Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.5163008.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 5x^{2} - 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.56754\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.0387751 | 0.0223868 | 0.0111934 | − | 0.999937i | \(-0.496437\pi\) | ||||
0.0111934 | + | 0.999937i | \(0.496437\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.61052 | 1.16746 | 0.583731 | − | 0.811947i | \(-0.301592\pi\) | ||||
0.583731 | + | 0.811947i | \(0.301592\pi\) | |||||||
\(6\) | 0.0387751 | 0.0158299 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.99850 | −0.999499 | ||||||||
\(10\) | 2.61052 | 0.825520 | ||||||||
\(11\) | 3.07158 | 0.926115 | 0.463057 | − | 0.886328i | \(-0.346752\pi\) | ||||
0.463057 | + | 0.886328i | \(0.346752\pi\) | |||||||
\(12\) | 0.0387751 | 0.0111934 | ||||||||
\(13\) | −2.08825 | −0.579176 | −0.289588 | − | 0.957151i | \(-0.593518\pi\) | ||||
−0.289588 | + | 0.957151i | \(0.593518\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.101223 | 0.0261358 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.761390 | −0.184664 | −0.0923321 | − | 0.995728i | \(-0.529432\pi\) | ||||
−0.0923321 | + | 0.995728i | \(0.529432\pi\) | |||||||
\(18\) | −2.99850 | −0.706752 | ||||||||
\(19\) | 7.09631 | 1.62801 | 0.814003 | − | 0.580861i | \(-0.197284\pi\) | ||||
0.814003 | + | 0.580861i | \(0.197284\pi\) | |||||||
\(20\) | 2.61052 | 0.583731 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.07158 | 0.654862 | ||||||||
\(23\) | 5.31219 | 1.10767 | 0.553835 | − | 0.832627i | \(-0.313164\pi\) | ||||
0.553835 | + | 0.832627i | \(0.313164\pi\) | |||||||
\(24\) | 0.0387751 | 0.00791494 | ||||||||
\(25\) | 1.81483 | 0.362966 | ||||||||
\(26\) | −2.08825 | −0.409539 | ||||||||
\(27\) | −0.232592 | −0.0447624 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.31533 | 0.429947 | 0.214973 | − | 0.976620i | \(-0.431033\pi\) | ||||
0.214973 | + | 0.976620i | \(0.431033\pi\) | |||||||
\(30\) | 0.101223 | 0.0184808 | ||||||||
\(31\) | 0.644105 | 0.115685 | 0.0578424 | − | 0.998326i | \(-0.481578\pi\) | ||||
0.0578424 | + | 0.998326i | \(0.481578\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.119101 | 0.0207328 | ||||||||
\(34\) | −0.761390 | −0.130577 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.99850 | −0.499749 | ||||||||
\(37\) | −9.45774 | −1.55484 | −0.777421 | − | 0.628980i | \(-0.783473\pi\) | ||||
−0.777421 | + | 0.628980i | \(0.783473\pi\) | |||||||
\(38\) | 7.09631 | 1.15117 | ||||||||
\(39\) | −0.0809720 | −0.0129659 | ||||||||
\(40\) | 2.61052 | 0.412760 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.79344 | 0.730993 | 0.365497 | − | 0.930813i | \(-0.380899\pi\) | ||||
0.365497 | + | 0.930813i | \(0.380899\pi\) | |||||||
\(44\) | 3.07158 | 0.463057 | ||||||||
\(45\) | −7.82764 | −1.16688 | ||||||||
\(46\) | 5.31219 | 0.783240 | ||||||||
\(47\) | 4.61388 | 0.673003 | 0.336501 | − | 0.941683i | \(-0.390756\pi\) | ||||
0.336501 | + | 0.941683i | \(0.390756\pi\) | |||||||
\(48\) | 0.0387751 | 0.00559671 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.81483 | 0.256656 | ||||||||
\(51\) | −0.0295230 | −0.00413405 | ||||||||
\(52\) | −2.08825 | −0.289588 | ||||||||
\(53\) | −6.27441 | −0.861856 | −0.430928 | − | 0.902386i | \(-0.641814\pi\) | ||||
−0.430928 | + | 0.902386i | \(0.641814\pi\) | |||||||
\(54\) | −0.232592 | −0.0316518 | ||||||||
\(55\) | 8.01842 | 1.08120 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.275160 | 0.0364459 | ||||||||
\(58\) | 2.31533 | 0.304018 | ||||||||
\(59\) | 14.3819 | 1.87236 | 0.936181 | − | 0.351518i | \(-0.114334\pi\) | ||||
0.936181 | + | 0.351518i | \(0.114334\pi\) | |||||||
\(60\) | 0.101223 | 0.0130679 | ||||||||
\(61\) | 3.84288 | 0.492030 | 0.246015 | − | 0.969266i | \(-0.420879\pi\) | ||||
0.246015 | + | 0.969266i | \(0.420879\pi\) | |||||||
\(62\) | 0.644105 | 0.0818015 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.45142 | −0.676165 | ||||||||
\(66\) | 0.119101 | 0.0146603 | ||||||||
\(67\) | 8.37335 | 1.02297 | 0.511484 | − | 0.859293i | \(-0.329096\pi\) | ||||
0.511484 | + | 0.859293i | \(0.329096\pi\) | |||||||
\(68\) | −0.761390 | −0.0923321 | ||||||||
\(69\) | 0.205981 | 0.0247972 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8481 | −1.28744 | −0.643718 | − | 0.765263i | \(-0.722609\pi\) | ||||
−0.643718 | + | 0.765263i | \(0.722609\pi\) | |||||||
\(72\) | −2.99850 | −0.353376 | ||||||||
\(73\) | 3.35938 | 0.393185 | 0.196593 | − | 0.980485i | \(-0.437012\pi\) | ||||
0.196593 | + | 0.980485i | \(0.437012\pi\) | |||||||
\(74\) | −9.45774 | −1.09944 | ||||||||
\(75\) | 0.0703702 | 0.00812565 | ||||||||
\(76\) | 7.09631 | 0.814003 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0809720 | −0.00916828 | ||||||||
\(79\) | −2.24510 | −0.252594 | −0.126297 | − | 0.991992i | \(-0.540309\pi\) | ||||
−0.126297 | + | 0.991992i | \(0.540309\pi\) | |||||||
\(80\) | 2.61052 | 0.291865 | ||||||||
\(81\) | 8.98647 | 0.998497 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 7.80581 | 0.856799 | 0.428399 | − | 0.903589i | \(-0.359078\pi\) | ||||
0.428399 | + | 0.903589i | \(0.359078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.98763 | −0.215588 | ||||||||
\(86\) | 4.79344 | 0.516890 | ||||||||
\(87\) | 0.0897774 | 0.00962515 | ||||||||
\(88\) | 3.07158 | 0.327431 | ||||||||
\(89\) | −5.93525 | −0.629135 | −0.314568 | − | 0.949235i | \(-0.601860\pi\) | ||||
−0.314568 | + | 0.949235i | \(0.601860\pi\) | |||||||
\(90\) | −7.82764 | −0.825106 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.31219 | 0.553835 | ||||||||
\(93\) | 0.0249753 | 0.00258981 | ||||||||
\(94\) | 4.61388 | 0.475885 | ||||||||
\(95\) | 18.5251 | 1.90063 | ||||||||
\(96\) | 0.0387751 | 0.00395747 | ||||||||
\(97\) | 16.7498 | 1.70069 | 0.850345 | − | 0.526226i | \(-0.176393\pi\) | ||||
0.850345 | + | 0.526226i | \(0.176393\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.21011 | −0.925651 | ||||||||
\(100\) | 1.81483 | 0.181483 | ||||||||
\(101\) | 10.4656 | 1.04137 | 0.520683 | − | 0.853750i | \(-0.325678\pi\) | ||||
0.520683 | + | 0.853750i | \(0.325678\pi\) | |||||||
\(102\) | −0.0295230 | −0.00292321 | ||||||||
\(103\) | −2.47421 | −0.243791 | −0.121896 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(104\) | −2.08825 | −0.204770 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.27441 | −0.609424 | ||||||||
\(107\) | −15.8124 | −1.52864 | −0.764320 | − | 0.644837i | \(-0.776925\pi\) | ||||
−0.764320 | + | 0.644837i | \(0.776925\pi\) | |||||||
\(108\) | −0.232592 | −0.0223812 | ||||||||
\(109\) | 6.57783 | 0.630042 | 0.315021 | − | 0.949085i | \(-0.397988\pi\) | ||||
0.315021 | + | 0.949085i | \(0.397988\pi\) | |||||||
\(110\) | 8.01842 | 0.764526 | ||||||||
\(111\) | −0.366725 | −0.0348080 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.34219 | 0.314407 | 0.157203 | − | 0.987566i | \(-0.449752\pi\) | ||||
0.157203 | + | 0.987566i | \(0.449752\pi\) | |||||||
