Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.618034 | −0.276393 | −0.138197 | − | 0.990405i | \(-0.544131\pi\) | ||||
−0.138197 | + | 0.990405i | \(0.544131\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 1.85410 | 0.700785 | 0.350392 | − | 0.936603i | \(-0.386048\pi\) | ||||
0.350392 | + | 0.936603i | \(0.386048\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.618034 | −0.195440 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | −6.47214 | −1.79505 | −0.897524 | − | 0.440966i | \(-0.854636\pi\) | ||||
−0.897524 | + | 0.440966i | \(0.854636\pi\) | |||||||
\(14\) | 1.85410 | 0.495530 | ||||||||
\(15\) | 1.23607 | 0.319151 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.61803 | 1.36257 | 0.681287 | − | 0.732017i | \(-0.261421\pi\) | ||||
0.681287 | + | 0.732017i | \(0.261421\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.618034 | −0.138197 | ||||||||
\(21\) | −3.70820 | −0.809196 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.14590 | −0.238936 | −0.119468 | − | 0.992838i | \(-0.538119\pi\) | ||||
−0.119468 | + | 0.992838i | \(0.538119\pi\) | |||||||
\(24\) | −2.00000 | −0.408248 | ||||||||
\(25\) | −4.61803 | −0.923607 | ||||||||
\(26\) | −6.47214 | −1.26929 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | 1.52786 | 0.283717 | 0.141859 | − | 0.989887i | \(-0.454692\pi\) | ||||
0.141859 | + | 0.989887i | \(0.454692\pi\) | |||||||
\(30\) | 1.23607 | 0.225674 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.61803 | 0.963485 | ||||||||
\(35\) | −1.14590 | −0.193692 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 12.9443 | 2.07274 | ||||||||
\(40\) | −0.618034 | −0.0977198 | ||||||||
\(41\) | −9.23607 | −1.44243 | −0.721216 | − | 0.692711i | \(-0.756416\pi\) | ||||
−0.721216 | + | 0.692711i | \(0.756416\pi\) | |||||||
\(42\) | −3.70820 | −0.572188 | ||||||||
\(43\) | 2.09017 | 0.318748 | 0.159374 | − | 0.987218i | \(-0.449052\pi\) | ||||
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.618034 | −0.0921311 | ||||||||
\(46\) | −1.14590 | −0.168953 | ||||||||
\(47\) | 3.61803 | 0.527744 | 0.263872 | − | 0.964558i | \(-0.415000\pi\) | ||||
0.263872 | + | 0.964558i | \(0.415000\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | −3.56231 | −0.508901 | ||||||||
\(50\) | −4.61803 | −0.653089 | ||||||||
\(51\) | −11.2361 | −1.57336 | ||||||||
\(52\) | −6.47214 | −0.897524 | ||||||||
\(53\) | −9.23607 | −1.26867 | −0.634336 | − | 0.773058i | \(-0.718726\pi\) | ||||
−0.634336 | + | 0.773058i | \(0.718726\pi\) | |||||||
\(54\) | 4.00000 | 0.544331 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.85410 | 0.247765 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 1.52786 | 0.200618 | ||||||||
\(59\) | −12.4721 | −1.62373 | −0.811867 | − | 0.583843i | \(-0.801549\pi\) | ||||
−0.811867 | + | 0.583843i | \(0.801549\pi\) | |||||||
\(60\) | 1.23607 | 0.159576 | ||||||||
\(61\) | 10.5623 | 1.35236 | 0.676182 | − | 0.736734i | \(-0.263633\pi\) | ||||
0.676182 | + | 0.736734i | \(0.263633\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 1.85410 | 0.233595 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.23607 | 0.884026 | 0.442013 | − | 0.897009i | \(-0.354264\pi\) | ||||
0.442013 | + | 0.897009i | \(0.354264\pi\) | |||||||
\(68\) | 5.61803 | 0.681287 | ||||||||
\(69\) | 2.29180 | 0.275900 | ||||||||
\(70\) | −1.14590 | −0.136961 | ||||||||
\(71\) | −12.9443 | −1.53620 | −0.768101 | − | 0.640328i | \(-0.778798\pi\) | ||||
−0.768101 | + | 0.640328i | \(0.778798\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −14.0000 | −1.63858 | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||||
−0.819288 | + | 0.573382i | \(0.805631\pi\) | |||||||
\(74\) | 4.00000 | 0.464991 | ||||||||
\(75\) | 9.23607 | 1.06649 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.9443 | 1.46565 | ||||||||
\(79\) | −9.70820 | −1.09226 | −0.546129 | − | 0.837701i | \(-0.683899\pi\) | ||||
−0.546129 | + | 0.837701i | \(0.683899\pi\) | |||||||
\(80\) | −0.618034 | −0.0690983 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −9.23607 | −1.01995 | ||||||||
\(83\) | 10.7984 | 1.18528 | 0.592638 | − | 0.805469i | \(-0.298087\pi\) | ||||
0.592638 | + | 0.805469i | \(0.298087\pi\) | |||||||
\(84\) | −3.70820 | −0.404598 | ||||||||
\(85\) | −3.47214 | −0.376606 | ||||||||
\(86\) | 2.09017 | 0.225389 | ||||||||
\(87\) | −3.05573 | −0.327608 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.76393 | 0.716975 | 0.358488 | − | 0.933534i | \(-0.383293\pi\) | ||||
0.358488 | + | 0.933534i | \(0.383293\pi\) | |||||||
\(90\) | −0.618034 | −0.0651465 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | −1.14590 | −0.119468 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | 3.61803 | 0.373172 | ||||||||
\(95\) | −0.618034 | −0.0634089 | ||||||||
\(96\) | −2.00000 | −0.204124 | ||||||||
\(97\) | −4.76393 | −0.483704 | −0.241852 | − | 0.970313i | \(-0.577755\pi\) | ||||
−0.241852 | + | 0.970313i | \(0.577755\pi\) | |||||||
\(98\) | −3.56231 | −0.359847 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.61803 | −0.461803 | ||||||||
\(101\) | 5.56231 | 0.553470 | 0.276735 | − | 0.960946i | \(-0.410748\pi\) | ||||
0.276735 | + | 0.960946i | \(0.410748\pi\) | |||||||
\(102\) | −11.2361 | −1.11254 | ||||||||
\(103\) | −9.23607 | −0.910057 | −0.455028 | − | 0.890477i | \(-0.650371\pi\) | ||||
−0.455028 | + | 0.890477i | \(0.650371\pi\) | |||||||
\(104\) | −6.47214 | −0.634645 | ||||||||
\(105\) | 2.29180 | 0.223656 | ||||||||
\(106\) | −9.23607 | −0.897086 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 4.00000 | 0.384900 | ||||||||
\(109\) | −1.23607 | −0.118394 | −0.0591969 | − | 0.998246i | \(-0.518854\pi\) | ||||
−0.0591969 | + | 0.998246i | \(0.518854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 1.85410 | 0.175196 | ||||||||
\(113\) | 14.4721 | 1.36142 | 0.680712 | − | 0.732551i | \(-0.261671\pi\) | ||||
0.680712 | + | 0.732551i | \(0.261671\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | 0.708204 | 0.0660404 | ||||||||
\(116\) | 1.52786 | 0.141859 | ||||||||
\(117\) | −6.47214 | −0.598349 | ||||||||
\(118\) | −12.4721 | −1.14815 | ||||||||
\(119\) | 10.4164 | 0.954871 | ||||||||
\(120\) | 1.23607 | 0.112837 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.5623 | 0.956266 | ||||||||
\(123\) | 18.4721 | 1.66558 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 5.94427 | 0.531672 | ||||||||
\(126\) | 1.85410 | 0.165177 | ||||||||
\(127\) | 7.41641 | 0.658100 | 0.329050 | − | 0.944313i | \(-0.393272\pi\) | ||||
0.329050 | + | 0.944313i | \(0.393272\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.18034 | −0.368058 | ||||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | −0.909830 | −0.0794922 | −0.0397461 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397461 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.85410 | 0.160771 | ||||||||
