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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.698857\) 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 | ||||||||
\(3\) | 1.43091 | 0.826135 | 0.413068 | − | 0.910700i | \(-0.364457\pi\) | ||||
0.413068 | + | 0.910700i | \(0.364457\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.301143 | −0.134675 | −0.0673376 | − | 0.997730i | \(-0.521450\pi\) | ||||
−0.0673376 | + | 0.997730i | \(0.521450\pi\) | |||||||
\(6\) | −1.43091 | −0.584166 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.952503 | −0.317501 | ||||||||
\(10\) | 0.301143 | 0.0952298 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.43091 | 0.413068 | ||||||||
\(13\) | 1.39771 | 0.387656 | 0.193828 | − | 0.981036i | \(-0.437910\pi\) | ||||
0.193828 | + | 0.981036i | \(0.437910\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.430908 | −0.111260 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.90931 | 0.948148 | 0.474074 | − | 0.880485i | \(-0.342783\pi\) | ||||
0.474074 | + | 0.880485i | \(0.342783\pi\) | |||||||
\(18\) | 0.952503 | 0.224507 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.301143 | −0.0673376 | ||||||||
\(21\) | 1.43091 | 0.312250 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.57498 | −0.745434 | −0.372717 | − | 0.927945i | \(-0.621574\pi\) | ||||
−0.372717 | + | 0.927945i | \(0.621574\pi\) | |||||||
\(24\) | −1.43091 | −0.292083 | ||||||||
\(25\) | −4.90931 | −0.981863 | ||||||||
\(26\) | −1.39771 | −0.274114 | ||||||||
\(27\) | −5.65567 | −1.08843 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.635480 | 0.118006 | 0.0590028 | − | 0.998258i | \(-0.481208\pi\) | ||||
0.0590028 | + | 0.998258i | \(0.481208\pi\) | |||||||
\(30\) | 0.430908 | 0.0786726 | ||||||||
\(31\) | −8.90089 | −1.59865 | −0.799324 | − | 0.600901i | \(-0.794809\pi\) | ||||
−0.799324 | + | 0.600901i | \(0.794809\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.90931 | −0.670442 | ||||||||
\(35\) | −0.301143 | −0.0509025 | ||||||||
\(36\) | −0.952503 | −0.158750 | ||||||||
\(37\) | −0.187258 | −0.0307851 | −0.0153925 | − | 0.999882i | \(-0.504900\pi\) | ||||
−0.0153925 | + | 0.999882i | \(0.504900\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0.301143 | 0.0476149 | ||||||||
\(41\) | −8.02908 | −1.25393 | −0.626966 | − | 0.779047i | \(-0.715703\pi\) | ||||
−0.626966 | + | 0.779047i | \(0.715703\pi\) | |||||||
\(42\) | −1.43091 | −0.220794 | ||||||||
\(43\) | 0.641364 | 0.0978071 | 0.0489035 | − | 0.998804i | \(-0.484427\pi\) | ||||
0.0489035 | + | 0.998804i | \(0.484427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.286840 | 0.0427595 | ||||||||
\(46\) | 3.57498 | 0.527101 | ||||||||
\(47\) | −7.55068 | −1.10138 | −0.550690 | − | 0.834710i | \(-0.685635\pi\) | ||||
−0.550690 | + | 0.834710i | \(0.685635\pi\) | |||||||
\(48\) | 1.43091 | 0.206534 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 4.90931 | 0.694282 | ||||||||
\(51\) | 5.59387 | 0.783298 | ||||||||
\(52\) | 1.39771 | 0.193828 | ||||||||
\(53\) | −0.919309 | −0.126277 | −0.0631384 | − | 0.998005i | \(-0.520111\pi\) | ||||
−0.0631384 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(54\) | 5.65567 | 0.769639 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −1.43091 | −0.189528 | ||||||||
\(58\) | −0.635480 | −0.0834426 | ||||||||
\(59\) | 0.502705 | 0.0654466 | 0.0327233 | − | 0.999464i | \(-0.489582\pi\) | ||||
0.0327233 | + | 0.999464i | \(0.489582\pi\) | |||||||
\(60\) | −0.430908 | −0.0556300 | ||||||||
\(61\) | 1.41072 | 0.180624 | 0.0903121 | − | 0.995914i | \(-0.471214\pi\) | ||||
0.0903121 | + | 0.995914i | \(0.471214\pi\) | |||||||
\(62\) | 8.90089 | 1.13041 | ||||||||
\(63\) | −0.952503 | −0.120004 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.420912 | −0.0522077 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.14454 | 0.995014 | 0.497507 | − | 0.867460i | \(-0.334249\pi\) | ||||
0.497507 | + | 0.867460i | \(0.334249\pi\) | |||||||
\(68\) | 3.90931 | 0.474074 | ||||||||
\(69\) | −5.11546 | −0.615829 | ||||||||
\(70\) | 0.301143 | 0.0359935 | ||||||||
\(71\) | 7.20634 | 0.855236 | 0.427618 | − | 0.903960i | \(-0.359353\pi\) | ||||
0.427618 | + | 0.903960i | \(0.359353\pi\) | |||||||
\(72\) | 0.952503 | 0.112254 | ||||||||
\(73\) | −4.86612 | −0.569537 | −0.284768 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284768 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(74\) | 0.187258 | 0.0217683 | ||||||||
\(75\) | −7.02477 | −0.811151 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −5.73363 | −0.645083 | −0.322542 | − | 0.946555i | \(-0.604537\pi\) | ||||
−0.322542 | + | 0.946555i | \(0.604537\pi\) | |||||||
\(80\) | −0.301143 | −0.0336688 | ||||||||
\(81\) | −5.23523 | −0.581692 | ||||||||
\(82\) | 8.02908 | 0.886664 | ||||||||
\(83\) | 14.9152 | 1.63716 | 0.818578 | − | 0.574396i | \(-0.194763\pi\) | ||||
0.818578 | + | 0.574396i | \(0.194763\pi\) | |||||||
\(84\) | 1.43091 | 0.156125 | ||||||||
\(85\) | −1.17726 | −0.127692 | ||||||||
\(86\) | −0.641364 | −0.0691600 | ||||||||
\(87\) | 0.909313 | 0.0974886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.76955 | 0.399572 | 0.199786 | − | 0.979840i | \(-0.435975\pi\) | ||||
0.199786 | + | 0.979840i | \(0.435975\pi\) | |||||||
\(90\) | −0.286840 | −0.0302355 | ||||||||
\(91\) | 1.39771 | 0.146520 | ||||||||
\(92\) | −3.57498 | −0.372717 | ||||||||
\(93\) | −12.7364 | −1.32070 | ||||||||
\(94\) | 7.55068 | 0.778793 | ||||||||
\(95\) | 0.301143 | 0.0308966 | ||||||||
\(96\) | −1.43091 | −0.146041 | ||||||||
\(97\) | −1.58641 | −0.161075 | −0.0805376 | − | 0.996752i | \(-0.525664\pi\) | ||||
−0.0805376 | + | 0.996752i | \(0.525664\pi\) | |||||||
\(98\) | 6.00000 | 0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.90931 | −0.490931 | ||||||||
\(101\) | −6.84751 | −0.681353 | −0.340676 | − | 0.940181i | \(-0.610656\pi\) | ||||
−0.340676 | + | 0.940181i | \(0.610656\pi\) | |||||||
\(102\) | −5.59387 | −0.553875 | ||||||||
