Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6029,2,Mod(1,6029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6029 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1418073786\) |
Analytic rank: | \(0\) |
Dimension: | \(268\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50934 | −1.77437 | −0.887186 | − | 0.461412i | \(-0.847343\pi\) | ||||
−0.887186 | + | 0.461412i | \(0.847343\pi\) | |||||||
\(3\) | −1.29295 | −0.746484 | −0.373242 | − | 0.927734i | \(-0.621754\pi\) | ||||
−0.373242 | + | 0.927734i | \(0.621754\pi\) | |||||||
\(4\) | 4.29679 | 2.14840 | ||||||||
\(5\) | −2.86314 | −1.28044 | −0.640218 | − | 0.768194i | \(-0.721156\pi\) | ||||
−0.640218 | + | 0.768194i | \(0.721156\pi\) | |||||||
\(6\) | 3.24445 | 1.32454 | ||||||||
\(7\) | 3.23051 | 1.22102 | 0.610508 | − | 0.792010i | \(-0.290965\pi\) | ||||
0.610508 | + | 0.792010i | \(0.290965\pi\) | |||||||
\(8\) | −5.76344 | −2.03768 | ||||||||
\(9\) | −1.32829 | −0.442762 | ||||||||
\(10\) | 7.18460 | 2.27197 | ||||||||
\(11\) | −0.163813 | −0.0493915 | −0.0246957 | − | 0.999695i | \(-0.507862\pi\) | ||||
−0.0246957 | + | 0.999695i | \(0.507862\pi\) | |||||||
\(12\) | −5.55553 | −1.60374 | ||||||||
\(13\) | −3.11485 | −0.863905 | −0.431952 | − | 0.901896i | \(-0.642175\pi\) | ||||
−0.431952 | + | 0.901896i | \(0.642175\pi\) | |||||||
\(14\) | −8.10644 | −2.16654 | ||||||||
\(15\) | 3.70189 | 0.955824 | ||||||||
\(16\) | 5.86886 | 1.46721 | ||||||||
\(17\) | −0.924070 | −0.224120 | −0.112060 | − | 0.993701i | \(-0.535745\pi\) | ||||
−0.112060 | + | 0.993701i | \(0.535745\pi\) | |||||||
\(18\) | 3.33312 | 0.785625 | ||||||||
\(19\) | −0.559171 | −0.128283 | −0.0641413 | − | 0.997941i | \(-0.520431\pi\) | ||||
−0.0641413 | + | 0.997941i | \(0.520431\pi\) | |||||||
\(20\) | −12.3023 | −2.75088 | ||||||||
\(21\) | −4.17688 | −0.911469 | ||||||||
\(22\) | 0.411063 | 0.0876389 | ||||||||
\(23\) | −3.51087 | −0.732067 | −0.366033 | − | 0.930602i | \(-0.619284\pi\) | ||||
−0.366033 | + | 0.930602i | \(0.619284\pi\) | |||||||
\(24\) | 7.45183 | 1.52110 | ||||||||
\(25\) | 3.19757 | 0.639515 | ||||||||
\(26\) | 7.81623 | 1.53289 | ||||||||
\(27\) | 5.59625 | 1.07700 | ||||||||
\(28\) | 13.8808 | 2.62323 | ||||||||
\(29\) | −7.35734 | −1.36622 | −0.683112 | − | 0.730314i | \(-0.739374\pi\) | ||||
−0.683112 | + | 0.730314i | \(0.739374\pi\) | |||||||
\(30\) | −9.28931 | −1.69599 | ||||||||
\(31\) | −11.0585 | −1.98617 | −0.993084 | − | 0.117405i | \(-0.962542\pi\) | ||||
−0.993084 | + | 0.117405i | \(0.962542\pi\) | |||||||
\(32\) | −3.20008 | −0.565699 | ||||||||
\(33\) | 0.211802 | 0.0368699 | ||||||||
\(34\) | 2.31881 | 0.397672 | ||||||||
\(35\) | −9.24939 | −1.56343 | ||||||||
\(36\) | −5.70737 | −0.951229 | ||||||||
\(37\) | −0.273151 | −0.0449057 | −0.0224528 | − | 0.999748i | \(-0.507148\pi\) | ||||
−0.0224528 | + | 0.999748i | \(0.507148\pi\) | |||||||
\(38\) | 1.40315 | 0.227621 | ||||||||
\(39\) | 4.02734 | 0.644891 | ||||||||
\(40\) | 16.5015 | 2.60912 | ||||||||
\(41\) | −10.7763 | −1.68297 | −0.841485 | − | 0.540281i | \(-0.818318\pi\) | ||||
−0.841485 | + | 0.540281i | \(0.818318\pi\) | |||||||
\(42\) | 10.4812 | 1.61729 | ||||||||
\(43\) | 9.53331 | 1.45382 | 0.726908 | − | 0.686734i | \(-0.240956\pi\) | ||||
0.726908 | + | 0.686734i | \(0.240956\pi\) | |||||||
\(44\) | −0.703871 | −0.106113 | ||||||||
\(45\) | 3.80307 | 0.566928 | ||||||||
\(46\) | 8.80997 | 1.29896 | ||||||||
\(47\) | 1.48887 | 0.217173 | 0.108587 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108587 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(48\) | −7.58812 | −1.09525 | ||||||||
\(49\) | 3.43617 | 0.490882 | ||||||||
\(50\) | −8.02380 | −1.13474 | ||||||||
\(51\) | 1.19477 | 0.167302 | ||||||||
\(52\) | −13.3839 | −1.85601 | ||||||||
\(53\) | −5.48181 | −0.752984 | −0.376492 | − | 0.926420i | \(-0.622870\pi\) | ||||
−0.376492 | + | 0.926420i | \(0.622870\pi\) | |||||||
\(54\) | −14.0429 | −1.91100 | ||||||||
\(55\) | 0.469020 | 0.0632426 | ||||||||
\(56\) | −18.6188 | −2.48805 | ||||||||
\(57\) | 0.722979 | 0.0957609 | ||||||||
\(58\) | 18.4621 | 2.42419 | ||||||||
\(59\) | −8.16820 | −1.06341 | −0.531704 | − | 0.846930i | \(-0.678448\pi\) | ||||
−0.531704 | + | 0.846930i | \(0.678448\pi\) | |||||||
\(60\) | 15.9063 | 2.05349 | ||||||||
\(61\) | 6.37058 | 0.815669 | 0.407834 | − | 0.913056i | \(-0.366284\pi\) | ||||
0.407834 | + | 0.913056i | \(0.366284\pi\) | |||||||
\(62\) | 27.7496 | 3.52420 | ||||||||
\(63\) | −4.29104 | −0.540620 | ||||||||
\(64\) | −3.70762 | −0.463453 | ||||||||
\(65\) | 8.91826 | 1.10617 | ||||||||
\(66\) | −0.531483 | −0.0654210 | ||||||||
\(67\) | −8.65926 | −1.05790 | −0.528949 | − | 0.848654i | \(-0.677414\pi\) | ||||
−0.528949 | + | 0.848654i | \(0.677414\pi\) | |||||||
\(68\) | −3.97054 | −0.481499 | ||||||||
\(69\) | 4.53937 | 0.546476 | ||||||||
\(70\) | 23.2099 | 2.77411 | ||||||||
\(71\) | 14.0143 | 1.66319 | 0.831597 | − | 0.555379i | \(-0.187427\pi\) | ||||
0.831597 | + | 0.555379i | \(0.187427\pi\) | |||||||
\(72\) | 7.65550 | 0.902209 | ||||||||
\(73\) | −11.0128 | −1.28895 | −0.644477 | − | 0.764624i | \(-0.722925\pi\) | ||||
−0.644477 | + | 0.764624i | \(0.722925\pi\) | |||||||
\(74\) | 0.685428 | 0.0796794 | ||||||||
\(75\) | −4.13430 | −0.477387 | ||||||||
\(76\) | −2.40264 | −0.275602 | ||||||||
\(77\) | −0.529199 | −0.0603078 | ||||||||
\(78\) | −10.1060 | −1.14428 | ||||||||
\(79\) | −2.09210 | −0.235380 | −0.117690 | − | 0.993050i | \(-0.537549\pi\) | ||||
−0.117690 | + | 0.993050i | \(0.537549\pi\) | |||||||
\(80\) | −16.8034 | −1.87867 | ||||||||
\(81\) | −3.25080 | −0.361200 | ||||||||
\(82\) | 27.0413 | 2.98621 | ||||||||
\(83\) | −16.7782 | −1.84164 | −0.920821 | − | 0.389985i | \(-0.872480\pi\) | ||||
−0.920821 | + | 0.389985i | \(0.872480\pi\) | |||||||
\(84\) | −17.9472 | −1.95820 | ||||||||
\(85\) | 2.64574 | 0.286971 | ||||||||
\(86\) | −23.9223 | −2.57961 | ||||||||
\(87\) | 9.51265 | 1.01986 | ||||||||
\(88\) | 0.944127 | 0.100644 | ||||||||
\(89\) | −5.64577 | −0.598450 | −0.299225 | − | 0.954183i | \(-0.596728\pi\) | ||||
−0.299225 | + | 0.954183i | \(0.596728\pi\) | |||||||
\(90\) | −9.54320 | −1.00594 | ||||||||
\(91\) | −10.0626 | −1.05484 | ||||||||
\(92\) | −15.0855 | −1.57277 | ||||||||
\(93\) | 14.2981 | 1.48264 | ||||||||
\(94\) | −3.73607 | −0.385346 | ||||||||
\(95\) | 1.60099 | 0.164258 | ||||||||
\(96\) | 4.13753 | 0.422285 | ||||||||
\(97\) | 13.5714 | 1.37797 | 0.688983 | − | 0.724778i | \(-0.258058\pi\) | ||||
0.688983 | + | 0.724778i | \(0.258058\pi\) | |||||||
\(98\) | −8.62253 | −0.871007 | ||||||||
\(99\) | 0.217591 | 0.0218687 | ||||||||
\(100\) | 13.7393 | 1.37393 | ||||||||
\(101\) | 17.5392 | 1.74521 | 0.872606 | − | 0.488425i | \(-0.162429\pi\) | ||||
0.872606 | + | 0.488425i | \(0.162429\pi\) | |||||||
\(102\) | −2.99810 | −0.296856 | ||||||||
\(103\) | 6.35488 | 0.626165 | 0.313082 | − | 0.949726i | \(-0.398638\pi\) | ||||
0.313082 | + | 0.949726i | \(0.398638\pi\) | |||||||
\(104\) | 17.9523 | 1.76037 | ||||||||
\(105\) | 11.9590 | 1.16708 | ||||||||
\(106\) | 13.7557 | 1.33607 | ||||||||
\(107\) | −3.80198 | −0.367551 | −0.183776 | − | 0.982968i | \(-0.558832\pi\) | ||||