\(134\) | 7.23607 | 0.625101 | ||||||||
\(135\) | −2.47214 | −0.212768 | ||||||||
\(136\) | 5.61803 | 0.481742 | ||||||||
\(137\) | −15.0902 | −1.28924 | −0.644620 | − | 0.764503i | \(-0.722984\pi\) | ||||
−0.644620 | + | 0.764503i | \(0.722984\pi\) | |||||||
\(138\) | 2.29180 | 0.195091 | ||||||||
\(139\) | 5.32624 | 0.451766 | 0.225883 | − | 0.974154i | \(-0.427473\pi\) | ||||
0.225883 | + | 0.974154i | \(0.427473\pi\) | |||||||
\(140\) | −1.14590 | −0.0968461 | ||||||||
\(141\) | −7.23607 | −0.609387 | ||||||||
\(142\) | −12.9443 | −1.08626 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.944272 | −0.0784175 | ||||||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | 7.12461 | 0.587628 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −20.4721 | −1.67714 | −0.838571 | − | 0.544792i | \(-0.816609\pi\) | ||||
−0.838571 | + | 0.544792i | \(0.816609\pi\) | |||||||
\(150\) | 9.23607 | 0.754122 | ||||||||
\(151\) | −0.291796 | −0.0237460 | −0.0118730 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118730 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 5.61803 | 0.454191 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.23607 | −0.0992834 | ||||||||
\(156\) | 12.9443 | 1.03637 | ||||||||
\(157\) | 7.67376 | 0.612433 | 0.306216 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306216 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(158\) | −9.70820 | −0.772343 | ||||||||
\(159\) | 18.4721 | 1.46494 | ||||||||
\(160\) | −0.618034 | −0.0488599 | ||||||||
\(161\) | −2.12461 | −0.167443 | ||||||||
\(162\) | −11.0000 | −0.864242 | ||||||||
\(163\) | −16.3262 | −1.27877 | −0.639385 | − | 0.768887i | \(-0.720811\pi\) | ||||
−0.639385 | + | 0.768887i | \(0.720811\pi\) | |||||||
\(164\) | −9.23607 | −0.721216 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.7984 | 0.838116 | ||||||||
\(167\) | −25.4164 | −1.96678 | −0.983390 | − | 0.181503i | \(-0.941904\pi\) | ||||
−0.983390 | + | 0.181503i | \(0.941904\pi\) | |||||||
\(168\) | −3.70820 | −0.286094 | ||||||||
\(169\) | 28.8885 | 2.22220 | ||||||||
\(170\) | −3.47214 | −0.266301 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 2.09017 | 0.159374 | ||||||||
\(173\) | −3.05573 | −0.232323 | −0.116161 | − | 0.993230i | \(-0.537059\pi\) | ||||
−0.116161 | + | 0.993230i | \(0.537059\pi\) | |||||||
\(174\) | −3.05573 | −0.231654 | ||||||||
\(175\) | −8.56231 | −0.647249 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.9443 | 1.87493 | ||||||||
\(178\) | 6.76393 | 0.506978 | ||||||||
\(179\) | −20.1803 | −1.50835 | −0.754175 | − | 0.656674i | \(-0.771963\pi\) | ||||
−0.754175 | + | 0.656674i | \(0.771963\pi\) | |||||||
\(180\) | −0.618034 | −0.0460655 | ||||||||
\(181\) | −13.7082 | −1.01892 | −0.509461 | − | 0.860494i | \(-0.670155\pi\) | ||||
−0.509461 | + | 0.860494i | \(0.670155\pi\) | |||||||
\(182\) | −12.0000 | −0.889499 | ||||||||
\(183\) | −21.1246 | −1.56158 | ||||||||
\(184\) | −1.14590 | −0.0844767 | ||||||||
\(185\) | −2.47214 | −0.181755 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.61803 | 0.263872 | ||||||||
\(189\) | 7.41641 | 0.539464 | ||||||||
\(190\) | −0.618034 | −0.0448369 | ||||||||
\(191\) | −24.0344 | −1.73907 | −0.869536 | − | 0.493870i | \(-0.835582\pi\) | ||||
−0.869536 | + | 0.493870i | \(0.835582\pi\) | |||||||
\(192\) | −2.00000 | −0.144338 | ||||||||
\(193\) | −21.1246 | −1.52058 | −0.760291 | − | 0.649582i | \(-0.774944\pi\) | ||||
−0.760291 | + | 0.649582i | \(0.774944\pi\) | |||||||
\(194\) | −4.76393 | −0.342030 | ||||||||
\(195\) | −8.00000 | −0.572892 | ||||||||
\(196\) | −3.56231 | −0.254450 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.56231 | −0.394301 | −0.197151 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197151 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(200\) | −4.61803 | −0.326544 | ||||||||
\(201\) | −14.4721 | −1.02079 | ||||||||
\(202\) | 5.56231 | 0.391362 | ||||||||
\(203\) | 2.83282 | 0.198825 | ||||||||
\(204\) | −11.2361 | −0.786682 | ||||||||
\(205\) | 5.70820 | 0.398678 | ||||||||
\(206\) | −9.23607 | −0.643507 | ||||||||
\(207\) | −1.14590 | −0.0796454 | ||||||||
\(208\) | −6.47214 | −0.448762 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.29180 | 0.158149 | ||||||||
\(211\) | −11.4164 | −0.785938 | −0.392969 | − | 0.919552i | \(-0.628552\pi\) | ||||
−0.392969 | + | 0.919552i | \(0.628552\pi\) | |||||||
\(212\) | −9.23607 | −0.634336 | ||||||||
\(213\) | 25.8885 | 1.77385 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | −1.29180 | −0.0880998 | ||||||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 3.70820 | 0.251729 | ||||||||
\(218\) | −1.23607 | −0.0837171 | ||||||||
\(219\) | 28.0000 | 1.89206 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.3607 | −2.44588 | ||||||||
\(222\) | −8.00000 | −0.536925 | ||||||||
\(223\) | 3.70820 | 0.248320 | 0.124160 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124160 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(224\) | 1.85410 | 0.123882 | ||||||||
\(225\) | −4.61803 | −0.307869 | ||||||||
\(226\) | 14.4721 | 0.962672 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | −2.00000 | −0.132453 | ||||||||
\(229\) | 24.2705 | 1.60384 | 0.801920 | − | 0.597431i | \(-0.203812\pi\) | ||||
0.801920 | + | 0.597431i | \(0.203812\pi\) | |||||||
\(230\) | 0.708204 | 0.0466976 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.52786 | 0.100309 | ||||||||
\(233\) | −18.7984 | −1.23152 | −0.615761 | − | 0.787933i | \(-0.711151\pi\) | ||||
−0.615761 | + | 0.787933i | \(0.711151\pi\) | |||||||
\(234\) | −6.47214 | −0.423097 | ||||||||
\(235\) | −2.23607 | −0.145865 | ||||||||
\(236\) | −12.4721 | −0.811867 | ||||||||
\(237\) | 19.4164 | 1.26123 | ||||||||
\(238\) | 10.4164 | 0.675195 | ||||||||
\(239\) | 2.67376 | 0.172951 | 0.0864756 | − | 0.996254i | \(-0.472440\pi\) | ||||
0.0864756 | + | 0.996254i | \(0.472440\pi\) | |||||||
\(240\) | 1.23607 | 0.0797878 | ||||||||
\(241\) | 10.0000 | 0.644157 | 0.322078 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322078 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 10.5623 | 0.676182 | ||||||||
\(245\) | 2.20163 | 0.140657 | ||||||||
\(246\) | 18.4721 | 1.17774 | ||||||||
\(247\) | −6.47214 | −0.411812 | ||||||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | −21.5967 | −1.36864 | ||||||||
\(250\) | 5.94427 | 0.375949 | ||||||||
\(251\) | 10.8541 | 0.685105 | 0.342552 | − | 0.939499i | \(-0.388709\pi\) | ||||
0.342552 | + | 0.939499i | \(0.388709\pi\) | |||||||
\(252\) | 1.85410 | 0.116797 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 7.41641 | 0.465347 | ||||||||
