Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28891 | −0.911397 | −0.455698 | − | 0.890134i | \(-0.650610\pi\) | ||||
−0.455698 | + | 0.890134i | \(0.650610\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.338712 | −0.169356 | ||||||||
\(5\) | 0.716613 | 0.320479 | 0.160240 | − | 0.987078i | \(-0.448773\pi\) | ||||
0.160240 | + | 0.987078i | \(0.448773\pi\) | |||||||
\(6\) | −1.28891 | −0.526195 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.01439 | 1.06575 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.923650 | −0.292084 | ||||||||
\(11\) | 5.42521 | 1.63576 | 0.817882 | − | 0.575386i | \(-0.195148\pi\) | ||||
0.817882 | + | 0.575386i | \(0.195148\pi\) | |||||||
\(12\) | −0.338712 | −0.0977778 | ||||||||
\(13\) | 3.53458 | 0.980315 | 0.490157 | − | 0.871634i | \(-0.336939\pi\) | ||||
0.490157 | + | 0.871634i | \(0.336939\pi\) | |||||||
\(14\) | −1.28891 | −0.344476 | ||||||||
\(15\) | 0.716613 | 0.185029 | ||||||||
\(16\) | −3.20785 | −0.801962 | ||||||||
\(17\) | 3.87656 | 0.940204 | 0.470102 | − | 0.882612i | \(-0.344217\pi\) | ||||
0.470102 | + | 0.882612i | \(0.344217\pi\) | |||||||
\(18\) | −1.28891 | −0.303799 | ||||||||
\(19\) | 5.75190 | 1.31958 | 0.659788 | − | 0.751452i | \(-0.270646\pi\) | ||||
0.659788 | + | 0.751452i | \(0.270646\pi\) | |||||||
\(20\) | −0.242726 | −0.0542751 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −6.99261 | −1.49083 | ||||||||
\(23\) | −3.07639 | −0.641473 | −0.320736 | − | 0.947169i | \(-0.603930\pi\) | ||||
−0.320736 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(24\) | 3.01439 | 0.615309 | ||||||||
\(25\) | −4.48647 | −0.897293 | ||||||||
\(26\) | −4.55575 | −0.893456 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.338712 | −0.0640106 | ||||||||
\(29\) | 1.93227 | 0.358814 | 0.179407 | − | 0.983775i | \(-0.442582\pi\) | ||||
0.179407 | + | 0.983775i | \(0.442582\pi\) | |||||||
\(30\) | −0.923650 | −0.168635 | ||||||||
\(31\) | 10.3463 | 1.85824 | 0.929122 | − | 0.369774i | \(-0.120565\pi\) | ||||
0.929122 | + | 0.369774i | \(0.120565\pi\) | |||||||
\(32\) | −1.89415 | −0.334841 | ||||||||
\(33\) | 5.42521 | 0.944409 | ||||||||
\(34\) | −4.99654 | −0.856899 | ||||||||
\(35\) | 0.716613 | 0.121130 | ||||||||
\(36\) | −0.338712 | −0.0564520 | ||||||||
\(37\) | 3.10093 | 0.509790 | 0.254895 | − | 0.966969i | \(-0.417959\pi\) | ||||
0.254895 | + | 0.966969i | \(0.417959\pi\) | |||||||
\(38\) | −7.41367 | −1.20266 | ||||||||
\(39\) | 3.53458 | 0.565985 | ||||||||
\(40\) | 2.16015 | 0.341550 | ||||||||
\(41\) | 0.243689 | 0.0380578 | 0.0190289 | − | 0.999819i | \(-0.493943\pi\) | ||||
0.0190289 | + | 0.999819i | \(0.493943\pi\) | |||||||
\(42\) | −1.28891 | −0.198883 | ||||||||
\(43\) | 8.67240 | 1.32253 | 0.661264 | − | 0.750153i | \(-0.270020\pi\) | ||||
0.661264 | + | 0.750153i | \(0.270020\pi\) | |||||||
\(44\) | −1.83759 | −0.277027 | ||||||||
\(45\) | 0.716613 | 0.106826 | ||||||||
\(46\) | 3.96519 | 0.584636 | ||||||||
\(47\) | 5.34819 | 0.780113 | 0.390056 | − | 0.920791i | \(-0.372455\pi\) | ||||
0.390056 | + | 0.920791i | \(0.372455\pi\) | |||||||
\(48\) | −3.20785 | −0.463013 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.78265 | 0.817790 | ||||||||
\(51\) | 3.87656 | 0.542827 | ||||||||
\(52\) | −1.19720 | −0.166022 | ||||||||
\(53\) | −2.95325 | −0.405661 | −0.202830 | − | 0.979214i | \(-0.565014\pi\) | ||||
−0.202830 | + | 0.979214i | \(0.565014\pi\) | |||||||
\(54\) | −1.28891 | −0.175398 | ||||||||
\(55\) | 3.88778 | 0.524228 | ||||||||
\(56\) | 3.01439 | 0.402815 | ||||||||
\(57\) | 5.75190 | 0.761857 | ||||||||
\(58\) | −2.49052 | −0.327022 | ||||||||
\(59\) | −6.43358 | −0.837581 | −0.418790 | − | 0.908083i | \(-0.637546\pi\) | ||||
−0.418790 | + | 0.908083i | \(0.637546\pi\) | |||||||
\(60\) | −0.242726 | −0.0313358 | ||||||||
\(61\) | −9.78399 | −1.25271 | −0.626356 | − | 0.779537i | \(-0.715454\pi\) | ||||
−0.626356 | + | 0.779537i | \(0.715454\pi\) | |||||||
\(62\) | −13.3354 | −1.69360 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.85709 | 1.10714 | ||||||||
\(65\) | 2.53292 | 0.314171 | ||||||||
\(66\) | −6.99261 | −0.860731 | ||||||||
\(67\) | 0.0125252 | 0.00153020 | 0.000765098 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000765098 | 1.00000i | \(0.499756\pi\) | ||||||||
\(68\) | −1.31304 | −0.159229 | ||||||||
\(69\) | −3.07639 | −0.370354 | ||||||||
\(70\) | −0.923650 | −0.110397 | ||||||||
\(71\) | −1.56317 | −0.185514 | −0.0927569 | − | 0.995689i | \(-0.529568\pi\) | ||||
−0.0927569 | + | 0.995689i | \(0.529568\pi\) | |||||||
\(72\) | 3.01439 | 0.355249 | ||||||||
\(73\) | −15.4518 | −1.80849 | −0.904245 | − | 0.427013i | \(-0.859566\pi\) | ||||
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(74\) | −3.99682 | −0.464621 | ||||||||
\(75\) | −4.48647 | −0.518052 | ||||||||
\(76\) | −1.94824 | −0.223478 | ||||||||
\(77\) | 5.42521 | 0.618261 | ||||||||
\(78\) | −4.55575 | −0.515837 | ||||||||
\(79\) | −5.55105 | −0.624542 | −0.312271 | − | 0.949993i | \(-0.601090\pi\) | ||||
−0.312271 | + | 0.949993i | \(0.601090\pi\) | |||||||
\(80\) | −2.29879 | −0.257012 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.314093 | −0.0346858 | ||||||||
\(83\) | 12.6372 | 1.38712 | 0.693559 | − | 0.720400i | \(-0.256042\pi\) | ||||
0.693559 | + | 0.720400i | \(0.256042\pi\) | |||||||
\(84\) | −0.338712 | −0.0369565 | ||||||||
\(85\) | 2.77800 | 0.301316 | ||||||||
\(86\) | −11.1779 | −1.20535 | ||||||||
\(87\) | 1.93227 | 0.207161 | ||||||||
\(88\) | 16.3537 | 1.74331 | ||||||||
\(89\) | −10.2353 | −1.08494 | −0.542472 | − | 0.840074i | \(-0.682512\pi\) | ||||
−0.542472 | + | 0.840074i | \(0.682512\pi\) | |||||||
\(90\) | −0.923650 | −0.0973612 | ||||||||
\(91\) | 3.53458 | 0.370524 | ||||||||
\(92\) | 1.04201 | 0.108637 | ||||||||
\(93\) | 10.3463 | 1.07286 | ||||||||
\(94\) | −6.89333 | −0.710992 | ||||||||
\(95\) | 4.12189 | 0.422897 | ||||||||
\(96\) | −1.89415 | −0.193321 | ||||||||
\(97\) | −18.5407 | −1.88252 | −0.941260 | − | 0.337684i | \(-0.890357\pi\) | ||||
−0.941260 | + | 0.337684i | \(0.890357\pi\) | |||||||
\(98\) | −1.28891 | −0.130200 | ||||||||
\(99\) | 5.42521 | 0.545255 | ||||||||
\(100\) | 1.51962 | 0.151962 | ||||||||
\(101\) | −5.99911 | −0.596934 | −0.298467 | − | 0.954420i | \(-0.596475\pi\) | ||||
−0.298467 | + | 0.954420i | \(0.596475\pi\) | |||||||
\(102\) | −4.99654 | −0.494731 | ||||||||
\(103\) | −14.0429 | −1.38368 | −0.691842 | − | 0.722049i | \(-0.743201\pi\) | ||||
−0.691842 | + | 0.722049i | \(0.743201\pi\) | |||||||
\(104\) | 10.6546 | 1.04477 | ||||||||
\(105\) | 0.716613 | 0.0699343 | ||||||||
\(106\) | 3.80648 | 0.369718 | ||||||||
\(107\) | −20.0752 | −1.94074 | −0.970370 | − | 0.241623i | \(-0.922320\pi\) | ||||
−0.970370 | + | 0.241623i | \(0.922320\pi\) | |||||||
\(108\) | −0.338712 | −0.0325926 | ||||||||
\(109\) | −5.64824 | −0.541003 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(110\) | −5.01100 | −0.477780 | ||||||||
\(111\) | 3.10093 | 0.294327 | ||||||||
\(112\) | −3.20785 | −0.303113 | ||||||||
\(113\) | 2.71733 | 0.255625 | 0.127812 | − | 0.991798i | \(-0.459204\pi\) | ||||
0.127812 | + | 0.991798i | \(0.459204\pi\) | |||||||