\(103\) | 5.20634 | 0.512996 | 0.256498 | − | 0.966545i | \(-0.417431\pi\) | ||||
0.256498 | + | 0.966545i | \(0.417431\pi\) | |||||||
\(104\) | −1.39771 | −0.137057 | ||||||||
\(105\) | −0.430908 | −0.0420523 | ||||||||
\(106\) | 0.919309 | 0.0892912 | ||||||||
\(107\) | 7.67997 | 0.742450 | 0.371225 | − | 0.928543i | \(-0.378938\pi\) | ||||
0.371225 | + | 0.928543i | \(0.378938\pi\) | |||||||
\(108\) | −5.65567 | −0.544217 | ||||||||
\(109\) | −11.1198 | −1.06508 | −0.532540 | − | 0.846405i | \(-0.678763\pi\) | ||||
−0.532540 | + | 0.846405i | \(0.678763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.267949 | −0.0254326 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −7.33180 | −0.689718 | −0.344859 | − | 0.938655i | \(-0.612073\pi\) | ||||
−0.344859 | + | 0.938655i | \(0.612073\pi\) | |||||||
\(114\) | 1.43091 | 0.134017 | ||||||||
\(115\) | 1.07658 | 0.100392 | ||||||||
\(116\) | 0.635480 | 0.0590028 | ||||||||
\(117\) | −1.33133 | −0.123081 | ||||||||
\(118\) | −0.502705 | −0.0462777 | ||||||||
\(119\) | 3.90931 | 0.358366 | ||||||||
\(120\) | 0.430908 | 0.0393363 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.41072 | −0.127721 | ||||||||
\(123\) | −11.4889 | −1.03592 | ||||||||
\(124\) | −8.90089 | −0.799324 | ||||||||
\(125\) | 2.98412 | 0.266908 | ||||||||
\(126\) | 0.952503 | 0.0848557 | ||||||||
\(127\) | −4.07816 | −0.361878 | −0.180939 | − | 0.983494i | \(-0.557914\pi\) | ||||
−0.180939 | + | 0.983494i | \(0.557914\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.917732 | 0.0808018 | ||||||||
\(130\) | 0.420912 | 0.0369164 | ||||||||
\(131\) | −6.73636 | −0.588558 | −0.294279 | − | 0.955720i | \(-0.595080\pi\) | ||||
−0.294279 | + | 0.955720i | \(0.595080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | −8.14454 | −0.703581 | ||||||||
\(135\) | 1.70316 | 0.146585 | ||||||||
\(136\) | −3.90931 | −0.335221 | ||||||||
\(137\) | −21.0107 | −1.79506 | −0.897531 | − | 0.440951i | \(-0.854641\pi\) | ||||
−0.897531 | + | 0.440951i | \(0.854641\pi\) | |||||||
\(138\) | 5.11546 | 0.435457 | ||||||||
\(139\) | −1.30272 | −0.110495 | −0.0552476 | − | 0.998473i | \(-0.517595\pi\) | ||||
−0.0552476 | + | 0.998473i | \(0.517595\pi\) | |||||||
\(140\) | −0.301143 | −0.0254512 | ||||||||
\(141\) | −10.8043 | −0.909888 | ||||||||
\(142\) | −7.20634 | −0.604743 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.952503 | −0.0793752 | ||||||||
\(145\) | −0.191370 | −0.0158924 | ||||||||
\(146\) | 4.86612 | 0.402723 | ||||||||
\(147\) | −8.58545 | −0.708116 | ||||||||
\(148\) | −0.187258 | −0.0153925 | ||||||||
\(149\) | 15.9514 | 1.30679 | 0.653395 | − | 0.757017i | \(-0.273344\pi\) | ||||
0.653395 | + | 0.757017i | \(0.273344\pi\) | |||||||
\(150\) | 7.02477 | 0.573570 | ||||||||
\(151\) | −0.910890 | −0.0741271 | −0.0370636 | − | 0.999313i | \(-0.511800\pi\) | ||||
−0.0370636 | + | 0.999313i | \(0.511800\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −3.72363 | −0.301038 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.68044 | 0.215298 | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 14.4848 | 1.15601 | 0.578005 | − | 0.816033i | \(-0.303831\pi\) | ||||
0.578005 | + | 0.816033i | \(0.303831\pi\) | |||||||
\(158\) | 5.73363 | 0.456143 | ||||||||
\(159\) | −1.31545 | −0.104322 | ||||||||
\(160\) | 0.301143 | 0.0238074 | ||||||||
\(161\) | −3.57498 | −0.281748 | ||||||||
\(162\) | 5.23523 | 0.411319 | ||||||||
\(163\) | −14.7364 | −1.15424 | −0.577120 | − | 0.816659i | \(-0.695824\pi\) | ||||
−0.577120 | + | 0.816659i | \(0.695824\pi\) | |||||||
\(164\) | −8.02908 | −0.626966 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9152 | −1.15764 | ||||||||
\(167\) | −16.4978 | −1.27664 | −0.638318 | − | 0.769773i | \(-0.720369\pi\) | ||||
−0.638318 | + | 0.769773i | \(0.720369\pi\) | |||||||
\(168\) | −1.43091 | −0.110397 | ||||||||
\(169\) | −11.0464 | −0.849723 | ||||||||
\(170\) | 1.17726 | 0.0902919 | ||||||||
\(171\) | 0.952503 | 0.0728397 | ||||||||
\(172\) | 0.641364 | 0.0489035 | ||||||||
\(173\) | 5.07638 | 0.385950 | 0.192975 | − | 0.981204i | \(-0.438186\pi\) | ||||
0.192975 | + | 0.981204i | \(0.438186\pi\) | |||||||
\(174\) | −0.909313 | −0.0689348 | ||||||||
\(175\) | −4.90931 | −0.371109 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.719324 | 0.0540677 | ||||||||
\(178\) | −3.76955 | −0.282540 | ||||||||
\(179\) | 4.26111 | 0.318490 | 0.159245 | − | 0.987239i | \(-0.449094\pi\) | ||||
0.159245 | + | 0.987239i | \(0.449094\pi\) | |||||||
\(180\) | 0.286840 | 0.0213798 | ||||||||
\(181\) | −11.2827 | −0.838639 | −0.419319 | − | 0.907839i | \(-0.637731\pi\) | ||||
−0.419319 | + | 0.907839i | \(0.637731\pi\) | |||||||
\(182\) | −1.39771 | −0.103605 | ||||||||
\(183\) | 2.01861 | 0.149220 | ||||||||
\(184\) | 3.57498 | 0.263551 | ||||||||
\(185\) | 0.0563915 | 0.00414598 | ||||||||
\(186\) | 12.7364 | 0.933875 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.55068 | −0.550690 | ||||||||
\(189\) | −5.65567 | −0.411389 | ||||||||
\(190\) | −0.301143 | −0.0218472 | ||||||||
\(191\) | −0.495719 | −0.0358690 | −0.0179345 | − | 0.999839i | \(-0.505709\pi\) | ||||
−0.0179345 | + | 0.999839i | \(0.505709\pi\) | |||||||
\(192\) | 1.43091 | 0.103267 | ||||||||
\(193\) | 19.3018 | 1.38937 | 0.694687 | − | 0.719312i | \(-0.255543\pi\) | ||||
0.694687 | + | 0.719312i | \(0.255543\pi\) | |||||||
\(194\) | 1.58641 | 0.113897 | ||||||||
\(195\) | −0.602286 | −0.0431306 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 22.9591 | 1.63577 | 0.817883 | − | 0.575385i | \(-0.195148\pi\) | ||||
0.817883 | + | 0.575385i | \(0.195148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.5611 | −1.74109 | −0.870547 | − | 0.492086i | \(-0.836235\pi\) | ||||
−0.870547 | + | 0.492086i | \(0.836235\pi\) | |||||||
\(200\) | 4.90931 | 0.347141 | ||||||||
\(201\) | 11.6541 | 0.822016 | ||||||||
\(202\) | 6.84751 | 0.481789 | ||||||||
\(203\) | 0.635480 | 0.0446019 | ||||||||
\(204\) | 5.59387 | 0.391649 | ||||||||
\(205\) | 2.41790 | 0.168874 | ||||||||
