Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −3.46410 | −1.54919 | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.73205 | 1.72828 | 0.864139 | − | 0.503253i | \(-0.167864\pi\) | ||||
0.864139 | + | 0.503253i | \(0.167864\pi\) | |||||||
\(12\) | 2.00000 | 0.577350 | ||||||||
\(13\) | 5.46410 | 1.51547 | 0.757735 | − | 0.652563i | \(-0.226306\pi\) | ||||
0.757735 | + | 0.652563i | \(0.226306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.46410 | 0.894427 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.535898 | 0.122944 | 0.0614718 | − | 0.998109i | \(-0.480421\pi\) | ||||
0.0614718 | + | 0.998109i | \(0.480421\pi\) | |||||||
\(20\) | 6.92820 | 1.54919 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.46410 | 1.13934 | 0.569672 | − | 0.821872i | \(-0.307070\pi\) | ||||
0.569672 | + | 0.821872i | \(0.307070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.00000 | 1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.19615 | −0.964901 | −0.482451 | − | 0.875923i | \(-0.660253\pi\) | ||||
−0.482451 | + | 0.875923i | \(0.660253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73205 | 1.02951 | 0.514753 | − | 0.857338i | \(-0.327883\pi\) | ||||
0.514753 | + | 0.857338i | \(0.327883\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.73205 | −0.997822 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.46410 | −0.874957 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.92820 | 1.51404 | 0.757018 | − | 0.653394i | \(-0.226655\pi\) | ||||
0.757018 | + | 0.653394i | \(0.226655\pi\) | |||||||
\(44\) | −11.4641 | −1.72828 | ||||||||
\(45\) | −3.46410 | −0.516398 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.9282 | −1.73991 | −0.869954 | − | 0.493134i | \(-0.835851\pi\) | ||||
−0.869954 | + | 0.493134i | \(0.835851\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | −10.9282 | −1.51547 | ||||||||
\(53\) | 10.9282 | 1.50110 | 0.750552 | − | 0.660811i | \(-0.229788\pi\) | ||||
0.750552 | + | 0.660811i | \(0.229788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.8564 | −2.67744 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.535898 | −0.0709815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | −6.92820 | −0.894427 | ||||||||
\(61\) | −1.73205 | −0.221766 | −0.110883 | − | 0.993833i | \(-0.535368\pi\) | ||||
−0.110883 | + | 0.993833i | \(0.535368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −18.9282 | −2.34775 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.46410 | 0.911885 | 0.455943 | − | 0.890009i | \(-0.349302\pi\) | ||||
0.455943 | + | 0.890009i | \(0.349302\pi\) | |||||||
\(68\) | −10.0000 | −1.21268 | ||||||||
\(69\) | −5.46410 | −0.657801 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1962 | 1.56610 | 0.783048 | − | 0.621962i | \(-0.213664\pi\) | ||||
0.783048 | + | 0.621962i | \(0.213664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.19615 | −1.07633 | −0.538164 | − | 0.842840i | \(-0.680882\pi\) | ||||
−0.538164 | + | 0.842840i | \(0.680882\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00000 | −0.808290 | ||||||||
\(76\) | −1.07180 | −0.122944 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.928203 | 0.104431 | 0.0522155 | − | 0.998636i | \(-0.483372\pi\) | ||||
0.0522155 | + | 0.998636i | \(0.483372\pi\) | |||||||
\(80\) | −13.8564 | −1.54919 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3205 | −1.87867 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.19615 | 0.557086 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.92820 | 0.946388 | 0.473194 | − | 0.880958i | \(-0.343101\pi\) | ||||
0.473194 | + | 0.880958i | \(0.343101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.9282 | −1.13934 | ||||||||
\(93\) | −5.73205 | −0.594386 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.85641 | −0.190463 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.39230 | 0.242902 | 0.121451 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121451 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.73205 | 0.576093 | ||||||||
\(100\) | −14.0000 | −1.40000 | ||||||||
\(101\) | 18.8564 | 1.87628 | 0.938141 | − | 0.346253i | \(-0.112546\pi\) | ||||
0.938141 | + | 0.346253i | \(0.112546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.19615 | −0.117860 | −0.0589302 | − | 0.998262i | \(-0.518769\pi\) | ||||
−0.0589302 | + | 0.998262i | \(0.518769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.46410 | −0.334887 | −0.167444 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167444 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(108\) | 2.00000 | 0.192450 | ||||||||
\(109\) | 2.53590 | 0.242895 | 0.121448 | − | 0.992598i | \(-0.461246\pi\) | ||||
0.121448 | + | 0.992598i | \(0.461246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | 0.0949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3205 | −1.62938 | −0.814688 | − | 0.579899i | \(-0.803092\pi\) | ||||
−0.814688 | + | 0.579899i | \(0.803092\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.9282 | −1.76506 | ||||||||
\(116\) | 10.3923 | 0.964901 | ||||||||
\(117\) | 5.46410 | 0.505156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.8564 | 1.98695 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −11.4641 | −1.02951 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8564 | 1.58450 | 0.792250 | − | 0.610197i | \(-0.208910\pi\) | ||||
0.792250 | + | 0.610197i | \(0.208910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.92820 | −0.874130 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5359 | −0.920526 | −0.460263 | − | 0.887783i | \(-0.652245\pi\) | ||||
−0.460263 | + | 0.887783i | \(0.652245\pi\) | |||||||
