0.0523075 | ||||||||
\(613\) | −0.187178 | −0.00756003 | −0.00378002 | − | 0.999993i | \(-0.501203\pi\) | ||||
−0.00378002 | + | 0.999993i | \(0.501203\pi\) | |||||||
\(614\) | −22.8301 | −0.921349 | ||||||||
\(615\) | 1.86270 | 0.0751111 | ||||||||
\(616\) | −4.32446 | −0.174237 | ||||||||
\(617\) | 21.2845 | 0.856880 | 0.428440 | − | 0.903570i | \(-0.359063\pi\) | ||||
0.428440 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(618\) | 10.8676 | 0.437158 | ||||||||
\(619\) | 26.4776 | 1.06422 | 0.532112 | − | 0.846674i | \(-0.321398\pi\) | ||||
0.532112 | + | 0.846674i | \(0.321398\pi\) | |||||||
\(620\) | 3.41517 | 0.137156 | ||||||||
\(621\) | 7.03342 | 0.282242 | ||||||||
\(622\) | 0.237512 | 0.00952338 | ||||||||
\(623\) | −13.6093 | −0.545247 | ||||||||
\(624\) | −21.0214 | −0.841529 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.8454 | 0.473438 | ||||||||
\(627\) | −3.74593 | −0.149598 | ||||||||
\(628\) | 28.7076 | 1.14556 | ||||||||
\(629\) | 2.63678 | 0.105135 | ||||||||
\(630\) | 9.19733 | 0.366431 | ||||||||
\(631\) | −15.3672 | −0.611757 | −0.305878 | − | 0.952071i | \(-0.598950\pi\) | ||||
−0.305878 | + | 0.952071i | \(0.598950\pi\) | |||||||
\(632\) | 8.08127 | 0.321455 | ||||||||
\(633\) | 26.4561 | 1.05153 | ||||||||
\(634\) | −2.36368 | −0.0938738 | ||||||||
\(635\) | 4.38227 | 0.173905 | ||||||||
\(636\) | 17.4361 | 0.691388 | ||||||||
\(637\) | 81.0750 | 3.21231 | ||||||||
\(638\) | −4.88822 | −0.193527 | ||||||||
\(639\) | −6.45925 | −0.255524 | ||||||||
\(640\) | 5.20157 | 0.205610 | ||||||||
\(641\) | 21.2377 | 0.838839 | 0.419420 | − | 0.907792i | \(-0.362234\pi\) | ||||
0.419420 | + | 0.907792i | \(0.362234\pi\) | |||||||
\(642\) | −9.53782 | −0.376428 | ||||||||
\(643\) | −9.46684 | −0.373336 | −0.186668 | − | 0.982423i | \(-0.559769\pi\) | ||||
−0.186668 | + | 0.982423i | \(0.559769\pi\) | |||||||
\(644\) | −72.1360 | −2.84256 | ||||||||
\(645\) | 2.32977 | 0.0917348 | ||||||||
\(646\) | 2.92989 | 0.115275 | ||||||||
\(647\) | −13.4251 | −0.527796 | −0.263898 | − | 0.964551i | \(-0.585008\pi\) | ||||
−0.263898 | + | 0.964551i | \(0.585008\pi\) | |||||||
\(648\) | −0.658463 | −0.0258669 | ||||||||
\(649\) | 1.25338 | 0.0491993 | ||||||||
\(650\) | −13.3742 | −0.524580 | ||||||||
\(651\) | −6.52494 | −0.255733 | ||||||||
\(652\) | −19.7139 | −0.772055 | ||||||||
\(653\) | 29.2982 | 1.14653 | 0.573264 | − | 0.819371i | \(-0.305677\pi\) | ||||
0.573264 | + | 0.819371i | \(0.305677\pi\) | |||||||
\(654\) | −32.5307 | −1.27205 | ||||||||
\(655\) | −2.38767 | −0.0932941 | ||||||||
\(656\) | −6.08306 | −0.237504 | ||||||||
\(657\) | −14.8625 | −0.579840 | ||||||||
\(658\) | −21.0660 | −0.821239 | ||||||||
