Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.09909 | −1.21191 | −0.605955 | − | 0.795499i | \(-0.707209\pi\) | ||||
−0.605955 | + | 0.795499i | \(0.707209\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36520 | 0.610534 | 0.305267 | − | 0.952267i | \(-0.401254\pi\) | ||||
0.305267 | + | 0.952267i | \(0.401254\pi\) | |||||||
\(6\) | 2.09909 | 0.856950 | ||||||||
\(7\) | 4.01442 | 1.51731 | 0.758654 | − | 0.651494i | \(-0.225858\pi\) | ||||
0.758654 | + | 0.651494i | \(0.225858\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.40618 | 0.468726 | ||||||||
\(10\) | −1.36520 | −0.431713 | ||||||||
\(11\) | 3.20824 | 0.967320 | 0.483660 | − | 0.875256i | \(-0.339307\pi\) | ||||
0.483660 | + | 0.875256i | \(0.339307\pi\) | |||||||
\(12\) | −2.09909 | −0.605955 | ||||||||
\(13\) | 6.79975 | 1.88591 | 0.942956 | − | 0.332918i | \(-0.108033\pi\) | ||||
0.942956 | + | 0.332918i | \(0.108033\pi\) | |||||||
\(14\) | −4.01442 | −1.07290 | ||||||||
\(15\) | −2.86567 | −0.739913 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.85135 | 0.449019 | 0.224509 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224509 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(18\) | −1.40618 | −0.331439 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.36520 | 0.305267 | ||||||||
\(21\) | −8.42662 | −1.83884 | ||||||||
\(22\) | −3.20824 | −0.683998 | ||||||||
\(23\) | −5.09179 | −1.06171 | −0.530856 | − | 0.847462i | \(-0.678130\pi\) | ||||
−0.530856 | + | 0.847462i | \(0.678130\pi\) | |||||||
\(24\) | 2.09909 | 0.428475 | ||||||||
\(25\) | −3.13624 | −0.627248 | ||||||||
\(26\) | −6.79975 | −1.33354 | ||||||||
\(27\) | 3.34558 | 0.643856 | ||||||||
\(28\) | 4.01442 | 0.758654 | ||||||||
\(29\) | 4.18921 | 0.777916 | 0.388958 | − | 0.921255i | \(-0.372835\pi\) | ||||
0.388958 | + | 0.921255i | \(0.372835\pi\) | |||||||
\(30\) | 2.86567 | 0.523197 | ||||||||
\(31\) | 0.712068 | 0.127891 | 0.0639456 | − | 0.997953i | \(-0.479632\pi\) | ||||
0.0639456 | + | 0.997953i | \(0.479632\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −6.73438 | −1.17230 | ||||||||
\(34\) | −1.85135 | −0.317504 | ||||||||
\(35\) | 5.48047 | 0.926368 | ||||||||
\(36\) | 1.40618 | 0.234363 | ||||||||
\(37\) | −6.50946 | −1.07015 | −0.535074 | − | 0.844805i | \(-0.679716\pi\) | ||||
−0.535074 | + | 0.844805i | \(0.679716\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −14.2733 | −2.28555 | ||||||||
\(40\) | −1.36520 | −0.215856 | ||||||||
\(41\) | 2.46268 | 0.384605 | 0.192303 | − | 0.981336i | \(-0.438404\pi\) | ||||
0.192303 | + | 0.981336i | \(0.438404\pi\) | |||||||
\(42\) | 8.42662 | 1.30026 | ||||||||
\(43\) | 10.2541 | 1.56373 | 0.781866 | − | 0.623447i | \(-0.214268\pi\) | ||||
0.781866 | + | 0.623447i | \(0.214268\pi\) | |||||||
\(44\) | 3.20824 | 0.483660 | ||||||||
\(45\) | 1.91971 | 0.286173 | ||||||||
\(46\) | 5.09179 | 0.750744 | ||||||||
\(47\) | −5.38403 | −0.785341 | −0.392671 | − | 0.919679i | \(-0.628449\pi\) | ||||
−0.392671 | + | 0.919679i | \(0.628449\pi\) | |||||||
\(48\) | −2.09909 | −0.302978 | ||||||||
\(49\) | 9.11555 | 1.30222 | ||||||||
\(50\) | 3.13624 | 0.443531 | ||||||||
\(51\) | −3.88615 | −0.544170 | ||||||||
\(52\) | 6.79975 | 0.942956 | ||||||||
\(53\) | 8.52058 | 1.17039 | 0.585196 | − | 0.810892i | \(-0.301018\pi\) | ||||
0.585196 | + | 0.810892i | \(0.301018\pi\) | |||||||
\(54\) | −3.34558 | −0.455275 | ||||||||
\(55\) | 4.37987 | 0.590582 | ||||||||
\(56\) | −4.01442 | −0.536449 | ||||||||
\(57\) | 2.09909 | 0.278031 | ||||||||
\(58\) | −4.18921 | −0.550070 | ||||||||
\(59\) | 10.3430 | 1.34654 | 0.673271 | − | 0.739396i | \(-0.264889\pi\) | ||||
0.673271 | + | 0.739396i | \(0.264889\pi\) | |||||||
\(60\) | −2.86567 | −0.369956 | ||||||||
\(61\) | 1.41889 | 0.181670 | 0.0908350 | − | 0.995866i | \(-0.471046\pi\) | ||||
0.0908350 | + | 0.995866i | \(0.471046\pi\) | |||||||
\(62\) | −0.712068 | −0.0904327 | ||||||||
\(63\) | 5.64498 | 0.711201 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.28299 | 1.15141 | ||||||||
\(66\) | 6.73438 | 0.828945 | ||||||||
\(67\) | 12.7000 | 1.55155 | 0.775773 | − | 0.631012i | \(-0.217360\pi\) | ||||
0.775773 | + | 0.631012i | \(0.217360\pi\) | |||||||
\(68\) | 1.85135 | 0.224509 | ||||||||
\(69\) | 10.6881 | 1.28670 | ||||||||
\(70\) | −5.48047 | −0.655041 | ||||||||
\(71\) | 4.06966 | 0.482980 | 0.241490 | − | 0.970403i | \(-0.422364\pi\) | ||||
0.241490 | + | 0.970403i | \(0.422364\pi\) | |||||||
\(72\) | −1.40618 | −0.165720 | ||||||||
\(73\) | −10.9181 | −1.27787 | −0.638935 | − | 0.769261i | \(-0.720625\pi\) | ||||
−0.638935 | + | 0.769261i | \(0.720625\pi\) | |||||||
\(74\) | 6.50946 | 0.756709 | ||||||||
\(75\) | 6.58325 | 0.760168 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 12.8792 | 1.46772 | ||||||||
\(78\) | 14.2733 | 1.61613 | ||||||||
\(79\) | −2.13278 | −0.239957 | −0.119978 | − | 0.992777i | \(-0.538283\pi\) | ||||
−0.119978 | + | 0.992777i | \(0.538283\pi\) | |||||||
\(80\) | 1.36520 | 0.152634 | ||||||||
\(81\) | −11.2412 | −1.24902 | ||||||||
\(82\) | −2.46268 | −0.271957 | ||||||||
\(83\) | −1.07045 | −0.117497 | −0.0587486 | − | 0.998273i | \(-0.518711\pi\) | ||||
−0.0587486 | + | 0.998273i | \(0.518711\pi\) | |||||||
\(84\) | −8.42662 | −0.919420 | ||||||||
\(85\) | 2.52746 | 0.274141 | ||||||||
\(86\) | −10.2541 | −1.10573 | ||||||||
\(87\) | −8.79352 | −0.942764 | ||||||||
\(88\) | −3.20824 | −0.341999 | ||||||||
\(89\) | −1.39280 | −0.147636 | −0.0738182 | − | 0.997272i | \(-0.523518\pi\) | ||||
−0.0738182 | + | 0.997272i | \(0.523518\pi\) | |||||||
\(90\) | −1.91971 | −0.202355 | ||||||||
\(91\) | 27.2970 | 2.86151 | ||||||||
\(92\) | −5.09179 | −0.530856 | ||||||||
\(93\) | −1.49469 | −0.154993 | ||||||||
\(94\) | 5.38403 | 0.555320 | ||||||||
\(95\) | −1.36520 | −0.140066 | ||||||||
\(96\) | 2.09909 | 0.214237 | ||||||||
\(97\) | 6.73244 | 0.683576 | 0.341788 | − | 0.939777i | \(-0.388968\pi\) | ||||
0.341788 | + | 0.939777i | \(0.388968\pi\) | |||||||
\(98\) | −9.11555 | −0.920809 | ||||||||
\(99\) | 4.51135 | 0.453408 | ||||||||
\(100\) | −3.13624 | −0.313624 | ||||||||
\(101\) | 4.93140 | 0.490693 | 0.245346 | − | 0.969435i | \(-0.421098\pi\) | ||||
0.245346 | + | 0.969435i | \(0.421098\pi\) | |||||||
\(102\) | 3.88615 | 0.384787 | ||||||||
\(103\) | −11.4164 | −1.12489 | −0.562446 | − | 0.826834i | \(-0.690140\pi\) | ||||
−0.562446 | + | 0.826834i | \(0.690140\pi\) | |||||||
\(104\) | −6.79975 | −0.666770 | ||||||||
\(105\) | −11.5040 | −1.12267 | ||||||||
\(106\) | −8.52058 | −0.827592 | ||||||||
\(107\) | −2.69435 | −0.260472 | −0.130236 | − | 0.991483i | \(-0.541574\pi\) | ||||
−0.130236 | + | 0.991483i | \(0.541574\pi\) | |||||||
\(108\) | 3.34558 | 0.321928 | ||||||||
\(109\) | 11.5555 | 1.10682 | 0.553408 | − | 0.832911i | \(-0.313327\pi\) | ||||
0.553408 | + | 0.832911i | \(0.313327\pi\) | |||||||
\(110\) | −4.37987 | −0.417605 | ||||||||
\(111\) | 13.6639 | 1.29692 | ||||||||
\(112\) | 4.01442 | 0.379327 | ||||||||
\(113\) | 3.46399 | 0.325865 | 0.162932 | − | 0.986637i | \(-0.447905\pi\) | ||||
0.162932 | + | 0.986637i | \(0.447905\pi\) | |||||||