\(114\) | 0.275160 | 0.0257711 | ||||||||
\(115\) | 13.8676 | 1.29316 | ||||||||
\(116\) | 2.31533 | 0.214973 | ||||||||
\(117\) | 6.26160 | 0.578885 | ||||||||
\(118\) | 14.3819 | 1.32396 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.101223 | 0.00924038 | ||||||||
\(121\) | −1.56542 | −0.142311 | ||||||||
\(122\) | 3.84288 | 0.347918 | ||||||||
\(123\) | −0.0387751 | −0.00349623 | ||||||||
\(124\) | 0.644105 | 0.0578424 | ||||||||
\(125\) | −8.31496 | −0.743713 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.37867 | −0.743487 | −0.371743 | − | 0.928335i | \(-0.621240\pi\) | ||||
−0.371743 | + | 0.928335i | \(0.621240\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.185866 | 0.0163646 | ||||||||
\(130\) | −5.45142 | −0.478121 | ||||||||
\(131\) | −12.7513 | −1.11409 | −0.557043 | − | 0.830483i | \(-0.688064\pi\) | ||||
−0.557043 | + | 0.830483i | \(0.688064\pi\) | |||||||
\(132\) | 0.119101 | 0.0103664 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.37335 | 0.723347 | ||||||||
\(135\) | −0.607188 | −0.0522584 | ||||||||
\(136\) | −0.761390 | −0.0652887 | ||||||||
\(137\) | 14.7866 | 1.26330 | 0.631651 | − | 0.775253i | \(-0.282377\pi\) | ||||
0.631651 | + | 0.775253i | \(0.282377\pi\) | |||||||
\(138\) | 0.205981 | 0.0175343 | ||||||||
\(139\) | 9.80861 | 0.831956 | 0.415978 | − | 0.909375i | \(-0.363439\pi\) | ||||
0.415978 | + | 0.909375i | \(0.363439\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.178904 | 0.0150664 | ||||||||
\(142\) | −10.8481 | −0.910355 | ||||||||
\(143\) | −6.41421 | −0.536383 | ||||||||
\(144\) | −2.99850 | −0.249875 | ||||||||
\(145\) | 6.04423 | 0.501946 | ||||||||
\(146\) | 3.35938 | 0.278024 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.45774 | −0.777421 | ||||||||
\(149\) | −12.1994 | −0.999412 | −0.499706 | − | 0.866195i | \(-0.666559\pi\) | ||||
−0.499706 | + | 0.866195i | \(0.666559\pi\) | |||||||
\(150\) | 0.0703702 | 0.00574570 | ||||||||
\(151\) | −20.5621 | −1.67332 | −0.836660 | − | 0.547722i | \(-0.815495\pi\) | ||||
−0.836660 | + | 0.547722i | \(0.815495\pi\) | |||||||
\(152\) | 7.09631 | 0.575587 | ||||||||
\(153\) | 2.28303 | 0.184572 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.68145 | 0.135057 | ||||||||
\(156\) | −0.0809720 | −0.00648295 | ||||||||
\(157\) | −4.63615 | −0.370005 | −0.185003 | − | 0.982738i | \(-0.559229\pi\) | ||||
−0.185003 | + | 0.982738i | \(0.559229\pi\) | |||||||
\(158\) | −2.24510 | −0.178611 | ||||||||
\(159\) | −0.243291 | −0.0192942 | ||||||||
\(160\) | 2.61052 | 0.206380 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.98647 | 0.706044 | ||||||||
\(163\) | 3.11486 | 0.243974 | 0.121987 | − | 0.992532i | \(-0.461073\pi\) | ||||
0.121987 | + | 0.992532i | \(0.461073\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 0.310915 | 0.0242047 | ||||||||
\(166\) | 7.80581 | 0.605848 | ||||||||
\(167\) | −4.77073 | −0.369170 | −0.184585 | − | 0.982817i | \(-0.559094\pi\) | ||||
−0.184585 | + | 0.982817i | \(0.559094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.63922 | −0.664556 | ||||||||
\(170\) | −1.98763 | −0.152444 | ||||||||
\(171\) | −21.2783 | −1.62719 | ||||||||
\(172\) | 4.79344 | 0.365497 | ||||||||
\(173\) | 2.15961 | 0.164192 | 0.0820959 | − | 0.996624i | \(-0.473839\pi\) | ||||
0.0820959 | + | 0.996624i | \(0.473839\pi\) | |||||||
\(174\) | 0.0897774 | 0.00680601 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.07158 | 0.231529 | ||||||||
\(177\) | 0.557659 | 0.0419163 | ||||||||
\(178\) | −5.93525 | −0.444866 | ||||||||
\(179\) | −20.1667 | −1.50733 | −0.753663 | − | 0.657261i | \(-0.771715\pi\) | ||||
−0.753663 | + | 0.657261i | \(0.771715\pi\) | |||||||
\(180\) | −7.82764 | −0.583438 | ||||||||
\(181\) | 7.51035 | 0.558240 | 0.279120 | − | 0.960256i | \(-0.409957\pi\) | ||||
0.279120 | + | 0.960256i | \(0.409957\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.149008 | 0.0110150 | ||||||||
\(184\) | 5.31219 | 0.391620 | ||||||||
\(185\) | −24.6896 | −1.81522 | ||||||||
\(186\) | 0.0249753 | 0.00183128 | ||||||||
\(187\) | −2.33867 | −0.171020 | ||||||||
\(188\) | 4.61388 | 0.336501 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.5251 | 1.34395 | ||||||||
\(191\) | 4.24153 | 0.306907 | 0.153453 | − | 0.988156i | \(-0.450961\pi\) | ||||
0.153453 | + | 0.988156i | \(0.450961\pi\) | |||||||
\(192\) | 0.0387751 | 0.00279835 | ||||||||
\(193\) | 13.7705 | 0.991224 | 0.495612 | − | 0.868544i | \(-0.334944\pi\) | ||||
0.495612 | + | 0.868544i | \(0.334944\pi\) | |||||||
\(194\) | 16.7498 | 1.20257 | ||||||||
\(195\) | −0.211379 | −0.0151372 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68951 | −0.191620 | −0.0958100 | − | 0.995400i | \(-0.530544\pi\) | ||||
−0.0958100 | + | 0.995400i | \(0.530544\pi\) | |||||||
\(198\) | −9.21011 | −0.654534 | ||||||||
\(199\) | −6.34370 | −0.449693 | −0.224847 | − | 0.974394i | \(-0.572188\pi\) | ||||
−0.224847 | + | 0.974394i | \(0.572188\pi\) | |||||||
\(200\) | 1.81483 | 0.128328 | ||||||||
\(201\) | 0.324678 | 0.0229010 | ||||||||
\(202\) | 10.4656 | 0.736356 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0295230 | −0.00206702 | ||||||||
\(205\) | −2.61052 | −0.182327 | ||||||||
\(206\) | −2.47421 | −0.172387 | ||||||||
\(207\) | −15.9286 | −1.10711 | ||||||||
\(208\) | −2.08825 | −0.144794 | ||||||||
\(209\) | 21.7969 | 1.50772 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.81048 | −0.193481 | −0.0967407 | − | 0.995310i | \(-0.530842\pi\) | ||||
−0.0967407 | + | 0.995310i | \(0.530842\pi\) | |||||||
\(212\) | −6.27441 | −0.430928 | ||||||||
\(213\) | −0.420638 | −0.0288216 | ||||||||
\(214\) | −15.8124 | −1.08091 | ||||||||
\(215\) | 12.5134 | 0.853407 | ||||||||
\(216\) | −0.232592 | −0.0158259 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.57783 | 0.445507 | ||||||||
\(219\) | 0.130260 | 0.00880217 | ||||||||
\(220\) | 8.01842 | 0.540602 | ||||||||
\(221\) | 1.58997 | 0.106953 | ||||||||
\(222\) | −0.366725 | −0.0246130 | ||||||||
\(223\) | 19.0157 | 1.27338 | 0.636692 | − | 0.771118i | \(-0.280302\pi\) | ||||
0.636692 | + | 0.771118i | \(0.280302\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.44176 | −0.362784 | ||||||||
\(226\) | 3.34219 | 0.222319 | ||||||||
\(227\) | 9.23513 | 0.612957 | 0.306478 | − | 0.951878i | \(-0.400849\pi\) | ||||
0.306478 | + | 0.951878i | \(0.400849\pi\) | |||||||
\(228\) | 0.275160 | 0.0182229 | ||||||||
\(229\) | −19.7514 | −1.30521 | −0.652605 | − | 0.757698i | \(-0.726324\pi\) | ||||
−0.652605 | + | 0.757698i | \(0.726324\pi\) | |||||||
\(230\) | 13.8676 | 0.914403 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.31533 | 0.152009 | ||||||||
\(233\) | −19.5991 | −1.28398 | −0.641990 | − | 0.766713i | \(-0.721891\pi\) | ||||
−0.641990 | + | 0.766713i | \(0.721891\pi\) | |||||||
\(234\) | 6.26160 | 0.409334 | ||||||||
\(235\) | 12.0446 | 0.785705 | ||||||||
\(236\) | 14.3819 | 0.936181 | ||||||||
