Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, 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("608.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(4.85490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.56155 | −1.14556 | −0.572781 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572781 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.561553 | 0.169315 | 0.0846573 | − | 0.996410i | \(-0.473020\pi\) | ||||
0.0846573 | + | 0.996410i | \(0.473020\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.56155 | −0.433097 | −0.216548 | − | 0.976272i | \(-0.569480\pi\) | ||||
−0.216548 | + | 0.976272i | \(0.569480\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.00000 | 1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.123106 | 0.0298575 | 0.0149287 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149287 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.68466 | −1.02228 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.56155 | 1.15966 | 0.579832 | − | 0.814736i | \(-0.303118\pi\) | ||||
0.579832 | + | 0.814736i | \(0.303118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.68466 | 0.869919 | 0.434960 | − | 0.900450i | \(-0.356763\pi\) | ||||
0.434960 | + | 0.900450i | \(0.356763\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.12311 | 1.63856 | 0.819279 | − | 0.573395i | \(-0.194374\pi\) | ||||
0.819279 | + | 0.573395i | \(0.194374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.876894 | −0.152648 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.68466 | −1.29894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.12311 | 1.17103 | 0.585516 | − | 0.810661i | \(-0.300892\pi\) | ||||
0.585516 | + | 0.810661i | \(0.300892\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.43845 | 0.390464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.43845 | 0.829355 | 0.414678 | − | 0.909968i | \(-0.363894\pi\) | ||||
0.414678 | + | 0.909968i | \(0.363894\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.43845 | 0.214431 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.68466 | −0.537463 | −0.268731 | − | 0.963215i | \(-0.586604\pi\) | ||||
−0.268731 | + | 0.963215i | \(0.586604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.192236 | −0.0269184 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43845 | −0.609668 | −0.304834 | − | 0.952406i | \(-0.598601\pi\) | ||||
−0.304834 | + | 0.952406i | \(0.598601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.43845 | −0.193960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.43845 | −0.577837 | −0.288918 | − | 0.957354i | \(-0.593296\pi\) | ||||
−0.288918 | + | 0.957354i | \(0.593296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.8078 | 1.89594 | 0.947970 | − | 0.318360i | \(-0.103132\pi\) | ||||
0.947970 | + | 0.318360i | \(0.103132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.68466 | −0.212247 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.438447 | −0.0535648 | −0.0267824 | − | 0.999641i | \(-0.508526\pi\) | ||||
−0.0267824 | + | 0.999641i | \(0.508526\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.68466 | −1.04551 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.24621 | −0.503933 | −0.251966 | − | 0.967736i | \(-0.581077\pi\) | ||||
−0.251966 | + | 0.967736i | \(0.581077\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.24621 | −1.08219 | −0.541094 | − | 0.840962i | \(-0.681990\pi\) | ||||
−0.541094 | + | 0.840962i | \(0.681990\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.43845 | −0.281568 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.68466 | 0.191985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.3693 | −1.90653 | −0.953265 | − | 0.302135i | \(-0.902301\pi\) | ||||
−0.953265 | + | 0.302135i | \(0.902301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.315342 | −0.0342036 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.31534 | −0.784287 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.3693 | −1.62914 | −0.814572 | − | 0.580062i | \(-0.803028\pi\) | ||||
−0.814572 | + | 0.580062i | \(0.803028\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68466 | −0.491086 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.2462 | −1.47726 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.56155 | −0.262810 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.12311 | 0.723242 | 0.361621 | − | 0.932325i | \(-0.382223\pi\) | ||||
0.361621 | + | 0.932325i | \(0.382223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.315342 | −0.0316930 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4924 | 1.42798 | 0.713990 | − | 0.700155i | \(-0.246886\pi\) | ||||
0.713990 | + | 0.700155i | \(0.246886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0000 | 1.17108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9309 | 1.63677 | 0.818384 | − | 0.574671i | \(-0.194870\pi\) | ||||
0.818384 | + | 0.574671i | \(0.194870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.56155 | −0.341135 | −0.170567 | − | 0.985346i | \(-0.554560\pi\) | ||||
−0.170567 | + | 0.985346i | \(0.554560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.1231 | −1.05576 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.87689 | 0.458780 | 0.229390 | − | 0.973335i | \(-0.426327\pi\) | ||||
0.229390 | + | 0.973335i | \(0.426327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.2462 | −1.32847 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.876894 | 0.0810689 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.369317 | 0.0338552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6847 | −0.971333 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.24621 | −0.563202 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.80776 | 0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1231 | 1.34196 | 0.670979 | − | 0.741476i | \(-0.265874\pi\) | ||||
0.670979 | + | 0.741476i | \(0.265874\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.49242 | −0.747716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.4384 | −1.17412 | −0.587061 | − | 0.809542i | \(-0.699715\pi\) | ||||