\(114\) | −2.09909 | −0.196598 | ||||||||
\(115\) | −6.95130 | −0.648212 | ||||||||
\(116\) | 4.18921 | 0.388958 | ||||||||
\(117\) | 9.56166 | 0.883976 | ||||||||
\(118\) | −10.3430 | −0.952149 | ||||||||
\(119\) | 7.43210 | 0.681299 | ||||||||
\(120\) | 2.86567 | 0.261599 | ||||||||
\(121\) | −0.707214 | −0.0642922 | ||||||||
\(122\) | −1.41889 | −0.128460 | ||||||||
\(123\) | −5.16938 | −0.466107 | ||||||||
\(124\) | 0.712068 | 0.0639456 | ||||||||
\(125\) | −11.1076 | −0.993491 | ||||||||
\(126\) | −5.64498 | −0.502895 | ||||||||
\(127\) | 12.7725 | 1.13337 | 0.566687 | − | 0.823933i | \(-0.308225\pi\) | ||||
0.566687 | + | 0.823933i | \(0.308225\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −21.5242 | −1.89510 | ||||||||
\(130\) | −9.28299 | −0.814172 | ||||||||
\(131\) | −2.47248 | −0.216022 | −0.108011 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108011 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(132\) | −6.73438 | −0.586152 | ||||||||
\(133\) | −4.01442 | −0.348094 | ||||||||
\(134\) | −12.7000 | −1.09711 | ||||||||
\(135\) | 4.56737 | 0.393096 | ||||||||
\(136\) | −1.85135 | −0.158752 | ||||||||
\(137\) | −6.95851 | −0.594506 | −0.297253 | − | 0.954799i | \(-0.596070\pi\) | ||||
−0.297253 | + | 0.954799i | \(0.596070\pi\) | |||||||
\(138\) | −10.6881 | −0.909834 | ||||||||
\(139\) | 2.69155 | 0.228294 | 0.114147 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114147 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(140\) | 5.48047 | 0.463184 | ||||||||
\(141\) | 11.3016 | 0.951763 | ||||||||
\(142\) | −4.06966 | −0.341518 | ||||||||
\(143\) | 21.8152 | 1.82428 | ||||||||
\(144\) | 1.40618 | 0.117181 | ||||||||
\(145\) | 5.71909 | 0.474945 | ||||||||
\(146\) | 10.9181 | 0.903590 | ||||||||
\(147\) | −19.1344 | −1.57817 | ||||||||
\(148\) | −6.50946 | −0.535074 | ||||||||
\(149\) | −20.5376 | −1.68251 | −0.841253 | − | 0.540642i | \(-0.818181\pi\) | ||||
−0.841253 | + | 0.540642i | \(0.818181\pi\) | |||||||
\(150\) | −6.58325 | −0.537520 | ||||||||
\(151\) | 3.78224 | 0.307795 | 0.153897 | − | 0.988087i | \(-0.450818\pi\) | ||||
0.153897 | + | 0.988087i | \(0.450818\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 2.60333 | 0.210467 | ||||||||
\(154\) | −12.8792 | −1.03784 | ||||||||
\(155\) | 0.972113 | 0.0780820 | ||||||||
\(156\) | −14.2733 | −1.14278 | ||||||||
\(157\) | 1.21829 | 0.0972299 | 0.0486150 | − | 0.998818i | \(-0.484519\pi\) | ||||
0.0486150 | + | 0.998818i | \(0.484519\pi\) | |||||||
\(158\) | 2.13278 | 0.169675 | ||||||||
\(159\) | −17.8855 | −1.41841 | ||||||||
\(160\) | −1.36520 | −0.107928 | ||||||||
\(161\) | −20.4406 | −1.61094 | ||||||||
\(162\) | 11.2412 | 0.883192 | ||||||||
\(163\) | 9.20183 | 0.720743 | 0.360371 | − | 0.932809i | \(-0.382650\pi\) | ||||
0.360371 | + | 0.932809i | \(0.382650\pi\) | |||||||
\(164\) | 2.46268 | 0.192303 | ||||||||
\(165\) | −9.19375 | −0.715732 | ||||||||
\(166\) | 1.07045 | 0.0830831 | ||||||||
\(167\) | −0.544945 | −0.0421691 | −0.0210846 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210846 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(168\) | 8.42662 | 0.650128 | ||||||||
\(169\) | 33.2366 | 2.55666 | ||||||||
\(170\) | −2.52746 | −0.193847 | ||||||||
\(171\) | −1.40618 | −0.107533 | ||||||||
\(172\) | 10.2541 | 0.781866 | ||||||||
\(173\) | 7.18185 | 0.546026 | 0.273013 | − | 0.962010i | \(-0.411980\pi\) | ||||
0.273013 | + | 0.962010i | \(0.411980\pi\) | |||||||
\(174\) | 8.79352 | 0.666635 | ||||||||
\(175\) | −12.5902 | −0.951728 | ||||||||
\(176\) | 3.20824 | 0.241830 | ||||||||
\(177\) | −21.7109 | −1.63189 | ||||||||
\(178\) | 1.39280 | 0.104395 | ||||||||
\(179\) | −12.2753 | −0.917498 | −0.458749 | − | 0.888566i | \(-0.651702\pi\) | ||||
−0.458749 | + | 0.888566i | \(0.651702\pi\) | |||||||
\(180\) | 1.91971 | 0.143087 | ||||||||
\(181\) | −2.93286 | −0.217997 | −0.108999 | − | 0.994042i | \(-0.534764\pi\) | ||||
−0.108999 | + | 0.994042i | \(0.534764\pi\) | |||||||
\(182\) | −27.2970 | −2.02339 | ||||||||
\(183\) | −2.97837 | −0.220168 | ||||||||
\(184\) | 5.09179 | 0.375372 | ||||||||
\(185\) | −8.88669 | −0.653362 | ||||||||
\(186\) | 1.49469 | 0.109596 | ||||||||
\(187\) | 5.93958 | 0.434345 | ||||||||
\(188\) | −5.38403 | −0.392671 | ||||||||
\(189\) | 13.4305 | 0.976928 | ||||||||
\(190\) | 1.36520 | 0.0990417 | ||||||||
\(191\) | 0.334793 | 0.0242248 | 0.0121124 | − | 0.999927i | \(-0.496144\pi\) | ||||
0.0121124 | + | 0.999927i | \(0.496144\pi\) | |||||||
\(192\) | −2.09909 | −0.151489 | ||||||||
\(193\) | −7.21710 | −0.519498 | −0.259749 | − | 0.965676i | \(-0.583640\pi\) | ||||
−0.259749 | + | 0.965676i | \(0.583640\pi\) | |||||||
\(194\) | −6.73244 | −0.483361 | ||||||||
\(195\) | −19.4858 | −1.39541 | ||||||||
\(196\) | 9.11555 | 0.651110 | ||||||||
\(197\) | 1.72510 | 0.122908 | 0.0614542 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614542 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(198\) | −4.51135 | −0.320608 | ||||||||
\(199\) | 7.92046 | 0.561466 | 0.280733 | − | 0.959786i | \(-0.409422\pi\) | ||||
0.280733 | + | 0.959786i | \(0.409422\pi\) | |||||||
\(200\) | 3.13624 | 0.221766 | ||||||||
\(201\) | −26.6584 | −1.88034 | ||||||||
\(202\) | −4.93140 | −0.346972 | ||||||||
\(203\) | 16.8172 | 1.18034 | ||||||||
\(204\) | −3.88615 | −0.272085 | ||||||||
\(205\) | 3.36204 | 0.234815 | ||||||||
\(206\) | 11.4164 | 0.795419 | ||||||||
\(207\) | −7.15997 | −0.497652 | ||||||||
\(208\) | 6.79975 | 0.471478 | ||||||||
\(209\) | −3.20824 | −0.221918 | ||||||||
\(210\) | 11.5040 | 0.793851 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | 8.52058 | 0.585196 | ||||||||
\(213\) | −8.54258 | −0.585328 | ||||||||
\(214\) | 2.69435 | 0.184182 | ||||||||
\(215\) | 13.9988 | 0.954712 | ||||||||
\(216\) | −3.34558 | −0.227638 | ||||||||
\(217\) | 2.85854 | 0.194050 | ||||||||
\(218\) | −11.5555 | −0.782637 | ||||||||
\(219\) | 22.9181 | 1.54866 | ||||||||
\(220\) | 4.37987 | 0.295291 | ||||||||
\(221\) | 12.5887 | 0.846810 | ||||||||
\(222\) | −13.6639 | −0.917064 | ||||||||
\(223\) | 9.60089 | 0.642923 | 0.321461 | − | 0.946923i | \(-0.395826\pi\) | ||||
0.321461 | + | 0.946923i | \(0.395826\pi\) | |||||||
\(224\) | −4.01442 | −0.268225 | ||||||||
\(225\) | −4.41011 | −0.294007 | ||||||||
\(226\) | −3.46399 | −0.230421 | ||||||||
\(227\) | −24.5848 | −1.63175 | −0.815875 | − | 0.578229i | \(-0.803744\pi\) | ||||
−0.815875 | + | 0.578229i | \(0.803744\pi\) | |||||||
\(228\) | 2.09909 | 0.139016 | ||||||||
\(229\) | 5.87183 | 0.388022 | 0.194011 | − | 0.980999i | \(-0.437850\pi\) | ||||
0.194011 | + | 0.980999i | \(0.437850\pi\) | |||||||
\(230\) | 6.95130 | 0.458355 | ||||||||
\(231\) | −27.0346 | −1.77875 | ||||||||
\(232\) | −4.18921 | −0.275035 | ||||||||
\(233\) | −28.7383 | −1.88271 | −0.941354 | − | 0.337421i | \(-0.890445\pi\) | ||||
−0.941354 | + | 0.337421i | \(0.890445\pi\) | |||||||
\(234\) | −9.56166 | −0.625065 | ||||||||
\(235\) | −7.35026 | −0.479478 | ||||||||
\(236\) | 10.3430 | 0.673271 | ||||||||
\(237\) | 4.47690 | 0.290806 | ||||||||
\(238\) | −7.43210 | −0.481751 | ||||||||
