Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.37 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.169015 | −0.0975810 | −0.0487905 | − | 0.998809i | \(-0.515537\pi\) | ||||
−0.0487905 | + | 0.998809i | \(0.515537\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.814742 | −0.364364 | −0.182182 | − | 0.983265i | \(-0.558316\pi\) | ||||
−0.182182 | + | 0.983265i | \(0.558316\pi\) | |||||||
\(6\) | 0.169015 | 0.0690002 | ||||||||
\(7\) | 3.07096 | 1.16071 | 0.580357 | − | 0.814362i | \(-0.302913\pi\) | ||||
0.580357 | + | 0.814362i | \(0.302913\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.97143 | −0.990478 | ||||||||
\(10\) | 0.814742 | 0.257644 | ||||||||
\(11\) | −2.65913 | −0.801758 | −0.400879 | − | 0.916131i | \(-0.631295\pi\) | ||||
−0.400879 | + | 0.916131i | \(0.631295\pi\) | |||||||
\(12\) | −0.169015 | −0.0487905 | ||||||||
\(13\) | −3.78538 | −1.04987 | −0.524937 | − | 0.851141i | \(-0.675911\pi\) | ||||
−0.524937 | + | 0.851141i | \(0.675911\pi\) | |||||||
\(14\) | −3.07096 | −0.820749 | ||||||||
\(15\) | 0.137704 | 0.0355550 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.48508 | −0.602721 | −0.301360 | − | 0.953510i | \(-0.597441\pi\) | ||||
−0.301360 | + | 0.953510i | \(0.597441\pi\) | |||||||
\(18\) | 2.97143 | 0.700374 | ||||||||
\(19\) | −7.18899 | −1.64927 | −0.824634 | − | 0.565667i | \(-0.808619\pi\) | ||||
−0.824634 | + | 0.565667i | \(0.808619\pi\) | |||||||
\(20\) | −0.814742 | −0.182182 | ||||||||
\(21\) | −0.519040 | −0.113264 | ||||||||
\(22\) | 2.65913 | 0.566928 | ||||||||
\(23\) | 3.37191 | 0.703092 | 0.351546 | − | 0.936171i | \(-0.385656\pi\) | ||||
0.351546 | + | 0.936171i | \(0.385656\pi\) | |||||||
\(24\) | 0.169015 | 0.0345001 | ||||||||
\(25\) | −4.33620 | −0.867239 | ||||||||
\(26\) | 3.78538 | 0.742373 | ||||||||
\(27\) | 1.00926 | 0.194233 | ||||||||
\(28\) | 3.07096 | 0.580357 | ||||||||
\(29\) | −5.80122 | −1.07726 | −0.538629 | − | 0.842543i | \(-0.681058\pi\) | ||||
−0.538629 | + | 0.842543i | \(0.681058\pi\) | |||||||
\(30\) | −0.137704 | −0.0251412 | ||||||||
\(31\) | 4.83287 | 0.868009 | 0.434005 | − | 0.900911i | \(-0.357100\pi\) | ||||
0.434005 | + | 0.900911i | \(0.357100\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.449434 | 0.0782364 | ||||||||
\(34\) | 2.48508 | 0.426188 | ||||||||
\(35\) | −2.50204 | −0.422922 | ||||||||
\(36\) | −2.97143 | −0.495239 | ||||||||
\(37\) | −7.94827 | −1.30669 | −0.653343 | − | 0.757062i | \(-0.726634\pi\) | ||||
−0.653343 | + | 0.757062i | \(0.726634\pi\) | |||||||
\(38\) | 7.18899 | 1.16621 | ||||||||
\(39\) | 0.639787 | 0.102448 | ||||||||
\(40\) | 0.814742 | 0.128822 | ||||||||
\(41\) | −4.40611 | −0.688119 | −0.344059 | − | 0.938948i | \(-0.611802\pi\) | ||||
−0.344059 | + | 0.938948i | \(0.611802\pi\) | |||||||
\(42\) | 0.519040 | 0.0800896 | ||||||||
\(43\) | −2.92068 | −0.445399 | −0.222700 | − | 0.974887i | \(-0.571487\pi\) | ||||
−0.222700 | + | 0.974887i | \(0.571487\pi\) | |||||||
\(44\) | −2.65913 | −0.400879 | ||||||||
\(45\) | 2.42095 | 0.360894 | ||||||||
\(46\) | −3.37191 | −0.497161 | ||||||||
\(47\) | 0.0383619 | 0.00559566 | 0.00279783 | − | 0.999996i | \(-0.499109\pi\) | ||||
0.00279783 | + | 0.999996i | \(0.499109\pi\) | |||||||
\(48\) | −0.169015 | −0.0243953 | ||||||||
\(49\) | 2.43081 | 0.347259 | ||||||||
\(50\) | 4.33620 | 0.613231 | ||||||||
\(51\) | 0.420017 | 0.0588141 | ||||||||
\(52\) | −3.78538 | −0.524937 | ||||||||
\(53\) | 8.11722 | 1.11499 | 0.557493 | − | 0.830182i | \(-0.311763\pi\) | ||||
0.557493 | + | 0.830182i | \(0.311763\pi\) | |||||||
\(54\) | −1.00926 | −0.137343 | ||||||||
\(55\) | 2.16650 | 0.292131 | ||||||||
\(56\) | −3.07096 | −0.410375 | ||||||||
\(57\) | 1.21505 | 0.160937 | ||||||||
\(58\) | 5.80122 | 0.761737 | ||||||||
\(59\) | −6.63420 | −0.863699 | −0.431849 | − | 0.901946i | \(-0.642139\pi\) | ||||
−0.431849 | + | 0.901946i | \(0.642139\pi\) | |||||||
\(60\) | 0.137704 | 0.0177775 | ||||||||
\(61\) | 13.5883 | 1.73980 | 0.869900 | − | 0.493228i | \(-0.164183\pi\) | ||||
0.869900 | + | 0.493228i | \(0.164183\pi\) | |||||||
\(62\) | −4.83287 | −0.613775 | ||||||||
\(63\) | −9.12516 | −1.14966 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.08410 | 0.382536 | ||||||||
\(66\) | −0.449434 | −0.0553215 | ||||||||
\(67\) | −10.0202 | −1.22417 | −0.612084 | − | 0.790793i | \(-0.709668\pi\) | ||||
−0.612084 | + | 0.790793i | \(0.709668\pi\) | |||||||
\(68\) | −2.48508 | −0.301360 | ||||||||
\(69\) | −0.569904 | −0.0686084 | ||||||||
\(70\) | 2.50204 | 0.299051 | ||||||||
\(71\) | 9.18773 | 1.09038 | 0.545191 | − | 0.838312i | \(-0.316457\pi\) | ||||
0.545191 | + | 0.838312i | \(0.316457\pi\) | |||||||
\(72\) | 2.97143 | 0.350187 | ||||||||
\(73\) | −4.01614 | −0.470053 | −0.235027 | − | 0.971989i | \(-0.575518\pi\) | ||||
−0.235027 | + | 0.971989i | \(0.575518\pi\) | |||||||
\(74\) | 7.94827 | 0.923967 | ||||||||
\(75\) | 0.732884 | 0.0846261 | ||||||||
\(76\) | −7.18899 | −0.824634 | ||||||||
\(77\) | −8.16609 | −0.930612 | ||||||||
\(78\) | −0.639787 | −0.0724416 | ||||||||
\(79\) | −2.45176 | −0.275845 | −0.137922 | − | 0.990443i | \(-0.544042\pi\) | ||||
−0.137922 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(80\) | −0.814742 | −0.0910909 | ||||||||
\(81\) | 8.74372 | 0.971524 | ||||||||
\(82\) | 4.40611 | 0.486573 | ||||||||
\(83\) | −1.24187 | −0.136313 | −0.0681565 | − | 0.997675i | \(-0.521712\pi\) | ||||
−0.0681565 | + | 0.997675i | \(0.521712\pi\) | |||||||
\(84\) | −0.519040 | −0.0566319 | ||||||||
\(85\) | 2.02470 | 0.219609 | ||||||||
\(86\) | 2.92068 | 0.314945 | ||||||||
\(87\) | 0.980494 | 0.105120 | ||||||||
\(88\) | 2.65913 | 0.283464 | ||||||||
\(89\) | 0.972868 | 0.103124 | 0.0515619 | − | 0.998670i | \(-0.483580\pi\) | ||||
0.0515619 | + | 0.998670i | \(0.483580\pi\) | |||||||
\(90\) | −2.42095 | −0.255191 | ||||||||
\(91\) | −11.6247 | −1.21860 | ||||||||
\(92\) | 3.37191 | 0.351546 | ||||||||
\(93\) | −0.816829 | −0.0847012 | ||||||||
\(94\) | −0.0383619 | −0.00395673 | ||||||||
\(95\) | 5.85717 | 0.600933 | ||||||||
\(96\) | 0.169015 | 0.0172501 | ||||||||
\(97\) | 18.0126 | 1.82890 | 0.914450 | − | 0.404700i | \(-0.132624\pi\) | ||||
0.914450 | + | 0.404700i | \(0.132624\pi\) | |||||||
\(98\) | −2.43081 | −0.245549 | ||||||||
\(99\) | 7.90143 | 0.794124 | ||||||||
\(100\) | −4.33620 | −0.433620 | ||||||||
\(101\) | 10.1712 | 1.01207 | 0.506036 | − | 0.862512i | \(-0.331110\pi\) | ||||
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(102\) | −0.420017 | −0.0415879 | ||||||||
\(103\) | −14.0294 | −1.38236 | −0.691179 | − | 0.722684i | \(-0.742908\pi\) | ||||
−0.691179 | + | 0.722684i | \(0.742908\pi\) | |||||||
\(104\) | 3.78538 | 0.371187 | ||||||||
\(105\) | 0.422883 | 0.0412692 | ||||||||
\(106\) | −8.11722 | −0.788414 | ||||||||
\(107\) | 15.0755 | 1.45740 | 0.728700 | − | 0.684833i | \(-0.240125\pi\) | ||||
0.728700 | + | 0.684833i | \(0.240125\pi\) | |||||||
\(108\) | 1.00926 | 0.0971165 | ||||||||
\(109\) | 4.89644 | 0.468994 | 0.234497 | − | 0.972117i | \(-0.424656\pi\) | ||||
0.234497 | + | 0.972117i | \(0.424656\pi\) | |||||||
\(110\) | −2.16650 | −0.206568 | ||||||||
\(111\) | 1.34338 | 0.127508 | ||||||||
\(112\) | 3.07096 | 0.290179 | ||||||||
