Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4680,2,Mod(1,4680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4680.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: | \(37.3699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.321637\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4680.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.53982 | −1.71589 | −0.857946 | − | 0.513740i | \(-0.828260\pi\) | ||||
−0.857946 | + | 0.513740i | \(0.828260\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.89655 | −1.77788 | −0.888938 | − | 0.458027i | \(-0.848556\pi\) | ||||
−0.888938 | + | 0.458027i | \(0.848556\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.53982 | 0.615998 | 0.307999 | − | 0.951387i | \(-0.400341\pi\) | ||||
0.307999 | + | 0.951387i | \(0.400341\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35673 | 0.311254 | 0.155627 | − | 0.987816i | \(-0.450260\pi\) | ||||
0.155627 | + | 0.987816i | \(0.450260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.25328 | 1.09538 | 0.547692 | − | 0.836680i | \(-0.315507\pi\) | ||||
0.547692 | + | 0.836680i | \(0.315507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.643274 | 0.119453 | 0.0597265 | − | 0.998215i | \(-0.480977\pi\) | ||||
0.0597265 | + | 0.998215i | \(0.480977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.53982 | −0.767370 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89655 | −0.640589 | −0.320294 | − | 0.947318i | \(-0.603782\pi\) | ||||
−0.320294 | + | 0.947318i | \(0.603782\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.89655 | −0.608539 | −0.304269 | − | 0.952586i | \(-0.598412\pi\) | ||||
−0.304269 | + | 0.952586i | \(0.598412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.79310 | −0.578442 | −0.289221 | − | 0.957262i | \(-0.593396\pi\) | ||||
−0.289221 | + | 0.957262i | \(0.593396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.79310 | −0.553280 | −0.276640 | − | 0.960974i | \(-0.589221\pi\) | ||||
−0.276640 | + | 0.960974i | \(0.589221\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.6100 | 1.94429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.10345 | 0.288931 | 0.144466 | − | 0.989510i | \(-0.453854\pi\) | ||||
0.144466 | + | 0.989510i | \(0.453854\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.89655 | −0.795091 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.103450 | 0.0132455 | 0.00662274 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662274 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.79310 | −0.707740 | −0.353870 | − | 0.935295i | \(-0.615134\pi\) | ||||
−0.353870 | + | 0.935295i | \(0.615134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.18310 | −0.377764 | −0.188882 | − | 0.982000i | \(-0.560486\pi\) | ||||
−0.188882 | + | 0.982000i | \(0.560486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4364 | 1.22149 | 0.610743 | − | 0.791829i | \(-0.290871\pi\) | ||||
0.610743 | + | 0.791829i | \(0.290871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26.7693 | 3.05064 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9762 | 1.23492 | 0.617459 | − | 0.786603i | \(-0.288162\pi\) | ||||
0.617459 | + | 0.786603i | \(0.288162\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.53982 | 0.275483 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6100 | 1.12466 | 0.562329 | − | 0.826914i | \(-0.309905\pi\) | ||||
0.562329 | + | 0.826914i | \(0.309905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.53982 | 0.475903 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.35673 | 0.139197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.46018 | 0.351328 | 0.175664 | − | 0.984450i | \(-0.443793\pi\) | ||||
0.175664 | + | 0.984450i | \(0.443793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1498 | 1.10945 | 0.554725 | − | 0.832034i | \(-0.312824\pi\) | ||||
0.554725 | + | 0.832034i | \(0.312824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0796 | 1.68291 | 0.841454 | − | 0.540329i | \(-0.181700\pi\) | ||||
0.841454 | + | 0.540329i | \(0.181700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.9762 | 1.06111 | 0.530555 | − | 0.847651i | \(-0.321984\pi\) | ||||
0.530555 | + | 0.847651i | \(0.321984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.43637 | −0.233362 | −0.116681 | − | 0.993169i | \(-0.537226\pi\) | ||||
−0.116681 | + | 0.993169i | \(0.537226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.35673 | −0.315774 | −0.157887 | − | 0.987457i | \(-0.550468\pi\) | ||||
