Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.38197 | −0.937989 | −0.468994 | − | 0.883201i | \(-0.655384\pi\) | ||||
−0.468994 | + | 0.883201i | \(0.655384\pi\) | |||||||
\(14\) | −3.23607 | −0.864876 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.09017 | 1.47708 | 0.738542 | − | 0.674208i | \(-0.235515\pi\) | ||||
0.738542 | + | 0.674208i | \(0.235515\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.85410 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246614\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246614\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.38197 | 0.663258 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.23607 | 0.611559 | ||||||||
\(29\) | 2.61803 | 0.486157 | 0.243078 | − | 0.970007i | \(-0.421843\pi\) | ||||
0.243078 | + | 0.970007i | \(0.421843\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −1.38197 | −0.248208 | −0.124104 | − | 0.992269i | \(-0.539606\pi\) | ||||
−0.124104 | + | 0.992269i | \(0.539606\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.09017 | −1.04446 | ||||||||
\(35\) | −3.23607 | −0.546995 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.38197 | −1.04919 | −0.524594 | − | 0.851352i | \(-0.675783\pi\) | ||||
−0.524594 | + | 0.851352i | \(0.675783\pi\) | |||||||
\(38\) | 1.23607 | 0.200517 | ||||||||
\(39\) | 3.38197 | 0.541548 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.23607 | −0.193041 | −0.0965207 | − | 0.995331i | \(-0.530771\pi\) | ||||
−0.0965207 | + | 0.995331i | \(0.530771\pi\) | |||||||
\(42\) | 3.23607 | 0.499336 | ||||||||
\(43\) | 0.0901699 | 0.0137508 | 0.00687539 | − | 0.999976i | \(-0.497811\pi\) | ||||
0.00687539 | + | 0.999976i | \(0.497811\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −6.85410 | −1.01058 | ||||||||
\(47\) | −4.32624 | −0.631047 | −0.315523 | − | 0.948918i | \(-0.602180\pi\) | ||||
−0.315523 | + | 0.948918i | \(0.602180\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.09017 | −0.852794 | ||||||||
\(52\) | −3.38197 | −0.468994 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.23607 | −0.432438 | ||||||||
\(57\) | 1.23607 | 0.163721 | ||||||||
\(58\) | −2.61803 | −0.343765 | ||||||||
\(59\) | 14.0902 | 1.83438 | 0.917192 | − | 0.398446i | \(-0.130450\pi\) | ||||
0.917192 | + | 0.398446i | \(0.130450\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | 1.38197 | 0.175510 | ||||||||
\(63\) | 3.23607 | 0.407706 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.38197 | 0.419481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.09017 | −0.621863 | −0.310932 | − | 0.950432i | \(-0.600641\pi\) | ||||
−0.310932 | + | 0.950432i | \(0.600641\pi\) | |||||||
\(68\) | 6.09017 | 0.738542 | ||||||||
\(69\) | −6.85410 | −0.825137 | ||||||||
\(70\) | 3.23607 | 0.386784 | ||||||||
\(71\) | 10.4721 | 1.24281 | 0.621407 | − | 0.783488i | \(-0.286561\pi\) | ||||
0.621407 | + | 0.783488i | \(0.286561\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −13.4164 | −1.57027 | −0.785136 | − | 0.619324i | \(-0.787407\pi\) | ||||
−0.785136 | + | 0.619324i | \(0.787407\pi\) | |||||||
\(74\) | 6.38197 | 0.741888 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.38197 | −0.382932 | ||||||||
\(79\) | 4.09017 | 0.460180 | 0.230090 | − | 0.973169i | \(-0.426098\pi\) | ||||
0.230090 | + | 0.973169i | \(0.426098\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.23607 | 0.136501 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −3.23607 | −0.353084 | ||||||||
\(85\) | −6.09017 | −0.660572 | ||||||||
\(86\) | −0.0901699 | −0.00972328 | ||||||||
\(87\) | −2.61803 | −0.280683 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.2361 | 1.82702 | 0.913510 | − | 0.406817i | \(-0.133361\pi\) | ||||
0.913510 | + | 0.406817i | \(0.133361\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −10.9443 | −1.14727 | ||||||||
\(92\) | 6.85410 | 0.714590 | ||||||||
\(93\) | 1.38197 | 0.143303 | ||||||||
\(94\) | 4.32624 | 0.446217 | ||||||||
\(95\) | 1.23607 | 0.126818 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 18.6525 | 1.89387 | 0.946936 | − | 0.321422i | \(-0.104161\pi\) | ||||
0.946936 | + | 0.321422i | \(0.104161\pi\) | |||||||
\(98\) | −3.47214 | −0.350739 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −15.6180 | −1.55405 | −0.777026 | − | 0.629468i | \(-0.783273\pi\) | ||||
−0.777026 | + | 0.629468i | \(0.783273\pi\) | |||||||
\(102\) | 6.09017 | 0.603017 | ||||||||
\(103\) | 6.76393 | 0.666470 | 0.333235 | − | 0.942844i | \(-0.391860\pi\) | ||||
0.333235 | + | 0.942844i | \(0.391860\pi\) | |||||||
\(104\) | 3.38197 | 0.331629 | ||||||||
\(105\) | 3.23607 | 0.315808 | ||||||||
\(106\) | −8.47214 | −0.822887 | ||||||||
\(107\) | −6.29180 | −0.608251 | −0.304125 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304125 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.47214 | 0.236788 | 0.118394 | − | 0.992967i | \(-0.462225\pi\) | ||||
0.118394 | + | 0.992967i | \(0.462225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.38197 | 0.605749 | ||||||||
\(112\) | 3.23607 | 0.305780 | ||||||||
\(113\) | −19.5623 | −1.84027 | −0.920133 | − | 0.391605i | \(-0.871920\pi\) | ||||
−0.920133 | + | 0.391605i | \(0.871920\pi\) | |||||||
\(114\) | −1.23607 | −0.115768 | ||||||||
\(115\) | −6.85410 | −0.639148 | ||||||||
\(116\) | 2.61803 | 0.243078 | ||||||||
\(117\) | −3.38197 | −0.312663 | ||||||||
\(118\) | −14.0902 | −1.29711 | ||||||||
\(119\) | 19.7082 | 1.80665 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.23607 | 0.111452 | ||||||||
\(124\) | −1.38197 | −0.124104 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.23607 | −0.288292 | ||||||||
\(127\) | −14.6525 | −1.30020 | −0.650098 | − | 0.759850i | \(-0.725272\pi\) | ||||
−0.650098 | + | 0.759850i | \(0.725272\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.0901699 | −0.00793902 | ||||||||
\(130\) | −3.38197 | −0.296618 | ||||||||
\(131\) | 3.38197 | 0.295484 | 0.147742 | − | 0.989026i | \(-0.452800\pi\) | ||||
0.147742 | + | 0.989026i | \(0.452800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | −0.346844 | ||||||||
\(134\) | 5.09017 | 0.439724 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −6.09017 | −0.522228 | ||||||||
\(137\) | −12.7984 | −1.09344 | −0.546719 | − | 0.837316i | \(-0.684124\pi\) | ||||
−0.546719 | + | 0.837316i | \(0.684124\pi\) | |||||||
\(138\) | 6.85410 | 0.583460 | ||||||||
\(139\) | −8.76393 | −0.743347 | −0.371674 | − | 0.928364i | \(-0.621216\pi\) | ||||
−0.371674 | + | 0.928364i | \(0.621216\pi\) | |||||||
\(140\) | −3.23607 | −0.273498 | ||||||||
\(141\) | 4.32624 | 0.364335 | ||||||||