\(659\) | −32.2265 | −1.25537 | −0.627684 | − | 0.778468i | \(-0.715997\pi\) | ||||
−0.627684 | + | 0.778468i | \(0.715997\pi\) | |||||||
\(660\) | −3.43744 | −0.133802 | ||||||||
\(661\) | −4.95749 | −0.192824 | −0.0964121 | − | 0.995342i | \(-0.530737\pi\) | ||||
−0.0964121 | + | 0.995342i | \(0.530737\pi\) | |||||||
\(662\) | 4.17327 | 0.162199 | ||||||||
\(663\) | −3.59510 | −0.139622 | ||||||||
\(664\) | 10.2493 | 0.397749 | ||||||||
\(665\) | −11.1766 | −0.433410 | ||||||||
\(666\) | 9.80916 | 0.380097 | ||||||||
\(667\) | −11.1534 | −0.431860 | ||||||||
\(668\) | −22.8408 | −0.883737 | ||||||||
\(669\) | 24.2406 | 0.937194 | ||||||||
\(670\) | 5.85069 | 0.226032 | ||||||||
\(671\) | −18.9806 | −0.732739 | ||||||||
\(672\) | −35.8656 | −1.38355 | ||||||||
\(673\) | 7.51400 | 0.289644 | 0.144822 | − | 0.989458i | \(-0.453739\pi\) | ||||
0.144822 | + | 0.989458i | \(0.453739\pi\) | |||||||
\(674\) | 36.0501 | 1.38860 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 65.8804 | 2.53386 | ||||||||
\(677\) | 32.9678 | 1.26706 | 0.633528 | − | 0.773720i | \(-0.281606\pi\) | ||||
0.633528 | + | 0.773720i | \(0.281606\pi\) | |||||||
\(678\) | 5.19276 | 0.199427 | ||||||||
\(679\) | −7.94163 | −0.304772 | ||||||||
\(680\) | 0.367757 | 0.0141028 | ||||||||
\(681\) | −11.6881 | −0.447889 | ||||||||
\(682\) | 4.54374 | 0.173989 | ||||||||
\(683\) | 29.6082 | 1.13293 | 0.566463 | − | 0.824087i | \(-0.308311\pi\) | ||||
0.566463 | + | 0.824087i | \(0.308311\pi\) | |||||||
\(684\) | 5.84985 | 0.223675 | ||||||||
\(685\) | −3.86352 | −0.147617 | ||||||||
\(686\) | 51.4612 | 1.96480 | ||||||||
\(687\) | 17.6754 | 0.674359 | ||||||||
\(688\) | −7.60841 | −0.290068 | ||||||||
\(689\) | 48.4419 | 1.84549 | ||||||||
\(690\) | −14.6135 | −0.556326 | ||||||||
\(691\) | −11.6840 | −0.444480 | −0.222240 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222240 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(692\) | −10.7109 | −0.407166 | ||||||||
\(693\) | 6.56750 | 0.249479 | ||||||||
\(694\) | −32.0974 | −1.21840 | ||||||||
\(695\) | 21.5796 | 0.818560 | ||||||||
\(696\) | 1.04417 | 0.0395791 | ||||||||
\(697\) | −1.04033 | −0.0394053 | ||||||||
\(698\) | 54.7762 | 2.07331 | ||||||||
\(699\) | 22.3503 | 0.845365 | ||||||||
\(700\) | −10.2562 | −0.387647 | ||||||||
\(701\) | 36.6032 | 1.38248 | 0.691242 | − | 0.722623i | \(-0.257064\pi\) | ||||
0.691242 | + | 0.722623i | \(0.257064\pi\) | |||||||
\(702\) | −13.3742 | −0.504777 | ||||||||
\(703\) | −11.9201 | −0.449574 | ||||||||
\(704\) | 15.2853 | 0.576085 | ||||||||
\(705\) | −2.29045 | −0.0862633 | ||||||||
\(706\) | −10.0092 | −0.376700 | ||||||||
\(707\) | −6.77419 | −0.254770 | ||||||||
\(708\) | −1.95734 | −0.0735614 | ||||||||