−0.157887 | + | 0.987457i | \(0.550468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.25328 | 0.489870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.5304 | −1.05699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.7693 | 2.16085 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.72292 | −0.849496 | −0.424748 | − | 0.905312i | \(-0.639637\pi\) | ||||
−0.424748 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.15930 | −0.534079 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.20690 | 0.188548 | 0.0942741 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942741 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1831 | 1.28781 | 0.643907 | − | 0.765104i | \(-0.277312\pi\) | ||||
0.643907 | + | 0.765104i | \(0.277312\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.89655 | 0.493094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.643274 | 0.0534210 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.7693 | 1.70149 | 0.850744 | − | 0.525581i | \(-0.176152\pi\) | ||||
0.850744 | + | 0.525581i | \(0.176152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7931 | 1.77350 | 0.886749 | − | 0.462252i | \(-0.152958\pi\) | ||||
0.886749 | + | 0.462252i | \(0.152958\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3662 | 1.30616 | 0.653082 | − | 0.757287i | \(-0.273476\pi\) | ||||
0.653082 | + | 0.757287i | \(0.273476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.8489 | −1.87956 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.4827 | 1.83931 | 0.919655 | − | 0.392726i | \(-0.128468\pi\) | ||||
0.919655 | + | 0.392726i | \(0.128468\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0796 | 1.01213 | 0.506067 | − | 0.862494i | \(-0.331099\pi\) | ||||
0.506067 | + | 0.862494i | \(0.331099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.5066 | −1.40703 | −0.703513 | − | 0.710682i | \(-0.748387\pi\) | ||||
−0.703513 | + | 0.710682i | \(0.748387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53982 | −0.343178 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.6433 | −0.945003 | −0.472501 | − | 0.881330i | \(-0.656649\pi\) | ||||
−0.472501 | + | 0.881330i | \(0.656649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.32345 | −0.693007 | −0.346503 | − | 0.938049i | \(-0.612631\pi\) | ||||
−0.346503 | + | 0.938049i | \(0.612631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.89655 | −0.286480 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.9762 | −1.09517 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7931 | −1.72161 | −0.860804 | − | 0.508936i | \(-0.830039\pi\) | ||||
−0.860804 | + | 0.508936i | \(0.830039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.53982 | 0.326784 | 0.163392 | − | 0.986561i | \(-0.447757\pi\) | ||||
0.163392 | + | 0.986561i | \(0.447757\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.50655 | −0.321078 | −0.160539 | − | 0.987029i | \(-0.551323\pi\) | ||||
−0.160539 | + | 0.987029i | \(0.551323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.42690 | −0.384703 | −0.192351 | − | 0.981326i | \(-0.561611\pi\) | ||||
−0.192351 | + | 0.981326i | \(0.561611\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.92035 | −0.204969 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.89655 | −0.272147 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7135 | 1.01292 | 0.506458 | − | 0.862265i | \(-0.330955\pi\) | ||||
0.506458 | + | 0.862265i | \(0.330955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.79310 | −0.258687 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.07965 | 0.616367 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.53982 | −0.170847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9429 | 1.40244 | 0.701221 | − | 0.712944i | \(-0.252639\pi\) | ||||
0.701221 | + | 0.712944i | \(0.252639\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.28655 | −0.350881 | −0.175440 | − | 0.984490i | \(-0.556135\pi\) | ||||
−0.175440 | + | 0.984490i | \(0.556135\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9298 | 0.788345 | 0.394172 | − | 0.919036i | \(-0.371031\pi\) | ||||
0.394172 | + | 0.919036i | \(0.371031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.173627 | 0.0113747 | 0.00568736 | − | 0.999984i | \(-0.498190\pi\) | ||||
0.00568736 | + | 0.999984i | \(0.498190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.79310 | −0.247434 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4827 | −1.64834 | −0.824171 | − | 0.566341i | \(-0.808358\pi\) | ||||
−0.824171 | + | 0.566341i | \(0.808358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.7455 | −1.78724 | −0.893622 | − | 0.448820i | \(-0.851844\pi\) | ||||