\(206\) | −5.20634 | −0.362743 | ||||||||
\(207\) | 3.40517 | 0.236676 | ||||||||
\(208\) | 1.39771 | 0.0969140 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.430908 | 0.0297355 | ||||||||
\(211\) | −13.0321 | −0.897166 | −0.448583 | − | 0.893741i | \(-0.648071\pi\) | ||||
−0.448583 | + | 0.893741i | \(0.648071\pi\) | |||||||
\(212\) | −0.919309 | −0.0631384 | ||||||||
\(213\) | 10.3116 | 0.706540 | ||||||||
\(214\) | −7.67997 | −0.524992 | ||||||||
\(215\) | −0.193142 | −0.0131722 | ||||||||
\(216\) | 5.65567 | 0.384819 | ||||||||
\(217\) | −8.90089 | −0.604232 | ||||||||
\(218\) | 11.1198 | 0.753126 | ||||||||
\(219\) | −6.96297 | −0.470514 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.46410 | 0.367555 | ||||||||
\(222\) | 0.267949 | 0.0179836 | ||||||||
\(223\) | −7.01450 | −0.469726 | −0.234863 | − | 0.972029i | \(-0.575464\pi\) | ||||
−0.234863 | + | 0.972029i | \(0.575464\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.67613 | 0.311742 | ||||||||
\(226\) | 7.33180 | 0.487704 | ||||||||
\(227\) | −2.63089 | −0.174618 | −0.0873092 | − | 0.996181i | \(-0.527827\pi\) | ||||
−0.0873092 | + | 0.996181i | \(0.527827\pi\) | |||||||
\(228\) | −1.43091 | −0.0947642 | ||||||||
\(229\) | −4.43961 | −0.293377 | −0.146689 | − | 0.989183i | \(-0.546862\pi\) | ||||
−0.146689 | + | 0.989183i | \(0.546862\pi\) | |||||||
\(230\) | −1.07658 | −0.0709875 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.635480 | −0.0417213 | ||||||||
\(233\) | −15.4482 | −1.01205 | −0.506023 | − | 0.862520i | \(-0.668885\pi\) | ||||
−0.506023 | + | 0.862520i | \(0.668885\pi\) | |||||||
\(234\) | 1.33133 | 0.0870315 | ||||||||
\(235\) | 2.27383 | 0.148329 | ||||||||
\(236\) | 0.502705 | 0.0327233 | ||||||||
\(237\) | −8.20429 | −0.532926 | ||||||||
\(238\) | −3.90931 | −0.253403 | ||||||||
\(239\) | −13.1489 | −0.850528 | −0.425264 | − | 0.905069i | \(-0.639819\pi\) | ||||
−0.425264 | + | 0.905069i | \(0.639819\pi\) | |||||||
\(240\) | −0.430908 | −0.0278150 | ||||||||
\(241\) | −16.1545 | −1.04061 | −0.520303 | − | 0.853982i | \(-0.674181\pi\) | ||||
−0.520303 | + | 0.853982i | \(0.674181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.47587 | 0.607877 | ||||||||
\(244\) | 1.41072 | 0.0903121 | ||||||||
\(245\) | 1.80686 | 0.115436 | ||||||||
\(246\) | 11.4889 | 0.732504 | ||||||||
\(247\) | −1.39771 | −0.0889344 | ||||||||
\(248\) | 8.90089 | 0.565207 | ||||||||
\(249\) | 21.3423 | 1.35251 | ||||||||
\(250\) | −2.98412 | −0.188732 | ||||||||
\(251\) | 4.74683 | 0.299617 | 0.149809 | − | 0.988715i | \(-0.452134\pi\) | ||||
0.149809 | + | 0.988715i | \(0.452134\pi\) | |||||||
\(252\) | −0.952503 | −0.0600020 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.07816 | 0.255886 | ||||||||
\(255\) | −1.68455 | −0.105491 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6804 | 1.29001 | 0.645005 | − | 0.764178i | \(-0.276855\pi\) | ||||
0.645005 | + | 0.764178i | \(0.276855\pi\) | |||||||
\(258\) | −0.917732 | −0.0571355 | ||||||||
\(259\) | −0.187258 | −0.0116357 | ||||||||
\(260\) | −0.420912 | −0.0261038 | ||||||||
\(261\) | −0.605296 | −0.0374669 | ||||||||
\(262\) | 6.73636 | 0.416174 | ||||||||
\(263\) | −16.2184 | −1.00007 | −0.500034 | − | 0.866006i | \(-0.666679\pi\) | ||||
−0.500034 | + | 0.866006i | \(0.666679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.276843 | 0.0170064 | ||||||||
\(266\) | 1.00000 | 0.0613139 | ||||||||
\(267\) | 5.39388 | 0.330100 | ||||||||
\(268\) | 8.14454 | 0.497507 | ||||||||
\(269\) | −1.93074 | −0.117719 | −0.0588596 | − | 0.998266i | \(-0.518746\pi\) | ||||
−0.0588596 | + | 0.998266i | \(0.518746\pi\) | |||||||
\(270\) | −1.70316 | −0.103651 | ||||||||
\(271\) | −4.51475 | −0.274252 | −0.137126 | − | 0.990554i | \(-0.543786\pi\) | ||||
−0.137126 | + | 0.990554i | \(0.543786\pi\) | |||||||
\(272\) | 3.90931 | 0.237037 | ||||||||
\(273\) | 2.00000 | 0.121046 | ||||||||
\(274\) | 21.0107 | 1.26930 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.11546 | −0.307915 | ||||||||
\(277\) | −12.6071 | −0.757485 | −0.378743 | − | 0.925502i | \(-0.623643\pi\) | ||||
−0.378743 | + | 0.925502i | \(0.623643\pi\) | |||||||
\(278\) | 1.30272 | 0.0781319 | ||||||||
\(279\) | 8.47813 | 0.507572 | ||||||||
\(280\) | 0.301143 | 0.0179967 | ||||||||
\(281\) | 13.3200 | 0.794607 | 0.397303 | − | 0.917687i | \(-0.369946\pi\) | ||||
0.397303 | + | 0.917687i | \(0.369946\pi\) | |||||||
\(282\) | 10.8043 | 0.643388 | ||||||||
\(283\) | 24.5772 | 1.46096 | 0.730482 | − | 0.682932i | \(-0.239295\pi\) | ||||
0.730482 | + | 0.682932i | \(0.239295\pi\) | |||||||
\(284\) | 7.20634 | 0.427618 | ||||||||
\(285\) | 0.430908 | 0.0255248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.02908 | −0.473942 | ||||||||
\(288\) | 0.952503 | 0.0561268 | ||||||||
\(289\) | −1.71727 | −0.101016 | ||||||||
\(290\) | 0.191370 | 0.0112376 | ||||||||
\(291\) | −2.27000 | −0.133070 | ||||||||
\(292\) | −4.86612 | −0.284768 | ||||||||
\(293\) | −6.95839 | −0.406513 | −0.203257 | − | 0.979125i | \(-0.565153\pi\) | ||||
−0.203257 | + | 0.979125i | \(0.565153\pi\) | |||||||
\(294\) | 8.58545 | 0.500713 | ||||||||
\(295\) | −0.151386 | −0.00881403 | ||||||||
\(296\) | 0.187258 | 0.0108842 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.9514 | −0.924040 | ||||||||
\(299\) | −4.99679 | −0.288972 | ||||||||
\(300\) | −7.02477 | −0.405576 | ||||||||
\(301\) | 0.641364 | 0.0369676 | ||||||||
\(302\) | 0.910890 | 0.0524158 | ||||||||
\(303\) | −9.79816 | −0.562890 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.424829 | −0.0243256 | ||||||||
\(306\) | 3.72363 | 0.212866 | ||||||||
\(307\) | 11.0608 | 0.631276 | 0.315638 | − | 0.948880i | \(-0.397782\pi\) | ||||
0.315638 | + | 0.948880i | \(0.397782\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.44980 | 0.423804 | ||||||||
\(310\) | −2.68044 | −0.152239 | ||||||||
\(311\) | 25.7857 | 1.46217 | 0.731087 | − | 0.682284i | \(-0.239013\pi\) | ||||