−0.587061 | + | 0.809542i | \(0.699715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.2462 | −1.22612 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3693 | 1.22765 | 0.613827 | − | 0.789441i | \(-0.289629\pi\) | ||||
0.613827 | + | 0.789441i | \(0.289629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.43845 | 0.461283 | 0.230642 | − | 0.973039i | \(-0.425918\pi\) | ||||
0.230642 | + | 0.973039i | \(0.425918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.75379 | 0.484556 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.876894 | −0.0733296 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.12311 | −0.257589 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5616 | 0.865236 | 0.432618 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432618 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4924 | −1.83041 | −0.915204 | − | 0.402992i | \(-0.867970\pi\) | ||||
−0.915204 | + | 0.402992i | \(0.867970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0691303 | −0.00558885 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.3693 | −1.87707 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.75379 | −0.618820 | −0.309410 | − | 0.950929i | \(-0.600131\pi\) | ||||
−0.309410 | + | 0.950929i | \(0.600131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.93087 | 0.549654 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.6847 | 1.31494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4924 | 1.29179 | 0.645893 | − | 0.763428i | \(-0.276485\pi\) | ||||
0.645893 | + | 0.763428i | \(0.276485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.24621 | 0.174867 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5616 | −0.812427 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.561553 | −0.0429430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.2462 | −1.53929 | −0.769645 | − | 0.638471i | \(-0.779567\pi\) | ||||
−0.769645 | + | 0.638471i | \(0.779567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.68466 | 0.354127 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.93087 | 0.520956 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.24621 | 0.167890 | 0.0839449 | − | 0.996470i | \(-0.473248\pi\) | ||||
0.0839449 | + | 0.996470i | \(0.473248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.246211 | −0.0183007 | −0.00915037 | − | 0.999958i | \(-0.502913\pi\) | ||||
−0.00915037 | + | 0.999958i | \(0.502913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.1231 | −1.70931 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.2462 | −1.34149 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0691303 | 0.00505531 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.6847 | 1.21363 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00000 | −0.0723575 | −0.0361787 | − | 0.999345i | \(-0.511519\pi\) | ||||
−0.0361787 | + | 0.999345i | \(0.511519\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.4924 | 1.33111 | 0.665557 | − | 0.746347i | \(-0.268194\pi\) | ||||
0.665557 | + | 0.746347i | \(0.268194\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.24621 | −0.447300 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3693 | 0.810030 | 0.405015 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405015 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.7386 | −1.68279 | −0.841394 | − | 0.540423i | \(-0.818264\pi\) | ||||
−0.841394 | + | 0.540423i | \(0.818264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.684658 | 0.0482921 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.0540 | 0.986396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2462 | −0.715626 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.12311 | −0.217071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.561553 | 0.0388434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5616 | 1.07130 | 0.535651 | − | 0.844440i | \(-0.320066\pi\) | ||||
0.535651 | + | 0.844440i | \(0.320066\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.63068 | 0.454327 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.9309 | −0.950077 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.3693 | 1.85795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4384 | 0.975660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.192236 | −0.0129312 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.36932 | −0.0916962 | −0.0458481 | − | 0.998948i | \(-0.514599\pi\) | ||||
−0.0458481 | + | 0.998948i | \(0.514599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.876894 | −0.0584596 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6847 | 1.10740 | 0.553700 | − | 0.832716i | \(-0.313216\pi\) | ||||
0.553700 | + | 0.832716i | \(0.313216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5616 | −0.830091 | −0.415045 | − | 0.909801i | \(-0.636234\pi\) | ||||
−0.415045 | + | 0.909801i | \(0.636234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.63068 | −0.173086 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.9309 | −1.30571 | −0.652857 | − | 0.757481i | \(-0.726430\pi\) | ||||
−0.652857 | + | 0.757481i | \(0.726430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.43845 | 0.615696 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.6155 | −1.01434 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2462 | −0.917679 | −0.458840 | − | 0.888519i | \(-0.651735\pi\) | ||||
−0.458840 | + | 0.888519i | \(0.651735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.12311 | −0.327303 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56155 | −0.0993592 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.1231 | 1.71886 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.68466 | 0.358812 | 0.179406 | − | 0.983775i | \(-0.442582\pi\) | ||||
0.179406 | + | 0.983775i | \(0.442582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.12311 | 0.196348 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.492423 | 0.0308367 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.2462 | 1.63719 | 0.818597 | − | 0.574369i | \(-0.194752\pi\) | ||||
