Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.40 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.85165 | 1.30931 | 0.654656 | − | 0.755927i | \(-0.272814\pi\) | ||||
0.654656 | + | 0.755927i | \(0.272814\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.42859 | 0.714296 | ||||||||
\(5\) | 1.52272 | 0.680983 | 0.340491 | − | 0.940248i | \(-0.389407\pi\) | ||||
0.340491 | + | 0.940248i | \(0.389407\pi\) | |||||||
\(6\) | −1.85165 | −0.755931 | ||||||||
\(7\) | 0.592895 | 0.224093 | 0.112047 | − | 0.993703i | \(-0.464259\pi\) | ||||
0.112047 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(8\) | −1.05805 | −0.374076 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.81954 | 0.891618 | ||||||||
\(11\) | 5.80574 | 1.75050 | 0.875248 | − | 0.483675i | \(-0.160698\pi\) | ||||
0.875248 | + | 0.483675i | \(0.160698\pi\) | |||||||
\(12\) | −1.42859 | −0.412399 | ||||||||
\(13\) | 0.790537 | 0.219255 | 0.109628 | − | 0.993973i | \(-0.465034\pi\) | ||||
0.109628 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(14\) | 1.09783 | 0.293408 | ||||||||
\(15\) | −1.52272 | −0.393166 | ||||||||
\(16\) | −4.81631 | −1.20408 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.85165 | 0.436437 | ||||||||
\(19\) | −8.36055 | −1.91804 | −0.959021 | − | 0.283336i | \(-0.908559\pi\) | ||||
−0.959021 | + | 0.283336i | \(0.908559\pi\) | |||||||
\(20\) | 2.17535 | 0.486423 | ||||||||
\(21\) | −0.592895 | −0.129380 | ||||||||
\(22\) | 10.7502 | 2.29194 | ||||||||
\(23\) | −4.55046 | −0.948836 | −0.474418 | − | 0.880300i | \(-0.657341\pi\) | ||||
−0.474418 | + | 0.880300i | \(0.657341\pi\) | |||||||
\(24\) | 1.05805 | 0.215973 | ||||||||
\(25\) | −2.68131 | −0.536263 | ||||||||
\(26\) | 1.46379 | 0.287074 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.847005 | 0.160069 | ||||||||
\(29\) | 4.33100 | 0.804246 | 0.402123 | − | 0.915586i | \(-0.368272\pi\) | ||||
0.402123 | + | 0.915586i | \(0.368272\pi\) | |||||||
\(30\) | −2.81954 | −0.514776 | ||||||||
\(31\) | −10.2152 | −1.83470 | −0.917350 | − | 0.398081i | \(-0.869676\pi\) | ||||
−0.917350 | + | 0.398081i | \(0.869676\pi\) | |||||||
\(32\) | −6.80201 | −1.20244 | ||||||||
\(33\) | −5.80574 | −1.01065 | ||||||||
\(34\) | −1.85165 | −0.317555 | ||||||||
\(35\) | 0.902816 | 0.152604 | ||||||||
\(36\) | 1.42859 | 0.238099 | ||||||||
\(37\) | −6.10080 | −1.00297 | −0.501483 | − | 0.865168i | \(-0.667212\pi\) | ||||
−0.501483 | + | 0.865168i | \(0.667212\pi\) | |||||||
\(38\) | −15.4808 | −2.51131 | ||||||||
\(39\) | −0.790537 | −0.126587 | ||||||||
\(40\) | −1.61111 | −0.254739 | ||||||||
\(41\) | −7.36631 | −1.15042 | −0.575212 | − | 0.818004i | \(-0.695081\pi\) | ||||
−0.575212 | + | 0.818004i | \(0.695081\pi\) | |||||||
\(42\) | −1.09783 | −0.169399 | ||||||||
\(43\) | −3.95148 | −0.602594 | −0.301297 | − | 0.953530i | \(-0.597420\pi\) | ||||
−0.301297 | + | 0.953530i | \(0.597420\pi\) | |||||||
\(44\) | 8.29402 | 1.25037 | ||||||||
\(45\) | 1.52272 | 0.226994 | ||||||||
\(46\) | −8.42583 | −1.24232 | ||||||||
\(47\) | −6.98813 | −1.01932 | −0.509662 | − | 0.860375i | \(-0.670229\pi\) | ||||
−0.509662 | + | 0.860375i | \(0.670229\pi\) | |||||||
\(48\) | 4.81631 | 0.695174 | ||||||||
\(49\) | −6.64847 | −0.949782 | ||||||||
\(50\) | −4.96484 | −0.702135 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.12935 | 0.156613 | ||||||||
\(53\) | −8.60881 | −1.18251 | −0.591256 | − | 0.806484i | \(-0.701368\pi\) | ||||
−0.591256 | + | 0.806484i | \(0.701368\pi\) | |||||||
\(54\) | −1.85165 | −0.251977 | ||||||||
\(55\) | 8.84053 | 1.19206 | ||||||||
\(56\) | −0.627311 | −0.0838279 | ||||||||
\(57\) | 8.36055 | 1.10738 | ||||||||
\(58\) | 8.01947 | 1.05301 | ||||||||
\(59\) | 10.5893 | 1.37861 | 0.689306 | − | 0.724471i | \(-0.257916\pi\) | ||||
0.689306 | + | 0.724471i | \(0.257916\pi\) | |||||||
\(60\) | −2.17535 | −0.280836 | ||||||||
\(61\) | 9.55763 | 1.22373 | 0.611864 | − | 0.790963i | \(-0.290420\pi\) | ||||
0.611864 | + | 0.790963i | \(0.290420\pi\) | |||||||
\(62\) | −18.9149 | −2.40219 | ||||||||
\(63\) | 0.592895 | 0.0746978 | ||||||||
\(64\) | −2.96228 | −0.370285 | ||||||||
\(65\) | 1.20377 | 0.149309 | ||||||||
\(66\) | −10.7502 | −1.32325 | ||||||||
\(67\) | 4.56547 | 0.557761 | 0.278881 | − | 0.960326i | \(-0.410037\pi\) | ||||
0.278881 | + | 0.960326i | \(0.410037\pi\) | |||||||
\(68\) | −1.42859 | −0.173242 | ||||||||
\(69\) | 4.55046 | 0.547811 | ||||||||
\(70\) | 1.67169 | 0.199806 | ||||||||
\(71\) | −8.15323 | −0.967611 | −0.483805 | − | 0.875176i | \(-0.660746\pi\) | ||||
−0.483805 | + | 0.875176i | \(0.660746\pi\) | |||||||
\(72\) | −1.05805 | −0.124692 | ||||||||
\(73\) | 12.0222 | 1.40709 | 0.703546 | − | 0.710650i | \(-0.251599\pi\) | ||||
0.703546 | + | 0.710650i | \(0.251599\pi\) | |||||||
\(74\) | −11.2965 | −1.31319 | ||||||||
\(75\) | 2.68131 | 0.309611 | ||||||||
\(76\) | −11.9438 | −1.37005 | ||||||||
\(77\) | 3.44219 | 0.392274 | ||||||||
\(78\) | −1.46379 | −0.165742 | ||||||||
\(79\) | 12.3113 | 1.38513 | 0.692564 | − | 0.721357i | \(-0.256481\pi\) | ||||
0.692564 | + | 0.721357i | \(0.256481\pi\) | |||||||
\(80\) | −7.33391 | −0.819956 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.6398 | −1.50626 | ||||||||
\(83\) | 8.32039 | 0.913281 | 0.456641 | − | 0.889651i | \(-0.349053\pi\) | ||||
0.456641 | + | 0.889651i | \(0.349053\pi\) | |||||||
\(84\) | −0.847005 | −0.0924159 | ||||||||
\(85\) | −1.52272 | −0.165163 | ||||||||
\(86\) | −7.31673 | −0.788983 | ||||||||
\(87\) | −4.33100 | −0.464332 | ||||||||
\(88\) | −6.14274 | −0.654818 | ||||||||
\(89\) | −17.9096 | −1.89841 | −0.949205 | − | 0.314657i | \(-0.898110\pi\) | ||||
−0.949205 | + | 0.314657i | \(0.898110\pi\) | |||||||
\(90\) | 2.81954 | 0.297206 | ||||||||
\(91\) | 0.468706 | 0.0491337 | ||||||||
\(92\) | −6.50074 | −0.677749 | ||||||||
\(93\) | 10.2152 | 1.05926 | ||||||||
\(94\) | −12.9395 | −1.33461 | ||||||||
\(95\) | −12.7308 | −1.30615 | ||||||||
\(96\) | 6.80201 | 0.694227 | ||||||||
\(97\) | 15.2579 | 1.54921 | 0.774603 | − | 0.632448i | \(-0.217950\pi\) | ||||
0.774603 | + | 0.632448i | \(0.217950\pi\) | |||||||
\(98\) | −12.3106 | −1.24356 | ||||||||
\(99\) | 5.80574 | 0.583498 | ||||||||
\(100\) | −3.83050 | −0.383050 | ||||||||
\(101\) | −13.9391 | −1.38699 | −0.693496 | − | 0.720460i | \(-0.743931\pi\) | ||||
−0.693496 | + | 0.720460i | \(0.743931\pi\) | |||||||
\(102\) | 1.85165 | 0.183340 | ||||||||
\(103\) | 7.10387 | 0.699966 | 0.349983 | − | 0.936756i | \(-0.386187\pi\) | ||||
0.349983 | + | 0.936756i | \(0.386187\pi\) | |||||||
\(104\) | −0.836425 | −0.0820182 | ||||||||
\(105\) | −0.902816 | −0.0881058 | ||||||||
\(106\) | −15.9405 | −1.54828 | ||||||||
\(107\) | 9.74860 | 0.942433 | 0.471217 | − | 0.882018i | \(-0.343815\pi\) | ||||
0.471217 | + | 0.882018i | \(0.343815\pi\) | |||||||
\(108\) | −1.42859 | −0.137466 | ||||||||
\(109\) | −0.523599 | −0.0501517 | −0.0250759 | − | 0.999686i | \(-0.507983\pi\) | ||||
−0.0250759 | + | 0.999686i | \(0.507983\pi\) | |||||||
\(110\) | 16.3695 | 1.56077 | ||||||||
\(111\) | 6.10080 | 0.579063 | ||||||||
\(112\) | −2.85557 | −0.269826 | ||||||||
