Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(12.1452461474\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35690 | 1.66658 | 0.833289 | − | 0.552838i | \(-0.186455\pi\) | ||||
0.833289 | + | 0.552838i | \(0.186455\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.55496 | 1.77748 | ||||||||
\(5\) | 3.69202 | 1.65112 | 0.825561 | − | 0.564313i | \(-0.190859\pi\) | ||||
0.825561 | + | 0.564313i | \(0.190859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.801938 | 0.303104 | 0.151552 | − | 0.988449i | \(-0.451573\pi\) | ||||
0.151552 | + | 0.988449i | \(0.451573\pi\) | |||||||
\(8\) | 3.66487 | 1.29573 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.70171 | 2.75172 | ||||||||
\(11\) | −2.85086 | −0.859565 | −0.429783 | − | 0.902932i | \(-0.641410\pi\) | ||||
−0.429783 | + | 0.902932i | \(0.641410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.89008 | 0.505146 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.52781 | 0.381953 | ||||||||
\(17\) | −2.93900 | −0.712812 | −0.356406 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356406 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44504 | 0.560931 | 0.280466 | − | 0.959864i | \(-0.409511\pi\) | ||||
0.280466 | + | 0.959864i | \(0.409511\pi\) | |||||||
\(20\) | 13.1250 | 2.93484 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.71917 | −1.43253 | ||||||||
\(23\) | 7.78986 | 1.62430 | 0.812149 | − | 0.583451i | \(-0.198298\pi\) | ||||
0.812149 | + | 0.583451i | \(0.198298\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.63102 | 1.72620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.85086 | 0.538761 | ||||||||
\(29\) | −3.85086 | −0.715086 | −0.357543 | − | 0.933897i | \(-0.616385\pi\) | ||||
−0.357543 | + | 0.933897i | \(0.616385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.34481 | −0.421141 | −0.210571 | − | 0.977579i | \(-0.567532\pi\) | ||||
−0.210571 | + | 0.977579i | \(0.567532\pi\) | |||||||
\(32\) | −3.72886 | −0.659175 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.92692 | −1.18796 | ||||||||
\(35\) | 2.96077 | 0.500462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.44504 | −1.22396 | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(38\) | 5.76271 | 0.934835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.5308 | 2.13941 | ||||||||
\(41\) | −0.850855 | −0.132881 | −0.0664406 | − | 0.997790i | \(-0.521164\pi\) | ||||
−0.0664406 | + | 0.997790i | \(0.521164\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61596 | −0.246431 | −0.123216 | − | 0.992380i | \(-0.539321\pi\) | ||||
−0.123216 | + | 0.992380i | \(0.539321\pi\) | |||||||
\(44\) | −10.1347 | −1.52786 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.3599 | 2.70702 | ||||||||
\(47\) | 2.44504 | 0.356646 | 0.178323 | − | 0.983972i | \(-0.442933\pi\) | ||||
0.178323 | + | 0.983972i | \(0.442933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35690 | −0.908128 | ||||||||
\(50\) | 20.3424 | 2.87685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.96077 | 1.36822 | 0.684109 | − | 0.729380i | \(-0.260191\pi\) | ||||
0.684109 | + | 0.729380i | \(0.260191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.5254 | −1.41925 | ||||||||
\(56\) | 2.93900 | 0.392741 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.07606 | −1.19175 | ||||||||
\(59\) | −5.38404 | −0.700943 | −0.350471 | − | 0.936573i | \(-0.613979\pi\) | ||||
−0.350471 | + | 0.936573i | \(0.613979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2567 | −1.69734 | −0.848671 | − | 0.528921i | \(-0.822597\pi\) | ||||
−0.848671 | + | 0.528921i | \(0.822597\pi\) | |||||||
\(62\) | −5.52648 | −0.701864 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.8442 | −1.48052 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.3937 | −1.75847 | −0.879237 | − | 0.476384i | \(-0.841947\pi\) | ||||
−0.879237 | + | 0.476384i | \(0.841947\pi\) | |||||||
\(68\) | −10.4480 | −1.26701 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.97823 | 0.834058 | ||||||||
\(71\) | 8.12498 | 0.964258 | 0.482129 | − | 0.876100i | \(-0.339864\pi\) | ||||
0.482129 | + | 0.876100i | \(0.339864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8877 | 1.39135 | 0.695674 | − | 0.718357i | \(-0.255106\pi\) | ||||
0.695674 | + | 0.718357i | \(0.255106\pi\) | |||||||
\(74\) | −17.5472 | −2.03982 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.69202 | 0.997043 | ||||||||
\(77\) | −2.28621 | −0.260538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.40581 | 0.608202 | 0.304101 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304101 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(80\) | 5.64071 | 0.630651 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00538 | −0.221457 | ||||||||
\(83\) | 7.04892 | 0.773719 | 0.386860 | − | 0.922139i | \(-0.373560\pi\) | ||||
0.386860 | + | 0.922139i | \(0.373560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8509 | −1.17694 | ||||||||
\(86\) | −3.80864 | −0.410696 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.4480 | −1.11376 | ||||||||
\(89\) | 1.13169 | 0.119959 | 0.0599793 | − | 0.998200i | \(-0.480897\pi\) | ||||
0.0599793 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 27.6926 | 2.88715 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.76271 | 0.594378 | ||||||||
\(95\) | 9.02715 | 0.926166 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.94438 | 0.603560 | 0.301780 | − | 0.953378i | \(-0.402419\pi\) | ||||
0.301780 | + | 0.953378i | \(0.402419\pi\) | |||||||
\(98\) | −14.9825 | −1.51347 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 30.6829 | 3.06829 | ||||||||
\(101\) | −4.62565 | −0.460269 | −0.230134 | − | 0.973159i | \(-0.573917\pi\) | ||||
−0.230134 | + | 0.973159i | \(0.573917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.20775 | 0.119003 | 0.0595016 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0595016 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 23.4765 | 2.28024 | ||||||||
\(107\) | 9.52111 | 0.920440 | 0.460220 | − | 0.887805i | \(-0.347771\pi\) | ||||
0.460220 | + | 0.887805i | \(0.347771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.78448 | 0.170922 | 0.0854611 | − | 0.996342i | \(-0.472764\pi\) | ||||
0.0854611 | + | 0.996342i | \(0.472764\pi\) | |||||||
\(110\) | −24.8073 | −2.36528 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.22521 | 0.115771 | ||||||||
\(113\) | −4.95108 | −0.465759 | −0.232879 | − | 0.972506i | \(-0.574815\pi\) | ||||
