Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29268.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 5x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.25548\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.14924 | −0.513954 | −0.256977 | − | 0.966417i | \(-0.582727\pi\) | ||||
−0.256977 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.14924 | 0.363421 | ||||||||
\(11\) | −2.16830 | −0.653767 | −0.326884 | − | 0.945065i | \(-0.605998\pi\) | ||||
−0.326884 | + | 0.945065i | \(0.605998\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.29847 | 0.637482 | 0.318741 | − | 0.947842i | \(-0.396740\pi\) | ||||
0.318741 | + | 0.947842i | \(0.396740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.14924 | 0.296732 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.99679 | −1.21190 | −0.605950 | − | 0.795503i | \(-0.707207\pi\) | ||||
−0.605950 | + | 0.795503i | \(0.707207\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.14924 | −0.256977 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.16830 | 0.462283 | ||||||||
\(23\) | −6.91567 | −1.44202 | −0.721008 | − | 0.692926i | \(-0.756321\pi\) | ||||
−0.721008 | + | 0.692926i | \(0.756321\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.67925 | −0.735851 | ||||||||
\(26\) | −2.29847 | −0.450768 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.76643 | 0.699409 | 0.349704 | − | 0.936860i | \(-0.386282\pi\) | ||||
0.349704 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(30\) | −1.14924 | −0.209821 | ||||||||
\(31\) | 4.38565 | 0.787686 | 0.393843 | − | 0.919178i | \(-0.371145\pi\) | ||||
0.393843 | + | 0.919178i | \(0.371145\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.16830 | 0.377453 | ||||||||
\(34\) | 4.99679 | 0.856943 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.660191 | 0.108535 | 0.0542674 | − | 0.998526i | \(-0.482718\pi\) | ||||
0.0542674 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −2.29847 | −0.368050 | ||||||||
\(40\) | 1.14924 | 0.181710 | ||||||||
\(41\) | 0.806583 | 0.125967 | 0.0629836 | − | 0.998015i | \(-0.479938\pi\) | ||||
0.0629836 | + | 0.998015i | \(0.479938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.08397 | −0.317802 | −0.158901 | − | 0.987295i | \(-0.550795\pi\) | ||||
−0.158901 | + | 0.987295i | \(0.550795\pi\) | |||||||
\(44\) | −2.16830 | −0.326884 | ||||||||
\(45\) | −1.14924 | −0.171318 | ||||||||
\(46\) | 6.91567 | 1.01966 | ||||||||
\(47\) | −3.72225 | −0.542946 | −0.271473 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271473 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.67925 | 0.520325 | ||||||||
\(51\) | 4.99679 | 0.699691 | ||||||||
\(52\) | 2.29847 | 0.318741 | ||||||||
\(53\) | −11.2713 | −1.54824 | −0.774118 | − | 0.633041i | \(-0.781806\pi\) | ||||
−0.774118 | + | 0.633041i | \(0.781806\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 2.49189 | 0.336006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −3.76643 | −0.494557 | ||||||||
\(59\) | 10.4266 | 1.35743 | 0.678715 | − | 0.734401i | \(-0.262537\pi\) | ||||
0.678715 | + | 0.734401i | \(0.262537\pi\) | |||||||
\(60\) | 1.14924 | 0.148366 | ||||||||
\(61\) | 2.57622 | 0.329852 | 0.164926 | − | 0.986306i | \(-0.447262\pi\) | ||||
0.164926 | + | 0.986306i | \(0.447262\pi\) | |||||||
\(62\) | −4.38565 | −0.556978 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.64149 | −0.327637 | ||||||||
\(66\) | −2.16830 | −0.266899 | ||||||||
\(67\) | 8.88568 | 1.08556 | 0.542779 | − | 0.839875i | \(-0.317372\pi\) | ||||
0.542779 | + | 0.839875i | \(0.317372\pi\) | |||||||
\(68\) | −4.99679 | −0.605950 | ||||||||
\(69\) | 6.91567 | 0.832549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.323591 | −0.0384031 | −0.0192016 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192016 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −4.72830 | −0.553406 | −0.276703 | − | 0.960955i | \(-0.589242\pi\) | ||||
−0.276703 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(74\) | −0.660191 | −0.0767457 | ||||||||
\(75\) | 3.67925 | 0.424844 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.29847 | 0.260251 | ||||||||
\(79\) | −7.59208 | −0.854175 | −0.427088 | − | 0.904210i | \(-0.640460\pi\) | ||||
−0.427088 | + | 0.904210i | \(0.640460\pi\) | |||||||
\(80\) | −1.14924 | −0.128489 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.806583 | −0.0890722 | ||||||||
\(83\) | 3.17435 | 0.348431 | 0.174215 | − | 0.984708i | \(-0.444261\pi\) | ||||
0.174215 | + | 0.984708i | \(0.444261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.74250 | 0.622861 | ||||||||
\(86\) | 2.08397 | 0.224720 | ||||||||
\(87\) | −3.76643 | −0.403804 | ||||||||
\(88\) | 2.16830 | 0.231142 | ||||||||
\(89\) | 12.3776 | 1.31202 | 0.656010 | − | 0.754752i | \(-0.272243\pi\) | ||||
0.656010 | + | 0.754752i | \(0.272243\pi\) | |||||||
\(90\) | 1.14924 | 0.121140 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.91567 | −0.721008 | ||||||||
\(93\) | −4.38565 | −0.454771 | ||||||||
\(94\) | 3.72225 | 0.383921 | ||||||||
\(95\) | −1.14924 | −0.117909 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −5.91567 | −0.600645 | −0.300323 | − | 0.953838i | \(-0.597094\pi\) | ||||
−0.300323 | + | 0.953838i | \(0.597094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.16830 | −0.217922 | ||||||||
\(100\) | −3.67925 | −0.367925 | ||||||||
\(101\) | −12.8683 | −1.28044 | −0.640221 | − | 0.768191i | \(-0.721157\pi\) | ||||
−0.640221 | + | 0.768191i | \(0.721157\pi\) | |||||||
\(102\) | −4.99679 | −0.494756 | ||||||||
\(103\) | 6.95582 | 0.685377 | 0.342689 | − | 0.939449i | \(-0.388662\pi\) | ||||
0.342689 | + | 0.939449i | \(0.388662\pi\) | |||||||
\(104\) | −2.29847 | −0.225384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2713 | 1.09477 | ||||||||
\(107\) | −12.3987 | −1.19862 | −0.599312 | − | 0.800516i | \(-0.704559\pi\) | ||||
−0.599312 | + | 0.800516i | \(0.704559\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.0568 | 1.72953 | 0.864765 | − | 0.502176i | \(-0.167467\pi\) | ||||
0.864765 | + | 0.502176i | \(0.167467\pi\) | |||||||
\(110\) | −2.49189 | −0.237592 | ||||||||
\(111\) | −0.660191 | −0.0626626 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.63792 | −0.812587 | −0.406294 | − | 0.913743i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913743i | \(0.633179\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 7.94774 | 0.741131 | ||||||||
\(116\) | 3.76643 | 0.349704 | ||||||||
\(117\) | 2.29847 | 0.212494 | ||||||||
\(118\) | −10.4266 | −0.959848 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.14924 | −0.104911 | ||||||||
\(121\) | −6.29847 | −0.572589 | ||||||||
\(122\) | −2.57622 | −0.233240 | ||||||||
\(123\) | −0.806583 | −0.0727271 | ||||||||
\(124\) | 4.38565 | 0.393843 | ||||||||
