Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.35168\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.30094 | 1.32845 | 0.664224 | − | 0.747534i | \(-0.268762\pi\) | ||||
0.664224 | + | 0.747534i | \(0.268762\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.62639 | 1.17456 | 0.587278 | − | 0.809385i | \(-0.300200\pi\) | ||||
0.587278 | + | 0.809385i | \(0.300200\pi\) | |||||||
\(6\) | 2.30094 | 0.939354 | ||||||||
\(7\) | 2.74200 | 1.03638 | 0.518188 | − | 0.855267i | \(-0.326607\pi\) | ||||
0.518188 | + | 0.855267i | \(0.326607\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.29431 | 0.764772 | ||||||||
\(10\) | 2.62639 | 0.830536 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.30094 | 0.664224 | ||||||||
\(13\) | 5.41693 | 1.50239 | 0.751193 | − | 0.660083i | \(-0.229479\pi\) | ||||
0.751193 | + | 0.660083i | \(0.229479\pi\) | |||||||
\(14\) | 2.74200 | 0.732829 | ||||||||
\(15\) | 6.04315 | 1.56034 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.27854 | −1.03770 | −0.518849 | − | 0.854866i | \(-0.673639\pi\) | ||||
−0.518849 | + | 0.854866i | \(0.673639\pi\) | |||||||
\(18\) | 2.29431 | 0.540775 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.62639 | 0.587278 | ||||||||
\(21\) | 6.30916 | 1.37677 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.21615 | −1.29616 | −0.648079 | − | 0.761573i | \(-0.724427\pi\) | ||||
−0.648079 | + | 0.761573i | \(0.724427\pi\) | |||||||
\(24\) | 2.30094 | 0.469677 | ||||||||
\(25\) | 1.89791 | 0.379581 | ||||||||
\(26\) | 5.41693 | 1.06235 | ||||||||
\(27\) | −1.62374 | −0.312489 | ||||||||
\(28\) | 2.74200 | 0.518188 | ||||||||
\(29\) | 5.99594 | 1.11342 | 0.556709 | − | 0.830708i | \(-0.312064\pi\) | ||||
0.556709 | + | 0.830708i | \(0.312064\pi\) | |||||||
\(30\) | 6.04315 | 1.10332 | ||||||||
\(31\) | −7.27922 | −1.30739 | −0.653693 | − | 0.756760i | \(-0.726781\pi\) | ||||
−0.653693 | + | 0.756760i | \(0.726781\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.27854 | −0.733763 | ||||||||
\(35\) | 7.20154 | 1.21728 | ||||||||
\(36\) | 2.29431 | 0.382386 | ||||||||
\(37\) | −3.97289 | −0.653139 | −0.326570 | − | 0.945173i | \(-0.605893\pi\) | ||||
−0.326570 | + | 0.945173i | \(0.605893\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 12.4640 | 1.99584 | ||||||||
\(40\) | 2.62639 | 0.415268 | ||||||||
\(41\) | 10.5357 | 1.64540 | 0.822699 | − | 0.568477i | \(-0.192467\pi\) | ||||
0.822699 | + | 0.568477i | \(0.192467\pi\) | |||||||
\(42\) | 6.30916 | 0.973525 | ||||||||
\(43\) | −0.306239 | −0.0467009 | −0.0233505 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233505 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.02576 | 0.898267 | ||||||||
\(46\) | −6.21615 | −0.916522 | ||||||||
\(47\) | −4.56638 | −0.666075 | −0.333038 | − | 0.942914i | \(-0.608074\pi\) | ||||
−0.333038 | + | 0.942914i | \(0.608074\pi\) | |||||||
\(48\) | 2.30094 | 0.332112 | ||||||||
\(49\) | 0.518537 | 0.0740767 | ||||||||
\(50\) | 1.89791 | 0.268404 | ||||||||
\(51\) | −9.84465 | −1.37853 | ||||||||
\(52\) | 5.41693 | 0.751193 | ||||||||
\(53\) | −3.72986 | −0.512335 | −0.256168 | − | 0.966632i | \(-0.582460\pi\) | ||||
−0.256168 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(54\) | −1.62374 | −0.220963 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.74200 | 0.366415 | ||||||||
\(57\) | −2.30094 | −0.304767 | ||||||||
\(58\) | 5.99594 | 0.787305 | ||||||||
\(59\) | 5.42719 | 0.706560 | 0.353280 | − | 0.935518i | \(-0.385066\pi\) | ||||
0.353280 | + | 0.935518i | \(0.385066\pi\) | |||||||
\(60\) | 6.04315 | 0.780168 | ||||||||
\(61\) | −10.1851 | −1.30407 | −0.652036 | − | 0.758188i | \(-0.726085\pi\) | ||||
−0.652036 | + | 0.758188i | \(0.726085\pi\) | |||||||
\(62\) | −7.27922 | −0.924462 | ||||||||
\(63\) | 6.29100 | 0.792591 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.2269 | 1.76464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0148030 | −0.00180848 | −0.000904239 | − | 1.00000i | \(-0.500288\pi\) | ||||
−0.000904239 | 1.00000i | \(0.500288\pi\) | ||||||||
\(68\) | −4.27854 | −0.518849 | ||||||||
\(69\) | −14.3030 | −1.72188 | ||||||||
\(70\) | 7.20154 | 0.860749 | ||||||||
\(71\) | 12.1074 | 1.43688 | 0.718440 | − | 0.695589i | \(-0.244856\pi\) | ||||
0.718440 | + | 0.695589i | \(0.244856\pi\) | |||||||
\(72\) | 2.29431 | 0.270388 | ||||||||
\(73\) | −13.8664 | −1.62294 | −0.811472 | − | 0.584392i | \(-0.801333\pi\) | ||||
−0.811472 | + | 0.584392i | \(0.801333\pi\) | |||||||
\(74\) | −3.97289 | −0.461839 | ||||||||
\(75\) | 4.36696 | 0.504254 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.4640 | 1.41127 | ||||||||
\(79\) | 11.8987 | 1.33871 | 0.669356 | − | 0.742942i | \(-0.266570\pi\) | ||||
0.669356 | + | 0.742942i | \(0.266570\pi\) | |||||||
\(80\) | 2.62639 | 0.293639 | ||||||||
\(81\) | −10.6191 | −1.17990 | ||||||||
\(82\) | 10.5357 | 1.16347 | ||||||||
\(83\) | 1.29710 | 0.142375 | 0.0711876 | − | 0.997463i | \(-0.477321\pi\) | ||||
0.0711876 | + | 0.997463i | \(0.477321\pi\) | |||||||
\(84\) | 6.30916 | 0.688386 | ||||||||
\(85\) | −11.2371 | −1.21883 | ||||||||
\(86\) | −0.306239 | −0.0330226 | ||||||||
\(87\) | 13.7963 | 1.47912 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5993 | −1.54753 | −0.773764 | − | 0.633474i | \(-0.781628\pi\) | ||||
−0.773764 | + | 0.633474i | \(0.781628\pi\) | |||||||
\(90\) | 6.02576 | 0.635171 | ||||||||
\(91\) | 14.8532 | 1.55704 | ||||||||
\(92\) | −6.21615 | −0.648079 | ||||||||
\(93\) | −16.7490 | −1.73679 | ||||||||
\(94\) | −4.56638 | −0.470986 | ||||||||
\(95\) | −2.62639 | −0.269462 | ||||||||
\(96\) | 2.30094 | 0.234838 | ||||||||
\(97\) | −10.0528 | −1.02071 | −0.510356 | − | 0.859963i | \(-0.670486\pi\) | ||||
−0.510356 | + | 0.859963i | \(0.670486\pi\) | |||||||
\(98\) | 0.518537 | 0.0523802 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.89791 | 0.189791 | ||||||||
\(101\) | 4.03837 | 0.401833 | 0.200916 | − | 0.979608i | \(-0.435608\pi\) | ||||
0.200916 | + | 0.979608i | \(0.435608\pi\) | |||||||
\(102\) | −9.84465 | −0.974765 | ||||||||
\(103\) | 12.3140 | 1.21333 | 0.606666 | − | 0.794957i | \(-0.292507\pi\) | ||||
0.606666 | + | 0.794957i | \(0.292507\pi\) | |||||||
\(104\) | 5.41693 | 0.531173 | ||||||||
\(105\) | 16.5703 | 1.61710 | ||||||||
\(106\) | −3.72986 | −0.362276 | ||||||||
\(107\) | −7.79569 | −0.753638 | −0.376819 | − | 0.926287i | \(-0.622982\pi\) | ||||
−0.376819 | + | 0.926287i | \(0.622982\pi\) | |||||||
\(108\) | −1.62374 | −0.156244 | ||||||||
\(109\) | −14.9495 | −1.43191 | −0.715953 | − | 0.698148i | \(-0.754008\pi\) | ||||
−0.715953 | + | 0.698148i | \(0.754008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.14138 | −0.867661 | ||||||||
\(112\) | 2.74200 | 0.259094 | ||||||||
\(113\) | 1.06888 | 0.100552 | 0.0502761 | − | 0.998735i | \(-0.483990\pi\) | ||||
0.0502761 | + | 0.998735i | \(0.483990\pi\) | |||||||
\(114\) | −2.30094 | −0.215503 | ||||||||
\(115\) | −16.3260 | −1.52241 | ||||||||
\(116\) | 5.99594 | 0.556709 | ||||||||
