Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 23x^{6} - 3x^{5} + 163x^{4} + 13x^{3} - 418x^{2} + 4x + 269 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.938106\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.938106 | −0.419534 | −0.209767 | − | 0.977751i | \(-0.567271\pi\) | ||||
−0.209767 | + | 0.977751i | \(0.567271\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.96672 | 1.87724 | 0.938621 | − | 0.344949i | \(-0.112104\pi\) | ||||
0.938621 | + | 0.344949i | \(0.112104\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.79099 | 1.14303 | 0.571513 | − | 0.820593i | \(-0.306357\pi\) | ||||
0.571513 | + | 0.820593i | \(0.306357\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.41916 | −1.50300 | −0.751502 | − | 0.659730i | \(-0.770670\pi\) | ||||
−0.751502 | + | 0.659730i | \(0.770670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.938106 | 0.242218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.64027 | −0.882895 | −0.441448 | − | 0.897287i | \(-0.645535\pi\) | ||||
−0.441448 | + | 0.897287i | \(0.645535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.92607 | 1.13012 | 0.565059 | − | 0.825051i | \(-0.308853\pi\) | ||||
0.565059 | + | 0.825051i | \(0.308853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.96672 | −1.08383 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.96672 | −0.827118 | −0.413559 | − | 0.910477i | \(-0.635714\pi\) | ||||
−0.413559 | + | 0.910477i | \(0.635714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.11996 | −0.823991 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2334 | −1.90030 | −0.950151 | − | 0.311791i | \(-0.899071\pi\) | ||||
−0.950151 | + | 0.311791i | \(0.899071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.29712 | −1.66981 | −0.834906 | − | 0.550393i | \(-0.814478\pi\) | ||||
−0.834906 | + | 0.550393i | \(0.814478\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.79099 | −0.659926 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.65931 | −0.787567 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.89525 | 0.475976 | 0.237988 | − | 0.971268i | \(-0.423512\pi\) | ||||
0.237988 | + | 0.971268i | \(0.423512\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.41916 | 0.867760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.61453 | −0.876842 | −0.438421 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438421 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.934214 | 0.142466 | 0.0712332 | − | 0.997460i | \(-0.477307\pi\) | ||||
0.0712332 | + | 0.997460i | \(0.477307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.938106 | −0.139845 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.64800 | −1.40731 | −0.703653 | − | 0.710544i | \(-0.748449\pi\) | ||||
−0.703653 | + | 0.710544i | \(0.748449\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.6683 | 2.52404 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.64027 | 0.509740 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.782015 | 0.107418 | 0.0537090 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537090 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.55635 | −0.479538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.92607 | −0.652474 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.0714 | 1.96214 | 0.981068 | − | 0.193665i | \(-0.0620373\pi\) | ||||
0.981068 | + | 0.193665i | \(0.0620373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5501 | −1.60687 | −0.803436 | − | 0.595391i | \(-0.796997\pi\) | ||||
−0.803436 | + | 0.595391i | \(0.796997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.96672 | 0.625748 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.08375 | 0.630561 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.96283 | 0.972814 | 0.486407 | − | 0.873732i | \(-0.338307\pi\) | ||||
0.486407 | + | 0.873732i | \(0.338307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.96672 | 0.477537 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.53856 | −1.01334 | −0.506670 | − | 0.862140i | \(-0.669124\pi\) | ||||
−0.506670 | + | 0.862140i | \(0.669124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.77746 | −0.676200 | −0.338100 | − | 0.941110i | \(-0.609784\pi\) | ||||
−0.338100 | + | 0.941110i | \(0.609784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.11996 | 0.475732 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.8288 | 2.14574 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.994199 | −0.111856 | −0.0559281 | − | 0.998435i | \(-0.517812\pi\) | ||||
−0.0559281 | + | 0.998435i | \(0.517812\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.08014 | 0.228325 | 0.114162 | − | 0.993462i | \(-0.463582\pi\) | ||||
0.114162 | + | 0.993462i | \(0.463582\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.41496 | 0.370404 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2334 | 1.09714 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.46795 | 1.00360 | 0.501801 | − | 0.864983i | \(-0.332671\pi\) | ||||
0.501801 | + | 0.864983i | \(0.332671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.9154 | −2.82150 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.29712 | 0.964066 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.62117 | −0.474122 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.16825 | 0.423221 | 0.211611 | − | 0.977354i | \(-0.432129\pi\) | ||||
0.211611 | + | 0.977354i | \(0.432129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.79099 | 0.381009 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.91578 | −0.787649 | −0.393825 | − | 0.919186i | \(-0.628848\pi\) | ||||
−0.393825 | + | 0.919186i | \(0.628848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.67646 | −0.460786 | −0.230393 | − | 0.973098i | \(-0.574001\pi\) | ||||
−0.230393 | + | 0.973098i | \(0.574001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.65931 | 0.454702 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6949 | −1.13059 | −0.565293 | − | 0.824890i | \(-0.691237\pi\) | ||||
−0.565293 | + | 0.824890i | \(0.691237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9966 | 1.53220 | 0.766100 | − | 0.642721i | \(-0.222195\pi\) | ||||
0.766100 | + | 0.642721i | \(0.222195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.89525 | −0.274805 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.39876 | −0.601944 | −0.300972 | − | 0.953633i | \(-0.597311\pi\) | ||||