−0.183776 | + | 0.982968i | \(0.558832\pi\) | |||||||
\(108\) | 24.0459 | 2.31382 | ||||||||
\(109\) | 13.6079 | 1.30340 | 0.651699 | − | 0.758478i | \(-0.274057\pi\) | ||||
0.651699 | + | 0.758478i | \(0.274057\pi\) | |||||||
\(110\) | −1.17693 | −0.112216 | ||||||||
\(111\) | 0.353169 | 0.0335214 | ||||||||
\(112\) | 18.9594 | 1.79149 | ||||||||
\(113\) | −7.93592 | −0.746549 | −0.373274 | − | 0.927721i | \(-0.621765\pi\) | ||||
−0.373274 | + | 0.927721i | \(0.621765\pi\) | |||||||
\(114\) | −1.81420 | −0.169916 | ||||||||
\(115\) | 10.0521 | 0.937364 | ||||||||
\(116\) | −31.6130 | −2.93519 | ||||||||
\(117\) | 4.13742 | 0.382504 | ||||||||
\(118\) | 20.4968 | 1.88688 | ||||||||
\(119\) | −2.98522 | −0.273654 | ||||||||
\(120\) | −21.3356 | −1.94767 | ||||||||
\(121\) | −10.9732 | −0.997560 | ||||||||
\(122\) | −15.9859 | −1.44730 | ||||||||
\(123\) | 13.9331 | 1.25631 | ||||||||
\(124\) | −47.5162 | −4.26708 | ||||||||
\(125\) | 5.16060 | 0.461578 | ||||||||
\(126\) | 10.7677 | 0.959261 | ||||||||
\(127\) | −8.44718 | −0.749566 | −0.374783 | − | 0.927113i | \(-0.622283\pi\) | ||||
−0.374783 | + | 0.927113i | \(0.622283\pi\) | |||||||
\(128\) | 15.7038 | 1.38804 | ||||||||
\(129\) | −12.3261 | −1.08525 | ||||||||
\(130\) | −22.3790 | −1.96276 | ||||||||
\(131\) | −14.6381 | −1.27894 | −0.639468 | − | 0.768818i | \(-0.720845\pi\) | ||||
−0.639468 | + | 0.768818i | \(0.720845\pi\) | |||||||
\(132\) | 0.910068 | 0.0792113 | ||||||||
\(133\) | −1.80641 | −0.156635 | ||||||||
\(134\) | 21.7290 | 1.87710 | ||||||||
\(135\) | −16.0228 | −1.37903 | ||||||||
\(136\) | 5.32583 | 0.456686 | ||||||||
\(137\) | −9.15192 | −0.781902 | −0.390951 | − | 0.920412i | \(-0.627854\pi\) | ||||
−0.390951 | + | 0.920412i | \(0.627854\pi\) | |||||||
\(138\) | −11.3908 | −0.969652 | ||||||||
\(139\) | 9.47319 | 0.803505 | 0.401753 | − | 0.915748i | \(-0.368401\pi\) | ||||
0.401753 | + | 0.915748i | \(0.368401\pi\) | |||||||
\(140\) | −39.7427 | −3.35888 | ||||||||
\(141\) | −1.92502 | −0.162116 | ||||||||
\(142\) | −35.1667 | −2.95113 | ||||||||
\(143\) | 0.510254 | 0.0426695 | ||||||||
\(144\) | −7.79552 | −0.649627 | ||||||||
\(145\) | 21.0651 | 1.74936 | ||||||||
\(146\) | 27.6349 | 2.28708 | ||||||||
\(147\) | −4.44279 | −0.366435 | ||||||||
\(148\) | −1.17367 | −0.0964752 | ||||||||
\(149\) | −15.3365 | −1.25641 | −0.628207 | − | 0.778046i | \(-0.716211\pi\) | ||||
−0.628207 | + | 0.778046i | \(0.716211\pi\) | |||||||
\(150\) | 10.3744 | 0.847063 | ||||||||
\(151\) | 21.6345 | 1.76059 | 0.880295 | − | 0.474427i | \(-0.157345\pi\) | ||||
0.880295 | + | 0.474427i | \(0.157345\pi\) | |||||||
\(152\) | 3.22275 | 0.261400 | ||||||||
\(153\) | 1.22743 | 0.0992318 | ||||||||
\(154\) | 1.32794 | 0.107009 | ||||||||
\(155\) | 31.6621 | 2.54316 | ||||||||
\(156\) | 17.3047 | 1.38548 | ||||||||
\(157\) | −13.3892 | −1.06858 | −0.534289 | − | 0.845302i | \(-0.679421\pi\) | ||||
−0.534289 | + | 0.845302i | \(0.679421\pi\) | |||||||
\(158\) | 5.24980 | 0.417651 | ||||||||
\(159\) | 7.08769 | 0.562090 | ||||||||
\(160\) | 9.16228 | 0.724341 | ||||||||
\(161\) | −11.3419 | −0.893866 | ||||||||
\(162\) | 8.15736 | 0.640903 | ||||||||
\(163\) | −22.5243 | −1.76424 | −0.882119 | − | 0.471027i | \(-0.843883\pi\) | ||||
−0.882119 | + | 0.471027i | \(0.843883\pi\) | |||||||
\(164\) | −46.3034 | −3.61569 | ||||||||
\(165\) | −0.606418 | −0.0472096 | ||||||||
\(166\) | 42.1021 | 3.26776 | ||||||||
\(167\) | −9.81058 | −0.759165 | −0.379583 | − | 0.925158i | \(-0.623932\pi\) | ||||
−0.379583 | + | 0.925158i | \(0.623932\pi\) | |||||||
\(168\) | 24.0732 | 1.85729 | ||||||||
\(169\) | −3.29769 | −0.253669 | ||||||||
\(170\) | −6.63907 | −0.509194 | ||||||||
\(171\) | 0.742739 | 0.0567987 | ||||||||
\(172\) | 40.9627 | 3.12338 | ||||||||
\(173\) | 12.6620 | 0.962672 | 0.481336 | − | 0.876536i | \(-0.340152\pi\) | ||||
0.481336 | + | 0.876536i | \(0.340152\pi\) | |||||||
\(174\) | −23.8705 | −1.80962 | ||||||||
\(175\) | 10.3298 | 0.780858 | ||||||||
\(176\) | −0.961395 | −0.0724679 | ||||||||
\(177\) | 10.5611 | 0.793817 | ||||||||
\(178\) | 14.1672 | 1.06187 | ||||||||
\(179\) | −6.07771 | −0.454269 | −0.227135 | − | 0.973863i | \(-0.572936\pi\) | ||||
−0.227135 | + | 0.973863i | \(0.572936\pi\) | |||||||
\(180\) | 16.3410 | 1.21799 | ||||||||
\(181\) | 15.1049 | 1.12274 | 0.561371 | − | 0.827564i | \(-0.310274\pi\) | ||||
0.561371 | + | 0.827564i | \(0.310274\pi\) | |||||||
\(182\) | 25.2504 | 1.87168 | ||||||||
\(183\) | −8.23682 | −0.608883 | ||||||||
\(184\) | 20.2347 | 1.49172 | ||||||||
\(185\) | 0.782068 | 0.0574988 | ||||||||
\(186\) | −35.8788 | −2.63076 | ||||||||
\(187\) | 0.151375 | 0.0110696 | ||||||||
\(188\) | 6.39735 | 0.466575 | ||||||||
\(189\) | 18.0787 | 1.31503 | ||||||||
\(190\) | −4.01742 | −0.291454 | ||||||||
\(191\) | −1.64721 | −0.119188 | −0.0595939 | − | 0.998223i | \(-0.518981\pi\) | ||||
−0.0595939 | + | 0.998223i | \(0.518981\pi\) | |||||||
\(192\) | 4.79376 | 0.345960 | ||||||||
\(193\) | −14.7815 | −1.06400 | −0.531999 | − | 0.846745i | \(-0.678559\pi\) | ||||
−0.531999 | + | 0.846745i | \(0.678559\pi\) | |||||||
\(194\) | −34.0552 | −2.44502 | ||||||||
\(195\) | −11.5308 | −0.825741 | ||||||||
\(196\) | 14.7645 | 1.05461 | ||||||||
\(197\) | −14.1902 | −1.01101 | −0.505505 | − | 0.862824i | \(-0.668694\pi\) | ||||
−0.505505 | + | 0.862824i | \(0.668694\pi\) | |||||||
\(198\) | −0.546009 | −0.0388032 | ||||||||
\(199\) | 4.04594 | 0.286809 | 0.143405 | − | 0.989664i | \(-0.454195\pi\) | ||||
0.143405 | + | 0.989664i | \(0.454195\pi\) | |||||||
\(200\) | −18.4290 | −1.30313 | ||||||||
\(201\) | 11.1960 | 0.789703 | ||||||||
\(202\) | −44.0117 | −3.09665 | ||||||||
\(203\) | −23.7679 | −1.66818 | ||||||||
\(204\) | 5.13370 | 0.359431 | ||||||||
\(205\) | 30.8539 | 2.15493 | ||||||||
\(206\) | −15.9466 | −1.11105 | ||||||||
\(207\) | 4.66344 | 0.324131 | ||||||||
\(208\) | −18.2806 | −1.26753 | ||||||||
\(209\) | 0.0915995 | 0.00633607 | ||||||||
\(210\) | −30.0092 | −2.07083 | ||||||||
\(211\) | −15.8689 | −1.09246 | −0.546229 | − | 0.837636i | \(-0.683937\pi\) | ||||
−0.546229 | + | 0.837636i | \(0.683937\pi\) | |||||||
\(212\) | −23.5542 | −1.61771 | ||||||||
\(213\) | −18.1198 | −1.24155 | ||||||||
\(214\) | 9.54047 | 0.652173 | ||||||||
\(215\) | −27.2952 | −1.86152 | ||||||||
\(216\) | −32.2537 | −2.19458 | ||||||||
\(217\) | −35.7246 | −2.42514 | ||||||||
\(218\) | −34.1468 | −2.31271 | ||||||||
\(219\) | 14.2390 | 0.962183 | ||||||||
\(220\) | 2.01528 | 0.135870 | ||||||||
\(221\) | 2.87834 | 0.193618 | ||||||||
\(222\) | −0.886223 | −0.0594794 | ||||||||
\(223\) | −23.2475 | −1.55677 | −0.778384 | − | 0.627789i | \(-0.783960\pi\) | ||||
−0.778384 | + | 0.627789i | \(0.783960\pi\) | |||||||
\(224\) | −10.3379 | −0.690728 | ||||||||
\(225\) | −4.24729 | −0.283153 | ||||||||
\(226\) | 19.9139 | 1.32466 | ||||||||
\(227\) | 6.21833 | 0.412725 | 0.206363 | − | 0.978476i | \(-0.433837\pi\) | ||||
0.206363 | + | 0.978476i | \(0.433837\pi\) | |||||||
\(228\) | 3.10649 | 0.205733 | ||||||||
\(229\) | 5.31004 | 0.350897 | 0.175449 | − | 0.984489i | \(-0.443862\pi\) | ||||
0.175449 | + | 0.984489i | \(0.443862\pi\) | |||||||
\(230\) | −25.2242 | −1.66323 | ||||||||