−0.232879 | + | 0.972506i | \(0.574815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.7603 | 2.68191 | ||||||||
\(116\) | −13.6896 | −1.27105 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.6896 | −1.16817 | ||||||||
\(119\) | −2.35690 | −0.216056 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.87263 | −0.261148 | ||||||||
\(122\) | −31.2446 | −2.82875 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.33572 | −0.748569 | ||||||||
\(125\) | 13.4058 | 1.19905 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.67025 | 0.503153 | 0.251577 | − | 0.967837i | \(-0.419051\pi\) | ||||
0.251577 | + | 0.967837i | \(0.419051\pi\) | |||||||
\(128\) | −20.4577 | −1.80822 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.2228 | −1.59213 | −0.796067 | − | 0.605208i | \(-0.793090\pi\) | ||||
−0.796067 | + | 0.605208i | \(0.793090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.96077 | 0.170020 | ||||||||
\(134\) | −33.9245 | −2.93063 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.7711 | −0.923612 | ||||||||
\(137\) | 9.45042 | 0.807404 | 0.403702 | − | 0.914891i | \(-0.367723\pi\) | ||||
0.403702 | + | 0.914891i | \(0.367723\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.01507 | 0.340553 | 0.170277 | − | 0.985396i | \(-0.445534\pi\) | ||||
0.170277 | + | 0.985396i | \(0.445534\pi\) | |||||||
\(140\) | 10.5254 | 0.889560 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.1497 | 1.60701 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.2174 | −1.18069 | ||||||||
\(146\) | 28.0180 | 2.31879 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26.4668 | −2.17556 | ||||||||
\(149\) | 19.4058 | 1.58979 | 0.794893 | − | 0.606750i | \(-0.207527\pi\) | ||||
0.794893 | + | 0.606750i | \(0.207527\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3623 | 1.00603 | 0.503014 | − | 0.864278i | \(-0.332225\pi\) | ||||
0.503014 | + | 0.864278i | \(0.332225\pi\) | |||||||
\(152\) | 8.96077 | 0.726815 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.38835 | −0.434206 | ||||||||
\(155\) | −8.65710 | −0.695355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6775 | −1.49063 | −0.745315 | − | 0.666712i | \(-0.767701\pi\) | ||||
−0.745315 | + | 0.666712i | \(0.767701\pi\) | |||||||
\(158\) | 12.7409 | 1.01361 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.7670 | −1.08838 | ||||||||
\(161\) | 6.24698 | 0.492331 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3394 | −0.966499 | −0.483250 | − | 0.875483i | \(-0.660544\pi\) | ||||
−0.483250 | + | 0.875483i | \(0.660544\pi\) | |||||||
\(164\) | −3.02475 | −0.236194 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.6136 | 1.28946 | ||||||||
\(167\) | 11.4940 | 0.889429 | 0.444715 | − | 0.895672i | \(-0.353305\pi\) | ||||
0.444715 | + | 0.895672i | \(0.353305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −25.5743 | −1.96146 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.74466 | −0.438026 | ||||||||
\(173\) | −12.1142 | −0.921028 | −0.460514 | − | 0.887653i | \(-0.652335\pi\) | ||||
−0.460514 | + | 0.887653i | \(0.652335\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.92154 | 0.523219 | ||||||||
\(176\) | −4.35557 | −0.328313 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.66727 | 0.199920 | ||||||||
\(179\) | 0.538565 | 0.0402542 | 0.0201271 | − | 0.999797i | \(-0.493593\pi\) | ||||
0.0201271 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.2838 | −1.73067 | −0.865336 | − | 0.501192i | \(-0.832895\pi\) | ||||
−0.865336 | + | 0.501192i | \(0.832895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 28.5488 | 2.10465 | ||||||||
\(185\) | −27.4873 | −2.02090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.37867 | 0.612709 | ||||||||
\(188\) | 8.69202 | 0.633931 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.2760 | 1.54353 | ||||||||
\(191\) | −16.7657 | −1.21312 | −0.606561 | − | 0.795037i | \(-0.707452\pi\) | ||||
−0.606561 | + | 0.795037i | \(0.707452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.7439 | −1.85309 | −0.926544 | − | 0.376186i | \(-0.877235\pi\) | ||||
−0.926544 | + | 0.376186i | \(0.877235\pi\) | |||||||
\(194\) | 14.0103 | 1.00588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.5985 | −1.61418 | ||||||||
\(197\) | 21.4209 | 1.52617 | 0.763087 | − | 0.646296i | \(-0.223683\pi\) | ||||
0.763087 | + | 0.646296i | \(0.223683\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.52781 | 0.250080 | 0.125040 | − | 0.992152i | \(-0.460094\pi\) | ||||
0.125040 | + | 0.992152i | \(0.460094\pi\) | |||||||
\(200\) | 31.6316 | 2.23669 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.9022 | −0.767074 | ||||||||
\(203\) | −3.08815 | −0.216745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.14138 | −0.219403 | ||||||||
\(206\) | 2.84654 | 0.198328 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.97046 | −0.482157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21552 | 0.0836799 | 0.0418399 | − | 0.999124i | \(-0.486678\pi\) | ||||
0.0418399 | + | 0.999124i | \(0.486678\pi\) | |||||||
\(212\) | 35.4101 | 2.43198 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.4403 | 1.53398 | ||||||||
\(215\) | −5.96615 | −0.406888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.88040 | −0.127650 | ||||||||
\(218\) | 4.20583 | 0.284855 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −37.4174 | −2.52268 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3884 | 1.16441 | 0.582205 | − | 0.813042i | \(-0.302190\pi\) | ||||
0.582205 | + | 0.813042i | \(0.302190\pi\) | |||||||
\(224\) | −2.99031 | −0.199799 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.6692 | −0.776223 | ||||||||
\(227\) | 17.4155 | 1.15591 | 0.577954 | − | 0.816070i | \(-0.303851\pi\) | ||||
0.577954 | + | 0.816070i | \(0.303851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7603 | −1.23972 | −0.619858 | − | 0.784714i | \(-0.712810\pi\) | ||||
−0.619858 | + | 0.784714i | \(0.712810\pi\) | |||||||
\(230\) | 67.7851 | 4.46962 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.1129 | −0.926557 | ||||||||
\(233\) | −3.95108 | −0.258844 | −0.129422 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129422 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.02715 | 0.588866 | ||||||||
\(236\) | −19.1400 | −1.24591 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.55496 | −0.360074 | ||||||||