\(113\) | 5.93044 | 0.557889 | 0.278945 | − | 0.960307i | \(-0.410015\pi\) | ||||
0.278945 | + | 0.960307i | \(0.410015\pi\) | |||||||
\(114\) | 15.4808 | 1.44991 | ||||||||
\(115\) | −6.92909 | −0.646141 | ||||||||
\(116\) | 6.18722 | 0.574469 | ||||||||
\(117\) | 0.790537 | 0.0730852 | ||||||||
\(118\) | 19.6077 | 1.80503 | ||||||||
\(119\) | −0.592895 | −0.0543506 | ||||||||
\(120\) | 1.61111 | 0.147074 | ||||||||
\(121\) | 22.7066 | 2.06423 | ||||||||
\(122\) | 17.6973 | 1.60224 | ||||||||
\(123\) | 7.36631 | 0.664198 | ||||||||
\(124\) | −14.5933 | −1.31052 | ||||||||
\(125\) | −11.6965 | −1.04617 | ||||||||
\(126\) | 1.09783 | 0.0978027 | ||||||||
\(127\) | −8.40692 | −0.745994 | −0.372997 | − | 0.927833i | \(-0.621670\pi\) | ||||
−0.372997 | + | 0.927833i | \(0.621670\pi\) | |||||||
\(128\) | 8.11891 | 0.717617 | ||||||||
\(129\) | 3.95148 | 0.347908 | ||||||||
\(130\) | 2.22895 | 0.195492 | ||||||||
\(131\) | 9.32937 | 0.815111 | 0.407555 | − | 0.913181i | \(-0.366381\pi\) | ||||
0.407555 | + | 0.913181i | \(0.366381\pi\) | |||||||
\(132\) | −8.29402 | −0.721902 | ||||||||
\(133\) | −4.95693 | −0.429820 | ||||||||
\(134\) | 8.45364 | 0.730283 | ||||||||
\(135\) | −1.52272 | −0.131055 | ||||||||
\(136\) | 1.05805 | 0.0907267 | ||||||||
\(137\) | −22.4372 | −1.91694 | −0.958469 | − | 0.285198i | \(-0.907941\pi\) | ||||
−0.958469 | + | 0.285198i | \(0.907941\pi\) | |||||||
\(138\) | 8.42583 | 0.717255 | ||||||||
\(139\) | −14.3859 | −1.22019 | −0.610097 | − | 0.792326i | \(-0.708870\pi\) | ||||
−0.610097 | + | 0.792326i | \(0.708870\pi\) | |||||||
\(140\) | 1.28975 | 0.109004 | ||||||||
\(141\) | 6.98813 | 0.588507 | ||||||||
\(142\) | −15.0969 | −1.26690 | ||||||||
\(143\) | 4.58965 | 0.383806 | ||||||||
\(144\) | −4.81631 | −0.401359 | ||||||||
\(145\) | 6.59491 | 0.547677 | ||||||||
\(146\) | 22.2608 | 1.84232 | ||||||||
\(147\) | 6.64847 | 0.548357 | ||||||||
\(148\) | −8.71555 | −0.716414 | ||||||||
\(149\) | −20.9710 | −1.71801 | −0.859005 | − | 0.511967i | \(-0.828917\pi\) | ||||
−0.859005 | + | 0.511967i | \(0.828917\pi\) | |||||||
\(150\) | 4.96484 | 0.405378 | ||||||||
\(151\) | 1.75453 | 0.142781 | 0.0713906 | − | 0.997448i | \(-0.477256\pi\) | ||||
0.0713906 | + | 0.997448i | \(0.477256\pi\) | |||||||
\(152\) | 8.84585 | 0.717493 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 6.37372 | 0.513609 | ||||||||
\(155\) | −15.5549 | −1.24940 | ||||||||
\(156\) | −1.12935 | −0.0904207 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 22.7961 | 1.81356 | ||||||||
\(159\) | 8.60881 | 0.682723 | ||||||||
\(160\) | −10.3576 | −0.818838 | ||||||||
\(161\) | −2.69795 | −0.212628 | ||||||||
\(162\) | 1.85165 | 0.145479 | ||||||||
\(163\) | 9.79492 | 0.767198 | 0.383599 | − | 0.923500i | \(-0.374685\pi\) | ||||
0.383599 | + | 0.923500i | \(0.374685\pi\) | |||||||
\(164\) | −10.5234 | −0.821743 | ||||||||
\(165\) | −8.84053 | −0.688234 | ||||||||
\(166\) | 15.4064 | 1.19577 | ||||||||
\(167\) | 21.4686 | 1.66129 | 0.830647 | − | 0.556800i | \(-0.187971\pi\) | ||||
0.830647 | + | 0.556800i | \(0.187971\pi\) | |||||||
\(168\) | 0.627311 | 0.0483981 | ||||||||
\(169\) | −12.3751 | −0.951927 | ||||||||
\(170\) | −2.81954 | −0.216249 | ||||||||
\(171\) | −8.36055 | −0.639347 | ||||||||
\(172\) | −5.64504 | −0.430430 | ||||||||
\(173\) | −10.3683 | −0.788286 | −0.394143 | − | 0.919049i | \(-0.628959\pi\) | ||||
−0.394143 | + | 0.919049i | \(0.628959\pi\) | |||||||
\(174\) | −8.01947 | −0.607955 | ||||||||
\(175\) | −1.58974 | −0.120173 | ||||||||
\(176\) | −27.9622 | −2.10773 | ||||||||
\(177\) | −10.5893 | −0.795942 | ||||||||
\(178\) | −33.1622 | −2.48561 | ||||||||
\(179\) | −18.4231 | −1.37701 | −0.688503 | − | 0.725234i | \(-0.741732\pi\) | ||||
−0.688503 | + | 0.725234i | \(0.741732\pi\) | |||||||
\(180\) | 2.17535 | 0.162141 | ||||||||
\(181\) | 14.4873 | 1.07684 | 0.538418 | − | 0.842678i | \(-0.319022\pi\) | ||||
0.538418 | + | 0.842678i | \(0.319022\pi\) | |||||||
\(182\) | 0.867877 | 0.0643313 | ||||||||
\(183\) | −9.55763 | −0.706520 | ||||||||
\(184\) | 4.81459 | 0.354937 | ||||||||
\(185\) | −9.28984 | −0.683002 | ||||||||
\(186\) | 18.9149 | 1.38691 | ||||||||
\(187\) | −5.80574 | −0.424557 | ||||||||
\(188\) | −9.98318 | −0.728098 | ||||||||
\(189\) | −0.592895 | −0.0431268 | ||||||||
\(190\) | −23.5729 | −1.71016 | ||||||||
\(191\) | 12.3486 | 0.893515 | 0.446758 | − | 0.894655i | \(-0.352579\pi\) | ||||
0.446758 | + | 0.894655i | \(0.352579\pi\) | |||||||
\(192\) | 2.96228 | 0.213784 | ||||||||
\(193\) | −16.8294 | −1.21140 | −0.605702 | − | 0.795692i | \(-0.707108\pi\) | ||||
−0.605702 | + | 0.795692i | \(0.707108\pi\) | |||||||
\(194\) | 28.2522 | 2.02839 | ||||||||
\(195\) | −1.20377 | −0.0862037 | ||||||||
\(196\) | −9.49795 | −0.678425 | ||||||||
\(197\) | 7.85567 | 0.559693 | 0.279847 | − | 0.960045i | \(-0.409716\pi\) | ||||
0.279847 | + | 0.960045i | \(0.409716\pi\) | |||||||
\(198\) | 10.7502 | 0.763981 | ||||||||
\(199\) | −3.33007 | −0.236062 | −0.118031 | − | 0.993010i | \(-0.537658\pi\) | ||||
−0.118031 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(200\) | 2.83695 | 0.200603 | ||||||||
\(201\) | −4.56547 | −0.322024 | ||||||||
\(202\) | −25.8103 | −1.81600 | ||||||||
\(203\) | 2.56783 | 0.180226 | ||||||||
\(204\) | 1.42859 | 0.100021 | ||||||||
\(205\) | −11.2169 | −0.783419 | ||||||||
\(206\) | 13.1539 | 0.916473 | ||||||||
\(207\) | −4.55046 | −0.316279 | ||||||||
\(208\) | −3.80747 | −0.264001 | ||||||||
\(209\) | −48.5391 | −3.35752 | ||||||||
\(210\) | −1.67169 | −0.115358 | ||||||||
\(211\) | −25.0736 | −1.72614 | −0.863070 | − | 0.505085i | \(-0.831461\pi\) | ||||
−0.863070 | + | 0.505085i | \(0.831461\pi\) | |||||||
\(212\) | −12.2985 | −0.844663 | ||||||||
\(213\) | 8.15323 | 0.558650 | ||||||||
\(214\) | 18.0510 | 1.23394 | ||||||||
\(215\) | −6.01700 | −0.410356 | ||||||||
\(216\) | 1.05805 | 0.0719909 | ||||||||
\(217\) | −6.05653 | −0.411144 | ||||||||
\(218\) | −0.969521 | −0.0656642 | ||||||||
\(219\) | −12.0222 | −0.812384 | ||||||||
\(220\) | 12.6295 | 0.851481 | ||||||||
\(221\) | −0.790537 | −0.0531773 | ||||||||
\(222\) | 11.2965 | 0.758173 | ||||||||
\(223\) | −2.69549 | −0.180503 | −0.0902516 | − | 0.995919i | \(-0.528767\pi\) | ||||
−0.0902516 | + | 0.995919i | \(0.528767\pi\) | |||||||
\(224\) | −4.03288 | −0.269458 | ||||||||
\(225\) | −2.68131 | −0.178754 | ||||||||
\(226\) | 10.9811 | 0.730450 | ||||||||
\(227\) | −27.4607 | −1.82263 | −0.911315 | − | 0.411710i | \(-0.864932\pi\) | ||||
−0.911315 | + | 0.411710i | \(0.864932\pi\) | |||||||
\(228\) | 11.9438 | 0.790998 | ||||||||
\(229\) | −3.09977 | −0.204838 | −0.102419 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102419 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(230\) | −12.8302 | −0.845999 | ||||||||
\(231\) | −3.44219 | −0.226480 | ||||||||
\(232\) | −4.58240 | −0.300849 | ||||||||
\(233\) | 20.0319 | 1.31233 | 0.656166 | − | 0.754616i | \(-0.272177\pi\) | ||||
0.656166 | + | 0.754616i | \(0.272177\pi\) | |||||||
\(234\) | 1.46379 | 0.0956912 | ||||||||
\(235\) | −10.6410 | −0.694141 | ||||||||
\(236\) | 15.1278 | 0.984736 | ||||||||