\(231\) | 0.684227 | 0.0450188 | ||||||||
\(232\) | 42.4036 | 2.78393 | ||||||||
\(233\) | −8.31997 | −0.545059 | −0.272530 | − | 0.962147i | \(-0.587860\pi\) | ||||
−0.272530 | + | 0.962147i | \(0.587860\pi\) | |||||||
\(234\) | −10.3822 | −0.678705 | ||||||||
\(235\) | −4.26283 | −0.278076 | ||||||||
\(236\) | −35.0971 | −2.28462 | ||||||||
\(237\) | 2.70498 | 0.175707 | ||||||||
\(238\) | 7.49092 | 0.485565 | ||||||||
\(239\) | 5.99454 | 0.387755 | 0.193877 | − | 0.981026i | \(-0.437894\pi\) | ||||
0.193877 | + | 0.981026i | \(0.437894\pi\) | |||||||
\(240\) | 21.7259 | 1.40240 | ||||||||
\(241\) | 2.78214 | 0.179213 | 0.0896067 | − | 0.995977i | \(-0.471439\pi\) | ||||
0.0896067 | + | 0.995977i | \(0.471439\pi\) | |||||||
\(242\) | 27.5354 | 1.77004 | ||||||||
\(243\) | −12.5856 | −0.807369 | ||||||||
\(244\) | 27.3731 | 1.75238 | ||||||||
\(245\) | −9.83824 | −0.628542 | ||||||||
\(246\) | −34.9630 | −2.22916 | ||||||||
\(247\) | 1.74174 | 0.110824 | ||||||||
\(248\) | 63.7351 | 4.04718 | ||||||||
\(249\) | 21.6933 | 1.37476 | ||||||||
\(250\) | −12.9497 | −0.819011 | ||||||||
\(251\) | 3.62912 | 0.229068 | 0.114534 | − | 0.993419i | \(-0.463463\pi\) | ||||
0.114534 | + | 0.993419i | \(0.463463\pi\) | |||||||
\(252\) | −18.4377 | −1.16147 | ||||||||
\(253\) | 0.575126 | 0.0361579 | ||||||||
\(254\) | 21.1968 | 1.33001 | ||||||||
\(255\) | −3.42081 | −0.214219 | ||||||||
\(256\) | −31.9911 | −1.99944 | ||||||||
\(257\) | 10.7342 | 0.669578 | 0.334789 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334789 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(258\) | 30.9303 | 1.92564 | ||||||||
\(259\) | −0.882415 | −0.0548306 | ||||||||
\(260\) | 38.3199 | 2.37650 | ||||||||
\(261\) | 9.77265 | 0.604912 | ||||||||
\(262\) | 36.7320 | 2.26931 | ||||||||
\(263\) | −19.7144 | −1.21564 | −0.607821 | − | 0.794074i | \(-0.707956\pi\) | ||||
−0.607821 | + | 0.794074i | \(0.707956\pi\) | |||||||
\(264\) | −1.22071 | −0.0751293 | ||||||||
\(265\) | 15.6952 | 0.964148 | ||||||||
\(266\) | 4.53289 | 0.277929 | ||||||||
\(267\) | 7.29968 | 0.446733 | ||||||||
\(268\) | −37.2071 | −2.27278 | ||||||||
\(269\) | 10.0446 | 0.612433 | 0.306216 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306216 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(270\) | 40.2068 | 2.44691 | ||||||||
\(271\) | −3.09015 | −0.187713 | −0.0938567 | − | 0.995586i | \(-0.529920\pi\) | ||||
−0.0938567 | + | 0.995586i | \(0.529920\pi\) | |||||||
\(272\) | −5.42324 | −0.328832 | ||||||||
\(273\) | 13.0104 | 0.787423 | ||||||||
\(274\) | 22.9653 | 1.38738 | ||||||||
\(275\) | −0.523804 | −0.0315866 | ||||||||
\(276\) | 19.5047 | 1.17405 | ||||||||
\(277\) | −24.6192 | −1.47923 | −0.739613 | − | 0.673032i | \(-0.764992\pi\) | ||||
−0.739613 | + | 0.673032i | \(0.764992\pi\) | |||||||
\(278\) | −23.7715 | −1.42572 | ||||||||
\(279\) | 14.6889 | 0.879400 | ||||||||
\(280\) | 53.3084 | 3.18578 | ||||||||
\(281\) | 14.0358 | 0.837308 | 0.418654 | − | 0.908146i | \(-0.362502\pi\) | ||||
0.418654 | + | 0.908146i | \(0.362502\pi\) | |||||||
\(282\) | 4.83054 | 0.287655 | ||||||||
\(283\) | −27.4258 | −1.63030 | −0.815149 | − | 0.579252i | \(-0.803345\pi\) | ||||
−0.815149 | + | 0.579252i | \(0.803345\pi\) | |||||||
\(284\) | 60.2167 | 3.57320 | ||||||||
\(285\) | −2.06999 | −0.122616 | ||||||||
\(286\) | −1.28040 | −0.0757117 | ||||||||
\(287\) | −34.8128 | −2.05493 | ||||||||
\(288\) | 4.25062 | 0.250470 | ||||||||
\(289\) | −16.1461 | −0.949770 | ||||||||
\(290\) | −52.8595 | −3.10402 | ||||||||
\(291\) | −17.5471 | −1.02863 | ||||||||
\(292\) | −47.3199 | −2.76919 | ||||||||
\(293\) | 12.5035 | 0.730459 | 0.365230 | − | 0.930917i | \(-0.380990\pi\) | ||||
0.365230 | + | 0.930917i | \(0.380990\pi\) | |||||||
\(294\) | 11.1485 | 0.650193 | ||||||||
\(295\) | 23.3867 | 1.36163 | ||||||||
\(296\) | 1.57429 | 0.0915036 | ||||||||
\(297\) | −0.916738 | −0.0531946 | ||||||||
\(298\) | 38.4845 | 2.22935 | ||||||||
\(299\) | 10.9358 | 0.632436 | ||||||||
\(300\) | −17.7642 | −1.02562 | ||||||||
\(301\) | 30.7974 | 1.77513 | ||||||||
\(302\) | −54.2883 | −3.12394 | ||||||||
\(303\) | −22.6772 | −1.30277 | ||||||||
\(304\) | −3.28169 | −0.188218 | ||||||||
\(305\) | −18.2399 | −1.04441 | ||||||||
\(306\) | −3.08004 | −0.176074 | ||||||||
\(307\) | 3.30503 | 0.188628 | 0.0943139 | − | 0.995543i | \(-0.469934\pi\) | ||||
0.0943139 | + | 0.995543i | \(0.469934\pi\) | |||||||
\(308\) | −2.27386 | −0.129565 | ||||||||
\(309\) | −8.21652 | −0.467422 | ||||||||
\(310\) | −79.4510 | −4.51251 | ||||||||
\(311\) | 15.0199 | 0.851703 | 0.425852 | − | 0.904793i | \(-0.359975\pi\) | ||||
0.425852 | + | 0.904793i | \(0.359975\pi\) | |||||||
\(312\) | −23.2114 | −1.31408 | ||||||||
\(313\) | 10.3320 | 0.584000 | 0.292000 | − | 0.956418i | \(-0.405679\pi\) | ||||
0.292000 | + | 0.956418i | \(0.405679\pi\) | |||||||
\(314\) | 33.5982 | 1.89605 | ||||||||
\(315\) | 12.2858 | 0.692229 | ||||||||
\(316\) | −8.98933 | −0.505689 | ||||||||
\(317\) | −5.24391 | −0.294527 | −0.147264 | − | 0.989097i | \(-0.547047\pi\) | ||||
−0.147264 | + | 0.989097i | \(0.547047\pi\) | |||||||
\(318\) | −17.7854 | −0.997358 | ||||||||
\(319\) | 1.20523 | 0.0674798 | ||||||||
\(320\) | 10.6154 | 0.593421 | ||||||||
\(321\) | 4.91576 | 0.274371 | ||||||||
\(322\) | 28.4607 | 1.58605 | ||||||||
\(323\) | 0.516714 | 0.0287507 | ||||||||
\(324\) | −13.9680 | −0.776001 | ||||||||
\(325\) | −9.95997 | −0.552480 | ||||||||
\(326\) | 56.5211 | 3.13041 | ||||||||
\(327\) | −17.5943 | −0.972965 | ||||||||
\(328\) | 62.1084 | 3.42936 | ||||||||
\(329\) | 4.80979 | 0.265172 | ||||||||
\(330\) | 1.52171 | 0.0837674 | ||||||||
\(331\) | 11.1948 | 0.615322 | 0.307661 | − | 0.951496i | \(-0.400454\pi\) | ||||
0.307661 | + | 0.951496i | \(0.400454\pi\) | |||||||
\(332\) | −72.0923 | −3.95658 | ||||||||
\(333\) | 0.362822 | 0.0198825 | ||||||||
\(334\) | 24.6181 | 1.34704 | ||||||||
\(335\) | 24.7927 | 1.35457 | ||||||||
\(336\) | −24.5135 | −1.33732 | ||||||||
\(337\) | 20.0997 | 1.09490 | 0.547451 | − | 0.836838i | \(-0.315598\pi\) | ||||
0.547451 | + | 0.836838i | \(0.315598\pi\) | |||||||
\(338\) | 8.27503 | 0.450102 | ||||||||
\(339\) | 10.2607 | 0.557287 | ||||||||
\(340\) | 11.3682 | 0.616528 | ||||||||
\(341\) | 1.81153 | 0.0980998 | ||||||||
\(342\) | −1.86379 | −0.100782 | ||||||||
\(343\) | −11.5130 | −0.621642 | ||||||||
\(344\) | −54.9447 | −2.96242 | ||||||||
\(345\) | −12.9969 | −0.699727 | ||||||||
\(346\) | −31.7732 | −1.70814 | ||||||||
\(347\) | 11.6576 | 0.625811 | 0.312905 | − | 0.949784i | \(-0.398698\pi\) | ||||
0.312905 | + | 0.949784i | \(0.398698\pi\) | |||||||
\(348\) | 40.8739 | 2.19107 | ||||||||
\(349\) | 16.1306 | 0.863450 | 0.431725 | − | 0.902005i | \(-0.357905\pi\) | ||||
0.431725 | + | 0.902005i | \(0.357905\pi\) | |||||||
\(350\) | −25.9210 | −1.38553 | ||||||||
\(351\) | −17.4315 | −0.930424 | ||||||||
\(352\) | 0.524215 | 0.0279407 | ||||||||
\(353\) | −15.2749 | −0.812999 | −0.406499 | − | 0.913651i | \(-0.633251\pi\) | ||||
−0.406499 | + | 0.913651i | \(0.633251\pi\) | |||||||
\(354\) | −26.5013 | −1.40853 | ||||||||
\(355\) | −40.1250 | −2.12961 | ||||||||
\(356\) | −24.2587 | −1.28571 | ||||||||
