Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, 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("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2855381023\) |
Analytic rank: | \(1\) |
Dimension: | \(217\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.54610 | −1.80037 | −0.900183 | − | 0.435511i | \(-0.856568\pi\) | ||||
−0.900183 | + | 0.435511i | \(0.856568\pi\) | |||||||
\(3\) | −2.31345 | −1.33567 | −0.667835 | − | 0.744310i | \(-0.732779\pi\) | ||||
−0.667835 | + | 0.744310i | \(0.732779\pi\) | |||||||
\(4\) | 4.48264 | 2.24132 | ||||||||
\(5\) | −3.02578 | −1.35317 | −0.676586 | − | 0.736364i | \(-0.736541\pi\) | ||||
−0.676586 | + | 0.736364i | \(0.736541\pi\) | |||||||
\(6\) | 5.89027 | 2.40469 | ||||||||
\(7\) | −2.15804 | −0.815661 | −0.407830 | − | 0.913058i | \(-0.633715\pi\) | ||||
−0.407830 | + | 0.913058i | \(0.633715\pi\) | |||||||
\(8\) | −6.32106 | −2.23483 | ||||||||
\(9\) | 2.35204 | 0.784013 | ||||||||
\(10\) | 7.70396 | 2.43621 | ||||||||
\(11\) | −1.11866 | −0.337290 | −0.168645 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168645 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(12\) | −10.3704 | −2.99366 | ||||||||
\(13\) | −5.26486 | −1.46021 | −0.730104 | − | 0.683336i | \(-0.760529\pi\) | ||||
−0.730104 | + | 0.683336i | \(0.760529\pi\) | |||||||
\(14\) | 5.49458 | 1.46849 | ||||||||
\(15\) | 6.99999 | 1.80739 | ||||||||
\(16\) | 7.12878 | 1.78220 | ||||||||
\(17\) | −6.53216 | −1.58428 | −0.792140 | − | 0.610339i | \(-0.791033\pi\) | ||||
−0.792140 | + | 0.610339i | \(0.791033\pi\) | |||||||
\(18\) | −5.98853 | −1.41151 | ||||||||
\(19\) | −6.25317 | −1.43458 | −0.717288 | − | 0.696777i | \(-0.754617\pi\) | ||||
−0.717288 | + | 0.696777i | \(0.754617\pi\) | |||||||
\(20\) | −13.5635 | −3.03289 | ||||||||
\(21\) | 4.99250 | 1.08945 | ||||||||
\(22\) | 2.84823 | 0.607245 | ||||||||
\(23\) | −1.84125 | −0.383928 | −0.191964 | − | 0.981402i | \(-0.561486\pi\) | ||||
−0.191964 | + | 0.981402i | \(0.561486\pi\) | |||||||
\(24\) | 14.6234 | 2.98500 | ||||||||
\(25\) | 4.15537 | 0.831074 | ||||||||
\(26\) | 13.4049 | 2.62891 | ||||||||
\(27\) | 1.49903 | 0.288488 | ||||||||
\(28\) | −9.67370 | −1.82816 | ||||||||
\(29\) | 1.34606 | 0.249957 | 0.124979 | − | 0.992159i | \(-0.460114\pi\) | ||||
0.124979 | + | 0.992159i | \(0.460114\pi\) | |||||||
\(30\) | −17.8227 | −3.25397 | ||||||||
\(31\) | 0.169506 | 0.0304442 | 0.0152221 | − | 0.999884i | \(-0.495154\pi\) | ||||
0.0152221 | + | 0.999884i | \(0.495154\pi\) | |||||||
\(32\) | −5.50850 | −0.973775 | ||||||||
\(33\) | 2.58797 | 0.450507 | ||||||||
\(34\) | 16.6315 | 2.85229 | ||||||||
\(35\) | 6.52975 | 1.10373 | ||||||||
\(36\) | 10.5433 | 1.75722 | ||||||||
\(37\) | −9.24432 | −1.51976 | −0.759878 | − | 0.650065i | \(-0.774741\pi\) | ||||
−0.759878 | + | 0.650065i | \(0.774741\pi\) | |||||||
\(38\) | 15.9212 | 2.58276 | ||||||||
\(39\) | 12.1800 | 1.95036 | ||||||||
\(40\) | 19.1262 | 3.02411 | ||||||||
\(41\) | 11.1562 | 1.74230 | 0.871152 | − | 0.491014i | \(-0.163374\pi\) | ||||
0.871152 | + | 0.491014i | \(0.163374\pi\) | |||||||
\(42\) | −12.7114 | −1.96142 | ||||||||
\(43\) | −1.50820 | −0.229998 | −0.114999 | − | 0.993366i | \(-0.536687\pi\) | ||||
−0.114999 | + | 0.993366i | \(0.536687\pi\) | |||||||
\(44\) | −5.01456 | −0.755974 | ||||||||
\(45\) | −7.11676 | −1.06090 | ||||||||
\(46\) | 4.68802 | 0.691211 | ||||||||
\(47\) | −4.48501 | −0.654206 | −0.327103 | − | 0.944989i | \(-0.606072\pi\) | ||||
−0.327103 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(48\) | −16.4921 | −2.38042 | ||||||||
\(49\) | −2.34288 | −0.334697 | ||||||||
\(50\) | −10.5800 | −1.49624 | ||||||||
\(51\) | 15.1118 | 2.11607 | ||||||||
\(52\) | −23.6005 | −3.27280 | ||||||||
\(53\) | 6.89328 | 0.946864 | 0.473432 | − | 0.880830i | \(-0.343015\pi\) | ||||
0.473432 | + | 0.880830i | \(0.343015\pi\) | |||||||
\(54\) | −3.81668 | −0.519384 | ||||||||
\(55\) | 3.38483 | 0.456411 | ||||||||
\(56\) | 13.6411 | 1.82286 | ||||||||
\(57\) | 14.4664 | 1.91612 | ||||||||
\(58\) | −3.42721 | −0.450015 | ||||||||
\(59\) | −2.12259 | −0.276338 | −0.138169 | − | 0.990409i | \(-0.544122\pi\) | ||||
−0.138169 | + | 0.990409i | \(0.544122\pi\) | |||||||
\(60\) | 31.3784 | 4.05094 | ||||||||
\(61\) | 8.00933 | 1.02549 | 0.512745 | − | 0.858541i | \(-0.328629\pi\) | ||||
0.512745 | + | 0.858541i | \(0.328629\pi\) | |||||||
\(62\) | −0.431580 | −0.0548107 | ||||||||
\(63\) | −5.07578 | −0.639488 | ||||||||
\(64\) | −0.232355 | −0.0290444 | ||||||||
\(65\) | 15.9303 | 1.97591 | ||||||||
\(66\) | −6.58923 | −0.811078 | ||||||||
\(67\) | −13.2349 | −1.61690 | −0.808450 | − | 0.588564i | \(-0.799693\pi\) | ||||
−0.808450 | + | 0.588564i | \(0.799693\pi\) | |||||||
\(68\) | −29.2813 | −3.55088 | ||||||||
\(69\) | 4.25964 | 0.512801 | ||||||||
\(70\) | −16.6254 | −1.98712 | ||||||||
\(71\) | −0.196267 | −0.0232925 | −0.0116463 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116463 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(72\) | −14.8674 | −1.75214 | ||||||||
\(73\) | −9.73800 | −1.13975 | −0.569874 | − | 0.821732i | \(-0.693008\pi\) | ||||
−0.569874 | + | 0.821732i | \(0.693008\pi\) | |||||||
\(74\) | 23.5370 | 2.73612 | ||||||||
\(75\) | −9.61323 | −1.11004 | ||||||||
\(76\) | −28.0307 | −3.21534 | ||||||||
\(77\) | 2.41411 | 0.275114 | ||||||||
\(78\) | −31.0115 | −3.51136 | ||||||||
\(79\) | −7.98632 | −0.898531 | −0.449266 | − | 0.893398i | \(-0.648314\pi\) | ||||
−0.449266 | + | 0.893398i | \(0.648314\pi\) | |||||||
\(80\) | −21.5702 | −2.41162 | ||||||||
\(81\) | −10.5240 | −1.16934 | ||||||||
\(82\) | −28.4048 | −3.13679 | ||||||||
\(83\) | 14.9679 | 1.64295 | 0.821473 | − | 0.570248i | \(-0.193153\pi\) | ||||
0.821473 | + | 0.570248i | \(0.193153\pi\) | |||||||
\(84\) | 22.3796 | 2.44181 | ||||||||
\(85\) | 19.7649 | 2.14380 | ||||||||
\(86\) | 3.84003 | 0.414081 | ||||||||
\(87\) | −3.11404 | −0.333860 | ||||||||
\(88\) | 7.07113 | 0.753785 | ||||||||
\(89\) | −4.50608 | −0.477643 | −0.238822 | − | 0.971063i | \(-0.576761\pi\) | ||||
−0.238822 | + | 0.971063i | \(0.576761\pi\) | |||||||
\(90\) | 18.1200 | 1.91002 | ||||||||
\(91\) | 11.3617 | 1.19103 | ||||||||
\(92\) | −8.25368 | −0.860506 | ||||||||
\(93\) | −0.392143 | −0.0406633 | ||||||||
\(94\) | 11.4193 | 1.17781 | ||||||||
\(95\) | 18.9208 | 1.94123 | ||||||||
\(96\) | 12.7436 | 1.30064 | ||||||||
\(97\) | 2.24387 | 0.227830 | 0.113915 | − | 0.993490i | \(-0.463661\pi\) | ||||
0.113915 | + | 0.993490i | \(0.463661\pi\) | |||||||
\(98\) | 5.96522 | 0.602578 | ||||||||
\(99\) | −2.63114 | −0.264439 | ||||||||
\(100\) | 18.6270 | 1.86270 | ||||||||
\(101\) | 1.54808 | 0.154039 | 0.0770196 | − | 0.997030i | \(-0.475460\pi\) | ||||
0.0770196 | + | 0.997030i | \(0.475460\pi\) | |||||||
\(102\) | −38.4762 | −3.80971 | ||||||||
\(103\) | 14.8966 | 1.46781 | 0.733905 | − | 0.679252i | \(-0.237696\pi\) | ||||
0.733905 | + | 0.679252i | \(0.237696\pi\) | |||||||
\(104\) | 33.2795 | 3.26332 | ||||||||
\(105\) | −15.1062 | −1.47422 | ||||||||
\(106\) | −17.5510 | −1.70470 | ||||||||
\(107\) | −4.51998 | −0.436963 | −0.218482 | − | 0.975841i | \(-0.570110\pi\) | ||||
