Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.20998 | −0.698581 | −0.349291 | − | 0.937014i | \(-0.613577\pi\) | ||||
−0.349291 | + | 0.937014i | \(0.613577\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.0448427 | 0.0200543 | 0.0100271 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100271 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(6\) | 1.20998 | 0.493972 | ||||||||
\(7\) | −2.73874 | −1.03515 | −0.517574 | − | 0.855639i | \(-0.673165\pi\) | ||||
−0.517574 | + | 0.855639i | \(0.673165\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.53595 | −0.511984 | ||||||||
\(10\) | −0.0448427 | −0.0141805 | ||||||||
\(11\) | 2.04170 | 0.615594 | 0.307797 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307797 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(12\) | −1.20998 | −0.349291 | ||||||||
\(13\) | 1.85754 | 0.515188 | 0.257594 | − | 0.966253i | \(-0.417070\pi\) | ||||
0.257594 | + | 0.966253i | \(0.417070\pi\) | |||||||
\(14\) | 2.73874 | 0.731960 | ||||||||
\(15\) | −0.0542587 | −0.0140095 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.92176 | 0.466095 | 0.233047 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233047 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(18\) | 1.53595 | 0.362027 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.0448427 | 0.0100271 | ||||||||
\(21\) | 3.31382 | 0.723135 | ||||||||
\(22\) | −2.04170 | −0.435291 | ||||||||
\(23\) | −2.83061 | −0.590223 | −0.295111 | − | 0.955463i | \(-0.595357\pi\) | ||||
−0.295111 | + | 0.955463i | \(0.595357\pi\) | |||||||
\(24\) | 1.20998 | 0.246986 | ||||||||
\(25\) | −4.99799 | −0.999598 | ||||||||
\(26\) | −1.85754 | −0.364293 | ||||||||
\(27\) | 5.48840 | 1.05624 | ||||||||
\(28\) | −2.73874 | −0.517574 | ||||||||
\(29\) | 6.47351 | 1.20210 | 0.601050 | − | 0.799211i | \(-0.294749\pi\) | ||||
0.601050 | + | 0.799211i | \(0.294749\pi\) | |||||||
\(30\) | 0.0542587 | 0.00990624 | ||||||||
\(31\) | −7.78208 | −1.39770 | −0.698851 | − | 0.715267i | \(-0.746305\pi\) | ||||
−0.698851 | + | 0.715267i | \(0.746305\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.47041 | −0.430043 | ||||||||
\(34\) | −1.92176 | −0.329579 | ||||||||
\(35\) | −0.122813 | −0.0207591 | ||||||||
\(36\) | −1.53595 | −0.255992 | ||||||||
\(37\) | −2.03660 | −0.334814 | −0.167407 | − | 0.985888i | \(-0.553539\pi\) | ||||
−0.167407 | + | 0.985888i | \(0.553539\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −2.24758 | −0.359901 | ||||||||
\(40\) | −0.0448427 | −0.00709025 | ||||||||
\(41\) | 4.98252 | 0.778138 | 0.389069 | − | 0.921209i | \(-0.372797\pi\) | ||||
0.389069 | + | 0.921209i | \(0.372797\pi\) | |||||||
\(42\) | −3.31382 | −0.511334 | ||||||||
\(43\) | −0.0680112 | −0.0103716 | −0.00518580 | − | 0.999987i | \(-0.501651\pi\) | ||||
−0.00518580 | + | 0.999987i | \(0.501651\pi\) | |||||||
\(44\) | 2.04170 | 0.307797 | ||||||||
\(45\) | −0.0688762 | −0.0102675 | ||||||||
\(46\) | 2.83061 | 0.417351 | ||||||||
\(47\) | 9.41398 | 1.37317 | 0.686585 | − | 0.727050i | \(-0.259109\pi\) | ||||
0.686585 | + | 0.727050i | \(0.259109\pi\) | |||||||
\(48\) | −1.20998 | −0.174645 | ||||||||
\(49\) | 0.500717 | 0.0715310 | ||||||||
\(50\) | 4.99799 | 0.706822 | ||||||||
\(51\) | −2.32529 | −0.325605 | ||||||||
\(52\) | 1.85754 | 0.257594 | ||||||||
\(53\) | −9.40770 | −1.29225 | −0.646123 | − | 0.763233i | \(-0.723611\pi\) | ||||
−0.646123 | + | 0.763233i | \(0.723611\pi\) | |||||||
\(54\) | −5.48840 | −0.746877 | ||||||||
\(55\) | 0.0915551 | 0.0123453 | ||||||||
\(56\) | 2.73874 | 0.365980 | ||||||||
\(57\) | 1.20998 | 0.160266 | ||||||||
\(58\) | −6.47351 | −0.850013 | ||||||||
\(59\) | 3.35189 | 0.436379 | 0.218190 | − | 0.975906i | \(-0.429985\pi\) | ||||
0.218190 | + | 0.975906i | \(0.429985\pi\) | |||||||
\(60\) | −0.0542587 | −0.00700477 | ||||||||
\(61\) | −7.94329 | −1.01703 | −0.508517 | − | 0.861052i | \(-0.669806\pi\) | ||||
−0.508517 | + | 0.861052i | \(0.669806\pi\) | |||||||
\(62\) | 7.78208 | 0.988325 | ||||||||
\(63\) | 4.20658 | 0.529979 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0832970 | 0.0103317 | ||||||||
\(66\) | 2.47041 | 0.304086 | ||||||||
\(67\) | 1.66761 | 0.203731 | 0.101866 | − | 0.994798i | \(-0.467519\pi\) | ||||
0.101866 | + | 0.994798i | \(0.467519\pi\) | |||||||
\(68\) | 1.92176 | 0.233047 | ||||||||
\(69\) | 3.42498 | 0.412319 | ||||||||
\(70\) | 0.122813 | 0.0146789 | ||||||||
\(71\) | −0.505292 | −0.0599672 | −0.0299836 | − | 0.999550i | \(-0.509546\pi\) | ||||
−0.0299836 | + | 0.999550i | \(0.509546\pi\) | |||||||
\(72\) | 1.53595 | 0.181014 | ||||||||
\(73\) | 0.785797 | 0.0919706 | 0.0459853 | − | 0.998942i | \(-0.485357\pi\) | ||||
0.0459853 | + | 0.998942i | \(0.485357\pi\) | |||||||
\(74\) | 2.03660 | 0.236750 | ||||||||
\(75\) | 6.04746 | 0.698300 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −5.59168 | −0.637231 | ||||||||
\(78\) | 2.24758 | 0.254488 | ||||||||
\(79\) | −13.5898 | −1.52897 | −0.764484 | − | 0.644643i | \(-0.777006\pi\) | ||||
−0.764484 | + | 0.644643i | \(0.777006\pi\) | |||||||
\(80\) | 0.0448427 | 0.00501357 | ||||||||
\(81\) | −2.03299 | −0.225888 | ||||||||
\(82\) | −4.98252 | −0.550227 | ||||||||
\(83\) | 14.9815 | 1.64443 | 0.822216 | − | 0.569175i | \(-0.192737\pi\) | ||||
0.822216 | + | 0.569175i | \(0.192737\pi\) | |||||||
\(84\) | 3.31382 | 0.361567 | ||||||||
\(85\) | 0.0861768 | 0.00934719 | ||||||||
\(86\) | 0.0680112 | 0.00733383 | ||||||||
\(87\) | −7.83281 | −0.839765 | ||||||||
\(88\) | −2.04170 | −0.217645 | ||||||||
\(89\) | −1.46405 | −0.155189 | −0.0775947 | − | 0.996985i | \(-0.524724\pi\) | ||||
−0.0775947 | + | 0.996985i | \(0.524724\pi\) | |||||||
\(90\) | 0.0688762 | 0.00726019 | ||||||||
\(91\) | −5.08732 | −0.533296 | ||||||||
\(92\) | −2.83061 | −0.295111 | ||||||||
\(93\) | 9.41615 | 0.976409 | ||||||||
\(94\) | −9.41398 | −0.970978 | ||||||||
\(95\) | −0.0448427 | −0.00460076 | ||||||||
\(96\) | 1.20998 | 0.123493 | ||||||||
\(97\) | −5.36599 | −0.544834 | −0.272417 | − | 0.962179i | \(-0.587823\pi\) | ||||
−0.272417 | + | 0.962179i | \(0.587823\pi\) | |||||||
\(98\) | −0.500717 | −0.0505800 | ||||||||
\(99\) | −3.13595 | −0.315174 | ||||||||
\(100\) | −4.99799 | −0.499799 | ||||||||
\(101\) | −0.764511 | −0.0760717 | −0.0380359 | − | 0.999276i | \(-0.512110\pi\) | ||||
−0.0380359 | + | 0.999276i | \(0.512110\pi\) | |||||||
\(102\) | 2.32529 | 0.230238 | ||||||||
\(103\) | 3.72634 | 0.367167 | 0.183583 | − | 0.983004i | \(-0.441230\pi\) | ||||
0.183583 | + | 0.983004i | \(0.441230\pi\) | |||||||
\(104\) | −1.85754 | −0.182147 | ||||||||
\(105\) | 0.148601 | 0.0145019 | ||||||||
\(106\) | 9.40770 | 0.913756 | ||||||||
\(107\) | −7.50454 | −0.725492 | −0.362746 | − | 0.931888i | \(-0.618161\pi\) | ||||
−0.362746 | + | 0.931888i | \(0.618161\pi\) | |||||||
\(108\) | 5.48840 | 0.528122 | ||||||||
\(109\) | −6.89890 | −0.660794 | −0.330397 | − | 0.943842i | \(-0.607183\pi\) | ||||
−0.330397 | + | 0.943842i | \(0.607183\pi\) | |||||||
\(110\) | −0.0915551 | −0.00872944 | ||||||||
\(111\) | 2.46424 | 0.233895 | ||||||||
\(112\) | −2.73874 | −0.258787 | ||||||||
\(113\) | −12.1419 | −1.14221 | −0.571106 | − | 0.820877i | \(-0.693485\pi\) | ||||
