Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.78139 | 1.96674 | 0.983369 | − | 0.181618i | \(-0.0581335\pi\) | ||||
0.983369 | + | 0.181618i | \(0.0581335\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.73612 | 2.86806 | ||||||||
\(5\) | −0.739443 | −0.330689 | −0.165344 | − | 0.986236i | \(-0.552874\pi\) | ||||
−0.165344 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(6\) | −2.78139 | −1.13550 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 10.3916 | 3.67398 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.05668 | −0.650378 | ||||||||
\(11\) | 4.44400 | 1.33992 | 0.669958 | − | 0.742399i | \(-0.266312\pi\) | ||||
0.669958 | + | 0.742399i | \(0.266312\pi\) | |||||||
\(12\) | −5.73612 | −1.65587 | ||||||||
\(13\) | −0.996618 | −0.276412 | −0.138206 | − | 0.990404i | \(-0.544134\pi\) | ||||
−0.138206 | + | 0.990404i | \(0.544134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.739443 | 0.190923 | ||||||||
\(16\) | 17.4308 | 4.35770 | ||||||||
\(17\) | 1.26311 | 0.306349 | 0.153174 | − | 0.988199i | \(-0.451050\pi\) | ||||
0.153174 | + | 0.988199i | \(0.451050\pi\) | |||||||
\(18\) | 2.78139 | 0.655579 | ||||||||
\(19\) | 1.98029 | 0.454310 | 0.227155 | − | 0.973859i | \(-0.427058\pi\) | ||||
0.227155 | + | 0.973859i | \(0.427058\pi\) | |||||||
\(20\) | −4.24153 | −0.948435 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 12.3605 | 2.63526 | ||||||||
\(23\) | 0.818638 | 0.170698 | 0.0853490 | − | 0.996351i | \(-0.472799\pi\) | ||||
0.0853490 | + | 0.996351i | \(0.472799\pi\) | |||||||
\(24\) | −10.3916 | −2.12118 | ||||||||
\(25\) | −4.45322 | −0.890645 | ||||||||
\(26\) | −2.77198 | −0.543630 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.261203 | −0.0485042 | −0.0242521 | − | 0.999706i | \(-0.507720\pi\) | ||||
−0.0242521 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(30\) | 2.05668 | 0.375496 | ||||||||
\(31\) | 7.23078 | 1.29869 | 0.649344 | − | 0.760495i | \(-0.275044\pi\) | ||||
0.649344 | + | 0.760495i | \(0.275044\pi\) | |||||||
\(32\) | 27.6987 | 4.89648 | ||||||||
\(33\) | −4.44400 | −0.773600 | ||||||||
\(34\) | 3.51319 | 0.602508 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.73612 | 0.956020 | ||||||||
\(37\) | −7.70796 | −1.26718 | −0.633591 | − | 0.773668i | \(-0.718420\pi\) | ||||
−0.633591 | + | 0.773668i | \(0.718420\pi\) | |||||||
\(38\) | 5.50796 | 0.893510 | ||||||||
\(39\) | 0.996618 | 0.159587 | ||||||||
\(40\) | −7.68399 | −1.21495 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.72101 | −0.719947 | −0.359974 | − | 0.932963i | \(-0.617214\pi\) | ||||
−0.359974 | + | 0.932963i | \(0.617214\pi\) | |||||||
\(44\) | 25.4913 | 3.84296 | ||||||||
\(45\) | −0.739443 | −0.110230 | ||||||||
\(46\) | 2.27695 | 0.335718 | ||||||||
\(47\) | 8.48773 | 1.23806 | 0.619031 | − | 0.785366i | \(-0.287525\pi\) | ||||
0.619031 | + | 0.785366i | \(0.287525\pi\) | |||||||
\(48\) | −17.4308 | −2.51592 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.3861 | −1.75167 | ||||||||
\(51\) | −1.26311 | −0.176871 | ||||||||
\(52\) | −5.71672 | −0.792766 | ||||||||
\(53\) | −10.1423 | −1.39316 | −0.696579 | − | 0.717480i | \(-0.745295\pi\) | ||||
−0.696579 | + | 0.717480i | \(0.745295\pi\) | |||||||
\(54\) | −2.78139 | −0.378499 | ||||||||
\(55\) | −3.28608 | −0.443095 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.98029 | −0.262296 | ||||||||
\(58\) | −0.726506 | −0.0953950 | ||||||||
\(59\) | 7.87031 | 1.02463 | 0.512313 | − | 0.858799i | \(-0.328789\pi\) | ||||
0.512313 | + | 0.858799i | \(0.328789\pi\) | |||||||
\(60\) | 4.24153 | 0.547579 | ||||||||
\(61\) | −6.85524 | −0.877723 | −0.438862 | − | 0.898555i | \(-0.644618\pi\) | ||||
−0.438862 | + | 0.898555i | \(0.644618\pi\) | |||||||
\(62\) | 20.1116 | 2.55418 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 42.1791 | 5.27239 | ||||||||
\(65\) | 0.736942 | 0.0914064 | ||||||||
\(66\) | −12.3605 | −1.52147 | ||||||||
\(67\) | 4.70290 | 0.574551 | 0.287276 | − | 0.957848i | \(-0.407250\pi\) | ||||
0.287276 | + | 0.957848i | \(0.407250\pi\) | |||||||
\(68\) | 7.24534 | 0.878626 | ||||||||
\(69\) | −0.818638 | −0.0985525 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60455 | −0.665138 | −0.332569 | − | 0.943079i | \(-0.607915\pi\) | ||||
−0.332569 | + | 0.943079i | \(0.607915\pi\) | |||||||
\(72\) | 10.3916 | 1.22466 | ||||||||
\(73\) | −10.6056 | −1.24129 | −0.620643 | − | 0.784093i | \(-0.713128\pi\) | ||||
−0.620643 | + | 0.784093i | \(0.713128\pi\) | |||||||
\(74\) | −21.4388 | −2.49221 | ||||||||
\(75\) | 4.45322 | 0.514214 | ||||||||
\(76\) | 11.3592 | 1.30299 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.77198 | 0.313865 | ||||||||
\(79\) | 1.81828 | 0.204572 | 0.102286 | − | 0.994755i | \(-0.467384\pi\) | ||||
0.102286 | + | 0.994755i | \(0.467384\pi\) | |||||||
\(80\) | −12.8891 | −1.44104 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.78139 | 0.307153 | ||||||||
\(83\) | 14.9327 | 1.63907 | 0.819537 | − | 0.573027i | \(-0.194231\pi\) | ||||
0.819537 | + | 0.573027i | \(0.194231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.933996 | −0.101306 | ||||||||
\(86\) | −13.1310 | −1.41595 | ||||||||
\(87\) | 0.261203 | 0.0280039 | ||||||||
\(88\) | 46.1802 | 4.92283 | ||||||||
\(89\) | −11.9846 | −1.27036 | −0.635181 | − | 0.772364i | \(-0.719074\pi\) | ||||
−0.635181 | + | 0.772364i | \(0.719074\pi\) | |||||||
\(90\) | −2.05668 | −0.216793 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.69581 | 0.489572 | ||||||||
\(93\) | −7.23078 | −0.749797 | ||||||||
\(94\) | 23.6077 | 2.43495 | ||||||||
\(95\) | −1.46431 | −0.150235 | ||||||||
\(96\) | −27.6987 | −2.82698 | ||||||||
\(97\) | 7.76174 | 0.788086 | 0.394043 | − | 0.919092i | \(-0.371076\pi\) | ||||
0.394043 | + | 0.919092i | \(0.371076\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.44400 | 0.446638 | ||||||||
\(100\) | −25.5442 | −2.55442 | ||||||||
\(101\) | −1.90481 | −0.189536 | −0.0947680 | − | 0.995499i | \(-0.530211\pi\) | ||||
−0.0947680 | + | 0.995499i | \(0.530211\pi\) | |||||||
\(102\) | −3.51319 | −0.347858 | ||||||||
\(103\) | 11.9010 | 1.17264 | 0.586318 | − | 0.810081i | \(-0.300577\pi\) | ||||
0.586318 | + | 0.810081i | \(0.300577\pi\) | |||||||
\(104\) | −10.3564 | −1.01553 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.2098 | −2.73998 | ||||||||
\(107\) | 20.1914 | 1.95197 | 0.975987 | − | 0.217828i | \(-0.0698973\pi\) | ||||
0.975987 | + | 0.217828i | \(0.0698973\pi\) | |||||||
\(108\) | −5.73612 | −0.551958 | ||||||||
\(109\) | 12.9034 | 1.23592 | 0.617959 | − | 0.786210i | \(-0.287960\pi\) | ||||
0.617959 | + | 0.786210i | \(0.287960\pi\) | |||||||
\(110\) | −9.13986 | −0.871452 | ||||||||
\(111\) | 7.70796 | 0.731608 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.91023 | 0.461916 | 0.230958 | − | 0.972964i | \(-0.425814\pi\) | ||||
0.230958 | + | 0.972964i | \(0.425814\pi\) | |||||||
\(114\) | −5.50796 | −0.515868 | ||||||||