\(125\) | 9.97452 | 0.892148 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8683 | −1.23061 | −0.615305 | − | 0.788289i | \(-0.710967\pi\) | ||||
−0.615305 | + | 0.788289i | \(0.710967\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.08397 | 0.183483 | ||||||||
\(130\) | 2.64149 | 0.231674 | ||||||||
\(131\) | 12.2113 | 1.06691 | 0.533453 | − | 0.845830i | \(-0.320894\pi\) | ||||
0.533453 | + | 0.845830i | \(0.320894\pi\) | |||||||
\(132\) | 2.16830 | 0.188726 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.88568 | −0.767606 | ||||||||
\(135\) | 1.14924 | 0.0989106 | ||||||||
\(136\) | 4.99679 | 0.428471 | ||||||||
\(137\) | 11.0808 | 0.946693 | 0.473347 | − | 0.880876i | \(-0.343046\pi\) | ||||
0.473347 | + | 0.880876i | \(0.343046\pi\) | |||||||
\(138\) | −6.91567 | −0.588701 | ||||||||
\(139\) | −11.0175 | −0.934494 | −0.467247 | − | 0.884127i | \(-0.654754\pi\) | ||||
−0.467247 | + | 0.884127i | \(0.654754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72225 | 0.313470 | ||||||||
\(142\) | 0.323591 | 0.0271551 | ||||||||
\(143\) | −4.98378 | −0.416765 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.32852 | −0.359464 | ||||||||
\(146\) | 4.72830 | 0.391317 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.660191 | 0.0542674 | ||||||||
\(149\) | −21.2170 | −1.73816 | −0.869082 | − | 0.494669i | \(-0.835289\pi\) | ||||
−0.869082 | + | 0.494669i | \(0.835289\pi\) | |||||||
\(150\) | −3.67925 | −0.300410 | ||||||||
\(151\) | 9.40187 | 0.765113 | 0.382557 | − | 0.923932i | \(-0.375044\pi\) | ||||
0.382557 | + | 0.923932i | \(0.375044\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −4.99679 | −0.403967 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.04015 | −0.404835 | ||||||||
\(156\) | −2.29847 | −0.184025 | ||||||||
\(157\) | 6.14721 | 0.490601 | 0.245300 | − | 0.969447i | \(-0.421113\pi\) | ||||
0.245300 | + | 0.969447i | \(0.421113\pi\) | |||||||
\(158\) | 7.59208 | 0.603993 | ||||||||
\(159\) | 11.2713 | 0.893875 | ||||||||
\(160\) | 1.14924 | 0.0908552 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.60793 | −0.674225 | −0.337113 | − | 0.941464i | \(-0.609450\pi\) | ||||
−0.337113 | + | 0.941464i | \(0.609450\pi\) | |||||||
\(164\) | 0.806583 | 0.0629836 | ||||||||
\(165\) | −2.49189 | −0.193993 | ||||||||
\(166\) | −3.17435 | −0.246378 | ||||||||
\(167\) | 11.9749 | 0.926644 | 0.463322 | − | 0.886190i | \(-0.346657\pi\) | ||||
0.463322 | + | 0.886190i | \(0.346657\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.71702 | −0.593617 | ||||||||
\(170\) | −5.74250 | −0.440429 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | −2.08397 | −0.158901 | ||||||||
\(173\) | 8.10185 | 0.615972 | 0.307986 | − | 0.951391i | \(-0.400345\pi\) | ||||
0.307986 | + | 0.951391i | \(0.400345\pi\) | |||||||
\(174\) | 3.76643 | 0.285532 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.16830 | −0.163442 | ||||||||
\(177\) | −10.4266 | −0.783713 | ||||||||
\(178\) | −12.3776 | −0.927738 | ||||||||
\(179\) | −6.84755 | −0.511810 | −0.255905 | − | 0.966702i | \(-0.582373\pi\) | ||||
−0.255905 | + | 0.966702i | \(0.582373\pi\) | |||||||
\(180\) | −1.14924 | −0.0856591 | ||||||||
\(181\) | −16.5905 | −1.23316 | −0.616582 | − | 0.787291i | \(-0.711483\pi\) | ||||
−0.616582 | + | 0.787291i | \(0.711483\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.57622 | −0.190440 | ||||||||
\(184\) | 6.91567 | 0.509830 | ||||||||
\(185\) | −0.758716 | −0.0557819 | ||||||||
\(186\) | 4.38565 | 0.321572 | ||||||||
\(187\) | 10.8345 | 0.792300 | ||||||||
\(188\) | −3.72225 | −0.271473 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.14924 | 0.0833744 | ||||||||
\(191\) | 15.8902 | 1.14977 | 0.574887 | − | 0.818233i | \(-0.305046\pi\) | ||||
0.574887 | + | 0.818233i | \(0.305046\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 6.49676 | 0.467647 | 0.233824 | − | 0.972279i | \(-0.424876\pi\) | ||||
0.233824 | + | 0.972279i | \(0.424876\pi\) | |||||||
\(194\) | 5.91567 | 0.424720 | ||||||||
\(195\) | 2.64149 | 0.189161 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.06491 | 0.0758713 | 0.0379357 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379357 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(198\) | 2.16830 | 0.154094 | ||||||||
\(199\) | 23.5917 | 1.67237 | 0.836186 | − | 0.548446i | \(-0.184780\pi\) | ||||
0.836186 | + | 0.548446i | \(0.184780\pi\) | |||||||
\(200\) | 3.67925 | 0.260163 | ||||||||
\(201\) | −8.88568 | −0.626748 | ||||||||
\(202\) | 12.8683 | 0.905409 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.99679 | 0.349845 | ||||||||
\(205\) | −0.926955 | −0.0647414 | ||||||||
\(206\) | −6.95582 | −0.484635 | ||||||||
\(207\) | −6.91567 | −0.480672 | ||||||||
\(208\) | 2.29847 | 0.159370 | ||||||||
\(209\) | −2.16830 | −0.149984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8699 | 1.23022 | 0.615109 | − | 0.788442i | \(-0.289112\pi\) | ||||
0.615109 | + | 0.788442i | \(0.289112\pi\) | |||||||
\(212\) | −11.2713 | −0.774118 | ||||||||
\(213\) | 0.323591 | 0.0221721 | ||||||||
\(214\) | 12.3987 | 0.847555 | ||||||||
\(215\) | 2.39497 | 0.163336 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.0568 | −1.22296 | ||||||||
\(219\) | 4.72830 | 0.319509 | ||||||||
\(220\) | 2.49189 | 0.168003 | ||||||||
\(221\) | −11.4850 | −0.772564 | ||||||||
\(222\) | 0.660191 | 0.0443091 | ||||||||
\(223\) | 4.44605 | 0.297729 | 0.148865 | − | 0.988858i | \(-0.452438\pi\) | ||||
0.148865 | + | 0.988858i | \(0.452438\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.67925 | −0.245284 | ||||||||
\(226\) | 8.63792 | 0.574586 | ||||||||
\(227\) | 20.0938 | 1.33367 | 0.666835 | − | 0.745205i | \(-0.267649\pi\) | ||||
0.666835 | + | 0.745205i | \(0.267649\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | 17.9555 | 1.18653 | 0.593265 | − | 0.805007i | \(-0.297839\pi\) | ||||
0.593265 | + | 0.805007i | \(0.297839\pi\) | |||||||
\(230\) | −7.94774 | −0.524059 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.76643 | −0.247278 | ||||||||
\(233\) | 10.2539 | 0.671757 | 0.335879 | − | 0.941905i | \(-0.390967\pi\) | ||||
0.335879 | + | 0.941905i | \(0.390967\pi\) | |||||||
\(234\) | −2.29847 | −0.150256 | ||||||||
\(235\) | 4.27775 | 0.279050 | ||||||||
\(236\) | 10.4266 | 0.678715 | ||||||||
\(237\) | 7.59208 | 0.493158 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.73965 | 0.112529 | 0.0562644 | − | 0.998416i | \(-0.482081\pi\) | ||||
0.0562644 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(240\) | 1.14924 | 0.0741829 | ||||||||
\(241\) | −20.8492 | −1.34302 | −0.671508 | − | 0.740997i | \(-0.734353\pi\) | ||||
−0.671508 | + | 0.740997i | \(0.734353\pi\) | |||||||
\(242\) | 6.29847 | 0.404881 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.57622 | 0.164926 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.806583 | 0.0514259 | ||||||||