−0.571106 | + | 0.820877i | \(0.693485\pi\) | |||||||
\(114\) | −1.20998 | −0.113325 | ||||||||
\(115\) | −0.126932 | −0.0118365 | ||||||||
\(116\) | 6.47351 | 0.601050 | ||||||||
\(117\) | −2.85309 | −0.263768 | ||||||||
\(118\) | −3.35189 | −0.308567 | ||||||||
\(119\) | −5.26320 | −0.482477 | ||||||||
\(120\) | 0.0542587 | 0.00495312 | ||||||||
\(121\) | −6.83148 | −0.621044 | ||||||||
\(122\) | 7.94329 | 0.719151 | ||||||||
\(123\) | −6.02874 | −0.543593 | ||||||||
\(124\) | −7.78208 | −0.698851 | ||||||||
\(125\) | −0.448337 | −0.0401005 | ||||||||
\(126\) | −4.20658 | −0.374752 | ||||||||
\(127\) | 11.5438 | 1.02435 | 0.512175 | − | 0.858881i | \(-0.328840\pi\) | ||||
0.512175 | + | 0.858881i | \(0.328840\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.0822920 | 0.00724541 | ||||||||
\(130\) | −0.0832970 | −0.00730563 | ||||||||
\(131\) | −2.66428 | −0.232779 | −0.116389 | − | 0.993204i | \(-0.537132\pi\) | ||||
−0.116389 | + | 0.993204i | \(0.537132\pi\) | |||||||
\(132\) | −2.47041 | −0.215021 | ||||||||
\(133\) | 2.73874 | 0.237479 | ||||||||
\(134\) | −1.66761 | −0.144060 | ||||||||
\(135\) | 0.246115 | 0.0211822 | ||||||||
\(136\) | −1.92176 | −0.164789 | ||||||||
\(137\) | −11.1215 | −0.950178 | −0.475089 | − | 0.879938i | \(-0.657584\pi\) | ||||
−0.475089 | + | 0.879938i | \(0.657584\pi\) | |||||||
\(138\) | −3.42498 | −0.291553 | ||||||||
\(139\) | 12.2154 | 1.03610 | 0.518049 | − | 0.855351i | \(-0.326659\pi\) | ||||
0.518049 | + | 0.855351i | \(0.326659\pi\) | |||||||
\(140\) | −0.122813 | −0.0103796 | ||||||||
\(141\) | −11.3907 | −0.959271 | ||||||||
\(142\) | 0.505292 | 0.0424032 | ||||||||
\(143\) | 3.79252 | 0.317147 | ||||||||
\(144\) | −1.53595 | −0.127996 | ||||||||
\(145\) | 0.290290 | 0.0241072 | ||||||||
\(146\) | −0.785797 | −0.0650330 | ||||||||
\(147\) | −0.605857 | −0.0499702 | ||||||||
\(148\) | −2.03660 | −0.167407 | ||||||||
\(149\) | 9.17304 | 0.751484 | 0.375742 | − | 0.926724i | \(-0.377388\pi\) | ||||
0.375742 | + | 0.926724i | \(0.377388\pi\) | |||||||
\(150\) | −6.04746 | −0.493773 | ||||||||
\(151\) | 9.99988 | 0.813779 | 0.406889 | − | 0.913477i | \(-0.366613\pi\) | ||||
0.406889 | + | 0.913477i | \(0.366613\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.95173 | −0.238633 | ||||||||
\(154\) | 5.59168 | 0.450590 | ||||||||
\(155\) | −0.348969 | −0.0280299 | ||||||||
\(156\) | −2.24758 | −0.179950 | ||||||||
\(157\) | −5.68658 | −0.453839 | −0.226919 | − | 0.973914i | \(-0.572865\pi\) | ||||
−0.226919 | + | 0.973914i | \(0.572865\pi\) | |||||||
\(158\) | 13.5898 | 1.08114 | ||||||||
\(159\) | 11.3831 | 0.902739 | ||||||||
\(160\) | −0.0448427 | −0.00354513 | ||||||||
\(161\) | 7.75231 | 0.610968 | ||||||||
\(162\) | 2.03299 | 0.159727 | ||||||||
\(163\) | 5.80869 | 0.454972 | 0.227486 | − | 0.973781i | \(-0.426949\pi\) | ||||
0.227486 | + | 0.973781i | \(0.426949\pi\) | |||||||
\(164\) | 4.98252 | 0.389069 | ||||||||
\(165\) | −0.110780 | −0.00862419 | ||||||||
\(166\) | −14.9815 | −1.16279 | ||||||||
\(167\) | −2.21510 | −0.171410 | −0.0857048 | − | 0.996321i | \(-0.527314\pi\) | ||||
−0.0857048 | + | 0.996321i | \(0.527314\pi\) | |||||||
\(168\) | −3.31382 | −0.255667 | ||||||||
\(169\) | −9.54956 | −0.734581 | ||||||||
\(170\) | −0.0861768 | −0.00660946 | ||||||||
\(171\) | 1.53595 | 0.117457 | ||||||||
\(172\) | −0.0680112 | −0.00518580 | ||||||||
\(173\) | −10.3281 | −0.785228 | −0.392614 | − | 0.919703i | \(-0.628429\pi\) | ||||
−0.392614 | + | 0.919703i | \(0.628429\pi\) | |||||||
\(174\) | 7.83281 | 0.593803 | ||||||||
\(175\) | 13.6882 | 1.03473 | ||||||||
\(176\) | 2.04170 | 0.153899 | ||||||||
\(177\) | −4.05572 | −0.304847 | ||||||||
\(178\) | 1.46405 | 0.109735 | ||||||||
\(179\) | −8.87410 | −0.663282 | −0.331641 | − | 0.943406i | \(-0.607602\pi\) | ||||
−0.331641 | + | 0.943406i | \(0.607602\pi\) | |||||||
\(180\) | −0.0688762 | −0.00513373 | ||||||||
\(181\) | 5.73170 | 0.426034 | 0.213017 | − | 0.977048i | \(-0.431671\pi\) | ||||
0.213017 | + | 0.977048i | \(0.431671\pi\) | |||||||
\(182\) | 5.08732 | 0.377097 | ||||||||
\(183\) | 9.61121 | 0.710481 | ||||||||
\(184\) | 2.83061 | 0.208675 | ||||||||
\(185\) | −0.0913265 | −0.00671446 | ||||||||
\(186\) | −9.41615 | −0.690425 | ||||||||
\(187\) | 3.92365 | 0.286925 | ||||||||
\(188\) | 9.41398 | 0.686585 | ||||||||
\(189\) | −15.0313 | −1.09337 | ||||||||
\(190\) | 0.0448427 | 0.00325323 | ||||||||
\(191\) | −7.40545 | −0.535839 | −0.267920 | − | 0.963441i | \(-0.586336\pi\) | ||||
−0.267920 | + | 0.963441i | \(0.586336\pi\) | |||||||
\(192\) | −1.20998 | −0.0873227 | ||||||||
\(193\) | 4.31071 | 0.310292 | 0.155146 | − | 0.987892i | \(-0.450415\pi\) | ||||
0.155146 | + | 0.987892i | \(0.450415\pi\) | |||||||
\(194\) | 5.36599 | 0.385256 | ||||||||
\(195\) | −0.100788 | −0.00721755 | ||||||||
\(196\) | 0.500717 | 0.0357655 | ||||||||
\(197\) | 6.81519 | 0.485562 | 0.242781 | − | 0.970081i | \(-0.421940\pi\) | ||||
0.242781 | + | 0.970081i | \(0.421940\pi\) | |||||||
\(198\) | 3.13595 | 0.222862 | ||||||||
\(199\) | 4.23326 | 0.300088 | 0.150044 | − | 0.988679i | \(-0.452058\pi\) | ||||
0.150044 | + | 0.988679i | \(0.452058\pi\) | |||||||
\(200\) | 4.99799 | 0.353411 | ||||||||
\(201\) | −2.01778 | −0.142323 | ||||||||
\(202\) | 0.764511 | 0.0537908 | ||||||||
\(203\) | −17.7293 | −1.24435 | ||||||||
\(204\) | −2.32529 | −0.162803 | ||||||||
\(205\) | 0.223429 | 0.0156050 | ||||||||
\(206\) | −3.72634 | −0.259626 | ||||||||
\(207\) | 4.34768 | 0.302185 | ||||||||
\(208\) | 1.85754 | 0.128797 | ||||||||
\(209\) | −2.04170 | −0.141227 | ||||||||
\(210\) | −0.148601 | −0.0102544 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −9.40770 | −0.646123 | ||||||||
\(213\) | 0.611393 | 0.0418919 | ||||||||
\(214\) | 7.50454 | 0.513000 | ||||||||
\(215\) | −0.00304980 | −0.000207995 0 | ||||||||
\(216\) | −5.48840 | −0.373439 | ||||||||
\(217\) | 21.3131 | 1.44683 | ||||||||
\(218\) | 6.89890 | 0.467252 | ||||||||
\(219\) | −0.950797 | −0.0642489 | ||||||||
\(220\) | 0.0915551 | 0.00617264 | ||||||||
\(221\) | 3.56974 | 0.240127 | ||||||||
\(222\) | −2.46424 | −0.165389 | ||||||||
\(223\) | −7.55745 | −0.506084 | −0.253042 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253042 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(224\) | 2.73874 | 0.182990 | ||||||||
\(225\) | 7.67667 | 0.511778 | ||||||||
\(226\) | 12.1419 | 0.807665 | ||||||||
\(227\) | 26.5914 | 1.76493 | 0.882466 | − | 0.470377i | \(-0.155882\pi\) | ||||
0.882466 | + | 0.470377i | \(0.155882\pi\) | |||||||
\(228\) | 1.20998 | 0.0801328 | ||||||||
\(229\) | 26.9239 | 1.77918 | 0.889591 | − | 0.456757i | \(-0.150989\pi\) | ||||
0.889591 | + | 0.456757i | \(0.150989\pi\) | |||||||
\(230\) | 0.126932 | 0.00836966 | ||||||||
\(231\) | 6.76581 | 0.445158 | ||||||||
\(232\) | −6.47351 | −0.425007 | ||||||||
\(233\) | −17.6009 | −1.15307 | −0.576536 | − | 0.817072i | \(-0.695596\pi\) | ||||
−0.576536 | + | 0.817072i | \(0.695596\pi\) | |||||||
\(234\) | 2.85309 | 0.186512 | ||||||||
\(235\) | 0.422148 | 0.0275379 | ||||||||
\(236\) | 3.35189 | 0.218190 | ||||||||
\(237\) | 16.4433 | 1.06811 | ||||||||
\(238\) | 5.26320 | 0.341163 | ||||||||