\(142\) | −10.4721 | −0.878802 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −2.61803 | −0.217416 | ||||||||
\(146\) | 13.4164 | 1.11035 | ||||||||
\(147\) | −3.47214 | −0.286377 | ||||||||
\(148\) | −6.38197 | −0.524594 | ||||||||
\(149\) | 7.61803 | 0.624094 | 0.312047 | − | 0.950067i | \(-0.398985\pi\) | ||||
0.312047 | + | 0.950067i | \(0.398985\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −20.9443 | −1.70442 | −0.852210 | − | 0.523199i | \(-0.824738\pi\) | ||||
−0.852210 | + | 0.523199i | \(0.824738\pi\) | |||||||
\(152\) | 1.23607 | 0.100258 | ||||||||
\(153\) | 6.09017 | 0.492361 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.38197 | 0.111002 | ||||||||
\(156\) | 3.38197 | 0.270774 | ||||||||
\(157\) | −9.27051 | −0.739867 | −0.369934 | − | 0.929058i | \(-0.620620\pi\) | ||||
−0.369934 | + | 0.929058i | \(0.620620\pi\) | |||||||
\(158\) | −4.09017 | −0.325396 | ||||||||
\(159\) | −8.47214 | −0.671884 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 22.1803 | 1.74806 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 0.854102 | 0.0668984 | 0.0334492 | − | 0.999440i | \(-0.489351\pi\) | ||||
0.0334492 | + | 0.999440i | \(0.489351\pi\) | |||||||
\(164\) | −1.23607 | −0.0965207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 13.2705 | 1.02690 | 0.513451 | − | 0.858119i | \(-0.328367\pi\) | ||||
0.513451 | + | 0.858119i | \(0.328367\pi\) | |||||||
\(168\) | 3.23607 | 0.249668 | ||||||||
\(169\) | −1.56231 | −0.120177 | ||||||||
\(170\) | 6.09017 | 0.467095 | ||||||||
\(171\) | −1.23607 | −0.0945245 | ||||||||
\(172\) | 0.0901699 | 0.00687539 | ||||||||
\(173\) | 9.52786 | 0.724390 | 0.362195 | − | 0.932102i | \(-0.382027\pi\) | ||||
0.362195 | + | 0.932102i | \(0.382027\pi\) | |||||||
\(174\) | 2.61803 | 0.198473 | ||||||||
\(175\) | 3.23607 | 0.244624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.0902 | −1.05908 | ||||||||
\(178\) | −17.2361 | −1.29190 | ||||||||
\(179\) | 18.1459 | 1.35629 | 0.678144 | − | 0.734929i | \(-0.262785\pi\) | ||||
0.678144 | + | 0.734929i | \(0.262785\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 21.8885 | 1.62696 | 0.813481 | − | 0.581591i | \(-0.197570\pi\) | ||||
0.813481 | + | 0.581591i | \(0.197570\pi\) | |||||||
\(182\) | 10.9443 | 0.811243 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.85410 | −0.505291 | ||||||||
\(185\) | 6.38197 | 0.469211 | ||||||||
\(186\) | −1.38197 | −0.101331 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.32624 | −0.315523 | ||||||||
\(189\) | −3.23607 | −0.235389 | ||||||||
\(190\) | −1.23607 | −0.0896738 | ||||||||
\(191\) | 9.23607 | 0.668298 | 0.334149 | − | 0.942520i | \(-0.391551\pi\) | ||||
0.334149 | + | 0.942520i | \(0.391551\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 20.9443 | 1.50760 | 0.753801 | − | 0.657103i | \(-0.228218\pi\) | ||||
0.753801 | + | 0.657103i | \(0.228218\pi\) | |||||||
\(194\) | −18.6525 | −1.33917 | ||||||||
\(195\) | −3.38197 | −0.242188 | ||||||||
\(196\) | 3.47214 | 0.248010 | ||||||||
\(197\) | −10.9443 | −0.779747 | −0.389874 | − | 0.920868i | \(-0.627481\pi\) | ||||
−0.389874 | + | 0.920868i | \(0.627481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9787 | 1.84158 | 0.920791 | − | 0.390056i | \(-0.127544\pi\) | ||||
0.920791 | + | 0.390056i | \(0.127544\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 5.09017 | 0.359033 | ||||||||
\(202\) | 15.6180 | 1.09888 | ||||||||
\(203\) | 8.47214 | 0.594627 | ||||||||
\(204\) | −6.09017 | −0.426397 | ||||||||
\(205\) | 1.23607 | 0.0863307 | ||||||||
\(206\) | −6.76393 | −0.471265 | ||||||||
\(207\) | 6.85410 | 0.476393 | ||||||||
\(208\) | −3.38197 | −0.234497 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.23607 | −0.223310 | ||||||||
\(211\) | 25.2361 | 1.73732 | 0.868661 | − | 0.495406i | \(-0.164981\pi\) | ||||
0.868661 | + | 0.495406i | \(0.164981\pi\) | |||||||
\(212\) | 8.47214 | 0.581869 | ||||||||
\(213\) | −10.4721 | −0.717539 | ||||||||
\(214\) | 6.29180 | 0.430098 | ||||||||
\(215\) | −0.0901699 | −0.00614954 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.47214 | −0.303588 | ||||||||
\(218\) | −2.47214 | −0.167434 | ||||||||
\(219\) | 13.4164 | 0.906597 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.5967 | −1.38549 | ||||||||
\(222\) | −6.38197 | −0.428330 | ||||||||
\(223\) | 7.23607 | 0.484563 | 0.242281 | − | 0.970206i | \(-0.422104\pi\) | ||||
0.242281 | + | 0.970206i | \(0.422104\pi\) | |||||||
\(224\) | −3.23607 | −0.216219 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 19.5623 | 1.30127 | ||||||||
\(227\) | −20.3607 | −1.35139 | −0.675693 | − | 0.737183i | \(-0.736155\pi\) | ||||
−0.675693 | + | 0.737183i | \(0.736155\pi\) | |||||||
\(228\) | 1.23607 | 0.0818606 | ||||||||
\(229\) | 0.763932 | 0.0504820 | 0.0252410 | − | 0.999681i | \(-0.491965\pi\) | ||||
0.0252410 | + | 0.999681i | \(0.491965\pi\) | |||||||
\(230\) | 6.85410 | 0.451946 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.61803 | −0.171882 | ||||||||
\(233\) | 4.43769 | 0.290723 | 0.145362 | − | 0.989379i | \(-0.453565\pi\) | ||||
0.145362 | + | 0.989379i | \(0.453565\pi\) | |||||||
\(234\) | 3.38197 | 0.221086 | ||||||||
\(235\) | 4.32624 | 0.282213 | ||||||||
\(236\) | 14.0902 | 0.917192 | ||||||||
\(237\) | −4.09017 | −0.265685 | ||||||||
\(238\) | −19.7082 | −1.27749 | ||||||||
\(239\) | 3.23607 | 0.209324 | 0.104662 | − | 0.994508i | \(-0.466624\pi\) | ||||
0.104662 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 23.8885 | 1.53880 | 0.769398 | − | 0.638769i | \(-0.220556\pi\) | ||||
0.769398 | + | 0.638769i | \(0.220556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.47214 | −0.221827 | ||||||||
\(246\) | −1.23607 | −0.0788088 | ||||||||
\(247\) | 4.18034 | 0.265989 | ||||||||
\(248\) | 1.38197 | 0.0877549 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 8.38197 | 0.529065 | 0.264533 | − | 0.964377i | \(-0.414782\pi\) | ||||
0.264533 | + | 0.964377i | \(0.414782\pi\) | |||||||
\(252\) | 3.23607 | 0.203853 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.6525 | 0.919378 | ||||||||
\(255\) | 6.09017 | 0.381381 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.3607 | 1.89385 | 0.946924 | − | 0.321459i | \(-0.104173\pi\) | ||||
0.946924 | + | 0.321459i | \(0.104173\pi\) | |||||||
\(258\) | 0.0901699 | 0.00561374 | ||||||||
\(259\) | −20.6525 | −1.28328 | ||||||||
\(260\) | 3.38197 | 0.209741 | ||||||||
\(261\) | 2.61803 | 0.162052 | ||||||||
\(262\) | −3.38197 | −0.208939 | ||||||||
\(263\) | −6.85410 | −0.422642 | −0.211321 | − | 0.977417i | \(-0.567777\pi\) | ||||
−0.211321 | + | 0.977417i | \(0.567777\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.47214 | −0.520439 | ||||||||