\(357\) | 3.85973 | 0.204278 | ||||||||
\(358\) | 15.2511 | 0.806043 | ||||||||
\(359\) | −30.4788 | −1.60861 | −0.804304 | − | 0.594218i | \(-0.797462\pi\) | ||||
−0.804304 | + | 0.594218i | \(0.797462\pi\) | |||||||
\(360\) | −21.9188 | −1.15522 | ||||||||
\(361\) | −18.6873 | −0.983544 | ||||||||
\(362\) | −37.9035 | −1.99216 | ||||||||
\(363\) | 14.1877 | 0.744663 | ||||||||
\(364\) | −43.2367 | −2.26622 | ||||||||
\(365\) | 31.5313 | 1.65042 | ||||||||
\(366\) | 20.6690 | 1.08039 | ||||||||
\(367\) | −6.70797 | −0.350153 | −0.175076 | − | 0.984555i | \(-0.556017\pi\) | ||||
−0.175076 | + | 0.984555i | \(0.556017\pi\) | |||||||
\(368\) | −20.6048 | −1.07410 | ||||||||
\(369\) | 14.3140 | 0.745155 | ||||||||
\(370\) | −1.96248 | −0.102024 | ||||||||
\(371\) | −17.7090 | −0.919406 | ||||||||
\(372\) | 61.4359 | 3.18530 | ||||||||
\(373\) | 11.9253 | 0.617469 | 0.308734 | − | 0.951148i | \(-0.400095\pi\) | ||||
0.308734 | + | 0.951148i | \(0.400095\pi\) | |||||||
\(374\) | −0.379851 | −0.0196416 | ||||||||
\(375\) | −6.67239 | −0.344561 | ||||||||
\(376\) | −8.58099 | −0.442531 | ||||||||
\(377\) | 22.9170 | 1.18029 | ||||||||
\(378\) | −45.3657 | −2.33336 | ||||||||
\(379\) | 28.1709 | 1.44704 | 0.723520 | − | 0.690303i | \(-0.242523\pi\) | ||||
0.723520 | + | 0.690303i | \(0.242523\pi\) | |||||||
\(380\) | 6.87911 | 0.352891 | ||||||||
\(381\) | 10.9218 | 0.559539 | ||||||||
\(382\) | 4.13341 | 0.211484 | ||||||||
\(383\) | −33.0567 | −1.68912 | −0.844559 | − | 0.535463i | \(-0.820137\pi\) | ||||
−0.844559 | + | 0.535463i | \(0.820137\pi\) | |||||||
\(384\) | −20.3043 | −1.03615 | ||||||||
\(385\) | 1.51517 | 0.0772203 | ||||||||
\(386\) | 37.0919 | 1.88793 | ||||||||
\(387\) | −12.6630 | −0.643695 | ||||||||
\(388\) | 58.3135 | 2.96042 | ||||||||
\(389\) | 18.5860 | 0.942349 | 0.471174 | − | 0.882040i | \(-0.343830\pi\) | ||||
0.471174 | + | 0.882040i | \(0.343830\pi\) | |||||||
\(390\) | 28.9348 | 1.46517 | ||||||||
\(391\) | 3.24429 | 0.164071 | ||||||||
\(392\) | −19.8042 | −1.00026 | ||||||||
\(393\) | 18.9263 | 0.954705 | ||||||||
\(394\) | 35.6081 | 1.79391 | ||||||||
\(395\) | 5.98998 | 0.301389 | ||||||||
\(396\) | 0.934942 | 0.0469826 | ||||||||
\(397\) | −15.6975 | −0.787837 | −0.393918 | − | 0.919145i | \(-0.628881\pi\) | ||||
−0.393918 | + | 0.919145i | \(0.628881\pi\) | |||||||
\(398\) | −10.1527 | −0.508907 | ||||||||
\(399\) | 2.33559 | 0.116926 | ||||||||
\(400\) | 18.7661 | 0.938305 | ||||||||
\(401\) | 32.3398 | 1.61497 | 0.807487 | − | 0.589886i | \(-0.200827\pi\) | ||||
0.807487 | + | 0.589886i | \(0.200827\pi\) | |||||||
\(402\) | −28.0945 | −1.40123 | ||||||||
\(403\) | 34.4457 | 1.71586 | ||||||||
\(404\) | 75.3622 | 3.74941 | ||||||||
\(405\) | 9.30749 | 0.462493 | ||||||||
\(406\) | 59.6418 | 2.95997 | ||||||||
\(407\) | 0.0447456 | 0.00221796 | ||||||||
\(408\) | −6.88602 | −0.340909 | ||||||||
\(409\) | −27.4380 | −1.35672 | −0.678361 | − | 0.734729i | \(-0.737309\pi\) | ||||
−0.678361 | + | 0.734729i | \(0.737309\pi\) | |||||||
\(410\) | −77.4231 | −3.82365 | ||||||||
\(411\) | 11.8330 | 0.583677 | ||||||||
\(412\) | 27.3056 | 1.34525 | ||||||||
\(413\) | −26.3874 | −1.29844 | ||||||||
\(414\) | −11.7022 | −0.575130 | ||||||||
\(415\) | 48.0382 | 2.35810 | ||||||||
\(416\) | 9.96777 | 0.488710 | ||||||||
\(417\) | −12.2483 | −0.599804 | ||||||||
\(418\) | −0.229854 | −0.0112426 | ||||||||
\(419\) | −14.4651 | −0.706664 | −0.353332 | − | 0.935498i | \(-0.614951\pi\) | ||||
−0.353332 | + | 0.935498i | \(0.614951\pi\) | |||||||
\(420\) | 51.3853 | 2.50735 | ||||||||
\(421\) | −8.80106 | −0.428938 | −0.214469 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214469 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(422\) | 39.8204 | 1.93843 | ||||||||
\(423\) | −1.97764 | −0.0961561 | ||||||||
\(424\) | 31.5941 | 1.53434 | ||||||||
\(425\) | −2.95478 | −0.143328 | ||||||||
\(426\) | 45.4688 | 2.20297 | ||||||||
\(427\) | 20.5802 | 0.995945 | ||||||||
\(428\) | −16.3363 | −0.789646 | ||||||||
\(429\) | −0.659731 | −0.0318521 | ||||||||
\(430\) | 68.4930 | 3.30303 | ||||||||
\(431\) | −16.7995 | −0.809202 | −0.404601 | − | 0.914493i | \(-0.632590\pi\) | ||||
−0.404601 | + | 0.914493i | \(0.632590\pi\) | |||||||
\(432\) | 32.8436 | 1.58019 | ||||||||
\(433\) | 27.6901 | 1.33070 | 0.665351 | − | 0.746531i | \(-0.268282\pi\) | ||||
0.665351 | + | 0.746531i | \(0.268282\pi\) | |||||||
\(434\) | 89.6452 | 4.30311 | ||||||||
\(435\) | −27.2361 | −1.30587 | ||||||||
\(436\) | 58.4702 | 2.80022 | ||||||||
\(437\) | 1.96318 | 0.0939115 | ||||||||
\(438\) | −35.7305 | −1.70727 | ||||||||
\(439\) | 31.6781 | 1.51191 | 0.755957 | − | 0.654621i | \(-0.227172\pi\) | ||||
0.755957 | + | 0.654621i | \(0.227172\pi\) | |||||||
\(440\) | −2.70317 | −0.128868 | ||||||||
\(441\) | −4.56422 | −0.217344 | ||||||||
\(442\) | −7.22275 | −0.343551 | ||||||||
\(443\) | −24.0322 | −1.14181 | −0.570903 | − | 0.821018i | \(-0.693407\pi\) | ||||
−0.570903 | + | 0.821018i | \(0.693407\pi\) | |||||||
\(444\) | 1.51750 | 0.0720172 | ||||||||
\(445\) | 16.1646 | 0.766276 | ||||||||
\(446\) | 58.3359 | 2.76228 | ||||||||
\(447\) | 19.8293 | 0.937893 | ||||||||
\(448\) | −11.9775 | −0.565883 | ||||||||
\(449\) | −31.6034 | −1.49146 | −0.745728 | − | 0.666250i | \(-0.767898\pi\) | ||||
−0.745728 | + | 0.666250i | \(0.767898\pi\) | |||||||
\(450\) | 10.6579 | 0.502419 | ||||||||
\(451\) | 1.76529 | 0.0831243 | ||||||||
\(452\) | −34.0990 | −1.60388 | ||||||||
\(453\) | −27.9723 | −1.31425 | ||||||||
\(454\) | −15.6039 | −0.732328 | ||||||||
\(455\) | 28.8105 | 1.35066 | ||||||||
\(456\) | −4.16685 | −0.195131 | ||||||||
\(457\) | 12.8000 | 0.598760 | 0.299380 | − | 0.954134i | \(-0.403220\pi\) | ||||
0.299380 | + | 0.954134i | \(0.403220\pi\) | |||||||
\(458\) | −13.3247 | −0.622622 | ||||||||
\(459\) | −5.17133 | −0.241377 | ||||||||
\(460\) | 43.1919 | 2.01383 | ||||||||
\(461\) | 30.7694 | 1.43307 | 0.716537 | − | 0.697549i | \(-0.245726\pi\) | ||||
0.716537 | + | 0.697549i | \(0.245726\pi\) | |||||||
\(462\) | −1.71696 | −0.0798801 | ||||||||
\(463\) | −26.3809 | −1.22602 | −0.613011 | − | 0.790074i | \(-0.710042\pi\) | ||||
−0.613011 | + | 0.790074i | \(0.710042\pi\) | |||||||
\(464\) | −43.1791 | −2.00454 | ||||||||
\(465\) | −40.9374 | −1.89843 | ||||||||
\(466\) | 20.8776 | 0.967138 | ||||||||
\(467\) | 12.4651 | 0.576818 | 0.288409 | − | 0.957507i | \(-0.406874\pi\) | ||||
0.288409 | + | 0.957507i | \(0.406874\pi\) | |||||||
\(468\) | 17.7776 | 0.821771 | ||||||||
\(469\) | −27.9738 | −1.29171 | ||||||||
\(470\) | 10.6969 | 0.493411 | ||||||||
\(471\) | 17.3116 | 0.797676 | ||||||||
\(472\) | 47.0769 | 2.16689 | ||||||||
\(473\) | −1.56168 | −0.0718062 | ||||||||
\(474\) | −6.78771 | −0.311770 | ||||||||
\(475\) | −1.78799 | −0.0820386 | ||||||||
\(476\) | −12.8269 | −0.587918 | ||||||||
\(477\) | 7.28141 | 0.333393 | ||||||||
\(478\) | −15.0423 | −0.688021 | ||||||||
\(479\) | −15.6696 | −0.715963 | −0.357982 | − | 0.933729i | \(-0.616535\pi\) | ||||
−0.357982 | + | 0.933729i | \(0.616535\pi\) | |||||||
\(480\) | −11.8463 | −0.540709 | ||||||||
\(481\) | 0.850824 | 0.0387942 | ||||||||
\(482\) | −6.98134 | −0.317991 | ||||||||