0.818597 | + | 0.574369i | \(0.194752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.3693 | 1.32782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.63068 | −0.162835 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0540 | 0.681617 | 0.340809 | − | 0.940133i | \(-0.389299\pi\) | ||||
0.340809 | + | 0.940133i | \(0.389299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.3693 | 0.698412 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0000 | 1.46878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4924 | −1.12750 | −0.563751 | − | 0.825944i | \(-0.690642\pi\) | ||||
−0.563751 | + | 0.825944i | \(0.690642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0540 | 0.610736 | 0.305368 | − | 0.952234i | \(-0.401221\pi\) | ||||
0.305368 | + | 0.952234i | \(0.401221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.31534 | 0.442745 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.876894 | 0.0528787 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6847 | −0.702063 | −0.351032 | − | 0.936364i | \(-0.614169\pi\) | ||||
−0.351032 | + | 0.936364i | \(0.614169\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.12311 | −0.306712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.630683 | −0.0376234 | −0.0188117 | − | 0.999823i | \(-0.505988\pi\) | ||||
−0.0188117 | + | 0.999823i | \(0.505988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.5616 | 1.69781 | 0.848904 | − | 0.528547i | \(-0.177263\pi\) | ||||
0.848904 | + | 0.528547i | \(0.177263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9848 | −0.999109 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.1231 | −0.652048 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3153 | 0.894732 | 0.447366 | − | 0.894351i | \(-0.352362\pi\) | ||||
0.447366 | + | 0.894351i | \(0.352362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3693 | 0.661947 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.12311 | 0.181221 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.68466 | −0.502247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3153 | 0.940401 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.384472 | 0.0220873 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −37.9309 | −2.17192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.63068 | 0.264287 | 0.132144 | − | 0.991231i | \(-0.457814\pi\) | ||||
0.132144 | + | 0.991231i | \(0.457814\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.6307 | −1.28741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.12311 | −0.347209 | −0.173605 | − | 0.984815i | \(-0.555542\pi\) | ||||
−0.173605 | + | 0.984815i | \(0.555542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.930870 | −0.0526159 | −0.0263079 | − | 0.999654i | \(-0.508375\pi\) | ||||
−0.0263079 | + | 0.999654i | \(0.508375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.31534 | 0.243142 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4384 | 0.923275 | 0.461638 | − | 0.887069i | \(-0.347262\pi\) | ||||
0.461638 | + | 0.887069i | \(0.347262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.63068 | 0.147290 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.4384 | −1.47565 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.123106 | 0.00684978 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.43845 | −0.135261 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.56155 | 0.307555 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.0540 | −0.609425 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.43845 | 0.243959 | 0.121980 | − | 0.992533i | \(-0.461076\pi\) | ||||
0.121980 | + | 0.992533i | \(0.461076\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.12311 | 0.0613618 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4924 | −1.11629 | −0.558147 | − | 0.829742i | \(-0.688487\pi\) | ||||
−0.558147 | + | 0.829742i | \(0.688487\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.61553 | −0.413619 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.12311 | 0.277432 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.2462 | 1.19770 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.56155 | −0.244877 | −0.122438 | − | 0.992476i | \(-0.539071\pi\) | ||||
−0.122438 | + | 0.992476i | \(0.539071\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6847 | 0.732523 | 0.366261 | − | 0.930512i | \(-0.380638\pi\) | ||||
0.366261 | + | 0.930512i | \(0.380638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.68466 | −0.463553 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.9309 | −1.53983 | −0.769917 | − | 0.638144i | \(-0.779703\pi\) | ||||
−0.769917 | + | 0.638144i | \(0.779703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8769 | 0.577286 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.576708 | −0.0305226 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.8769 | 1.47129 | 0.735643 | − | 0.677369i | \(-0.236880\pi\) | ||||
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.6847 | 0.875717 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.6847 | 1.23971 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.0000 | −1.04399 | −0.521996 | − | 0.852948i | \(-0.674812\pi\) | ||||
−0.521996 | + | 0.852948i | \(0.674812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.24621 | −0.116933 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.3153 | −0.691298 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9309 | −0.773091 | −0.386546 | − | 0.922270i | \(-0.626332\pi\) | ||||
−0.386546 | + | 0.922270i | \(0.626332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.7538 | −0.710243 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.31534 | −0.376759 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0540 | 0.824637 | 0.412319 | − | 0.911040i | \(-0.364719\pi\) | ||||