\(239\) | −13.1897 | −0.853169 | −0.426584 | − | 0.904448i | \(-0.640283\pi\) | ||||
−0.426584 | + | 0.904448i | \(0.640283\pi\) | |||||||
\(240\) | −0.0542587 | −0.00350238 | ||||||||
\(241\) | 2.57390 | 0.165800 | 0.0828999 | − | 0.996558i | \(-0.473582\pi\) | ||||
0.0828999 | + | 0.996558i | \(0.473582\pi\) | |||||||
\(242\) | 6.83148 | 0.439144 | ||||||||
\(243\) | −14.0053 | −0.898443 | ||||||||
\(244\) | −7.94329 | −0.508517 | ||||||||
\(245\) | 0.0224535 | 0.00143450 | ||||||||
\(246\) | 6.02874 | 0.384378 | ||||||||
\(247\) | −1.85754 | −0.118192 | ||||||||
\(248\) | 7.78208 | 0.494162 | ||||||||
\(249\) | −18.1273 | −1.14877 | ||||||||
\(250\) | 0.448337 | 0.0283553 | ||||||||
\(251\) | 3.43499 | 0.216815 | 0.108407 | − | 0.994107i | \(-0.465425\pi\) | ||||
0.108407 | + | 0.994107i | \(0.465425\pi\) | |||||||
\(252\) | 4.20658 | 0.264990 | ||||||||
\(253\) | −5.77924 | −0.363338 | ||||||||
\(254\) | −11.5438 | −0.724325 | ||||||||
\(255\) | −0.104272 | −0.00652977 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.6341 | −1.28712 | −0.643561 | − | 0.765395i | \(-0.722544\pi\) | ||||
−0.643561 | + | 0.765395i | \(0.722544\pi\) | |||||||
\(258\) | −0.0822920 | −0.00512328 | ||||||||
\(259\) | 5.57772 | 0.346582 | ||||||||
\(260\) | 0.0832970 | 0.00516586 | ||||||||
\(261\) | −9.94300 | −0.615456 | ||||||||
\(262\) | 2.66428 | 0.164599 | ||||||||
\(263\) | 18.0576 | 1.11348 | 0.556741 | − | 0.830686i | \(-0.312052\pi\) | ||||
0.556741 | + | 0.830686i | \(0.312052\pi\) | |||||||
\(264\) | 2.47041 | 0.152043 | ||||||||
\(265\) | −0.421866 | −0.0259150 | ||||||||
\(266\) | −2.73874 | −0.167923 | ||||||||
\(267\) | 1.77147 | 0.108412 | ||||||||
\(268\) | 1.66761 | 0.101866 | ||||||||
\(269\) | 30.3245 | 1.84892 | 0.924460 | − | 0.381280i | \(-0.124517\pi\) | ||||
0.924460 | + | 0.381280i | \(0.124517\pi\) | |||||||
\(270\) | −0.246115 | −0.0149781 | ||||||||
\(271\) | 7.46687 | 0.453580 | 0.226790 | − | 0.973944i | \(-0.427177\pi\) | ||||
0.226790 | + | 0.973944i | \(0.427177\pi\) | |||||||
\(272\) | 1.92176 | 0.116524 | ||||||||
\(273\) | 6.15555 | 0.372551 | ||||||||
\(274\) | 11.1215 | 0.671877 | ||||||||
\(275\) | −10.2044 | −0.615347 | ||||||||
\(276\) | 3.42498 | 0.206159 | ||||||||
\(277\) | 31.8582 | 1.91417 | 0.957087 | − | 0.289800i | \(-0.0935888\pi\) | ||||
0.957087 | + | 0.289800i | \(0.0935888\pi\) | |||||||
\(278\) | −12.2154 | −0.732632 | ||||||||
\(279\) | 11.9529 | 0.715601 | ||||||||
\(280\) | 0.122813 | 0.00733946 | ||||||||
\(281\) | −3.05766 | −0.182405 | −0.0912024 | − | 0.995832i | \(-0.529071\pi\) | ||||
−0.0912024 | + | 0.995832i | \(0.529071\pi\) | |||||||
\(282\) | 11.3907 | 0.678307 | ||||||||
\(283\) | 17.5142 | 1.04111 | 0.520556 | − | 0.853828i | \(-0.325725\pi\) | ||||
0.520556 | + | 0.853828i | \(0.325725\pi\) | |||||||
\(284\) | −0.505292 | −0.0299836 | ||||||||
\(285\) | 0.0542587 | 0.00321401 | ||||||||
\(286\) | −3.79252 | −0.224257 | ||||||||
\(287\) | −13.6458 | −0.805488 | ||||||||
\(288\) | 1.53595 | 0.0905068 | ||||||||
\(289\) | −13.3068 | −0.782755 | ||||||||
\(290\) | −0.290290 | −0.0170464 | ||||||||
\(291\) | 6.49273 | 0.380611 | ||||||||
\(292\) | 0.785797 | 0.0459853 | ||||||||
\(293\) | 25.1596 | 1.46984 | 0.734919 | − | 0.678154i | \(-0.237220\pi\) | ||||
0.734919 | + | 0.678154i | \(0.237220\pi\) | |||||||
\(294\) | 0.605857 | 0.0353343 | ||||||||
\(295\) | 0.150308 | 0.00875127 | ||||||||
\(296\) | 2.03660 | 0.118375 | ||||||||
\(297\) | 11.2056 | 0.650218 | ||||||||
\(298\) | −9.17304 | −0.531380 | ||||||||
\(299\) | −5.25796 | −0.304076 | ||||||||
\(300\) | 6.04746 | 0.349150 | ||||||||
\(301\) | 0.186265 | 0.0107361 | ||||||||
\(302\) | −9.99988 | −0.575429 | ||||||||
\(303\) | 0.925042 | 0.0531423 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.356198 | −0.0203959 | ||||||||
\(306\) | 2.95173 | 0.168739 | ||||||||
\(307\) | 7.27043 | 0.414945 | 0.207473 | − | 0.978241i | \(-0.433476\pi\) | ||||
0.207473 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(308\) | −5.59168 | −0.318616 | ||||||||
\(309\) | −4.50879 | −0.256496 | ||||||||
\(310\) | 0.348969 | 0.0198201 | ||||||||
\(311\) | 2.71336 | 0.153861 | 0.0769304 | − | 0.997036i | \(-0.475488\pi\) | ||||
0.0769304 | + | 0.997036i | \(0.475488\pi\) | |||||||
\(312\) | 2.24758 | 0.127244 | ||||||||
\(313\) | −20.8311 | −1.17744 | −0.588722 | − | 0.808336i | \(-0.700369\pi\) | ||||
−0.588722 | + | 0.808336i | \(0.700369\pi\) | |||||||
\(314\) | 5.68658 | 0.320913 | ||||||||
\(315\) | 0.188634 | 0.0106283 | ||||||||
\(316\) | −13.5898 | −0.764484 | ||||||||
\(317\) | 16.4333 | 0.922983 | 0.461492 | − | 0.887145i | \(-0.347314\pi\) | ||||
0.461492 | + | 0.887145i | \(0.347314\pi\) | |||||||
\(318\) | −11.3831 | −0.638333 | ||||||||
\(319\) | 13.2169 | 0.740006 | ||||||||
\(320\) | 0.0448427 | 0.00250678 | ||||||||
\(321\) | 9.08034 | 0.506815 | ||||||||
\(322\) | −7.75231 | −0.432020 | ||||||||
\(323\) | −1.92176 | −0.106930 | ||||||||
\(324\) | −2.03299 | −0.112944 | ||||||||
\(325\) | −9.28395 | −0.514981 | ||||||||
\(326\) | −5.80869 | −0.321714 | ||||||||
\(327\) | 8.34752 | 0.461619 | ||||||||
\(328\) | −4.98252 | −0.275113 | ||||||||
\(329\) | −25.7825 | −1.42143 | ||||||||
\(330\) | 0.110780 | 0.00609822 | ||||||||
\(331\) | −12.7091 | −0.698557 | −0.349278 | − | 0.937019i | \(-0.613573\pi\) | ||||
−0.349278 | + | 0.937019i | \(0.613573\pi\) | |||||||
\(332\) | 14.9815 | 0.822216 | ||||||||
\(333\) | 3.12812 | 0.171420 | ||||||||
\(334\) | 2.21510 | 0.121205 | ||||||||
\(335\) | 0.0747803 | 0.00408568 | ||||||||
\(336\) | 3.31382 | 0.180784 | ||||||||
\(337\) | −7.40878 | −0.403582 | −0.201791 | − | 0.979429i | \(-0.564676\pi\) | ||||
−0.201791 | + | 0.979429i | \(0.564676\pi\) | |||||||
\(338\) | 9.54956 | 0.519427 | ||||||||
\(339\) | 14.6914 | 0.797927 | ||||||||
\(340\) | 0.0861768 | 0.00467360 | ||||||||
\(341\) | −15.8886 | −0.860418 | ||||||||
\(342\) | −1.53595 | −0.0830548 | ||||||||
\(343\) | 17.7999 | 0.961103 | ||||||||
\(344\) | 0.0680112 | 0.00366692 | ||||||||
\(345\) | 0.153585 | 0.00826875 | ||||||||
\(346\) | 10.3281 | 0.555240 | ||||||||
\(347\) | 15.7189 | 0.843834 | 0.421917 | − | 0.906635i | \(-0.361357\pi\) | ||||
0.421917 | + | 0.906635i | \(0.361357\pi\) | |||||||
\(348\) | −7.83281 | −0.419882 | ||||||||
\(349\) | −2.98915 | −0.160005 | −0.0800027 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800027 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(350\) | −13.6882 | −0.731666 | ||||||||
\(351\) | 10.1949 | 0.544164 | ||||||||
\(352\) | −2.04170 | −0.108823 | ||||||||
\(353\) | −0.786860 | −0.0418803 | −0.0209402 | − | 0.999781i | \(-0.506666\pi\) | ||||
−0.0209402 | + | 0.999781i | \(0.506666\pi\) | |||||||
\(354\) | 4.05572 | 0.215559 | ||||||||
\(355\) | −0.0226587 | −0.00120260 | ||||||||
\(356\) | −1.46405 | −0.0775947 | ||||||||
\(357\) | 6.36836 | 0.337050 | ||||||||
\(358\) | 8.87410 | 0.469011 | ||||||||
\(359\) | −15.5405 | −0.820195 | −0.410097 | − | 0.912042i | \(-0.634505\pi\) | ||||
−0.410097 | + | 0.912042i | \(0.634505\pi\) | |||||||
\(360\) | 0.0688762 | 0.00363010 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.73170 | −0.301252 | ||||||||
\(363\) | 8.26594 | 0.433850 | ||||||||