\(709\) | −32.2651 | −1.21174 | −0.605871 | − | 0.795563i | \(-0.707175\pi\) | ||||
−0.605871 | + | 0.795563i | \(0.707175\pi\) | |||||||
\(710\) | 13.4205 | 0.503662 | ||||||||
\(711\) | −12.2729 | −0.460270 | ||||||||
\(712\) | −2.02439 | −0.0758671 | ||||||||
\(713\) | 10.3674 | 0.388261 | ||||||||
\(714\) | −5.13678 | −0.192239 | ||||||||
\(715\) | −9.55007 | −0.357152 | ||||||||
\(716\) | −3.11044 | −0.116243 | ||||||||
\(717\) | −3.42123 | −0.127768 | ||||||||
\(718\) | 64.0065 | 2.38870 | ||||||||
\(719\) | 0.320817 | 0.0119645 | 0.00598223 | − | 0.999982i | \(-0.498096\pi\) | ||||
0.00598223 | + | 0.999982i | \(0.498096\pi\) | |||||||
\(720\) | −3.26573 | −0.121707 | ||||||||
\(721\) | 23.1537 | 0.862290 | ||||||||
\(722\) | 26.2316 | 0.976237 | ||||||||
\(723\) | 24.3443 | 0.905374 | ||||||||
\(724\) | 21.7442 | 0.808118 | ||||||||
\(725\) | −1.58577 | −0.0588939 | ||||||||
\(726\) | 18.2815 | 0.678491 | ||||||||
\(727\) | −6.07116 | −0.225167 | −0.112583 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112583 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(728\) | 18.7624 | 0.695380 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.8801 | 1.14292 | ||||||||
\(731\) | −1.30120 | −0.0481265 | ||||||||
\(732\) | 29.6412 | 1.09557 | ||||||||
\(733\) | −39.7977 | −1.46996 | −0.734982 | − | 0.678087i | \(-0.762809\pi\) | ||||
−0.734982 | + | 0.678087i | \(0.762809\pi\) | |||||||
\(734\) | 4.28867 | 0.158298 | ||||||||
\(735\) | 12.5952 | 0.464582 | ||||||||
\(736\) | 56.9862 | 2.10054 | ||||||||
\(737\) | 4.17778 | 0.153891 | ||||||||
\(738\) | −3.87016 | −0.142462 | ||||||||
\(739\) | −10.5971 | −0.389821 | −0.194910 | − | 0.980821i | \(-0.562442\pi\) | ||||
−0.194910 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(740\) | −10.9384 | −0.402105 | ||||||||
\(741\) | 16.2523 | 0.597044 | ||||||||
\(742\) | 69.2153 | 2.54097 | ||||||||
\(743\) | −45.3111 | −1.66230 | −0.831152 | − | 0.556045i | \(-0.812318\pi\) | ||||
−0.831152 | + | 0.556045i | \(0.812318\pi\) | |||||||
\(744\) | −0.970584 | −0.0355833 | ||||||||
\(745\) | 14.5330 | 0.532449 | ||||||||
\(746\) | −45.9816 | −1.68351 | ||||||||
\(747\) | −15.5654 | −0.569510 | ||||||||
\(748\) | 1.91984 | 0.0701963 | ||||||||
\(749\) | −20.3206 | −0.742500 | ||||||||
\(750\) | −2.07772 | −0.0758676 | ||||||||
\(751\) | 3.56157 | 0.129964 | 0.0649818 | − | 0.997886i | \(-0.479301\pi\) | ||||
0.0649818 | + | 0.997886i | \(0.479301\pi\) | |||||||
\(752\) | 7.47999 | 0.272767 | ||||||||
\(753\) | −28.3171 | −1.03193 | ||||||||
\(754\) | 21.2084 | 0.772363 | ||||||||
\(755\) | 14.8051 | 0.538813 | ||||||||
\(756\) | −10.2562 | −0.373014 | ||||||||