−0.893622 | + | 0.448820i | \(0.851844\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.6100 | 0.869511 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.35673 | −0.0863264 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.27708 | −0.143728 | −0.0718639 | − | 0.997414i | \(-0.522895\pi\) | ||||
−0.0718639 | + | 0.997414i | \(0.522895\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.9762 | −1.94746 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.6433 | 1.28769 | 0.643846 | − | 0.765155i | \(-0.277338\pi\) | ||||
0.643846 | + | 0.765155i | \(0.277338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6896 | 1.09918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1498 | 0.687528 | 0.343764 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343764 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.10345 | 0.129214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2295 | −0.989528 | −0.494764 | − | 0.869027i | \(-0.664746\pi\) | ||||
−0.494764 | + | 0.869027i | \(0.664746\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.366196 | −0.0222449 | −0.0111224 | − | 0.999938i | \(-0.503540\pi\) | ||||
−0.0111224 | + | 0.999938i | \(0.503540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.89655 | −0.355575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 33.1724 | 1.99314 | 0.996568 | − | 0.0827774i | \(-0.0263791\pi\) | ||||
0.996568 | + | 0.0827774i | \(0.0263791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.1593 | −1.67984 | −0.839921 | − | 0.542708i | \(-0.817399\pi\) | ||||
−0.839921 | + | 0.542708i | \(0.817399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.57310 | 0.390730 | 0.195365 | − | 0.980731i | \(-0.437411\pi\) | ||||
0.195365 | + | 0.980731i | \(0.437411\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.6896 | 1.04419 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5493 | −0.620547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.28655 | 0.192002 | 0.0960011 | − | 0.995381i | \(-0.469395\pi\) | ||||
0.0960011 | + | 0.995381i | \(0.469395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.25328 | −0.303805 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.2200 | 0.992544 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.103450 | 0.00592356 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.6100 | 1.51871 | 0.759356 | − | 0.650675i | \(-0.225514\pi\) | ||||
0.759356 | + | 0.650675i | \(0.225514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.3793 | 1.77936 | 0.889678 | − | 0.456588i | \(-0.150929\pi\) | ||||
0.889678 | + | 0.456588i | \(0.150929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0796 | 0.852352 | 0.426176 | − | 0.904640i | \(-0.359860\pi\) | ||||
0.426176 | + | 0.904640i | \(0.359860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5862 | 1.21240 | 0.606201 | − | 0.795312i | \(-0.292693\pi\) | ||||
0.606201 | + | 0.795312i | \(0.292693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.79310 | −0.212373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.44584 | 0.191732 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.2200 | 0.949369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.8157 | −1.85868 | −0.929339 | − | 0.369228i | \(-0.879622\pi\) | ||||
−0.929339 | + | 0.369228i | \(0.879622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.79310 | −0.316511 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1593 | 1.31604 | 0.658020 | − | 0.753000i | \(-0.271394\pi\) | ||||
0.658020 | + | 0.753000i | \(0.271394\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7931 | 0.638632 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −30.0082 | −1.62029 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.89655 | −0.101812 | −0.0509061 | − | 0.998703i | \(-0.516211\pi\) | ||||
−0.0509061 | + | 0.998703i | \(0.516211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.8157 | −1.81011 | −0.905056 | − | 0.425293i | \(-0.860171\pi\) | ||||
−0.905056 | + | 0.425293i | \(0.860171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.7324 | −1.20992 | −0.604962 | − | 0.796255i | \(-0.706812\pi\) | ||||
−0.604962 | + | 0.796255i | \(0.706812\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.18310 | −0.168941 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.5862 | 0.822608 | 0.411304 | − | 0.911498i | \(-0.365073\pi\) | ||||
0.411304 | + | 0.911498i | \(0.365073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1593 | −0.903121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4364 | 0.546265 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.7455 | −1.76150 | −0.880750 | − | 0.473581i | \(-0.842961\pi\) | ||||