−0.300972 | + | 0.953633i | \(0.597311\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.72120 | 0.347004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.41916 | −0.501002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.0802 | −1.65741 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37159 | 0.306508 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.61453 | 0.506245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.55549 | 0.765226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.89284 | −0.256698 | −0.128349 | − | 0.991729i | \(-0.540968\pi\) | ||||
−0.128349 | + | 0.991729i | \(0.540968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.934214 | −0.0822530 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.96987 | −0.783701 | −0.391850 | − | 0.920029i | \(-0.628165\pi\) | ||||
−0.391850 | + | 0.920029i | \(0.628165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.4664 | 2.12151 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.938106 | 0.0807393 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.6172 | −1.50514 | −0.752570 | − | 0.658512i | \(-0.771186\pi\) | ||||
−0.752570 | + | 0.658512i | \(0.771186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9504 | −0.928803 | −0.464402 | − | 0.885625i | \(-0.653731\pi\) | ||||
−0.464402 | + | 0.885625i | \(0.653731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.64800 | 0.812508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.5440 | −1.71797 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.60005 | 0.797241 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.6683 | −1.45726 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.7367 | −0.879581 | −0.439790 | − | 0.898100i | \(-0.644947\pi\) | ||||
−0.439790 | + | 0.898100i | \(0.644947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.776575 | −0.0631968 | −0.0315984 | − | 0.999501i | \(-0.510060\pi\) | ||||
−0.0315984 | + | 0.999501i | \(0.510060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.64027 | −0.294298 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.72168 | 0.700542 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39402 | −0.590107 | −0.295054 | − | 0.955481i | \(-0.595338\pi\) | ||||
−0.295054 | + | 0.955481i | \(0.595338\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.782015 | −0.0620178 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7016 | −1.55270 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.8717 | 1.32149 | 0.660746 | − | 0.750609i | \(-0.270240\pi\) | ||||
0.660746 | + | 0.750609i | \(0.270240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.55635 | 0.276861 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3673 | 1.25902 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.92607 | 0.376706 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.4626 | −1.40368 | −0.701842 | − | 0.712333i | \(-0.747639\pi\) | ||||
−0.701842 | + | 0.712333i | \(0.747639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.4627 | −1.54683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.0714 | −1.13284 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1981 | 1.06122 | 0.530609 | − | 0.847617i | \(-0.321963\pi\) | ||||
0.530609 | + | 0.847617i | \(0.321963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3089 | 1.36089 | 0.680443 | − | 0.732801i | \(-0.261787\pi\) | ||||
0.680443 | + | 0.732801i | \(0.261787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5501 | 0.927728 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.71605 | −0.199688 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8002 | −1.00917 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.96672 | −0.361276 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4667 | 0.974413 | 0.487206 | − | 0.873287i | \(-0.338016\pi\) | ||||
0.487206 | + | 0.873287i | \(0.338016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6449 | 0.982184 | 0.491092 | − | 0.871108i | \(-0.336598\pi\) | ||||
0.491092 | + | 0.871108i | \(0.336598\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.08375 | −0.364055 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.9789 | 1.49468 | 0.747342 | − | 0.664439i | \(-0.231330\pi\) | ||||
0.747342 | + | 0.664439i | \(0.231330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0296 | −0.923647 | −0.461823 | − | 0.886972i | \(-0.652805\pi\) | ||||
−0.461823 | + | 0.886972i | \(0.652805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.96283 | −0.561654 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −50.8266 | −3.56733 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.26702 | 0.367865 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.96672 | −0.275706 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.6747 | 1.29175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2109 | 1.25369 | 0.626845 | − | 0.779144i | \(-0.284346\pi\) | ||||
0.626845 | + | 0.779144i | \(0.284346\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.53856 | 0.585052 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.876392 | −0.0597694 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −46.1762 | −3.13464 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.77746 | 0.390404 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.7272 | 1.32700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9336 | 1.13396 | 0.566978 | − | 0.823733i | \(-0.308112\pi\) | ||||
0.566978 | + | 0.823733i | \(0.308112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.11996 | −0.274664 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.66081 | 0.242976 | 0.121488 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121488 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7283 | −1.56801 | −0.784004 | − | 0.620756i | \(-0.786826\pi\) | ||||
−0.784004 | + | 0.620756i | \(0.786826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.8288 | −1.23884 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.4226 | −0.813834 | −0.406917 | − | 0.913465i | \(-0.633396\pi\) | ||||
−0.406917 | + | 0.913465i | \(0.633396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.05085 | 0.590412 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.994199 | 0.0645802 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.7982 | −1.41001 | −0.705003 | − | 0.709204i | \(-0.749055\pi\) | ||||