\(757\) | 22.7490 | 0.826826 | 0.413413 | − | 0.910544i | \(-0.364337\pi\) | ||||
0.413413 | + | 0.910544i | \(0.364337\pi\) | |||||||
\(758\) | −44.2561 | −1.60746 | ||||||||
\(759\) | −10.4350 | −0.378766 | ||||||||
\(760\) | −1.66252 | −0.0603058 | ||||||||
\(761\) | 43.4393 | 1.57467 | 0.787336 | − | 0.616524i | \(-0.211460\pi\) | ||||
0.787336 | + | 0.616524i | \(0.211460\pi\) | |||||||
\(762\) | −9.10513 | −0.329844 | ||||||||
\(763\) | −69.3078 | −2.50911 | ||||||||
\(764\) | −36.2191 | −1.31036 | ||||||||
\(765\) | −0.558508 | −0.0201929 | ||||||||
\(766\) | 34.1045 | 1.23224 | ||||||||
\(767\) | −5.43798 | −0.196354 | ||||||||
\(768\) | 9.79785 | 0.353549 | ||||||||
\(769\) | 51.0460 | 1.84076 | 0.920382 | − | 0.391020i | \(-0.127878\pi\) | ||||
0.920382 | + | 0.391020i | \(0.127878\pi\) | |||||||
\(770\) | −13.6454 | −0.491747 | ||||||||
\(771\) | −23.2754 | −0.838245 | ||||||||
\(772\) | −2.60824 | −0.0938725 | ||||||||
\(773\) | −24.1477 | −0.868533 | −0.434266 | − | 0.900785i | \(-0.642992\pi\) | ||||
−0.434266 | + | 0.900785i | \(0.642992\pi\) | |||||||
\(774\) | −4.84062 | −0.173992 | ||||||||
\(775\) | 1.47401 | 0.0529481 | ||||||||
\(776\) | −1.18132 | −0.0424068 | ||||||||
\(777\) | 20.8987 | 0.749738 | ||||||||
\(778\) | −31.5459 | −1.13097 | ||||||||
\(779\) | 4.70301 | 0.168503 | ||||||||
\(780\) | 14.9139 | 0.534004 | ||||||||
\(781\) | 9.58312 | 0.342911 | ||||||||
\(782\) | 8.16174 | 0.291863 | ||||||||
\(783\) | −1.58577 | −0.0566707 | ||||||||
\(784\) | −41.1326 | −1.46902 | ||||||||
\(785\) | 12.3905 | 0.442234 | ||||||||
\(786\) | 4.96091 | 0.176950 | ||||||||
\(787\) | 50.3061 | 1.79322 | 0.896610 | − | 0.442821i | \(-0.146022\pi\) | ||||
0.896610 | + | 0.442821i | \(0.146022\pi\) | |||||||
\(788\) | −48.0761 | −1.71264 | ||||||||
\(789\) | 21.2062 | 0.754961 | ||||||||
\(790\) | 25.4997 | 0.907237 | ||||||||
\(791\) | 11.0633 | 0.393367 | ||||||||
\(792\) | 0.976915 | 0.0347132 | ||||||||
\(793\) | 82.3506 | 2.92436 | ||||||||
\(794\) | −15.0111 | −0.532722 | ||||||||
\(795\) | 7.52558 | 0.266905 | ||||||||
\(796\) | 36.6487 | 1.29898 | ||||||||
\(797\) | 46.9664 | 1.66364 | 0.831818 | − | 0.555049i | \(-0.187300\pi\) | ||||
0.831818 | + | 0.555049i | \(0.187300\pi\) | |||||||
\(798\) | 23.2218 | 0.822044 | ||||||||
\(799\) | 1.27923 | 0.0452560 | ||||||||
\(800\) | 8.10220 | 0.286456 | ||||||||
\(801\) | 3.07441 | 0.108629 | ||||||||
\(802\) | −2.07772 | −0.0733668 | ||||||||
\(803\) | 22.0504 | 0.778141 | ||||||||
\(804\) | −6.52425 | −0.230093 | ||||||||
\(805\) | −31.1345 | −1.09735 | ||||||||
\(806\) | −19.7138 | −0.694387 | ||||||||
\(807\) | 29.1884 | 1.02748 | ||||||||
\(808\) | −1.00766 | −0.0354493 | ||||||||