0.731087 | + | 0.682284i | \(0.239013\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | −17.3016 | −0.977945 | −0.488973 | − | 0.872299i | \(-0.662628\pi\) | ||||
−0.488973 | + | 0.872299i | \(0.662628\pi\) | |||||||
\(314\) | −14.4848 | −0.817423 | ||||||||
\(315\) | 0.286840 | 0.0161616 | ||||||||
\(316\) | −5.73363 | −0.322542 | ||||||||
\(317\) | −11.8272 | −0.664284 | −0.332142 | − | 0.943229i | \(-0.607771\pi\) | ||||
−0.332142 | + | 0.943229i | \(0.607771\pi\) | |||||||
\(318\) | 1.31545 | 0.0737666 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.301143 | −0.0168344 | ||||||||
\(321\) | 10.9893 | 0.613364 | ||||||||
\(322\) | 3.57498 | 0.199226 | ||||||||
\(323\) | −3.90931 | −0.217520 | ||||||||
\(324\) | −5.23523 | −0.290846 | ||||||||
\(325\) | −6.86182 | −0.380625 | ||||||||
\(326\) | 14.7364 | 0.816171 | ||||||||
\(327\) | −15.9114 | −0.879900 | ||||||||
\(328\) | 8.02908 | 0.443332 | ||||||||
\(329\) | −7.55068 | −0.416282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.1398 | −1.16195 | −0.580973 | − | 0.813923i | \(-0.697328\pi\) | ||||
−0.580973 | + | 0.813923i | \(0.697328\pi\) | |||||||
\(332\) | 14.9152 | 0.818578 | ||||||||
\(333\) | 0.178364 | 0.00977428 | ||||||||
\(334\) | 16.4978 | 0.902718 | ||||||||
\(335\) | −2.45267 | −0.134004 | ||||||||
\(336\) | 1.43091 | 0.0780624 | ||||||||
\(337\) | 3.64725 | 0.198678 | 0.0993391 | − | 0.995054i | \(-0.468327\pi\) | ||||
0.0993391 | + | 0.995054i | \(0.468327\pi\) | |||||||
\(338\) | 11.0464 | 0.600845 | ||||||||
\(339\) | −10.4911 | −0.569800 | ||||||||
\(340\) | −1.17726 | −0.0638460 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.952503 | −0.0515055 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −0.641364 | −0.0345800 | ||||||||
\(345\) | 1.54049 | 0.0829369 | ||||||||
\(346\) | −5.07638 | −0.272908 | ||||||||
\(347\) | 5.70933 | 0.306493 | 0.153246 | − | 0.988188i | \(-0.451027\pi\) | ||||
0.153246 | + | 0.988188i | \(0.451027\pi\) | |||||||
\(348\) | 0.909313 | 0.0487443 | ||||||||
\(349\) | 7.82910 | 0.419082 | 0.209541 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209541 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(350\) | 4.90931 | 0.262414 | ||||||||
\(351\) | −7.90501 | −0.421938 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.13708 | 0.166970 | 0.0834850 | − | 0.996509i | \(-0.473395\pi\) | ||||
0.0834850 | + | 0.996509i | \(0.473395\pi\) | |||||||
\(354\) | −0.719324 | −0.0382316 | ||||||||
\(355\) | −2.17014 | −0.115179 | ||||||||
\(356\) | 3.76955 | 0.199786 | ||||||||
\(357\) | 5.59387 | 0.296059 | ||||||||
\(358\) | −4.26111 | −0.225206 | ||||||||
\(359\) | −9.10566 | −0.480578 | −0.240289 | − | 0.970701i | \(-0.577242\pi\) | ||||
−0.240289 | + | 0.970701i | \(0.577242\pi\) | |||||||
\(360\) | −0.286840 | −0.0151178 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 11.2827 | 0.593007 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.39771 | 0.0732601 | ||||||||
\(365\) | 1.46540 | 0.0767025 | ||||||||
\(366\) | −2.01861 | −0.105514 | ||||||||
\(367\) | 1.30291 | 0.0680116 | 0.0340058 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340058 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(368\) | −3.57498 | −0.186359 | ||||||||
\(369\) | 7.64772 | 0.398125 | ||||||||
\(370\) | −0.0563915 | −0.00293165 | ||||||||
\(371\) | −0.919309 | −0.0477281 | ||||||||
\(372\) | −12.7364 | −0.660349 | ||||||||
\(373\) | −0.845461 | −0.0437763 | −0.0218882 | − | 0.999760i | \(-0.506968\pi\) | ||||
−0.0218882 | + | 0.999760i | \(0.506968\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.27000 | 0.220502 | ||||||||
\(376\) | 7.55068 | 0.389396 | ||||||||
\(377\) | 0.888219 | 0.0457456 | ||||||||
\(378\) | 5.65567 | 0.290896 | ||||||||
\(379\) | −16.4689 | −0.845950 | −0.422975 | − | 0.906141i | \(-0.639014\pi\) | ||||
−0.422975 | + | 0.906141i | \(0.639014\pi\) | |||||||
\(380\) | 0.301143 | 0.0154483 | ||||||||
\(381\) | −5.83546 | −0.298960 | ||||||||
\(382\) | 0.495719 | 0.0253632 | ||||||||
\(383\) | 14.8014 | 0.756319 | 0.378159 | − | 0.925741i | \(-0.376557\pi\) | ||||
0.378159 | + | 0.925741i | \(0.376557\pi\) | |||||||
\(384\) | −1.43091 | −0.0730207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.3018 | −0.982436 | ||||||||
\(387\) | −0.610901 | −0.0310538 | ||||||||
\(388\) | −1.58641 | −0.0805376 | ||||||||
\(389\) | −3.91931 | −0.198717 | −0.0993584 | − | 0.995052i | \(-0.531679\pi\) | ||||
−0.0993584 | + | 0.995052i | \(0.531679\pi\) | |||||||
\(390\) | 0.602286 | 0.0304979 | ||||||||
\(391\) | −13.9757 | −0.706782 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | −9.63911 | −0.486229 | ||||||||
\(394\) | −22.9591 | −1.15666 | ||||||||
\(395\) | 1.72664 | 0.0868768 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.9082 | 0.647845 | 0.323922 | − | 0.946084i | \(-0.394998\pi\) | ||||
0.323922 | + | 0.946084i | \(0.394998\pi\) | |||||||
\(398\) | 24.5611 | 1.23114 | ||||||||
\(399\) | −1.43091 | −0.0716350 | ||||||||
\(400\) | −4.90931 | −0.245466 | ||||||||
\(401\) | −2.53413 | −0.126548 | −0.0632741 | − | 0.997996i | \(-0.520154\pi\) | ||||
−0.0632741 | + | 0.997996i | \(0.520154\pi\) | |||||||
\(402\) | −11.6541 | −0.581253 | ||||||||
\(403\) | −12.4409 | −0.619726 | ||||||||
\(404\) | −6.84751 | −0.340676 | ||||||||
\(405\) | 1.57655 | 0.0783395 | ||||||||
\(406\) | −0.635480 | −0.0315383 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.59387 | −0.276938 | ||||||||
\(409\) | −28.3472 | −1.40168 | −0.700841 | − | 0.713318i | \(-0.747192\pi\) | ||||
−0.700841 | + | 0.713318i | \(0.747192\pi\) | |||||||
\(410\) | −2.41790 | −0.119412 | ||||||||
\(411\) | −30.0643 | −1.48296 | ||||||||
\(412\) | 5.20634 | 0.256498 | ||||||||
\(413\) | 0.502705 | 0.0247365 | ||||||||
\(414\) | −3.40517 | −0.167355 | ||||||||
\(415\) | −4.49161 | −0.220484 | ||||||||
\(416\) | −1.39771 | −0.0685286 | ||||||||
\(417\) | −1.86407 | −0.0912840 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.82561 | −0.0891870 | −0.0445935 | − | 0.999005i | \(-0.514199\pi\) | ||||