\(239\) | 0.818331 | 0.0529334 | 0.0264667 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264667 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.03252 | −0.388589 | −0.194295 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194295 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(242\) | −6.77048 | −0.435223 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −47.1269 | −3.01699 | ||||||||
\(245\) | −23.4698 | −1.49943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.59345 | −0.545685 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 31.5961 | 1.99831 | ||||||||
\(251\) | 26.8799 | 1.69665 | 0.848323 | − | 0.529479i | \(-0.177613\pi\) | ||||
0.848323 | + | 0.529479i | \(0.177613\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.2078 | −1.39619 | ||||||||
\(254\) | 13.3642 | 0.838544 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.5284 | −1.53303 | ||||||||
\(257\) | 9.05323 | 0.564725 | 0.282362 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282362 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.97046 | −0.370986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.9493 | −2.65342 | ||||||||
\(263\) | −23.1511 | −1.42756 | −0.713778 | − | 0.700372i | \(-0.753017\pi\) | ||||
−0.713778 | + | 0.700372i | \(0.753017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.7754 | 2.25909 | ||||||||
\(266\) | 4.62133 | 0.283352 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −51.1691 | −3.12565 | ||||||||
\(269\) | 2.42088 | 0.147604 | 0.0738018 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0738018 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4450 | 1.30269 | 0.651347 | − | 0.758780i | \(-0.274204\pi\) | ||||
0.651347 | + | 0.758780i | \(0.274204\pi\) | |||||||
\(272\) | −4.49024 | −0.272261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.2737 | 1.34560 | ||||||||
\(275\) | −24.6058 | −1.48379 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8073 | −0.889685 | −0.444843 | − | 0.895609i | \(-0.646740\pi\) | ||||
−0.444843 | + | 0.895609i | \(0.646740\pi\) | |||||||
\(278\) | 9.46309 | 0.567558 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.8509 | 0.648463 | ||||||||
\(281\) | 14.5036 | 0.865215 | 0.432608 | − | 0.901582i | \(-0.357594\pi\) | ||||
0.432608 | + | 0.901582i | \(0.357594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6722 | 1.52605 | 0.763026 | − | 0.646368i | \(-0.223713\pi\) | ||||
0.763026 | + | 0.646368i | \(0.223713\pi\) | |||||||
\(284\) | 28.8840 | 1.71395 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.682333 | −0.0402768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.36227 | −0.491898 | ||||||||
\(290\) | −33.5090 | −1.96772 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 42.2602 | 2.47309 | ||||||||
\(293\) | −26.5230 | −1.54949 | −0.774746 | − | 0.632273i | \(-0.782122\pi\) | ||||
−0.774746 | + | 0.632273i | \(0.782122\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.8780 | −1.15734 | ||||||||
\(296\) | −27.2851 | −1.58592 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 45.7375 | 2.64950 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29590 | −0.0746943 | ||||||||
\(302\) | 29.1366 | 1.67662 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.73556 | 0.214249 | ||||||||
\(305\) | −48.9439 | −2.80252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.24698 | 0.470680 | 0.235340 | − | 0.971913i | \(-0.424380\pi\) | ||||
0.235340 | + | 0.971913i | \(0.424380\pi\) | |||||||
\(308\) | −8.12737 | −0.463100 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.4039 | −1.15886 | ||||||||
\(311\) | 14.4179 | 0.817564 | 0.408782 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408782 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2338 | 0.804544 | 0.402272 | − | 0.915520i | \(-0.368221\pi\) | ||||
0.402272 | + | 0.915520i | \(0.368221\pi\) | |||||||
\(314\) | −44.0210 | −2.48425 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2174 | 1.08107 | ||||||||
\(317\) | −6.84415 | −0.384406 | −0.192203 | − | 0.981355i | \(-0.561563\pi\) | ||||
−0.192203 | + | 0.981355i | \(0.561563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.9782 | 0.614663 | ||||||||
\(320\) | −43.7289 | −2.44452 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.7235 | 0.820507 | ||||||||
\(323\) | −7.18598 | −0.399839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.0828 | −1.61075 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.11828 | −0.172178 | ||||||||
\(329\) | 1.96077 | 0.108101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.44265 | −0.519015 | −0.259507 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259507 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(332\) | 25.0586 | 1.37527 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.0901 | 1.48230 | ||||||||
\(335\) | −53.1420 | −2.90346 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64310 | 0.143979 | 0.0719895 | − | 0.997405i | \(-0.477065\pi\) | ||||
0.0719895 | + | 0.997405i | \(0.477065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −38.5743 | −2.09199 | ||||||||
\(341\) | 6.68473 | 0.361998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.7114 | −0.578361 | ||||||||
\(344\) | −5.92228 | −0.319308 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.5520 | −1.53496 | ||||||||
\(347\) | 10.1588 | 0.545355 | 0.272677 | − | 0.962106i | \(-0.412091\pi\) | ||||
0.272677 | + | 0.962106i | \(0.412091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4397 | −0.558822 | −0.279411 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279411 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(350\) | 16.3134 | 0.871986 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.6304 | 0.566604 | ||||||||
\(353\) | 18.2911 | 0.973538 | 0.486769 | − | 0.873531i | \(-0.338175\pi\) | ||||
0.486769 | + | 0.873531i | \(0.338175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.9976 | 1.59211 | ||||||||
\(356\) | 4.02310 | 0.213224 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.26934 | 0.0670867 | ||||||||
\(359\) | −15.2731 | −0.806081 | −0.403041 | − | 0.915182i | \(-0.632047\pi\) | ||||
−0.403041 | + | 0.915182i | \(0.632047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0218 | −0.685356 | ||||||||
\(362\) | −54.8775 | −2.88430 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.8896 | 2.29729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.2717 | −1.16258 | −0.581288 | − | 0.813698i | \(-0.697451\pi\) | ||||
−0.581288 | + | 0.813698i | \(0.697451\pi\) | |||||||
\(368\) | 11.9014 | 0.620405 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −64.7846 | −3.36799 | ||||||||