\(115\) | −0.605336 | −0.0564479 | ||||||||
\(116\) | −1.49829 | −0.139113 | ||||||||
\(117\) | −0.996618 | −0.0921373 | ||||||||
\(118\) | 21.8904 | 2.01517 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.68399 | 0.701449 | ||||||||
\(121\) | 8.74910 | 0.795373 | ||||||||
\(122\) | −19.0671 | −1.72625 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 41.4766 | 3.72471 | ||||||||
\(125\) | 6.99012 | 0.625215 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3656 | 1.18600 | 0.593001 | − | 0.805201i | \(-0.297943\pi\) | ||||
0.593001 | + | 0.805201i | \(0.297943\pi\) | |||||||
\(128\) | 61.9191 | 5.47293 | ||||||||
\(129\) | 4.72101 | 0.415662 | ||||||||
\(130\) | 2.04972 | 0.179772 | ||||||||
\(131\) | 6.39618 | 0.558836 | 0.279418 | − | 0.960169i | \(-0.409858\pi\) | ||||
0.279418 | + | 0.960169i | \(0.409858\pi\) | |||||||
\(132\) | −25.4913 | −2.21873 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.0806 | 1.12999 | ||||||||
\(135\) | 0.739443 | 0.0636411 | ||||||||
\(136\) | 13.1257 | 1.12552 | ||||||||
\(137\) | −17.7906 | −1.51995 | −0.759977 | − | 0.649950i | \(-0.774790\pi\) | ||||
−0.759977 | + | 0.649950i | \(0.774790\pi\) | |||||||
\(138\) | −2.27695 | −0.193827 | ||||||||
\(139\) | −17.9649 | −1.52376 | −0.761881 | − | 0.647717i | \(-0.775724\pi\) | ||||
−0.761881 | + | 0.647717i | \(0.775724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.48773 | −0.714796 | ||||||||
\(142\) | −15.5884 | −1.30815 | ||||||||
\(143\) | −4.42897 | −0.370369 | ||||||||
\(144\) | 17.4308 | 1.45257 | ||||||||
\(145\) | 0.193145 | 0.0160398 | ||||||||
\(146\) | −29.4982 | −2.44128 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −44.2138 | −3.63435 | ||||||||
\(149\) | 9.87073 | 0.808642 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(150\) | 12.3861 | 1.01132 | ||||||||
\(151\) | 2.97270 | 0.241915 | 0.120957 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120957 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(152\) | 20.5784 | 1.66913 | ||||||||
\(153\) | 1.26311 | 0.102116 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.34675 | −0.429461 | ||||||||
\(156\) | 5.71672 | 0.457704 | ||||||||
\(157\) | −7.59023 | −0.605766 | −0.302883 | − | 0.953028i | \(-0.597949\pi\) | ||||
−0.302883 | + | 0.953028i | \(0.597949\pi\) | |||||||
\(158\) | 5.05734 | 0.402340 | ||||||||
\(159\) | 10.1423 | 0.804340 | ||||||||
\(160\) | −20.4816 | −1.61921 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.78139 | 0.218526 | ||||||||
\(163\) | 3.51811 | 0.275560 | 0.137780 | − | 0.990463i | \(-0.456003\pi\) | ||||
0.137780 | + | 0.990463i | \(0.456003\pi\) | |||||||
\(164\) | 5.73612 | 0.447916 | ||||||||
\(165\) | 3.28608 | 0.255821 | ||||||||
\(166\) | 41.5335 | 3.22363 | ||||||||
\(167\) | −11.7196 | −0.906890 | −0.453445 | − | 0.891284i | \(-0.649805\pi\) | ||||
−0.453445 | + | 0.891284i | \(0.649805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0068 | −0.923596 | ||||||||
\(170\) | −2.59781 | −0.199243 | ||||||||
\(171\) | 1.98029 | 0.151437 | ||||||||
\(172\) | −27.0803 | −2.06485 | ||||||||
\(173\) | 1.24977 | 0.0950180 | 0.0475090 | − | 0.998871i | \(-0.484872\pi\) | ||||
0.0475090 | + | 0.998871i | \(0.484872\pi\) | |||||||
\(174\) | 0.726506 | 0.0550763 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 77.4625 | 5.83895 | ||||||||
\(177\) | −7.87031 | −0.591569 | ||||||||
\(178\) | −33.3337 | −2.49847 | ||||||||
\(179\) | −22.2805 | −1.66532 | −0.832661 | − | 0.553783i | \(-0.813184\pi\) | ||||
−0.832661 | + | 0.553783i | \(0.813184\pi\) | |||||||
\(180\) | −4.24153 | −0.316145 | ||||||||
\(181\) | −22.0862 | −1.64166 | −0.820828 | − | 0.571175i | \(-0.806488\pi\) | ||||
−0.820828 | + | 0.571175i | \(0.806488\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.85524 | 0.506754 | ||||||||
\(184\) | 8.50696 | 0.627141 | ||||||||
\(185\) | 5.69960 | 0.419043 | ||||||||
\(186\) | −20.1116 | −1.47466 | ||||||||
\(187\) | 5.61325 | 0.410481 | ||||||||
\(188\) | 48.6866 | 3.55084 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.07282 | −0.295474 | ||||||||
\(191\) | −10.3978 | −0.752362 | −0.376181 | − | 0.926546i | \(-0.622763\pi\) | ||||
−0.376181 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(192\) | −42.1791 | −3.04402 | ||||||||
\(193\) | 7.05716 | 0.507985 | 0.253993 | − | 0.967206i | \(-0.418256\pi\) | ||||
0.253993 | + | 0.967206i | \(0.418256\pi\) | |||||||
\(194\) | 21.5884 | 1.54996 | ||||||||
\(195\) | −0.736942 | −0.0527735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0301 | 0.999604 | 0.499802 | − | 0.866140i | \(-0.333406\pi\) | ||||
0.499802 | + | 0.866140i | \(0.333406\pi\) | |||||||
\(198\) | 12.3605 | 0.878421 | ||||||||
\(199\) | −18.5358 | −1.31397 | −0.656984 | − | 0.753904i | \(-0.728168\pi\) | ||||
−0.656984 | + | 0.753904i | \(0.728168\pi\) | |||||||
\(200\) | −46.2761 | −3.27221 | ||||||||
\(201\) | −4.70290 | −0.331717 | ||||||||
\(202\) | −5.29802 | −0.372768 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.24534 | −0.507275 | ||||||||
\(205\) | −0.739443 | −0.0516449 | ||||||||
\(206\) | 33.1012 | 2.30627 | ||||||||
\(207\) | 0.818638 | 0.0568993 | ||||||||
\(208\) | −17.3719 | −1.20452 | ||||||||
\(209\) | 8.80041 | 0.608737 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.96301 | −0.341668 | −0.170834 | − | 0.985300i | \(-0.554646\pi\) | ||||
−0.170834 | + | 0.985300i | \(0.554646\pi\) | |||||||
\(212\) | −58.1777 | −3.99566 | ||||||||
\(213\) | 5.60455 | 0.384018 | ||||||||
\(214\) | 56.1601 | 3.83902 | ||||||||
\(215\) | 3.49092 | 0.238078 | ||||||||
\(216\) | −10.3916 | −0.707058 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 35.8893 | 2.43073 | ||||||||
\(219\) | 10.6056 | 0.716657 | ||||||||
\(220\) | −18.8493 | −1.27082 | ||||||||
\(221\) | −1.25884 | −0.0846785 | ||||||||
\(222\) | 21.4388 | 1.43888 | ||||||||
\(223\) | −28.3618 | −1.89924 | −0.949622 | − | 0.313398i | \(-0.898533\pi\) | ||||
−0.949622 | + | 0.313398i | \(0.898533\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.45322 | −0.296882 | ||||||||
\(226\) | 13.6573 | 0.908468 | ||||||||
\(227\) | −12.3166 | −0.817482 | −0.408741 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408741 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(228\) | −11.3592 | −0.752281 | ||||||||
\(229\) | 28.5546 | 1.88694 | 0.943470 | − | 0.331459i | \(-0.107541\pi\) | ||||
0.943470 | + | 0.331459i | \(0.107541\pi\) | |||||||
\(230\) | −1.68367 | −0.111018 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.71431 | −0.178203 | ||||||||
\(233\) | 4.44452 | 0.291170 | 0.145585 | − | 0.989346i | \(-0.453493\pi\) | ||||
0.145585 | + | 0.989346i | \(0.453493\pi\) | |||||||
\(234\) | −2.77198 | −0.181210 | ||||||||
\(235\) | −6.27619 | −0.409413 | ||||||||
\(236\) | 45.1450 | 2.93869 | ||||||||
\(237\) | −1.81828 | −0.118110 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.27584 | 0.405950 | 0.202975 | − | 0.979184i | \(-0.434939\pi\) | ||||