\(809\) | 46.2457 | 1.62591 | 0.812956 | − | 0.582326i | \(-0.197857\pi\) | ||||
0.812956 | + | 0.582326i | \(0.197857\pi\) | |||||||
\(810\) | −2.07772 | −0.0730036 | ||||||||
\(811\) | 19.8260 | 0.696186 | 0.348093 | − | 0.937460i | \(-0.386829\pi\) | ||||
0.348093 | + | 0.937460i | \(0.386829\pi\) | |||||||
\(812\) | 16.2639 | 0.570751 | ||||||||
\(813\) | 25.6360 | 0.899093 | ||||||||
\(814\) | −14.5531 | −0.510087 | ||||||||
\(815\) | −8.50867 | −0.298046 | ||||||||
\(816\) | 1.82394 | 0.0638506 | ||||||||
\(817\) | 5.88231 | 0.205796 | ||||||||
\(818\) | −13.9140 | −0.486492 | ||||||||
\(819\) | −28.4942 | −0.995668 | ||||||||
\(820\) | 4.31571 | 0.150711 | ||||||||
\(821\) | 38.3828 | 1.33957 | 0.669784 | − | 0.742556i | \(-0.266387\pi\) | ||||
0.669784 | + | 0.742556i | \(0.266387\pi\) | |||||||
\(822\) | 8.02730 | 0.279984 | ||||||||
\(823\) | −21.1217 | −0.736256 | −0.368128 | − | 0.929775i | \(-0.620001\pi\) | ||||
−0.368128 | + | 0.929775i | \(0.620001\pi\) | |||||||
\(824\) | 3.44411 | 0.119981 | ||||||||
\(825\) | −1.48363 | −0.0516533 | ||||||||
\(826\) | −7.76995 | −0.270351 | ||||||||
\(827\) | 12.2201 | 0.424936 | 0.212468 | − | 0.977168i | \(-0.431850\pi\) | ||||
0.212468 | + | 0.977168i | \(0.431850\pi\) | |||||||
\(828\) | 16.2959 | 0.566320 | ||||||||
\(829\) | 4.75174 | 0.165035 | 0.0825174 | − | 0.996590i | \(-0.473704\pi\) | ||||
0.0825174 | + | 0.996590i | \(0.473704\pi\) | |||||||
\(830\) | 32.3406 | 1.12256 | ||||||||
\(831\) | −10.7203 | −0.371882 | ||||||||
\(832\) | −66.3177 | −2.29915 | ||||||||
\(833\) | −7.03454 | −0.243732 | ||||||||
\(834\) | −44.8363 | −1.55255 | ||||||||
\(835\) | −9.85827 | −0.341160 | ||||||||
\(836\) | −8.67900 | −0.300170 | ||||||||
\(837\) | 1.47401 | 0.0509493 | ||||||||
\(838\) | 7.42955 | 0.256649 | ||||||||
\(839\) | −5.57124 | −0.192340 | −0.0961702 | − | 0.995365i | \(-0.530659\pi\) | ||||
−0.0961702 | + | 0.995365i | \(0.530659\pi\) | |||||||
\(840\) | 2.91479 | 0.100570 | ||||||||
\(841\) | −26.4853 | −0.913288 | ||||||||
\(842\) | 6.21556 | 0.214202 | ||||||||
\(843\) | 27.2623 | 0.938963 | ||||||||
\(844\) | 61.2965 | 2.10991 | ||||||||
\(845\) | 28.4345 | 0.978178 | ||||||||
\(846\) | 4.75891 | 0.163615 | ||||||||
\(847\) | 38.9494 | 1.33832 | ||||||||
\(848\) | −24.5765 | −0.843961 | ||||||||
\(849\) | 5.89342 | 0.202262 | ||||||||
\(850\) | 1.16042 | 0.0398022 | ||||||||
\(851\) | −33.2056 | −1.13827 | ||||||||
\(852\) | −14.9655 | −0.512711 | ||||||||
\(853\) | 30.6515 | 1.04949 | 0.524744 | − | 0.851260i | \(-0.324161\pi\) | ||||
0.524744 | + | 0.851260i | \(0.324161\pi\) | |||||||
\(854\) | 117.665 | 4.02642 | ||||||||
\(855\) | 2.52484 | 0.0863478 | ||||||||
\(856\) | −3.02269 | −0.103313 | ||||||||