\(371\) | 7.98792 | 0.414712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.12631 | 0.213652 | 0.106826 | − | 0.994278i | \(-0.465931\pi\) | ||||
0.106826 | + | 0.994278i | \(0.465931\pi\) | |||||||
\(374\) | 19.7476 | 1.02113 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.96077 | 0.462116 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7071 | 0.549986 | 0.274993 | − | 0.961446i | \(-0.411324\pi\) | ||||
0.274993 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(380\) | 32.0911 | 1.64624 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −39.5150 | −2.02176 | ||||||||
\(383\) | 6.52648 | 0.333488 | 0.166744 | − | 0.986000i | \(-0.446675\pi\) | ||||
0.166744 | + | 0.986000i | \(0.446675\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44073 | −0.430179 | ||||||||
\(386\) | −60.6757 | −3.08831 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21.1320 | 1.07282 | ||||||||
\(389\) | 11.7922 | 0.597891 | 0.298945 | − | 0.954270i | \(-0.403365\pi\) | ||||
0.298945 | + | 0.954270i | \(0.403365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8944 | −1.15782 | ||||||||
\(392\) | −23.2972 | −1.17669 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 50.4868 | 2.54349 | ||||||||
\(395\) | 19.9584 | 1.00422 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5429 | 0.629509 | 0.314754 | − | 0.949173i | \(-0.398078\pi\) | ||||
0.314754 | + | 0.949173i | \(0.398078\pi\) | |||||||
\(398\) | 8.31468 | 0.416777 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.1866 | 0.659329 | ||||||||
\(401\) | 17.8702 | 0.892397 | 0.446198 | − | 0.894934i | \(-0.352778\pi\) | ||||
0.446198 | + | 0.894934i | \(0.352778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −16.4440 | −0.818118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.27844 | −0.361223 | ||||||||
\(407\) | 21.2247 | 1.05207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9119 | 1.38015 | 0.690076 | − | 0.723737i | \(-0.257577\pi\) | ||||
0.690076 | + | 0.723737i | \(0.257577\pi\) | |||||||
\(410\) | −7.40389 | −0.365652 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.29350 | 0.211526 | ||||||||
\(413\) | −4.31767 | −0.212459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.0248 | 1.27750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.4286 | −0.803551 | ||||||||
\(419\) | 16.4034 | 0.801360 | 0.400680 | − | 0.916218i | \(-0.368774\pi\) | ||||
0.400680 | + | 0.916218i | \(0.368774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.03684 | 0.148006 | 0.0740032 | − | 0.997258i | \(-0.476423\pi\) | ||||
0.0740032 | + | 0.997258i | \(0.476423\pi\) | |||||||
\(422\) | 2.86486 | 0.139459 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 36.5050 | 1.77284 | ||||||||
\(425\) | −25.3666 | −1.23046 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6310 | −0.514471 | ||||||||
\(428\) | 33.8471 | 1.63606 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0616 | −0.678110 | ||||||||
\(431\) | −3.33811 | −0.160791 | −0.0803955 | − | 0.996763i | \(-0.525618\pi\) | ||||
−0.0803955 | + | 0.996763i | \(0.525618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9028 | 0.572010 | 0.286005 | − | 0.958228i | \(-0.407673\pi\) | ||||
0.286005 | + | 0.958228i | \(0.407673\pi\) | |||||||
\(434\) | −4.43190 | −0.212738 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.34375 | 0.303810 | ||||||||
\(437\) | 19.0465 | 0.911119 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.71810 | 0.177455 | 0.0887277 | − | 0.996056i | \(-0.471720\pi\) | ||||
0.0887277 | + | 0.996056i | \(0.471720\pi\) | |||||||
\(440\) | −38.5743 | −1.83896 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.45712 | −0.0692300 | −0.0346150 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346150 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.17821 | 0.198066 | ||||||||
\(446\) | 40.9825 | 1.94058 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.49827 | −0.448751 | ||||||||
\(449\) | −12.1274 | −0.572326 | −0.286163 | − | 0.958181i | \(-0.592380\pi\) | ||||
−0.286163 | + | 0.958181i | \(0.592380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.42566 | 0.114220 | ||||||||
\(452\) | −17.6009 | −0.827876 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 41.0465 | 1.92641 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.44803 | 0.161292 | 0.0806459 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806459 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(458\) | −44.2161 | −2.06608 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 102.242 | 4.76704 | ||||||||
\(461\) | −6.75600 | −0.314658 | −0.157329 | − | 0.987546i | \(-0.550288\pi\) | ||||
−0.157329 | + | 0.987546i | \(0.550288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.45175 | 0.346312 | 0.173156 | − | 0.984894i | \(-0.444604\pi\) | ||||
0.173156 | + | 0.984894i | \(0.444604\pi\) | |||||||
\(464\) | −5.88338 | −0.273129 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.31229 | −0.431384 | ||||||||
\(467\) | −32.6098 | −1.50900 | −0.754502 | − | 0.656298i | \(-0.772121\pi\) | ||||
−0.754502 | + | 0.656298i | \(0.772121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5429 | −0.533001 | ||||||||
\(470\) | 21.2760 | 0.981391 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −19.7318 | −0.908232 | ||||||||
\(473\) | 4.60686 | 0.211824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.1032 | 0.968282 | ||||||||
\(476\) | −8.37867 | −0.384036 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.92872 | 0.0882177 | ||||||||
\(479\) | 2.82908 | 0.129264 | 0.0646321 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646321 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.2180 | −0.647614 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.2121 | −0.464185 | ||||||||
\(485\) | 21.9468 | 0.996552 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.2935 | 1.87119 | 0.935594 | − | 0.353079i | \(-0.114865\pi\) | ||||
0.935594 | + | 0.353079i | \(0.114865\pi\) | |||||||
\(488\) | −48.5840 | −2.19930 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −55.3159 | −2.49892 | ||||||||
\(491\) | 34.6698 | 1.56463 | 0.782313 | − | 0.622886i | \(-0.214040\pi\) | ||||
0.782313 | + | 0.622886i | \(0.214040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.3177 | 0.509722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.58243 | −0.160856 | ||||||||
\(497\) | 6.51573 | 0.292270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9409 | −0.803146 | −0.401573 | − | 0.915827i | \(-0.631536\pi\) | ||||