−0.705003 | + | 0.709204i | \(0.749055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.02354 | 0.323594 | 0.161797 | − | 0.986824i | \(-0.448271\pi\) | ||||
0.161797 | + | 0.986824i | \(0.448271\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5747 | −1.05892 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.6952 | −1.69857 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.08014 | −0.131823 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.2662 | −0.647999 | −0.324000 | − | 0.946057i | \(-0.605028\pi\) | ||||
−0.324000 | + | 0.946057i | \(0.605028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.0378 | −0.945417 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.41496 | −0.213853 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.9857 | −0.747650 | −0.373825 | − | 0.927499i | \(-0.621954\pi\) | ||||
−0.373825 | + | 0.927499i | \(0.621954\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.3799 | 0.893522 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2334 | −0.633434 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.9764 | −1.66344 | −0.831719 | − | 0.555197i | \(-0.812643\pi\) | ||||
−0.831719 | + | 0.555197i | \(0.812643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.733613 | −0.0450655 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.46795 | −0.579429 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.3337 | 1.78851 | 0.894254 | − | 0.447559i | \(-0.147707\pi\) | ||||
0.894254 | + | 0.447559i | \(0.147707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.4504 | 0.695564 | 0.347782 | − | 0.937575i | \(-0.386935\pi\) | ||||
0.347782 | + | 0.937575i | \(0.386935\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.9154 | 1.62900 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.6187 | −0.941844 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.10038 | 0.126199 | 0.0630997 | − | 0.998007i | \(-0.479901\pi\) | ||||
0.0630997 | + | 0.998007i | \(0.479901\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.29712 | −0.556604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.37932 | −0.141938 | −0.0709691 | − | 0.997479i | \(-0.522609\pi\) | ||||
−0.0709691 | + | 0.997479i | \(0.522609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0104 | −1.66504 | −0.832522 | − | 0.553991i | \(-0.813104\pi\) | ||||
−0.832522 | + | 0.553991i | \(0.813104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.62117 | 0.273735 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.8858 | −1.64605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.74843 | −0.220496 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.16825 | −0.244347 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.26096 | −0.365769 | −0.182885 | − | 0.983134i | \(-0.558543\pi\) | ||||
−0.182885 | + | 0.983134i | \(0.558543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.1386 | −0.823182 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.79099 | −0.219975 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.4963 | 1.24316 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.63998 | 0.267444 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.91578 | 0.454749 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.7733 | 0.674137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.9131 | −1.70723 | −0.853617 | − | 0.520902i | \(-0.825596\pi\) | ||||
−0.853617 | + | 0.520902i | \(0.825596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.67646 | 0.266035 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.6641 | 0.944933 | 0.472467 | − | 0.881349i | \(-0.343364\pi\) | ||||
0.472467 | + | 0.881349i | \(0.343364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.82677 | 0.103255 | 0.0516276 | − | 0.998666i | \(-0.483559\pi\) | ||||
0.0516276 | + | 0.998666i | \(0.483559\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.65931 | −0.262522 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.80617 | −0.382273 | −0.191136 | − | 0.981563i | \(-0.561217\pi\) | ||||
−0.191136 | + | 0.981563i | \(0.561217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38.7948 | −2.17209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6949 | 0.652745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.9322 | −0.997776 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.3267 | 1.23846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.9966 | −0.884616 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −47.9189 | −2.64185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.7166 | 1.85323 | 0.926615 | − | 0.376011i | \(-0.122705\pi\) | ||||
0.926615 | + | 0.376011i | \(0.122705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.89525 | 0.158659 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.46997 | −0.408128 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.7686 | −1.67607 | −0.838036 | − | 0.545615i | \(-0.816296\pi\) | ||||
−0.838036 | + | 0.545615i | \(0.816296\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.39876 | 0.347533 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.2453 | −1.90864 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 52.9863 | 2.86099 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.72120 | −0.200343 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.35902 | 0.287687 | 0.143844 | − | 0.989600i | \(-0.454054\pi\) | ||||
0.143844 | + | 0.989600i | \(0.454054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0047 | −0.910239 | −0.455119 | − | 0.890430i | \(-0.650403\pi\) | ||||
−0.455119 | + | 0.890430i | \(0.650403\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41916 | 0.289253 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9678 | 0.636984 | 0.318492 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318492 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.01007 | 0.425130 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.0802 | 0.956906 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0766 | −0.531823 | −0.265912 | − | 0.963997i | \(-0.585673\pi\) | ||||