\(237\) | −12.3113 | −0.799704 | ||||||||
\(238\) | −1.09783 | −0.0711619 | ||||||||
\(239\) | −17.0924 | −1.10562 | −0.552808 | − | 0.833309i | \(-0.686444\pi\) | ||||
−0.552808 | + | 0.833309i | \(0.686444\pi\) | |||||||
\(240\) | 7.33391 | 0.473402 | ||||||||
\(241\) | 17.3130 | 1.11523 | 0.557615 | − | 0.830100i | \(-0.311717\pi\) | ||||
0.557615 | + | 0.830100i | \(0.311717\pi\) | |||||||
\(242\) | 42.0445 | 2.70272 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.6539 | 0.874104 | ||||||||
\(245\) | −10.1238 | −0.646785 | ||||||||
\(246\) | 13.6398 | 0.869642 | ||||||||
\(247\) | −6.60932 | −0.420541 | ||||||||
\(248\) | 10.8081 | 0.686317 | ||||||||
\(249\) | −8.32039 | −0.527283 | ||||||||
\(250\) | −21.6578 | −1.36976 | ||||||||
\(251\) | 18.0587 | 1.13985 | 0.569926 | − | 0.821696i | \(-0.306972\pi\) | ||||
0.569926 | + | 0.821696i | \(0.306972\pi\) | |||||||
\(252\) | 0.847005 | 0.0533563 | ||||||||
\(253\) | −26.4187 | −1.66093 | ||||||||
\(254\) | −15.5666 | −0.976738 | ||||||||
\(255\) | 1.52272 | 0.0953566 | ||||||||
\(256\) | 20.9579 | 1.30987 | ||||||||
\(257\) | −1.98632 | −0.123903 | −0.0619517 | − | 0.998079i | \(-0.519732\pi\) | ||||
−0.0619517 | + | 0.998079i | \(0.519732\pi\) | |||||||
\(258\) | 7.31673 | 0.455520 | ||||||||
\(259\) | −3.61714 | −0.224758 | ||||||||
\(260\) | 1.71969 | 0.106651 | ||||||||
\(261\) | 4.33100 | 0.268082 | ||||||||
\(262\) | 17.2747 | 1.06723 | ||||||||
\(263\) | 1.85794 | 0.114565 | 0.0572827 | − | 0.998358i | \(-0.481756\pi\) | ||||
0.0572827 | + | 0.998358i | \(0.481756\pi\) | |||||||
\(264\) | 6.14274 | 0.378059 | ||||||||
\(265\) | −13.1088 | −0.805270 | ||||||||
\(266\) | −9.17848 | −0.562769 | ||||||||
\(267\) | 17.9096 | 1.09605 | ||||||||
\(268\) | 6.52219 | 0.398406 | ||||||||
\(269\) | 16.4997 | 1.00600 | 0.503001 | − | 0.864286i | \(-0.332229\pi\) | ||||
0.503001 | + | 0.864286i | \(0.332229\pi\) | |||||||
\(270\) | −2.81954 | −0.171592 | ||||||||
\(271\) | 17.2735 | 1.04929 | 0.524645 | − | 0.851321i | \(-0.324198\pi\) | ||||
0.524645 | + | 0.851321i | \(0.324198\pi\) | |||||||
\(272\) | 4.81631 | 0.292032 | ||||||||
\(273\) | −0.468706 | −0.0283674 | ||||||||
\(274\) | −41.5457 | −2.50987 | ||||||||
\(275\) | −15.5670 | −0.938725 | ||||||||
\(276\) | 6.50074 | 0.391299 | ||||||||
\(277\) | 19.5227 | 1.17300 | 0.586502 | − | 0.809948i | \(-0.300505\pi\) | ||||
0.586502 | + | 0.809948i | \(0.300505\pi\) | |||||||
\(278\) | −26.6376 | −1.59761 | ||||||||
\(279\) | −10.2152 | −0.611567 | ||||||||
\(280\) | −0.955221 | −0.0570854 | ||||||||
\(281\) | −6.83926 | −0.407996 | −0.203998 | − | 0.978971i | \(-0.565394\pi\) | ||||
−0.203998 | + | 0.978971i | \(0.565394\pi\) | |||||||
\(282\) | 12.9395 | 0.770538 | ||||||||
\(283\) | 1.47130 | 0.0874599 | 0.0437299 | − | 0.999043i | \(-0.486076\pi\) | ||||
0.0437299 | + | 0.999043i | \(0.486076\pi\) | |||||||
\(284\) | −11.6476 | −0.691160 | ||||||||
\(285\) | 12.7308 | 0.754108 | ||||||||
\(286\) | 8.49840 | 0.502521 | ||||||||
\(287\) | −4.36745 | −0.257803 | ||||||||
\(288\) | −6.80201 | −0.400812 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 12.2114 | 0.717080 | ||||||||
\(291\) | −15.2579 | −0.894434 | ||||||||
\(292\) | 17.1748 | 1.00508 | ||||||||
\(293\) | −15.0191 | −0.877423 | −0.438711 | − | 0.898628i | \(-0.644565\pi\) | ||||
−0.438711 | + | 0.898628i | \(0.644565\pi\) | |||||||
\(294\) | 12.3106 | 0.717970 | ||||||||
\(295\) | 16.1246 | 0.938810 | ||||||||
\(296\) | 6.45493 | 0.375185 | ||||||||
\(297\) | −5.80574 | −0.336883 | ||||||||
\(298\) | −38.8308 | −2.24941 | ||||||||
\(299\) | −3.59730 | −0.208037 | ||||||||
\(300\) | 3.83050 | 0.221154 | ||||||||
\(301\) | −2.34281 | −0.135037 | ||||||||
\(302\) | 3.24876 | 0.186945 | ||||||||
\(303\) | 13.9391 | 0.800780 | ||||||||
\(304\) | 40.2670 | 2.30947 | ||||||||
\(305\) | 14.5536 | 0.833338 | ||||||||
\(306\) | −1.85165 | −0.105852 | ||||||||
\(307\) | 24.0001 | 1.36976 | 0.684878 | − | 0.728658i | \(-0.259855\pi\) | ||||
0.684878 | + | 0.728658i | \(0.259855\pi\) | |||||||
\(308\) | 4.91749 | 0.280200 | ||||||||
\(309\) | −7.10387 | −0.404125 | ||||||||
\(310\) | −28.8021 | −1.63585 | ||||||||
\(311\) | 29.6667 | 1.68225 | 0.841123 | − | 0.540844i | \(-0.181895\pi\) | ||||
0.841123 | + | 0.540844i | \(0.181895\pi\) | |||||||
\(312\) | 0.836425 | 0.0473532 | ||||||||
\(313\) | 5.39192 | 0.304769 | 0.152385 | − | 0.988321i | \(-0.451305\pi\) | ||||
0.152385 | + | 0.988321i | \(0.451305\pi\) | |||||||
\(314\) | −1.85165 | −0.104494 | ||||||||
\(315\) | 0.902816 | 0.0508679 | ||||||||
\(316\) | 17.5878 | 0.989390 | ||||||||
\(317\) | −9.67677 | −0.543501 | −0.271751 | − | 0.962368i | \(-0.587603\pi\) | ||||
−0.271751 | + | 0.962368i | \(0.587603\pi\) | |||||||
\(318\) | 15.9405 | 0.893897 | ||||||||
\(319\) | 25.1446 | 1.40783 | ||||||||
\(320\) | −4.51074 | −0.252158 | ||||||||
\(321\) | −9.74860 | −0.544114 | ||||||||
\(322\) | −4.99564 | −0.278396 | ||||||||
\(323\) | 8.36055 | 0.465193 | ||||||||
\(324\) | 1.42859 | 0.0793662 | ||||||||
\(325\) | −2.11968 | −0.117579 | ||||||||
\(326\) | 18.1367 | 1.00450 | ||||||||
\(327\) | 0.523599 | 0.0289551 | ||||||||
\(328\) | 7.79390 | 0.430346 | ||||||||
\(329\) | −4.14323 | −0.228424 | ||||||||
\(330\) | −16.3695 | −0.901113 | ||||||||
\(331\) | −13.8446 | −0.760969 | −0.380485 | − | 0.924787i | \(-0.624243\pi\) | ||||
−0.380485 | + | 0.924787i | \(0.624243\pi\) | |||||||
\(332\) | 11.8864 | 0.652353 | ||||||||
\(333\) | −6.10080 | −0.334322 | ||||||||
\(334\) | 39.7523 | 2.17515 | ||||||||
\(335\) | 6.95195 | 0.379826 | ||||||||
\(336\) | 2.85557 | 0.155784 | ||||||||
\(337\) | −9.10708 | −0.496094 | −0.248047 | − | 0.968748i | \(-0.579789\pi\) | ||||
−0.248047 | + | 0.968748i | \(0.579789\pi\) | |||||||
\(338\) | −22.9142 | −1.24637 | ||||||||
\(339\) | −5.93044 | −0.322097 | ||||||||
\(340\) | −2.17535 | −0.117975 | ||||||||
\(341\) | −59.3066 | −3.21163 | ||||||||
\(342\) | −15.4808 | −0.837104 | ||||||||
\(343\) | −8.09212 | −0.436933 | ||||||||
\(344\) | 4.18084 | 0.225416 | ||||||||
\(345\) | 6.92909 | 0.373050 | ||||||||
\(346\) | −19.1984 | −1.03211 | ||||||||
\(347\) | −30.5201 | −1.63840 | −0.819202 | − | 0.573505i | \(-0.805583\pi\) | ||||
−0.819202 | + | 0.573505i | \(0.805583\pi\) | |||||||
\(348\) | −6.18722 | −0.331670 | ||||||||
\(349\) | −18.7346 | −1.00284 | −0.501420 | − | 0.865204i | \(-0.667189\pi\) | ||||
−0.501420 | + | 0.865204i | \(0.667189\pi\) | |||||||
\(350\) | −2.94363 | −0.157344 | ||||||||
\(351\) | −0.790537 | −0.0421957 | ||||||||
\(352\) | −39.4906 | −2.10486 | ||||||||
\(353\) | −0.0549497 | −0.00292468 | −0.00146234 | − | 0.999999i | \(-0.500465\pi\) | ||||
−0.00146234 | + | 0.999999i | \(0.500465\pi\) | |||||||
\(354\) | −19.6077 | −1.04214 | ||||||||
\(355\) | −12.4151 | −0.658926 | ||||||||
\(356\) | −25.5855 | −1.35603 | ||||||||
\(357\) | 0.592895 | 0.0313794 | ||||||||
\(358\) | −34.1130 | −1.80293 | ||||||||
\(359\) | −1.15478 | −0.0609468 | −0.0304734 | − | 0.999536i | \(-0.509701\pi\) | ||||
−0.0304734 | + | 0.999536i | \(0.509701\pi\) | |||||||
\(360\) | −1.61111 | −0.0849131 | ||||||||
\(361\) | 50.8988 | 2.67888 | ||||||||