−0.401573 | + | 0.915827i | \(0.631536\pi\) | |||||||
\(500\) | 47.6571 | 2.13129 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 63.3532 | 2.82759 | ||||||||
\(503\) | 26.1812 | 1.16736 | 0.583681 | − | 0.811983i | \(-0.301612\pi\) | ||||
0.583681 | + | 0.811983i | \(0.301612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0780 | −0.759960 | ||||||||
\(506\) | −52.3414 | −2.32686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.1575 | 0.894345 | ||||||||
\(509\) | −5.50604 | −0.244051 | −0.122025 | − | 0.992527i | \(-0.538939\pi\) | ||||
−0.122025 | + | 0.992527i | \(0.538939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.53319 | 0.421723 | ||||||||
\(512\) | −16.8955 | −0.746681 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.3375 | 0.941158 | ||||||||
\(515\) | 4.45904 | 0.196489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.97046 | −0.306560 | ||||||||
\(518\) | −14.0718 | −0.618277 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.7211 | 1.17067 | 0.585336 | − | 0.810791i | \(-0.300963\pi\) | ||||
0.585336 | + | 0.810791i | \(0.300963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.5230 | 1.59704 | 0.798520 | − | 0.601968i | \(-0.205617\pi\) | ||||
0.798520 | + | 0.601968i | \(0.205617\pi\) | |||||||
\(524\) | −64.7813 | −2.82999 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −54.5646 | −2.37913 | ||||||||
\(527\) | 6.89141 | 0.300195 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.6819 | 1.63834 | ||||||||
\(530\) | 86.6757 | 3.76495 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.97046 | 0.302208 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.1521 | 1.51976 | ||||||||
\(536\) | −52.7512 | −2.27851 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.70576 | 0.245993 | ||||||||
\(539\) | 18.1226 | 0.780595 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4655 | −0.793893 | −0.396947 | − | 0.917842i | \(-0.629930\pi\) | ||||
−0.396947 | + | 0.917842i | \(0.629930\pi\) | |||||||
\(542\) | 50.5437 | 2.17104 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.9591 | 0.469868 | ||||||||
\(545\) | 6.58834 | 0.282213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8471 | 1.70374 | 0.851870 | − | 0.523753i | \(-0.175468\pi\) | ||||
0.851870 | + | 0.523753i | \(0.175468\pi\) | |||||||
\(548\) | 33.5958 | 1.43514 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −57.9933 | −2.47284 | ||||||||
\(551\) | −9.41550 | −0.401114 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.33513 | 0.184348 | ||||||||
\(554\) | −34.8993 | −1.48273 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.2734 | 0.605327 | ||||||||
\(557\) | 9.20477 | 0.390018 | 0.195009 | − | 0.980801i | \(-0.437526\pi\) | ||||
0.195009 | + | 0.980801i | \(0.437526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.52350 | 0.191153 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.1836 | 1.44195 | ||||||||
\(563\) | 0.975246 | 0.0411017 | 0.0205509 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205509 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.2795 | −0.769024 | ||||||||
\(566\) | 60.5066 | 2.54328 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.7770 | 1.24942 | ||||||||
\(569\) | 16.8944 | 0.708250 | 0.354125 | − | 0.935198i | \(-0.384779\pi\) | ||||
0.354125 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.3226 | −1.85484 | −0.927421 | − | 0.374019i | \(-0.877979\pi\) | ||||
−0.927421 | + | 0.374019i | \(0.877979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.60819 | −0.0671244 | ||||||||
\(575\) | 67.2344 | 2.80387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.56704 | −0.148498 | −0.0742489 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742489 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(578\) | −19.7090 | −0.819787 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −50.5424 | −2.09866 | ||||||||
\(581\) | 5.65279 | 0.234517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.3967 | −1.17607 | ||||||||
\(584\) | 43.5669 | 1.80281 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −62.5120 | −2.58235 | ||||||||
\(587\) | −16.1172 | −0.665229 | −0.332614 | − | 0.943063i | \(-0.607931\pi\) | ||||
−0.332614 | + | 0.943063i | \(0.607931\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.73317 | −0.236231 | ||||||||
\(590\) | −46.8504 | −1.92880 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.3746 | −0.467494 | ||||||||
\(593\) | −42.8611 | −1.76010 | −0.880048 | − | 0.474885i | \(-0.842490\pi\) | ||||
−0.880048 | + | 0.474885i | \(0.842490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.70171 | −0.356735 | ||||||||
\(596\) | 68.9869 | 2.82581 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.9420 | −1.67284 | −0.836422 | − | 0.548086i | \(-0.815357\pi\) | ||||
−0.836422 | + | 0.548086i | \(0.815357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18705 | 0.0484206 | 0.0242103 | − | 0.999707i | \(-0.492293\pi\) | ||||
0.0242103 | + | 0.999707i | \(0.492293\pi\) | |||||||
\(602\) | −3.05429 | −0.124484 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 43.9474 | 1.78819 | ||||||||
\(605\) | −10.6058 | −0.431187 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.9922 | 0.811460 | 0.405730 | − | 0.913993i | \(-0.367017\pi\) | ||||
0.405730 | + | 0.913993i | \(0.367017\pi\) | |||||||
\(608\) | −9.11721 | −0.369752 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −115.356 | −4.67062 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.3618 | 1.34747 | 0.673735 | − | 0.738973i | \(-0.264689\pi\) | ||||
0.673735 | + | 0.738973i | \(0.264689\pi\) | |||||||
\(614\) | 19.4373 | 0.784424 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.37867 | −0.337586 | ||||||||
\(617\) | 11.6233 | 0.467935 | 0.233967 | − | 0.972244i | \(-0.424829\pi\) | ||||
0.233967 | + | 0.972244i | \(0.424829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5381 | 0.664722 | 0.332361 | − | 0.943152i | \(-0.392155\pi\) | ||||
0.332361 | + | 0.943152i | \(0.392155\pi\) | |||||||
\(620\) | −30.7756 | −1.23598 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.9815 | 1.36253 | ||||||||
\(623\) | 0.907542 | 0.0363599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33944 | 0.253577 | ||||||||
\(626\) | 33.5477 | 1.34083 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −66.3979 | −2.64956 | ||||||||
\(629\) | 21.8810 | 0.872452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.4416 | 1.45072 | 0.725358 | − | 0.688372i | \(-0.241674\pi\) | ||||