\(237\) | −0.0870541 | −0.00565477 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.41493 | −0.544317 | −0.272158 | − | 0.962252i | \(-0.587737\pi\) | ||||
−0.272158 | + | 0.962252i | \(0.587737\pi\) | |||||||
\(240\) | 0.101223 | 0.00653394 | ||||||||
\(241\) | 3.36585 | 0.216813 | 0.108407 | − | 0.994107i | \(-0.465425\pi\) | ||||
0.108407 | + | 0.994107i | \(0.465425\pi\) | |||||||
\(242\) | −1.56542 | −0.100629 | ||||||||
\(243\) | 1.04623 | 0.0671156 | ||||||||
\(244\) | 3.84288 | 0.246015 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0387751 | −0.00247221 | ||||||||
\(247\) | −14.8189 | −0.942901 | ||||||||
\(248\) | 0.644105 | 0.0409007 | ||||||||
\(249\) | 0.302671 | 0.0191810 | ||||||||
\(250\) | −8.31496 | −0.525884 | ||||||||
\(251\) | 2.97894 | 0.188029 | 0.0940144 | − | 0.995571i | \(-0.470030\pi\) | ||||
0.0940144 | + | 0.995571i | \(0.470030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.3168 | 1.02583 | ||||||||
\(254\) | −8.37867 | −0.525725 | ||||||||
\(255\) | −0.0770704 | −0.00482634 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.74010 | 0.420436 | 0.210218 | − | 0.977655i | \(-0.432583\pi\) | ||||
0.210218 | + | 0.977655i | \(0.432583\pi\) | |||||||
\(258\) | 0.185866 | 0.0115715 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.45142 | −0.338083 | ||||||||
\(261\) | −6.94252 | −0.429731 | ||||||||
\(262\) | −12.7513 | −0.787778 | ||||||||
\(263\) | 21.7936 | 1.34385 | 0.671926 | − | 0.740618i | \(-0.265467\pi\) | ||||
0.671926 | + | 0.740618i | \(0.265467\pi\) | |||||||
\(264\) | 0.119101 | 0.00733014 | ||||||||
\(265\) | −16.3795 | −1.00618 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.230140 | −0.0140843 | ||||||||
\(268\) | 8.37335 | 0.511484 | ||||||||
\(269\) | 26.2079 | 1.59793 | 0.798963 | − | 0.601380i | \(-0.205382\pi\) | ||||
0.798963 | + | 0.601380i | \(0.205382\pi\) | |||||||
\(270\) | −0.607188 | −0.0369523 | ||||||||
\(271\) | −19.9240 | −1.21030 | −0.605149 | − | 0.796112i | \(-0.706887\pi\) | ||||
−0.605149 | + | 0.796112i | \(0.706887\pi\) | |||||||
\(272\) | −0.761390 | −0.0461660 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.7866 | 0.893290 | ||||||||
\(275\) | 5.57438 | 0.336148 | ||||||||
\(276\) | 0.205981 | 0.0123986 | ||||||||
\(277\) | 20.0693 | 1.20585 | 0.602923 | − | 0.797799i | \(-0.294003\pi\) | ||||
0.602923 | + | 0.797799i | \(0.294003\pi\) | |||||||
\(278\) | 9.80861 | 0.588282 | ||||||||
\(279\) | −1.93135 | −0.115627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8047 | 1.36041 | 0.680207 | − | 0.733020i | \(-0.261890\pi\) | ||||
0.680207 | + | 0.733020i | \(0.261890\pi\) | |||||||
\(282\) | 0.178904 | 0.0106536 | ||||||||
\(283\) | −20.5397 | −1.22096 | −0.610479 | − | 0.792033i | \(-0.709023\pi\) | ||||
−0.610479 | + | 0.792033i | \(0.709023\pi\) | |||||||
\(284\) | −10.8481 | −0.643718 | ||||||||
\(285\) | 0.718312 | 0.0425491 | ||||||||
\(286\) | −6.41421 | −0.379280 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.99850 | −0.176688 | ||||||||
\(289\) | −16.4203 | −0.965899 | ||||||||
\(290\) | 6.04423 | 0.354930 | ||||||||
\(291\) | 0.649477 | 0.0380730 | ||||||||
\(292\) | 3.35938 | 0.196593 | ||||||||
\(293\) | −26.9744 | −1.57586 | −0.787930 | − | 0.615764i | \(-0.788847\pi\) | ||||
−0.787930 | + | 0.615764i | \(0.788847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37.5442 | 2.18591 | ||||||||
\(296\) | −9.45774 | −0.549720 | ||||||||
\(297\) | −0.714425 | −0.0414552 | ||||||||
\(298\) | −12.1994 | −0.706691 | ||||||||
\(299\) | −11.0932 | −0.641535 | ||||||||
\(300\) | 0.0703702 | 0.00406283 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.5621 | −1.18322 | ||||||||
\(303\) | 0.405805 | 0.0233129 | ||||||||
\(304\) | 7.09631 | 0.407001 | ||||||||
\(305\) | 10.0319 | 0.574426 | ||||||||
\(306\) | 2.28303 | 0.130512 | ||||||||
\(307\) | 11.9580 | 0.682476 | 0.341238 | − | 0.939977i | \(-0.389154\pi\) | ||||
0.341238 | + | 0.939977i | \(0.389154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0959379 | −0.00545772 | ||||||||
\(310\) | 1.68145 | 0.0955001 | ||||||||
\(311\) | −17.8581 | −1.01264 | −0.506319 | − | 0.862346i | \(-0.668994\pi\) | ||||
−0.506319 | + | 0.862346i | \(0.668994\pi\) | |||||||
\(312\) | −0.0809720 | −0.00458414 | ||||||||
\(313\) | 10.1352 | 0.572876 | 0.286438 | − | 0.958099i | \(-0.407529\pi\) | ||||
0.286438 | + | 0.958099i | \(0.407529\pi\) | |||||||
\(314\) | −4.63615 | −0.261633 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.24510 | −0.126297 | ||||||||
\(317\) | 11.6642 | 0.655127 | 0.327564 | − | 0.944829i | \(-0.393772\pi\) | ||||
0.327564 | + | 0.944829i | \(0.393772\pi\) | |||||||
\(318\) | −0.243291 | −0.0136431 | ||||||||
\(319\) | 7.11173 | 0.398180 | ||||||||
\(320\) | 2.61052 | 0.145933 | ||||||||
\(321\) | −0.613127 | −0.0342214 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.40306 | −0.300634 | ||||||||
\(324\) | 8.98647 | 0.499248 | ||||||||
\(325\) | −3.78981 | −0.210221 | ||||||||
\(326\) | 3.11486 | 0.172516 | ||||||||
\(327\) | 0.255056 | 0.0141046 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.310915 | 0.0171153 | ||||||||
\(331\) | −12.3608 | −0.679413 | −0.339707 | − | 0.940531i | \(-0.610328\pi\) | ||||
−0.339707 | + | 0.940531i | \(0.610328\pi\) | |||||||
\(332\) | 7.80581 | 0.428399 | ||||||||
\(333\) | 28.3590 | 1.55406 | ||||||||
\(334\) | −4.77073 | −0.261043 | ||||||||
\(335\) | 21.8588 | 1.19428 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.7851 | 1.51355 | 0.756776 | − | 0.653675i | \(-0.226774\pi\) | ||||
0.756776 | + | 0.653675i | \(0.226774\pi\) | |||||||
\(338\) | −8.63922 | −0.469912 | ||||||||
\(339\) | 0.129594 | 0.00703857 | ||||||||
\(340\) | −1.98763 | −0.107794 | ||||||||
\(341\) | 1.97842 | 0.107137 | ||||||||
\(342\) | −21.2783 | −1.15060 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.79344 | 0.258445 | ||||||||
\(345\) | 0.537718 | 0.0289498 | ||||||||
\(346\) | 2.15961 | 0.116101 | ||||||||
\(347\) | 2.25401 | 0.121002 | 0.0605008 | − | 0.998168i | \(-0.480730\pi\) | ||||
0.0605008 | + | 0.998168i | \(0.480730\pi\) | |||||||
\(348\) | 0.0897774 | 0.00481257 | ||||||||
\(349\) | −17.0144 | −0.910762 | −0.455381 | − | 0.890297i | \(-0.650497\pi\) | ||||
−0.455381 | + | 0.890297i | \(0.650497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.485711 | 0.0259253 | ||||||||
\(352\) | 3.07158 | 0.163716 | ||||||||
\(353\) | −17.9998 | −0.958032 | −0.479016 | − | 0.877806i | \(-0.659006\pi\) | ||||
−0.479016 | + | 0.877806i | \(0.659006\pi\) | |||||||
\(354\) | 0.557659 | 0.0296393 | ||||||||
\(355\) | −28.3193 | −1.50303 | ||||||||
\(356\) | −5.93525 | −0.314568 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.1667 | −1.06584 | ||||||||
\(359\) | 9.57429 | 0.505312 | 0.252656 | − | 0.967556i | \(-0.418696\pi\) | ||||
0.252656 | + | 0.967556i | \(0.418696\pi\) | |||||||
\(360\) | −7.82764 | −0.412553 | ||||||||
\(361\) | 31.3576 | 1.65040 | ||||||||
\(362\) | 7.51035 | 0.394735 | ||||||||