\(362\) | 26.8254 | 1.40991 | ||||||||
\(363\) | −22.7066 | −1.19179 | ||||||||
\(364\) | 0.669589 | 0.0350960 | ||||||||
\(365\) | 18.3065 | 0.958205 | ||||||||
\(366\) | −17.6973 | −0.925055 | ||||||||
\(367\) | −9.32154 | −0.486580 | −0.243290 | − | 0.969954i | \(-0.578227\pi\) | ||||
−0.243290 | + | 0.969954i | \(0.578227\pi\) | |||||||
\(368\) | 21.9164 | 1.14247 | ||||||||
\(369\) | −7.36631 | −0.383475 | ||||||||
\(370\) | −17.2015 | −0.894262 | ||||||||
\(371\) | −5.10413 | −0.264993 | ||||||||
\(372\) | 14.5933 | 0.756628 | ||||||||
\(373\) | −24.8604 | −1.28722 | −0.643611 | − | 0.765353i | \(-0.722564\pi\) | ||||
−0.643611 | + | 0.765353i | \(0.722564\pi\) | |||||||
\(374\) | −10.7502 | −0.555878 | ||||||||
\(375\) | 11.6965 | 0.604005 | ||||||||
\(376\) | 7.39376 | 0.381304 | ||||||||
\(377\) | 3.42381 | 0.176335 | ||||||||
\(378\) | −1.09783 | −0.0564664 | ||||||||
\(379\) | −15.2568 | −0.783688 | −0.391844 | − | 0.920032i | \(-0.628163\pi\) | ||||
−0.391844 | + | 0.920032i | \(0.628163\pi\) | |||||||
\(380\) | −18.1871 | −0.932979 | ||||||||
\(381\) | 8.40692 | 0.430700 | ||||||||
\(382\) | 22.8653 | 1.16989 | ||||||||
\(383\) | 37.6542 | 1.92404 | 0.962020 | − | 0.272979i | \(-0.0880089\pi\) | ||||
0.962020 | + | 0.272979i | \(0.0880089\pi\) | |||||||
\(384\) | −8.11891 | −0.414316 | ||||||||
\(385\) | 5.24151 | 0.267132 | ||||||||
\(386\) | −31.1620 | −1.58611 | ||||||||
\(387\) | −3.95148 | −0.200865 | ||||||||
\(388\) | 21.7973 | 1.10659 | ||||||||
\(389\) | 2.08505 | 0.105716 | 0.0528581 | − | 0.998602i | \(-0.483167\pi\) | ||||
0.0528581 | + | 0.998602i | \(0.483167\pi\) | |||||||
\(390\) | −2.22895 | −0.112867 | ||||||||
\(391\) | 4.55046 | 0.230127 | ||||||||
\(392\) | 7.03440 | 0.355291 | ||||||||
\(393\) | −9.32937 | −0.470604 | ||||||||
\(394\) | 14.5459 | 0.732813 | ||||||||
\(395\) | 18.7467 | 0.943248 | ||||||||
\(396\) | 8.29402 | 0.416790 | ||||||||
\(397\) | −19.3637 | −0.971836 | −0.485918 | − | 0.874005i | \(-0.661515\pi\) | ||||
−0.485918 | + | 0.874005i | \(0.661515\pi\) | |||||||
\(398\) | −6.16611 | −0.309079 | ||||||||
\(399\) | 4.95693 | 0.248157 | ||||||||
\(400\) | 12.9140 | 0.645702 | ||||||||
\(401\) | 36.2545 | 1.81046 | 0.905231 | − | 0.424920i | \(-0.139698\pi\) | ||||
0.905231 | + | 0.424920i | \(0.139698\pi\) | |||||||
\(402\) | −8.45364 | −0.421629 | ||||||||
\(403\) | −8.07548 | −0.402268 | ||||||||
\(404\) | −19.9133 | −0.990722 | ||||||||
\(405\) | 1.52272 | 0.0756647 | ||||||||
\(406\) | 4.75471 | 0.235972 | ||||||||
\(407\) | −35.4196 | −1.75569 | ||||||||
\(408\) | −1.05805 | −0.0523811 | ||||||||
\(409\) | 26.0246 | 1.28683 | 0.643416 | − | 0.765517i | \(-0.277517\pi\) | ||||
0.643416 | + | 0.765517i | \(0.277517\pi\) | |||||||
\(410\) | −20.7696 | −1.02574 | ||||||||
\(411\) | 22.4372 | 1.10674 | ||||||||
\(412\) | 10.1485 | 0.499982 | ||||||||
\(413\) | 6.27836 | 0.308938 | ||||||||
\(414\) | −8.42583 | −0.414107 | ||||||||
\(415\) | 12.6696 | 0.621929 | ||||||||
\(416\) | −5.37724 | −0.263641 | ||||||||
\(417\) | 14.3859 | 0.704480 | ||||||||
\(418\) | −89.8773 | −4.39604 | ||||||||
\(419\) | 8.94675 | 0.437077 | 0.218539 | − | 0.975828i | \(-0.429871\pi\) | ||||
0.218539 | + | 0.975828i | \(0.429871\pi\) | |||||||
\(420\) | −1.28975 | −0.0629336 | ||||||||
\(421\) | −19.3800 | −0.944523 | −0.472261 | − | 0.881459i | \(-0.656562\pi\) | ||||
−0.472261 | + | 0.881459i | \(0.656562\pi\) | |||||||
\(422\) | −46.4275 | −2.26005 | ||||||||
\(423\) | −6.98813 | −0.339774 | ||||||||
\(424\) | 9.10852 | 0.442349 | ||||||||
\(425\) | 2.68131 | 0.130063 | ||||||||
\(426\) | 15.0969 | 0.731447 | ||||||||
\(427\) | 5.66667 | 0.274230 | ||||||||
\(428\) | 13.9268 | 0.673176 | ||||||||
\(429\) | −4.58965 | −0.221590 | ||||||||
\(430\) | −11.1414 | −0.537284 | ||||||||
\(431\) | 24.5160 | 1.18089 | 0.590446 | − | 0.807077i | \(-0.298952\pi\) | ||||
0.590446 | + | 0.807077i | \(0.298952\pi\) | |||||||
\(432\) | 4.81631 | 0.231725 | ||||||||
\(433\) | 6.54669 | 0.314614 | 0.157307 | − | 0.987550i | \(-0.449719\pi\) | ||||
0.157307 | + | 0.987550i | \(0.449719\pi\) | |||||||
\(434\) | −11.2146 | −0.538316 | ||||||||
\(435\) | −6.59491 | −0.316202 | ||||||||
\(436\) | −0.748010 | −0.0358232 | ||||||||
\(437\) | 38.0443 | 1.81991 | ||||||||
\(438\) | −22.2608 | −1.06366 | ||||||||
\(439\) | 22.4568 | 1.07180 | 0.535902 | − | 0.844280i | \(-0.319972\pi\) | ||||
0.535902 | + | 0.844280i | \(0.319972\pi\) | |||||||
\(440\) | −9.35369 | −0.445920 | ||||||||
\(441\) | −6.64847 | −0.316594 | ||||||||
\(442\) | −1.46379 | −0.0696256 | ||||||||
\(443\) | 28.8903 | 1.37262 | 0.686309 | − | 0.727310i | \(-0.259230\pi\) | ||||
0.686309 | + | 0.727310i | \(0.259230\pi\) | |||||||
\(444\) | 8.71555 | 0.413622 | ||||||||
\(445\) | −27.2713 | −1.29278 | ||||||||
\(446\) | −4.99109 | −0.236335 | ||||||||
\(447\) | 20.9710 | 0.991894 | ||||||||
\(448\) | −1.75632 | −0.0829785 | ||||||||
\(449\) | −15.6886 | −0.740390 | −0.370195 | − | 0.928954i | \(-0.620709\pi\) | ||||
−0.370195 | + | 0.928954i | \(0.620709\pi\) | |||||||
\(450\) | −4.96484 | −0.234045 | ||||||||
\(451\) | −42.7669 | −2.01381 | ||||||||
\(452\) | 8.47218 | 0.398498 | ||||||||
\(453\) | −1.75453 | −0.0824348 | ||||||||
\(454\) | −50.8475 | −2.38639 | ||||||||
\(455\) | 0.713709 | 0.0334592 | ||||||||
\(456\) | −8.84585 | −0.414245 | ||||||||
\(457\) | 4.99318 | 0.233571 | 0.116786 | − | 0.993157i | \(-0.462741\pi\) | ||||
0.116786 | + | 0.993157i | \(0.462741\pi\) | |||||||
\(458\) | −5.73967 | −0.268197 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −9.89883 | −0.461536 | ||||||||
\(461\) | 9.76476 | 0.454790 | 0.227395 | − | 0.973803i | \(-0.426979\pi\) | ||||
0.227395 | + | 0.973803i | \(0.426979\pi\) | |||||||
\(462\) | −6.37372 | −0.296532 | ||||||||
\(463\) | −6.34394 | −0.294828 | −0.147414 | − | 0.989075i | \(-0.547095\pi\) | ||||
−0.147414 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(464\) | −20.8594 | −0.968374 | ||||||||
\(465\) | 15.5549 | 0.721341 | ||||||||
\(466\) | 37.0920 | 1.71825 | ||||||||
\(467\) | −18.0623 | −0.835822 | −0.417911 | − | 0.908488i | \(-0.637238\pi\) | ||||
−0.417911 | + | 0.908488i | \(0.637238\pi\) | |||||||
\(468\) | 1.12935 | 0.0522044 | ||||||||
\(469\) | 2.70685 | 0.124991 | ||||||||
\(470\) | −19.7033 | −0.908847 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −11.2040 | −0.515705 | ||||||||
\(473\) | −22.9412 | −1.05484 | ||||||||
\(474\) | −22.7961 | −1.04706 | ||||||||
\(475\) | 22.4172 | 1.02857 | ||||||||
\(476\) | −0.847005 | −0.0388224 | ||||||||
\(477\) | −8.60881 | −0.394170 | ||||||||
\(478\) | −31.6491 | −1.44759 | ||||||||
\(479\) | −20.6472 | −0.943395 | −0.471698 | − | 0.881760i | \(-0.656359\pi\) | ||||
−0.471698 | + | 0.881760i | \(0.656359\pi\) | |||||||
\(480\) | 10.3576 | 0.472756 | ||||||||
\(481\) | −4.82291 | −0.219906 | ||||||||
\(482\) | 32.0576 | 1.46018 | ||||||||
\(483\) | 2.69795 | 0.122761 | ||||||||
\(484\) | 32.4384 | 1.47447 | ||||||||
\(485\) | 23.2336 | 1.05498 | ||||||||
\(486\) | −1.85165 | −0.0839923 | ||||||||
\(487\) | −18.3023 | −0.829356 | −0.414678 | − | 0.909968i | \(-0.636106\pi\) | ||||