\(114\) | −7.41367 | −0.694354 | ||||||||
\(115\) | −2.20459 | −0.205579 | ||||||||
\(116\) | −0.654484 | −0.0607673 | ||||||||
\(117\) | 3.53458 | 0.326772 | ||||||||
\(118\) | 8.29230 | 0.763368 | ||||||||
\(119\) | 3.87656 | 0.355364 | ||||||||
\(120\) | 2.16015 | 0.197194 | ||||||||
\(121\) | 18.4330 | 1.67572 | ||||||||
\(122\) | 12.6107 | 1.14172 | ||||||||
\(123\) | 0.243689 | 0.0219727 | ||||||||
\(124\) | −3.50441 | −0.314705 | ||||||||
\(125\) | −6.79813 | −0.608043 | ||||||||
\(126\) | −1.28891 | −0.114825 | ||||||||
\(127\) | 0.0339105 | 0.00300907 | 0.00150453 | − | 0.999999i | \(-0.499521\pi\) | ||||
0.00150453 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(128\) | −7.62768 | −0.674198 | ||||||||
\(129\) | 8.67240 | 0.763562 | ||||||||
\(130\) | −3.26471 | −0.286334 | ||||||||
\(131\) | 10.3981 | 0.908486 | 0.454243 | − | 0.890878i | \(-0.349910\pi\) | ||||
0.454243 | + | 0.890878i | \(0.349910\pi\) | |||||||
\(132\) | −1.83759 | −0.159941 | ||||||||
\(133\) | 5.75190 | 0.498753 | ||||||||
\(134\) | −0.0161439 | −0.00139462 | ||||||||
\(135\) | 0.716613 | 0.0616763 | ||||||||
\(136\) | 11.6855 | 1.00202 | ||||||||
\(137\) | 3.92674 | 0.335484 | 0.167742 | − | 0.985831i | \(-0.446352\pi\) | ||||
0.167742 | + | 0.985831i | \(0.446352\pi\) | |||||||
\(138\) | 3.96519 | 0.337540 | ||||||||
\(139\) | −14.8936 | −1.26326 | −0.631629 | − | 0.775271i | \(-0.717613\pi\) | ||||
−0.631629 | + | 0.775271i | \(0.717613\pi\) | |||||||
\(140\) | −0.242726 | −0.0205141 | ||||||||
\(141\) | 5.34819 | 0.450398 | ||||||||
\(142\) | 2.01478 | 0.169077 | ||||||||
\(143\) | 19.1758 | 1.60356 | ||||||||
\(144\) | −3.20785 | −0.267321 | ||||||||
\(145\) | 1.38469 | 0.114992 | ||||||||
\(146\) | 19.9159 | 1.64825 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −1.05032 | −0.0863360 | ||||||||
\(149\) | 19.9744 | 1.63637 | 0.818184 | − | 0.574957i | \(-0.194981\pi\) | ||||
0.818184 | + | 0.574957i | \(0.194981\pi\) | |||||||
\(150\) | 5.78265 | 0.472151 | ||||||||
\(151\) | 7.80032 | 0.634781 | 0.317391 | − | 0.948295i | \(-0.397193\pi\) | ||||
0.317391 | + | 0.948295i | \(0.397193\pi\) | |||||||
\(152\) | 17.3384 | 1.40633 | ||||||||
\(153\) | 3.87656 | 0.313401 | ||||||||
\(154\) | −6.99261 | −0.563481 | ||||||||
\(155\) | 7.41427 | 0.595528 | ||||||||
\(156\) | −1.19720 | −0.0958530 | ||||||||
\(157\) | −13.1463 | −1.04919 | −0.524595 | − | 0.851352i | \(-0.675783\pi\) | ||||
−0.524595 | + | 0.851352i | \(0.675783\pi\) | |||||||
\(158\) | 7.15481 | 0.569206 | ||||||||
\(159\) | −2.95325 | −0.234208 | ||||||||
\(160\) | −1.35737 | −0.107310 | ||||||||
\(161\) | −3.07639 | −0.242454 | ||||||||
\(162\) | −1.28891 | −0.101266 | ||||||||
\(163\) | −15.5010 | −1.21414 | −0.607068 | − | 0.794650i | \(-0.707654\pi\) | ||||
−0.607068 | + | 0.794650i | \(0.707654\pi\) | |||||||
\(164\) | −0.0825405 | −0.00644533 | ||||||||
\(165\) | 3.88778 | 0.302663 | ||||||||
\(166\) | −16.2883 | −1.26421 | ||||||||
\(167\) | 6.08456 | 0.470838 | 0.235419 | − | 0.971894i | \(-0.424354\pi\) | ||||
0.235419 | + | 0.971894i | \(0.424354\pi\) | |||||||
\(168\) | 3.01439 | 0.232565 | ||||||||
\(169\) | −0.506775 | −0.0389827 | ||||||||
\(170\) | −3.58058 | −0.274618 | ||||||||
\(171\) | 5.75190 | 0.439858 | ||||||||
\(172\) | −2.93745 | −0.223978 | ||||||||
\(173\) | −9.91974 | −0.754184 | −0.377092 | − | 0.926176i | \(-0.623076\pi\) | ||||
−0.377092 | + | 0.926176i | \(0.623076\pi\) | |||||||
\(174\) | −2.49052 | −0.188806 | ||||||||
\(175\) | −4.48647 | −0.339145 | ||||||||
\(176\) | −17.4033 | −1.31182 | ||||||||
\(177\) | −6.43358 | −0.483578 | ||||||||
\(178\) | 13.1924 | 0.988814 | ||||||||
\(179\) | 4.88013 | 0.364758 | 0.182379 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182379 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(180\) | −0.242726 | −0.0180917 | ||||||||
\(181\) | −3.43394 | −0.255243 | −0.127621 | − | 0.991823i | \(-0.540734\pi\) | ||||
−0.127621 | + | 0.991823i | \(0.540734\pi\) | |||||||
\(182\) | −4.55575 | −0.337695 | ||||||||
\(183\) | −9.78399 | −0.723254 | ||||||||
\(184\) | −9.27345 | −0.683648 | ||||||||
\(185\) | 2.22217 | 0.163377 | ||||||||
\(186\) | −13.3354 | −0.977799 | ||||||||
\(187\) | 21.0312 | 1.53795 | ||||||||
\(188\) | −1.81150 | −0.132117 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −5.31274 | −0.385426 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | 8.85709 | 0.639205 | ||||||||
\(193\) | −9.55231 | −0.687590 | −0.343795 | − | 0.939045i | \(-0.611713\pi\) | ||||
−0.343795 | + | 0.939045i | \(0.611713\pi\) | |||||||
\(194\) | 23.8972 | 1.71572 | ||||||||
\(195\) | 2.53292 | 0.181386 | ||||||||
\(196\) | −0.338712 | −0.0241937 | ||||||||
\(197\) | 11.2246 | 0.799722 | 0.399861 | − | 0.916576i | \(-0.369058\pi\) | ||||
0.399861 | + | 0.916576i | \(0.369058\pi\) | |||||||
\(198\) | −6.99261 | −0.496943 | ||||||||
\(199\) | 17.0021 | 1.20525 | 0.602624 | − | 0.798025i | \(-0.294122\pi\) | ||||
0.602624 | + | 0.798025i | \(0.294122\pi\) | |||||||
\(200\) | −13.5239 | −0.956288 | ||||||||
\(201\) | 0.0125252 | 0.000883460 0 | ||||||||
\(202\) | 7.73231 | 0.544044 | ||||||||
\(203\) | 1.93227 | 0.135619 | ||||||||
\(204\) | −1.31304 | −0.0919311 | ||||||||
\(205\) | 0.174631 | 0.0121967 | ||||||||
\(206\) | 18.1000 | 1.26108 | ||||||||
\(207\) | −3.07639 | −0.213824 | ||||||||
\(208\) | −11.3384 | −0.786176 | ||||||||
\(209\) | 31.2053 | 2.15851 | ||||||||
\(210\) | −0.923650 | −0.0637379 | ||||||||
\(211\) | 11.2161 | 0.772146 | 0.386073 | − | 0.922468i | \(-0.373831\pi\) | ||||
0.386073 | + | 0.922468i | \(0.373831\pi\) | |||||||
\(212\) | 1.00030 | 0.0687011 | ||||||||
\(213\) | −1.56317 | −0.107106 | ||||||||
\(214\) | 25.8751 | 1.76878 | ||||||||
\(215\) | 6.21476 | 0.423843 | ||||||||
\(216\) | 3.01439 | 0.205103 | ||||||||
\(217\) | 10.3463 | 0.702350 | ||||||||
\(218\) | 7.28007 | 0.493068 | ||||||||
\(219\) | −15.4518 | −1.04413 | ||||||||
\(220\) | −1.31684 | −0.0887813 | ||||||||
\(221\) | 13.7020 | 0.921696 | ||||||||
\(222\) | −3.99682 | −0.268249 | ||||||||
\(223\) | −28.2613 | −1.89252 | −0.946258 | − | 0.323413i | \(-0.895170\pi\) | ||||
−0.946258 | + | 0.323413i | \(0.895170\pi\) | |||||||
\(224\) | −1.89415 | −0.126558 | ||||||||
\(225\) | −4.48647 | −0.299098 | ||||||||
\(226\) | −3.50239 | −0.232976 | ||||||||
\(227\) | 14.8970 | 0.988750 | 0.494375 | − | 0.869249i | \(-0.335397\pi\) | ||||
0.494375 | + | 0.869249i | \(0.335397\pi\) | |||||||
\(228\) | −1.94824 | −0.129025 | ||||||||
\(229\) | −19.6728 | −1.30002 | −0.650009 | − | 0.759926i | \(-0.725235\pi\) | ||||
−0.650009 | + | 0.759926i | \(0.725235\pi\) | |||||||
\(230\) | 2.84151 | 0.187364 | ||||||||
\(231\) | 5.42521 | 0.356953 | ||||||||
\(232\) | 5.82462 | 0.382405 | ||||||||
\(233\) | −5.32816 | −0.349059 | −0.174530 | − | 0.984652i | \(-0.555840\pi\) | ||||
−0.174530 | + | 0.984652i | \(0.555840\pi\) | |||||||
\(234\) | −4.55575 | −0.297819 | ||||||||
\(235\) | 3.83258 | 0.250010 | ||||||||
\(236\) | 2.17913 | 0.141849 | ||||||||
\(237\) | −5.55105 | −0.360580 | ||||||||
\(238\) | −4.99654 | −0.323877 | ||||||||