−0.880750 | + | 0.473581i | \(0.842961\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.54929 | −0.495775 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4269 | 0.591663 | 0.295831 | − | 0.955240i | \(-0.404403\pi\) | ||||
0.295831 | + | 0.955240i | \(0.404403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.643274 | −0.0331303 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.56363 | −0.491251 | −0.245625 | − | 0.969365i | \(-0.578993\pi\) | ||||
−0.245625 | + | 0.969365i | \(0.578993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.8727 | −1.67972 | −0.839859 | − | 0.542804i | \(-0.817363\pi\) | ||||
−0.839859 | + | 0.542804i | \(0.817363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.7693 | 1.36429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.502920 | 0.0254991 | 0.0127495 | − | 0.999919i | \(-0.495942\pi\) | ||||
0.0127495 | + | 0.999919i | \(0.495942\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.3424 | 0.674754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9762 | 0.552272 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.68965 | 0.185178 | 0.0925891 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925891 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2865 | 0.563623 | 0.281812 | − | 0.959470i | \(-0.409065\pi\) | ||||
0.281812 | + | 0.959470i | \(0.409065\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.9762 | 1.13889 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0796 | −0.745641 | −0.372820 | − | 0.927904i | \(-0.621609\pi\) | ||||
−0.372820 | + | 0.927904i | \(0.621609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.1593 | 0.893561 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7705 | −0.575028 | −0.287514 | − | 0.957776i | \(-0.592829\pi\) | ||||
−0.287514 | + | 0.957776i | \(0.592829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.65638 | 0.373149 | 0.186574 | − | 0.982441i | \(-0.440261\pi\) | ||||
0.186574 | + | 0.982441i | \(0.440261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.53982 | 0.123200 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.469647 | −0.0227278 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.4458 | 1.32202 | 0.661010 | − | 0.750377i | \(-0.270128\pi\) | ||||
0.661010 | + | 0.750377i | \(0.270128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2200 | −0.923654 | −0.461827 | − | 0.886970i | \(-0.652806\pi\) | ||||
−0.461827 | + | 0.886970i | \(0.652806\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.12725 | 0.340943 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.39000 | −0.161796 | −0.0808979 | − | 0.996722i | \(-0.525779\pi\) | ||||
−0.0808979 | + | 0.996722i | \(0.525779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.26275 | 0.202529 | 0.101265 | − | 0.994860i | \(-0.467711\pi\) | ||||
0.101265 | + | 0.994860i | \(0.467711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6100 | 0.502962 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.18310 | −0.433377 | −0.216689 | − | 0.976241i | \(-0.569526\pi\) | ||||
−0.216689 | + | 0.976241i | \(0.569526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.9762 | 1.08191 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.53982 | 0.212830 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.5529 | −1.19532 | −0.597658 | − | 0.801751i | \(-0.703902\pi\) | ||||
−0.597658 | + | 0.801751i | \(0.703902\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.2627 | 1.03688 | 0.518440 | − | 0.855114i | \(-0.326513\pi\) | ||||
0.518440 | + | 0.855114i | \(0.326513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.4791 | 0.812323 | 0.406162 | − | 0.913801i | \(-0.366867\pi\) | ||||
0.406162 | + | 0.913801i | \(0.366867\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.7693 | −0.498344 | −0.249172 | − | 0.968459i | \(-0.580158\pi\) | ||||
−0.249172 | + | 0.968459i | \(0.580158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2996 | 1.21440 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.3662 | 1.02840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.35673 | 0.0622508 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.9097 | 1.41230 | 0.706149 | − | 0.708063i | \(-0.250431\pi\) | ||||
0.706149 | + | 0.708063i | \(0.250431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.89655 | 0.177667 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.46018 | 0.157119 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.2664 | 1.28087 | 0.640436 | − | 0.768012i | \(-0.278754\pi\) | ||||
0.640436 | + | 0.768012i | \(0.278754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.9429 | −1.39643 | −0.698217 | − | 0.715886i | \(-0.746023\pi\) | ||||