\(117\) | 12.4281 | 1.14898 | ||||||||
\(118\) | 5.42719 | 0.499613 | ||||||||
\(119\) | −11.7317 | −1.07545 | ||||||||
\(120\) | 6.04315 | 0.551662 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −10.1851 | −0.922118 | ||||||||
\(123\) | 24.2420 | 2.18582 | ||||||||
\(124\) | −7.27922 | −0.653693 | ||||||||
\(125\) | −8.14730 | −0.728716 | ||||||||
\(126\) | 6.29100 | 0.560447 | ||||||||
\(127\) | 1.63724 | 0.145281 | 0.0726407 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726407 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.704636 | −0.0620397 | ||||||||
\(130\) | 14.2269 | 1.24779 | ||||||||
\(131\) | −21.5141 | −1.87970 | −0.939849 | − | 0.341592i | \(-0.889034\pi\) | ||||
−0.939849 | + | 0.341592i | \(0.889034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.74200 | −0.237761 | ||||||||
\(134\) | −0.0148030 | −0.00127879 | ||||||||
\(135\) | −4.26456 | −0.367035 | ||||||||
\(136\) | −4.27854 | −0.366882 | ||||||||
\(137\) | 6.40013 | 0.546800 | 0.273400 | − | 0.961900i | \(-0.411852\pi\) | ||||
0.273400 | + | 0.961900i | \(0.411852\pi\) | |||||||
\(138\) | −14.3030 | −1.21755 | ||||||||
\(139\) | −7.37781 | −0.625778 | −0.312889 | − | 0.949790i | \(-0.601297\pi\) | ||||
−0.312889 | + | 0.949790i | \(0.601297\pi\) | |||||||
\(140\) | 7.20154 | 0.608641 | ||||||||
\(141\) | −10.5070 | −0.884846 | ||||||||
\(142\) | 12.1074 | 1.01603 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.29431 | 0.191193 | ||||||||
\(145\) | 15.7477 | 1.30777 | ||||||||
\(146\) | −13.8664 | −1.14759 | ||||||||
\(147\) | 1.19312 | 0.0984070 | ||||||||
\(148\) | −3.97289 | −0.326570 | ||||||||
\(149\) | 6.70635 | 0.549405 | 0.274703 | − | 0.961529i | \(-0.411421\pi\) | ||||
0.274703 | + | 0.961529i | \(0.411421\pi\) | |||||||
\(150\) | 4.36696 | 0.356561 | ||||||||
\(151\) | 17.7575 | 1.44508 | 0.722542 | − | 0.691327i | \(-0.242973\pi\) | ||||
0.722542 | + | 0.691327i | \(0.242973\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −9.81631 | −0.793602 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1180 | −1.53560 | ||||||||
\(156\) | 12.4640 | 0.997920 | ||||||||
\(157\) | 1.60819 | 0.128348 | 0.0641738 | − | 0.997939i | \(-0.479559\pi\) | ||||
0.0641738 | + | 0.997939i | \(0.479559\pi\) | |||||||
\(158\) | 11.8987 | 0.946612 | ||||||||
\(159\) | −8.58217 | −0.680610 | ||||||||
\(160\) | 2.62639 | 0.207634 | ||||||||
\(161\) | −17.0447 | −1.34331 | ||||||||
\(162\) | −10.6191 | −0.834312 | ||||||||
\(163\) | 21.6766 | 1.69784 | 0.848922 | − | 0.528518i | \(-0.177252\pi\) | ||||
0.848922 | + | 0.528518i | \(0.177252\pi\) | |||||||
\(164\) | 10.5357 | 0.822699 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.29710 | 0.100674 | ||||||||
\(167\) | 12.2081 | 0.944693 | 0.472346 | − | 0.881413i | \(-0.343407\pi\) | ||||
0.472346 | + | 0.881413i | \(0.343407\pi\) | |||||||
\(168\) | 6.30916 | 0.486762 | ||||||||
\(169\) | 16.3431 | 1.25716 | ||||||||
\(170\) | −11.2371 | −0.861846 | ||||||||
\(171\) | −2.29431 | −0.175451 | ||||||||
\(172\) | −0.306239 | −0.0233505 | ||||||||
\(173\) | 11.5446 | 0.877720 | 0.438860 | − | 0.898556i | \(-0.355382\pi\) | ||||
0.438860 | + | 0.898556i | \(0.355382\pi\) | |||||||
\(174\) | 13.7963 | 1.04589 | ||||||||
\(175\) | 5.20405 | 0.393389 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4876 | 0.938627 | ||||||||
\(178\) | −14.5993 | −1.09427 | ||||||||
\(179\) | −0.875261 | −0.0654201 | −0.0327100 | − | 0.999465i | \(-0.510414\pi\) | ||||
−0.0327100 | + | 0.999465i | \(0.510414\pi\) | |||||||
\(180\) | 6.02576 | 0.449133 | ||||||||
\(181\) | 5.60684 | 0.416753 | 0.208377 | − | 0.978049i | \(-0.433182\pi\) | ||||
0.208377 | + | 0.978049i | \(0.433182\pi\) | |||||||
\(182\) | 14.8532 | 1.10099 | ||||||||
\(183\) | −23.4353 | −1.73239 | ||||||||
\(184\) | −6.21615 | −0.458261 | ||||||||
\(185\) | −10.4343 | −0.767149 | ||||||||
\(186\) | −16.7490 | −1.22810 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.56638 | −0.333038 | ||||||||
\(189\) | −4.45228 | −0.323856 | ||||||||
\(190\) | −2.62639 | −0.190538 | ||||||||
\(191\) | −9.79138 | −0.708480 | −0.354240 | − | 0.935155i | \(-0.615260\pi\) | ||||
−0.354240 | + | 0.935155i | \(0.615260\pi\) | |||||||
\(192\) | 2.30094 | 0.166056 | ||||||||
\(193\) | 8.40525 | 0.605023 | 0.302512 | − | 0.953146i | \(-0.402175\pi\) | ||||
0.302512 | + | 0.953146i | \(0.402175\pi\) | |||||||
\(194\) | −10.0528 | −0.721752 | ||||||||
\(195\) | 32.7353 | 2.34422 | ||||||||
\(196\) | 0.518537 | 0.0370384 | ||||||||
\(197\) | −3.91660 | −0.279046 | −0.139523 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139523 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.808932 | 0.0573437 | 0.0286718 | − | 0.999589i | \(-0.490872\pi\) | ||||
0.0286718 | + | 0.999589i | \(0.490872\pi\) | |||||||
\(200\) | 1.89791 | 0.134202 | ||||||||
\(201\) | −0.0340609 | −0.00240247 | ||||||||
\(202\) | 4.03837 | 0.284139 | ||||||||
\(203\) | 16.4408 | 1.15392 | ||||||||
\(204\) | −9.84465 | −0.689263 | ||||||||
\(205\) | 27.6708 | 1.93261 | ||||||||
\(206\) | 12.3140 | 0.857955 | ||||||||
\(207\) | −14.2618 | −0.991265 | ||||||||
\(208\) | 5.41693 | 0.375596 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 16.5703 | 1.14346 | ||||||||
\(211\) | 13.8172 | 0.951214 | 0.475607 | − | 0.879658i | \(-0.342228\pi\) | ||||
0.475607 | + | 0.879658i | \(0.342228\pi\) | |||||||
\(212\) | −3.72986 | −0.256168 | ||||||||
\(213\) | 27.8583 | 1.90882 | ||||||||
\(214\) | −7.79569 | −0.532902 | ||||||||
\(215\) | −0.804301 | −0.0548529 | ||||||||
\(216\) | −1.62374 | −0.110481 | ||||||||
\(217\) | −19.9596 | −1.35494 | ||||||||
\(218\) | −14.9495 | −1.01251 | ||||||||
\(219\) | −31.9058 | −2.15599 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.1765 | −1.55902 | ||||||||
\(222\) | −9.14138 | −0.613529 | ||||||||
\(223\) | 1.06868 | 0.0715638 | 0.0357819 | − | 0.999360i | \(-0.488608\pi\) | ||||
0.0357819 | + | 0.999360i | \(0.488608\pi\) | |||||||
\(224\) | 2.74200 | 0.183207 | ||||||||
\(225\) | 4.35439 | 0.290293 | ||||||||
\(226\) | 1.06888 | 0.0711011 | ||||||||
\(227\) | −20.1639 | −1.33833 | −0.669164 | − | 0.743115i | \(-0.733348\pi\) | ||||
−0.669164 | + | 0.743115i | \(0.733348\pi\) | |||||||
\(228\) | −2.30094 | −0.152383 | ||||||||
\(229\) | 25.5481 | 1.68827 | 0.844133 | − | 0.536134i | \(-0.180116\pi\) | ||||
0.844133 | + | 0.536134i | \(0.180116\pi\) | |||||||
\(230\) | −16.3260 | −1.07651 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.99594 | 0.393653 | ||||||||
\(233\) | 11.3403 | 0.742928 | 0.371464 | − | 0.928447i | \(-0.378856\pi\) | ||||
0.371464 | + | 0.928447i | \(0.378856\pi\) | |||||||
\(234\) | 12.4281 | 0.812453 | ||||||||
\(235\) | −11.9931 | −0.782342 | ||||||||
\(236\) | 5.42719 | 0.353280 | ||||||||
\(237\) | 27.3782 | 1.77841 | ||||||||
\(238\) | −11.7317 | −0.760455 | ||||||||
\(239\) | −1.78866 | −0.115699 | −0.0578495 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578495 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(240\) | 6.04315 | 0.390084 | ||||||||