−0.0445935 | + | 0.999005i | \(0.514199\pi\) | |||||||
\(420\) | −0.430908 | −0.0210261 | ||||||||
\(421\) | 24.0238 | 1.17085 | 0.585425 | − | 0.810727i | \(-0.300928\pi\) | ||||
0.585425 | + | 0.810727i | \(0.300928\pi\) | |||||||
\(422\) | 13.0321 | 0.634392 | ||||||||
\(423\) | 7.19204 | 0.349689 | ||||||||
\(424\) | 0.919309 | 0.0446456 | ||||||||
\(425\) | −19.1920 | −0.930951 | ||||||||
\(426\) | −10.3116 | −0.499599 | ||||||||
\(427\) | 1.41072 | 0.0682695 | ||||||||
\(428\) | 7.67997 | 0.371225 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.193142 | 0.00931414 | ||||||||
\(431\) | −21.4490 | −1.03316 | −0.516582 | − | 0.856238i | \(-0.672796\pi\) | ||||
−0.516582 | + | 0.856238i | \(0.672796\pi\) | |||||||
\(432\) | −5.65567 | −0.272108 | ||||||||
\(433\) | −7.85455 | −0.377466 | −0.188733 | − | 0.982028i | \(-0.560438\pi\) | ||||
−0.188733 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(434\) | 8.90089 | 0.427257 | ||||||||
\(435\) | −0.273833 | −0.0131293 | ||||||||
\(436\) | −11.1198 | −0.532540 | ||||||||
\(437\) | 3.57498 | 0.171014 | ||||||||
\(438\) | 6.96297 | 0.332704 | ||||||||
\(439\) | −0.650885 | −0.0310650 | −0.0155325 | − | 0.999879i | \(-0.504944\pi\) | ||||
−0.0155325 | + | 0.999879i | \(0.504944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71502 | 0.272144 | ||||||||
\(442\) | −5.46410 | −0.259901 | ||||||||
\(443\) | 4.53815 | 0.215614 | 0.107807 | − | 0.994172i | \(-0.465617\pi\) | ||||
0.107807 | + | 0.994172i | \(0.465617\pi\) | |||||||
\(444\) | −0.267949 | −0.0127163 | ||||||||
\(445\) | −1.13517 | −0.0538124 | ||||||||
\(446\) | 7.01450 | 0.332146 | ||||||||
\(447\) | 22.8250 | 1.07958 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 37.3091 | 1.76073 | 0.880363 | − | 0.474300i | \(-0.157299\pi\) | ||||
0.880363 | + | 0.474300i | \(0.157299\pi\) | |||||||
\(450\) | −4.67613 | −0.220435 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.33180 | −0.344859 | ||||||||
\(453\) | −1.30340 | −0.0612390 | ||||||||
\(454\) | 2.63089 | 0.123474 | ||||||||
\(455\) | −0.420912 | −0.0197326 | ||||||||
\(456\) | 1.43091 | 0.0670084 | ||||||||
\(457\) | −21.3693 | −0.999614 | −0.499807 | − | 0.866137i | \(-0.666596\pi\) | ||||
−0.499807 | + | 0.866137i | \(0.666596\pi\) | |||||||
\(458\) | 4.43961 | 0.207449 | ||||||||
\(459\) | −22.1098 | −1.03200 | ||||||||
\(460\) | 1.07658 | 0.0501958 | ||||||||
\(461\) | 9.44157 | 0.439738 | 0.219869 | − | 0.975529i | \(-0.429437\pi\) | ||||
0.219869 | + | 0.975529i | \(0.429437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4976 | −0.720233 | −0.360117 | − | 0.932907i | \(-0.617263\pi\) | ||||
−0.360117 | + | 0.932907i | \(0.617263\pi\) | |||||||
\(464\) | 0.635480 | 0.0295014 | ||||||||
\(465\) | 3.83546 | 0.177865 | ||||||||
\(466\) | 15.4482 | 0.715625 | ||||||||
\(467\) | −5.81733 | −0.269194 | −0.134597 | − | 0.990900i | \(-0.542974\pi\) | ||||
−0.134597 | + | 0.990900i | \(0.542974\pi\) | |||||||
\(468\) | −1.33133 | −0.0615406 | ||||||||
\(469\) | 8.14454 | 0.376080 | ||||||||
\(470\) | −2.27383 | −0.104884 | ||||||||
\(471\) | 20.7264 | 0.955020 | ||||||||
\(472\) | −0.502705 | −0.0231389 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.20429 | 0.376836 | ||||||||
\(475\) | 4.90931 | 0.225255 | ||||||||
\(476\) | 3.90931 | 0.179183 | ||||||||
\(477\) | 0.875644 | 0.0400930 | ||||||||
\(478\) | 13.1489 | 0.601414 | ||||||||
\(479\) | 24.8407 | 1.13500 | 0.567501 | − | 0.823373i | \(-0.307910\pi\) | ||||
0.567501 | + | 0.823373i | \(0.307910\pi\) | |||||||
\(480\) | 0.430908 | 0.0196682 | ||||||||
\(481\) | −0.261733 | −0.0119340 | ||||||||
\(482\) | 16.1545 | 0.735819 | ||||||||
\(483\) | −5.11546 | −0.232762 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.477735 | 0.0216928 | ||||||||
\(486\) | −9.47587 | −0.429834 | ||||||||
\(487\) | −10.5918 | −0.479961 | −0.239980 | − | 0.970778i | \(-0.577141\pi\) | ||||
−0.239980 | + | 0.970778i | \(0.577141\pi\) | |||||||
\(488\) | −1.41072 | −0.0638603 | ||||||||
\(489\) | −21.0864 | −0.953559 | ||||||||
\(490\) | −1.80686 | −0.0816255 | ||||||||
\(491\) | 38.6077 | 1.74234 | 0.871170 | − | 0.490981i | \(-0.163362\pi\) | ||||
0.871170 | + | 0.490981i | \(0.163362\pi\) | |||||||
\(492\) | −11.4889 | −0.517959 | ||||||||
\(493\) | 2.48429 | 0.111887 | ||||||||
\(494\) | 1.39771 | 0.0628861 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.90089 | −0.399662 | ||||||||
\(497\) | 7.20634 | 0.323249 | ||||||||
\(498\) | −21.3423 | −0.956370 | ||||||||
\(499\) | 4.54198 | 0.203327 | 0.101663 | − | 0.994819i | \(-0.467584\pi\) | ||||
0.101663 | + | 0.994819i | \(0.467584\pi\) | |||||||
\(500\) | 2.98412 | 0.133454 | ||||||||
\(501\) | −23.6068 | −1.05467 | ||||||||
\(502\) | −4.74683 | −0.211861 | ||||||||
\(503\) | 34.6954 | 1.54699 | 0.773496 | − | 0.633801i | \(-0.218506\pi\) | ||||
0.773496 | + | 0.633801i | \(0.218506\pi\) | |||||||
\(504\) | 0.952503 | 0.0424278 | ||||||||
\(505\) | 2.06208 | 0.0917614 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.8064 | −0.701986 | ||||||||
\(508\) | −4.07816 | −0.180939 | ||||||||
\(509\) | 25.2232 | 1.11800 | 0.558999 | − | 0.829168i | \(-0.311186\pi\) | ||||
0.558999 | + | 0.829168i | \(0.311186\pi\) | |||||||
\(510\) | 1.68455 | 0.0745933 | ||||||||
\(511\) | −4.86612 | −0.215265 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.65567 | 0.249704 | ||||||||
\(514\) | −20.6804 | −0.912175 | ||||||||
\(515\) | −1.56785 | −0.0690879 | ||||||||
\(516\) | 0.917732 | 0.0404009 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.187258 | 0.00822765 | ||||||||
\(519\) | 7.26384 | 0.318847 | ||||||||
\(520\) | 0.420912 | 0.0184582 | ||||||||
\(521\) | −2.72459 | −0.119366 | −0.0596832 | − | 0.998217i | \(-0.519009\pi\) | ||||
−0.0596832 | + | 0.998217i | \(0.519009\pi\) | |||||||
\(522\) | 0.605296 | 0.0264931 | ||||||||
\(523\) | −22.7787 | −0.996044 | −0.498022 | − | 0.867164i | \(-0.665940\pi\) | ||||
−0.498022 | + | 0.867164i | \(0.665940\pi\) | |||||||