\(857\) | −8.67392 | −0.296295 | −0.148148 | − | 0.988965i | \(-0.547331\pi\) | ||||
−0.148148 | + | 0.988965i | \(0.547331\pi\) | |||||||
\(858\) | 19.8424 | 0.677407 | ||||||||
\(859\) | 4.22187 | 0.144048 | 0.0720242 | − | 0.997403i | \(-0.477054\pi\) | ||||
0.0720242 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(860\) | 5.39789 | 0.184067 | ||||||||
\(861\) | −8.24550 | −0.281006 | ||||||||
\(862\) | −12.4120 | −0.422753 | ||||||||
\(863\) | 6.39200 | 0.217586 | 0.108793 | − | 0.994064i | \(-0.465301\pi\) | ||||
0.108793 | + | 0.994064i | \(0.465301\pi\) | |||||||
\(864\) | 8.10220 | 0.275642 | ||||||||
\(865\) | −4.62289 | −0.157183 | ||||||||
\(866\) | −33.7969 | −1.14847 | ||||||||
\(867\) | −16.6881 | −0.566757 | ||||||||
\(868\) | −15.1177 | −0.513130 | ||||||||
\(869\) | 18.2084 | 0.617679 | ||||||||
\(870\) | 3.29478 | 0.111703 | ||||||||
\(871\) | −18.1260 | −0.614176 | ||||||||
\(872\) | −10.3095 | −0.349125 | ||||||||
\(873\) | 1.79405 | 0.0607194 | ||||||||
\(874\) | −36.8967 | −1.24805 | ||||||||
\(875\) | −4.42665 | −0.149648 | ||||||||
\(876\) | −34.4351 | −1.16345 | ||||||||
\(877\) | −48.5065 | −1.63795 | −0.818974 | − | 0.573830i | \(-0.805457\pi\) | ||||
−0.818974 | + | 0.573830i | \(0.805457\pi\) | |||||||
\(878\) | 75.6721 | 2.55381 | ||||||||
\(879\) | 4.62191 | 0.155893 | ||||||||
\(880\) | 4.84513 | 0.163329 | ||||||||
\(881\) | −45.1632 | −1.52159 | −0.760794 | − | 0.648993i | \(-0.775190\pi\) | ||||
−0.760794 | + | 0.648993i | \(0.775190\pi\) | |||||||
\(882\) | −26.1693 | −0.881168 | ||||||||
\(883\) | 41.8945 | 1.40986 | 0.704931 | − | 0.709275i | \(-0.250978\pi\) | ||||
0.704931 | + | 0.709275i | \(0.250978\pi\) | |||||||
\(884\) | −8.32954 | −0.280153 | ||||||||
\(885\) | −0.844805 | −0.0283978 | ||||||||
\(886\) | −16.8627 | −0.566513 | ||||||||
\(887\) | −0.865938 | −0.0290754 | −0.0145377 | − | 0.999894i | \(-0.504628\pi\) | ||||
−0.0145377 | + | 0.999894i | \(0.504628\pi\) | |||||||
\(888\) | 3.10868 | 0.104321 | ||||||||
\(889\) | −19.3988 | −0.650614 | ||||||||
\(890\) | −6.38776 | −0.214118 | ||||||||
\(891\) | −1.48363 | −0.0497034 | ||||||||
\(892\) | 56.1633 | 1.88049 | ||||||||
\(893\) | −5.78302 | −0.193521 | ||||||||
\(894\) | −30.1955 | −1.00989 | ||||||||
\(895\) | −1.34249 | −0.0448746 | ||||||||
\(896\) | −23.0255 | −0.769229 | ||||||||
\(897\) | 45.2739 | 1.51165 | ||||||||
\(898\) | 39.0774 | 1.30403 | ||||||||
\(899\) | −2.33744 | −0.0779580 | ||||||||
\(900\) | 2.31692 | 0.0772305 | ||||||||
\(901\) | −4.20310 | −0.140025 | ||||||||
\(902\) | 5.74188 | 0.191184 | ||||||||
\(903\) | −10.3131 | −0.343198 | ||||||||
\(904\) | 1.64567 | 0.0547342 | ||||||||
\(905\) | 9.38498 | 0.311967 | ||||||||