\(483\) | 14.6645 | 0.667256 | ||||||||
\(484\) | −47.1494 | −2.14316 | ||||||||
\(485\) | −38.8568 | −1.76440 | ||||||||
\(486\) | 31.5816 | 1.43257 | ||||||||
\(487\) | 15.1152 | 0.684936 | 0.342468 | − | 0.939529i | \(-0.388737\pi\) | ||||
0.342468 | + | 0.939529i | \(0.388737\pi\) | |||||||
\(488\) | −36.7164 | −1.66208 | ||||||||
\(489\) | 29.1227 | 1.31697 | ||||||||
\(490\) | 24.6875 | 1.11527 | ||||||||
\(491\) | 6.07639 | 0.274224 | 0.137112 | − | 0.990556i | \(-0.456218\pi\) | ||||
0.137112 | + | 0.990556i | \(0.456218\pi\) | |||||||
\(492\) | 59.8679 | 2.69905 | ||||||||
\(493\) | 6.79870 | 0.306198 | ||||||||
\(494\) | −4.37061 | −0.196643 | ||||||||
\(495\) | −0.622992 | −0.0280014 | ||||||||
\(496\) | −64.9008 | −2.91413 | ||||||||
\(497\) | 45.2734 | 2.03079 | ||||||||
\(498\) | −54.4359 | −2.43933 | ||||||||
\(499\) | −31.2213 | −1.39766 | −0.698829 | − | 0.715288i | \(-0.746295\pi\) | ||||
−0.698829 | + | 0.715288i | \(0.746295\pi\) | |||||||
\(500\) | 22.1740 | 0.991653 | ||||||||
\(501\) | 12.6846 | 0.566705 | ||||||||
\(502\) | −9.10669 | −0.406451 | ||||||||
\(503\) | −21.7349 | −0.969110 | −0.484555 | − | 0.874761i | \(-0.661018\pi\) | ||||
−0.484555 | + | 0.874761i | \(0.661018\pi\) | |||||||
\(504\) | 24.7311 | 1.10161 | ||||||||
\(505\) | −50.2171 | −2.23463 | ||||||||
\(506\) | −1.44319 | −0.0641575 | ||||||||
\(507\) | 4.26374 | 0.189359 | ||||||||
\(508\) | −36.2958 | −1.61036 | ||||||||
\(509\) | 20.8270 | 0.923139 | 0.461569 | − | 0.887104i | \(-0.347287\pi\) | ||||
0.461569 | + | 0.887104i | \(0.347287\pi\) | |||||||
\(510\) | 8.58398 | 0.380105 | ||||||||
\(511\) | −35.5770 | −1.57383 | ||||||||
\(512\) | 48.8688 | 2.15972 | ||||||||
\(513\) | −3.12926 | −0.138160 | ||||||||
\(514\) | −26.9357 | −1.18808 | ||||||||
\(515\) | −18.1949 | −0.801763 | ||||||||
\(516\) | −52.9626 | −2.33155 | ||||||||
\(517\) | −0.243896 | −0.0107265 | ||||||||
\(518\) | 2.21428 | 0.0972899 | ||||||||
\(519\) | −16.3713 | −0.718619 | ||||||||
\(520\) | −51.3999 | −2.25403 | ||||||||
\(521\) | 20.2559 | 0.887429 | 0.443715 | − | 0.896168i | \(-0.353660\pi\) | ||||
0.443715 | + | 0.896168i | \(0.353660\pi\) | |||||||
\(522\) | −24.5229 | −1.07334 | ||||||||
\(523\) | 14.7323 | 0.644199 | 0.322099 | − | 0.946706i | \(-0.395611\pi\) | ||||
0.322099 | + | 0.946706i | \(0.395611\pi\) | |||||||
\(524\) | −62.8969 | −2.74766 | ||||||||
\(525\) | −13.3559 | −0.582898 | ||||||||
\(526\) | 49.4702 | 2.15700 | ||||||||
\(527\) | 10.2188 | 0.445140 | ||||||||
\(528\) | 1.24303 | 0.0540961 | ||||||||
\(529\) | −10.6738 | −0.464078 | ||||||||
\(530\) | −39.3846 | −1.71076 | ||||||||
\(531\) | 10.8497 | 0.470837 | ||||||||
\(532\) | −7.76176 | −0.336515 | ||||||||
\(533\) | 33.5665 | 1.45393 | ||||||||
\(534\) | −18.3174 | −0.792671 | ||||||||
\(535\) | 10.8856 | 0.470626 | ||||||||
\(536\) | 49.9072 | 2.15566 | ||||||||
\(537\) | 7.85816 | 0.339105 | ||||||||
\(538\) | −25.2054 | −1.08668 | ||||||||
\(539\) | −0.562890 | −0.0242454 | ||||||||
\(540\) | −68.8469 | −2.96270 | ||||||||
\(541\) | −1.84350 | −0.0792581 | −0.0396291 | − | 0.999214i | \(-0.512618\pi\) | ||||
−0.0396291 | + | 0.999214i | \(0.512618\pi\) | |||||||
\(542\) | 7.75425 | 0.333073 | ||||||||
\(543\) | −19.5299 | −0.838109 | ||||||||
\(544\) | 2.95710 | 0.126785 | ||||||||
\(545\) | −38.9612 | −1.66892 | ||||||||
\(546\) | −32.6474 | −1.39718 | ||||||||
\(547\) | 21.3997 | 0.914986 | 0.457493 | − | 0.889213i | \(-0.348747\pi\) | ||||
0.457493 | + | 0.889213i | \(0.348747\pi\) | |||||||
\(548\) | −39.3239 | −1.67984 | ||||||||
\(549\) | −8.46195 | −0.361147 | ||||||||
\(550\) | 1.31440 | 0.0560464 | ||||||||
\(551\) | 4.11401 | 0.175263 | ||||||||
\(552\) | −26.1624 | −1.11355 | ||||||||
\(553\) | −6.75855 | −0.287403 | ||||||||
\(554\) | 61.7781 | 2.62470 | ||||||||
\(555\) | −1.01117 | −0.0429219 | ||||||||
\(556\) | 40.7043 | 1.72625 | ||||||||
\(557\) | −0.130409 | −0.00552561 | −0.00276280 | − | 0.999996i | \(-0.500879\pi\) | ||||
−0.00276280 | + | 0.999996i | \(0.500879\pi\) | |||||||
\(558\) | −36.8594 | −1.56038 | ||||||||
\(559\) | −29.6949 | −1.25596 | ||||||||
\(560\) | −54.2834 | −2.29389 | ||||||||
\(561\) | −0.195720 | −0.00826329 | ||||||||
\(562\) | −35.2207 | −1.48570 | ||||||||
\(563\) | 46.3199 | 1.95215 | 0.976076 | − | 0.217430i | \(-0.0697673\pi\) | ||||
0.976076 | + | 0.217430i | \(0.0697673\pi\) | |||||||
\(564\) | −8.27144 | −0.348290 | ||||||||
\(565\) | 22.7217 | 0.955908 | ||||||||
\(566\) | 68.8208 | 2.89275 | ||||||||
\(567\) | −10.5017 | −0.441031 | ||||||||
\(568\) | −80.7708 | −3.38907 | ||||||||
\(569\) | 13.7850 | 0.577896 | 0.288948 | − | 0.957345i | \(-0.406695\pi\) | ||||
0.288948 | + | 0.957345i | \(0.406695\pi\) | |||||||
\(570\) | 5.19431 | 0.217566 | ||||||||
\(571\) | −38.8825 | −1.62718 | −0.813591 | − | 0.581438i | \(-0.802490\pi\) | ||||
−0.813591 | + | 0.581438i | \(0.802490\pi\) | |||||||
\(572\) | 2.19245 | 0.0916711 | ||||||||
\(573\) | 2.12975 | 0.0889718 | ||||||||
\(574\) | 87.3572 | 3.64622 | ||||||||
\(575\) | −11.2263 | −0.468168 | ||||||||
\(576\) | 4.92478 | 0.205199 | ||||||||
\(577\) | 13.7898 | 0.574078 | 0.287039 | − | 0.957919i | \(-0.407329\pi\) | ||||
0.287039 | + | 0.957919i | \(0.407329\pi\) | |||||||
\(578\) | 40.5161 | 1.68525 | ||||||||
\(579\) | 19.1118 | 0.794258 | ||||||||
\(580\) | 90.5124 | 3.75832 | ||||||||
\(581\) | −54.2019 | −2.24868 | ||||||||
\(582\) | 44.0317 | 1.82517 | ||||||||
\(583\) | 0.897992 | 0.0371910 | ||||||||
\(584\) | 63.4718 | 2.62648 | ||||||||
\(585\) | −11.8460 | −0.489772 | ||||||||
\(586\) | −31.3754 | −1.29611 | ||||||||
\(587\) | 43.2967 | 1.78704 | 0.893522 | − | 0.449018i | \(-0.148226\pi\) | ||||
0.893522 | + | 0.449018i | \(0.148226\pi\) | |||||||
\(588\) | −19.0898 | −0.787249 | ||||||||
\(589\) | 6.18360 | 0.254791 | ||||||||
\(590\) | −58.6852 | −2.41603 | ||||||||
\(591\) | 18.3472 | 0.754703 | ||||||||
\(592\) | −1.60308 | −0.0658862 | ||||||||
\(593\) | −18.5331 | −0.761064 | −0.380532 | − | 0.924768i | \(-0.624259\pi\) | ||||
−0.380532 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(594\) | 2.30041 | 0.0943869 | ||||||||
\(595\) | 8.54709 | 0.350397 | ||||||||
\(596\) | −65.8978 | −2.69928 | ||||||||
\(597\) | −5.23120 | −0.214099 | ||||||||
\(598\) | −27.4418 | −1.12218 | ||||||||
\(599\) | 2.75983 | 0.112764 | 0.0563819 | − | 0.998409i | \(-0.482044\pi\) | ||||
0.0563819 | + | 0.998409i | \(0.482044\pi\) | |||||||
\(600\) | 23.8278 | 0.972765 | ||||||||
\(601\) | −11.3059 | −0.461178 | −0.230589 | − | 0.973051i | \(-0.574065\pi\) | ||||
−0.230589 | + | 0.973051i | \(0.574065\pi\) | |||||||
\(602\) | −77.2813 | −3.14975 | ||||||||
\(603\) | 11.5020 | 0.468397 | ||||||||
\(604\) | 92.9589 | 3.78245 | ||||||||
\(605\) | 31.4177 | 1.27731 | ||||||||
\(606\) | 56.9049 | 2.31160 | ||||||||
\(607\) | 37.7519 | 1.53230 | 0.766151 | − | 0.642660i | \(-0.222169\pi\) | ||||
0.766151 | + | 0.642660i | \(0.222169\pi\) | |||||||
\(608\) | 1.78939 | 0.0725694 | ||||||||
\(609\) | 30.7307 | 1.24527 | ||||||||
\(610\) | 45.7700 | 1.85317 | ||||||||
\(611\) | −4.63760 | −0.187617 | ||||||||
\(612\) | 5.27401 | 0.213189 | ||||||||