\(239\) | −18.0598 | −1.16819 | −0.584096 | − | 0.811684i | \(-0.698551\pi\) | ||||
−0.584096 | + | 0.811684i | \(0.698551\pi\) | |||||||
\(240\) | −2.86567 | −0.184978 | ||||||||
\(241\) | 6.33711 | 0.408209 | 0.204105 | − | 0.978949i | \(-0.434572\pi\) | ||||
0.204105 | + | 0.978949i | \(0.434572\pi\) | |||||||
\(242\) | 0.707214 | 0.0454614 | ||||||||
\(243\) | 13.5596 | 0.869846 | ||||||||
\(244\) | 1.41889 | 0.0908350 | ||||||||
\(245\) | 12.4445 | 0.795051 | ||||||||
\(246\) | 5.16938 | 0.329587 | ||||||||
\(247\) | −6.79975 | −0.432658 | ||||||||
\(248\) | −0.712068 | −0.0452164 | ||||||||
\(249\) | 2.24697 | 0.142396 | ||||||||
\(250\) | 11.1076 | 0.702504 | ||||||||
\(251\) | 10.5272 | 0.664470 | 0.332235 | − | 0.943197i | \(-0.392197\pi\) | ||||
0.332235 | + | 0.943197i | \(0.392197\pi\) | |||||||
\(252\) | 5.64498 | 0.355601 | ||||||||
\(253\) | −16.3357 | −1.02702 | ||||||||
\(254\) | −12.7725 | −0.801417 | ||||||||
\(255\) | −5.30536 | −0.332235 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.4516 | 0.839087 | 0.419544 | − | 0.907735i | \(-0.362190\pi\) | ||||
0.419544 | + | 0.907735i | \(0.362190\pi\) | |||||||
\(258\) | 21.5242 | 1.34004 | ||||||||
\(259\) | −26.1317 | −1.62374 | ||||||||
\(260\) | 9.28299 | 0.575707 | ||||||||
\(261\) | 5.89077 | 0.364629 | ||||||||
\(262\) | 2.47248 | 0.152750 | ||||||||
\(263\) | −27.4111 | −1.69024 | −0.845122 | − | 0.534574i | \(-0.820472\pi\) | ||||
−0.845122 | + | 0.534574i | \(0.820472\pi\) | |||||||
\(264\) | 6.73438 | 0.414472 | ||||||||
\(265\) | 11.6323 | 0.714564 | ||||||||
\(266\) | 4.01442 | 0.246140 | ||||||||
\(267\) | 2.92361 | 0.178922 | ||||||||
\(268\) | 12.7000 | 0.775773 | ||||||||
\(269\) | −15.0893 | −0.920011 | −0.460005 | − | 0.887916i | \(-0.652153\pi\) | ||||
−0.460005 | + | 0.887916i | \(0.652153\pi\) | |||||||
\(270\) | −4.56737 | −0.277961 | ||||||||
\(271\) | −11.0613 | −0.671926 | −0.335963 | − | 0.941875i | \(-0.609062\pi\) | ||||
−0.335963 | + | 0.941875i | \(0.609062\pi\) | |||||||
\(272\) | 1.85135 | 0.112255 | ||||||||
\(273\) | −57.2989 | −3.46789 | ||||||||
\(274\) | 6.95851 | 0.420379 | ||||||||
\(275\) | −10.0618 | −0.606749 | ||||||||
\(276\) | 10.6881 | 0.643350 | ||||||||
\(277\) | −9.23931 | −0.555136 | −0.277568 | − | 0.960706i | \(-0.589528\pi\) | ||||
−0.277568 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(278\) | −2.69155 | −0.161428 | ||||||||
\(279\) | 1.00129 | 0.0599459 | ||||||||
\(280\) | −5.48047 | −0.327521 | ||||||||
\(281\) | −1.98630 | −0.118493 | −0.0592464 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592464 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(282\) | −11.3016 | −0.672998 | ||||||||
\(283\) | 22.3346 | 1.32765 | 0.663827 | − | 0.747886i | \(-0.268931\pi\) | ||||
0.663827 | + | 0.747886i | \(0.268931\pi\) | |||||||
\(284\) | 4.06966 | 0.241490 | ||||||||
\(285\) | 2.86567 | 0.169748 | ||||||||
\(286\) | −21.8152 | −1.28996 | ||||||||
\(287\) | 9.88621 | 0.583564 | ||||||||
\(288\) | −1.40618 | −0.0828598 | ||||||||
\(289\) | −13.5725 | −0.798382 | ||||||||
\(290\) | −5.71909 | −0.335836 | ||||||||
\(291\) | −14.1320 | −0.828433 | ||||||||
\(292\) | −10.9181 | −0.638935 | ||||||||
\(293\) | 7.92357 | 0.462900 | 0.231450 | − | 0.972847i | \(-0.425653\pi\) | ||||
0.231450 | + | 0.972847i | \(0.425653\pi\) | |||||||
\(294\) | 19.1344 | 1.11594 | ||||||||
\(295\) | 14.1202 | 0.822111 | ||||||||
\(296\) | 6.50946 | 0.378355 | ||||||||
\(297\) | 10.7334 | 0.622815 | ||||||||
\(298\) | 20.5376 | 1.18971 | ||||||||
\(299\) | −34.6229 | −2.00230 | ||||||||
\(300\) | 6.58325 | 0.380084 | ||||||||
\(301\) | 41.1641 | 2.37266 | ||||||||
\(302\) | −3.78224 | −0.217644 | ||||||||
\(303\) | −10.3515 | −0.594675 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 1.93706 | 0.110916 | ||||||||
\(306\) | −2.60333 | −0.148822 | ||||||||
\(307\) | 5.90593 | 0.337069 | 0.168535 | − | 0.985696i | \(-0.446097\pi\) | ||||
0.168535 | + | 0.985696i | \(0.446097\pi\) | |||||||
\(308\) | 12.8792 | 0.733861 | ||||||||
\(309\) | 23.9641 | 1.36327 | ||||||||
\(310\) | −0.972113 | −0.0552123 | ||||||||
\(311\) | −0.881378 | −0.0499783 | −0.0249892 | − | 0.999688i | \(-0.507955\pi\) | ||||
−0.0249892 | + | 0.999688i | \(0.507955\pi\) | |||||||
\(312\) | 14.2733 | 0.808066 | ||||||||
\(313\) | −21.3977 | −1.20947 | −0.604734 | − | 0.796428i | \(-0.706720\pi\) | ||||
−0.604734 | + | 0.796428i | \(0.706720\pi\) | |||||||
\(314\) | −1.21829 | −0.0687519 | ||||||||
\(315\) | 7.70651 | 0.434213 | ||||||||
\(316\) | −2.13278 | −0.119978 | ||||||||
\(317\) | 2.33800 | 0.131315 | 0.0656577 | − | 0.997842i | \(-0.479085\pi\) | ||||
0.0656577 | + | 0.997842i | \(0.479085\pi\) | |||||||
\(318\) | 17.8855 | 1.00297 | ||||||||
\(319\) | 13.4400 | 0.752494 | ||||||||
\(320\) | 1.36520 | 0.0763168 | ||||||||
\(321\) | 5.65567 | 0.315669 | ||||||||
\(322\) | 20.4406 | 1.13911 | ||||||||
\(323\) | −1.85135 | −0.103012 | ||||||||
\(324\) | −11.2412 | −0.624511 | ||||||||
\(325\) | −21.3256 | −1.18293 | ||||||||
\(326\) | −9.20183 | −0.509642 | ||||||||
\(327\) | −24.2560 | −1.34136 | ||||||||
\(328\) | −2.46268 | −0.135979 | ||||||||
\(329\) | −21.6137 | −1.19160 | ||||||||
\(330\) | 9.19375 | 0.506099 | ||||||||
\(331\) | 3.12286 | 0.171648 | 0.0858240 | − | 0.996310i | \(-0.472648\pi\) | ||||
0.0858240 | + | 0.996310i | \(0.472648\pi\) | |||||||
\(332\) | −1.07045 | −0.0587486 | ||||||||
\(333\) | −9.15346 | −0.501606 | ||||||||
\(334\) | 0.544945 | 0.0298181 | ||||||||
\(335\) | 17.3379 | 0.947273 | ||||||||
\(336\) | −8.42662 | −0.459710 | ||||||||
\(337\) | 8.89853 | 0.484734 | 0.242367 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242367 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(338\) | −33.2366 | −1.80783 | ||||||||
\(339\) | −7.27122 | −0.394919 | ||||||||
\(340\) | 2.52746 | 0.137071 | ||||||||
\(341\) | 2.28448 | 0.123712 | ||||||||
\(342\) | 1.40618 | 0.0760374 | ||||||||
\(343\) | 8.49269 | 0.458562 | ||||||||
\(344\) | −10.2541 | −0.552863 | ||||||||
\(345\) | 14.5914 | 0.785574 | ||||||||
\(346\) | −7.18185 | −0.386099 | ||||||||
\(347\) | −5.82350 | −0.312622 | −0.156311 | − | 0.987708i | \(-0.549960\pi\) | ||||
−0.156311 | + | 0.987708i | \(0.549960\pi\) | |||||||
\(348\) | −8.79352 | −0.471382 | ||||||||
\(349\) | −22.3662 | −1.19724 | −0.598618 | − | 0.801035i | \(-0.704283\pi\) | ||||
−0.598618 | + | 0.801035i | \(0.704283\pi\) | |||||||
\(350\) | 12.5902 | 0.672973 | ||||||||
\(351\) | 22.7491 | 1.21426 | ||||||||
\(352\) | −3.20824 | −0.171000 | ||||||||
\(353\) | −14.8098 | −0.788246 | −0.394123 | − | 0.919058i | \(-0.628952\pi\) | ||||
−0.394123 | + | 0.919058i | \(0.628952\pi\) | |||||||
\(354\) | 21.7109 | 1.15392 | ||||||||
\(355\) | 5.55588 | 0.294876 | ||||||||
\(356\) | −1.39280 | −0.0738182 | ||||||||
\(357\) | −15.6006 | −0.825674 | ||||||||
\(358\) | 12.2753 | 0.648769 | ||||||||
\(359\) | 30.4912 | 1.60927 | 0.804633 | − | 0.593773i | \(-0.202362\pi\) | ||||
0.804633 | + | 0.593773i | \(0.202362\pi\) | |||||||
\(360\) | −1.91971 | −0.101178 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 2.93286 | 0.154148 | ||||||||