\(247\) | 2.29847 | 0.146248 | ||||||||
\(248\) | −4.38565 | −0.278489 | ||||||||
\(249\) | −3.17435 | −0.201166 | ||||||||
\(250\) | −9.97452 | −0.630844 | ||||||||
\(251\) | 3.19663 | 0.201769 | 0.100885 | − | 0.994898i | \(-0.467833\pi\) | ||||
0.100885 | + | 0.994898i | \(0.467833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.9952 | 0.942743 | ||||||||
\(254\) | 13.8683 | 0.870173 | ||||||||
\(255\) | −5.74250 | −0.359609 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.0219 | −0.937041 | −0.468520 | − | 0.883453i | \(-0.655213\pi\) | ||||
−0.468520 | + | 0.883453i | \(0.655213\pi\) | |||||||
\(258\) | −2.08397 | −0.129742 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.64149 | −0.163818 | ||||||||
\(261\) | 3.76643 | 0.233136 | ||||||||
\(262\) | −12.2113 | −0.754416 | ||||||||
\(263\) | 10.6760 | 0.658313 | 0.329157 | − | 0.944275i | \(-0.393236\pi\) | ||||
0.329157 | + | 0.944275i | \(0.393236\pi\) | |||||||
\(264\) | −2.16830 | −0.133450 | ||||||||
\(265\) | 12.9534 | 0.795723 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.3776 | −0.757495 | ||||||||
\(268\) | 8.88568 | 0.542779 | ||||||||
\(269\) | −3.24906 | −0.198099 | −0.0990494 | − | 0.995083i | \(-0.531580\pi\) | ||||
−0.0990494 | + | 0.995083i | \(0.531580\pi\) | |||||||
\(270\) | −1.14924 | −0.0699403 | ||||||||
\(271\) | 18.0349 | 1.09554 | 0.547772 | − | 0.836628i | \(-0.315476\pi\) | ||||
0.547772 | + | 0.836628i | \(0.315476\pi\) | |||||||
\(272\) | −4.99679 | −0.302975 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.0808 | −0.669413 | ||||||||
\(275\) | 7.97773 | 0.481075 | ||||||||
\(276\) | 6.91567 | 0.416274 | ||||||||
\(277\) | 22.2839 | 1.33891 | 0.669455 | − | 0.742852i | \(-0.266528\pi\) | ||||
0.669455 | + | 0.742852i | \(0.266528\pi\) | |||||||
\(278\) | 11.0175 | 0.660787 | ||||||||
\(279\) | 4.38565 | 0.262562 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.10790 | 0.424022 | 0.212011 | − | 0.977267i | \(-0.431999\pi\) | ||||
0.212011 | + | 0.977267i | \(0.431999\pi\) | |||||||
\(282\) | −3.72225 | −0.221657 | ||||||||
\(283\) | −15.7474 | −0.936084 | −0.468042 | − | 0.883706i | \(-0.655040\pi\) | ||||
−0.468042 | + | 0.883706i | \(0.655040\pi\) | |||||||
\(284\) | −0.323591 | −0.0192016 | ||||||||
\(285\) | 1.14924 | 0.0680749 | ||||||||
\(286\) | 4.98378 | 0.294697 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.96793 | 0.468702 | ||||||||
\(290\) | 4.32852 | 0.254180 | ||||||||
\(291\) | 5.91567 | 0.346783 | ||||||||
\(292\) | −4.72830 | −0.276703 | ||||||||
\(293\) | 22.0139 | 1.28607 | 0.643034 | − | 0.765837i | \(-0.277675\pi\) | ||||
0.643034 | + | 0.765837i | \(0.277675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9827 | −0.697657 | ||||||||
\(296\) | −0.660191 | −0.0383728 | ||||||||
\(297\) | 2.16830 | 0.125818 | ||||||||
\(298\) | 21.2170 | 1.22907 | ||||||||
\(299\) | −15.8955 | −0.919260 | ||||||||
\(300\) | 3.67925 | 0.212422 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.40187 | −0.541017 | ||||||||
\(303\) | 12.8683 | 0.739263 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −2.96069 | −0.169529 | ||||||||
\(306\) | 4.99679 | 0.285648 | ||||||||
\(307\) | 14.3776 | 0.820571 | 0.410286 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410286 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.95582 | −0.395703 | ||||||||
\(310\) | 5.04015 | 0.286261 | ||||||||
\(311\) | −2.97452 | −0.168670 | −0.0843348 | − | 0.996437i | \(-0.526877\pi\) | ||||
−0.0843348 | + | 0.996437i | \(0.526877\pi\) | |||||||
\(312\) | 2.29847 | 0.130125 | ||||||||
\(313\) | −16.7588 | −0.947265 | −0.473633 | − | 0.880723i | \(-0.657058\pi\) | ||||
−0.473633 | + | 0.880723i | \(0.657058\pi\) | |||||||
\(314\) | −6.14721 | −0.346907 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.59208 | −0.427088 | ||||||||
\(317\) | −2.81061 | −0.157860 | −0.0789298 | − | 0.996880i | \(-0.525150\pi\) | ||||
−0.0789298 | + | 0.996880i | \(0.525150\pi\) | |||||||
\(318\) | −11.2713 | −0.632065 | ||||||||
\(319\) | −8.16675 | −0.457250 | ||||||||
\(320\) | −1.14924 | −0.0642443 | ||||||||
\(321\) | 12.3987 | 0.692026 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.99679 | −0.278029 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −8.45667 | −0.469092 | ||||||||
\(326\) | 8.60793 | 0.476749 | ||||||||
\(327\) | −18.0568 | −0.998545 | ||||||||
\(328\) | −0.806583 | −0.0445361 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.49189 | 0.137174 | ||||||||
\(331\) | −10.1391 | −0.557294 | −0.278647 | − | 0.960394i | \(-0.589886\pi\) | ||||
−0.278647 | + | 0.960394i | \(0.589886\pi\) | |||||||
\(332\) | 3.17435 | 0.174215 | ||||||||
\(333\) | 0.660191 | 0.0361782 | ||||||||
\(334\) | −11.9749 | −0.655236 | ||||||||
\(335\) | −10.2118 | −0.557928 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4364 | 1.16772 | 0.583858 | − | 0.811856i | \(-0.301542\pi\) | ||||
0.583858 | + | 0.811856i | \(0.301542\pi\) | |||||||
\(338\) | 7.71702 | 0.419750 | ||||||||
\(339\) | 8.63792 | 0.469147 | ||||||||
\(340\) | 5.74250 | 0.311431 | ||||||||
\(341\) | −9.50941 | −0.514963 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.08397 | 0.112360 | ||||||||
\(345\) | −7.94774 | −0.427892 | ||||||||
\(346\) | −8.10185 | −0.435558 | ||||||||
\(347\) | 29.1826 | 1.56660 | 0.783302 | − | 0.621641i | \(-0.213534\pi\) | ||||
0.783302 | + | 0.621641i | \(0.213534\pi\) | |||||||
\(348\) | −3.76643 | −0.201902 | ||||||||
\(349\) | 9.36208 | 0.501141 | 0.250570 | − | 0.968098i | \(-0.419382\pi\) | ||||
0.250570 | + | 0.968098i | \(0.419382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.29847 | −0.122683 | ||||||||
\(352\) | 2.16830 | 0.115571 | ||||||||
\(353\) | 33.5994 | 1.78832 | 0.894159 | − | 0.447750i | \(-0.147775\pi\) | ||||
0.894159 | + | 0.447750i | \(0.147775\pi\) | |||||||
\(354\) | 10.4266 | 0.554169 | ||||||||
\(355\) | 0.371882 | 0.0197375 | ||||||||
\(356\) | 12.3776 | 0.656010 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.84755 | 0.361905 | ||||||||
\(359\) | −24.3630 | −1.28583 | −0.642915 | − | 0.765937i | \(-0.722275\pi\) | ||||
−0.642915 | + | 0.765937i | \(0.722275\pi\) | |||||||
\(360\) | 1.14924 | 0.0605701 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 16.5905 | 0.871979 | ||||||||
\(363\) | 6.29847 | 0.330584 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.43394 | 0.284426 | ||||||||
\(366\) | 2.57622 | 0.134661 | ||||||||
\(367\) | −33.1571 | −1.73079 | −0.865394 | − | 0.501092i | \(-0.832932\pi\) | ||||
−0.865394 | + | 0.501092i | \(0.832932\pi\) | |||||||
\(368\) | −6.91567 | −0.360504 | ||||||||
\(369\) | 0.806583 | 0.0419890 | ||||||||
\(370\) | 0.758716 | 0.0394438 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.38565 | −0.227385 | ||||||||
