Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8112,2,Mod(1,8112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8112.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: | \(64.7746461197\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 1.1 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8112.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.69202 | −1.65112 | −0.825561 | − | 0.564313i | \(-0.809141\pi\) | ||||
−0.825561 | + | 0.564313i | \(0.809141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.801938 | −0.303104 | −0.151552 | − | 0.988449i | \(-0.548427\pi\) | ||||
−0.151552 | + | 0.988449i | \(0.548427\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.85086 | −0.859565 | −0.429783 | − | 0.902932i | \(-0.641410\pi\) | ||||
−0.429783 | + | 0.902932i | \(0.641410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.69202 | −0.953276 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.93900 | 0.712812 | 0.356406 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356406 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44504 | −0.560931 | −0.280466 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280466 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.801938 | −0.174997 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.85086 | 0.715086 | 0.357543 | − | 0.933897i | \(-0.383615\pi\) | ||||
0.357543 | + | 0.933897i | \(0.383615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.34481 | 0.421141 | 0.210571 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210571 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.85086 | −0.496270 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.96077 | 0.500462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.44504 | −1.22396 | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.850855 | 0.132881 | 0.0664406 | − | 0.997790i | \(-0.478836\pi\) | ||||
0.0664406 | + | 0.997790i | \(0.478836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61596 | 0.246431 | 0.123216 | − | 0.992380i | \(-0.460679\pi\) | ||||
0.123216 | + | 0.992380i | \(0.460679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.69202 | −0.550374 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.93900 | 0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.96077 | −1.36822 | −0.684109 | − | 0.729380i | \(-0.739809\pi\) | ||||
−0.684109 | + | 0.729380i | \(0.739809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.5254 | 1.41925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.44504 | −0.323854 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −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 | \(0.822597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.801938 | −0.101035 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3937 | 1.75847 | 0.879237 | − | 0.476384i | \(-0.158053\pi\) | ||||
0.879237 | + | 0.476384i | \(0.158053\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.78986 | 0.937788 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 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 | \(0.255106\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.63102 | 0.996625 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.28621 | 0.260538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.40581 | −0.608202 | −0.304101 | − | 0.952640i | \(-0.598356\pi\) | ||||
−0.304101 | + | 0.952640i | \(0.598356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.85086 | 0.412855 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.13169 | −0.119959 | −0.0599793 | − | 0.998200i | \(-0.519103\pi\) | ||||
−0.0599793 | + | 0.998200i | \(0.519103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34481 | 0.243146 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.02715 | 0.926166 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.94438 | 0.603560 | 0.301780 | − | 0.953378i | \(-0.402419\pi\) | ||||
0.301780 | + | 0.953378i | \(0.402419\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.85086 | −0.286522 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.62565 | 0.460269 | 0.230134 | − | 0.973159i | \(-0.426083\pi\) | ||||
0.230134 | + | 0.973159i | \(0.426083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.20775 | −0.119003 | −0.0595016 | − | 0.998228i | \(-0.518951\pi\) | ||||
−0.0595016 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.96077 | 0.288942 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | \(0.472764\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.44504 | −0.706652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.95108 | 0.465759 | 0.232879 | − | 0.972506i | \(-0.425185\pi\) | ||||
0.232879 | + | 0.972506i | \(0.425185\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −28.7603 | −2.68191 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.35690 | −0.216056 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.87263 | −0.261148 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.850855 | 0.0767190 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.4058 | −1.19905 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.67025 | −0.503153 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.61596 | 0.142277 | ||||||||
\(130\) | 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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.69202 | −0.317759 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.45042 | −0.807404 | −0.403702 | − | 0.914891i | \(-0.632277\pi\) | ||||
−0.403702 | + | 0.914891i | \(0.632277\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.01507 | −0.340553 | −0.170277 | − | 0.985396i | \(-0.554466\pi\) | ||||