\(363\) | 1.48451 | 0.0779164 | ||||||||
\(364\) | 27.2970 | 1.43075 | ||||||||
\(365\) | −14.9054 | −0.780183 | ||||||||
\(366\) | 2.97837 | 0.155682 | ||||||||
\(367\) | 33.5656 | 1.75211 | 0.876054 | − | 0.482213i | \(-0.160167\pi\) | ||||
0.876054 | + | 0.482213i | \(0.160167\pi\) | |||||||
\(368\) | −5.09179 | −0.265428 | ||||||||
\(369\) | 3.46296 | 0.180274 | ||||||||
\(370\) | 8.88669 | 0.461997 | ||||||||
\(371\) | 34.2052 | 1.77584 | ||||||||
\(372\) | −1.49469 | −0.0774963 | ||||||||
\(373\) | 12.1478 | 0.628991 | 0.314495 | − | 0.949259i | \(-0.398165\pi\) | ||||
0.314495 | + | 0.949259i | \(0.398165\pi\) | |||||||
\(374\) | −5.93958 | −0.307128 | ||||||||
\(375\) | 23.3158 | 1.20402 | ||||||||
\(376\) | 5.38403 | 0.277660 | ||||||||
\(377\) | 28.4856 | 1.46708 | ||||||||
\(378\) | −13.4305 | −0.690792 | ||||||||
\(379\) | 6.92608 | 0.355769 | 0.177884 | − | 0.984051i | \(-0.443075\pi\) | ||||
0.177884 | + | 0.984051i | \(0.443075\pi\) | |||||||
\(380\) | −1.36520 | −0.0700331 | ||||||||
\(381\) | −26.8106 | −1.37355 | ||||||||
\(382\) | −0.334793 | −0.0171295 | ||||||||
\(383\) | −9.79457 | −0.500479 | −0.250239 | − | 0.968184i | \(-0.580509\pi\) | ||||
−0.250239 | + | 0.968184i | \(0.580509\pi\) | |||||||
\(384\) | 2.09909 | 0.107119 | ||||||||
\(385\) | 17.5826 | 0.896094 | ||||||||
\(386\) | 7.21710 | 0.367341 | ||||||||
\(387\) | 14.4191 | 0.732962 | ||||||||
\(388\) | 6.73244 | 0.341788 | ||||||||
\(389\) | 34.1871 | 1.73335 | 0.866676 | − | 0.498871i | \(-0.166252\pi\) | ||||
0.866676 | + | 0.498871i | \(0.166252\pi\) | |||||||
\(390\) | 19.4858 | 0.986704 | ||||||||
\(391\) | −9.42670 | −0.476729 | ||||||||
\(392\) | −9.11555 | −0.460405 | ||||||||
\(393\) | 5.18996 | 0.261799 | ||||||||
\(394\) | −1.72510 | −0.0869094 | ||||||||
\(395\) | −2.91167 | −0.146502 | ||||||||
\(396\) | 4.51135 | 0.226704 | ||||||||
\(397\) | 16.0565 | 0.805852 | 0.402926 | − | 0.915233i | \(-0.367993\pi\) | ||||
0.402926 | + | 0.915233i | \(0.367993\pi\) | |||||||
\(398\) | −7.92046 | −0.397017 | ||||||||
\(399\) | 8.42662 | 0.421859 | ||||||||
\(400\) | −3.13624 | −0.156812 | ||||||||
\(401\) | −12.0767 | −0.603084 | −0.301542 | − | 0.953453i | \(-0.597501\pi\) | ||||
−0.301542 | + | 0.953453i | \(0.597501\pi\) | |||||||
\(402\) | 26.6584 | 1.32960 | ||||||||
\(403\) | 4.84189 | 0.241191 | ||||||||
\(404\) | 4.93140 | 0.245346 | ||||||||
\(405\) | −15.3464 | −0.762571 | ||||||||
\(406\) | −16.8172 | −0.834625 | ||||||||
\(407\) | −20.8839 | −1.03518 | ||||||||
\(408\) | 3.88615 | 0.192393 | ||||||||
\(409\) | −9.59680 | −0.474531 | −0.237266 | − | 0.971445i | \(-0.576251\pi\) | ||||
−0.237266 | + | 0.971445i | \(0.576251\pi\) | |||||||
\(410\) | −3.36204 | −0.166039 | ||||||||
\(411\) | 14.6065 | 0.720487 | ||||||||
\(412\) | −11.4164 | −0.562446 | ||||||||
\(413\) | 41.5211 | 2.04312 | ||||||||
\(414\) | 7.15997 | 0.351893 | ||||||||
\(415\) | −1.46138 | −0.0717361 | ||||||||
\(416\) | −6.79975 | −0.333385 | ||||||||
\(417\) | −5.64980 | −0.276672 | ||||||||
\(418\) | 3.20824 | 0.156920 | ||||||||
\(419\) | −17.7597 | −0.867620 | −0.433810 | − | 0.901004i | \(-0.642831\pi\) | ||||
−0.433810 | + | 0.901004i | \(0.642831\pi\) | |||||||
\(420\) | −11.5040 | −0.561337 | ||||||||
\(421\) | −32.4693 | −1.58245 | −0.791227 | − | 0.611522i | \(-0.790558\pi\) | ||||
−0.791227 | + | 0.611522i | \(0.790558\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −7.57090 | −0.368110 | ||||||||
\(424\) | −8.52058 | −0.413796 | ||||||||
\(425\) | −5.80628 | −0.281646 | ||||||||
\(426\) | 8.54258 | 0.413889 | ||||||||
\(427\) | 5.69601 | 0.275649 | ||||||||
\(428\) | −2.69435 | −0.130236 | ||||||||
\(429\) | −45.7921 | −2.21086 | ||||||||
\(430\) | −13.9988 | −0.675083 | ||||||||
\(431\) | −26.6865 | −1.28544 | −0.642721 | − | 0.766100i | \(-0.722194\pi\) | ||||
−0.642721 | + | 0.766100i | \(0.722194\pi\) | |||||||
\(432\) | 3.34558 | 0.160964 | ||||||||
\(433\) | 2.53135 | 0.121649 | 0.0608246 | − | 0.998148i | \(-0.480627\pi\) | ||||
0.0608246 | + | 0.998148i | \(0.480627\pi\) | |||||||
\(434\) | −2.85854 | −0.137214 | ||||||||
\(435\) | −12.0049 | −0.575590 | ||||||||
\(436\) | 11.5555 | 0.553408 | ||||||||
\(437\) | 5.09179 | 0.243574 | ||||||||
\(438\) | −22.9181 | −1.09507 | ||||||||
\(439\) | 3.05361 | 0.145741 | 0.0728704 | − | 0.997341i | \(-0.476784\pi\) | ||||
0.0728704 | + | 0.997341i | \(0.476784\pi\) | |||||||
\(440\) | −4.37987 | −0.208802 | ||||||||
\(441\) | 12.8181 | 0.610385 | ||||||||
\(442\) | −12.5887 | −0.598785 | ||||||||
\(443\) | −23.5422 | −1.11852 | −0.559261 | − | 0.828992i | \(-0.688915\pi\) | ||||
−0.559261 | + | 0.828992i | \(0.688915\pi\) | |||||||
\(444\) | 13.6639 | 0.648462 | ||||||||
\(445\) | −1.90144 | −0.0901371 | ||||||||
\(446\) | −9.60089 | −0.454615 | ||||||||
\(447\) | 43.1103 | 2.03905 | ||||||||
\(448\) | 4.01442 | 0.189663 | ||||||||
\(449\) | −28.4555 | −1.34290 | −0.671448 | − | 0.741052i | \(-0.734327\pi\) | ||||
−0.671448 | + | 0.741052i | \(0.734327\pi\) | |||||||
\(450\) | 4.41011 | 0.207895 | ||||||||
\(451\) | 7.90085 | 0.372036 | ||||||||
\(452\) | 3.46399 | 0.162932 | ||||||||
\(453\) | −7.93927 | −0.373019 | ||||||||
\(454\) | 24.5848 | 1.15382 | ||||||||
\(455\) | 37.2658 | 1.74705 | ||||||||
\(456\) | −2.09909 | −0.0982989 | ||||||||
\(457\) | −21.6748 | −1.01390 | −0.506952 | − | 0.861974i | \(-0.669228\pi\) | ||||
−0.506952 | + | 0.861974i | \(0.669228\pi\) | |||||||
\(458\) | −5.87183 | −0.274373 | ||||||||
\(459\) | 6.19384 | 0.289104 | ||||||||
\(460\) | −6.95130 | −0.324106 | ||||||||
\(461\) | 38.6715 | 1.80111 | 0.900556 | − | 0.434740i | \(-0.143160\pi\) | ||||
0.900556 | + | 0.434740i | \(0.143160\pi\) | |||||||
\(462\) | 27.0346 | 1.25776 | ||||||||
\(463\) | 17.3366 | 0.805702 | 0.402851 | − | 0.915266i | \(-0.368019\pi\) | ||||
0.402851 | + | 0.915266i | \(0.368019\pi\) | |||||||
\(464\) | 4.18921 | 0.194479 | ||||||||
\(465\) | −2.04055 | −0.0946283 | ||||||||
\(466\) | 28.7383 | 1.33128 | ||||||||
\(467\) | −22.9253 | −1.06086 | −0.530429 | − | 0.847729i | \(-0.677969\pi\) | ||||
−0.530429 | + | 0.847729i | \(0.677969\pi\) | |||||||
\(468\) | 9.56166 | 0.441988 | ||||||||
\(469\) | 50.9829 | 2.35417 | ||||||||
\(470\) | 7.35026 | 0.339042 | ||||||||
\(471\) | −2.55729 | −0.117834 | ||||||||
\(472\) | −10.3430 | −0.476075 | ||||||||
\(473\) | 32.8975 | 1.51263 | ||||||||
\(474\) | −4.47690 | −0.205631 | ||||||||
\(475\) | 3.13624 | 0.143901 | ||||||||
\(476\) | 7.43210 | 0.340650 | ||||||||
\(477\) | 11.9814 | 0.548593 | ||||||||
\(478\) | 18.0598 | 0.826037 | ||||||||
\(479\) | 37.0920 | 1.69478 | 0.847388 | − | 0.530974i | \(-0.178174\pi\) | ||||
0.847388 | + | 0.530974i | \(0.178174\pi\) | |||||||
\(480\) | 2.86567 | 0.130799 | ||||||||
\(481\) | −44.2627 | −2.01821 | ||||||||
\(482\) | −6.33711 | −0.288648 | ||||||||
\(483\) | 42.9066 | 1.95232 | ||||||||
\(484\) | −0.707214 | −0.0321461 | ||||||||
\(485\) | 9.19111 | 0.417347 | ||||||||
\(486\) | −13.5596 | −0.615074 | ||||||||
\(487\) | −15.8194 | −0.716847 | −0.358423 | − | 0.933559i | \(-0.616686\pi\) | ||||
−0.358423 | + | 0.933559i | \(0.616686\pi\) | |||||||