−0.414678 | + | 0.909968i | \(0.636106\pi\) | |||||||
\(488\) | −10.1124 | −0.457767 | ||||||||
\(489\) | −9.79492 | −0.442942 | ||||||||
\(490\) | −18.7457 | −0.846843 | ||||||||
\(491\) | −2.68600 | −0.121218 | −0.0606089 | − | 0.998162i | \(-0.519304\pi\) | ||||
−0.0606089 | + | 0.998162i | \(0.519304\pi\) | |||||||
\(492\) | 10.5234 | 0.474434 | ||||||||
\(493\) | −4.33100 | −0.195058 | ||||||||
\(494\) | −12.2381 | −0.550619 | ||||||||
\(495\) | 8.84053 | 0.397352 | ||||||||
\(496\) | 49.1995 | 2.20912 | ||||||||
\(497\) | −4.83402 | −0.216835 | ||||||||
\(498\) | −15.4064 | −0.690378 | ||||||||
\(499\) | −28.0367 | −1.25509 | −0.627547 | − | 0.778579i | \(-0.715941\pi\) | ||||
−0.627547 | + | 0.778579i | \(0.715941\pi\) | |||||||
\(500\) | −16.7095 | −0.747273 | ||||||||
\(501\) | −21.4686 | −0.959148 | ||||||||
\(502\) | 33.4382 | 1.49242 | ||||||||
\(503\) | 9.14819 | 0.407898 | 0.203949 | − | 0.978982i | \(-0.434622\pi\) | ||||
0.203949 | + | 0.978982i | \(0.434622\pi\) | |||||||
\(504\) | −0.627311 | −0.0279426 | ||||||||
\(505\) | −21.2254 | −0.944518 | ||||||||
\(506\) | −48.9182 | −2.17468 | ||||||||
\(507\) | 12.3751 | 0.549595 | ||||||||
\(508\) | −12.0101 | −0.532860 | ||||||||
\(509\) | 25.2113 | 1.11747 | 0.558735 | − | 0.829346i | \(-0.311287\pi\) | ||||
0.558735 | + | 0.829346i | \(0.311287\pi\) | |||||||
\(510\) | 2.81954 | 0.124852 | ||||||||
\(511\) | 7.12790 | 0.315320 | ||||||||
\(512\) | 22.5688 | 0.997410 | ||||||||
\(513\) | 8.36055 | 0.369127 | ||||||||
\(514\) | −3.67797 | −0.162228 | ||||||||
\(515\) | 10.8172 | 0.476664 | ||||||||
\(516\) | 5.64504 | 0.248509 | ||||||||
\(517\) | −40.5712 | −1.78432 | ||||||||
\(518\) | −6.69766 | −0.294278 | ||||||||
\(519\) | 10.3683 | 0.455117 | ||||||||
\(520\) | −1.27364 | −0.0558530 | ||||||||
\(521\) | −11.7648 | −0.515426 | −0.257713 | − | 0.966222i | \(-0.582969\pi\) | ||||
−0.257713 | + | 0.966222i | \(0.582969\pi\) | |||||||
\(522\) | 8.01947 | 0.351003 | ||||||||
\(523\) | −12.9905 | −0.568033 | −0.284016 | − | 0.958819i | \(-0.591667\pi\) | ||||
−0.284016 | + | 0.958819i | \(0.591667\pi\) | |||||||
\(524\) | 13.3279 | 0.582230 | ||||||||
\(525\) | 1.58974 | 0.0693819 | ||||||||
\(526\) | 3.44025 | 0.150002 | ||||||||
\(527\) | 10.2152 | 0.444980 | ||||||||
\(528\) | 27.9622 | 1.21690 | ||||||||
\(529\) | −2.29334 | −0.0997105 | ||||||||
\(530\) | −24.2729 | −1.05435 | ||||||||
\(531\) | 10.5893 | 0.459537 | ||||||||
\(532\) | −7.08143 | −0.307019 | ||||||||
\(533\) | −5.82334 | −0.252237 | ||||||||
\(534\) | 33.1622 | 1.43507 | ||||||||
\(535\) | 14.8444 | 0.641780 | ||||||||
\(536\) | −4.83048 | −0.208645 | ||||||||
\(537\) | 18.4231 | 0.795015 | ||||||||
\(538\) | 30.5515 | 1.31717 | ||||||||
\(539\) | −38.5993 | −1.66259 | ||||||||
\(540\) | −2.17535 | −0.0936121 | ||||||||
\(541\) | −24.5817 | −1.05685 | −0.528426 | − | 0.848980i | \(-0.677217\pi\) | ||||
−0.528426 | + | 0.848980i | \(0.677217\pi\) | |||||||
\(542\) | 31.9844 | 1.37385 | ||||||||
\(543\) | −14.4873 | −0.621711 | ||||||||
\(544\) | 6.80201 | 0.291634 | ||||||||
\(545\) | −0.797297 | −0.0341525 | ||||||||
\(546\) | −0.867877 | −0.0371417 | ||||||||
\(547\) | −10.7030 | −0.457629 | −0.228814 | − | 0.973470i | \(-0.573485\pi\) | ||||
−0.228814 | + | 0.973470i | \(0.573485\pi\) | |||||||
\(548\) | −32.0536 | −1.36926 | ||||||||
\(549\) | 9.55763 | 0.407910 | ||||||||
\(550\) | −28.8246 | −1.22908 | ||||||||
\(551\) | −36.2095 | −1.54258 | ||||||||
\(552\) | −4.81459 | −0.204923 | ||||||||
\(553\) | 7.29930 | 0.310398 | ||||||||
\(554\) | 36.1491 | 1.53583 | ||||||||
\(555\) | 9.28984 | 0.394332 | ||||||||
\(556\) | −20.5515 | −0.871580 | ||||||||
\(557\) | 16.9136 | 0.716654 | 0.358327 | − | 0.933596i | \(-0.383347\pi\) | ||||
0.358327 | + | 0.933596i | \(0.383347\pi\) | |||||||
\(558\) | −18.9149 | −0.800731 | ||||||||
\(559\) | −3.12379 | −0.132122 | ||||||||
\(560\) | −4.34824 | −0.183747 | ||||||||
\(561\) | 5.80574 | 0.245118 | ||||||||
\(562\) | −12.6639 | −0.534194 | ||||||||
\(563\) | −21.7343 | −0.915990 | −0.457995 | − | 0.888955i | \(-0.651432\pi\) | ||||
−0.457995 | + | 0.888955i | \(0.651432\pi\) | |||||||
\(564\) | 9.98318 | 0.420368 | ||||||||
\(565\) | 9.03042 | 0.379913 | ||||||||
\(566\) | 2.72433 | 0.114512 | ||||||||
\(567\) | 0.592895 | 0.0248993 | ||||||||
\(568\) | 8.62650 | 0.361960 | ||||||||
\(569\) | −38.6392 | −1.61984 | −0.809920 | − | 0.586541i | \(-0.800489\pi\) | ||||
−0.809920 | + | 0.586541i | \(0.800489\pi\) | |||||||
\(570\) | 23.5729 | 0.987362 | ||||||||
\(571\) | 20.8146 | 0.871065 | 0.435533 | − | 0.900173i | \(-0.356560\pi\) | ||||
0.435533 | + | 0.900173i | \(0.356560\pi\) | |||||||
\(572\) | 6.55673 | 0.274151 | ||||||||
\(573\) | −12.3486 | −0.515871 | ||||||||
\(574\) | −8.08697 | −0.337544 | ||||||||
\(575\) | 12.2012 | 0.508825 | ||||||||
\(576\) | −2.96228 | −0.123428 | ||||||||
\(577\) | −46.1050 | −1.91938 | −0.959688 | − | 0.281066i | \(-0.909312\pi\) | ||||
−0.959688 | + | 0.281066i | \(0.909312\pi\) | |||||||
\(578\) | 1.85165 | 0.0770183 | ||||||||
\(579\) | 16.8294 | 0.699405 | ||||||||
\(580\) | 9.42143 | 0.391204 | ||||||||
\(581\) | 4.93312 | 0.204660 | ||||||||
\(582\) | −28.2522 | −1.17109 | ||||||||
\(583\) | −49.9805 | −2.06998 | ||||||||
\(584\) | −12.7200 | −0.526359 | ||||||||
\(585\) | 1.20377 | 0.0497697 | ||||||||
\(586\) | −27.8100 | −1.14882 | ||||||||
\(587\) | −26.9114 | −1.11075 | −0.555376 | − | 0.831600i | \(-0.687426\pi\) | ||||
−0.555376 | + | 0.831600i | \(0.687426\pi\) | |||||||
\(588\) | 9.49795 | 0.391689 | ||||||||
\(589\) | 85.4045 | 3.51903 | ||||||||
\(590\) | 29.8570 | 1.22919 | ||||||||
\(591\) | −7.85567 | −0.323139 | ||||||||
\(592\) | 29.3834 | 1.20765 | ||||||||
\(593\) | 2.40357 | 0.0987028 | 0.0493514 | − | 0.998781i | \(-0.484285\pi\) | ||||
0.0493514 | + | 0.998781i | \(0.484285\pi\) | |||||||
\(594\) | −10.7502 | −0.441085 | ||||||||
\(595\) | −0.902816 | −0.0370118 | ||||||||
\(596\) | −29.9590 | −1.22717 | ||||||||
\(597\) | 3.33007 | 0.136291 | ||||||||
\(598\) | −6.66093 | −0.272386 | ||||||||
\(599\) | 40.2253 | 1.64356 | 0.821781 | − | 0.569804i | \(-0.192981\pi\) | ||||
0.821781 | + | 0.569804i | \(0.192981\pi\) | |||||||
\(600\) | −2.83695 | −0.115818 | ||||||||
\(601\) | −16.6753 | −0.680198 | −0.340099 | − | 0.940390i | \(-0.610461\pi\) | ||||
−0.340099 | + | 0.940390i | \(0.610461\pi\) | |||||||
\(602\) | −4.33806 | −0.176806 | ||||||||
\(603\) | 4.56547 | 0.185920 | ||||||||
\(604\) | 2.50650 | 0.101988 | ||||||||
\(605\) | 34.5758 | 1.40571 | ||||||||
\(606\) | 25.8103 | 1.04847 | ||||||||
\(607\) | 17.9768 | 0.729657 | 0.364829 | − | 0.931075i | \(-0.381128\pi\) | ||||
0.364829 | + | 0.931075i | \(0.381128\pi\) | |||||||
\(608\) | 56.8685 | 2.30632 | ||||||||
\(609\) | −2.56783 | −0.104054 | ||||||||
\(610\) | 26.9481 | 1.09110 | ||||||||
\(611\) | −5.52437 | −0.223492 | ||||||||
\(612\) | −1.42859 | −0.0577474 | ||||||||
\(613\) | −2.57498 | −0.104003 | −0.0520013 | − | 0.998647i | \(-0.516560\pi\) | ||||
−0.0520013 | + | 0.998647i | \(0.516560\pi\) | |||||||
\(614\) | 44.4396 | 1.79344 | ||||||||
\(615\) | 11.2169 | 0.452307 | ||||||||