0.412319 | + | 0.911040i | \(0.364719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.6155 | −1.20986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.2462 | 1.23892 | 0.619462 | − | 0.785027i | \(-0.287351\pi\) | ||||
0.619462 | + | 0.785027i | \(0.287351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.31534 | −0.219930 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.05398 | −0.155242 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.8078 | 1.35921 | 0.679604 | − | 0.733579i | \(-0.262152\pi\) | ||||
0.679604 | + | 0.733579i | \(0.262152\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.684658 | 0.0346247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.9848 | 1.05855 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.6155 | −1.28886 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.43845 | −0.272948 | −0.136474 | − | 0.990644i | \(-0.543577\pi\) | ||||
−0.136474 | + | 0.990644i | \(0.543577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.68466 | −0.234526 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3693 | 1.16701 | 0.583504 | − | 0.812110i | \(-0.301681\pi\) | ||||
0.583504 | + | 0.812110i | \(0.301681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.2462 | −0.709654 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.9309 | 0.890992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00000 | 0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.8769 | 0.933402 | 0.466701 | − | 0.884415i | \(-0.345442\pi\) | ||||
0.466701 | + | 0.884415i | \(0.345442\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.4384 | −1.10681 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3153 | −0.655205 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.4924 | 2.18405 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.49242 | −0.415876 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.2462 | −1.28221 | −0.641106 | − | 0.767453i | \(-0.721524\pi\) | ||||
−0.641106 | + | 0.767453i | \(0.721524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0540 | 0.977371 | 0.488685 | − | 0.872460i | \(-0.337477\pi\) | ||||
0.488685 | + | 0.872460i | \(0.337477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.06913 | 0.100605 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.192236 | 0.00932481 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.4233 | 2.14979 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.36932 | 0.0661112 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.1231 | −1.49915 | −0.749574 | − | 0.661921i | \(-0.769741\pi\) | ||||
−0.749574 | + | 0.661921i | \(0.769741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.6155 | 1.90380 | 0.951900 | − | 0.306408i | \(-0.0991271\pi\) | ||||
0.951900 | + | 0.306408i | \(0.0991271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.7386 | 0.898449 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.56155 | 0.266045 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.75379 | 0.0837038 | 0.0418519 | − | 0.999124i | \(-0.486674\pi\) | ||||
0.0418519 | + | 0.999124i | \(0.486674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.12311 | −0.0534812 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.68466 | 0.0800405 | 0.0400203 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400203 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.3693 | 1.86628 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.4924 | −0.780065 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.1231 | −0.713703 | −0.356852 | − | 0.934161i | \(-0.616150\pi\) | ||||
−0.356852 | + | 0.934161i | \(0.616150\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24621 | 0.105770 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 35.1231 | 1.65023 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.1231 | −1.68977 | −0.844884 | − | 0.534950i | \(-0.820330\pi\) | ||||
−0.844884 | + | 0.534950i | \(0.820330\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.684658 | 0.0319571 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.9309 | −1.58032 | −0.790159 | − | 0.612902i | \(-0.790002\pi\) | ||||
−0.790159 | + | 0.612902i | \(0.790002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0540 | 0.699618 | 0.349809 | − | 0.936821i | \(-0.386247\pi\) | ||||
0.349809 | + | 0.936821i | \(0.386247\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 36.4924 | 1.69230 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.6847 | 0.818348 | 0.409174 | − | 0.912456i | \(-0.365817\pi\) | ||||
0.409174 | + | 0.912456i | \(0.365817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.31534 | −0.0607368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1080 | 0.557905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.05398 | 0.140422 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.56155 | 0.0716490 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.49242 | 0.114120 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.2462 | −0.650926 | −0.325463 | − | 0.945555i | \(-0.605520\pi\) | ||||
−0.325463 | + | 0.945555i | \(0.605520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1231 | −0.507170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.0540 | −1.18550 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.2462 | −0.828518 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.49242 | −0.294200 | −0.147100 | − | 0.989122i | \(-0.546994\pi\) | ||||
−0.147100 | + | 0.989122i | \(0.546994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.7538 | −1.16463 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.4924 | −1.46636 | −0.733181 | − | 0.680033i | \(-0.761965\pi\) | ||||
−0.733181 | + | 0.680033i | \(0.761965\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.576708 | 0.0259736 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.807764 | 0.0363063 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.7386 | −0.571406 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.68466 | −0.164948 | −0.0824740 | − | 0.996593i | \(-0.526282\pi\) | ||||
−0.0824740 | + | 0.996593i | \(0.526282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.43845 | −0.108725 | −0.0543625 | − | 0.998521i | \(-0.517313\pi\) | ||||