\(488\) | −1.41889 | −0.0642301 | ||||||||
\(489\) | −19.3155 | −0.873476 | ||||||||
\(490\) | −12.4445 | −0.562186 | ||||||||
\(491\) | 29.5626 | 1.33414 | 0.667072 | − | 0.744994i | \(-0.267547\pi\) | ||||
0.667072 | + | 0.744994i | \(0.267547\pi\) | |||||||
\(492\) | −5.16938 | −0.233054 | ||||||||
\(493\) | 7.75570 | 0.349299 | ||||||||
\(494\) | 6.79975 | 0.305935 | ||||||||
\(495\) | 6.15888 | 0.276821 | ||||||||
\(496\) | 0.712068 | 0.0319728 | ||||||||
\(497\) | 16.3373 | 0.732829 | ||||||||
\(498\) | −2.24697 | −0.100689 | ||||||||
\(499\) | −14.7836 | −0.661804 | −0.330902 | − | 0.943665i | \(-0.607353\pi\) | ||||
−0.330902 | + | 0.943665i | \(0.607353\pi\) | |||||||
\(500\) | −11.1076 | −0.496745 | ||||||||
\(501\) | 1.14389 | 0.0511052 | ||||||||
\(502\) | −10.5272 | −0.469852 | ||||||||
\(503\) | −6.57703 | −0.293255 | −0.146628 | − | 0.989192i | \(-0.546842\pi\) | ||||
−0.146628 | + | 0.989192i | \(0.546842\pi\) | |||||||
\(504\) | −5.64498 | −0.251448 | ||||||||
\(505\) | 6.73233 | 0.299585 | ||||||||
\(506\) | 16.3357 | 0.726210 | ||||||||
\(507\) | −69.7666 | −3.09844 | ||||||||
\(508\) | 12.7725 | 0.566687 | ||||||||
\(509\) | −6.46511 | −0.286561 | −0.143280 | − | 0.989682i | \(-0.545765\pi\) | ||||
−0.143280 | + | 0.989682i | \(0.545765\pi\) | |||||||
\(510\) | 5.30536 | 0.234925 | ||||||||
\(511\) | −43.8299 | −1.93892 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.34558 | −0.147711 | ||||||||
\(514\) | −13.4516 | −0.593324 | ||||||||
\(515\) | −15.5856 | −0.686785 | ||||||||
\(516\) | −21.5242 | −0.947551 | ||||||||
\(517\) | −17.2732 | −0.759676 | ||||||||
\(518\) | 26.1317 | 1.14816 | ||||||||
\(519\) | −15.0754 | −0.661735 | ||||||||
\(520\) | −9.28299 | −0.407086 | ||||||||
\(521\) | −30.2026 | −1.32320 | −0.661600 | − | 0.749857i | \(-0.730122\pi\) | ||||
−0.661600 | + | 0.749857i | \(0.730122\pi\) | |||||||
\(522\) | −5.89077 | −0.257832 | ||||||||
\(523\) | 34.8479 | 1.52379 | 0.761897 | − | 0.647698i | \(-0.224268\pi\) | ||||
0.761897 | + | 0.647698i | \(0.224268\pi\) | |||||||
\(524\) | −2.47248 | −0.108011 | ||||||||
\(525\) | 26.4279 | 1.15341 | ||||||||
\(526\) | 27.4111 | 1.19518 | ||||||||
\(527\) | 1.31829 | 0.0574256 | ||||||||
\(528\) | −6.73438 | −0.293076 | ||||||||
\(529\) | 2.92637 | 0.127233 | ||||||||
\(530\) | −11.6323 | −0.505273 | ||||||||
\(531\) | 14.5441 | 0.631159 | ||||||||
\(532\) | −4.01442 | −0.174047 | ||||||||
\(533\) | 16.7456 | 0.725331 | ||||||||
\(534\) | −2.92361 | −0.126517 | ||||||||
\(535\) | −3.67831 | −0.159027 | ||||||||
\(536\) | −12.7000 | −0.548555 | ||||||||
\(537\) | 25.7669 | 1.11193 | ||||||||
\(538\) | 15.0893 | 0.650546 | ||||||||
\(539\) | 29.2448 | 1.25966 | ||||||||
\(540\) | 4.56737 | 0.196548 | ||||||||
\(541\) | 12.1188 | 0.521026 | 0.260513 | − | 0.965470i | \(-0.416108\pi\) | ||||
0.260513 | + | 0.965470i | \(0.416108\pi\) | |||||||
\(542\) | 11.0613 | 0.475123 | ||||||||
\(543\) | 6.15633 | 0.264193 | ||||||||
\(544\) | −1.85135 | −0.0793761 | ||||||||
\(545\) | 15.7755 | 0.675749 | ||||||||
\(546\) | 57.2989 | 2.45217 | ||||||||
\(547\) | 14.5532 | 0.622251 | 0.311126 | − | 0.950369i | \(-0.399294\pi\) | ||||
0.311126 | + | 0.950369i | \(0.399294\pi\) | |||||||
\(548\) | −6.95851 | −0.297253 | ||||||||
\(549\) | 1.99521 | 0.0851535 | ||||||||
\(550\) | 10.0618 | 0.429037 | ||||||||
\(551\) | −4.18921 | −0.178466 | ||||||||
\(552\) | −10.6881 | −0.454917 | ||||||||
\(553\) | −8.56188 | −0.364088 | ||||||||
\(554\) | 9.23931 | 0.392541 | ||||||||
\(555\) | 18.6540 | 0.791816 | ||||||||
\(556\) | 2.69155 | 0.114147 | ||||||||
\(557\) | −16.4156 | −0.695552 | −0.347776 | − | 0.937578i | \(-0.613063\pi\) | ||||
−0.347776 | + | 0.937578i | \(0.613063\pi\) | |||||||
\(558\) | −1.00129 | −0.0423882 | ||||||||
\(559\) | 69.7251 | 2.94906 | ||||||||
\(560\) | 5.48047 | 0.231592 | ||||||||
\(561\) | −12.4677 | −0.526387 | ||||||||
\(562\) | 1.98630 | 0.0837870 | ||||||||
\(563\) | −28.9442 | −1.21985 | −0.609925 | − | 0.792459i | \(-0.708801\pi\) | ||||
−0.609925 | + | 0.792459i | \(0.708801\pi\) | |||||||
\(564\) | 11.3016 | 0.475882 | ||||||||
\(565\) | 4.72902 | 0.198952 | ||||||||
\(566\) | −22.3346 | −0.938793 | ||||||||
\(567\) | −45.1269 | −1.89515 | ||||||||
\(568\) | −4.06966 | −0.170759 | ||||||||
\(569\) | −1.36758 | −0.0573320 | −0.0286660 | − | 0.999589i | \(-0.509126\pi\) | ||||
−0.0286660 | + | 0.999589i | \(0.509126\pi\) | |||||||
\(570\) | −2.86567 | −0.120030 | ||||||||
\(571\) | 33.7948 | 1.41427 | 0.707134 | − | 0.707079i | \(-0.249988\pi\) | ||||
0.707134 | + | 0.707079i | \(0.249988\pi\) | |||||||
\(572\) | 21.8152 | 0.912140 | ||||||||
\(573\) | −0.702762 | −0.0293583 | ||||||||
\(574\) | −9.88621 | −0.412642 | ||||||||
\(575\) | 15.9691 | 0.665957 | ||||||||
\(576\) | 1.40618 | 0.0585907 | ||||||||
\(577\) | 13.6874 | 0.569813 | 0.284907 | − | 0.958555i | \(-0.408037\pi\) | ||||
0.284907 | + | 0.958555i | \(0.408037\pi\) | |||||||
\(578\) | 13.5725 | 0.564541 | ||||||||
\(579\) | 15.1493 | 0.629585 | ||||||||
\(580\) | 5.71909 | 0.237472 | ||||||||
\(581\) | −4.29724 | −0.178279 | ||||||||
\(582\) | 14.1320 | 0.585790 | ||||||||
\(583\) | 27.3360 | 1.13214 | ||||||||
\(584\) | 10.9181 | 0.451795 | ||||||||
\(585\) | 13.0535 | 0.539697 | ||||||||
\(586\) | −7.92357 | −0.327320 | ||||||||
\(587\) | −6.75410 | −0.278772 | −0.139386 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139386 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(588\) | −19.1344 | −0.789087 | ||||||||
\(589\) | −0.712068 | −0.0293403 | ||||||||
\(590\) | −14.1202 | −0.581320 | ||||||||
\(591\) | −3.62114 | −0.148954 | ||||||||
\(592\) | −6.50946 | −0.267537 | ||||||||
\(593\) | 8.99007 | 0.369178 | 0.184589 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184589 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(594\) | −10.7334 | −0.440397 | ||||||||
\(595\) | 10.1463 | 0.415957 | ||||||||
\(596\) | −20.5376 | −0.841253 | ||||||||
\(597\) | −16.6257 | −0.680447 | ||||||||
\(598\) | 34.6229 | 1.41584 | ||||||||
\(599\) | 23.5439 | 0.961977 | 0.480988 | − | 0.876727i | \(-0.340278\pi\) | ||||
0.480988 | + | 0.876727i | \(0.340278\pi\) | |||||||
\(600\) | −6.58325 | −0.268760 | ||||||||
\(601\) | 30.8591 | 1.25877 | 0.629385 | − | 0.777093i | \(-0.283307\pi\) | ||||
0.629385 | + | 0.777093i | \(0.283307\pi\) | |||||||
\(602\) | −41.1641 | −1.67772 | ||||||||
\(603\) | 17.8584 | 0.727250 | ||||||||
\(604\) | 3.78224 | 0.153897 | ||||||||
\(605\) | −0.965486 | −0.0392526 | ||||||||
\(606\) | 10.3515 | 0.420499 | ||||||||
\(607\) | 32.0409 | 1.30050 | 0.650250 | − | 0.759720i | \(-0.274664\pi\) | ||||
0.650250 | + | 0.759720i | \(0.274664\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −35.3009 | −1.43046 | ||||||||
\(610\) | −1.93706 | −0.0784293 | ||||||||
\(611\) | −36.6101 | −1.48108 | ||||||||
\(612\) | 2.60333 | 0.105233 | ||||||||
\(613\) | −3.46021 | −0.139757 | −0.0698784 | − | 0.997556i | \(-0.522261\pi\) | ||||
−0.0698784 | + | 0.997556i | \(0.522261\pi\) | |||||||
\(614\) | −5.90593 | −0.238344 | ||||||||
\(615\) | −7.05721 | −0.284574 | ||||||||