\(241\) | −19.8713 | −1.28002 | −0.640011 | − | 0.768366i | \(-0.721070\pi\) | ||||
−0.640011 | + | 0.768366i | \(0.721070\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.5626 | −1.25494 | ||||||||
\(244\) | −10.1851 | −0.652036 | ||||||||
\(245\) | 1.36188 | 0.0870072 | ||||||||
\(246\) | 24.2420 | 1.54561 | ||||||||
\(247\) | −5.41693 | −0.344671 | ||||||||
\(248\) | −7.27922 | −0.462231 | ||||||||
\(249\) | 2.98454 | 0.189138 | ||||||||
\(250\) | −8.14730 | −0.515280 | ||||||||
\(251\) | 11.0409 | 0.696898 | 0.348449 | − | 0.937328i | \(-0.386708\pi\) | ||||
0.348449 | + | 0.937328i | \(0.386708\pi\) | |||||||
\(252\) | 6.29100 | 0.396296 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.63724 | 0.102729 | ||||||||
\(255\) | −25.8559 | −1.61916 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.40353 | −0.399441 | −0.199721 | − | 0.979853i | \(-0.564003\pi\) | ||||
−0.199721 | + | 0.979853i | \(0.564003\pi\) | |||||||
\(258\) | −0.704636 | −0.0438687 | ||||||||
\(259\) | −10.8936 | −0.676898 | ||||||||
\(260\) | 14.2269 | 0.882318 | ||||||||
\(261\) | 13.7566 | 0.851510 | ||||||||
\(262\) | −21.5141 | −1.32915 | ||||||||
\(263\) | 4.26381 | 0.262918 | 0.131459 | − | 0.991322i | \(-0.458034\pi\) | ||||
0.131459 | + | 0.991322i | \(0.458034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.79604 | −0.601766 | ||||||||
\(266\) | −2.74200 | −0.168123 | ||||||||
\(267\) | −33.5922 | −2.05581 | ||||||||
\(268\) | −0.0148030 | −0.000904239 0 | ||||||||
\(269\) | −2.60318 | −0.158719 | −0.0793595 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793595 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(270\) | −4.26456 | −0.259533 | ||||||||
\(271\) | 9.55649 | 0.580515 | 0.290258 | − | 0.956949i | \(-0.406259\pi\) | ||||
0.290258 | + | 0.956949i | \(0.406259\pi\) | |||||||
\(272\) | −4.27854 | −0.259424 | ||||||||
\(273\) | 34.1763 | 2.06844 | ||||||||
\(274\) | 6.40013 | 0.386646 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.3030 | −0.860938 | ||||||||
\(277\) | 9.48715 | 0.570027 | 0.285014 | − | 0.958523i | \(-0.408002\pi\) | ||||
0.285014 | + | 0.958523i | \(0.408002\pi\) | |||||||
\(278\) | −7.37781 | −0.442492 | ||||||||
\(279\) | −16.7008 | −0.999852 | ||||||||
\(280\) | 7.20154 | 0.430374 | ||||||||
\(281\) | −9.15958 | −0.546415 | −0.273207 | − | 0.961955i | \(-0.588085\pi\) | ||||
−0.273207 | + | 0.961955i | \(0.588085\pi\) | |||||||
\(282\) | −10.5070 | −0.625680 | ||||||||
\(283\) | 21.1581 | 1.25772 | 0.628860 | − | 0.777519i | \(-0.283522\pi\) | ||||
0.628860 | + | 0.777519i | \(0.283522\pi\) | |||||||
\(284\) | 12.1074 | 0.718440 | ||||||||
\(285\) | −6.04315 | −0.357965 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.8888 | 1.70525 | ||||||||
\(288\) | 2.29431 | 0.135194 | ||||||||
\(289\) | 1.30588 | 0.0768165 | ||||||||
\(290\) | 15.7477 | 0.924734 | ||||||||
\(291\) | −23.1310 | −1.35596 | ||||||||
\(292\) | −13.8664 | −0.811472 | ||||||||
\(293\) | 22.1069 | 1.29150 | 0.645749 | − | 0.763550i | \(-0.276545\pi\) | ||||
0.645749 | + | 0.763550i | \(0.276545\pi\) | |||||||
\(294\) | 1.19312 | 0.0695843 | ||||||||
\(295\) | 14.2539 | 0.829894 | ||||||||
\(296\) | −3.97289 | −0.230920 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.70635 | 0.388488 | ||||||||
\(299\) | −33.6725 | −1.94733 | ||||||||
\(300\) | 4.36696 | 0.252127 | ||||||||
\(301\) | −0.839705 | −0.0483998 | ||||||||
\(302\) | 17.7575 | 1.02183 | ||||||||
\(303\) | 9.29204 | 0.533814 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −26.7501 | −1.53171 | ||||||||
\(306\) | −9.81631 | −0.561161 | ||||||||
\(307\) | 14.5129 | 0.828296 | 0.414148 | − | 0.910209i | \(-0.364080\pi\) | ||||
0.414148 | + | 0.910209i | \(0.364080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.3337 | 1.61185 | ||||||||
\(310\) | −19.1180 | −1.08583 | ||||||||
\(311\) | −29.2145 | −1.65660 | −0.828300 | − | 0.560285i | \(-0.810692\pi\) | ||||
−0.828300 | + | 0.560285i | \(0.810692\pi\) | |||||||
\(312\) | 12.4640 | 0.705636 | ||||||||
\(313\) | −27.0783 | −1.53055 | −0.765277 | − | 0.643702i | \(-0.777398\pi\) | ||||
−0.765277 | + | 0.643702i | \(0.777398\pi\) | |||||||
\(314\) | 1.60819 | 0.0907555 | ||||||||
\(315\) | 16.5226 | 0.930943 | ||||||||
\(316\) | 11.8987 | 0.669356 | ||||||||
\(317\) | 27.2677 | 1.53151 | 0.765754 | − | 0.643134i | \(-0.222366\pi\) | ||||
0.765754 | + | 0.643134i | \(0.222366\pi\) | |||||||
\(318\) | −8.58217 | −0.481264 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 2.62639 | 0.146819 | ||||||||
\(321\) | −17.9374 | −1.00117 | ||||||||
\(322\) | −17.0447 | −0.949862 | ||||||||
\(323\) | 4.27854 | 0.238064 | ||||||||
\(324\) | −10.6191 | −0.589948 | ||||||||
\(325\) | 10.2808 | 0.570277 | ||||||||
\(326\) | 21.6766 | 1.20056 | ||||||||
\(327\) | −34.3980 | −1.90221 | ||||||||
\(328\) | 10.5357 | 0.581736 | ||||||||
\(329\) | −12.5210 | −0.690305 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1001 | 0.884941 | 0.442471 | − | 0.896783i | \(-0.354102\pi\) | ||||
0.442471 | + | 0.896783i | \(0.354102\pi\) | |||||||
\(332\) | 1.29710 | 0.0711876 | ||||||||
\(333\) | −9.11506 | −0.499502 | ||||||||
\(334\) | 12.2081 | 0.667999 | ||||||||
\(335\) | −0.0388785 | −0.00212416 | ||||||||
\(336\) | 6.30916 | 0.344193 | ||||||||
\(337\) | 22.6353 | 1.23303 | 0.616513 | − | 0.787345i | \(-0.288545\pi\) | ||||
0.616513 | + | 0.787345i | \(0.288545\pi\) | |||||||
\(338\) | 16.3431 | 0.888948 | ||||||||
\(339\) | 2.45944 | 0.133578 | ||||||||
\(340\) | −11.2371 | −0.609417 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.29431 | −0.124062 | ||||||||
\(343\) | −17.7721 | −0.959605 | ||||||||
\(344\) | −0.306239 | −0.0165113 | ||||||||
\(345\) | −37.5652 | −2.02244 | ||||||||
\(346\) | 11.5446 | 0.620642 | ||||||||
\(347\) | −18.8940 | −1.01428 | −0.507142 | − | 0.861863i | \(-0.669298\pi\) | ||||
−0.507142 | + | 0.861863i | \(0.669298\pi\) | |||||||
\(348\) | 13.7963 | 0.739558 | ||||||||
\(349\) | 16.3651 | 0.876002 | 0.438001 | − | 0.898974i | \(-0.355687\pi\) | ||||
0.438001 | + | 0.898974i | \(0.355687\pi\) | |||||||
\(350\) | 5.20405 | 0.278168 | ||||||||
\(351\) | −8.79567 | −0.469478 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.7651 | −1.53101 | −0.765506 | − | 0.643429i | \(-0.777511\pi\) | ||||
−0.765506 | + | 0.643429i | \(0.777511\pi\) | |||||||
\(354\) | 12.4876 | 0.663710 | ||||||||
\(355\) | 31.7986 | 1.68770 | ||||||||
\(356\) | −14.5993 | −0.773764 | ||||||||
\(357\) | −26.9940 | −1.42867 | ||||||||
\(358\) | −0.875261 | −0.0462590 | ||||||||
\(359\) | −22.4187 | −1.18321 | −0.591606 | − | 0.806228i | \(-0.701506\pi\) | ||||
−0.591606 | + | 0.806228i | \(0.701506\pi\) | |||||||
\(360\) | 6.02576 | 0.317585 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.60684 | 0.294689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.8532 | 0.778519 | ||||||||
\(365\) | −36.4186 | −1.90624 | ||||||||
\(366\) | −23.4353 | −1.22499 | ||||||||
\(367\) | 21.2032 | 1.10680 | 0.553399 | − | 0.832916i | \(-0.313330\pi\) | ||||