0.202975 | + | 0.979184i | \(0.434939\pi\) | |||||||
\(240\) | 12.8891 | 0.831987 | ||||||||
\(241\) | 1.02263 | 0.0658735 | 0.0329367 | − | 0.999457i | \(-0.489514\pi\) | ||||
0.0329367 | + | 0.999457i | \(0.489514\pi\) | |||||||
\(242\) | 24.3347 | 1.56429 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −39.3224 | −2.51736 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.78139 | −0.177335 | ||||||||
\(247\) | −1.97360 | −0.125577 | ||||||||
\(248\) | 75.1394 | 4.77135 | ||||||||
\(249\) | −14.9327 | −0.946319 | ||||||||
\(250\) | 19.4422 | 1.22963 | ||||||||
\(251\) | −14.9031 | −0.940675 | −0.470338 | − | 0.882486i | \(-0.655868\pi\) | ||||
−0.470338 | + | 0.882486i | \(0.655868\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.63803 | 0.228721 | ||||||||
\(254\) | 37.1748 | 2.33256 | ||||||||
\(255\) | 0.933996 | 0.0584891 | ||||||||
\(256\) | 87.8629 | 5.49143 | ||||||||
\(257\) | 12.2433 | 0.763716 | 0.381858 | − | 0.924221i | \(-0.375284\pi\) | ||||
0.381858 | + | 0.924221i | \(0.375284\pi\) | |||||||
\(258\) | 13.1310 | 0.817498 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.22718 | 0.262159 | ||||||||
\(261\) | −0.261203 | −0.0161681 | ||||||||
\(262\) | 17.7902 | 1.09908 | ||||||||
\(263\) | 14.3878 | 0.887190 | 0.443595 | − | 0.896227i | \(-0.353703\pi\) | ||||
0.443595 | + | 0.896227i | \(0.353703\pi\) | |||||||
\(264\) | −46.1802 | −2.84220 | ||||||||
\(265\) | 7.49968 | 0.460702 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9846 | 0.733443 | ||||||||
\(268\) | 26.9764 | 1.64785 | ||||||||
\(269\) | 15.4040 | 0.939200 | 0.469600 | − | 0.882879i | \(-0.344398\pi\) | ||||
0.469600 | + | 0.882879i | \(0.344398\pi\) | |||||||
\(270\) | 2.05668 | 0.125165 | ||||||||
\(271\) | 23.6110 | 1.43427 | 0.717134 | − | 0.696936i | \(-0.245454\pi\) | ||||
0.717134 | + | 0.696936i | \(0.245454\pi\) | |||||||
\(272\) | 22.0170 | 1.33498 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −49.4826 | −2.98935 | ||||||||
\(275\) | −19.7901 | −1.19339 | ||||||||
\(276\) | −4.69581 | −0.282654 | ||||||||
\(277\) | −22.5841 | −1.35695 | −0.678473 | − | 0.734626i | \(-0.737358\pi\) | ||||
−0.678473 | + | 0.734626i | \(0.737358\pi\) | |||||||
\(278\) | −49.9673 | −2.99684 | ||||||||
\(279\) | 7.23078 | 0.432896 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.9736 | −1.01256 | −0.506280 | − | 0.862369i | \(-0.668980\pi\) | ||||
−0.506280 | + | 0.862369i | \(0.668980\pi\) | |||||||
\(282\) | −23.6077 | −1.40582 | ||||||||
\(283\) | 21.2050 | 1.26051 | 0.630254 | − | 0.776389i | \(-0.282951\pi\) | ||||
0.630254 | + | 0.776389i | \(0.282951\pi\) | |||||||
\(284\) | −32.1484 | −1.90766 | ||||||||
\(285\) | 1.46431 | 0.0867384 | ||||||||
\(286\) | −12.3187 | −0.728418 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 27.6987 | 1.63216 | ||||||||
\(289\) | −15.4046 | −0.906150 | ||||||||
\(290\) | 0.537210 | 0.0315460 | ||||||||
\(291\) | −7.76174 | −0.455001 | ||||||||
\(292\) | −60.8347 | −3.56008 | ||||||||
\(293\) | −2.59209 | −0.151431 | −0.0757156 | − | 0.997129i | \(-0.524124\pi\) | ||||
−0.0757156 | + | 0.997129i | \(0.524124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.81964 | −0.338833 | ||||||||
\(296\) | −80.0980 | −4.65560 | ||||||||
\(297\) | −4.44400 | −0.257867 | ||||||||
\(298\) | 27.4543 | 1.59039 | ||||||||
\(299\) | −0.815870 | −0.0471830 | ||||||||
\(300\) | 25.5442 | 1.47480 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.26822 | 0.475783 | ||||||||
\(303\) | 1.90481 | 0.109429 | ||||||||
\(304\) | 34.5181 | 1.97975 | ||||||||
\(305\) | 5.06905 | 0.290253 | ||||||||
\(306\) | 3.51319 | 0.200836 | ||||||||
\(307\) | −6.79604 | −0.387871 | −0.193935 | − | 0.981014i | \(-0.562125\pi\) | ||||
−0.193935 | + | 0.981014i | \(0.562125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.9010 | −0.677022 | ||||||||
\(310\) | −14.8714 | −0.844638 | ||||||||
\(311\) | −30.4275 | −1.72538 | −0.862692 | − | 0.505730i | \(-0.831223\pi\) | ||||
−0.862692 | + | 0.505730i | \(0.831223\pi\) | |||||||
\(312\) | 10.3564 | 0.586318 | ||||||||
\(313\) | −17.2644 | −0.975841 | −0.487921 | − | 0.872888i | \(-0.662244\pi\) | ||||
−0.487921 | + | 0.872888i | \(0.662244\pi\) | |||||||
\(314\) | −21.1114 | −1.19138 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4299 | 0.586725 | ||||||||
\(317\) | 34.1992 | 1.92082 | 0.960409 | − | 0.278593i | \(-0.0898679\pi\) | ||||
0.960409 | + | 0.278593i | \(0.0898679\pi\) | |||||||
\(318\) | 28.2098 | 1.58193 | ||||||||
\(319\) | −1.16078 | −0.0649915 | ||||||||
\(320\) | −31.1890 | −1.74352 | ||||||||
\(321\) | −20.1914 | −1.12697 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.50132 | 0.139177 | ||||||||
\(324\) | 5.73612 | 0.318673 | ||||||||
\(325\) | 4.43816 | 0.246185 | ||||||||
\(326\) | 9.78524 | 0.541954 | ||||||||
\(327\) | −12.9034 | −0.713558 | ||||||||
\(328\) | 10.3916 | 0.573780 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.13986 | 0.503133 | ||||||||
\(331\) | −9.26778 | −0.509403 | −0.254702 | − | 0.967020i | \(-0.581977\pi\) | ||||
−0.254702 | + | 0.967020i | \(0.581977\pi\) | |||||||
\(332\) | 85.6555 | 4.70096 | ||||||||
\(333\) | −7.70796 | −0.422394 | ||||||||
\(334\) | −32.5968 | −1.78362 | ||||||||
\(335\) | −3.47753 | −0.189998 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.87332 | 0.374414 | 0.187207 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187207 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(338\) | −33.3954 | −1.81647 | ||||||||
\(339\) | −4.91023 | −0.266687 | ||||||||
\(340\) | −5.35751 | −0.290552 | ||||||||
\(341\) | 32.1336 | 1.74013 | ||||||||
\(342\) | 5.50796 | 0.297837 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −49.0588 | −2.64507 | ||||||||
\(345\) | 0.605336 | 0.0325902 | ||||||||
\(346\) | 3.47609 | 0.186876 | ||||||||
\(347\) | −24.8500 | −1.33402 | −0.667008 | − | 0.745050i | \(-0.732425\pi\) | ||||
−0.667008 | + | 0.745050i | \(0.732425\pi\) | |||||||
\(348\) | 1.49829 | 0.0803168 | ||||||||
\(349\) | −9.14773 | −0.489667 | −0.244833 | − | 0.969565i | \(-0.578733\pi\) | ||||
−0.244833 | + | 0.969565i | \(0.578733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.996618 | 0.0531955 | ||||||||
\(352\) | 123.093 | 6.56087 | ||||||||
\(353\) | −13.1852 | −0.701775 | −0.350887 | − | 0.936418i | \(-0.614120\pi\) | ||||
−0.350887 | + | 0.936418i | \(0.614120\pi\) | |||||||
\(354\) | −21.8904 | −1.16346 | ||||||||
\(355\) | 4.14425 | 0.219954 | ||||||||
\(356\) | −68.7449 | −3.64347 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61.9707 | −3.27525 | ||||||||
\(359\) | 19.9471 | 1.05277 | 0.526383 | − | 0.850247i | \(-0.323548\pi\) | ||||
0.526383 | + | 0.850247i | \(0.323548\pi\) | |||||||
\(360\) | −7.68399 | −0.404982 | ||||||||
\(361\) | −15.0784 | −0.793602 | ||||||||
\(362\) | −61.4304 | −3.22871 | ||||||||