\(616\) | −3.64200 | −0.146740 | ||||||||
\(617\) | 19.4272 | 0.782110 | 0.391055 | − | 0.920367i | \(-0.372110\pi\) | ||||
0.391055 | + | 0.920367i | \(0.372110\pi\) | |||||||
\(618\) | −13.1539 | −0.529126 | ||||||||
\(619\) | 38.8528 | 1.56162 | 0.780812 | − | 0.624766i | \(-0.214806\pi\) | ||||
0.780812 | + | 0.624766i | \(0.214806\pi\) | |||||||
\(620\) | −22.2216 | −0.892440 | ||||||||
\(621\) | 4.55046 | 0.182604 | ||||||||
\(622\) | 54.9323 | 2.20258 | ||||||||
\(623\) | −10.6185 | −0.425421 | ||||||||
\(624\) | 3.80747 | 0.152421 | ||||||||
\(625\) | −4.40399 | −0.176160 | ||||||||
\(626\) | 9.98392 | 0.399038 | ||||||||
\(627\) | 48.5391 | 1.93847 | ||||||||
\(628\) | −1.42859 | −0.0570070 | ||||||||
\(629\) | 6.10080 | 0.243255 | ||||||||
\(630\) | 1.67169 | 0.0666019 | ||||||||
\(631\) | 34.3397 | 1.36704 | 0.683521 | − | 0.729931i | \(-0.260448\pi\) | ||||
0.683521 | + | 0.729931i | \(0.260448\pi\) | |||||||
\(632\) | −13.0259 | −0.518143 | ||||||||
\(633\) | 25.0736 | 0.996587 | ||||||||
\(634\) | −17.9179 | −0.711612 | ||||||||
\(635\) | −12.8014 | −0.508009 | ||||||||
\(636\) | 12.2985 | 0.487666 | ||||||||
\(637\) | −5.25586 | −0.208245 | ||||||||
\(638\) | 46.5589 | 1.84329 | ||||||||
\(639\) | −8.15323 | −0.322537 | ||||||||
\(640\) | 12.3629 | 0.488685 | ||||||||
\(641\) | −35.3955 | −1.39804 | −0.699019 | − | 0.715103i | \(-0.746380\pi\) | ||||
−0.699019 | + | 0.715103i | \(0.746380\pi\) | |||||||
\(642\) | −18.0510 | −0.712414 | ||||||||
\(643\) | 16.4750 | 0.649709 | 0.324854 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324854 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(644\) | −3.85426 | −0.151879 | ||||||||
\(645\) | 6.01700 | 0.236919 | ||||||||
\(646\) | 15.4808 | 0.609083 | ||||||||
\(647\) | 13.9775 | 0.549512 | 0.274756 | − | 0.961514i | \(-0.411403\pi\) | ||||
0.274756 | + | 0.961514i | \(0.411403\pi\) | |||||||
\(648\) | −1.05805 | −0.0415640 | ||||||||
\(649\) | 61.4788 | 2.41325 | ||||||||
\(650\) | −3.92489 | −0.153947 | ||||||||
\(651\) | 6.05653 | 0.237374 | ||||||||
\(652\) | 13.9929 | 0.548006 | ||||||||
\(653\) | −35.0114 | −1.37010 | −0.685052 | − | 0.728494i | \(-0.740220\pi\) | ||||
−0.685052 | + | 0.728494i | \(0.740220\pi\) | |||||||
\(654\) | 0.969521 | 0.0379113 | ||||||||
\(655\) | 14.2060 | 0.555076 | ||||||||
\(656\) | 35.4784 | 1.38520 | ||||||||
\(657\) | 12.0222 | 0.469030 | ||||||||
\(658\) | −7.67179 | −0.299078 | ||||||||
\(659\) | 22.7875 | 0.887674 | 0.443837 | − | 0.896107i | \(-0.353617\pi\) | ||||
0.443837 | + | 0.896107i | \(0.353617\pi\) | |||||||
\(660\) | −12.6295 | −0.491603 | ||||||||
\(661\) | 31.6182 | 1.22980 | 0.614902 | − | 0.788604i | \(-0.289196\pi\) | ||||
0.614902 | + | 0.788604i | \(0.289196\pi\) | |||||||
\(662\) | −25.6353 | −0.996345 | ||||||||
\(663\) | 0.790537 | 0.0307019 | ||||||||
\(664\) | −8.80335 | −0.341636 | ||||||||
\(665\) | −7.54803 | −0.292700 | ||||||||
\(666\) | −11.2965 | −0.437731 | ||||||||
\(667\) | −19.7080 | −0.763097 | ||||||||
\(668\) | 30.6699 | 1.18665 | ||||||||
\(669\) | 2.69549 | 0.104214 | ||||||||
\(670\) | 12.8725 | 0.497310 | ||||||||
\(671\) | 55.4890 | 2.14213 | ||||||||
\(672\) | 4.03288 | 0.155572 | ||||||||
\(673\) | −43.9719 | −1.69499 | −0.847496 | − | 0.530802i | \(-0.821891\pi\) | ||||
−0.847496 | + | 0.530802i | \(0.821891\pi\) | |||||||
\(674\) | −16.8631 | −0.649541 | ||||||||
\(675\) | 2.68131 | 0.103204 | ||||||||
\(676\) | −17.6789 | −0.679957 | ||||||||
\(677\) | 29.5774 | 1.13675 | 0.568377 | − | 0.822768i | \(-0.307572\pi\) | ||||
0.568377 | + | 0.822768i | \(0.307572\pi\) | |||||||
\(678\) | −10.9811 | −0.421726 | ||||||||
\(679\) | 9.04634 | 0.347167 | ||||||||
\(680\) | 1.61111 | 0.0617833 | ||||||||
\(681\) | 27.4607 | 1.05230 | ||||||||
\(682\) | −109.815 | −4.20503 | ||||||||
\(683\) | 16.4680 | 0.630130 | 0.315065 | − | 0.949070i | \(-0.397974\pi\) | ||||
0.315065 | + | 0.949070i | \(0.397974\pi\) | |||||||
\(684\) | −11.9438 | −0.456683 | ||||||||
\(685\) | −34.1656 | −1.30540 | ||||||||
\(686\) | −14.9837 | −0.572082 | ||||||||
\(687\) | 3.09977 | 0.118263 | ||||||||
\(688\) | 19.0315 | 0.725570 | ||||||||
\(689\) | −6.80558 | −0.259272 | ||||||||
\(690\) | 12.8302 | 0.488438 | ||||||||
\(691\) | −22.4688 | −0.854754 | −0.427377 | − | 0.904074i | \(-0.640562\pi\) | ||||
−0.427377 | + | 0.904074i | \(0.640562\pi\) | |||||||
\(692\) | −14.8120 | −0.563070 | ||||||||
\(693\) | 3.44219 | 0.130758 | ||||||||
\(694\) | −56.5124 | −2.14518 | ||||||||
\(695\) | −21.9057 | −0.830931 | ||||||||
\(696\) | 4.58240 | 0.173695 | ||||||||
\(697\) | 7.36631 | 0.279019 | ||||||||
\(698\) | −34.6898 | −1.31303 | ||||||||
\(699\) | −20.0319 | −0.757676 | ||||||||
\(700\) | −2.27109 | −0.0858390 | ||||||||
\(701\) | −10.1228 | −0.382331 | −0.191166 | − | 0.981558i | \(-0.561227\pi\) | ||||
−0.191166 | + | 0.981558i | \(0.561227\pi\) | |||||||
\(702\) | −1.46379 | −0.0552473 | ||||||||
\(703\) | 51.0061 | 1.92373 | ||||||||
\(704\) | −17.1982 | −0.648183 | ||||||||
\(705\) | 10.6410 | 0.400763 | ||||||||
\(706\) | −0.101747 | −0.00382931 | ||||||||
\(707\) | −8.26443 | −0.310816 | ||||||||
\(708\) | −15.1278 | −0.568538 | ||||||||
\(709\) | 43.0622 | 1.61723 | 0.808617 | − | 0.588336i | \(-0.200217\pi\) | ||||
0.808617 | + | 0.588336i | \(0.200217\pi\) | |||||||
\(710\) | −22.9884 | −0.862739 | ||||||||
\(711\) | 12.3113 | 0.461709 | ||||||||
\(712\) | 18.9492 | 0.710150 | ||||||||
\(713\) | 46.4837 | 1.74083 | ||||||||
\(714\) | 1.09783 | 0.0410853 | ||||||||
\(715\) | 6.98876 | 0.261365 | ||||||||
\(716\) | −26.3191 | −0.983589 | ||||||||
\(717\) | 17.0924 | 0.638327 | ||||||||
\(718\) | −2.13824 | −0.0797983 | ||||||||
\(719\) | −19.9392 | −0.743606 | −0.371803 | − | 0.928312i | \(-0.621260\pi\) | ||||
−0.371803 | + | 0.928312i | \(0.621260\pi\) | |||||||
\(720\) | −7.33391 | −0.273319 | ||||||||
\(721\) | 4.21185 | 0.156858 | ||||||||
\(722\) | 94.2465 | 3.50749 | ||||||||
\(723\) | −17.3130 | −0.643878 | ||||||||
\(724\) | 20.6965 | 0.769179 | ||||||||
\(725\) | −11.6128 | −0.431287 | ||||||||
\(726\) | −42.0445 | −1.56042 | ||||||||
\(727\) | −17.0629 | −0.632827 | −0.316413 | − | 0.948621i | \(-0.602479\pi\) | ||||
−0.316413 | + | 0.948621i | \(0.602479\pi\) | |||||||
\(728\) | −0.495912 | −0.0183797 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 33.8971 | 1.25459 | ||||||||
\(731\) | 3.95148 | 0.146151 | ||||||||
\(732\) | −13.6539 | −0.504664 | ||||||||
\(733\) | −26.2776 | −0.970585 | −0.485293 | − | 0.874352i | \(-0.661287\pi\) | ||||
−0.485293 | + | 0.874352i | \(0.661287\pi\) | |||||||
\(734\) | −17.2602 | −0.637085 | ||||||||
\(735\) | 10.1238 | 0.373422 | ||||||||
\(736\) | 30.9522 | 1.14091 | ||||||||
\(737\) | 26.5059 | 0.976358 | ||||||||
\(738\) | −13.6398 | −0.502088 | ||||||||
\(739\) | −8.07199 | −0.296933 | −0.148466 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148466 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(740\) | −13.2714 | −0.487866 | ||||||||
\(741\) | 6.60932 | 0.242800 | ||||||||
\(742\) | −9.45103 | −0.346958 | ||||||||
\(743\) | 16.8378 | 0.617719 | 0.308860 | − | 0.951108i | \(-0.400053\pi\) | ||||