\(524\) | −6.73636 | −0.294279 | ||||||||
\(525\) | −7.02477 | −0.306586 | ||||||||
\(526\) | 16.2184 | 0.707155 | ||||||||
\(527\) | −34.7964 | −1.51575 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2195 | −0.444328 | ||||||||
\(530\) | −0.276843 | −0.0120253 | ||||||||
\(531\) | −0.478828 | −0.0207793 | ||||||||
\(532\) | −1.00000 | −0.0433555 | ||||||||
\(533\) | −11.2224 | −0.486094 | ||||||||
\(534\) | −5.39388 | −0.233416 | ||||||||
\(535\) | −2.31277 | −0.0999897 | ||||||||
\(536\) | −8.14454 | −0.351791 | ||||||||
\(537\) | 6.09725 | 0.263116 | ||||||||
\(538\) | 1.93074 | 0.0832401 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.70316 | 0.0732925 | ||||||||
\(541\) | 12.8536 | 0.552619 | 0.276310 | − | 0.961069i | \(-0.410889\pi\) | ||||
0.276310 | + | 0.961069i | \(0.410889\pi\) | |||||||
\(542\) | 4.51475 | 0.193925 | ||||||||
\(543\) | −16.1445 | −0.692829 | ||||||||
\(544\) | −3.90931 | −0.167610 | ||||||||
\(545\) | 3.34864 | 0.143440 | ||||||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | 31.7903 | 1.35926 | 0.679628 | − | 0.733557i | \(-0.262141\pi\) | ||||
0.679628 | + | 0.733557i | \(0.262141\pi\) | |||||||
\(548\) | −21.0107 | −0.897531 | ||||||||
\(549\) | −1.34372 | −0.0573484 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.635480 | −0.0270723 | ||||||||
\(552\) | 5.11546 | 0.217728 | ||||||||
\(553\) | −5.73363 | −0.243819 | ||||||||
\(554\) | 12.6071 | 0.535623 | ||||||||
\(555\) | 0.0806910 | 0.00342514 | ||||||||
\(556\) | −1.30272 | −0.0552476 | ||||||||
\(557\) | −3.20457 | −0.135782 | −0.0678910 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678910 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(558\) | −8.47813 | −0.358908 | ||||||||
\(559\) | 0.896443 | 0.0379155 | ||||||||
\(560\) | −0.301143 | −0.0127256 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3200 | −0.561872 | ||||||||
\(563\) | −0.824315 | −0.0347407 | −0.0173704 | − | 0.999849i | \(-0.505529\pi\) | ||||
−0.0173704 | + | 0.999849i | \(0.505529\pi\) | |||||||
\(564\) | −10.8043 | −0.454944 | ||||||||
\(565\) | 2.20792 | 0.0928879 | ||||||||
\(566\) | −24.5772 | −1.03306 | ||||||||
\(567\) | −5.23523 | −0.219859 | ||||||||
\(568\) | −7.20634 | −0.302371 | ||||||||
\(569\) | −16.0832 | −0.674244 | −0.337122 | − | 0.941461i | \(-0.609453\pi\) | ||||
−0.337122 | + | 0.941461i | \(0.609453\pi\) | |||||||
\(570\) | −0.430908 | −0.0180487 | ||||||||
\(571\) | −26.7916 | −1.12119 | −0.560597 | − | 0.828089i | \(-0.689428\pi\) | ||||
−0.560597 | + | 0.828089i | \(0.689428\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.709328 | −0.0296326 | ||||||||
\(574\) | 8.02908 | 0.335127 | ||||||||
\(575\) | 17.5507 | 0.731914 | ||||||||
\(576\) | −0.952503 | −0.0396876 | ||||||||
\(577\) | 19.2616 | 0.801870 | 0.400935 | − | 0.916106i | \(-0.368685\pi\) | ||||
0.400935 | + | 0.916106i | \(0.368685\pi\) | |||||||
\(578\) | 1.71727 | 0.0714291 | ||||||||
\(579\) | 27.6191 | 1.14781 | ||||||||
\(580\) | −0.191370 | −0.00794622 | ||||||||
\(581\) | 14.9152 | 0.618787 | ||||||||
\(582\) | 2.27000 | 0.0940946 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.86612 | 0.201362 | ||||||||
\(585\) | 0.400920 | 0.0165760 | ||||||||
\(586\) | 6.95839 | 0.287448 | ||||||||
\(587\) | −38.6661 | −1.59592 | −0.797961 | − | 0.602709i | \(-0.794088\pi\) | ||||
−0.797961 | + | 0.602709i | \(0.794088\pi\) | |||||||
\(588\) | −8.58545 | −0.354058 | ||||||||
\(589\) | 8.90089 | 0.366755 | ||||||||
\(590\) | 0.151386 | 0.00623246 | ||||||||
\(591\) | 32.8523 | 1.35136 | ||||||||
\(592\) | −0.187258 | −0.00769626 | ||||||||
\(593\) | 38.0454 | 1.56234 | 0.781169 | − | 0.624319i | \(-0.214623\pi\) | ||||
0.781169 | + | 0.624319i | \(0.214623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.17726 | −0.0482630 | ||||||||
\(596\) | 15.9514 | 0.653395 | ||||||||
\(597\) | −35.1447 | −1.43838 | ||||||||
\(598\) | 4.99679 | 0.204334 | ||||||||
\(599\) | 31.7240 | 1.29621 | 0.648104 | − | 0.761552i | \(-0.275562\pi\) | ||||
0.648104 | + | 0.761552i | \(0.275562\pi\) | |||||||
\(600\) | 7.02477 | 0.286785 | ||||||||
\(601\) | −47.9295 | −1.95508 | −0.977542 | − | 0.210739i | \(-0.932413\pi\) | ||||
−0.977542 | + | 0.210739i | \(0.932413\pi\) | |||||||
\(602\) | −0.641364 | −0.0261400 | ||||||||
\(603\) | −7.75770 | −0.315918 | ||||||||
\(604\) | −0.910890 | −0.0370636 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.79816 | 0.398023 | ||||||||
\(607\) | 35.2950 | 1.43258 | 0.716289 | − | 0.697803i | \(-0.245839\pi\) | ||||
0.716289 | + | 0.697803i | \(0.245839\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0.909313 | 0.0368472 | ||||||||
\(610\) | 0.424829 | 0.0172008 | ||||||||
\(611\) | −10.5537 | −0.426956 | ||||||||
\(612\) | −3.72363 | −0.150519 | ||||||||
\(613\) | −16.4588 | −0.664763 | −0.332381 | − | 0.943145i | \(-0.607852\pi\) | ||||
−0.332381 | + | 0.943145i | \(0.607852\pi\) | |||||||
\(614\) | −11.0608 | −0.446379 | ||||||||
\(615\) | 3.45979 | 0.139512 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0456 | 0.766748 | 0.383374 | − | 0.923593i | \(-0.374762\pi\) | ||||
0.383374 | + | 0.923593i | \(0.374762\pi\) | |||||||
\(618\) | −7.44980 | −0.299675 | ||||||||
\(619\) | −15.5372 | −0.624492 | −0.312246 | − | 0.950001i | \(-0.601081\pi\) | ||||
−0.312246 | + | 0.950001i | \(0.601081\pi\) | |||||||
\(620\) | 2.68044 | 0.107649 | ||||||||
\(621\) | 20.2189 | 0.811356 | ||||||||
\(622\) | −25.7857 | −1.03391 | ||||||||
\(623\) | 3.76955 | 0.151024 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 23.6479 | 0.945917 | ||||||||
\(626\) | 17.3016 | 0.691512 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.4848 | 0.578005 | ||||||||
\(629\) | −0.732051 | −0.0291888 | ||||||||
\(630\) | −0.286840 | −0.0114280 | ||||||||
\(631\) | −17.1545 | −0.682908 | −0.341454 | − | 0.939898i | \(-0.610919\pi\) | ||||
−0.341454 | + | 0.939898i | \(0.610919\pi\) | |||||||
\(632\) | 5.73363 | 0.228071 | ||||||||
\(633\) | −18.6477 | −0.741180 | ||||||||