\(132\) | 11.4641 | 0.997822 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.46410 | 0.298142 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.80385 | 0.239549 | 0.119774 | − | 0.992801i | \(-0.461783\pi\) | ||||
0.119774 | + | 0.992801i | \(0.461783\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4641 | −0.972372 | −0.486186 | − | 0.873855i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873855i | \(0.661612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9282 | 1.00454 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.3205 | 2.61915 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 18.0000 | 1.49482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −13.8564 | −1.13516 | −0.567581 | − | 0.823318i | \(-0.692120\pi\) | ||||
−0.567581 | + | 0.823318i | \(0.692120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3923 | 1.65950 | 0.829751 | − | 0.558134i | \(-0.188482\pi\) | ||||
0.829751 | + | 0.558134i | \(0.188482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00000 | 0.404226 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.8564 | −1.59490 | ||||||||
\(156\) | 10.9282 | 0.874957 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.9282 | −0.866663 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9282 | −1.40425 | −0.702123 | − | 0.712056i | \(-0.747764\pi\) | ||||
−0.702123 | + | 0.712056i | \(0.747764\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 19.8564 | 1.54582 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.9282 | −1.46471 | −0.732354 | − | 0.680924i | \(-0.761578\pi\) | ||||
−0.732354 | + | 0.680924i | \(0.761578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.535898 | 0.0409812 | ||||||||
\(172\) | −19.8564 | −1.51404 | ||||||||
\(173\) | 7.07180 | 0.537659 | 0.268829 | − | 0.963188i | \(-0.413363\pi\) | ||||
0.268829 | + | 0.963188i | \(0.413363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.9282 | 1.72828 | ||||||||
\(177\) | 6.92820 | 0.520756 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5885 | 1.16514 | 0.582568 | − | 0.812782i | \(-0.302048\pi\) | ||||
0.582568 | + | 0.812782i | \(0.302048\pi\) | |||||||
\(180\) | 6.92820 | 0.516398 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.73205 | 0.128037 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.46410 | 0.254686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.6603 | 2.09585 | ||||||||
\(188\) | 23.8564 | 1.73991 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3923 | −0.751961 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | −7.32051 | −0.526942 | −0.263471 | − | 0.964667i | \(-0.584867\pi\) | ||||
−0.263471 | + | 0.964667i | \(0.584867\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.9282 | 1.35548 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.535898 | 0.0381812 | 0.0190906 | − | 0.999818i | \(-0.493923\pi\) | ||||
0.0190906 | + | 0.999818i | \(0.493923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.3205 | 1.79492 | 0.897462 | − | 0.441093i | \(-0.145409\pi\) | ||||
0.897462 | + | 0.441093i | \(0.145409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.46410 | −0.526477 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.0000 | 0.700140 | ||||||||
\(205\) | 3.46410 | 0.241943 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.46410 | 0.379781 | ||||||||
\(208\) | 21.8564 | 1.51547 | ||||||||
\(209\) | 3.07180 | 0.212481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9282 | 1.02770 | 0.513850 | − | 0.857880i | \(-0.328219\pi\) | ||||
0.513850 | + | 0.857880i | \(0.328219\pi\) | |||||||
\(212\) | −21.8564 | −1.50110 | ||||||||
\(213\) | −13.1962 | −0.904185 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −34.3923 | −2.34554 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.19615 | 0.621418 | ||||||||
\(220\) | 39.7128 | 2.67744 | ||||||||
\(221\) | 27.3205 | 1.83778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.53590 | 0.571606 | 0.285803 | − | 0.958288i | \(-0.407740\pi\) | ||||
0.285803 | + | 0.958288i | \(0.407740\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.00000 | 0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.0717968 | −0.00476532 | −0.00238266 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238266 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(228\) | 1.07180 | 0.0709815 | ||||||||
\(229\) | 8.92820 | 0.589992 | 0.294996 | − | 0.955498i | \(-0.404682\pi\) | ||||
0.294996 | + | 0.955498i | \(0.404682\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8564 | −0.907763 | −0.453882 | − | 0.891062i | \(-0.649961\pi\) | ||||
−0.453882 | + | 0.891062i | \(0.649961\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.3205 | 2.69545 | ||||||||
\(236\) | 13.8564 | 0.901975 | ||||||||
\(237\) | −0.928203 | −0.0602933 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4641 | −1.00029 | −0.500145 | − | 0.865942i | \(-0.666720\pi\) | ||||
−0.500145 | + | 0.865942i | \(0.666720\pi\) | |||||||
\(240\) | 13.8564 | 0.894427 | ||||||||
\(241\) | −5.19615 | −0.334714 | −0.167357 | − | 0.985896i | \(-0.553523\pi\) | ||||
−0.167357 | + | 0.985896i | \(0.553523\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.46410 | 0.221766 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.92820 | 0.186317 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | −0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.46410 | −0.471130 | −0.235565 | − | 0.971859i | \(-0.575694\pi\) | ||||
−0.235565 | + | 0.971859i | \(0.575694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.3205 | 1.96910 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.3205 | 1.08465 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 37.8564 | 2.34775 | ||||||||