\(113\) | 14.5861 | 1.37215 | 0.686075 | − | 0.727531i | \(-0.259332\pi\) | ||||
0.686075 | + | 0.727531i | \(0.259332\pi\) | |||||||
\(114\) | −1.21505 | −0.113800 | ||||||||
\(115\) | −2.74723 | −0.256181 | ||||||||
\(116\) | −5.80122 | −0.538629 | ||||||||
\(117\) | 11.2480 | 1.03988 | ||||||||
\(118\) | 6.63420 | 0.610727 | ||||||||
\(119\) | −7.63159 | −0.699587 | ||||||||
\(120\) | −0.137704 | −0.0125706 | ||||||||
\(121\) | −3.92903 | −0.357184 | ||||||||
\(122\) | −13.5883 | −1.23022 | ||||||||
\(123\) | 0.744700 | 0.0671473 | ||||||||
\(124\) | 4.83287 | 0.434005 | ||||||||
\(125\) | 7.60659 | 0.680354 | ||||||||
\(126\) | 9.12516 | 0.812934 | ||||||||
\(127\) | −10.1576 | −0.901337 | −0.450669 | − | 0.892691i | \(-0.648814\pi\) | ||||
−0.450669 | + | 0.892691i | \(0.648814\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.493639 | 0.0434625 | ||||||||
\(130\) | −3.08410 | −0.270494 | ||||||||
\(131\) | 6.40092 | 0.559251 | 0.279625 | − | 0.960109i | \(-0.409790\pi\) | ||||
0.279625 | + | 0.960109i | \(0.409790\pi\) | |||||||
\(132\) | 0.449434 | 0.0391182 | ||||||||
\(133\) | −22.0771 | −1.91433 | ||||||||
\(134\) | 10.0202 | 0.865617 | ||||||||
\(135\) | −0.822289 | −0.0707714 | ||||||||
\(136\) | 2.48508 | 0.213094 | ||||||||
\(137\) | 12.3450 | 1.05470 | 0.527351 | − | 0.849648i | \(-0.323185\pi\) | ||||
0.527351 | + | 0.849648i | \(0.323185\pi\) | |||||||
\(138\) | 0.569904 | 0.0485135 | ||||||||
\(139\) | 8.03274 | 0.681328 | 0.340664 | − | 0.940185i | \(-0.389348\pi\) | ||||
0.340664 | + | 0.940185i | \(0.389348\pi\) | |||||||
\(140\) | −2.50204 | −0.211461 | ||||||||
\(141\) | −0.00648375 | −0.000546031 0 | ||||||||
\(142\) | −9.18773 | −0.771017 | ||||||||
\(143\) | 10.0658 | 0.841745 | ||||||||
\(144\) | −2.97143 | −0.247619 | ||||||||
\(145\) | 4.72649 | 0.392514 | ||||||||
\(146\) | 4.01614 | 0.332378 | ||||||||
\(147\) | −0.410844 | −0.0338859 | ||||||||
\(148\) | −7.94827 | −0.653343 | ||||||||
\(149\) | −11.1522 | −0.913625 | −0.456813 | − | 0.889563i | \(-0.651009\pi\) | ||||
−0.456813 | + | 0.889563i | \(0.651009\pi\) | |||||||
\(150\) | −0.732884 | −0.0598397 | ||||||||
\(151\) | 7.09851 | 0.577668 | 0.288834 | − | 0.957379i | \(-0.406732\pi\) | ||||
0.288834 | + | 0.957379i | \(0.406732\pi\) | |||||||
\(152\) | 7.18899 | 0.583104 | ||||||||
\(153\) | 7.38426 | 0.596982 | ||||||||
\(154\) | 8.16609 | 0.658042 | ||||||||
\(155\) | −3.93754 | −0.316271 | ||||||||
\(156\) | 0.639787 | 0.0512239 | ||||||||
\(157\) | 5.41650 | 0.432284 | 0.216142 | − | 0.976362i | \(-0.430653\pi\) | ||||
0.216142 | + | 0.976362i | \(0.430653\pi\) | |||||||
\(158\) | 2.45176 | 0.195052 | ||||||||
\(159\) | −1.37194 | −0.108802 | ||||||||
\(160\) | 0.814742 | 0.0644110 | ||||||||
\(161\) | 10.3550 | 0.816089 | ||||||||
\(162\) | −8.74372 | −0.686972 | ||||||||
\(163\) | 23.5997 | 1.84847 | 0.924234 | − | 0.381827i | \(-0.124705\pi\) | ||||
0.924234 | + | 0.381827i | \(0.124705\pi\) | |||||||
\(164\) | −4.40611 | −0.344059 | ||||||||
\(165\) | −0.366172 | −0.0285065 | ||||||||
\(166\) | 1.24187 | 0.0963878 | ||||||||
\(167\) | −16.7950 | −1.29964 | −0.649819 | − | 0.760089i | \(-0.725156\pi\) | ||||
−0.649819 | + | 0.760089i | \(0.725156\pi\) | |||||||
\(168\) | 0.519040 | 0.0400448 | ||||||||
\(169\) | 1.32908 | 0.102237 | ||||||||
\(170\) | −2.02470 | −0.155287 | ||||||||
\(171\) | 21.3616 | 1.63356 | ||||||||
\(172\) | −2.92068 | −0.222700 | ||||||||
\(173\) | 8.69062 | 0.660735 | 0.330368 | − | 0.943852i | \(-0.392827\pi\) | ||||
0.330368 | + | 0.943852i | \(0.392827\pi\) | |||||||
\(174\) | −0.980494 | −0.0743311 | ||||||||
\(175\) | −13.3163 | −1.00662 | ||||||||
\(176\) | −2.65913 | −0.200439 | ||||||||
\(177\) | 1.12128 | 0.0842806 | ||||||||
\(178\) | −0.972868 | −0.0729196 | ||||||||
\(179\) | 0.867658 | 0.0648518 | 0.0324259 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324259 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(180\) | 2.42095 | 0.180447 | ||||||||
\(181\) | −2.06989 | −0.153854 | −0.0769270 | − | 0.997037i | \(-0.524511\pi\) | ||||
−0.0769270 | + | 0.997037i | \(0.524511\pi\) | |||||||
\(182\) | 11.6247 | 0.861684 | ||||||||
\(183\) | −2.29663 | −0.169771 | ||||||||
\(184\) | −3.37191 | −0.248580 | ||||||||
\(185\) | 6.47578 | 0.476109 | ||||||||
\(186\) | 0.816829 | 0.0598928 | ||||||||
\(187\) | 6.60816 | 0.483236 | ||||||||
\(188\) | 0.0383619 | 0.00279783 | ||||||||
\(189\) | 3.09941 | 0.225449 | ||||||||
\(190\) | −5.85717 | −0.424924 | ||||||||
\(191\) | 1.35941 | 0.0983632 | 0.0491816 | − | 0.998790i | \(-0.484339\pi\) | ||||
0.0491816 | + | 0.998790i | \(0.484339\pi\) | |||||||
\(192\) | −0.169015 | −0.0121976 | ||||||||
\(193\) | −15.9083 | −1.14510 | −0.572551 | − | 0.819869i | \(-0.694046\pi\) | ||||
−0.572551 | + | 0.819869i | \(0.694046\pi\) | |||||||
\(194\) | −18.0126 | −1.29323 | ||||||||
\(195\) | −0.521261 | −0.0373283 | ||||||||
\(196\) | 2.43081 | 0.173629 | ||||||||
\(197\) | 14.9004 | 1.06161 | 0.530805 | − | 0.847494i | \(-0.321890\pi\) | ||||
0.530805 | + | 0.847494i | \(0.321890\pi\) | |||||||
\(198\) | −7.90143 | −0.561530 | ||||||||
\(199\) | −11.8598 | −0.840719 | −0.420359 | − | 0.907358i | \(-0.638096\pi\) | ||||
−0.420359 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(200\) | 4.33620 | 0.306615 | ||||||||
\(201\) | 1.69357 | 0.119455 | ||||||||
\(202\) | −10.1712 | −0.715644 | ||||||||
\(203\) | −17.8153 | −1.25039 | ||||||||
\(204\) | 0.420017 | 0.0294071 | ||||||||
\(205\) | 3.58984 | 0.250725 | ||||||||
\(206\) | 14.0294 | 0.977475 | ||||||||
\(207\) | −10.0194 | −0.696397 | ||||||||
\(208\) | −3.78538 | −0.262469 | ||||||||
\(209\) | 19.1165 | 1.32231 | ||||||||
\(210\) | −0.422883 | −0.0291817 | ||||||||
\(211\) | −9.12273 | −0.628034 | −0.314017 | − | 0.949417i | \(-0.601675\pi\) | ||||
−0.314017 | + | 0.949417i | \(0.601675\pi\) | |||||||
\(212\) | 8.11722 | 0.557493 | ||||||||
\(213\) | −1.55287 | −0.106401 | ||||||||
\(214\) | −15.0755 | −1.03054 | ||||||||
\(215\) | 2.37960 | 0.162287 | ||||||||
\(216\) | −1.00926 | −0.0686717 | ||||||||
\(217\) | 14.8416 | 1.00751 | ||||||||
\(218\) | −4.89644 | −0.331629 | ||||||||
\(219\) | 0.678788 | 0.0458683 | ||||||||
\(220\) | 2.16650 | 0.146066 | ||||||||
\(221\) | 9.40697 | 0.632781 | ||||||||
\(222\) | −1.34338 | −0.0901617 | ||||||||
\(223\) | 2.63638 | 0.176545 | 0.0882725 | − | 0.996096i | \(-0.471865\pi\) | ||||
0.0882725 | + | 0.996096i | \(0.471865\pi\) | |||||||
\(224\) | −3.07096 | −0.205187 | ||||||||
\(225\) | 12.8847 | 0.858981 | ||||||||
\(226\) | −14.5861 | −0.970256 | ||||||||
\(227\) | −8.03189 | −0.533095 | −0.266548 | − | 0.963822i | \(-0.585883\pi\) | ||||
−0.266548 | + | 0.963822i | \(0.585883\pi\) | |||||||
\(228\) | 1.21505 | 0.0804686 | ||||||||
\(229\) | 12.1310 | 0.801640 | 0.400820 | − | 0.916157i | \(-0.368725\pi\) | ||||
0.400820 | + | 0.916157i | \(0.368725\pi\) | |||||||
\(230\) | 2.74723 | 0.181147 | ||||||||
\(231\) | 1.38019 | 0.0908101 | ||||||||
\(232\) | 5.80122 | 0.380868 | ||||||||
\(233\) | 2.20968 | 0.144761 | 0.0723805 | − | 0.997377i | \(-0.476940\pi\) | ||||
0.0723805 | + | 0.997377i | \(0.476940\pi\) | |||||||
\(234\) | −11.2480 | −0.735305 | ||||||||