\(363\) | −8.74910 | −0.459209 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.84220 | 0.410479 | ||||||||
\(366\) | 19.0671 | 0.996652 | ||||||||
\(367\) | 12.8609 | 0.671332 | 0.335666 | − | 0.941981i | \(-0.391039\pi\) | ||||
0.335666 | + | 0.941981i | \(0.391039\pi\) | |||||||
\(368\) | 14.2695 | 0.743851 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 15.8528 | 0.824147 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −41.4766 | −2.15046 | ||||||||
\(373\) | 24.4376 | 1.26533 | 0.632666 | − | 0.774425i | \(-0.281961\pi\) | ||||
0.632666 | + | 0.774425i | \(0.281961\pi\) | |||||||
\(374\) | 15.6126 | 0.807309 | ||||||||
\(375\) | −6.99012 | −0.360968 | ||||||||
\(376\) | 88.2010 | 4.54862 | ||||||||
\(377\) | 0.260319 | 0.0134071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0687 | −0.619929 | −0.309965 | − | 0.950748i | \(-0.600317\pi\) | ||||
−0.309965 | + | 0.950748i | \(0.600317\pi\) | |||||||
\(380\) | −8.39947 | −0.430884 | ||||||||
\(381\) | −13.3656 | −0.684739 | ||||||||
\(382\) | −28.9204 | −1.47970 | ||||||||
\(383\) | −22.0469 | −1.12654 | −0.563272 | − | 0.826272i | \(-0.690458\pi\) | ||||
−0.563272 | + | 0.826272i | \(0.690458\pi\) | |||||||
\(384\) | −61.9191 | −3.15980 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.6287 | 0.999074 | ||||||||
\(387\) | −4.72101 | −0.239982 | ||||||||
\(388\) | 44.5223 | 2.26028 | ||||||||
\(389\) | −25.3972 | −1.28769 | −0.643844 | − | 0.765157i | \(-0.722662\pi\) | ||||
−0.643844 | + | 0.765157i | \(0.722662\pi\) | |||||||
\(390\) | −2.04972 | −0.103792 | ||||||||
\(391\) | 1.03403 | 0.0522931 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.39618 | −0.322644 | ||||||||
\(394\) | 39.0232 | 1.96596 | ||||||||
\(395\) | −1.34451 | −0.0676498 | ||||||||
\(396\) | 25.4913 | 1.28099 | ||||||||
\(397\) | −8.21500 | −0.412299 | −0.206149 | − | 0.978521i | \(-0.566093\pi\) | ||||
−0.206149 | + | 0.978521i | \(0.566093\pi\) | |||||||
\(398\) | −51.5553 | −2.58423 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −77.6233 | −3.88117 | ||||||||
\(401\) | −17.4105 | −0.869438 | −0.434719 | − | 0.900566i | \(-0.643152\pi\) | ||||
−0.434719 | + | 0.900566i | \(0.643152\pi\) | |||||||
\(402\) | −13.0806 | −0.652401 | ||||||||
\(403\) | −7.20633 | −0.358973 | ||||||||
\(404\) | −10.9262 | −0.543600 | ||||||||
\(405\) | −0.739443 | −0.0367432 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.2542 | −1.69792 | ||||||||
\(408\) | −13.1257 | −0.649819 | ||||||||
\(409\) | 32.4066 | 1.60241 | 0.801203 | − | 0.598393i | \(-0.204194\pi\) | ||||
0.801203 | + | 0.598393i | \(0.204194\pi\) | |||||||
\(410\) | −2.05668 | −0.101572 | ||||||||
\(411\) | 17.7906 | 0.877546 | ||||||||
\(412\) | 68.2653 | 3.36319 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.27695 | 0.111906 | ||||||||
\(415\) | −11.0419 | −0.542023 | ||||||||
\(416\) | −27.6050 | −1.35345 | ||||||||
\(417\) | 17.9649 | 0.879745 | ||||||||
\(418\) | 24.4774 | 1.19723 | ||||||||
\(419\) | −30.3528 | −1.48283 | −0.741417 | − | 0.671045i | \(-0.765846\pi\) | ||||
−0.741417 | + | 0.671045i | \(0.765846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4240 | −0.556772 | −0.278386 | − | 0.960469i | \(-0.589799\pi\) | ||||
−0.278386 | + | 0.960469i | \(0.589799\pi\) | |||||||
\(422\) | −13.8041 | −0.671971 | ||||||||
\(423\) | 8.48773 | 0.412688 | ||||||||
\(424\) | −105.395 | −5.11844 | ||||||||
\(425\) | −5.62490 | −0.272848 | ||||||||
\(426\) | 15.5884 | 0.755262 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 115.820 | 5.59838 | ||||||||
\(429\) | 4.42897 | 0.213832 | ||||||||
\(430\) | 9.70959 | 0.468238 | ||||||||
\(431\) | −20.2073 | −0.973353 | −0.486677 | − | 0.873582i | \(-0.661791\pi\) | ||||
−0.486677 | + | 0.873582i | \(0.661791\pi\) | |||||||
\(432\) | −17.4308 | −0.838641 | ||||||||
\(433\) | 6.32439 | 0.303931 | 0.151965 | − | 0.988386i | \(-0.451440\pi\) | ||||
0.151965 | + | 0.988386i | \(0.451440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.193145 | −0.00926057 | ||||||||
\(436\) | 74.0153 | 3.54469 | ||||||||
\(437\) | 1.62114 | 0.0775498 | ||||||||
\(438\) | 29.4982 | 1.40948 | ||||||||
\(439\) | −24.0627 | −1.14845 | −0.574226 | − | 0.818697i | \(-0.694697\pi\) | ||||
−0.574226 | + | 0.818697i | \(0.694697\pi\) | |||||||
\(440\) | −34.1476 | −1.62792 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.50131 | −0.166540 | ||||||||
\(443\) | 15.6018 | 0.741263 | 0.370631 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370631 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(444\) | 44.2138 | 2.09829 | ||||||||
\(445\) | 8.86190 | 0.420094 | ||||||||
\(446\) | −78.8850 | −3.73531 | ||||||||
\(447\) | −9.87073 | −0.466870 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.0234 | −1.70005 | −0.850025 | − | 0.526742i | \(-0.823413\pi\) | ||||
−0.850025 | + | 0.526742i | \(0.823413\pi\) | |||||||
\(450\) | −12.3861 | −0.583888 | ||||||||
\(451\) | 4.44400 | 0.209260 | ||||||||
\(452\) | 28.1657 | 1.32480 | ||||||||
\(453\) | −2.97270 | −0.139669 | ||||||||
\(454\) | −34.2573 | −1.60777 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.5784 | −0.963672 | ||||||||
\(457\) | 26.2316 | 1.22706 | 0.613532 | − | 0.789670i | \(-0.289748\pi\) | ||||
0.613532 | + | 0.789670i | \(0.289748\pi\) | |||||||
\(458\) | 79.4213 | 3.71112 | ||||||||
\(459\) | −1.26311 | −0.0589568 | ||||||||
\(460\) | −3.47228 | −0.161896 | ||||||||
\(461\) | −28.3632 | −1.32101 | −0.660503 | − | 0.750823i | \(-0.729657\pi\) | ||||
−0.660503 | + | 0.750823i | \(0.729657\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.1426 | 0.703737 | 0.351869 | − | 0.936049i | \(-0.385546\pi\) | ||||
0.351869 | + | 0.936049i | \(0.385546\pi\) | |||||||
\(464\) | −4.55298 | −0.211367 | ||||||||
\(465\) | 5.34675 | 0.247950 | ||||||||
\(466\) | 12.3619 | 0.572656 | ||||||||
\(467\) | 32.0316 | 1.48225 | 0.741124 | − | 0.671369i | \(-0.234293\pi\) | ||||
0.741124 | + | 0.671369i | \(0.234293\pi\) | |||||||
\(468\) | −5.71672 | −0.264255 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.4565 | −0.805209 | ||||||||
\(471\) | 7.59023 | 0.349739 | ||||||||
\(472\) | 81.7850 | 3.76446 | ||||||||
\(473\) | −20.9801 | −0.964668 | ||||||||
\(474\) | −5.05734 | −0.232291 | ||||||||
\(475\) | −8.81869 | −0.404629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.1423 | −0.464386 | ||||||||
\(478\) | 17.4555 | 0.798398 | ||||||||
\(479\) | 1.91570 | 0.0875304 | 0.0437652 | − | 0.999042i | \(-0.486065\pi\) | ||||
0.0437652 | + | 0.999042i | \(0.486065\pi\) | |||||||
\(480\) | 20.4816 | 0.934852 | ||||||||
\(481\) | 7.68189 | 0.350264 | ||||||||
\(482\) | 2.84434 | 0.129556 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 50.1859 | 2.28118 | ||||||||
\(485\) | −5.73936 | −0.260611 | ||||||||
\(486\) | −2.78139 | −0.126166 | ||||||||
\(487\) | 3.36168 | 0.152332 | 0.0761661 | − | 0.997095i | \(-0.475732\pi\) | ||||
0.0761661 | + | 0.997095i | \(0.475732\pi\) | |||||||
\(488\) | −71.2368 | −3.22474 | ||||||||