\(364\) | −5.08732 | −0.266648 | ||||||||
\(365\) | 0.0352372 | 0.00184440 | ||||||||
\(366\) | −9.61121 | −0.502386 | ||||||||
\(367\) | −17.0403 | −0.889495 | −0.444748 | − | 0.895656i | \(-0.646707\pi\) | ||||
−0.444748 | + | 0.895656i | \(0.646707\pi\) | |||||||
\(368\) | −2.83061 | −0.147556 | ||||||||
\(369\) | −7.65291 | −0.398394 | ||||||||
\(370\) | 0.0913265 | 0.00474784 | ||||||||
\(371\) | 25.7653 | 1.33767 | ||||||||
\(372\) | 9.41615 | 0.488205 | ||||||||
\(373\) | 16.6854 | 0.863940 | 0.431970 | − | 0.901888i | \(-0.357819\pi\) | ||||
0.431970 | + | 0.901888i | \(0.357819\pi\) | |||||||
\(374\) | −3.92365 | −0.202887 | ||||||||
\(375\) | 0.542478 | 0.0280134 | ||||||||
\(376\) | −9.41398 | −0.485489 | ||||||||
\(377\) | 12.0248 | 0.619308 | ||||||||
\(378\) | 15.0313 | 0.773128 | ||||||||
\(379\) | 20.9333 | 1.07527 | 0.537636 | − | 0.843177i | \(-0.319318\pi\) | ||||
0.537636 | + | 0.843177i | \(0.319318\pi\) | |||||||
\(380\) | −0.0448427 | −0.00230038 | ||||||||
\(381\) | −13.9678 | −0.715592 | ||||||||
\(382\) | 7.40545 | 0.378896 | ||||||||
\(383\) | 27.8816 | 1.42468 | 0.712341 | − | 0.701834i | \(-0.247635\pi\) | ||||
0.712341 | + | 0.701834i | \(0.247635\pi\) | |||||||
\(384\) | 1.20998 | 0.0617465 | ||||||||
\(385\) | −0.250746 | −0.0127792 | ||||||||
\(386\) | −4.31071 | −0.219410 | ||||||||
\(387\) | 0.104462 | 0.00531010 | ||||||||
\(388\) | −5.36599 | −0.272417 | ||||||||
\(389\) | −16.9170 | −0.857726 | −0.428863 | − | 0.903370i | \(-0.641086\pi\) | ||||
−0.428863 | + | 0.903370i | \(0.641086\pi\) | |||||||
\(390\) | 0.100788 | 0.00510358 | ||||||||
\(391\) | −5.43975 | −0.275100 | ||||||||
\(392\) | −0.500717 | −0.0252900 | ||||||||
\(393\) | 3.22372 | 0.162615 | ||||||||
\(394\) | −6.81519 | −0.343344 | ||||||||
\(395\) | −0.609402 | −0.0306623 | ||||||||
\(396\) | −3.13595 | −0.157587 | ||||||||
\(397\) | −4.90896 | −0.246374 | −0.123187 | − | 0.992384i | \(-0.539311\pi\) | ||||
−0.123187 | + | 0.992384i | \(0.539311\pi\) | |||||||
\(398\) | −4.23326 | −0.212194 | ||||||||
\(399\) | −3.31382 | −0.165899 | ||||||||
\(400\) | −4.99799 | −0.249899 | ||||||||
\(401\) | −3.24262 | −0.161929 | −0.0809644 | − | 0.996717i | \(-0.525800\pi\) | ||||
−0.0809644 | + | 0.996717i | \(0.525800\pi\) | |||||||
\(402\) | 2.01778 | 0.100638 | ||||||||
\(403\) | −14.4555 | −0.720080 | ||||||||
\(404\) | −0.764511 | −0.0380359 | ||||||||
\(405\) | −0.0911650 | −0.00453002 | ||||||||
\(406\) | 17.7293 | 0.879889 | ||||||||
\(407\) | −4.15811 | −0.206110 | ||||||||
\(408\) | 2.32529 | 0.115119 | ||||||||
\(409\) | −10.5525 | −0.521786 | −0.260893 | − | 0.965368i | \(-0.584017\pi\) | ||||
−0.260893 | + | 0.965368i | \(0.584017\pi\) | |||||||
\(410\) | −0.223429 | −0.0110344 | ||||||||
\(411\) | 13.4568 | 0.663776 | ||||||||
\(412\) | 3.72634 | 0.183583 | ||||||||
\(413\) | −9.17998 | −0.451717 | ||||||||
\(414\) | −4.34768 | −0.213677 | ||||||||
\(415\) | 0.671811 | 0.0329779 | ||||||||
\(416\) | −1.85754 | −0.0910733 | ||||||||
\(417\) | −14.7804 | −0.723798 | ||||||||
\(418\) | 2.04170 | 0.0998626 | ||||||||
\(419\) | −31.7266 | −1.54994 | −0.774972 | − | 0.631996i | \(-0.782236\pi\) | ||||
−0.774972 | + | 0.631996i | \(0.782236\pi\) | |||||||
\(420\) | 0.148601 | 0.00725097 | ||||||||
\(421\) | 23.7832 | 1.15912 | 0.579562 | − | 0.814928i | \(-0.303224\pi\) | ||||
0.579562 | + | 0.814928i | \(0.303224\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −14.4594 | −0.703041 | ||||||||
\(424\) | 9.40770 | 0.456878 | ||||||||
\(425\) | −9.60493 | −0.465908 | ||||||||
\(426\) | −0.611393 | −0.0296221 | ||||||||
\(427\) | 21.7546 | 1.05278 | ||||||||
\(428\) | −7.50454 | −0.362746 | ||||||||
\(429\) | −4.58887 | −0.221553 | ||||||||
\(430\) | 0.00304980 | 0.000147075 0 | ||||||||
\(431\) | −3.13657 | −0.151083 | −0.0755417 | − | 0.997143i | \(-0.524069\pi\) | ||||
−0.0755417 | + | 0.997143i | \(0.524069\pi\) | |||||||
\(432\) | 5.48840 | 0.264061 | ||||||||
\(433\) | 24.2943 | 1.16751 | 0.583754 | − | 0.811931i | \(-0.301583\pi\) | ||||
0.583754 | + | 0.811931i | \(0.301583\pi\) | |||||||
\(434\) | −21.3131 | −1.02306 | ||||||||
\(435\) | −0.351244 | −0.0168409 | ||||||||
\(436\) | −6.89890 | −0.330397 | ||||||||
\(437\) | 2.83061 | 0.135406 | ||||||||
\(438\) | 0.950797 | 0.0454309 | ||||||||
\(439\) | −6.37754 | −0.304383 | −0.152192 | − | 0.988351i | \(-0.548633\pi\) | ||||
−0.152192 | + | 0.988351i | \(0.548633\pi\) | |||||||
\(440\) | −0.0915551 | −0.00436472 | ||||||||
\(441\) | −0.769077 | −0.0366227 | ||||||||
\(442\) | −3.56974 | −0.169795 | ||||||||
\(443\) | 15.8222 | 0.751735 | 0.375867 | − | 0.926673i | \(-0.377345\pi\) | ||||
0.375867 | + | 0.926673i | \(0.377345\pi\) | |||||||
\(444\) | 2.46424 | 0.116948 | ||||||||
\(445\) | −0.0656521 | −0.00311221 | ||||||||
\(446\) | 7.55745 | 0.357856 | ||||||||
\(447\) | −11.0992 | −0.524973 | ||||||||
\(448\) | −2.73874 | −0.129393 | ||||||||
\(449\) | 0.375322 | 0.0177125 | 0.00885626 | − | 0.999961i | \(-0.497181\pi\) | ||||
0.00885626 | + | 0.999961i | \(0.497181\pi\) | |||||||
\(450\) | −7.67667 | −0.361882 | ||||||||
\(451\) | 10.1728 | 0.479017 | ||||||||
\(452\) | −12.1419 | −0.571106 | ||||||||
\(453\) | −12.0996 | −0.568491 | ||||||||
\(454\) | −26.5914 | −1.24799 | ||||||||
\(455\) | −0.228129 | −0.0106949 | ||||||||
\(456\) | −1.20998 | −0.0566624 | ||||||||
\(457\) | 9.07588 | 0.424552 | 0.212276 | − | 0.977210i | \(-0.431912\pi\) | ||||
0.212276 | + | 0.977210i | \(0.431912\pi\) | |||||||
\(458\) | −26.9239 | −1.25807 | ||||||||
\(459\) | 10.5474 | 0.492310 | ||||||||
\(460\) | −0.126932 | −0.00591824 | ||||||||
\(461\) | −36.3391 | −1.69248 | −0.846240 | − | 0.532801i | \(-0.821139\pi\) | ||||
−0.846240 | + | 0.532801i | \(0.821139\pi\) | |||||||
\(462\) | −6.76581 | −0.314774 | ||||||||
\(463\) | −28.6466 | −1.33132 | −0.665660 | − | 0.746255i | \(-0.731850\pi\) | ||||
−0.665660 | + | 0.746255i | \(0.731850\pi\) | |||||||
\(464\) | 6.47351 | 0.300525 | ||||||||
\(465\) | 0.422245 | 0.0195812 | ||||||||
\(466\) | 17.6009 | 0.815345 | ||||||||
\(467\) | −5.09899 | −0.235953 | −0.117977 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117977 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(468\) | −2.85309 | −0.131884 | ||||||||
\(469\) | −4.56717 | −0.210892 | ||||||||
\(470\) | −0.422148 | −0.0194722 | ||||||||
\(471\) | 6.88064 | 0.317043 | ||||||||
\(472\) | −3.35189 | −0.154283 | ||||||||
\(473\) | −0.138858 | −0.00638470 | ||||||||
\(474\) | −16.4433 | −0.755267 | ||||||||
\(475\) | 4.99799 | 0.229323 | ||||||||
\(476\) | −5.26320 | −0.241239 | ||||||||
\(477\) | 14.4498 | 0.661610 | ||||||||
\(478\) | 13.1897 | 0.603281 | ||||||||
\(479\) | 8.74345 | 0.399498 | 0.199749 | − | 0.979847i | \(-0.435987\pi\) | ||||
0.199749 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(480\) | 0.0542587 | 0.00247656 | ||||||||
\(481\) | −3.78305 | −0.172492 | ||||||||
\(482\) | −2.57390 | −0.117238 | ||||||||
\(483\) | −9.38013 | −0.426811 | ||||||||
\(484\) | −6.83148 | −0.310522 | ||||||||
\(485\) | −0.240626 | −0.0109262 | ||||||||
\(486\) | 14.0053 | 0.635295 | ||||||||
\(487\) | −1.45780 | −0.0660594 | −0.0330297 | − | 0.999454i | \(-0.510516\pi\) | ||||