\(235\) | −0.0312551 | −0.00203886 | ||||||||
\(236\) | −6.63420 | −0.431849 | ||||||||
\(237\) | 0.414385 | 0.0269172 | ||||||||
\(238\) | 7.63159 | 0.494683 | ||||||||
\(239\) | 7.70534 | 0.498417 | 0.249208 | − | 0.968450i | \(-0.419830\pi\) | ||||
0.249208 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(240\) | 0.137704 | 0.00888874 | ||||||||
\(241\) | 23.9056 | 1.53990 | 0.769949 | − | 0.638106i | \(-0.220282\pi\) | ||||
0.769949 | + | 0.638106i | \(0.220282\pi\) | |||||||
\(242\) | 3.92903 | 0.252567 | ||||||||
\(243\) | −4.50561 | −0.289035 | ||||||||
\(244\) | 13.5883 | 0.869900 | ||||||||
\(245\) | −1.98048 | −0.126528 | ||||||||
\(246\) | −0.744700 | −0.0474803 | ||||||||
\(247\) | 27.2130 | 1.73152 | ||||||||
\(248\) | −4.83287 | −0.306888 | ||||||||
\(249\) | 0.209895 | 0.0133016 | ||||||||
\(250\) | −7.60659 | −0.481083 | ||||||||
\(251\) | −23.1486 | −1.46112 | −0.730562 | − | 0.682846i | \(-0.760742\pi\) | ||||
−0.730562 | + | 0.682846i | \(0.760742\pi\) | |||||||
\(252\) | −9.12516 | −0.574831 | ||||||||
\(253\) | −8.96634 | −0.563709 | ||||||||
\(254\) | 10.1576 | 0.637342 | ||||||||
\(255\) | −0.342205 | −0.0214297 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.33938 | 0.333062 | 0.166531 | − | 0.986036i | \(-0.446743\pi\) | ||||
0.166531 | + | 0.986036i | \(0.446743\pi\) | |||||||
\(258\) | −0.493639 | −0.0307326 | ||||||||
\(259\) | −24.4088 | −1.51669 | ||||||||
\(260\) | 3.08410 | 0.191268 | ||||||||
\(261\) | 17.2379 | 1.06700 | ||||||||
\(262\) | −6.40092 | −0.395450 | ||||||||
\(263\) | 3.15421 | 0.194497 | 0.0972483 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972483 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(264\) | −0.449434 | −0.0276607 | ||||||||
\(265\) | −6.61344 | −0.406260 | ||||||||
\(266\) | 22.0771 | 1.35363 | ||||||||
\(267\) | −0.164430 | −0.0100629 | ||||||||
\(268\) | −10.0202 | −0.612084 | ||||||||
\(269\) | −13.1864 | −0.803988 | −0.401994 | − | 0.915642i | \(-0.631683\pi\) | ||||
−0.401994 | + | 0.915642i | \(0.631683\pi\) | |||||||
\(270\) | 0.822289 | 0.0500429 | ||||||||
\(271\) | 10.5521 | 0.640995 | 0.320497 | − | 0.947249i | \(-0.396150\pi\) | ||||
0.320497 | + | 0.947249i | \(0.396150\pi\) | |||||||
\(272\) | −2.48508 | −0.150680 | ||||||||
\(273\) | 1.96476 | 0.118913 | ||||||||
\(274\) | −12.3450 | −0.745787 | ||||||||
\(275\) | 11.5305 | 0.695316 | ||||||||
\(276\) | −0.569904 | −0.0343042 | ||||||||
\(277\) | −25.7575 | −1.54762 | −0.773808 | − | 0.633420i | \(-0.781651\pi\) | ||||
−0.773808 | + | 0.633420i | \(0.781651\pi\) | |||||||
\(278\) | −8.03274 | −0.481772 | ||||||||
\(279\) | −14.3606 | −0.859744 | ||||||||
\(280\) | 2.50204 | 0.149526 | ||||||||
\(281\) | 4.45765 | 0.265921 | 0.132961 | − | 0.991121i | \(-0.457552\pi\) | ||||
0.132961 | + | 0.991121i | \(0.457552\pi\) | |||||||
\(282\) | 0.00648375 | 0.000386102 0 | ||||||||
\(283\) | 1.07317 | 0.0637935 | 0.0318968 | − | 0.999491i | \(-0.489845\pi\) | ||||
0.0318968 | + | 0.999491i | \(0.489845\pi\) | |||||||
\(284\) | 9.18773 | 0.545191 | ||||||||
\(285\) | −0.989951 | −0.0586397 | ||||||||
\(286\) | −10.0658 | −0.595204 | ||||||||
\(287\) | −13.5310 | −0.798709 | ||||||||
\(288\) | 2.97143 | 0.175093 | ||||||||
\(289\) | −10.8244 | −0.636728 | ||||||||
\(290\) | −4.72649 | −0.277549 | ||||||||
\(291\) | −3.04440 | −0.178466 | ||||||||
\(292\) | −4.01614 | −0.235027 | ||||||||
\(293\) | −21.7034 | −1.26793 | −0.633964 | − | 0.773363i | \(-0.718573\pi\) | ||||
−0.633964 | + | 0.773363i | \(0.718573\pi\) | |||||||
\(294\) | 0.410844 | 0.0239609 | ||||||||
\(295\) | 5.40516 | 0.314700 | ||||||||
\(296\) | 7.94827 | 0.461984 | ||||||||
\(297\) | −2.68376 | −0.155728 | ||||||||
\(298\) | 11.1522 | 0.646031 | ||||||||
\(299\) | −12.7639 | −0.738158 | ||||||||
\(300\) | 0.732884 | 0.0423131 | ||||||||
\(301\) | −8.96929 | −0.516981 | ||||||||
\(302\) | −7.09851 | −0.408473 | ||||||||
\(303\) | −1.71909 | −0.0987591 | ||||||||
\(304\) | −7.18899 | −0.412317 | ||||||||
\(305\) | −11.0709 | −0.633920 | ||||||||
\(306\) | −7.38426 | −0.422130 | ||||||||
\(307\) | −8.66351 | −0.494453 | −0.247226 | − | 0.968958i | \(-0.579519\pi\) | ||||
−0.247226 | + | 0.968958i | \(0.579519\pi\) | |||||||
\(308\) | −8.16609 | −0.465306 | ||||||||
\(309\) | 2.37118 | 0.134892 | ||||||||
\(310\) | 3.93754 | 0.223637 | ||||||||
\(311\) | 15.2654 | 0.865623 | 0.432812 | − | 0.901484i | \(-0.357522\pi\) | ||||
0.432812 | + | 0.901484i | \(0.357522\pi\) | |||||||
\(312\) | −0.639787 | −0.0362208 | ||||||||
\(313\) | −17.2240 | −0.973557 | −0.486778 | − | 0.873526i | \(-0.661828\pi\) | ||||
−0.486778 | + | 0.873526i | \(0.661828\pi\) | |||||||
\(314\) | −5.41650 | −0.305671 | ||||||||
\(315\) | 7.43465 | 0.418895 | ||||||||
\(316\) | −2.45176 | −0.137922 | ||||||||
\(317\) | −14.5111 | −0.815023 | −0.407512 | − | 0.913200i | \(-0.633603\pi\) | ||||
−0.407512 | + | 0.913200i | \(0.633603\pi\) | |||||||
\(318\) | 1.37194 | 0.0769343 | ||||||||
\(319\) | 15.4262 | 0.863701 | ||||||||
\(320\) | −0.814742 | −0.0455454 | ||||||||
\(321\) | −2.54798 | −0.142215 | ||||||||
\(322\) | −10.3550 | −0.577062 | ||||||||
\(323\) | 17.8652 | 0.994048 | ||||||||
\(324\) | 8.74372 | 0.485762 | ||||||||
\(325\) | 16.4141 | 0.910492 | ||||||||
\(326\) | −23.5997 | −1.30706 | ||||||||
\(327\) | −0.827573 | −0.0457649 | ||||||||
\(328\) | 4.40611 | 0.243287 | ||||||||
\(329\) | 0.117808 | 0.00649497 | ||||||||
\(330\) | 0.366172 | 0.0201571 | ||||||||
\(331\) | −19.6185 | −1.07833 | −0.539165 | − | 0.842200i | \(-0.681260\pi\) | ||||
−0.539165 | + | 0.842200i | \(0.681260\pi\) | |||||||
\(332\) | −1.24187 | −0.0681565 | ||||||||
\(333\) | 23.6177 | 1.29424 | ||||||||
\(334\) | 16.7950 | 0.918984 | ||||||||
\(335\) | 8.16391 | 0.446042 | ||||||||
\(336\) | −0.519040 | −0.0283159 | ||||||||
\(337\) | 5.02933 | 0.273965 | 0.136983 | − | 0.990573i | \(-0.456260\pi\) | ||||
0.136983 | + | 0.990573i | \(0.456260\pi\) | |||||||
\(338\) | −1.32908 | −0.0722923 | ||||||||
\(339\) | −2.46528 | −0.133896 | ||||||||
\(340\) | 2.02470 | 0.109805 | ||||||||
\(341\) | −12.8512 | −0.695933 | ||||||||
\(342\) | −21.3616 | −1.15510 | ||||||||
\(343\) | −14.0318 | −0.757647 | ||||||||
\(344\) | 2.92068 | 0.157472 | ||||||||
\(345\) | 0.464325 | 0.0249984 | ||||||||
\(346\) | −8.69062 | −0.467210 | ||||||||
\(347\) | 2.17304 | 0.116655 | 0.0583275 | − | 0.998298i | \(-0.481423\pi\) | ||||
0.0583275 | + | 0.998298i | \(0.481423\pi\) | |||||||
\(348\) | 0.980494 | 0.0525600 | ||||||||
\(349\) | −21.0770 | −1.12823 | −0.564113 | − | 0.825698i | \(-0.690782\pi\) | ||||
−0.564113 | + | 0.825698i | \(0.690782\pi\) | |||||||
\(350\) | 13.3163 | 0.711786 | ||||||||
\(351\) | −3.82044 | −0.203920 | ||||||||
\(352\) | 2.65913 | 0.141732 | ||||||||
\(353\) | 12.5787 | 0.669495 | 0.334748 | − | 0.942308i | \(-0.391349\pi\) | ||||
0.334748 | + | 0.942308i | \(0.391349\pi\) | |||||||
\(354\) | −1.12128 | −0.0595954 | ||||||||
\(355\) | −7.48562 | −0.397296 | ||||||||
\(356\) | 0.972868 | 0.0515619 | ||||||||
\(357\) | 1.28986 | 0.0682664 | ||||||||
\(358\) | −0.867658 | −0.0458571 | ||||||||
\(359\) | −2.31276 | −0.122063 | −0.0610315 | − | 0.998136i | \(-0.519439\pi\) | ||||
−0.0610315 | + | 0.998136i | \(0.519439\pi\) | |||||||