−0.170277 | + | 0.985396i | \(0.554466\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.44504 | 0.205910 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.2174 | −1.18069 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.35690 | −0.524308 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.4058 | −1.58979 | −0.794893 | − | 0.606750i | \(-0.792473\pi\) | ||||
−0.794893 | + | 0.606750i | \(0.792473\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.3623 | −1.00603 | −0.503014 | − | 0.864278i | \(-0.667775\pi\) | ||||
−0.503014 | + | 0.864278i | \(0.667775\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.93900 | 0.237604 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.65710 | −0.695355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6775 | −1.49063 | −0.745315 | − | 0.666712i | \(-0.767701\pi\) | ||||
−0.745315 | + | 0.666712i | \(0.767701\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.96077 | −0.789941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.24698 | −0.492331 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3394 | 0.966499 | 0.483250 | − | 0.875483i | \(-0.339456\pi\) | ||||
0.483250 | + | 0.875483i | \(0.339456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.5254 | 0.819403 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4940 | 0.889429 | 0.444715 | − | 0.895672i | \(-0.353305\pi\) | ||||
0.444715 | + | 0.895672i | \(0.353305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.44504 | −0.186977 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.1142 | 0.921028 | 0.460514 | − | 0.887653i | \(-0.347665\pi\) | ||||
0.460514 | + | 0.887653i | \(0.347665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.92154 | −0.523219 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.38404 | −0.404689 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | ||||||||
\(183\) | −13.2567 | −0.979961 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.4873 | 2.02090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.37867 | −0.612709 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.801938 | −0.0583324 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −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 | \(0.877235\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.4209 | −1.52617 | −0.763087 | − | 0.646296i | \(-0.776317\pi\) | ||||
−0.763087 | + | 0.646296i | \(0.776317\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.52781 | −0.250080 | −0.125040 | − | 0.992152i | \(-0.539906\pi\) | ||||
−0.125040 | + | 0.992152i | \(0.539906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3937 | 1.01526 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.08815 | −0.216745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.14138 | −0.219403 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.78986 | 0.541432 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.97046 | 0.482157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.21552 | −0.0836799 | −0.0418399 | − | 0.999124i | \(-0.513322\pi\) | ||||
−0.0418399 | + | 0.999124i | \(0.513322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.12498 | 0.556715 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.96615 | −0.406888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.88040 | −0.127650 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.8877 | 0.803296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3884 | −1.16441 | −0.582205 | − | 0.813042i | \(-0.697810\pi\) | ||||
−0.582205 | + | 0.813042i | \(0.697810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.63102 | 0.575402 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 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 | \(0.712810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.28621 | 0.150421 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.95108 | 0.258844 | 0.129422 | − | 0.991590i | \(-0.458688\pi\) | ||||
0.129422 | + | 0.991590i | \(0.458688\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.02715 | −0.588866 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.40581 | −0.351145 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(0.562242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.4698 | 1.49943 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.04892 | 0.446707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.8509 | −0.679507 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.05323 | −0.564725 | −0.282362 | − | 0.959308i | \(-0.591118\pi\) | ||||
−0.282362 | + | 0.959308i | \(0.591118\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.97046 | 0.370986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85086 | 0.238362 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.13169 | −0.0692581 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.42088 | −0.147604 | −0.0738018 | − | 0.997273i | \(-0.523513\pi\) | ||||
−0.0738018 | + | 0.997273i | \(0.523513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.4450 | −1.30269 | −0.651347 | − | 0.758780i | \(-0.725796\pi\) | ||||
−0.651347 | + | 0.758780i | \(0.725796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −24.6058 | −1.48379 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8073 | −0.889685 | −0.444843 | − | 0.895609i | \(-0.646740\pi\) | ||||
−0.444843 | + | 0.895609i | \(0.646740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.34481 | 0.140380 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.5036 | −0.865215 | −0.432608 | − | 0.901582i | \(-0.642406\pi\) | ||||
−0.432608 | + | 0.901582i | \(0.642406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.6722 | −1.52605 | −0.763026 | − | 0.646368i | \(-0.776287\pi\) | ||||
−0.763026 | + | 0.646368i | \(0.776287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.02715 | 0.534722 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.682333 | −0.0402768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.36227 | −0.491898 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.94438 | 0.348466 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.5230 | 1.54949 | 0.774746 | − | 0.632273i | \(-0.217878\pi\) | ||||