0.553399 | + | 0.832916i | \(0.313330\pi\) | |||||||
\(368\) | −6.21615 | −0.324039 | ||||||||
\(369\) | 24.1722 | 1.25835 | ||||||||
\(370\) | −10.4343 | −0.542456 | ||||||||
\(371\) | −10.2272 | −0.530972 | ||||||||
\(372\) | −16.7490 | −0.868397 | ||||||||
\(373\) | 34.6222 | 1.79267 | 0.896334 | − | 0.443379i | \(-0.146220\pi\) | ||||
0.896334 | + | 0.443379i | \(0.146220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.7464 | −0.968061 | ||||||||
\(376\) | −4.56638 | −0.235493 | ||||||||
\(377\) | 32.4796 | 1.67278 | ||||||||
\(378\) | −4.45228 | −0.229001 | ||||||||
\(379\) | 18.9799 | 0.974933 | 0.487467 | − | 0.873142i | \(-0.337921\pi\) | ||||
0.487467 | + | 0.873142i | \(0.337921\pi\) | |||||||
\(380\) | −2.62639 | −0.134731 | ||||||||
\(381\) | 3.76718 | 0.192999 | ||||||||
\(382\) | −9.79138 | −0.500971 | ||||||||
\(383\) | 15.4258 | 0.788219 | 0.394110 | − | 0.919063i | \(-0.371053\pi\) | ||||
0.394110 | + | 0.919063i | \(0.371053\pi\) | |||||||
\(384\) | 2.30094 | 0.117419 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.40525 | 0.427816 | ||||||||
\(387\) | −0.702608 | −0.0357156 | ||||||||
\(388\) | −10.0528 | −0.510356 | ||||||||
\(389\) | −18.1318 | −0.919317 | −0.459659 | − | 0.888096i | \(-0.652028\pi\) | ||||
−0.459659 | + | 0.888096i | \(0.652028\pi\) | |||||||
\(390\) | 32.7353 | 1.65762 | ||||||||
\(391\) | 26.5960 | 1.34502 | ||||||||
\(392\) | 0.518537 | 0.0261901 | ||||||||
\(393\) | −49.5026 | −2.49708 | ||||||||
\(394\) | −3.91660 | −0.197315 | ||||||||
\(395\) | 31.2507 | 1.57239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44526 | 0.474044 | 0.237022 | − | 0.971504i | \(-0.423829\pi\) | ||||
0.237022 | + | 0.971504i | \(0.423829\pi\) | |||||||
\(398\) | 0.808932 | 0.0405481 | ||||||||
\(399\) | −6.30916 | −0.315853 | ||||||||
\(400\) | 1.89791 | 0.0948953 | ||||||||
\(401\) | 26.3735 | 1.31703 | 0.658515 | − | 0.752568i | \(-0.271185\pi\) | ||||
0.658515 | + | 0.752568i | \(0.271185\pi\) | |||||||
\(402\) | −0.0340609 | −0.00169880 | ||||||||
\(403\) | −39.4310 | −1.96420 | ||||||||
\(404\) | 4.03837 | 0.200916 | ||||||||
\(405\) | −27.8898 | −1.38585 | ||||||||
\(406\) | 16.4408 | 0.815945 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.84465 | −0.487383 | ||||||||
\(409\) | −27.1570 | −1.34283 | −0.671413 | − | 0.741083i | \(-0.734312\pi\) | ||||
−0.671413 | + | 0.741083i | \(0.734312\pi\) | |||||||
\(410\) | 27.6708 | 1.36656 | ||||||||
\(411\) | 14.7263 | 0.726395 | ||||||||
\(412\) | 12.3140 | 0.606666 | ||||||||
\(413\) | 14.8813 | 0.732262 | ||||||||
\(414\) | −14.2618 | −0.700930 | ||||||||
\(415\) | 3.40668 | 0.167228 | ||||||||
\(416\) | 5.41693 | 0.265587 | ||||||||
\(417\) | −16.9759 | −0.831312 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5473 | 0.808387 | 0.404193 | − | 0.914674i | \(-0.367552\pi\) | ||||
0.404193 | + | 0.914674i | \(0.367552\pi\) | |||||||
\(420\) | 16.5703 | 0.808548 | ||||||||
\(421\) | −37.0039 | −1.80346 | −0.901731 | − | 0.432298i | \(-0.857703\pi\) | ||||
−0.901731 | + | 0.432298i | \(0.857703\pi\) | |||||||
\(422\) | 13.8172 | 0.672610 | ||||||||
\(423\) | −10.4767 | −0.509395 | ||||||||
\(424\) | −3.72986 | −0.181138 | ||||||||
\(425\) | −8.12026 | −0.393891 | ||||||||
\(426\) | 27.8583 | 1.34974 | ||||||||
\(427\) | −27.9276 | −1.35151 | ||||||||
\(428\) | −7.79569 | −0.376819 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.804301 | −0.0387868 | ||||||||
\(431\) | −11.7109 | −0.564096 | −0.282048 | − | 0.959400i | \(-0.591014\pi\) | ||||
−0.282048 | + | 0.959400i | \(0.591014\pi\) | |||||||
\(432\) | −1.62374 | −0.0781221 | ||||||||
\(433\) | 2.12441 | 0.102093 | 0.0510463 | − | 0.998696i | \(-0.483744\pi\) | ||||
0.0510463 | + | 0.998696i | \(0.483744\pi\) | |||||||
\(434\) | −19.9596 | −0.958091 | ||||||||
\(435\) | 36.2344 | 1.73730 | ||||||||
\(436\) | −14.9495 | −0.715953 | ||||||||
\(437\) | 6.21615 | 0.297359 | ||||||||
\(438\) | −31.9058 | −1.52452 | ||||||||
\(439\) | 17.7590 | 0.847591 | 0.423795 | − | 0.905758i | \(-0.360698\pi\) | ||||
0.423795 | + | 0.905758i | \(0.360698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.18969 | 0.0566518 | ||||||||
\(442\) | −23.1765 | −1.10239 | ||||||||
\(443\) | 7.42988 | 0.353004 | 0.176502 | − | 0.984300i | \(-0.443522\pi\) | ||||
0.176502 | + | 0.984300i | \(0.443522\pi\) | |||||||
\(444\) | −9.14138 | −0.433831 | ||||||||
\(445\) | −38.3435 | −1.81766 | ||||||||
\(446\) | 1.06868 | 0.0506033 | ||||||||
\(447\) | 15.4309 | 0.729856 | ||||||||
\(448\) | 2.74200 | 0.129547 | ||||||||
\(449\) | −19.0848 | −0.900668 | −0.450334 | − | 0.892860i | \(-0.648695\pi\) | ||||
−0.450334 | + | 0.892860i | \(0.648695\pi\) | |||||||
\(450\) | 4.35439 | 0.205268 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.06888 | 0.0502761 | ||||||||
\(453\) | 40.8589 | 1.91972 | ||||||||
\(454\) | −20.1639 | −0.946341 | ||||||||
\(455\) | 39.0102 | 1.82883 | ||||||||
\(456\) | −2.30094 | −0.107751 | ||||||||
\(457\) | −2.89775 | −0.135551 | −0.0677755 | − | 0.997701i | \(-0.521590\pi\) | ||||
−0.0677755 | + | 0.997701i | \(0.521590\pi\) | |||||||
\(458\) | 25.5481 | 1.19378 | ||||||||
\(459\) | 6.94722 | 0.324269 | ||||||||
\(460\) | −16.3260 | −0.761205 | ||||||||
\(461\) | −7.89943 | −0.367913 | −0.183957 | − | 0.982934i | \(-0.558891\pi\) | ||||
−0.183957 | + | 0.982934i | \(0.558891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8107 | 0.967155 | 0.483578 | − | 0.875301i | \(-0.339337\pi\) | ||||
0.483578 | + | 0.875301i | \(0.339337\pi\) | |||||||
\(464\) | 5.99594 | 0.278354 | ||||||||
\(465\) | −43.9894 | −2.03996 | ||||||||
\(466\) | 11.3403 | 0.525329 | ||||||||
\(467\) | −31.5622 | −1.46052 | −0.730262 | − | 0.683168i | \(-0.760602\pi\) | ||||
−0.730262 | + | 0.683168i | \(0.760602\pi\) | |||||||
\(468\) | 12.4281 | 0.574491 | ||||||||
\(469\) | −0.0405898 | −0.00187426 | ||||||||
\(470\) | −11.9931 | −0.553200 | ||||||||
\(471\) | 3.70035 | 0.170503 | ||||||||
\(472\) | 5.42719 | 0.249807 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 27.3782 | 1.25752 | ||||||||
\(475\) | −1.89791 | −0.0870819 | ||||||||
\(476\) | −11.7317 | −0.537723 | ||||||||
\(477\) | −8.55746 | −0.391819 | ||||||||
\(478\) | −1.78866 | −0.0818116 | ||||||||
\(479\) | 23.7066 | 1.08318 | 0.541591 | − | 0.840642i | \(-0.317822\pi\) | ||||
0.541591 | + | 0.840642i | \(0.317822\pi\) | |||||||
\(480\) | 6.04315 | 0.275831 | ||||||||
\(481\) | −21.5209 | −0.981267 | ||||||||
\(482\) | −19.8713 | −0.905112 | ||||||||
\(483\) | −39.2187 | −1.78451 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.4027 | −1.19888 | ||||||||
\(486\) | −19.5626 | −0.887377 | ||||||||
\(487\) | −24.6716 | −1.11798 | −0.558988 | − | 0.829176i | \(-0.688810\pi\) | ||||
−0.558988 | + | 0.829176i | \(0.688810\pi\) | |||||||
\(488\) | −10.1851 | −0.461059 | ||||||||
\(489\) | 49.8766 | 2.25550 | ||||||||
\(490\) | 1.36188 | 0.0615234 | ||||||||
\(491\) | 34.1976 | 1.54332 | 0.771658 | − | 0.636038i | \(-0.219428\pi\) | ||||