\(360\) | −2.42095 | −0.127595 | ||||||||
\(361\) | 32.6816 | 1.72008 | ||||||||
\(362\) | 2.06989 | 0.108791 | ||||||||
\(363\) | 0.664066 | 0.0348544 | ||||||||
\(364\) | −11.6247 | −0.609302 | ||||||||
\(365\) | 3.27211 | 0.171270 | ||||||||
\(366\) | 2.29663 | 0.120047 | ||||||||
\(367\) | −0.557091 | −0.0290799 | −0.0145400 | − | 0.999894i | \(-0.504628\pi\) | ||||
−0.0145400 | + | 0.999894i | \(0.504628\pi\) | |||||||
\(368\) | 3.37191 | 0.175773 | ||||||||
\(369\) | 13.0925 | 0.681566 | ||||||||
\(370\) | −6.47578 | −0.336660 | ||||||||
\(371\) | 24.9277 | 1.29418 | ||||||||
\(372\) | −0.816829 | −0.0423506 | ||||||||
\(373\) | −10.9109 | −0.564943 | −0.282471 | − | 0.959276i | \(-0.591154\pi\) | ||||
−0.282471 | + | 0.959276i | \(0.591154\pi\) | |||||||
\(374\) | −6.60816 | −0.341700 | ||||||||
\(375\) | −1.28563 | −0.0663896 | ||||||||
\(376\) | −0.0383619 | −0.00197837 | ||||||||
\(377\) | 21.9598 | 1.13099 | ||||||||
\(378\) | −3.09941 | −0.159417 | ||||||||
\(379\) | 18.4773 | 0.949113 | 0.474557 | − | 0.880225i | \(-0.342608\pi\) | ||||
0.474557 | + | 0.880225i | \(0.342608\pi\) | |||||||
\(380\) | 5.85717 | 0.300466 | ||||||||
\(381\) | 1.71678 | 0.0879534 | ||||||||
\(382\) | −1.35941 | −0.0695533 | ||||||||
\(383\) | −19.6251 | −1.00279 | −0.501397 | − | 0.865217i | \(-0.667180\pi\) | ||||
−0.501397 | + | 0.865217i | \(0.667180\pi\) | |||||||
\(384\) | 0.169015 | 0.00862503 | ||||||||
\(385\) | 6.65325 | 0.339081 | ||||||||
\(386\) | 15.9083 | 0.809709 | ||||||||
\(387\) | 8.67860 | 0.441158 | ||||||||
\(388\) | 18.0126 | 0.914450 | ||||||||
\(389\) | −25.5547 | −1.29567 | −0.647837 | − | 0.761779i | \(-0.724326\pi\) | ||||
−0.647837 | + | 0.761779i | \(0.724326\pi\) | |||||||
\(390\) | 0.521261 | 0.0263951 | ||||||||
\(391\) | −8.37947 | −0.423768 | ||||||||
\(392\) | −2.43081 | −0.122774 | ||||||||
\(393\) | −1.08185 | −0.0545723 | ||||||||
\(394\) | −14.9004 | −0.750672 | ||||||||
\(395\) | 1.99755 | 0.100508 | ||||||||
\(396\) | 7.90143 | 0.397062 | ||||||||
\(397\) | −24.6808 | −1.23870 | −0.619348 | − | 0.785117i | \(-0.712603\pi\) | ||||
−0.619348 | + | 0.785117i | \(0.712603\pi\) | |||||||
\(398\) | 11.8598 | 0.594478 | ||||||||
\(399\) | 3.73137 | 0.186802 | ||||||||
\(400\) | −4.33620 | −0.216810 | ||||||||
\(401\) | 20.4996 | 1.02370 | 0.511850 | − | 0.859075i | \(-0.328960\pi\) | ||||
0.511850 | + | 0.859075i | \(0.328960\pi\) | |||||||
\(402\) | −1.69357 | −0.0844678 | ||||||||
\(403\) | −18.2942 | −0.911301 | ||||||||
\(404\) | 10.1712 | 0.506036 | ||||||||
\(405\) | −7.12387 | −0.353988 | ||||||||
\(406\) | 17.8153 | 0.884159 | ||||||||
\(407\) | 21.1355 | 1.04765 | ||||||||
\(408\) | −0.420017 | −0.0207939 | ||||||||
\(409\) | 13.6234 | 0.673632 | 0.336816 | − | 0.941570i | \(-0.390650\pi\) | ||||
0.336816 | + | 0.941570i | \(0.390650\pi\) | |||||||
\(410\) | −3.58984 | −0.177290 | ||||||||
\(411\) | −2.08649 | −0.102919 | ||||||||
\(412\) | −14.0294 | −0.691179 | ||||||||
\(413\) | −20.3734 | −1.00251 | ||||||||
\(414\) | 10.0194 | 0.492427 | ||||||||
\(415\) | 1.01180 | 0.0496675 | ||||||||
\(416\) | 3.78538 | 0.185593 | ||||||||
\(417\) | −1.35766 | −0.0664847 | ||||||||
\(418\) | −19.1165 | −0.935017 | ||||||||
\(419\) | −0.236224 | −0.0115403 | −0.00577015 | − | 0.999983i | \(-0.501837\pi\) | ||||
−0.00577015 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(420\) | 0.422883 | 0.0206346 | ||||||||
\(421\) | −40.4372 | −1.97079 | −0.985394 | − | 0.170288i | \(-0.945530\pi\) | ||||
−0.985394 | + | 0.170288i | \(0.945530\pi\) | |||||||
\(422\) | 9.12273 | 0.444087 | ||||||||
\(423\) | −0.113990 | −0.00554238 | ||||||||
\(424\) | −8.11722 | −0.394207 | ||||||||
\(425\) | 10.7758 | 0.522703 | ||||||||
\(426\) | 1.55287 | 0.0752366 | ||||||||
\(427\) | 41.7291 | 2.01941 | ||||||||
\(428\) | 15.0755 | 0.728700 | ||||||||
\(429\) | −1.70128 | −0.0821384 | ||||||||
\(430\) | −2.37960 | −0.114754 | ||||||||
\(431\) | 38.0549 | 1.83304 | 0.916520 | − | 0.399988i | \(-0.130986\pi\) | ||||
0.916520 | + | 0.399988i | \(0.130986\pi\) | |||||||
\(432\) | 1.00926 | 0.0485582 | ||||||||
\(433\) | 15.0745 | 0.724437 | 0.362218 | − | 0.932093i | \(-0.382019\pi\) | ||||
0.362218 | + | 0.932093i | \(0.382019\pi\) | |||||||
\(434\) | −14.8416 | −0.712418 | ||||||||
\(435\) | −0.798850 | −0.0383019 | ||||||||
\(436\) | 4.89644 | 0.234497 | ||||||||
\(437\) | −24.2406 | −1.15959 | ||||||||
\(438\) | −0.678788 | −0.0324338 | ||||||||
\(439\) | 31.0098 | 1.48002 | 0.740008 | − | 0.672598i | \(-0.234822\pi\) | ||||
0.740008 | + | 0.672598i | \(0.234822\pi\) | |||||||
\(440\) | −2.16650 | −0.103284 | ||||||||
\(441\) | −7.22299 | −0.343952 | ||||||||
\(442\) | −9.40697 | −0.447444 | ||||||||
\(443\) | −25.9257 | −1.23177 | −0.615883 | − | 0.787837i | \(-0.711201\pi\) | ||||
−0.615883 | + | 0.787837i | \(0.711201\pi\) | |||||||
\(444\) | 1.34338 | 0.0637539 | ||||||||
\(445\) | −0.792636 | −0.0375746 | ||||||||
\(446\) | −2.63638 | −0.124836 | ||||||||
\(447\) | 1.88490 | 0.0891525 | ||||||||
\(448\) | 3.07096 | 0.145089 | ||||||||
\(449\) | 18.0562 | 0.852124 | 0.426062 | − | 0.904694i | \(-0.359901\pi\) | ||||
0.426062 | + | 0.904694i | \(0.359901\pi\) | |||||||
\(450\) | −12.8847 | −0.607391 | ||||||||
\(451\) | 11.7164 | 0.551705 | ||||||||
\(452\) | 14.5861 | 0.686075 | ||||||||
\(453\) | −1.19976 | −0.0563695 | ||||||||
\(454\) | 8.03189 | 0.376955 | ||||||||
\(455\) | 9.47117 | 0.444015 | ||||||||
\(456\) | −1.21505 | −0.0568999 | ||||||||
\(457\) | 9.37221 | 0.438413 | 0.219207 | − | 0.975678i | \(-0.429653\pi\) | ||||
0.219207 | + | 0.975678i | \(0.429653\pi\) | |||||||
\(458\) | −12.1310 | −0.566845 | ||||||||
\(459\) | −2.50810 | −0.117068 | ||||||||
\(460\) | −2.74723 | −0.128090 | ||||||||
\(461\) | 28.3684 | 1.32125 | 0.660623 | − | 0.750718i | \(-0.270292\pi\) | ||||
0.660623 | + | 0.750718i | \(0.270292\pi\) | |||||||
\(462\) | −1.38019 | −0.0642124 | ||||||||
\(463\) | 11.6167 | 0.539873 | 0.269936 | − | 0.962878i | \(-0.412997\pi\) | ||||
0.269936 | + | 0.962878i | \(0.412997\pi\) | |||||||
\(464\) | −5.80122 | −0.269315 | ||||||||
\(465\) | 0.665505 | 0.0308620 | ||||||||
\(466\) | −2.20968 | −0.102362 | ||||||||
\(467\) | 28.8799 | 1.33640 | 0.668200 | − | 0.743981i | \(-0.267065\pi\) | ||||
0.668200 | + | 0.743981i | \(0.267065\pi\) | |||||||
\(468\) | 11.2480 | 0.519939 | ||||||||
\(469\) | −30.7718 | −1.42091 | ||||||||
\(470\) | 0.0312551 | 0.00144169 | ||||||||
\(471\) | −0.915471 | −0.0421827 | ||||||||
\(472\) | 6.63420 | 0.305364 | ||||||||
\(473\) | 7.76646 | 0.357102 | ||||||||
\(474\) | −0.414385 | −0.0190334 | ||||||||
\(475\) | 31.1729 | 1.43031 | ||||||||
\(476\) | −7.63159 | −0.349793 | ||||||||
\(477\) | −24.1198 | −1.10437 | ||||||||
\(478\) | −7.70534 | −0.352434 | ||||||||
\(479\) | 14.5624 | 0.665372 | 0.332686 | − | 0.943038i | \(-0.392045\pi\) | ||||
0.332686 | + | 0.943038i | \(0.392045\pi\) | |||||||
\(480\) | −0.137704 | −0.00628529 | ||||||||
\(481\) | 30.0872 | 1.37186 | ||||||||
\(482\) | −23.9056 | −1.08887 | ||||||||
\(483\) | −1.75015 | −0.0796348 | ||||||||
\(484\) | −3.92903 | −0.178592 | ||||||||
\(485\) | −14.6756 | −0.666384 | ||||||||
\(486\) | 4.50561 | 0.204379 | ||||||||