−0.265912 | + | 0.963997i | \(0.585673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.26615 | 0.277166 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.37159 | −0.176963 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.41987 | 0.283689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.9226 | 1.82295 | 0.911473 | − | 0.411360i | \(-0.134946\pi\) | ||||
0.911473 | + | 0.411360i | \(0.134946\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.61453 | −0.292281 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.88405 | 0.201650 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.7963 | −1.33568 | −0.667842 | − | 0.744303i | \(-0.732782\pi\) | ||||
−0.667842 | + | 0.744303i | \(0.732782\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.55549 | −0.441803 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 55.4566 | 2.85616 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7412 | 0.551736 | 0.275868 | − | 0.961196i | \(-0.411035\pi\) | ||||
0.275868 | + | 0.961196i | \(0.411035\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.89284 | 0.148205 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.2013 | −1.54322 | −0.771608 | − | 0.636098i | \(-0.780547\pi\) | ||||
−0.771608 | + | 0.636098i | \(0.780547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.6634 | −0.900209 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.934214 | 0.0474888 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.09465 | −0.156905 | −0.0784525 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784525 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.4399 | 0.730258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.96987 | 0.452470 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.932664 | 0.0469274 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.86237 | −0.444790 | −0.222395 | − | 0.974957i | \(-0.571387\pi\) | ||||
−0.222395 | + | 0.974957i | \(0.571387\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.4664 | −1.22485 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.5081 | −0.724499 | −0.362249 | − | 0.932081i | \(-0.617991\pi\) | ||||
−0.362249 | + | 0.932081i | \(0.617991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.3826 | 2.50973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.938106 | −0.0466149 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.9759 | 0.544053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.7417 | −1.56953 | −0.784763 | − | 0.619796i | \(-0.787215\pi\) | ||||
−0.784763 | + | 0.619796i | \(0.787215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.6172 | 0.868993 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 74.8556 | 3.68340 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.95139 | −0.0957899 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9504 | 0.536245 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.47217 | 0.120773 | 0.0603866 | − | 0.998175i | \(-0.480767\pi\) | ||||
0.0603866 | + | 0.998175i | \(0.480767\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.7214 | 1.74096 | 0.870478 | − | 0.492207i | \(-0.163810\pi\) | ||||
0.870478 | + | 0.492207i | \(0.163810\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.64800 | −0.469102 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.9978 | 0.727498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −62.3327 | −3.01649 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.5440 | 0.991872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1608 | −1.01928 | −0.509639 | − | 0.860388i | \(-0.670221\pi\) | ||||
−0.509639 | + | 0.860388i | \(0.670221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.61648 | 0.462138 | 0.231069 | − | 0.972937i | \(-0.425778\pi\) | ||||
0.231069 | + | 0.972937i | \(0.425778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.60005 | −0.460287 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.5403 | −0.934740 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.51986 | 0.454358 | 0.227179 | − | 0.973853i | \(-0.427050\pi\) | ||||
0.227179 | + | 0.973853i | \(0.427050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6683 | 0.841347 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5948 | 0.788441 | 0.394220 | − | 0.919016i | \(-0.371015\pi\) | ||||
0.394220 | + | 0.919016i | \(0.371015\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.88194 | −0.421045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.7367 | 0.507826 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.7360 | −0.601050 | −0.300525 | − | 0.953774i | \(-0.597162\pi\) | ||||
−0.300525 | + | 0.953774i | \(0.597162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.2846 | −1.00225 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.776575 | 0.0364867 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.2495 | 1.18372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.9605 | 1.07405 | 0.537024 | − | 0.843567i | \(-0.319548\pi\) | ||||
0.537024 | + | 0.843567i | \(0.319548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.64027 | 0.169913 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.7347 | 1.19859 | 0.599293 | − | 0.800530i | \(-0.295449\pi\) | ||||
0.599293 | + | 0.800530i | \(0.295449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.3604 | 1.82923 | 0.914616 | − | 0.404323i | \(-0.132493\pi\) | ||||
0.914616 | + | 0.404323i | \(0.132493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.72168 | −0.404458 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9555 | 0.692058 | 0.346029 | − | 0.938224i | \(-0.387530\pi\) | ||||
0.346029 | + | 0.938224i | \(0.387530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.5491 | 1.82621 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.39402 | 0.340699 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.54160 | 0.162843 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.2952 | −0.931207 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.782015 | 0.0358060 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.494235 | 0.0225822 | 0.0112911 | − | 0.999936i | \(-0.496406\pi\) | ||||
0.0112911 | + | 0.999936i | \(0.496406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6898 | −0.715394 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.7016 | 0.896452 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.91026 | −0.177556 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.27382 | −0.0577222 | −0.0288611 | − | 0.999583i | \(-0.509188\pi\) | ||||