\(239\) | −3.27976 | −0.212150 | −0.106075 | − | 0.994358i | \(-0.533828\pi\) | ||||
−0.106075 | + | 0.994358i | \(0.533828\pi\) | |||||||
\(240\) | −2.29879 | −0.148386 | ||||||||
\(241\) | 11.7854 | 0.759165 | 0.379582 | − | 0.925158i | \(-0.376068\pi\) | ||||
0.379582 | + | 0.925158i | \(0.376068\pi\) | |||||||
\(242\) | −23.7584 | −1.52725 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.31396 | 0.212154 | ||||||||
\(245\) | 0.716613 | 0.0457827 | ||||||||
\(246\) | −0.314093 | −0.0200259 | ||||||||
\(247\) | 20.3305 | 1.29360 | ||||||||
\(248\) | 31.1877 | 1.98042 | ||||||||
\(249\) | 12.6372 | 0.800853 | ||||||||
\(250\) | 8.76217 | 0.554168 | ||||||||
\(251\) | −14.6941 | −0.927485 | −0.463743 | − | 0.885970i | \(-0.653494\pi\) | ||||
−0.463743 | + | 0.885970i | \(0.653494\pi\) | |||||||
\(252\) | −0.338712 | −0.0213369 | ||||||||
\(253\) | −16.6901 | −1.04930 | ||||||||
\(254\) | −0.0437075 | −0.00274245 | ||||||||
\(255\) | 2.77800 | 0.173965 | ||||||||
\(256\) | −7.88278 | −0.492674 | ||||||||
\(257\) | 12.1910 | 0.760455 | 0.380228 | − | 0.924893i | \(-0.375846\pi\) | ||||
0.380228 | + | 0.924893i | \(0.375846\pi\) | |||||||
\(258\) | −11.1779 | −0.695908 | ||||||||
\(259\) | 3.10093 | 0.192682 | ||||||||
\(260\) | −0.857932 | −0.0532067 | ||||||||
\(261\) | 1.93227 | 0.119605 | ||||||||
\(262\) | −13.4022 | −0.827991 | ||||||||
\(263\) | 2.82742 | 0.174346 | 0.0871730 | − | 0.996193i | \(-0.472217\pi\) | ||||
0.0871730 | + | 0.996193i | \(0.472217\pi\) | |||||||
\(264\) | 16.3537 | 1.00650 | ||||||||
\(265\) | −2.11634 | −0.130006 | ||||||||
\(266\) | −7.41367 | −0.454561 | ||||||||
\(267\) | −10.2353 | −0.626393 | ||||||||
\(268\) | −0.00424244 | −0.000259148 0 | ||||||||
\(269\) | −19.8290 | −1.20900 | −0.604498 | − | 0.796607i | \(-0.706626\pi\) | ||||
−0.604498 | + | 0.796607i | \(0.706626\pi\) | |||||||
\(270\) | −0.923650 | −0.0562115 | ||||||||
\(271\) | 22.0669 | 1.34047 | 0.670233 | − | 0.742151i | \(-0.266194\pi\) | ||||
0.670233 | + | 0.742151i | \(0.266194\pi\) | |||||||
\(272\) | −12.4354 | −0.754008 | ||||||||
\(273\) | 3.53458 | 0.213922 | ||||||||
\(274\) | −5.06122 | −0.305759 | ||||||||
\(275\) | −24.3400 | −1.46776 | ||||||||
\(276\) | 1.04201 | 0.0627218 | ||||||||
\(277\) | 6.98114 | 0.419456 | 0.209728 | − | 0.977760i | \(-0.432742\pi\) | ||||
0.209728 | + | 0.977760i | \(0.432742\pi\) | |||||||
\(278\) | 19.1965 | 1.15133 | ||||||||
\(279\) | 10.3463 | 0.619415 | ||||||||
\(280\) | 2.16015 | 0.129094 | ||||||||
\(281\) | 26.5918 | 1.58633 | 0.793166 | − | 0.609006i | \(-0.208431\pi\) | ||||
0.793166 | + | 0.609006i | \(0.208431\pi\) | |||||||
\(282\) | −6.89333 | −0.410492 | ||||||||
\(283\) | 15.2797 | 0.908287 | 0.454143 | − | 0.890929i | \(-0.349945\pi\) | ||||
0.454143 | + | 0.890929i | \(0.349945\pi\) | |||||||
\(284\) | 0.529464 | 0.0314179 | ||||||||
\(285\) | 4.12189 | 0.244159 | ||||||||
\(286\) | −24.7159 | −1.46148 | ||||||||
\(287\) | 0.243689 | 0.0143845 | ||||||||
\(288\) | −1.89415 | −0.111614 | ||||||||
\(289\) | −1.97228 | −0.116016 | ||||||||
\(290\) | −1.78474 | −0.104804 | ||||||||
\(291\) | −18.5407 | −1.08687 | ||||||||
\(292\) | 5.23370 | 0.306279 | ||||||||
\(293\) | 25.8528 | 1.51034 | 0.755168 | − | 0.655531i | \(-0.227555\pi\) | ||||
0.755168 | + | 0.655531i | \(0.227555\pi\) | |||||||
\(294\) | −1.28891 | −0.0751707 | ||||||||
\(295\) | −4.61039 | −0.268427 | ||||||||
\(296\) | 9.34741 | 0.543307 | ||||||||
\(297\) | 5.42521 | 0.314803 | ||||||||
\(298\) | −25.7452 | −1.49138 | ||||||||
\(299\) | −10.8737 | −0.628845 | ||||||||
\(300\) | 1.51962 | 0.0877353 | ||||||||
\(301\) | 8.67240 | 0.499869 | ||||||||
\(302\) | −10.0539 | −0.578538 | ||||||||
\(303\) | −5.99911 | −0.344640 | ||||||||
\(304\) | −18.4512 | −1.05825 | ||||||||
\(305\) | −7.01134 | −0.401468 | ||||||||
\(306\) | −4.99654 | −0.285633 | ||||||||
\(307\) | −23.8691 | −1.36228 | −0.681140 | − | 0.732154i | \(-0.738515\pi\) | ||||
−0.681140 | + | 0.732154i | \(0.738515\pi\) | |||||||
\(308\) | −1.83759 | −0.104706 | ||||||||
\(309\) | −14.0429 | −0.798870 | ||||||||
\(310\) | −9.55632 | −0.542763 | ||||||||
\(311\) | −13.5790 | −0.769996 | −0.384998 | − | 0.922917i | \(-0.625798\pi\) | ||||
−0.384998 | + | 0.922917i | \(0.625798\pi\) | |||||||
\(312\) | 10.6546 | 0.603197 | ||||||||
\(313\) | 16.4100 | 0.927546 | 0.463773 | − | 0.885954i | \(-0.346495\pi\) | ||||
0.463773 | + | 0.885954i | \(0.346495\pi\) | |||||||
\(314\) | 16.9444 | 0.956228 | ||||||||
\(315\) | 0.716613 | 0.0403766 | ||||||||
\(316\) | 1.88021 | 0.105770 | ||||||||
\(317\) | 6.08345 | 0.341681 | 0.170840 | − | 0.985299i | \(-0.445352\pi\) | ||||
0.170840 | + | 0.985299i | \(0.445352\pi\) | |||||||
\(318\) | 3.80648 | 0.213457 | ||||||||
\(319\) | 10.4830 | 0.586934 | ||||||||
\(320\) | 6.34711 | 0.354814 | ||||||||
\(321\) | −20.0752 | −1.12049 | ||||||||
\(322\) | 3.96519 | 0.220972 | ||||||||
\(323\) | 22.2976 | 1.24067 | ||||||||
\(324\) | −0.338712 | −0.0188173 | ||||||||
\(325\) | −15.8578 | −0.879630 | ||||||||
\(326\) | 19.9795 | 1.10656 | ||||||||
\(327\) | −5.64824 | −0.312348 | ||||||||
\(328\) | 0.734574 | 0.0405600 | ||||||||
\(329\) | 5.34819 | 0.294855 | ||||||||
\(330\) | −5.01100 | −0.275846 | ||||||||
\(331\) | −22.8441 | −1.25563 | −0.627814 | − | 0.778364i | \(-0.716050\pi\) | ||||
−0.627814 | + | 0.778364i | \(0.716050\pi\) | |||||||
\(332\) | −4.28039 | −0.234917 | ||||||||
\(333\) | 3.10093 | 0.169930 | ||||||||
\(334\) | −7.84245 | −0.429120 | ||||||||
\(335\) | 0.00897573 | 0.000490396 0 | ||||||||
\(336\) | −3.20785 | −0.175003 | ||||||||
\(337\) | −1.12003 | −0.0610119 | −0.0305059 | − | 0.999535i | \(-0.509712\pi\) | ||||
−0.0305059 | + | 0.999535i | \(0.509712\pi\) | |||||||
\(338\) | 0.653187 | 0.0355287 | ||||||||
\(339\) | 2.71733 | 0.147585 | ||||||||
\(340\) | −0.940941 | −0.0510297 | ||||||||
\(341\) | 56.1307 | 3.03965 | ||||||||
\(342\) | −7.41367 | −0.400886 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 26.1420 | 1.40948 | ||||||||
\(345\) | −2.20459 | −0.118691 | ||||||||
\(346\) | 12.7856 | 0.687360 | ||||||||
\(347\) | −4.30026 | −0.230850 | −0.115425 | − | 0.993316i | \(-0.536823\pi\) | ||||
−0.115425 | + | 0.993316i | \(0.536823\pi\) | |||||||
\(348\) | −0.654484 | −0.0350840 | ||||||||
\(349\) | 17.0512 | 0.912728 | 0.456364 | − | 0.889793i | \(-0.349151\pi\) | ||||
0.456364 | + | 0.889793i | \(0.349151\pi\) | |||||||
\(350\) | 5.78265 | 0.309096 | ||||||||
\(351\) | 3.53458 | 0.188662 | ||||||||
\(352\) | −10.2762 | −0.547721 | ||||||||
\(353\) | 0.0960293 | 0.00511112 | 0.00255556 | − | 0.999997i | \(-0.499187\pi\) | ||||
0.00255556 | + | 0.999997i | \(0.499187\pi\) | |||||||
\(354\) | 8.29230 | 0.440731 | ||||||||
\(355\) | −1.12019 | −0.0594533 | ||||||||
\(356\) | 3.46683 | 0.183742 | ||||||||
\(357\) | 3.87656 | 0.205169 | ||||||||
\(358\) | −6.29004 | −0.332439 | ||||||||
\(359\) | −30.5766 | −1.61377 | −0.806885 | − | 0.590709i | \(-0.798848\pi\) | ||||
−0.806885 | + | 0.590709i | \(0.798848\pi\) | |||||||
\(360\) | 2.16015 | 0.113850 | ||||||||
\(361\) | 14.0843 | 0.741279 | ||||||||
\(362\) | 4.42604 | 0.232627 | ||||||||
\(363\) | 18.4330 | 0.967479 | ||||||||