\(489\) | −3.51811 | −0.159095 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.9652 | 1.48770 | 0.743848 | − | 0.668348i | \(-0.232998\pi\) | ||||
0.743848 | + | 0.668348i | \(0.232998\pi\) | |||||||
\(492\) | −5.73612 | −0.258604 | ||||||||
\(493\) | −0.329927 | −0.0148592 | ||||||||
\(494\) | −5.48933 | −0.246977 | ||||||||
\(495\) | −3.28608 | −0.147698 | ||||||||
\(496\) | 126.038 | 5.65929 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −41.5335 | −1.86116 | ||||||||
\(499\) | −41.8130 | −1.87180 | −0.935902 | − | 0.352259i | \(-0.885414\pi\) | ||||
−0.935902 | + | 0.352259i | \(0.885414\pi\) | |||||||
\(500\) | 40.0961 | 1.79315 | ||||||||
\(501\) | 11.7196 | 0.523593 | ||||||||
\(502\) | −41.4513 | −1.85006 | ||||||||
\(503\) | 25.0498 | 1.11692 | 0.558458 | − | 0.829533i | \(-0.311393\pi\) | ||||
0.558458 | + | 0.829533i | \(0.311393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.40850 | 0.0626774 | ||||||||
\(506\) | 10.1188 | 0.449834 | ||||||||
\(507\) | 12.0068 | 0.533239 | ||||||||
\(508\) | 76.6665 | 3.40153 | ||||||||
\(509\) | −30.3007 | −1.34306 | −0.671529 | − | 0.740979i | \(-0.734362\pi\) | ||||
−0.671529 | + | 0.740979i | \(0.734362\pi\) | |||||||
\(510\) | 2.59781 | 0.115033 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 120.543 | 5.32728 | ||||||||
\(513\) | −1.98029 | −0.0874321 | ||||||||
\(514\) | 34.0534 | 1.50203 | ||||||||
\(515\) | −8.80008 | −0.387778 | ||||||||
\(516\) | 27.0803 | 1.19214 | ||||||||
\(517\) | 37.7194 | 1.65890 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.24977 | −0.0548587 | ||||||||
\(520\) | 7.65800 | 0.335825 | ||||||||
\(521\) | −24.0337 | −1.05293 | −0.526467 | − | 0.850195i | \(-0.676484\pi\) | ||||
−0.526467 | + | 0.850195i | \(0.676484\pi\) | |||||||
\(522\) | −0.726506 | −0.0317983 | ||||||||
\(523\) | −0.910581 | −0.0398169 | −0.0199085 | − | 0.999802i | \(-0.506337\pi\) | ||||
−0.0199085 | + | 0.999802i | \(0.506337\pi\) | |||||||
\(524\) | 36.6892 | 1.60278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.0181 | 1.74487 | ||||||||
\(527\) | 9.13326 | 0.397851 | ||||||||
\(528\) | −77.4625 | −3.37112 | ||||||||
\(529\) | −22.3298 | −0.970862 | ||||||||
\(530\) | 20.8595 | 0.906080 | ||||||||
\(531\) | 7.87031 | 0.341542 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.996618 | −0.0431683 | ||||||||
\(534\) | 33.3337 | 1.44249 | ||||||||
\(535\) | −14.9304 | −0.645496 | ||||||||
\(536\) | 48.8707 | 2.11089 | ||||||||
\(537\) | 22.2805 | 0.961475 | ||||||||
\(538\) | 42.8446 | 1.84716 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.24153 | 0.182526 | ||||||||
\(541\) | −19.6023 | −0.842769 | −0.421385 | − | 0.906882i | \(-0.638456\pi\) | ||||
−0.421385 | + | 0.906882i | \(0.638456\pi\) | |||||||
\(542\) | 65.6714 | 2.82083 | ||||||||
\(543\) | 22.0862 | 0.947811 | ||||||||
\(544\) | 34.9864 | 1.50003 | ||||||||
\(545\) | −9.54130 | −0.408705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.48929 | −0.0636774 | −0.0318387 | − | 0.999493i | \(-0.510136\pi\) | ||||
−0.0318387 | + | 0.999493i | \(0.510136\pi\) | |||||||
\(548\) | −102.049 | −4.35932 | ||||||||
\(549\) | −6.85524 | −0.292574 | ||||||||
\(550\) | −55.0440 | −2.34708 | ||||||||
\(551\) | −0.517258 | −0.0220359 | ||||||||
\(552\) | −8.50696 | −0.362080 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −62.8151 | −2.66876 | ||||||||
\(555\) | −5.69960 | −0.241934 | ||||||||
\(556\) | −103.049 | −4.37024 | ||||||||
\(557\) | 3.84524 | 0.162928 | 0.0814641 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814641 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(558\) | 20.1116 | 0.851392 | ||||||||
\(559\) | 4.70504 | 0.199002 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.61325 | −0.236992 | ||||||||
\(562\) | −47.2102 | −1.99144 | ||||||||
\(563\) | −33.2100 | −1.39963 | −0.699817 | − | 0.714322i | \(-0.746735\pi\) | ||||
−0.699817 | + | 0.714322i | \(0.746735\pi\) | |||||||
\(564\) | −48.6866 | −2.05008 | ||||||||
\(565\) | −3.63084 | −0.152750 | ||||||||
\(566\) | 58.9794 | 2.47909 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −58.2402 | −2.44371 | ||||||||
\(569\) | −23.5829 | −0.988648 | −0.494324 | − | 0.869278i | \(-0.664584\pi\) | ||||
−0.494324 | + | 0.869278i | \(0.664584\pi\) | |||||||
\(570\) | 4.07282 | 0.170592 | ||||||||
\(571\) | 12.4917 | 0.522763 | 0.261381 | − | 0.965236i | \(-0.415822\pi\) | ||||
0.261381 | + | 0.965236i | \(0.415822\pi\) | |||||||
\(572\) | −25.4051 | −1.06224 | ||||||||
\(573\) | 10.3978 | 0.434376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.64558 | −0.152031 | ||||||||
\(576\) | 42.1791 | 1.75746 | ||||||||
\(577\) | 0.650901 | 0.0270973 | 0.0135487 | − | 0.999908i | \(-0.495687\pi\) | ||||
0.0135487 | + | 0.999908i | \(0.495687\pi\) | |||||||
\(578\) | −42.8460 | −1.78216 | ||||||||
\(579\) | −7.05716 | −0.293285 | ||||||||
\(580\) | 1.10790 | 0.0460030 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.5884 | −0.894869 | ||||||||
\(583\) | −45.0725 | −1.86671 | ||||||||
\(584\) | −110.209 | −4.56046 | ||||||||
\(585\) | 0.736942 | 0.0304688 | ||||||||
\(586\) | −7.20960 | −0.297826 | ||||||||
\(587\) | −7.71470 | −0.318420 | −0.159210 | − | 0.987245i | \(-0.550895\pi\) | ||||
−0.159210 | + | 0.987245i | \(0.550895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.3191 | 0.590007 | ||||||||
\(590\) | −16.1867 | −0.666395 | ||||||||
\(591\) | −14.0301 | −0.577122 | ||||||||
\(592\) | −134.356 | −5.52200 | ||||||||
\(593\) | −4.01641 | −0.164934 | −0.0824671 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824671 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(594\) | −12.3605 | −0.507157 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 56.6197 | 2.31923 | ||||||||
\(597\) | 18.5358 | 0.758620 | ||||||||
\(598\) | −2.26925 | −0.0927965 | ||||||||
\(599\) | −6.86492 | −0.280493 | −0.140247 | − | 0.990117i | \(-0.544790\pi\) | ||||
−0.140247 | + | 0.990117i | \(0.544790\pi\) | |||||||
\(600\) | 46.2761 | 1.88921 | ||||||||
\(601\) | −13.0763 | −0.533393 | −0.266697 | − | 0.963781i | \(-0.585932\pi\) | ||||
−0.266697 | + | 0.963781i | \(0.585932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.70290 | 0.191517 | ||||||||
\(604\) | 17.0517 | 0.693825 | ||||||||
\(605\) | −6.46946 | −0.263021 | ||||||||
\(606\) | 5.29802 | 0.215218 | ||||||||
\(607\) | 43.1382 | 1.75093 | 0.875463 | − | 0.483285i | \(-0.160556\pi\) | ||||
0.875463 | + | 0.483285i | \(0.160556\pi\) | |||||||
\(608\) | 54.8515 | 2.22452 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0990 | 0.570852 | ||||||||
\(611\) | −8.45902 | −0.342215 | ||||||||
\(612\) | 7.24534 | 0.292875 | ||||||||
\(613\) | 12.2221 | 0.493646 | 0.246823 | − | 0.969061i | \(-0.420613\pi\) | ||||
0.246823 | + | 0.969061i | \(0.420613\pi\) | |||||||
\(614\) | −18.9024 | −0.762840 | ||||||||