0.308860 | + | 0.951108i | \(0.400053\pi\) | |||||||
\(744\) | −10.8081 | −0.396245 | ||||||||
\(745\) | −31.9330 | −1.16994 | ||||||||
\(746\) | −46.0326 | −1.68537 | ||||||||
\(747\) | 8.32039 | 0.304427 | ||||||||
\(748\) | −8.29402 | −0.303260 | ||||||||
\(749\) | 5.77990 | 0.211193 | ||||||||
\(750\) | 21.6578 | 0.790831 | ||||||||
\(751\) | 13.6448 | 0.497907 | 0.248954 | − | 0.968515i | \(-0.419913\pi\) | ||||
0.248954 | + | 0.968515i | \(0.419913\pi\) | |||||||
\(752\) | 33.6570 | 1.22734 | ||||||||
\(753\) | −18.0587 | −0.658094 | ||||||||
\(754\) | 6.33969 | 0.230878 | ||||||||
\(755\) | 2.67166 | 0.0972316 | ||||||||
\(756\) | −0.847005 | −0.0308053 | ||||||||
\(757\) | 20.8405 | 0.757460 | 0.378730 | − | 0.925507i | \(-0.376361\pi\) | ||||
0.378730 | + | 0.925507i | \(0.376361\pi\) | |||||||
\(758\) | −28.2501 | −1.02609 | ||||||||
\(759\) | 26.4187 | 0.958940 | ||||||||
\(760\) | 13.4698 | 0.488600 | ||||||||
\(761\) | 13.2014 | 0.478552 | 0.239276 | − | 0.970952i | \(-0.423090\pi\) | ||||
0.239276 | + | 0.970952i | \(0.423090\pi\) | |||||||
\(762\) | 15.5666 | 0.563920 | ||||||||
\(763\) | −0.310440 | −0.0112387 | ||||||||
\(764\) | 17.6411 | 0.638234 | ||||||||
\(765\) | −1.52272 | −0.0550542 | ||||||||
\(766\) | 69.7222 | 2.51917 | ||||||||
\(767\) | 8.37124 | 0.302268 | ||||||||
\(768\) | −20.9579 | −0.756254 | ||||||||
\(769\) | 12.2469 | 0.441634 | 0.220817 | − | 0.975315i | \(-0.429128\pi\) | ||||
0.220817 | + | 0.975315i | \(0.429128\pi\) | |||||||
\(770\) | 9.70542 | 0.349759 | ||||||||
\(771\) | 1.98632 | 0.0715357 | ||||||||
\(772\) | −24.0423 | −0.865301 | ||||||||
\(773\) | −28.8898 | −1.03909 | −0.519546 | − | 0.854442i | \(-0.673899\pi\) | ||||
−0.519546 | + | 0.854442i | \(0.673899\pi\) | |||||||
\(774\) | −7.31673 | −0.262994 | ||||||||
\(775\) | 27.3901 | 0.983881 | ||||||||
\(776\) | −16.1436 | −0.579520 | ||||||||
\(777\) | 3.61714 | 0.129764 | ||||||||
\(778\) | 3.86077 | 0.138415 | ||||||||
\(779\) | 61.5864 | 2.20656 | ||||||||
\(780\) | −1.71969 | −0.0615749 | ||||||||
\(781\) | −47.3355 | −1.69380 | ||||||||
\(782\) | 8.42583 | 0.301307 | ||||||||
\(783\) | −4.33100 | −0.154777 | ||||||||
\(784\) | 32.0211 | 1.14361 | ||||||||
\(785\) | −1.52272 | −0.0543483 | ||||||||
\(786\) | −17.2747 | −0.616168 | ||||||||
\(787\) | −5.82375 | −0.207594 | −0.103797 | − | 0.994598i | \(-0.533099\pi\) | ||||
−0.103797 | + | 0.994598i | \(0.533099\pi\) | |||||||
\(788\) | 11.2225 | 0.399786 | ||||||||
\(789\) | −1.85794 | −0.0661444 | ||||||||
\(790\) | 34.7122 | 1.23500 | ||||||||
\(791\) | 3.51613 | 0.125019 | ||||||||
\(792\) | −6.14274 | −0.218273 | ||||||||
\(793\) | 7.55566 | 0.268309 | ||||||||
\(794\) | −35.8547 | −1.27244 | ||||||||
\(795\) | 13.1088 | 0.464923 | ||||||||
\(796\) | −4.75731 | −0.168618 | ||||||||
\(797\) | 27.3577 | 0.969059 | 0.484529 | − | 0.874775i | \(-0.338991\pi\) | ||||
0.484529 | + | 0.874775i | \(0.338991\pi\) | |||||||
\(798\) | 9.17848 | 0.324915 | ||||||||
\(799\) | 6.98813 | 0.247222 | ||||||||
\(800\) | 18.2383 | 0.644822 | ||||||||
\(801\) | −17.9096 | −0.632804 | ||||||||
\(802\) | 67.1304 | 2.37046 | ||||||||
\(803\) | 69.7977 | 2.46311 | ||||||||
\(804\) | −6.52219 | −0.230020 | ||||||||
\(805\) | −4.10822 | −0.144796 | ||||||||
\(806\) | −14.9529 | −0.526694 | ||||||||
\(807\) | −16.4997 | −0.580816 | ||||||||
\(808\) | 14.7482 | 0.518840 | ||||||||
\(809\) | −48.4762 | −1.70433 | −0.852166 | − | 0.523272i | \(-0.824711\pi\) | ||||
−0.852166 | + | 0.523272i | \(0.824711\pi\) | |||||||
\(810\) | 2.81954 | 0.0990687 | ||||||||
\(811\) | 1.62819 | 0.0571735 | 0.0285868 | − | 0.999591i | \(-0.490899\pi\) | ||||
0.0285868 | + | 0.999591i | \(0.490899\pi\) | |||||||
\(812\) | 3.66838 | 0.128735 | ||||||||
\(813\) | −17.2735 | −0.605808 | ||||||||
\(814\) | −65.5846 | −2.29874 | ||||||||
\(815\) | 14.9150 | 0.522448 | ||||||||
\(816\) | −4.81631 | −0.168605 | ||||||||
\(817\) | 33.0365 | 1.15580 | ||||||||
\(818\) | 48.1883 | 1.68486 | ||||||||
\(819\) | 0.468706 | 0.0163779 | ||||||||
\(820\) | −16.0243 | −0.559593 | ||||||||
\(821\) | 2.22097 | 0.0775124 | 0.0387562 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387562 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(822\) | 41.5457 | 1.44907 | ||||||||
\(823\) | −48.9827 | −1.70743 | −0.853714 | − | 0.520742i | \(-0.825655\pi\) | ||||
−0.853714 | + | 0.520742i | \(0.825655\pi\) | |||||||
\(824\) | −7.51623 | −0.261840 | ||||||||
\(825\) | 15.5670 | 0.541973 | ||||||||
\(826\) | 11.6253 | 0.404496 | ||||||||
\(827\) | 2.95069 | 0.102606 | 0.0513028 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513028 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(828\) | −6.50074 | −0.225916 | ||||||||
\(829\) | 35.7698 | 1.24234 | 0.621168 | − | 0.783678i | \(-0.286659\pi\) | ||||
0.621168 | + | 0.783678i | \(0.286659\pi\) | |||||||
\(830\) | 23.4597 | 0.814298 | ||||||||
\(831\) | −19.5227 | −0.677234 | ||||||||
\(832\) | −2.34179 | −0.0811871 | ||||||||
\(833\) | 6.64847 | 0.230356 | ||||||||
\(834\) | 26.6376 | 0.922383 | ||||||||
\(835\) | 32.6908 | 1.13131 | ||||||||
\(836\) | −69.3426 | −2.39826 | ||||||||
\(837\) | 10.2152 | 0.353088 | ||||||||
\(838\) | 16.5662 | 0.572270 | ||||||||
\(839\) | −8.24737 | −0.284731 | −0.142365 | − | 0.989814i | \(-0.545471\pi\) | ||||
−0.142365 | + | 0.989814i | \(0.545471\pi\) | |||||||
\(840\) | 0.955221 | 0.0329583 | ||||||||
\(841\) | −10.2425 | −0.353189 | ||||||||
\(842\) | −35.8849 | −1.23667 | ||||||||
\(843\) | 6.83926 | 0.235557 | ||||||||
\(844\) | −35.8200 | −1.23297 | ||||||||
\(845\) | −18.8438 | −0.648246 | ||||||||
\(846\) | −12.9395 | −0.444870 | ||||||||
\(847\) | 13.4626 | 0.462581 | ||||||||
\(848\) | 41.4627 | 1.42384 | ||||||||
\(849\) | −1.47130 | −0.0504950 | ||||||||
\(850\) | 4.96484 | 0.170293 | ||||||||
\(851\) | 27.7614 | 0.951650 | ||||||||
\(852\) | 11.6476 | 0.399042 | ||||||||
\(853\) | 4.11677 | 0.140956 | 0.0704778 | − | 0.997513i | \(-0.477548\pi\) | ||||
0.0704778 | + | 0.997513i | \(0.477548\pi\) | |||||||
\(854\) | 10.4927 | 0.359052 | ||||||||
\(855\) | −12.7308 | −0.435384 | ||||||||
\(856\) | −10.3145 | −0.352541 | ||||||||
\(857\) | 14.8778 | 0.508216 | 0.254108 | − | 0.967176i | \(-0.418218\pi\) | ||||
0.254108 | + | 0.967176i | \(0.418218\pi\) | |||||||
\(858\) | −8.49840 | −0.290131 | ||||||||
\(859\) | −14.5402 | −0.496104 | −0.248052 | − | 0.968747i | \(-0.579790\pi\) | ||||
−0.248052 | + | 0.968747i | \(0.579790\pi\) | |||||||
\(860\) | −8.59584 | −0.293116 | ||||||||
\(861\) | 4.36745 | 0.148842 | ||||||||
\(862\) | 45.3949 | 1.54616 | ||||||||
\(863\) | −13.3109 | −0.453109 | −0.226554 | − | 0.973999i | \(-0.572746\pi\) | ||||
−0.226554 | + | 0.973999i | \(0.572746\pi\) | |||||||
\(864\) | 6.80201 | 0.231409 | ||||||||
\(865\) | −15.7880 | −0.536809 | ||||||||
\(866\) | 12.1221 | 0.411927 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −8.65231 | −0.293679 | ||||||||
\(869\) | 71.4760 | 2.42466 | ||||||||
\(870\) | −12.2114 | −0.414006 | ||||||||
\(871\) | 3.60917 | 0.122292 | ||||||||
\(872\) | 0.553992 | 0.0187606 | ||||||||
\(873\) | 15.2579 | 0.516402 | ||||||||