\(613\) | 39.9266 | 1.61262 | 0.806310 | − | 0.591493i | \(-0.201461\pi\) | ||||
0.806310 | + | 0.591493i | \(0.201461\pi\) | |||||||
\(614\) | −8.29344 | −0.334696 | ||||||||
\(615\) | −39.8925 | −1.60862 | ||||||||
\(616\) | 3.05001 | 0.122888 | ||||||||
\(617\) | −3.50635 | −0.141161 | −0.0705803 | − | 0.997506i | \(-0.522485\pi\) | ||||
−0.0705803 | + | 0.997506i | \(0.522485\pi\) | |||||||
\(618\) | 20.6181 | 0.829380 | ||||||||
\(619\) | 26.0803 | 1.04826 | 0.524129 | − | 0.851639i | \(-0.324391\pi\) | ||||
0.524129 | + | 0.851639i | \(0.324391\pi\) | |||||||
\(620\) | 136.045 | 5.46372 | ||||||||
\(621\) | −19.6477 | −0.788435 | ||||||||
\(622\) | −37.6902 | −1.51124 | ||||||||
\(623\) | −18.2387 | −0.730717 | ||||||||
\(624\) | 23.6359 | 0.946193 | ||||||||
\(625\) | −30.7634 | −1.23054 | ||||||||
\(626\) | −25.9266 | −1.03623 | ||||||||
\(627\) | −0.118433 | −0.00472977 | ||||||||
\(628\) | −57.5308 | −2.29573 | ||||||||
\(629\) | 0.252410 | 0.0100643 | ||||||||
\(630\) | −30.8294 | −1.22827 | ||||||||
\(631\) | 44.1554 | 1.75780 | 0.878899 | − | 0.477007i | \(-0.158278\pi\) | ||||
0.878899 | + | 0.477007i | \(0.158278\pi\) | |||||||
\(632\) | 12.0577 | 0.479630 | ||||||||
\(633\) | 20.5176 | 0.815503 | ||||||||
\(634\) | 13.1588 | 0.522601 | ||||||||
\(635\) | 24.1855 | 0.959770 | ||||||||
\(636\) | 30.4544 | 1.20759 | ||||||||
\(637\) | −10.7032 | −0.424075 | ||||||||
\(638\) | −3.02433 | −0.119734 | ||||||||
\(639\) | −18.6150 | −0.736399 | ||||||||
\(640\) | −44.9623 | −1.77729 | ||||||||
\(641\) | 44.3860 | 1.75314 | 0.876571 | − | 0.481273i | \(-0.159825\pi\) | ||||
0.876571 | + | 0.481273i | \(0.159825\pi\) | |||||||
\(642\) | −12.3353 | −0.486837 | ||||||||
\(643\) | 22.9109 | 0.903518 | 0.451759 | − | 0.892140i | \(-0.350797\pi\) | ||||
0.451759 | + | 0.892140i | \(0.350797\pi\) | |||||||
\(644\) | −48.7338 | −1.92038 | ||||||||
\(645\) | 35.2913 | 1.38959 | ||||||||
\(646\) | −1.29661 | −0.0510145 | ||||||||
\(647\) | 41.1369 | 1.61726 | 0.808629 | − | 0.588318i | \(-0.200210\pi\) | ||||
0.808629 | + | 0.588318i | \(0.200210\pi\) | |||||||
\(648\) | 18.7358 | 0.736011 | ||||||||
\(649\) | 1.33806 | 0.0525233 | ||||||||
\(650\) | 24.9930 | 0.980305 | ||||||||
\(651\) | 46.1901 | 1.81033 | ||||||||
\(652\) | −96.7822 | −3.79028 | ||||||||
\(653\) | −45.3144 | −1.77329 | −0.886644 | − | 0.462453i | \(-0.846970\pi\) | ||||
−0.886644 | + | 0.462453i | \(0.846970\pi\) | |||||||
\(654\) | 44.1500 | 1.72640 | ||||||||
\(655\) | 41.9109 | 1.63759 | ||||||||
\(656\) | −63.2443 | −2.46928 | ||||||||
\(657\) | 14.6282 | 0.570700 | ||||||||
\(658\) | −12.0694 | −0.470514 | ||||||||
\(659\) | −18.2261 | −0.709989 | −0.354995 | − | 0.934868i | \(-0.615517\pi\) | ||||
−0.354995 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(660\) | −2.60565 | −0.101425 | ||||||||
\(661\) | 34.7371 | 1.35112 | 0.675558 | − | 0.737307i | \(-0.263903\pi\) | ||||
0.675558 | + | 0.737307i | \(0.263903\pi\) | |||||||
\(662\) | −28.0916 | −1.09181 | ||||||||
\(663\) | −3.72155 | −0.144533 | ||||||||
\(664\) | 96.6999 | 3.75269 | ||||||||
\(665\) | 5.17199 | 0.200561 | ||||||||
\(666\) | −0.910445 | −0.0352790 | ||||||||
\(667\) | 25.8306 | 1.00017 | ||||||||
\(668\) | −42.1540 | −1.63099 | ||||||||
\(669\) | 30.0578 | 1.16210 | ||||||||
\(670\) | −62.2133 | −2.40351 | ||||||||
\(671\) | −1.04358 | −0.0402871 | ||||||||
\(672\) | 13.3663 | 0.515617 | ||||||||
\(673\) | −11.2892 | −0.435166 | −0.217583 | − | 0.976042i | \(-0.569817\pi\) | ||||
−0.217583 | + | 0.976042i | \(0.569817\pi\) | |||||||
\(674\) | −50.4371 | −1.94276 | ||||||||
\(675\) | 17.8944 | 0.688756 | ||||||||
\(676\) | −14.1695 | −0.544981 | ||||||||
\(677\) | −13.6990 | −0.526496 | −0.263248 | − | 0.964728i | \(-0.584794\pi\) | ||||
−0.263248 | + | 0.964728i | \(0.584794\pi\) | |||||||
\(678\) | −25.7477 | −0.988834 | ||||||||
\(679\) | 43.8425 | 1.68252 | ||||||||
\(680\) | −15.2486 | −0.584757 | ||||||||
\(681\) | −8.03998 | −0.308093 | ||||||||
\(682\) | −4.54574 | −0.174066 | ||||||||
\(683\) | 21.6109 | 0.826918 | 0.413459 | − | 0.910523i | \(-0.364320\pi\) | ||||
0.413459 | + | 0.910523i | \(0.364320\pi\) | |||||||
\(684\) | 3.19140 | 0.122026 | ||||||||
\(685\) | 26.2032 | 1.00117 | ||||||||
\(686\) | 28.8900 | 1.10302 | ||||||||
\(687\) | −6.86560 | −0.261939 | ||||||||
\(688\) | 55.9496 | 2.13306 | ||||||||
\(689\) | 17.0750 | 0.650507 | ||||||||
\(690\) | 32.6136 | 1.24158 | ||||||||
\(691\) | 37.4593 | 1.42502 | 0.712509 | − | 0.701663i | \(-0.247559\pi\) | ||||
0.712509 | + | 0.701663i | \(0.247559\pi\) | |||||||
\(692\) | 54.4059 | 2.06820 | ||||||||
\(693\) | 0.702928 | 0.0267020 | ||||||||
\(694\) | −29.2528 | −1.11042 | ||||||||
\(695\) | −27.1231 | −1.02884 | ||||||||
\(696\) | −54.8256 | −2.07816 | ||||||||
\(697\) | 9.95802 | 0.377187 | ||||||||
\(698\) | −40.4771 | −1.53208 | ||||||||
\(699\) | 10.7573 | 0.406878 | ||||||||
\(700\) | 44.3850 | 1.67759 | ||||||||
\(701\) | 9.58853 | 0.362154 | 0.181077 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181077 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(702\) | 43.7416 | 1.65092 | ||||||||
\(703\) | 0.152738 | 0.00576062 | ||||||||
\(704\) | 0.607357 | 0.0228906 | ||||||||
\(705\) | 5.51162 | 0.207579 | ||||||||
\(706\) | 38.3298 | 1.44256 | ||||||||
\(707\) | 56.6604 | 2.13093 | ||||||||
\(708\) | 45.3787 | 1.70544 | ||||||||
\(709\) | −35.2991 | −1.32569 | −0.662843 | − | 0.748759i | \(-0.730650\pi\) | ||||
−0.662843 | + | 0.748759i | \(0.730650\pi\) | |||||||
\(710\) | 100.687 | 3.77873 | ||||||||
\(711\) | 2.77891 | 0.104217 | ||||||||
\(712\) | 32.5390 | 1.21945 | ||||||||
\(713\) | 38.8250 | 1.45401 | ||||||||
\(714\) | −9.68537 | −0.362466 | ||||||||
\(715\) | −1.46093 | −0.0546356 | ||||||||
\(716\) | −26.1147 | −0.975951 | ||||||||
\(717\) | −7.75063 | −0.289452 | ||||||||
\(718\) | 76.4816 | 2.85427 | ||||||||
\(719\) | −14.3086 | −0.533621 | −0.266811 | − | 0.963749i | \(-0.585970\pi\) | ||||
−0.266811 | + | 0.963749i | \(0.585970\pi\) | |||||||
\(720\) | 22.3197 | 0.831805 | ||||||||
\(721\) | 20.5295 | 0.764557 | ||||||||
\(722\) | 46.8929 | 1.74517 | ||||||||
\(723\) | −3.59716 | −0.133780 | ||||||||
\(724\) | 64.9029 | 2.41210 | ||||||||
\(725\) | −23.5256 | −0.873720 | ||||||||
\(726\) | −35.6019 | −1.32131 | ||||||||
\(727\) | −38.3133 | −1.42096 | −0.710480 | − | 0.703717i | \(-0.751522\pi\) | ||||
−0.710480 | + | 0.703717i | \(0.751522\pi\) | |||||||
\(728\) | 57.9949 | 2.14944 | ||||||||
\(729\) | 26.0250 | 0.963887 | ||||||||
\(730\) | −79.1227 | −2.92846 | ||||||||
\(731\) | −8.80945 | −0.325829 | ||||||||
\(732\) | −35.3919 | −1.30812 | ||||||||
\(733\) | −9.43115 | −0.348348 | −0.174174 | − | 0.984715i | \(-0.555725\pi\) | ||||
−0.174174 | + | 0.984715i | \(0.555725\pi\) | |||||||
\(734\) | 16.8326 | 0.621302 | ||||||||
\(735\) | 12.7203 | 0.469197 | ||||||||
\(736\) | 11.2351 | 0.414130 | ||||||||
\(737\) | 1.41850 | 0.0522511 | ||||||||
\(738\) | −35.9186 | −1.32218 | ||||||||
\(739\) | 13.4781 | 0.495800 | 0.247900 | − | 0.968786i | \(-0.420260\pi\) | ||||
0.247900 | + | 0.968786i | \(0.420260\pi\) | |||||||
\(740\) | 3.36039 | 0.123530 | ||||||||
\(741\) | −2.25197 | −0.0827283 | ||||||||