\(363\) | −0.0606995 | −0.00318590 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.76973 | 0.459029 | ||||||||
\(366\) | 0.149008 | 0.00778877 | ||||||||
\(367\) | 13.8966 | 0.725396 | 0.362698 | − | 0.931907i | \(-0.381856\pi\) | ||||
0.362698 | + | 0.931907i | \(0.381856\pi\) | |||||||
\(368\) | 5.31219 | 0.276917 | ||||||||
\(369\) | 2.99850 | 0.156095 | ||||||||
\(370\) | −24.6896 | −1.28355 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.0249753 | 0.00129491 | ||||||||
\(373\) | −30.4692 | −1.57764 | −0.788818 | − | 0.614627i | \(-0.789307\pi\) | ||||
−0.788818 | + | 0.614627i | \(0.789307\pi\) | |||||||
\(374\) | −2.33867 | −0.120930 | ||||||||
\(375\) | −0.322414 | −0.0166494 | ||||||||
\(376\) | 4.61388 | 0.237942 | ||||||||
\(377\) | −4.83499 | −0.249015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9617 | 0.665799 | 0.332900 | − | 0.942962i | \(-0.391973\pi\) | ||||
0.332900 | + | 0.942962i | \(0.391973\pi\) | |||||||
\(380\) | 18.5251 | 0.950317 | ||||||||
\(381\) | −0.324884 | −0.0166443 | ||||||||
\(382\) | 4.24153 | 0.217016 | ||||||||
\(383\) | −14.7064 | −0.751460 | −0.375730 | − | 0.926729i | \(-0.622608\pi\) | ||||
−0.375730 | + | 0.926729i | \(0.622608\pi\) | |||||||
\(384\) | 0.0387751 | 0.00197873 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.7705 | 0.700902 | ||||||||
\(387\) | −14.3731 | −0.730627 | ||||||||
\(388\) | 16.7498 | 0.850345 | ||||||||
\(389\) | −27.1877 | −1.37847 | −0.689235 | − | 0.724537i | \(-0.742053\pi\) | ||||
−0.689235 | + | 0.724537i | \(0.742053\pi\) | |||||||
\(390\) | −0.211379 | −0.0107036 | ||||||||
\(391\) | −4.04465 | −0.204547 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.494433 | −0.0249409 | ||||||||
\(394\) | −2.68951 | −0.135496 | ||||||||
\(395\) | −5.86089 | −0.294894 | ||||||||
\(396\) | −9.21011 | −0.462825 | ||||||||
\(397\) | −35.1116 | −1.76220 | −0.881100 | − | 0.472930i | \(-0.843196\pi\) | ||||
−0.881100 | + | 0.472930i | \(0.843196\pi\) | |||||||
\(398\) | −6.34370 | −0.317981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.81483 | 0.0907414 | ||||||||
\(401\) | −13.7763 | −0.687958 | −0.343979 | − | 0.938977i | \(-0.611775\pi\) | ||||
−0.343979 | + | 0.938977i | \(0.611775\pi\) | |||||||
\(402\) | 0.324678 | 0.0161935 | ||||||||
\(403\) | −1.34505 | −0.0670018 | ||||||||
\(404\) | 10.4656 | 0.520683 | ||||||||
\(405\) | 23.4594 | 1.16571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.0502 | −1.43996 | ||||||||
\(408\) | −0.0295230 | −0.00146161 | ||||||||
\(409\) | 27.4007 | 1.35487 | 0.677437 | − | 0.735580i | \(-0.263090\pi\) | ||||
0.677437 | + | 0.735580i | \(0.263090\pi\) | |||||||
\(410\) | −2.61052 | −0.128925 | ||||||||
\(411\) | 0.573351 | 0.0282813 | ||||||||
\(412\) | −2.47421 | −0.121896 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −15.9286 | −0.782848 | ||||||||
\(415\) | 20.3772 | 1.00028 | ||||||||
\(416\) | −2.08825 | −0.102385 | ||||||||
\(417\) | 0.380330 | 0.0186248 | ||||||||
\(418\) | 21.7969 | 1.06612 | ||||||||
\(419\) | −29.5386 | −1.44305 | −0.721527 | − | 0.692386i | \(-0.756559\pi\) | ||||
−0.721527 | + | 0.692386i | \(0.756559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.26049 | 0.256380 | 0.128190 | − | 0.991750i | \(-0.459083\pi\) | ||||
0.128190 | + | 0.991750i | \(0.459083\pi\) | |||||||
\(422\) | −2.81048 | −0.136812 | ||||||||
\(423\) | −13.8347 | −0.672666 | ||||||||
\(424\) | −6.27441 | −0.304712 | ||||||||
\(425\) | −1.38179 | −0.0670268 | ||||||||
\(426\) | −0.420638 | −0.0203800 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.8124 | −0.764320 | ||||||||
\(429\) | −0.248712 | −0.0120079 | ||||||||
\(430\) | 12.5134 | 0.603450 | ||||||||
\(431\) | −34.4649 | −1.66012 | −0.830059 | − | 0.557676i | \(-0.811693\pi\) | ||||
−0.830059 | + | 0.557676i | \(0.811693\pi\) | |||||||
\(432\) | −0.232592 | −0.0111906 | ||||||||
\(433\) | −8.66488 | −0.416408 | −0.208204 | − | 0.978085i | \(-0.566762\pi\) | ||||
−0.208204 | + | 0.978085i | \(0.566762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.234366 | 0.0112370 | ||||||||
\(436\) | 6.57783 | 0.315021 | ||||||||
\(437\) | 37.6970 | 1.80329 | ||||||||
\(438\) | 0.130260 | 0.00622408 | ||||||||
\(439\) | 7.77642 | 0.371148 | 0.185574 | − | 0.982630i | \(-0.440586\pi\) | ||||
0.185574 | + | 0.982630i | \(0.440586\pi\) | |||||||
\(440\) | 8.01842 | 0.382263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.58997 | 0.0756272 | ||||||||
\(443\) | −10.7928 | −0.512782 | −0.256391 | − | 0.966573i | \(-0.582533\pi\) | ||||
−0.256391 | + | 0.966573i | \(0.582533\pi\) | |||||||
\(444\) | −0.366725 | −0.0174040 | ||||||||
\(445\) | −15.4941 | −0.734491 | ||||||||
\(446\) | 19.0157 | 0.900419 | ||||||||
\(447\) | −0.473032 | −0.0223737 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.4966 | −0.825717 | −0.412859 | − | 0.910795i | \(-0.635470\pi\) | ||||
−0.412859 | + | 0.910795i | \(0.635470\pi\) | |||||||
\(450\) | −5.44176 | −0.256527 | ||||||||
\(451\) | −3.07158 | −0.144635 | ||||||||
\(452\) | 3.34219 | 0.157203 | ||||||||
\(453\) | −0.797298 | −0.0374603 | ||||||||
\(454\) | 9.23513 | 0.433426 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.275160 | 0.0128856 | ||||||||
\(457\) | 2.68726 | 0.125705 | 0.0628524 | − | 0.998023i | \(-0.479980\pi\) | ||||
0.0628524 | + | 0.998023i | \(0.479980\pi\) | |||||||
\(458\) | −19.7514 | −0.922923 | ||||||||
\(459\) | 0.177094 | 0.00826602 | ||||||||
\(460\) | 13.8676 | 0.646580 | ||||||||
\(461\) | −8.15008 | −0.379587 | −0.189794 | − | 0.981824i | \(-0.560782\pi\) | ||||
−0.189794 | + | 0.981824i | \(0.560782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1325 | 0.517372 | 0.258686 | − | 0.965961i | \(-0.416711\pi\) | ||||
0.258686 | + | 0.965961i | \(0.416711\pi\) | |||||||
\(464\) | 2.31533 | 0.107487 | ||||||||
\(465\) | 0.0651985 | 0.00302351 | ||||||||
\(466\) | −19.5991 | −0.907911 | ||||||||
\(467\) | 33.9394 | 1.57053 | 0.785265 | − | 0.619160i | \(-0.212527\pi\) | ||||
0.785265 | + | 0.619160i | \(0.212527\pi\) | |||||||
\(468\) | 6.26160 | 0.289443 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 12.0446 | 0.555577 | ||||||||
\(471\) | −0.179767 | −0.00828324 | ||||||||
\(472\) | 14.3819 | 0.661980 | ||||||||
\(473\) | 14.7234 | 0.676984 | ||||||||
\(474\) | −0.0870541 | −0.00399853 | ||||||||
\(475\) | 12.8786 | 0.590910 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.8138 | 0.861424 | ||||||||
\(478\) | −8.41493 | −0.384890 | ||||||||
\(479\) | −4.31877 | −0.197329 | −0.0986647 | − | 0.995121i | \(-0.531457\pi\) | ||||
−0.0986647 | + | 0.995121i | \(0.531457\pi\) | |||||||
\(480\) | 0.101223 | 0.00462019 | ||||||||
\(481\) | 19.7501 | 0.900527 | ||||||||
\(482\) | 3.36585 | 0.153310 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.56542 | −0.0711556 | ||||||||
\(485\) | 43.7259 | 1.98549 | ||||||||
\(486\) | 1.04623 | 0.0474579 | ||||||||
\(487\) | 9.08302 | 0.411591 | 0.205795 | − | 0.978595i | \(-0.434022\pi\) | ||||
0.205795 | + | 0.978595i | \(0.434022\pi\) | |||||||