\(616\) | −12.8792 | −0.518918 | ||||||||
\(617\) | −23.6533 | −0.952245 | −0.476122 | − | 0.879379i | \(-0.657958\pi\) | ||||
−0.476122 | + | 0.879379i | \(0.657958\pi\) | |||||||
\(618\) | −23.9641 | −0.963976 | ||||||||
\(619\) | −37.8759 | −1.52236 | −0.761180 | − | 0.648541i | \(-0.775380\pi\) | ||||
−0.761180 | + | 0.648541i | \(0.775380\pi\) | |||||||
\(620\) | 0.972113 | 0.0390410 | ||||||||
\(621\) | −17.0350 | −0.683590 | ||||||||
\(622\) | 0.881378 | 0.0353400 | ||||||||
\(623\) | −5.59128 | −0.224010 | ||||||||
\(624\) | −14.2733 | −0.571389 | ||||||||
\(625\) | 0.517193 | 0.0206877 | ||||||||
\(626\) | 21.3977 | 0.855222 | ||||||||
\(627\) | 6.73438 | 0.268945 | ||||||||
\(628\) | 1.21829 | 0.0486150 | ||||||||
\(629\) | −12.0513 | −0.480517 | ||||||||
\(630\) | −7.70651 | −0.307035 | ||||||||
\(631\) | −11.2238 | −0.446811 | −0.223405 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223405 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(632\) | 2.13278 | 0.0848375 | ||||||||
\(633\) | −2.09909 | −0.0834313 | ||||||||
\(634\) | −2.33800 | −0.0928539 | ||||||||
\(635\) | 17.4369 | 0.691964 | ||||||||
\(636\) | −17.8855 | −0.709205 | ||||||||
\(637\) | 61.9834 | 2.45587 | ||||||||
\(638\) | −13.4400 | −0.532093 | ||||||||
\(639\) | 5.72267 | 0.226385 | ||||||||
\(640\) | −1.36520 | −0.0539641 | ||||||||
\(641\) | −7.97255 | −0.314897 | −0.157448 | − | 0.987527i | \(-0.550327\pi\) | ||||
−0.157448 | + | 0.987527i | \(0.550327\pi\) | |||||||
\(642\) | −5.65567 | −0.223212 | ||||||||
\(643\) | 39.9487 | 1.57542 | 0.787711 | − | 0.616045i | \(-0.211266\pi\) | ||||
0.787711 | + | 0.616045i | \(0.211266\pi\) | |||||||
\(644\) | −20.4406 | −0.805472 | ||||||||
\(645\) | −29.3848 | −1.15702 | ||||||||
\(646\) | 1.85135 | 0.0728405 | ||||||||
\(647\) | 1.94128 | 0.0763196 | 0.0381598 | − | 0.999272i | \(-0.487850\pi\) | ||||
0.0381598 | + | 0.999272i | \(0.487850\pi\) | |||||||
\(648\) | 11.2412 | 0.441596 | ||||||||
\(649\) | 33.1828 | 1.30254 | ||||||||
\(650\) | 21.3256 | 0.836461 | ||||||||
\(651\) | −6.00033 | −0.235171 | ||||||||
\(652\) | 9.20183 | 0.360371 | ||||||||
\(653\) | −19.3525 | −0.757322 | −0.378661 | − | 0.925535i | \(-0.623615\pi\) | ||||
−0.378661 | + | 0.925535i | \(0.623615\pi\) | |||||||
\(654\) | 24.2560 | 0.948485 | ||||||||
\(655\) | −3.37542 | −0.131889 | ||||||||
\(656\) | 2.46268 | 0.0961513 | ||||||||
\(657\) | −15.3528 | −0.598970 | ||||||||
\(658\) | 21.6137 | 0.842591 | ||||||||
\(659\) | 19.3530 | 0.753886 | 0.376943 | − | 0.926236i | \(-0.376975\pi\) | ||||
0.376943 | + | 0.926236i | \(0.376975\pi\) | |||||||
\(660\) | −9.19375 | −0.357866 | ||||||||
\(661\) | −44.0744 | −1.71430 | −0.857148 | − | 0.515070i | \(-0.827766\pi\) | ||||
−0.857148 | + | 0.515070i | \(0.827766\pi\) | |||||||
\(662\) | −3.12286 | −0.121373 | ||||||||
\(663\) | −26.4249 | −1.02626 | ||||||||
\(664\) | 1.07045 | 0.0415416 | ||||||||
\(665\) | −5.48047 | −0.212523 | ||||||||
\(666\) | 9.15346 | 0.354689 | ||||||||
\(667\) | −21.3306 | −0.825923 | ||||||||
\(668\) | −0.544945 | −0.0210846 | ||||||||
\(669\) | −20.1531 | −0.779165 | ||||||||
\(670\) | −17.3379 | −0.669823 | ||||||||
\(671\) | 4.55213 | 0.175733 | ||||||||
\(672\) | 8.42662 | 0.325064 | ||||||||
\(673\) | −13.7683 | −0.530731 | −0.265365 | − | 0.964148i | \(-0.585493\pi\) | ||||
−0.265365 | + | 0.964148i | \(0.585493\pi\) | |||||||
\(674\) | −8.89853 | −0.342758 | ||||||||
\(675\) | −10.4925 | −0.403858 | ||||||||
\(676\) | 33.2366 | 1.27833 | ||||||||
\(677\) | 37.4217 | 1.43823 | 0.719117 | − | 0.694889i | \(-0.244546\pi\) | ||||
0.719117 | + | 0.694889i | \(0.244546\pi\) | |||||||
\(678\) | 7.27122 | 0.279250 | ||||||||
\(679\) | 27.0268 | 1.03719 | ||||||||
\(680\) | −2.52746 | −0.0969236 | ||||||||
\(681\) | 51.6057 | 1.97753 | ||||||||
\(682\) | −2.28448 | −0.0874774 | ||||||||
\(683\) | 11.6717 | 0.446603 | 0.223302 | − | 0.974749i | \(-0.428317\pi\) | ||||
0.223302 | + | 0.974749i | \(0.428317\pi\) | |||||||
\(684\) | −1.40618 | −0.0537666 | ||||||||
\(685\) | −9.49973 | −0.362966 | ||||||||
\(686\) | −8.49269 | −0.324252 | ||||||||
\(687\) | −12.3255 | −0.470247 | ||||||||
\(688\) | 10.2541 | 0.390933 | ||||||||
\(689\) | 57.9378 | 2.20725 | ||||||||
\(690\) | −14.5914 | −0.555485 | ||||||||
\(691\) | 2.80943 | 0.106876 | 0.0534379 | − | 0.998571i | \(-0.482982\pi\) | ||||
0.0534379 | + | 0.998571i | \(0.482982\pi\) | |||||||
\(692\) | 7.18185 | 0.273013 | ||||||||
\(693\) | 18.1104 | 0.687959 | ||||||||
\(694\) | 5.82350 | 0.221057 | ||||||||
\(695\) | 3.67449 | 0.139381 | ||||||||
\(696\) | 8.79352 | 0.333318 | ||||||||
\(697\) | 4.55928 | 0.172695 | ||||||||
\(698\) | 22.3662 | 0.846574 | ||||||||
\(699\) | 60.3242 | 2.28167 | ||||||||
\(700\) | −12.5902 | −0.475864 | ||||||||
\(701\) | 11.3301 | 0.427934 | 0.213967 | − | 0.976841i | \(-0.431362\pi\) | ||||
0.213967 | + | 0.976841i | \(0.431362\pi\) | |||||||
\(702\) | −22.7491 | −0.858609 | ||||||||
\(703\) | 6.50946 | 0.245509 | ||||||||
\(704\) | 3.20824 | 0.120915 | ||||||||
\(705\) | 15.4288 | 0.581084 | ||||||||
\(706\) | 14.8098 | 0.557374 | ||||||||
\(707\) | 19.7967 | 0.744532 | ||||||||
\(708\) | −21.7109 | −0.815944 | ||||||||
\(709\) | −48.9067 | −1.83673 | −0.918364 | − | 0.395736i | \(-0.870489\pi\) | ||||
−0.918364 | + | 0.395736i | \(0.870489\pi\) | |||||||
\(710\) | −5.55588 | −0.208509 | ||||||||
\(711\) | −2.99907 | −0.112474 | ||||||||
\(712\) | 1.39280 | 0.0521974 | ||||||||
\(713\) | −3.62570 | −0.135784 | ||||||||
\(714\) | 15.6006 | 0.583839 | ||||||||
\(715\) | 29.7820 | 1.11379 | ||||||||
\(716\) | −12.2753 | −0.458749 | ||||||||
\(717\) | 37.9092 | 1.41574 | ||||||||
\(718\) | −30.4912 | −1.13792 | ||||||||
\(719\) | 18.1079 | 0.675312 | 0.337656 | − | 0.941270i | \(-0.390366\pi\) | ||||
0.337656 | + | 0.941270i | \(0.390366\pi\) | |||||||
\(720\) | 1.91971 | 0.0715433 | ||||||||
\(721\) | −45.8302 | −1.70681 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −13.3022 | −0.494713 | ||||||||
\(724\) | −2.93286 | −0.108999 | ||||||||
\(725\) | −13.1384 | −0.487946 | ||||||||
\(726\) | −1.48451 | −0.0550952 | ||||||||
\(727\) | 9.15818 | 0.339658 | 0.169829 | − | 0.985474i | \(-0.445678\pi\) | ||||
0.169829 | + | 0.985474i | \(0.445678\pi\) | |||||||
\(728\) | −27.2970 | −1.01170 | ||||||||
\(729\) | 5.26087 | 0.194847 | ||||||||
\(730\) | 14.9054 | 0.551673 | ||||||||
\(731\) | 18.9839 | 0.702145 | ||||||||
\(732\) | −2.97837 | −0.110084 | ||||||||
\(733\) | −36.0381 | −1.33110 | −0.665549 | − | 0.746354i | \(-0.731803\pi\) | ||||
−0.665549 | + | 0.746354i | \(0.731803\pi\) | |||||||
\(734\) | −33.5656 | −1.23893 | ||||||||
\(735\) | −26.1221 | −0.963530 | ||||||||
\(736\) | 5.09179 | 0.187686 | ||||||||
\(737\) | 40.7445 | 1.50084 | ||||||||
\(738\) | −3.46296 | −0.127473 | ||||||||
\(739\) | 17.8157 | 0.655360 | 0.327680 | − | 0.944789i | \(-0.393733\pi\) | ||||
0.327680 | + | 0.944789i | \(0.393733\pi\) | |||||||
\(740\) | −8.88669 | −0.326681 | ||||||||
\(741\) | 14.2733 | 0.524342 | ||||||||
\(742\) | −34.2052 | −1.25571 | ||||||||
\(743\) | 36.6957 | 1.34623 | 0.673117 | − | 0.739536i | \(-0.264955\pi\) | ||||