\(742\) | 44.4380 | 1.63137 | ||||||||
\(743\) | 51.0013 | 1.87106 | 0.935529 | − | 0.353250i | \(-0.114923\pi\) | ||||
0.935529 | + | 0.353250i | \(0.114923\pi\) | |||||||
\(744\) | −82.4062 | −3.02116 | ||||||||
\(745\) | 43.9105 | 1.60876 | ||||||||
\(746\) | −29.9247 | −1.09562 | ||||||||
\(747\) | 22.2862 | 0.815409 | ||||||||
\(748\) | 0.650426 | 0.0237819 | ||||||||
\(749\) | −12.2823 | −0.448786 | ||||||||
\(750\) | 16.7433 | 0.611379 | ||||||||
\(751\) | −18.2002 | −0.664133 | −0.332067 | − | 0.943256i | \(-0.607746\pi\) | ||||
−0.332067 | + | 0.943256i | \(0.607746\pi\) | |||||||
\(752\) | 8.73793 | 0.318640 | ||||||||
\(753\) | −4.69226 | −0.170995 | ||||||||
\(754\) | −57.5066 | −2.09427 | ||||||||
\(755\) | −61.9426 | −2.25432 | ||||||||
\(756\) | 77.6805 | 2.82521 | ||||||||
\(757\) | 42.9009 | 1.55926 | 0.779630 | − | 0.626240i | \(-0.215407\pi\) | ||||
0.779630 | + | 0.626240i | \(0.215407\pi\) | |||||||
\(758\) | −70.6904 | −2.56759 | ||||||||
\(759\) | −0.743608 | −0.0269913 | ||||||||
\(760\) | −9.22719 | −0.334705 | ||||||||
\(761\) | −21.6162 | −0.783587 | −0.391793 | − | 0.920053i | \(-0.628145\pi\) | ||||
−0.391793 | + | 0.920053i | \(0.628145\pi\) | |||||||
\(762\) | −27.4064 | −0.992830 | ||||||||
\(763\) | 43.9603 | 1.59147 | ||||||||
\(764\) | −7.07772 | −0.256063 | ||||||||
\(765\) | −3.51430 | −0.127060 | ||||||||
\(766\) | 82.9505 | 2.99712 | ||||||||
\(767\) | 25.4427 | 0.918684 | ||||||||
\(768\) | 41.3628 | 1.49255 | ||||||||
\(769\) | 41.2256 | 1.48663 | 0.743316 | − | 0.668941i | \(-0.233252\pi\) | ||||
0.743316 | + | 0.668941i | \(0.233252\pi\) | |||||||
\(770\) | −3.80208 | −0.137018 | ||||||||
\(771\) | −13.8787 | −0.499829 | ||||||||
\(772\) | −63.5133 | −2.28589 | ||||||||
\(773\) | 12.4493 | 0.447769 | 0.223884 | − | 0.974616i | \(-0.428126\pi\) | ||||
0.223884 | + | 0.974616i | \(0.428126\pi\) | |||||||
\(774\) | 31.7757 | 1.14215 | ||||||||
\(775\) | −35.3604 | −1.27018 | ||||||||
\(776\) | −78.2179 | −2.80786 | ||||||||
\(777\) | 1.14092 | 0.0409301 | ||||||||
\(778\) | −46.6387 | −1.67208 | ||||||||
\(779\) | 6.02577 | 0.215896 | ||||||||
\(780\) | −49.5457 | −1.77402 | ||||||||
\(781\) | −2.29573 | −0.0821477 | ||||||||
\(782\) | −8.14103 | −0.291123 | ||||||||
\(783\) | −41.1735 | −1.47142 | ||||||||
\(784\) | 20.1664 | 0.720229 | ||||||||
\(785\) | 38.3353 | 1.36824 | ||||||||
\(786\) | −47.4925 | −1.69400 | ||||||||
\(787\) | −41.2236 | −1.46946 | −0.734731 | − | 0.678359i | \(-0.762691\pi\) | ||||
−0.734731 | + | 0.678359i | \(0.762691\pi\) | |||||||
\(788\) | −60.9724 | −2.17205 | ||||||||
\(789\) | 25.4897 | 0.907458 | ||||||||
\(790\) | −15.0309 | −0.534776 | ||||||||
\(791\) | −25.6371 | −0.911549 | ||||||||
\(792\) | −1.25407 | −0.0445615 | ||||||||
\(793\) | −19.8434 | −0.704660 | ||||||||
\(794\) | 39.3905 | 1.39792 | ||||||||
\(795\) | −20.2931 | −0.719721 | ||||||||
\(796\) | 17.3846 | 0.616181 | ||||||||
\(797\) | 45.8627 | 1.62454 | 0.812270 | − | 0.583281i | \(-0.198231\pi\) | ||||
0.812270 | + | 0.583281i | \(0.198231\pi\) | |||||||
\(798\) | −5.86079 | −0.207470 | ||||||||
\(799\) | −1.37582 | −0.0486729 | ||||||||
\(800\) | −10.2325 | −0.361773 | ||||||||
\(801\) | 7.49919 | 0.264971 | ||||||||
\(802\) | −81.1517 | −2.86556 | ||||||||
\(803\) | 1.80404 | 0.0636633 | ||||||||
\(804\) | 48.1068 | 1.69660 | ||||||||
\(805\) | 32.4734 | 1.14454 | ||||||||
\(806\) | −86.4359 | −3.04457 | ||||||||
\(807\) | −12.9872 | −0.457171 | ||||||||
\(808\) | −101.086 | −3.55619 | ||||||||
\(809\) | 33.0979 | 1.16366 | 0.581831 | − | 0.813310i | \(-0.302337\pi\) | ||||
0.581831 | + | 0.813310i | \(0.302337\pi\) | |||||||
\(810\) | −23.3557 | −0.820635 | ||||||||
\(811\) | 7.26574 | 0.255135 | 0.127567 | − | 0.991830i | \(-0.459283\pi\) | ||||
0.127567 | + | 0.991830i | \(0.459283\pi\) | |||||||
\(812\) | −102.126 | −3.58392 | ||||||||
\(813\) | 3.99541 | 0.140125 | ||||||||
\(814\) | −0.112282 | −0.00393548 | ||||||||
\(815\) | 64.4902 | 2.25899 | ||||||||
\(816\) | 7.01196 | 0.245468 | ||||||||
\(817\) | −5.33075 | −0.186499 | ||||||||
\(818\) | 68.8513 | 2.40733 | ||||||||
\(819\) | 13.3659 | 0.467044 | ||||||||
\(820\) | 132.573 | 4.62965 | ||||||||
\(821\) | −0.337702 | −0.0117859 | −0.00589295 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589295 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(822\) | −29.6929 | −1.03566 | ||||||||
\(823\) | 38.6426 | 1.34700 | 0.673499 | − | 0.739188i | \(-0.264791\pi\) | ||||
0.673499 | + | 0.739188i | \(0.264791\pi\) | |||||||
\(824\) | −36.6260 | −1.27593 | ||||||||
\(825\) | 0.677251 | 0.0235789 | ||||||||
\(826\) | 66.2150 | 2.30392 | ||||||||
\(827\) | 39.6551 | 1.37894 | 0.689472 | − | 0.724313i | \(-0.257843\pi\) | ||||
0.689472 | + | 0.724313i | \(0.257843\pi\) | |||||||
\(828\) | 20.0378 | 0.696363 | ||||||||
\(829\) | 11.6416 | 0.404328 | 0.202164 | − | 0.979352i | \(-0.435203\pi\) | ||||
0.202164 | + | 0.979352i | \(0.435203\pi\) | |||||||
\(830\) | −120.544 | −4.18415 | ||||||||
\(831\) | 31.8314 | 1.10422 | ||||||||
\(832\) | 11.5487 | 0.400379 | ||||||||
\(833\) | −3.17527 | −0.110016 | ||||||||
\(834\) | 30.7353 | 1.06428 | ||||||||
\(835\) | 28.0891 | 0.972062 | ||||||||
\(836\) | 0.393584 | 0.0136124 | ||||||||
\(837\) | −61.8862 | −2.13910 | ||||||||
\(838\) | 36.2978 | 1.25389 | ||||||||
\(839\) | −19.8923 | −0.686758 | −0.343379 | − | 0.939197i | \(-0.611571\pi\) | ||||
−0.343379 | + | 0.939197i | \(0.611571\pi\) | |||||||
\(840\) | −68.9249 | −2.37814 | ||||||||
\(841\) | 25.1304 | 0.866565 | ||||||||
\(842\) | 22.0849 | 0.761095 | ||||||||
\(843\) | −18.1476 | −0.625037 | ||||||||
\(844\) | −68.1853 | −2.34704 | ||||||||
\(845\) | 9.44175 | 0.324806 | ||||||||
\(846\) | 4.96257 | 0.170617 | ||||||||
\(847\) | −35.4489 | −1.21804 | ||||||||
\(848\) | −32.1719 | −1.10479 | ||||||||
\(849\) | 35.4602 | 1.21699 | ||||||||
\(850\) | 7.41456 | 0.254317 | ||||||||
\(851\) | 0.958996 | 0.0328740 | ||||||||
\(852\) | −77.8570 | −2.66734 | ||||||||
\(853\) | 5.57752 | 0.190971 | 0.0954853 | − | 0.995431i | \(-0.469560\pi\) | ||||
0.0954853 | + | 0.995431i | \(0.469560\pi\) | |||||||
\(854\) | −51.6427 | −1.76718 | ||||||||
\(855\) | −2.12657 | −0.0727271 | ||||||||
\(856\) | 21.9125 | 0.748954 | ||||||||
\(857\) | 49.8657 | 1.70338 | 0.851691 | − | 0.524045i | \(-0.175578\pi\) | ||||
0.851691 | + | 0.524045i | \(0.175578\pi\) | |||||||
\(858\) | 1.65549 | 0.0565175 | ||||||||
\(859\) | 20.5409 | 0.700846 | 0.350423 | − | 0.936592i | \(-0.386038\pi\) | ||||
0.350423 | + | 0.936592i | \(0.386038\pi\) | |||||||
\(860\) | −117.282 | −3.99928 | ||||||||
\(861\) | 45.0111 | 1.53397 | ||||||||
\(862\) | 42.1556 | 1.43583 | ||||||||
\(863\) | −13.2325 | −0.450438 | −0.225219 | − | 0.974308i | \(-0.572310\pi\) | ||||
−0.225219 | + | 0.974308i | \(0.572310\pi\) | |||||||
\(864\) | −17.9084 | −0.609257 | ||||||||
\(865\) | −36.2530 | −1.23264 | ||||||||
\(866\) | −69.4839 | −2.36116 | ||||||||
\(867\) | 20.8761 | 0.708988 | ||||||||
\(868\) | −153.501 | −5.21017 | ||||||||
\(869\) | 0.342713 | 0.0116258 | ||||||||
\(870\) | 68.3446 | 2.31710 | ||||||||
\(871\) | 26.9723 | 0.913922 | ||||||||
\(872\) | −78.4282 | −2.65591 | ||||||||