−0.0543625 | + | 0.998521i | \(0.517313\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.630683 | 0.0280650 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.4924 | 0.732454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6155 | −0.869443 | −0.434721 | − | 0.900565i | \(-0.643153\pi\) | ||||
−0.434721 | + | 0.900565i | \(0.643153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7386 | −1.22708 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56155 | 0.245549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.1231 | −1.63584 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.06913 | −0.0910002 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.6155 | 1.38777 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.3693 | 1.02383 | 0.511914 | − | 0.859037i | \(-0.328937\pi\) | ||||
0.511914 | + | 0.859037i | \(0.328937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.5464 | −1.42315 | −0.711577 | − | 0.702608i | \(-0.752019\pi\) | ||||
−0.711577 | + | 0.702608i | \(0.752019\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.31534 | −0.319268 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12311 | 0.0489232 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.93087 | 0.344820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.49242 | 0.108162 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.24621 | −0.270553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.3693 | −1.87502 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50758 | −0.151363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.12311 | 0.0483756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.4384 | −1.52362 | −0.761809 | − | 0.647802i | \(-0.775688\pi\) | ||||
−0.761809 | + | 0.647802i | \(0.775688\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.384472 | 0.0164993 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.12311 | 0.390791 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4924 | 1.04722 | 0.523610 | − | 0.851958i | \(-0.324585\pi\) | ||||
0.523610 | + | 0.851958i | \(0.324585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.31534 | −0.354890 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.68466 | 0.199573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | 1.27573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.4924 | 1.20944 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.9309 | −0.759755 | −0.379878 | − | 0.925037i | \(-0.624034\pi\) | ||||
−0.379878 | + | 0.925037i | \(0.624034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.49242 | −0.359191 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.107951 | −0.00455768 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.2462 | −1.27473 | −0.637363 | − | 0.770564i | \(-0.719975\pi\) | ||||
−0.637363 | + | 0.770564i | \(0.719975\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.4924 | −0.525560 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.0000 | −0.881917 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.7386 | −1.12094 | −0.560471 | − | 0.828174i | \(-0.689380\pi\) | ||||
−0.560471 | + | 0.828174i | \(0.689380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.56155 | 0.0652348 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.68466 | 0.362175 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.24621 | 0.218403 | 0.109201 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109201 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.8769 | −1.20008 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −52.1080 | −2.16180 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.49242 | −0.103226 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.24621 | −0.0928694 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.9309 | −1.40048 | −0.700238 | − | 0.713909i | \(-0.746923\pi\) | ||||
−0.700238 | + | 0.713909i | \(0.746923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.12311 | 0.375911 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.7538 | −0.730293 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.7386 | 1.34441 | 0.672207 | − | 0.740363i | \(-0.265346\pi\) | ||||
0.672207 | + | 0.740363i | \(0.265346\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.946025 | −0.0387832 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.0691 | 1.51714 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.8617 | 1.79214 | 0.896071 | − | 0.443911i | \(-0.146409\pi\) | ||||
0.896071 | + | 0.443911i | \(0.146409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.63068 | −0.188890 | −0.0944448 | − | 0.995530i | \(-0.530108\pi\) | ||||
−0.0944448 | + | 0.995530i | \(0.530108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.246211 | 0.0100265 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.3693 | 1.11272 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.8769 | −0.522657 | −0.261329 | − | 0.965250i | \(-0.584161\pi\) | ||||
−0.261329 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.9460 | −0.889298 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.75379 | 0.232773 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.5464 | −1.67804 | −0.839022 | − | 0.544098i | \(-0.816872\pi\) | ||||
−0.839022 | + | 0.544098i | \(0.816872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6847 | 0.872991 | 0.436496 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436496 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.1231 | −1.89404 | −0.947019 | − | 0.321178i | \(-0.895921\pi\) | ||||
−0.947019 | + | 0.321178i | \(0.895921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.9309 | 1.24121 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.1080 | −1.84728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.876894 | −0.0350198 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.876894 | 0.0349641 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.3002 | −1.80337 | −0.901686 | − | 0.432391i | \(-0.857670\pi\) | ||||