\(266\) | 4.00000 | 0.245256 | ||||||||
\(267\) | −17.2361 | −1.05483 | ||||||||
\(268\) | −5.09017 | −0.310932 | ||||||||
\(269\) | 3.20163 | 0.195207 | 0.0976033 | − | 0.995225i | \(-0.468882\pi\) | ||||
0.0976033 | + | 0.995225i | \(0.468882\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 6.38197 | 0.387677 | 0.193838 | − | 0.981033i | \(-0.437906\pi\) | ||||
0.193838 | + | 0.981033i | \(0.437906\pi\) | |||||||
\(272\) | 6.09017 | 0.369271 | ||||||||
\(273\) | 10.9443 | 0.662377 | ||||||||
\(274\) | 12.7984 | 0.773178 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.85410 | −0.412568 | ||||||||
\(277\) | 23.5066 | 1.41237 | 0.706187 | − | 0.708026i | \(-0.250414\pi\) | ||||
0.706187 | + | 0.708026i | \(0.250414\pi\) | |||||||
\(278\) | 8.76393 | 0.525626 | ||||||||
\(279\) | −1.38197 | −0.0827361 | ||||||||
\(280\) | 3.23607 | 0.193392 | ||||||||
\(281\) | 7.52786 | 0.449075 | 0.224537 | − | 0.974465i | \(-0.427913\pi\) | ||||
0.224537 | + | 0.974465i | \(0.427913\pi\) | |||||||
\(282\) | −4.32624 | −0.257624 | ||||||||
\(283\) | 22.3262 | 1.32716 | 0.663579 | − | 0.748107i | \(-0.269037\pi\) | ||||
0.663579 | + | 0.748107i | \(0.269037\pi\) | |||||||
\(284\) | 10.4721 | 0.621407 | ||||||||
\(285\) | −1.23607 | −0.0732183 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 20.0902 | 1.18177 | ||||||||
\(290\) | 2.61803 | 0.153736 | ||||||||
\(291\) | −18.6525 | −1.09343 | ||||||||
\(292\) | −13.4164 | −0.785136 | ||||||||
\(293\) | 20.0000 | 1.16841 | 0.584206 | − | 0.811605i | \(-0.301406\pi\) | ||||
0.584206 | + | 0.811605i | \(0.301406\pi\) | |||||||
\(294\) | 3.47214 | 0.202499 | ||||||||
\(295\) | −14.0902 | −0.820361 | ||||||||
\(296\) | 6.38197 | 0.370944 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.61803 | −0.441301 | ||||||||
\(299\) | −23.1803 | −1.34055 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0.291796 | 0.0168188 | ||||||||
\(302\) | 20.9443 | 1.20521 | ||||||||
\(303\) | 15.6180 | 0.897233 | ||||||||
\(304\) | −1.23607 | −0.0708934 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.09017 | −0.348152 | ||||||||
\(307\) | 33.4508 | 1.90914 | 0.954570 | − | 0.297985i | \(-0.0963147\pi\) | ||||
0.954570 | + | 0.297985i | \(0.0963147\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.76393 | −0.384787 | ||||||||
\(310\) | −1.38197 | −0.0784904 | ||||||||
\(311\) | 9.23607 | 0.523729 | 0.261865 | − | 0.965105i | \(-0.415663\pi\) | ||||
0.261865 | + | 0.965105i | \(0.415663\pi\) | |||||||
\(312\) | −3.38197 | −0.191466 | ||||||||
\(313\) | 8.47214 | 0.478873 | 0.239437 | − | 0.970912i | \(-0.423037\pi\) | ||||
0.239437 | + | 0.970912i | \(0.423037\pi\) | |||||||
\(314\) | 9.27051 | 0.523165 | ||||||||
\(315\) | −3.23607 | −0.182332 | ||||||||
\(316\) | 4.09017 | 0.230090 | ||||||||
\(317\) | −27.4164 | −1.53986 | −0.769929 | − | 0.638129i | \(-0.779709\pi\) | ||||
−0.769929 | + | 0.638129i | \(0.779709\pi\) | |||||||
\(318\) | 8.47214 | 0.475094 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 6.29180 | 0.351174 | ||||||||
\(322\) | −22.1803 | −1.23606 | ||||||||
\(323\) | −7.52786 | −0.418862 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.38197 | −0.187598 | ||||||||
\(326\) | −0.854102 | −0.0473043 | ||||||||
\(327\) | −2.47214 | −0.136709 | ||||||||
\(328\) | 1.23607 | 0.0682504 | ||||||||
\(329\) | −14.0000 | −0.771845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.23607 | 0.507660 | 0.253830 | − | 0.967249i | \(-0.418310\pi\) | ||||
0.253830 | + | 0.967249i | \(0.418310\pi\) | |||||||
\(332\) | −4.00000 | −0.219529 | ||||||||
\(333\) | −6.38197 | −0.349730 | ||||||||
\(334\) | −13.2705 | −0.726130 | ||||||||
\(335\) | 5.09017 | 0.278106 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | 15.2361 | 0.829962 | 0.414981 | − | 0.909830i | \(-0.363788\pi\) | ||||
0.414981 | + | 0.909830i | \(0.363788\pi\) | |||||||
\(338\) | 1.56231 | 0.0849782 | ||||||||
\(339\) | 19.5623 | 1.06248 | ||||||||
\(340\) | −6.09017 | −0.330286 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.23607 | 0.0668389 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | −0.0901699 | −0.00486164 | ||||||||
\(345\) | 6.85410 | 0.369012 | ||||||||
\(346\) | −9.52786 | −0.512221 | ||||||||
\(347\) | −35.8885 | −1.92660 | −0.963299 | − | 0.268431i | \(-0.913495\pi\) | ||||
−0.963299 | + | 0.268431i | \(0.913495\pi\) | |||||||
\(348\) | −2.61803 | −0.140341 | ||||||||
\(349\) | 11.4164 | 0.611106 | 0.305553 | − | 0.952175i | \(-0.401159\pi\) | ||||
0.305553 | + | 0.952175i | \(0.401159\pi\) | |||||||
\(350\) | −3.23607 | −0.172975 | ||||||||
\(351\) | 3.38197 | 0.180516 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.6180 | 1.25706 | 0.628531 | − | 0.777785i | \(-0.283657\pi\) | ||||
0.628531 | + | 0.777785i | \(0.283657\pi\) | |||||||
\(354\) | 14.0902 | 0.748884 | ||||||||
\(355\) | −10.4721 | −0.555803 | ||||||||
\(356\) | 17.2361 | 0.913510 | ||||||||
\(357\) | −19.7082 | −1.04307 | ||||||||
\(358\) | −18.1459 | −0.959041 | ||||||||
\(359\) | 12.1803 | 0.642854 | 0.321427 | − | 0.946934i | \(-0.395838\pi\) | ||||
0.321427 | + | 0.946934i | \(0.395838\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | −21.8885 | −1.15044 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.9443 | −0.573636 | ||||||||
\(365\) | 13.4164 | 0.702247 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.7639 | −1.39707 | −0.698533 | − | 0.715578i | \(-0.746163\pi\) | ||||
−0.698533 | + | 0.715578i | \(0.746163\pi\) | |||||||
\(368\) | 6.85410 | 0.357295 | ||||||||
\(369\) | −1.23607 | −0.0643471 | ||||||||
\(370\) | −6.38197 | −0.331783 | ||||||||
\(371\) | 27.4164 | 1.42339 | ||||||||
\(372\) | 1.38197 | 0.0716516 | ||||||||
\(373\) | 11.5279 | 0.596890 | 0.298445 | − | 0.954427i | \(-0.403532\pi\) | ||||
0.298445 | + | 0.954427i | \(0.403532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 4.32624 | 0.223109 | ||||||||
\(377\) | −8.85410 | −0.456009 | ||||||||
\(378\) | 3.23607 | 0.166445 | ||||||||
\(379\) | −12.3607 | −0.634925 | −0.317463 | − | 0.948271i | \(-0.602831\pi\) | ||||
−0.317463 | + | 0.948271i | \(0.602831\pi\) | |||||||
\(380\) | 1.23607 | 0.0634089 | ||||||||
\(381\) | 14.6525 | 0.750669 | ||||||||
\(382\) | −9.23607 | −0.472558 | ||||||||
\(383\) | −0.326238 | −0.0166700 | −0.00833499 | − | 0.999965i | \(-0.502653\pi\) | ||||
−0.00833499 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.9443 | −1.06604 | ||||||||
\(387\) | 0.0901699 | 0.00458360 | ||||||||
\(388\) | 18.6525 | 0.946936 | ||||||||
\(389\) | 6.85410 | 0.347517 | 0.173758 | − | 0.984788i | \(-0.444409\pi\) | ||||