0.673117 | + | 0.739536i | \(0.264955\pi\) | |||||||
\(744\) | 1.49469 | 0.0547982 | ||||||||
\(745\) | −28.0379 | −1.02723 | ||||||||
\(746\) | −12.1478 | −0.444764 | ||||||||
\(747\) | −1.50524 | −0.0550740 | ||||||||
\(748\) | 5.93958 | 0.217172 | ||||||||
\(749\) | −10.8162 | −0.395216 | ||||||||
\(750\) | −23.3158 | −0.851372 | ||||||||
\(751\) | 3.91941 | 0.143021 | 0.0715106 | − | 0.997440i | \(-0.477218\pi\) | ||||
0.0715106 | + | 0.997440i | \(0.477218\pi\) | |||||||
\(752\) | −5.38403 | −0.196335 | ||||||||
\(753\) | −22.0975 | −0.805278 | ||||||||
\(754\) | −28.4856 | −1.03738 | ||||||||
\(755\) | 5.16350 | 0.187919 | ||||||||
\(756\) | 13.4305 | 0.488464 | ||||||||
\(757\) | 22.5512 | 0.819637 | 0.409818 | − | 0.912167i | \(-0.365592\pi\) | ||||
0.409818 | + | 0.912167i | \(0.365592\pi\) | |||||||
\(758\) | −6.92608 | −0.251567 | ||||||||
\(759\) | 34.2901 | 1.24465 | ||||||||
\(760\) | 1.36520 | 0.0495209 | ||||||||
\(761\) | 27.4817 | 0.996210 | 0.498105 | − | 0.867117i | \(-0.334029\pi\) | ||||
0.498105 | + | 0.867117i | \(0.334029\pi\) | |||||||
\(762\) | 26.8106 | 0.971245 | ||||||||
\(763\) | 46.3886 | 1.67938 | ||||||||
\(764\) | 0.334793 | 0.0121124 | ||||||||
\(765\) | 3.55406 | 0.128497 | ||||||||
\(766\) | 9.79457 | 0.353892 | ||||||||
\(767\) | 70.3298 | 2.53946 | ||||||||
\(768\) | −2.09909 | −0.0757444 | ||||||||
\(769\) | 35.7216 | 1.28815 | 0.644077 | − | 0.764961i | \(-0.277242\pi\) | ||||
0.644077 | + | 0.764961i | \(0.277242\pi\) | |||||||
\(770\) | −17.5826 | −0.633634 | ||||||||
\(771\) | −28.2361 | −1.01690 | ||||||||
\(772\) | −7.21710 | −0.259749 | ||||||||
\(773\) | 5.71637 | 0.205603 | 0.102802 | − | 0.994702i | \(-0.467219\pi\) | ||||
0.102802 | + | 0.994702i | \(0.467219\pi\) | |||||||
\(774\) | −14.4191 | −0.518282 | ||||||||
\(775\) | −2.23322 | −0.0802195 | ||||||||
\(776\) | −6.73244 | −0.241681 | ||||||||
\(777\) | 54.8528 | 1.96783 | ||||||||
\(778\) | −34.1871 | −1.22567 | ||||||||
\(779\) | −2.46268 | −0.0882345 | ||||||||
\(780\) | −19.4858 | −0.697705 | ||||||||
\(781\) | 13.0564 | 0.467196 | ||||||||
\(782\) | 9.42670 | 0.337098 | ||||||||
\(783\) | 14.0153 | 0.500866 | ||||||||
\(784\) | 9.11555 | 0.325555 | ||||||||
\(785\) | 1.66320 | 0.0593622 | ||||||||
\(786\) | −5.18996 | −0.185120 | ||||||||
\(787\) | −8.51979 | −0.303698 | −0.151849 | − | 0.988404i | \(-0.548523\pi\) | ||||
−0.151849 | + | 0.988404i | \(0.548523\pi\) | |||||||
\(788\) | 1.72510 | 0.0614542 | ||||||||
\(789\) | 57.5385 | 2.04842 | ||||||||
\(790\) | 2.91167 | 0.103592 | ||||||||
\(791\) | 13.9059 | 0.494437 | ||||||||
\(792\) | −4.51135 | −0.160304 | ||||||||
\(793\) | 9.64809 | 0.342614 | ||||||||
\(794\) | −16.0565 | −0.569823 | ||||||||
\(795\) | −24.4172 | −0.865987 | ||||||||
\(796\) | 7.92046 | 0.280733 | ||||||||
\(797\) | −29.3299 | −1.03892 | −0.519460 | − | 0.854495i | \(-0.673867\pi\) | ||||
−0.519460 | + | 0.854495i | \(0.673867\pi\) | |||||||
\(798\) | −8.42662 | −0.298299 | ||||||||
\(799\) | −9.96773 | −0.352633 | ||||||||
\(800\) | 3.13624 | 0.110883 | ||||||||
\(801\) | −1.95852 | −0.0692010 | ||||||||
\(802\) | 12.0767 | 0.426445 | ||||||||
\(803\) | −35.0279 | −1.23611 | ||||||||
\(804\) | −26.6584 | −0.940168 | ||||||||
\(805\) | −27.9054 | −0.983537 | ||||||||
\(806\) | −4.84189 | −0.170548 | ||||||||
\(807\) | 31.6738 | 1.11497 | ||||||||
\(808\) | −4.93140 | −0.173486 | ||||||||
\(809\) | 17.5296 | 0.616307 | 0.308154 | − | 0.951337i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951337i | \(0.400289\pi\) | |||||||
\(810\) | 15.3464 | 0.539219 | ||||||||
\(811\) | 17.4583 | 0.613042 | 0.306521 | − | 0.951864i | \(-0.400835\pi\) | ||||
0.306521 | + | 0.951864i | \(0.400835\pi\) | |||||||
\(812\) | 16.8172 | 0.590169 | ||||||||
\(813\) | 23.2187 | 0.814314 | ||||||||
\(814\) | 20.8839 | 0.731980 | ||||||||
\(815\) | 12.5623 | 0.440038 | ||||||||
\(816\) | −3.88615 | −0.136043 | ||||||||
\(817\) | −10.2541 | −0.358745 | ||||||||
\(818\) | 9.59680 | 0.335544 | ||||||||
\(819\) | 38.3845 | 1.34126 | ||||||||
\(820\) | 3.36204 | 0.117407 | ||||||||
\(821\) | 20.5697 | 0.717886 | 0.358943 | − | 0.933359i | \(-0.383137\pi\) | ||||
0.358943 | + | 0.933359i | \(0.383137\pi\) | |||||||
\(822\) | −14.6065 | −0.509462 | ||||||||
\(823\) | 47.7009 | 1.66275 | 0.831375 | − | 0.555712i | \(-0.187554\pi\) | ||||
0.831375 | + | 0.555712i | \(0.187554\pi\) | |||||||
\(824\) | 11.4164 | 0.397710 | ||||||||
\(825\) | 21.1206 | 0.735326 | ||||||||
\(826\) | −41.5211 | −1.44470 | ||||||||
\(827\) | −34.8192 | −1.21078 | −0.605391 | − | 0.795928i | \(-0.706983\pi\) | ||||
−0.605391 | + | 0.795928i | \(0.706983\pi\) | |||||||
\(828\) | −7.15997 | −0.248826 | ||||||||
\(829\) | 5.13640 | 0.178394 | 0.0891972 | − | 0.996014i | \(-0.471570\pi\) | ||||
0.0891972 | + | 0.996014i | \(0.471570\pi\) | |||||||
\(830\) | 1.46138 | 0.0507251 | ||||||||
\(831\) | 19.3941 | 0.672775 | ||||||||
\(832\) | 6.79975 | 0.235739 | ||||||||
\(833\) | 16.8761 | 0.584722 | ||||||||
\(834\) | 5.64980 | 0.195636 | ||||||||
\(835\) | −0.743957 | −0.0257457 | ||||||||
\(836\) | −3.20824 | −0.110959 | ||||||||
\(837\) | 2.38228 | 0.0823436 | ||||||||
\(838\) | 17.7597 | 0.613500 | ||||||||
\(839\) | −30.2316 | −1.04371 | −0.521855 | − | 0.853034i | \(-0.674760\pi\) | ||||
−0.521855 | + | 0.853034i | \(0.674760\pi\) | |||||||
\(840\) | 11.5040 | 0.396925 | ||||||||
\(841\) | −11.4505 | −0.394846 | ||||||||
\(842\) | 32.4693 | 1.11896 | ||||||||
\(843\) | 4.16942 | 0.143603 | ||||||||
\(844\) | 1.00000 | 0.0344214 | ||||||||
\(845\) | 45.3745 | 1.56093 | ||||||||
\(846\) | 7.57090 | 0.260293 | ||||||||
\(847\) | −2.83905 | −0.0975510 | ||||||||
\(848\) | 8.52058 | 0.292598 | ||||||||
\(849\) | −46.8823 | −1.60900 | ||||||||
\(850\) | 5.80628 | 0.199154 | ||||||||
\(851\) | 33.1448 | 1.13619 | ||||||||
\(852\) | −8.54258 | −0.292664 | ||||||||
\(853\) | −13.5929 | −0.465413 | −0.232706 | − | 0.972547i | \(-0.574758\pi\) | ||||
−0.232706 | + | 0.972547i | \(0.574758\pi\) | |||||||
\(854\) | −5.69601 | −0.194914 | ||||||||
\(855\) | −1.91971 | −0.0656526 | ||||||||
\(856\) | 2.69435 | 0.0920908 | ||||||||
\(857\) | 24.8412 | 0.848560 | 0.424280 | − | 0.905531i | \(-0.360527\pi\) | ||||
0.424280 | + | 0.905531i | \(0.360527\pi\) | |||||||
\(858\) | 45.7921 | 1.56332 | ||||||||
\(859\) | 31.0539 | 1.05955 | 0.529773 | − | 0.848140i | \(-0.322277\pi\) | ||||
0.529773 | + | 0.848140i | \(0.322277\pi\) | |||||||
\(860\) | 13.9988 | 0.477356 | ||||||||
\(861\) | −20.7520 | −0.707227 | ||||||||
\(862\) | 26.6865 | 0.908945 | ||||||||
\(863\) | −4.29609 | −0.146241 | −0.0731203 | − | 0.997323i | \(-0.523296\pi\) | ||||
−0.0731203 | + | 0.997323i | \(0.523296\pi\) | |||||||
\(864\) | −3.34558 | −0.113819 | ||||||||
\(865\) | 9.80464 | 0.333368 | ||||||||
\(866\) | −2.53135 | −0.0860189 | ||||||||
\(867\) | 28.4899 | 0.967567 | ||||||||
\(868\) | 2.85854 | 0.0970251 | ||||||||
\(869\) | −6.84247 | −0.232115 | ||||||||
\(870\) | 12.0049 | 0.407004 | ||||||||
\(871\) | 86.3565 | 2.92608 | ||||||||
\(872\) | −11.5555 | −0.391318 | ||||||||