\(874\) | 70.4446 | 2.38282 | ||||||||
\(875\) | −6.93481 | −0.234439 | ||||||||
\(876\) | −17.1748 | −0.580283 | ||||||||
\(877\) | −45.5288 | −1.53740 | −0.768699 | − | 0.639611i | \(-0.779096\pi\) | ||||
−0.768699 | + | 0.639611i | \(0.779096\pi\) | |||||||
\(878\) | 41.5820 | 1.40332 | ||||||||
\(879\) | 15.0191 | 0.506580 | ||||||||
\(880\) | −42.5787 | −1.43533 | ||||||||
\(881\) | −23.8946 | −0.805030 | −0.402515 | − | 0.915413i | \(-0.631864\pi\) | ||||
−0.402515 | + | 0.915413i | \(0.631864\pi\) | |||||||
\(882\) | −12.3106 | −0.414520 | ||||||||
\(883\) | 36.5644 | 1.23049 | 0.615245 | − | 0.788336i | \(-0.289057\pi\) | ||||
0.615245 | + | 0.788336i | \(0.289057\pi\) | |||||||
\(884\) | −1.12935 | −0.0379843 | ||||||||
\(885\) | −16.1246 | −0.542022 | ||||||||
\(886\) | 53.4945 | 1.79718 | ||||||||
\(887\) | −56.5770 | −1.89967 | −0.949834 | − | 0.312753i | \(-0.898749\pi\) | ||||
−0.949834 | + | 0.312753i | \(0.898749\pi\) | |||||||
\(888\) | −6.45493 | −0.216613 | ||||||||
\(889\) | −4.98443 | −0.167172 | ||||||||
\(890\) | −50.4968 | −1.69266 | ||||||||
\(891\) | 5.80574 | 0.194499 | ||||||||
\(892\) | −3.85075 | −0.128933 | ||||||||
\(893\) | 58.4246 | 1.95510 | ||||||||
\(894\) | 38.8308 | 1.29870 | ||||||||
\(895\) | −28.0533 | −0.937717 | ||||||||
\(896\) | 4.81367 | 0.160813 | ||||||||
\(897\) | 3.59730 | 0.120110 | ||||||||
\(898\) | −29.0497 | −0.969401 | ||||||||
\(899\) | −44.2419 | −1.47555 | ||||||||
\(900\) | −3.83050 | −0.127683 | ||||||||
\(901\) | 8.60881 | 0.286801 | ||||||||
\(902\) | −79.1891 | −2.63671 | ||||||||
\(903\) | 2.34281 | 0.0779639 | ||||||||
\(904\) | −6.27468 | −0.208693 | ||||||||
\(905\) | 22.0602 | 0.733306 | ||||||||
\(906\) | −3.24876 | −0.107933 | ||||||||
\(907\) | −21.7146 | −0.721023 | −0.360511 | − | 0.932755i | \(-0.617398\pi\) | ||||
−0.360511 | + | 0.932755i | \(0.617398\pi\) | |||||||
\(908\) | −39.2301 | −1.30190 | ||||||||
\(909\) | −13.9391 | −0.462331 | ||||||||
\(910\) | 1.32154 | 0.0438085 | ||||||||
\(911\) | −1.17482 | −0.0389237 | −0.0194618 | − | 0.999811i | \(-0.506195\pi\) | ||||
−0.0194618 | + | 0.999811i | \(0.506195\pi\) | |||||||
\(912\) | −40.2670 | −1.33337 | ||||||||
\(913\) | 48.3060 | 1.59869 | ||||||||
\(914\) | 9.24560 | 0.305817 | ||||||||
\(915\) | −14.5536 | −0.481128 | ||||||||
\(916\) | −4.42830 | −0.146315 | ||||||||
\(917\) | 5.53134 | 0.182661 | ||||||||
\(918\) | 1.85165 | 0.0611134 | ||||||||
\(919\) | 43.5319 | 1.43599 | 0.717993 | − | 0.696050i | \(-0.245061\pi\) | ||||
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(920\) | 7.33130 | 0.241706 | ||||||||
\(921\) | −24.0001 | −0.790829 | ||||||||
\(922\) | 18.0809 | 0.595462 | ||||||||
\(923\) | −6.44543 | −0.212154 | ||||||||
\(924\) | −4.91749 | −0.161773 | ||||||||
\(925\) | 16.3582 | 0.537853 | ||||||||
\(926\) | −11.7467 | −0.386021 | ||||||||
\(927\) | 7.10387 | 0.233322 | ||||||||
\(928\) | −29.4595 | −0.967054 | ||||||||
\(929\) | −31.0750 | −1.01954 | −0.509769 | − | 0.860311i | \(-0.670269\pi\) | ||||
−0.509769 | + | 0.860311i | \(0.670269\pi\) | |||||||
\(930\) | 28.8021 | 0.944460 | ||||||||
\(931\) | 55.5849 | 1.82172 | ||||||||
\(932\) | 28.6174 | 0.937394 | ||||||||
\(933\) | −29.6667 | −0.971245 | ||||||||
\(934\) | −33.4449 | −1.09435 | ||||||||
\(935\) | −8.84053 | −0.289116 | ||||||||
\(936\) | −0.836425 | −0.0273394 | ||||||||
\(937\) | −31.2913 | −1.02224 | −0.511121 | − | 0.859509i | \(-0.670770\pi\) | ||||
−0.511121 | + | 0.859509i | \(0.670770\pi\) | |||||||
\(938\) | 5.01212 | 0.163652 | ||||||||
\(939\) | −5.39192 | −0.175959 | ||||||||
\(940\) | −15.2016 | −0.495822 | ||||||||
\(941\) | −12.3214 | −0.401665 | −0.200832 | − | 0.979626i | \(-0.564365\pi\) | ||||
−0.200832 | + | 0.979626i | \(0.564365\pi\) | |||||||
\(942\) | 1.85165 | 0.0603299 | ||||||||
\(943\) | 33.5201 | 1.09156 | ||||||||
\(944\) | −51.0014 | −1.65995 | ||||||||
\(945\) | −0.902816 | −0.0293686 | ||||||||
\(946\) | −42.4790 | −1.38111 | ||||||||
\(947\) | −23.6727 | −0.769259 | −0.384630 | − | 0.923071i | \(-0.625671\pi\) | ||||
−0.384630 | + | 0.923071i | \(0.625671\pi\) | |||||||
\(948\) | −17.5878 | −0.571225 | ||||||||
\(949\) | 9.50399 | 0.308512 | ||||||||
\(950\) | 41.5088 | 1.34672 | ||||||||
\(951\) | 9.67677 | 0.313791 | ||||||||
\(952\) | 0.627311 | 0.0203313 | ||||||||
\(953\) | −46.1271 | −1.49420 | −0.747101 | − | 0.664710i | \(-0.768555\pi\) | ||||
−0.747101 | + | 0.664710i | \(0.768555\pi\) | |||||||
\(954\) | −15.9405 | −0.516092 | ||||||||
\(955\) | 18.8035 | 0.608468 | ||||||||
\(956\) | −24.4181 | −0.789736 | ||||||||
\(957\) | −25.1446 | −0.812810 | ||||||||
\(958\) | −38.2313 | −1.23520 | ||||||||
\(959\) | −13.3029 | −0.429573 | ||||||||
\(960\) | 4.51074 | 0.145583 | ||||||||
\(961\) | 73.3499 | 2.36613 | ||||||||
\(962\) | −8.93032 | −0.287925 | ||||||||
\(963\) | 9.74860 | 0.314144 | ||||||||
\(964\) | 24.7332 | 0.796604 | ||||||||
\(965\) | −25.6265 | −0.824945 | ||||||||
\(966\) | 4.99564 | 0.160732 | ||||||||
\(967\) | −12.6008 | −0.405213 | −0.202607 | − | 0.979260i | \(-0.564941\pi\) | ||||
−0.202607 | + | 0.979260i | \(0.564941\pi\) | |||||||
\(968\) | −24.0246 | −0.772180 | ||||||||
\(969\) | −8.36055 | −0.268580 | ||||||||
\(970\) | 43.0203 | 1.38130 | ||||||||
\(971\) | −4.23955 | −0.136054 | −0.0680268 | − | 0.997683i | \(-0.521670\pi\) | ||||
−0.0680268 | + | 0.997683i | \(0.521670\pi\) | |||||||
\(972\) | −1.42859 | −0.0458221 | ||||||||
\(973\) | −8.52932 | −0.273438 | ||||||||
\(974\) | −33.8894 | −1.08589 | ||||||||
\(975\) | 2.11968 | 0.0678840 | ||||||||
\(976\) | −46.0325 | −1.47346 | ||||||||
\(977\) | −16.2196 | −0.518911 | −0.259455 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259455 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(978\) | −18.1367 | −0.579949 | ||||||||
\(979\) | −103.978 | −3.32316 | ||||||||
\(980\) | −14.4628 | −0.461996 | ||||||||
\(981\) | −0.523599 | −0.0167172 | ||||||||
\(982\) | −4.97353 | −0.158712 | ||||||||
\(983\) | −3.05502 | −0.0974399 | −0.0487199 | − | 0.998812i | \(-0.515514\pi\) | ||||
−0.0487199 | + | 0.998812i | \(0.515514\pi\) | |||||||
\(984\) | −7.79390 | −0.248460 | ||||||||
\(985\) | 11.9620 | 0.381141 | ||||||||
\(986\) | −8.01947 | −0.255392 | ||||||||
\(987\) | 4.14323 | 0.131880 | ||||||||
\(988\) | −9.44202 | −0.300391 | ||||||||
\(989\) | 17.9810 | 0.571763 | ||||||||
\(990\) | 16.3695 | 0.520258 | ||||||||
\(991\) | 45.4318 | 1.44319 | 0.721594 | − | 0.692316i | \(-0.243410\pi\) | ||||
0.721594 | + | 0.692316i | \(0.243410\pi\) | |||||||
\(992\) | 69.4837 | 2.20611 | ||||||||
\(993\) | 13.8446 | 0.439346 | ||||||||
\(994\) | −8.95088 | −0.283905 | ||||||||
\(995\) | −5.07078 | −0.160754 | ||||||||
\(996\) | −11.8864 | −0.376636 | ||||||||
\(997\) | −12.1999 | −0.386375 | −0.193188 | − | 0.981162i | \(-0.561883\pi\) | ||||
−0.193188 | + | 0.981162i | \(0.561883\pi\) | |||||||
\(998\) | −51.9140 | −1.64331 | ||||||||
\(999\) | 6.10080 | 0.193021 |
(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 | 8007.2.a.f.1.40 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.40 | ✓ | 48 | 1.1 | even | 1 | trivial |