\(261\) | −5.19615 | −0.321634 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.1244 | −1.24092 | −0.620460 | − | 0.784238i | \(-0.713054\pi\) | ||||
−0.620460 | + | 0.784238i | \(0.713054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.8564 | −2.32550 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.92820 | −0.546397 | ||||||||
\(268\) | −14.9282 | −0.911885 | ||||||||
\(269\) | −17.4641 | −1.06481 | −0.532403 | − | 0.846491i | \(-0.678711\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5885 | 0.703949 | 0.351974 | − | 0.936010i | \(-0.385510\pi\) | ||||
0.351974 | + | 0.936010i | \(0.385510\pi\) | |||||||
\(272\) | 20.0000 | 1.21268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 40.1244 | 2.41959 | ||||||||
\(276\) | 10.9282 | 0.657801 | ||||||||
\(277\) | −21.9282 | −1.31754 | −0.658769 | − | 0.752345i | \(-0.728923\pi\) | ||||
−0.658769 | + | 0.752345i | \(0.728923\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.73205 | 0.343169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.124356 | −0.00741844 | −0.00370922 | − | 0.999993i | \(-0.501181\pi\) | ||||
−0.00370922 | + | 0.999993i | \(0.501181\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.66025 | −0.277023 | −0.138512 | − | 0.990361i | \(-0.544232\pi\) | ||||
−0.138512 | + | 0.990361i | \(0.544232\pi\) | |||||||
\(284\) | −26.3923 | −1.56610 | ||||||||
\(285\) | 1.85641 | 0.109964 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.39230 | −0.140239 | ||||||||
\(292\) | 18.3923 | 1.07633 | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.0000 | 1.39733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.73205 | −0.332607 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.8564 | 1.72664 | ||||||||
\(300\) | 14.0000 | 0.808290 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.8564 | −1.08327 | ||||||||
\(304\) | 2.14359 | 0.122944 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.2679 | −0.814315 | −0.407157 | − | 0.913358i | \(-0.633480\pi\) | ||||
−0.407157 | + | 0.913358i | \(0.633480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.19615 | 0.0680467 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.8564 | −1.46618 | −0.733091 | − | 0.680130i | \(-0.761923\pi\) | ||||
−0.733091 | + | 0.680130i | \(0.761923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.92820 | −0.165512 | −0.0827559 | − | 0.996570i | \(-0.526372\pi\) | ||||
−0.0827559 | + | 0.996570i | \(0.526372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.85641 | −0.104431 | ||||||||
\(317\) | 22.8038 | 1.28079 | 0.640396 | − | 0.768045i | \(-0.278770\pi\) | ||||
0.640396 | + | 0.768045i | \(0.278770\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −29.7846 | −1.66762 | ||||||||
\(320\) | 27.7128 | 1.54919 | ||||||||
\(321\) | 3.46410 | 0.193347 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.67949 | 0.149091 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 38.2487 | 2.12166 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.53590 | −0.140236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2487 | 0.893110 | 0.446555 | − | 0.894756i | \(-0.352651\pi\) | ||||
0.446555 | + | 0.894756i | \(0.352651\pi\) | |||||||
\(332\) | −20.0000 | −1.09764 | ||||||||
\(333\) | −1.00000 | −0.0547997 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.8564 | −1.41269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.0000 | 1.57973 | 0.789865 | − | 0.613280i | \(-0.210150\pi\) | ||||
0.789865 | + | 0.613280i | \(0.210150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3205 | 0.940721 | ||||||||
\(340\) | 34.6410 | 1.87867 | ||||||||
\(341\) | 32.8564 | 1.77927 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.9282 | 1.01906 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.66025 | −0.250176 | −0.125088 | − | 0.992146i | \(-0.539921\pi\) | ||||
−0.125088 | + | 0.992146i | \(0.539921\pi\) | |||||||
\(348\) | −10.3923 | −0.557086 | ||||||||
\(349\) | −3.58846 | −0.192086 | −0.0960429 | − | 0.995377i | \(-0.530619\pi\) | ||||
−0.0960429 | + | 0.995377i | \(0.530619\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46410 | −0.291652 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3205 | −0.708979 | −0.354490 | − | 0.935060i | \(-0.615345\pi\) | ||||
−0.354490 | + | 0.935060i | \(0.615345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −45.7128 | −2.42618 | ||||||||
\(356\) | −17.8564 | −0.946388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.7128 | 1.67374 | 0.836869 | − | 0.547403i | \(-0.184384\pi\) | ||||
0.836869 | + | 0.547403i | \(0.184384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7128 | −0.984885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.8564 | −1.14716 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.8564 | 1.66744 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0526 | 0.785737 | 0.392869 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392869 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(368\) | 21.8564 | 1.13934 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 11.4641 | 0.594386 | ||||||||
\(373\) | 7.14359 | 0.369881 | 0.184941 | − | 0.982750i | \(-0.440791\pi\) | ||||
0.184941 | + | 0.982750i | \(0.440791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.3923 | −1.46228 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 3.71281 | 0.190463 | ||||||||
\(381\) | −17.8564 | −0.914811 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.9282 | −1.83585 | −0.917923 | − | 0.396759i | \(-0.870135\pi\) | ||||
−0.917923 | + | 0.396759i | \(0.870135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.92820 | 0.504679 | ||||||||
\(388\) | −4.78461 | −0.242902 | ||||||||
\(389\) | −6.78461 | −0.343993 | −0.171997 | − | 0.985098i | \(-0.555022\pi\) | ||||