\(634\) | 11.8272 | 0.469720 | ||||||||
\(635\) | 1.22811 | 0.0487360 | ||||||||
\(636\) | −1.31545 | −0.0521608 | ||||||||
\(637\) | −8.38628 | −0.332277 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.86406 | −0.271538 | ||||||||
\(640\) | 0.301143 | 0.0119037 | ||||||||
\(641\) | 3.65547 | 0.144382 | 0.0721912 | − | 0.997391i | \(-0.477001\pi\) | ||||
0.0721912 | + | 0.997391i | \(0.477001\pi\) | |||||||
\(642\) | −10.9893 | −0.433714 | ||||||||
\(643\) | 47.9841 | 1.89231 | 0.946154 | − | 0.323716i | \(-0.104932\pi\) | ||||
0.946154 | + | 0.323716i | \(0.104932\pi\) | |||||||
\(644\) | −3.57498 | −0.140874 | ||||||||
\(645\) | −0.276369 | −0.0108820 | ||||||||
\(646\) | 3.90931 | 0.153810 | ||||||||
\(647\) | −44.3431 | −1.74331 | −0.871654 | − | 0.490121i | \(-0.836953\pi\) | ||||
−0.871654 | + | 0.490121i | \(0.836953\pi\) | |||||||
\(648\) | 5.23523 | 0.205659 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.86182 | 0.269143 | ||||||||
\(651\) | −12.7364 | −0.499177 | ||||||||
\(652\) | −14.7364 | −0.577120 | ||||||||
\(653\) | −36.1754 | −1.41565 | −0.707826 | − | 0.706386i | \(-0.750324\pi\) | ||||
−0.707826 | + | 0.706386i | \(0.750324\pi\) | |||||||
\(654\) | 15.9114 | 0.622184 | ||||||||
\(655\) | 2.02861 | 0.0792642 | ||||||||
\(656\) | −8.02908 | −0.313483 | ||||||||
\(657\) | 4.63500 | 0.180828 | ||||||||
\(658\) | 7.55068 | 0.294356 | ||||||||
\(659\) | −27.7848 | −1.08234 | −0.541171 | − | 0.840912i | \(-0.682019\pi\) | ||||
−0.541171 | + | 0.840912i | \(0.682019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.1358 | −0.588716 | −0.294358 | − | 0.955695i | \(-0.595106\pi\) | ||||
−0.294358 | + | 0.955695i | \(0.595106\pi\) | |||||||
\(662\) | 21.1398 | 0.821620 | ||||||||
\(663\) | 7.81863 | 0.303650 | ||||||||
\(664\) | −14.9152 | −0.578822 | ||||||||
\(665\) | 0.301143 | 0.0116778 | ||||||||
\(666\) | −0.178364 | −0.00691146 | ||||||||
\(667\) | −2.27182 | −0.0879654 | ||||||||
\(668\) | −16.4978 | −0.638318 | ||||||||
\(669\) | −10.0371 | −0.388057 | ||||||||
\(670\) | 2.45267 | 0.0947550 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.43091 | −0.0551985 | ||||||||
\(673\) | 2.79968 | 0.107920 | 0.0539598 | − | 0.998543i | \(-0.482816\pi\) | ||||
0.0539598 | + | 0.998543i | \(0.482816\pi\) | |||||||
\(674\) | −3.64725 | −0.140487 | ||||||||
\(675\) | 27.7654 | 1.06869 | ||||||||
\(676\) | −11.0464 | −0.424861 | ||||||||
\(677\) | 0.584013 | 0.0224455 | 0.0112227 | − | 0.999937i | \(-0.496428\pi\) | ||||
0.0112227 | + | 0.999937i | \(0.496428\pi\) | |||||||
\(678\) | 10.4911 | 0.402909 | ||||||||
\(679\) | −1.58641 | −0.0608807 | ||||||||
\(680\) | 1.17726 | 0.0451459 | ||||||||
\(681\) | −3.76457 | −0.144258 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.43455 | 0.207947 | 0.103974 | − | 0.994580i | \(-0.466844\pi\) | ||||
0.103974 | + | 0.994580i | \(0.466844\pi\) | |||||||
\(684\) | 0.952503 | 0.0364199 | ||||||||
\(685\) | 6.32721 | 0.241750 | ||||||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | −6.35267 | −0.242369 | ||||||||
\(688\) | 0.641364 | 0.0244518 | ||||||||
\(689\) | −1.28493 | −0.0489520 | ||||||||
\(690\) | −1.54049 | −0.0586453 | ||||||||
\(691\) | −2.27124 | −0.0864020 | −0.0432010 | − | 0.999066i | \(-0.513756\pi\) | ||||
−0.0432010 | + | 0.999066i | \(0.513756\pi\) | |||||||
\(692\) | 5.07638 | 0.192975 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.70933 | −0.216723 | ||||||||
\(695\) | 0.392305 | 0.0148810 | ||||||||
\(696\) | −0.909313 | −0.0344674 | ||||||||
\(697\) | −31.3882 | −1.18891 | ||||||||
\(698\) | −7.82910 | −0.296336 | ||||||||
\(699\) | −22.1050 | −0.836087 | ||||||||
\(700\) | −4.90931 | −0.185555 | ||||||||
\(701\) | −25.4477 | −0.961145 | −0.480572 | − | 0.876955i | \(-0.659571\pi\) | ||||
−0.480572 | + | 0.876955i | \(0.659571\pi\) | |||||||
\(702\) | 7.90501 | 0.298355 | ||||||||
\(703\) | 0.187258 | 0.00706258 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.25365 | 0.122539 | ||||||||
\(706\) | −3.13708 | −0.118066 | ||||||||
\(707\) | −6.84751 | −0.257527 | ||||||||
\(708\) | 0.719324 | 0.0270338 | ||||||||
\(709\) | −10.9778 | −0.412278 | −0.206139 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206139 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(710\) | 2.17014 | 0.0814439 | ||||||||
\(711\) | 5.46130 | 0.204815 | ||||||||
\(712\) | −3.76955 | −0.141270 | ||||||||
\(713\) | 31.8205 | 1.19169 | ||||||||
\(714\) | −5.59387 | −0.209345 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.26111 | 0.159245 | ||||||||
\(717\) | −18.8148 | −0.702651 | ||||||||
\(718\) | 9.10566 | 0.339820 | ||||||||
\(719\) | −32.1855 | −1.20032 | −0.600158 | − | 0.799882i | \(-0.704896\pi\) | ||||
−0.600158 | + | 0.799882i | \(0.704896\pi\) | |||||||
\(720\) | 0.286840 | 0.0106899 | ||||||||
\(721\) | 5.20634 | 0.193894 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −23.1157 | −0.859681 | ||||||||
\(724\) | −11.2827 | −0.419319 | ||||||||
\(725\) | −3.11977 | −0.115865 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.1057 | 1.74705 | 0.873526 | − | 0.486778i | \(-0.161828\pi\) | ||||
0.873526 | + | 0.486778i | \(0.161828\pi\) | |||||||
\(728\) | −1.39771 | −0.0518027 | ||||||||
\(729\) | 29.2648 | 1.08388 | ||||||||
\(730\) | −1.46540 | −0.0542368 | ||||||||
\(731\) | 2.50729 | 0.0927355 | ||||||||
\(732\) | 2.01861 | 0.0746100 | ||||||||
\(733\) | −39.3132 | −1.45207 | −0.726033 | − | 0.687660i | \(-0.758638\pi\) | ||||
−0.726033 | + | 0.687660i | \(0.758638\pi\) | |||||||
\(734\) | −1.30291 | −0.0480915 | ||||||||
\(735\) | 2.58545 | 0.0953657 | ||||||||
\(736\) | 3.57498 | 0.131775 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −7.64772 | −0.281517 | ||||||||
\(739\) | 29.1248 | 1.07137 | 0.535687 | − | 0.844417i | \(-0.320053\pi\) | ||||
0.535687 | + | 0.844417i | \(0.320053\pi\) | |||||||
\(740\) | 0.0563915 | 0.00207299 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0.919309 | 0.0337489 | ||||||||