\(364\) | −1.19720 | −0.0627505 | ||||||||
\(365\) | −11.0729 | −0.579584 | ||||||||
\(366\) | 12.6107 | 0.659171 | ||||||||
\(367\) | 32.4082 | 1.69169 | 0.845847 | − | 0.533425i | \(-0.179095\pi\) | ||||
0.845847 | + | 0.533425i | \(0.179095\pi\) | |||||||
\(368\) | 9.86861 | 0.514437 | ||||||||
\(369\) | 0.243689 | 0.0126859 | ||||||||
\(370\) | −2.86417 | −0.148901 | ||||||||
\(371\) | −2.95325 | −0.153325 | ||||||||
\(372\) | −3.50441 | −0.181695 | ||||||||
\(373\) | −15.3890 | −0.796811 | −0.398406 | − | 0.917209i | \(-0.630436\pi\) | ||||
−0.398406 | + | 0.917209i | \(0.630436\pi\) | |||||||
\(374\) | −27.1073 | −1.40168 | ||||||||
\(375\) | −6.79813 | −0.351054 | ||||||||
\(376\) | 16.1215 | 0.831403 | ||||||||
\(377\) | 6.82976 | 0.351750 | ||||||||
\(378\) | −1.28891 | −0.0662944 | ||||||||
\(379\) | 8.37059 | 0.429968 | 0.214984 | − | 0.976618i | \(-0.431030\pi\) | ||||
0.214984 | + | 0.976618i | \(0.431030\pi\) | |||||||
\(380\) | −1.39613 | −0.0716201 | ||||||||
\(381\) | 0.0339105 | 0.00173729 | ||||||||
\(382\) | −1.28891 | −0.0659463 | ||||||||
\(383\) | −17.0519 | −0.871314 | −0.435657 | − | 0.900113i | \(-0.643484\pi\) | ||||
−0.435657 | + | 0.900113i | \(0.643484\pi\) | |||||||
\(384\) | −7.62768 | −0.389249 | ||||||||
\(385\) | 3.88778 | 0.198140 | ||||||||
\(386\) | 12.3121 | 0.626667 | ||||||||
\(387\) | 8.67240 | 0.440843 | ||||||||
\(388\) | 6.27995 | 0.318816 | ||||||||
\(389\) | 20.4796 | 1.03835 | 0.519177 | − | 0.854667i | \(-0.326238\pi\) | ||||
0.519177 | + | 0.854667i | \(0.326238\pi\) | |||||||
\(390\) | −3.26471 | −0.165315 | ||||||||
\(391\) | −11.9258 | −0.603115 | ||||||||
\(392\) | 3.01439 | 0.152250 | ||||||||
\(393\) | 10.3981 | 0.524515 | ||||||||
\(394\) | −14.4675 | −0.728864 | ||||||||
\(395\) | −3.97796 | −0.200153 | ||||||||
\(396\) | −1.83759 | −0.0923422 | ||||||||
\(397\) | −18.3972 | −0.923331 | −0.461665 | − | 0.887054i | \(-0.652748\pi\) | ||||
−0.461665 | + | 0.887054i | \(0.652748\pi\) | |||||||
\(398\) | −21.9142 | −1.09846 | ||||||||
\(399\) | 5.75190 | 0.287955 | ||||||||
\(400\) | 14.3919 | 0.719595 | ||||||||
\(401\) | −25.6981 | −1.28330 | −0.641650 | − | 0.766998i | \(-0.721750\pi\) | ||||
−0.641650 | + | 0.766998i | \(0.721750\pi\) | |||||||
\(402\) | −0.0161439 | −0.000805182 0 | ||||||||
\(403\) | 36.5696 | 1.82166 | ||||||||
\(404\) | 2.03197 | 0.101094 | ||||||||
\(405\) | 0.716613 | 0.0356088 | ||||||||
\(406\) | −2.49052 | −0.123603 | ||||||||
\(407\) | 16.8232 | 0.833896 | ||||||||
\(408\) | 11.6855 | 0.578516 | ||||||||
\(409\) | −0.688587 | −0.0340485 | −0.0170242 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170242 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(410\) | −0.225083 | −0.0111161 | ||||||||
\(411\) | 3.92674 | 0.193692 | ||||||||
\(412\) | 4.75649 | 0.234335 | ||||||||
\(413\) | −6.43358 | −0.316576 | ||||||||
\(414\) | 3.96519 | 0.194879 | ||||||||
\(415\) | 9.05602 | 0.444542 | ||||||||
\(416\) | −6.69501 | −0.328250 | ||||||||
\(417\) | −14.8936 | −0.729343 | ||||||||
\(418\) | −40.2208 | −1.96726 | ||||||||
\(419\) | −3.66524 | −0.179059 | −0.0895293 | − | 0.995984i | \(-0.528536\pi\) | ||||
−0.0895293 | + | 0.995984i | \(0.528536\pi\) | |||||||
\(420\) | −0.242726 | −0.0118438 | ||||||||
\(421\) | −13.6438 | −0.664959 | −0.332479 | − | 0.943111i | \(-0.607885\pi\) | ||||
−0.332479 | + | 0.943111i | \(0.607885\pi\) | |||||||
\(422\) | −14.4565 | −0.703731 | ||||||||
\(423\) | 5.34819 | 0.260038 | ||||||||
\(424\) | −8.90226 | −0.432332 | ||||||||
\(425\) | −17.3921 | −0.843639 | ||||||||
\(426\) | 2.01478 | 0.0976165 | ||||||||
\(427\) | −9.78399 | −0.473481 | ||||||||
\(428\) | 6.79971 | 0.328676 | ||||||||
\(429\) | 19.1758 | 0.925818 | ||||||||
\(430\) | −8.01026 | −0.386289 | ||||||||
\(431\) | −4.25103 | −0.204765 | −0.102382 | − | 0.994745i | \(-0.532647\pi\) | ||||
−0.102382 | + | 0.994745i | \(0.532647\pi\) | |||||||
\(432\) | −3.20785 | −0.154338 | ||||||||
\(433\) | −36.6191 | −1.75980 | −0.879902 | − | 0.475156i | \(-0.842392\pi\) | ||||
−0.879902 | + | 0.475156i | \(0.842392\pi\) | |||||||
\(434\) | −13.3354 | −0.640119 | ||||||||
\(435\) | 1.38469 | 0.0663909 | ||||||||
\(436\) | 1.91313 | 0.0916221 | ||||||||
\(437\) | −17.6951 | −0.846471 | ||||||||
\(438\) | 19.9159 | 0.951619 | ||||||||
\(439\) | 7.26399 | 0.346691 | 0.173346 | − | 0.984861i | \(-0.444542\pi\) | ||||
0.173346 | + | 0.984861i | \(0.444542\pi\) | |||||||
\(440\) | 11.7193 | 0.558695 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −17.6606 | −0.840031 | ||||||||
\(443\) | 32.9289 | 1.56450 | 0.782251 | − | 0.622964i | \(-0.214072\pi\) | ||||
0.782251 | + | 0.622964i | \(0.214072\pi\) | |||||||
\(444\) | −1.05032 | −0.0498461 | ||||||||
\(445\) | −7.33478 | −0.347702 | ||||||||
\(446\) | 36.4262 | 1.72483 | ||||||||
\(447\) | 19.9744 | 0.944757 | ||||||||
\(448\) | 8.85709 | 0.418458 | ||||||||
\(449\) | −9.19664 | −0.434016 | −0.217008 | − | 0.976170i | \(-0.569630\pi\) | ||||
−0.217008 | + | 0.976170i | \(0.569630\pi\) | |||||||
\(450\) | 5.78265 | 0.272597 | ||||||||
\(451\) | 1.32207 | 0.0622536 | ||||||||
\(452\) | −0.920392 | −0.0432916 | ||||||||
\(453\) | 7.80032 | 0.366491 | ||||||||
\(454\) | −19.2009 | −0.901143 | ||||||||
\(455\) | 2.53292 | 0.118745 | ||||||||
\(456\) | 17.3384 | 0.811947 | ||||||||
\(457\) | −13.9780 | −0.653864 | −0.326932 | − | 0.945048i | \(-0.606015\pi\) | ||||
−0.326932 | + | 0.945048i | \(0.606015\pi\) | |||||||
\(458\) | 25.3565 | 1.18483 | ||||||||
\(459\) | 3.87656 | 0.180942 | ||||||||
\(460\) | 0.746720 | 0.0348160 | ||||||||
\(461\) | 38.4887 | 1.79260 | 0.896299 | − | 0.443450i | \(-0.146246\pi\) | ||||
0.896299 | + | 0.443450i | \(0.146246\pi\) | |||||||
\(462\) | −6.99261 | −0.325326 | ||||||||
\(463\) | 19.0064 | 0.883303 | 0.441652 | − | 0.897187i | \(-0.354393\pi\) | ||||
0.441652 | + | 0.897187i | \(0.354393\pi\) | |||||||
\(464\) | −6.19843 | −0.287755 | ||||||||
\(465\) | 7.41427 | 0.343829 | ||||||||
\(466\) | 6.86751 | 0.318131 | ||||||||
\(467\) | −25.2053 | −1.16636 | −0.583182 | − | 0.812342i | \(-0.698193\pi\) | ||||
−0.583182 | + | 0.812342i | \(0.698193\pi\) | |||||||
\(468\) | −1.19720 | −0.0553408 | ||||||||
\(469\) | 0.0125252 | 0.000578360 0 | ||||||||
\(470\) | −4.93985 | −0.227858 | ||||||||
\(471\) | −13.1463 | −0.605750 | ||||||||
\(472\) | −19.3933 | −0.892650 | ||||||||
\(473\) | 47.0496 | 2.16334 | ||||||||
\(474\) | 7.15481 | 0.328631 | ||||||||
\(475\) | −25.8057 | −1.18405 | ||||||||
\(476\) | −1.31304 | −0.0601830 | ||||||||
\(477\) | −2.95325 | −0.135220 | ||||||||
\(478\) | 4.22731 | 0.193353 | ||||||||
\(479\) | −5.20589 | −0.237863 | −0.118932 | − | 0.992902i | \(-0.537947\pi\) | ||||
−0.118932 | + | 0.992902i | \(0.537947\pi\) | |||||||
\(480\) | −1.35737 | −0.0619553 | ||||||||
\(481\) | 10.9605 | 0.499754 | ||||||||
\(482\) | −15.1903 | −0.691900 | ||||||||
\(483\) | −3.07639 | −0.139981 | ||||||||
\(484\) | −6.24347 | −0.283794 | ||||||||
\(485\) | −13.2865 | −0.603308 | ||||||||
\(486\) | −1.28891 | −0.0584661 | ||||||||
\(487\) | −11.7313 | −0.531596 | −0.265798 | − | 0.964029i | \(-0.585635\pi\) | ||||
−0.265798 | + | 0.964029i | \(0.585635\pi\) | |||||||