\(255\) | 6.94427 | 0.434867 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.9443 | −0.682685 | −0.341342 | − | 0.939939i | \(-0.610882\pi\) | ||||
−0.341342 | + | 0.939939i | \(0.610882\pi\) | |||||||
\(258\) | −4.18034 | −0.260257 | ||||||||
\(259\) | 7.41641 | 0.460833 | ||||||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 1.52786 | 0.0945724 | ||||||||
\(262\) | −0.909830 | −0.0562095 | ||||||||
\(263\) | 6.47214 | 0.399089 | 0.199544 | − | 0.979889i | \(-0.436054\pi\) | ||||
0.199544 | + | 0.979889i | \(0.436054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.70820 | 0.350652 | ||||||||
\(266\) | 1.85410 | 0.113682 | ||||||||
\(267\) | −13.5279 | −0.827892 | ||||||||
\(268\) | 7.23607 | 0.442013 | ||||||||
\(269\) | 18.6525 | 1.13726 | 0.568631 | − | 0.822593i | \(-0.307473\pi\) | ||||
0.568631 | + | 0.822593i | \(0.307473\pi\) | |||||||
\(270\) | −2.47214 | −0.150449 | ||||||||
\(271\) | −31.2148 | −1.89616 | −0.948081 | − | 0.318028i | \(-0.896980\pi\) | ||||
−0.948081 | + | 0.318028i | \(0.896980\pi\) | |||||||
\(272\) | 5.61803 | 0.340643 | ||||||||
\(273\) | 24.0000 | 1.45255 | ||||||||
\(274\) | −15.0902 | −0.911631 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.29180 | 0.137950 | ||||||||
\(277\) | −3.52786 | −0.211969 | −0.105984 | − | 0.994368i | \(-0.533799\pi\) | ||||
−0.105984 | + | 0.994368i | \(0.533799\pi\) | |||||||
\(278\) | 5.32624 | 0.319447 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | −1.14590 | −0.0684805 | ||||||||
\(281\) | 4.65248 | 0.277543 | 0.138772 | − | 0.990324i | \(-0.455685\pi\) | ||||
0.138772 | + | 0.990324i | \(0.455685\pi\) | |||||||
\(282\) | −7.23607 | −0.430902 | ||||||||
\(283\) | −9.56231 | −0.568420 | −0.284210 | − | 0.958762i | \(-0.591731\pi\) | ||||
−0.284210 | + | 0.958762i | \(0.591731\pi\) | |||||||
\(284\) | −12.9443 | −0.768101 | ||||||||
\(285\) | 1.23607 | 0.0732183 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.1246 | −1.01083 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 14.5623 | 0.856606 | ||||||||
\(290\) | −0.944272 | −0.0554496 | ||||||||
\(291\) | 9.52786 | 0.558533 | ||||||||
\(292\) | −14.0000 | −0.819288 | ||||||||
\(293\) | 0.652476 | 0.0381180 | 0.0190590 | − | 0.999818i | \(-0.493933\pi\) | ||||
0.0190590 | + | 0.999818i | \(0.493933\pi\) | |||||||
\(294\) | 7.12461 | 0.415516 | ||||||||
\(295\) | 7.70820 | 0.448789 | ||||||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.4721 | −1.18592 | ||||||||
\(299\) | 7.41641 | 0.428902 | ||||||||
\(300\) | 9.23607 | 0.533245 | ||||||||
\(301\) | 3.87539 | 0.223374 | ||||||||
\(302\) | −0.291796 | −0.0167910 | ||||||||
\(303\) | −11.1246 | −0.639092 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −6.52786 | −0.373784 | ||||||||
\(306\) | 5.61803 | 0.321162 | ||||||||
\(307\) | −27.4164 | −1.56474 | −0.782369 | − | 0.622816i | \(-0.785989\pi\) | ||||
−0.782369 | + | 0.622816i | \(0.785989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.4721 | 1.05084 | ||||||||
\(310\) | −1.23607 | −0.0702039 | ||||||||
\(311\) | −4.20163 | −0.238252 | −0.119126 | − | 0.992879i | \(-0.538009\pi\) | ||||
−0.119126 | + | 0.992879i | \(0.538009\pi\) | |||||||
\(312\) | 12.9443 | 0.732825 | ||||||||
\(313\) | −0.0901699 | −0.00509671 | −0.00254835 | − | 0.999997i | \(-0.500811\pi\) | ||||
−0.00254835 | + | 0.999997i | \(0.500811\pi\) | |||||||
\(314\) | 7.67376 | 0.433055 | ||||||||
\(315\) | −1.14590 | −0.0645640 | ||||||||
\(316\) | −9.70820 | −0.546129 | ||||||||
\(317\) | 2.18034 | 0.122460 | 0.0612300 | − | 0.998124i | \(-0.480498\pi\) | ||||
0.0612300 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(318\) | 18.4721 | 1.03587 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.618034 | −0.0345492 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | −2.12461 | −0.118400 | ||||||||
\(323\) | 5.61803 | 0.312596 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 29.8885 | 1.65792 | ||||||||
\(326\) | −16.3262 | −0.904227 | ||||||||
\(327\) | 2.47214 | 0.136709 | ||||||||
\(328\) | −9.23607 | −0.509977 | ||||||||
\(329\) | 6.70820 | 0.369835 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.70820 | −0.533611 | −0.266806 | − | 0.963750i | \(-0.585968\pi\) | ||||
−0.266806 | + | 0.963750i | \(0.585968\pi\) | |||||||
\(332\) | 10.7984 | 0.592638 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | −25.4164 | −1.39072 | ||||||||
\(335\) | −4.47214 | −0.244339 | ||||||||
\(336\) | −3.70820 | −0.202299 | ||||||||
\(337\) | −17.0557 | −0.929085 | −0.464542 | − | 0.885551i | \(-0.653781\pi\) | ||||
−0.464542 | + | 0.885551i | \(0.653781\pi\) | |||||||
\(338\) | 28.8885 | 1.57133 | ||||||||
\(339\) | −28.9443 | −1.57204 | ||||||||
\(340\) | −3.47214 | −0.188303 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −19.5836 | −1.05741 | ||||||||
\(344\) | 2.09017 | 0.112694 | ||||||||
\(345\) | −1.41641 | −0.0762568 | ||||||||
\(346\) | −3.05573 | −0.164277 | ||||||||
\(347\) | 8.56231 | 0.459649 | 0.229824 | − | 0.973232i | \(-0.426185\pi\) | ||||
0.229824 | + | 0.973232i | \(0.426185\pi\) | |||||||
\(348\) | −3.05573 | −0.163804 | ||||||||
\(349\) | 20.9787 | 1.12296 | 0.561482 | − | 0.827489i | \(-0.310231\pi\) | ||||
0.561482 | + | 0.827489i | \(0.310231\pi\) | |||||||
\(350\) | −8.56231 | −0.457675 | ||||||||
\(351\) | −25.8885 | −1.38183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.3820 | 0.818699 | 0.409350 | − | 0.912378i | \(-0.365756\pi\) | ||||
0.409350 | + | 0.912378i | \(0.365756\pi\) | |||||||
\(354\) | 24.9443 | 1.32577 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 6.76393 | 0.358488 | ||||||||
\(357\) | −20.8328 | −1.10259 | ||||||||
\(358\) | −20.1803 | −1.06656 | ||||||||
\(359\) | −6.09017 | −0.321427 | −0.160713 | − | 0.987001i | \(-0.551379\pi\) | ||||
−0.160713 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(360\) | −0.618034 | −0.0325733 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −13.7082 | −0.720487 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | 8.65248 | 0.452891 | ||||||||
\(366\) | −21.1246 | −1.10420 | ||||||||
\(367\) | −21.5623 | −1.12554 | −0.562772 | − | 0.826612i | \(-0.690265\pi\) | ||||
−0.562772 | + | 0.826612i | \(0.690265\pi\) | |||||||
\(368\) | −1.14590 | −0.0597341 | ||||||||
\(369\) | −9.23607 | −0.480810 | ||||||||
\(370\) | −2.47214 | −0.128520 | ||||||||
\(371\) | −17.1246 | −0.889066 | ||||||||
\(372\) | −4.00000 | −0.207390 | ||||||||
\(373\) | −30.3607 | −1.57202 | −0.786008 | − | 0.618216i | \(-0.787856\pi\) | ||||
−0.786008 | + | 0.618216i | \(0.787856\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.8885 | −0.613922 | ||||||||
\(376\) | 3.61803 | 0.186586 | ||||||||
\(377\) | −9.88854 | −0.509286 | ||||||||
\(378\) | 7.41641 | 0.381459 | ||||||||