0.173758 | + | 0.984788i | \(0.444409\pi\) | |||||||
\(390\) | 3.38197 | 0.171253 | ||||||||
\(391\) | 41.7426 | 2.11102 | ||||||||
\(392\) | −3.47214 | −0.175369 | ||||||||
\(393\) | −3.38197 | −0.170598 | ||||||||
\(394\) | 10.9443 | 0.551364 | ||||||||
\(395\) | −4.09017 | −0.205799 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20163 | 0.110496 | 0.0552482 | − | 0.998473i | \(-0.482405\pi\) | ||||
0.0552482 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(398\) | −25.9787 | −1.30220 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 22.0689 | 1.10207 | 0.551034 | − | 0.834483i | \(-0.314234\pi\) | ||||
0.551034 | + | 0.834483i | \(0.314234\pi\) | |||||||
\(402\) | −5.09017 | −0.253875 | ||||||||
\(403\) | 4.67376 | 0.232817 | ||||||||
\(404\) | −15.6180 | −0.777026 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −8.47214 | −0.420465 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.09017 | 0.301508 | ||||||||
\(409\) | −12.9787 | −0.641756 | −0.320878 | − | 0.947121i | \(-0.603978\pi\) | ||||
−0.320878 | + | 0.947121i | \(0.603978\pi\) | |||||||
\(410\) | −1.23607 | −0.0610450 | ||||||||
\(411\) | 12.7984 | 0.631297 | ||||||||
\(412\) | 6.76393 | 0.333235 | ||||||||
\(413\) | 45.5967 | 2.24367 | ||||||||
\(414\) | −6.85410 | −0.336861 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 3.38197 | 0.165815 | ||||||||
\(417\) | 8.76393 | 0.429172 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.8541 | 1.11650 | 0.558248 | − | 0.829674i | \(-0.311474\pi\) | ||||
0.558248 | + | 0.829674i | \(0.311474\pi\) | |||||||
\(420\) | 3.23607 | 0.157904 | ||||||||
\(421\) | −2.47214 | −0.120485 | −0.0602423 | − | 0.998184i | \(-0.519187\pi\) | ||||
−0.0602423 | + | 0.998184i | \(0.519187\pi\) | |||||||
\(422\) | −25.2361 | −1.22847 | ||||||||
\(423\) | −4.32624 | −0.210349 | ||||||||
\(424\) | −8.47214 | −0.411443 | ||||||||
\(425\) | 6.09017 | 0.295417 | ||||||||
\(426\) | 10.4721 | 0.507377 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.29180 | −0.304125 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0901699 | 0.00434838 | ||||||||
\(431\) | −22.3607 | −1.07708 | −0.538538 | − | 0.842601i | \(-0.681023\pi\) | ||||
−0.538538 | + | 0.842601i | \(0.681023\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.8328 | −1.09728 | −0.548638 | − | 0.836060i | \(-0.684853\pi\) | ||||
−0.548638 | + | 0.836060i | \(0.684853\pi\) | |||||||
\(434\) | 4.47214 | 0.214669 | ||||||||
\(435\) | 2.61803 | 0.125525 | ||||||||
\(436\) | 2.47214 | 0.118394 | ||||||||
\(437\) | −8.47214 | −0.405277 | ||||||||
\(438\) | −13.4164 | −0.641061 | ||||||||
\(439\) | −1.67376 | −0.0798843 | −0.0399422 | − | 0.999202i | \(-0.512717\pi\) | ||||
−0.0399422 | + | 0.999202i | \(0.512717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47214 | 0.165340 | ||||||||
\(442\) | 20.5967 | 0.979687 | ||||||||
\(443\) | −18.6525 | −0.886206 | −0.443103 | − | 0.896471i | \(-0.646122\pi\) | ||||
−0.443103 | + | 0.896471i | \(0.646122\pi\) | |||||||
\(444\) | 6.38197 | 0.302875 | ||||||||
\(445\) | −17.2361 | −0.817068 | ||||||||
\(446\) | −7.23607 | −0.342638 | ||||||||
\(447\) | −7.61803 | −0.360321 | ||||||||
\(448\) | 3.23607 | 0.152890 | ||||||||
\(449\) | −11.1246 | −0.525003 | −0.262501 | − | 0.964932i | \(-0.584547\pi\) | ||||
−0.262501 | + | 0.964932i | \(0.584547\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −19.5623 | −0.920133 | ||||||||
\(453\) | 20.9443 | 0.984048 | ||||||||
\(454\) | 20.3607 | 0.955574 | ||||||||
\(455\) | 10.9443 | 0.513075 | ||||||||
\(456\) | −1.23607 | −0.0578842 | ||||||||
\(457\) | −4.65248 | −0.217634 | −0.108817 | − | 0.994062i | \(-0.534706\pi\) | ||||
−0.108817 | + | 0.994062i | \(0.534706\pi\) | |||||||
\(458\) | −0.763932 | −0.0356962 | ||||||||
\(459\) | −6.09017 | −0.284265 | ||||||||
\(460\) | −6.85410 | −0.319574 | ||||||||
\(461\) | −23.2148 | −1.08122 | −0.540610 | − | 0.841273i | \(-0.681807\pi\) | ||||
−0.540610 | + | 0.841273i | \(0.681807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8885 | 0.552507 | 0.276254 | − | 0.961085i | \(-0.410907\pi\) | ||||
0.276254 | + | 0.961085i | \(0.410907\pi\) | |||||||
\(464\) | 2.61803 | 0.121539 | ||||||||
\(465\) | −1.38197 | −0.0640871 | ||||||||
\(466\) | −4.43769 | −0.205572 | ||||||||
\(467\) | 28.5410 | 1.32072 | 0.660360 | − | 0.750949i | \(-0.270404\pi\) | ||||
0.660360 | + | 0.750949i | \(0.270404\pi\) | |||||||
\(468\) | −3.38197 | −0.156331 | ||||||||
\(469\) | −16.4721 | −0.760613 | ||||||||
\(470\) | −4.32624 | −0.199554 | ||||||||
\(471\) | 9.27051 | 0.427163 | ||||||||
\(472\) | −14.0902 | −0.648553 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.09017 | 0.187868 | ||||||||
\(475\) | −1.23607 | −0.0567147 | ||||||||
\(476\) | 19.7082 | 0.903324 | ||||||||
\(477\) | 8.47214 | 0.387912 | ||||||||
\(478\) | −3.23607 | −0.148014 | ||||||||
\(479\) | −12.7639 | −0.583199 | −0.291599 | − | 0.956541i | \(-0.594187\pi\) | ||||
−0.291599 | + | 0.956541i | \(0.594187\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 21.5836 | 0.984127 | ||||||||
\(482\) | −23.8885 | −1.08809 | ||||||||
\(483\) | −22.1803 | −1.00924 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.6525 | −0.846965 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 11.4164 | 0.517327 | 0.258663 | − | 0.965968i | \(-0.416718\pi\) | ||||
0.258663 | + | 0.965968i | \(0.416718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.854102 | −0.0386238 | ||||||||
\(490\) | 3.47214 | 0.156855 | ||||||||
\(491\) | −28.0344 | −1.26518 | −0.632588 | − | 0.774488i | \(-0.718007\pi\) | ||||
−0.632588 | + | 0.774488i | \(0.718007\pi\) | |||||||
\(492\) | 1.23607 | 0.0557262 | ||||||||
\(493\) | 15.9443 | 0.718094 | ||||||||
\(494\) | −4.18034 | −0.188082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.38197 | −0.0620521 | ||||||||
\(497\) | 33.8885 | 1.52011 | ||||||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | −32.4721 | −1.45365 | −0.726826 | − | 0.686821i | \(-0.759005\pi\) | ||||
−0.726826 | + | 0.686821i | \(0.759005\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −13.2705 | −0.592883 | ||||||||
\(502\) | −8.38197 | −0.374105 | ||||||||
\(503\) | 24.3262 | 1.08465 | 0.542327 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542327 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(504\) | −3.23607 | −0.144146 | ||||||||
\(505\) | 15.6180 | 0.694993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.56231 | 0.0693844 | ||||||||
\(508\) | −14.6525 | −0.650098 | ||||||||
\(509\) | 8.79837 | 0.389981 | 0.194991 | − | 0.980805i | \(-0.437532\pi\) | ||||