−0.218482 | + | 0.975841i | \(0.570110\pi\) | |||||||
\(108\) | 6.71960 | 0.646594 | ||||||||
\(109\) | 9.46619 | 0.906696 | 0.453348 | − | 0.891334i | \(-0.350229\pi\) | ||||
0.453348 | + | 0.891334i | \(0.350229\pi\) | |||||||
\(110\) | −8.61813 | −0.821707 | ||||||||
\(111\) | 21.3862 | 2.02989 | ||||||||
\(112\) | −15.3842 | −1.45367 | ||||||||
\(113\) | −3.25496 | −0.306200 | −0.153100 | − | 0.988211i | \(-0.548926\pi\) | ||||
−0.153100 | + | 0.988211i | \(0.548926\pi\) | |||||||
\(114\) | −36.8329 | −3.44972 | ||||||||
\(115\) | 5.57124 | 0.519521 | ||||||||
\(116\) | 6.03391 | 0.560234 | ||||||||
\(117\) | −12.3831 | −1.14482 | ||||||||
\(118\) | 5.40434 | 0.497510 | ||||||||
\(119\) | 14.0966 | 1.29224 | ||||||||
\(120\) | −44.2474 | −4.03921 | ||||||||
\(121\) | −9.74859 | −0.886236 | ||||||||
\(122\) | −20.3926 | −1.84626 | ||||||||
\(123\) | −25.8092 | −2.32714 | ||||||||
\(124\) | 0.759834 | 0.0682351 | ||||||||
\(125\) | 2.55566 | 0.228586 | ||||||||
\(126\) | 12.9235 | 1.15131 | ||||||||
\(127\) | −4.37884 | −0.388559 | −0.194279 | − | 0.980946i | \(-0.562237\pi\) | ||||
−0.194279 | + | 0.980946i | \(0.562237\pi\) | |||||||
\(128\) | 11.6086 | 1.02607 | ||||||||
\(129\) | 3.48914 | 0.307202 | ||||||||
\(130\) | −40.5602 | −3.55737 | ||||||||
\(131\) | 2.76271 | 0.241379 | 0.120689 | − | 0.992690i | \(-0.461490\pi\) | ||||
0.120689 | + | 0.992690i | \(0.461490\pi\) | |||||||
\(132\) | 11.6009 | 1.00973 | ||||||||
\(133\) | 13.4946 | 1.17013 | ||||||||
\(134\) | 33.6974 | 2.91101 | ||||||||
\(135\) | −4.53573 | −0.390374 | ||||||||
\(136\) | 41.2901 | 3.54060 | ||||||||
\(137\) | −11.2697 | −0.962839 | −0.481419 | − | 0.876490i | \(-0.659879\pi\) | ||||
−0.481419 | + | 0.876490i | \(0.659879\pi\) | |||||||
\(138\) | −10.8455 | −0.923230 | ||||||||
\(139\) | 17.9048 | 1.51866 | 0.759331 | − | 0.650705i | \(-0.225527\pi\) | ||||
0.759331 | + | 0.650705i | \(0.225527\pi\) | |||||||
\(140\) | 29.2705 | 2.47381 | ||||||||
\(141\) | 10.3758 | 0.873803 | ||||||||
\(142\) | 0.499715 | 0.0419351 | ||||||||
\(143\) | 5.88960 | 0.492513 | ||||||||
\(144\) | 16.7672 | 1.39726 | ||||||||
\(145\) | −4.07289 | −0.338235 | ||||||||
\(146\) | 24.7940 | 2.05196 | ||||||||
\(147\) | 5.42013 | 0.447045 | ||||||||
\(148\) | −41.4390 | −3.40626 | ||||||||
\(149\) | 0.878309 | 0.0719539 | 0.0359769 | − | 0.999353i | \(-0.488546\pi\) | ||||
0.0359769 | + | 0.999353i | \(0.488546\pi\) | |||||||
\(150\) | 24.4763 | 1.99848 | ||||||||
\(151\) | −21.3497 | −1.73741 | −0.868707 | − | 0.495326i | \(-0.835049\pi\) | ||||
−0.868707 | + | 0.495326i | \(0.835049\pi\) | |||||||
\(152\) | 39.5267 | 3.20604 | ||||||||
\(153\) | −15.3639 | −1.24210 | ||||||||
\(154\) | −6.14658 | −0.495306 | ||||||||
\(155\) | −0.512888 | −0.0411962 | ||||||||
\(156\) | 54.5984 | 4.37137 | ||||||||
\(157\) | 11.1660 | 0.891143 | 0.445572 | − | 0.895246i | \(-0.353000\pi\) | ||||
0.445572 | + | 0.895246i | \(0.353000\pi\) | |||||||
\(158\) | 20.3340 | 1.61769 | ||||||||
\(159\) | −15.9472 | −1.26470 | ||||||||
\(160\) | 16.6675 | 1.31768 | ||||||||
\(161\) | 3.97349 | 0.313155 | ||||||||
\(162\) | 26.7953 | 2.10524 | ||||||||
\(163\) | 12.3511 | 0.967411 | 0.483705 | − | 0.875231i | \(-0.339291\pi\) | ||||
0.483705 | + | 0.875231i | \(0.339291\pi\) | |||||||
\(164\) | 50.0092 | 3.90506 | ||||||||
\(165\) | −7.83063 | −0.609614 | ||||||||
\(166\) | −38.1099 | −2.95790 | ||||||||
\(167\) | 19.1792 | 1.48413 | 0.742067 | − | 0.670326i | \(-0.233846\pi\) | ||||
0.742067 | + | 0.670326i | \(0.233846\pi\) | |||||||
\(168\) | −31.5579 | −2.43474 | ||||||||
\(169\) | 14.7187 | 1.13221 | ||||||||
\(170\) | −50.3235 | −3.85963 | ||||||||
\(171\) | −14.7077 | −1.12473 | ||||||||
\(172\) | −6.76072 | −0.515500 | ||||||||
\(173\) | 11.1174 | 0.845239 | 0.422619 | − | 0.906307i | \(-0.361111\pi\) | ||||
0.422619 | + | 0.906307i | \(0.361111\pi\) | |||||||
\(174\) | 7.92867 | 0.601071 | ||||||||
\(175\) | −8.96744 | −0.677875 | ||||||||
\(176\) | −7.97471 | −0.601116 | ||||||||
\(177\) | 4.91051 | 0.369097 | ||||||||
\(178\) | 11.4729 | 0.859933 | ||||||||
\(179\) | 17.3640 | 1.29784 | 0.648921 | − | 0.760855i | \(-0.275220\pi\) | ||||
0.648921 | + | 0.760855i | \(0.275220\pi\) | |||||||
\(180\) | −31.9019 | −2.37783 | ||||||||
\(181\) | −20.7141 | −1.53967 | −0.769833 | − | 0.638245i | \(-0.779661\pi\) | ||||
−0.769833 | + | 0.638245i | \(0.779661\pi\) | |||||||
\(182\) | −28.9282 | −2.14430 | ||||||||
\(183\) | −18.5292 | −1.36972 | ||||||||
\(184\) | 11.6387 | 0.858014 | ||||||||
\(185\) | 27.9713 | 2.05649 | ||||||||
\(186\) | 0.998437 | 0.0732089 | ||||||||
\(187\) | 7.30728 | 0.534361 | ||||||||
\(188\) | −20.1047 | −1.46629 | ||||||||
\(189\) | −3.23495 | −0.235308 | ||||||||
\(190\) | −48.1742 | −3.49492 | ||||||||
\(191\) | −0.136049 | −0.00984415 | −0.00492208 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492208 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(192\) | 0.537541 | 0.0387937 | ||||||||
\(193\) | −4.33713 | −0.312193 | −0.156097 | − | 0.987742i | \(-0.549891\pi\) | ||||
−0.156097 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(194\) | −5.71312 | −0.410178 | ||||||||
\(195\) | −36.8540 | −2.63917 | ||||||||
\(196\) | −10.5023 | −0.750164 | ||||||||
\(197\) | −17.8907 | −1.27466 | −0.637331 | − | 0.770590i | \(-0.719962\pi\) | ||||
−0.637331 | + | 0.770590i | \(0.719962\pi\) | |||||||
\(198\) | 6.69915 | 0.476088 | ||||||||
\(199\) | −12.0588 | −0.854825 | −0.427413 | − | 0.904057i | \(-0.640575\pi\) | ||||
−0.427413 | + | 0.904057i | \(0.640575\pi\) | |||||||
\(200\) | −26.2663 | −1.85731 | ||||||||
\(201\) | 30.6182 | 2.15964 | ||||||||
\(202\) | −3.94156 | −0.277327 | ||||||||
\(203\) | −2.90485 | −0.203880 | ||||||||
\(204\) | 67.7408 | 4.74280 | ||||||||
\(205\) | −33.7562 | −2.35764 | ||||||||
\(206\) | −37.9284 | −2.64260 | ||||||||
\(207\) | −4.33070 | −0.301004 | ||||||||
\(208\) | −37.5320 | −2.60238 | ||||||||
\(209\) | 6.99519 | 0.483868 | ||||||||
\(210\) | 38.4620 | 2.65413 | ||||||||
\(211\) | 18.4728 | 1.27172 | 0.635859 | − | 0.771806i | \(-0.280646\pi\) | ||||
0.635859 | + | 0.771806i | \(0.280646\pi\) | |||||||
\(212\) | 30.9001 | 2.12223 | ||||||||
\(213\) | 0.454052 | 0.0311111 | ||||||||
\(214\) | 11.5083 | 0.786694 | ||||||||
\(215\) | 4.56349 | 0.311227 | ||||||||
\(216\) | −9.47543 | −0.644722 | ||||||||
\(217\) | −0.365800 | −0.0248321 | ||||||||
\(218\) | −24.1019 | −1.63239 | ||||||||
\(219\) | 22.5284 | 1.52233 | ||||||||
\(220\) | 15.1730 | 1.02296 | ||||||||
\(221\) | 34.3909 | 2.31338 | ||||||||
\(222\) | −54.4516 | −3.65455 | ||||||||
\(223\) | 10.1377 | 0.678870 | 0.339435 | − | 0.940630i | \(-0.389764\pi\) | ||||
0.339435 | + | 0.940630i | \(0.389764\pi\) | |||||||
\(224\) | 11.8875 | 0.794270 | ||||||||
\(225\) | 9.77359 | 0.651573 | ||||||||
\(226\) | 8.28745 | 0.551273 | ||||||||
\(227\) | −18.9122 | −1.25525 | −0.627623 | − | 0.778517i | \(-0.715972\pi\) | ||||
−0.627623 | + | 0.778517i | \(0.715972\pi\) | |||||||
\(228\) | 64.8476 | 4.29464 | ||||||||
\(229\) | 12.0998 | 0.799575 | 0.399787 | − | 0.916608i | \(-0.369084\pi\) | ||||
0.399787 | + | 0.916608i | \(0.369084\pi\) | |||||||
\(230\) | −14.1849 | −0.935328 | ||||||||