−0.698217 | + | 0.715886i | \(0.746023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.63380 | 0.0735828 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4507 | 0.648203 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1498 | −0.946796 | −0.473398 | − | 0.880849i | \(-0.656973\pi\) | ||||
−0.473398 | + | 0.880849i | \(0.656973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.4495 | −1.49144 | −0.745719 | − | 0.666260i | \(-0.767894\pi\) | ||||
−0.745719 | + | 0.666260i | \(0.767894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1498 | 0.496161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.2627 | −0.809482 | −0.404741 | − | 0.914431i | \(-0.632638\pi\) | ||||
−0.404741 | + | 0.914431i | \(0.632638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −47.3793 | −2.09594 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.0796 | 0.752619 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.3662 | 0.983664 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0796 | 0.748273 | 0.374136 | − | 0.927374i | \(-0.377939\pi\) | ||||
0.374136 | + | 0.927374i | \(0.377939\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.42690 | −0.412210 | −0.206105 | − | 0.978530i | \(-0.566079\pi\) | ||||
−0.206105 | + | 0.978530i | \(0.566079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.07965 | −0.221273 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.59690 | 0.199865 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.89655 | 0.168778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9762 | 0.474542 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −80.2520 | −3.45670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.8026 | 0.894372 | 0.447186 | − | 0.894441i | \(-0.352426\pi\) | ||||
0.447186 | + | 0.894441i | \(0.352426\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.43637 | −0.104363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.36620 | 0.101171 | 0.0505856 | − | 0.998720i | \(-0.483891\pi\) | ||||
0.0505856 | + | 0.998720i | \(0.483891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.872747 | 0.0371803 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.8300 | −2.11899 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.159296 | −0.00674957 | −0.00337478 | − | 0.999994i | \(-0.501074\pi\) | ||||
−0.00337478 | + | 0.999994i | \(0.501074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.79310 | 0.160431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.6289 | −1.79660 | −0.898298 | − | 0.439387i | \(-0.855196\pi\) | ||||
−0.898298 | + | 0.439387i | \(0.855196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.35673 | −0.141219 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.2389 | 0.471161 | 0.235581 | − | 0.971855i | \(-0.424301\pi\) | ||||
0.235581 | + | 0.971855i | \(0.424301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.9762 | 1.12892 | 0.564459 | − | 0.825461i | \(-0.309085\pi\) | ||||
0.564459 | + | 0.825461i | \(0.309085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.25328 | 0.219077 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.75983 | 0.239785 | 0.119892 | − | 0.992787i | \(-0.461745\pi\) | ||||
0.119892 | + | 0.992787i | \(0.461745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.1593 | 0.753375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.4031 | −0.513684 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8727 | 0.861510 | 0.430755 | − | 0.902469i | \(-0.358247\pi\) | ||||
0.430755 | + | 0.902469i | \(0.358247\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.71345 | −0.111806 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.0131 | 0.945035 | 0.472517 | − | 0.881321i | \(-0.343345\pi\) | ||||
0.472517 | + | 0.881321i | \(0.343345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.5304 | −0.472698 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.9524 | −0.896951 | −0.448475 | − | 0.893795i | \(-0.648033\pi\) | ||||
−0.448475 | + | 0.893795i | \(0.648033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9762 | −0.529310 | −0.264655 | − | 0.964343i | \(-0.585258\pi\) | ||||
−0.264655 | + | 0.964343i | \(0.585258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.7693 | 0.966359 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.5862 | 1.60675 | 0.803377 | − | 0.595471i | \(-0.203034\pi\) | ||||
0.803377 | + | 0.595471i | \(0.203034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.79310 | 0.153452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.6896 | −1.92617 | −0.963083 | − | 0.269203i | \(-0.913240\pi\) | ||||
−0.963083 | + | 0.269203i | \(0.913240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.85965 | 0.396934 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.78363 | −0.111883 | −0.0559417 | − | 0.998434i | \(-0.517816\pi\) | ||||