−0.0330297 | + | 0.999454i | \(0.510516\pi\) | |||||||
\(488\) | 7.94329 | 0.359576 | ||||||||
\(489\) | −7.02840 | −0.317835 | ||||||||
\(490\) | −0.0224535 | −0.00101435 | ||||||||
\(491\) | 18.2117 | 0.821884 | 0.410942 | − | 0.911662i | \(-0.365200\pi\) | ||||
0.410942 | + | 0.911662i | \(0.365200\pi\) | |||||||
\(492\) | −6.02874 | −0.271796 | ||||||||
\(493\) | 12.4405 | 0.560293 | ||||||||
\(494\) | 1.85754 | 0.0835745 | ||||||||
\(495\) | −0.140624 | −0.00632059 | ||||||||
\(496\) | −7.78208 | −0.349426 | ||||||||
\(497\) | 1.38387 | 0.0620749 | ||||||||
\(498\) | 18.1273 | 0.812303 | ||||||||
\(499\) | 6.37347 | 0.285316 | 0.142658 | − | 0.989772i | \(-0.454435\pi\) | ||||
0.142658 | + | 0.989772i | \(0.454435\pi\) | |||||||
\(500\) | −0.448337 | −0.0200502 | ||||||||
\(501\) | 2.68022 | 0.119744 | ||||||||
\(502\) | −3.43499 | −0.153311 | ||||||||
\(503\) | 39.2616 | 1.75059 | 0.875293 | − | 0.483593i | \(-0.160668\pi\) | ||||
0.875293 | + | 0.483593i | \(0.160668\pi\) | |||||||
\(504\) | −4.20658 | −0.187376 | ||||||||
\(505\) | −0.0342828 | −0.00152556 | ||||||||
\(506\) | 5.77924 | 0.256919 | ||||||||
\(507\) | 11.5548 | 0.513165 | ||||||||
\(508\) | 11.5438 | 0.512175 | ||||||||
\(509\) | 34.9816 | 1.55053 | 0.775266 | − | 0.631634i | \(-0.217616\pi\) | ||||
0.775266 | + | 0.631634i | \(0.217616\pi\) | |||||||
\(510\) | 0.104272 | 0.00461725 | ||||||||
\(511\) | −2.15210 | −0.0952031 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.48840 | −0.242319 | ||||||||
\(514\) | 20.6341 | 0.910132 | ||||||||
\(515\) | 0.167099 | 0.00736326 | ||||||||
\(516\) | 0.0822920 | 0.00362270 | ||||||||
\(517\) | 19.2205 | 0.845316 | ||||||||
\(518\) | −5.57772 | −0.245071 | ||||||||
\(519\) | 12.4967 | 0.548546 | ||||||||
\(520\) | −0.0832970 | −0.00365281 | ||||||||
\(521\) | 24.5132 | 1.07394 | 0.536971 | − | 0.843601i | \(-0.319568\pi\) | ||||
0.536971 | + | 0.843601i | \(0.319568\pi\) | |||||||
\(522\) | 9.94300 | 0.435193 | ||||||||
\(523\) | −18.4689 | −0.807588 | −0.403794 | − | 0.914850i | \(-0.632309\pi\) | ||||
−0.403794 | + | 0.914850i | \(0.632309\pi\) | |||||||
\(524\) | −2.66428 | −0.116389 | ||||||||
\(525\) | −16.5624 | −0.722844 | ||||||||
\(526\) | −18.0576 | −0.787351 | ||||||||
\(527\) | −14.9553 | −0.651462 | ||||||||
\(528\) | −2.47041 | −0.107511 | ||||||||
\(529\) | −14.9876 | −0.651637 | ||||||||
\(530\) | 0.421866 | 0.0183247 | ||||||||
\(531\) | −5.14835 | −0.223419 | ||||||||
\(532\) | 2.73874 | 0.118740 | ||||||||
\(533\) | 9.25521 | 0.400888 | ||||||||
\(534\) | −1.77147 | −0.0766592 | ||||||||
\(535\) | −0.336524 | −0.0145492 | ||||||||
\(536\) | −1.66761 | −0.0720299 | ||||||||
\(537\) | 10.7375 | 0.463356 | ||||||||
\(538\) | −30.3245 | −1.30738 | ||||||||
\(539\) | 1.02231 | 0.0440341 | ||||||||
\(540\) | 0.246115 | 0.0105911 | ||||||||
\(541\) | 28.7139 | 1.23451 | 0.617253 | − | 0.786765i | \(-0.288246\pi\) | ||||
0.617253 | + | 0.786765i | \(0.288246\pi\) | |||||||
\(542\) | −7.46687 | −0.320729 | ||||||||
\(543\) | −6.93524 | −0.297619 | ||||||||
\(544\) | −1.92176 | −0.0823947 | ||||||||
\(545\) | −0.309365 | −0.0132517 | ||||||||
\(546\) | −6.15555 | −0.263433 | ||||||||
\(547\) | 31.2204 | 1.33489 | 0.667444 | − | 0.744660i | \(-0.267389\pi\) | ||||
0.667444 | + | 0.744660i | \(0.267389\pi\) | |||||||
\(548\) | −11.1215 | −0.475089 | ||||||||
\(549\) | 12.2005 | 0.520705 | ||||||||
\(550\) | 10.2044 | 0.435116 | ||||||||
\(551\) | −6.47351 | −0.275781 | ||||||||
\(552\) | −3.42498 | −0.145777 | ||||||||
\(553\) | 37.2189 | 1.58271 | ||||||||
\(554\) | −31.8582 | −1.35353 | ||||||||
\(555\) | 0.110503 | 0.00469059 | ||||||||
\(556\) | 12.2154 | 0.518049 | ||||||||
\(557\) | 17.2103 | 0.729224 | 0.364612 | − | 0.931160i | \(-0.381202\pi\) | ||||
0.364612 | + | 0.931160i | \(0.381202\pi\) | |||||||
\(558\) | −11.9529 | −0.506007 | ||||||||
\(559\) | −0.126333 | −0.00534333 | ||||||||
\(560\) | −0.122813 | −0.00518978 | ||||||||
\(561\) | −4.74753 | −0.200441 | ||||||||
\(562\) | 3.05766 | 0.128980 | ||||||||
\(563\) | −7.12262 | −0.300183 | −0.150091 | − | 0.988672i | \(-0.547957\pi\) | ||||
−0.150091 | + | 0.988672i | \(0.547957\pi\) | |||||||
\(564\) | −11.3907 | −0.479635 | ||||||||
\(565\) | −0.544474 | −0.0229062 | ||||||||
\(566\) | −17.5142 | −0.736177 | ||||||||
\(567\) | 5.56785 | 0.233828 | ||||||||
\(568\) | 0.505292 | 0.0212016 | ||||||||
\(569\) | −30.1132 | −1.26241 | −0.631205 | − | 0.775616i | \(-0.717439\pi\) | ||||
−0.631205 | + | 0.775616i | \(0.717439\pi\) | |||||||
\(570\) | −0.0542587 | −0.00227265 | ||||||||
\(571\) | 8.50857 | 0.356072 | 0.178036 | − | 0.984024i | \(-0.443026\pi\) | ||||
0.178036 | + | 0.984024i | \(0.443026\pi\) | |||||||
\(572\) | 3.79252 | 0.158573 | ||||||||
\(573\) | 8.96043 | 0.374327 | ||||||||
\(574\) | 13.6458 | 0.569566 | ||||||||
\(575\) | 14.1474 | 0.589986 | ||||||||
\(576\) | −1.53595 | −0.0639980 | ||||||||
\(577\) | −8.70274 | −0.362300 | −0.181150 | − | 0.983456i | \(-0.557982\pi\) | ||||
−0.181150 | + | 0.983456i | \(0.557982\pi\) | |||||||
\(578\) | 13.3068 | 0.553492 | ||||||||
\(579\) | −5.21587 | −0.216764 | ||||||||
\(580\) | 0.290290 | 0.0120536 | ||||||||
\(581\) | −41.0305 | −1.70223 | ||||||||
\(582\) | −6.49273 | −0.269133 | ||||||||
\(583\) | −19.2076 | −0.795499 | ||||||||
\(584\) | −0.785797 | −0.0325165 | ||||||||
\(585\) | −0.127940 | −0.00528967 | ||||||||
\(586\) | −25.1596 | −1.03933 | ||||||||
\(587\) | 46.2495 | 1.90892 | 0.954461 | − | 0.298334i | \(-0.0964311\pi\) | ||||
0.954461 | + | 0.298334i | \(0.0964311\pi\) | |||||||
\(588\) | −0.605857 | −0.0249851 | ||||||||
\(589\) | 7.78208 | 0.320655 | ||||||||
\(590\) | −0.150308 | −0.00618808 | ||||||||
\(591\) | −8.24623 | −0.339204 | ||||||||
\(592\) | −2.03660 | −0.0837036 | ||||||||
\(593\) | 26.3507 | 1.08209 | 0.541047 | − | 0.840993i | \(-0.318028\pi\) | ||||
0.541047 | + | 0.840993i | \(0.318028\pi\) | |||||||
\(594\) | −11.2056 | −0.459773 | ||||||||
\(595\) | −0.236016 | −0.00967572 | ||||||||
\(596\) | 9.17304 | 0.375742 | ||||||||
\(597\) | −5.12216 | −0.209636 | ||||||||
\(598\) | 5.25796 | 0.215014 | ||||||||
\(599\) | −17.9714 | −0.734291 | −0.367146 | − | 0.930163i | \(-0.619665\pi\) | ||||
−0.367146 | + | 0.930163i | \(0.619665\pi\) | |||||||
\(600\) | −6.04746 | −0.246886 | ||||||||
\(601\) | 23.9345 | 0.976308 | 0.488154 | − | 0.872757i | \(-0.337670\pi\) | ||||
0.488154 | + | 0.872757i | \(0.337670\pi\) | |||||||
\(602\) | −0.186265 | −0.00759160 | ||||||||
\(603\) | −2.56137 | −0.104307 | ||||||||
\(604\) | 9.99988 | 0.406889 | ||||||||
\(605\) | −0.306342 | −0.0124546 | ||||||||
\(606\) | −0.925042 | −0.0375773 | ||||||||
\(607\) | 17.5506 | 0.712358 | 0.356179 | − | 0.934418i | \(-0.384079\pi\) | ||||
0.356179 | + | 0.934418i | \(0.384079\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 21.4520 | 0.869281 | ||||||||
\(610\) | 0.356198 | 0.0144220 | ||||||||
\(611\) | 17.4868 | 0.707441 | ||||||||
\(612\) | −2.95173 | −0.119317 | ||||||||
\(613\) | 25.7385 | 1.03957 | 0.519783 | − | 0.854298i | \(-0.326013\pi\) | ||||
0.519783 | + | 0.854298i | \(0.326013\pi\) | |||||||
\(614\) | −7.27043 | −0.293411 | ||||||||
\(615\) | −0.270345 | −0.0109014 | ||||||||