\(231\) | −5.58493 | −0.367461 | ||||||||
\(232\) | −8.50853 | −0.558612 | ||||||||
\(233\) | −0.123894 | −0.00811658 | −0.00405829 | − | 0.999992i | \(-0.501292\pi\) | ||||
−0.00405829 | + | 0.999992i | \(0.501292\pi\) | |||||||
\(234\) | 31.5288 | 2.06110 | ||||||||
\(235\) | 13.5707 | 0.885254 | ||||||||
\(236\) | −9.51483 | −0.619363 | ||||||||
\(237\) | 18.4759 | 1.20014 | ||||||||
\(238\) | −35.8915 | −2.32650 | ||||||||
\(239\) | −4.64682 | −0.300578 | −0.150289 | − | 0.988642i | \(-0.548020\pi\) | ||||
−0.150289 | + | 0.988642i | \(0.548020\pi\) | |||||||
\(240\) | 49.9014 | 3.22112 | ||||||||
\(241\) | 8.69431 | 0.560049 | 0.280025 | − | 0.959993i | \(-0.409657\pi\) | ||||
0.280025 | + | 0.959993i | \(0.409657\pi\) | |||||||
\(242\) | 24.8209 | 1.59555 | ||||||||
\(243\) | 19.8497 | 1.27336 | ||||||||
\(244\) | 35.9029 | 2.29845 | ||||||||
\(245\) | 7.08906 | 0.452903 | ||||||||
\(246\) | 65.7130 | 4.18971 | ||||||||
\(247\) | 32.9221 | 2.09478 | ||||||||
\(248\) | −1.07146 | −0.0680376 | ||||||||
\(249\) | −34.6276 | −2.19443 | ||||||||
\(250\) | −6.50698 | −0.411538 | ||||||||
\(251\) | 14.6695 | 0.925929 | 0.462965 | − | 0.886377i | \(-0.346786\pi\) | ||||
0.462965 | + | 0.886377i | \(0.346786\pi\) | |||||||
\(252\) | −22.7529 | −1.43330 | ||||||||
\(253\) | 2.05974 | 0.129495 | ||||||||
\(254\) | 11.1490 | 0.699548 | ||||||||
\(255\) | −45.7250 | −2.86341 | ||||||||
\(256\) | −29.0920 | −1.81825 | ||||||||
\(257\) | 14.2408 | 0.888319 | 0.444159 | − | 0.895948i | \(-0.353502\pi\) | ||||
0.444159 | + | 0.895948i | \(0.353502\pi\) | |||||||
\(258\) | −8.88371 | −0.553076 | ||||||||
\(259\) | 19.9496 | 1.23961 | ||||||||
\(260\) | 71.4099 | 4.42865 | ||||||||
\(261\) | 3.16599 | 0.195970 | ||||||||
\(262\) | −7.03413 | −0.434570 | ||||||||
\(263\) | 23.6715 | 1.45965 | 0.729823 | − | 0.683636i | \(-0.239602\pi\) | ||||
0.729823 | + | 0.683636i | \(0.239602\pi\) | |||||||
\(264\) | −16.3587 | −1.00681 | ||||||||
\(265\) | −20.8576 | −1.28127 | ||||||||
\(266\) | −34.3586 | −2.10666 | ||||||||
\(267\) | 10.4246 | 0.637973 | ||||||||
\(268\) | −59.3273 | −3.62399 | ||||||||
\(269\) | 17.6373 | 1.07536 | 0.537681 | − | 0.843148i | \(-0.319300\pi\) | ||||
0.537681 | + | 0.843148i | \(0.319300\pi\) | |||||||
\(270\) | 11.5484 | 0.702816 | ||||||||
\(271\) | −21.3323 | −1.29584 | −0.647922 | − | 0.761706i | \(-0.724362\pi\) | ||||
−0.647922 | + | 0.761706i | \(0.724362\pi\) | |||||||
\(272\) | −46.5663 | −2.82350 | ||||||||
\(273\) | −26.2848 | −1.59083 | ||||||||
\(274\) | 28.6939 | 1.73346 | ||||||||
\(275\) | −4.64846 | −0.280313 | ||||||||
\(276\) | 19.0945 | 1.14935 | ||||||||
\(277\) | 12.9240 | 0.776526 | 0.388263 | − | 0.921549i | \(-0.373075\pi\) | ||||
0.388263 | + | 0.921549i | \(0.373075\pi\) | |||||||
\(278\) | −45.5873 | −2.73415 | ||||||||
\(279\) | 0.398684 | 0.0238686 | ||||||||
\(280\) | −41.2749 | −2.46665 | ||||||||
\(281\) | 3.65752 | 0.218189 | 0.109095 | − | 0.994031i | \(-0.465205\pi\) | ||||
0.109095 | + | 0.994031i | \(0.465205\pi\) | |||||||
\(282\) | −26.4180 | −1.57317 | ||||||||
\(283\) | 0.0449931 | 0.00267456 | 0.00133728 | − | 0.999999i | \(-0.499574\pi\) | ||||
0.00133728 | + | 0.999999i | \(0.499574\pi\) | |||||||
\(284\) | −0.879792 | −0.0522061 | ||||||||
\(285\) | −43.7722 | −2.59284 | ||||||||
\(286\) | −14.9955 | −0.886704 | ||||||||
\(287\) | −24.0754 | −1.42113 | ||||||||
\(288\) | −12.9562 | −0.763452 | ||||||||
\(289\) | 25.6691 | 1.50994 | ||||||||
\(290\) | 10.3700 | 0.608947 | ||||||||
\(291\) | −5.19107 | −0.304306 | ||||||||
\(292\) | −43.6520 | −2.55454 | ||||||||
\(293\) | 0.922965 | 0.0539202 | 0.0269601 | − | 0.999637i | \(-0.491417\pi\) | ||||
0.0269601 | + | 0.999637i | \(0.491417\pi\) | |||||||
\(294\) | −13.8002 | −0.804845 | ||||||||
\(295\) | 6.42251 | 0.373933 | ||||||||
\(296\) | 58.4339 | 3.39640 | ||||||||
\(297\) | −1.67691 | −0.0973039 | ||||||||
\(298\) | −2.23627 | −0.129543 | ||||||||
\(299\) | 9.69394 | 0.560615 | ||||||||
\(300\) | −43.0927 | −2.48796 | ||||||||
\(301\) | 3.25475 | 0.187601 | ||||||||
\(302\) | 54.3585 | 3.12798 | ||||||||
\(303\) | −3.58139 | −0.205745 | ||||||||
\(304\) | −44.5775 | −2.55670 | ||||||||
\(305\) | −24.2345 | −1.38766 | ||||||||
\(306\) | 39.1180 | 2.23623 | ||||||||
\(307\) | −7.64583 | −0.436371 | −0.218185 | − | 0.975907i | \(-0.570014\pi\) | ||||
−0.218185 | + | 0.975907i | \(0.570014\pi\) | |||||||
\(308\) | 10.8216 | 0.616618 | ||||||||
\(309\) | −34.4626 | −1.96051 | ||||||||
\(310\) | 1.30587 | 0.0741682 | ||||||||
\(311\) | −27.1648 | −1.54037 | −0.770187 | − | 0.637819i | \(-0.779837\pi\) | ||||
−0.770187 | + | 0.637819i | \(0.779837\pi\) | |||||||
\(312\) | −76.9903 | −4.35872 | ||||||||
\(313\) | 22.7039 | 1.28330 | 0.641651 | − | 0.766997i | \(-0.278250\pi\) | ||||
0.641651 | + | 0.766997i | \(0.278250\pi\) | |||||||
\(314\) | −28.4298 | −1.60438 | ||||||||
\(315\) | 15.3582 | 0.865338 | ||||||||
\(316\) | −35.7998 | −2.01390 | ||||||||
\(317\) | −19.8243 | −1.11345 | −0.556723 | − | 0.830698i | \(-0.687941\pi\) | ||||
−0.556723 | + | 0.830698i | \(0.687941\pi\) | |||||||
\(318\) | 40.6033 | 2.27692 | ||||||||
\(319\) | −1.50579 | −0.0843080 | ||||||||
\(320\) | 0.703056 | 0.0393020 | ||||||||
\(321\) | 10.4567 | 0.583638 | ||||||||
\(322\) | −10.1169 | −0.563794 | ||||||||
\(323\) | 40.8467 | 2.27277 | ||||||||
\(324\) | −47.1754 | −2.62086 | ||||||||
\(325\) | −21.8774 | −1.21354 | ||||||||
\(326\) | −31.4471 | −1.74169 | ||||||||
\(327\) | −21.8995 | −1.21105 | ||||||||
\(328\) | −70.5189 | −3.89375 | ||||||||
\(329\) | 9.67882 | 0.533610 | ||||||||
\(330\) | 19.9376 | 1.09753 | ||||||||
\(331\) | 5.94560 | 0.326800 | 0.163400 | − | 0.986560i | \(-0.447754\pi\) | ||||
0.163400 | + | 0.986560i | \(0.447754\pi\) | |||||||
\(332\) | 67.0959 | 3.68237 | ||||||||
\(333\) | −21.7430 | −1.19151 | ||||||||
\(334\) | −48.8323 | −2.67198 | ||||||||
\(335\) | 40.0460 | 2.18794 | ||||||||
\(336\) | 35.5905 | 1.94162 | ||||||||
\(337\) | 11.7125 | 0.638020 | 0.319010 | − | 0.947751i | \(-0.396650\pi\) | ||||
0.319010 | + | 0.947751i | \(0.396650\pi\) | |||||||
\(338\) | −37.4754 | −2.03839 | ||||||||
\(339\) | 7.53017 | 0.408983 | ||||||||
\(340\) | 88.5989 | 4.80495 | ||||||||
\(341\) | −0.189620 | −0.0102685 | ||||||||
\(342\) | 37.4473 | 2.02492 | ||||||||
\(343\) | 20.1623 | 1.08866 | ||||||||
\(344\) | 9.53342 | 0.514007 | ||||||||
\(345\) | −12.8888 | −0.693908 | ||||||||
\(346\) | −28.3060 | −1.52174 | ||||||||
\(347\) | −18.1724 | −0.975548 | −0.487774 | − | 0.872970i | \(-0.662191\pi\) | ||||
−0.487774 | + | 0.872970i | \(0.662191\pi\) | |||||||
\(348\) | −13.9591 | −0.748288 | ||||||||
\(349\) | −0.0279519 | −0.00149623 | −0.000748116 | − | 1.00000i | \(-0.500238\pi\) | ||||
−0.000748116 | 1.00000i | \(0.500238\pi\) | ||||||||
\(350\) | 22.8320 | 1.22042 | ||||||||
\(351\) | −7.89216 | −0.421252 | ||||||||
\(352\) | 6.16216 | 0.328444 | ||||||||
\(353\) | 3.52057 | 0.187381 | 0.0936905 | − | 0.995601i | \(-0.470134\pi\) | ||||
0.0936905 | + | 0.995601i | \(0.470134\pi\) | |||||||
\(354\) | −12.5027 | −0.664509 | ||||||||
\(355\) | 0.593860 | 0.0315188 | ||||||||
\(356\) | −20.1991 | −1.07055 | ||||||||