−0.901686 | + | 0.432391i | \(0.857670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.3002 | −0.965846 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.7386 | −1.53730 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.12311 | −0.123742 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.38447 | 0.0943282 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.1080 | 0.952207 | 0.476103 | − | 0.879389i | \(-0.342049\pi\) | ||||
0.476103 | + | 0.879389i | \(0.342049\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.3002 | 1.07661 | 0.538307 | − | 0.842749i | \(-0.319064\pi\) | ||||
0.538307 | + | 0.842749i | \(0.319064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.7538 | 0.856555 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.0000 | 1.84776 | 0.923880 | − | 0.382682i | \(-0.124999\pi\) | ||||
0.923880 | + | 0.382682i | \(0.124999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.49242 | −0.0978361 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −42.7386 | −1.67506 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.80776 | 0.344674 | 0.172337 | − | 0.985038i | \(-0.444868\pi\) | ||||
0.172337 | + | 0.985038i | \(0.444868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.4233 | 1.34503 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.19224 | 0.202568 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.5464 | −1.26783 | −0.633914 | − | 0.773404i | \(-0.718553\pi\) | ||||
−0.633914 | + | 0.773404i | \(0.718553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1771 | −0.823693 | −0.411846 | − | 0.911253i | \(-0.635116\pi\) | ||||
−0.411846 | + | 0.911253i | \(0.635116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.300187 | 0.0116583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.68466 | −0.297998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.0540 | 1.00881 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.13826 | 0.0826699 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.31534 | 0.321010 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1231 | −0.814236 | −0.407118 | − | 0.913376i | \(-0.633466\pi\) | ||||
−0.407118 | + | 0.913376i | \(0.633466\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.68466 | 0.334273 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.43845 | −0.0937171 | −0.0468586 | − | 0.998902i | \(-0.514921\pi\) | ||||
−0.0468586 | + | 0.998902i | \(0.514921\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.3693 | 0.820079 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0540 | −0.998391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.7538 | −0.679330 | −0.339665 | − | 0.940547i | \(-0.610314\pi\) | ||||
−0.339665 | + | 0.940547i | \(0.610314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.8078 | −1.40635 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.6155 | 0.748379 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.93087 | 0.264045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −45.0540 | −1.71393 | −0.856967 | − | 0.515371i | \(-0.827654\pi\) | ||||
−0.856967 | + | 0.515371i | \(0.827654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.946025 | −0.0359365 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.9309 | −0.528428 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.492423 | 0.0186518 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.1231 | 1.17718 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.6155 | 0.514251 | 0.257126 | − | 0.966378i | \(-0.417225\pi\) | ||||
0.257126 | + | 0.966378i | \(0.417225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.12311 | 0.268653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.7386 | −0.555089 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.738634 | −0.0277792 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 50.4924 | 1.89628 | 0.948141 | − | 0.317849i | \(-0.102960\pi\) | ||||
0.948141 | + | 0.317849i | \(0.102960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.61553 | −0.210599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.7386 | 1.90018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.24621 | 0.0840035 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.4233 | −0.874759 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4924 | 0.876120 | 0.438060 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438060 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.4773 | 1.61918 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.2462 | 0.827345 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.31534 | 0.271685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.3693 | 0.829632 | 0.414816 | − | 0.909905i | \(-0.363846\pi\) | ||||
0.414816 | + | 0.909905i | \(0.363846\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.669503 | 0.0247625 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.36932 | 0.124449 | 0.0622243 | − | 0.998062i | \(-0.480181\pi\) | ||||
0.0622243 | + | 0.998062i | \(0.480181\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.00000 | 0.295084 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.246211 | −0.00906931 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.43845 | 0.0529141 | 0.0264571 | − | 0.999650i | \(-0.491577\pi\) | ||||
0.0264571 | + | 0.999650i | \(0.491577\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.43845 | 0.0895786 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8769 | 0.839272 | 0.419636 | − | 0.907693i | \(-0.362158\pi\) | ||||
0.419636 | + | 0.907693i | \(0.362158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.0540 | −0.991181 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.75379 | 0.356872 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.7926 | 1.85592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.87689 | −0.323492 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.6155 | 2.09684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.0540 | 0.765220 | 0.382610 | − | 0.923910i | \(-0.375025\pi\) | ||||