0.774746 | + | 0.632273i | \(0.217878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.8780 | 1.15734 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.85086 | −0.165423 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29590 | −0.0746943 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.62565 | 0.265736 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.9439 | 2.80252 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.24698 | −0.470680 | −0.235340 | − | 0.971913i | \(-0.575620\pi\) | ||||
−0.235340 | + | 0.971913i | \(0.575620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.20775 | −0.0687066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(0.368221\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.96077 | 0.166821 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.84415 | 0.384406 | 0.192203 | − | 0.981355i | \(-0.438437\pi\) | ||||
0.192203 | + | 0.981355i | \(0.438437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.9782 | −0.614663 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.52111 | 0.531416 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.18598 | −0.399839 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78448 | 0.0986819 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.96077 | −0.108101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.44265 | 0.519015 | 0.259507 | − | 0.965741i | \(-0.416440\pi\) | ||||
0.259507 | + | 0.965741i | \(0.416440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.44504 | −0.407986 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −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 | ||||||||
\(339\) | 4.95108 | 0.268906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.68473 | −0.361998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.7114 | 0.578361 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28.7603 | −1.54840 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | \(0.590139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.2911 | −0.973538 | −0.486769 | − | 0.873531i | \(-0.661825\pi\) | ||||
−0.486769 | + | 0.873531i | \(0.661825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.9976 | −1.59211 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.35690 | −0.124740 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.87263 | −0.150774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.8896 | −2.29729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2717 | 1.16258 | 0.581288 | − | 0.813698i | \(-0.302549\pi\) | ||||
0.581288 | + | 0.813698i | \(0.302549\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.850855 | 0.0442937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.98792 | 0.414712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.12631 | 0.213652 | 0.106826 | − | 0.994278i | \(-0.465931\pi\) | ||||
0.106826 | + | 0.994278i | \(0.465931\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.4058 | −0.692273 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.7071 | −0.549986 | −0.274993 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274993 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.67025 | −0.290496 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.61596 | 0.0821437 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.7922 | −0.597891 | −0.298945 | − | 0.954270i | \(-0.596635\pi\) | ||||
−0.298945 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.8944 | 1.15782 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.2228 | −0.919219 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.9584 | 1.00422 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5429 | 0.629509 | 0.314754 | − | 0.949173i | \(-0.398078\pi\) | ||||
0.314754 | + | 0.949173i | \(0.398078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.96077 | 0.0981613 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8702 | −0.892397 | −0.446198 | − | 0.894934i | \(-0.647222\pi\) | ||||
−0.446198 | + | 0.894934i | \(0.647222\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.69202 | −0.183458 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.2247 | 1.05207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.9119 | 1.38015 | 0.690076 | − | 0.723737i | \(-0.257577\pi\) | ||||
0.690076 | + | 0.723737i | \(0.257577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.45042 | −0.466155 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.31767 | 0.212459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.0248 | −1.27750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.01507 | −0.196619 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 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 | \(0.476423\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.44504 | 0.118882 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.3666 | 1.23046 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6310 | 0.514471 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | \(0.407673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.2174 | −0.681674 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.0465 | −0.911119 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.71810 | −0.177455 | −0.0887277 | − | 0.996056i | \(-0.528280\pi\) | ||||
−0.0887277 | + | 0.996056i | \(0.528280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.35690 | −0.302709 | ||||||||
\(442\) | 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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.4058 | −0.917863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.1274 | 0.572326 | 0.286163 | − | 0.958181i | \(-0.407620\pi\) | ||||