\(357\) | −32.6118 | −1.72600 | ||||||||
\(358\) | −44.2104 | −2.33659 | ||||||||
\(359\) | −33.3893 | −1.76222 | −0.881109 | − | 0.472914i | \(-0.843202\pi\) | ||||
−0.881109 | + | 0.472914i | \(0.843202\pi\) | |||||||
\(360\) | 44.9854 | 2.37094 | ||||||||
\(361\) | 20.1022 | 1.05801 | ||||||||
\(362\) | 52.7402 | 2.77196 | ||||||||
\(363\) | 22.5529 | 1.18372 | ||||||||
\(364\) | 50.9306 | 2.66949 | ||||||||
\(365\) | 29.4651 | 1.54227 | ||||||||
\(366\) | 47.1772 | 2.46599 | ||||||||
\(367\) | −9.05997 | −0.472927 | −0.236463 | − | 0.971640i | \(-0.575988\pi\) | ||||
−0.236463 | + | 0.971640i | \(0.575988\pi\) | |||||||
\(368\) | −13.1259 | −0.684235 | ||||||||
\(369\) | 26.2398 | 1.36599 | ||||||||
\(370\) | −71.2178 | −3.70244 | ||||||||
\(371\) | −14.8759 | −0.772320 | ||||||||
\(372\) | −1.75784 | −0.0911396 | ||||||||
\(373\) | −22.6728 | −1.17396 | −0.586978 | − | 0.809603i | \(-0.699682\pi\) | ||||
−0.586978 | + | 0.809603i | \(0.699682\pi\) | |||||||
\(374\) | −18.6051 | −0.962046 | ||||||||
\(375\) | −5.91239 | −0.305315 | ||||||||
\(376\) | 28.3500 | 1.46204 | ||||||||
\(377\) | −7.08682 | −0.364990 | ||||||||
\(378\) | 8.23652 | 0.423641 | ||||||||
\(379\) | 6.89468 | 0.354156 | 0.177078 | − | 0.984197i | \(-0.443335\pi\) | ||||
0.177078 | + | 0.984197i | \(0.443335\pi\) | |||||||
\(380\) | 84.8149 | 4.35091 | ||||||||
\(381\) | 10.1302 | 0.518986 | ||||||||
\(382\) | 0.346395 | 0.0177231 | ||||||||
\(383\) | 28.3483 | 1.44853 | 0.724265 | − | 0.689521i | \(-0.242179\pi\) | ||||
0.724265 | + | 0.689521i | \(0.242179\pi\) | |||||||
\(384\) | −26.8559 | −1.37048 | ||||||||
\(385\) | −7.30459 | −0.372276 | ||||||||
\(386\) | 11.0428 | 0.562062 | ||||||||
\(387\) | −3.54734 | −0.180322 | ||||||||
\(388\) | 10.0584 | 0.510640 | ||||||||
\(389\) | 3.61541 | 0.183309 | 0.0916543 | − | 0.995791i | \(-0.470785\pi\) | ||||
0.0916543 | + | 0.995791i | \(0.470785\pi\) | |||||||
\(390\) | 93.8340 | 4.75147 | ||||||||
\(391\) | 12.0274 | 0.608250 | ||||||||
\(392\) | 14.8095 | 0.747992 | ||||||||
\(393\) | −6.39137 | −0.322402 | ||||||||
\(394\) | 45.5517 | 2.29486 | ||||||||
\(395\) | 24.1649 | 1.21587 | ||||||||
\(396\) | −11.7944 | −0.592693 | ||||||||
\(397\) | 24.5672 | 1.23299 | 0.616497 | − | 0.787357i | \(-0.288551\pi\) | ||||
0.616497 | + | 0.787357i | \(0.288551\pi\) | |||||||
\(398\) | 30.7029 | 1.53900 | ||||||||
\(399\) | −31.2190 | −1.56290 | ||||||||
\(400\) | 29.6227 | 1.48114 | ||||||||
\(401\) | 30.6801 | 1.53209 | 0.766045 | − | 0.642787i | \(-0.222222\pi\) | ||||
0.766045 | + | 0.642787i | \(0.222222\pi\) | |||||||
\(402\) | −77.9572 | −3.88815 | ||||||||
\(403\) | −0.892425 | −0.0444548 | ||||||||
\(404\) | 6.93946 | 0.345251 | ||||||||
\(405\) | 31.8435 | 1.58231 | ||||||||
\(406\) | 7.39604 | 0.367059 | ||||||||
\(407\) | 10.3413 | 0.512598 | ||||||||
\(408\) | −95.5226 | −4.72907 | ||||||||
\(409\) | 0.984912 | 0.0487007 | 0.0243504 | − | 0.999703i | \(-0.492248\pi\) | ||||
0.0243504 | + | 0.999703i | \(0.492248\pi\) | |||||||
\(410\) | 85.9468 | 4.24461 | ||||||||
\(411\) | 26.0719 | 1.28603 | ||||||||
\(412\) | 66.7763 | 3.28983 | ||||||||
\(413\) | 4.58064 | 0.225398 | ||||||||
\(414\) | 11.0264 | 0.541918 | ||||||||
\(415\) | −45.2898 | −2.22319 | ||||||||
\(416\) | 29.0015 | 1.42191 | ||||||||
\(417\) | −41.4217 | −2.02843 | ||||||||
\(418\) | −17.8105 | −0.871139 | ||||||||
\(419\) | −2.30116 | −0.112419 | −0.0562096 | − | 0.998419i | \(-0.517902\pi\) | ||||
−0.0562096 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(420\) | −67.7158 | −3.30419 | ||||||||
\(421\) | 29.9506 | 1.45970 | 0.729851 | − | 0.683606i | \(-0.239589\pi\) | ||||
0.729851 | + | 0.683606i | \(0.239589\pi\) | |||||||
\(422\) | −47.0335 | −2.28956 | ||||||||
\(423\) | −10.5489 | −0.512906 | ||||||||
\(424\) | −43.5728 | −2.11608 | ||||||||
\(425\) | −27.1435 | −1.31665 | ||||||||
\(426\) | −1.15606 | −0.0560115 | ||||||||
\(427\) | −17.2844 | −0.836452 | ||||||||
\(428\) | −20.2615 | −0.979374 | ||||||||
\(429\) | −13.6253 | −0.657835 | ||||||||
\(430\) | −11.6191 | −0.560323 | ||||||||
\(431\) | −20.8300 | −1.00335 | −0.501673 | − | 0.865057i | \(-0.667282\pi\) | ||||
−0.501673 | + | 0.865057i | \(0.667282\pi\) | |||||||
\(432\) | 10.6862 | 0.514142 | ||||||||
\(433\) | −33.8117 | −1.62488 | −0.812442 | − | 0.583042i | \(-0.801862\pi\) | ||||
−0.812442 | + | 0.583042i | \(0.801862\pi\) | |||||||
\(434\) | 0.931364 | 0.0447069 | ||||||||
\(435\) | 9.42242 | 0.451770 | ||||||||
\(436\) | 42.4335 | 2.03220 | ||||||||
\(437\) | 11.5137 | 0.550774 | ||||||||
\(438\) | −57.3595 | −2.74074 | ||||||||
\(439\) | −12.3996 | −0.591798 | −0.295899 | − | 0.955219i | \(-0.595619\pi\) | ||||
−0.295899 | + | 0.955219i | \(0.595619\pi\) | |||||||
\(440\) | −21.3957 | −1.02000 | ||||||||
\(441\) | −5.51055 | −0.262407 | ||||||||
\(442\) | −87.5627 | −4.16493 | ||||||||
\(443\) | −26.9209 | −1.27905 | −0.639526 | − | 0.768770i | \(-0.720869\pi\) | ||||
−0.639526 | + | 0.768770i | \(0.720869\pi\) | |||||||
\(444\) | 95.8668 | 4.54964 | ||||||||
\(445\) | 13.6344 | 0.646333 | ||||||||
\(446\) | −25.8116 | −1.22222 | ||||||||
\(447\) | −2.03192 | −0.0961066 | ||||||||
\(448\) | 0.501430 | 0.0236903 | ||||||||
\(449\) | 29.9104 | 1.41156 | 0.705779 | − | 0.708432i | \(-0.250597\pi\) | ||||
0.705779 | + | 0.708432i | \(0.250597\pi\) | |||||||
\(450\) | −24.8846 | −1.17307 | ||||||||
\(451\) | −12.4800 | −0.587661 | ||||||||
\(452\) | −14.5908 | −0.686293 | ||||||||
\(453\) | 49.3914 | 2.32061 | ||||||||
\(454\) | 48.1524 | 2.25990 | ||||||||
\(455\) | −34.3782 | −1.61168 | ||||||||
\(456\) | −91.4429 | −4.28220 | ||||||||
\(457\) | 4.79167 | 0.224145 | 0.112072 | − | 0.993700i | \(-0.464251\pi\) | ||||
0.112072 | + | 0.993700i | \(0.464251\pi\) | |||||||
\(458\) | −30.8072 | −1.43953 | ||||||||
\(459\) | −9.79188 | −0.457046 | ||||||||
\(460\) | 24.9739 | 1.16441 | ||||||||
\(461\) | 6.91366 | 0.322001 | 0.161001 | − | 0.986954i | \(-0.448528\pi\) | ||||
0.161001 | + | 0.986954i | \(0.448528\pi\) | |||||||
\(462\) | 14.2198 | 0.661565 | ||||||||
\(463\) | −29.1807 | −1.35614 | −0.678071 | − | 0.734997i | \(-0.737184\pi\) | ||||
−0.678071 | + | 0.734997i | \(0.737184\pi\) | |||||||
\(464\) | 9.59578 | 0.445473 | ||||||||
\(465\) | 1.18654 | 0.0550245 | ||||||||
\(466\) | 0.315447 | 0.0146128 | ||||||||
\(467\) | −12.0740 | −0.558719 | −0.279360 | − | 0.960187i | \(-0.590122\pi\) | ||||
−0.279360 | + | 0.960187i | \(0.590122\pi\) | |||||||
\(468\) | −55.5092 | −2.56591 | ||||||||
\(469\) | 28.5614 | 1.31884 | ||||||||
\(470\) | −34.5523 | −1.59378 | ||||||||
\(471\) | −25.8319 | −1.19027 | ||||||||
\(472\) | 13.4170 | 0.617570 | ||||||||
\(473\) | 1.68717 | 0.0775760 | ||||||||
\(474\) | −47.0416 | −2.16069 | ||||||||
\(475\) | −25.9843 | −1.19224 | ||||||||
\(476\) | 63.1901 | 2.89631 | ||||||||
\(477\) | 16.2132 | 0.742354 | ||||||||
\(478\) | 11.8313 | 0.541150 | ||||||||
\(479\) | −25.2183 | −1.15225 | −0.576127 | − | 0.817360i | \(-0.695437\pi\) | ||||
−0.576127 | + | 0.817360i | \(0.695437\pi\) | |||||||
\(480\) | −38.5595 | −1.75999 | ||||||||
\(481\) | 48.6700 | 2.21916 | ||||||||
\(482\) | −22.1366 | −1.00829 | ||||||||