0.382610 | + | 0.923910i | \(0.375025\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.87689 | −0.177020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.8617 | −1.48124 | −0.740618 | − | 0.671926i | \(-0.765467\pi\) | ||||
−0.740618 | + | 0.671926i | \(0.765467\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6847 | −0.386811 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.177081 | 0.00640237 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.93087 | 0.250259 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.3693 | 0.446049 | 0.223024 | − | 0.974813i | \(-0.428407\pi\) | ||||
0.223024 | + | 0.974813i | \(0.428407\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.9848 | −1.47603 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.0540 | −1.15290 | −0.576451 | − | 0.817132i | \(-0.695563\pi\) | ||||
−0.576451 | + | 0.817132i | \(0.695563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.2462 | 0.511739 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.3693 | −1.19712 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00000 | 0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.38447 | −0.0853231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.0540 | 0.931093 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.8617 | 0.708896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4384 | 0.799844 | 0.399922 | − | 0.916549i | \(-0.369037\pi\) | ||||
0.399922 | + | 0.916549i | \(0.369037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.2614 | −0.614521 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6307 | 0.520207 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.1231 | −0.821126 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.7538 | −0.629662 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.68466 | −0.0950955 | −0.0475477 | − | 0.998869i | \(-0.515141\pi\) | ||||
−0.0475477 | + | 0.998869i | \(0.515141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.453602 | −0.0160473 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.63068 | 0.304950 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.19224 | −0.183230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.7386 | −1.50634 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.8769 | 1.01651 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.12311 | 0.215277 | 0.107638 | − | 0.994190i | \(-0.465671\pi\) | ||||
0.107638 | + | 0.994190i | \(0.465671\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4233 | −0.401126 | −0.200563 | − | 0.979681i | \(-0.564277\pi\) | ||||
−0.200563 | + | 0.979681i | \(0.564277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.6998 | −0.550616 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.2462 | −1.47982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.43845 | 0.190267 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.63068 | 0.0919235 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.31534 | 0.150606 | 0.0753032 | − | 0.997161i | \(-0.476008\pi\) | ||||
0.0753032 | + | 0.997161i | \(0.476008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3693 | 0.710030 | 0.355015 | − | 0.934861i | \(-0.384476\pi\) | ||||
0.355015 | + | 0.934861i | \(0.384476\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.36932 | −0.0476735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5616 | 0.680222 | 0.340111 | − | 0.940385i | \(-0.389535\pi\) | ||||
0.340111 | + | 0.940385i | \(0.389535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.5464 | 0.644143 | 0.322072 | − | 0.946715i | \(-0.395621\pi\) | ||||
0.322072 | + | 0.946715i | \(0.395621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2462 | 0.632954 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.246211 | 0.00853071 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 50.7386 | 1.75378 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.6155 | 1.02244 | 0.511221 | − | 0.859449i | \(-0.329193\pi\) | ||||
0.511221 | + | 0.859449i | \(0.329193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.05398 | −0.243241 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.984845 | 0.0339199 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.0540 | 0.930685 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.0540 | −1.10139 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.6004 | −1.53068 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.6155 | 1.35800 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.2462 | 1.10409 | 0.552045 | − | 0.833815i | \(-0.313848\pi\) | ||||
0.552045 | + | 0.833815i | \(0.313848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.43845 | 0.0491939 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.6307 | 0.431456 | 0.215728 | − | 0.976454i | \(-0.430788\pi\) | ||||
0.215728 | + | 0.976454i | \(0.430788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.9309 | −1.22595 | −0.612973 | − | 0.790104i | \(-0.710026\pi\) | ||||
−0.612973 | + | 0.790104i | \(0.710026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.7386 | −0.638611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.6307 | 0.770357 | 0.385179 | − | 0.922842i | \(-0.374140\pi\) | ||||
0.385179 | + | 0.922842i | \(0.374140\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.8617 | 1.76335 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.5227 | 0.900759 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.61553 | 0.190494 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.684658 | 0.0231988 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.4233 | 0.893270 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.68466 | 0.0906545 | 0.0453272 | − | 0.998972i | \(-0.485567\pi\) | ||||
0.0453272 | + | 0.998972i | \(0.485567\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.9157 | −0.806657 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.6847 | 1.67392 | 0.836959 | − | 0.547265i | \(-0.184331\pi\) | ||||
0.836959 | + | 0.547265i | \(0.184331\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.0691303 | 0.00232642 | 0.00116321 | − | 0.999999i | \(-0.499630\pi\) | ||||