0.286163 | + | 0.958181i | \(0.407620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.42566 | −0.114220 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.3623 | −0.580830 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.44803 | 0.161292 | 0.0806459 | − | 0.996743i | \(-0.474302\pi\) | ||||
0.0806459 | + | 0.996743i | \(0.474302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.93900 | 0.137181 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.75600 | 0.314658 | 0.157329 | − | 0.987546i | \(-0.449712\pi\) | ||||
0.157329 | + | 0.987546i | \(0.449712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.45175 | −0.346312 | −0.173156 | − | 0.984894i | \(-0.555396\pi\) | ||||
−0.173156 | + | 0.984894i | \(0.555396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.65710 | −0.401464 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.6775 | −0.860616 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.60686 | −0.211824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.1032 | −0.968282 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.96077 | −0.456072 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.82908 | 0.129264 | 0.0646321 | − | 0.997909i | \(-0.479413\pi\) | ||||
0.0646321 | + | 0.997909i | \(0.479413\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.24698 | −0.284247 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.9468 | −0.996552 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −41.2935 | −1.87119 | −0.935594 | − | 0.353079i | \(-0.885135\pi\) | ||||
−0.935594 | + | 0.353079i | \(0.885135\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.3394 | 0.558009 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 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 | ||||||||
\(495\) | 10.5254 | 0.473082 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.51573 | −0.292270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.9409 | 0.803146 | 0.401573 | − | 0.915827i | \(-0.368464\pi\) | ||||
0.401573 | + | 0.915827i | \(0.368464\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.4940 | 0.513512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.50604 | 0.244051 | 0.122025 | − | 0.992527i | \(-0.461061\pi\) | ||||
0.122025 | + | 0.992527i | \(0.461061\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.53319 | −0.421723 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.44504 | −0.107951 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.45904 | 0.196489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.97046 | −0.306560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.1142 | 0.531756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7211 | −1.17067 | −0.585336 | − | 0.810791i | \(-0.699037\pi\) | ||||
−0.585336 | + | 0.810791i | \(0.699037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.5230 | −1.59704 | −0.798520 | − | 0.601968i | \(-0.794383\pi\) | ||||
−0.798520 | + | 0.601968i | \(0.794383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.92154 | −0.302081 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.89141 | 0.300195 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.6819 | 1.63834 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.38404 | −0.233648 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.1521 | −1.51976 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.538565 | 0.0232408 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.1226 | 0.780595 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4655 | −0.793893 | −0.396947 | − | 0.917842i | \(-0.629930\pi\) | ||||
−0.396947 | + | 0.917842i | \(0.629930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.2838 | −0.999204 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.58834 | −0.282213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8471 | −1.70374 | −0.851870 | − | 0.523753i | \(-0.824532\pi\) | ||||
−0.851870 | + | 0.523753i | \(0.824532\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.2567 | −0.565781 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.41550 | −0.401114 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.33513 | 0.184348 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.4873 | 1.16677 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.20477 | −0.390018 | −0.195009 | − | 0.980801i | \(-0.562474\pi\) | ||||
−0.195009 | + | 0.980801i | \(0.562474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.37867 | −0.353748 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.801938 | −0.0336782 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.8944 | −0.708250 | −0.354125 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354125 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.3226 | 1.85484 | 0.927421 | − | 0.374019i | \(-0.122021\pi\) | ||||
0.927421 | + | 0.374019i | \(0.122021\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7657 | −0.700397 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 67.2344 | 2.80387 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.56704 | −0.148498 | −0.0742489 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742489 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.7439 | −1.06988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.65279 | −0.234517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.3967 | 1.17607 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.4209 | −0.881137 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.8611 | 1.76010 | 0.880048 | − | 0.474885i | \(-0.157510\pi\) | ||||
0.880048 | + | 0.474885i | \(0.157510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.70171 | 0.356735 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.52781 | −0.144384 | ||||||||