\(379\) | 1.23607 | 0.0634925 | 0.0317463 | − | 0.999496i | \(-0.489893\pi\) | ||||
0.0317463 | + | 0.999496i | \(0.489893\pi\) | |||||||
\(380\) | −0.618034 | −0.0317045 | ||||||||
\(381\) | −14.8328 | −0.759908 | ||||||||
\(382\) | −24.0344 | −1.22971 | ||||||||
\(383\) | 14.9443 | 0.763617 | 0.381808 | − | 0.924242i | \(-0.375301\pi\) | ||||
0.381808 | + | 0.924242i | \(0.375301\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.1246 | −1.07521 | ||||||||
\(387\) | 2.09017 | 0.106249 | ||||||||
\(388\) | −4.76393 | −0.241852 | ||||||||
\(389\) | 13.0344 | 0.660872 | 0.330436 | − | 0.943828i | \(-0.392804\pi\) | ||||
0.330436 | + | 0.943828i | \(0.392804\pi\) | |||||||
\(390\) | −8.00000 | −0.405096 | ||||||||
\(391\) | −6.43769 | −0.325568 | ||||||||
\(392\) | −3.56231 | −0.179924 | ||||||||
\(393\) | 1.81966 | 0.0917897 | ||||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8541 | 1.04664 | 0.523319 | − | 0.852137i | \(-0.324694\pi\) | ||||
0.523319 | + | 0.852137i | \(0.324694\pi\) | |||||||
\(398\) | −5.56231 | −0.278813 | ||||||||
\(399\) | −3.70820 | −0.185642 | ||||||||
\(400\) | −4.61803 | −0.230902 | ||||||||
\(401\) | 12.4721 | 0.622829 | 0.311414 | − | 0.950274i | \(-0.399197\pi\) | ||||
0.311414 | + | 0.950274i | \(0.399197\pi\) | |||||||
\(402\) | −14.4721 | −0.721805 | ||||||||
\(403\) | −12.9443 | −0.644800 | ||||||||
\(404\) | 5.56231 | 0.276735 | ||||||||
\(405\) | 6.79837 | 0.337814 | ||||||||
\(406\) | 2.83282 | 0.140590 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −11.2361 | −0.556268 | ||||||||
\(409\) | −22.9443 | −1.13452 | −0.567261 | − | 0.823538i | \(-0.691997\pi\) | ||||
−0.567261 | + | 0.823538i | \(0.691997\pi\) | |||||||
\(410\) | 5.70820 | 0.281908 | ||||||||
\(411\) | 30.1803 | 1.48869 | ||||||||
\(412\) | −9.23607 | −0.455028 | ||||||||
\(413\) | −23.1246 | −1.13789 | ||||||||
\(414\) | −1.14590 | −0.0563178 | ||||||||
\(415\) | −6.67376 | −0.327602 | ||||||||
\(416\) | −6.47214 | −0.317323 | ||||||||
\(417\) | −10.6525 | −0.521654 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.32624 | 0.455617 | 0.227808 | − | 0.973706i | \(-0.426844\pi\) | ||||
0.227808 | + | 0.973706i | \(0.426844\pi\) | |||||||
\(420\) | 2.29180 | 0.111828 | ||||||||
\(421\) | 28.0000 | 1.36464 | 0.682318 | − | 0.731055i | \(-0.260972\pi\) | ||||
0.682318 | + | 0.731055i | \(0.260972\pi\) | |||||||
\(422\) | −11.4164 | −0.555742 | ||||||||
\(423\) | 3.61803 | 0.175915 | ||||||||
\(424\) | −9.23607 | −0.448543 | ||||||||
\(425\) | −25.9443 | −1.25848 | ||||||||
\(426\) | 25.8885 | 1.25430 | ||||||||
\(427\) | 19.5836 | 0.947716 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.29180 | −0.0622959 | ||||||||
\(431\) | 35.8885 | 1.72869 | 0.864345 | − | 0.502899i | \(-0.167733\pi\) | ||||
0.864345 | + | 0.502899i | \(0.167733\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 5.52786 | 0.265652 | 0.132826 | − | 0.991139i | \(-0.457595\pi\) | ||||
0.132826 | + | 0.991139i | \(0.457595\pi\) | |||||||
\(434\) | 3.70820 | 0.177999 | ||||||||
\(435\) | 1.88854 | 0.0905487 | ||||||||
\(436\) | −1.23607 | −0.0591969 | ||||||||
\(437\) | −1.14590 | −0.0548157 | ||||||||
\(438\) | 28.0000 | 1.33789 | ||||||||
\(439\) | 23.1246 | 1.10368 | 0.551839 | − | 0.833951i | \(-0.313926\pi\) | ||||
0.551839 | + | 0.833951i | \(0.313926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.56231 | −0.169634 | ||||||||
\(442\) | −36.3607 | −1.72950 | ||||||||
\(443\) | 14.2148 | 0.675365 | 0.337682 | − | 0.941260i | \(-0.390357\pi\) | ||||
0.337682 | + | 0.941260i | \(0.390357\pi\) | |||||||
\(444\) | −8.00000 | −0.379663 | ||||||||
\(445\) | −4.18034 | −0.198167 | ||||||||
\(446\) | 3.70820 | 0.175589 | ||||||||
\(447\) | 40.9443 | 1.93660 | ||||||||
\(448\) | 1.85410 | 0.0875981 | ||||||||
\(449\) | −8.18034 | −0.386054 | −0.193027 | − | 0.981193i | \(-0.561831\pi\) | ||||
−0.193027 | + | 0.981193i | \(0.561831\pi\) | |||||||
\(450\) | −4.61803 | −0.217696 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.4721 | 0.680712 | ||||||||
\(453\) | 0.583592 | 0.0274196 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.41641 | 0.347687 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −23.3820 | −1.09376 | −0.546881 | − | 0.837210i | \(-0.684185\pi\) | ||||
−0.546881 | + | 0.837210i | \(0.684185\pi\) | |||||||
\(458\) | 24.2705 | 1.13409 | ||||||||
\(459\) | 22.4721 | 1.04891 | ||||||||
\(460\) | 0.708204 | 0.0330202 | ||||||||
\(461\) | 5.20163 | 0.242264 | 0.121132 | − | 0.992636i | \(-0.461348\pi\) | ||||
0.121132 | + | 0.992636i | \(0.461348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.79837 | 0.130051 | 0.0650257 | − | 0.997884i | \(-0.479287\pi\) | ||||
0.0650257 | + | 0.997884i | \(0.479287\pi\) | |||||||
\(464\) | 1.52786 | 0.0709293 | ||||||||
\(465\) | 2.47214 | 0.114643 | ||||||||
\(466\) | −18.7984 | −0.870818 | ||||||||
\(467\) | 31.0902 | 1.43868 | 0.719341 | − | 0.694657i | \(-0.244444\pi\) | ||||
0.719341 | + | 0.694657i | \(0.244444\pi\) | |||||||
\(468\) | −6.47214 | −0.299175 | ||||||||
\(469\) | 13.4164 | 0.619512 | ||||||||
\(470\) | −2.23607 | −0.103142 | ||||||||
\(471\) | −15.3475 | −0.707177 | ||||||||
\(472\) | −12.4721 | −0.574077 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 19.4164 | 0.891825 | ||||||||
\(475\) | −4.61803 | −0.211890 | ||||||||
\(476\) | 10.4164 | 0.477435 | ||||||||
\(477\) | −9.23607 | −0.422891 | ||||||||
\(478\) | 2.67376 | 0.122295 | ||||||||
\(479\) | −10.0902 | −0.461032 | −0.230516 | − | 0.973069i | \(-0.574041\pi\) | ||||
−0.230516 | + | 0.973069i | \(0.574041\pi\) | |||||||
\(480\) | 1.23607 | 0.0564185 | ||||||||
\(481\) | −25.8885 | −1.18042 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 4.24922 | 0.193346 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.94427 | 0.133693 | ||||||||
\(486\) | 10.0000 | 0.453609 | ||||||||
\(487\) | 10.0000 | 0.453143 | 0.226572 | − | 0.973995i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973995i | \(0.427248\pi\) | |||||||
\(488\) | 10.5623 | 0.478133 | ||||||||
\(489\) | 32.6525 | 1.47660 | ||||||||
\(490\) | 2.20163 | 0.0994593 | ||||||||
\(491\) | −10.1459 | −0.457878 | −0.228939 | − | 0.973441i | \(-0.573526\pi\) | ||||
−0.228939 | + | 0.973441i | \(0.573526\pi\) | |||||||
\(492\) | 18.4721 | 0.832788 | ||||||||
\(493\) | 8.58359 | 0.386586 | ||||||||
\(494\) | −6.47214 | −0.291195 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −24.0000 | −1.07655 | ||||||||
\(498\) | −21.5967 | −0.967773 | ||||||||
\(499\) | 17.5623 | 0.786197 | 0.393098 | − | 0.919496i | \(-0.371403\pi\) | ||||
0.393098 | + | 0.919496i | \(0.371403\pi\) | |||||||
\(500\) | 5.94427 | 0.265836 | ||||||||
\(501\) | 50.8328 | 2.27104 | ||||||||
\(502\) | 10.8541 | 0.484442 | ||||||||