\(488\) | −29.4928 | −1.33507 | ||||||||
\(489\) | −15.5010 | −0.700982 | ||||||||
\(490\) | −0.923650 | −0.0417262 | ||||||||
\(491\) | 39.1571 | 1.76713 | 0.883567 | − | 0.468304i | \(-0.155135\pi\) | ||||
0.883567 | + | 0.468304i | \(0.155135\pi\) | |||||||
\(492\) | −0.0825405 | −0.00372121 | ||||||||
\(493\) | 7.49057 | 0.337358 | ||||||||
\(494\) | −26.2042 | −1.17898 | ||||||||
\(495\) | 3.88778 | 0.174743 | ||||||||
\(496\) | −33.1893 | −1.49024 | ||||||||
\(497\) | −1.56317 | −0.0701176 | ||||||||
\(498\) | −16.2883 | −0.729895 | ||||||||
\(499\) | −34.4988 | −1.54438 | −0.772188 | − | 0.635394i | \(-0.780838\pi\) | ||||
−0.772188 | + | 0.635394i | \(0.780838\pi\) | |||||||
\(500\) | 2.30261 | 0.102976 | ||||||||
\(501\) | 6.08456 | 0.271838 | ||||||||
\(502\) | 18.9394 | 0.845307 | ||||||||
\(503\) | 28.0256 | 1.24960 | 0.624800 | − | 0.780785i | \(-0.285181\pi\) | ||||
0.624800 | + | 0.780785i | \(0.285181\pi\) | |||||||
\(504\) | 3.01439 | 0.134272 | ||||||||
\(505\) | −4.29904 | −0.191305 | ||||||||
\(506\) | 21.5120 | 0.956326 | ||||||||
\(507\) | −0.506775 | −0.0225067 | ||||||||
\(508\) | −0.0114859 | −0.000509604 0 | ||||||||
\(509\) | −37.8404 | −1.67725 | −0.838623 | − | 0.544712i | \(-0.816639\pi\) | ||||
−0.838623 | + | 0.544712i | \(0.816639\pi\) | |||||||
\(510\) | −3.58058 | −0.158551 | ||||||||
\(511\) | −15.4518 | −0.683545 | ||||||||
\(512\) | 25.4156 | 1.12322 | ||||||||
\(513\) | 5.75190 | 0.253952 | ||||||||
\(514\) | −15.7131 | −0.693076 | ||||||||
\(515\) | −10.0633 | −0.443442 | ||||||||
\(516\) | −2.93745 | −0.129314 | ||||||||
\(517\) | 29.0151 | 1.27608 | ||||||||
\(518\) | −3.99682 | −0.175610 | ||||||||
\(519\) | −9.91974 | −0.435428 | ||||||||
\(520\) | 7.63522 | 0.334826 | ||||||||
\(521\) | −22.6377 | −0.991777 | −0.495889 | − | 0.868386i | \(-0.665158\pi\) | ||||
−0.495889 | + | 0.868386i | \(0.665158\pi\) | |||||||
\(522\) | −2.49052 | −0.109007 | ||||||||
\(523\) | 17.9243 | 0.783777 | 0.391889 | − | 0.920013i | \(-0.371822\pi\) | ||||
0.391889 | + | 0.920013i | \(0.371822\pi\) | |||||||
\(524\) | −3.52196 | −0.153858 | ||||||||
\(525\) | −4.48647 | −0.195805 | ||||||||
\(526\) | −3.64428 | −0.158898 | ||||||||
\(527\) | 40.1079 | 1.74713 | ||||||||
\(528\) | −17.4033 | −0.757380 | ||||||||
\(529\) | −13.5358 | −0.588513 | ||||||||
\(530\) | 2.72777 | 0.118487 | ||||||||
\(531\) | −6.43358 | −0.279194 | ||||||||
\(532\) | −1.94824 | −0.0844668 | ||||||||
\(533\) | 0.861338 | 0.0373087 | ||||||||
\(534\) | 13.1924 | 0.570892 | ||||||||
\(535\) | −14.3861 | −0.621967 | ||||||||
\(536\) | 0.0377558 | 0.00163080 | ||||||||
\(537\) | 4.88013 | 0.210593 | ||||||||
\(538\) | 25.5578 | 1.10187 | ||||||||
\(539\) | 5.42521 | 0.233681 | ||||||||
\(540\) | −0.242726 | −0.0104453 | ||||||||
\(541\) | −19.7848 | −0.850614 | −0.425307 | − | 0.905049i | \(-0.639834\pi\) | ||||
−0.425307 | + | 0.905049i | \(0.639834\pi\) | |||||||
\(542\) | −28.4422 | −1.22170 | ||||||||
\(543\) | −3.43394 | −0.147365 | ||||||||
\(544\) | −7.34278 | −0.314819 | ||||||||
\(545\) | −4.04760 | −0.173380 | ||||||||
\(546\) | −4.55575 | −0.194968 | ||||||||
\(547\) | −39.3259 | −1.68145 | −0.840726 | − | 0.541460i | \(-0.817872\pi\) | ||||
−0.840726 | + | 0.541460i | \(0.817872\pi\) | |||||||
\(548\) | −1.33004 | −0.0568163 | ||||||||
\(549\) | −9.78399 | −0.417571 | ||||||||
\(550\) | 31.3721 | 1.33771 | ||||||||
\(551\) | 11.1142 | 0.473482 | ||||||||
\(552\) | −9.27345 | −0.394704 | ||||||||
\(553\) | −5.55105 | −0.236055 | ||||||||
\(554\) | −8.99806 | −0.382291 | ||||||||
\(555\) | 2.22217 | 0.0943258 | ||||||||
\(556\) | 5.04464 | 0.213941 | ||||||||
\(557\) | −1.55498 | −0.0658864 | −0.0329432 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329432 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(558\) | −13.3354 | −0.564532 | ||||||||
\(559\) | 30.6532 | 1.29649 | ||||||||
\(560\) | −2.29879 | −0.0971415 | ||||||||
\(561\) | 21.0312 | 0.887937 | ||||||||
\(562\) | −34.2744 | −1.44578 | ||||||||
\(563\) | 11.9985 | 0.505677 | 0.252838 | − | 0.967509i | \(-0.418636\pi\) | ||||
0.252838 | + | 0.967509i | \(0.418636\pi\) | |||||||
\(564\) | −1.81150 | −0.0762777 | ||||||||
\(565\) | 1.94727 | 0.0819224 | ||||||||
\(566\) | −19.6942 | −0.827809 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.71199 | −0.197711 | ||||||||
\(569\) | −10.1682 | −0.426272 | −0.213136 | − | 0.977023i | \(-0.568368\pi\) | ||||
−0.213136 | + | 0.977023i | \(0.568368\pi\) | |||||||
\(570\) | −5.31274 | −0.222526 | ||||||||
\(571\) | 10.6798 | 0.446934 | 0.223467 | − | 0.974711i | \(-0.428262\pi\) | ||||
0.223467 | + | 0.974711i | \(0.428262\pi\) | |||||||
\(572\) | −6.49509 | −0.271573 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −0.314093 | −0.0131100 | ||||||||
\(575\) | 13.8021 | 0.575589 | ||||||||
\(576\) | 8.85709 | 0.369045 | ||||||||
\(577\) | 46.7618 | 1.94672 | 0.973359 | − | 0.229286i | \(-0.0736390\pi\) | ||||
0.973359 | + | 0.229286i | \(0.0736390\pi\) | |||||||
\(578\) | 2.54209 | 0.105737 | ||||||||
\(579\) | −9.55231 | −0.396980 | ||||||||
\(580\) | −0.469012 | −0.0194747 | ||||||||
\(581\) | 12.6372 | 0.524281 | ||||||||
\(582\) | 23.8972 | 0.990572 | ||||||||
\(583\) | −16.0220 | −0.663565 | ||||||||
\(584\) | −46.5776 | −1.92739 | ||||||||
\(585\) | 2.53292 | 0.104724 | ||||||||
\(586\) | −33.3219 | −1.37652 | ||||||||
\(587\) | −13.8301 | −0.570828 | −0.285414 | − | 0.958404i | \(-0.592131\pi\) | ||||
−0.285414 | + | 0.958404i | \(0.592131\pi\) | |||||||
\(588\) | −0.338712 | −0.0139683 | ||||||||
\(589\) | 59.5106 | 2.45209 | ||||||||
\(590\) | 5.94238 | 0.244644 | ||||||||
\(591\) | 11.2246 | 0.461720 | ||||||||
\(592\) | −9.94732 | −0.408832 | ||||||||
\(593\) | 24.6222 | 1.01111 | 0.505556 | − | 0.862794i | \(-0.331287\pi\) | ||||
0.505556 | + | 0.862794i | \(0.331287\pi\) | |||||||
\(594\) | −6.99261 | −0.286910 | ||||||||
\(595\) | 2.77800 | 0.113887 | ||||||||
\(596\) | −6.76558 | −0.277129 | ||||||||
\(597\) | 17.0021 | 0.695851 | ||||||||
\(598\) | 14.0153 | 0.573127 | ||||||||
\(599\) | 43.7878 | 1.78912 | 0.894560 | − | 0.446948i | \(-0.147489\pi\) | ||||
0.894560 | + | 0.446948i | \(0.147489\pi\) | |||||||
\(600\) | −13.5239 | −0.552113 | ||||||||
\(601\) | 3.54445 | 0.144581 | 0.0722906 | − | 0.997384i | \(-0.476969\pi\) | ||||
0.0722906 | + | 0.997384i | \(0.476969\pi\) | |||||||
\(602\) | −11.1779 | −0.455579 | ||||||||
\(603\) | 0.0125252 | 0.000510066 0 | ||||||||
\(604\) | −2.64206 | −0.107504 | ||||||||
\(605\) | 13.2093 | 0.537034 | ||||||||
\(606\) | 7.73231 | 0.314104 | ||||||||
\(607\) | 26.4064 | 1.07180 | 0.535901 | − | 0.844281i | \(-0.319972\pi\) | ||||
0.535901 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(608\) | −10.8949 | −0.441848 | ||||||||
\(609\) | 1.93227 | 0.0782996 | ||||||||
\(610\) | 9.03698 | 0.365897 | ||||||||
\(611\) | 18.9036 | 0.764756 | ||||||||
\(612\) | −1.31304 | −0.0530764 | ||||||||
\(613\) | 21.7769 | 0.879559 | 0.439780 | − | 0.898106i | \(-0.355057\pi\) | ||||
0.439780 | + | 0.898106i | \(0.355057\pi\) | |||||||
\(614\) | 30.7651 | 1.24158 | ||||||||
\(615\) | 0.174631 | 0.00704180 | ||||||||