0.771658 | + | 0.636038i | \(0.219428\pi\) | |||||||
\(492\) | 24.2420 | 1.09291 | ||||||||
\(493\) | −25.6538 | −1.15539 | ||||||||
\(494\) | −5.41693 | −0.243719 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.27922 | −0.326847 | ||||||||
\(497\) | 33.1983 | 1.48915 | ||||||||
\(498\) | 2.98454 | 0.133741 | ||||||||
\(499\) | 23.0706 | 1.03278 | 0.516390 | − | 0.856353i | \(-0.327275\pi\) | ||||
0.516390 | + | 0.856353i | \(0.327275\pi\) | |||||||
\(500\) | −8.14730 | −0.364358 | ||||||||
\(501\) | 28.0901 | 1.25497 | ||||||||
\(502\) | 11.0409 | 0.492782 | ||||||||
\(503\) | −20.1071 | −0.896532 | −0.448266 | − | 0.893900i | \(-0.647958\pi\) | ||||
−0.448266 | + | 0.893900i | \(0.647958\pi\) | |||||||
\(504\) | 6.29100 | 0.280223 | ||||||||
\(505\) | 10.6063 | 0.471975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.6045 | 1.67007 | ||||||||
\(508\) | 1.63724 | 0.0726407 | ||||||||
\(509\) | 30.9152 | 1.37029 | 0.685145 | − | 0.728406i | \(-0.259739\pi\) | ||||
0.685145 | + | 0.728406i | \(0.259739\pi\) | |||||||
\(510\) | −25.8559 | −1.14492 | ||||||||
\(511\) | −38.0217 | −1.68198 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.62374 | 0.0716898 | ||||||||
\(514\) | −6.40353 | −0.282448 | ||||||||
\(515\) | 32.3412 | 1.42513 | ||||||||
\(516\) | −0.704636 | −0.0310199 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.8936 | −0.478639 | ||||||||
\(519\) | 26.5634 | 1.16600 | ||||||||
\(520\) | 14.2269 | 0.623893 | ||||||||
\(521\) | −24.5075 | −1.07369 | −0.536845 | − | 0.843681i | \(-0.680384\pi\) | ||||
−0.536845 | + | 0.843681i | \(0.680384\pi\) | |||||||
\(522\) | 13.7566 | 0.602109 | ||||||||
\(523\) | 0.648533 | 0.0283584 | 0.0141792 | − | 0.999899i | \(-0.495486\pi\) | ||||
0.0141792 | + | 0.999899i | \(0.495486\pi\) | |||||||
\(524\) | −21.5141 | −0.939849 | ||||||||
\(525\) | 11.9742 | 0.522597 | ||||||||
\(526\) | 4.26381 | 0.185911 | ||||||||
\(527\) | 31.1444 | 1.35667 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.6406 | 0.680025 | ||||||||
\(530\) | −9.79604 | −0.425513 | ||||||||
\(531\) | 12.4517 | 0.540357 | ||||||||
\(532\) | −2.74200 | −0.118881 | ||||||||
\(533\) | 57.0711 | 2.47202 | ||||||||
\(534\) | −33.5922 | −1.45368 | ||||||||
\(535\) | −20.4745 | −0.885190 | ||||||||
\(536\) | −0.0148030 | −0.000639394 0 | ||||||||
\(537\) | −2.01392 | −0.0869071 | ||||||||
\(538\) | −2.60318 | −0.112231 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.26456 | −0.183518 | ||||||||
\(541\) | −0.839279 | −0.0360834 | −0.0180417 | − | 0.999837i | \(-0.505743\pi\) | ||||
−0.0180417 | + | 0.999837i | \(0.505743\pi\) | |||||||
\(542\) | 9.55649 | 0.410486 | ||||||||
\(543\) | 12.9010 | 0.553635 | ||||||||
\(544\) | −4.27854 | −0.183441 | ||||||||
\(545\) | −39.2633 | −1.68185 | ||||||||
\(546\) | 34.1763 | 1.46261 | ||||||||
\(547\) | 35.5183 | 1.51865 | 0.759327 | − | 0.650709i | \(-0.225528\pi\) | ||||
0.759327 | + | 0.650709i | \(0.225528\pi\) | |||||||
\(548\) | 6.40013 | 0.273400 | ||||||||
\(549\) | −23.3679 | −0.997317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.99594 | −0.255436 | ||||||||
\(552\) | −14.3030 | −0.608775 | ||||||||
\(553\) | 32.6263 | 1.38741 | ||||||||
\(554\) | 9.48715 | 0.403070 | ||||||||
\(555\) | −24.0088 | −1.01912 | ||||||||
\(556\) | −7.37781 | −0.312889 | ||||||||
\(557\) | 11.6586 | 0.493990 | 0.246995 | − | 0.969017i | \(-0.420557\pi\) | ||||
0.246995 | + | 0.969017i | \(0.420557\pi\) | |||||||
\(558\) | −16.7008 | −0.707002 | ||||||||
\(559\) | −1.65887 | −0.0701628 | ||||||||
\(560\) | 7.20154 | 0.304321 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.15958 | −0.386374 | ||||||||
\(563\) | 2.58856 | 0.109095 | 0.0545473 | − | 0.998511i | \(-0.482628\pi\) | ||||
0.0545473 | + | 0.998511i | \(0.482628\pi\) | |||||||
\(564\) | −10.5070 | −0.442423 | ||||||||
\(565\) | 2.80730 | 0.118104 | ||||||||
\(566\) | 21.1581 | 0.889342 | ||||||||
\(567\) | −29.1174 | −1.22282 | ||||||||
\(568\) | 12.1074 | 0.508014 | ||||||||
\(569\) | −11.8494 | −0.496751 | −0.248376 | − | 0.968664i | \(-0.579897\pi\) | ||||
−0.248376 | + | 0.968664i | \(0.579897\pi\) | |||||||
\(570\) | −6.04315 | −0.253120 | ||||||||
\(571\) | −7.12206 | −0.298049 | −0.149024 | − | 0.988834i | \(-0.547613\pi\) | ||||
−0.149024 | + | 0.988834i | \(0.547613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.5294 | −0.941178 | ||||||||
\(574\) | 28.8888 | 1.20580 | ||||||||
\(575\) | −11.7977 | −0.491997 | ||||||||
\(576\) | 2.29431 | 0.0955964 | ||||||||
\(577\) | −40.0598 | −1.66771 | −0.833855 | − | 0.551984i | \(-0.813871\pi\) | ||||
−0.833855 | + | 0.551984i | \(0.813871\pi\) | |||||||
\(578\) | 1.30588 | 0.0543175 | ||||||||
\(579\) | 19.3400 | 0.803741 | ||||||||
\(580\) | 15.7477 | 0.653886 | ||||||||
\(581\) | 3.55664 | 0.147554 | ||||||||
\(582\) | −23.1310 | −0.958810 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −13.8664 | −0.573797 | ||||||||
\(585\) | 32.6411 | 1.34954 | ||||||||
\(586\) | 22.1069 | 0.913227 | ||||||||
\(587\) | 10.7483 | 0.443631 | 0.221815 | − | 0.975089i | \(-0.428802\pi\) | ||||
0.221815 | + | 0.975089i | \(0.428802\pi\) | |||||||
\(588\) | 1.19312 | 0.0492035 | ||||||||
\(589\) | 7.27922 | 0.299935 | ||||||||
\(590\) | 14.2539 | 0.586824 | ||||||||
\(591\) | −9.01184 | −0.370698 | ||||||||
\(592\) | −3.97289 | −0.163285 | ||||||||
\(593\) | 15.0714 | 0.618909 | 0.309454 | − | 0.950914i | \(-0.399854\pi\) | ||||
0.309454 | + | 0.950914i | \(0.399854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.8121 | −1.26317 | ||||||||
\(596\) | 6.70635 | 0.274703 | ||||||||
\(597\) | 1.86130 | 0.0761781 | ||||||||
\(598\) | −33.6725 | −1.37697 | ||||||||
\(599\) | 22.2653 | 0.909737 | 0.454868 | − | 0.890559i | \(-0.349686\pi\) | ||||
0.454868 | + | 0.890559i | \(0.349686\pi\) | |||||||
\(600\) | 4.36696 | 0.178281 | ||||||||
\(601\) | 15.6242 | 0.637326 | 0.318663 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318663 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(602\) | −0.839705 | −0.0342238 | ||||||||
\(603\) | −0.0339628 | −0.00138307 | ||||||||
\(604\) | 17.7575 | 0.722542 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.29204 | 0.377463 | ||||||||
\(607\) | −17.3993 | −0.706217 | −0.353109 | − | 0.935582i | \(-0.614875\pi\) | ||||
−0.353109 | + | 0.935582i | \(0.614875\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 37.8293 | 1.53292 | ||||||||
\(610\) | −26.7501 | −1.08308 | ||||||||
\(611\) | −24.7358 | −1.00070 | ||||||||
\(612\) | −9.81631 | −0.396801 | ||||||||
\(613\) | 45.7036 | 1.84595 | 0.922975 | − | 0.384860i | \(-0.125750\pi\) | ||||
0.922975 | + | 0.384860i | \(0.125750\pi\) | |||||||
\(614\) | 14.5129 | 0.585694 | ||||||||
\(615\) | 63.6688 | 2.56737 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1087 | −0.608252 | −0.304126 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304126 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(618\) | 28.3337 | 1.13975 | ||||||||