−0.171997 | + | 0.985098i | \(0.555022\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.3205 | 1.38166 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5359 | 0.531466 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.21539 | −0.161784 | ||||||||
\(396\) | −11.4641 | −0.576093 | ||||||||
\(397\) | 17.4641 | 0.876498 | 0.438249 | − | 0.898854i | \(-0.355599\pi\) | ||||
0.438249 | + | 0.898854i | \(0.355599\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000 | 1.40000 | ||||||||
\(401\) | −17.0718 | −0.852525 | −0.426262 | − | 0.904600i | \(-0.640170\pi\) | ||||
−0.426262 | + | 0.904600i | \(0.640170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.3205 | 1.56019 | ||||||||
\(404\) | −37.7128 | −1.87628 | ||||||||
\(405\) | −3.46410 | −0.172133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.73205 | −0.284127 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.73205 | 0.283432 | 0.141716 | − | 0.989907i | \(-0.454738\pi\) | ||||
0.141716 | + | 0.989907i | \(0.454738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.80385 | −0.138304 | ||||||||
\(412\) | 2.39230 | 0.117860 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.6410 | −1.70046 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.4641 | 0.561399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.7128 | 1.54927 | 0.774636 | − | 0.632407i | \(-0.217933\pi\) | ||||
0.774636 | + | 0.632407i | \(0.217933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4641 | 1.24104 | 0.620522 | − | 0.784189i | \(-0.286921\pi\) | ||||
0.620522 | + | 0.784189i | \(0.286921\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.9282 | −0.579969 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 35.0000 | 1.69775 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.92820 | 0.334887 | ||||||||
\(429\) | −31.3205 | −1.51217 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.53590 | 0.122150 | 0.0610750 | − | 0.998133i | \(-0.480547\pi\) | ||||
0.0610750 | + | 0.998133i | \(0.480547\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | 31.5885 | 1.51804 | 0.759022 | − | 0.651065i | \(-0.225677\pi\) | ||||
0.759022 | + | 0.651065i | \(0.225677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.0000 | −0.863034 | ||||||||
\(436\) | −5.07180 | −0.242895 | ||||||||
\(437\) | 2.92820 | 0.140075 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.5359 | 1.36194 | 0.680972 | − | 0.732309i | \(-0.261557\pi\) | ||||
0.680972 | + | 0.732309i | \(0.261557\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.60770 | 0.171407 | 0.0857034 | − | 0.996321i | \(-0.472686\pi\) | ||||
0.0857034 | + | 0.996321i | \(0.472686\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | −30.9282 | −1.46614 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8564 | 0.655386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.3205 | −1.10056 | −0.550281 | − | 0.834979i | \(-0.685480\pi\) | ||||
−0.550281 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.73205 | −0.269912 | ||||||||
\(452\) | 34.6410 | 1.62938 | ||||||||
\(453\) | −20.3923 | −0.958114 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.6410 | −1.80755 | −0.903775 | − | 0.428007i | \(-0.859216\pi\) | ||||
−0.903775 | + | 0.428007i | \(0.859216\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 37.8564 | 1.76506 | ||||||||
\(461\) | 24.2487 | 1.12938 | 0.564688 | − | 0.825305i | \(-0.308997\pi\) | ||||
0.564688 | + | 0.825305i | \(0.308997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.39230 | 0.390023 | 0.195012 | − | 0.980801i | \(-0.437526\pi\) | ||||
0.195012 | + | 0.980801i | \(0.437526\pi\) | |||||||
\(464\) | −20.7846 | −0.964901 | ||||||||
\(465\) | 19.8564 | 0.920819 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.535898 | 0.0247984 | 0.0123992 | − | 0.999923i | \(-0.496053\pi\) | ||||
0.0123992 | + | 0.999923i | \(0.496053\pi\) | |||||||
\(468\) | −10.9282 | −0.505156 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0000 | 0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56.9090 | 2.61668 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.75129 | 0.172121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.9282 | 0.500368 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.7128 | −1.86022 | −0.930108 | − | 0.367286i | \(-0.880287\pi\) | ||||
−0.930108 | + | 0.367286i | \(0.880287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.46410 | −0.249142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −43.7128 | −1.98695 | ||||||||
\(485\) | −8.28719 | −0.376302 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.07180 | 0.0938821 | 0.0469410 | − | 0.998898i | \(-0.485053\pi\) | ||||
0.0469410 | + | 0.998898i | \(0.485053\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.9282 | 0.810741 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.85641 | 0.174037 | 0.0870186 | − | 0.996207i | \(-0.472266\pi\) | ||||
0.0870186 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | −25.9808 | −1.17011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.8564 | −0.892479 | ||||||||
\(496\) | 22.9282 | 1.02951 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.46410 | −0.0655422 | −0.0327711 | − | 0.999463i | \(-0.510433\pi\) | ||||
−0.0327711 | + | 0.999463i | \(0.510433\pi\) | |||||||
\(500\) | 13.8564 | 0.619677 | ||||||||
\(501\) | 18.9282 | 0.845650 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7846 | 0.525450 | 0.262725 | − | 0.964871i | \(-0.415379\pi\) | ||||
0.262725 | + | 0.964871i | \(0.415379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −65.3205 | −2.90672 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.8564 | −0.748619 | ||||||||