0.194991 | + | 0.980805i | \(0.437532\pi\) | |||||||
\(510\) | −6.09017 | −0.269677 | ||||||||
\(511\) | −43.4164 | −1.92063 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.23607 | 0.0545737 | ||||||||
\(514\) | −30.3607 | −1.33915 | ||||||||
\(515\) | −6.76393 | −0.298054 | ||||||||
\(516\) | −0.0901699 | −0.00396951 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 20.6525 | 0.907418 | ||||||||
\(519\) | −9.52786 | −0.418227 | ||||||||
\(520\) | −3.38197 | −0.148309 | ||||||||
\(521\) | −2.36068 | −0.103423 | −0.0517116 | − | 0.998662i | \(-0.516468\pi\) | ||||
−0.0517116 | + | 0.998662i | \(0.516468\pi\) | |||||||
\(522\) | −2.61803 | −0.114588 | ||||||||
\(523\) | −38.8328 | −1.69804 | −0.849020 | − | 0.528360i | \(-0.822807\pi\) | ||||
−0.849020 | + | 0.528360i | \(0.822807\pi\) | |||||||
\(524\) | 3.38197 | 0.147742 | ||||||||
\(525\) | −3.23607 | −0.141234 | ||||||||
\(526\) | 6.85410 | 0.298853 | ||||||||
\(527\) | −8.41641 | −0.366624 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.9787 | 1.04255 | ||||||||
\(530\) | 8.47214 | 0.368006 | ||||||||
\(531\) | 14.0902 | 0.611461 | ||||||||
\(532\) | −4.00000 | −0.173422 | ||||||||
\(533\) | 4.18034 | 0.181071 | ||||||||
\(534\) | 17.2361 | 0.745878 | ||||||||
\(535\) | 6.29180 | 0.272018 | ||||||||
\(536\) | 5.09017 | 0.219862 | ||||||||
\(537\) | −18.1459 | −0.783053 | ||||||||
\(538\) | −3.20163 | −0.138032 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −26.0689 | −1.12079 | −0.560394 | − | 0.828226i | \(-0.689350\pi\) | ||||
−0.560394 | + | 0.828226i | \(0.689350\pi\) | |||||||
\(542\) | −6.38197 | −0.274129 | ||||||||
\(543\) | −21.8885 | −0.939327 | ||||||||
\(544\) | −6.09017 | −0.261114 | ||||||||
\(545\) | −2.47214 | −0.105895 | ||||||||
\(546\) | −10.9443 | −0.468372 | ||||||||
\(547\) | −34.3262 | −1.46768 | −0.733842 | − | 0.679320i | \(-0.762275\pi\) | ||||
−0.733842 | + | 0.679320i | \(0.762275\pi\) | |||||||
\(548\) | −12.7984 | −0.546719 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.23607 | −0.137861 | ||||||||
\(552\) | 6.85410 | 0.291730 | ||||||||
\(553\) | 13.2361 | 0.562855 | ||||||||
\(554\) | −23.5066 | −0.998699 | ||||||||
\(555\) | −6.38197 | −0.270899 | ||||||||
\(556\) | −8.76393 | −0.371674 | ||||||||
\(557\) | 35.1246 | 1.48828 | 0.744139 | − | 0.668025i | \(-0.232860\pi\) | ||||
0.744139 | + | 0.668025i | \(0.232860\pi\) | |||||||
\(558\) | 1.38197 | 0.0585033 | ||||||||
\(559\) | −0.304952 | −0.0128981 | ||||||||
\(560\) | −3.23607 | −0.136749 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.52786 | −0.317544 | ||||||||
\(563\) | −17.0557 | −0.718813 | −0.359407 | − | 0.933181i | \(-0.617021\pi\) | ||||
−0.359407 | + | 0.933181i | \(0.617021\pi\) | |||||||
\(564\) | 4.32624 | 0.182167 | ||||||||
\(565\) | 19.5623 | 0.822992 | ||||||||
\(566\) | −22.3262 | −0.938442 | ||||||||
\(567\) | 3.23607 | 0.135902 | ||||||||
\(568\) | −10.4721 | −0.439401 | ||||||||
\(569\) | 25.4164 | 1.06551 | 0.532756 | − | 0.846269i | \(-0.321156\pi\) | ||||
0.532756 | + | 0.846269i | \(0.321156\pi\) | |||||||
\(570\) | 1.23607 | 0.0517732 | ||||||||
\(571\) | 28.3607 | 1.18686 | 0.593429 | − | 0.804887i | \(-0.297774\pi\) | ||||
0.593429 | + | 0.804887i | \(0.297774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.23607 | −0.385842 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 6.85410 | 0.285836 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.0557 | 0.710039 | 0.355020 | − | 0.934859i | \(-0.384474\pi\) | ||||
0.355020 | + | 0.934859i | \(0.384474\pi\) | |||||||
\(578\) | −20.0902 | −0.835641 | ||||||||
\(579\) | −20.9443 | −0.870414 | ||||||||
\(580\) | −2.61803 | −0.108708 | ||||||||
\(581\) | −12.9443 | −0.537019 | ||||||||
\(582\) | 18.6525 | 0.773170 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.4164 | 0.555175 | ||||||||
\(585\) | 3.38197 | 0.139827 | ||||||||
\(586\) | −20.0000 | −0.826192 | ||||||||
\(587\) | −26.2918 | −1.08518 | −0.542589 | − | 0.839998i | \(-0.682556\pi\) | ||||
−0.542589 | + | 0.839998i | \(0.682556\pi\) | |||||||
\(588\) | −3.47214 | −0.143188 | ||||||||
\(589\) | 1.70820 | 0.0703853 | ||||||||
\(590\) | 14.0902 | 0.580083 | ||||||||
\(591\) | 10.9443 | 0.450187 | ||||||||
\(592\) | −6.38197 | −0.262297 | ||||||||
\(593\) | 17.6738 | 0.725774 | 0.362887 | − | 0.931833i | \(-0.381791\pi\) | ||||
0.362887 | + | 0.931833i | \(0.381791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.7082 | −0.807958 | ||||||||
\(596\) | 7.61803 | 0.312047 | ||||||||
\(597\) | −25.9787 | −1.06324 | ||||||||
\(598\) | 23.1803 | 0.947915 | ||||||||
\(599\) | 18.1803 | 0.742829 | 0.371414 | − | 0.928467i | \(-0.378873\pi\) | ||||
0.371414 | + | 0.928467i | \(0.378873\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 18.9443 | 0.772753 | 0.386376 | − | 0.922341i | \(-0.373727\pi\) | ||||
0.386376 | + | 0.922341i | \(0.373727\pi\) | |||||||
\(602\) | −0.291796 | −0.0118927 | ||||||||
\(603\) | −5.09017 | −0.207288 | ||||||||
\(604\) | −20.9443 | −0.852210 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.6180 | −0.634439 | ||||||||
\(607\) | 4.47214 | 0.181518 | 0.0907592 | − | 0.995873i | \(-0.471071\pi\) | ||||
0.0907592 | + | 0.995873i | \(0.471071\pi\) | |||||||
\(608\) | 1.23607 | 0.0501292 | ||||||||
\(609\) | −8.47214 | −0.343308 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6312 | 0.591915 | ||||||||
\(612\) | 6.09017 | 0.246181 | ||||||||
\(613\) | −6.00000 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(614\) | −33.4508 | −1.34997 | ||||||||
\(615\) | −1.23607 | −0.0498431 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.3607 | 1.06124 | 0.530621 | − | 0.847610i | \(-0.321959\pi\) | ||||
0.530621 | + | 0.847610i | \(0.321959\pi\) | |||||||
\(618\) | 6.76393 | 0.272085 | ||||||||
\(619\) | 9.52786 | 0.382957 | 0.191479 | − | 0.981497i | \(-0.438672\pi\) | ||||
0.191479 | + | 0.981497i | \(0.438672\pi\) | |||||||
\(620\) | 1.38197 | 0.0555011 | ||||||||
\(621\) | −6.85410 | −0.275046 | ||||||||
\(622\) | −9.23607 | −0.370333 | ||||||||
\(623\) | 55.7771 | 2.23466 | ||||||||
\(624\) | 3.38197 | 0.135387 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.47214 | −0.338615 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.27051 | −0.369934 | ||||||||
\(629\) | −38.8673 | −1.54974 | ||||||||
\(630\) | 3.23607 | 0.128928 | ||||||||
\(631\) | −5.67376 | −0.225869 | −0.112934 | − | 0.993602i | \(-0.536025\pi\) | ||||
−0.112934 | + | 0.993602i | \(0.536025\pi\) | |||||||
\(632\) | −4.09017 | −0.162698 | ||||||||
\(633\) | −25.2361 | −1.00304 | ||||||||
\(634\) | 27.4164 | 1.08884 | ||||||||
\(635\) | 14.6525 | 0.581466 | ||||||||