\(619\) | 15.8931 | 0.638799 | 0.319399 | − | 0.947620i | \(-0.396519\pi\) | ||||
0.319399 | + | 0.947620i | \(0.396519\pi\) | |||||||
\(620\) | −19.1180 | −0.767799 | ||||||||
\(621\) | 10.0934 | 0.405034 | ||||||||
\(622\) | −29.2145 | −1.17139 | ||||||||
\(623\) | −40.0313 | −1.60382 | ||||||||
\(624\) | 12.4640 | 0.498960 | ||||||||
\(625\) | −30.8875 | −1.23550 | ||||||||
\(626\) | −27.0783 | −1.08226 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.60819 | 0.0641738 | ||||||||
\(629\) | 16.9982 | 0.677761 | ||||||||
\(630\) | 16.5226 | 0.658276 | ||||||||
\(631\) | −20.2056 | −0.804371 | −0.402185 | − | 0.915558i | \(-0.631749\pi\) | ||||
−0.402185 | + | 0.915558i | \(0.631749\pi\) | |||||||
\(632\) | 11.8987 | 0.473306 | ||||||||
\(633\) | 31.7925 | 1.26364 | ||||||||
\(634\) | 27.2677 | 1.08294 | ||||||||
\(635\) | 4.30002 | 0.170641 | ||||||||
\(636\) | −8.58217 | −0.340305 | ||||||||
\(637\) | 2.80888 | 0.111292 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 27.7781 | 1.09889 | ||||||||
\(640\) | 2.62639 | 0.103817 | ||||||||
\(641\) | 33.5188 | 1.32391 | 0.661957 | − | 0.749542i | \(-0.269726\pi\) | ||||
0.661957 | + | 0.749542i | \(0.269726\pi\) | |||||||
\(642\) | −17.9374 | −0.707933 | ||||||||
\(643\) | −38.5327 | −1.51958 | −0.759791 | − | 0.650167i | \(-0.774699\pi\) | ||||
−0.759791 | + | 0.650167i | \(0.774699\pi\) | |||||||
\(644\) | −17.0447 | −0.671654 | ||||||||
\(645\) | −1.85065 | −0.0728691 | ||||||||
\(646\) | 4.27854 | 0.168337 | ||||||||
\(647\) | 15.4199 | 0.606221 | 0.303110 | − | 0.952955i | \(-0.401975\pi\) | ||||
0.303110 | + | 0.952955i | \(0.401975\pi\) | |||||||
\(648\) | −10.6191 | −0.417156 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 10.2808 | 0.403247 | ||||||||
\(651\) | −45.9258 | −1.79997 | ||||||||
\(652\) | 21.6766 | 0.848922 | ||||||||
\(653\) | −47.1190 | −1.84391 | −0.921955 | − | 0.387297i | \(-0.873409\pi\) | ||||
−0.921955 | + | 0.387297i | \(0.873409\pi\) | |||||||
\(654\) | −34.3980 | −1.34507 | ||||||||
\(655\) | −56.5044 | −2.20781 | ||||||||
\(656\) | 10.5357 | 0.411350 | ||||||||
\(657\) | −31.8140 | −1.24118 | ||||||||
\(658\) | −12.5210 | −0.488119 | ||||||||
\(659\) | −42.9260 | −1.67216 | −0.836080 | − | 0.548608i | \(-0.815158\pi\) | ||||
−0.836080 | + | 0.548608i | \(0.815158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7231 | −0.572663 | −0.286331 | − | 0.958131i | \(-0.592436\pi\) | ||||
−0.286331 | + | 0.958131i | \(0.592436\pi\) | |||||||
\(662\) | 16.1001 | 0.625748 | ||||||||
\(663\) | −53.3277 | −2.07108 | ||||||||
\(664\) | 1.29710 | 0.0503372 | ||||||||
\(665\) | −7.20154 | −0.279264 | ||||||||
\(666\) | −9.11506 | −0.353202 | ||||||||
\(667\) | −37.2717 | −1.44317 | ||||||||
\(668\) | 12.2081 | 0.472346 | ||||||||
\(669\) | 2.45896 | 0.0950688 | ||||||||
\(670\) | −0.0388785 | −0.00150201 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 6.30916 | 0.243381 | ||||||||
\(673\) | 1.95301 | 0.0752829 | 0.0376415 | − | 0.999291i | \(-0.488016\pi\) | ||||
0.0376415 | + | 0.999291i | \(0.488016\pi\) | |||||||
\(674\) | 22.6353 | 0.871881 | ||||||||
\(675\) | −3.08170 | −0.118615 | ||||||||
\(676\) | 16.3431 | 0.628581 | ||||||||
\(677\) | −22.6415 | −0.870183 | −0.435091 | − | 0.900386i | \(-0.643284\pi\) | ||||
−0.435091 | + | 0.900386i | \(0.643284\pi\) | |||||||
\(678\) | 2.45944 | 0.0944541 | ||||||||
\(679\) | −27.5649 | −1.05784 | ||||||||
\(680\) | −11.2371 | −0.430923 | ||||||||
\(681\) | −46.3960 | −1.77790 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.4520 | −1.62438 | −0.812191 | − | 0.583392i | \(-0.801725\pi\) | ||||
−0.812191 | + | 0.583392i | \(0.801725\pi\) | |||||||
\(684\) | −2.29431 | −0.0877253 | ||||||||
\(685\) | 16.8092 | 0.642247 | ||||||||
\(686\) | −17.7721 | −0.678543 | ||||||||
\(687\) | 58.7846 | 2.24277 | ||||||||
\(688\) | −0.306239 | −0.0116752 | ||||||||
\(689\) | −20.2044 | −0.769725 | ||||||||
\(690\) | −37.5652 | −1.43008 | ||||||||
\(691\) | −2.80082 | −0.106548 | −0.0532741 | − | 0.998580i | \(-0.516966\pi\) | ||||
−0.0532741 | + | 0.998580i | \(0.516966\pi\) | |||||||
\(692\) | 11.5446 | 0.438860 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.8940 | −0.717207 | ||||||||
\(695\) | −19.3770 | −0.735011 | ||||||||
\(696\) | 13.7963 | 0.522947 | ||||||||
\(697\) | −45.0773 | −1.70743 | ||||||||
\(698\) | 16.3651 | 0.619427 | ||||||||
\(699\) | 26.0933 | 0.986940 | ||||||||
\(700\) | 5.20405 | 0.196695 | ||||||||
\(701\) | −42.0175 | −1.58698 | −0.793489 | − | 0.608585i | \(-0.791738\pi\) | ||||
−0.793489 | + | 0.608585i | \(0.791738\pi\) | |||||||
\(702\) | −8.79567 | −0.331971 | ||||||||
\(703\) | 3.97289 | 0.149840 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.5953 | −1.03930 | ||||||||
\(706\) | −28.7651 | −1.08259 | ||||||||
\(707\) | 11.0732 | 0.416450 | ||||||||
\(708\) | 12.4876 | 0.469314 | ||||||||
\(709\) | 16.1992 | 0.608375 | 0.304187 | − | 0.952612i | \(-0.401615\pi\) | ||||
0.304187 | + | 0.952612i | \(0.401615\pi\) | |||||||
\(710\) | 31.7986 | 1.19338 | ||||||||
\(711\) | 27.2994 | 1.02381 | ||||||||
\(712\) | −14.5993 | −0.547134 | ||||||||
\(713\) | 45.2488 | 1.69458 | ||||||||
\(714\) | −26.9940 | −1.01022 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.875261 | −0.0327100 | ||||||||
\(717\) | −4.11561 | −0.153700 | ||||||||
\(718\) | −22.4187 | −0.836657 | ||||||||
\(719\) | 8.51612 | 0.317598 | 0.158799 | − | 0.987311i | \(-0.449238\pi\) | ||||
0.158799 | + | 0.987311i | \(0.449238\pi\) | |||||||
\(720\) | 6.02576 | 0.224567 | ||||||||
\(721\) | 33.7648 | 1.25747 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −45.7226 | −1.70044 | ||||||||
\(724\) | 5.60684 | 0.208377 | ||||||||
\(725\) | 11.3797 | 0.422632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.0860 | −1.26418 | −0.632091 | − | 0.774895i | \(-0.717803\pi\) | ||||
−0.632091 | + | 0.774895i | \(0.717803\pi\) | |||||||
\(728\) | 14.8532 | 0.550496 | ||||||||
\(729\) | −13.1551 | −0.487226 | ||||||||
\(730\) | −36.4186 | −1.34791 | ||||||||
\(731\) | 1.31025 | 0.0484615 | ||||||||
\(732\) | −23.4353 | −0.866195 | ||||||||
\(733\) | 19.6418 | 0.725485 | 0.362743 | − | 0.931889i | \(-0.381840\pi\) | ||||
0.362743 | + | 0.931889i | \(0.381840\pi\) | |||||||
\(734\) | 21.2032 | 0.782624 | ||||||||
\(735\) | 3.13360 | 0.115585 | ||||||||
\(736\) | −6.21615 | −0.229130 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 24.1722 | 0.889791 | ||||||||
\(739\) | −0.422833 | −0.0155542 | −0.00777709 | − | 0.999970i | \(-0.502476\pi\) | ||||
−0.00777709 | + | 0.999970i | \(0.502476\pi\) | |||||||
\(740\) | −10.4343 | −0.383574 | ||||||||
\(741\) | −12.4640 | −0.457877 | ||||||||
\(742\) | −10.2272 | −0.375454 | ||||||||
\(743\) | 8.69396 | 0.318950 | 0.159475 | − | 0.987202i | \(-0.449020\pi\) | ||||
0.159475 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(744\) | −16.7490 | −0.614049 | ||||||||
\(745\) | 17.6135 | 0.645307 | ||||||||
\(746\) | 34.6222 | 1.26761 | ||||||||