\(503\) | −29.3050 | −1.30664 | −0.653322 | − | 0.757080i | \(-0.726625\pi\) | ||||
−0.653322 | + | 0.757080i | \(0.726625\pi\) | |||||||
\(504\) | 1.85410 | 0.0825883 | ||||||||
\(505\) | −3.43769 | −0.152975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −57.7771 | −2.56597 | ||||||||
\(508\) | 7.41641 | 0.329050 | ||||||||
\(509\) | 20.2918 | 0.899418 | 0.449709 | − | 0.893175i | \(-0.351528\pi\) | ||||
0.449709 | + | 0.893175i | \(0.351528\pi\) | |||||||
\(510\) | 6.94427 | 0.307498 | ||||||||
\(511\) | −25.9574 | −1.14829 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.00000 | 0.176604 | ||||||||
\(514\) | −10.9443 | −0.482731 | ||||||||
\(515\) | 5.70820 | 0.251534 | ||||||||
\(516\) | −4.18034 | −0.184029 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.41641 | 0.325858 | ||||||||
\(519\) | 6.11146 | 0.268263 | ||||||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | 2.18034 | 0.0955224 | 0.0477612 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477612 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(522\) | 1.52786 | 0.0668728 | ||||||||
\(523\) | −29.1246 | −1.27353 | −0.636765 | − | 0.771058i | \(-0.719728\pi\) | ||||
−0.636765 | + | 0.771058i | \(0.719728\pi\) | |||||||
\(524\) | −0.909830 | −0.0397461 | ||||||||
\(525\) | 17.1246 | 0.747379 | ||||||||
\(526\) | 6.47214 | 0.282199 | ||||||||
\(527\) | 11.2361 | 0.489451 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6869 | −0.942909 | ||||||||
\(530\) | 5.70820 | 0.247949 | ||||||||
\(531\) | −12.4721 | −0.541245 | ||||||||
\(532\) | 1.85410 | 0.0803855 | ||||||||
\(533\) | 59.7771 | 2.58923 | ||||||||
\(534\) | −13.5279 | −0.585408 | ||||||||
\(535\) | −3.70820 | −0.160320 | ||||||||
\(536\) | 7.23607 | 0.312551 | ||||||||
\(537\) | 40.3607 | 1.74169 | ||||||||
\(538\) | 18.6525 | 0.804165 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.47214 | −0.106384 | ||||||||
\(541\) | 27.1459 | 1.16709 | 0.583547 | − | 0.812080i | \(-0.301665\pi\) | ||||
0.583547 | + | 0.812080i | \(0.301665\pi\) | |||||||
\(542\) | −31.2148 | −1.34079 | ||||||||
\(543\) | 27.4164 | 1.17655 | ||||||||
\(544\) | 5.61803 | 0.240871 | ||||||||
\(545\) | 0.763932 | 0.0327233 | ||||||||
\(546\) | 24.0000 | 1.02711 | ||||||||
\(547\) | 6.29180 | 0.269018 | 0.134509 | − | 0.990912i | \(-0.457054\pi\) | ||||
0.134509 | + | 0.990912i | \(0.457054\pi\) | |||||||
\(548\) | −15.0902 | −0.644620 | ||||||||
\(549\) | 10.5623 | 0.450788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.52786 | 0.0650892 | ||||||||
\(552\) | 2.29180 | 0.0975453 | ||||||||
\(553\) | −18.0000 | −0.765438 | ||||||||
\(554\) | −3.52786 | −0.149885 | ||||||||
\(555\) | 4.94427 | 0.209873 | ||||||||
\(556\) | 5.32624 | 0.225883 | ||||||||
\(557\) | 35.4508 | 1.50210 | 0.751050 | − | 0.660245i | \(-0.229548\pi\) | ||||
0.751050 | + | 0.660245i | \(0.229548\pi\) | |||||||
\(558\) | 2.00000 | 0.0846668 | ||||||||
\(559\) | −13.5279 | −0.572168 | ||||||||
\(560\) | −1.14590 | −0.0484230 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.65248 | 0.196253 | ||||||||
\(563\) | −9.70820 | −0.409152 | −0.204576 | − | 0.978851i | \(-0.565582\pi\) | ||||
−0.204576 | + | 0.978851i | \(0.565582\pi\) | |||||||
\(564\) | −7.23607 | −0.304693 | ||||||||
\(565\) | −8.94427 | −0.376288 | ||||||||
\(566\) | −9.56231 | −0.401934 | ||||||||
\(567\) | −20.3951 | −0.856515 | ||||||||
\(568\) | −12.9443 | −0.543130 | ||||||||
\(569\) | −16.6525 | −0.698108 | −0.349054 | − | 0.937103i | \(-0.613497\pi\) | ||||
−0.349054 | + | 0.937103i | \(0.613497\pi\) | |||||||
\(570\) | 1.23607 | 0.0517732 | ||||||||
\(571\) | 6.14590 | 0.257198 | 0.128599 | − | 0.991697i | \(-0.458952\pi\) | ||||
0.128599 | + | 0.991697i | \(0.458952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.0689 | 2.00811 | ||||||||
\(574\) | −17.1246 | −0.714767 | ||||||||
\(575\) | 5.29180 | 0.220683 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 12.4721 | 0.519222 | 0.259611 | − | 0.965713i | \(-0.416406\pi\) | ||||
0.259611 | + | 0.965713i | \(0.416406\pi\) | |||||||
\(578\) | 14.5623 | 0.605712 | ||||||||
\(579\) | 42.2492 | 1.75582 | ||||||||
\(580\) | −0.944272 | −0.0392088 | ||||||||
\(581\) | 20.0213 | 0.830623 | ||||||||
\(582\) | 9.52786 | 0.394943 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 4.00000 | 0.165380 | ||||||||
\(586\) | 0.652476 | 0.0269535 | ||||||||
\(587\) | 28.9443 | 1.19466 | 0.597329 | − | 0.801996i | \(-0.296229\pi\) | ||||
0.597329 | + | 0.801996i | \(0.296229\pi\) | |||||||
\(588\) | 7.12461 | 0.293814 | ||||||||
\(589\) | 2.00000 | 0.0824086 | ||||||||
\(590\) | 7.70820 | 0.317342 | ||||||||
\(591\) | 36.0000 | 1.48084 | ||||||||
\(592\) | 4.00000 | 0.164399 | ||||||||
\(593\) | −44.4508 | −1.82538 | −0.912689 | − | 0.408655i | \(-0.865998\pi\) | ||||
−0.912689 | + | 0.408655i | \(0.865998\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.43769 | −0.263920 | ||||||||
\(596\) | −20.4721 | −0.838571 | ||||||||
\(597\) | 11.1246 | 0.455300 | ||||||||
\(598\) | 7.41641 | 0.303279 | ||||||||
\(599\) | 15.5967 | 0.637266 | 0.318633 | − | 0.947878i | \(-0.396776\pi\) | ||||
0.318633 | + | 0.947878i | \(0.396776\pi\) | |||||||
\(600\) | 9.23607 | 0.377061 | ||||||||
\(601\) | 31.7082 | 1.29340 | 0.646702 | − | 0.762743i | \(-0.276148\pi\) | ||||
0.646702 | + | 0.762743i | \(0.276148\pi\) | |||||||
\(602\) | 3.87539 | 0.157949 | ||||||||
\(603\) | 7.23607 | 0.294675 | ||||||||
\(604\) | −0.291796 | −0.0118730 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.1246 | −0.451906 | ||||||||
\(607\) | 24.9443 | 1.01246 | 0.506228 | − | 0.862399i | \(-0.331039\pi\) | ||||
0.506228 | + | 0.862399i | \(0.331039\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −5.66563 | −0.229583 | ||||||||
\(610\) | −6.52786 | −0.264305 | ||||||||
\(611\) | −23.4164 | −0.947326 | ||||||||
\(612\) | 5.61803 | 0.227096 | ||||||||
\(613\) | −7.72949 | −0.312191 | −0.156096 | − | 0.987742i | \(-0.549891\pi\) | ||||
−0.156096 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(614\) | −27.4164 | −1.10644 | ||||||||
\(615\) | −11.4164 | −0.460354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.7214 | 1.71990 | 0.859949 | − | 0.510381i | \(-0.170495\pi\) | ||||
0.859949 | + | 0.510381i | \(0.170495\pi\) | |||||||
\(618\) | 18.4721 | 0.743058 | ||||||||
\(619\) | 12.5623 | 0.504922 | 0.252461 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252461 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(620\) | −1.23607 | −0.0496417 | ||||||||
\(621\) | −4.58359 | −0.183933 | ||||||||
\(622\) | −4.20163 | −0.168470 | ||||||||
\(623\) | 12.5410 | 0.502445 | ||||||||
\(624\) | 12.9443 | 0.518186 | ||||||||
\(625\) | 19.4164 | 0.776656 | ||||||||