−0.0559417 | + | 0.998434i | \(0.517816\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.1675 | −1.92979 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.89655 | −0.394601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.12725 | −0.204113 | −0.102056 | − | 0.994779i | \(-0.532542\pi\) | ||||
−0.102056 | + | 0.994779i | \(0.532542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.6100 | −0.539248 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.15930 | 0.0852870 | 0.0426435 | − | 0.999090i | \(-0.486422\pi\) | ||||
0.0426435 | + | 0.999090i | \(0.486422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.1962 | 1.50631 | 0.753156 | − | 0.657843i | \(-0.228531\pi\) | ||||
0.753156 | + | 0.657843i | \(0.228531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.41257 | −0.134162 | −0.0670810 | − | 0.997748i | \(-0.521369\pi\) | ||||
−0.0670810 | + | 0.997748i | \(0.521369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.5862 | 0.925839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.93929 | −0.349822 | −0.174911 | − | 0.984584i | \(-0.555964\pi\) | ||||
−0.174911 | + | 0.984584i | \(0.555964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.72292 | −0.379906 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5029 | −0.487045 | −0.243522 | − | 0.969895i | \(-0.578303\pi\) | ||||
−0.243522 | + | 0.969895i | \(0.578303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1688 | 0.901161 | 0.450580 | − | 0.892736i | \(-0.351217\pi\) | ||||
0.450580 | + | 0.892736i | \(0.351217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.15930 | −0.238847 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.37930 | 0.130847 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.610001 | −0.0235488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.0451 | 1.77491 | 0.887455 | − | 0.460895i | \(-0.152471\pi\) | ||||
0.887455 | + | 0.460895i | \(0.152471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.9286 | −1.57301 | −0.786507 | − | 0.617582i | \(-0.788113\pi\) | ||||
−0.786507 | + | 0.617582i | \(0.788113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7086 | −0.602840 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.3317 | 1.73457 | 0.867284 | − | 0.497813i | \(-0.165863\pi\) | ||||
0.867284 | + | 0.497813i | \(0.165863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.20690 | 0.0843214 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.10345 | −0.0801351 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6753 | 1.28107 | 0.640535 | − | 0.767929i | \(-0.278713\pi\) | ||||
0.640535 | + | 0.767929i | \(0.278713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.1831 | 0.575928 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.89655 | −0.374859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4553 | 1.15028 | 0.575141 | − | 0.818055i | \(-0.304947\pi\) | ||||
0.575141 | + | 0.818055i | \(0.304947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.28655 | −0.199386 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.6182 | −1.90369 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.94292 | 0.335859 | 0.167929 | − | 0.985799i | \(-0.446292\pi\) | ||||
0.167929 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.5066 | −0.393473 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.89655 | 0.220518 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.2996 | −1.57751 | −0.788755 | − | 0.614707i | \(-0.789274\pi\) | ||||
−0.788755 | + | 0.614707i | \(0.789274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −77.5386 | −2.88769 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.643274 | 0.0238906 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.3793 | 1.60885 | 0.804425 | − | 0.594055i | \(-0.202474\pi\) | ||||
0.804425 | + | 0.594055i | \(0.202474\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.63380 | −0.356319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.6289 | −1.05743 | −0.528717 | − | 0.848798i | \(-0.677327\pi\) | ||||
−0.528717 | + | 0.848798i | \(0.677327\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.1593 | 1.25827 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5636 | −0.940373 | −0.470187 | − | 0.882567i | \(-0.655813\pi\) | ||||
−0.470187 | + | 0.882567i | \(0.655813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.7324 | −0.467106 | −0.233553 | − | 0.972344i | \(-0.575035\pi\) | ||||