−0.0288611 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.8717 | −0.762964 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.45413 | −0.155883 | −0.0779415 | − | 0.996958i | \(-0.524835\pi\) | ||||
−0.0779415 | + | 0.996958i | \(0.524835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.2525 | 1.67777 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.55635 | −0.159846 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.4086 | −1.90229 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0025 | 0.626839 | 0.313420 | − | 0.949615i | \(-0.398525\pi\) | ||||
0.313420 | + | 0.949615i | \(0.398525\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5706 | −0.738848 | −0.369424 | − | 0.929261i | \(-0.620445\pi\) | ||||
−0.369424 | + | 0.929261i | \(0.620445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.42584 | 0.330445 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.3673 | −0.726897 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.9733 | 1.06260 | 0.531299 | − | 0.847184i | \(-0.321704\pi\) | ||||
0.531299 | + | 0.847184i | \(0.321704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.6950 | −1.26939 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.92607 | −0.217491 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.38702 | 0.193315 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.5754 | −1.60859 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.4626 | 0.810417 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.77526 | 0.340640 | 0.170320 | − | 0.985389i | \(-0.445520\pi\) | ||||
0.170320 | + | 0.985389i | \(0.445520\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.1796 | −1.53830 | −0.769149 | − | 0.639069i | \(-0.779320\pi\) | ||||
−0.769149 | + | 0.639069i | \(0.779320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.4627 | 0.893064 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.8440 | 1.47427 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.26515 | −0.315876 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.0714 | 0.654045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.4260 | 1.31790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9710 | 0.474319 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.1981 | −0.612694 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 66.9802 | 2.88504 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.5670 | 1.40017 | 0.700083 | − | 0.714062i | \(-0.253146\pi\) | ||||
0.700083 | + | 0.714062i | \(0.253146\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.3089 | −0.785708 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0065 | −0.642810 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.59032 | 0.367296 | 0.183648 | − | 0.982992i | \(-0.441209\pi\) | ||||
0.183648 | + | 0.982992i | \(0.441209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.5501 | −0.535624 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −50.4106 | −2.14756 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.93791 | −0.209981 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.71605 | 0.115290 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.86029 | −0.163566 | −0.0817830 | − | 0.996650i | \(-0.526061\pi\) | ||||
−0.0817830 | + | 0.996650i | \(0.526061\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.06266 | −0.214128 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.8002 | 0.582646 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8475 | 0.667891 | 0.333946 | − | 0.942592i | \(-0.391620\pi\) | ||||
0.333946 | + | 0.942592i | \(0.391620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00271 | 0.252536 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.96672 | 0.208583 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.8436 | 1.33496 | 0.667478 | − | 0.744630i | \(-0.267374\pi\) | ||||
0.667478 | + | 0.744630i | \(0.267374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.7301 | −1.45341 | −0.726706 | − | 0.686949i | \(-0.758950\pi\) | ||||
−0.726706 | + | 0.686949i | \(0.758950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.4667 | −0.562577 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.3427 | 0.681538 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7968 | −0.865783 | −0.432892 | − | 0.901446i | \(-0.642507\pi\) | ||||
−0.432892 | + | 0.901446i | \(0.642507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.6449 | −0.567064 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3315 | 0.428621 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.96461 | 0.122782 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.08375 | 0.210187 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.8987 | −1.39915 | −0.699574 | − | 0.714560i | \(-0.746627\pi\) | ||||
−0.699574 | + | 0.714560i | \(0.746627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.7982 | −1.88708 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9789 | −0.862956 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.7423 | −1.05711 | −0.528554 | − | 0.848900i | \(-0.677266\pi\) | ||||
−0.528554 | + | 0.848900i | \(0.677266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.9611 | 0.695339 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.0296 | 0.533268 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.85022 | −0.157316 | −0.0786578 | − | 0.996902i | \(-0.525063\pi\) | ||||
−0.0786578 | + | 0.996902i | \(0.525063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.44645 | −0.0997930 | −0.0498965 | − | 0.998754i | \(-0.515889\pi\) | ||||
−0.0498965 | + | 0.998754i | \(0.515889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.96283 | 0.324271 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.16291 | −0.128590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.3391 | 1.92143 | 0.960717 | − | 0.277529i | \(-0.0895156\pi\) | ||||
0.960717 | + | 0.277529i | \(0.0895156\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50.8266 | 2.05960 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.2841 | 2.11519 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.1587 | 0.975762 | 0.487881 | − | 0.872910i | \(-0.337770\pi\) | ||||