\(483\) | −9.19246 | −0.418272 | ||||||||
\(484\) | −43.6994 | −1.98634 | ||||||||
\(485\) | −6.78946 | −0.308293 | ||||||||
\(486\) | −50.5394 | −2.29251 | ||||||||
\(487\) | 9.99182 | 0.452772 | 0.226386 | − | 0.974038i | \(-0.427309\pi\) | ||||
0.226386 | + | 0.974038i | \(0.427309\pi\) | |||||||
\(488\) | −50.6274 | −2.29180 | ||||||||
\(489\) | −28.5736 | −1.29214 | ||||||||
\(490\) | −18.0495 | −0.815392 | ||||||||
\(491\) | 7.59133 | 0.342592 | 0.171296 | − | 0.985220i | \(-0.445205\pi\) | ||||
0.171296 | + | 0.985220i | \(0.445205\pi\) | |||||||
\(492\) | −115.694 | −5.21587 | ||||||||
\(493\) | −8.79268 | −0.396003 | ||||||||
\(494\) | −83.8230 | −3.77137 | ||||||||
\(495\) | 7.96125 | 0.357832 | ||||||||
\(496\) | 1.20837 | 0.0542575 | ||||||||
\(497\) | 0.423550 | 0.0189988 | ||||||||
\(498\) | 88.1653 | 3.95078 | ||||||||
\(499\) | 8.02626 | 0.359305 | 0.179652 | − | 0.983730i | \(-0.442503\pi\) | ||||
0.179652 | + | 0.983730i | \(0.442503\pi\) | |||||||
\(500\) | 11.4561 | 0.512333 | ||||||||
\(501\) | −44.3701 | −1.98231 | ||||||||
\(502\) | −37.3500 | −1.66701 | ||||||||
\(503\) | 28.8795 | 1.28767 | 0.643836 | − | 0.765163i | \(-0.277342\pi\) | ||||
0.643836 | + | 0.765163i | \(0.277342\pi\) | |||||||
\(504\) | 32.0843 | 1.42915 | ||||||||
\(505\) | −4.68414 | −0.208442 | ||||||||
\(506\) | −5.24432 | −0.233138 | ||||||||
\(507\) | −34.0510 | −1.51226 | ||||||||
\(508\) | −19.6287 | −0.870885 | ||||||||
\(509\) | 13.5685 | 0.601412 | 0.300706 | − | 0.953717i | \(-0.402778\pi\) | ||||
0.300706 | + | 0.953717i | \(0.402778\pi\) | |||||||
\(510\) | 116.421 | 5.15519 | ||||||||
\(511\) | 21.0150 | 0.929647 | ||||||||
\(512\) | 50.8540 | 2.24745 | ||||||||
\(513\) | −9.37367 | −0.413858 | ||||||||
\(514\) | −36.2586 | −1.59930 | ||||||||
\(515\) | −45.0740 | −1.98620 | ||||||||
\(516\) | 15.6406 | 0.688537 | ||||||||
\(517\) | 5.01722 | 0.220657 | ||||||||
\(518\) | −50.7937 | −2.23174 | ||||||||
\(519\) | −25.7195 | −1.12896 | ||||||||
\(520\) | −100.696 | −4.41583 | ||||||||
\(521\) | −8.64002 | −0.378526 | −0.189263 | − | 0.981926i | \(-0.560610\pi\) | ||||
−0.189263 | + | 0.981926i | \(0.560610\pi\) | |||||||
\(522\) | −8.06093 | −0.352817 | ||||||||
\(523\) | 38.3582 | 1.67729 | 0.838645 | − | 0.544679i | \(-0.183349\pi\) | ||||
0.838645 | + | 0.544679i | \(0.183349\pi\) | |||||||
\(524\) | 12.3842 | 0.541007 | ||||||||
\(525\) | 20.7457 | 0.905416 | ||||||||
\(526\) | −60.2701 | −2.62790 | ||||||||
\(527\) | −1.10724 | −0.0482321 | ||||||||
\(528\) | 18.4491 | 0.802892 | ||||||||
\(529\) | −19.6098 | −0.852599 | ||||||||
\(530\) | 53.1055 | 2.30676 | ||||||||
\(531\) | −4.99242 | −0.216653 | ||||||||
\(532\) | 60.4913 | 2.62263 | ||||||||
\(533\) | −58.7357 | −2.54413 | ||||||||
\(534\) | −26.5420 | −1.14859 | ||||||||
\(535\) | 13.6765 | 0.591286 | ||||||||
\(536\) | 83.6586 | 3.61350 | ||||||||
\(537\) | −40.1706 | −1.73349 | ||||||||
\(538\) | −44.9063 | −1.93605 | ||||||||
\(539\) | 2.62090 | 0.112890 | ||||||||
\(540\) | −20.3321 | −0.874952 | ||||||||
\(541\) | −12.0929 | −0.519916 | −0.259958 | − | 0.965620i | \(-0.583709\pi\) | ||||
−0.259958 | + | 0.965620i | \(0.583709\pi\) | |||||||
\(542\) | 54.3142 | 2.33300 | ||||||||
\(543\) | 47.9210 | 2.05649 | ||||||||
\(544\) | 35.9824 | 1.54273 | ||||||||
\(545\) | −28.6426 | −1.22692 | ||||||||
\(546\) | 66.9238 | 2.86408 | ||||||||
\(547\) | 6.79584 | 0.290569 | 0.145284 | − | 0.989390i | \(-0.453590\pi\) | ||||
0.145284 | + | 0.989390i | \(0.453590\pi\) | |||||||
\(548\) | −50.5182 | −2.15803 | ||||||||
\(549\) | 18.8382 | 0.803997 | ||||||||
\(550\) | 11.8355 | 0.504666 | ||||||||
\(551\) | −8.41715 | −0.358583 | ||||||||
\(552\) | −26.9255 | −1.14602 | ||||||||
\(553\) | 17.2348 | 0.732897 | ||||||||
\(554\) | −32.9058 | −1.39803 | ||||||||
\(555\) | −64.7102 | −2.74679 | ||||||||
\(556\) | 80.2606 | 3.40381 | ||||||||
\(557\) | −5.81733 | −0.246488 | −0.123244 | − | 0.992376i | \(-0.539330\pi\) | ||||
−0.123244 | + | 0.992376i | \(0.539330\pi\) | |||||||
\(558\) | −1.01509 | −0.0429722 | ||||||||
\(559\) | 7.94045 | 0.335845 | ||||||||
\(560\) | 46.5492 | 1.96706 | ||||||||
\(561\) | −16.9050 | −0.713730 | ||||||||
\(562\) | −9.31243 | −0.392821 | ||||||||
\(563\) | −27.3558 | −1.15291 | −0.576456 | − | 0.817128i | \(-0.695565\pi\) | ||||
−0.576456 | + | 0.817128i | \(0.695565\pi\) | |||||||
\(564\) | 46.5112 | 1.95847 | ||||||||
\(565\) | 9.84879 | 0.414342 | ||||||||
\(566\) | −0.114557 | −0.00481519 | ||||||||
\(567\) | 22.7112 | 0.953782 | ||||||||
\(568\) | 1.24061 | 0.0520549 | ||||||||
\(569\) | −13.7344 | −0.575775 | −0.287887 | − | 0.957664i | \(-0.592953\pi\) | ||||
−0.287887 | + | 0.957664i | \(0.592953\pi\) | |||||||
\(570\) | 111.448 | 4.66806 | ||||||||
\(571\) | 0.218398 | 0.00913966 | 0.00456983 | − | 0.999990i | \(-0.498545\pi\) | ||||
0.00456983 | + | 0.999990i | \(0.498545\pi\) | |||||||
\(572\) | 26.4010 | 1.10388 | ||||||||
\(573\) | 0.314742 | 0.0131485 | ||||||||
\(574\) | 61.2986 | 2.55855 | ||||||||
\(575\) | −7.65109 | −0.319073 | ||||||||
\(576\) | −0.546507 | −0.0227711 | ||||||||
\(577\) | −37.2260 | −1.54974 | −0.774870 | − | 0.632121i | \(-0.782185\pi\) | ||||
−0.774870 | + | 0.632121i | \(0.782185\pi\) | |||||||
\(578\) | −65.3561 | −2.71845 | ||||||||
\(579\) | 10.0337 | 0.416987 | ||||||||
\(580\) | −18.2573 | −0.758093 | ||||||||
\(581\) | −32.3014 | −1.34009 | ||||||||
\(582\) | 13.2170 | 0.547862 | ||||||||
\(583\) | −7.71125 | −0.319367 | ||||||||
\(584\) | 61.5545 | 2.54714 | ||||||||
\(585\) | 37.4687 | 1.54914 | ||||||||
\(586\) | −2.34996 | −0.0970761 | ||||||||
\(587\) | 27.7337 | 1.14469 | 0.572346 | − | 0.820012i | \(-0.306033\pi\) | ||||
0.572346 | + | 0.820012i | \(0.306033\pi\) | |||||||
\(588\) | 24.2965 | 1.00197 | ||||||||
\(589\) | −1.05995 | −0.0436745 | ||||||||
\(590\) | −16.3524 | −0.673217 | ||||||||
\(591\) | 41.3893 | 1.70253 | ||||||||
\(592\) | −65.9007 | −2.70850 | ||||||||
\(593\) | −27.9161 | −1.14638 | −0.573189 | − | 0.819423i | \(-0.694294\pi\) | ||||
−0.573189 | + | 0.819423i | \(0.694294\pi\) | |||||||
\(594\) | 4.26957 | 0.175183 | ||||||||
\(595\) | −42.6533 | −1.74862 | ||||||||
\(596\) | 3.93714 | 0.161272 | ||||||||
\(597\) | 27.8974 | 1.14176 | ||||||||
\(598\) | −24.6818 | −1.00931 | ||||||||
\(599\) | −4.71962 | −0.192838 | −0.0964192 | − | 0.995341i | \(-0.530739\pi\) | ||||
−0.0964192 | + | 0.995341i | \(0.530739\pi\) | |||||||
\(600\) | 60.7658 | 2.48075 | ||||||||
\(601\) | 3.85608 | 0.157293 | 0.0786463 | − | 0.996903i | \(-0.474940\pi\) | ||||
0.0786463 | + | 0.996903i | \(0.474940\pi\) | |||||||
\(602\) | −8.28692 | −0.337750 | ||||||||
\(603\) | −31.1290 | −1.26767 | ||||||||
\(604\) | −95.7030 | −3.89410 | ||||||||
\(605\) | 29.4971 | 1.19923 | ||||||||
\(606\) | 9.11859 | 0.370417 | ||||||||
\(607\) | 35.6084 | 1.44530 | 0.722650 | − | 0.691214i | \(-0.242924\pi\) | ||||
0.722650 | + | 0.691214i | \(0.242924\pi\) | |||||||
\(608\) | 34.4456 | 1.39695 | ||||||||
\(609\) | 6.72021 | 0.272317 | ||||||||
\(610\) | 61.7036 | 2.49830 | ||||||||
\(611\) | 23.6129 | 0.955278 | ||||||||
\(612\) | −68.8707 | −2.78393 | ||||||||