0.00116321 | + | 0.999999i | \(0.499630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.7538 | −0.596787 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.2311 | −1.25010 | −0.625048 | − | 0.780586i | \(-0.714921\pi\) | ||||
−0.625048 | + | 0.780586i | \(0.714921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.3693 | 1.52164 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.93087 | −0.131689 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.68466 | −0.123302 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.75379 | −0.192328 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.5616 | 0.452807 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.7386 | 1.42541 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.546398 | −0.0182032 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.4773 | −0.847830 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.630683 | 0.0209646 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.5616 | −0.516713 | −0.258356 | − | 0.966050i | \(-0.583181\pi\) | ||||
−0.258356 | + | 0.966050i | \(0.583181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.138261 | 0.00458582 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.12311 | −0.302262 | −0.151131 | − | 0.988514i | \(-0.548292\pi\) | ||||
−0.151131 | + | 0.988514i | \(0.548292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.75379 | −0.322803 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 59.2311 | 1.95812 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.3153 | −1.33133 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.3002 | −0.801589 | −0.400795 | − | 0.916168i | \(-0.631266\pi\) | ||||
−0.400795 | + | 0.916168i | \(0.631266\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.23106 | −0.238271 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.63068 | 0.218252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1231 | 0.365725 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.13826 | −0.267296 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −55.1771 | −1.81030 | −0.905151 | − | 0.425091i | \(-0.860242\pi\) | ||||
−0.905151 | + | 0.425091i | \(0.860242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.56155 | 0.313031 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.177081 | −0.00579117 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.7538 | −0.416648 | −0.208324 | − | 0.978060i | \(-0.566801\pi\) | ||||
−0.208324 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.45360 | 0.0474365 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.3002 | 0.596569 | 0.298285 | − | 0.954477i | \(-0.403586\pi\) | ||||
0.298285 | + | 0.954477i | \(0.403586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.2462 | 0.724436 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −42.7386 | −1.39029 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.9848 | 1.20185 | 0.600923 | − | 0.799307i | \(-0.294800\pi\) | ||||
0.600923 | + | 0.799307i | \(0.294800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.4384 | 0.468692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6695 | −0.832391 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.24621 | −0.267121 | −0.133560 | − | 0.991041i | \(-0.542641\pi\) | ||||
−0.133560 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.56155 | 0.0828899 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.10795 | −0.132791 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.1080 | 1.39203 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.2311 | 1.68487 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.50758 | −0.306377 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.3693 | −1.52487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0000 | −0.771788 | −0.385894 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385894 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.192236 | −0.00617551 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.5076 | −0.754394 | −0.377197 | − | 0.926133i | \(-0.623112\pi\) | ||||
−0.377197 | + | 0.926133i | \(0.623112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.3153 | 0.523046 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.80776 | 0.121946 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.6155 | −1.71531 | −0.857656 | − | 0.514223i | \(-0.828080\pi\) | ||||
−0.857656 | + | 0.514223i | \(0.828080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.63068 | −0.275838 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.6155 | 0.370478 | 0.185239 | − | 0.982694i | \(-0.440694\pi\) | ||||
0.185239 | + | 0.982694i | \(0.440694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.1231 | −0.927939 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.2614 | 0.549435 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.2462 | 0.961774 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.2462 | −0.579610 | −0.289805 | − | 0.957086i | \(-0.593590\pi\) | ||||
−0.289805 | + | 0.957086i | \(0.593590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.93087 | −0.219945 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.8078 | 1.92774 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.9157 | −1.48584 | −0.742918 | − | 0.669383i | \(-0.766559\pi\) | ||||
−0.742918 | + | 0.669383i | \(0.766559\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.6155 | 1.25338 |
(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 | 608.2.a.h.1.1 | yes | 2 | |
3.2 | odd | 2 | 5472.2.a.bf.1.2 | 2 | |||
4.3 | odd | 2 | 608.2.a.g.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 1216.2.a.t.1.1 | 2 | |||
8.5 | even | 2 | 1216.2.a.s.1.2 | 2 | |||
12.11 | even | 2 | 5472.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.g.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
608.2.a.h.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1216.2.a.s.1.2 | 2 | 8.5 | even | 2 | |||
1216.2.a.t.1.1 | 2 | 8.3 | odd | 2 | |||
5472.2.a.bc.1.2 | 2 | 12.11 | even | 2 | |||
5472.2.a.bf.1.2 | 2 | 3.2 | odd | 2 |