\(487\) | −29.8995 | −1.35487 | −0.677437 | − | 0.735581i | \(-0.736909\pi\) | ||||
−0.677437 | + | 0.735581i | \(0.736909\pi\) | |||||||
\(488\) | −13.5883 | −0.615112 | ||||||||
\(489\) | −3.98870 | −0.180375 | ||||||||
\(490\) | 1.98048 | 0.0894691 | ||||||||
\(491\) | 30.1072 | 1.35872 | 0.679359 | − | 0.733806i | \(-0.262258\pi\) | ||||
0.679359 | + | 0.733806i | \(0.262258\pi\) | |||||||
\(492\) | 0.744700 | 0.0335737 | ||||||||
\(493\) | 14.4165 | 0.649286 | ||||||||
\(494\) | −27.2130 | −1.22437 | ||||||||
\(495\) | −6.43762 | −0.289350 | ||||||||
\(496\) | 4.83287 | 0.217002 | ||||||||
\(497\) | 28.2152 | 1.26562 | ||||||||
\(498\) | −0.209895 | −0.00940562 | ||||||||
\(499\) | 35.4216 | 1.58569 | 0.792845 | − | 0.609424i | \(-0.208599\pi\) | ||||
0.792845 | + | 0.609424i | \(0.208599\pi\) | |||||||
\(500\) | 7.60659 | 0.340177 | ||||||||
\(501\) | 2.83862 | 0.126820 | ||||||||
\(502\) | 23.1486 | 1.03317 | ||||||||
\(503\) | 7.53970 | 0.336179 | 0.168089 | − | 0.985772i | \(-0.446240\pi\) | ||||
0.168089 | + | 0.985772i | \(0.446240\pi\) | |||||||
\(504\) | 9.12516 | 0.406467 | ||||||||
\(505\) | −8.28691 | −0.368763 | ||||||||
\(506\) | 8.96634 | 0.398603 | ||||||||
\(507\) | −0.224634 | −0.00997637 | ||||||||
\(508\) | −10.1576 | −0.450669 | ||||||||
\(509\) | 2.55867 | 0.113411 | 0.0567055 | − | 0.998391i | \(-0.481940\pi\) | ||||
0.0567055 | + | 0.998391i | \(0.481940\pi\) | |||||||
\(510\) | 0.342205 | 0.0151531 | ||||||||
\(511\) | −12.3334 | −0.545597 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −7.25559 | −0.320342 | ||||||||
\(514\) | −5.33938 | −0.235510 | ||||||||
\(515\) | 11.4303 | 0.503681 | ||||||||
\(516\) | 0.493639 | 0.0217312 | ||||||||
\(517\) | −0.102009 | −0.00448637 | ||||||||
\(518\) | 24.4088 | 1.07246 | ||||||||
\(519\) | −1.46885 | −0.0644752 | ||||||||
\(520\) | −3.08410 | −0.135247 | ||||||||
\(521\) | −7.45017 | −0.326398 | −0.163199 | − | 0.986593i | \(-0.552181\pi\) | ||||
−0.163199 | + | 0.986593i | \(0.552181\pi\) | |||||||
\(522\) | −17.2379 | −0.754484 | ||||||||
\(523\) | 3.51052 | 0.153504 | 0.0767521 | − | 0.997050i | \(-0.475545\pi\) | ||||
0.0767521 | + | 0.997050i | \(0.475545\pi\) | |||||||
\(524\) | 6.40092 | 0.279625 | ||||||||
\(525\) | 2.25066 | 0.0982268 | ||||||||
\(526\) | −3.15421 | −0.137530 | ||||||||
\(527\) | −12.0101 | −0.523167 | ||||||||
\(528\) | 0.449434 | 0.0195591 | ||||||||
\(529\) | −11.6302 | −0.505662 | ||||||||
\(530\) | 6.61344 | 0.287269 | ||||||||
\(531\) | 19.7131 | 0.855475 | ||||||||
\(532\) | −22.0771 | −0.957164 | ||||||||
\(533\) | 16.6788 | 0.722438 | ||||||||
\(534\) | 0.164430 | 0.00711557 | ||||||||
\(535\) | −12.2826 | −0.531023 | ||||||||
\(536\) | 10.0202 | 0.432808 | ||||||||
\(537\) | −0.146647 | −0.00632831 | ||||||||
\(538\) | 13.1864 | 0.568505 | ||||||||
\(539\) | −6.46384 | −0.278417 | ||||||||
\(540\) | −0.822289 | −0.0353857 | ||||||||
\(541\) | 4.26827 | 0.183507 | 0.0917537 | − | 0.995782i | \(-0.470753\pi\) | ||||
0.0917537 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(542\) | −10.5521 | −0.453252 | ||||||||
\(543\) | 0.349844 | 0.0150132 | ||||||||
\(544\) | 2.48508 | 0.106547 | ||||||||
\(545\) | −3.98933 | −0.170884 | ||||||||
\(546\) | −1.96476 | −0.0840840 | ||||||||
\(547\) | −30.3139 | −1.29613 | −0.648065 | − | 0.761585i | \(-0.724421\pi\) | ||||
−0.648065 | + | 0.761585i | \(0.724421\pi\) | |||||||
\(548\) | 12.3450 | 0.527351 | ||||||||
\(549\) | −40.3766 | −1.72323 | ||||||||
\(550\) | −11.5305 | −0.491663 | ||||||||
\(551\) | 41.7049 | 1.77669 | ||||||||
\(552\) | 0.569904 | 0.0242567 | ||||||||
\(553\) | −7.52927 | −0.320177 | ||||||||
\(554\) | 25.7575 | 1.09433 | ||||||||
\(555\) | −1.09451 | −0.0464592 | ||||||||
\(556\) | 8.03274 | 0.340664 | ||||||||
\(557\) | 40.5246 | 1.71708 | 0.858540 | − | 0.512746i | \(-0.171372\pi\) | ||||
0.858540 | + | 0.512746i | \(0.171372\pi\) | |||||||
\(558\) | 14.3606 | 0.607931 | ||||||||
\(559\) | 11.0559 | 0.467613 | ||||||||
\(560\) | −2.50204 | −0.105731 | ||||||||
\(561\) | −1.11688 | −0.0471547 | ||||||||
\(562\) | −4.45765 | −0.188035 | ||||||||
\(563\) | −9.44003 | −0.397850 | −0.198925 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198925 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(564\) | −0.00648375 | −0.000273015 0 | ||||||||
\(565\) | −11.8839 | −0.499961 | ||||||||
\(566\) | −1.07317 | −0.0451088 | ||||||||
\(567\) | 26.8516 | 1.12766 | ||||||||
\(568\) | −9.18773 | −0.385508 | ||||||||
\(569\) | 26.1437 | 1.09600 | 0.548000 | − | 0.836478i | \(-0.315389\pi\) | ||||
0.548000 | + | 0.836478i | \(0.315389\pi\) | |||||||
\(570\) | 0.989951 | 0.0414645 | ||||||||
\(571\) | 1.60146 | 0.0670192 | 0.0335096 | − | 0.999438i | \(-0.489332\pi\) | ||||
0.0335096 | + | 0.999438i | \(0.489332\pi\) | |||||||
\(572\) | 10.0658 | 0.420873 | ||||||||
\(573\) | −0.229761 | −0.00959839 | ||||||||
\(574\) | 13.5310 | 0.564773 | ||||||||
\(575\) | −14.6213 | −0.609749 | ||||||||
\(576\) | −2.97143 | −0.123810 | ||||||||
\(577\) | −31.9091 | −1.32839 | −0.664197 | − | 0.747558i | \(-0.731226\pi\) | ||||
−0.664197 | + | 0.747558i | \(0.731226\pi\) | |||||||
\(578\) | 10.8244 | 0.450234 | ||||||||
\(579\) | 2.68874 | 0.111740 | ||||||||
\(580\) | 4.72649 | 0.196257 | ||||||||
\(581\) | −3.81374 | −0.158220 | ||||||||
\(582\) | 3.04440 | 0.126194 | ||||||||
\(583\) | −21.5848 | −0.893949 | ||||||||
\(584\) | 4.01614 | 0.166189 | ||||||||
\(585\) | −9.16421 | −0.378894 | ||||||||
\(586\) | 21.7034 | 0.896560 | ||||||||
\(587\) | −11.1644 | −0.460806 | −0.230403 | − | 0.973095i | \(-0.574004\pi\) | ||||
−0.230403 | + | 0.973095i | \(0.574004\pi\) | |||||||
\(588\) | −0.410844 | −0.0169429 | ||||||||
\(589\) | −34.7435 | −1.43158 | ||||||||
\(590\) | −5.40516 | −0.222527 | ||||||||
\(591\) | −2.51840 | −0.103593 | ||||||||
\(592\) | −7.94827 | −0.326672 | ||||||||
\(593\) | 38.4459 | 1.57879 | 0.789393 | − | 0.613888i | \(-0.210395\pi\) | ||||
0.789393 | + | 0.613888i | \(0.210395\pi\) | |||||||
\(594\) | 2.68376 | 0.110116 | ||||||||
\(595\) | 6.21778 | 0.254904 | ||||||||
\(596\) | −11.1522 | −0.456813 | ||||||||
\(597\) | 2.00449 | 0.0820382 | ||||||||
\(598\) | 12.7639 | 0.521956 | ||||||||
\(599\) | −37.0267 | −1.51287 | −0.756434 | − | 0.654070i | \(-0.773060\pi\) | ||||
−0.756434 | + | 0.654070i | \(0.773060\pi\) | |||||||
\(600\) | −0.732884 | −0.0299198 | ||||||||
\(601\) | −2.15567 | −0.0879316 | −0.0439658 | − | 0.999033i | \(-0.513999\pi\) | ||||
−0.0439658 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(602\) | 8.96929 | 0.365561 | ||||||||
\(603\) | 29.7745 | 1.21251 | ||||||||
\(604\) | 7.09851 | 0.288834 | ||||||||
\(605\) | 3.20114 | 0.130145 | ||||||||
\(606\) | 1.71909 | 0.0698333 | ||||||||
\(607\) | −6.24324 | −0.253405 | −0.126703 | − | 0.991941i | \(-0.540439\pi\) | ||||
−0.126703 | + | 0.991941i | \(0.540439\pi\) | |||||||
\(608\) | 7.18899 | 0.291552 | ||||||||
\(609\) | 3.01106 | 0.122014 | ||||||||
\(610\) | 11.0709 | 0.448249 | ||||||||
\(611\) | −0.145214 | −0.00587474 | ||||||||
\(612\) | 7.38426 | 0.298491 | ||||||||
\(613\) | 19.4918 | 0.787266 | 0.393633 | − | 0.919268i | \(-0.371218\pi\) | ||||
0.393633 | + | 0.919268i | \(0.371218\pi\) | |||||||