\(906\) | −30.7608 | −1.02196 | ||||||||
\(907\) | 18.2532 | 0.606088 | 0.303044 | − | 0.952977i | \(-0.401997\pi\) | ||||
0.303044 | + | 0.952977i | \(0.401997\pi\) | |||||||
\(908\) | −27.0803 | −0.898692 | ||||||||
\(909\) | 1.53032 | 0.0507575 | ||||||||
\(910\) | 59.2029 | 1.96256 | ||||||||
\(911\) | −4.37970 | −0.145106 | −0.0725530 | − | 0.997365i | \(-0.523115\pi\) | ||||
−0.0725530 | + | 0.997365i | \(0.523115\pi\) | |||||||
\(912\) | −8.24546 | −0.273034 | ||||||||
\(913\) | 23.0933 | 0.764278 | ||||||||
\(914\) | −59.8785 | −1.98061 | ||||||||
\(915\) | 12.7934 | 0.422936 | ||||||||
\(916\) | 40.9525 | 1.35311 | ||||||||
\(917\) | 10.5694 | 0.349032 | ||||||||
\(918\) | 1.16042 | 0.0382997 | ||||||||
\(919\) | 9.08279 | 0.299614 | 0.149807 | − | 0.988715i | \(-0.452135\pi\) | ||||
0.149807 | + | 0.988715i | \(0.452135\pi\) | |||||||
\(920\) | −4.63125 | −0.152688 | ||||||||
\(921\) | 10.9881 | 0.362069 | ||||||||
\(922\) | 87.8464 | 2.89307 | ||||||||
\(923\) | −41.5780 | −1.36856 | ||||||||
\(924\) | 15.2164 | 0.500581 | ||||||||
\(925\) | −4.72112 | −0.155229 | ||||||||
\(926\) | 42.8520 | 1.40820 | ||||||||
\(927\) | −5.23053 | −0.171793 | ||||||||
\(928\) | −12.8482 | −0.421763 | ||||||||
\(929\) | 15.3679 | 0.504205 | 0.252103 | − | 0.967700i | \(-0.418878\pi\) | ||||
0.252103 | + | 0.967700i | \(0.418878\pi\) | |||||||
\(930\) | −3.06259 | −0.100426 | ||||||||
\(931\) | 31.8010 | 1.04223 | ||||||||
\(932\) | 51.7837 | 1.69623 | ||||||||
\(933\) | −0.114314 | −0.00374247 | ||||||||
\(934\) | −7.10736 | −0.232560 | ||||||||
\(935\) | 0.828618 | 0.0270987 | ||||||||
\(936\) | −4.23851 | −0.138540 | ||||||||
\(937\) | −35.4554 | −1.15828 | −0.579139 | − | 0.815229i | \(-0.696611\pi\) | ||||
−0.579139 | + | 0.815229i | \(0.696611\pi\) | |||||||
\(938\) | −25.8990 | −0.845631 | ||||||||
\(939\) | −5.70116 | −0.186050 | ||||||||
\(940\) | −5.30678 | −0.173088 | ||||||||
\(941\) | −30.3805 | −0.990375 | −0.495187 | − | 0.868786i | \(-0.664901\pi\) | ||||
−0.495187 | + | 0.868786i | \(0.664901\pi\) | |||||||
\(942\) | −25.7439 | −0.838781 | ||||||||
\(943\) | 13.1011 | 0.426631 | ||||||||
\(944\) | 2.75890 | 0.0897947 | ||||||||
\(945\) | −4.42665 | −0.143999 | ||||||||
\(946\) | 7.18167 | 0.233496 | ||||||||
\(947\) | −23.5258 | −0.764487 | −0.382243 | − | 0.924062i | \(-0.624848\pi\) | ||||
−0.382243 | + | 0.924062i | \(0.624848\pi\) | |||||||
\(948\) | −28.4353 | −0.923536 | ||||||||
\(949\) | −95.6693 | −3.10556 | ||||||||
\(950\) | −5.24591 | −0.170200 | ||||||||
\(951\) | 1.13763 | 0.0368903 | ||||||||
\(952\) | −1.62793 | −0.0527616 | ||||||||
\(953\) | −45.2597 | −1.46610 | −0.733052 | − | 0.680172i | \(-0.761905\pi\) | ||||