\(616\) | 16.3537 | 0.658910 | ||||||||
\(617\) | 5.59619 | 0.225294 | 0.112647 | − | 0.993635i | \(-0.464067\pi\) | ||||
0.112647 | + | 0.993635i | \(0.464067\pi\) | |||||||
\(618\) | 18.1000 | 0.728088 | ||||||||
\(619\) | −31.5824 | −1.26941 | −0.634703 | − | 0.772756i | \(-0.718878\pi\) | ||||
−0.634703 | + | 0.772756i | \(0.718878\pi\) | |||||||
\(620\) | −2.51130 | −0.100856 | ||||||||
\(621\) | −3.07639 | −0.123451 | ||||||||
\(622\) | 17.5021 | 0.701772 | ||||||||
\(623\) | −10.2353 | −0.410070 | ||||||||
\(624\) | −11.3384 | −0.453899 | ||||||||
\(625\) | 17.5607 | 0.702428 | ||||||||
\(626\) | −21.1510 | −0.845363 | ||||||||
\(627\) | 31.2053 | 1.24622 | ||||||||
\(628\) | 4.45281 | 0.177687 | ||||||||
\(629\) | 12.0209 | 0.479306 | ||||||||
\(630\) | −0.923650 | −0.0367991 | ||||||||
\(631\) | 33.1442 | 1.31945 | 0.659724 | − | 0.751508i | \(-0.270673\pi\) | ||||
0.659724 | + | 0.751508i | \(0.270673\pi\) | |||||||
\(632\) | −16.7330 | −0.665604 | ||||||||
\(633\) | 11.2161 | 0.445799 | ||||||||
\(634\) | −7.84102 | −0.311407 | ||||||||
\(635\) | 0.0243007 | 0.000964344 0 | ||||||||
\(636\) | 1.00030 | 0.0396646 | ||||||||
\(637\) | 3.53458 | 0.140045 | ||||||||
\(638\) | −13.5116 | −0.534930 | ||||||||
\(639\) | −1.56317 | −0.0618379 | ||||||||
\(640\) | −5.46610 | −0.216067 | ||||||||
\(641\) | 7.28068 | 0.287569 | 0.143785 | − | 0.989609i | \(-0.454073\pi\) | ||||
0.143785 | + | 0.989609i | \(0.454073\pi\) | |||||||
\(642\) | 25.8751 | 1.02121 | ||||||||
\(643\) | −20.9999 | −0.828156 | −0.414078 | − | 0.910241i | \(-0.635896\pi\) | ||||
−0.414078 | + | 0.910241i | \(0.635896\pi\) | |||||||
\(644\) | 1.04201 | 0.0410610 | ||||||||
\(645\) | 6.21476 | 0.244706 | ||||||||
\(646\) | −28.7396 | −1.13074 | ||||||||
\(647\) | −6.15247 | −0.241879 | −0.120939 | − | 0.992660i | \(-0.538591\pi\) | ||||
−0.120939 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(648\) | 3.01439 | 0.118416 | ||||||||
\(649\) | −34.9036 | −1.37008 | ||||||||
\(650\) | 20.4392 | 0.801692 | ||||||||
\(651\) | 10.3463 | 0.405502 | ||||||||
\(652\) | 5.25039 | 0.205621 | ||||||||
\(653\) | 0.236684 | 0.00926217 | 0.00463109 | − | 0.999989i | \(-0.498526\pi\) | ||||
0.00463109 | + | 0.999989i | \(0.498526\pi\) | |||||||
\(654\) | 7.28007 | 0.284673 | ||||||||
\(655\) | 7.45142 | 0.291151 | ||||||||
\(656\) | −0.781718 | −0.0305210 | ||||||||
\(657\) | −15.4518 | −0.602830 | ||||||||
\(658\) | −6.89333 | −0.268730 | ||||||||
\(659\) | 8.67219 | 0.337821 | 0.168910 | − | 0.985631i | \(-0.445975\pi\) | ||||
0.168910 | + | 0.985631i | \(0.445975\pi\) | |||||||
\(660\) | −1.31684 | −0.0512579 | ||||||||
\(661\) | 27.7143 | 1.07796 | 0.538980 | − | 0.842319i | \(-0.318810\pi\) | ||||
0.538980 | + | 0.842319i | \(0.318810\pi\) | |||||||
\(662\) | 29.4440 | 1.14437 | ||||||||
\(663\) | 13.7020 | 0.532141 | ||||||||
\(664\) | 38.0936 | 1.47832 | ||||||||
\(665\) | 4.12189 | 0.159840 | ||||||||
\(666\) | −3.99682 | −0.154874 | ||||||||
\(667\) | −5.94443 | −0.230169 | ||||||||
\(668\) | −2.06092 | −0.0797393 | ||||||||
\(669\) | −28.2613 | −1.09264 | ||||||||
\(670\) | −0.0115689 | −0.000446946 0 | ||||||||
\(671\) | −53.0803 | −2.04914 | ||||||||
\(672\) | −1.89415 | −0.0730684 | ||||||||
\(673\) | −6.39286 | −0.246427 | −0.123213 | − | 0.992380i | \(-0.539320\pi\) | ||||
−0.123213 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(674\) | 1.44362 | 0.0556060 | ||||||||
\(675\) | −4.48647 | −0.172684 | ||||||||
\(676\) | 0.171651 | 0.00660196 | ||||||||
\(677\) | 33.3563 | 1.28199 | 0.640994 | − | 0.767546i | \(-0.278522\pi\) | ||||
0.640994 | + | 0.767546i | \(0.278522\pi\) | |||||||
\(678\) | −3.50239 | −0.134509 | ||||||||
\(679\) | −18.5407 | −0.711525 | ||||||||
\(680\) | 8.37396 | 0.321127 | ||||||||
\(681\) | 14.8970 | 0.570855 | ||||||||
\(682\) | −72.3474 | −2.77032 | ||||||||
\(683\) | 26.5556 | 1.01612 | 0.508060 | − | 0.861322i | \(-0.330363\pi\) | ||||
0.508060 | + | 0.861322i | \(0.330363\pi\) | |||||||
\(684\) | −1.94824 | −0.0744927 | ||||||||
\(685\) | 2.81396 | 0.107516 | ||||||||
\(686\) | −1.28891 | −0.0492108 | ||||||||
\(687\) | −19.6728 | −0.750566 | ||||||||
\(688\) | −27.8197 | −1.06062 | ||||||||
\(689\) | −10.4385 | −0.397675 | ||||||||
\(690\) | 2.84151 | 0.108174 | ||||||||
\(691\) | −19.3607 | −0.736515 | −0.368257 | − | 0.929724i | \(-0.620045\pi\) | ||||
−0.368257 | + | 0.929724i | \(0.620045\pi\) | |||||||
\(692\) | 3.35994 | 0.127726 | ||||||||
\(693\) | 5.42521 | 0.206087 | ||||||||
\(694\) | 5.54265 | 0.210396 | ||||||||
\(695\) | −10.6729 | −0.404848 | ||||||||
\(696\) | 5.82462 | 0.220781 | ||||||||
\(697\) | 0.944676 | 0.0357821 | ||||||||
\(698\) | −21.9774 | −0.831857 | ||||||||
\(699\) | −5.32816 | −0.201529 | ||||||||
\(700\) | 1.51962 | 0.0574363 | ||||||||
\(701\) | −29.2639 | −1.10528 | −0.552642 | − | 0.833419i | \(-0.686380\pi\) | ||||
−0.552642 | + | 0.833419i | \(0.686380\pi\) | |||||||
\(702\) | −4.55575 | −0.171946 | ||||||||
\(703\) | 17.8362 | 0.672706 | ||||||||
\(704\) | 48.0516 | 1.81101 | ||||||||
\(705\) | 3.83258 | 0.144343 | ||||||||
\(706\) | −0.123773 | −0.00465826 | ||||||||
\(707\) | −5.99911 | −0.225620 | ||||||||
\(708\) | 2.17913 | 0.0818968 | ||||||||
\(709\) | −17.6673 | −0.663511 | −0.331755 | − | 0.943365i | \(-0.607641\pi\) | ||||
−0.331755 | + | 0.943365i | \(0.607641\pi\) | |||||||
\(710\) | 1.44382 | 0.0541856 | ||||||||
\(711\) | −5.55105 | −0.208181 | ||||||||
\(712\) | −30.8533 | −1.15628 | ||||||||
\(713\) | −31.8292 | −1.19201 | ||||||||
\(714\) | −4.99654 | −0.186991 | ||||||||
\(715\) | 13.7417 | 0.513909 | ||||||||
\(716\) | −1.65296 | −0.0617739 | ||||||||
\(717\) | −3.27976 | −0.122485 | ||||||||
\(718\) | 39.4104 | 1.47078 | ||||||||
\(719\) | 10.3621 | 0.386441 | 0.193220 | − | 0.981155i | \(-0.438107\pi\) | ||||
0.193220 | + | 0.981155i | \(0.438107\pi\) | |||||||
\(720\) | −2.29879 | −0.0856708 | ||||||||
\(721\) | −14.0429 | −0.522983 | ||||||||
\(722\) | −18.1534 | −0.675599 | ||||||||
\(723\) | 11.7854 | 0.438304 | ||||||||
\(724\) | 1.16312 | 0.0432269 | ||||||||
\(725\) | −8.66907 | −0.321961 | ||||||||
\(726\) | −23.7584 | −0.881757 | ||||||||
\(727\) | −4.85081 | −0.179907 | −0.0899534 | − | 0.995946i | \(-0.528672\pi\) | ||||
−0.0899534 | + | 0.995946i | \(0.528672\pi\) | |||||||
\(728\) | 10.6546 | 0.394885 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.2720 | 0.528231 | ||||||||
\(731\) | 33.6191 | 1.24345 | ||||||||
\(732\) | 3.31396 | 0.122487 | ||||||||
\(733\) | −2.36363 | −0.0873026 | −0.0436513 | − | 0.999047i | \(-0.513899\pi\) | ||||
−0.0436513 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(734\) | −41.7713 | −1.54181 | ||||||||
\(735\) | 0.716613 | 0.0264327 | ||||||||
\(736\) | 5.82715 | 0.214792 | ||||||||
\(737\) | 0.0679519 | 0.00250304 | ||||||||
\(738\) | −0.314093 | −0.0115619 | ||||||||
\(739\) | 5.61438 | 0.206528 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(740\) | −0.752675 | −0.0276689 | ||||||||
\(741\) | 20.3305 | 0.746860 | ||||||||
\(742\) | 3.80648 | 0.139740 | ||||||||
\(743\) | −2.27545 | −0.0834782 | −0.0417391 | − | 0.999129i | \(-0.513290\pi\) | ||||