0.487881 | + | 0.872910i | \(0.337770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.26702 | −0.212387 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6706 | 1.15424 | 0.577118 | − | 0.816661i | \(-0.304177\pi\) | ||||
0.577118 | + | 0.816661i | \(0.304177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.44432 | −0.339406 | −0.169703 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169703 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.96672 | 0.159179 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.0247 | 1.88400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5738 | 0.502953 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.6747 | −0.745794 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.5395 | −0.420237 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9953 | 0.676574 | 0.338287 | − | 0.941043i | \(-0.390153\pi\) | ||||
0.338287 | + | 0.941043i | \(0.390153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.2109 | −0.723819 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.71379 | 0.107694 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −95.7473 | −3.79364 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.53856 | −0.337780 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.16277 | −0.203917 | −0.101959 | − | 0.994789i | \(-0.532511\pi\) | ||||
−0.101959 | + | 0.994789i | \(0.532511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2816 | 0.839266 | 0.419633 | − | 0.907694i | \(-0.362159\pi\) | ||||
0.419633 | + | 0.907694i | \(0.362159\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.876392 | 0.0345079 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0273 | 0.630099 | 0.315049 | − | 0.949075i | \(-0.397979\pi\) | ||||
0.315049 | + | 0.949075i | \(0.397979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.1357 | 2.24277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 46.1762 | 1.80979 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.626015 | 0.0244979 | 0.0122489 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122489 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.41468 | 0.328789 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.77746 | −0.225400 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.5268 | 0.487974 | 0.243987 | − | 0.969778i | \(-0.421545\pi\) | ||||
0.243987 | + | 0.969778i | \(0.421545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7520 | −1.66286 | −0.831431 | − | 0.555628i | \(-0.812478\pi\) | ||||
−0.831431 | + | 0.555628i | \(0.812478\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.7272 | −0.766142 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.9521 | −0.890043 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.5932 | 1.57177 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.9336 | −0.654690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.5772 | −1.83670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.4562 | −1.40528 | −0.702641 | − | 0.711545i | \(-0.747996\pi\) | ||||
−0.702641 | + | 0.711545i | \(0.747996\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.11996 | 0.158577 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1589 | −0.505738 | −0.252869 | − | 0.967501i | \(-0.581374\pi\) | ||||
−0.252869 | + | 0.967501i | \(0.581374\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7025 | 0.794489 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.66081 | −0.140282 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.9825 | −1.03246 | −0.516228 | − | 0.856451i | \(-0.672664\pi\) | ||||
−0.516228 | + | 0.856451i | \(0.672664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5268 | 0.631457 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.7283 | 0.905289 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.23786 | −0.161450 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.8616 | −1.85878 | −0.929391 | − | 0.369098i | \(-0.879667\pi\) | ||||
−0.929391 | + | 0.369098i | \(0.879667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.8288 | 0.715246 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.2727 | 0.389664 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4384 | 0.774160 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.4226 | 0.469867 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.66374 | −0.176147 | −0.0880735 | − | 0.996114i | \(-0.528071\pi\) | ||||
−0.0880735 | + | 0.996114i | \(0.528071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2622 | 0.537909 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.05085 | −0.340875 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.3154 | −1.47861 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0634 | −0.603272 | −0.301636 | − | 0.953423i | \(-0.597533\pi\) | ||||
−0.301636 | + | 0.953423i | \(0.597533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.994199 | −0.0372854 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.8790 | 1.38113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.2724 | 0.720748 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.7982 | 0.814068 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.91597 | 0.146041 | 0.0730204 | − | 0.997330i | \(-0.476736\pi\) | ||||
0.0730204 | + | 0.997330i | \(0.476736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2267 | −0.865007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.02354 | −0.186827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 42.1613 | 1.56583 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.871641 | −0.0323274 | −0.0161637 | − | 0.999869i | \(-0.505145\pi\) | ||||
−0.0161637 | + | 0.999869i | \(0.505145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.40079 | −0.125783 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8543 | 0.770270 | 0.385135 | − | 0.922860i | \(-0.374155\pi\) | ||||
0.385135 | + | 0.922860i | \(0.374155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.5747 | 0.611368 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1870 | 1.11195 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.8564 | −0.767217 | −0.383608 | − | 0.923496i | \(-0.625319\pi\) | ||||
−0.383608 | + | 0.923496i | \(0.625319\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.6952 | 0.980671 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.26706 | −0.266603 | −0.133301 | − | 0.991076i | \(-0.542558\pi\) | ||||