\(614\) | 8.66351 | 0.349631 | ||||||||
\(615\) | −0.606738 | −0.0244660 | ||||||||
\(616\) | 8.16609 | 0.329021 | ||||||||
\(617\) | −36.1792 | −1.45652 | −0.728260 | − | 0.685301i | \(-0.759671\pi\) | ||||
−0.728260 | + | 0.685301i | \(0.759671\pi\) | |||||||
\(618\) | −2.37118 | −0.0953830 | ||||||||
\(619\) | −29.1030 | −1.16975 | −0.584875 | − | 0.811124i | \(-0.698856\pi\) | ||||
−0.584875 | + | 0.811124i | \(0.698856\pi\) | |||||||
\(620\) | −3.93754 | −0.158135 | ||||||||
\(621\) | 3.40315 | 0.136564 | ||||||||
\(622\) | −15.2654 | −0.612088 | ||||||||
\(623\) | 2.98764 | 0.119697 | ||||||||
\(624\) | 0.639787 | 0.0256120 | ||||||||
\(625\) | 15.4836 | 0.619343 | ||||||||
\(626\) | 17.2240 | 0.688408 | ||||||||
\(627\) | −3.23097 | −0.129033 | ||||||||
\(628\) | 5.41650 | 0.216142 | ||||||||
\(629\) | 19.7521 | 0.787567 | ||||||||
\(630\) | −7.43465 | −0.296204 | ||||||||
\(631\) | 7.13286 | 0.283955 | 0.141977 | − | 0.989870i | \(-0.454654\pi\) | ||||
0.141977 | + | 0.989870i | \(0.454654\pi\) | |||||||
\(632\) | 2.45176 | 0.0975259 | ||||||||
\(633\) | 1.54188 | 0.0612843 | ||||||||
\(634\) | 14.5111 | 0.576309 | ||||||||
\(635\) | 8.27579 | 0.328415 | ||||||||
\(636\) | −1.37194 | −0.0544008 | ||||||||
\(637\) | −9.20153 | −0.364578 | ||||||||
\(638\) | −15.4262 | −0.610729 | ||||||||
\(639\) | −27.3007 | −1.08000 | ||||||||
\(640\) | 0.814742 | 0.0322055 | ||||||||
\(641\) | 32.3133 | 1.27630 | 0.638150 | − | 0.769912i | \(-0.279700\pi\) | ||||
0.638150 | + | 0.769912i | \(0.279700\pi\) | |||||||
\(642\) | 2.54798 | 0.100561 | ||||||||
\(643\) | −36.6551 | −1.44554 | −0.722769 | − | 0.691090i | \(-0.757131\pi\) | ||||
−0.722769 | + | 0.691090i | \(0.757131\pi\) | |||||||
\(644\) | 10.3550 | 0.408044 | ||||||||
\(645\) | −0.402188 | −0.0158362 | ||||||||
\(646\) | −17.8652 | −0.702898 | ||||||||
\(647\) | 9.96599 | 0.391804 | 0.195902 | − | 0.980624i | \(-0.437237\pi\) | ||||
0.195902 | + | 0.980624i | \(0.437237\pi\) | |||||||
\(648\) | −8.74372 | −0.343486 | ||||||||
\(649\) | 17.6412 | 0.692477 | ||||||||
\(650\) | −16.4141 | −0.643815 | ||||||||
\(651\) | −2.50845 | −0.0983140 | ||||||||
\(652\) | 23.5997 | 0.924234 | ||||||||
\(653\) | 3.84625 | 0.150515 | 0.0752576 | − | 0.997164i | \(-0.476022\pi\) | ||||
0.0752576 | + | 0.997164i | \(0.476022\pi\) | |||||||
\(654\) | 0.827573 | 0.0323607 | ||||||||
\(655\) | −5.21509 | −0.203771 | ||||||||
\(656\) | −4.40611 | −0.172030 | ||||||||
\(657\) | 11.9337 | 0.465577 | ||||||||
\(658\) | −0.117808 | −0.00459264 | ||||||||
\(659\) | −7.45776 | −0.290513 | −0.145256 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145256 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(660\) | −0.366172 | −0.0142532 | ||||||||
\(661\) | 19.6195 | 0.763109 | 0.381554 | − | 0.924346i | \(-0.375389\pi\) | ||||
0.381554 | + | 0.924346i | \(0.375389\pi\) | |||||||
\(662\) | 19.6185 | 0.762495 | ||||||||
\(663\) | −1.58992 | −0.0617475 | ||||||||
\(664\) | 1.24187 | 0.0481939 | ||||||||
\(665\) | 17.9871 | 0.697512 | ||||||||
\(666\) | −23.6177 | −0.915169 | ||||||||
\(667\) | −19.5612 | −0.757411 | ||||||||
\(668\) | −16.7950 | −0.649819 | ||||||||
\(669\) | −0.445588 | −0.0172274 | ||||||||
\(670\) | −8.16391 | −0.315399 | ||||||||
\(671\) | −36.1330 | −1.39490 | ||||||||
\(672\) | 0.519040 | 0.0200224 | ||||||||
\(673\) | −1.84451 | −0.0711007 | −0.0355504 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355504 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(674\) | −5.02933 | −0.193723 | ||||||||
\(675\) | −4.37637 | −0.168446 | ||||||||
\(676\) | 1.32908 | 0.0511184 | ||||||||
\(677\) | −19.0178 | −0.730914 | −0.365457 | − | 0.930828i | \(-0.619087\pi\) | ||||
−0.365457 | + | 0.930828i | \(0.619087\pi\) | |||||||
\(678\) | 2.46528 | 0.0946786 | ||||||||
\(679\) | 55.3159 | 2.12283 | ||||||||
\(680\) | −2.02470 | −0.0776437 | ||||||||
\(681\) | 1.35751 | 0.0520200 | ||||||||
\(682\) | 12.8512 | 0.492099 | ||||||||
\(683\) | 32.5115 | 1.24402 | 0.622010 | − | 0.783010i | \(-0.286317\pi\) | ||||
0.622010 | + | 0.783010i | \(0.286317\pi\) | |||||||
\(684\) | 21.3616 | 0.816781 | ||||||||
\(685\) | −10.0580 | −0.384295 | ||||||||
\(686\) | 14.0318 | 0.535737 | ||||||||
\(687\) | −2.05033 | −0.0782248 | ||||||||
\(688\) | −2.92068 | −0.111350 | ||||||||
\(689\) | −30.7267 | −1.17060 | ||||||||
\(690\) | −0.464325 | −0.0176765 | ||||||||
\(691\) | 2.91815 | 0.111012 | 0.0555058 | − | 0.998458i | \(-0.482323\pi\) | ||||
0.0555058 | + | 0.998458i | \(0.482323\pi\) | |||||||
\(692\) | 8.69062 | 0.330368 | ||||||||
\(693\) | 24.2650 | 0.921751 | ||||||||
\(694\) | −2.17304 | −0.0824875 | ||||||||
\(695\) | −6.54461 | −0.248251 | ||||||||
\(696\) | −0.980494 | −0.0371655 | ||||||||
\(697\) | 10.9495 | 0.414743 | ||||||||
\(698\) | 21.0770 | 0.797776 | ||||||||
\(699\) | −0.373470 | −0.0141259 | ||||||||
\(700\) | −13.3163 | −0.503309 | ||||||||
\(701\) | −5.30444 | −0.200346 | −0.100173 | − | 0.994970i | \(-0.531940\pi\) | ||||
−0.100173 | + | 0.994970i | \(0.531940\pi\) | |||||||
\(702\) | 3.82044 | 0.144193 | ||||||||
\(703\) | 57.1400 | 2.15508 | ||||||||
\(704\) | −2.65913 | −0.100220 | ||||||||
\(705\) | 0.00528258 | 0.000198954 0 | ||||||||
\(706\) | −12.5787 | −0.473404 | ||||||||
\(707\) | 31.2354 | 1.17473 | ||||||||
\(708\) | 1.12128 | 0.0421403 | ||||||||
\(709\) | 12.4448 | 0.467374 | 0.233687 | − | 0.972312i | \(-0.424921\pi\) | ||||
0.233687 | + | 0.972312i | \(0.424921\pi\) | |||||||
\(710\) | 7.48562 | 0.280930 | ||||||||
\(711\) | 7.28525 | 0.273218 | ||||||||
\(712\) | −0.972868 | −0.0364598 | ||||||||
\(713\) | 16.2960 | 0.610290 | ||||||||
\(714\) | −1.28986 | −0.0482716 | ||||||||
\(715\) | −8.20103 | −0.306701 | ||||||||
\(716\) | 0.867658 | 0.0324259 | ||||||||
\(717\) | −1.30232 | −0.0486360 | ||||||||
\(718\) | 2.31276 | 0.0863116 | ||||||||
\(719\) | −12.6156 | −0.470483 | −0.235241 | − | 0.971937i | \(-0.575588\pi\) | ||||
−0.235241 | + | 0.971937i | \(0.575588\pi\) | |||||||
\(720\) | 2.42095 | 0.0902235 | ||||||||
\(721\) | −43.0838 | −1.60452 | ||||||||
\(722\) | −32.6816 | −1.21628 | ||||||||
\(723\) | −4.04042 | −0.150265 | ||||||||
\(724\) | −2.06989 | −0.0769270 | ||||||||
\(725\) | 25.1552 | 0.934241 | ||||||||
\(726\) | −0.664066 | −0.0246458 | ||||||||
\(727\) | −50.3308 | −1.86667 | −0.933333 | − | 0.359011i | \(-0.883114\pi\) | ||||
−0.933333 | + | 0.359011i | \(0.883114\pi\) | |||||||
\(728\) | 11.6247 | 0.430842 | ||||||||
\(729\) | −25.4696 | −0.943320 | ||||||||
\(730\) | −3.27211 | −0.121106 | ||||||||
\(731\) | 7.25812 | 0.268451 | ||||||||
\(732\) | −2.29663 | −0.0848857 | ||||||||
\(733\) | 16.8222 | 0.621343 | 0.310671 | − | 0.950517i | \(-0.399446\pi\) | ||||
0.310671 | + | 0.950517i | \(0.399446\pi\) | |||||||
\(734\) | 0.557091 | 0.0205626 | ||||||||
\(735\) | 0.334732 | 0.0123468 | ||||||||
\(736\) | −3.37191 | −0.124290 | ||||||||
\(737\) | 26.6451 | 0.981486 | ||||||||
\(738\) | −13.0925 | −0.481940 | ||||||||
\(739\) | 9.38710 | 0.345310 | 0.172655 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172655 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(740\) | 6.47578 | 0.238055 | ||||||||
\(741\) | −4.59942 | −0.168964 | ||||||||