\(626\) | −0.0901699 | −0.00360392 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.67376 | 0.306216 | ||||||||
\(629\) | 22.4721 | 0.896023 | ||||||||
\(630\) | −1.14590 | −0.0456537 | ||||||||
\(631\) | −24.3607 | −0.969783 | −0.484892 | − | 0.874574i | \(-0.661141\pi\) | ||||
−0.484892 | + | 0.874574i | \(0.661141\pi\) | |||||||
\(632\) | −9.70820 | −0.386172 | ||||||||
\(633\) | 22.8328 | 0.907523 | ||||||||
\(634\) | 2.18034 | 0.0865924 | ||||||||
\(635\) | −4.58359 | −0.181894 | ||||||||
\(636\) | 18.4721 | 0.732468 | ||||||||
\(637\) | 23.0557 | 0.913501 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.9443 | −0.512067 | ||||||||
\(640\) | −0.618034 | −0.0244299 | ||||||||
\(641\) | 21.3050 | 0.841495 | 0.420747 | − | 0.907178i | \(-0.361768\pi\) | ||||
0.420747 | + | 0.907178i | \(0.361768\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | 20.9230 | 0.825122 | 0.412561 | − | 0.910930i | \(-0.364634\pi\) | ||||
0.412561 | + | 0.910930i | \(0.364634\pi\) | |||||||
\(644\) | −2.12461 | −0.0837214 | ||||||||
\(645\) | 2.58359 | 0.101729 | ||||||||
\(646\) | 5.61803 | 0.221039 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | −11.0000 | −0.432121 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 29.8885 | 1.17233 | ||||||||
\(651\) | −7.41641 | −0.290672 | ||||||||
\(652\) | −16.3262 | −0.639385 | ||||||||
\(653\) | −1.61803 | −0.0633186 | −0.0316593 | − | 0.999499i | \(-0.510079\pi\) | ||||
−0.0316593 | + | 0.999499i | \(0.510079\pi\) | |||||||
\(654\) | 2.47214 | 0.0966682 | ||||||||
\(655\) | 0.562306 | 0.0219711 | ||||||||
\(656\) | −9.23607 | −0.360608 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 6.70820 | 0.261513 | ||||||||
\(659\) | 20.2918 | 0.790456 | 0.395228 | − | 0.918583i | \(-0.370666\pi\) | ||||
0.395228 | + | 0.918583i | \(0.370666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5967 | 0.762225 | 0.381113 | − | 0.924529i | \(-0.375541\pi\) | ||||
0.381113 | + | 0.924529i | \(0.375541\pi\) | |||||||
\(662\) | −9.70820 | −0.377320 | ||||||||
\(663\) | 72.7214 | 2.82426 | ||||||||
\(664\) | 10.7984 | 0.419058 | ||||||||
\(665\) | −1.14590 | −0.0444360 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | −1.75078 | −0.0677903 | ||||||||
\(668\) | −25.4164 | −0.983390 | ||||||||
\(669\) | −7.41641 | −0.286735 | ||||||||
\(670\) | −4.47214 | −0.172774 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.70820 | −0.143047 | ||||||||
\(673\) | −45.0132 | −1.73513 | −0.867565 | − | 0.497324i | \(-0.834316\pi\) | ||||
−0.867565 | + | 0.497324i | \(0.834316\pi\) | |||||||
\(674\) | −17.0557 | −0.656962 | ||||||||
\(675\) | −18.4721 | −0.710993 | ||||||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | 33.7082 | 1.29551 | 0.647756 | − | 0.761848i | \(-0.275708\pi\) | ||||
0.647756 | + | 0.761848i | \(0.275708\pi\) | |||||||
\(678\) | −28.9443 | −1.11160 | ||||||||
\(679\) | −8.83282 | −0.338972 | ||||||||
\(680\) | −3.47214 | −0.133150 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.0689 | −0.767914 | −0.383957 | − | 0.923351i | \(-0.625439\pi\) | ||||
−0.383957 | + | 0.923351i | \(0.625439\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 9.32624 | 0.356337 | ||||||||
\(686\) | −19.5836 | −0.747705 | ||||||||
\(687\) | −48.5410 | −1.85196 | ||||||||
\(688\) | 2.09017 | 0.0796870 | ||||||||
\(689\) | 59.7771 | 2.27733 | ||||||||
\(690\) | −1.41641 | −0.0539217 | ||||||||
\(691\) | −20.3262 | −0.773247 | −0.386623 | − | 0.922238i | \(-0.626359\pi\) | ||||
−0.386623 | + | 0.922238i | \(0.626359\pi\) | |||||||
\(692\) | −3.05573 | −0.116161 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.56231 | 0.325021 | ||||||||
\(695\) | −3.29180 | −0.124865 | ||||||||
\(696\) | −3.05573 | −0.115827 | ||||||||
\(697\) | −51.8885 | −1.96542 | ||||||||
\(698\) | 20.9787 | 0.794056 | ||||||||
\(699\) | 37.5967 | 1.42204 | ||||||||
\(700\) | −8.56231 | −0.323625 | ||||||||
\(701\) | 14.7426 | 0.556822 | 0.278411 | − | 0.960462i | \(-0.410192\pi\) | ||||
0.278411 | + | 0.960462i | \(0.410192\pi\) | |||||||
\(702\) | −25.8885 | −0.977100 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.47214 | 0.168430 | ||||||||
\(706\) | 15.3820 | 0.578908 | ||||||||
\(707\) | 10.3131 | 0.387863 | ||||||||
\(708\) | 24.9443 | 0.937463 | ||||||||
\(709\) | 5.20163 | 0.195351 | 0.0976756 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976756 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | −9.70820 | −0.364086 | ||||||||
\(712\) | 6.76393 | 0.253489 | ||||||||
\(713\) | −2.29180 | −0.0858284 | ||||||||
\(714\) | −20.8328 | −0.779649 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −20.1803 | −0.754175 | ||||||||
\(717\) | −5.34752 | −0.199707 | ||||||||
\(718\) | −6.09017 | −0.227283 | ||||||||
\(719\) | −20.3262 | −0.758041 | −0.379020 | − | 0.925388i | \(-0.623739\pi\) | ||||
−0.379020 | + | 0.925388i | \(0.623739\pi\) | |||||||
\(720\) | −0.618034 | −0.0230328 | ||||||||
\(721\) | −17.1246 | −0.637754 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −20.0000 | −0.743808 | ||||||||
\(724\) | −13.7082 | −0.509461 | ||||||||
\(725\) | −7.05573 | −0.262043 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.8541 | 0.699260 | 0.349630 | − | 0.936888i | \(-0.386307\pi\) | ||||
0.349630 | + | 0.936888i | \(0.386307\pi\) | |||||||
\(728\) | −12.0000 | −0.444750 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 8.65248 | 0.320242 | ||||||||
\(731\) | 11.7426 | 0.434317 | ||||||||
\(732\) | −21.1246 | −0.780788 | ||||||||
\(733\) | 44.3262 | 1.63723 | 0.818613 | − | 0.574345i | \(-0.194743\pi\) | ||||
0.818613 | + | 0.574345i | \(0.194743\pi\) | |||||||
\(734\) | −21.5623 | −0.795879 | ||||||||
\(735\) | −4.40325 | −0.162416 | ||||||||
\(736\) | −1.14590 | −0.0422384 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −9.23607 | −0.339984 | ||||||||
\(739\) | −43.4508 | −1.59837 | −0.799183 | − | 0.601088i | \(-0.794734\pi\) | ||||
−0.799183 | + | 0.601088i | \(0.794734\pi\) | |||||||
\(740\) | −2.47214 | −0.0908775 | ||||||||
\(741\) | 12.9443 | 0.475520 | ||||||||
\(742\) | −17.1246 | −0.628664 | ||||||||
\(743\) | 28.6525 | 1.05116 | 0.525579 | − | 0.850745i | \(-0.323849\pi\) | ||||
0.525579 | + | 0.850745i | \(0.323849\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | 12.6525 | 0.463551 | ||||||||
\(746\) | −30.3607 | −1.11158 | ||||||||
\(747\) | 10.7984 | 0.395092 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1246 | 0.406484 | ||||||||
\(750\) | −11.8885 | −0.434108 | ||||||||
\(751\) | −37.4164 | −1.36534 | −0.682672 | − | 0.730725i | \(-0.739182\pi\) | ||||
−0.682672 | + | 0.730725i | \(0.739182\pi\) | |||||||
\(752\) | 3.61803 | 0.131936 | ||||||||
\(753\) | −21.7082 | −0.791091 | ||||||||
\(754\) | −9.88854 | −0.360120 | ||||||||