−0.133301 | + | 0.991076i | \(0.542558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0721 | 0.369014 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.08014 | 0.0761082 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −58.0852 | −2.12239 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7011 | 0.572943 | 0.286471 | − | 0.958089i | \(-0.407518\pi\) | ||||
0.286471 | + | 0.958089i | \(0.407518\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.2662 | 0.374122 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.728510 | 0.0265132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.4685 | −1.14374 | −0.571870 | − | 0.820344i | \(-0.693782\pi\) | ||||
−0.571870 | + | 0.820344i | \(0.693782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0378 | 0.545837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6417 | −0.385760 | −0.192880 | − | 0.981222i | \(-0.561783\pi\) | ||||
−0.192880 | + | 0.981222i | \(0.561783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 79.4508 | 2.87631 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.41496 | 0.123468 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −81.6746 | −2.94910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.4970 | 0.775201 | 0.387601 | − | 0.921827i | \(-0.373304\pi\) | ||||
0.387601 | + | 0.921827i | \(0.373304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9857 | 0.431656 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0847 | 0.866267 | 0.433134 | − | 0.901330i | \(-0.357408\pi\) | ||||
0.433134 | + | 0.901330i | \(0.357408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.3037 | 1.37591 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.3799 | −0.515875 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27.6576 | −0.990935 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3696 | −1.15827 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.2334 | 0.365713 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.93638 | 0.247570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.23370 | −0.186561 | −0.0932807 | − | 0.995640i | \(-0.529735\pi\) | ||||
−0.0932807 | + | 0.995640i | \(0.529735\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.9764 | 0.960386 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.7808 | −1.13000 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.0109 | 2.41514 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.733613 | 0.0260186 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.8380 | −1.41113 | −0.705567 | − | 0.708643i | \(-0.749308\pi\) | ||||
−0.705567 | + | 0.708643i | \(0.749308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.1213 | 1.24250 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.46795 | 0.334534 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.9023 | −0.772915 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4822 | 0.651410 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.3337 | −1.03260 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.0976 | −1.12849 | −0.564245 | − | 0.825607i | \(-0.690833\pi\) | ||||
−0.564245 | + | 0.825607i | \(0.690833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.75780 | 0.342643 | 0.171321 | − | 0.985215i | \(-0.445196\pi\) | ||||
0.171321 | + | 0.985215i | \(0.445196\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4504 | −0.401584 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.8274 | −0.554411 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.60200 | 0.161004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.9154 | −0.940502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3362 | −0.779539 | −0.389770 | − | 0.920912i | \(-0.627445\pi\) | ||||
−0.389770 | + | 0.920912i | \(0.627445\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2312 | −0.391496 | −0.195748 | − | 0.980654i | \(-0.562714\pi\) | ||||
−0.195748 | + | 0.980654i | \(0.562714\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.6187 | 0.543774 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4558 | −0.815639 | −0.407819 | − | 0.913063i | \(-0.633711\pi\) | ||||
−0.407819 | + | 0.913063i | \(0.633711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4725 | −0.537381 | −0.268690 | − | 0.963227i | \(-0.586591\pi\) | ||||
−0.268690 | + | 0.963227i | \(0.586591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.10038 | −0.0728613 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −64.3173 | −2.22846 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.938106 | −0.0324645 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.29712 | 0.321355 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.61128 | −0.0556276 | −0.0278138 | − | 0.999613i | \(-0.508855\pi\) | ||||
−0.0278138 | + | 0.999613i | \(0.508855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.7232 | 2.61115 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.37932 | 0.0819481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.3543 | −0.528203 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.7457 | 0.575390 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0104 | 0.961314 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4846 | −0.393688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.22499 | −0.110421 | −0.0552107 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552107 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.62117 | −0.158041 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.31541 | −0.0449334 | −0.0224667 | − | 0.999748i | \(-0.507152\pi\) | ||||
−0.0224667 | + | 0.999748i | \(0.507152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.03496 | 0.0694320 | 0.0347160 | − | 0.999397i | \(-0.488947\pi\) | ||||
0.0347160 | + | 0.999397i | \(0.488947\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.8858 | 0.950345 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.2917 | −0.894981 | −0.447490 | − | 0.894289i | \(-0.647682\pi\) | ||||
−0.447490 | + | 0.894289i | \(0.647682\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.3198 | 0.588893 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.74843 | 0.127303 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.76900 | −0.127854 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.1518 | −1.46214 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.16825 | 0.141074 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.4927 | 1.43651 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.99857 | 0.135022 | 0.0675111 | − | 0.997719i | \(-0.478494\pi\) | ||||