0.725358 | + | 0.688372i | \(0.241674\pi\) | |||||||
\(632\) | 19.8116 | 0.788064 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.1309 | −0.640642 | ||||||||
\(635\) | 20.9347 | 0.830768 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25.8745 | 1.02438 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −75.5303 | −2.98560 | ||||||||
\(641\) | −27.2067 | −1.07460 | −0.537300 | − | 0.843391i | \(-0.680556\pi\) | ||||
−0.537300 | + | 0.843391i | \(0.680556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.06962 | 0.199926 | 0.0999632 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999632 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(644\) | 22.2078 | 0.875108 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.9366 | −0.666362 | ||||||||
\(647\) | −19.3207 | −0.759573 | −0.379787 | − | 0.925074i | \(-0.624003\pi\) | ||||
−0.379787 | + | 0.925074i | \(0.624003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.3491 | 0.602506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −43.8662 | −1.71793 | ||||||||
\(653\) | −35.2355 | −1.37887 | −0.689436 | − | 0.724347i | \(-0.742141\pi\) | ||||
−0.689436 | + | 0.724347i | \(0.742141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −67.2790 | −2.62881 | ||||||||
\(656\) | −1.29995 | −0.0507544 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.62133 | 0.180158 | ||||||||
\(659\) | 4.36168 | 0.169907 | 0.0849535 | − | 0.996385i | \(-0.472926\pi\) | ||||
0.0849535 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4709 | 0.601747 | 0.300873 | − | 0.953664i | \(-0.402722\pi\) | ||||
0.300873 | + | 0.953664i | \(0.402722\pi\) | |||||||
\(662\) | −22.2553 | −0.864978 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.8334 | 1.00253 | ||||||||
\(665\) | 7.23921 | 0.280725 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.9976 | −1.16151 | ||||||||
\(668\) | 40.8605 | 1.58094 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −125.250 | −4.83883 | ||||||||
\(671\) | 37.7928 | 1.45898 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.7409 | −0.452580 | −0.226290 | − | 0.974060i | \(-0.572660\pi\) | ||||
−0.226290 | + | 0.974060i | \(0.572660\pi\) | |||||||
\(674\) | 6.22952 | 0.239952 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.44504 | −0.132404 | −0.0662019 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662019 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.76702 | 0.182941 | ||||||||
\(680\) | −39.7670 | −1.52500 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.7552 | 0.603298 | ||||||||
\(683\) | 20.4058 | 0.780807 | 0.390403 | − | 0.920644i | \(-0.372336\pi\) | ||||
0.390403 | + | 0.920644i | \(0.372336\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.8911 | 1.33312 | ||||||||
\(686\) | −25.2457 | −0.963883 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.46888 | −0.0941251 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.8039 | −1.05771 | −0.528854 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528854 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(692\) | −43.0656 | −1.63711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.9433 | 0.908876 | ||||||||
\(695\) | 14.8237 | 0.562295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.50066 | 0.0947194 | ||||||||
\(698\) | −24.6052 | −0.931321 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.6058 | 0.930012 | ||||||||
\(701\) | −11.9715 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2034 | −0.686556 | ||||||||
\(704\) | 33.7660 | 1.27260 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 43.1102 | 1.62248 | ||||||||
\(707\) | −3.70948 | −0.139509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.2664 | −1.21179 | −0.605894 | − | 0.795545i | \(-0.707185\pi\) | ||||
−0.605894 | + | 0.795545i | \(0.707185\pi\) | |||||||
\(710\) | 70.7012 | 2.65337 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.14749 | 0.155434 | ||||||||
\(713\) | −18.2658 | −0.684058 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.91457 | 0.0715510 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.9970 | −1.34340 | ||||||||
\(719\) | −12.1086 | −0.451574 | −0.225787 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225787 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.968541 | 0.0360704 | ||||||||
\(722\) | −30.6910 | −1.14220 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −82.7730 | −3.07623 | ||||||||
\(725\) | −33.2368 | −1.23438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6200 | −0.616402 | −0.308201 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308201 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 103.443 | 3.82861 | ||||||||
\(731\) | 4.74930 | 0.175659 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7912 | −0.657132 | −0.328566 | − | 0.944481i | \(-0.606565\pi\) | ||||
−0.328566 | + | 0.944481i | \(0.606565\pi\) | |||||||
\(734\) | −52.4922 | −1.93752 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29.0473 | −1.07070 | ||||||||
\(737\) | 41.0344 | 1.51152 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.3618 | 1.00652 | 0.503260 | − | 0.864135i | \(-0.332134\pi\) | ||||
0.503260 | + | 0.864135i | \(0.332134\pi\) | |||||||
\(740\) | −97.7160 | −3.59211 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.8267 | 0.691150 | ||||||||
\(743\) | 8.38596 | 0.307651 | 0.153826 | − | 0.988098i | \(-0.450841\pi\) | ||||
0.153826 | + | 0.988098i | \(0.450841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 71.6467 | 2.62493 | ||||||||
\(746\) | 9.72528 | 0.356068 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29.7858 | 1.08908 | ||||||||
\(749\) | 7.63533 | 0.278989 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7778 | −1.41502 | −0.707511 | − | 0.706703i | \(-0.750182\pi\) | ||||
−0.707511 | + | 0.706703i | \(0.750182\pi\) | |||||||
\(752\) | 3.73556 | 0.136222 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.6418 | 1.66107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.9729 | 0.471506 | 0.235753 | − | 0.971813i | \(-0.424244\pi\) | ||||
0.235753 | + | 0.971813i | \(0.424244\pi\) | |||||||
\(758\) | 25.2355 | 0.916594 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 33.0834 | 1.20006 | ||||||||
\(761\) | −5.15585 | −0.186899 | −0.0934497 | − | 0.995624i | \(-0.529789\pi\) | ||||
−0.0934497 | + | 0.995624i | \(0.529789\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.43104 | 0.0518072 | ||||||||