\(616\) | 5.59168 | 0.225295 | ||||||||
\(617\) | 29.7041 | 1.19584 | 0.597921 | − | 0.801555i | \(-0.295994\pi\) | ||||
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(618\) | 4.50879 | 0.181370 | ||||||||
\(619\) | −16.0381 | −0.644624 | −0.322312 | − | 0.946633i | \(-0.604460\pi\) | ||||
−0.322312 | + | 0.946633i | \(0.604460\pi\) | |||||||
\(620\) | −0.348969 | −0.0140149 | ||||||||
\(621\) | −15.5355 | −0.623419 | ||||||||
\(622\) | −2.71336 | −0.108796 | ||||||||
\(623\) | 4.00967 | 0.160644 | ||||||||
\(624\) | −2.24758 | −0.0899752 | ||||||||
\(625\) | 24.9698 | 0.998794 | ||||||||
\(626\) | 20.8311 | 0.832579 | ||||||||
\(627\) | 2.47041 | 0.0986586 | ||||||||
\(628\) | −5.68658 | −0.226919 | ||||||||
\(629\) | −3.91385 | −0.156055 | ||||||||
\(630\) | −0.188634 | −0.00751537 | ||||||||
\(631\) | −25.1387 | −1.00075 | −0.500377 | − | 0.865807i | \(-0.666805\pi\) | ||||
−0.500377 | + | 0.865807i | \(0.666805\pi\) | |||||||
\(632\) | 13.5898 | 0.540572 | ||||||||
\(633\) | −1.20998 | −0.0480923 | ||||||||
\(634\) | −16.4333 | −0.652648 | ||||||||
\(635\) | 0.517657 | 0.0205426 | ||||||||
\(636\) | 11.3831 | 0.451370 | ||||||||
\(637\) | 0.930100 | 0.0368519 | ||||||||
\(638\) | −13.2169 | −0.523263 | ||||||||
\(639\) | 0.776105 | 0.0307022 | ||||||||
\(640\) | −0.0448427 | −0.00177256 | ||||||||
\(641\) | −40.7984 | −1.61144 | −0.805721 | − | 0.592295i | \(-0.798222\pi\) | ||||
−0.805721 | + | 0.592295i | \(0.798222\pi\) | |||||||
\(642\) | −9.08034 | −0.358372 | ||||||||
\(643\) | 38.1025 | 1.50261 | 0.751307 | − | 0.659953i | \(-0.229424\pi\) | ||||
0.751307 | + | 0.659953i | \(0.229424\pi\) | |||||||
\(644\) | 7.75231 | 0.305484 | ||||||||
\(645\) | 0.00369020 | 0.000145301 0 | ||||||||
\(646\) | 1.92176 | 0.0756106 | ||||||||
\(647\) | −45.5527 | −1.79086 | −0.895431 | − | 0.445200i | \(-0.853133\pi\) | ||||
−0.895431 | + | 0.445200i | \(0.853133\pi\) | |||||||
\(648\) | 2.03299 | 0.0798636 | ||||||||
\(649\) | 6.84354 | 0.268633 | ||||||||
\(650\) | 9.28395 | 0.364147 | ||||||||
\(651\) | −25.7884 | −1.01073 | ||||||||
\(652\) | 5.80869 | 0.227486 | ||||||||
\(653\) | 10.2061 | 0.399397 | 0.199699 | − | 0.979857i | \(-0.436004\pi\) | ||||
0.199699 | + | 0.979857i | \(0.436004\pi\) | |||||||
\(654\) | −8.34752 | −0.326414 | ||||||||
\(655\) | −0.119473 | −0.00466821 | ||||||||
\(656\) | 4.98252 | 0.194535 | ||||||||
\(657\) | −1.20695 | −0.0470875 | ||||||||
\(658\) | 25.7825 | 1.00511 | ||||||||
\(659\) | 44.5937 | 1.73712 | 0.868561 | − | 0.495582i | \(-0.165045\pi\) | ||||
0.868561 | + | 0.495582i | \(0.165045\pi\) | |||||||
\(660\) | −0.110780 | −0.00431209 | ||||||||
\(661\) | 16.1901 | 0.629724 | 0.314862 | − | 0.949138i | \(-0.398042\pi\) | ||||
0.314862 | + | 0.949138i | \(0.398042\pi\) | |||||||
\(662\) | 12.7091 | 0.493954 | ||||||||
\(663\) | −4.31931 | −0.167748 | ||||||||
\(664\) | −14.9815 | −0.581395 | ||||||||
\(665\) | 0.122813 | 0.00476247 | ||||||||
\(666\) | −3.12812 | −0.121212 | ||||||||
\(667\) | −18.3240 | −0.709507 | ||||||||
\(668\) | −2.21510 | −0.0857048 | ||||||||
\(669\) | 9.14435 | 0.353541 | ||||||||
\(670\) | −0.0747803 | −0.00288901 | ||||||||
\(671\) | −16.2178 | −0.626080 | ||||||||
\(672\) | −3.31382 | −0.127833 | ||||||||
\(673\) | 15.3128 | 0.590263 | 0.295132 | − | 0.955457i | \(-0.404636\pi\) | ||||
0.295132 | + | 0.955457i | \(0.404636\pi\) | |||||||
\(674\) | 7.40878 | 0.285375 | ||||||||
\(675\) | −27.4310 | −1.05582 | ||||||||
\(676\) | −9.54956 | −0.367291 | ||||||||
\(677\) | 35.7116 | 1.37251 | 0.686255 | − | 0.727361i | \(-0.259253\pi\) | ||||
0.686255 | + | 0.727361i | \(0.259253\pi\) | |||||||
\(678\) | −14.6914 | −0.564220 | ||||||||
\(679\) | 14.6961 | 0.563984 | ||||||||
\(680\) | −0.0861768 | −0.00330473 | ||||||||
\(681\) | −32.1750 | −1.23295 | ||||||||
\(682\) | 15.8886 | 0.608407 | ||||||||
\(683\) | −1.49599 | −0.0572423 | −0.0286212 | − | 0.999590i | \(-0.509112\pi\) | ||||
−0.0286212 | + | 0.999590i | \(0.509112\pi\) | |||||||
\(684\) | 1.53595 | 0.0587286 | ||||||||
\(685\) | −0.498720 | −0.0190551 | ||||||||
\(686\) | −17.7999 | −0.679602 | ||||||||
\(687\) | −32.5774 | −1.24290 | ||||||||
\(688\) | −0.0680112 | −0.00259290 | ||||||||
\(689\) | −17.4751 | −0.665750 | ||||||||
\(690\) | −0.153585 | −0.00584689 | ||||||||
\(691\) | −38.4899 | −1.46422 | −0.732112 | − | 0.681184i | \(-0.761465\pi\) | ||||
−0.732112 | + | 0.681184i | \(0.761465\pi\) | |||||||
\(692\) | −10.3281 | −0.392614 | ||||||||
\(693\) | 8.58855 | 0.326252 | ||||||||
\(694\) | −15.7189 | −0.596680 | ||||||||
\(695\) | 0.547772 | 0.0207782 | ||||||||
\(696\) | 7.83281 | 0.296902 | ||||||||
\(697\) | 9.57519 | 0.362686 | ||||||||
\(698\) | 2.98915 | 0.113141 | ||||||||
\(699\) | 21.2967 | 0.805515 | ||||||||
\(700\) | 13.6882 | 0.517366 | ||||||||
\(701\) | −36.3287 | −1.37211 | −0.686057 | − | 0.727548i | \(-0.740660\pi\) | ||||
−0.686057 | + | 0.727548i | \(0.740660\pi\) | |||||||
\(702\) | −10.1949 | −0.384782 | ||||||||
\(703\) | 2.03660 | 0.0768117 | ||||||||
\(704\) | 2.04170 | 0.0769493 | ||||||||
\(705\) | −0.510790 | −0.0192375 | ||||||||
\(706\) | 0.786860 | 0.0296139 | ||||||||
\(707\) | 2.09380 | 0.0787455 | ||||||||
\(708\) | −4.05572 | −0.152423 | ||||||||
\(709\) | −30.9061 | −1.16070 | −0.580352 | − | 0.814366i | \(-0.697085\pi\) | ||||
−0.580352 | + | 0.814366i | \(0.697085\pi\) | |||||||
\(710\) | 0.0226587 | 0.000850365 0 | ||||||||
\(711\) | 20.8732 | 0.782807 | ||||||||
\(712\) | 1.46405 | 0.0548677 | ||||||||
\(713\) | 22.0280 | 0.824956 | ||||||||
\(714\) | −6.36836 | −0.238330 | ||||||||
\(715\) | 0.170067 | 0.00636015 | ||||||||
\(716\) | −8.87410 | −0.331641 | ||||||||
\(717\) | 15.9592 | 0.596008 | ||||||||
\(718\) | 15.5405 | 0.579965 | ||||||||
\(719\) | 44.5382 | 1.66100 | 0.830498 | − | 0.557022i | \(-0.188056\pi\) | ||||
0.830498 | + | 0.557022i | \(0.188056\pi\) | |||||||
\(720\) | −0.0688762 | −0.00256687 | ||||||||
\(721\) | −10.2055 | −0.380072 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −3.11437 | −0.115825 | ||||||||
\(724\) | 5.73170 | 0.213017 | ||||||||
\(725\) | −32.3545 | −1.20162 | ||||||||
\(726\) | −8.26594 | −0.306778 | ||||||||
\(727\) | 11.7787 | 0.436847 | 0.218424 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218424 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(728\) | 5.08732 | 0.188549 | ||||||||
\(729\) | 23.0451 | 0.853524 | ||||||||
\(730\) | −0.0352372 | −0.00130419 | ||||||||
\(731\) | −0.130701 | −0.00483415 | ||||||||
\(732\) | 9.61121 | 0.355240 | ||||||||
\(733\) | −12.6876 | −0.468627 | −0.234313 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234313 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(734\) | 17.0403 | 0.628968 | ||||||||
\(735\) | −0.0271682 | −0.00100212 | ||||||||
\(736\) | 2.83061 | 0.104338 | ||||||||
\(737\) | 3.40476 | 0.125416 | ||||||||
\(738\) | 7.65291 | 0.281707 | ||||||||
\(739\) | 17.7407 | 0.652603 | 0.326301 | − | 0.945266i | \(-0.394198\pi\) | ||||
0.326301 | + | 0.945266i | \(0.394198\pi\) | |||||||
\(740\) | −0.0913265 | −0.00335723 | ||||||||
\(741\) | 2.24758 | 0.0825669 | ||||||||
\(742\) | −25.7653 | −0.945873 | ||||||||
\(743\) | 20.1383 | 0.738804 | 0.369402 | − | 0.929270i | \(-0.379563\pi\) | ||||
0.369402 | + | 0.929270i | \(0.379563\pi\) | |||||||
\(744\) | −9.41615 | −0.345213 | ||||||||
\(745\) | 0.411344 | 0.0150705 | ||||||||
\(746\) | −16.6854 | −0.610898 | ||||||||
\(747\) | −23.0109 | −0.841923 | ||||||||
\(748\) | 3.92365 | 0.143463 | ||||||||
\(749\) | 20.5530 | 0.750991 | ||||||||
\(750\) | −0.542478 | −0.0198085 | ||||||||
\(751\) | 26.2753 | 0.958801 | 0.479400 | − | 0.877596i | \(-0.340854\pi\) | ||||
0.479400 | + | 0.877596i | \(0.340854\pi\) | |||||||
\(752\) | 9.41398 | 0.343292 | ||||||||
\(753\) | −4.15626 | −0.151463 | ||||||||
\(754\) | −12.0248 | −0.437917 | ||||||||
\(755\) | 0.448422 | 0.0163197 | ||||||||
\(756\) | −15.0313 | −0.546684 | ||||||||
\(757\) | −13.6533 | −0.496237 | −0.248119 | − | 0.968730i | \(-0.579812\pi\) | ||||
−0.248119 | + | 0.968730i | \(0.579812\pi\) | |||||||
\(758\) | −20.9333 | −0.760332 | ||||||||
\(759\) | 6.99276 | 0.253821 | ||||||||
\(760\) | 0.0448427 | 0.00162662 | ||||||||
\(761\) | −20.3777 | −0.738692 | −0.369346 | − | 0.929292i | \(-0.620418\pi\) | ||||
−0.369346 | + | 0.929292i | \(0.620418\pi\) | |||||||
\(762\) | 13.9678 | 0.506000 | ||||||||
\(763\) | 18.8943 | 0.684020 | ||||||||
\(764\) | −7.40545 | −0.267920 | ||||||||
\(765\) | −0.132363 | −0.00478561 | ||||||||
\(766\) | −27.8816 | −1.00740 | ||||||||
\(767\) | 6.22627 | 0.224817 | ||||||||
\(768\) | −1.20998 | −0.0436613 | ||||||||
\(769\) | 18.4729 | 0.666148 | 0.333074 | − | 0.942901i | \(-0.391914\pi\) | ||||
0.333074 | + | 0.942901i | \(0.391914\pi\) | |||||||
\(770\) | 0.250746 | 0.00903626 | ||||||||
\(771\) | 24.9668 | 0.899159 | ||||||||
\(772\) | 4.31071 | 0.155146 | ||||||||
\(773\) | 12.9924 | 0.467304 | 0.233652 | − | 0.972320i | \(-0.424932\pi\) | ||||
0.233652 | + | 0.972320i | \(0.424932\pi\) | |||||||
\(774\) | −0.104462 | −0.00375480 | ||||||||
\(775\) | 38.8947 | 1.39714 | ||||||||
\(776\) | 5.36599 | 0.192628 | ||||||||
\(777\) | −6.74892 | −0.242116 | ||||||||
\(778\) | 16.9170 | 0.606504 | ||||||||
\(779\) | −4.98252 | −0.178517 | ||||||||
\(780\) | −0.100788 | −0.00360877 | ||||||||
\(781\) | −1.03165 | −0.0369154 | ||||||||
\(782\) | 5.43975 | 0.194525 | ||||||||
\(783\) | 35.5292 | 1.26971 | ||||||||
\(784\) | 0.500717 | 0.0178827 | ||||||||
\(785\) | −0.255002 | −0.00910140 | ||||||||
\(786\) | −3.22372 | −0.114986 | ||||||||
\(787\) | −2.57559 | −0.0918098 | −0.0459049 | − | 0.998946i | \(-0.514617\pi\) | ||||
−0.0459049 | + | 0.998946i | \(0.514617\pi\) | |||||||
\(788\) | 6.81519 | 0.242781 | ||||||||
\(789\) | −21.8494 | −0.777858 | ||||||||
\(790\) | 0.609402 | 0.0216815 | ||||||||
\(791\) | 33.2535 | 1.18236 | ||||||||
\(792\) | 3.13595 | 0.111431 | ||||||||
\(793\) | −14.7549 | −0.523964 | ||||||||
\(794\) | 4.90896 | 0.174212 | ||||||||
\(795\) | 0.510449 | 0.0181038 | ||||||||
\(796\) | 4.23326 | 0.150044 | ||||||||
\(797\) | 43.2715 | 1.53276 | 0.766378 | − | 0.642390i | \(-0.222057\pi\) | ||||
0.766378 | + | 0.642390i | \(0.222057\pi\) | |||||||
\(798\) | 3.31382 | 0.117308 | ||||||||
\(799\) | 18.0914 | 0.640028 | ||||||||
\(800\) | 4.99799 | 0.176706 | ||||||||
\(801\) | 2.24872 | 0.0794545 | ||||||||
\(802\) | 3.24262 | 0.114501 | ||||||||
\(803\) | 1.60436 | 0.0566166 | ||||||||
\(804\) | −2.01778 | −0.0711615 | ||||||||
\(805\) | 0.347635 | 0.0122525 | ||||||||
\(806\) | 14.4555 | 0.509173 | ||||||||
\(807\) | −36.6920 | −1.29162 | ||||||||
\(808\) | 0.764511 | 0.0268954 | ||||||||
\(809\) | 7.86728 | 0.276599 | 0.138299 | − | 0.990390i | \(-0.455836\pi\) | ||||
0.138299 | + | 0.990390i | \(0.455836\pi\) | |||||||
\(810\) | 0.0911650 | 0.00320321 | ||||||||
\(811\) | 42.8850 | 1.50590 | 0.752949 | − | 0.658079i | \(-0.228631\pi\) | ||||
0.752949 | + | 0.658079i | \(0.228631\pi\) | |||||||
\(812\) | −17.7293 | −0.622176 | ||||||||
\(813\) | −9.03475 | −0.316863 | ||||||||
\(814\) | 4.15811 | 0.145742 | ||||||||
\(815\) | 0.260477 | 0.00912413 | ||||||||
\(816\) | −2.32529 | −0.0814013 | ||||||||
\(817\) | 0.0680112 | 0.00237941 | ||||||||
\(818\) | 10.5525 | 0.368958 | ||||||||
\(819\) | 7.81388 | 0.273039 | ||||||||
\(820\) | 0.223429 | 0.00780249 | ||||||||
\(821\) | 15.1335 | 0.528161 | 0.264081 | − | 0.964501i | \(-0.414932\pi\) | ||||
0.264081 | + | 0.964501i | \(0.414932\pi\) | |||||||
\(822\) | −13.4568 | −0.469361 | ||||||||
\(823\) | 12.2086 | 0.425564 | 0.212782 | − | 0.977100i | \(-0.431748\pi\) | ||||
0.212782 | + | 0.977100i | \(0.431748\pi\) | |||||||
\(824\) | −3.72634 | −0.129813 | ||||||||
\(825\) | 12.3471 | 0.429870 | ||||||||
\(826\) | 9.17998 | 0.319412 | ||||||||
\(827\) | −26.0440 | −0.905638 | −0.452819 | − | 0.891602i | \(-0.649582\pi\) | ||||
−0.452819 | + | 0.891602i | \(0.649582\pi\) | |||||||
\(828\) | 4.34768 | 0.151092 | ||||||||
\(829\) | 46.0399 | 1.59903 | 0.799516 | − | 0.600644i | \(-0.205089\pi\) | ||||
0.799516 | + | 0.600644i | \(0.205089\pi\) | |||||||
\(830\) | −0.671811 | −0.0233189 | ||||||||
\(831\) | −38.5478 | −1.33721 | ||||||||
\(832\) | 1.85754 | 0.0643985 | ||||||||
\(833\) | 0.962257 | 0.0333402 | ||||||||
\(834\) | 14.7804 | 0.511803 | ||||||||
\(835\) | −0.0993310 | −0.00343749 | ||||||||
\(836\) | −2.04170 | −0.0706135 | ||||||||
\(837\) | −42.7112 | −1.47631 | ||||||||
\(838\) | 31.7266 | 1.09598 | ||||||||
\(839\) | 51.6147 | 1.78194 | 0.890968 | − | 0.454066i | \(-0.150027\pi\) | ||||
0.890968 | + | 0.454066i | \(0.150027\pi\) | |||||||
\(840\) | −0.148601 | −0.00512721 | ||||||||
\(841\) | 12.9063 | 0.445045 | ||||||||
\(842\) | −23.7832 | −0.819625 | ||||||||
\(843\) | 3.69970 | 0.127425 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | −0.428228 | −0.0147315 | ||||||||
\(846\) | 14.4594 | 0.497125 | ||||||||
\(847\) | 18.7097 | 0.642872 | ||||||||
\(848\) | −9.40770 | −0.323062 | ||||||||
\(849\) | −21.1918 | −0.727301 | ||||||||
\(850\) | 9.60493 | 0.329446 | ||||||||
\(851\) | 5.76481 | 0.197615 | ||||||||
\(852\) | 0.611393 | 0.0209460 | ||||||||
\(853\) | 46.8320 | 1.60350 | 0.801748 | − | 0.597662i | \(-0.203904\pi\) | ||||
0.801748 | + | 0.597662i | \(0.203904\pi\) | |||||||
\(854\) | −21.7546 | −0.744428 | ||||||||
\(855\) | 0.0688762 | 0.00235552 | ||||||||
\(856\) | 7.50454 | 0.256500 | ||||||||
\(857\) | 1.40124 | 0.0478654 | 0.0239327 | − | 0.999714i | \(-0.492381\pi\) | ||||
0.0239327 | + | 0.999714i | \(0.492381\pi\) | |||||||
\(858\) | 4.58887 | 0.156662 | ||||||||
\(859\) | 27.1497 | 0.926337 | 0.463169 | − | 0.886270i | \(-0.346712\pi\) | ||||
0.463169 | + | 0.886270i | \(0.346712\pi\) | |||||||
\(860\) | −0.00304980 | −0.000103997 0 | ||||||||
\(861\) | 16.5112 | 0.562699 | ||||||||
\(862\) | 3.13657 | 0.106832 | ||||||||
\(863\) | −5.29111 | −0.180111 | −0.0900557 | − | 0.995937i | \(-0.528705\pi\) | ||||
−0.0900557 | + | 0.995937i | \(0.528705\pi\) | |||||||
\(864\) | −5.48840 | −0.186719 | ||||||||
\(865\) | −0.463138 | −0.0157472 | ||||||||
\(866\) | −24.2943 | −0.825552 | ||||||||
\(867\) | 16.1010 | 0.546818 | ||||||||
\(868\) | 21.3131 | 0.723414 | ||||||||
\(869\) | −27.7462 | −0.941224 | ||||||||
\(870\) | 0.351244 | 0.0119083 | ||||||||
\(871\) | 3.09765 | 0.104960 | ||||||||
\(872\) | 6.89890 | 0.233626 | ||||||||