−0.0417391 | + | 0.999129i | \(0.513290\pi\) | |||||||
\(744\) | 31.1877 | 1.14339 | ||||||||
\(745\) | 14.3139 | 0.524422 | ||||||||
\(746\) | 19.8350 | 0.726211 | ||||||||
\(747\) | 12.6372 | 0.462373 | ||||||||
\(748\) | −7.12352 | −0.260462 | ||||||||
\(749\) | −20.0752 | −0.733531 | ||||||||
\(750\) | 8.76217 | 0.319949 | ||||||||
\(751\) | −4.50828 | −0.164509 | −0.0822546 | − | 0.996611i | \(-0.526212\pi\) | ||||
−0.0822546 | + | 0.996611i | \(0.526212\pi\) | |||||||
\(752\) | −17.1562 | −0.625621 | ||||||||
\(753\) | −14.6941 | −0.535484 | ||||||||
\(754\) | −8.80294 | −0.320584 | ||||||||
\(755\) | 5.58982 | 0.203434 | ||||||||
\(756\) | −0.338712 | −0.0123188 | ||||||||
\(757\) | 38.5415 | 1.40081 | 0.700407 | − | 0.713744i | \(-0.253002\pi\) | ||||
0.700407 | + | 0.713744i | \(0.253002\pi\) | |||||||
\(758\) | −10.7889 | −0.391872 | ||||||||
\(759\) | −16.6901 | −0.605812 | ||||||||
\(760\) | 12.4250 | 0.450701 | ||||||||
\(761\) | 34.5119 | 1.25106 | 0.625528 | − | 0.780202i | \(-0.284884\pi\) | ||||
0.625528 | + | 0.780202i | \(0.284884\pi\) | |||||||
\(762\) | −0.0437075 | −0.00158336 | ||||||||
\(763\) | −5.64824 | −0.204480 | ||||||||
\(764\) | −0.338712 | −0.0122542 | ||||||||
\(765\) | 2.77800 | 0.100439 | ||||||||
\(766\) | 21.9784 | 0.794112 | ||||||||
\(767\) | −22.7400 | −0.821093 | ||||||||
\(768\) | −7.88278 | −0.284445 | ||||||||
\(769\) | −35.7693 | −1.28988 | −0.644938 | − | 0.764235i | \(-0.723117\pi\) | ||||
−0.644938 | + | 0.764235i | \(0.723117\pi\) | |||||||
\(770\) | −5.01100 | −0.180584 | ||||||||
\(771\) | 12.1910 | 0.439049 | ||||||||
\(772\) | 3.23548 | 0.116448 | ||||||||
\(773\) | −8.79838 | −0.316456 | −0.158228 | − | 0.987403i | \(-0.550578\pi\) | ||||
−0.158228 | + | 0.987403i | \(0.550578\pi\) | |||||||
\(774\) | −11.1779 | −0.401783 | ||||||||
\(775\) | −46.4181 | −1.66739 | ||||||||
\(776\) | −55.8888 | −2.00629 | ||||||||
\(777\) | 3.10093 | 0.111245 | ||||||||
\(778\) | −26.3963 | −0.946353 | ||||||||
\(779\) | 1.40167 | 0.0502202 | ||||||||
\(780\) | −0.857932 | −0.0307189 | ||||||||
\(781\) | −8.48052 | −0.303457 | ||||||||
\(782\) | 15.3713 | 0.549677 | ||||||||
\(783\) | 1.93227 | 0.0690537 | ||||||||
\(784\) | −3.20785 | −0.114566 | ||||||||
\(785\) | −9.42082 | −0.336243 | ||||||||
\(786\) | −13.4022 | −0.478041 | ||||||||
\(787\) | −34.3816 | −1.22557 | −0.612785 | − | 0.790250i | \(-0.709951\pi\) | ||||
−0.612785 | + | 0.790250i | \(0.709951\pi\) | |||||||
\(788\) | −3.80192 | −0.135438 | ||||||||
\(789\) | 2.82742 | 0.100659 | ||||||||
\(790\) | 5.12723 | 0.182419 | ||||||||
\(791\) | 2.71733 | 0.0966171 | ||||||||
\(792\) | 16.3537 | 0.581104 | ||||||||
\(793\) | −34.5823 | −1.22805 | ||||||||
\(794\) | 23.7124 | 0.841521 | ||||||||
\(795\) | −2.11634 | −0.0750589 | ||||||||
\(796\) | −5.75883 | −0.204116 | ||||||||
\(797\) | −17.5399 | −0.621294 | −0.310647 | − | 0.950525i | \(-0.600546\pi\) | ||||
−0.310647 | + | 0.950525i | \(0.600546\pi\) | |||||||
\(798\) | −7.41367 | −0.262441 | ||||||||
\(799\) | 20.7326 | 0.733465 | ||||||||
\(800\) | 8.49803 | 0.300451 | ||||||||
\(801\) | −10.2353 | −0.361648 | ||||||||
\(802\) | 33.1225 | 1.16960 | ||||||||
\(803\) | −83.8291 | −2.95826 | ||||||||
\(804\) | −0.00424244 | −0.000149619 0 | ||||||||
\(805\) | −2.20459 | −0.0777014 | ||||||||
\(806\) | −47.1350 | −1.66026 | ||||||||
\(807\) | −19.8290 | −0.698014 | ||||||||
\(808\) | −18.0837 | −0.636181 | ||||||||
\(809\) | −43.3301 | −1.52341 | −0.761703 | − | 0.647926i | \(-0.775637\pi\) | ||||
−0.761703 | + | 0.647926i | \(0.775637\pi\) | |||||||
\(810\) | −0.923650 | −0.0324537 | ||||||||
\(811\) | −14.1553 | −0.497060 | −0.248530 | − | 0.968624i | \(-0.579947\pi\) | ||||
−0.248530 | + | 0.968624i | \(0.579947\pi\) | |||||||
\(812\) | −0.654484 | −0.0229679 | ||||||||
\(813\) | 22.0669 | 0.773918 | ||||||||
\(814\) | −21.6836 | −0.760010 | ||||||||
\(815\) | −11.1083 | −0.389105 | ||||||||
\(816\) | −12.4354 | −0.435327 | ||||||||
\(817\) | 49.8827 | 1.74518 | ||||||||
\(818\) | 0.887527 | 0.0310316 | ||||||||
\(819\) | 3.53458 | 0.123508 | ||||||||
\(820\) | −0.0591496 | −0.00206559 | ||||||||
\(821\) | −31.7951 | −1.10966 | −0.554829 | − | 0.831965i | \(-0.687216\pi\) | ||||
−0.554829 | + | 0.831965i | \(0.687216\pi\) | |||||||
\(822\) | −5.06122 | −0.176530 | ||||||||
\(823\) | 11.2600 | 0.392499 | 0.196250 | − | 0.980554i | \(-0.437124\pi\) | ||||
0.196250 | + | 0.980554i | \(0.437124\pi\) | |||||||
\(824\) | −42.3306 | −1.47466 | ||||||||
\(825\) | −24.3400 | −0.847411 | ||||||||
\(826\) | 8.29230 | 0.288526 | ||||||||
\(827\) | 4.18435 | 0.145504 | 0.0727521 | − | 0.997350i | \(-0.476822\pi\) | ||||
0.0727521 | + | 0.997350i | \(0.476822\pi\) | |||||||
\(828\) | 1.04201 | 0.0362124 | ||||||||
\(829\) | 20.3502 | 0.706791 | 0.353395 | − | 0.935474i | \(-0.385027\pi\) | ||||
0.353395 | + | 0.935474i | \(0.385027\pi\) | |||||||
\(830\) | −11.6724 | −0.405154 | ||||||||
\(831\) | 6.98114 | 0.242173 | ||||||||
\(832\) | 31.3060 | 1.08534 | ||||||||
\(833\) | 3.87656 | 0.134315 | ||||||||
\(834\) | 19.1965 | 0.664720 | ||||||||
\(835\) | 4.36028 | 0.150894 | ||||||||
\(836\) | −10.5696 | −0.365557 | ||||||||
\(837\) | 10.3463 | 0.357619 | ||||||||
\(838\) | 4.72416 | 0.163193 | ||||||||
\(839\) | 16.5287 | 0.570634 | 0.285317 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285317 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(840\) | 2.16015 | 0.0745323 | ||||||||
\(841\) | −25.2663 | −0.871253 | ||||||||
\(842\) | 17.5856 | 0.606041 | ||||||||
\(843\) | 26.5918 | 0.915869 | ||||||||
\(844\) | −3.79902 | −0.130768 | ||||||||
\(845\) | −0.363162 | −0.0124931 | ||||||||
\(846\) | −6.89333 | −0.236997 | ||||||||
\(847\) | 18.4330 | 0.633364 | ||||||||
\(848\) | 9.47360 | 0.325325 | ||||||||
\(849\) | 15.2797 | 0.524400 | ||||||||
\(850\) | 22.4168 | 0.768889 | ||||||||
\(851\) | −9.53968 | −0.327016 | ||||||||
\(852\) | 0.529464 | 0.0181391 | ||||||||
\(853\) | −20.1898 | −0.691286 | −0.345643 | − | 0.938366i | \(-0.612339\pi\) | ||||
−0.345643 | + | 0.938366i | \(0.612339\pi\) | |||||||
\(854\) | 12.6107 | 0.431529 | ||||||||
\(855\) | 4.12189 | 0.140966 | ||||||||
\(856\) | −60.5144 | −2.06834 | ||||||||
\(857\) | 42.9661 | 1.46769 | 0.733847 | − | 0.679315i | \(-0.237723\pi\) | ||||
0.733847 | + | 0.679315i | \(0.237723\pi\) | |||||||
\(858\) | −24.7159 | −0.843787 | ||||||||
\(859\) | −31.6244 | −1.07901 | −0.539505 | − | 0.841983i | \(-0.681388\pi\) | ||||
−0.539505 | + | 0.841983i | \(0.681388\pi\) | |||||||
\(860\) | −2.10501 | −0.0717804 | ||||||||
\(861\) | 0.243689 | 0.00830490 | ||||||||
\(862\) | 5.47919 | 0.186622 | ||||||||
\(863\) | −22.8383 | −0.777424 | −0.388712 | − | 0.921359i | \(-0.627080\pi\) | ||||
−0.388712 | + | 0.921359i | \(0.627080\pi\) | |||||||
\(864\) | −1.89415 | −0.0644403 | ||||||||
\(865\) | −7.10862 | −0.241700 | ||||||||
\(866\) | 47.1987 | 1.60388 | ||||||||
\(867\) | −1.97228 | −0.0669820 | ||||||||
\(868\) | −3.50441 | −0.118947 | ||||||||
\(869\) | −30.1157 | −1.02160 | ||||||||
\(870\) | −1.78474 | −0.0605084 | ||||||||
\(871\) | 0.0442713 | 0.00150007 | ||||||||
\(872\) | −17.0260 | −0.576572 | ||||||||