\(488\) | 3.84288 | 0.173959 | ||||||||
\(489\) | 0.120779 | 0.00546181 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.4075 | −1.55279 | −0.776393 | − | 0.630249i | \(-0.782953\pi\) | ||||
−0.776393 | + | 0.630249i | \(0.782953\pi\) | |||||||
\(492\) | −0.0387751 | −0.00174812 | ||||||||
\(493\) | −1.76287 | −0.0793958 | ||||||||
\(494\) | −14.8189 | −0.666732 | ||||||||
\(495\) | −24.0432 | −1.08066 | ||||||||
\(496\) | 0.644105 | 0.0289212 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.302671 | 0.0135630 | ||||||||
\(499\) | 13.8869 | 0.621665 | 0.310833 | − | 0.950465i | \(-0.399392\pi\) | ||||
0.310833 | + | 0.950465i | \(0.399392\pi\) | |||||||
\(500\) | −8.31496 | −0.371856 | ||||||||
\(501\) | −0.184986 | −0.00826455 | ||||||||
\(502\) | 2.97894 | 0.132956 | ||||||||
\(503\) | −16.1893 | −0.721847 | −0.360923 | − | 0.932595i | \(-0.617538\pi\) | ||||
−0.360923 | + | 0.932595i | \(0.617538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.3207 | 1.21575 | ||||||||
\(506\) | 16.3168 | 0.725371 | ||||||||
\(507\) | −0.334987 | −0.0148773 | ||||||||
\(508\) | −8.37867 | −0.371743 | ||||||||
\(509\) | 26.6050 | 1.17925 | 0.589623 | − | 0.807679i | \(-0.299276\pi\) | ||||
0.589623 | + | 0.807679i | \(0.299276\pi\) | |||||||
\(510\) | −0.0770704 | −0.00341274 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.65055 | −0.0728735 | ||||||||
\(514\) | 6.74010 | 0.297293 | ||||||||
\(515\) | −6.45899 | −0.284617 | ||||||||
\(516\) | 0.185866 | 0.00818231 | ||||||||
\(517\) | 14.1719 | 0.623278 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0837389 | 0.00367573 | ||||||||
\(520\) | −5.45142 | −0.239060 | ||||||||
\(521\) | −21.8148 | −0.955722 | −0.477861 | − | 0.878436i | \(-0.658588\pi\) | ||||
−0.477861 | + | 0.878436i | \(0.658588\pi\) | |||||||
\(522\) | −6.94252 | −0.303866 | ||||||||
\(523\) | −31.0649 | −1.35838 | −0.679188 | − | 0.733965i | \(-0.737668\pi\) | ||||
−0.679188 | + | 0.733965i | \(0.737668\pi\) | |||||||
\(524\) | −12.7513 | −0.557043 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.7936 | 0.950247 | ||||||||
\(527\) | −0.490415 | −0.0213628 | ||||||||
\(528\) | 0.119101 | 0.00518319 | ||||||||
\(529\) | 5.21941 | 0.226931 | ||||||||
\(530\) | −16.3795 | −0.711479 | ||||||||
\(531\) | −43.1240 | −1.87142 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.08825 | 0.0904520 | ||||||||
\(534\) | −0.230140 | −0.00995914 | ||||||||
\(535\) | −41.2785 | −1.78463 | ||||||||
\(536\) | 8.37335 | 0.361674 | ||||||||
\(537\) | −0.781964 | −0.0337443 | ||||||||
\(538\) | 26.2079 | 1.12990 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.607188 | −0.0261292 | ||||||||
\(541\) | 15.6807 | 0.674166 | 0.337083 | − | 0.941475i | \(-0.390560\pi\) | ||||
0.337083 | + | 0.941475i | \(0.390560\pi\) | |||||||
\(542\) | −19.9240 | −0.855810 | ||||||||
\(543\) | 0.291215 | 0.0124972 | ||||||||
\(544\) | −0.761390 | −0.0326443 | ||||||||
\(545\) | 17.1716 | 0.735549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.18783 | −0.221816 | −0.110908 | − | 0.993831i | \(-0.535376\pi\) | ||||
−0.110908 | + | 0.993831i | \(0.535376\pi\) | |||||||
\(548\) | 14.7866 | 0.631651 | ||||||||
\(549\) | −11.5229 | −0.491783 | ||||||||
\(550\) | 5.57438 | 0.237693 | ||||||||
\(551\) | 16.4303 | 0.699956 | ||||||||
\(552\) | 0.205981 | 0.00876713 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.0693 | 0.852662 | ||||||||
\(555\) | −0.957344 | −0.0406370 | ||||||||
\(556\) | 9.80861 | 0.415978 | ||||||||
\(557\) | −20.5638 | −0.871318 | −0.435659 | − | 0.900112i | \(-0.643485\pi\) | ||||
−0.435659 | + | 0.900112i | \(0.643485\pi\) | |||||||
\(558\) | −1.93135 | −0.0817605 | ||||||||
\(559\) | −10.0099 | −0.423374 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0906821 | −0.00382860 | ||||||||
\(562\) | 22.8047 | 0.961957 | ||||||||
\(563\) | 30.8588 | 1.30054 | 0.650271 | − | 0.759702i | \(-0.274655\pi\) | ||||
0.650271 | + | 0.759702i | \(0.274655\pi\) | |||||||
\(564\) | 0.178904 | 0.00753320 | ||||||||
\(565\) | 8.72486 | 0.367058 | ||||||||
\(566\) | −20.5397 | −0.863347 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.8481 | −0.455178 | ||||||||
\(569\) | 34.7113 | 1.45517 | 0.727587 | − | 0.686016i | \(-0.240642\pi\) | ||||
0.727587 | + | 0.686016i | \(0.240642\pi\) | |||||||
\(570\) | 0.718312 | 0.0300868 | ||||||||
\(571\) | 8.47738 | 0.354767 | 0.177384 | − | 0.984142i | \(-0.443237\pi\) | ||||
0.177384 | + | 0.984142i | \(0.443237\pi\) | |||||||
\(572\) | −6.41421 | −0.268192 | ||||||||
\(573\) | 0.164466 | 0.00687067 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64072 | 0.402046 | ||||||||
\(576\) | −2.99850 | −0.124937 | ||||||||
\(577\) | −16.7833 | −0.698697 | −0.349348 | − | 0.936993i | \(-0.613597\pi\) | ||||
−0.349348 | + | 0.936993i | \(0.613597\pi\) | |||||||
\(578\) | −16.4203 | −0.682994 | ||||||||
\(579\) | 0.533954 | 0.0221904 | ||||||||
\(580\) | 6.04423 | 0.250973 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.649477 | 0.0269217 | ||||||||
\(583\) | −19.2723 | −0.798178 | ||||||||
\(584\) | 3.35938 | 0.139012 | ||||||||
\(585\) | 16.3461 | 0.675826 | ||||||||
\(586\) | −26.9744 | −1.11430 | ||||||||
\(587\) | −17.1051 | −0.706003 | −0.353001 | − | 0.935623i | \(-0.614839\pi\) | ||||
−0.353001 | + | 0.935623i | \(0.614839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.57077 | 0.188335 | ||||||||
\(590\) | 37.5442 | 1.54567 | ||||||||
\(591\) | −0.104286 | −0.00428976 | ||||||||
\(592\) | −9.45774 | −0.388711 | ||||||||
\(593\) | −23.4517 | −0.963047 | −0.481523 | − | 0.876433i | \(-0.659916\pi\) | ||||
−0.481523 | + | 0.876433i | \(0.659916\pi\) | |||||||
\(594\) | −0.714425 | −0.0293132 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.1994 | −0.499706 | ||||||||
\(597\) | −0.245978 | −0.0100672 | ||||||||
\(598\) | −11.0932 | −0.453634 | ||||||||
\(599\) | −20.3118 | −0.829917 | −0.414958 | − | 0.909840i | \(-0.636204\pi\) | ||||
−0.414958 | + | 0.909840i | \(0.636204\pi\) | |||||||
\(600\) | 0.0703702 | 0.00287285 | ||||||||
\(601\) | −21.9226 | −0.894240 | −0.447120 | − | 0.894474i | \(-0.647550\pi\) | ||||
−0.447120 | + | 0.894474i | \(0.647550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.1075 | −1.02246 | ||||||||
\(604\) | −20.5621 | −0.836660 | ||||||||
\(605\) | −4.08657 | −0.166143 | ||||||||
\(606\) | 0.405805 | 0.0164847 | ||||||||
\(607\) | −0.152226 | −0.00617865 | −0.00308932 | − | 0.999995i | \(-0.500983\pi\) | ||||
−0.00308932 | + | 0.999995i | \(0.500983\pi\) | |||||||
\(608\) | 7.09631 | 0.287793 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.0319 | 0.406180 | ||||||||
\(611\) | −9.63491 | −0.389787 | ||||||||
\(612\) | 2.28303 | 0.0922858 | ||||||||
\(613\) | 16.8306 | 0.679782 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(614\) | 11.9580 | 0.482584 | ||||||||
\(615\) | −0.101223 | −0.00408172 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.5730 | 1.67366 | 0.836832 | − | 0.547459i | \(-0.184405\pi\) | ||||