\(747\) | 2.97595 | 0.108884 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.3757 | −0.781053 | ||||||||
\(750\) | −18.7464 | −0.684523 | ||||||||
\(751\) | 16.7911 | 0.612715 | 0.306357 | − | 0.951917i | \(-0.400890\pi\) | ||||
0.306357 | + | 0.951917i | \(0.400890\pi\) | |||||||
\(752\) | −4.56638 | −0.166519 | ||||||||
\(753\) | 25.4045 | 0.925792 | ||||||||
\(754\) | 32.4796 | 1.18284 | ||||||||
\(755\) | 46.6380 | 1.69733 | ||||||||
\(756\) | −4.45228 | −0.161928 | ||||||||
\(757\) | 23.9419 | 0.870183 | 0.435091 | − | 0.900386i | \(-0.356716\pi\) | ||||
0.435091 | + | 0.900386i | \(0.356716\pi\) | |||||||
\(758\) | 18.9799 | 0.689382 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.62639 | −0.0952691 | ||||||||
\(761\) | 7.13012 | 0.258467 | 0.129233 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129233 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(762\) | 3.76718 | 0.136471 | ||||||||
\(763\) | −40.9916 | −1.48399 | ||||||||
\(764\) | −9.79138 | −0.354240 | ||||||||
\(765\) | −25.7814 | −0.932129 | ||||||||
\(766\) | 15.4258 | 0.557355 | ||||||||
\(767\) | 29.3987 | 1.06152 | ||||||||
\(768\) | 2.30094 | 0.0830279 | ||||||||
\(769\) | −9.77470 | −0.352485 | −0.176242 | − | 0.984347i | \(-0.556394\pi\) | ||||
−0.176242 | + | 0.984347i | \(0.556394\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7341 | −0.530637 | ||||||||
\(772\) | 8.40525 | 0.302512 | ||||||||
\(773\) | 6.37683 | 0.229359 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(774\) | −0.702608 | −0.0252547 | ||||||||
\(775\) | −13.8153 | −0.496259 | ||||||||
\(776\) | −10.0528 | −0.360876 | ||||||||
\(777\) | −25.0656 | −0.899224 | ||||||||
\(778\) | −18.1318 | −0.650055 | ||||||||
\(779\) | −10.5357 | −0.377480 | ||||||||
\(780\) | 32.7353 | 1.17211 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.5960 | 0.951073 | ||||||||
\(783\) | −9.73583 | −0.347930 | ||||||||
\(784\) | 0.518537 | 0.0185192 | ||||||||
\(785\) | 4.22373 | 0.150751 | ||||||||
\(786\) | −49.5026 | −1.76570 | ||||||||
\(787\) | 31.8703 | 1.13605 | 0.568027 | − | 0.823010i | \(-0.307707\pi\) | ||||
0.568027 | + | 0.823010i | \(0.307707\pi\) | |||||||
\(788\) | −3.91660 | −0.139523 | ||||||||
\(789\) | 9.81075 | 0.349272 | ||||||||
\(790\) | 31.2507 | 1.11185 | ||||||||
\(791\) | 2.93088 | 0.104210 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −55.1721 | −1.95922 | ||||||||
\(794\) | 9.44526 | 0.335200 | ||||||||
\(795\) | −22.5401 | −0.799414 | ||||||||
\(796\) | 0.808932 | 0.0286718 | ||||||||
\(797\) | 7.17570 | 0.254176 | 0.127088 | − | 0.991891i | \(-0.459437\pi\) | ||||
0.127088 | + | 0.991891i | \(0.459437\pi\) | |||||||
\(798\) | −6.30916 | −0.223342 | ||||||||
\(799\) | 19.5374 | 0.691185 | ||||||||
\(800\) | 1.89791 | 0.0671011 | ||||||||
\(801\) | −33.4955 | −1.18351 | ||||||||
\(802\) | 26.3735 | 0.931281 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.0340609 | −0.00120123 | ||||||||
\(805\) | −44.7659 | −1.57779 | ||||||||
\(806\) | −39.4310 | −1.38890 | ||||||||
\(807\) | −5.98976 | −0.210850 | ||||||||
\(808\) | 4.03837 | 0.142069 | ||||||||
\(809\) | 0.228395 | 0.00802993 | 0.00401496 | − | 0.999992i | \(-0.498722\pi\) | ||||
0.00401496 | + | 0.999992i | \(0.498722\pi\) | |||||||
\(810\) | −27.8898 | −0.979947 | ||||||||
\(811\) | 2.94450 | 0.103395 | 0.0516976 | − | 0.998663i | \(-0.483537\pi\) | ||||
0.0516976 | + | 0.998663i | \(0.483537\pi\) | |||||||
\(812\) | 16.4408 | 0.576960 | ||||||||
\(813\) | 21.9889 | 0.771184 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 56.9312 | 1.99421 | ||||||||
\(816\) | −9.84465 | −0.344632 | ||||||||
\(817\) | 0.306239 | 0.0107139 | ||||||||
\(818\) | −27.1570 | −0.949522 | ||||||||
\(819\) | 34.0779 | 1.19078 | ||||||||
\(820\) | 27.6708 | 0.966306 | ||||||||
\(821\) | −31.6730 | −1.10540 | −0.552698 | − | 0.833382i | \(-0.686402\pi\) | ||||
−0.552698 | + | 0.833382i | \(0.686402\pi\) | |||||||
\(822\) | 14.7263 | 0.513639 | ||||||||
\(823\) | −15.9174 | −0.554847 | −0.277424 | − | 0.960748i | \(-0.589481\pi\) | ||||
−0.277424 | + | 0.960748i | \(0.589481\pi\) | |||||||
\(824\) | 12.3140 | 0.428977 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.8813 | 0.517787 | ||||||||
\(827\) | 45.1869 | 1.57130 | 0.785650 | − | 0.618671i | \(-0.212328\pi\) | ||||
0.785650 | + | 0.618671i | \(0.212328\pi\) | |||||||
\(828\) | −14.2618 | −0.495632 | ||||||||
\(829\) | 7.99671 | 0.277737 | 0.138869 | − | 0.990311i | \(-0.455653\pi\) | ||||
0.138869 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(830\) | 3.40668 | 0.118248 | ||||||||
\(831\) | 21.8293 | 0.757251 | ||||||||
\(832\) | 5.41693 | 0.187798 | ||||||||
\(833\) | −2.21858 | −0.0768693 | ||||||||
\(834\) | −16.9759 | −0.587827 | ||||||||
\(835\) | 32.0632 | 1.10959 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.8195 | 0.408543 | ||||||||
\(838\) | 16.5473 | 0.571616 | ||||||||
\(839\) | −48.9847 | −1.69114 | −0.845570 | − | 0.533864i | \(-0.820739\pi\) | ||||
−0.845570 | + | 0.533864i | \(0.820739\pi\) | |||||||
\(840\) | 16.5703 | 0.571729 | ||||||||
\(841\) | 6.95128 | 0.239699 | ||||||||
\(842\) | −37.0039 | −1.27524 | ||||||||
\(843\) | −21.0756 | −0.725883 | ||||||||
\(844\) | 13.8172 | 0.475607 | ||||||||
\(845\) | 42.9233 | 1.47661 | ||||||||
\(846\) | −10.4767 | −0.360197 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.72986 | −0.128084 | ||||||||
\(849\) | 48.6835 | 1.67081 | ||||||||
\(850\) | −8.12026 | −0.278523 | ||||||||
\(851\) | 24.6961 | 0.846572 | ||||||||
\(852\) | 27.8583 | 0.954410 | ||||||||
\(853\) | 5.48357 | 0.187754 | 0.0938770 | − | 0.995584i | \(-0.470074\pi\) | ||||
0.0938770 | + | 0.995584i | \(0.470074\pi\) | |||||||
\(854\) | −27.9276 | −0.955662 | ||||||||
\(855\) | −6.02576 | −0.206077 | ||||||||
\(856\) | −7.79569 | −0.266451 | ||||||||
\(857\) | −47.1600 | −1.61096 | −0.805478 | − | 0.592626i | \(-0.798091\pi\) | ||||
−0.805478 | + | 0.592626i | \(0.798091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.3677 | 1.20673 | 0.603364 | − | 0.797466i | \(-0.293826\pi\) | ||||
0.603364 | + | 0.797466i | \(0.293826\pi\) | |||||||
\(860\) | −0.804301 | −0.0274264 | ||||||||
\(861\) | 66.4714 | 2.26534 | ||||||||
\(862\) | −11.7109 | −0.398876 | ||||||||
\(863\) | 20.0753 | 0.683370 | 0.341685 | − | 0.939815i | \(-0.389002\pi\) | ||||
0.341685 | + | 0.939815i | \(0.389002\pi\) | |||||||
\(864\) | −1.62374 | −0.0552407 | ||||||||
\(865\) | 30.3206 | 1.03093 | ||||||||
\(866\) | 2.12441 | 0.0721904 | ||||||||
\(867\) | 3.00475 | 0.102047 | ||||||||
\(868\) | −19.9596 | −0.677472 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 36.2344 | 1.22846 | ||||||||
\(871\) | −0.0801869 | −0.00271703 | ||||||||
\(872\) | −14.9495 | −0.506255 | ||||||||
\(873\) | −23.0644 | −0.780611 | ||||||||
\(874\) | 6.21615 | 0.210265 | ||||||||
\(875\) | −22.3399 | −0.755225 | ||||||||
\(876\) | −31.9058 | −1.07800 | ||||||||
\(877\) | 13.6785 | 0.461890 | 0.230945 | − | 0.972967i | \(-0.425818\pi\) | ||||
0.230945 | + | 0.972967i | \(0.425818\pi\) | |||||||