\(598\) | 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 | \(0.492293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3937 | 0.586158 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6058 | 0.431187 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9922 | −0.811460 | −0.405730 | − | 0.913993i | \(-0.632983\pi\) | ||||
−0.405730 | + | 0.913993i | \(0.632983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.08815 | −0.125138 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.3618 | 1.34747 | 0.673735 | − | 0.738973i | \(-0.264689\pi\) | ||||
0.673735 | + | 0.738973i | \(0.264689\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.14138 | −0.126672 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6233 | −0.467935 | −0.233967 | − | 0.972244i | \(-0.575171\pi\) | ||||
−0.233967 | + | 0.972244i | \(0.575171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5381 | −0.664722 | −0.332361 | − | 0.943152i | \(-0.607845\pi\) | ||||
−0.332361 | + | 0.943152i | \(0.607845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.78986 | 0.312596 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.907542 | 0.0363599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33944 | 0.253577 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.97046 | 0.278373 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.8810 | −0.872452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4416 | −1.45072 | −0.725358 | − | 0.688372i | \(-0.758326\pi\) | ||||
−0.725358 | + | 0.688372i | \(0.758326\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.21552 | −0.0483126 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.9347 | 0.830768 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.12498 | 0.321419 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.2067 | 1.07460 | 0.537300 | − | 0.843391i | \(-0.319444\pi\) | ||||
0.537300 | + | 0.843391i | \(0.319444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.06962 | −0.199926 | −0.0999632 | − | 0.994991i | \(-0.531873\pi\) | ||||
−0.0999632 | + | 0.994991i | \(0.531873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.96615 | −0.234917 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −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 | ||||||||
\(651\) | −1.88040 | −0.0736985 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.2355 | 1.37887 | 0.689436 | − | 0.724347i | \(-0.257859\pi\) | ||||
0.689436 | + | 0.724347i | \(0.257859\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 67.2790 | 2.62881 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.8877 | 0.463783 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(0.402722\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.23921 | −0.280725 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.9976 | 1.16151 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.3884 | −0.672273 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.7928 | 1.45898 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.7409 | −0.452580 | −0.226290 | − | 0.974060i | \(-0.572660\pi\) | ||||
−0.226290 | + | 0.974060i | \(0.572660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.63102 | 0.332208 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.44504 | 0.132404 | 0.0662019 | − | 0.997806i | \(-0.478912\pi\) | ||||
0.0662019 | + | 0.997806i | \(0.478912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.76702 | −0.182941 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4155 | 0.667363 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7603 | −0.715751 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.8039 | 1.05771 | 0.528854 | − | 0.848713i | \(-0.322622\pi\) | ||||
0.528854 | + | 0.848713i | \(0.322622\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.28621 | 0.0868459 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.8237 | 0.562295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.50066 | 0.0947194 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.95108 | 0.149444 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9715 | 0.452158 | 0.226079 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226079 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2034 | 0.686556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.02715 | −0.339982 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.70948 | −0.139509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.2664 | −1.21179 | −0.605894 | − | 0.795545i | \(-0.707185\pi\) | ||||
−0.605894 | + | 0.795545i | \(0.707185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.40581 | −0.202734 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.2658 | 0.684058 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.818331 | 0.0305611 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.03252 | −0.224352 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.2368 | 1.23438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.6200 | 0.616402 | 0.308201 | − | 0.951321i | \(-0.400273\pi\) | ||||
0.308201 | + | 0.951321i | \(0.400273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.74930 | 0.175659 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7912 | −0.657132 | −0.328566 | − | 0.944481i | \(-0.606565\pi\) | ||||
−0.328566 | + | 0.944481i | \(0.606565\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.4698 | 0.865696 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.0344 | −1.51152 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.3618 | −1.00652 | −0.503260 | − | 0.864135i | \(-0.667866\pi\) | ||||
−0.503260 | + | 0.864135i | \(0.667866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.04892 | 0.257906 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.63533 | −0.278989 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.7778 | 1.41502 | 0.707511 | − | 0.706703i | \(-0.249818\pi\) | ||||