\(873\) | −18.5407 | −0.627506 | ||||||||
\(874\) | 22.8074 | 0.771471 | ||||||||
\(875\) | −6.79813 | −0.229819 | ||||||||
\(876\) | 5.23370 | 0.176830 | ||||||||
\(877\) | 6.92005 | 0.233673 | 0.116837 | − | 0.993151i | \(-0.462725\pi\) | ||||
0.116837 | + | 0.993151i | \(0.462725\pi\) | |||||||
\(878\) | −9.36262 | −0.315973 | ||||||||
\(879\) | 25.8528 | 0.871993 | ||||||||
\(880\) | −12.4714 | −0.420411 | ||||||||
\(881\) | −6.28431 | −0.211724 | −0.105862 | − | 0.994381i | \(-0.533760\pi\) | ||||
−0.105862 | + | 0.994381i | \(0.533760\pi\) | |||||||
\(882\) | −1.28891 | −0.0433998 | ||||||||
\(883\) | −34.4540 | −1.15947 | −0.579735 | − | 0.814805i | \(-0.696844\pi\) | ||||
−0.579735 | + | 0.814805i | \(0.696844\pi\) | |||||||
\(884\) | −4.64103 | −0.156095 | ||||||||
\(885\) | −4.61039 | −0.154977 | ||||||||
\(886\) | −42.4424 | −1.42588 | ||||||||
\(887\) | −21.0920 | −0.708200 | −0.354100 | − | 0.935208i | \(-0.615213\pi\) | ||||
−0.354100 | + | 0.935208i | \(0.615213\pi\) | |||||||
\(888\) | 9.34741 | 0.313678 | ||||||||
\(889\) | 0.0339105 | 0.00113732 | ||||||||
\(890\) | 9.45387 | 0.316894 | ||||||||
\(891\) | 5.42521 | 0.181752 | ||||||||
\(892\) | 9.57244 | 0.320509 | ||||||||
\(893\) | 30.7622 | 1.02942 | ||||||||
\(894\) | −25.7452 | −0.861049 | ||||||||
\(895\) | 3.49716 | 0.116897 | ||||||||
\(896\) | −7.62768 | −0.254823 | ||||||||
\(897\) | −10.8737 | −0.363064 | ||||||||
\(898\) | 11.8536 | 0.395561 | ||||||||
\(899\) | 19.9918 | 0.666763 | ||||||||
\(900\) | 1.51962 | 0.0506540 | ||||||||
\(901\) | −11.4485 | −0.381404 | ||||||||
\(902\) | −1.70402 | −0.0567378 | ||||||||
\(903\) | 8.67240 | 0.288599 | ||||||||
\(904\) | 8.19108 | 0.272431 | ||||||||
\(905\) | −2.46081 | −0.0818000 | ||||||||
\(906\) | −10.0539 | −0.334019 | ||||||||
\(907\) | −53.5819 | −1.77916 | −0.889580 | − | 0.456780i | \(-0.849003\pi\) | ||||
−0.889580 | + | 0.456780i | \(0.849003\pi\) | |||||||
\(908\) | −5.04580 | −0.167451 | ||||||||
\(909\) | −5.99911 | −0.198978 | ||||||||
\(910\) | −3.26471 | −0.108224 | ||||||||
\(911\) | 36.9670 | 1.22477 | 0.612386 | − | 0.790559i | \(-0.290210\pi\) | ||||
0.612386 | + | 0.790559i | \(0.290210\pi\) | |||||||
\(912\) | −18.4512 | −0.610981 | ||||||||
\(913\) | 68.5598 | 2.26900 | ||||||||
\(914\) | 18.0164 | 0.595930 | ||||||||
\(915\) | −7.01134 | −0.231788 | ||||||||
\(916\) | 6.66343 | 0.220166 | ||||||||
\(917\) | 10.3981 | 0.343376 | ||||||||
\(918\) | −4.99654 | −0.164910 | ||||||||
\(919\) | 21.1835 | 0.698778 | 0.349389 | − | 0.936978i | \(-0.386389\pi\) | ||||
0.349389 | + | 0.936978i | \(0.386389\pi\) | |||||||
\(920\) | −6.64548 | −0.219095 | ||||||||
\(921\) | −23.8691 | −0.786512 | ||||||||
\(922\) | −49.6085 | −1.63377 | ||||||||
\(923\) | −5.52513 | −0.181862 | ||||||||
\(924\) | −1.83759 | −0.0604522 | ||||||||
\(925\) | −13.9122 | −0.457431 | ||||||||
\(926\) | −24.4976 | −0.805040 | ||||||||
\(927\) | −14.0429 | −0.461228 | ||||||||
\(928\) | −3.66001 | −0.120146 | ||||||||
\(929\) | −31.1858 | −1.02317 | −0.511586 | − | 0.859232i | \(-0.670942\pi\) | ||||
−0.511586 | + | 0.859232i | \(0.670942\pi\) | |||||||
\(930\) | −9.55632 | −0.313364 | ||||||||
\(931\) | 5.75190 | 0.188511 | ||||||||
\(932\) | 1.80471 | 0.0591153 | ||||||||
\(933\) | −13.5790 | −0.444557 | ||||||||
\(934\) | 32.4874 | 1.06302 | ||||||||
\(935\) | 15.0712 | 0.492882 | ||||||||
\(936\) | 10.6546 | 0.348256 | ||||||||
\(937\) | 28.4722 | 0.930145 | 0.465072 | − | 0.885273i | \(-0.346028\pi\) | ||||
0.465072 | + | 0.885273i | \(0.346028\pi\) | |||||||
\(938\) | −0.0161439 | −0.000527115 0 | ||||||||
\(939\) | 16.4100 | 0.535519 | ||||||||
\(940\) | −1.29814 | −0.0423407 | ||||||||
\(941\) | −34.2874 | −1.11774 | −0.558868 | − | 0.829257i | \(-0.688764\pi\) | ||||
−0.558868 | + | 0.829257i | \(0.688764\pi\) | |||||||
\(942\) | 16.9444 | 0.552078 | ||||||||
\(943\) | −0.749684 | −0.0244131 | ||||||||
\(944\) | 20.6380 | 0.671708 | ||||||||
\(945\) | 0.716613 | 0.0233114 | ||||||||
\(946\) | −60.6427 | −1.97166 | ||||||||
\(947\) | −53.9405 | −1.75283 | −0.876415 | − | 0.481557i | \(-0.840071\pi\) | ||||
−0.876415 | + | 0.481557i | \(0.840071\pi\) | |||||||
\(948\) | 1.88021 | 0.0610664 | ||||||||
\(949\) | −54.6154 | −1.77289 | ||||||||
\(950\) | 33.2612 | 1.07914 | ||||||||
\(951\) | 6.08345 | 0.197270 | ||||||||
\(952\) | 11.6855 | 0.378728 | ||||||||
\(953\) | 10.4268 | 0.337756 | 0.168878 | − | 0.985637i | \(-0.445986\pi\) | ||||
0.168878 | + | 0.985637i | \(0.445986\pi\) | |||||||
\(954\) | 3.80648 | 0.123239 | ||||||||
\(955\) | 0.716613 | 0.0231891 | ||||||||
\(956\) | 1.11089 | 0.0359289 | ||||||||
\(957\) | 10.4830 | 0.338867 | ||||||||
\(958\) | 6.70992 | 0.216788 | ||||||||
\(959\) | 3.92674 | 0.126801 | ||||||||
\(960\) | 6.34711 | 0.204852 | ||||||||
\(961\) | 76.0451 | 2.45307 | ||||||||
\(962\) | −14.1271 | −0.455475 | ||||||||
\(963\) | −20.0752 | −0.646913 | ||||||||
\(964\) | −3.99186 | −0.128569 | ||||||||
\(965\) | −6.84531 | −0.220358 | ||||||||
\(966\) | 3.96519 | 0.127578 | ||||||||
\(967\) | −24.5004 | −0.787881 | −0.393940 | − | 0.919136i | \(-0.628888\pi\) | ||||
−0.393940 | + | 0.919136i | \(0.628888\pi\) | |||||||
\(968\) | 55.5641 | 1.78590 | ||||||||
\(969\) | 22.2976 | 0.716301 | ||||||||
\(970\) | 17.1251 | 0.549853 | ||||||||
\(971\) | 25.9523 | 0.832848 | 0.416424 | − | 0.909170i | \(-0.363283\pi\) | ||||
0.416424 | + | 0.909170i | \(0.363283\pi\) | |||||||
\(972\) | −0.338712 | −0.0108642 | ||||||||
\(973\) | −14.8936 | −0.477467 | ||||||||
\(974\) | 15.1206 | 0.484495 | ||||||||
\(975\) | −15.8578 | −0.507854 | ||||||||
\(976\) | 31.3856 | 1.00463 | ||||||||
\(977\) | 20.8782 | 0.667951 | 0.333976 | − | 0.942582i | \(-0.391610\pi\) | ||||
0.333976 | + | 0.942582i | \(0.391610\pi\) | |||||||
\(978\) | 19.9795 | 0.638872 | ||||||||
\(979\) | −55.5289 | −1.77471 | ||||||||
\(980\) | −0.242726 | −0.00775359 | ||||||||
\(981\) | −5.64824 | −0.180334 | ||||||||
\(982\) | −50.4699 | −1.61056 | ||||||||
\(983\) | 32.5924 | 1.03954 | 0.519768 | − | 0.854308i | \(-0.326019\pi\) | ||||
0.519768 | + | 0.854308i | \(0.326019\pi\) | |||||||
\(984\) | 0.734574 | 0.0234174 | ||||||||
\(985\) | 8.04372 | 0.256294 | ||||||||
\(986\) | −9.65466 | −0.307467 | ||||||||
\(987\) | 5.34819 | 0.170235 | ||||||||
\(988\) | −6.88619 | −0.219079 | ||||||||
\(989\) | −26.6797 | −0.848366 | ||||||||
\(990\) | −5.01100 | −0.159260 | ||||||||
\(991\) | −30.6977 | −0.975144 | −0.487572 | − | 0.873083i | \(-0.662117\pi\) | ||||
−0.487572 | + | 0.873083i | \(0.662117\pi\) | |||||||
\(992\) | −19.5974 | −0.622217 | ||||||||
\(993\) | −22.8441 | −0.724937 | ||||||||
\(994\) | 2.01478 | 0.0639050 | ||||||||
\(995\) | 12.1840 | 0.386257 | ||||||||
\(996\) | −4.28039 | −0.135629 | ||||||||
\(997\) | −2.51877 | −0.0797702 | −0.0398851 | − | 0.999204i | \(-0.512699\pi\) | ||||
−0.0398851 | + | 0.999204i | \(0.512699\pi\) | |||||||
\(998\) | 44.4658 | 1.40754 | ||||||||
\(999\) | 3.10093 | 0.0981091 |
(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 | 4011.2.a.k.1.7 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.k.1.7 | ✓ | 27 | 1.1 | even | 1 | trivial |