\(373\) | −22.5460 | −1.16739 | −0.583693 | − | 0.811974i | \(-0.698393\pi\) | ||||
−0.583693 | + | 0.811974i | \(0.698393\pi\) | |||||||
\(374\) | −10.8345 | −0.560241 | ||||||||
\(375\) | −9.97452 | −0.515082 | ||||||||
\(376\) | 3.72225 | 0.191960 | ||||||||
\(377\) | 8.65704 | 0.445860 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7616 | 0.963717 | 0.481858 | − | 0.876249i | \(-0.339962\pi\) | ||||
0.481858 | + | 0.876249i | \(0.339962\pi\) | |||||||
\(380\) | −1.14924 | −0.0589546 | ||||||||
\(381\) | 13.8683 | 0.710494 | ||||||||
\(382\) | −15.8902 | −0.813013 | ||||||||
\(383\) | −8.11770 | −0.414795 | −0.207398 | − | 0.978257i | \(-0.566499\pi\) | ||||
−0.207398 | + | 0.978257i | \(0.566499\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.49676 | −0.330676 | ||||||||
\(387\) | −2.08397 | −0.105934 | ||||||||
\(388\) | −5.91567 | −0.300323 | ||||||||
\(389\) | −35.0034 | −1.77474 | −0.887371 | − | 0.461056i | \(-0.847471\pi\) | ||||
−0.887371 | + | 0.461056i | \(0.847471\pi\) | |||||||
\(390\) | −2.64149 | −0.133757 | ||||||||
\(391\) | 34.5562 | 1.74758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.2113 | −0.615978 | ||||||||
\(394\) | −1.06491 | −0.0536491 | ||||||||
\(395\) | 8.72510 | 0.439007 | ||||||||
\(396\) | −2.16830 | −0.108961 | ||||||||
\(397\) | 15.0219 | 0.753928 | 0.376964 | − | 0.926228i | \(-0.376968\pi\) | ||||
0.376964 | + | 0.926228i | \(0.376968\pi\) | |||||||
\(398\) | −23.5917 | −1.18255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.67925 | −0.183963 | ||||||||
\(401\) | −26.6287 | −1.32977 | −0.664886 | − | 0.746945i | \(-0.731520\pi\) | ||||
−0.664886 | + | 0.746945i | \(0.731520\pi\) | |||||||
\(402\) | 8.88568 | 0.443178 | ||||||||
\(403\) | 10.0803 | 0.502136 | ||||||||
\(404\) | −12.8683 | −0.640221 | ||||||||
\(405\) | −1.14924 | −0.0571060 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.43149 | −0.0709565 | ||||||||
\(408\) | −4.99679 | −0.247378 | ||||||||
\(409\) | 27.6489 | 1.36715 | 0.683575 | − | 0.729880i | \(-0.260424\pi\) | ||||
0.683575 | + | 0.729880i | \(0.260424\pi\) | |||||||
\(410\) | 0.926955 | 0.0457791 | ||||||||
\(411\) | −11.0808 | −0.546574 | ||||||||
\(412\) | 6.95582 | 0.342689 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.91567 | 0.339887 | ||||||||
\(415\) | −3.64808 | −0.179077 | ||||||||
\(416\) | −2.29847 | −0.112692 | ||||||||
\(417\) | 11.0175 | 0.539530 | ||||||||
\(418\) | 2.16830 | 0.106055 | ||||||||
\(419\) | 1.91888 | 0.0937433 | 0.0468716 | − | 0.998901i | \(-0.485075\pi\) | ||||
0.0468716 | + | 0.998901i | \(0.485075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.9815 | 1.26626 | 0.633130 | − | 0.774046i | \(-0.281770\pi\) | ||||
0.633130 | + | 0.774046i | \(0.281770\pi\) | |||||||
\(422\) | −17.8699 | −0.869895 | ||||||||
\(423\) | −3.72225 | −0.180982 | ||||||||
\(424\) | 11.2713 | 0.547384 | ||||||||
\(425\) | 18.3845 | 0.891778 | ||||||||
\(426\) | −0.323591 | −0.0156780 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.3987 | −0.599312 | ||||||||
\(429\) | 4.98378 | 0.240619 | ||||||||
\(430\) | −2.39497 | −0.115496 | ||||||||
\(431\) | 0.965082 | 0.0464864 | 0.0232432 | − | 0.999730i | \(-0.492601\pi\) | ||||
0.0232432 | + | 0.999730i | \(0.492601\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −5.93960 | −0.285439 | −0.142720 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142720 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.32852 | 0.207537 | ||||||||
\(436\) | 18.0568 | 0.864765 | ||||||||
\(437\) | −6.91567 | −0.330821 | ||||||||
\(438\) | −4.72830 | −0.225927 | ||||||||
\(439\) | 21.5921 | 1.03053 | 0.515267 | − | 0.857030i | \(-0.327693\pi\) | ||||
0.515267 | + | 0.857030i | \(0.327693\pi\) | |||||||
\(440\) | −2.49189 | −0.118796 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.4850 | 0.546286 | ||||||||
\(443\) | 13.9344 | 0.662042 | 0.331021 | − | 0.943623i | \(-0.392607\pi\) | ||||
0.331021 | + | 0.943623i | \(0.392607\pi\) | |||||||
\(444\) | −0.660191 | −0.0313313 | ||||||||
\(445\) | −14.2248 | −0.674318 | ||||||||
\(446\) | −4.44605 | −0.210527 | ||||||||
\(447\) | 21.2170 | 1.00353 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3273 | 0.676149 | 0.338074 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338074 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(450\) | 3.67925 | 0.173442 | ||||||||
\(451\) | −1.74891 | −0.0823532 | ||||||||
\(452\) | −8.63792 | −0.406294 | ||||||||
\(453\) | −9.40187 | −0.441738 | ||||||||
\(454\) | −20.0938 | −0.943047 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 32.2981 | 1.51084 | 0.755421 | − | 0.655240i | \(-0.227432\pi\) | ||||
0.755421 | + | 0.655240i | \(0.227432\pi\) | |||||||
\(458\) | −17.9555 | −0.839003 | ||||||||
\(459\) | 4.99679 | 0.233230 | ||||||||
\(460\) | 7.94774 | 0.370565 | ||||||||
\(461\) | 0.375849 | 0.0175050 | 0.00875252 | − | 0.999962i | \(-0.497214\pi\) | ||||
0.00875252 | + | 0.999962i | \(0.497214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.80824 | 0.362880 | 0.181440 | − | 0.983402i | \(-0.441924\pi\) | ||||
0.181440 | + | 0.983402i | \(0.441924\pi\) | |||||||
\(464\) | 3.76643 | 0.174852 | ||||||||
\(465\) | 5.04015 | 0.233731 | ||||||||
\(466\) | −10.2539 | −0.475004 | ||||||||
\(467\) | −12.2555 | −0.567116 | −0.283558 | − | 0.958955i | \(-0.591515\pi\) | ||||
−0.283558 | + | 0.958955i | \(0.591515\pi\) | |||||||
\(468\) | 2.29847 | 0.106247 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.27775 | −0.197318 | ||||||||
\(471\) | −6.14721 | −0.283249 | ||||||||
\(472\) | −10.4266 | −0.479924 | ||||||||
\(473\) | 4.51867 | 0.207769 | ||||||||
\(474\) | −7.59208 | −0.348716 | ||||||||
\(475\) | −3.67925 | −0.168816 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.2713 | −0.516079 | ||||||||
\(478\) | −1.73965 | −0.0795699 | ||||||||
\(479\) | 27.0751 | 1.23709 | 0.618546 | − | 0.785749i | \(-0.287722\pi\) | ||||
0.618546 | + | 0.785749i | \(0.287722\pi\) | |||||||
\(480\) | −1.14924 | −0.0524553 | ||||||||
\(481\) | 1.51743 | 0.0691889 | ||||||||
\(482\) | 20.8492 | 0.949656 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.29847 | −0.286294 | ||||||||
\(485\) | 6.79850 | 0.308704 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 29.7498 | 1.34809 | 0.674047 | − | 0.738688i | \(-0.264554\pi\) | ||||
0.674047 | + | 0.738688i | \(0.264554\pi\) | |||||||
\(488\) | −2.57622 | −0.116620 | ||||||||
\(489\) | 8.60793 | 0.389264 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4381 | 0.832099 | 0.416050 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416050 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(492\) | −0.806583 | −0.0363636 | ||||||||
\(493\) | −18.8201 | −0.847613 | ||||||||
\(494\) | −2.29847 | −0.103413 | ||||||||
\(495\) | 2.49189 | 0.112002 | ||||||||