0.707511 | + | 0.706703i | \(0.249818\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.8799 | 0.979559 | ||||||||
\(754\) | 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 | \(0.424244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.2078 | −0.806090 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.15585 | 0.186899 | 0.0934497 | − | 0.995624i | \(-0.470211\pi\) | ||||
0.0934497 | + | 0.995624i | \(0.470211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.43104 | −0.0518072 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.8509 | −0.392313 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.5013 | 1.28021 | 0.640104 | − | 0.768288i | \(-0.278891\pi\) | ||||
0.640104 | + | 0.768288i | \(0.278891\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.05323 | −0.326044 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.15585 | 0.221411 | 0.110705 | − | 0.993853i | \(-0.464689\pi\) | ||||
0.110705 | + | 0.993853i | \(0.464689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.2381 | 0.726976 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.97046 | 0.214189 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.08038 | −0.0745372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1631 | −0.828843 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.85086 | 0.137618 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 68.9579 | 2.46121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.2107 | 0.506558 | 0.253279 | − | 0.967393i | \(-0.418491\pi\) | ||||
0.253279 | + | 0.967393i | \(0.418491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.1511 | −0.824200 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.97046 | −0.141173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 36.7754 | 1.30429 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.9022 | 0.421596 | 0.210798 | − | 0.977530i | \(-0.432394\pi\) | ||||
0.210798 | + | 0.977530i | \(0.432394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.18598 | 0.254222 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.13169 | −0.0399862 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.8901 | −1.19596 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0640 | 0.812899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.42088 | −0.0852190 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.61596 | 0.0568140 | 0.0284070 | − | 0.999596i | \(-0.490957\pi\) | ||||
0.0284070 | + | 0.999596i | \(0.490957\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.9657 | −1.82476 | −0.912381 | − | 0.409342i | \(-0.865758\pi\) | ||||
−0.912381 | + | 0.409342i | \(0.865758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.4450 | −0.752110 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45.5575 | −1.59581 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.95108 | −0.138231 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.8327 | −1.91367 | −0.956837 | − | 0.290627i | \(-0.906136\pi\) | ||||
−0.956837 | + | 0.290627i | \(0.906136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.8514 | 1.63314 | 0.816569 | − | 0.577247i | \(-0.195873\pi\) | ||||
0.816569 | + | 0.577247i | \(0.195873\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.6058 | −0.856664 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 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 | \(0.397075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.8073 | −0.513660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6829 | −0.647325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.4359 | −1.46856 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34481 | 0.0810486 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.5036 | −0.499532 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.30367 | 0.0791549 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.6722 | −0.881067 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.9958 | −1.98807 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.13036 | 0.244139 | 0.122069 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122069 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.02715 | 0.308722 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7741 | −1.52945 | −0.764726 | − | 0.644355i | \(-0.777126\pi\) | ||||
−0.764726 | + | 0.644355i | \(0.777126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.3782 | −1.95772 | −0.978859 | − | 0.204535i | \(-0.934432\pi\) | ||||
−0.978859 | + | 0.204535i | \(0.934432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.682333 | −0.0232538 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.36227 | −0.283998 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.4112 | 0.522789 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.94438 | 0.201187 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.7506 | 0.363438 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.2983 | −0.854263 | −0.427131 | − | 0.904190i | \(-0.640476\pi\) | ||||
−0.427131 | + | 0.904190i | \(0.640476\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.5230 | 0.894599 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.3787 | −1.19194 | −0.595969 | − | 0.803008i | \(-0.703232\pi\) | ||||
−0.595969 | + | 0.803008i | \(0.703232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.5851 | 0.389869 | 0.194935 | − | 0.980816i | \(-0.437551\pi\) | ||||
0.194935 | + | 0.980816i | \(0.437551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8780 | 0.668192 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.85086 | −0.0955072 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.97823 | −0.200054 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.98839 | −0.0664646 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.02954 | 0.301152 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.2747 | −0.975282 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.29590 | −0.0431247 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 85.9643 | 2.85755 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.4219 | 1.01014 | 0.505072 | − | 0.863077i | \(-0.331466\pi\) | ||||