\(873\) | 9.46701 | 0.320410 | ||||||||
\(874\) | −5.09179 | −0.172233 | ||||||||
\(875\) | −44.5904 | −1.50743 | ||||||||
\(876\) | 22.9181 | 0.774331 | ||||||||
\(877\) | 46.7308 | 1.57799 | 0.788994 | − | 0.614401i | \(-0.210602\pi\) | ||||
0.788994 | + | 0.614401i | \(0.210602\pi\) | |||||||
\(878\) | −3.05361 | −0.103054 | ||||||||
\(879\) | −16.6323 | −0.560993 | ||||||||
\(880\) | 4.37987 | 0.147645 | ||||||||
\(881\) | 51.3965 | 1.73159 | 0.865796 | − | 0.500398i | \(-0.166813\pi\) | ||||
0.865796 | + | 0.500398i | \(0.166813\pi\) | |||||||
\(882\) | −12.8181 | −0.431607 | ||||||||
\(883\) | 6.00177 | 0.201976 | 0.100988 | − | 0.994888i | \(-0.467800\pi\) | ||||
0.100988 | + | 0.994888i | \(0.467800\pi\) | |||||||
\(884\) | 12.5887 | 0.423405 | ||||||||
\(885\) | −29.6396 | −0.996324 | ||||||||
\(886\) | 23.5422 | 0.790914 | ||||||||
\(887\) | 26.9133 | 0.903659 | 0.451829 | − | 0.892104i | \(-0.350772\pi\) | ||||
0.451829 | + | 0.892104i | \(0.350772\pi\) | |||||||
\(888\) | −13.6639 | −0.458532 | ||||||||
\(889\) | 51.2741 | 1.71968 | ||||||||
\(890\) | 1.90144 | 0.0637366 | ||||||||
\(891\) | −36.0644 | −1.20820 | ||||||||
\(892\) | 9.60089 | 0.321461 | ||||||||
\(893\) | 5.38403 | 0.180170 | ||||||||
\(894\) | −43.1103 | −1.44182 | ||||||||
\(895\) | −16.7582 | −0.560164 | ||||||||
\(896\) | −4.01442 | −0.134112 | ||||||||
\(897\) | 72.6766 | 2.42660 | ||||||||
\(898\) | 28.4555 | 0.949571 | ||||||||
\(899\) | 2.98300 | 0.0994886 | ||||||||
\(900\) | −4.41011 | −0.147004 | ||||||||
\(901\) | 15.7746 | 0.525528 | ||||||||
\(902\) | −7.90085 | −0.263069 | ||||||||
\(903\) | −86.4072 | −2.87545 | ||||||||
\(904\) | −3.46399 | −0.115211 | ||||||||
\(905\) | −4.00392 | −0.133095 | ||||||||
\(906\) | 7.93927 | 0.263764 | ||||||||
\(907\) | 58.5145 | 1.94294 | 0.971472 | − | 0.237156i | \(-0.0762153\pi\) | ||||
0.971472 | + | 0.237156i | \(0.0762153\pi\) | |||||||
\(908\) | −24.5848 | −0.815875 | ||||||||
\(909\) | 6.93443 | 0.230000 | ||||||||
\(910\) | −37.2658 | −1.23535 | ||||||||
\(911\) | −37.4134 | −1.23956 | −0.619781 | − | 0.784775i | \(-0.712779\pi\) | ||||
−0.619781 | + | 0.784775i | \(0.712779\pi\) | |||||||
\(912\) | 2.09909 | 0.0695078 | ||||||||
\(913\) | −3.43426 | −0.113657 | ||||||||
\(914\) | 21.6748 | 0.716938 | ||||||||
\(915\) | −4.06607 | −0.134420 | ||||||||
\(916\) | 5.87183 | 0.194011 | ||||||||
\(917\) | −9.92557 | −0.327771 | ||||||||
\(918\) | −6.19384 | −0.204427 | ||||||||
\(919\) | 12.2240 | 0.403234 | 0.201617 | − | 0.979464i | \(-0.435380\pi\) | ||||
0.201617 | + | 0.979464i | \(0.435380\pi\) | |||||||
\(920\) | 6.95130 | 0.229178 | ||||||||
\(921\) | −12.3971 | −0.408497 | ||||||||
\(922\) | −38.6715 | −1.27358 | ||||||||
\(923\) | 27.6727 | 0.910857 | ||||||||
\(924\) | −27.0346 | −0.889373 | ||||||||
\(925\) | 20.4152 | 0.671248 | ||||||||
\(926\) | −17.3366 | −0.569717 | ||||||||
\(927\) | −16.0535 | −0.527266 | ||||||||
\(928\) | −4.18921 | −0.137517 | ||||||||
\(929\) | −33.6650 | −1.10451 | −0.552257 | − | 0.833674i | \(-0.686233\pi\) | ||||
−0.552257 | + | 0.833674i | \(0.686233\pi\) | |||||||
\(930\) | 2.04055 | 0.0669123 | ||||||||
\(931\) | −9.11555 | −0.298750 | ||||||||
\(932\) | −28.7383 | −0.941354 | ||||||||
\(933\) | 1.85009 | 0.0605693 | ||||||||
\(934\) | 22.9253 | 0.750140 | ||||||||
\(935\) | 8.10869 | 0.265182 | ||||||||
\(936\) | −9.56166 | −0.312533 | ||||||||
\(937\) | 33.4928 | 1.09416 | 0.547081 | − | 0.837079i | \(-0.315739\pi\) | ||||
0.547081 | + | 0.837079i | \(0.315739\pi\) | |||||||
\(938\) | −50.9829 | −1.66465 | ||||||||
\(939\) | 44.9156 | 1.46577 | ||||||||
\(940\) | −7.35026 | −0.239739 | ||||||||
\(941\) | −51.1775 | −1.66834 | −0.834169 | − | 0.551509i | \(-0.814052\pi\) | ||||
−0.834169 | + | 0.551509i | \(0.814052\pi\) | |||||||
\(942\) | 2.55729 | 0.0833212 | ||||||||
\(943\) | −12.5394 | −0.408340 | ||||||||
\(944\) | 10.3430 | 0.336636 | ||||||||
\(945\) | 18.3353 | 0.596448 | ||||||||
\(946\) | −32.8975 | −1.06959 | ||||||||
\(947\) | −3.16912 | −0.102982 | −0.0514912 | − | 0.998673i | \(-0.516397\pi\) | ||||
−0.0514912 | + | 0.998673i | \(0.516397\pi\) | |||||||
\(948\) | 4.47690 | 0.145403 | ||||||||
\(949\) | −74.2405 | −2.40995 | ||||||||
\(950\) | −3.13624 | −0.101753 | ||||||||
\(951\) | −4.90768 | −0.159142 | ||||||||
\(952\) | −7.43210 | −0.240876 | ||||||||
\(953\) | −47.9786 | −1.55418 | −0.777089 | − | 0.629391i | \(-0.783304\pi\) | ||||
−0.777089 | + | 0.629391i | \(0.783304\pi\) | |||||||
\(954\) | −11.9814 | −0.387914 | ||||||||
\(955\) | 0.457059 | 0.0147901 | ||||||||
\(956\) | −18.0598 | −0.584096 | ||||||||
\(957\) | −28.2117 | −0.911955 | ||||||||
\(958\) | −37.0920 | −1.19839 | ||||||||
\(959\) | −27.9344 | −0.902048 | ||||||||
\(960\) | −2.86567 | −0.0924891 | ||||||||
\(961\) | −30.4930 | −0.983644 | ||||||||
\(962\) | 44.2627 | 1.42709 | ||||||||
\(963\) | −3.78873 | −0.122090 | ||||||||
\(964\) | 6.33711 | 0.204105 | ||||||||
\(965\) | −9.85275 | −0.317171 | ||||||||
\(966\) | −42.9066 | −1.38050 | ||||||||
\(967\) | −11.8867 | −0.382251 | −0.191126 | − | 0.981566i | \(-0.561214\pi\) | ||||
−0.191126 | + | 0.981566i | \(0.561214\pi\) | |||||||
\(968\) | 0.707214 | 0.0227307 | ||||||||
\(969\) | 3.88615 | 0.124841 | ||||||||
\(970\) | −9.19111 | −0.295109 | ||||||||
\(971\) | −3.64315 | −0.116914 | −0.0584571 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584571 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(972\) | 13.5596 | 0.434923 | ||||||||
\(973\) | 10.8050 | 0.346392 | ||||||||
\(974\) | 15.8194 | 0.506887 | ||||||||
\(975\) | 44.7644 | 1.43361 | ||||||||
\(976\) | 1.41889 | 0.0454175 | ||||||||
\(977\) | 16.9679 | 0.542852 | 0.271426 | − | 0.962459i | \(-0.412505\pi\) | ||||
0.271426 | + | 0.962459i | \(0.412505\pi\) | |||||||
\(978\) | 19.3155 | 0.617640 | ||||||||
\(979\) | −4.46843 | −0.142812 | ||||||||
\(980\) | 12.4445 | 0.397525 | ||||||||
\(981\) | 16.2491 | 0.518793 | ||||||||
\(982\) | −29.5626 | −0.943382 | ||||||||
\(983\) | 13.2719 | 0.423306 | 0.211653 | − | 0.977345i | \(-0.432115\pi\) | ||||
0.211653 | + | 0.977345i | \(0.432115\pi\) | |||||||
\(984\) | 5.16938 | 0.164794 | ||||||||
\(985\) | 2.35510 | 0.0750398 | ||||||||
\(986\) | −7.75570 | −0.246992 | ||||||||
\(987\) | 45.3692 | 1.44412 | ||||||||
\(988\) | −6.79975 | −0.216329 | ||||||||
\(989\) | −52.2116 | −1.66023 | ||||||||
\(990\) | −6.15888 | −0.195742 | ||||||||
\(991\) | −7.97607 | −0.253368 | −0.126684 | − | 0.991943i | \(-0.540433\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540433\pi\) | |||||||
\(992\) | −0.712068 | −0.0226082 | ||||||||
\(993\) | −6.55517 | −0.208022 | ||||||||
\(994\) | −16.3373 | −0.518188 | ||||||||
\(995\) | 10.8130 | 0.342794 | ||||||||
\(996\) | 2.24697 | 0.0711981 | ||||||||
\(997\) | 4.07981 | 0.129209 | 0.0646044 | − | 0.997911i | \(-0.479421\pi\) | ||||
0.0646044 | + | 0.997911i | \(0.479421\pi\) | |||||||
\(998\) | 14.7836 | 0.467966 | ||||||||
\(999\) | −21.7779 | −0.689022 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.h.1.7 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.h.1.7 | ✓ | 41 | 1.1 | even | 1 | trivial |