\(615\) | 0.739443 | 0.0298172 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.82789 | 0.0735882 | 0.0367941 | − | 0.999323i | \(-0.488285\pi\) | ||||
0.0367941 | + | 0.999323i | \(0.488285\pi\) | |||||||
\(618\) | −33.1012 | −1.33152 | ||||||||
\(619\) | 27.7081 | 1.11368 | 0.556842 | − | 0.830618i | \(-0.312013\pi\) | ||||
0.556842 | + | 0.830618i | \(0.312013\pi\) | |||||||
\(620\) | −30.6696 | −1.23172 | ||||||||
\(621\) | −0.818638 | −0.0328508 | ||||||||
\(622\) | −84.6306 | −3.39338 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.3719 | 0.695431 | ||||||||
\(625\) | 17.0973 | 0.683893 | ||||||||
\(626\) | −48.0190 | −1.91922 | ||||||||
\(627\) | −8.80041 | −0.351455 | ||||||||
\(628\) | −43.5385 | −1.73737 | ||||||||
\(629\) | −9.73599 | −0.388200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.4494 | 0.535413 | 0.267707 | − | 0.963501i | \(-0.413734\pi\) | ||||
0.267707 | + | 0.963501i | \(0.413734\pi\) | |||||||
\(632\) | 18.8948 | 0.751595 | ||||||||
\(633\) | 4.96301 | 0.197262 | ||||||||
\(634\) | 95.1213 | 3.77775 | ||||||||
\(635\) | −9.88308 | −0.392198 | ||||||||
\(636\) | 58.1777 | 2.30690 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.22859 | −0.127821 | ||||||||
\(639\) | −5.60455 | −0.221713 | ||||||||
\(640\) | −45.7857 | −1.80984 | ||||||||
\(641\) | −20.7826 | −0.820863 | −0.410432 | − | 0.911891i | \(-0.634622\pi\) | ||||
−0.410432 | + | 0.911891i | \(0.634622\pi\) | |||||||
\(642\) | −56.1601 | −2.21646 | ||||||||
\(643\) | −43.3748 | −1.71054 | −0.855268 | − | 0.518186i | \(-0.826607\pi\) | ||||
−0.855268 | + | 0.518186i | \(0.826607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.49092 | −0.137455 | ||||||||
\(646\) | 6.95715 | 0.273726 | ||||||||
\(647\) | 22.5713 | 0.887369 | 0.443685 | − | 0.896183i | \(-0.353671\pi\) | ||||
0.443685 | + | 0.896183i | \(0.353671\pi\) | |||||||
\(648\) | 10.3916 | 0.408220 | ||||||||
\(649\) | 34.9756 | 1.37291 | ||||||||
\(650\) | 12.3443 | 0.484181 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.1803 | 0.790322 | ||||||||
\(653\) | −38.7485 | −1.51635 | −0.758173 | − | 0.652053i | \(-0.773908\pi\) | ||||
−0.758173 | + | 0.652053i | \(0.773908\pi\) | |||||||
\(654\) | −35.8893 | −1.40338 | ||||||||
\(655\) | −4.72960 | −0.184801 | ||||||||
\(656\) | 17.4308 | 0.680559 | ||||||||
\(657\) | −10.6056 | −0.413762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.1448 | 1.40800 | 0.704001 | − | 0.710199i | \(-0.251395\pi\) | ||||
0.704001 | + | 0.710199i | \(0.251395\pi\) | |||||||
\(660\) | 18.8493 | 0.733710 | ||||||||
\(661\) | −22.4151 | −0.871846 | −0.435923 | − | 0.899984i | \(-0.643578\pi\) | ||||
−0.435923 | + | 0.899984i | \(0.643578\pi\) | |||||||
\(662\) | −25.7773 | −1.00186 | ||||||||
\(663\) | 1.25884 | 0.0488891 | ||||||||
\(664\) | 155.174 | 6.02193 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.4388 | −0.830738 | ||||||||
\(667\) | −0.213831 | −0.00827956 | ||||||||
\(668\) | −67.2250 | −2.60101 | ||||||||
\(669\) | 28.3618 | 1.09653 | ||||||||
\(670\) | −9.67235 | −0.373676 | ||||||||
\(671\) | −30.4646 | −1.17607 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.9476 | 1.50132 | 0.750660 | − | 0.660688i | \(-0.229735\pi\) | ||||
0.750660 | + | 0.660688i | \(0.229735\pi\) | |||||||
\(674\) | 19.1174 | 0.736374 | ||||||||
\(675\) | 4.45322 | 0.171405 | ||||||||
\(676\) | −68.8722 | −2.64893 | ||||||||
\(677\) | 46.3643 | 1.78192 | 0.890962 | − | 0.454077i | \(-0.150031\pi\) | ||||
0.890962 | + | 0.454077i | \(0.150031\pi\) | |||||||
\(678\) | −13.6573 | −0.524504 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.70571 | −0.372197 | ||||||||
\(681\) | 12.3166 | 0.471974 | ||||||||
\(682\) | 89.3759 | 3.42238 | ||||||||
\(683\) | −25.7755 | −0.986271 | −0.493135 | − | 0.869953i | \(-0.664149\pi\) | ||||
−0.493135 | + | 0.869953i | \(0.664149\pi\) | |||||||
\(684\) | 11.3592 | 0.434330 | ||||||||
\(685\) | 13.1551 | 0.502632 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.5546 | −1.08942 | ||||||||
\(688\) | −82.2910 | −3.13732 | ||||||||
\(689\) | 10.1080 | 0.385086 | ||||||||
\(690\) | 1.68367 | 0.0640964 | ||||||||
\(691\) | 43.5702 | 1.65749 | 0.828744 | − | 0.559628i | \(-0.189056\pi\) | ||||
0.828744 | + | 0.559628i | \(0.189056\pi\) | |||||||
\(692\) | 7.16881 | 0.272517 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −69.1174 | −2.62366 | ||||||||
\(695\) | 13.2840 | 0.503891 | ||||||||
\(696\) | 2.71431 | 0.102886 | ||||||||
\(697\) | 1.26311 | 0.0478436 | ||||||||
\(698\) | −25.4434 | −0.963047 | ||||||||
\(699\) | −4.44452 | −0.168107 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0873 | 0.985305 | 0.492652 | − | 0.870226i | \(-0.336027\pi\) | ||||
0.492652 | + | 0.870226i | \(0.336027\pi\) | |||||||
\(702\) | 2.77198 | 0.104622 | ||||||||
\(703\) | −15.2640 | −0.575694 | ||||||||
\(704\) | 187.444 | 7.06456 | ||||||||
\(705\) | 6.27619 | 0.236375 | ||||||||
\(706\) | −36.6730 | −1.38021 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −45.1450 | −1.69665 | ||||||||
\(709\) | −5.54993 | −0.208432 | −0.104216 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104216 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(710\) | 11.5268 | 0.432591 | ||||||||
\(711\) | 1.81828 | 0.0681908 | ||||||||
\(712\) | −124.539 | −4.66729 | ||||||||
\(713\) | 5.91940 | 0.221683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.27497 | 0.122477 | ||||||||
\(716\) | −127.804 | −4.77624 | ||||||||
\(717\) | −6.27584 | −0.234375 | ||||||||
\(718\) | 55.4806 | 2.07052 | ||||||||
\(719\) | −12.7308 | −0.474777 | −0.237388 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237388 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(720\) | −12.8891 | −0.480348 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −41.9390 | −1.56081 | ||||||||
\(723\) | −1.02263 | −0.0380321 | ||||||||
\(724\) | −126.689 | −4.70837 | ||||||||
\(725\) | 1.16319 | 0.0432000 | ||||||||
\(726\) | −24.3347 | −0.903144 | ||||||||
\(727\) | 8.95982 | 0.332301 | 0.166151 | − | 0.986100i | \(-0.446866\pi\) | ||||
0.166151 | + | 0.986100i | \(0.446866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 21.8122 | 0.807306 | ||||||||
\(731\) | −5.96315 | −0.220555 | ||||||||
\(732\) | 39.3224 | 1.45340 | ||||||||
\(733\) | −22.4833 | −0.830438 | −0.415219 | − | 0.909721i | \(-0.636295\pi\) | ||||
−0.415219 | + | 0.909721i | \(0.636295\pi\) | |||||||
\(734\) | 35.7711 | 1.32033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.6752 | 0.835819 | ||||||||
\(737\) | 20.8997 | 0.769850 | ||||||||
\(738\) | 2.78139 | 0.102384 | ||||||||
\(739\) | −41.6105 | −1.53067 | −0.765334 | − | 0.643633i | \(-0.777426\pi\) | ||||
−0.765334 | + | 0.643633i | \(0.777426\pi\) | |||||||
\(740\) | 32.6936 | 1.20184 | ||||||||
\(741\) | 1.97360 | 0.0725018 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.94361 | −0.218050 | −0.109025 | − | 0.994039i | \(-0.534773\pi\) | ||||
−0.109025 | + | 0.994039i | \(0.534773\pi\) | |||||||