\(508\) | −35.7128 | −1.58450 | ||||||||
\(509\) | −8.07180 | −0.357776 | −0.178888 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178888 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.535898 | −0.0236605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.14359 | 0.182589 | ||||||||
\(516\) | 19.8564 | 0.874130 | ||||||||
\(517\) | −68.3731 | −3.00704 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.07180 | −0.310417 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.85641 | −0.300385 | −0.150192 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150192 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1769 | −1.36327 | −0.681636 | − | 0.731692i | \(-0.738731\pi\) | ||||
−0.681636 | + | 0.731692i | \(0.738731\pi\) | |||||||
\(524\) | 21.0718 | 0.920526 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.6603 | 1.24846 | ||||||||
\(528\) | −22.9282 | −0.997822 | ||||||||
\(529\) | 6.85641 | 0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.92820 | −0.300658 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.46410 | −0.236677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | 0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.5885 | −0.672692 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.92820 | −0.298142 | ||||||||
\(541\) | 3.07180 | 0.132067 | 0.0660334 | − | 0.997817i | \(-0.478966\pi\) | ||||
0.0660334 | + | 0.997817i | \(0.478966\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0000 | 0.858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.78461 | −0.376291 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3923 | −1.38499 | −0.692497 | − | 0.721420i | \(-0.743490\pi\) | ||||
−0.692497 | + | 0.721420i | \(0.743490\pi\) | |||||||
\(548\) | −5.60770 | −0.239549 | ||||||||
\(549\) | −1.73205 | −0.0739221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.78461 | −0.118628 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.46410 | −0.147043 | ||||||||
\(556\) | 22.9282 | 0.972372 | ||||||||
\(557\) | −34.5167 | −1.46252 | −0.731259 | − | 0.682100i | \(-0.761067\pi\) | ||||
−0.731259 | + | 0.682100i | \(0.761067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.2487 | 2.29448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.6603 | −1.21004 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.92820 | −0.334134 | −0.167067 | − | 0.985946i | \(-0.553430\pi\) | ||||
−0.167067 | + | 0.985946i | \(0.553430\pi\) | |||||||
\(564\) | −23.8564 | −1.00454 | ||||||||
\(565\) | 60.0000 | 2.52422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.2487 | 0.932714 | 0.466357 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466357 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.0718 | 0.881827 | 0.440914 | − | 0.897550i | \(-0.354655\pi\) | ||||
0.440914 | + | 0.897550i | \(0.354655\pi\) | |||||||
\(572\) | −62.6410 | −2.61915 | ||||||||
\(573\) | 10.3923 | 0.434145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.2487 | 1.59508 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 0.679492 | 0.0282876 | 0.0141438 | − | 0.999900i | \(-0.495498\pi\) | ||||
0.0141438 | + | 0.999900i | \(0.495498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.32051 | 0.304230 | ||||||||
\(580\) | −36.0000 | −1.49482 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 62.6410 | 2.59433 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.9282 | −0.782585 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0718 | 1.15865 | 0.579324 | − | 0.815098i | \(-0.303317\pi\) | ||||
0.579324 | + | 0.815098i | \(0.303317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.07180 | 0.126571 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.535898 | −0.0220439 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | 12.7128 | 0.522053 | 0.261026 | − | 0.965332i | \(-0.415939\pi\) | ||||
0.261026 | + | 0.965332i | \(0.415939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.7128 | 1.13516 | ||||||||
\(597\) | −25.3205 | −1.03630 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.24871 | 0.336472 | 0.168236 | − | 0.985747i | \(-0.446193\pi\) | ||||
0.168236 | + | 0.985747i | \(0.446193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.46410 | 0.303962 | ||||||||
\(604\) | −40.7846 | −1.65950 | ||||||||
\(605\) | −75.7128 | −3.07816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.24871 | −0.172450 | −0.0862249 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862249 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −65.1769 | −2.63678 | ||||||||
\(612\) | −10.0000 | −0.404226 | ||||||||
\(613\) | 36.6410 | 1.47992 | 0.739958 | − | 0.672653i | \(-0.234845\pi\) | ||||
0.739958 | + | 0.672653i | \(0.234845\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.46410 | −0.139686 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.85641 | 0.316287 | 0.158144 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158144 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.8038 | −1.07734 | −0.538669 | − | 0.842518i | \(-0.681073\pi\) | ||||
−0.538669 | + | 0.842518i | \(0.681073\pi\) | |||||||
\(620\) | 39.7128 | 1.59490 | ||||||||
\(621\) | −5.46410 | −0.219267 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21.8564 | −0.874957 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.07180 | −0.122676 | ||||||||
\(628\) | 20.0000 | 0.798087 | ||||||||
\(629\) | −5.00000 | −0.199363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.9282 | 0.554473 | 0.277237 | − | 0.960802i | \(-0.410581\pi\) | ||||
0.277237 | + | 0.960802i | \(0.410581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9282 | −0.593343 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −61.8564 | −2.45470 | ||||||||