\(764\) | −59.6013 | −2.15630 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.3822 | 0.555783 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.5013 | 1.28021 | 0.640104 | − | 0.768288i | \(-0.278891\pi\) | ||||
0.640104 | + | 0.768288i | \(0.278891\pi\) | |||||||
\(770\) | −19.8939 | −0.716927 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −91.5186 | −3.29383 | ||||||||
\(773\) | −6.15585 | −0.221411 | −0.110705 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110705 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.2381 | −0.726976 | ||||||||
\(776\) | 21.7854 | 0.782050 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.7931 | 0.996431 | ||||||||
\(779\) | −2.08038 | −0.0745372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1631 | −0.828843 | ||||||||
\(782\) | −53.9597 | −1.92960 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.71214 | −0.346862 | ||||||||
\(785\) | −68.9579 | −2.46121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2107 | −0.506558 | −0.253279 | − | 0.967393i | \(-0.581509\pi\) | ||||
−0.253279 | + | 0.967393i | \(0.581509\pi\) | |||||||
\(788\) | 76.1503 | 2.71274 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 47.0398 | 1.67360 | ||||||||
\(791\) | −3.97046 | −0.141173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 29.5623 | 1.04913 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.5412 | 0.444512 | ||||||||
\(797\) | −11.9022 | −0.421596 | −0.210798 | − | 0.977530i | \(-0.567606\pi\) | ||||
−0.210798 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.18598 | −0.254222 | ||||||||
\(800\) | −32.1839 | −1.13787 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 42.1183 | 1.48725 | ||||||||
\(803\) | −33.8901 | −1.19596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0640 | 0.812899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.9524 | −0.596384 | ||||||||
\(809\) | −1.61596 | −0.0568140 | −0.0284070 | − | 0.999596i | \(-0.509043\pi\) | ||||
−0.0284070 | + | 0.999596i | \(0.509043\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.9657 | 1.82476 | 0.912381 | − | 0.409342i | \(-0.134242\pi\) | ||||
0.912381 | + | 0.409342i | \(0.134242\pi\) | |||||||
\(812\) | −10.9782 | −0.385260 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 50.0245 | 1.75336 | ||||||||
\(815\) | −45.5575 | −1.59581 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.95108 | −0.138231 | ||||||||
\(818\) | 65.7853 | 2.30013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.1675 | −0.389985 | ||||||||
\(821\) | 54.8327 | 1.91367 | 0.956837 | − | 0.290627i | \(-0.0938638\pi\) | ||||
0.956837 | + | 0.290627i | \(0.0938638\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.8514 | −1.63314 | −0.816569 | − | 0.577247i | \(-0.804127\pi\) | ||||
−0.816569 | + | 0.577247i | \(0.804127\pi\) | |||||||
\(824\) | 4.42626 | 0.154196 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.1763 | −0.354078 | ||||||||
\(827\) | 21.2021 | 0.737270 | 0.368635 | − | 0.929574i | \(-0.379825\pi\) | ||||
0.368635 | + | 0.929574i | \(0.379825\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.2972 | 0.635489 | 0.317744 | − | 0.948176i | \(-0.397075\pi\) | ||||
0.317744 | + | 0.948176i | \(0.397075\pi\) | |||||||
\(830\) | 61.3376 | 2.12906 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.6829 | 0.647325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.4359 | 1.46856 | ||||||||
\(836\) | −24.7797 | −0.857024 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 38.6612 | 1.33553 | ||||||||
\(839\) | 21.1414 | 0.729881 | 0.364941 | − | 0.931031i | \(-0.381089\pi\) | ||||
0.364941 | + | 0.931031i | \(0.381089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1709 | −0.488652 | ||||||||
\(842\) | 7.15751 | 0.246664 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.32113 | 0.148739 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.30367 | −0.0791549 | ||||||||
\(848\) | 15.2182 | 0.522594 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59.7864 | −2.05066 | ||||||||
\(851\) | −57.9958 | −1.98807 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.13036 | 0.244139 | 0.122069 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122069 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(854\) | −25.0562 | −0.857406 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 34.8937 | 1.19264 | ||||||||
\(857\) | 44.7741 | 1.52945 | 0.764726 | − | 0.644355i | \(-0.222874\pi\) | ||||
0.764726 | + | 0.644355i | \(0.222874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.3782 | 1.95772 | 0.978859 | − | 0.204535i | \(-0.0655681\pi\) | ||||
0.978859 | + | 0.204535i | \(0.0655681\pi\) | |||||||
\(860\) | −21.2094 | −0.723235 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.86758 | −0.267971 | ||||||||
\(863\) | −6.67563 | −0.227241 | −0.113621 | − | 0.993524i | \(-0.536245\pi\) | ||||
−0.113621 | + | 0.993524i | \(0.536245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.7260 | −1.52073 | ||||||||
\(866\) | 28.0536 | 0.953299 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.68473 | −0.226894 | ||||||||
\(869\) | −15.4112 | −0.522789 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.53989 | 0.221469 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44.8907 | 1.51845 | ||||||||
\(875\) | 10.7506 | 0.363438 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2983 | −0.854263 | −0.427131 | − | 0.904190i | \(-0.640476\pi\) | ||||
−0.427131 | + | 0.904190i | \(0.640476\pi\) | |||||||
\(878\) | 8.76318 | 0.295743 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.0809 | −0.542085 | ||||||||
\(881\) | 35.3787 | 1.19194 | 0.595969 | − | 0.803008i | \(-0.296768\pi\) | ||||
0.595969 | + | 0.803008i | \(0.296768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.5851 | −0.389869 | −0.194935 | − | 0.980816i | \(-0.562449\pi\) | ||||
−0.194935 | + | 0.980816i | \(0.562449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.43429 | −0.115377 | ||||||||
\(887\) | 27.2892 | 0.916281 | 0.458141 | − | 0.888880i | \(-0.348516\pi\) | ||||
0.458141 | + | 0.888880i | \(0.348516\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.54719 | 0.152508 | ||||||||
\(890\) | 9.84761 | 0.330093 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 61.8149 | 2.06972 | ||||||||
\(893\) | 5.97823 | 0.200054 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.98839 | 0.0664646 | ||||||||
\(896\) | −16.4058 | −0.548080 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.5830 | −0.953826 | ||||||||