\(744\) | −75.1394 | −2.75474 | ||||||||
\(745\) | −7.29884 | −0.267409 | ||||||||
\(746\) | 67.9705 | 2.48858 | ||||||||
\(747\) | 14.9327 | 0.546358 | ||||||||
\(748\) | 32.1983 | 1.17728 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.4422 | −0.709930 | ||||||||
\(751\) | −33.6224 | −1.22690 | −0.613450 | − | 0.789734i | \(-0.710219\pi\) | ||||
−0.613450 | + | 0.789734i | \(0.710219\pi\) | |||||||
\(752\) | 147.948 | 5.39511 | ||||||||
\(753\) | 14.9031 | 0.543099 | ||||||||
\(754\) | 0.724049 | 0.0263683 | ||||||||
\(755\) | −2.19814 | −0.0799984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.503440 | −0.0182978 | −0.00914892 | − | 0.999958i | \(-0.502912\pi\) | ||||
−0.00914892 | + | 0.999958i | \(0.502912\pi\) | |||||||
\(758\) | −33.5678 | −1.21924 | ||||||||
\(759\) | −3.63803 | −0.132052 | ||||||||
\(760\) | −15.2165 | −0.551962 | ||||||||
\(761\) | −33.1318 | −1.20103 | −0.600513 | − | 0.799615i | \(-0.705037\pi\) | ||||
−0.600513 | + | 0.799615i | \(0.705037\pi\) | |||||||
\(762\) | −37.1748 | −1.34670 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −59.6433 | −2.15782 | ||||||||
\(765\) | −0.933996 | −0.0337687 | ||||||||
\(766\) | −61.3210 | −2.21562 | ||||||||
\(767\) | −7.84369 | −0.283219 | ||||||||
\(768\) | −87.8629 | −3.17048 | ||||||||
\(769\) | 17.7871 | 0.641419 | 0.320710 | − | 0.947178i | \(-0.396079\pi\) | ||||
0.320710 | + | 0.947178i | \(0.396079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.2433 | −0.440932 | ||||||||
\(772\) | 40.4807 | 1.45693 | ||||||||
\(773\) | −9.30219 | −0.334577 | −0.167288 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167288 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(774\) | −13.1310 | −0.471983 | ||||||||
\(775\) | −32.2003 | −1.15667 | ||||||||
\(776\) | 80.6569 | 2.89541 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −70.6394 | −2.53255 | ||||||||
\(779\) | 1.98029 | 0.0709514 | ||||||||
\(780\) | −4.22718 | −0.151357 | ||||||||
\(781\) | −24.9066 | −0.891229 | ||||||||
\(782\) | 2.87604 | 0.102847 | ||||||||
\(783\) | 0.261203 | 0.00933463 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.61254 | 0.200320 | ||||||||
\(786\) | −17.7902 | −0.634557 | ||||||||
\(787\) | 1.42985 | 0.0509687 | 0.0254844 | − | 0.999675i | \(-0.491887\pi\) | ||||
0.0254844 | + | 0.999675i | \(0.491887\pi\) | |||||||
\(788\) | 80.4784 | 2.86692 | ||||||||
\(789\) | −14.3878 | −0.512219 | ||||||||
\(790\) | −3.73961 | −0.133049 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 46.1802 | 1.64094 | ||||||||
\(793\) | 6.83205 | 0.242613 | ||||||||
\(794\) | −22.8491 | −0.810884 | ||||||||
\(795\) | −7.49968 | −0.265986 | ||||||||
\(796\) | −106.324 | −3.76854 | ||||||||
\(797\) | −22.3072 | −0.790163 | −0.395081 | − | 0.918646i | \(-0.629284\pi\) | ||||
−0.395081 | + | 0.918646i | \(0.629284\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7209 | 0.379279 | ||||||||
\(800\) | −123.348 | −4.36102 | ||||||||
\(801\) | −11.9846 | −0.423454 | ||||||||
\(802\) | −48.4253 | −1.70996 | ||||||||
\(803\) | −47.1310 | −1.66322 | ||||||||
\(804\) | −26.9764 | −0.951385 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0436 | −0.706005 | ||||||||
\(807\) | −15.4040 | −0.542247 | ||||||||
\(808\) | −19.7940 | −0.696352 | ||||||||
\(809\) | −13.6353 | −0.479392 | −0.239696 | − | 0.970848i | \(-0.577048\pi\) | ||||
−0.239696 | + | 0.970848i | \(0.577048\pi\) | |||||||
\(810\) | −2.05668 | −0.0722643 | ||||||||
\(811\) | 13.4034 | 0.470659 | 0.235329 | − | 0.971916i | \(-0.424383\pi\) | ||||
0.235329 | + | 0.971916i | \(0.424383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6110 | −0.828074 | ||||||||
\(814\) | −95.2741 | −3.33936 | ||||||||
\(815\) | −2.60144 | −0.0911246 | ||||||||
\(816\) | −22.0170 | −0.770749 | ||||||||
\(817\) | −9.34898 | −0.327079 | ||||||||
\(818\) | 90.1355 | 3.15151 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.24153 | −0.148121 | ||||||||
\(821\) | 50.9993 | 1.77989 | 0.889944 | − | 0.456070i | \(-0.150743\pi\) | ||||
0.889944 | + | 0.456070i | \(0.150743\pi\) | |||||||
\(822\) | 49.4826 | 1.72590 | ||||||||
\(823\) | −46.0488 | −1.60516 | −0.802580 | − | 0.596545i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596545i | \(0.796540\pi\) | |||||||
\(824\) | 123.670 | 4.30825 | ||||||||
\(825\) | 19.7901 | 0.689003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.3779 | −1.16066 | −0.580332 | − | 0.814380i | \(-0.697077\pi\) | ||||
−0.580332 | + | 0.814380i | \(0.697077\pi\) | |||||||
\(828\) | 4.69581 | 0.163191 | ||||||||
\(829\) | 13.5451 | 0.470440 | 0.235220 | − | 0.971942i | \(-0.424419\pi\) | ||||
0.235220 | + | 0.971942i | \(0.424419\pi\) | |||||||
\(830\) | −30.7117 | −1.06602 | ||||||||
\(831\) | 22.5841 | 0.783433 | ||||||||
\(832\) | −42.0365 | −1.45735 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 49.9673 | 1.73023 | ||||||||
\(835\) | 8.66597 | 0.299898 | ||||||||
\(836\) | 50.4802 | 1.74589 | ||||||||
\(837\) | −7.23078 | −0.249932 | ||||||||
\(838\) | −84.4230 | −2.91634 | ||||||||
\(839\) | −37.2031 | −1.28439 | −0.642196 | − | 0.766540i | \(-0.721977\pi\) | ||||
−0.642196 | + | 0.766540i | \(0.721977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9318 | −0.997647 | ||||||||
\(842\) | −31.7746 | −1.09503 | ||||||||
\(843\) | 16.9736 | 0.584602 | ||||||||
\(844\) | −28.4684 | −0.979923 | ||||||||
\(845\) | 8.87831 | 0.305423 | ||||||||
\(846\) | 23.6077 | 0.811648 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −176.789 | −6.07097 | ||||||||
\(849\) | −21.2050 | −0.727755 | ||||||||
\(850\) | −15.6450 | −0.536621 | ||||||||
\(851\) | −6.31004 | −0.216305 | ||||||||
\(852\) | 32.1484 | 1.10139 | ||||||||
\(853\) | 6.70239 | 0.229486 | 0.114743 | − | 0.993395i | \(-0.463396\pi\) | ||||
0.114743 | + | 0.993395i | \(0.463396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.46431 | −0.0500785 | ||||||||
\(856\) | 209.821 | 7.17152 | ||||||||
\(857\) | −35.3173 | −1.20642 | −0.603208 | − | 0.797584i | \(-0.706111\pi\) | ||||
−0.603208 | + | 0.797584i | \(0.706111\pi\) | |||||||
\(858\) | 12.3187 | 0.420552 | ||||||||
\(859\) | 48.0851 | 1.64064 | 0.820322 | − | 0.571902i | \(-0.193794\pi\) | ||||
0.820322 | + | 0.571902i | \(0.193794\pi\) | |||||||
\(860\) | 20.0243 | 0.682823 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −56.2044 | −1.91433 | ||||||||
\(863\) | 0.553632 | 0.0188458 | 0.00942292 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00942292 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(864\) | −27.6987 | −0.942328 | ||||||||
\(865\) | −0.924131 | −0.0314214 | ||||||||
\(866\) | 17.5906 | 0.597752 | ||||||||
\(867\) | 15.4046 | 0.523166 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.08042 | 0.274110 | ||||||||
\(870\) | −0.537210 | −0.0182131 | ||||||||
\(871\) | −4.68700 | −0.158813 | ||||||||
\(872\) | 134.087 | 4.54075 | ||||||||
\(873\) | 7.76174 | 0.262695 | ||||||||