\(636\) | 21.8564 | 0.866663 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1962 | 0.522032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.5167 | −1.67931 | −0.839654 | − | 0.543122i | \(-0.817242\pi\) | ||||
−0.839654 | + | 0.543122i | \(0.817242\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2487 | 1.50838 | 0.754191 | − | 0.656655i | \(-0.228029\pi\) | ||||
0.754191 | + | 0.656655i | \(0.228029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34.3923 | 1.35420 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.92820 | −0.115120 | −0.0575598 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575598 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.7128 | −1.55886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.8564 | 1.40425 | ||||||||
\(653\) | −12.6603 | −0.495434 | −0.247717 | − | 0.968832i | \(-0.579680\pi\) | ||||
−0.247717 | + | 0.968832i | \(0.579680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.4974 | 1.42607 | ||||||||
\(656\) | −4.00000 | −0.156174 | ||||||||
\(657\) | −9.19615 | −0.358776 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5359 | −0.488329 | −0.244165 | − | 0.969734i | \(-0.578514\pi\) | ||||
−0.244165 | + | 0.969734i | \(0.578514\pi\) | |||||||
\(660\) | −39.7128 | −1.54582 | ||||||||
\(661\) | −30.6410 | −1.19180 | −0.595899 | − | 0.803060i | \(-0.703204\pi\) | ||||
−0.595899 | + | 0.803060i | \(0.703204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.3205 | −1.06104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.3923 | −1.09935 | ||||||||
\(668\) | 37.8564 | 1.46471 | ||||||||
\(669\) | −8.53590 | −0.330017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.92820 | −0.383274 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.4641 | 0.596097 | 0.298049 | − | 0.954551i | \(-0.403664\pi\) | ||||
0.298049 | + | 0.954551i | \(0.403664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00000 | −0.269430 | ||||||||
\(676\) | −33.7128 | −1.29665 | ||||||||
\(677\) | 3.85641 | 0.148214 | 0.0741069 | − | 0.997250i | \(-0.476389\pi\) | ||||
0.0741069 | + | 0.997250i | \(0.476389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0717968 | 0.00275126 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2487 | −0.468684 | −0.234342 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234342 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(684\) | −1.07180 | −0.0409812 | ||||||||
\(685\) | −9.71281 | −0.371108 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.92820 | −0.340632 | ||||||||
\(688\) | 39.7128 | 1.51404 | ||||||||
\(689\) | 59.7128 | 2.27488 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.1769 | 1.56644 | 0.783222 | − | 0.621742i | \(-0.213575\pi\) | ||||
0.783222 | + | 0.621742i | \(0.213575\pi\) | |||||||
\(692\) | −14.1436 | −0.537659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.7128 | 1.50639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00000 | −0.189389 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.8564 | 0.524097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.4641 | −0.584071 | −0.292036 | − | 0.956407i | \(-0.594333\pi\) | ||||
−0.292036 | + | 0.956407i | \(0.594333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.535898 | −0.0202118 | ||||||||
\(704\) | −45.8564 | −1.72828 | ||||||||
\(705\) | −41.3205 | −1.55622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.8564 | −0.520756 | ||||||||
\(709\) | 33.3205 | 1.25138 | 0.625689 | − | 0.780073i | \(-0.284818\pi\) | ||||
0.625689 | + | 0.780073i | \(0.284818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.928203 | 0.0348103 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.3205 | 1.17296 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −108.497 | −4.05757 | ||||||||
\(716\) | −31.1769 | −1.16514 | ||||||||
\(717\) | 15.4641 | 0.577517 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0000 | 0.633993 | 0.316997 | − | 0.948427i | \(-0.397326\pi\) | ||||
0.316997 | + | 0.948427i | \(0.397326\pi\) | |||||||
\(720\) | −13.8564 | −0.516398 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.19615 | 0.193247 | ||||||||
\(724\) | 40.0000 | 1.48659 | ||||||||
\(725\) | −36.3731 | −1.35086 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.6410 | 1.06224 | 0.531118 | − | 0.847298i | \(-0.321772\pi\) | ||||
0.531118 | + | 0.847298i | \(0.321772\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 49.6410 | 1.83604 | ||||||||
\(732\) | −3.46410 | −0.128037 | ||||||||
\(733\) | 29.9808 | 1.10736 | 0.553682 | − | 0.832728i | \(-0.313222\pi\) | ||||
0.553682 | + | 0.832728i | \(0.313222\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.7846 | 1.57599 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.78461 | 0.286361 | 0.143181 | − | 0.989697i | \(-0.454267\pi\) | ||||
0.143181 | + | 0.989697i | \(0.454267\pi\) | |||||||
\(740\) | −6.92820 | −0.254686 | ||||||||
\(741\) | −2.92820 | −0.107570 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.4641 | 1.00756 | 0.503780 | − | 0.863832i | \(-0.331942\pi\) | ||||
0.503780 | + | 0.863832i | \(0.331942\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.0000 | 1.75858 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.0000 | 0.365881 | ||||||||
\(748\) | −57.3205 | −2.09585 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2487 | −0.884848 | −0.442424 | − | 0.896806i | \(-0.645881\pi\) | ||||
−0.442424 | + | 0.896806i | \(0.645881\pi\) | |||||||
\(752\) | −47.7128 | −1.73991 | ||||||||
\(753\) | 7.46410 | 0.272007 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −70.6410 | −2.57089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.8564 | 0.576311 | 0.288155 | − | 0.957584i | \(-0.406958\pi\) | ||||