0.836832 | + | 0.547459i | \(0.184405\pi\) | |||||||
\(618\) | −0.0959379 | −0.00385919 | ||||||||
\(619\) | −1.19822 | −0.0481604 | −0.0240802 | − | 0.999710i | \(-0.507666\pi\) | ||||
−0.0240802 | + | 0.999710i | \(0.507666\pi\) | |||||||
\(620\) | 1.68145 | 0.0675287 | ||||||||
\(621\) | −1.23558 | −0.0495820 | ||||||||
\(622\) | −17.8581 | −0.716043 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.0809720 | −0.00324148 | ||||||||
\(625\) | −30.7805 | −1.23122 | ||||||||
\(626\) | 10.1352 | 0.405085 | ||||||||
\(627\) | 0.845176 | 0.0337531 | ||||||||
\(628\) | −4.63615 | −0.185003 | ||||||||
\(629\) | 7.20103 | 0.287124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.6115 | 0.661292 | 0.330646 | − | 0.943755i | \(-0.392733\pi\) | ||||
0.330646 | + | 0.943755i | \(0.392733\pi\) | |||||||
\(632\) | −2.24510 | −0.0893054 | ||||||||
\(633\) | −0.108977 | −0.00433143 | ||||||||
\(634\) | 11.6642 | 0.463245 | ||||||||
\(635\) | −21.8727 | −0.867992 | ||||||||
\(636\) | −0.243291 | −0.00964711 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.11173 | 0.281556 | ||||||||
\(639\) | 32.5281 | 1.28679 | ||||||||
\(640\) | 2.61052 | 0.103190 | ||||||||
\(641\) | −43.1532 | −1.70445 | −0.852225 | − | 0.523176i | \(-0.824747\pi\) | ||||
−0.852225 | + | 0.523176i | \(0.824747\pi\) | |||||||
\(642\) | −0.613127 | −0.0241982 | ||||||||
\(643\) | −36.4417 | −1.43712 | −0.718559 | − | 0.695466i | \(-0.755198\pi\) | ||||
−0.718559 | + | 0.695466i | \(0.755198\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.485208 | 0.0191051 | ||||||||
\(646\) | −5.40306 | −0.212581 | ||||||||
\(647\) | 18.1008 | 0.711616 | 0.355808 | − | 0.934559i | \(-0.384206\pi\) | ||||
0.355808 | + | 0.934559i | \(0.384206\pi\) | |||||||
\(648\) | 8.98647 | 0.353022 | ||||||||
\(649\) | 44.1751 | 1.73402 | ||||||||
\(650\) | −3.78981 | −0.148649 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.11486 | 0.121987 | ||||||||
\(653\) | −26.7064 | −1.04510 | −0.522551 | − | 0.852608i | \(-0.675020\pi\) | ||||
−0.522551 | + | 0.852608i | \(0.675020\pi\) | |||||||
\(654\) | 0.255056 | 0.00997348 | ||||||||
\(655\) | −33.2876 | −1.30065 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −10.0731 | −0.392988 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.7015 | −1.93609 | −0.968047 | − | 0.250767i | \(-0.919317\pi\) | ||||
−0.968047 | + | 0.250767i | \(0.919317\pi\) | |||||||
\(660\) | 0.310915 | 0.0121024 | ||||||||
\(661\) | 12.2909 | 0.478061 | 0.239030 | − | 0.971012i | \(-0.423170\pi\) | ||||
0.239030 | + | 0.971012i | \(0.423170\pi\) | |||||||
\(662\) | −12.3608 | −0.480418 | ||||||||
\(663\) | 0.0616513 | 0.00239434 | ||||||||
\(664\) | 7.80581 | 0.302924 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.3590 | 1.09889 | ||||||||
\(667\) | 12.2995 | 0.476239 | ||||||||
\(668\) | −4.77073 | −0.184585 | ||||||||
\(669\) | 0.737336 | 0.0285070 | ||||||||
\(670\) | 21.8588 | 0.844480 | ||||||||
\(671\) | 11.8037 | 0.455676 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.11146 | 0.119938 | 0.0599689 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599689 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(674\) | 27.7851 | 1.07024 | ||||||||
\(675\) | −0.422115 | −0.0162472 | ||||||||
\(676\) | −8.63922 | −0.332278 | ||||||||
\(677\) | 24.4512 | 0.939736 | 0.469868 | − | 0.882737i | \(-0.344301\pi\) | ||||
0.469868 | + | 0.882737i | \(0.344301\pi\) | |||||||
\(678\) | 0.129594 | 0.00497702 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.98763 | −0.0762220 | ||||||||
\(681\) | 0.358093 | 0.0137222 | ||||||||
\(682\) | 1.97842 | 0.0757576 | ||||||||
\(683\) | 17.3445 | 0.663669 | 0.331834 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331834 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(684\) | −21.2783 | −0.813595 | ||||||||
\(685\) | 38.6007 | 1.47486 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.765863 | −0.0292195 | ||||||||
\(688\) | 4.79344 | 0.182748 | ||||||||
\(689\) | 13.1025 | 0.499166 | ||||||||
\(690\) | 0.537718 | 0.0204706 | ||||||||
\(691\) | −43.8282 | −1.66730 | −0.833652 | − | 0.552290i | \(-0.813754\pi\) | ||||
−0.833652 | + | 0.552290i | \(0.813754\pi\) | |||||||
\(692\) | 2.15961 | 0.0820959 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.25401 | 0.0855610 | ||||||||
\(695\) | 25.6056 | 0.971276 | ||||||||
\(696\) | 0.0897774 | 0.00340300 | ||||||||
\(697\) | 0.761390 | 0.0288397 | ||||||||
\(698\) | −17.0144 | −0.644006 | ||||||||
\(699\) | −0.759958 | −0.0287442 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.1293 | −1.74228 | −0.871139 | − | 0.491036i | \(-0.836618\pi\) | ||||
−0.871139 | + | 0.491036i | \(0.836618\pi\) | |||||||
\(702\) | 0.485711 | 0.0183320 | ||||||||
\(703\) | −67.1151 | −2.53129 | ||||||||
\(704\) | 3.07158 | 0.115764 | ||||||||
\(705\) | 0.467032 | 0.0175894 | ||||||||
\(706\) | −17.9998 | −0.677431 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.557659 | 0.0209581 | ||||||||
\(709\) | −44.6646 | −1.67741 | −0.838707 | − | 0.544583i | \(-0.816688\pi\) | ||||
−0.838707 | + | 0.544583i | \(0.816688\pi\) | |||||||
\(710\) | −28.3193 | −1.06280 | ||||||||
\(711\) | 6.73193 | 0.252467 | ||||||||
\(712\) | −5.93525 | −0.222433 | ||||||||
\(713\) | 3.42161 | 0.128140 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.7444 | −0.626207 | ||||||||
\(716\) | −20.1667 | −0.753663 | ||||||||
\(717\) | −0.326290 | −0.0121855 | ||||||||
\(718\) | 9.57429 | 0.357309 | ||||||||
\(719\) | −12.9542 | −0.483110 | −0.241555 | − | 0.970387i | \(-0.577657\pi\) | ||||
−0.241555 | + | 0.970387i | \(0.577657\pi\) | |||||||
\(720\) | −7.82764 | −0.291719 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 31.3576 | 1.16701 | ||||||||
\(723\) | 0.130511 | 0.00485376 | ||||||||
\(724\) | 7.51035 | 0.279120 | ||||||||
\(725\) | 4.20194 | 0.156056 | ||||||||
\(726\) | −0.0606995 | −0.00225277 | ||||||||
\(727\) | 24.3968 | 0.904827 | 0.452414 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452414 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9188 | −0.996994 | ||||||||
\(730\) | 8.76973 | 0.324582 | ||||||||
\(731\) | −3.64968 | −0.134988 | ||||||||
\(732\) | 0.149008 | 0.00550749 | ||||||||
\(733\) | −25.5066 | −0.942106 | −0.471053 | − | 0.882105i | \(-0.656126\pi\) | ||||
−0.471053 | + | 0.882105i | \(0.656126\pi\) | |||||||
\(734\) | 13.8966 | 0.512932 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.31219 | 0.195810 | ||||||||
\(737\) | 25.7194 | 0.947386 | ||||||||
\(738\) | 2.99850 | 0.110376 | ||||||||
\(739\) | 50.7786 | 1.86792 | 0.933961 | − | 0.357376i | \(-0.116328\pi\) | ||||
0.933961 | + | 0.357376i | \(0.116328\pi\) | |||||||
\(740\) | −24.6896 | −0.907609 | ||||||||
\(741\) | −0.574603 | −0.0211086 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.81231 | 0.286606 | 0.143303 | − | 0.989679i | \(-0.454228\pi\) | ||||
0.143303 | + | 0.989679i | \(0.454228\pi\) | |||||||