0.505072 | + | 0.863077i | \(0.331466\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.62565 | 0.153423 | ||||||||
\(910\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.9439 | 1.61804 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.6136 | 0.482582 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.1672 | 1.19305 | 0.596523 | − | 0.802596i | \(-0.296549\pi\) | ||||
0.596523 | + | 0.802596i | \(0.296549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.24698 | −0.271747 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.2583 | −2.11280 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.20775 | −0.0396677 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.3478 | 0.437927 | 0.218964 | − | 0.975733i | \(-0.429732\pi\) | ||||
0.218964 | + | 0.975733i | \(0.429732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.5429 | 0.509397 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.4179 | 0.472021 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.9342 | 1.01166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6872 | 1.26386 | 0.631928 | − | 0.775027i | \(-0.282264\pi\) | ||||
0.631928 | + | 0.775027i | \(0.282264\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.2338 | 0.464504 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.7275 | −1.16468 | −0.582342 | − | 0.812944i | \(-0.697864\pi\) | ||||
−0.582342 | + | 0.812944i | \(0.697864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.62804 | 0.215839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.96077 | 0.0963139 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.8436 | −0.579838 | −0.289919 | − | 0.957051i | \(-0.593628\pi\) | ||||
−0.289919 | + | 0.957051i | \(0.593628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.84415 | 0.221937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.1691 | 0.653342 | 0.326671 | − | 0.945138i | \(-0.394073\pi\) | ||||
0.326671 | + | 0.945138i | \(0.394073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.8993 | 2.00301 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9782 | −0.354876 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.57865 | 0.244727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5018 | −0.822640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.52111 | 0.306813 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 95.0471 | 3.05967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.7894 | −1.05444 | −0.527218 | − | 0.849730i | \(-0.676765\pi\) | ||||
−0.527218 | + | 0.849730i | \(0.676765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.18598 | −0.230847 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.9571 | 0.542504 | 0.271252 | − | 0.962508i | \(-0.412562\pi\) | ||||
0.271252 | + | 0.962508i | \(0.412562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.22627 | 0.103112 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78448 | 0.0569740 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −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 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.96077 | −0.0624120 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.5881 | 0.400277 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.64310 | −0.242791 | −0.121396 | − | 0.992604i | \(-0.538737\pi\) | ||||
−0.121396 | + | 0.992604i | \(0.538737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.44265 | 0.299653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0248 | 0.412912 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.1256 | 1.14411 | 0.572054 | − | 0.820216i | \(-0.306147\pi\) | ||||
0.572054 | + | 0.820216i | \(0.306147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.44504 | −0.235551 |
(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 | 8112.2.a.cg.1.1 | 3 | ||
4.3 | odd | 2 | 507.2.a.i.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 1521.2.a.s.1.2 | 3 | |||
13.12 | even | 2 | 8112.2.a.cp.1.3 | 3 | |||
52.3 | odd | 6 | 507.2.e.l.22.2 | 6 | |||
52.7 | even | 12 | 507.2.j.i.361.2 | 12 | |||
52.11 | even | 12 | 507.2.j.i.316.5 | 12 | |||
52.15 | even | 12 | 507.2.j.i.316.2 | 12 | |||
52.19 | even | 12 | 507.2.j.i.361.5 | 12 | |||
52.23 | odd | 6 | 507.2.e.i.22.2 | 6 | |||
52.31 | even | 4 | 507.2.b.f.337.5 | 6 | |||
52.35 | odd | 6 | 507.2.e.l.484.2 | 6 | |||
52.43 | odd | 6 | 507.2.e.i.484.2 | 6 | |||
52.47 | even | 4 | 507.2.b.f.337.2 | 6 | |||
52.51 | odd | 2 | 507.2.a.l.1.2 | yes | 3 | ||
156.47 | odd | 4 | 1521.2.b.k.1351.5 | 6 | |||
156.83 | odd | 4 | 1521.2.b.k.1351.2 | 6 | |||
156.155 | even | 2 | 1521.2.a.n.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
507.2.a.l.1.2 | yes | 3 | 52.51 | odd | 2 | ||
507.2.b.f.337.2 | 6 | 52.47 | even | 4 | |||
507.2.b.f.337.5 | 6 | 52.31 | even | 4 | |||
507.2.e.i.22.2 | 6 | 52.23 | odd | 6 | |||
507.2.e.i.484.2 | 6 | 52.43 | odd | 6 | |||
507.2.e.l.22.2 | 6 | 52.3 | odd | 6 | |||
507.2.e.l.484.2 | 6 | 52.35 | odd | 6 | |||
507.2.j.i.316.2 | 12 | 52.15 | even | 12 | |||
507.2.j.i.316.5 | 12 | 52.11 | even | 12 | |||
507.2.j.i.361.2 | 12 | 52.7 | even | 12 | |||
507.2.j.i.361.5 | 12 | 52.19 | even | 12 | |||
1521.2.a.n.1.2 | 3 | 156.155 | even | 2 | |||
1521.2.a.s.1.2 | 3 | 12.11 | even | 2 | |||
1521.2.b.k.1351.2 | 6 | 156.83 | odd | 4 | |||
1521.2.b.k.1351.5 | 6 | 156.47 | odd | 4 | |||
8112.2.a.cg.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8112.2.a.cp.1.3 | 3 | 13.12 | even | 2 |