0.288155 | + | 0.957584i | \(0.406958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.3205 | −1.13686 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.2487 | −0.371515 | −0.185758 | − | 0.982596i | \(-0.559474\pi\) | ||||
−0.185758 | + | 0.982596i | \(0.559474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.7846 | 0.751961 | ||||||||
\(765\) | −17.3205 | −0.626224 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.8564 | −1.36692 | ||||||||
\(768\) | −16.0000 | −0.577350 | ||||||||
\(769\) | 2.80385 | 0.101109 | 0.0505547 | − | 0.998721i | \(-0.483901\pi\) | ||||
0.0505547 | + | 0.998721i | \(0.483901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00000 | 0.108042 | ||||||||
\(772\) | 14.6410 | 0.526942 | ||||||||
\(773\) | 3.14359 | 0.113067 | 0.0565336 | − | 0.998401i | \(-0.481995\pi\) | ||||
0.0565336 | + | 0.998401i | \(0.481995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.1244 | 1.44131 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.535898 | −0.0192006 | ||||||||
\(780\) | −37.8564 | −1.35548 | ||||||||
\(781\) | 75.6410 | 2.70665 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.19615 | 0.185695 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34.6410 | 1.23639 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5167 | 0.945217 | 0.472608 | − | 0.881273i | \(-0.343313\pi\) | ||||
0.472608 | + | 0.881273i | \(0.343313\pi\) | |||||||
\(788\) | −1.07180 | −0.0381812 | ||||||||
\(789\) | 20.1244 | 0.716446 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.46410 | −0.336080 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.8564 | 1.34263 | ||||||||
\(796\) | −50.6410 | −1.79492 | ||||||||
\(797\) | 19.8564 | 0.703350 | 0.351675 | − | 0.936122i | \(-0.385612\pi\) | ||||
0.351675 | + | 0.936122i | \(0.385612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.6410 | −2.10995 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.92820 | 0.315463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.7128 | −1.86019 | ||||||||
\(804\) | 14.9282 | 0.526477 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.4641 | 0.614765 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.0718 | −1.44401 | −0.722004 | − | 0.691889i | \(-0.756779\pi\) | ||||
−0.722004 | + | 0.691889i | \(0.756779\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.73205 | 0.0608205 | 0.0304103 | − | 0.999538i | \(-0.490319\pi\) | ||||
0.0304103 | + | 0.999538i | \(0.490319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.5885 | −0.406425 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 62.1051 | 2.17545 | ||||||||
\(816\) | −20.0000 | −0.700140 | ||||||||
\(817\) | 5.32051 | 0.186141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.92820 | −0.241943 | ||||||||
\(821\) | −8.67949 | −0.302916 | −0.151458 | − | 0.988464i | \(-0.548397\pi\) | ||||
−0.151458 | + | 0.988464i | \(0.548397\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.5692 | 1.37930 | 0.689648 | − | 0.724145i | \(-0.257765\pi\) | ||||
0.689648 | + | 0.724145i | \(0.257765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −40.1244 | −1.39695 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.1962 | −1.57162 | −0.785812 | − | 0.618465i | \(-0.787755\pi\) | ||||
−0.785812 | + | 0.618465i | \(0.787755\pi\) | |||||||
\(828\) | −10.9282 | −0.379781 | ||||||||
\(829\) | −15.0526 | −0.522797 | −0.261398 | − | 0.965231i | \(-0.584184\pi\) | ||||
−0.261398 | + | 0.965231i | \(0.584184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.9282 | 0.760681 | ||||||||
\(832\) | −43.7128 | −1.51547 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.5692 | 2.26912 | ||||||||
\(836\) | −6.14359 | −0.212481 | ||||||||
\(837\) | −5.73205 | −0.198129 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.0000 | −1.51905 | −0.759524 | − | 0.650479i | \(-0.774568\pi\) | ||||
−0.759524 | + | 0.650479i | \(0.774568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00000 | −0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.124356 | 0.00428304 | ||||||||
\(844\) | −29.8564 | −1.02770 | ||||||||
\(845\) | −58.3923 | −2.00876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 43.7128 | 1.50110 | ||||||||
\(849\) | 4.66025 | 0.159940 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.46410 | −0.187307 | ||||||||
\(852\) | 26.3923 | 0.904185 | ||||||||
\(853\) | 51.7128 | 1.77061 | 0.885306 | − | 0.465008i | \(-0.153949\pi\) | ||||
0.885306 | + | 0.465008i | \(0.153949\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.85641 | −0.0634878 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.2487 | −1.16991 | −0.584957 | − | 0.811064i | \(-0.698889\pi\) | ||||
−0.584957 | + | 0.811064i | \(0.698889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.80385 | −0.0956660 | −0.0478330 | − | 0.998855i | \(-0.515232\pi\) | ||||
−0.0478330 | + | 0.998855i | \(0.515232\pi\) | |||||||
\(860\) | 68.7846 | 2.34554 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.6795 | 0.499696 | 0.249848 | − | 0.968285i | \(-0.419619\pi\) | ||||
0.249848 | + | 0.968285i | \(0.419619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.4974 | −0.832937 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.32051 | 0.180486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.7846 | 1.38193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.39230 | 0.0809673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.3923 | −0.621418 | ||||||||
\(877\) | 28.0718 | 0.947917 | 0.473959 | − | 0.880547i | \(-0.342825\pi\) | ||||
0.473959 | + | 0.880547i | \(0.342825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.00000 | −0.303562 | ||||||||
\(880\) | −79.4256 | −2.67744 | ||||||||