\(755\) | 0.180340 | 0.00656324 | ||||||||
\(756\) | 7.41641 | 0.269732 | ||||||||
\(757\) | 1.41641 | 0.0514802 | 0.0257401 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257401 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(758\) | 1.23607 | 0.0448960 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.618034 | −0.0224184 | ||||||||
\(761\) | 51.3050 | 1.85980 | 0.929902 | − | 0.367809i | \(-0.119892\pi\) | ||||
0.929902 | + | 0.367809i | \(0.119892\pi\) | |||||||
\(762\) | −14.8328 | −0.537336 | ||||||||
\(763\) | −2.29180 | −0.0829686 | ||||||||
\(764\) | −24.0344 | −0.869536 | ||||||||
\(765\) | −3.47214 | −0.125535 | ||||||||
\(766\) | 14.9443 | 0.539958 | ||||||||
\(767\) | 80.7214 | 2.91468 | ||||||||
\(768\) | −2.00000 | −0.0721688 | ||||||||
\(769\) | 34.5066 | 1.24434 | 0.622170 | − | 0.782883i | \(-0.286251\pi\) | ||||
0.622170 | + | 0.782883i | \(0.286251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.8885 | 0.788297 | ||||||||
\(772\) | −21.1246 | −0.760291 | ||||||||
\(773\) | −33.5967 | −1.20839 | −0.604196 | − | 0.796836i | \(-0.706505\pi\) | ||||
−0.604196 | + | 0.796836i | \(0.706505\pi\) | |||||||
\(774\) | 2.09017 | 0.0751296 | ||||||||
\(775\) | −9.23607 | −0.331769 | ||||||||
\(776\) | −4.76393 | −0.171015 | ||||||||
\(777\) | −14.8328 | −0.532124 | ||||||||
\(778\) | 13.0344 | 0.467307 | ||||||||
\(779\) | −9.23607 | −0.330916 | ||||||||
\(780\) | −8.00000 | −0.286446 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −6.43769 | −0.230211 | ||||||||
\(783\) | 6.11146 | 0.218406 | ||||||||
\(784\) | −3.56231 | −0.127225 | ||||||||
\(785\) | −4.74265 | −0.169272 | ||||||||
\(786\) | 1.81966 | 0.0649051 | ||||||||
\(787\) | −42.9443 | −1.53080 | −0.765399 | − | 0.643556i | \(-0.777458\pi\) | ||||
−0.765399 | + | 0.643556i | \(0.777458\pi\) | |||||||
\(788\) | −18.0000 | −0.641223 | ||||||||
\(789\) | −12.9443 | −0.460828 | ||||||||
\(790\) | 6.00000 | 0.213470 | ||||||||
\(791\) | 26.8328 | 0.954065 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.3607 | −2.42756 | ||||||||
\(794\) | 20.8541 | 0.740084 | ||||||||
\(795\) | −11.4164 | −0.404898 | ||||||||
\(796\) | −5.56231 | −0.197151 | ||||||||
\(797\) | −53.7771 | −1.90488 | −0.952441 | − | 0.304723i | \(-0.901436\pi\) | ||||
−0.952441 | + | 0.304723i | \(0.901436\pi\) | |||||||
\(798\) | −3.70820 | −0.131269 | ||||||||
\(799\) | 20.3262 | 0.719091 | ||||||||
\(800\) | −4.61803 | −0.163272 | ||||||||
\(801\) | 6.76393 | 0.238992 | ||||||||
\(802\) | 12.4721 | 0.440406 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.4721 | −0.510393 | ||||||||
\(805\) | 1.31308 | 0.0462801 | ||||||||
\(806\) | −12.9443 | −0.455943 | ||||||||
\(807\) | −37.3050 | −1.31320 | ||||||||
\(808\) | 5.56231 | 0.195681 | ||||||||
\(809\) | 5.56231 | 0.195560 | 0.0977801 | − | 0.995208i | \(-0.468826\pi\) | ||||
0.0977801 | + | 0.995208i | \(0.468826\pi\) | |||||||
\(810\) | 6.79837 | 0.238871 | ||||||||
\(811\) | −40.2492 | −1.41334 | −0.706671 | − | 0.707543i | \(-0.749804\pi\) | ||||
−0.706671 | + | 0.707543i | \(0.749804\pi\) | |||||||
\(812\) | 2.83282 | 0.0994123 | ||||||||
\(813\) | 62.4296 | 2.18950 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.0902 | 0.353443 | ||||||||
\(816\) | −11.2361 | −0.393341 | ||||||||
\(817\) | 2.09017 | 0.0731258 | ||||||||
\(818\) | −22.9443 | −0.802228 | ||||||||
\(819\) | −12.0000 | −0.419314 | ||||||||
\(820\) | 5.70820 | 0.199339 | ||||||||
\(821\) | 3.90983 | 0.136454 | 0.0682270 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682270 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(822\) | 30.1803 | 1.05266 | ||||||||
\(823\) | 13.8541 | 0.482924 | 0.241462 | − | 0.970410i | \(-0.422373\pi\) | ||||
0.241462 | + | 0.970410i | \(0.422373\pi\) | |||||||
\(824\) | −9.23607 | −0.321754 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.1246 | −0.804608 | ||||||||
\(827\) | 28.2492 | 0.982322 | 0.491161 | − | 0.871069i | \(-0.336573\pi\) | ||||
0.491161 | + | 0.871069i | \(0.336573\pi\) | |||||||
\(828\) | −1.14590 | −0.0398227 | ||||||||
\(829\) | −18.8328 | −0.654091 | −0.327045 | − | 0.945009i | \(-0.606053\pi\) | ||||
−0.327045 | + | 0.945009i | \(0.606053\pi\) | |||||||
\(830\) | −6.67376 | −0.231650 | ||||||||
\(831\) | 7.05573 | 0.244760 | ||||||||
\(832\) | −6.47214 | −0.224381 | ||||||||
\(833\) | −20.0132 | −0.693415 | ||||||||
\(834\) | −10.6525 | −0.368865 | ||||||||
\(835\) | 15.7082 | 0.543605 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 9.32624 | 0.322170 | ||||||||
\(839\) | −24.1803 | −0.834798 | −0.417399 | − | 0.908723i | \(-0.637058\pi\) | ||||
−0.417399 | + | 0.908723i | \(0.637058\pi\) | |||||||
\(840\) | 2.29180 | 0.0790745 | ||||||||
\(841\) | −26.6656 | −0.919505 | ||||||||
\(842\) | 28.0000 | 0.964944 | ||||||||
\(843\) | −9.30495 | −0.320480 | ||||||||
\(844\) | −11.4164 | −0.392969 | ||||||||
\(845\) | −17.8541 | −0.614200 | ||||||||
\(846\) | 3.61803 | 0.124391 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.23607 | −0.317168 | ||||||||
\(849\) | 19.1246 | 0.656355 | ||||||||
\(850\) | −25.9443 | −0.889881 | ||||||||
\(851\) | −4.58359 | −0.157124 | ||||||||
\(852\) | 25.8885 | 0.886927 | ||||||||
\(853\) | −4.27051 | −0.146219 | −0.0731097 | − | 0.997324i | \(-0.523292\pi\) | ||||
−0.0731097 | + | 0.997324i | \(0.523292\pi\) | |||||||
\(854\) | 19.5836 | 0.670137 | ||||||||
\(855\) | −0.618034 | −0.0211363 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | −19.0132 | −0.649477 | −0.324739 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324739 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6869 | 1.14938 | 0.574691 | − | 0.818370i | \(-0.305122\pi\) | ||||
0.574691 | + | 0.818370i | \(0.305122\pi\) | |||||||
\(860\) | −1.29180 | −0.0440499 | ||||||||
\(861\) | 34.2492 | 1.16721 | ||||||||
\(862\) | 35.8885 | 1.22237 | ||||||||
\(863\) | 48.1803 | 1.64008 | 0.820039 | − | 0.572308i | \(-0.193952\pi\) | ||||
0.820039 | + | 0.572308i | \(0.193952\pi\) | |||||||
\(864\) | 4.00000 | 0.136083 | ||||||||
\(865\) | 1.88854 | 0.0642124 | ||||||||
\(866\) | 5.52786 | 0.187844 | ||||||||
\(867\) | −29.1246 | −0.989124 | ||||||||
\(868\) | 3.70820 | 0.125865 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.88854 | 0.0640276 | ||||||||
\(871\) | −46.8328 | −1.58687 | ||||||||
\(872\) | −1.23607 | −0.0418585 | ||||||||
\(873\) | −4.76393 | −0.161235 | ||||||||
\(874\) | −1.14590 | −0.0387606 | ||||||||
\(875\) | 11.0213 | 0.372587 | ||||||||
\(876\) | 28.0000 | 0.946032 | ||||||||
\(877\) | −14.5836 | −0.492453 | −0.246226 | − | 0.969212i | \(-0.579191\pi\) | ||||
−0.246226 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(878\) | 23.1246 | 0.780418 | ||||||||