\(613\) | −3.38207 | −0.136601 | −0.0683003 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683003 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(614\) | 19.4671 | 0.785627 | ||||||||
\(615\) | 78.0932 | 3.14902 | ||||||||
\(616\) | −15.2598 | −0.614833 | ||||||||
\(617\) | −43.2857 | −1.74262 | −0.871308 | − | 0.490737i | \(-0.836728\pi\) | ||||
−0.871308 | + | 0.490737i | \(0.836728\pi\) | |||||||
\(618\) | 87.7453 | 3.52963 | ||||||||
\(619\) | −23.6178 | −0.949280 | −0.474640 | − | 0.880180i | \(-0.657422\pi\) | ||||
−0.474640 | + | 0.880180i | \(0.657422\pi\) | |||||||
\(620\) | −2.29909 | −0.0923338 | ||||||||
\(621\) | −2.76009 | −0.110759 | ||||||||
\(622\) | 69.1643 | 2.77324 | ||||||||
\(623\) | 9.72427 | 0.389595 | ||||||||
\(624\) | 86.8284 | 3.47592 | ||||||||
\(625\) | −28.5097 | −1.14039 | ||||||||
\(626\) | −57.8065 | −2.31041 | ||||||||
\(627\) | −16.1830 | −0.646287 | ||||||||
\(628\) | 50.0531 | 1.99734 | ||||||||
\(629\) | 60.3853 | 2.40772 | ||||||||
\(630\) | −39.1036 | −1.55792 | ||||||||
\(631\) | 2.28587 | 0.0909990 | 0.0454995 | − | 0.998964i | \(-0.485512\pi\) | ||||
0.0454995 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(632\) | 50.4820 | 2.00807 | ||||||||
\(633\) | −42.7358 | −1.69859 | ||||||||
\(634\) | 50.4748 | 2.00461 | ||||||||
\(635\) | 13.2494 | 0.525787 | ||||||||
\(636\) | −71.4857 | −2.83459 | ||||||||
\(637\) | 12.3349 | 0.488728 | ||||||||
\(638\) | 3.83389 | 0.151785 | ||||||||
\(639\) | −0.461626 | −0.0182617 | ||||||||
\(640\) | −35.1251 | −1.38844 | ||||||||
\(641\) | −39.0478 | −1.54229 | −0.771147 | − | 0.636657i | \(-0.780317\pi\) | ||||
−0.771147 | + | 0.636657i | \(0.780317\pi\) | |||||||
\(642\) | −26.6239 | −1.05076 | ||||||||
\(643\) | −3.64472 | −0.143734 | −0.0718669 | − | 0.997414i | \(-0.522896\pi\) | ||||
−0.0718669 | + | 0.997414i | \(0.522896\pi\) | |||||||
\(644\) | 17.8117 | 0.701881 | ||||||||
\(645\) | −10.5574 | −0.415697 | ||||||||
\(646\) | −104.000 | −4.09182 | ||||||||
\(647\) | 2.37465 | 0.0933571 | 0.0466785 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466785 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(648\) | 66.5230 | 2.61327 | ||||||||
\(649\) | 2.37447 | 0.0932060 | ||||||||
\(650\) | 55.7022 | 2.18482 | ||||||||
\(651\) | 0.846259 | 0.0331675 | ||||||||
\(652\) | 55.3654 | 2.16828 | ||||||||
\(653\) | −41.9990 | −1.64355 | −0.821774 | − | 0.569814i | \(-0.807015\pi\) | ||||
−0.821774 | + | 0.569814i | \(0.807015\pi\) | |||||||
\(654\) | 55.7584 | 2.18033 | ||||||||
\(655\) | −8.35935 | −0.326627 | ||||||||
\(656\) | 79.5300 | 3.10513 | ||||||||
\(657\) | −22.9042 | −0.893576 | ||||||||
\(658\) | −24.6433 | −0.960694 | ||||||||
\(659\) | 41.3762 | 1.61179 | 0.805894 | − | 0.592059i | \(-0.201685\pi\) | ||||
0.805894 | + | 0.592059i | \(0.201685\pi\) | |||||||
\(660\) | −35.1019 | −1.36634 | ||||||||
\(661\) | −47.6937 | −1.85507 | −0.927535 | − | 0.373735i | \(-0.878077\pi\) | ||||
−0.927535 | + | 0.373735i | \(0.878077\pi\) | |||||||
\(662\) | −15.1381 | −0.588360 | ||||||||
\(663\) | −79.5615 | −3.08991 | ||||||||
\(664\) | −94.6133 | −3.67171 | ||||||||
\(665\) | −40.8317 | −1.58338 | ||||||||
\(666\) | 55.3599 | 2.14515 | ||||||||
\(667\) | −2.47844 | −0.0959656 | ||||||||
\(668\) | 85.9736 | 3.32642 | ||||||||
\(669\) | −23.4530 | −0.906746 | ||||||||
\(670\) | −101.961 | −3.93910 | ||||||||
\(671\) | −8.95974 | −0.345887 | ||||||||
\(672\) | −27.5012 | −1.06088 | ||||||||
\(673\) | −48.6598 | −1.87570 | −0.937850 | − | 0.347042i | \(-0.887186\pi\) | ||||
−0.937850 | + | 0.347042i | \(0.887186\pi\) | |||||||
\(674\) | −29.8212 | −1.14867 | ||||||||
\(675\) | 6.22901 | 0.239755 | ||||||||
\(676\) | 65.9787 | 2.53764 | ||||||||
\(677\) | −15.9423 | −0.612711 | −0.306355 | − | 0.951917i | \(-0.599110\pi\) | ||||
−0.306355 | + | 0.951917i | \(0.599110\pi\) | |||||||
\(678\) | −19.1726 | −0.736319 | ||||||||
\(679\) | −4.84235 | −0.185832 | ||||||||
\(680\) | −124.935 | −4.79104 | ||||||||
\(681\) | 43.7524 | 1.67659 | ||||||||
\(682\) | 0.482792 | 0.0184871 | ||||||||
\(683\) | 3.83176 | 0.146618 | 0.0733092 | − | 0.997309i | \(-0.476644\pi\) | ||||
0.0733092 | + | 0.997309i | \(0.476644\pi\) | |||||||
\(684\) | −65.9293 | −2.52087 | ||||||||
\(685\) | 34.0998 | 1.30289 | ||||||||
\(686\) | −51.3352 | −1.95999 | ||||||||
\(687\) | −27.9922 | −1.06797 | ||||||||
\(688\) | −10.7516 | −0.409902 | ||||||||
\(689\) | −36.2921 | −1.38262 | ||||||||
\(690\) | 32.8161 | 1.24929 | ||||||||
\(691\) | −11.6515 | −0.443245 | −0.221622 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221622 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(692\) | 49.8352 | 1.89445 | ||||||||
\(693\) | 5.67809 | 0.215693 | ||||||||
\(694\) | 46.2689 | 1.75634 | ||||||||
\(695\) | −54.1759 | −2.05501 | ||||||||
\(696\) | 19.6840 | 0.746122 | ||||||||
\(697\) | −72.8739 | −2.76030 | ||||||||
\(698\) | 0.0711685 | 0.00269377 | ||||||||
\(699\) | 0.286623 | 0.0108411 | ||||||||
\(700\) | −40.1978 | −1.51933 | ||||||||
\(701\) | −31.6364 | −1.19489 | −0.597445 | − | 0.801910i | \(-0.703817\pi\) | ||||
−0.597445 | + | 0.801910i | \(0.703817\pi\) | |||||||
\(702\) | 20.0943 | 0.758409 | ||||||||
\(703\) | 57.8063 | 2.18021 | ||||||||
\(704\) | 0.259927 | 0.00979636 | ||||||||
\(705\) | −31.3951 | −1.18241 | ||||||||
\(706\) | −8.96374 | −0.337355 | ||||||||
\(707\) | −3.34080 | −0.125644 | ||||||||
\(708\) | 22.0121 | 0.827264 | ||||||||
\(709\) | −32.7582 | −1.23026 | −0.615130 | − | 0.788426i | \(-0.710897\pi\) | ||||
−0.615130 | + | 0.788426i | \(0.710897\pi\) | |||||||
\(710\) | −1.51203 | −0.0567454 | ||||||||
\(711\) | −18.7841 | −0.704460 | ||||||||
\(712\) | 28.4832 | 1.06745 | ||||||||
\(713\) | −0.312104 | −0.0116884 | ||||||||
\(714\) | 83.0330 | 3.10743 | ||||||||
\(715\) | −17.8207 | −0.666455 | ||||||||
\(716\) | 77.8364 | 2.90888 | ||||||||
\(717\) | 10.7502 | 0.401472 | ||||||||
\(718\) | 85.0125 | 3.17264 | ||||||||
\(719\) | −26.0367 | −0.971006 | −0.485503 | − | 0.874235i | \(-0.661363\pi\) | ||||
−0.485503 | + | 0.874235i | \(0.661363\pi\) | |||||||
\(720\) | −50.7338 | −1.89074 | ||||||||
\(721\) | −32.1475 | −1.19723 | ||||||||
\(722\) | −51.1822 | −1.90480 | ||||||||
\(723\) | −20.1138 | −0.748041 | ||||||||
\(724\) | −92.8539 | −3.45089 | ||||||||
\(725\) | 5.59338 | 0.207733 | ||||||||
\(726\) | −57.4219 | −2.13113 | ||||||||
\(727\) | −20.2033 | −0.749298 | −0.374649 | − | 0.927167i | \(-0.622237\pi\) | ||||
−0.374649 | + | 0.927167i | \(0.622237\pi\) | |||||||
\(728\) | −71.8183 | −2.66176 | ||||||||
\(729\) | −14.3492 | −0.531450 | ||||||||
\(730\) | −75.0212 | −2.77666 | ||||||||
\(731\) | 9.85179 | 0.364382 | ||||||||
\(732\) | −83.0596 | −3.06997 | ||||||||
\(733\) | −26.7064 | −0.986423 | −0.493212 | − | 0.869909i | \(-0.664177\pi\) | ||||
−0.493212 | + | 0.869909i | \(0.664177\pi\) | |||||||
\(734\) | 23.0676 | 0.851442 | ||||||||
\(735\) | −16.4002 | −0.604929 | ||||||||
\(736\) | 10.1426 | 0.373859 | ||||||||
\(737\) | 14.8054 | 0.545364 | ||||||||
\(738\) | −66.8092 | −2.45928 | ||||||||
\(739\) | −6.02930 | −0.221791 | −0.110896 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110896 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(740\) | 125.385 | 4.60926 | ||||||||