\(496\) | 4.38565 | 0.196922 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.17435 | 0.142246 | ||||||||
\(499\) | 33.1570 | 1.48431 | 0.742156 | − | 0.670227i | \(-0.233803\pi\) | ||||
0.742156 | + | 0.670227i | \(0.233803\pi\) | |||||||
\(500\) | 9.97452 | 0.446074 | ||||||||
\(501\) | −11.9749 | −0.534998 | ||||||||
\(502\) | −3.19663 | −0.142672 | ||||||||
\(503\) | 12.8678 | 0.573747 | 0.286873 | − | 0.957968i | \(-0.407384\pi\) | ||||
0.286873 | + | 0.957968i | \(0.407384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7887 | 0.658089 | ||||||||
\(506\) | −14.9952 | −0.666620 | ||||||||
\(507\) | 7.71702 | 0.342725 | ||||||||
\(508\) | −13.8683 | −0.615305 | ||||||||
\(509\) | 8.70235 | 0.385725 | 0.192862 | − | 0.981226i | \(-0.438223\pi\) | ||||
0.192862 | + | 0.981226i | \(0.438223\pi\) | |||||||
\(510\) | 5.74250 | 0.254282 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 15.0219 | 0.662588 | ||||||||
\(515\) | −7.99389 | −0.352253 | ||||||||
\(516\) | 2.08397 | 0.0917416 | ||||||||
\(517\) | 8.07096 | 0.354960 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.10185 | −0.355632 | ||||||||
\(520\) | 2.64149 | 0.115837 | ||||||||
\(521\) | 37.7965 | 1.65590 | 0.827948 | − | 0.560805i | \(-0.189508\pi\) | ||||
0.827948 | + | 0.560805i | \(0.189508\pi\) | |||||||
\(522\) | −3.76643 | −0.164852 | ||||||||
\(523\) | 42.3364 | 1.85124 | 0.925620 | − | 0.378455i | \(-0.123545\pi\) | ||||
0.925620 | + | 0.378455i | \(0.123545\pi\) | |||||||
\(524\) | 12.2113 | 0.533453 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.6760 | −0.465498 | ||||||||
\(527\) | −21.9142 | −0.954597 | ||||||||
\(528\) | 2.16830 | 0.0943632 | ||||||||
\(529\) | 24.8265 | 1.07941 | ||||||||
\(530\) | −12.9534 | −0.562661 | ||||||||
\(531\) | 10.4266 | 0.452477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.85391 | 0.0803018 | ||||||||
\(534\) | 12.3776 | 0.535630 | ||||||||
\(535\) | 14.2490 | 0.616038 | ||||||||
\(536\) | −8.88568 | −0.383803 | ||||||||
\(537\) | 6.84755 | 0.295494 | ||||||||
\(538\) | 3.24906 | 0.140077 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.14924 | 0.0494553 | ||||||||
\(541\) | 8.01146 | 0.344440 | 0.172220 | − | 0.985059i | \(-0.444906\pi\) | ||||
0.172220 | + | 0.985059i | \(0.444906\pi\) | |||||||
\(542\) | −18.0349 | −0.774666 | ||||||||
\(543\) | 16.5905 | 0.711968 | ||||||||
\(544\) | 4.99679 | 0.214236 | ||||||||
\(545\) | −20.7516 | −0.888900 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.1587 | −1.46052 | −0.730260 | − | 0.683170i | \(-0.760601\pi\) | ||||
−0.730260 | + | 0.683170i | \(0.760601\pi\) | |||||||
\(548\) | 11.0808 | 0.473347 | ||||||||
\(549\) | 2.57622 | 0.109951 | ||||||||
\(550\) | −7.97773 | −0.340171 | ||||||||
\(551\) | 3.76643 | 0.160455 | ||||||||
\(552\) | −6.91567 | −0.294350 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.2839 | −0.946753 | ||||||||
\(555\) | 0.758716 | 0.0322057 | ||||||||
\(556\) | −11.0175 | −0.467247 | ||||||||
\(557\) | −40.4791 | −1.71515 | −0.857576 | − | 0.514357i | \(-0.828031\pi\) | ||||
−0.857576 | + | 0.514357i | \(0.828031\pi\) | |||||||
\(558\) | −4.38565 | −0.185659 | ||||||||
\(559\) | −4.78995 | −0.202593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.8345 | −0.457435 | ||||||||
\(562\) | −7.10790 | −0.299829 | ||||||||
\(563\) | 18.2044 | 0.767224 | 0.383612 | − | 0.923494i | \(-0.374680\pi\) | ||||
0.383612 | + | 0.923494i | \(0.374680\pi\) | |||||||
\(564\) | 3.72225 | 0.156735 | ||||||||
\(565\) | 9.92702 | 0.417633 | ||||||||
\(566\) | 15.7474 | 0.661911 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.323591 | 0.0135776 | ||||||||
\(569\) | −16.0253 | −0.671815 | −0.335908 | − | 0.941895i | \(-0.609043\pi\) | ||||
−0.335908 | + | 0.941895i | \(0.609043\pi\) | |||||||
\(570\) | −1.14924 | −0.0481362 | ||||||||
\(571\) | 7.02630 | 0.294041 | 0.147021 | − | 0.989133i | \(-0.453032\pi\) | ||||
0.147021 | + | 0.989133i | \(0.453032\pi\) | |||||||
\(572\) | −4.98378 | −0.208382 | ||||||||
\(573\) | −15.8902 | −0.663822 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.4445 | 1.06111 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.9109 | 0.953794 | 0.476897 | − | 0.878959i | \(-0.341762\pi\) | ||||
0.476897 | + | 0.878959i | \(0.341762\pi\) | |||||||
\(578\) | −7.96793 | −0.331422 | ||||||||
\(579\) | −6.49676 | −0.269996 | ||||||||
\(580\) | −4.32852 | −0.179732 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.91567 | −0.245212 | ||||||||
\(583\) | 24.4396 | 1.01219 | ||||||||
\(584\) | 4.72830 | 0.195659 | ||||||||
\(585\) | −2.64149 | −0.109212 | ||||||||
\(586\) | −22.0139 | −0.909388 | ||||||||
\(587\) | −9.55395 | −0.394334 | −0.197167 | − | 0.980370i | \(-0.563174\pi\) | ||||
−0.197167 | + | 0.980370i | \(0.563174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.38565 | 0.180708 | ||||||||
\(590\) | 11.9827 | 0.493318 | ||||||||
\(591\) | −1.06491 | −0.0438043 | ||||||||
\(592\) | 0.660191 | 0.0271337 | ||||||||
\(593\) | 8.10672 | 0.332903 | 0.166452 | − | 0.986050i | \(-0.446769\pi\) | ||||
0.166452 | + | 0.986050i | \(0.446769\pi\) | |||||||
\(594\) | −2.16830 | −0.0889664 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.2170 | −0.869082 | ||||||||
\(597\) | −23.5917 | −0.965545 | ||||||||
\(598\) | 15.8955 | 0.650015 | ||||||||
\(599\) | −18.3172 | −0.748419 | −0.374210 | − | 0.927344i | \(-0.622086\pi\) | ||||
−0.374210 | + | 0.927344i | \(0.622086\pi\) | |||||||
\(600\) | −3.67925 | −0.150205 | ||||||||
\(601\) | 15.5629 | 0.634824 | 0.317412 | − | 0.948288i | \(-0.397186\pi\) | ||||
0.317412 | + | 0.948288i | \(0.397186\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.88568 | 0.361853 | ||||||||
\(604\) | 9.40187 | 0.382557 | ||||||||
\(605\) | 7.23844 | 0.294284 | ||||||||
\(606\) | −12.8683 | −0.522738 | ||||||||
\(607\) | 28.3918 | 1.15239 | 0.576193 | − | 0.817314i | \(-0.304538\pi\) | ||||
0.576193 | + | 0.817314i | \(0.304538\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.96069 | 0.119875 | ||||||||
\(611\) | −8.55550 | −0.346118 | ||||||||
\(612\) | −4.99679 | −0.201983 | ||||||||
\(613\) | −35.4409 | −1.43145 | −0.715723 | − | 0.698384i | \(-0.753903\pi\) | ||||
−0.715723 | + | 0.698384i | \(0.753903\pi\) | |||||||
\(614\) | −14.3776 | −0.580232 | ||||||||
\(615\) | 0.926955 | 0.0373784 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.6964 | 1.11502 | 0.557508 | − | 0.830172i | \(-0.311758\pi\) | ||||
0.557508 | + | 0.830172i | \(0.311758\pi\) | |||||||
\(618\) | 6.95582 | 0.279804 | ||||||||
\(619\) | −26.3914 | −1.06076 | −0.530380 | − | 0.847760i | \(-0.677951\pi\) | ||||
−0.530380 | + | 0.847760i | \(0.677951\pi\) | |||||||
\(620\) | −5.04015 | −0.202417 | ||||||||
\(621\) | 6.91567 | 0.277516 | ||||||||