\(742\) | −24.9277 | −0.915124 | ||||||||
\(743\) | 7.13519 | 0.261765 | 0.130882 | − | 0.991398i | \(-0.458219\pi\) | ||||
0.130882 | + | 0.991398i | \(0.458219\pi\) | |||||||
\(744\) | 0.816829 | 0.0299464 | ||||||||
\(745\) | 9.08618 | 0.332892 | ||||||||
\(746\) | 10.9109 | 0.399475 | ||||||||
\(747\) | 3.69013 | 0.135015 | ||||||||
\(748\) | 6.60816 | 0.241618 | ||||||||
\(749\) | 46.2962 | 1.69163 | ||||||||
\(750\) | 1.28563 | 0.0469446 | ||||||||
\(751\) | 3.62153 | 0.132151 | 0.0660757 | − | 0.997815i | \(-0.478952\pi\) | ||||
0.0660757 | + | 0.997815i | \(0.478952\pi\) | |||||||
\(752\) | 0.0383619 | 0.00139892 | ||||||||
\(753\) | 3.91246 | 0.142578 | ||||||||
\(754\) | −21.9598 | −0.799728 | ||||||||
\(755\) | −5.78345 | −0.210481 | ||||||||
\(756\) | 3.09941 | 0.112724 | ||||||||
\(757\) | −31.8496 | −1.15759 | −0.578797 | − | 0.815472i | \(-0.696478\pi\) | ||||
−0.578797 | + | 0.815472i | \(0.696478\pi\) | |||||||
\(758\) | −18.4773 | −0.671124 | ||||||||
\(759\) | 1.51545 | 0.0550073 | ||||||||
\(760\) | −5.85717 | −0.212462 | ||||||||
\(761\) | 44.7731 | 1.62302 | 0.811511 | − | 0.584337i | \(-0.198645\pi\) | ||||
0.811511 | + | 0.584337i | \(0.198645\pi\) | |||||||
\(762\) | −1.71678 | −0.0621925 | ||||||||
\(763\) | 15.0368 | 0.544368 | ||||||||
\(764\) | 1.35941 | 0.0491816 | ||||||||
\(765\) | −6.01626 | −0.217518 | ||||||||
\(766\) | 19.6251 | 0.709082 | ||||||||
\(767\) | 25.1129 | 0.906776 | ||||||||
\(768\) | −0.169015 | −0.00609882 | ||||||||
\(769\) | 40.3762 | 1.45600 | 0.728002 | − | 0.685575i | \(-0.240449\pi\) | ||||
0.728002 | + | 0.685575i | \(0.240449\pi\) | |||||||
\(770\) | −6.65325 | −0.239767 | ||||||||
\(771\) | −0.902438 | −0.0325005 | ||||||||
\(772\) | −15.9083 | −0.572551 | ||||||||
\(773\) | 3.98968 | 0.143499 | 0.0717495 | − | 0.997423i | \(-0.477142\pi\) | ||||
0.0717495 | + | 0.997423i | \(0.477142\pi\) | |||||||
\(774\) | −8.67860 | −0.311946 | ||||||||
\(775\) | −20.9563 | −0.752772 | ||||||||
\(776\) | −18.0126 | −0.646614 | ||||||||
\(777\) | 4.12547 | 0.148000 | ||||||||
\(778\) | 25.5547 | 0.916180 | ||||||||
\(779\) | 31.6755 | 1.13489 | ||||||||
\(780\) | −0.521261 | −0.0186641 | ||||||||
\(781\) | −24.4314 | −0.874223 | ||||||||
\(782\) | 8.37947 | 0.299649 | ||||||||
\(783\) | −5.85496 | −0.209239 | ||||||||
\(784\) | 2.43081 | 0.0868146 | ||||||||
\(785\) | −4.41305 | −0.157508 | ||||||||
\(786\) | 1.08185 | 0.0385884 | ||||||||
\(787\) | −24.2218 | −0.863416 | −0.431708 | − | 0.902014i | \(-0.642089\pi\) | ||||
−0.431708 | + | 0.902014i | \(0.642089\pi\) | |||||||
\(788\) | 14.9004 | 0.530805 | ||||||||
\(789\) | −0.533109 | −0.0189792 | ||||||||
\(790\) | −1.99755 | −0.0710697 | ||||||||
\(791\) | 44.7935 | 1.59267 | ||||||||
\(792\) | −7.90143 | −0.280765 | ||||||||
\(793\) | −51.4367 | −1.82657 | ||||||||
\(794\) | 24.6808 | 0.875890 | ||||||||
\(795\) | 1.11777 | 0.0396433 | ||||||||
\(796\) | −11.8598 | −0.420359 | ||||||||
\(797\) | 39.5164 | 1.39974 | 0.699871 | − | 0.714270i | \(-0.253241\pi\) | ||||
0.699871 | + | 0.714270i | \(0.253241\pi\) | |||||||
\(798\) | −3.73137 | −0.132089 | ||||||||
\(799\) | −0.0953325 | −0.00337262 | ||||||||
\(800\) | 4.33620 | 0.153308 | ||||||||
\(801\) | −2.89081 | −0.102142 | ||||||||
\(802\) | −20.4996 | −0.723865 | ||||||||
\(803\) | 10.6794 | 0.376869 | ||||||||
\(804\) | 1.69357 | 0.0597277 | ||||||||
\(805\) | −8.43665 | −0.297353 | ||||||||
\(806\) | 18.2942 | 0.644387 | ||||||||
\(807\) | 2.22870 | 0.0784540 | ||||||||
\(808\) | −10.1712 | −0.357822 | ||||||||
\(809\) | 26.8957 | 0.945604 | 0.472802 | − | 0.881169i | \(-0.343243\pi\) | ||||
0.472802 | + | 0.881169i | \(0.343243\pi\) | |||||||
\(810\) | 7.12387 | 0.250307 | ||||||||
\(811\) | 13.5426 | 0.475547 | 0.237773 | − | 0.971321i | \(-0.423582\pi\) | ||||
0.237773 | + | 0.971321i | \(0.423582\pi\) | |||||||
\(812\) | −17.8153 | −0.625195 | ||||||||
\(813\) | −1.78347 | −0.0625489 | ||||||||
\(814\) | −21.1355 | −0.740798 | ||||||||
\(815\) | −19.2276 | −0.673514 | ||||||||
\(816\) | 0.420017 | 0.0147035 | ||||||||
\(817\) | 20.9967 | 0.734582 | ||||||||
\(818\) | −13.6234 | −0.476330 | ||||||||
\(819\) | 34.5422 | 1.20700 | ||||||||
\(820\) | 3.58984 | 0.125363 | ||||||||
\(821\) | −53.7470 | −1.87578 | −0.937892 | − | 0.346927i | \(-0.887225\pi\) | ||||
−0.937892 | + | 0.346927i | \(0.887225\pi\) | |||||||
\(822\) | 2.08649 | 0.0727747 | ||||||||
\(823\) | 41.2143 | 1.43664 | 0.718320 | − | 0.695713i | \(-0.244911\pi\) | ||||
0.718320 | + | 0.695713i | \(0.244911\pi\) | |||||||
\(824\) | 14.0294 | 0.488737 | ||||||||
\(825\) | −1.94883 | −0.0678496 | ||||||||
\(826\) | 20.3734 | 0.708880 | ||||||||
\(827\) | −25.6253 | −0.891078 | −0.445539 | − | 0.895263i | \(-0.646988\pi\) | ||||
−0.445539 | + | 0.895263i | \(0.646988\pi\) | |||||||
\(828\) | −10.0194 | −0.348198 | ||||||||
\(829\) | 7.20305 | 0.250172 | 0.125086 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125086 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(830\) | −1.01180 | −0.0351202 | ||||||||
\(831\) | 4.35341 | 0.151018 | ||||||||
\(832\) | −3.78538 | −0.131234 | ||||||||
\(833\) | −6.04076 | −0.209300 | ||||||||
\(834\) | 1.35766 | 0.0470118 | ||||||||
\(835\) | 13.6836 | 0.473541 | ||||||||
\(836\) | 19.1165 | 0.661157 | ||||||||
\(837\) | 4.87764 | 0.168596 | ||||||||
\(838\) | 0.236224 | 0.00816023 | ||||||||
\(839\) | 40.6571 | 1.40364 | 0.701820 | − | 0.712355i | \(-0.252371\pi\) | ||||
0.701820 | + | 0.712355i | \(0.252371\pi\) | |||||||
\(840\) | −0.422883 | −0.0145909 | ||||||||
\(841\) | 4.65410 | 0.160486 | ||||||||
\(842\) | 40.4372 | 1.39356 | ||||||||
\(843\) | −0.753412 | −0.0259489 | ||||||||
\(844\) | −9.12273 | −0.314017 | ||||||||
\(845\) | −1.08285 | −0.0372513 | ||||||||
\(846\) | 0.113990 | 0.00391905 | ||||||||
\(847\) | −12.0659 | −0.414589 | ||||||||
\(848\) | 8.11722 | 0.278747 | ||||||||
\(849\) | −0.181383 | −0.00622504 | ||||||||
\(850\) | −10.7758 | −0.369607 | ||||||||
\(851\) | −26.8008 | −0.918720 | ||||||||
\(852\) | −1.55287 | −0.0532003 | ||||||||
\(853\) | −13.5529 | −0.464044 | −0.232022 | − | 0.972711i | \(-0.574534\pi\) | ||||
−0.232022 | + | 0.972711i | \(0.574534\pi\) | |||||||
\(854\) | −41.7291 | −1.42794 | ||||||||
\(855\) | −17.4042 | −0.595211 | ||||||||
\(856\) | −15.0755 | −0.515269 | ||||||||
\(857\) | −27.2976 | −0.932467 | −0.466234 | − | 0.884662i | \(-0.654389\pi\) | ||||
−0.466234 | + | 0.884662i | \(0.654389\pi\) | |||||||
\(858\) | 1.70128 | 0.0580806 | ||||||||
\(859\) | 0.705554 | 0.0240732 | 0.0120366 | − | 0.999928i | \(-0.496169\pi\) | ||||
0.0120366 | + | 0.999928i | \(0.496169\pi\) | |||||||
\(860\) | 2.37960 | 0.0811436 | ||||||||
\(861\) | 2.28695 | 0.0779389 | ||||||||
\(862\) | −38.0549 | −1.29616 | ||||||||
\(863\) | 24.6526 | 0.839183 | 0.419591 | − | 0.907713i | \(-0.362173\pi\) | ||||
0.419591 | + | 0.907713i | \(0.362173\pi\) | |||||||
\(864\) | −1.00926 | −0.0343359 | ||||||||
\(865\) | −7.08061 | −0.240748 | ||||||||
\(866\) | −15.0745 | −0.512254 | ||||||||
\(867\) | 1.82948 | 0.0621325 | ||||||||
\(868\) | 14.8416 | 0.503756 | ||||||||
\(869\) | 6.51956 | 0.221161 | ||||||||
\(870\) | 0.798850 | 0.0270835 | ||||||||
\(871\) | 37.9304 | 1.28522 | ||||||||