\(881\) | −26.5359 | −0.894017 | −0.447009 | − | 0.894530i | \(-0.647511\pi\) | ||||
−0.447009 | + | 0.894530i | \(0.647511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.5692 | 1.33161 | 0.665805 | − | 0.746126i | \(-0.268088\pi\) | ||||
0.665805 | + | 0.746126i | \(0.268088\pi\) | |||||||
\(884\) | −54.6410 | −1.83778 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8564 | 0.700290 | 0.350145 | − | 0.936696i | \(-0.386132\pi\) | ||||
0.350145 | + | 0.936696i | \(0.386132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.73205 | 0.192031 | ||||||||
\(892\) | −17.0718 | −0.571606 | ||||||||
\(893\) | −6.39230 | −0.213910 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54.0000 | −1.80502 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.8564 | −0.996876 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.7846 | −0.993372 | ||||||||
\(900\) | −14.0000 | −0.466667 | ||||||||
\(901\) | 54.6410 | 1.82036 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 69.2820 | 2.30301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.85641 | 0.194459 | 0.0972294 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972294 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(908\) | 0.143594 | 0.00476532 | ||||||||
\(909\) | 18.8564 | 0.625428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.7846 | −0.556099 | −0.278049 | − | 0.960567i | \(-0.589688\pi\) | ||||
−0.278049 | + | 0.960567i | \(0.589688\pi\) | |||||||
\(912\) | −2.14359 | −0.0709815 | ||||||||
\(913\) | 57.3205 | 1.89703 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −17.8564 | −0.589992 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.4641 | −0.839983 | −0.419992 | − | 0.907528i | \(-0.637967\pi\) | ||||
−0.419992 | + | 0.907528i | \(0.637967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.2679 | 0.470145 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.1051 | 2.37337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.00000 | −0.230159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.19615 | −0.0392868 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.7846 | 1.43653 | 0.718263 | − | 0.695771i | \(-0.244937\pi\) | ||||
0.718263 | + | 0.695771i | \(0.244937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27.7128 | 0.907763 | ||||||||
\(933\) | 25.8564 | 0.846501 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −99.2820 | −3.24687 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.07180 | −0.165688 | −0.0828442 | − | 0.996563i | \(-0.526400\pi\) | ||||
−0.0828442 | + | 0.996563i | \(0.526400\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.92820 | 0.0955583 | ||||||||
\(940\) | −82.6410 | −2.69545 | ||||||||
\(941\) | −33.3205 | −1.08622 | −0.543109 | − | 0.839662i | \(-0.682753\pi\) | ||||
−0.543109 | + | 0.839662i | \(0.682753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.46410 | −0.177936 | ||||||||
\(944\) | −27.7128 | −0.901975 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0718 | 0.749733 | 0.374866 | − | 0.927079i | \(-0.377689\pi\) | ||||
0.374866 | + | 0.927079i | \(0.377689\pi\) | |||||||
\(948\) | 1.85641 | 0.0602933 | ||||||||
\(949\) | −50.2487 | −1.63114 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.8038 | −0.739465 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6795 | −0.669874 | −0.334937 | − | 0.942240i | \(-0.608715\pi\) | ||||
−0.334937 | + | 0.942240i | \(0.608715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.0000 | 1.16493 | ||||||||
\(956\) | 30.9282 | 1.00029 | ||||||||
\(957\) | 29.7846 | 0.962800 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −27.7128 | −0.894427 | ||||||||
\(961\) | 1.85641 | 0.0598841 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.46410 | −0.111629 | ||||||||
\(964\) | 10.3923 | 0.334714 | ||||||||
\(965\) | 25.3590 | 0.816335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.2487 | −1.16568 | −0.582840 | − | 0.812587i | \(-0.698059\pi\) | ||||
−0.582840 | + | 0.812587i | \(0.698059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.67949 | −0.0860777 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0718 | −0.451585 | −0.225793 | − | 0.974175i | \(-0.572497\pi\) | ||||
−0.225793 | + | 0.974175i | \(0.572497\pi\) | |||||||
\(972\) | 2.00000 | 0.0641500 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.2487 | −1.22494 | ||||||||
\(976\) | −6.92820 | −0.221766 | ||||||||
\(977\) | 13.9808 | 0.447284 | 0.223642 | − | 0.974671i | \(-0.428205\pi\) | ||||
0.223642 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.1769 | 1.63562 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.53590 | 0.0809650 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.7846 | 0.471556 | 0.235778 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235778 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.85641 | −0.0591500 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.85641 | −0.186317 | ||||||||
\(989\) | 54.2487 | 1.72501 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1051 | −0.765724 | −0.382862 | − | 0.923805i | \(-0.625062\pi\) | ||||
−0.382862 | + | 0.923805i | \(0.625062\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.2487 | −0.515637 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −87.7128 | −2.78068 | ||||||||
\(996\) | 20.0000 | 0.633724 | ||||||||
\(997\) | −21.1769 | −0.670680 | −0.335340 | − | 0.942097i | \(-0.608851\pi\) | ||||
−0.335340 | + | 0.942097i | \(0.608851\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.00000 | 0.0316386 |
(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 | 6027.2.a.l.1.1 | ✓ | 2 | |
7.6 | odd | 2 | 6027.2.a.n.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6027.2.a.n.1.2 | yes | 2 | 7.6 | odd | 2 |