−0.233553 | + | 0.972344i | \(0.575035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7693 | 0.760928 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.8300 | −1.82075 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.5624 | −0.969276 | −0.484638 | − | 0.874715i | \(-0.661049\pi\) | ||||
−0.484638 | + | 0.874715i | \(0.661049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7931 | 0.793132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5993 | −1.11215 | −0.556075 | − | 0.831132i | \(-0.687693\pi\) | ||||
−0.556075 | + | 0.831132i | \(0.687693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1404 | −0.512587 | −0.256294 | − | 0.966599i | \(-0.582501\pi\) | ||||
−0.256294 | + | 0.966599i | \(0.582501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0607 | 0.400424 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | 0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.58620 | −0.201443 | −0.100722 | − | 0.994915i | \(-0.532115\pi\) | ||||
−0.100722 | + | 0.994915i | \(0.532115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.2389 | 1.19552 | 0.597761 | − | 0.801674i | \(-0.296057\pi\) | ||||
0.597761 | + | 0.801674i | \(0.296057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.28655 | −0.189410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.7693 | 0.671618 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.3662 | 0.584135 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5066 | −0.873564 | −0.436782 | − | 0.899567i | \(-0.643882\pi\) | ||||
−0.436782 | + | 0.899567i | \(0.643882\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2389 | 0.541834 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.103450 | −0.00367363 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.8489 | −0.703086 | −0.351543 | − | 0.936172i | \(-0.614343\pi\) | ||||
−0.351543 | + | 0.936172i | \(0.614343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.63380 | −0.340819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61.5386 | −2.17165 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.8489 | −0.840565 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.7455 | −1.04580 | −0.522898 | − | 0.852395i | \(-0.675149\pi\) | ||||
−0.522898 | + | 0.852395i | \(0.675149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.277078 | −0.00972952 | −0.00486476 | − | 0.999988i | \(-0.501549\pi\) | ||||
−0.00486476 | + | 0.999988i | \(0.501549\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.4827 | 0.822565 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.14619 | −0.180043 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.5624 | 1.69484 | 0.847420 | − | 0.530924i | \(-0.178155\pi\) | ||||
0.847420 | + | 0.530924i | \(0.178155\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.4589 | 0.992016 | 0.496008 | − | 0.868318i | \(-0.334799\pi\) | ||||
0.496008 | + | 0.868318i | \(0.334799\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.3793 | 0.812978 | 0.406489 | − | 0.913656i | \(-0.366753\pi\) | ||||
0.406489 | + | 0.913656i | \(0.366753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.1593 | 0.839087 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.5670 | 1.19768 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.0796 | 0.452640 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.4220 | 0.912190 | 0.456095 | − | 0.889931i | \(-0.349248\pi\) | ||||
0.456095 | + | 0.889931i | \(0.349248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5862 | −0.985731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −107.908 | −3.70778 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4696 | −0.701690 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0558 | 0.892135 | 0.446068 | − | 0.894999i | \(-0.352824\pi\) | ||||
0.446068 | + | 0.894999i | \(0.352824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.6326 | 1.66126 | 0.830629 | − | 0.556827i | \(-0.187981\pi\) | ||||
0.830629 | + | 0.556827i | \(0.187981\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.2627 | −1.10079 | −0.550395 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550395 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4113 | 1.57986 | 0.789930 | − | 0.613197i | \(-0.210117\pi\) | ||||
0.789930 | + | 0.613197i | \(0.210117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.5066 | −0.629242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −64.7217 | −2.19553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79310 | 0.196292 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.53982 | −0.153474 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.5731 | −0.424563 | −0.212282 | − | 0.977209i | \(-0.568089\pi\) | ||||
−0.212282 | + | 0.977209i | \(0.568089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.6658 | 0.561487 | 0.280743 | − | 0.959783i | \(-0.409419\pi\) | ||||