\(874\) | 4.50903 | 0.152520 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 60.8347 | 2.05541 | ||||||||
\(877\) | −13.8660 | −0.468222 | −0.234111 | − | 0.972210i | \(-0.575218\pi\) | ||||
−0.234111 | + | 0.972210i | \(0.575218\pi\) | |||||||
\(878\) | −66.9278 | −2.25870 | ||||||||
\(879\) | 2.59209 | 0.0874289 | ||||||||
\(880\) | −57.2791 | −1.93088 | ||||||||
\(881\) | 8.62496 | 0.290582 | 0.145291 | − | 0.989389i | \(-0.453588\pi\) | ||||
0.145291 | + | 0.989389i | \(0.453588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.1227 | 0.946404 | 0.473202 | − | 0.880954i | \(-0.343098\pi\) | ||||
0.473202 | + | 0.880954i | \(0.343098\pi\) | |||||||
\(884\) | −7.22083 | −0.242863 | ||||||||
\(885\) | 5.81964 | 0.195625 | ||||||||
\(886\) | 43.3946 | 1.45787 | ||||||||
\(887\) | 28.6430 | 0.961737 | 0.480869 | − | 0.876793i | \(-0.340321\pi\) | ||||
0.480869 | + | 0.876793i | \(0.340321\pi\) | |||||||
\(888\) | 80.0980 | 2.68791 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.6484 | 0.826215 | ||||||||
\(891\) | 4.44400 | 0.148879 | ||||||||
\(892\) | −162.686 | −5.44714 | ||||||||
\(893\) | 16.8082 | 0.562465 | ||||||||
\(894\) | −27.4543 | −0.918210 | ||||||||
\(895\) | 16.4752 | 0.550704 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.815870 | 0.0272411 | ||||||||
\(898\) | −100.195 | −3.34355 | ||||||||
\(899\) | −1.88870 | −0.0629917 | ||||||||
\(900\) | −25.5442 | −0.851474 | ||||||||
\(901\) | −12.8109 | −0.426792 | ||||||||
\(902\) | 12.3605 | 0.411559 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 51.0252 | 1.69707 | ||||||||
\(905\) | 16.3315 | 0.542878 | ||||||||
\(906\) | −8.26822 | −0.274693 | ||||||||
\(907\) | 15.9653 | 0.530119 | 0.265060 | − | 0.964232i | \(-0.414608\pi\) | ||||
0.265060 | + | 0.964232i | \(0.414608\pi\) | |||||||
\(908\) | −70.6495 | −2.34459 | ||||||||
\(909\) | −1.90481 | −0.0631787 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.29604 | 0.175466 | 0.0877328 | − | 0.996144i | \(-0.472038\pi\) | ||||
0.0877328 | + | 0.996144i | \(0.472038\pi\) | |||||||
\(912\) | −34.5181 | −1.14301 | ||||||||
\(913\) | 66.3607 | 2.19622 | ||||||||
\(914\) | 72.9604 | 2.41332 | ||||||||
\(915\) | −5.06905 | −0.167578 | ||||||||
\(916\) | 163.792 | 5.41185 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.51319 | −0.115953 | ||||||||
\(919\) | 37.9280 | 1.25113 | 0.625564 | − | 0.780173i | \(-0.284869\pi\) | ||||
0.625564 | + | 0.780173i | \(0.284869\pi\) | |||||||
\(920\) | −6.29041 | −0.207389 | ||||||||
\(921\) | 6.79604 | 0.223937 | ||||||||
\(922\) | −78.8891 | −2.59807 | ||||||||
\(923\) | 5.58560 | 0.183852 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.3253 | 1.12861 | ||||||||
\(926\) | 42.1175 | 1.38407 | ||||||||
\(927\) | 11.9010 | 0.390879 | ||||||||
\(928\) | −7.23497 | −0.237500 | ||||||||
\(929\) | −48.1695 | −1.58039 | −0.790195 | − | 0.612855i | \(-0.790021\pi\) | ||||
−0.790195 | + | 0.612855i | \(0.790021\pi\) | |||||||
\(930\) | 14.8714 | 0.487652 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.4943 | 0.835094 | ||||||||
\(933\) | 30.4275 | 0.996150 | ||||||||
\(934\) | 89.0924 | 2.91519 | ||||||||
\(935\) | −4.15068 | −0.135742 | ||||||||
\(936\) | −10.3564 | −0.338511 | ||||||||
\(937\) | −57.1372 | −1.86659 | −0.933295 | − | 0.359111i | \(-0.883080\pi\) | ||||
−0.933295 | + | 0.359111i | \(0.883080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2644 | 0.563402 | ||||||||
\(940\) | −36.0010 | −1.17422 | ||||||||
\(941\) | 47.0404 | 1.53347 | 0.766736 | − | 0.641962i | \(-0.221879\pi\) | ||||
0.766736 | + | 0.641962i | \(0.221879\pi\) | |||||||
\(942\) | 21.1114 | 0.687846 | ||||||||
\(943\) | 0.818638 | 0.0266585 | ||||||||
\(944\) | 137.186 | 4.46502 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −58.3539 | −1.89725 | ||||||||
\(947\) | −2.12620 | −0.0690922 | −0.0345461 | − | 0.999403i | \(-0.510999\pi\) | ||||
−0.0345461 | + | 0.999403i | \(0.510999\pi\) | |||||||
\(948\) | −10.4299 | −0.338746 | ||||||||
\(949\) | 10.5697 | 0.343106 | ||||||||
\(950\) | −24.5282 | −0.795800 | ||||||||
\(951\) | −34.1992 | −1.10899 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.1574 | 1.17125 | 0.585627 | − | 0.810581i | \(-0.300848\pi\) | ||||
0.585627 | + | 0.810581i | \(0.300848\pi\) | |||||||
\(954\) | −28.2098 | −0.913326 | ||||||||
\(955\) | 7.68861 | 0.248798 | ||||||||
\(956\) | 35.9989 | 1.16429 | ||||||||
\(957\) | 1.16078 | 0.0375228 | ||||||||
\(958\) | 5.32829 | 0.172149 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 31.1890 | 1.00662 | ||||||||
\(961\) | 21.2842 | 0.686588 | ||||||||
\(962\) | 21.3663 | 0.688878 | ||||||||
\(963\) | 20.1914 | 0.650658 | ||||||||
\(964\) | 5.86594 | 0.188929 | ||||||||
\(965\) | −5.21836 | −0.167985 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.8312 | 1.37736 | 0.688679 | − | 0.725066i | \(-0.258191\pi\) | ||||
0.688679 | + | 0.725066i | \(0.258191\pi\) | |||||||
\(968\) | 90.9171 | 2.92219 | ||||||||
\(969\) | −2.50132 | −0.0803541 | ||||||||
\(970\) | −15.9634 | −0.512554 | ||||||||
\(971\) | 7.63406 | 0.244988 | 0.122494 | − | 0.992469i | \(-0.460911\pi\) | ||||
0.122494 | + | 0.992469i | \(0.460911\pi\) | |||||||
\(972\) | −5.73612 | −0.183986 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.35013 | 0.299597 | ||||||||
\(975\) | −4.43816 | −0.142135 | ||||||||
\(976\) | −119.492 | −3.82486 | ||||||||
\(977\) | 31.7537 | 1.01589 | 0.507945 | − | 0.861390i | \(-0.330405\pi\) | ||||
0.507945 | + | 0.861390i | \(0.330405\pi\) | |||||||
\(978\) | −9.78524 | −0.312897 | ||||||||
\(979\) | −53.2594 | −1.70218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9034 | 0.411973 | ||||||||
\(982\) | 91.6889 | 2.92591 | ||||||||
\(983\) | 17.8060 | 0.567924 | 0.283962 | − | 0.958836i | \(-0.408351\pi\) | ||||
0.283962 | + | 0.958836i | \(0.408351\pi\) | |||||||
\(984\) | −10.3916 | −0.331272 | ||||||||
\(985\) | −10.3745 | −0.330558 | ||||||||
\(986\) | −0.917656 | −0.0292241 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11.3208 | −0.360162 | ||||||||
\(989\) | −3.86480 | −0.122893 | ||||||||
\(990\) | −9.13986 | −0.290484 | ||||||||
\(991\) | 37.4634 | 1.19007 | 0.595033 | − | 0.803702i | \(-0.297139\pi\) | ||||
0.595033 | + | 0.803702i | \(0.297139\pi\) | |||||||
\(992\) | 200.283 | 6.35899 | ||||||||
\(993\) | 9.26778 | 0.294104 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.7062 | 0.434515 | ||||||||
\(996\) | −85.6555 | −2.71410 | ||||||||
\(997\) | 24.7442 | 0.783657 | 0.391829 | − | 0.920038i | \(-0.371843\pi\) | ||||
0.391829 | + | 0.920038i | \(0.371843\pi\) | |||||||
\(998\) | −116.298 | −3.68135 | ||||||||
\(999\) | 7.70796 | 0.243869 |
(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 | 6027.2.a.bn.1.24 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.24 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.24 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.24 | yes | 24 | 7.6 | odd | 2 |