\(879\) | −1.30495 | −0.0440149 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.4164 | 0.856301 | 0.428150 | − | 0.903708i | \(-0.359165\pi\) | ||||
0.428150 | + | 0.903708i | \(0.359165\pi\) | |||||||
\(882\) | −3.56231 | −0.119949 | ||||||||
\(883\) | −24.3951 | −0.820961 | −0.410481 | − | 0.911869i | \(-0.634639\pi\) | ||||
−0.410481 | + | 0.911869i | \(0.634639\pi\) | |||||||
\(884\) | −36.3607 | −1.22294 | ||||||||
\(885\) | −15.4164 | −0.518217 | ||||||||
\(886\) | 14.2148 | 0.477555 | ||||||||
\(887\) | 12.1115 | 0.406663 | 0.203331 | − | 0.979110i | \(-0.434823\pi\) | ||||
0.203331 | + | 0.979110i | \(0.434823\pi\) | |||||||
\(888\) | −8.00000 | −0.268462 | ||||||||
\(889\) | 13.7508 | 0.461186 | ||||||||
\(890\) | −4.18034 | −0.140125 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.70820 | 0.124160 | ||||||||
\(893\) | 3.61803 | 0.121073 | ||||||||
\(894\) | 40.9443 | 1.36938 | ||||||||
\(895\) | 12.4721 | 0.416898 | ||||||||
\(896\) | 1.85410 | 0.0619412 | ||||||||
\(897\) | −14.8328 | −0.495253 | ||||||||
\(898\) | −8.18034 | −0.272981 | ||||||||
\(899\) | 3.05573 | 0.101914 | ||||||||
\(900\) | −4.61803 | −0.153934 | ||||||||
\(901\) | −51.8885 | −1.72866 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.75078 | −0.257930 | ||||||||
\(904\) | 14.4721 | 0.481336 | ||||||||
\(905\) | 8.47214 | 0.281623 | ||||||||
\(906\) | 0.583592 | 0.0193886 | ||||||||
\(907\) | −30.8328 | −1.02379 | −0.511893 | − | 0.859049i | \(-0.671056\pi\) | ||||
−0.511893 | + | 0.859049i | \(0.671056\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.56231 | 0.184490 | ||||||||
\(910\) | 7.41641 | 0.245852 | ||||||||
\(911\) | 13.4164 | 0.444505 | 0.222253 | − | 0.974989i | \(-0.428659\pi\) | ||||
0.222253 | + | 0.974989i | \(0.428659\pi\) | |||||||
\(912\) | −2.00000 | −0.0662266 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −23.3820 | −0.773407 | ||||||||
\(915\) | 13.0557 | 0.431609 | ||||||||
\(916\) | 24.2705 | 0.801920 | ||||||||
\(917\) | −1.68692 | −0.0557069 | ||||||||
\(918\) | 22.4721 | 0.741691 | ||||||||
\(919\) | −28.6869 | −0.946294 | −0.473147 | − | 0.880983i | \(-0.656882\pi\) | ||||
−0.473147 | + | 0.880983i | \(0.656882\pi\) | |||||||
\(920\) | 0.708204 | 0.0233488 | ||||||||
\(921\) | 54.8328 | 1.80680 | ||||||||
\(922\) | 5.20163 | 0.171306 | ||||||||
\(923\) | 83.7771 | 2.75756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.4721 | −0.607360 | ||||||||
\(926\) | 2.79837 | 0.0919603 | ||||||||
\(927\) | −9.23607 | −0.303352 | ||||||||
\(928\) | 1.52786 | 0.0501546 | ||||||||
\(929\) | 48.2705 | 1.58370 | 0.791852 | − | 0.610713i | \(-0.209117\pi\) | ||||
0.791852 | + | 0.610713i | \(0.209117\pi\) | |||||||
\(930\) | 2.47214 | 0.0810645 | ||||||||
\(931\) | −3.56231 | −0.116750 | ||||||||
\(932\) | −18.7984 | −0.615761 | ||||||||
\(933\) | 8.40325 | 0.275110 | ||||||||
\(934\) | 31.0902 | 1.01730 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.47214 | −0.211548 | ||||||||
\(937\) | 56.8115 | 1.85595 | 0.927976 | − | 0.372640i | \(-0.121547\pi\) | ||||
0.927976 | + | 0.372640i | \(0.121547\pi\) | |||||||
\(938\) | 13.4164 | 0.438061 | ||||||||
\(939\) | 0.180340 | 0.00588517 | ||||||||
\(940\) | −2.23607 | −0.0729325 | ||||||||
\(941\) | 8.94427 | 0.291575 | 0.145787 | − | 0.989316i | \(-0.453428\pi\) | ||||
0.145787 | + | 0.989316i | \(0.453428\pi\) | |||||||
\(942\) | −15.3475 | −0.500049 | ||||||||
\(943\) | 10.5836 | 0.344649 | ||||||||
\(944\) | −12.4721 | −0.405933 | ||||||||
\(945\) | −4.58359 | −0.149104 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.9230 | −1.23233 | −0.616166 | − | 0.787617i | \(-0.711315\pi\) | ||||
−0.616166 | + | 0.787617i | \(0.711315\pi\) | |||||||
\(948\) | 19.4164 | 0.630616 | ||||||||
\(949\) | 90.6099 | 2.94132 | ||||||||
\(950\) | −4.61803 | −0.149829 | ||||||||
\(951\) | −4.36068 | −0.141405 | ||||||||
\(952\) | 10.4164 | 0.337598 | ||||||||
\(953\) | 49.7771 | 1.61244 | 0.806219 | − | 0.591617i | \(-0.201510\pi\) | ||||
0.806219 | + | 0.591617i | \(0.201510\pi\) | |||||||
\(954\) | −9.23607 | −0.299029 | ||||||||
\(955\) | 14.8541 | 0.480667 | ||||||||
\(956\) | 2.67376 | 0.0864756 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0902 | −0.325999 | ||||||||
\(959\) | −27.9787 | −0.903480 | ||||||||
\(960\) | 1.23607 | 0.0398939 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −25.8885 | −0.834680 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | 13.0557 | 0.420279 | ||||||||
\(966\) | 4.24922 | 0.136717 | ||||||||
\(967\) | −58.2705 | −1.87385 | −0.936927 | − | 0.349526i | \(-0.886343\pi\) | ||||
−0.936927 | + | 0.349526i | \(0.886343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.2361 | −0.360955 | ||||||||
\(970\) | 2.94427 | 0.0945349 | ||||||||
\(971\) | −34.3607 | −1.10269 | −0.551343 | − | 0.834278i | \(-0.685885\pi\) | ||||
−0.551343 | + | 0.834278i | \(0.685885\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | 9.87539 | 0.316590 | ||||||||
\(974\) | 10.0000 | 0.320421 | ||||||||
\(975\) | −59.7771 | −1.91440 | ||||||||
\(976\) | 10.5623 | 0.338091 | ||||||||
\(977\) | 8.83282 | 0.282587 | 0.141293 | − | 0.989968i | \(-0.454874\pi\) | ||||
0.141293 | + | 0.989968i | \(0.454874\pi\) | |||||||
\(978\) | 32.6525 | 1.04411 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.20163 | 0.0703284 | ||||||||
\(981\) | −1.23607 | −0.0394646 | ||||||||
\(982\) | −10.1459 | −0.323769 | ||||||||
\(983\) | −58.1378 | −1.85431 | −0.927153 | − | 0.374682i | \(-0.877752\pi\) | ||||
−0.927153 | + | 0.374682i | \(0.877752\pi\) | |||||||
\(984\) | 18.4721 | 0.588870 | ||||||||
\(985\) | 11.1246 | 0.354460 | ||||||||
\(986\) | 8.58359 | 0.273357 | ||||||||
\(987\) | −13.4164 | −0.427049 | ||||||||
\(988\) | −6.47214 | −0.205906 | ||||||||
\(989\) | −2.39512 | −0.0761604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3607 | −0.837375 | −0.418687 | − | 0.908130i | \(-0.637510\pi\) | ||||
−0.418687 | + | 0.908130i | \(0.637510\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | 19.4164 | 0.616161 | ||||||||
\(994\) | −24.0000 | −0.761234 | ||||||||
\(995\) | 3.43769 | 0.108982 | ||||||||
\(996\) | −21.5967 | −0.684319 | ||||||||
\(997\) | −21.2705 | −0.673644 | −0.336822 | − | 0.941568i | \(-0.609352\pi\) | ||||
−0.336822 | + | 0.941568i | \(0.609352\pi\) | |||||||
\(998\) | 17.5623 | 0.555925 | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 4598.2.a.bb.1.1 | 2 | ||
11.5 | even | 5 | 418.2.f.d.267.1 | yes | 4 | ||
11.9 | even | 5 | 418.2.f.d.191.1 | ✓ | 4 | ||
11.10 | odd | 2 | 4598.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.d.191.1 | ✓ | 4 | 11.9 | even | 5 | ||
418.2.f.d.267.1 | yes | 4 | 11.5 | even | 5 | ||
4598.2.a.t.1.1 | 2 | 11.10 | odd | 2 | |||
4598.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial |