Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, 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("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1557568940\) |
Analytic rank: | \(1\) |
Dimension: | \(159\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70494 | −1.91268 | −0.956339 | − | 0.292259i | \(-0.905593\pi\) | ||||
−0.956339 | + | 0.292259i | \(0.905593\pi\) | |||||||
\(3\) | 2.29108 | 1.32276 | 0.661378 | − | 0.750053i | \(-0.269972\pi\) | ||||
0.661378 | + | 0.750053i | \(0.269972\pi\) | |||||||
\(4\) | 5.31668 | 2.65834 | ||||||||
\(5\) | −3.64034 | −1.62801 | −0.814004 | − | 0.580859i | \(-0.802717\pi\) | ||||
−0.814004 | + | 0.580859i | \(0.802717\pi\) | |||||||
\(6\) | −6.19723 | −2.53001 | ||||||||
\(7\) | 2.95034 | 1.11512 | 0.557561 | − | 0.830136i | \(-0.311737\pi\) | ||||
0.557561 | + | 0.830136i | \(0.311737\pi\) | |||||||
\(8\) | −8.97141 | −3.17187 | ||||||||
\(9\) | 2.24905 | 0.749683 | ||||||||
\(10\) | 9.84688 | 3.11386 | ||||||||
\(11\) | 0.0557392 | 0.0168060 | 0.00840300 | − | 0.999965i | \(-0.497325\pi\) | ||||
0.00840300 | + | 0.999965i | \(0.497325\pi\) | |||||||
\(12\) | 12.1809 | 3.51633 | ||||||||
\(13\) | 0.308532 | 0.0855715 | 0.0427857 | − | 0.999084i | \(-0.486377\pi\) | ||||
0.0427857 | + | 0.999084i | \(0.486377\pi\) | |||||||
\(14\) | −7.98047 | −2.13287 | ||||||||
\(15\) | −8.34031 | −2.15346 | ||||||||
\(16\) | 13.6337 | 3.40843 | ||||||||
\(17\) | 0.0875711 | 0.0212391 | 0.0106196 | − | 0.999944i | \(-0.496620\pi\) | ||||
0.0106196 | + | 0.999944i | \(0.496620\pi\) | |||||||
\(18\) | −6.08354 | −1.43390 | ||||||||
\(19\) | 5.39100 | 1.23678 | 0.618390 | − | 0.785871i | \(-0.287785\pi\) | ||||
0.618390 | + | 0.785871i | \(0.287785\pi\) | |||||||
\(20\) | −19.3545 | −4.32780 | ||||||||
\(21\) | 6.75946 | 1.47503 | ||||||||
\(22\) | −0.150771 | −0.0321445 | ||||||||
\(23\) | −9.19884 | −1.91809 | −0.959045 | − | 0.283253i | \(-0.908586\pi\) | ||||
−0.959045 | + | 0.283253i | \(0.908586\pi\) | |||||||
\(24\) | −20.5542 | −4.19561 | ||||||||
\(25\) | 8.25206 | 1.65041 | ||||||||
\(26\) | −0.834560 | −0.163671 | ||||||||
\(27\) | −1.72049 | −0.331108 | ||||||||
\(28\) | 15.6860 | 2.96437 | ||||||||
\(29\) | 5.34661 | 0.992840 | 0.496420 | − | 0.868083i | \(-0.334648\pi\) | ||||
0.496420 | + | 0.868083i | \(0.334648\pi\) | |||||||
\(30\) | 22.5600 | 4.11887 | ||||||||
\(31\) | −5.28856 | −0.949853 | −0.474926 | − | 0.880025i | \(-0.657525\pi\) | ||||
−0.474926 | + | 0.880025i | \(0.657525\pi\) | |||||||
\(32\) | −18.9355 | −3.34736 | ||||||||
\(33\) | 0.127703 | 0.0222302 | ||||||||
\(34\) | −0.236874 | −0.0406236 | ||||||||
\(35\) | −10.7402 | −1.81543 | ||||||||
\(36\) | 11.9575 | 1.99291 | ||||||||
\(37\) | −9.66142 | −1.58833 | −0.794164 | − | 0.607704i | \(-0.792091\pi\) | ||||
−0.794164 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(38\) | −14.5823 | −2.36556 | ||||||||
\(39\) | 0.706873 | 0.113190 | ||||||||
\(40\) | 32.6589 | 5.16383 | ||||||||
\(41\) | 10.2560 | 1.60172 | 0.800859 | − | 0.598853i | \(-0.204377\pi\) | ||||
0.800859 | + | 0.598853i | \(0.204377\pi\) | |||||||
\(42\) | −18.2839 | −2.82127 | ||||||||
\(43\) | −3.32164 | −0.506545 | −0.253272 | − | 0.967395i | \(-0.581507\pi\) | ||||
−0.253272 | + | 0.967395i | \(0.581507\pi\) | |||||||
\(44\) | 0.296347 | 0.0446760 | ||||||||
\(45\) | −8.18730 | −1.22049 | ||||||||
\(46\) | 24.8823 | 3.66869 | ||||||||
\(47\) | −12.7133 | −1.85443 | −0.927214 | − | 0.374533i | \(-0.877803\pi\) | ||||
−0.927214 | + | 0.374533i | \(0.877803\pi\) | |||||||
\(48\) | 31.2359 | 4.50852 | ||||||||
\(49\) | 1.70448 | 0.243498 | ||||||||
\(50\) | −22.3213 | −3.15671 | ||||||||
\(51\) | 0.200633 | 0.0280942 | ||||||||
\(52\) | 1.64037 | 0.227478 | ||||||||
\(53\) | −12.0783 | −1.65908 | −0.829542 | − | 0.558444i | \(-0.811399\pi\) | ||||
−0.829542 | + | 0.558444i | \(0.811399\pi\) | |||||||
\(54\) | 4.65380 | 0.633303 | ||||||||
\(55\) | −0.202909 | −0.0273603 | ||||||||
\(56\) | −26.4687 | −3.53702 | ||||||||
\(57\) | 12.3512 | 1.63596 | ||||||||
\(58\) | −14.4622 | −1.89898 | ||||||||
\(59\) | 4.08845 | 0.532271 | 0.266135 | − | 0.963936i | \(-0.414253\pi\) | ||||
0.266135 | + | 0.963936i | \(0.414253\pi\) | |||||||
\(60\) | −44.3427 | −5.72462 | ||||||||
\(61\) | −9.71062 | −1.24332 | −0.621659 | − | 0.783288i | \(-0.713541\pi\) | ||||
−0.621659 | + | 0.783288i | \(0.713541\pi\) | |||||||
\(62\) | 14.3052 | 1.81676 | ||||||||
\(63\) | 6.63545 | 0.835989 | ||||||||
\(64\) | 23.9520 | 2.99399 | ||||||||
\(65\) | −1.12316 | −0.139311 | ||||||||
\(66\) | −0.345428 | −0.0425193 | ||||||||
\(67\) | 4.90596 | 0.599358 | 0.299679 | − | 0.954040i | \(-0.403120\pi\) | ||||
0.299679 | + | 0.954040i | \(0.403120\pi\) | |||||||
\(68\) | 0.465588 | 0.0564608 | ||||||||
\(69\) | −21.0753 | −2.53717 | ||||||||
\(70\) | 29.0516 | 3.47233 | ||||||||
\(71\) | 8.92690 | 1.05943 | 0.529714 | − | 0.848176i | \(-0.322299\pi\) | ||||
0.529714 | + | 0.848176i | \(0.322299\pi\) | |||||||
\(72\) | −20.1771 | −2.37790 | ||||||||
\(73\) | 4.01351 | 0.469746 | 0.234873 | − | 0.972026i | \(-0.424533\pi\) | ||||
0.234873 | + | 0.972026i | \(0.424533\pi\) | |||||||
\(74\) | 26.1335 | 3.03796 | ||||||||
\(75\) | 18.9061 | 2.18309 | ||||||||
\(76\) | 28.6622 | 3.28778 | ||||||||
\(77\) | 0.164449 | 0.0187407 | ||||||||
\(78\) | −1.91205 | −0.216497 | ||||||||
\(79\) | 4.32177 | 0.486237 | 0.243118 | − | 0.969997i | \(-0.421830\pi\) | ||||
0.243118 | + | 0.969997i | \(0.421830\pi\) | |||||||
\(80\) | −49.6313 | −5.54895 | ||||||||
\(81\) | −10.6889 | −1.18766 | ||||||||
\(82\) | −27.7418 | −3.06357 | ||||||||
\(83\) | 12.7382 | 1.39820 | 0.699102 | − | 0.715022i | \(-0.253584\pi\) | ||||
0.699102 | + | 0.715022i | \(0.253584\pi\) | |||||||
\(84\) | 35.9379 | 3.92114 | ||||||||
\(85\) | −0.318789 | −0.0345775 | ||||||||
\(86\) | 8.98481 | 0.968857 | ||||||||
\(87\) | 12.2495 | 1.31328 | ||||||||
\(88\) | −0.500059 | −0.0533064 | ||||||||
\(89\) | 14.7033 | 1.55854 | 0.779272 | − | 0.626686i | \(-0.215589\pi\) | ||||
0.779272 | + | 0.626686i | \(0.215589\pi\) | |||||||
\(90\) | 22.1461 | 2.33441 | ||||||||
\(91\) | 0.910274 | 0.0954227 | ||||||||
\(92\) | −48.9073 | −5.09894 | ||||||||
\(93\) | −12.1165 | −1.25642 | ||||||||
\(94\) | 34.3887 | 3.54692 | ||||||||
\(95\) | −19.6251 | −2.01349 | ||||||||
\(96\) | −43.3828 | −4.42774 | ||||||||
\(97\) | −16.4466 | −1.66990 | −0.834948 | − | 0.550329i | \(-0.814502\pi\) | ||||
−0.834948 | + | 0.550329i | \(0.814502\pi\) | |||||||
\(98\) | −4.61052 | −0.465733 | ||||||||
\(99\) | 0.125360 | 0.0125992 | ||||||||
\(100\) | 43.8736 | 4.38736 | ||||||||
\(101\) | −0.955208 | −0.0950467 | −0.0475234 | − | 0.998870i | \(-0.515133\pi\) | ||||
−0.0475234 | + | 0.998870i | \(0.515133\pi\) | |||||||
\(102\) | −0.542698 | −0.0537351 | ||||||||
\(103\) | −8.26485 | −0.814360 | −0.407180 | − | 0.913348i | \(-0.633488\pi\) | ||||
−0.407180 | + | 0.913348i | \(0.633488\pi\) | |||||||
\(104\) | −2.76797 | −0.271422 | ||||||||
\(105\) | −24.6067 | −2.40137 | ||||||||
\(106\) | 32.6711 | 3.17330 | ||||||||
\(107\) | 0.444664 | 0.0429873 | 0.0214937 | − | 0.999769i | \(-0.493158\pi\) | ||||
0.0214937 | + | 0.999769i | \(0.493158\pi\) | |||||||
\(108\) | −9.14727 | −0.880197 | ||||||||
\(109\) | −11.1928 | −1.07208 | −0.536038 | − | 0.844194i | \(-0.680080\pi\) | ||||
−0.536038 | + | 0.844194i | \(0.680080\pi\) | |||||||
\(110\) | 0.548857 | 0.0523315 | ||||||||
\(111\) | −22.1351 | −2.10097 | ||||||||
\(112\) | 40.2241 | 3.80082 | ||||||||
\(113\) | 4.77855 | 0.449528 | 0.224764 | − | 0.974413i | \(-0.427839\pi\) | ||||
0.224764 | + | 0.974413i | \(0.427839\pi\) | |||||||
\(114\) | −33.4092 | −3.12906 | ||||||||
\(115\) | 33.4869 | 3.12267 | ||||||||
\(116\) | 28.4262 | 2.63930 | ||||||||
\(117\) | 0.693905 | 0.0641515 | ||||||||
\(118\) | −11.0590 | −1.01806 | ||||||||
\(119\) | 0.258364 | 0.0236842 | ||||||||
\(120\) | 74.8243 | 6.83049 | ||||||||
\(121\) | −10.9969 | −0.999718 | ||||||||
\(122\) | 26.2666 | 2.37807 | ||||||||
\(123\) | 23.4973 | 2.11868 | ||||||||
\(124\) | −28.1176 | −2.52503 | ||||||||
\(125\) | −11.8386 | −1.05888 | ||||||||
\(126\) | −17.9485 | −1.59898 | ||||||||
\(127\) | 9.27930 | 0.823405 | 0.411702 | − | 0.911318i | \(-0.364934\pi\) | ||||
0.411702 | + | 0.911318i | \(0.364934\pi\) | |||||||
\(128\) | −26.9175 | −2.37919 | ||||||||
\(129\) | −7.61013 | −0.670035 | ||||||||
\(130\) | 3.03808 | 0.266457 | ||||||||
\(131\) | −2.63832 | −0.230511 | −0.115256 | − | 0.993336i | \(-0.536769\pi\) | ||||
−0.115256 | + | 0.993336i | \(0.536769\pi\) | |||||||
\(132\) | 0.678956 | 0.0590955 | ||||||||
\(133\) | 15.9053 | 1.37916 | ||||||||
\(134\) | −13.2703 | −1.14638 | ||||||||
\(135\) | 6.26315 | 0.539046 | ||||||||
\(136\) | −0.785636 | −0.0673677 | ||||||||
\(137\) | 12.0878 | 1.03273 | 0.516365 | − | 0.856368i | \(-0.327285\pi\) | ||||
0.516365 | + | 0.856368i | \(0.327285\pi\) | |||||||
\(138\) | 57.0073 | 4.85278 | ||||||||
\(139\) | 18.6926 | 1.58548 | 0.792742 | − | 0.609558i | \(-0.208653\pi\) | ||||
0.792742 | + | 0.609558i | \(0.208653\pi\) | |||||||
\(140\) | −57.1023 | −4.82603 | ||||||||
\(141\) | −29.1272 | −2.45295 | ||||||||
\(142\) | −24.1467 | −2.02635 | ||||||||
\(143\) | 0.0171973 | 0.00143811 | ||||||||
\(144\) | 30.6629 | 2.55524 | ||||||||
\(145\) | −19.4634 | −1.61635 | ||||||||
\(146\) | −10.8563 | −0.898472 | ||||||||
\(147\) | 3.90511 | 0.322088 | ||||||||
\(148\) | −51.3667 | −4.22231 | ||||||||
\(149\) | −7.97920 | −0.653682 | −0.326841 | − | 0.945079i | \(-0.605984\pi\) | ||||
−0.326841 | + | 0.945079i | \(0.605984\pi\) | |||||||
\(150\) | −51.1399 | −4.17555 | ||||||||
\(151\) | −7.39471 | −0.601773 | −0.300886 | − | 0.953660i | \(-0.597282\pi\) | ||||
−0.300886 | + | 0.953660i | \(0.597282\pi\) | |||||||
\(152\) | −48.3648 | −3.92291 | ||||||||
\(153\) | 0.196952 | 0.0159226 | ||||||||
\(154\) | −0.444825 | −0.0358450 | ||||||||
\(155\) | 19.2521 | 1.54637 | ||||||||
\(156\) | 3.75822 | 0.300898 | ||||||||
\(157\) | −7.28696 | −0.581563 | −0.290781 | − | 0.956790i | \(-0.593915\pi\) | ||||
−0.290781 | + | 0.956790i | \(0.593915\pi\) | |||||||
\(158\) | −11.6901 | −0.930014 | ||||||||
\(159\) | −27.6724 | −2.19456 | ||||||||
\(160\) | 68.9317 | 5.44953 | ||||||||
\(161\) | −27.1397 | −2.13891 | ||||||||
\(162\) | 28.9129 | 2.27161 | ||||||||
\(163\) | −21.3759 | −1.67429 | −0.837145 | − | 0.546981i | \(-0.815777\pi\) | ||||
−0.837145 | + | 0.546981i | \(0.815777\pi\) | |||||||
\(164\) | 54.5279 | 4.25791 | ||||||||
\(165\) | −0.464882 | −0.0361910 | ||||||||
\(166\) | −34.4561 | −2.67431 | ||||||||
\(167\) | −17.3736 | −1.34441 | −0.672205 | − | 0.740365i | \(-0.734652\pi\) | ||||
−0.672205 | + | 0.740365i | \(0.734652\pi\) | |||||||
\(168\) | −60.6418 | −4.67862 | ||||||||
\(169\) | −12.9048 | −0.992678 | ||||||||
\(170\) | 0.862303 | 0.0661356 | ||||||||
\(171\) | 12.1246 | 0.927194 | ||||||||
\(172\) | −17.6601 | −1.34657 | ||||||||
\(173\) | −19.2011 | −1.45983 | −0.729915 | − | 0.683538i | \(-0.760440\pi\) | ||||
−0.729915 | + | 0.683538i | \(0.760440\pi\) | |||||||
\(174\) | −33.1341 | −2.51189 | ||||||||
\(175\) | 24.3464 | 1.84041 | ||||||||
\(176\) | 0.759932 | 0.0572821 | ||||||||
\(177\) | 9.36697 | 0.704064 | ||||||||
\(178\) | −39.7714 | −2.98099 | ||||||||
\(179\) | −14.9536 | −1.11769 | −0.558843 | − | 0.829274i | \(-0.688754\pi\) | ||||
−0.558843 | + | 0.829274i | \(0.688754\pi\) | |||||||
\(180\) | −43.5293 | −3.24448 | ||||||||
\(181\) | −10.9716 | −0.815515 | −0.407757 | − | 0.913090i | \(-0.633689\pi\) | ||||
−0.407757 | + | 0.913090i | \(0.633689\pi\) | |||||||
\(182\) | −2.46223 | −0.182513 | ||||||||
\(183\) | −22.2478 | −1.64461 | ||||||||
\(184\) | 82.5265 | 6.08393 | ||||||||
\(185\) | 35.1708 | 2.58581 | ||||||||
\(186\) | 32.7744 | 2.40313 | ||||||||
\(187\) | 0.00488114 | 0.000356945 0 | ||||||||
\(188\) | −67.5926 | −4.92970 | ||||||||
\(189\) | −5.07601 | −0.369226 | ||||||||
\(190\) | 53.0845 | 3.85116 | ||||||||
\(191\) | −5.41905 | −0.392109 | −0.196054 | − | 0.980593i | \(-0.562813\pi\) | ||||
−0.196054 | + | 0.980593i | \(0.562813\pi\) | |||||||
\(192\) | 54.8759 | 3.96032 | ||||||||
\(193\) | −4.22668 | −0.304243 | −0.152122 | − | 0.988362i | \(-0.548611\pi\) | ||||
−0.152122 | + | 0.988362i | \(0.548611\pi\) | |||||||
\(194\) | 44.4869 | 3.19397 | ||||||||
\(195\) | −2.57326 | −0.184275 | ||||||||
\(196\) | 9.06220 | 0.647300 | ||||||||
\(197\) | 10.1157 | 0.720712 | 0.360356 | − | 0.932815i | \(-0.382655\pi\) | ||||
0.360356 | + | 0.932815i | \(0.382655\pi\) | |||||||
\(198\) | −0.339091 | −0.0240982 | ||||||||
\(199\) | −7.87397 | −0.558171 | −0.279085 | − | 0.960266i | \(-0.590031\pi\) | ||||
−0.279085 | + | 0.960266i | \(0.590031\pi\) | |||||||
\(200\) | −74.0326 | −5.23489 | ||||||||
\(201\) | 11.2399 | 0.792804 | ||||||||
\(202\) | 2.58378 | 0.181794 | ||||||||
\(203\) | 15.7743 | 1.10714 | ||||||||
\(204\) | 1.06670 | 0.0746839 | ||||||||
\(205\) | −37.3353 | −2.60761 | ||||||||
\(206\) | 22.3559 | 1.55761 | ||||||||
\(207\) | −20.6887 | −1.43796 | ||||||||
\(208\) | 4.20644 | 0.291664 | ||||||||
\(209\) | 0.300490 | 0.0207853 | ||||||||
\(210\) | 66.5596 | 4.59305 | ||||||||
\(211\) | −12.2701 | −0.844710 | −0.422355 | − | 0.906430i | \(-0.638796\pi\) | ||||
−0.422355 | + | 0.906430i | \(0.638796\pi\) | |||||||
\(212\) | −64.2165 | −4.41041 | ||||||||
\(213\) | 20.4523 | 1.40137 | ||||||||
\(214\) | −1.20279 | −0.0822209 | ||||||||
\(215\) | 12.0919 | 0.824659 | ||||||||
\(216\) | 15.4352 | 1.05023 | ||||||||
\(217\) | −15.6030 | −1.05920 | ||||||||
\(218\) | 30.2758 | 2.05054 | ||||||||
\(219\) | 9.19527 | 0.621359 | ||||||||
\(220\) | −1.07880 | −0.0727330 | ||||||||
\(221\) | 0.0270185 | 0.00181746 | ||||||||
\(222\) | 59.8740 | 4.01848 | ||||||||
\(223\) | 12.8492 | 0.860448 | 0.430224 | − | 0.902722i | \(-0.358435\pi\) | ||||
0.430224 | + | 0.902722i | \(0.358435\pi\) | |||||||
\(224\) | −55.8662 | −3.73272 | ||||||||
\(225\) | 18.5593 | 1.23729 | ||||||||
\(226\) | −12.9257 | −0.859803 | ||||||||
\(227\) | 12.1830 | 0.808615 | 0.404307 | − | 0.914623i | \(-0.367513\pi\) | ||||
0.404307 | + | 0.914623i | \(0.367513\pi\) | |||||||
\(228\) | 65.6674 | 4.34893 | ||||||||
\(229\) | 25.5787 | 1.69029 | 0.845145 | − | 0.534538i | \(-0.179514\pi\) | ||||
0.845145 | + | 0.534538i | \(0.179514\pi\) | |||||||
\(230\) | −90.5799 | −5.97266 | ||||||||
\(231\) | 0.376767 | 0.0247894 | ||||||||
\(232\) | −47.9666 | −3.14916 | ||||||||
\(233\) | 7.24926 | 0.474915 | 0.237457 | − | 0.971398i | \(-0.423686\pi\) | ||||
0.237457 | + | 0.971398i | \(0.423686\pi\) | |||||||
\(234\) | −1.87697 | −0.122701 | ||||||||
\(235\) | 46.2808 | 3.01902 | ||||||||
\(236\) | 21.7370 | 1.41496 | ||||||||
\(237\) | 9.90151 | 0.643172 | ||||||||
\(238\) | −0.698859 | −0.0453003 | ||||||||
\(239\) | 12.9354 | 0.836725 | 0.418362 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418362 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(240\) | −113.709 | −7.33991 | ||||||||
\(241\) | 6.62577 | 0.426803 | 0.213402 | − | 0.976965i | \(-0.431546\pi\) | ||||
0.213402 | + | 0.976965i | \(0.431546\pi\) | |||||||
\(242\) | 29.7459 | 1.91214 | ||||||||
\(243\) | −19.3277 | −1.23987 | ||||||||
\(244\) | −51.6283 | −3.30516 | ||||||||
\(245\) | −6.20490 | −0.396416 | ||||||||
\(246\) | −63.5588 | −4.05236 | ||||||||
\(247\) | 1.66330 | 0.105833 | ||||||||
\(248\) | 47.4458 | 3.01281 | ||||||||
\(249\) | 29.1843 | 1.84948 | ||||||||
\(250\) | 32.0227 | 2.02529 | ||||||||
\(251\) | −15.6506 | −0.987860 | −0.493930 | − | 0.869502i | \(-0.664440\pi\) | ||||
−0.493930 | + | 0.869502i | \(0.664440\pi\) | |||||||
\(252\) | 35.2786 | 2.22234 | ||||||||
\(253\) | −0.512736 | −0.0322354 | ||||||||
\(254\) | −25.0999 | −1.57491 | ||||||||
\(255\) | −0.730370 | −0.0457376 | ||||||||
\(256\) | 24.9061 | 1.55663 | ||||||||
\(257\) | −0.393204 | −0.0245274 | −0.0122637 | − | 0.999925i | \(-0.503904\pi\) | ||||
−0.0122637 | + | 0.999925i | \(0.503904\pi\) | |||||||
\(258\) | 20.5849 | 1.28156 | ||||||||
\(259\) | −28.5044 | −1.77118 | ||||||||
\(260\) | −5.97149 | −0.370336 | ||||||||
\(261\) | 12.0248 | 0.744315 | ||||||||
\(262\) | 7.13650 | 0.440894 | ||||||||
\(263\) | −14.6232 | −0.901704 | −0.450852 | − | 0.892599i | \(-0.648880\pi\) | ||||
−0.450852 | + | 0.892599i | \(0.648880\pi\) | |||||||
\(264\) | −1.14567 | −0.0705114 | ||||||||
\(265\) | 43.9692 | 2.70100 | ||||||||
\(266\) | −43.0227 | −2.63789 | ||||||||
\(267\) | 33.6864 | 2.06157 | ||||||||
\(268\) | 26.0834 | 1.59330 | ||||||||
\(269\) | −0.823071 | −0.0501835 | −0.0250917 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250917 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(270\) | −16.9414 | −1.03102 | ||||||||
\(271\) | −6.49379 | −0.394470 | −0.197235 | − | 0.980356i | \(-0.563196\pi\) | ||||
−0.197235 | + | 0.980356i | \(0.563196\pi\) | |||||||
\(272\) | 1.19392 | 0.0723921 | ||||||||
\(273\) | 2.08551 | 0.126221 | ||||||||
\(274\) | −32.6967 | −1.97528 | ||||||||
\(275\) | 0.459963 | 0.0277368 | ||||||||
\(276\) | −112.051 | −6.74465 | ||||||||
\(277\) | 16.6222 | 0.998730 | 0.499365 | − | 0.866392i | \(-0.333567\pi\) | ||||
0.499365 | + | 0.866392i | \(0.333567\pi\) | |||||||
\(278\) | −50.5622 | −3.03252 | ||||||||
\(279\) | −11.8942 | −0.712089 | ||||||||
\(280\) | 96.3549 | 5.75831 | ||||||||
\(281\) | −13.4768 | −0.803957 | −0.401979 | − | 0.915649i | \(-0.631677\pi\) | ||||
−0.401979 | + | 0.915649i | \(0.631677\pi\) | |||||||
\(282\) | 78.7873 | 4.69171 | ||||||||
\(283\) | 6.28908 | 0.373847 | 0.186923 | − | 0.982374i | \(-0.440148\pi\) | ||||
0.186923 | + | 0.982374i | \(0.440148\pi\) | |||||||
\(284\) | 47.4615 | 2.81632 | ||||||||
\(285\) | −44.9626 | −2.66335 | ||||||||
\(286\) | −0.0465177 | −0.00275065 | ||||||||
\(287\) | 30.2587 | 1.78611 | ||||||||
\(288\) | −42.5870 | −2.50946 | ||||||||
\(289\) | −16.9923 | −0.999549 | ||||||||
\(290\) | 52.6474 | 3.09156 | ||||||||
\(291\) | −37.6804 | −2.20887 | ||||||||
\(292\) | 21.3385 | 1.24874 | ||||||||
\(293\) | 12.6587 | 0.739530 | 0.369765 | − | 0.929125i | \(-0.379438\pi\) | ||||
0.369765 | + | 0.929125i | \(0.379438\pi\) | |||||||
\(294\) | −10.5631 | −0.616051 | ||||||||
\(295\) | −14.8833 | −0.866541 | ||||||||
\(296\) | 86.6765 | 5.03797 | ||||||||
\(297\) | −0.0958985 | −0.00556459 | ||||||||
\(298\) | 21.5832 | 1.25028 | ||||||||
\(299\) | −2.83814 | −0.164134 | ||||||||
\(300\) | 100.518 | 5.80340 | ||||||||
\(301\) | −9.79994 | −0.564859 | ||||||||
\(302\) | 20.0022 | 1.15100 | ||||||||
\(303\) | −2.18846 | −0.125724 | ||||||||
\(304\) | 73.4994 | 4.21548 | ||||||||
\(305\) | 35.3499 | 2.02413 | ||||||||
\(306\) | −0.532742 | −0.0304549 | ||||||||
\(307\) | −14.5728 | −0.831715 | −0.415857 | − | 0.909430i | \(-0.636518\pi\) | ||||
−0.415857 | + | 0.909430i | \(0.636518\pi\) | |||||||
\(308\) | 0.874324 | 0.0498193 | ||||||||
\(309\) | −18.9354 | −1.07720 | ||||||||
\(310\) | −52.0758 | −2.95771 | ||||||||
\(311\) | 22.2480 | 1.26157 | 0.630785 | − | 0.775958i | \(-0.282733\pi\) | ||||
0.630785 | + | 0.775958i | \(0.282733\pi\) | |||||||
\(312\) | −6.34164 | −0.359025 | ||||||||
\(313\) | −26.0567 | −1.47281 | −0.736407 | − | 0.676539i | \(-0.763479\pi\) | ||||
−0.736407 | + | 0.676539i | \(0.763479\pi\) | |||||||
\(314\) | 19.7108 | 1.11234 | ||||||||
\(315\) | −24.1553 | −1.36100 | ||||||||
\(316\) | 22.9774 | 1.29258 | ||||||||
\(317\) | 9.86820 | 0.554253 | 0.277127 | − | 0.960833i | \(-0.410618\pi\) | ||||
0.277127 | + | 0.960833i | \(0.410618\pi\) | |||||||
\(318\) | 74.8521 | 4.19750 | ||||||||
\(319\) | 0.298015 | 0.0166857 | ||||||||
\(320\) | −87.1932 | −4.87425 | ||||||||
\(321\) | 1.01876 | 0.0568617 | ||||||||
\(322\) | 73.4111 | 4.09104 | ||||||||
\(323\) | 0.472096 | 0.0262681 | ||||||||
\(324\) | −56.8296 | −3.15720 | ||||||||
\(325\) | 2.54603 | 0.141228 | ||||||||
\(326\) | 57.8204 | 3.20238 | ||||||||
\(327\) | −25.6436 | −1.41810 | ||||||||
\(328\) | −92.0107 | −5.08044 | ||||||||
\(329\) | −37.5085 | −2.06791 | ||||||||
\(330\) | 1.25748 | 0.0692218 | ||||||||
\(331\) | −9.04341 | −0.497071 | −0.248535 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248535 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(332\) | 67.7251 | 3.71690 | ||||||||
\(333\) | −21.7290 | −1.19074 | ||||||||
\(334\) | 46.9945 | 2.57142 | ||||||||
\(335\) | −17.8593 | −0.975760 | ||||||||
\(336\) | 92.1566 | 5.02755 | ||||||||
\(337\) | 16.2383 | 0.884558 | 0.442279 | − | 0.896877i | \(-0.354170\pi\) | ||||
0.442279 | + | 0.896877i | \(0.354170\pi\) | |||||||
\(338\) | 34.9067 | 1.89867 | ||||||||
\(339\) | 10.9480 | 0.594616 | ||||||||
\(340\) | −1.69490 | −0.0919187 | ||||||||
\(341\) | −0.294780 | −0.0159632 | ||||||||
\(342\) | −32.7963 | −1.77342 | ||||||||
\(343\) | −15.6236 | −0.843593 | ||||||||
\(344\) | 29.7997 | 1.60669 | ||||||||
\(345\) | 76.7211 | 4.13053 | ||||||||
\(346\) | 51.9376 | 2.79218 | ||||||||
\(347\) | −31.3678 | −1.68391 | −0.841956 | − | 0.539547i | \(-0.818596\pi\) | ||||
−0.841956 | + | 0.539547i | \(0.818596\pi\) | |||||||
\(348\) | 65.1267 | 3.49116 | ||||||||
\(349\) | 16.8525 | 0.902096 | 0.451048 | − | 0.892500i | \(-0.351050\pi\) | ||||
0.451048 | + | 0.892500i | \(0.351050\pi\) | |||||||
\(350\) | −65.8553 | −3.52012 | ||||||||
\(351\) | −0.530826 | −0.0283334 | ||||||||
\(352\) | −1.05545 | −0.0562557 | ||||||||
\(353\) | −10.7676 | −0.573104 | −0.286552 | − | 0.958065i | \(-0.592509\pi\) | ||||
−0.286552 | + | 0.958065i | \(0.592509\pi\) | |||||||
\(354\) | −25.3370 | −1.34665 | ||||||||
\(355\) | −32.4969 | −1.72476 | ||||||||
\(356\) | 78.1726 | 4.14314 | ||||||||
\(357\) | 0.591933 | 0.0313284 | ||||||||
\(358\) | 40.4486 | 2.13777 | ||||||||
\(359\) | −12.1766 | −0.642654 | −0.321327 | − | 0.946968i | \(-0.604129\pi\) | ||||
−0.321327 | + | 0.946968i | \(0.604129\pi\) | |||||||
\(360\) | 73.4516 | 3.87124 | ||||||||
\(361\) | 10.0629 | 0.529625 | ||||||||
\(362\) | 29.6776 | 1.55982 | ||||||||
\(363\) | −25.1948 | −1.32238 | ||||||||
\(364\) | 4.83964 | 0.253666 | ||||||||
\(365\) | −14.6105 | −0.764750 | ||||||||
\(366\) | 60.1789 | 3.14560 | ||||||||
\(367\) | 31.5158 | 1.64511 | 0.822555 | − | 0.568685i | \(-0.192548\pi\) | ||||
0.822555 | + | 0.568685i | \(0.192548\pi\) | |||||||
\(368\) | −125.414 | −6.53768 | ||||||||
\(369\) | 23.0663 | 1.20078 | ||||||||
\(370\) | −95.1348 | −4.94582 | ||||||||
\(371\) | −35.6351 | −1.85008 | ||||||||
\(372\) | −64.4196 | −3.34000 | ||||||||
\(373\) | −28.0341 | −1.45155 | −0.725775 | − | 0.687932i | \(-0.758519\pi\) | ||||
−0.725775 | + | 0.687932i | \(0.758519\pi\) | |||||||
\(374\) | −0.0132032 | −0.000682720 0 | ||||||||
\(375\) | −27.1232 | −1.40064 | ||||||||
\(376\) | 114.056 | 5.88200 | ||||||||
\(377\) | 1.64960 | 0.0849588 | ||||||||
\(378\) | 13.7303 | 0.706210 | ||||||||
\(379\) | −23.9854 | −1.23205 | −0.616023 | − | 0.787729i | \(-0.711257\pi\) | ||||
−0.616023 | + | 0.787729i | \(0.711257\pi\) | |||||||
\(380\) | −104.340 | −5.35254 | ||||||||
\(381\) | 21.2596 | 1.08916 | ||||||||
\(382\) | 14.6582 | 0.749978 | ||||||||
\(383\) | 5.95479 | 0.304275 | 0.152138 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152138 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(384\) | −61.6700 | −3.14709 | ||||||||
\(385\) | −0.598651 | −0.0305101 | ||||||||
\(386\) | 11.4329 | 0.581919 | ||||||||
\(387\) | −7.47052 | −0.379748 | ||||||||
\(388\) | −87.4411 | −4.43915 | ||||||||
\(389\) | 18.6180 | 0.943970 | 0.471985 | − | 0.881607i | \(-0.343538\pi\) | ||||
0.471985 | + | 0.881607i | \(0.343538\pi\) | |||||||
\(390\) | 6.96049 | 0.352458 | ||||||||
\(391\) | −0.805553 | −0.0407386 | ||||||||
\(392\) | −15.2916 | −0.772343 | ||||||||
\(393\) | −6.04461 | −0.304910 | ||||||||
\(394\) | −27.3623 | −1.37849 | ||||||||
\(395\) | −15.7327 | −0.791597 | ||||||||
\(396\) | 0.666500 | 0.0334929 | ||||||||
\(397\) | 0.513203 | 0.0257569 | 0.0128785 | − | 0.999917i | \(-0.495901\pi\) | ||||
0.0128785 | + | 0.999917i | \(0.495901\pi\) | |||||||
\(398\) | 21.2986 | 1.06760 | ||||||||
\(399\) | 36.4402 | 1.82429 | ||||||||
\(400\) | 112.506 | 5.62531 | ||||||||
\(401\) | 23.2637 | 1.16173 | 0.580867 | − | 0.813999i | \(-0.302714\pi\) | ||||
0.580867 | + | 0.813999i | \(0.302714\pi\) | |||||||
\(402\) | −30.4033 | −1.51638 | ||||||||
\(403\) | −1.63169 | −0.0812803 | ||||||||
\(404\) | −5.07853 | −0.252666 | ||||||||
\(405\) | 38.9113 | 1.93352 | ||||||||
\(406\) | −42.6684 | −2.11760 | ||||||||
\(407\) | −0.538520 | −0.0266934 | ||||||||
\(408\) | −1.79996 | −0.0891111 | ||||||||
\(409\) | −16.8777 | −0.834549 | −0.417275 | − | 0.908780i | \(-0.637015\pi\) | ||||
−0.417275 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(410\) | 100.990 | 4.98752 | ||||||||
\(411\) | 27.6941 | 1.36605 | ||||||||
\(412\) | −43.9416 | −2.16485 | ||||||||
\(413\) | 12.0623 | 0.593547 | ||||||||
\(414\) | 55.9615 | 2.75036 | ||||||||
\(415\) | −46.3715 | −2.27629 | ||||||||
\(416\) | −5.84222 | −0.286439 | ||||||||
\(417\) | 42.8262 | 2.09721 | ||||||||
\(418\) | −0.812806 | −0.0397556 | ||||||||
\(419\) | −24.2427 | −1.18433 | −0.592166 | − | 0.805816i | \(-0.701727\pi\) | ||||
−0.592166 | + | 0.805816i | \(0.701727\pi\) | |||||||
\(420\) | −130.826 | −6.38366 | ||||||||
\(421\) | −38.6264 | −1.88253 | −0.941267 | − | 0.337663i | \(-0.890364\pi\) | ||||
−0.941267 | + | 0.337663i | \(0.890364\pi\) | |||||||
\(422\) | 33.1899 | 1.61566 | ||||||||
\(423\) | −28.5929 | −1.39023 | ||||||||
\(424\) | 108.359 | 5.26240 | ||||||||
\(425\) | 0.722642 | 0.0350533 | ||||||||
\(426\) | −55.3220 | −2.68036 | ||||||||
\(427\) | −28.6496 | −1.38645 | ||||||||
\(428\) | 2.36414 | 0.114275 | ||||||||
\(429\) | 0.0394005 | 0.00190227 | ||||||||
\(430\) | −32.7077 | −1.57731 | ||||||||
\(431\) | −27.4211 | −1.32083 | −0.660413 | − | 0.750903i | \(-0.729619\pi\) | ||||
−0.660413 | + | 0.750903i | \(0.729619\pi\) | |||||||
\(432\) | −23.4566 | −1.12856 | ||||||||
\(433\) | −8.86253 | −0.425906 | −0.212953 | − | 0.977062i | \(-0.568308\pi\) | ||||
−0.212953 | + | 0.977062i | \(0.568308\pi\) | |||||||
\(434\) | 42.2052 | 2.02591 | ||||||||
\(435\) | −44.5923 | −2.13804 | ||||||||
\(436\) | −59.5086 | −2.84994 | ||||||||
\(437\) | −49.5909 | −2.37226 | ||||||||
\(438\) | −24.8726 | −1.18846 | ||||||||
\(439\) | 28.7215 | 1.37080 | 0.685402 | − | 0.728165i | \(-0.259627\pi\) | ||||
0.685402 | + | 0.728165i | \(0.259627\pi\) | |||||||
\(440\) | 1.82038 | 0.0867834 | ||||||||
\(441\) | 3.83347 | 0.182546 | ||||||||
\(442\) | −0.0730834 | −0.00347622 | ||||||||
\(443\) | −11.9513 | −0.567825 | −0.283912 | − | 0.958850i | \(-0.591633\pi\) | ||||
−0.283912 | + | 0.958850i | \(0.591633\pi\) | |||||||
\(444\) | −117.685 | −5.58509 | ||||||||
\(445\) | −53.5249 | −2.53732 | ||||||||
\(446\) | −34.7563 | −1.64576 | ||||||||
\(447\) | −18.2810 | −0.864662 | ||||||||
\(448\) | 70.6663 | 3.33867 | ||||||||
\(449\) | −36.4429 | −1.71985 | −0.859924 | − | 0.510422i | \(-0.829489\pi\) | ||||
−0.859924 | + | 0.510422i | \(0.829489\pi\) | |||||||
\(450\) | −50.2017 | −2.36653 | ||||||||
\(451\) | 0.571661 | 0.0269185 | ||||||||
\(452\) | 25.4060 | 1.19500 | ||||||||
\(453\) | −16.9419 | −0.795998 | ||||||||
\(454\) | −32.9543 | −1.54662 | ||||||||
\(455\) | −3.31371 | −0.155349 | ||||||||
\(456\) | −110.808 | −5.18905 | ||||||||
\(457\) | −5.58640 | −0.261321 | −0.130660 | − | 0.991427i | \(-0.541710\pi\) | ||||
−0.130660 | + | 0.991427i | \(0.541710\pi\) | |||||||
\(458\) | −69.1888 | −3.23298 | ||||||||
\(459\) | −0.150665 | −0.00703244 | ||||||||
\(460\) | 178.039 | 8.30111 | ||||||||
\(461\) | 10.7489 | 0.500628 | 0.250314 | − | 0.968165i | \(-0.419466\pi\) | ||||
0.250314 | + | 0.968165i | \(0.419466\pi\) | |||||||
\(462\) | −1.01913 | −0.0474142 | ||||||||
\(463\) | 15.3458 | 0.713178 | 0.356589 | − | 0.934261i | \(-0.383940\pi\) | ||||
0.356589 | + | 0.934261i | \(0.383940\pi\) | |||||||
\(464\) | 72.8941 | 3.38402 | ||||||||
\(465\) | 44.1082 | 2.04547 | ||||||||
\(466\) | −19.6088 | −0.908360 | ||||||||
\(467\) | −22.8959 | −1.05950 | −0.529748 | − | 0.848155i | \(-0.677714\pi\) | ||||
−0.529748 | + | 0.848155i | \(0.677714\pi\) | |||||||
\(468\) | 3.68927 | 0.170537 | ||||||||
\(469\) | 14.4742 | 0.668357 | ||||||||
\(470\) | −125.186 | −5.77442 | ||||||||
\(471\) | −16.6950 | −0.769266 | ||||||||
\(472\) | −36.6791 | −1.68829 | ||||||||
\(473\) | −0.185145 | −0.00851299 | ||||||||
\(474\) | −26.7830 | −1.23018 | ||||||||
\(475\) | 44.4869 | 2.04120 | ||||||||
\(476\) | 1.37364 | 0.0629607 | ||||||||
\(477\) | −27.1647 | −1.24379 | ||||||||
\(478\) | −34.9896 | −1.60039 | ||||||||
\(479\) | −0.759954 | −0.0347232 | −0.0173616 | − | 0.999849i | \(-0.505527\pi\) | ||||
−0.0173616 | + | 0.999849i | \(0.505527\pi\) | |||||||
\(480\) | 157.928 | 7.20840 | ||||||||
\(481\) | −2.98086 | −0.135916 | ||||||||
\(482\) | −17.9223 | −0.816337 | ||||||||
\(483\) | −62.1792 | −2.82925 | ||||||||
\(484\) | −58.4670 | −2.65759 | ||||||||
\(485\) | 59.8711 | 2.71861 | ||||||||
\(486\) | 52.2803 | 2.37148 | ||||||||
\(487\) | 36.3345 | 1.64647 | 0.823236 | − | 0.567699i | \(-0.192166\pi\) | ||||
0.823236 | + | 0.567699i | \(0.192166\pi\) | |||||||
\(488\) | 87.1179 | 3.94364 | ||||||||
\(489\) | −48.9739 | −2.21468 | ||||||||
\(490\) | 16.7839 | 0.758217 | ||||||||
\(491\) | −12.1803 | −0.549691 | −0.274845 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274845 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(492\) | 124.928 | 5.63218 | ||||||||
\(493\) | 0.468208 | 0.0210870 | ||||||||
\(494\) | −4.49911 | −0.202425 | ||||||||
\(495\) | −0.456354 | −0.0205116 | ||||||||
\(496\) | −72.1027 | −3.23751 | ||||||||
\(497\) | 26.3374 | 1.18139 | ||||||||
\(498\) | −78.9417 | −3.53746 | ||||||||
\(499\) | −28.1849 | −1.26173 | −0.630866 | − | 0.775892i | \(-0.717300\pi\) | ||||
−0.630866 | + | 0.775892i | \(0.717300\pi\) | |||||||
\(500\) | −62.9421 | −2.81485 | ||||||||
\(501\) | −39.8043 | −1.77833 | ||||||||
\(502\) | 42.3340 | 1.88946 | ||||||||
\(503\) | −19.7762 | −0.881778 | −0.440889 | − | 0.897562i | \(-0.645337\pi\) | ||||
−0.440889 | + | 0.897562i | \(0.645337\pi\) | |||||||
\(504\) | −59.5294 | −2.65165 | ||||||||
\(505\) | 3.47728 | 0.154737 | ||||||||
\(506\) | 1.38692 | 0.0616560 | ||||||||
\(507\) | −29.5660 | −1.31307 | ||||||||
\(508\) | 49.3350 | 2.18889 | ||||||||
\(509\) | 3.98402 | 0.176589 | 0.0882944 | − | 0.996094i | \(-0.471858\pi\) | ||||
0.0882944 | + | 0.996094i | \(0.471858\pi\) | |||||||
\(510\) | 1.97560 | 0.0874813 | ||||||||
\(511\) | 11.8412 | 0.523824 | ||||||||
\(512\) | −13.5344 | −0.598143 | ||||||||
\(513\) | −9.27514 | −0.409507 | ||||||||
\(514\) | 1.06359 | 0.0469130 | ||||||||
\(515\) | 30.0869 | 1.32579 | ||||||||
\(516\) | −40.4606 | −1.78118 | ||||||||
\(517\) | −0.708630 | −0.0311655 | ||||||||
\(518\) | 77.1027 | 3.38770 | ||||||||
\(519\) | −43.9912 | −1.93100 | ||||||||
\(520\) | 10.0763 | 0.441877 | ||||||||
\(521\) | −29.4263 | −1.28919 | −0.644595 | − | 0.764524i | \(-0.722974\pi\) | ||||
−0.644595 | + | 0.764524i | \(0.722974\pi\) | |||||||
\(522\) | −32.5263 | −1.42364 | ||||||||
\(523\) | 21.6341 | 0.945993 | 0.472996 | − | 0.881064i | \(-0.343172\pi\) | ||||
0.472996 | + | 0.881064i | \(0.343172\pi\) | |||||||
\(524\) | −14.0271 | −0.612778 | ||||||||
\(525\) | 55.7795 | 2.43442 | ||||||||
\(526\) | 39.5548 | 1.72467 | ||||||||
\(527\) | −0.463125 | −0.0201740 | ||||||||
\(528\) | 1.74107 | 0.0757702 | ||||||||
\(529\) | 61.6186 | 2.67907 | ||||||||
\(530\) | −118.934 | −5.16615 | ||||||||
\(531\) | 9.19513 | 0.399035 | ||||||||
\(532\) | 84.5632 | 3.66628 | ||||||||
\(533\) | 3.16431 | 0.137061 | ||||||||
\(534\) | −91.1195 | −3.94313 | ||||||||
\(535\) | −1.61873 | −0.0699837 | ||||||||
\(536\) | −44.0133 | −1.90109 | ||||||||
\(537\) | −34.2599 | −1.47843 | ||||||||
\(538\) | 2.22635 | 0.0959849 | ||||||||
\(539\) | 0.0950066 | 0.00409222 | ||||||||
\(540\) | 33.2992 | 1.43297 | ||||||||
\(541\) | 3.33019 | 0.143176 | 0.0715880 | − | 0.997434i | \(-0.477193\pi\) | ||||
0.0715880 | + | 0.997434i | \(0.477193\pi\) | |||||||
\(542\) | 17.5653 | 0.754494 | ||||||||
\(543\) | −25.1369 | −1.07873 | ||||||||
\(544\) | −1.65821 | −0.0710950 | ||||||||
\(545\) | 40.7456 | 1.74535 | ||||||||
\(546\) | −5.64118 | −0.241420 | ||||||||
\(547\) | 3.15290 | 0.134808 | 0.0674042 | − | 0.997726i | \(-0.478528\pi\) | ||||
0.0674042 | + | 0.997726i | \(0.478528\pi\) | |||||||
\(548\) | 64.2670 | 2.74535 | ||||||||
\(549\) | −21.8397 | −0.932095 | ||||||||
\(550\) | −1.24417 | −0.0530516 | ||||||||
\(551\) | 28.8235 | 1.22792 | ||||||||
\(552\) | 189.075 | 8.04756 | ||||||||
\(553\) | 12.7507 | 0.542213 | ||||||||
\(554\) | −44.9619 | −1.91025 | ||||||||
\(555\) | 80.5792 | 3.42040 | ||||||||
\(556\) | 99.3824 | 4.21475 | ||||||||
\(557\) | 2.64369 | 0.112017 | 0.0560083 | − | 0.998430i | \(-0.482163\pi\) | ||||
0.0560083 | + | 0.998430i | \(0.482163\pi\) | |||||||
\(558\) | 32.1731 | 1.36200 | ||||||||
\(559\) | −1.02483 | −0.0433458 | ||||||||
\(560\) | −146.429 | −6.18776 | ||||||||
\(561\) | 0.0111831 | 0.000472151 0 | ||||||||
\(562\) | 36.4538 | 1.53771 | ||||||||
\(563\) | −24.3531 | −1.02636 | −0.513180 | − | 0.858281i | \(-0.671532\pi\) | ||||
−0.513180 | + | 0.858281i | \(0.671532\pi\) | |||||||
\(564\) | −154.860 | −6.52079 | ||||||||
\(565\) | −17.3955 | −0.731836 | ||||||||
\(566\) | −17.0116 | −0.715049 | ||||||||
\(567\) | −31.5359 | −1.32438 | ||||||||
\(568\) | −80.0869 | −3.36037 | ||||||||
\(569\) | 26.2539 | 1.10062 | 0.550310 | − | 0.834960i | \(-0.314509\pi\) | ||||
0.550310 | + | 0.834960i | \(0.314509\pi\) | |||||||
\(570\) | 121.621 | 5.09414 | ||||||||
\(571\) | 27.0258 | 1.13099 | 0.565497 | − | 0.824751i | \(-0.308684\pi\) | ||||
0.565497 | + | 0.824751i | \(0.308684\pi\) | |||||||
\(572\) | 0.0914328 | 0.00382300 | ||||||||
\(573\) | −12.4155 | −0.518664 | ||||||||
\(574\) | −81.8477 | −3.41626 | ||||||||
\(575\) | −75.9094 | −3.16564 | ||||||||
\(576\) | 53.8692 | 2.24455 | ||||||||
\(577\) | 8.35160 | 0.347682 | 0.173841 | − | 0.984774i | \(-0.444382\pi\) | ||||
0.173841 | + | 0.984774i | \(0.444382\pi\) | |||||||
\(578\) | 45.9632 | 1.91182 | ||||||||
\(579\) | −9.68367 | −0.402439 | ||||||||
\(580\) | −103.481 | −4.29681 | ||||||||
\(581\) | 37.5821 | 1.55917 | ||||||||
\(582\) | 101.923 | 4.22485 | ||||||||
\(583\) | −0.673236 | −0.0278826 | ||||||||
\(584\) | −36.0068 | −1.48997 | ||||||||
\(585\) | −2.52605 | −0.104439 | ||||||||
\(586\) | −34.2410 | −1.41448 | ||||||||
\(587\) | −9.09715 | −0.375480 | −0.187740 | − | 0.982219i | \(-0.560116\pi\) | ||||
−0.187740 | + | 0.982219i | \(0.560116\pi\) | |||||||
\(588\) | 20.7622 | 0.856220 | ||||||||
\(589\) | −28.5106 | −1.17476 | ||||||||
\(590\) | 40.2585 | 1.65742 | ||||||||
\(591\) | 23.1758 | 0.953326 | ||||||||
\(592\) | −131.721 | −5.41370 | ||||||||
\(593\) | −26.5313 | −1.08951 | −0.544754 | − | 0.838596i | \(-0.683377\pi\) | ||||
−0.544754 | + | 0.838596i | \(0.683377\pi\) | |||||||
\(594\) | 0.259399 | 0.0106433 | ||||||||
\(595\) | −0.940533 | −0.0385581 | ||||||||
\(596\) | −42.4229 | −1.73771 | ||||||||
\(597\) | −18.0399 | −0.738324 | ||||||||
\(598\) | 7.67699 | 0.313935 | ||||||||
\(599\) | −44.4492 | −1.81615 | −0.908073 | − | 0.418812i | \(-0.862446\pi\) | ||||
−0.908073 | + | 0.418812i | \(0.862446\pi\) | |||||||
\(600\) | −169.615 | −6.92449 | ||||||||
\(601\) | 19.1121 | 0.779601 | 0.389800 | − | 0.920899i | \(-0.372544\pi\) | ||||
0.389800 | + | 0.920899i | \(0.372544\pi\) | |||||||
\(602\) | 26.5082 | 1.08039 | ||||||||
\(603\) | 11.0337 | 0.449329 | ||||||||
\(604\) | −39.3153 | −1.59972 | ||||||||
\(605\) | 40.0324 | 1.62755 | ||||||||
\(606\) | 5.91964 | 0.240469 | ||||||||
\(607\) | −38.6939 | −1.57054 | −0.785269 | − | 0.619154i | \(-0.787476\pi\) | ||||
−0.785269 | + | 0.619154i | \(0.787476\pi\) | |||||||
\(608\) | −102.081 | −4.13995 | ||||||||
\(609\) | 36.1402 | 1.46447 | ||||||||
\(610\) | −95.6193 | −3.87151 | ||||||||
\(611\) | −3.92247 | −0.158686 | ||||||||
\(612\) | 1.04713 | 0.0423277 | ||||||||
\(613\) | 35.7708 | 1.44477 | 0.722384 | − | 0.691493i | \(-0.243047\pi\) | ||||
0.722384 | + | 0.691493i | \(0.243047\pi\) | |||||||
\(614\) | 39.4186 | 1.59080 | ||||||||
\(615\) | −85.5382 | −3.44923 | ||||||||
\(616\) | −1.47534 | −0.0594432 | ||||||||
\(617\) | −17.5074 | −0.704821 | −0.352411 | − | 0.935845i | \(-0.614638\pi\) | ||||
−0.352411 | + | 0.935845i | \(0.614638\pi\) | |||||||
\(618\) | 51.2192 | 2.06034 | ||||||||
\(619\) | −0.268718 | −0.0108007 | −0.00540035 | − | 0.999985i | \(-0.501719\pi\) | ||||
−0.00540035 | + | 0.999985i | \(0.501719\pi\) | |||||||
\(620\) | 102.357 | 4.11077 | ||||||||
\(621\) | 15.8265 | 0.635095 | ||||||||
\(622\) | −60.1795 | −2.41298 | ||||||||
\(623\) | 43.3796 | 1.73797 | ||||||||
\(624\) | 9.63730 | 0.385801 | ||||||||
\(625\) | 1.83621 | 0.0734484 | ||||||||
\(626\) | 70.4818 | 2.81702 | ||||||||
\(627\) | 0.688447 | 0.0274939 | ||||||||
\(628\) | −38.7424 | −1.54599 | ||||||||
\(629\) | −0.846061 | −0.0337347 | ||||||||
\(630\) | 65.3385 | 2.60315 | ||||||||
\(631\) | 3.75402 | 0.149445 | 0.0747226 | − | 0.997204i | \(-0.476193\pi\) | ||||
0.0747226 | + | 0.997204i | \(0.476193\pi\) | |||||||
\(632\) | −38.7723 | −1.54228 | ||||||||
\(633\) | −28.1118 | −1.11735 | ||||||||
\(634\) | −26.6929 | −1.06011 | ||||||||
\(635\) | −33.7798 | −1.34051 | ||||||||
\(636\) | −147.125 | −5.83390 | ||||||||
\(637\) | 0.525889 | 0.0208365 | ||||||||
\(638\) | −0.806113 | −0.0319143 | ||||||||
\(639\) | 20.0771 | 0.794236 | ||||||||
\(640\) | 97.9886 | 3.87334 | ||||||||
\(641\) | −29.1855 | −1.15276 | −0.576380 | − | 0.817182i | \(-0.695535\pi\) | ||||
−0.576380 | + | 0.817182i | \(0.695535\pi\) | |||||||
\(642\) | −2.75569 | −0.108758 | ||||||||
\(643\) | 38.4436 | 1.51607 | 0.758035 | − | 0.652214i | \(-0.226160\pi\) | ||||
0.758035 | + | 0.652214i | \(0.226160\pi\) | |||||||
\(644\) | −144.293 | −5.68594 | ||||||||
\(645\) | 27.7035 | 1.09082 | ||||||||
\(646\) | −1.27699 | −0.0502425 | ||||||||
\(647\) | −7.86962 | −0.309387 | −0.154693 | − | 0.987963i | \(-0.549439\pi\) | ||||
−0.154693 | + | 0.987963i | \(0.549439\pi\) | |||||||
\(648\) | 95.8947 | 3.76710 | ||||||||
\(649\) | 0.227887 | 0.00894534 | ||||||||
\(650\) | −6.88684 | −0.270124 | ||||||||
\(651\) | −35.7478 | −1.40107 | ||||||||
\(652\) | −113.649 | −4.45083 | ||||||||
\(653\) | 13.5511 | 0.530295 | 0.265148 | − | 0.964208i | \(-0.414579\pi\) | ||||
0.265148 | + | 0.964208i | \(0.414579\pi\) | |||||||
\(654\) | 69.3644 | 2.71236 | ||||||||
\(655\) | 9.60439 | 0.375275 | ||||||||
\(656\) | 139.827 | 5.45934 | ||||||||
\(657\) | 9.02658 | 0.352160 | ||||||||
\(658\) | 101.458 | 3.95525 | ||||||||
\(659\) | −14.8092 | −0.576883 | −0.288442 | − | 0.957497i | \(-0.593137\pi\) | ||||
−0.288442 | + | 0.957497i | \(0.593137\pi\) | |||||||
\(660\) | −2.47163 | −0.0962080 | ||||||||
\(661\) | 10.4107 | 0.404929 | 0.202464 | − | 0.979290i | \(-0.435105\pi\) | ||||
0.202464 | + | 0.979290i | \(0.435105\pi\) | |||||||
\(662\) | 24.4619 | 0.950737 | ||||||||
\(663\) | 0.0619016 | 0.00240406 | ||||||||
\(664\) | −114.280 | −4.43492 | ||||||||
\(665\) | −57.9005 | −2.24529 | ||||||||
\(666\) | 58.7756 | 2.27751 | ||||||||
\(667\) | −49.1826 | −1.90436 | ||||||||
\(668\) | −92.3698 | −3.57390 | ||||||||
\(669\) | 29.4386 | 1.13816 | ||||||||
\(670\) | 48.3084 | 1.86632 | ||||||||
\(671\) | −0.541262 | −0.0208952 | ||||||||
\(672\) | −127.994 | −4.93747 | ||||||||
\(673\) | 11.3851 | 0.438862 | 0.219431 | − | 0.975628i | \(-0.429580\pi\) | ||||
0.219431 | + | 0.975628i | \(0.429580\pi\) | |||||||
\(674\) | −43.9236 | −1.69188 | ||||||||
\(675\) | −14.1976 | −0.546464 | ||||||||
\(676\) | −68.6107 | −2.63887 | ||||||||
\(677\) | −2.43282 | −0.0935010 | −0.0467505 | − | 0.998907i | \(-0.514887\pi\) | ||||
−0.0467505 | + | 0.998907i | \(0.514887\pi\) | |||||||
\(678\) | −29.6138 | −1.13731 | ||||||||
\(679\) | −48.5229 | −1.86214 | ||||||||
\(680\) | 2.85998 | 0.109675 | ||||||||
\(681\) | 27.9122 | 1.06960 | ||||||||
\(682\) | 0.797361 | 0.0305325 | ||||||||
\(683\) | 18.2028 | 0.696509 | 0.348255 | − | 0.937400i | \(-0.386774\pi\) | ||||
0.348255 | + | 0.937400i | \(0.386774\pi\) | |||||||
\(684\) | 64.4628 | 2.46480 | ||||||||
\(685\) | −44.0037 | −1.68129 | ||||||||
\(686\) | 42.2607 | 1.61352 | ||||||||
\(687\) | 58.6029 | 2.23584 | ||||||||
\(688\) | −45.2862 | −1.72652 | ||||||||
\(689\) | −3.72655 | −0.141970 | ||||||||
\(690\) | −207.526 | −7.90037 | ||||||||
\(691\) | 27.5374 | 1.04757 | 0.523787 | − | 0.851849i | \(-0.324519\pi\) | ||||
0.523787 | + | 0.851849i | \(0.324519\pi\) | |||||||
\(692\) | −102.086 | −3.88072 | ||||||||
\(693\) | 0.369855 | 0.0140496 | ||||||||
\(694\) | 84.8479 | 3.22078 | ||||||||
\(695\) | −68.0473 | −2.58118 | ||||||||
\(696\) | −109.895 | −4.16557 | ||||||||
\(697\) | 0.898130 | 0.0340191 | ||||||||
\(698\) | −45.5850 | −1.72542 | ||||||||
\(699\) | 16.6086 | 0.628197 | ||||||||
\(700\) | 129.442 | 4.89244 | ||||||||
\(701\) | 29.1269 | 1.10011 | 0.550055 | − | 0.835129i | \(-0.314607\pi\) | ||||
0.550055 | + | 0.835129i | \(0.314607\pi\) | |||||||
\(702\) | 1.43585 | 0.0541927 | ||||||||
\(703\) | −52.0847 | −1.96441 | ||||||||
\(704\) | 1.33506 | 0.0503171 | ||||||||
\(705\) | 106.033 | 3.99343 | ||||||||
\(706\) | 29.1258 | 1.09616 | ||||||||
\(707\) | −2.81818 | −0.105989 | ||||||||
\(708\) | 49.8012 | 1.87164 | ||||||||
\(709\) | 7.84561 | 0.294648 | 0.147324 | − | 0.989088i | \(-0.452934\pi\) | ||||
0.147324 | + | 0.989088i | \(0.452934\pi\) | |||||||
\(710\) | 87.9022 | 3.29891 | ||||||||
\(711\) | 9.71987 | 0.364524 | ||||||||
\(712\) | −131.909 | −4.94350 | ||||||||
\(713\) | 48.6486 | 1.82190 | ||||||||
\(714\) | −1.60114 | −0.0599212 | ||||||||
\(715\) | −0.0626041 | −0.00234126 | ||||||||
\(716\) | −79.5036 | −2.97119 | ||||||||
\(717\) | 29.6362 | 1.10678 | ||||||||
\(718\) | 32.9368 | 1.22919 | ||||||||
\(719\) | 12.4554 | 0.464508 | 0.232254 | − | 0.972655i | \(-0.425390\pi\) | ||||
0.232254 | + | 0.972655i | \(0.425390\pi\) | |||||||
\(720\) | −111.623 | −4.15996 | ||||||||
\(721\) | −24.3841 | −0.908111 | ||||||||
\(722\) | −27.2194 | −1.01300 | ||||||||
\(723\) | 15.1802 | 0.564556 | ||||||||
\(724\) | −58.3326 | −2.16791 | ||||||||
\(725\) | 44.1205 | 1.63859 | ||||||||
\(726\) | 68.1502 | 2.52929 | ||||||||
\(727\) | 28.3786 | 1.05250 | 0.526251 | − | 0.850329i | \(-0.323597\pi\) | ||||
0.526251 | + | 0.850329i | \(0.323597\pi\) | |||||||
\(728\) | −8.16644 | −0.302668 | ||||||||
\(729\) | −12.2146 | −0.452393 | ||||||||
\(730\) | 39.5205 | 1.46272 | ||||||||
\(731\) | −0.290879 | −0.0107586 | ||||||||
\(732\) | −118.285 | −4.37192 | ||||||||
\(733\) | 1.24568 | 0.0460101 | 0.0230051 | − | 0.999735i | \(-0.492677\pi\) | ||||
0.0230051 | + | 0.999735i | \(0.492677\pi\) | |||||||
\(734\) | −85.2482 | −3.14657 | ||||||||
\(735\) | −14.2159 | −0.524362 | ||||||||
\(736\) | 174.185 | 6.42054 | ||||||||
\(737\) | 0.273454 | 0.0100728 | ||||||||
\(738\) | −62.3928 | −2.29671 | ||||||||
\(739\) | 30.9573 | 1.13878 | 0.569391 | − | 0.822067i | \(-0.307179\pi\) | ||||
0.569391 | + | 0.822067i | \(0.307179\pi\) | |||||||
\(740\) | 186.992 | 6.87396 | ||||||||
\(741\) | 3.81075 | 0.139991 | ||||||||
\(742\) | 96.3907 | 3.53861 | ||||||||
\(743\) | 38.4267 | 1.40974 | 0.704869 | − | 0.709337i | \(-0.251006\pi\) | ||||
0.704869 | + | 0.709337i | \(0.251006\pi\) | |||||||
\(744\) | 108.702 | 3.98521 | ||||||||
\(745\) | 29.0470 | 1.06420 | ||||||||
\(746\) | 75.8305 | 2.77635 | ||||||||
\(747\) | 28.6489 | 1.04821 | ||||||||
\(748\) | 0.0259515 | 0.000948880 0 | ||||||||
\(749\) | 1.31191 | 0.0479361 | ||||||||
\(750\) | 73.3665 | 2.67897 | ||||||||
\(751\) | 21.2600 | 0.775789 | 0.387895 | − | 0.921704i | \(-0.373202\pi\) | ||||
0.387895 | + | 0.921704i | \(0.373202\pi\) | |||||||
\(752\) | −173.330 | −6.32068 | ||||||||
\(753\) | −35.8569 | −1.30670 | ||||||||
\(754\) | −4.46207 | −0.162499 | ||||||||
\(755\) | 26.9192 | 0.979691 | ||||||||
\(756\) | −26.9875 | −0.981527 | ||||||||
\(757\) | 6.20929 | 0.225681 | 0.112840 | − | 0.993613i | \(-0.464005\pi\) | ||||
0.112840 | + | 0.993613i | \(0.464005\pi\) | |||||||
\(758\) | 64.8789 | 2.35651 | ||||||||
\(759\) | −1.17472 | −0.0426396 | ||||||||
\(760\) | 176.064 | 6.38653 | ||||||||
\(761\) | 3.91027 | 0.141747 | 0.0708736 | − | 0.997485i | \(-0.477421\pi\) | ||||
0.0708736 | + | 0.997485i | \(0.477421\pi\) | |||||||
\(762\) | −57.5059 | −2.08322 | ||||||||
\(763\) | −33.0225 | −1.19550 | ||||||||
\(764\) | −28.8114 | −1.04236 | ||||||||
\(765\) | −0.716972 | −0.0259222 | ||||||||
\(766\) | −16.1073 | −0.581981 | ||||||||
\(767\) | 1.26142 | 0.0455472 | ||||||||
\(768\) | 57.0618 | 2.05904 | ||||||||
\(769\) | 1.90872 | 0.0688302 | 0.0344151 | − | 0.999408i | \(-0.489043\pi\) | ||||
0.0344151 | + | 0.999408i | \(0.489043\pi\) | |||||||
\(770\) | 1.61931 | 0.0583560 | ||||||||
\(771\) | −0.900862 | −0.0324437 | ||||||||
\(772\) | −22.4719 | −0.808782 | ||||||||
\(773\) | −38.1640 | −1.37267 | −0.686333 | − | 0.727288i | \(-0.740781\pi\) | ||||
−0.686333 | + | 0.727288i | \(0.740781\pi\) | |||||||
\(774\) | 20.2073 | 0.726336 | ||||||||
\(775\) | −43.6415 | −1.56765 | ||||||||
\(776\) | 147.549 | 5.29669 | ||||||||
\(777\) | −65.3060 | −2.34284 | ||||||||
\(778\) | −50.3605 | −1.80551 | ||||||||
\(779\) | 55.2901 | 1.98097 | ||||||||
\(780\) | −13.6812 | −0.489865 | ||||||||
\(781\) | 0.497578 | 0.0178048 | ||||||||
\(782\) | 2.17897 | 0.0779198 | ||||||||
\(783\) | −9.19876 | −0.328737 | ||||||||
\(784\) | 23.2385 | 0.829945 | ||||||||
\(785\) | 26.5270 | 0.946789 | ||||||||
\(786\) | 16.3503 | 0.583196 | ||||||||
\(787\) | −6.92428 | −0.246824 | −0.123412 | − | 0.992356i | \(-0.539384\pi\) | ||||
−0.123412 | + | 0.992356i | \(0.539384\pi\) | |||||||
\(788\) | 53.7818 | 1.91590 | ||||||||
\(789\) | −33.5029 | −1.19273 | ||||||||
\(790\) | 42.5559 | 1.51407 | ||||||||
\(791\) | 14.0983 | 0.501279 | ||||||||
\(792\) | −1.12466 | −0.0399630 | ||||||||
\(793\) | −2.99604 | −0.106393 | ||||||||
\(794\) | −1.38818 | −0.0492647 | ||||||||
\(795\) | 100.737 | 3.57277 | ||||||||
\(796\) | −41.8634 | −1.48381 | ||||||||
\(797\) | −20.7141 | −0.733730 | −0.366865 | − | 0.930274i | \(-0.619569\pi\) | ||||
−0.366865 | + | 0.930274i | \(0.619569\pi\) | |||||||
\(798\) | −98.5685 | −3.48929 | ||||||||
\(799\) | −1.11332 | −0.0393864 | ||||||||
\(800\) | −156.257 | −5.52452 | ||||||||
\(801\) | 33.0684 | 1.16841 | ||||||||
\(802\) | −62.9268 | −2.22202 | ||||||||
\(803\) | 0.223710 | 0.00789454 | ||||||||
\(804\) | 59.7592 | 2.10754 | ||||||||
\(805\) | 98.7976 | 3.48216 | ||||||||
\(806\) | 4.41362 | 0.155463 | ||||||||
\(807\) | −1.88572 | −0.0663805 | ||||||||
\(808\) | 8.56955 | 0.301476 | ||||||||
\(809\) | −11.3197 | −0.397981 | −0.198990 | − | 0.980001i | \(-0.563766\pi\) | ||||
−0.198990 | + | 0.980001i | \(0.563766\pi\) | |||||||
\(810\) | −105.253 | −3.69820 | ||||||||
\(811\) | −28.6002 | −1.00429 | −0.502145 | − | 0.864783i | \(-0.667456\pi\) | ||||
−0.502145 | + | 0.864783i | \(0.667456\pi\) | |||||||
\(812\) | 83.8668 | 2.94315 | ||||||||
\(813\) | −14.8778 | −0.521787 | ||||||||
\(814\) | 1.45666 | 0.0510559 | ||||||||
\(815\) | 77.8155 | 2.72576 | ||||||||
\(816\) | 2.73537 | 0.0957570 | ||||||||
\(817\) | −17.9069 | −0.626484 | ||||||||
\(818\) | 45.6531 | 1.59622 | ||||||||
\(819\) | 2.04725 | 0.0715368 | ||||||||
\(820\) | −198.500 | −6.93192 | ||||||||
\(821\) | 48.7945 | 1.70294 | 0.851469 | − | 0.524404i | \(-0.175712\pi\) | ||||
0.851469 | + | 0.524404i | \(0.175712\pi\) | |||||||
\(822\) | −74.9108 | −2.61282 | ||||||||
\(823\) | −8.69685 | −0.303153 | −0.151577 | − | 0.988446i | \(-0.548435\pi\) | ||||
−0.151577 | + | 0.988446i | \(0.548435\pi\) | |||||||
\(824\) | 74.1474 | 2.58305 | ||||||||
\(825\) | 1.05381 | 0.0366890 | ||||||||
\(826\) | −32.6277 | −1.13526 | ||||||||
\(827\) | −40.4758 | −1.40748 | −0.703741 | − | 0.710456i | \(-0.748489\pi\) | ||||
−0.703741 | + | 0.710456i | \(0.748489\pi\) | |||||||
\(828\) | −109.995 | −3.82259 | ||||||||
\(829\) | −8.30921 | −0.288591 | −0.144295 | − | 0.989535i | \(-0.546092\pi\) | ||||
−0.144295 | + | 0.989535i | \(0.546092\pi\) | |||||||
\(830\) | 125.432 | 4.35381 | ||||||||
\(831\) | 38.0828 | 1.32108 | ||||||||
\(832\) | 7.38995 | 0.256201 | ||||||||
\(833\) | 0.149264 | 0.00517168 | ||||||||
\(834\) | −115.842 | −4.01128 | ||||||||
\(835\) | 63.2458 | 2.18871 | ||||||||
\(836\) | 1.59761 | 0.0552544 | ||||||||
\(837\) | 9.09889 | 0.314504 | ||||||||
\(838\) | 65.5749 | 2.26525 | ||||||||
\(839\) | −39.3013 | −1.35683 | −0.678416 | − | 0.734678i | \(-0.737333\pi\) | ||||
−0.678416 | + | 0.734678i | \(0.737333\pi\) | |||||||
\(840\) | 220.757 | 7.61683 | ||||||||
\(841\) | −0.413815 | −0.0142695 | ||||||||
\(842\) | 104.482 | 3.60068 | ||||||||
\(843\) | −30.8764 | −1.06344 | ||||||||
\(844\) | −65.2363 | −2.24553 | ||||||||
\(845\) | 46.9779 | 1.61609 | ||||||||
\(846\) | 77.3419 | 2.65907 | ||||||||
\(847\) | −32.4445 | −1.11481 | ||||||||
\(848\) | −164.672 | −5.65487 | ||||||||
\(849\) | 14.4088 | 0.494508 | ||||||||
\(850\) | −1.95470 | −0.0670457 | ||||||||
\(851\) | 88.8738 | 3.04656 | ||||||||
\(852\) | 108.738 | 3.72531 | ||||||||
\(853\) | −49.3940 | −1.69122 | −0.845609 | − | 0.533803i | \(-0.820762\pi\) | ||||
−0.845609 | + | 0.533803i | \(0.820762\pi\) | |||||||
\(854\) | 77.4953 | 2.65184 | ||||||||
\(855\) | −44.1377 | −1.50948 | ||||||||
\(856\) | −3.98926 | −0.136350 | ||||||||
\(857\) | −3.62130 | −0.123701 | −0.0618506 | − | 0.998085i | \(-0.519700\pi\) | ||||
−0.0618506 | + | 0.998085i | \(0.519700\pi\) | |||||||
\(858\) | −0.106576 | −0.00363844 | ||||||||
\(859\) | 43.6033 | 1.48773 | 0.743863 | − | 0.668332i | \(-0.232991\pi\) | ||||
0.743863 | + | 0.668332i | \(0.232991\pi\) | |||||||
\(860\) | 64.2886 | 2.19222 | ||||||||
\(861\) | 69.3250 | 2.36259 | ||||||||
\(862\) | 74.1722 | 2.52632 | ||||||||
\(863\) | −23.4576 | −0.798507 | −0.399253 | − | 0.916841i | \(-0.630731\pi\) | ||||
−0.399253 | + | 0.916841i | \(0.630731\pi\) | |||||||
\(864\) | 32.5783 | 1.10834 | ||||||||
\(865\) | 69.8983 | 2.37661 | ||||||||
\(866\) | 23.9726 | 0.814621 | ||||||||
\(867\) | −38.9308 | −1.32216 | ||||||||
\(868\) | −82.9563 | −2.81572 | ||||||||
\(869\) | 0.240892 | 0.00817169 | ||||||||
\(870\) | 120.619 | 4.08938 | ||||||||
\(871\) | 1.51365 | 0.0512880 | ||||||||
\(872\) | 100.415 | 3.40049 | ||||||||
\(873\) | −36.9892 | −1.25189 | ||||||||
\(874\) | 134.140 | 4.53736 | ||||||||
\(875\) | −34.9279 | −1.18078 | ||||||||
\(876\) | 48.8883 | 1.65178 | ||||||||
\(877\) | −3.71082 | −0.125306 | −0.0626528 | − | 0.998035i | \(-0.519956\pi\) | ||||
−0.0626528 | + | 0.998035i | \(0.519956\pi\) | |||||||
\(878\) | −77.6899 | −2.62191 | ||||||||
\(879\) | 29.0021 | 0.978217 | ||||||||
\(880\) | −2.76641 | −0.0932557 | ||||||||
\(881\) | 6.83985 | 0.230440 | 0.115220 | − | 0.993340i | \(-0.463243\pi\) | ||||
0.115220 | + | 0.993340i | \(0.463243\pi\) | |||||||
\(882\) | −10.3693 | −0.349152 | ||||||||
\(883\) | 0.0532323 | 0.00179141 | 0.000895705 | − | 1.00000i | \(-0.499715\pi\) | ||||
0.000895705 | 1.00000i | \(0.499715\pi\) | ||||||||
\(884\) | 0.143649 | 0.00483143 | ||||||||
\(885\) | −34.0989 | −1.14622 | ||||||||
\(886\) | 32.3276 | 1.08607 | ||||||||
\(887\) | 50.7192 | 1.70298 | 0.851491 | − | 0.524369i | \(-0.175699\pi\) | ||||
0.851491 | + | 0.524369i | \(0.175699\pi\) | |||||||
\(888\) | 198.583 | 6.66400 | ||||||||
\(889\) | 27.3770 | 0.918197 | ||||||||
\(890\) | 144.781 | 4.85308 | ||||||||
\(891\) | −0.595792 | −0.0199598 | ||||||||
\(892\) | 68.3152 | 2.28736 | ||||||||
\(893\) | −68.5374 | −2.29352 | ||||||||
\(894\) | 49.4489 | 1.65382 | ||||||||
\(895\) | 54.4362 | 1.81960 | ||||||||
\(896\) | −79.4155 | −2.65309 | ||||||||
\(897\) | −6.50241 | −0.217109 | ||||||||
\(898\) | 98.5758 | 3.28952 | ||||||||
\(899\) | −28.2758 | −0.943052 | ||||||||
\(900\) | 98.6739 | 3.28913 | ||||||||
\(901\) | −1.05771 | −0.0352375 | ||||||||
\(902\) | −1.54631 | −0.0514864 | ||||||||
\(903\) | −22.4525 | −0.747171 | ||||||||
\(904\) | −42.8703 | −1.42585 | ||||||||
\(905\) | 39.9404 | 1.32766 | ||||||||
\(906\) | 45.8267 | 1.52249 | ||||||||
\(907\) | −12.7213 | −0.422403 | −0.211201 | − | 0.977443i | \(-0.567738\pi\) | ||||
−0.211201 | + | 0.977443i | \(0.567738\pi\) | |||||||
\(908\) | 64.7731 | 2.14957 | ||||||||
\(909\) | −2.14831 | −0.0712549 | ||||||||
\(910\) | 8.96336 | 0.297133 | ||||||||
\(911\) | 41.7710 | 1.38393 | 0.691967 | − | 0.721929i | \(-0.256744\pi\) | ||||
0.691967 | + | 0.721929i | \(0.256744\pi\) | |||||||
\(912\) | 168.393 | 5.57605 | ||||||||
\(913\) | 0.710019 | 0.0234982 | ||||||||
\(914\) | 15.1109 | 0.499823 | ||||||||
\(915\) | 80.9896 | 2.67743 | ||||||||
\(916\) | 135.994 | 4.49336 | ||||||||
\(917\) | −7.78394 | −0.257048 | ||||||||
\(918\) | 0.407539 | 0.0134508 | ||||||||
\(919\) | 16.0793 | 0.530408 | 0.265204 | − | 0.964192i | \(-0.414561\pi\) | ||||
0.265204 | + | 0.964192i | \(0.414561\pi\) | |||||||
\(920\) | −300.424 | −9.90470 | ||||||||
\(921\) | −33.3875 | −1.10016 | ||||||||
\(922\) | −29.0752 | −0.957540 | ||||||||
\(923\) | 2.75424 | 0.0906569 | ||||||||
\(924\) | 2.00315 | 0.0658987 | ||||||||
\(925\) | −79.7266 | −2.62139 | ||||||||
\(926\) | −41.5093 | −1.36408 | ||||||||
\(927\) | −18.5881 | −0.610512 | ||||||||
\(928\) | −101.241 | −3.32339 | ||||||||
\(929\) | −32.4133 | −1.06345 | −0.531724 | − | 0.846918i | \(-0.678455\pi\) | ||||
−0.531724 | + | 0.846918i | \(0.678455\pi\) | |||||||
\(930\) | −119.310 | −3.91232 | ||||||||
\(931\) | 9.18887 | 0.301153 | ||||||||
\(932\) | 38.5420 | 1.26249 | ||||||||
\(933\) | 50.9720 | 1.66875 | ||||||||
\(934\) | 61.9320 | 2.02648 | ||||||||
\(935\) | −0.0177690 | −0.000581109 0 | ||||||||
\(936\) | −6.22530 | −0.203480 | ||||||||
\(937\) | −58.3735 | −1.90698 | −0.953490 | − | 0.301424i | \(-0.902538\pi\) | ||||
−0.953490 | + | 0.301424i | \(0.902538\pi\) | |||||||
\(938\) | −39.1518 | −1.27835 | ||||||||
\(939\) | −59.6981 | −1.94817 | ||||||||
\(940\) | 246.060 | 8.02559 | ||||||||
\(941\) | −53.4042 | −1.74093 | −0.870463 | − | 0.492234i | \(-0.836180\pi\) | ||||
−0.870463 | + | 0.492234i | \(0.836180\pi\) | |||||||
\(942\) | 45.1589 | 1.47136 | ||||||||
\(943\) | −94.3433 | −3.07224 | ||||||||
\(944\) | 55.7408 | 1.81421 | ||||||||
\(945\) | 18.4784 | 0.601102 | ||||||||
\(946\) | 0.500806 | 0.0162826 | ||||||||
\(947\) | 21.9724 | 0.714008 | 0.357004 | − | 0.934103i | \(-0.383798\pi\) | ||||
0.357004 | + | 0.934103i | \(0.383798\pi\) | |||||||
\(948\) | 52.6432 | 1.70977 | ||||||||
\(949\) | 1.23830 | 0.0401968 | ||||||||
\(950\) | −120.334 | −3.90415 | ||||||||
\(951\) | 22.6088 | 0.733142 | ||||||||
\(952\) | −2.31789 | −0.0751233 | ||||||||
\(953\) | −11.9508 | −0.387126 | −0.193563 | − | 0.981088i | \(-0.562004\pi\) | ||||
−0.193563 | + | 0.981088i | \(0.562004\pi\) | |||||||
\(954\) | 73.4789 | 2.37897 | ||||||||
\(955\) | 19.7272 | 0.638356 | ||||||||
\(956\) | 68.7736 | 2.22430 | ||||||||
\(957\) | 0.682777 | 0.0220711 | ||||||||
\(958\) | 2.05563 | 0.0664143 | ||||||||
\(959\) | 35.6631 | 1.15162 | ||||||||
\(960\) | −199.767 | −6.44744 | ||||||||
\(961\) | −3.03116 | −0.0977794 | ||||||||
\(962\) | 8.06304 | 0.259963 | ||||||||
\(963\) | 1.00007 | 0.0322269 | ||||||||
\(964\) | 35.2271 | 1.13459 | ||||||||
\(965\) | 15.3865 | 0.495310 | ||||||||
\(966\) | 168.191 | 5.41145 | ||||||||
\(967\) | 8.42422 | 0.270905 | 0.135452 | − | 0.990784i | \(-0.456751\pi\) | ||||
0.135452 | + | 0.990784i | \(0.456751\pi\) | |||||||
\(968\) | 98.6576 | 3.17097 | ||||||||
\(969\) | 1.08161 | 0.0347463 | ||||||||
\(970\) | −161.947 | −5.19982 | ||||||||
\(971\) | 8.39926 | 0.269545 | 0.134773 | − | 0.990877i | \(-0.456970\pi\) | ||||
0.134773 | + | 0.990877i | \(0.456970\pi\) | |||||||
\(972\) | −102.759 | −3.29601 | ||||||||
\(973\) | 55.1494 | 1.76801 | ||||||||
\(974\) | −98.2825 | −3.14917 | ||||||||
\(975\) | 5.83316 | 0.186811 | ||||||||
\(976\) | −132.392 | −4.23776 | ||||||||
\(977\) | −34.4356 | −1.10169 | −0.550846 | − | 0.834607i | \(-0.685695\pi\) | ||||
−0.550846 | + | 0.834607i | \(0.685695\pi\) | |||||||
\(978\) | 132.471 | 4.23596 | ||||||||
\(979\) | 0.819549 | 0.0261929 | ||||||||
\(980\) | −32.9895 | −1.05381 | ||||||||
\(981\) | −25.1732 | −0.803718 | ||||||||
\(982\) | 32.9470 | 1.05138 | ||||||||
\(983\) | 0.294686 | 0.00939902 | 0.00469951 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469951 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(984\) | −210.804 | −6.72019 | ||||||||
\(985\) | −36.8245 | −1.17333 | ||||||||
\(986\) | −1.26647 | −0.0403327 | ||||||||
\(987\) | −85.9351 | −2.73534 | ||||||||
\(988\) | 8.84322 | 0.281340 | ||||||||
\(989\) | 30.5552 | 0.971598 | ||||||||
\(990\) | 1.23441 | 0.0392320 | ||||||||
\(991\) | −47.0066 | −1.49321 | −0.746607 | − | 0.665266i | \(-0.768318\pi\) | ||||
−0.746607 | + | 0.665266i | \(0.768318\pi\) | |||||||
\(992\) | 100.142 | 3.17950 | ||||||||
\(993\) | −20.7192 | −0.657504 | ||||||||
\(994\) | −71.2409 | −2.25962 | ||||||||
\(995\) | 28.6639 | 0.908707 | ||||||||
\(996\) | 155.164 | 4.91655 | ||||||||
\(997\) | 5.23646 | 0.165840 | 0.0829202 | − | 0.996556i | \(-0.473575\pi\) | ||||
0.0829202 | + | 0.996556i | \(0.473575\pi\) | |||||||
\(998\) | 76.2385 | 2.41329 | ||||||||
\(999\) | 16.6223 | 0.525907 |
(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 | 4027.2.a.b.1.6 | ✓ | 159 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.b.1.6 | ✓ | 159 | 1.1 | even | 1 | trivial |