\(636\) | −8.47214 | −0.335942 | ||||||||
\(637\) | −11.7426 | −0.465261 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.4721 | 0.414271 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 12.1803 | 0.481095 | 0.240547 | − | 0.970637i | \(-0.422673\pi\) | ||||
0.240547 | + | 0.970637i | \(0.422673\pi\) | |||||||
\(642\) | −6.29180 | −0.248317 | ||||||||
\(643\) | −4.79837 | −0.189229 | −0.0946147 | − | 0.995514i | \(-0.530162\pi\) | ||||
−0.0946147 | + | 0.995514i | \(0.530162\pi\) | |||||||
\(644\) | 22.1803 | 0.874028 | ||||||||
\(645\) | 0.0901699 | 0.00355044 | ||||||||
\(646\) | 7.52786 | 0.296180 | ||||||||
\(647\) | −12.3820 | −0.486785 | −0.243393 | − | 0.969928i | \(-0.578260\pi\) | ||||
−0.243393 | + | 0.969928i | \(0.578260\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.38197 | 0.132652 | ||||||||
\(651\) | 4.47214 | 0.175277 | ||||||||
\(652\) | 0.854102 | 0.0334492 | ||||||||
\(653\) | 24.5410 | 0.960364 | 0.480182 | − | 0.877169i | \(-0.340571\pi\) | ||||
0.480182 | + | 0.877169i | \(0.340571\pi\) | |||||||
\(654\) | 2.47214 | 0.0966682 | ||||||||
\(655\) | −3.38197 | −0.132144 | ||||||||
\(656\) | −1.23607 | −0.0482603 | ||||||||
\(657\) | −13.4164 | −0.523424 | ||||||||
\(658\) | 14.0000 | 0.545777 | ||||||||
\(659\) | 15.4164 | 0.600538 | 0.300269 | − | 0.953855i | \(-0.402924\pi\) | ||||
0.300269 | + | 0.953855i | \(0.402924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.36068 | 0.325193 | 0.162596 | − | 0.986693i | \(-0.448013\pi\) | ||||
0.162596 | + | 0.986693i | \(0.448013\pi\) | |||||||
\(662\) | −9.23607 | −0.358970 | ||||||||
\(663\) | 20.5967 | 0.799911 | ||||||||
\(664\) | 4.00000 | 0.155230 | ||||||||
\(665\) | 4.00000 | 0.155113 | ||||||||
\(666\) | 6.38197 | 0.247296 | ||||||||
\(667\) | 17.9443 | 0.694805 | ||||||||
\(668\) | 13.2705 | 0.513451 | ||||||||
\(669\) | −7.23607 | −0.279763 | ||||||||
\(670\) | −5.09017 | −0.196650 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.23607 | 0.124834 | ||||||||
\(673\) | 15.7082 | 0.605507 | 0.302753 | − | 0.953069i | \(-0.402094\pi\) | ||||
0.302753 | + | 0.953069i | \(0.402094\pi\) | |||||||
\(674\) | −15.2361 | −0.586871 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −1.56231 | −0.0600887 | ||||||||
\(677\) | −27.2361 | −1.04677 | −0.523384 | − | 0.852097i | \(-0.675330\pi\) | ||||
−0.523384 | + | 0.852097i | \(0.675330\pi\) | |||||||
\(678\) | −19.5623 | −0.751286 | ||||||||
\(679\) | 60.3607 | 2.31643 | ||||||||
\(680\) | 6.09017 | 0.233547 | ||||||||
\(681\) | 20.3607 | 0.780223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.1246 | 0.808311 | 0.404155 | − | 0.914690i | \(-0.367565\pi\) | ||||
0.404155 | + | 0.914690i | \(0.367565\pi\) | |||||||
\(684\) | −1.23607 | −0.0472622 | ||||||||
\(685\) | 12.7984 | 0.489001 | ||||||||
\(686\) | 11.4164 | 0.435880 | ||||||||
\(687\) | −0.763932 | −0.0291458 | ||||||||
\(688\) | 0.0901699 | 0.00343770 | ||||||||
\(689\) | −28.6525 | −1.09157 | ||||||||
\(690\) | −6.85410 | −0.260931 | ||||||||
\(691\) | −20.6525 | −0.785657 | −0.392829 | − | 0.919612i | \(-0.628503\pi\) | ||||
−0.392829 | + | 0.919612i | \(0.628503\pi\) | |||||||
\(692\) | 9.52786 | 0.362195 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 35.8885 | 1.36231 | ||||||||
\(695\) | 8.76393 | 0.332435 | ||||||||
\(696\) | 2.61803 | 0.0992363 | ||||||||
\(697\) | −7.52786 | −0.285138 | ||||||||
\(698\) | −11.4164 | −0.432117 | ||||||||
\(699\) | −4.43769 | −0.167849 | ||||||||
\(700\) | 3.23607 | 0.122312 | ||||||||
\(701\) | 3.52786 | 0.133246 | 0.0666228 | − | 0.997778i | \(-0.478778\pi\) | ||||
0.0666228 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(702\) | −3.38197 | −0.127644 | ||||||||
\(703\) | 7.88854 | 0.297522 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.32624 | −0.162936 | ||||||||
\(706\) | −23.6180 | −0.888876 | ||||||||
\(707\) | −50.5410 | −1.90079 | ||||||||
\(708\) | −14.0902 | −0.529541 | ||||||||
\(709\) | −10.5836 | −0.397475 | −0.198738 | − | 0.980053i | \(-0.563684\pi\) | ||||
−0.198738 | + | 0.980053i | \(0.563684\pi\) | |||||||
\(710\) | 10.4721 | 0.393012 | ||||||||
\(711\) | 4.09017 | 0.153393 | ||||||||
\(712\) | −17.2361 | −0.645949 | ||||||||
\(713\) | −9.47214 | −0.354734 | ||||||||
\(714\) | 19.7082 | 0.737561 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.1459 | 0.678144 | ||||||||
\(717\) | −3.23607 | −0.120853 | ||||||||
\(718\) | −12.1803 | −0.454566 | ||||||||
\(719\) | 40.6525 | 1.51608 | 0.758041 | − | 0.652207i | \(-0.226157\pi\) | ||||
0.758041 | + | 0.652207i | \(0.226157\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 21.8885 | 0.815172 | ||||||||
\(722\) | 17.4721 | 0.650246 | ||||||||
\(723\) | −23.8885 | −0.888425 | ||||||||
\(724\) | 21.8885 | 0.813481 | ||||||||
\(725\) | 2.61803 | 0.0972313 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.1803 | −1.86109 | −0.930543 | − | 0.366183i | \(-0.880664\pi\) | ||||
−0.930543 | + | 0.366183i | \(0.880664\pi\) | |||||||
\(728\) | 10.9443 | 0.405622 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.4164 | −0.496564 | ||||||||
\(731\) | 0.549150 | 0.0203111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.3262 | −1.89578 | −0.947889 | − | 0.318601i | \(-0.896787\pi\) | ||||
−0.947889 | + | 0.318601i | \(0.896787\pi\) | |||||||
\(734\) | 26.7639 | 0.987875 | ||||||||
\(735\) | 3.47214 | 0.128072 | ||||||||
\(736\) | −6.85410 | −0.252646 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.23607 | 0.0455003 | ||||||||
\(739\) | −27.0132 | −0.993695 | −0.496847 | − | 0.867838i | \(-0.665509\pi\) | ||||
−0.496847 | + | 0.867838i | \(0.665509\pi\) | |||||||
\(740\) | 6.38197 | 0.234606 | ||||||||
\(741\) | −4.18034 | −0.153569 | ||||||||
\(742\) | −27.4164 | −1.00649 | ||||||||
\(743\) | −10.7984 | −0.396154 | −0.198077 | − | 0.980186i | \(-0.563470\pi\) | ||||
−0.198077 | + | 0.980186i | \(0.563470\pi\) | |||||||
\(744\) | −1.38197 | −0.0506653 | ||||||||
\(745\) | −7.61803 | −0.279103 | ||||||||
\(746\) | −11.5279 | −0.422065 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.3607 | −0.743963 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −29.0344 | −1.05948 | −0.529741 | − | 0.848160i | \(-0.677711\pi\) | ||||
−0.529741 | + | 0.848160i | \(0.677711\pi\) | |||||||
\(752\) | −4.32624 | −0.157762 | ||||||||
\(753\) | −8.38197 | −0.305456 | ||||||||
\(754\) | 8.85410 | 0.322447 | ||||||||
\(755\) | 20.9443 | 0.762240 | ||||||||
\(756\) | −3.23607 | −0.117695 | ||||||||
\(757\) | −53.8541 | −1.95736 | −0.978680 | − | 0.205389i | \(-0.934154\pi\) | ||||
−0.978680 | + | 0.205389i | \(0.934154\pi\) | |||||||