\(744\) | 0.0249753 | 0.000915638 0 | ||||||||
\(745\) | −31.8468 | −1.16677 | ||||||||
\(746\) | −30.4692 | −1.11556 | ||||||||
\(747\) | −23.4057 | −0.856370 | ||||||||
\(748\) | −2.33867 | −0.0855101 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.322414 | −0.0117729 | ||||||||
\(751\) | 27.5822 | 1.00649 | 0.503245 | − | 0.864144i | \(-0.332139\pi\) | ||||
0.503245 | + | 0.864144i | \(0.332139\pi\) | |||||||
\(752\) | 4.61388 | 0.168251 | ||||||||
\(753\) | 0.115509 | 0.00420937 | ||||||||
\(754\) | −4.83499 | −0.176080 | ||||||||
\(755\) | −53.6778 | −1.95354 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.6468 | −1.44099 | −0.720493 | − | 0.693462i | \(-0.756085\pi\) | ||||
−0.720493 | + | 0.693462i | \(0.756085\pi\) | |||||||
\(758\) | 12.9617 | 0.470791 | ||||||||
\(759\) | 0.632686 | 0.0229651 | ||||||||
\(760\) | 18.5251 | 0.671975 | ||||||||
\(761\) | −32.1470 | −1.16533 | −0.582665 | − | 0.812713i | \(-0.697990\pi\) | ||||
−0.582665 | + | 0.812713i | \(0.697990\pi\) | |||||||
\(762\) | −0.324884 | −0.0117693 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.24153 | 0.153453 | ||||||||
\(765\) | 5.95989 | 0.215480 | ||||||||
\(766\) | −14.7064 | −0.531362 | ||||||||
\(767\) | −30.0329 | −1.08443 | ||||||||
\(768\) | 0.0387751 | 0.00139918 | ||||||||
\(769\) | 23.9039 | 0.861998 | 0.430999 | − | 0.902353i | \(-0.358161\pi\) | ||||
0.430999 | + | 0.902353i | \(0.358161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.261348 | 0.00941222 | ||||||||
\(772\) | 13.7705 | 0.495612 | ||||||||
\(773\) | 8.23647 | 0.296245 | 0.148123 | − | 0.988969i | \(-0.452677\pi\) | ||||
0.148123 | + | 0.988969i | \(0.452677\pi\) | |||||||
\(774\) | −14.3731 | −0.516631 | ||||||||
\(775\) | 1.16894 | 0.0419896 | ||||||||
\(776\) | 16.7498 | 0.601284 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −27.1877 | −0.974726 | ||||||||
\(779\) | −7.09631 | −0.254252 | ||||||||
\(780\) | −0.211379 | −0.00756860 | ||||||||
\(781\) | −33.3209 | −1.19231 | ||||||||
\(782\) | −4.04465 | −0.144636 | ||||||||
\(783\) | −0.538529 | −0.0192455 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.1028 | −0.431967 | ||||||||
\(786\) | −0.494433 | −0.0176359 | ||||||||
\(787\) | −21.2691 | −0.758163 | −0.379082 | − | 0.925363i | \(-0.623760\pi\) | ||||
−0.379082 | + | 0.925363i | \(0.623760\pi\) | |||||||
\(788\) | −2.68951 | −0.0958100 | ||||||||
\(789\) | 0.845050 | 0.0300846 | ||||||||
\(790\) | −5.86089 | −0.208521 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.21011 | −0.327267 | ||||||||
\(793\) | −8.02488 | −0.284972 | ||||||||
\(794\) | −35.1116 | −1.24606 | ||||||||
\(795\) | −0.635116 | −0.0225253 | ||||||||
\(796\) | −6.34370 | −0.224847 | ||||||||
\(797\) | 19.7091 | 0.698133 | 0.349067 | − | 0.937098i | \(-0.386499\pi\) | ||||
0.349067 | + | 0.937098i | \(0.386499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.51296 | −0.124280 | ||||||||
\(800\) | 1.81483 | 0.0641639 | ||||||||
\(801\) | 17.7968 | 0.628820 | ||||||||
\(802\) | −13.7763 | −0.486460 | ||||||||
\(803\) | 10.3186 | 0.364135 | ||||||||
\(804\) | 0.324678 | 0.0114505 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.34505 | −0.0473774 | ||||||||
\(807\) | 1.01622 | 0.0357725 | ||||||||
\(808\) | 10.4656 | 0.368178 | ||||||||
\(809\) | −20.9287 | −0.735813 | −0.367907 | − | 0.929863i | \(-0.619925\pi\) | ||||
−0.367907 | + | 0.929863i | \(0.619925\pi\) | |||||||
\(810\) | 23.4594 | 0.824279 | ||||||||
\(811\) | −6.04921 | −0.212417 | −0.106208 | − | 0.994344i | \(-0.533871\pi\) | ||||
−0.106208 | + | 0.994344i | \(0.533871\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.772557 | −0.0270947 | ||||||||
\(814\) | −29.0502 | −1.01821 | ||||||||
\(815\) | 8.13140 | 0.284831 | ||||||||
\(816\) | −0.0295230 | −0.00103351 | ||||||||
\(817\) | 34.0158 | 1.19006 | ||||||||
\(818\) | 27.4007 | 0.958041 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.61052 | −0.0911634 | ||||||||
\(821\) | 9.72428 | 0.339380 | 0.169690 | − | 0.985498i | \(-0.445723\pi\) | ||||
0.169690 | + | 0.985498i | \(0.445723\pi\) | |||||||
\(822\) | 0.573351 | 0.0199979 | ||||||||
\(823\) | −13.8729 | −0.483578 | −0.241789 | − | 0.970329i | \(-0.577734\pi\) | ||||
−0.241789 | + | 0.970329i | \(0.577734\pi\) | |||||||
\(824\) | −2.47421 | −0.0861933 | ||||||||
\(825\) | 0.216147 | 0.00752529 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.1407 | −0.978547 | −0.489273 | − | 0.872130i | \(-0.662738\pi\) | ||||
−0.489273 | + | 0.872130i | \(0.662738\pi\) | |||||||
\(828\) | −15.9286 | −0.553557 | ||||||||
\(829\) | −23.1463 | −0.803904 | −0.401952 | − | 0.915661i | \(-0.631668\pi\) | ||||
−0.401952 | + | 0.915661i | \(0.631668\pi\) | |||||||
\(830\) | 20.3772 | 0.707304 | ||||||||
\(831\) | 0.778189 | 0.0269951 | ||||||||
\(832\) | −2.08825 | −0.0723970 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.380330 | 0.0131698 | ||||||||
\(835\) | −12.4541 | −0.430992 | ||||||||
\(836\) | 21.7969 | 0.753860 | ||||||||
\(837\) | −0.149814 | −0.00517833 | ||||||||
\(838\) | −29.5386 | −1.02039 | ||||||||
\(839\) | −24.5774 | −0.848508 | −0.424254 | − | 0.905543i | \(-0.639464\pi\) | ||||
−0.424254 | + | 0.905543i | \(0.639464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.6392 | −0.815146 | ||||||||
\(842\) | 5.26049 | 0.181288 | ||||||||
\(843\) | 0.884254 | 0.0304553 | ||||||||
\(844\) | −2.81048 | −0.0967407 | ||||||||
\(845\) | −22.5529 | −0.775843 | ||||||||
\(846\) | −13.8347 | −0.475646 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.27441 | −0.215464 | ||||||||
\(849\) | −0.796429 | −0.0273334 | ||||||||
\(850\) | −1.38179 | −0.0473951 | ||||||||
\(851\) | −50.2414 | −1.72225 | ||||||||
\(852\) | −0.420638 | −0.0144108 | ||||||||
\(853\) | −49.7805 | −1.70445 | −0.852225 | − | 0.523175i | \(-0.824747\pi\) | ||||
−0.852225 | + | 0.523175i | \(0.824747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −55.5474 | −1.89968 | ||||||||
\(856\) | −15.8124 | −0.540456 | ||||||||
\(857\) | 27.5930 | 0.942559 | 0.471280 | − | 0.881984i | \(-0.343792\pi\) | ||||
0.471280 | + | 0.881984i | \(0.343792\pi\) | |||||||
\(858\) | −0.248712 | −0.00849088 | ||||||||
\(859\) | −26.1523 | −0.892306 | −0.446153 | − | 0.894957i | \(-0.647206\pi\) | ||||
−0.446153 | + | 0.894957i | \(0.647206\pi\) | |||||||
\(860\) | 12.5134 | 0.426703 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.4649 | −1.17388 | ||||||||
\(863\) | 38.4067 | 1.30738 | 0.653689 | − | 0.756763i | \(-0.273220\pi\) | ||||
0.653689 | + | 0.756763i | \(0.273220\pi\) | |||||||
\(864\) | −0.232592 | −0.00791295 | ||||||||
\(865\) | 5.63770 | 0.191687 | ||||||||
\(866\) | −8.66488 | −0.294445 | ||||||||
\(867\) | −0.636699 | −0.0216234 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.89600 | −0.233931 | ||||||||
\(870\) | 0.234366 | 0.00794575 | ||||||||
\(871\) | −17.4856 | −0.592478 | ||||||||
\(872\) | 6.57783 | 0.222753 | ||||||||
\(873\) | −50.2244 | −1.69984 | ||||||||