\(873\) | 8.24191 | 0.278946 | ||||||||
\(874\) | −2.83061 | −0.0957468 | ||||||||
\(875\) | 1.22788 | 0.0415099 | ||||||||
\(876\) | −0.950797 | −0.0321245 | ||||||||
\(877\) | 39.3548 | 1.32892 | 0.664458 | − | 0.747326i | \(-0.268663\pi\) | ||||
0.664458 | + | 0.747326i | \(0.268663\pi\) | |||||||
\(878\) | 6.37754 | 0.215231 | ||||||||
\(879\) | −30.4426 | −1.02680 | ||||||||
\(880\) | 0.0915551 | 0.00308632 | ||||||||
\(881\) | −28.8075 | −0.970548 | −0.485274 | − | 0.874362i | \(-0.661280\pi\) | ||||
−0.485274 | + | 0.874362i | \(0.661280\pi\) | |||||||
\(882\) | 0.769077 | 0.0258962 | ||||||||
\(883\) | 6.50521 | 0.218918 | 0.109459 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109459 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(884\) | 3.56974 | 0.120063 | ||||||||
\(885\) | −0.181869 | −0.00611347 | ||||||||
\(886\) | −15.8222 | −0.531557 | ||||||||
\(887\) | 0.656669 | 0.0220488 | 0.0110244 | − | 0.999939i | \(-0.496491\pi\) | ||||
0.0110244 | + | 0.999939i | \(0.496491\pi\) | |||||||
\(888\) | −2.46424 | −0.0826944 | ||||||||
\(889\) | −31.6156 | −1.06035 | ||||||||
\(890\) | 0.0656521 | 0.00220066 | ||||||||
\(891\) | −4.15076 | −0.139056 | ||||||||
\(892\) | −7.55745 | −0.253042 | ||||||||
\(893\) | −9.41398 | −0.315027 | ||||||||
\(894\) | 11.0992 | 0.371212 | ||||||||
\(895\) | −0.397939 | −0.0133016 | ||||||||
\(896\) | 2.73874 | 0.0914950 | ||||||||
\(897\) | 6.36202 | 0.212422 | ||||||||
\(898\) | −0.375322 | −0.0125246 | ||||||||
\(899\) | −50.3773 | −1.68018 | ||||||||
\(900\) | 7.67667 | 0.255889 | ||||||||
\(901\) | −18.0793 | −0.602310 | ||||||||
\(902\) | −10.1728 | −0.338716 | ||||||||
\(903\) | −0.225377 | −0.00750007 | ||||||||
\(904\) | 12.1419 | 0.403833 | ||||||||
\(905\) | 0.257025 | 0.00854380 | ||||||||
\(906\) | 12.0996 | 0.401984 | ||||||||
\(907\) | 52.6931 | 1.74965 | 0.874823 | − | 0.484444i | \(-0.160978\pi\) | ||||
0.874823 | + | 0.484444i | \(0.160978\pi\) | |||||||
\(908\) | 26.5914 | 0.882466 | ||||||||
\(909\) | 1.17425 | 0.0389475 | ||||||||
\(910\) | 0.228129 | 0.00756240 | ||||||||
\(911\) | −47.8000 | −1.58368 | −0.791842 | − | 0.610725i | \(-0.790878\pi\) | ||||
−0.791842 | + | 0.610725i | \(0.790878\pi\) | |||||||
\(912\) | 1.20998 | 0.0400664 | ||||||||
\(913\) | 30.5876 | 1.01230 | ||||||||
\(914\) | −9.07588 | −0.300203 | ||||||||
\(915\) | 0.430992 | 0.0142482 | ||||||||
\(916\) | 26.9239 | 0.889591 | ||||||||
\(917\) | 7.29677 | 0.240960 | ||||||||
\(918\) | −10.5474 | −0.348116 | ||||||||
\(919\) | 56.6714 | 1.86942 | 0.934709 | − | 0.355414i | \(-0.115660\pi\) | ||||
0.934709 | + | 0.355414i | \(0.115660\pi\) | |||||||
\(920\) | 0.126932 | 0.00418483 | ||||||||
\(921\) | −8.79706 | −0.289873 | ||||||||
\(922\) | 36.3391 | 1.19676 | ||||||||
\(923\) | −0.938599 | −0.0308944 | ||||||||
\(924\) | 6.76581 | 0.222579 | ||||||||
\(925\) | 10.1789 | 0.334680 | ||||||||
\(926\) | 28.6466 | 0.941385 | ||||||||
\(927\) | −5.72347 | −0.187983 | ||||||||
\(928\) | −6.47351 | −0.212503 | ||||||||
\(929\) | 8.23766 | 0.270269 | 0.135134 | − | 0.990827i | \(-0.456853\pi\) | ||||
0.135134 | + | 0.990827i | \(0.456853\pi\) | |||||||
\(930\) | −0.422245 | −0.0138460 | ||||||||
\(931\) | −0.500717 | −0.0164103 | ||||||||
\(932\) | −17.6009 | −0.576536 | ||||||||
\(933\) | −3.28311 | −0.107484 | ||||||||
\(934\) | 5.09899 | 0.166844 | ||||||||
\(935\) | 0.175947 | 0.00575408 | ||||||||
\(936\) | 2.85309 | 0.0932561 | ||||||||
\(937\) | −1.85542 | −0.0606138 | −0.0303069 | − | 0.999541i | \(-0.509648\pi\) | ||||
−0.0303069 | + | 0.999541i | \(0.509648\pi\) | |||||||
\(938\) | 4.56717 | 0.149123 | ||||||||
\(939\) | 25.2052 | 0.822540 | ||||||||
\(940\) | 0.422148 | 0.0137690 | ||||||||
\(941\) | −1.27161 | −0.0414534 | −0.0207267 | − | 0.999785i | \(-0.506598\pi\) | ||||
−0.0207267 | + | 0.999785i | \(0.506598\pi\) | |||||||
\(942\) | −6.88064 | −0.224184 | ||||||||
\(943\) | −14.1036 | −0.459275 | ||||||||
\(944\) | 3.35189 | 0.109095 | ||||||||
\(945\) | −0.674045 | −0.0219267 | ||||||||
\(946\) | 0.138858 | 0.00451466 | ||||||||
\(947\) | 52.9885 | 1.72190 | 0.860948 | − | 0.508694i | \(-0.169871\pi\) | ||||
0.860948 | + | 0.508694i | \(0.169871\pi\) | |||||||
\(948\) | 16.4433 | 0.534054 | ||||||||
\(949\) | 1.45965 | 0.0473821 | ||||||||
\(950\) | −4.99799 | −0.162156 | ||||||||
\(951\) | −19.8839 | −0.644779 | ||||||||
\(952\) | 5.26320 | 0.170581 | ||||||||
\(953\) | 49.7872 | 1.61277 | 0.806383 | − | 0.591394i | \(-0.201422\pi\) | ||||
0.806383 | + | 0.591394i | \(0.201422\pi\) | |||||||
\(954\) | −14.4498 | −0.467829 | ||||||||
\(955\) | −0.332080 | −0.0107459 | ||||||||
\(956\) | −13.1897 | −0.426584 | ||||||||
\(957\) | −15.9922 | −0.516954 | ||||||||
\(958\) | −8.74345 | −0.282488 | ||||||||
\(959\) | 30.4591 | 0.983574 | ||||||||
\(960\) | −0.0542587 | −0.00175119 | ||||||||
\(961\) | 29.5607 | 0.953573 | ||||||||
\(962\) | 3.78305 | 0.121971 | ||||||||
\(963\) | 11.5266 | 0.371440 | ||||||||
\(964\) | 2.57390 | 0.0828999 | ||||||||
\(965\) | 0.193304 | 0.00622268 | ||||||||
\(966\) | 9.38013 | 0.301801 | ||||||||
\(967\) | −15.6632 | −0.503696 | −0.251848 | − | 0.967767i | \(-0.581038\pi\) | ||||
−0.251848 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(968\) | 6.83148 | 0.219572 | ||||||||
\(969\) | 2.32529 | 0.0746990 | ||||||||
\(970\) | 0.240626 | 0.00772602 | ||||||||
\(971\) | 29.8628 | 0.958343 | 0.479171 | − | 0.877721i | \(-0.340937\pi\) | ||||
0.479171 | + | 0.877721i | \(0.340937\pi\) | |||||||
\(972\) | −14.0053 | −0.449221 | ||||||||
\(973\) | −33.4549 | −1.07251 | ||||||||
\(974\) | 1.45780 | 0.0467111 | ||||||||
\(975\) | 11.2334 | 0.359756 | ||||||||
\(976\) | −7.94329 | −0.254258 | ||||||||
\(977\) | −40.6488 | −1.30047 | −0.650235 | − | 0.759733i | \(-0.725329\pi\) | ||||
−0.650235 | + | 0.759733i | \(0.725329\pi\) | |||||||
\(978\) | 7.02840 | 0.224743 | ||||||||
\(979\) | −2.98915 | −0.0955337 | ||||||||
\(980\) | 0.0224535 | 0.000717250 0 | ||||||||
\(981\) | 10.5964 | 0.338316 | ||||||||
\(982\) | −18.2117 | −0.581159 | ||||||||
\(983\) | 47.9337 | 1.52885 | 0.764424 | − | 0.644714i | \(-0.223023\pi\) | ||||
0.764424 | + | 0.644714i | \(0.223023\pi\) | |||||||
\(984\) | 6.02874 | 0.192189 | ||||||||
\(985\) | 0.305611 | 0.00973758 | ||||||||
\(986\) | −12.4405 | −0.396187 | ||||||||
\(987\) | 31.1962 | 0.992987 | ||||||||
\(988\) | −1.85754 | −0.0590961 | ||||||||
\(989\) | 0.192513 | 0.00612156 | ||||||||
\(990\) | 0.140624 | 0.00446933 | ||||||||
\(991\) | 6.70873 | 0.213110 | 0.106555 | − | 0.994307i | \(-0.466018\pi\) | ||||
0.106555 | + | 0.994307i | \(0.466018\pi\) | |||||||
\(992\) | 7.78208 | 0.247081 | ||||||||
\(993\) | 15.3778 | 0.487999 | ||||||||
\(994\) | −1.38387 | −0.0438936 | ||||||||
\(995\) | 0.189831 | 0.00601804 | ||||||||
\(996\) | −18.1273 | −0.574385 | ||||||||
\(997\) | −42.5743 | −1.34834 | −0.674170 | − | 0.738576i | \(-0.735499\pi\) | ||||
−0.674170 | + | 0.738576i | \(0.735499\pi\) | |||||||
\(998\) | −6.37347 | −0.201749 | ||||||||
\(999\) | −11.1777 | −0.353646 |
(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 | 8018.2.a.h.1.14 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.h.1.14 | ✓ | 41 | 1.1 | even | 1 | trivial |