\(873\) | −18.0267 | −0.610111 | ||||||||
\(874\) | −4.92628 | −0.166634 | ||||||||
\(875\) | 16.6714 | 0.563595 | ||||||||
\(876\) | 61.1821 | 2.06715 | ||||||||
\(877\) | −56.9530 | −1.92317 | −0.961583 | − | 0.274515i | \(-0.911483\pi\) | ||||
−0.961583 | + | 0.274515i | \(0.911483\pi\) | |||||||
\(878\) | −79.4912 | −2.68270 | ||||||||
\(879\) | −16.1663 | −0.545276 | ||||||||
\(880\) | 2.75261 | 0.0927904 | ||||||||
\(881\) | −52.3819 | −1.76479 | −0.882395 | − | 0.470509i | \(-0.844070\pi\) | ||||
−0.882395 | + | 0.470509i | \(0.844070\pi\) | |||||||
\(882\) | 11.4532 | 0.385649 | ||||||||
\(883\) | −13.0096 | −0.437808 | −0.218904 | − | 0.975746i | \(-0.570248\pi\) | ||||
−0.218904 | + | 0.975746i | \(0.570248\pi\) | |||||||
\(884\) | 12.3677 | 0.415969 | ||||||||
\(885\) | −30.2378 | −1.01643 | ||||||||
\(886\) | 60.3051 | 2.02599 | ||||||||
\(887\) | −35.0352 | −1.17637 | −0.588184 | − | 0.808727i | \(-0.700157\pi\) | ||||
−0.588184 | + | 0.808727i | \(0.700157\pi\) | |||||||
\(888\) | −2.03547 | −0.0683060 | ||||||||
\(889\) | −27.2887 | −0.915232 | ||||||||
\(890\) | −40.5626 | −1.35966 | ||||||||
\(891\) | 0.532523 | 0.0178402 | ||||||||
\(892\) | −99.8897 | −3.34455 | ||||||||
\(893\) | −0.832530 | −0.0278596 | ||||||||
\(894\) | −49.7584 | −1.66417 | ||||||||
\(895\) | 17.4013 | 0.581663 | ||||||||
\(896\) | 50.7314 | 1.69482 | ||||||||
\(897\) | −14.1395 | −0.472103 | ||||||||
\(898\) | 79.3037 | 2.64640 | ||||||||
\(899\) | 81.3612 | 2.71355 | ||||||||
\(900\) | −18.2497 | −0.608325 | ||||||||
\(901\) | 5.06558 | 0.168759 | ||||||||
\(902\) | −4.42972 | −0.147494 | ||||||||
\(903\) | −39.8195 | −1.32511 | ||||||||
\(904\) | 45.7382 | 1.52123 | ||||||||
\(905\) | −43.2476 | −1.43760 | ||||||||
\(906\) | 70.1919 | 2.33197 | ||||||||
\(907\) | −5.95374 | −0.197691 | −0.0988454 | − | 0.995103i | \(-0.531515\pi\) | ||||
−0.0988454 | + | 0.995103i | \(0.531515\pi\) | |||||||
\(908\) | 26.7189 | 0.886697 | ||||||||
\(909\) | −23.2970 | −0.772713 | ||||||||
\(910\) | −72.2954 | −2.39657 | ||||||||
\(911\) | −7.94120 | −0.263104 | −0.131552 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131552 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(912\) | 4.24306 | 0.140502 | ||||||||
\(913\) | 2.74848 | 0.0909614 | ||||||||
\(914\) | −32.1196 | −1.06242 | ||||||||
\(915\) | 23.5832 | 0.779636 | ||||||||
\(916\) | 22.8161 | 0.753866 | ||||||||
\(917\) | −47.2884 | −1.56160 | ||||||||
\(918\) | 12.9766 | 0.428292 | ||||||||
\(919\) | −36.4422 | −1.20212 | −0.601059 | − | 0.799205i | \(-0.705254\pi\) | ||||
−0.601059 | + | 0.799205i | \(0.705254\pi\) | |||||||
\(920\) | −57.9348 | −1.91005 | ||||||||
\(921\) | −4.27323 | −0.140808 | ||||||||
\(922\) | −77.2110 | −2.54281 | ||||||||
\(923\) | −43.6526 | −1.43684 | ||||||||
\(924\) | 2.93998 | 0.0967183 | ||||||||
\(925\) | −0.873419 | −0.0287178 | ||||||||
\(926\) | 66.1986 | 2.17542 | ||||||||
\(927\) | −8.44109 | −0.277242 | ||||||||
\(928\) | 23.5441 | 0.772871 | ||||||||
\(929\) | −26.5933 | −0.872498 | −0.436249 | − | 0.899826i | \(-0.643693\pi\) | ||||
−0.436249 | + | 0.899826i | \(0.643693\pi\) | |||||||
\(930\) | 102.726 | 3.36852 | ||||||||
\(931\) | −1.92141 | −0.0629716 | ||||||||
\(932\) | −35.7492 | −1.17100 | ||||||||
\(933\) | −19.4200 | −0.635783 | ||||||||
\(934\) | −31.2793 | −1.02349 | ||||||||
\(935\) | −0.433407 | −0.0141739 | ||||||||
\(936\) | −23.8458 | −0.779423 | ||||||||
\(937\) | −10.7660 | −0.351711 | −0.175855 | − | 0.984416i | \(-0.556269\pi\) | ||||
−0.175855 | + | 0.984416i | \(0.556269\pi\) | |||||||
\(938\) | 70.1958 | 2.29197 | ||||||||
\(939\) | −13.3588 | −0.435947 | ||||||||
\(940\) | −18.3165 | −0.597419 | ||||||||
\(941\) | 13.9752 | 0.455578 | 0.227789 | − | 0.973711i | \(-0.426850\pi\) | ||||
0.227789 | + | 0.973711i | \(0.426850\pi\) | |||||||
\(942\) | −43.4407 | −1.41537 | ||||||||
\(943\) | 37.8340 | 1.23205 | ||||||||
\(944\) | −47.9380 | −1.56025 | ||||||||
\(945\) | −51.7619 | −1.68381 | ||||||||
\(946\) | 3.91879 | 0.127411 | ||||||||
\(947\) | 10.5098 | 0.341522 | 0.170761 | − | 0.985313i | \(-0.445377\pi\) | ||||
0.170761 | + | 0.985313i | \(0.445377\pi\) | |||||||
\(948\) | 11.6227 | 0.377489 | ||||||||
\(949\) | 34.3033 | 1.11353 | ||||||||
\(950\) | 4.48668 | 0.145567 | ||||||||
\(951\) | 6.78010 | 0.219860 | ||||||||
\(952\) | 17.2051 | 0.557621 | ||||||||
\(953\) | 54.8893 | 1.77804 | 0.889019 | − | 0.457870i | \(-0.151388\pi\) | ||||
0.889019 | + | 0.457870i | \(0.151388\pi\) | |||||||
\(954\) | −18.2715 | −0.591563 | ||||||||
\(955\) | 4.71619 | 0.152612 | ||||||||
\(956\) | 25.7573 | 0.833051 | ||||||||
\(957\) | −1.55830 | −0.0503726 | ||||||||
\(958\) | 39.3204 | 1.27039 | ||||||||
\(959\) | −29.5654 | −0.954715 | ||||||||
\(960\) | −13.7252 | −0.442979 | ||||||||
\(961\) | 91.2908 | 2.94486 | ||||||||
\(962\) | −2.13501 | −0.0688354 | ||||||||
\(963\) | 5.05012 | 0.162738 | ||||||||
\(964\) | 11.9543 | 0.385022 | ||||||||
\(965\) | 42.3216 | 1.36238 | ||||||||
\(966\) | −36.7982 | −1.18396 | ||||||||
\(967\) | −50.7638 | −1.63245 | −0.816226 | − | 0.577732i | \(-0.803938\pi\) | ||||
−0.816226 | + | 0.577732i | \(0.803938\pi\) | |||||||
\(968\) | 63.2432 | 2.03271 | ||||||||
\(969\) | −0.668084 | −0.0214619 | ||||||||
\(970\) | 97.5050 | 3.13070 | ||||||||
\(971\) | 14.2416 | 0.457034 | 0.228517 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228517 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(972\) | −54.0779 | −1.73455 | ||||||||
\(973\) | 30.6032 | 0.981094 | ||||||||
\(974\) | −37.9293 | −1.21533 | ||||||||
\(975\) | 12.8777 | 0.412417 | ||||||||
\(976\) | 37.3880 | 1.19676 | ||||||||
\(977\) | 23.0523 | 0.737508 | 0.368754 | − | 0.929527i | \(-0.379785\pi\) | ||||
0.368754 | + | 0.929527i | \(0.379785\pi\) | |||||||
\(978\) | −73.0788 | −2.33680 | ||||||||
\(979\) | 0.924850 | 0.0295583 | ||||||||
\(980\) | −42.2729 | −1.35036 | ||||||||
\(981\) | −18.0751 | −0.577095 | ||||||||
\(982\) | −15.2477 | −0.486575 | ||||||||
\(983\) | −2.94466 | −0.0939200 | −0.0469600 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469600 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(984\) | −80.3029 | −2.55996 | ||||||||
\(985\) | 40.6286 | 1.29453 | ||||||||
\(986\) | −17.0603 | −0.543309 | ||||||||
\(987\) | −6.21881 | −0.197947 | ||||||||
\(988\) | 7.48388 | 0.238094 | ||||||||
\(989\) | −33.4702 | −1.06429 | ||||||||
\(990\) | 1.56330 | 0.0496850 | ||||||||
\(991\) | 5.95963 | 0.189314 | 0.0946569 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946569 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(992\) | 35.3881 | 1.12357 | ||||||||
\(993\) | −14.4743 | −0.459328 | ||||||||
\(994\) | −113.606 | −3.60338 | ||||||||
\(995\) | −11.5841 | −0.367241 | ||||||||
\(996\) | 93.2116 | 2.95352 | ||||||||
\(997\) | 50.9814 | 1.61460 | 0.807298 | − | 0.590144i | \(-0.200929\pi\) | ||||
0.807298 | + | 0.590144i | \(0.200929\pi\) | |||||||
\(998\) | 78.3450 | 2.47997 | ||||||||
\(999\) | −1.52862 | −0.0483633 |
(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 | 6029.2.a.b.1.20 | ✓ | 268 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6029.2.a.b.1.20 | ✓ | 268 | 1.1 | even | 1 | trivial |