\(741\) | −76.1634 | −2.79793 | ||||||||
\(742\) | 37.8757 | 1.39046 | ||||||||
\(743\) | 2.64757 | 0.0971300 | 0.0485650 | − | 0.998820i | \(-0.484535\pi\) | ||||
0.0485650 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(744\) | 2.47876 | 0.0908757 | ||||||||
\(745\) | −2.65757 | −0.0973660 | ||||||||
\(746\) | 57.7274 | 2.11355 | ||||||||
\(747\) | 35.2052 | 1.28809 | ||||||||
\(748\) | 32.7559 | 1.19767 | ||||||||
\(749\) | 9.75428 | 0.356414 | ||||||||
\(750\) | 15.0536 | 0.549678 | ||||||||
\(751\) | 45.9015 | 1.67497 | 0.837485 | − | 0.546460i | \(-0.184025\pi\) | ||||
0.837485 | + | 0.546460i | \(0.184025\pi\) | |||||||
\(752\) | −31.9727 | −1.16592 | ||||||||
\(753\) | −33.9371 | −1.23674 | ||||||||
\(754\) | 18.0438 | 0.657116 | ||||||||
\(755\) | 64.5996 | 2.35102 | ||||||||
\(756\) | −14.5011 | −0.527401 | ||||||||
\(757\) | 23.7709 | 0.863966 | 0.431983 | − | 0.901882i | \(-0.357814\pi\) | ||||
0.431983 | + | 0.901882i | \(0.357814\pi\) | |||||||
\(758\) | −17.5546 | −0.637611 | ||||||||
\(759\) | −4.76511 | −0.172962 | ||||||||
\(760\) | −119.599 | −4.33832 | ||||||||
\(761\) | −14.3488 | −0.520144 | −0.260072 | − | 0.965589i | \(-0.583746\pi\) | ||||
−0.260072 | + | 0.965589i | \(0.583746\pi\) | |||||||
\(762\) | −25.7925 | −0.934365 | ||||||||
\(763\) | −20.4284 | −0.739556 | ||||||||
\(764\) | −0.609858 | −0.0220639 | ||||||||
\(765\) | 46.4878 | 1.68077 | ||||||||
\(766\) | −72.1777 | −2.60789 | ||||||||
\(767\) | 11.1752 | 0.403512 | ||||||||
\(768\) | 67.3028 | 2.42858 | ||||||||
\(769\) | −15.8726 | −0.572382 | −0.286191 | − | 0.958173i | \(-0.592389\pi\) | ||||
−0.286191 | + | 0.958173i | \(0.592389\pi\) | |||||||
\(770\) | 18.5982 | 0.670234 | ||||||||
\(771\) | −32.9454 | −1.18650 | ||||||||
\(772\) | −19.4418 | −0.699725 | ||||||||
\(773\) | 42.7407 | 1.53728 | 0.768639 | − | 0.639683i | \(-0.220934\pi\) | ||||
0.768639 | + | 0.639683i | \(0.220934\pi\) | |||||||
\(774\) | 9.03190 | 0.324645 | ||||||||
\(775\) | 0.704360 | 0.0253014 | ||||||||
\(776\) | −14.1836 | −0.509162 | ||||||||
\(777\) | −46.1523 | −1.65570 | ||||||||
\(778\) | −9.20521 | −0.330023 | ||||||||
\(779\) | −69.7616 | −2.49947 | ||||||||
\(780\) | −165.203 | −5.91522 | ||||||||
\(781\) | 0.219556 | 0.00785633 | ||||||||
\(782\) | −30.6229 | −1.09507 | ||||||||
\(783\) | 2.01778 | 0.0721096 | ||||||||
\(784\) | −16.7019 | −0.596497 | ||||||||
\(785\) | −33.7859 | −1.20587 | ||||||||
\(786\) | 16.2731 | 0.580442 | ||||||||
\(787\) | 17.0715 | 0.608533 | 0.304266 | − | 0.952587i | \(-0.401589\pi\) | ||||
0.304266 | + | 0.952587i | \(0.401589\pi\) | |||||||
\(788\) | −80.1978 | −2.85693 | ||||||||
\(789\) | −54.7627 | −1.94961 | ||||||||
\(790\) | −61.5263 | −2.18901 | ||||||||
\(791\) | 7.02431 | 0.249756 | ||||||||
\(792\) | 16.6316 | 0.590977 | ||||||||
\(793\) | −42.1680 | −1.49743 | ||||||||
\(794\) | −62.5507 | −2.21984 | ||||||||
\(795\) | 48.2529 | 1.71135 | ||||||||
\(796\) | −54.0552 | −1.91594 | ||||||||
\(797\) | 34.1268 | 1.20883 | 0.604417 | − | 0.796668i | \(-0.293406\pi\) | ||||
0.604417 | + | 0.796668i | \(0.293406\pi\) | |||||||
\(798\) | 79.4867 | 2.81380 | ||||||||
\(799\) | 29.2968 | 1.03645 | ||||||||
\(800\) | −22.8899 | −0.809279 | ||||||||
\(801\) | −10.5985 | −0.374478 | ||||||||
\(802\) | −78.1146 | −2.75832 | ||||||||
\(803\) | 10.8935 | 0.384425 | ||||||||
\(804\) | 137.251 | 4.84046 | ||||||||
\(805\) | −12.0229 | −0.423753 | ||||||||
\(806\) | 2.27220 | 0.0800350 | ||||||||
\(807\) | −40.8029 | −1.43633 | ||||||||
\(808\) | −9.78547 | −0.344252 | ||||||||
\(809\) | 43.8724 | 1.54247 | 0.771236 | − | 0.636549i | \(-0.219639\pi\) | ||||
0.771236 | + | 0.636549i | \(0.219639\pi\) | |||||||
\(810\) | −81.0767 | −2.84875 | ||||||||
\(811\) | −0.487573 | −0.0171210 | −0.00856051 | − | 0.999963i | \(-0.502725\pi\) | ||||
−0.00856051 | + | 0.999963i | \(0.502725\pi\) | |||||||
\(812\) | −13.0214 | −0.456961 | ||||||||
\(813\) | 49.3511 | 1.73082 | ||||||||
\(814\) | −26.3300 | −0.922864 | ||||||||
\(815\) | −37.3717 | −1.30907 | ||||||||
\(816\) | 107.729 | 3.77126 | ||||||||
\(817\) | 9.43103 | 0.329950 | ||||||||
\(818\) | −2.50769 | −0.0876792 | ||||||||
\(819\) | 26.7233 | 0.933786 | ||||||||
\(820\) | −151.317 | −5.28422 | ||||||||
\(821\) | −3.39195 | −0.118380 | −0.0591900 | − | 0.998247i | \(-0.518852\pi\) | ||||
−0.0591900 | + | 0.998247i | \(0.518852\pi\) | |||||||
\(822\) | −66.3818 | −2.31533 | ||||||||
\(823\) | 2.28824 | 0.0797629 | 0.0398814 | − | 0.999204i | \(-0.487302\pi\) | ||||
0.0398814 | + | 0.999204i | \(0.487302\pi\) | |||||||
\(824\) | −94.1625 | −3.28031 | ||||||||
\(825\) | 10.7540 | 0.374405 | ||||||||
\(826\) | −11.6628 | −0.405800 | ||||||||
\(827\) | 14.9974 | 0.521511 | 0.260756 | − | 0.965405i | \(-0.416028\pi\) | ||||
0.260756 | + | 0.965405i | \(0.416028\pi\) | |||||||
\(828\) | −19.4130 | −0.674647 | ||||||||
\(829\) | −46.8989 | −1.62887 | −0.814433 | − | 0.580257i | \(-0.802952\pi\) | ||||
−0.814433 | + | 0.580257i | \(0.802952\pi\) | |||||||
\(830\) | 115.312 | 4.00255 | ||||||||
\(831\) | −29.8989 | −1.03718 | ||||||||
\(832\) | 1.22332 | 0.0424108 | ||||||||
\(833\) | 15.3041 | 0.530255 | ||||||||
\(834\) | 105.464 | 3.65192 | ||||||||
\(835\) | −58.0322 | −2.00829 | ||||||||
\(836\) | 31.3569 | 1.08450 | ||||||||
\(837\) | 0.254094 | 0.00878277 | ||||||||
\(838\) | 5.85900 | 0.202396 | ||||||||
\(839\) | 34.0396 | 1.17518 | 0.587588 | − | 0.809160i | \(-0.300078\pi\) | ||||
0.587588 | + | 0.809160i | \(0.300078\pi\) | |||||||
\(840\) | 95.4874 | 3.29463 | ||||||||
\(841\) | −27.1881 | −0.937521 | ||||||||
\(842\) | −76.2573 | −2.62800 | ||||||||
\(843\) | −8.46148 | −0.291429 | ||||||||
\(844\) | 82.8067 | 2.85033 | ||||||||
\(845\) | −44.5357 | −1.53207 | ||||||||
\(846\) | 26.8586 | 0.923419 | ||||||||
\(847\) | 21.0378 | 0.722868 | ||||||||
\(848\) | 49.1407 | 1.68750 | ||||||||
\(849\) | −0.104089 | −0.00357233 | ||||||||
\(850\) | 69.1102 | 2.37046 | ||||||||
\(851\) | 17.0211 | 0.583477 | ||||||||
\(852\) | 2.03535 | 0.0697300 | ||||||||
\(853\) | −5.66104 | −0.193830 | −0.0969151 | − | 0.995293i | \(-0.530898\pi\) | ||||
−0.0969151 | + | 0.995293i | \(0.530898\pi\) | |||||||
\(854\) | 44.0079 | 1.50592 | ||||||||
\(855\) | 44.5023 | 1.52195 | ||||||||
\(856\) | 28.5711 | 0.976539 | ||||||||
\(857\) | 10.3392 | 0.353181 | 0.176590 | − | 0.984284i | \(-0.443493\pi\) | ||||
0.176590 | + | 0.984284i | \(0.443493\pi\) | |||||||
\(858\) | 34.6914 | 1.18434 | ||||||||
\(859\) | 51.8642 | 1.76958 | 0.884791 | − | 0.465988i | \(-0.154301\pi\) | ||||
0.884791 | + | 0.465988i | \(0.154301\pi\) | |||||||
\(860\) | 20.4565 | 0.697560 | ||||||||
\(861\) | 55.6973 | 1.89816 | ||||||||
\(862\) | 53.0354 | 1.80639 | ||||||||
\(863\) | 15.6714 | 0.533460 | 0.266730 | − | 0.963771i | \(-0.414057\pi\) | ||||
0.266730 | + | 0.963771i | \(0.414057\pi\) | |||||||
\(864\) | −8.25739 | −0.280922 | ||||||||
\(865\) | −33.6388 | −1.14375 | ||||||||
\(866\) | 86.0880 | 2.92539 | ||||||||
\(867\) | −59.3840 | −2.01679 | ||||||||
\(868\) | −1.63975 | −0.0556567 | ||||||||
\(869\) | 8.93400 | 0.303065 | ||||||||
\(870\) | −23.9904 | −0.813352 | ||||||||