\(872\) | −4.89644 | −0.165814 | ||||||||
\(873\) | −53.5232 | −1.81148 | ||||||||
\(874\) | 24.2406 | 0.819951 | ||||||||
\(875\) | 23.3595 | 0.789697 | ||||||||
\(876\) | 0.678788 | 0.0229341 | ||||||||
\(877\) | 49.5757 | 1.67405 | 0.837025 | − | 0.547164i | \(-0.184293\pi\) | ||||
0.837025 | + | 0.547164i | \(0.184293\pi\) | |||||||
\(878\) | −31.0098 | −1.04653 | ||||||||
\(879\) | 3.66821 | 0.123726 | ||||||||
\(880\) | 2.16650 | 0.0730328 | ||||||||
\(881\) | −19.7620 | −0.665798 | −0.332899 | − | 0.942963i | \(-0.608027\pi\) | ||||
−0.332899 | + | 0.942963i | \(0.608027\pi\) | |||||||
\(882\) | 7.22299 | 0.243211 | ||||||||
\(883\) | 5.58022 | 0.187789 | 0.0938946 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938946 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(884\) | 9.40697 | 0.316391 | ||||||||
\(885\) | −0.913554 | −0.0307088 | ||||||||
\(886\) | 25.9257 | 0.870991 | ||||||||
\(887\) | 27.8003 | 0.933441 | 0.466721 | − | 0.884405i | \(-0.345435\pi\) | ||||
0.466721 | + | 0.884405i | \(0.345435\pi\) | |||||||
\(888\) | −1.34338 | −0.0450808 | ||||||||
\(889\) | −31.1935 | −1.04620 | ||||||||
\(890\) | 0.792636 | 0.0265692 | ||||||||
\(891\) | −23.2507 | −0.778927 | ||||||||
\(892\) | 2.63638 | 0.0882725 | ||||||||
\(893\) | −0.275783 | −0.00922874 | ||||||||
\(894\) | −1.88490 | −0.0630404 | ||||||||
\(895\) | −0.706917 | −0.0236296 | ||||||||
\(896\) | −3.07096 | −0.102594 | ||||||||
\(897\) | 2.15730 | 0.0720302 | ||||||||
\(898\) | −18.0562 | −0.602543 | ||||||||
\(899\) | −28.0365 | −0.935070 | ||||||||
\(900\) | 12.8847 | 0.429491 | ||||||||
\(901\) | −20.1720 | −0.672025 | ||||||||
\(902\) | −11.7164 | −0.390114 | ||||||||
\(903\) | 1.51595 | 0.0504476 | ||||||||
\(904\) | −14.5861 | −0.485128 | ||||||||
\(905\) | 1.68643 | 0.0560588 | ||||||||
\(906\) | 1.19976 | 0.0398592 | ||||||||
\(907\) | 3.99944 | 0.132799 | 0.0663997 | − | 0.997793i | \(-0.478849\pi\) | ||||
0.0663997 | + | 0.997793i | \(0.478849\pi\) | |||||||
\(908\) | −8.03189 | −0.266548 | ||||||||
\(909\) | −30.2231 | −1.00244 | ||||||||
\(910\) | −9.47117 | −0.313966 | ||||||||
\(911\) | −28.1964 | −0.934190 | −0.467095 | − | 0.884207i | \(-0.654699\pi\) | ||||
−0.467095 | + | 0.884207i | \(0.654699\pi\) | |||||||
\(912\) | 1.21505 | 0.0402343 | ||||||||
\(913\) | 3.30229 | 0.109290 | ||||||||
\(914\) | −9.37221 | −0.310005 | ||||||||
\(915\) | 1.87116 | 0.0618585 | ||||||||
\(916\) | 12.1310 | 0.400820 | ||||||||
\(917\) | 19.6570 | 0.649130 | ||||||||
\(918\) | 2.50810 | 0.0827797 | ||||||||
\(919\) | 25.6955 | 0.847616 | 0.423808 | − | 0.905752i | \(-0.360693\pi\) | ||||
0.423808 | + | 0.905752i | \(0.360693\pi\) | |||||||
\(920\) | 2.74723 | 0.0905736 | ||||||||
\(921\) | 1.46427 | 0.0482492 | ||||||||
\(922\) | −28.3684 | −0.934262 | ||||||||
\(923\) | −34.7790 | −1.14476 | ||||||||
\(924\) | 1.38019 | 0.0454051 | ||||||||
\(925\) | 34.4652 | 1.13321 | ||||||||
\(926\) | −11.6167 | −0.381748 | ||||||||
\(927\) | 41.6874 | 1.36919 | ||||||||
\(928\) | 5.80122 | 0.190434 | ||||||||
\(929\) | −47.9780 | −1.57411 | −0.787053 | − | 0.616885i | \(-0.788394\pi\) | ||||
−0.787053 | + | 0.616885i | \(0.788394\pi\) | |||||||
\(930\) | −0.665505 | −0.0218228 | ||||||||
\(931\) | −17.4751 | −0.572722 | ||||||||
\(932\) | 2.20968 | 0.0723805 | ||||||||
\(933\) | −2.58009 | −0.0844684 | ||||||||
\(934\) | −28.8799 | −0.944978 | ||||||||
\(935\) | −5.38394 | −0.176074 | ||||||||
\(936\) | −11.2480 | −0.367652 | ||||||||
\(937\) | 3.12031 | 0.101936 | 0.0509680 | − | 0.998700i | \(-0.483769\pi\) | ||||
0.0509680 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(938\) | 30.7718 | 1.00473 | ||||||||
\(939\) | 2.91112 | 0.0950007 | ||||||||
\(940\) | −0.0312551 | −0.00101943 | ||||||||
\(941\) | 48.9185 | 1.59470 | 0.797349 | − | 0.603519i | \(-0.206235\pi\) | ||||
0.797349 | + | 0.603519i | \(0.206235\pi\) | |||||||
\(942\) | 0.915471 | 0.0298277 | ||||||||
\(943\) | −14.8570 | −0.483810 | ||||||||
\(944\) | −6.63420 | −0.215925 | ||||||||
\(945\) | −2.52522 | −0.0821454 | ||||||||
\(946\) | −7.76646 | −0.252509 | ||||||||
\(947\) | 21.1680 | 0.687867 | 0.343933 | − | 0.938994i | \(-0.388241\pi\) | ||||
0.343933 | + | 0.938994i | \(0.388241\pi\) | |||||||
\(948\) | 0.414385 | 0.0134586 | ||||||||
\(949\) | 15.2026 | 0.493497 | ||||||||
\(950\) | −31.1729 | −1.01138 | ||||||||
\(951\) | 2.45259 | 0.0795308 | ||||||||
\(952\) | 7.63159 | 0.247341 | ||||||||
\(953\) | −7.17049 | −0.232275 | −0.116137 | − | 0.993233i | \(-0.537051\pi\) | ||||
−0.116137 | + | 0.993233i | \(0.537051\pi\) | |||||||
\(954\) | 24.1198 | 0.780907 | ||||||||
\(955\) | −1.10757 | −0.0358400 | ||||||||
\(956\) | 7.70534 | 0.249208 | ||||||||
\(957\) | −2.60726 | −0.0842808 | ||||||||
\(958\) | −14.5624 | −0.470489 | ||||||||
\(959\) | 37.9109 | 1.22421 | ||||||||
\(960\) | 0.137704 | 0.00444437 | ||||||||
\(961\) | −7.64336 | −0.246560 | ||||||||
\(962\) | −30.0872 | −0.970050 | ||||||||
\(963\) | −44.7957 | −1.44352 | ||||||||
\(964\) | 23.9056 | 0.769949 | ||||||||
\(965\) | 12.9611 | 0.417233 | ||||||||
\(966\) | 1.75015 | 0.0563103 | ||||||||
\(967\) | 45.5372 | 1.46438 | 0.732188 | − | 0.681102i | \(-0.238499\pi\) | ||||
0.732188 | + | 0.681102i | \(0.238499\pi\) | |||||||
\(968\) | 3.92903 | 0.126284 | ||||||||
\(969\) | −3.01950 | −0.0970002 | ||||||||
\(970\) | 14.6756 | 0.471205 | ||||||||
\(971\) | −15.9227 | −0.510985 | −0.255492 | − | 0.966811i | \(-0.582238\pi\) | ||||
−0.255492 | + | 0.966811i | \(0.582238\pi\) | |||||||
\(972\) | −4.50561 | −0.144518 | ||||||||
\(973\) | 24.6682 | 0.790827 | ||||||||
\(974\) | 29.8995 | 0.958041 | ||||||||
\(975\) | −2.77424 | −0.0888468 | ||||||||
\(976\) | 13.5883 | 0.434950 | ||||||||
\(977\) | −8.23938 | −0.263601 | −0.131801 | − | 0.991276i | \(-0.542076\pi\) | ||||
−0.131801 | + | 0.991276i | \(0.542076\pi\) | |||||||
\(978\) | 3.98870 | 0.127545 | ||||||||
\(979\) | −2.58698 | −0.0826803 | ||||||||
\(980\) | −1.98048 | −0.0632642 | ||||||||
\(981\) | −14.5494 | −0.464528 | ||||||||
\(982\) | −30.1072 | −0.960759 | ||||||||
\(983\) | 19.2525 | 0.614060 | 0.307030 | − | 0.951700i | \(-0.400665\pi\) | ||||
0.307030 | + | 0.951700i | \(0.400665\pi\) | |||||||
\(984\) | −0.744700 | −0.0237402 | ||||||||
\(985\) | −12.1400 | −0.386812 | ||||||||
\(986\) | −14.4165 | −0.459115 | ||||||||
\(987\) | −0.0199114 | −0.000633786 0 | ||||||||
\(988\) | 27.2130 | 0.865762 | ||||||||
\(989\) | −9.84825 | −0.313156 | ||||||||
\(990\) | 6.43762 | 0.204601 | ||||||||
\(991\) | 15.1501 | 0.481260 | 0.240630 | − | 0.970617i | \(-0.422646\pi\) | ||||
0.240630 | + | 0.970617i | \(0.422646\pi\) | |||||||
\(992\) | −4.83287 | −0.153444 | ||||||||
\(993\) | 3.31583 | 0.105225 | ||||||||
\(994\) | −28.2152 | −0.894931 | ||||||||
\(995\) | 9.66267 | 0.306327 | ||||||||
\(996\) | 0.209895 | 0.00665078 | ||||||||
\(997\) | 39.9948 | 1.26665 | 0.633324 | − | 0.773887i | \(-0.281690\pi\) | ||||
0.633324 | + | 0.773887i | \(0.281690\pi\) | |||||||
\(998\) | −35.4216 | −1.12125 | ||||||||
\(999\) | −8.02190 | −0.253802 |
(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 | 8002.2.a.e.1.37 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.37 | ✓ | 77 | 1.1 | even | 1 | trivial |