\(622\) | 2.97452 | 0.119267 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.29847 | −0.0920126 | ||||||||
\(625\) | 6.93318 | 0.277327 | ||||||||
\(626\) | 16.7588 | 0.669818 | ||||||||
\(627\) | 2.16830 | 0.0865936 | ||||||||
\(628\) | 6.14721 | 0.245300 | ||||||||
\(629\) | −3.29884 | −0.131533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3293 | 0.849105 | 0.424553 | − | 0.905403i | \(-0.360431\pi\) | ||||
0.424553 | + | 0.905403i | \(0.360431\pi\) | |||||||
\(632\) | 7.59208 | 0.301997 | ||||||||
\(633\) | −17.8699 | −0.710266 | ||||||||
\(634\) | 2.81061 | 0.111624 | ||||||||
\(635\) | 15.9379 | 0.632478 | ||||||||
\(636\) | 11.2713 | 0.446937 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.16675 | 0.323325 | ||||||||
\(639\) | −0.323591 | −0.0128010 | ||||||||
\(640\) | 1.14924 | 0.0454276 | ||||||||
\(641\) | 19.0070 | 0.750730 | 0.375365 | − | 0.926877i | \(-0.377517\pi\) | ||||
0.375365 | + | 0.926877i | \(0.377517\pi\) | |||||||
\(642\) | −12.3987 | −0.489336 | ||||||||
\(643\) | 3.46630 | 0.136697 | 0.0683487 | − | 0.997661i | \(-0.478227\pi\) | ||||
0.0683487 | + | 0.997661i | \(0.478227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.39497 | −0.0943020 | ||||||||
\(646\) | 4.99679 | 0.196596 | ||||||||
\(647\) | 12.3609 | 0.485957 | 0.242979 | − | 0.970032i | \(-0.421876\pi\) | ||||
0.242979 | + | 0.970032i | \(0.421876\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −22.6080 | −0.887444 | ||||||||
\(650\) | 8.45667 | 0.331698 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.60793 | −0.337113 | ||||||||
\(653\) | 50.7123 | 1.98452 | 0.992262 | − | 0.124161i | \(-0.0396239\pi\) | ||||
0.992262 | + | 0.124161i | \(0.0396239\pi\) | |||||||
\(654\) | 18.0568 | 0.706078 | ||||||||
\(655\) | −14.0337 | −0.548341 | ||||||||
\(656\) | 0.806583 | 0.0314918 | ||||||||
\(657\) | −4.72830 | −0.184469 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.4985 | −1.14910 | −0.574549 | − | 0.818470i | \(-0.694822\pi\) | ||||
−0.574549 | + | 0.818470i | \(0.694822\pi\) | |||||||
\(660\) | −2.49189 | −0.0969967 | ||||||||
\(661\) | −37.8979 | −1.47406 | −0.737029 | − | 0.675861i | \(-0.763772\pi\) | ||||
−0.737029 | + | 0.675861i | \(0.763772\pi\) | |||||||
\(662\) | 10.1391 | 0.394066 | ||||||||
\(663\) | 11.4850 | 0.446040 | ||||||||
\(664\) | −3.17435 | −0.123189 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.660191 | −0.0255819 | ||||||||
\(667\) | −26.0474 | −1.00856 | ||||||||
\(668\) | 11.9749 | 0.463322 | ||||||||
\(669\) | −4.44605 | −0.171894 | ||||||||
\(670\) | 10.2118 | 0.394514 | ||||||||
\(671\) | −5.58602 | −0.215646 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.234048 | −0.00902187 | −0.00451094 | − | 0.999990i | \(-0.501436\pi\) | ||||
−0.00451094 | + | 0.999990i | \(0.501436\pi\) | |||||||
\(674\) | −21.4364 | −0.825700 | ||||||||
\(675\) | 3.67925 | 0.141615 | ||||||||
\(676\) | −7.71702 | −0.296808 | ||||||||
\(677\) | −11.2235 | −0.431353 | −0.215676 | − | 0.976465i | \(-0.569196\pi\) | ||||
−0.215676 | + | 0.976465i | \(0.569196\pi\) | |||||||
\(678\) | −8.63792 | −0.331737 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.74250 | −0.220215 | ||||||||
\(681\) | −20.0938 | −0.769995 | ||||||||
\(682\) | 9.50941 | 0.364134 | ||||||||
\(683\) | 16.5187 | 0.632072 | 0.316036 | − | 0.948747i | \(-0.397648\pi\) | ||||
0.316036 | + | 0.948747i | \(0.397648\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −12.7344 | −0.486557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.9555 | −0.685043 | ||||||||
\(688\) | −2.08397 | −0.0794506 | ||||||||
\(689\) | −25.9069 | −0.986973 | ||||||||
\(690\) | 7.94774 | 0.302565 | ||||||||
\(691\) | 41.4575 | 1.57712 | 0.788559 | − | 0.614959i | \(-0.210827\pi\) | ||||
0.788559 | + | 0.614959i | \(0.210827\pi\) | |||||||
\(692\) | 8.10185 | 0.307986 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.1826 | −1.10776 | ||||||||
\(695\) | 12.6617 | 0.480287 | ||||||||
\(696\) | 3.76643 | 0.142766 | ||||||||
\(697\) | −4.03033 | −0.152660 | ||||||||
\(698\) | −9.36208 | −0.354360 | ||||||||
\(699\) | −10.2539 | −0.387839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9202 | 1.01676 | 0.508380 | − | 0.861133i | \(-0.330244\pi\) | ||||
0.508380 | + | 0.861133i | \(0.330244\pi\) | |||||||
\(702\) | 2.29847 | 0.0867503 | ||||||||
\(703\) | 0.660191 | 0.0248996 | ||||||||
\(704\) | −2.16830 | −0.0817209 | ||||||||
\(705\) | −4.27775 | −0.161109 | ||||||||
\(706\) | −33.5994 | −1.26453 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10.4266 | −0.391856 | ||||||||
\(709\) | 29.6206 | 1.11242 | 0.556212 | − | 0.831040i | \(-0.312254\pi\) | ||||
0.556212 | + | 0.831040i | \(0.312254\pi\) | |||||||
\(710\) | −0.371882 | −0.0139565 | ||||||||
\(711\) | −7.59208 | −0.284725 | ||||||||
\(712\) | −12.3776 | −0.463869 | ||||||||
\(713\) | −30.3297 | −1.13586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.72755 | 0.214198 | ||||||||
\(716\) | −6.84755 | −0.255905 | ||||||||
\(717\) | −1.73965 | −0.0649685 | ||||||||
\(718\) | 24.3630 | 0.909220 | ||||||||
\(719\) | −26.5038 | −0.988425 | −0.494213 | − | 0.869341i | \(-0.664544\pi\) | ||||
−0.494213 | + | 0.869341i | \(0.664544\pi\) | |||||||
\(720\) | −1.14924 | −0.0428295 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 20.8492 | 0.775391 | ||||||||
\(724\) | −16.5905 | −0.616582 | ||||||||
\(725\) | −13.8577 | −0.514661 | ||||||||
\(726\) | −6.29847 | −0.233758 | ||||||||
\(727\) | 27.4510 | 1.01810 | 0.509051 | − | 0.860736i | \(-0.329996\pi\) | ||||
0.509051 | + | 0.860736i | \(0.329996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.43394 | −0.201119 | ||||||||
\(731\) | 10.4132 | 0.385144 | ||||||||
\(732\) | −2.57622 | −0.0952199 | ||||||||
\(733\) | −14.1651 | −0.523200 | −0.261600 | − | 0.965176i | \(-0.584250\pi\) | ||||
−0.261600 | + | 0.965176i | \(0.584250\pi\) | |||||||
\(734\) | 33.1571 | 1.22385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.91567 | 0.254915 | ||||||||
\(737\) | −19.2668 | −0.709703 | ||||||||
\(738\) | −0.806583 | −0.0296907 | ||||||||
\(739\) | 7.54018 | 0.277370 | 0.138685 | − | 0.990337i | \(-0.455712\pi\) | ||||
0.138685 | + | 0.990337i | \(0.455712\pi\) | |||||||
\(740\) | −0.758716 | −0.0278910 | ||||||||
\(741\) | −2.29847 | −0.0844365 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −53.8226 | −1.97456 | −0.987279 | − | 0.158997i | \(-0.949174\pi\) | ||||
−0.987279 | + | 0.158997i | \(0.949174\pi\) | |||||||
\(744\) | 4.38565 | 0.160786 | ||||||||
\(745\) | 24.3833 | 0.893337 | ||||||||
\(746\) | 22.5460 | 0.825467 | ||||||||
\(747\) | 3.17435 | 0.116144 | ||||||||
\(748\) | 10.8345 | 0.396150 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.97452 | 0.364218 | ||||||||
\(751\) | 20.7762 | 0.758136 | 0.379068 | − | 0.925369i | \(-0.376245\pi\) | ||||
0.379068 | + | 0.925369i | \(0.376245\pi\) | |||||||