\(758\) | 12.3607 | 0.448960 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.23607 | −0.0448369 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | −14.6525 | −0.530803 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | 9.23607 | 0.334149 | ||||||||
\(765\) | −6.09017 | −0.220191 | ||||||||
\(766\) | 0.326238 | 0.0117875 | ||||||||
\(767\) | −47.6525 | −1.72063 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 24.4508 | 0.881720 | 0.440860 | − | 0.897576i | \(-0.354673\pi\) | ||||
0.440860 | + | 0.897576i | \(0.354673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.3607 | −1.09341 | ||||||||
\(772\) | 20.9443 | 0.753801 | ||||||||
\(773\) | 19.5967 | 0.704846 | 0.352423 | − | 0.935841i | \(-0.385358\pi\) | ||||
0.352423 | + | 0.935841i | \(0.385358\pi\) | |||||||
\(774\) | −0.0901699 | −0.00324109 | ||||||||
\(775\) | −1.38197 | −0.0496417 | ||||||||
\(776\) | −18.6525 | −0.669585 | ||||||||
\(777\) | 20.6525 | 0.740903 | ||||||||
\(778\) | −6.85410 | −0.245731 | ||||||||
\(779\) | 1.52786 | 0.0547414 | ||||||||
\(780\) | −3.38197 | −0.121094 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −41.7426 | −1.49271 | ||||||||
\(783\) | −2.61803 | −0.0935609 | ||||||||
\(784\) | 3.47214 | 0.124005 | ||||||||
\(785\) | 9.27051 | 0.330879 | ||||||||
\(786\) | 3.38197 | 0.120631 | ||||||||
\(787\) | −21.0344 | −0.749797 | −0.374898 | − | 0.927066i | \(-0.622322\pi\) | ||||
−0.374898 | + | 0.927066i | \(0.622322\pi\) | |||||||
\(788\) | −10.9443 | −0.389874 | ||||||||
\(789\) | 6.85410 | 0.244012 | ||||||||
\(790\) | 4.09017 | 0.145522 | ||||||||
\(791\) | −63.3050 | −2.25086 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2.20163 | −0.0781328 | ||||||||
\(795\) | 8.47214 | 0.300476 | ||||||||
\(796\) | 25.9787 | 0.920791 | ||||||||
\(797\) | −21.7082 | −0.768944 | −0.384472 | − | 0.923137i | \(-0.625616\pi\) | ||||
−0.384472 | + | 0.923137i | \(0.625616\pi\) | |||||||
\(798\) | −4.00000 | −0.141598 | ||||||||
\(799\) | −26.3475 | −0.932108 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 17.2361 | 0.609007 | ||||||||
\(802\) | −22.0689 | −0.779279 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.09017 | 0.179516 | ||||||||
\(805\) | −22.1803 | −0.781754 | ||||||||
\(806\) | −4.67376 | −0.164626 | ||||||||
\(807\) | −3.20163 | −0.112703 | ||||||||
\(808\) | 15.6180 | 0.549441 | ||||||||
\(809\) | 2.65248 | 0.0932561 | 0.0466280 | − | 0.998912i | \(-0.485152\pi\) | ||||
0.0466280 | + | 0.998912i | \(0.485152\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 4.58359 | 0.160952 | 0.0804758 | − | 0.996757i | \(-0.474356\pi\) | ||||
0.0804758 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(812\) | 8.47214 | 0.297314 | ||||||||
\(813\) | −6.38197 | −0.223825 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.854102 | −0.0299179 | ||||||||
\(816\) | −6.09017 | −0.213199 | ||||||||
\(817\) | −0.111456 | −0.00389936 | ||||||||
\(818\) | 12.9787 | 0.453790 | ||||||||
\(819\) | −10.9443 | −0.382424 | ||||||||
\(820\) | 1.23607 | 0.0431654 | ||||||||
\(821\) | 43.3050 | 1.51135 | 0.755677 | − | 0.654945i | \(-0.227308\pi\) | ||||
0.755677 | + | 0.654945i | \(0.227308\pi\) | |||||||
\(822\) | −12.7984 | −0.446395 | ||||||||
\(823\) | −12.7639 | −0.444923 | −0.222461 | − | 0.974942i | \(-0.571409\pi\) | ||||
−0.222461 | + | 0.974942i | \(0.571409\pi\) | |||||||
\(824\) | −6.76393 | −0.235633 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.5967 | −1.58651 | ||||||||
\(827\) | −30.2918 | −1.05335 | −0.526674 | − | 0.850067i | \(-0.676561\pi\) | ||||
−0.526674 | + | 0.850067i | \(0.676561\pi\) | |||||||
\(828\) | 6.85410 | 0.238197 | ||||||||
\(829\) | 35.5967 | 1.23633 | 0.618163 | − | 0.786050i | \(-0.287877\pi\) | ||||
0.618163 | + | 0.786050i | \(0.287877\pi\) | |||||||
\(830\) | −4.00000 | −0.138842 | ||||||||
\(831\) | −23.5066 | −0.815434 | ||||||||
\(832\) | −3.38197 | −0.117249 | ||||||||
\(833\) | 21.1459 | 0.732662 | ||||||||
\(834\) | −8.76393 | −0.303470 | ||||||||
\(835\) | −13.2705 | −0.459245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.38197 | 0.0477677 | ||||||||
\(838\) | −22.8541 | −0.789482 | ||||||||
\(839\) | −23.3475 | −0.806046 | −0.403023 | − | 0.915190i | \(-0.632041\pi\) | ||||
−0.403023 | + | 0.915190i | \(0.632041\pi\) | |||||||
\(840\) | −3.23607 | −0.111655 | ||||||||
\(841\) | −22.1459 | −0.763652 | ||||||||
\(842\) | 2.47214 | 0.0851954 | ||||||||
\(843\) | −7.52786 | −0.259273 | ||||||||
\(844\) | 25.2361 | 0.868661 | ||||||||
\(845\) | 1.56231 | 0.0537450 | ||||||||
\(846\) | 4.32624 | 0.148739 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.47214 | 0.290934 | ||||||||
\(849\) | −22.3262 | −0.766235 | ||||||||
\(850\) | −6.09017 | −0.208891 | ||||||||
\(851\) | −43.7426 | −1.49948 | ||||||||
\(852\) | −10.4721 | −0.358769 | ||||||||
\(853\) | 27.5279 | 0.942536 | 0.471268 | − | 0.881990i | \(-0.343796\pi\) | ||||
0.471268 | + | 0.881990i | \(0.343796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.23607 | 0.0422726 | ||||||||
\(856\) | 6.29180 | 0.215049 | ||||||||
\(857\) | −24.1591 | −0.825258 | −0.412629 | − | 0.910899i | \(-0.635389\pi\) | ||||
−0.412629 | + | 0.910899i | \(0.635389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.1246 | −0.652523 | −0.326262 | − | 0.945279i | \(-0.605789\pi\) | ||||
−0.326262 | + | 0.945279i | \(0.605789\pi\) | |||||||
\(860\) | −0.0901699 | −0.00307477 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 22.3607 | 0.761608 | ||||||||
\(863\) | −44.3394 | −1.50933 | −0.754665 | − | 0.656110i | \(-0.772201\pi\) | ||||
−0.754665 | + | 0.656110i | \(0.772201\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −9.52786 | −0.323957 | ||||||||
\(866\) | 22.8328 | 0.775891 | ||||||||
\(867\) | −20.0902 | −0.682298 | ||||||||
\(868\) | −4.47214 | −0.151794 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −2.61803 | −0.0887597 | ||||||||
\(871\) | 17.2148 | 0.583301 | ||||||||
\(872\) | −2.47214 | −0.0837171 | ||||||||
\(873\) | 18.6525 | 0.631291 | ||||||||
\(874\) | 8.47214 | 0.286574 | ||||||||
\(875\) | −3.23607 | −0.109399 | ||||||||
\(876\) | 13.4164 | 0.453298 | ||||||||
\(877\) | −18.9656 | −0.640421 | −0.320211 | − | 0.947346i | \(-0.603754\pi\) | ||||
−0.320211 | + | 0.947346i | \(0.603754\pi\) | |||||||
\(878\) | 1.67376 | 0.0564867 | ||||||||
\(879\) | −20.0000 | −0.674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.00000 | 0.269527 | 0.134763 | − | 0.990878i | \(-0.456973\pi\) | ||||
0.134763 | + | 0.990878i | \(0.456973\pi\) | |||||||
\(882\) | −3.47214 | −0.116913 | ||||||||
\(883\) | −4.67376 | −0.157285 | −0.0786423 | − | 0.996903i | \(-0.525058\pi\) | ||||