\(874\) | 37.6970 | 1.27512 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.130260 | 0.00440109 | ||||||||
\(877\) | −5.62482 | −0.189937 | −0.0949683 | − | 0.995480i | \(-0.530275\pi\) | ||||
−0.0949683 | + | 0.995480i | \(0.530275\pi\) | |||||||
\(878\) | 7.77642 | 0.262441 | ||||||||
\(879\) | −1.04594 | −0.0352785 | ||||||||
\(880\) | 8.01842 | 0.270301 | ||||||||
\(881\) | 49.5452 | 1.66922 | 0.834610 | − | 0.550841i | \(-0.185693\pi\) | ||||
0.834610 | + | 0.550841i | \(0.185693\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0172 | −0.404409 | −0.202205 | − | 0.979343i | \(-0.564811\pi\) | ||||
−0.202205 | + | 0.979343i | \(0.564811\pi\) | |||||||
\(884\) | 1.58997 | 0.0534765 | ||||||||
\(885\) | 1.45578 | 0.0489356 | ||||||||
\(886\) | −10.7928 | −0.362592 | ||||||||
\(887\) | 44.5177 | 1.49476 | 0.747379 | − | 0.664398i | \(-0.231312\pi\) | ||||
0.747379 | + | 0.664398i | \(0.231312\pi\) | |||||||
\(888\) | −0.366725 | −0.0123065 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.4941 | −0.519364 | ||||||||
\(891\) | 27.6026 | 0.924723 | ||||||||
\(892\) | 19.0157 | 0.636692 | ||||||||
\(893\) | 32.7415 | 1.09565 | ||||||||
\(894\) | −0.473032 | −0.0158206 | ||||||||
\(895\) | −52.6455 | −1.75975 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.430139 | −0.0143619 | ||||||||
\(898\) | −17.4966 | −0.583870 | ||||||||
\(899\) | 1.49132 | 0.0497383 | ||||||||
\(900\) | −5.44176 | −0.181392 | ||||||||
\(901\) | 4.77727 | 0.159154 | ||||||||
\(902\) | −3.07158 | −0.102272 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.34219 | 0.111160 | ||||||||
\(905\) | 19.6059 | 0.651723 | ||||||||
\(906\) | −0.797298 | −0.0264885 | ||||||||
\(907\) | 12.3361 | 0.409612 | 0.204806 | − | 0.978803i | \(-0.434344\pi\) | ||||
0.204806 | + | 0.978803i | \(0.434344\pi\) | |||||||
\(908\) | 9.23513 | 0.306478 | ||||||||
\(909\) | −31.3810 | −1.04084 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.3470 | 1.89999 | 0.949996 | − | 0.312262i | \(-0.101087\pi\) | ||||
0.949996 | + | 0.312262i | \(0.101087\pi\) | |||||||
\(912\) | 0.275160 | 0.00911147 | ||||||||
\(913\) | 23.9761 | 0.793494 | ||||||||
\(914\) | 2.68726 | 0.0888867 | ||||||||
\(915\) | 0.388989 | 0.0128596 | ||||||||
\(916\) | −19.7514 | −0.652605 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.177094 | 0.00584496 | ||||||||
\(919\) | 51.2205 | 1.68961 | 0.844804 | − | 0.535075i | \(-0.179717\pi\) | ||||
0.844804 | + | 0.535075i | \(0.179717\pi\) | |||||||
\(920\) | 13.8676 | 0.457201 | ||||||||
\(921\) | 0.463671 | 0.0152785 | ||||||||
\(922\) | −8.15008 | −0.268409 | ||||||||
\(923\) | 22.6536 | 0.745652 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1642 | −0.564355 | ||||||||
\(926\) | 11.1325 | 0.365837 | ||||||||
\(927\) | 7.41892 | 0.243669 | ||||||||
\(928\) | 2.31533 | 0.0760046 | ||||||||
\(929\) | 21.9800 | 0.721140 | 0.360570 | − | 0.932732i | \(-0.382582\pi\) | ||||
0.360570 | + | 0.932732i | \(0.382582\pi\) | |||||||
\(930\) | 0.0651985 | 0.00213794 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.5991 | −0.641990 | ||||||||
\(933\) | −0.692449 | −0.0226698 | ||||||||
\(934\) | 33.9394 | 1.11053 | ||||||||
\(935\) | −6.10514 | −0.199660 | ||||||||
\(936\) | 6.26160 | 0.204667 | ||||||||
\(937\) | 34.1101 | 1.11433 | 0.557164 | − | 0.830403i | \(-0.311890\pi\) | ||||
0.557164 | + | 0.830403i | \(0.311890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.392994 | 0.0128249 | ||||||||
\(940\) | 12.0446 | 0.392852 | ||||||||
\(941\) | 37.0147 | 1.20665 | 0.603323 | − | 0.797497i | \(-0.293843\pi\) | ||||
0.603323 | + | 0.797497i | \(0.293843\pi\) | |||||||
\(942\) | −0.179767 | −0.00585713 | ||||||||
\(943\) | −5.31219 | −0.172989 | ||||||||
\(944\) | 14.3819 | 0.468091 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.7234 | 0.478700 | ||||||||
\(947\) | 11.6847 | 0.379703 | 0.189851 | − | 0.981813i | \(-0.439199\pi\) | ||||
0.189851 | + | 0.981813i | \(0.439199\pi\) | |||||||
\(948\) | −0.0870541 | −0.00282739 | ||||||||
\(949\) | −7.01521 | −0.227723 | ||||||||
\(950\) | 12.8786 | 0.417837 | ||||||||
\(951\) | 0.452281 | 0.0146662 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.1180 | −1.33194 | −0.665971 | − | 0.745978i | \(-0.731982\pi\) | ||||
−0.665971 | + | 0.745978i | \(0.731982\pi\) | |||||||
\(954\) | 18.8138 | 0.609119 | ||||||||
\(955\) | 11.0726 | 0.358302 | ||||||||
\(956\) | −8.41493 | −0.272158 | ||||||||
\(957\) | 0.275758 | 0.00891399 | ||||||||
\(958\) | −4.31877 | −0.139533 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.101223 | 0.00326697 | ||||||||
\(961\) | −30.5851 | −0.986617 | ||||||||
\(962\) | 19.7501 | 0.636769 | ||||||||
\(963\) | 47.4133 | 1.52787 | ||||||||
\(964\) | 3.36585 | 0.108407 | ||||||||
\(965\) | 35.9483 | 1.15722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.6510 | 0.728407 | 0.364203 | − | 0.931319i | \(-0.381341\pi\) | ||||
0.364203 | + | 0.931319i | \(0.381341\pi\) | |||||||
\(968\) | −1.56542 | −0.0503146 | ||||||||
\(969\) | −0.209504 | −0.00673025 | ||||||||
\(970\) | 43.7259 | 1.40395 | ||||||||
\(971\) | 5.04506 | 0.161904 | 0.0809518 | − | 0.996718i | \(-0.474204\pi\) | ||||
0.0809518 | + | 0.996718i | \(0.474204\pi\) | |||||||
\(972\) | 1.04623 | 0.0335578 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.08302 | 0.291039 | ||||||||
\(975\) | −0.146950 | −0.00470618 | ||||||||
\(976\) | 3.84288 | 0.123008 | ||||||||
\(977\) | 11.8207 | 0.378178 | 0.189089 | − | 0.981960i | \(-0.439447\pi\) | ||||
0.189089 | + | 0.981960i | \(0.439447\pi\) | |||||||
\(978\) | 0.120779 | 0.00386208 | ||||||||
\(979\) | −18.2306 | −0.582652 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.7236 | −0.629726 | ||||||||
\(982\) | −34.4075 | −1.09799 | ||||||||
\(983\) | 44.6385 | 1.42375 | 0.711873 | − | 0.702308i | \(-0.247847\pi\) | ||||
0.711873 | + | 0.702308i | \(0.247847\pi\) | |||||||
\(984\) | −0.0387751 | −0.00123611 | ||||||||
\(985\) | −7.02104 | −0.223709 | ||||||||
\(986\) | −1.76287 | −0.0561413 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.8189 | −0.471451 | ||||||||
\(989\) | 25.4637 | 0.809699 | ||||||||
\(990\) | −24.0432 | −0.764143 | ||||||||
\(991\) | 37.0298 | 1.17629 | 0.588146 | − | 0.808755i | \(-0.299858\pi\) | ||||
0.588146 | + | 0.808755i | \(0.299858\pi\) | |||||||
\(992\) | 0.644105 | 0.0204504 | ||||||||
\(993\) | −0.479293 | −0.0152099 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.5604 | −0.524999 | ||||||||
\(996\) | 0.302671 | 0.00959050 | ||||||||
\(997\) | −46.9480 | −1.48686 | −0.743429 | − | 0.668815i | \(-0.766802\pi\) | ||||
−0.743429 | + | 0.668815i | \(0.766802\pi\) | |||||||
\(998\) | 13.8869 | 0.439584 | ||||||||
\(999\) | 2.19980 | 0.0695986 |
(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 | 4018.2.a.bq.1.3 | yes | 6 | |
7.6 | odd | 2 | 4018.2.a.bp.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.bp.1.4 | ✓ | 6 | 7.6 | odd | 2 | ||
4018.2.a.bq.1.3 | yes | 6 | 1.1 | even | 1 | trivial |