\(752\) | −3.72225 | −0.135737 | ||||||||
\(753\) | −3.19663 | −0.116492 | ||||||||
\(754\) | −8.65704 | −0.315271 | ||||||||
\(755\) | −10.8050 | −0.393233 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9757 | −0.580647 | −0.290323 | − | 0.956929i | \(-0.593763\pi\) | ||||
−0.290323 | + | 0.956929i | \(0.593763\pi\) | |||||||
\(758\) | −18.7616 | −0.681451 | ||||||||
\(759\) | −14.9952 | −0.544293 | ||||||||
\(760\) | 1.14924 | 0.0416872 | ||||||||
\(761\) | 14.1830 | 0.514132 | 0.257066 | − | 0.966394i | \(-0.417244\pi\) | ||||
0.257066 | + | 0.966394i | \(0.417244\pi\) | |||||||
\(762\) | −13.8683 | −0.502395 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.8902 | 0.574887 | ||||||||
\(765\) | 5.74250 | 0.207620 | ||||||||
\(766\) | 8.11770 | 0.293305 | ||||||||
\(767\) | 23.9653 | 0.865338 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −39.7426 | −1.43316 | −0.716578 | − | 0.697507i | \(-0.754292\pi\) | ||||
−0.716578 | + | 0.697507i | \(0.754292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0219 | 0.541001 | ||||||||
\(772\) | 6.49676 | 0.233824 | ||||||||
\(773\) | 0.183792 | 0.00661053 | 0.00330527 | − | 0.999995i | \(-0.498948\pi\) | ||||
0.00330527 | + | 0.999995i | \(0.498948\pi\) | |||||||
\(774\) | 2.08397 | 0.0749067 | ||||||||
\(775\) | −16.1359 | −0.579620 | ||||||||
\(776\) | 5.91567 | 0.212360 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.0034 | 1.25493 | ||||||||
\(779\) | 0.806583 | 0.0288988 | ||||||||
\(780\) | 2.64149 | 0.0945806 | ||||||||
\(781\) | 0.701641 | 0.0251067 | ||||||||
\(782\) | −34.5562 | −1.23573 | ||||||||
\(783\) | −3.76643 | −0.134601 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.06460 | −0.252146 | ||||||||
\(786\) | 12.2113 | 0.435563 | ||||||||
\(787\) | −20.2158 | −0.720616 | −0.360308 | − | 0.932833i | \(-0.617328\pi\) | ||||
−0.360308 | + | 0.932833i | \(0.617328\pi\) | |||||||
\(788\) | 1.06491 | 0.0379357 | ||||||||
\(789\) | −10.6760 | −0.380077 | ||||||||
\(790\) | −8.72510 | −0.310425 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.16830 | 0.0770472 | ||||||||
\(793\) | 5.92138 | 0.210274 | ||||||||
\(794\) | −15.0219 | −0.533108 | ||||||||
\(795\) | −12.9534 | −0.459411 | ||||||||
\(796\) | 23.5917 | 0.836186 | ||||||||
\(797\) | −33.9377 | −1.20213 | −0.601067 | − | 0.799198i | \(-0.705258\pi\) | ||||
−0.601067 | + | 0.799198i | \(0.705258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.5993 | 0.657996 | ||||||||
\(800\) | 3.67925 | 0.130081 | ||||||||
\(801\) | 12.3776 | 0.437340 | ||||||||
\(802\) | 26.6287 | 0.940291 | ||||||||
\(803\) | 10.2524 | 0.361799 | ||||||||
\(804\) | −8.88568 | −0.313374 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.0803 | −0.355064 | ||||||||
\(807\) | 3.24906 | 0.114372 | ||||||||
\(808\) | 12.8683 | 0.452705 | ||||||||
\(809\) | −34.7190 | −1.22066 | −0.610328 | − | 0.792149i | \(-0.708962\pi\) | ||||
−0.610328 | + | 0.792149i | \(0.708962\pi\) | |||||||
\(810\) | 1.14924 | 0.0403801 | ||||||||
\(811\) | 44.1620 | 1.55074 | 0.775369 | − | 0.631509i | \(-0.217564\pi\) | ||||
0.775369 | + | 0.631509i | \(0.217564\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.0349 | −0.632512 | ||||||||
\(814\) | 1.43149 | 0.0501738 | ||||||||
\(815\) | 9.89255 | 0.346521 | ||||||||
\(816\) | 4.99679 | 0.174923 | ||||||||
\(817\) | −2.08397 | −0.0729088 | ||||||||
\(818\) | −27.6489 | −0.966721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.926955 | −0.0323707 | ||||||||
\(821\) | 12.1074 | 0.422552 | 0.211276 | − | 0.977426i | \(-0.432238\pi\) | ||||
0.211276 | + | 0.977426i | \(0.432238\pi\) | |||||||
\(822\) | 11.0808 | 0.386486 | ||||||||
\(823\) | 3.69623 | 0.128843 | 0.0644213 | − | 0.997923i | \(-0.479480\pi\) | ||||
0.0644213 | + | 0.997923i | \(0.479480\pi\) | |||||||
\(824\) | −6.95582 | −0.242317 | ||||||||
\(825\) | −7.97773 | −0.277749 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8614 | −0.412461 | −0.206230 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206230 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(828\) | −6.91567 | −0.240336 | ||||||||
\(829\) | 34.2921 | 1.19101 | 0.595506 | − | 0.803351i | \(-0.296952\pi\) | ||||
0.595506 | + | 0.803351i | \(0.296952\pi\) | |||||||
\(830\) | 3.64808 | 0.126627 | ||||||||
\(831\) | −22.2839 | −0.773021 | ||||||||
\(832\) | 2.29847 | 0.0796852 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11.0175 | −0.381505 | ||||||||
\(835\) | −13.7620 | −0.476253 | ||||||||
\(836\) | −2.16830 | −0.0749922 | ||||||||
\(837\) | −4.38565 | −0.151590 | ||||||||
\(838\) | −1.91888 | −0.0662865 | ||||||||
\(839\) | 23.5395 | 0.812672 | 0.406336 | − | 0.913724i | \(-0.366806\pi\) | ||||
0.406336 | + | 0.913724i | \(0.366806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8140 | −0.510827 | ||||||||
\(842\) | −25.9815 | −0.895381 | ||||||||
\(843\) | −7.10790 | −0.244809 | ||||||||
\(844\) | 17.8699 | 0.615109 | ||||||||
\(845\) | 8.86868 | 0.305092 | ||||||||
\(846\) | 3.72225 | 0.127974 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.2713 | −0.387059 | ||||||||
\(849\) | 15.7474 | 0.540448 | ||||||||
\(850\) | −18.3845 | −0.630582 | ||||||||
\(851\) | −4.56566 | −0.156509 | ||||||||
\(852\) | 0.323591 | 0.0110860 | ||||||||
\(853\) | −54.9855 | −1.88267 | −0.941334 | − | 0.337477i | \(-0.890427\pi\) | ||||
−0.941334 | + | 0.337477i | \(0.890427\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14924 | −0.0393031 | ||||||||
\(856\) | 12.3987 | 0.423777 | ||||||||
\(857\) | 58.1333 | 1.98579 | 0.992897 | − | 0.118976i | \(-0.0379612\pi\) | ||||
0.992897 | + | 0.118976i | \(0.0379612\pi\) | |||||||
\(858\) | −4.98378 | −0.170143 | ||||||||
\(859\) | 11.6517 | 0.397550 | 0.198775 | − | 0.980045i | \(-0.436304\pi\) | ||||
0.198775 | + | 0.980045i | \(0.436304\pi\) | |||||||
\(860\) | 2.39497 | 0.0816679 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.965082 | −0.0328708 | ||||||||
\(863\) | −9.64470 | −0.328309 | −0.164155 | − | 0.986435i | \(-0.552490\pi\) | ||||
−0.164155 | + | 0.986435i | \(0.552490\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −9.31094 | −0.316582 | ||||||||
\(866\) | 5.93960 | 0.201836 | ||||||||
\(867\) | −7.96793 | −0.270605 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.4619 | 0.558432 | ||||||||
\(870\) | −4.32852 | −0.146751 | ||||||||
\(871\) | 20.4235 | 0.692024 | ||||||||
\(872\) | −18.0568 | −0.611481 | ||||||||
\(873\) | −5.91567 | −0.200215 | ||||||||
\(874\) | 6.91567 | 0.233926 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.72830 | 0.159755 | ||||||||
\(877\) | −51.9199 | −1.75321 | −0.876605 | − | 0.481211i | \(-0.840197\pi\) | ||||
−0.876605 | + | 0.481211i | \(0.840197\pi\) | |||||||
\(878\) | −21.5921 | −0.728697 | ||||||||
\(879\) | −22.0139 | −0.742512 | ||||||||