\(871\) | 69.6799 | 2.36101 | ||||||||
\(872\) | −59.8363 | −2.02631 | ||||||||
\(873\) | 5.27766 | 0.178622 | ||||||||
\(874\) | −29.3150 | −0.991595 | ||||||||
\(875\) | −5.51521 | −0.186448 | ||||||||
\(876\) | 100.987 | 3.41202 | ||||||||
\(877\) | 41.7811 | 1.41085 | 0.705424 | − | 0.708786i | \(-0.250757\pi\) | ||||
0.705424 | + | 0.708786i | \(0.250757\pi\) | |||||||
\(878\) | 31.5705 | 1.06545 | ||||||||
\(879\) | −2.13523 | −0.0720195 | ||||||||
\(880\) | 24.1297 | 0.813413 | ||||||||
\(881\) | 50.2244 | 1.69210 | 0.846052 | − | 0.533100i | \(-0.178973\pi\) | ||||
0.846052 | + | 0.533100i | \(0.178973\pi\) | |||||||
\(882\) | 14.0304 | 0.472429 | ||||||||
\(883\) | 33.1248 | 1.11474 | 0.557369 | − | 0.830265i | \(-0.311811\pi\) | ||||
0.557369 | + | 0.830265i | \(0.311811\pi\) | |||||||
\(884\) | 154.162 | 5.18503 | ||||||||
\(885\) | −14.8581 | −0.499451 | ||||||||
\(886\) | 68.5434 | 2.30276 | ||||||||
\(887\) | −32.0100 | −1.07479 | −0.537396 | − | 0.843330i | \(-0.680592\pi\) | ||||
−0.537396 | + | 0.843330i | \(0.680592\pi\) | |||||||
\(888\) | −135.184 | −4.53647 | ||||||||
\(889\) | 9.44968 | 0.316932 | ||||||||
\(890\) | −34.7146 | −1.16364 | ||||||||
\(891\) | 11.7728 | 0.394405 | ||||||||
\(892\) | 45.4436 | 1.52157 | ||||||||
\(893\) | 28.0456 | 0.938509 | ||||||||
\(894\) | 5.17348 | 0.173027 | ||||||||
\(895\) | −52.5396 | −1.75620 | ||||||||
\(896\) | −25.0518 | −0.836921 | ||||||||
\(897\) | −22.4264 | −0.748796 | ||||||||
\(898\) | −76.1549 | −2.54132 | ||||||||
\(899\) | 0.228165 | 0.00760974 | ||||||||
\(900\) | 43.8115 | 1.46038 | ||||||||
\(901\) | −45.0280 | −1.50010 | ||||||||
\(902\) | 31.7754 | 1.05800 | ||||||||
\(903\) | −7.52969 | −0.250572 | ||||||||
\(904\) | 20.5748 | 0.684306 | ||||||||
\(905\) | 62.6764 | 2.08343 | ||||||||
\(906\) | −125.756 | −4.17795 | ||||||||
\(907\) | −51.8138 | −1.72045 | −0.860225 | − | 0.509915i | \(-0.829677\pi\) | ||||
−0.860225 | + | 0.509915i | \(0.829677\pi\) | |||||||
\(908\) | −84.7766 | −2.81341 | ||||||||
\(909\) | 3.64113 | 0.120769 | ||||||||
\(910\) | 87.5304 | 2.90161 | ||||||||
\(911\) | −1.01322 | −0.0335694 | −0.0167847 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167847 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(912\) | 103.128 | 3.41490 | ||||||||
\(913\) | −16.7441 | −0.554148 | ||||||||
\(914\) | −12.2001 | −0.403543 | ||||||||
\(915\) | 56.0653 | 1.85346 | ||||||||
\(916\) | 54.2389 | 1.79210 | ||||||||
\(917\) | −5.96202 | −0.196883 | ||||||||
\(918\) | 24.9311 | 0.822850 | ||||||||
\(919\) | 44.4151 | 1.46512 | 0.732559 | − | 0.680704i | \(-0.238326\pi\) | ||||
0.732559 | + | 0.680704i | \(0.238326\pi\) | |||||||
\(920\) | −35.2161 | −1.16104 | ||||||||
\(921\) | 17.6882 | 0.582847 | ||||||||
\(922\) | −17.6029 | −0.579721 | ||||||||
\(923\) | 1.03332 | 0.0340120 | ||||||||
\(924\) | −25.0352 | −0.823598 | ||||||||
\(925\) | −38.4136 | −1.26303 | ||||||||
\(926\) | 74.2970 | 2.44155 | ||||||||
\(927\) | 35.0375 | 1.15078 | ||||||||
\(928\) | −7.41478 | −0.243402 | ||||||||
\(929\) | −3.62621 | −0.118972 | −0.0594860 | − | 0.998229i | \(-0.518946\pi\) | ||||
−0.0594860 | + | 0.998229i | \(0.518946\pi\) | |||||||
\(930\) | −3.02105 | −0.0990643 | ||||||||
\(931\) | 14.6504 | 0.480149 | ||||||||
\(932\) | −0.555373 | −0.0181918 | ||||||||
\(933\) | 62.8443 | 2.05743 | ||||||||
\(934\) | 30.7417 | 1.00590 | ||||||||
\(935\) | −22.1103 | −0.723083 | ||||||||
\(936\) | 78.2746 | 2.55848 | ||||||||
\(937\) | 13.5578 | 0.442914 | 0.221457 | − | 0.975170i | \(-0.428919\pi\) | ||||
0.221457 | + | 0.975170i | \(0.428919\pi\) | |||||||
\(938\) | −72.7202 | −2.37440 | ||||||||
\(939\) | −52.5243 | −1.71407 | ||||||||
\(940\) | 60.8325 | 1.98414 | ||||||||
\(941\) | 22.5394 | 0.734764 | 0.367382 | − | 0.930070i | \(-0.380254\pi\) | ||||
0.367382 | + | 0.930070i | \(0.380254\pi\) | |||||||
\(942\) | 65.7708 | 2.14293 | ||||||||
\(943\) | −20.5414 | −0.668919 | ||||||||
\(944\) | −15.1315 | −0.492489 | ||||||||
\(945\) | 9.78827 | 0.318412 | ||||||||
\(946\) | −4.29570 | −0.139665 | ||||||||
\(947\) | 29.0633 | 0.944429 | 0.472214 | − | 0.881484i | \(-0.343455\pi\) | ||||
0.472214 | + | 0.881484i | \(0.343455\pi\) | |||||||
\(948\) | 82.8210 | 2.68990 | ||||||||
\(949\) | 51.2692 | 1.66427 | ||||||||
\(950\) | 66.1586 | 2.14647 | ||||||||
\(951\) | 45.8625 | 1.48719 | ||||||||
\(952\) | −89.1056 | −2.88793 | ||||||||
\(953\) | −0.340675 | −0.0110356 | −0.00551778 | − | 0.999985i | \(-0.501756\pi\) | ||||
−0.00551778 | + | 0.999985i | \(0.501756\pi\) | |||||||
\(954\) | −41.2806 | −1.33651 | ||||||||
\(955\) | 0.411655 | 0.0133208 | ||||||||
\(956\) | −20.8300 | −0.673690 | ||||||||
\(957\) | 3.48356 | 0.112608 | ||||||||
\(958\) | 64.2084 | 2.07448 | ||||||||
\(959\) | 24.3205 | 0.785350 | ||||||||
\(960\) | −1.62648 | −0.0524945 | ||||||||
\(961\) | −30.9713 | −0.999073 | ||||||||
\(962\) | −123.919 | −3.99530 | ||||||||
\(963\) | −10.6312 | −0.342585 | ||||||||
\(964\) | 38.9734 | 1.25525 | ||||||||
\(965\) | 13.1232 | 0.422451 | ||||||||
\(966\) | 23.4050 | 0.753042 | ||||||||
\(967\) | 0.227348 | 0.00731102 | 0.00365551 | − | 0.999993i | \(-0.498836\pi\) | ||||
0.00365551 | + | 0.999993i | \(0.498836\pi\) | |||||||
\(968\) | 61.6214 | 1.98059 | ||||||||
\(969\) | −94.4967 | −3.03567 | ||||||||
\(970\) | 17.2867 | 0.555041 | ||||||||
\(971\) | 53.3032 | 1.71058 | 0.855291 | − | 0.518148i | \(-0.173378\pi\) | ||||
0.855291 | + | 0.518148i | \(0.173378\pi\) | |||||||
\(972\) | 88.9791 | 2.85401 | ||||||||
\(973\) | −38.6391 | −1.23871 | ||||||||
\(974\) | −25.4402 | −0.815156 | ||||||||
\(975\) | 50.6123 | 1.62089 | ||||||||
\(976\) | 57.0968 | 1.82762 | ||||||||
\(977\) | −55.6819 | −1.78142 | −0.890712 | − | 0.454569i | \(-0.849793\pi\) | ||||
−0.890712 | + | 0.454569i | \(0.849793\pi\) | |||||||
\(978\) | 72.7512 | 2.32633 | ||||||||
\(979\) | 5.04078 | 0.161104 | ||||||||
\(980\) | 31.7777 | 1.01510 | ||||||||
\(981\) | 22.2648 | 0.710861 | ||||||||
\(982\) | −19.3283 | −0.616791 | ||||||||
\(983\) | −29.7370 | −0.948462 | −0.474231 | − | 0.880400i | \(-0.657274\pi\) | ||||
−0.474231 | + | 0.880400i | \(0.657274\pi\) | |||||||
\(984\) | 163.142 | 5.20077 | ||||||||
\(985\) | 54.1335 | 1.72484 | ||||||||
\(986\) | 22.3871 | 0.712950 | ||||||||
\(987\) | −22.3914 | −0.712727 | ||||||||
\(988\) | 147.578 | 4.69507 | ||||||||
\(989\) | 2.77698 | 0.0883028 | ||||||||
\(990\) | −20.2702 | −0.644228 | ||||||||
\(991\) | 37.0786 | 1.17784 | 0.588920 | − | 0.808191i | \(-0.299553\pi\) | ||||
0.588920 | + | 0.808191i | \(0.299553\pi\) | |||||||
\(992\) | −0.933724 | −0.0296458 | ||||||||
\(993\) | −13.7548 | −0.436497 | ||||||||
\(994\) | −1.07840 | −0.0342048 | ||||||||
\(995\) | 36.4873 | 1.15673 | ||||||||
\(996\) | −155.223 | −4.91842 | ||||||||
\(997\) | 22.3345 | 0.707341 | 0.353671 | − | 0.935370i | \(-0.384933\pi\) | ||||
0.353671 | + | 0.935370i | \(0.384933\pi\) | |||||||
\(998\) | −20.4357 | −0.646880 | ||||||||
\(999\) | −13.8575 | −0.438431 |
(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 | 6047.2.a.a.1.13 | ✓ | 217 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.a.1.13 | ✓ | 217 | 1.1 | even | 1 | trivial |