0.0675111 | + | 0.997719i | \(0.478494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.26096 | 0.211177 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.8878 | 1.24278 | 0.621391 | − | 0.783501i | \(-0.286568\pi\) | ||||
0.621391 | + | 0.783501i | \(0.286568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5716 | 0.692290 | 0.346145 | − | 0.938181i | \(-0.387491\pi\) | ||||
0.346145 | + | 0.938181i | \(0.387491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.1386 | 0.475264 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.4419 | −1.12287 | −0.561435 | − | 0.827521i | \(-0.689750\pi\) | ||||
−0.561435 | + | 0.827521i | \(0.689750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.3679 | −0.481885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79099 | 0.127003 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −47.5267 | −1.59042 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.3193 | −0.445217 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4963 | −0.717740 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 95.1415 | 3.17315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.84675 | −0.0948388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.63998 | −0.154409 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.1756 | −0.570938 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.4819 | 1.44379 | 0.721897 | − | 0.692001i | \(-0.243270\pi\) | ||||
0.721897 | + | 0.692001i | \(0.243270\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.91578 | −0.262550 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.34014 | 0.243190 | 0.121595 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121595 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.88577 | 0.260981 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.7733 | −0.389213 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.5508 | −1.47120 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1239 | 0.333957 | 0.166978 | − | 0.985961i | \(-0.446599\pi\) | ||||
0.166978 | + | 0.985961i | \(0.446599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.9131 | 0.985671 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.2718 | 1.52306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.9283 | −0.392200 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.67646 | −0.153595 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.3148 | 0.338419 | 0.169210 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169210 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 87.0352 | 2.85246 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.6641 | −0.545557 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.9461 | 0.423382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.4046 | −0.503247 | −0.251623 | − | 0.967825i | \(-0.580964\pi\) | ||||
−0.251623 | + | 0.967825i | \(0.580964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.82677 | −0.0596144 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.3822 | 1.64241 | 0.821207 | − | 0.570630i | \(-0.193301\pi\) | ||||
0.821207 | + | 0.570630i | \(0.193301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.2712 | 0.725252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.65931 | 0.151567 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.6479 | 0.638472 | 0.319236 | − | 0.947675i | \(-0.396574\pi\) | ||||
0.319236 | + | 0.947675i | \(0.396574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.3090 | 1.01633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.80617 | 0.220705 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.92780 | −0.159627 | −0.0798136 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798136 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6331 | −0.408799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.7948 | 1.25406 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −87.4998 | −2.82551 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.4364 | 1.78827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.6949 | −0.376862 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8004 | −0.412059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.1654 | 0.777107 | 0.388554 | − | 0.921426i | \(-0.372975\pi\) | ||||
0.388554 | + | 0.921426i | \(0.372975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.9322 | 0.576066 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9672 | −0.640780 | −0.320390 | − | 0.947286i | \(-0.603814\pi\) | ||||
−0.320390 | + | 0.947286i | \(0.603814\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.3877 | −1.74359 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −22.3267 | −0.715027 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.2739 | 1.67239 | 0.836195 | − | 0.548432i | \(-0.184775\pi\) | ||||
0.836195 | + | 0.548432i | \(0.184775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.8929 | 1.14714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.9966 | 0.510734 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.5159 | 0.845726 | 0.422863 | − | 0.906194i | \(-0.361025\pi\) | ||||
0.422863 | + | 0.906194i | \(0.361025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.6804 | −0.627070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.9189 | 1.52527 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.70576 | −0.117836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6727 | −0.751988 | −0.375994 | − | 0.926622i | \(-0.622699\pi\) | ||||
−0.375994 | + | 0.926622i | \(0.622699\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.7166 | −1.06996 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2232 | 0.387501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.5729 | −0.936584 | −0.468292 | − | 0.883574i | \(-0.655131\pi\) | ||||
−0.468292 | + | 0.883574i | \(0.655131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.89525 | −0.0916016 |
(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 | 4008.2.a.h.1.4 | ✓ | 8 | |
4.3 | odd | 2 | 8016.2.a.y.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.h.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
8016.2.a.y.1.4 | 8 | 4.3 | odd | 2 |