0.280743 | + | 0.959783i | \(0.409419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.5386 | −1.39788 | −0.698942 | − | 0.715178i | \(-0.746346\pi\) | ||||
−0.698942 | + | 0.715178i | \(0.746346\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.1926 | 0.745154 | 0.372577 | − | 0.928001i | \(-0.378474\pi\) | ||||
0.372577 | + | 0.928001i | \(0.378474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.14619 | −0.172211 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.6433 | −0.422618 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.28655 | −0.0429088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.34239 | 0.177981 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.32345 | −0.309922 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.5386 | −1.64490 | −0.822451 | − | 0.568836i | \(-0.807394\pi\) | ||||
−0.822451 | + | 0.568836i | \(0.807394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.4589 | −0.677835 | −0.338918 | − | 0.940816i | \(-0.610061\pi\) | ||||
−0.338918 | + | 0.940816i | \(0.610061\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.5862 | 0.780589 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.1404 | 1.45764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.5624 | 0.348421 | 0.174211 | − | 0.984708i | \(-0.444263\pi\) | ||||
0.174211 | + | 0.984708i | \(0.444263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.18310 | 0.104773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.89655 | −0.128118 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.18310 | 0.0388162 | 0.0194081 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194081 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4650 | 0.605167 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.9762 | −0.489774 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.0796 | −1.27668 | −0.638338 | − | 0.769756i | \(-0.720378\pi\) | ||||
−0.638338 | + | 0.769756i | \(0.720378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.7504 | 0.741640 | 0.370820 | − | 0.928705i | \(-0.379077\pi\) | ||||
0.370820 | + | 0.928705i | \(0.379077\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.4696 | −0.666583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.9524 | −0.583374 | −0.291687 | − | 0.956514i | \(-0.594217\pi\) | ||||
−0.291687 | + | 0.956514i | \(0.594217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4364 | −0.338779 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.7788 | −0.705483 | −0.352742 | − | 0.935721i | \(-0.614751\pi\) | ||||
−0.352742 | + | 0.935721i | \(0.614751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.7931 | −0.769927 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0189 | −0.323528 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.53982 | 0.146142 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.21637 | 0.0391159 | 0.0195579 | − | 0.999809i | \(-0.493774\pi\) | ||||
0.0195579 | + | 0.999809i | \(0.493774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.85018 | −0.155650 | −0.0778248 | − | 0.996967i | \(-0.524797\pi\) | ||||
−0.0778248 | + | 0.996967i | \(0.524797\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −68.9286 | −2.20975 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0131 | 0.992197 | 0.496098 | − | 0.868266i | \(-0.334765\pi\) | ||||
0.496098 | + | 0.868266i | \(0.334765\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −62.5624 | −1.99950 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.7324 | 1.17158 | 0.585791 | − | 0.810462i | \(-0.300784\pi\) | ||||
0.585791 | + | 0.810462i | \(0.300784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.50655 | −0.143591 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.9262 | −0.633616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.7824 | 1.77199 | 0.885993 | − | 0.463698i | \(-0.153478\pi\) | ||||
0.885993 | + | 0.463698i | \(0.153478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.42690 | −0.172044 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.84070 | 0.121636 | 0.0608182 | − | 0.998149i | \(-0.480629\pi\) | ||||
0.0608182 | + | 0.998149i | \(0.480629\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4680.2.a.bj.1.1 | yes | 3 | |
3.2 | odd | 2 | 4680.2.a.bg.1.1 | ✓ | 3 | ||
4.3 | odd | 2 | 9360.2.a.de.1.3 | 3 | |||
12.11 | even | 2 | 9360.2.a.cz.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4680.2.a.bg.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
4680.2.a.bj.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
9360.2.a.cz.1.3 | 3 | 12.11 | even | 2 | |||
9360.2.a.de.1.3 | 3 | 4.3 | odd | 2 |