\(878\) | 17.7590 | 0.599337 | ||||||||
\(879\) | 50.8666 | 1.71569 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.3568 | −1.49442 | −0.747209 | − | 0.664590i | \(-0.768606\pi\) | ||||
−0.747209 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(882\) | 1.18969 | 0.0400589 | ||||||||
\(883\) | 24.4649 | 0.823308 | 0.411654 | − | 0.911340i | \(-0.364951\pi\) | ||||
0.411654 | + | 0.911340i | \(0.364951\pi\) | |||||||
\(884\) | −23.1765 | −0.779511 | ||||||||
\(885\) | 32.7973 | 1.10247 | ||||||||
\(886\) | 7.42988 | 0.249612 | ||||||||
\(887\) | 9.44528 | 0.317141 | 0.158571 | − | 0.987348i | \(-0.449311\pi\) | ||||
0.158571 | + | 0.987348i | \(0.449311\pi\) | |||||||
\(888\) | −9.14138 | −0.306765 | ||||||||
\(889\) | 4.48930 | 0.150566 | ||||||||
\(890\) | −38.3435 | −1.28528 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.06868 | 0.0357819 | ||||||||
\(893\) | 4.56638 | 0.152808 | ||||||||
\(894\) | 15.4309 | 0.516086 | ||||||||
\(895\) | −2.29877 | −0.0768395 | ||||||||
\(896\) | 2.74200 | 0.0916036 | ||||||||
\(897\) | −77.4782 | −2.58692 | ||||||||
\(898\) | −19.0848 | −0.636869 | ||||||||
\(899\) | −43.6458 | −1.45567 | ||||||||
\(900\) | 4.35439 | 0.145146 | ||||||||
\(901\) | 15.9583 | 0.531649 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.93211 | −0.0642965 | ||||||||
\(904\) | 1.06888 | 0.0355506 | ||||||||
\(905\) | 14.7257 | 0.489500 | ||||||||
\(906\) | 40.8589 | 1.35745 | ||||||||
\(907\) | −19.0258 | −0.631741 | −0.315870 | − | 0.948802i | \(-0.602296\pi\) | ||||
−0.315870 | + | 0.948802i | \(0.602296\pi\) | |||||||
\(908\) | −20.1639 | −0.669164 | ||||||||
\(909\) | 9.26529 | 0.307310 | ||||||||
\(910\) | 39.0102 | 1.29318 | ||||||||
\(911\) | −31.4552 | −1.04216 | −0.521079 | − | 0.853509i | \(-0.674470\pi\) | ||||
−0.521079 | + | 0.853509i | \(0.674470\pi\) | |||||||
\(912\) | −2.30094 | −0.0761917 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.89775 | −0.0958490 | ||||||||
\(915\) | −61.5503 | −2.03479 | ||||||||
\(916\) | 25.5481 | 0.844133 | ||||||||
\(917\) | −58.9916 | −1.94807 | ||||||||
\(918\) | 6.94722 | 0.229293 | ||||||||
\(919\) | 1.56648 | 0.0516734 | 0.0258367 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258367 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(920\) | −16.3260 | −0.538253 | ||||||||
\(921\) | 33.3933 | 1.10035 | ||||||||
\(922\) | −7.89943 | −0.260154 | ||||||||
\(923\) | 65.5847 | 2.15875 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.54018 | −0.247919 | ||||||||
\(926\) | 20.8107 | 0.683882 | ||||||||
\(927\) | 28.2521 | 0.927921 | ||||||||
\(928\) | 5.99594 | 0.196826 | ||||||||
\(929\) | −9.10446 | −0.298708 | −0.149354 | − | 0.988784i | \(-0.547719\pi\) | ||||
−0.149354 | + | 0.988784i | \(0.547719\pi\) | |||||||
\(930\) | −43.9894 | −1.44247 | ||||||||
\(931\) | −0.518537 | −0.0169944 | ||||||||
\(932\) | 11.3403 | 0.371464 | ||||||||
\(933\) | −67.2206 | −2.20071 | ||||||||
\(934\) | −31.5622 | −1.03275 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.4281 | 0.406226 | ||||||||
\(937\) | 11.1056 | 0.362805 | 0.181402 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181402 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(938\) | −0.0405898 | −0.00132531 | ||||||||
\(939\) | −62.3054 | −2.03326 | ||||||||
\(940\) | −11.9931 | −0.391171 | ||||||||
\(941\) | −34.2505 | −1.11654 | −0.558268 | − | 0.829661i | \(-0.688534\pi\) | ||||
−0.558268 | + | 0.829661i | \(0.688534\pi\) | |||||||
\(942\) | 3.70035 | 0.120564 | ||||||||
\(943\) | −65.4915 | −2.13270 | ||||||||
\(944\) | 5.42719 | 0.176640 | ||||||||
\(945\) | −11.6934 | −0.380387 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.0662 | 1.23699 | 0.618493 | − | 0.785791i | \(-0.287744\pi\) | ||||
0.618493 | + | 0.785791i | \(0.287744\pi\) | |||||||
\(948\) | 27.3782 | 0.889204 | ||||||||
\(949\) | −75.1134 | −2.43829 | ||||||||
\(950\) | −1.89791 | −0.0615762 | ||||||||
\(951\) | 62.7413 | 2.03453 | ||||||||
\(952\) | −11.7317 | −0.380227 | ||||||||
\(953\) | 14.8133 | 0.479848 | 0.239924 | − | 0.970792i | \(-0.422877\pi\) | ||||
0.239924 | + | 0.970792i | \(0.422877\pi\) | |||||||
\(954\) | −8.55746 | −0.277058 | ||||||||
\(955\) | −25.7160 | −0.832149 | ||||||||
\(956\) | −1.78866 | −0.0578495 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.7066 | 0.765926 | ||||||||
\(959\) | 17.5491 | 0.566691 | ||||||||
\(960\) | 6.04315 | 0.195042 | ||||||||
\(961\) | 21.9870 | 0.709259 | ||||||||
\(962\) | −21.5209 | −0.693861 | ||||||||
\(963\) | −17.8858 | −0.576361 | ||||||||
\(964\) | −19.8713 | −0.640011 | ||||||||
\(965\) | 22.0754 | 0.710633 | ||||||||
\(966\) | −39.2187 | −1.26184 | ||||||||
\(967\) | 33.3782 | 1.07337 | 0.536684 | − | 0.843783i | \(-0.319677\pi\) | ||||
0.536684 | + | 0.843783i | \(0.319677\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.84465 | 0.316256 | ||||||||
\(970\) | −26.4027 | −0.847738 | ||||||||
\(971\) | 43.0686 | 1.38214 | 0.691069 | − | 0.722789i | \(-0.257140\pi\) | ||||
0.691069 | + | 0.722789i | \(0.257140\pi\) | |||||||
\(972\) | −19.5626 | −0.627470 | ||||||||
\(973\) | −20.2299 | −0.648541 | ||||||||
\(974\) | −24.6716 | −0.790528 | ||||||||
\(975\) | 23.6555 | 0.757583 | ||||||||
\(976\) | −10.1851 | −0.326018 | ||||||||
\(977\) | −29.7229 | −0.950919 | −0.475459 | − | 0.879738i | \(-0.657718\pi\) | ||||
−0.475459 | + | 0.879738i | \(0.657718\pi\) | |||||||
\(978\) | 49.8766 | 1.59488 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.36188 | 0.0435036 | ||||||||
\(981\) | −34.2990 | −1.09508 | ||||||||
\(982\) | 34.1976 | 1.09129 | ||||||||
\(983\) | 21.5927 | 0.688699 | 0.344349 | − | 0.938842i | \(-0.388100\pi\) | ||||
0.344349 | + | 0.938842i | \(0.388100\pi\) | |||||||
\(984\) | 24.2420 | 0.772806 | ||||||||
\(985\) | −10.2865 | −0.327755 | ||||||||
\(986\) | −25.6538 | −0.816985 | ||||||||
\(987\) | −28.8100 | −0.917033 | ||||||||
\(988\) | −5.41693 | −0.172335 | ||||||||
\(989\) | 1.90363 | 0.0605318 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9486 | −0.728987 | −0.364494 | − | 0.931206i | \(-0.618758\pi\) | ||||
−0.364494 | + | 0.931206i | \(0.618758\pi\) | |||||||
\(992\) | −7.27922 | −0.231115 | ||||||||
\(993\) | 37.0453 | 1.17560 | ||||||||
\(994\) | 33.1983 | 1.05299 | ||||||||
\(995\) | 2.12457 | 0.0673534 | ||||||||
\(996\) | 2.98454 | 0.0945689 | ||||||||
\(997\) | −41.3888 | −1.31080 | −0.655399 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655399 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(998\) | 23.0706 | 0.730286 | ||||||||
\(999\) | 6.45094 | 0.204099 |
(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 | 4598.2.a.ca.1.7 | 8 | ||
11.3 | even | 5 | 418.2.f.f.229.1 | yes | 16 | ||
11.4 | even | 5 | 418.2.f.f.115.1 | ✓ | 16 | ||
11.10 | odd | 2 | 4598.2.a.bx.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.f.115.1 | ✓ | 16 | 11.4 | even | 5 | ||
418.2.f.f.229.1 | yes | 16 | 11.3 | even | 5 | ||
4598.2.a.bx.1.7 | 8 | 11.10 | odd | 2 | |||
4598.2.a.ca.1.7 | 8 | 1.1 | even | 1 | trivial |