−0.0786423 | + | 0.996903i | \(0.525058\pi\) | |||||||
\(884\) | −20.5967 | −0.692744 | ||||||||
\(885\) | 14.0902 | 0.473636 | ||||||||
\(886\) | 18.6525 | 0.626642 | ||||||||
\(887\) | 42.4508 | 1.42536 | 0.712680 | − | 0.701489i | \(-0.247481\pi\) | ||||
0.712680 | + | 0.701489i | \(0.247481\pi\) | |||||||
\(888\) | −6.38197 | −0.214165 | ||||||||
\(889\) | −47.4164 | −1.59030 | ||||||||
\(890\) | 17.2361 | 0.577754 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.23607 | 0.242281 | ||||||||
\(893\) | 5.34752 | 0.178948 | ||||||||
\(894\) | 7.61803 | 0.254785 | ||||||||
\(895\) | −18.1459 | −0.606550 | ||||||||
\(896\) | −3.23607 | −0.108109 | ||||||||
\(897\) | 23.1803 | 0.773969 | ||||||||
\(898\) | 11.1246 | 0.371233 | ||||||||
\(899\) | −3.61803 | −0.120668 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 51.5967 | 1.71894 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.291796 | −0.00971037 | ||||||||
\(904\) | 19.5623 | 0.650633 | ||||||||
\(905\) | −21.8885 | −0.727600 | ||||||||
\(906\) | −20.9443 | −0.695827 | ||||||||
\(907\) | −23.5066 | −0.780523 | −0.390262 | − | 0.920704i | \(-0.627615\pi\) | ||||
−0.390262 | + | 0.920704i | \(0.627615\pi\) | |||||||
\(908\) | −20.3607 | −0.675693 | ||||||||
\(909\) | −15.6180 | −0.518017 | ||||||||
\(910\) | −10.9443 | −0.362799 | ||||||||
\(911\) | 3.52786 | 0.116883 | 0.0584417 | − | 0.998291i | \(-0.481387\pi\) | ||||
0.0584417 | + | 0.998291i | \(0.481387\pi\) | |||||||
\(912\) | 1.23607 | 0.0409303 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 4.65248 | 0.153890 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.763932 | 0.0252410 | ||||||||
\(917\) | 10.9443 | 0.361412 | ||||||||
\(918\) | 6.09017 | 0.201006 | ||||||||
\(919\) | −46.3394 | −1.52860 | −0.764298 | − | 0.644863i | \(-0.776914\pi\) | ||||
−0.764298 | + | 0.644863i | \(0.776914\pi\) | |||||||
\(920\) | 6.85410 | 0.225973 | ||||||||
\(921\) | −33.4508 | −1.10224 | ||||||||
\(922\) | 23.2148 | 0.764538 | ||||||||
\(923\) | −35.4164 | −1.16575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.38197 | −0.209838 | ||||||||
\(926\) | −11.8885 | −0.390682 | ||||||||
\(927\) | 6.76393 | 0.222157 | ||||||||
\(928\) | −2.61803 | −0.0859412 | ||||||||
\(929\) | −30.4721 | −0.999758 | −0.499879 | − | 0.866095i | \(-0.666622\pi\) | ||||
−0.499879 | + | 0.866095i | \(0.666622\pi\) | |||||||
\(930\) | 1.38197 | 0.0453165 | ||||||||
\(931\) | −4.29180 | −0.140658 | ||||||||
\(932\) | 4.43769 | 0.145362 | ||||||||
\(933\) | −9.23607 | −0.302375 | ||||||||
\(934\) | −28.5410 | −0.933891 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.38197 | 0.110543 | ||||||||
\(937\) | 42.6525 | 1.39340 | 0.696698 | − | 0.717365i | \(-0.254652\pi\) | ||||
0.696698 | + | 0.717365i | \(0.254652\pi\) | |||||||
\(938\) | 16.4721 | 0.537834 | ||||||||
\(939\) | −8.47214 | −0.276478 | ||||||||
\(940\) | 4.32624 | 0.141106 | ||||||||
\(941\) | −1.02129 | −0.0332930 | −0.0166465 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166465 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(942\) | −9.27051 | −0.302050 | ||||||||
\(943\) | −8.47214 | −0.275891 | ||||||||
\(944\) | 14.0902 | 0.458596 | ||||||||
\(945\) | 3.23607 | 0.105269 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −4.09017 | −0.132843 | ||||||||
\(949\) | 45.3738 | 1.47290 | ||||||||
\(950\) | 1.23607 | 0.0401033 | ||||||||
\(951\) | 27.4164 | 0.889038 | ||||||||
\(952\) | −19.7082 | −0.638747 | ||||||||
\(953\) | 59.2148 | 1.91815 | 0.959077 | − | 0.283144i | \(-0.0913774\pi\) | ||||
0.959077 | + | 0.283144i | \(0.0913774\pi\) | |||||||
\(954\) | −8.47214 | −0.274296 | ||||||||
\(955\) | −9.23607 | −0.298872 | ||||||||
\(956\) | 3.23607 | 0.104662 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.7639 | 0.412384 | ||||||||
\(959\) | −41.4164 | −1.33741 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −29.0902 | −0.938393 | ||||||||
\(962\) | −21.5836 | −0.695883 | ||||||||
\(963\) | −6.29180 | −0.202750 | ||||||||
\(964\) | 23.8885 | 0.769398 | ||||||||
\(965\) | −20.9443 | −0.674220 | ||||||||
\(966\) | 22.1803 | 0.713641 | ||||||||
\(967\) | −53.3050 | −1.71417 | −0.857086 | − | 0.515174i | \(-0.827727\pi\) | ||||
−0.857086 | + | 0.515174i | \(0.827727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.52786 | 0.241830 | ||||||||
\(970\) | 18.6525 | 0.598895 | ||||||||
\(971\) | 8.36068 | 0.268307 | 0.134153 | − | 0.990961i | \(-0.457168\pi\) | ||||
0.134153 | + | 0.990961i | \(0.457168\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −28.3607 | −0.909202 | ||||||||
\(974\) | −11.4164 | −0.365805 | ||||||||
\(975\) | 3.38197 | 0.108310 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8328 | 0.922443 | 0.461222 | − | 0.887285i | \(-0.347411\pi\) | ||||
0.461222 | + | 0.887285i | \(0.347411\pi\) | |||||||
\(978\) | 0.854102 | 0.0273112 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.47214 | −0.110913 | ||||||||
\(981\) | 2.47214 | 0.0789292 | ||||||||
\(982\) | 28.0344 | 0.894615 | ||||||||
\(983\) | −51.1935 | −1.63282 | −0.816409 | − | 0.577473i | \(-0.804039\pi\) | ||||
−0.816409 | + | 0.577473i | \(0.804039\pi\) | |||||||
\(984\) | −1.23607 | −0.0394044 | ||||||||
\(985\) | 10.9443 | 0.348713 | ||||||||
\(986\) | −15.9443 | −0.507769 | ||||||||
\(987\) | 14.0000 | 0.445625 | ||||||||
\(988\) | 4.18034 | 0.132994 | ||||||||
\(989\) | 0.618034 | 0.0196523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5197 | 1.73188 | 0.865938 | − | 0.500151i | \(-0.166722\pi\) | ||||
0.865938 | + | 0.500151i | \(0.166722\pi\) | |||||||
\(992\) | 1.38197 | 0.0438775 | ||||||||
\(993\) | −9.23607 | −0.293098 | ||||||||
\(994\) | −33.8885 | −1.07488 | ||||||||
\(995\) | −25.9787 | −0.823581 | ||||||||
\(996\) | 4.00000 | 0.126745 | ||||||||
\(997\) | 25.0344 | 0.792849 | 0.396424 | − | 0.918067i | \(-0.370251\pi\) | ||||
0.396424 | + | 0.918067i | \(0.370251\pi\) | |||||||
\(998\) | 32.4721 | 1.02789 | ||||||||
\(999\) | 6.38197 | 0.201916 |
(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 | 3630.2.a.bb.1.2 | 2 | ||
11.2 | odd | 10 | 330.2.m.b.301.1 | yes | 4 | ||
11.6 | odd | 10 | 330.2.m.b.91.1 | ✓ | 4 | ||
11.10 | odd | 2 | 3630.2.a.bj.1.1 | 2 | |||
33.2 | even | 10 | 990.2.n.e.631.1 | 4 | |||
33.17 | even | 10 | 990.2.n.e.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.b.91.1 | ✓ | 4 | 11.6 | odd | 10 | ||
330.2.m.b.301.1 | yes | 4 | 11.2 | odd | 10 | ||
990.2.n.e.91.1 | 4 | 33.17 | even | 10 | |||
990.2.n.e.631.1 | 4 | 33.2 | even | 10 | |||
3630.2.a.bb.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3630.2.a.bj.1.1 | 2 | 11.10 | odd | 2 |