−0.733052 | + | 0.680172i | \(0.761905\pi\) | |||||||
\(954\) | −15.6360 | −0.506236 | ||||||||
\(955\) | −15.6325 | −0.505855 | ||||||||
\(956\) | −7.92671 | −0.256368 | ||||||||
\(957\) | 2.35269 | 0.0760516 | ||||||||
\(958\) | −63.2570 | −2.04374 | ||||||||
\(959\) | 17.1024 | 0.552266 | ||||||||
\(960\) | −10.3026 | −0.332516 | ||||||||
\(961\) | −28.8273 | −0.929912 | ||||||||
\(962\) | 63.1412 | 2.03575 | ||||||||
\(963\) | 4.59052 | 0.147928 | ||||||||
\(964\) | 56.4037 | 1.81664 | ||||||||
\(965\) | −1.12574 | −0.0362387 | ||||||||
\(966\) | 64.6887 | 2.08133 | ||||||||
\(967\) | −28.1933 | −0.906634 | −0.453317 | − | 0.891349i | \(-0.649759\pi\) | ||||
−0.453317 | + | 0.891349i | \(0.649759\pi\) | |||||||
\(968\) | 5.79372 | 0.186217 | ||||||||
\(969\) | −1.41015 | −0.0453004 | ||||||||
\(970\) | −3.72753 | −0.119684 | ||||||||
\(971\) | −24.9658 | −0.801192 | −0.400596 | − | 0.916255i | \(-0.631197\pi\) | ||||
−0.400596 | + | 0.916255i | \(0.631197\pi\) | |||||||
\(972\) | 2.31692 | 0.0743151 | ||||||||
\(973\) | −95.5252 | −3.06240 | ||||||||
\(974\) | 35.1224 | 1.12540 | ||||||||
\(975\) | 6.43697 | 0.206148 | ||||||||
\(976\) | −41.7798 | −1.33734 | ||||||||
\(977\) | −8.55294 | −0.273633 | −0.136816 | − | 0.990596i | \(-0.543687\pi\) | ||||
−0.136816 | + | 0.990596i | \(0.543687\pi\) | |||||||
\(978\) | 17.6786 | 0.565300 | ||||||||
\(979\) | −4.56128 | −0.145779 | ||||||||
\(980\) | 29.1821 | 0.932188 | ||||||||
\(981\) | 15.6570 | 0.499888 | ||||||||
\(982\) | −75.0185 | −2.39394 | ||||||||
\(983\) | −39.1357 | −1.24824 | −0.624118 | − | 0.781330i | \(-0.714541\pi\) | ||||
−0.624118 | + | 0.781330i | \(0.714541\pi\) | |||||||
\(984\) | −1.22652 | −0.0390999 | ||||||||
\(985\) | −20.7500 | −0.661151 | ||||||||
\(986\) | −1.84016 | −0.0586026 | ||||||||
\(987\) | 10.1390 | 0.322728 | ||||||||
\(988\) | 37.6553 | 1.19797 | ||||||||
\(989\) | 16.3863 | 0.521054 | ||||||||
\(990\) | 3.08256 | 0.0979703 | ||||||||
\(991\) | 13.2902 | 0.422178 | 0.211089 | − | 0.977467i | \(-0.432299\pi\) | ||||
0.211089 | + | 0.977467i | \(0.432299\pi\) | |||||||
\(992\) | 11.9427 | 0.379183 | ||||||||
\(993\) | −2.00858 | −0.0637404 | ||||||||
\(994\) | −59.4079 | −1.88430 | ||||||||
\(995\) | 15.8179 | 0.501460 | ||||||||
\(996\) | −36.0638 | −1.14273 | ||||||||
\(997\) | −21.4461 | −0.679205 | −0.339603 | − | 0.940569i | \(-0.610293\pi\) | ||||
−0.339603 | + | 0.940569i | \(0.610293\pi\) | |||||||
\(998\) | −5.58911 | −0.176920 | ||||||||
\(999\) | −4.72112 | −0.149370 |
(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 | 6015.2.a.i.1.7 | ✓ | 43 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6015.2.a.i.1.7 | ✓ | 43 | 1.1 | even | 1 | trivial |