\(880\) | 2.49189 | 0.0840016 | ||||||||
\(881\) | 1.32443 | 0.0446213 | 0.0223106 | − | 0.999751i | \(-0.492898\pi\) | ||||
0.0223106 | + | 0.999751i | \(0.492898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.6432 | −1.53602 | −0.768009 | − | 0.640439i | \(-0.778752\pi\) | ||||
−0.768009 | + | 0.640439i | \(0.778752\pi\) | |||||||
\(884\) | −11.4850 | −0.386282 | ||||||||
\(885\) | 11.9827 | 0.402793 | ||||||||
\(886\) | −13.9344 | −0.468134 | ||||||||
\(887\) | 5.18089 | 0.173957 | 0.0869786 | − | 0.996210i | \(-0.472279\pi\) | ||||
0.0869786 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(888\) | 0.660191 | 0.0221546 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.2248 | 0.476815 | ||||||||
\(891\) | −2.16830 | −0.0726408 | ||||||||
\(892\) | 4.44605 | 0.148865 | ||||||||
\(893\) | −3.72225 | −0.124560 | ||||||||
\(894\) | −21.2170 | −0.709602 | ||||||||
\(895\) | 7.86946 | 0.263047 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.8955 | 0.530735 | ||||||||
\(898\) | −14.3273 | −0.478109 | ||||||||
\(899\) | 16.5183 | 0.550915 | ||||||||
\(900\) | −3.67925 | −0.122642 | ||||||||
\(901\) | 56.3205 | 1.87631 | ||||||||
\(902\) | 1.74891 | 0.0582325 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.63792 | 0.287293 | ||||||||
\(905\) | 19.0665 | 0.633790 | ||||||||
\(906\) | 9.40187 | 0.312356 | ||||||||
\(907\) | 58.5017 | 1.94252 | 0.971258 | − | 0.238028i | \(-0.0765008\pi\) | ||||
0.971258 | + | 0.238028i | \(0.0765008\pi\) | |||||||
\(908\) | 20.0938 | 0.666835 | ||||||||
\(909\) | −12.8683 | −0.426814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2344 | 0.769790 | 0.384895 | − | 0.922960i | \(-0.374238\pi\) | ||||
0.384895 | + | 0.922960i | \(0.374238\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | −6.88295 | −0.227792 | ||||||||
\(914\) | −32.2981 | −1.06833 | ||||||||
\(915\) | 2.96069 | 0.0978774 | ||||||||
\(916\) | 17.9555 | 0.593265 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.99679 | −0.164919 | ||||||||
\(919\) | 17.8751 | 0.589644 | 0.294822 | − | 0.955552i | \(-0.404740\pi\) | ||||
0.294822 | + | 0.955552i | \(0.404740\pi\) | |||||||
\(920\) | −7.94774 | −0.262029 | ||||||||
\(921\) | −14.3776 | −0.473757 | ||||||||
\(922\) | −0.375849 | −0.0123779 | ||||||||
\(923\) | −0.743764 | −0.0244813 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.42901 | −0.0798654 | ||||||||
\(926\) | −7.80824 | −0.256595 | ||||||||
\(927\) | 6.95582 | 0.228459 | ||||||||
\(928\) | −3.76643 | −0.123639 | ||||||||
\(929\) | 46.4492 | 1.52395 | 0.761974 | − | 0.647607i | \(-0.224230\pi\) | ||||
0.761974 | + | 0.647607i | \(0.224230\pi\) | |||||||
\(930\) | −5.04015 | −0.165273 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.2539 | 0.335879 | ||||||||
\(933\) | 2.97452 | 0.0973814 | ||||||||
\(934\) | 12.2555 | 0.401011 | ||||||||
\(935\) | −12.4515 | −0.407206 | ||||||||
\(936\) | −2.29847 | −0.0751280 | ||||||||
\(937\) | −42.3561 | −1.38371 | −0.691857 | − | 0.722034i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722034i | \(0.743207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.7588 | 0.546904 | ||||||||
\(940\) | 4.27775 | 0.139525 | ||||||||
\(941\) | −46.4969 | −1.51576 | −0.757878 | − | 0.652396i | \(-0.773764\pi\) | ||||
−0.757878 | + | 0.652396i | \(0.773764\pi\) | |||||||
\(942\) | 6.14721 | 0.200287 | ||||||||
\(943\) | −5.57806 | −0.181647 | ||||||||
\(944\) | 10.4266 | 0.339358 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.51867 | −0.146915 | ||||||||
\(947\) | 47.2657 | 1.53593 | 0.767964 | − | 0.640493i | \(-0.221270\pi\) | ||||
0.767964 | + | 0.640493i | \(0.221270\pi\) | |||||||
\(948\) | 7.59208 | 0.246579 | ||||||||
\(949\) | −10.8679 | −0.352786 | ||||||||
\(950\) | 3.67925 | 0.119371 | ||||||||
\(951\) | 2.81061 | 0.0911403 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.673201 | −0.0218071 | −0.0109036 | − | 0.999941i | \(-0.503471\pi\) | ||||
−0.0109036 | + | 0.999941i | \(0.503471\pi\) | |||||||
\(954\) | 11.2713 | 0.364923 | ||||||||
\(955\) | −18.2616 | −0.590931 | ||||||||
\(956\) | 1.73965 | 0.0562644 | ||||||||
\(957\) | 8.16675 | 0.263994 | ||||||||
\(958\) | −27.0751 | −0.874756 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.14924 | 0.0370915 | ||||||||
\(961\) | −11.7661 | −0.379551 | ||||||||
\(962\) | −1.51743 | −0.0489240 | ||||||||
\(963\) | −12.3987 | −0.399541 | ||||||||
\(964\) | −20.8492 | −0.671508 | ||||||||
\(965\) | −7.46632 | −0.240349 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.83609 | 0.0590447 | 0.0295224 | − | 0.999564i | \(-0.490601\pi\) | ||||
0.0295224 | + | 0.999564i | \(0.490601\pi\) | |||||||
\(968\) | 6.29847 | 0.202441 | ||||||||
\(969\) | 4.99679 | 0.160520 | ||||||||
\(970\) | −6.79850 | −0.218287 | ||||||||
\(971\) | 12.6488 | 0.405921 | 0.202960 | − | 0.979187i | \(-0.434944\pi\) | ||||
0.202960 | + | 0.979187i | \(0.434944\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.7498 | −0.953247 | ||||||||
\(975\) | 8.45667 | 0.270830 | ||||||||
\(976\) | 2.57622 | 0.0824629 | ||||||||
\(977\) | 21.3457 | 0.682909 | 0.341454 | − | 0.939898i | \(-0.389081\pi\) | ||||
0.341454 | + | 0.939898i | \(0.389081\pi\) | |||||||
\(978\) | −8.60793 | −0.275251 | ||||||||
\(979\) | −26.8383 | −0.857756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0568 | 0.576510 | ||||||||
\(982\) | −18.4381 | −0.588383 | ||||||||
\(983\) | 25.7268 | 0.820558 | 0.410279 | − | 0.911960i | \(-0.365431\pi\) | ||||
0.410279 | + | 0.911960i | \(0.365431\pi\) | |||||||
\(984\) | 0.806583 | 0.0257129 | ||||||||
\(985\) | −1.22383 | −0.0389944 | ||||||||
\(986\) | 18.8201 | 0.599353 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.29847 | 0.0731242 | ||||||||
\(989\) | 14.4120 | 0.458276 | ||||||||
\(990\) | −2.49189 | −0.0791975 | ||||||||
\(991\) | −58.1823 | −1.84822 | −0.924111 | − | 0.382124i | \(-0.875193\pi\) | ||||
−0.924111 | + | 0.382124i | \(0.875193\pi\) | |||||||
\(992\) | −4.38565 | −0.139245 | ||||||||
\(993\) | 10.1391 | 0.321754 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.1125 | −0.859523 | ||||||||
\(996\) | −3.17435 | −0.100583 | ||||||||
\(997\) | −51.2792 | −1.62403 | −0.812014 | − | 0.583638i | \(-0.801629\pi\) | ||||
−0.812014 | + | 0.583638i | \(0.801629\pi\) | |||||||
\(998\) | −33.1570 | −1.04957 | ||||||||
\(999\) | −0.660191 | −0.0208875 |
(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 | 5586.2.a.bw.1.2 | 4 | ||
7.2 | even | 3 | 798.2.j.l.571.3 | yes | 8 | ||
7.4 | even | 3 | 798.2.j.l.457.3 | ✓ | 8 | ||
7.6 | odd | 2 | 5586.2.a.bz.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.l.457.3 | ✓ | 8 | 7.4 | even | 3 | ||
798.2.j.l.571.3 | yes | 8 | 7.2 | even | 3 | ||
5586.2.a.bw.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5586.2.a.bz.1.3 | 4 | 7.6 | odd | 2 |