\(899\) | 9.02954 | 0.301152 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.2747 | −0.975282 | ||||||||
\(902\) | 5.71704 | 0.190357 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.1451 | −0.603497 | ||||||||
\(905\) | −85.9643 | −2.85755 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.4219 | −1.01014 | −0.505072 | − | 0.863077i | \(-0.668534\pi\) | ||||
−0.505072 | + | 0.863077i | \(0.668534\pi\) | |||||||
\(908\) | 61.9114 | 2.05460 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.5719 | −1.77492 | −0.887459 | − | 0.460887i | \(-0.847531\pi\) | ||||
−0.887459 | + | 0.460887i | \(0.847531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0954 | −0.665062 | ||||||||
\(914\) | 8.12664 | 0.268805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −66.6921 | −2.20357 | ||||||||
\(917\) | −14.6136 | −0.482582 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.1672 | −1.19305 | −0.596523 | − | 0.802596i | \(-0.703451\pi\) | ||||
−0.596523 | + | 0.802596i | \(0.703451\pi\) | |||||||
\(920\) | 105.403 | 3.47503 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.9232 | −0.524403 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.2583 | −2.11280 | ||||||||
\(926\) | 17.5630 | 0.577156 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 14.3593 | 0.471367 | ||||||||
\(929\) | −13.3478 | −0.437927 | −0.218964 | − | 0.975733i | \(-0.570268\pi\) | ||||
−0.218964 | + | 0.975733i | \(0.570268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.5429 | −0.509397 | ||||||||
\(932\) | −14.0459 | −0.460090 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −76.8580 | −2.51487 | ||||||||
\(935\) | 30.9342 | 1.01166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6872 | 1.26386 | 0.631928 | − | 0.775027i | \(-0.282264\pi\) | ||||
0.631928 | + | 0.775027i | \(0.282264\pi\) | |||||||
\(938\) | −27.2054 | −0.888286 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 32.0911 | 1.04670 | ||||||||
\(941\) | 35.7275 | 1.16468 | 0.582342 | − | 0.812944i | \(-0.302136\pi\) | ||||
0.582342 | + | 0.812944i | \(0.302136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.62804 | −0.215839 | ||||||||
\(944\) | −8.22580 | −0.267727 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.8579 | 0.353020 | ||||||||
\(947\) | −17.8436 | −0.579838 | −0.289919 | − | 0.957051i | \(-0.593628\pi\) | ||||
−0.289919 | + | 0.957051i | \(0.593628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 49.7381 | 1.61372 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.63773 | −0.279950 | ||||||||
\(953\) | −20.1691 | −0.653342 | −0.326671 | − | 0.945138i | \(-0.605927\pi\) | ||||
−0.326671 | + | 0.945138i | \(0.605927\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −61.8993 | −2.00301 | ||||||||
\(956\) | 2.90913 | 0.0940881 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.66786 | 0.215429 | ||||||||
\(959\) | 7.57865 | 0.244727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5018 | −0.822640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.4454 | −0.690709 | ||||||||
\(965\) | −95.0471 | −3.05967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.7894 | 1.05444 | 0.527218 | − | 0.849730i | \(-0.323235\pi\) | ||||
0.527218 | + | 0.849730i | \(0.323235\pi\) | |||||||
\(968\) | −10.5278 | −0.338377 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 51.7263 | 1.66083 | ||||||||
\(971\) | 26.9845 | 0.865973 | 0.432986 | − | 0.901401i | \(-0.357460\pi\) | ||||
0.432986 | + | 0.901401i | \(0.357460\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.21983 | 0.103223 | ||||||||
\(974\) | 97.3245 | 3.11848 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.2537 | −0.648305 | ||||||||
\(977\) | −16.9571 | −0.542504 | −0.271252 | − | 0.962508i | \(-0.587438\pi\) | ||||
−0.271252 | + | 0.962508i | \(0.587438\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.22627 | −0.103112 | ||||||||
\(980\) | −83.4341 | −2.66521 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 81.7131 | 2.60757 | ||||||||
\(983\) | −32.6631 | −1.04179 | −0.520895 | − | 0.853621i | \(-0.674402\pi\) | ||||
−0.520895 | + | 0.853621i | \(0.674402\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 79.0863 | 2.51990 | ||||||||
\(986\) | 26.6746 | 0.849491 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.5881 | −0.400277 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.64310 | 0.242791 | 0.121396 | − | 0.992604i | \(-0.461263\pi\) | ||||
0.121396 | + | 0.992604i | \(0.461263\pi\) | |||||||
\(992\) | 8.74348 | 0.277606 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.3569 | 0.487091 | ||||||||
\(995\) | 13.0248 | 0.412912 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.1256 | 1.14411 | 0.572054 | − | 0.820216i | \(-0.306147\pi\) | ||||
0.572054 | + | 0.820216i | \(0.306147\pi\) | |||||||
\(998\) | −42.2849 | −1.33850 | ||||||||
\(999\) | 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 | 1521.2.a.s.1.2 | 3 | ||
3.2 | odd | 2 | 507.2.a.i.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 8112.2.a.cg.1.1 | 3 | |||
13.5 | odd | 4 | 1521.2.b.k.1351.2 | 6 | |||
13.8 | odd | 4 | 1521.2.b.k.1351.5 | 6 | |||
13.12 | even | 2 | 1521.2.a.n.1.2 | 3 | |||
39.2 | even | 12 | 507.2.j.i.316.2 | 12 | |||
39.5 | even | 4 | 507.2.b.f.337.5 | 6 | |||
39.8 | even | 4 | 507.2.b.f.337.2 | 6 | |||
39.11 | even | 12 | 507.2.j.i.316.5 | 12 | |||
39.17 | odd | 6 | 507.2.e.i.484.2 | 6 | |||
39.20 | even | 12 | 507.2.j.i.361.2 | 12 | |||
39.23 | odd | 6 | 507.2.e.i.22.2 | 6 | |||
39.29 | odd | 6 | 507.2.e.l.22.2 | 6 | |||
39.32 | even | 12 | 507.2.j.i.361.5 | 12 | |||
39.35 | odd | 6 | 507.2.e.l.484.2 | 6 | |||
39.38 | odd | 2 | 507.2.a.l.1.2 | yes | 3 | ||
156.155 | even | 2 | 8112.2.a.cp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
507.2.a.l.1.2 | yes | 3 | 39.38 | odd | 2 | ||
507.2.b.f.337.2 | 6 | 39.8 | even | 4 | |||
507.2.b.f.337.5 | 6 | 39.5 | even | 4 | |||
507.2.e.i.22.2 | 6 | 39.23 | odd | 6 | |||
507.2.e.i.484.2 | 6 | 39.17 | odd | 6 | |||
507.2.e.l.22.2 | 6 | 39.29 | odd | 6 | |||
507.2.e.l.484.2 | 6 | 39.35 | odd | 6 | |||
507.2.j.i.316.2 | 12 | 39.2 | even | 12 | |||
507.2.j.i.316.5 | 12 | 39.11 | even | 12 | |||
507.2.j.i.361.2 | 12 | 39.20 | even | 12 | |||
507.2.j.i.361.5 | 12 | 39.32 | even | 12 | |||
1521.2.a.n.1.2 | 3 | 13.12 | even | 2 | |||
1521.2.a.s.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1521.2.b.k.1351.2 | 6 | 13.5 | odd | 4 | |||
1521.2.b.k.1351.5 | 6 | 13.8 | odd | 4 | |||
8112.2.a.cg.1.1 | 3 | 12.11 | even | 2 | |||
8112.2.a.cp.1.3 | 3 | 156.155 | even | 2 |