\(743\) | 16.7650 | 0.615047 | 0.307523 | − | 0.951540i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951540i | \(0.400500\pi\) | |||||||
\(744\) | 12.7364 | 0.466938 | ||||||||
\(745\) | −4.80365 | −0.175992 | ||||||||
\(746\) | 0.845461 | 0.0309545 | ||||||||
\(747\) | −14.2068 | −0.519798 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.67997 | 0.280620 | ||||||||
\(750\) | −4.27000 | −0.155918 | ||||||||
\(751\) | 19.0714 | 0.695927 | 0.347964 | − | 0.937508i | \(-0.386873\pi\) | ||||
0.347964 | + | 0.937508i | \(0.386873\pi\) | |||||||
\(752\) | −7.55068 | −0.275345 | ||||||||
\(753\) | 6.79227 | 0.247524 | ||||||||
\(754\) | −0.888219 | −0.0323470 | ||||||||
\(755\) | 0.274308 | 0.00998309 | ||||||||
\(756\) | −5.65567 | −0.205695 | ||||||||
\(757\) | −51.1070 | −1.85752 | −0.928759 | − | 0.370685i | \(-0.879123\pi\) | ||||
−0.928759 | + | 0.370685i | \(0.879123\pi\) | |||||||
\(758\) | 16.4689 | 0.598177 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.301143 | −0.0109236 | ||||||||
\(761\) | 13.0980 | 0.474802 | 0.237401 | − | 0.971412i | \(-0.423704\pi\) | ||||
0.237401 | + | 0.971412i | \(0.423704\pi\) | |||||||
\(762\) | 5.83546 | 0.211397 | ||||||||
\(763\) | −11.1198 | −0.402563 | ||||||||
\(764\) | −0.495719 | −0.0179345 | ||||||||
\(765\) | 1.12135 | 0.0405423 | ||||||||
\(766\) | −14.8014 | −0.534798 | ||||||||
\(767\) | 0.702637 | 0.0253708 | ||||||||
\(768\) | 1.43091 | 0.0516334 | ||||||||
\(769\) | 23.8480 | 0.859980 | 0.429990 | − | 0.902834i | \(-0.358517\pi\) | ||||
0.429990 | + | 0.902834i | \(0.358517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.5918 | 1.06572 | ||||||||
\(772\) | 19.3018 | 0.694687 | ||||||||
\(773\) | −15.1475 | −0.544817 | −0.272408 | − | 0.962182i | \(-0.587820\pi\) | ||||
−0.272408 | + | 0.962182i | \(0.587820\pi\) | |||||||
\(774\) | 0.610901 | 0.0219584 | ||||||||
\(775\) | 43.6973 | 1.56965 | ||||||||
\(776\) | 1.58641 | 0.0569487 | ||||||||
\(777\) | −0.267949 | −0.00961262 | ||||||||
\(778\) | 3.91931 | 0.140514 | ||||||||
\(779\) | 8.02908 | 0.287672 | ||||||||
\(780\) | −0.602286 | −0.0215653 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 13.9757 | 0.499770 | ||||||||
\(783\) | −3.59406 | −0.128441 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | −4.36198 | −0.155686 | ||||||||
\(786\) | 9.63911 | 0.343816 | ||||||||
\(787\) | −10.5856 | −0.377335 | −0.188668 | − | 0.982041i | \(-0.560417\pi\) | ||||
−0.188668 | + | 0.982041i | \(0.560417\pi\) | |||||||
\(788\) | 22.9591 | 0.817883 | ||||||||
\(789\) | −23.2070 | −0.826192 | ||||||||
\(790\) | −1.72664 | −0.0614312 | ||||||||
\(791\) | −7.33180 | −0.260689 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.97178 | 0.0700201 | ||||||||
\(794\) | −12.9082 | −0.458095 | ||||||||
\(795\) | 0.396137 | 0.0140495 | ||||||||
\(796\) | −24.5611 | −0.870547 | ||||||||
\(797\) | −31.4937 | −1.11556 | −0.557781 | − | 0.829988i | \(-0.688347\pi\) | ||||
−0.557781 | + | 0.829988i | \(0.688347\pi\) | |||||||
\(798\) | 1.43091 | 0.0506536 | ||||||||
\(799\) | −29.5180 | −1.04427 | ||||||||
\(800\) | 4.90931 | 0.173570 | ||||||||
\(801\) | −3.59051 | −0.126864 | ||||||||
\(802\) | 2.53413 | 0.0894831 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.6541 | 0.411008 | ||||||||
\(805\) | 1.07658 | 0.0379444 | ||||||||
\(806\) | 12.4409 | 0.438212 | ||||||||
\(807\) | −2.76271 | −0.0972520 | ||||||||
\(808\) | 6.84751 | 0.240895 | ||||||||
\(809\) | 4.29264 | 0.150921 | 0.0754606 | − | 0.997149i | \(-0.475957\pi\) | ||||
0.0754606 | + | 0.997149i | \(0.475957\pi\) | |||||||
\(810\) | −1.57655 | −0.0553944 | ||||||||
\(811\) | 45.3464 | 1.59233 | 0.796163 | − | 0.605082i | \(-0.206860\pi\) | ||||
0.796163 | + | 0.605082i | \(0.206860\pi\) | |||||||
\(812\) | 0.635480 | 0.0223010 | ||||||||
\(813\) | −6.46019 | −0.226569 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.43775 | 0.155448 | ||||||||
\(816\) | 5.59387 | 0.195824 | ||||||||
\(817\) | −0.641364 | −0.0224385 | ||||||||
\(818\) | 28.3472 | 0.991138 | ||||||||
\(819\) | −1.33133 | −0.0465203 | ||||||||
\(820\) | 2.41790 | 0.0844368 | ||||||||
\(821\) | −26.1744 | −0.913492 | −0.456746 | − | 0.889597i | \(-0.650985\pi\) | ||||
−0.456746 | + | 0.889597i | \(0.650985\pi\) | |||||||
\(822\) | 30.0643 | 1.04861 | ||||||||
\(823\) | −42.1604 | −1.46962 | −0.734810 | − | 0.678273i | \(-0.762729\pi\) | ||||
−0.734810 | + | 0.678273i | \(0.762729\pi\) | |||||||
\(824\) | −5.20634 | −0.181372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.502705 | −0.0174913 | ||||||||
\(827\) | 29.8252 | 1.03712 | 0.518562 | − | 0.855040i | \(-0.326468\pi\) | ||||
0.518562 | + | 0.855040i | \(0.326468\pi\) | |||||||
\(828\) | 3.40517 | 0.118338 | ||||||||
\(829\) | −27.5800 | −0.957894 | −0.478947 | − | 0.877844i | \(-0.658981\pi\) | ||||
−0.478947 | + | 0.877844i | \(0.658981\pi\) | |||||||
\(830\) | 4.49161 | 0.155906 | ||||||||
\(831\) | −18.0396 | −0.625785 | ||||||||
\(832\) | 1.39771 | 0.0484570 | ||||||||
\(833\) | −23.4559 | −0.812698 | ||||||||
\(834\) | 1.86407 | 0.0645475 | ||||||||
\(835\) | 4.96819 | 0.171931 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 50.3405 | 1.74002 | ||||||||
\(838\) | 1.82561 | 0.0630647 | ||||||||
\(839\) | −38.6032 | −1.33273 | −0.666364 | − | 0.745626i | \(-0.732150\pi\) | ||||
−0.666364 | + | 0.745626i | \(0.732150\pi\) | |||||||
\(840\) | 0.430908 | 0.0148677 | ||||||||
\(841\) | −28.5962 | −0.986075 | ||||||||
\(842\) | −24.0238 | −0.827915 | ||||||||
\(843\) | 19.0597 | 0.656452 | ||||||||
\(844\) | −13.0321 | −0.448583 | ||||||||
\(845\) | 3.32654 | 0.114437 | ||||||||
\(846\) | −7.19204 | −0.247267 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.919309 | −0.0315692 | ||||||||
\(849\) | 35.1677 | 1.20695 | ||||||||
\(850\) | 19.1920 | 0.658282 | ||||||||
\(851\) | 0.669444 | 0.0229482 | ||||||||
\(852\) | 10.3116 | 0.353270 | ||||||||
\(853\) | 30.2567 | 1.03597 | 0.517985 | − | 0.855390i | \(-0.326682\pi\) | ||||
0.517985 | + | 0.855390i | \(0.326682\pi\) | |||||||
\(854\) | −1.41072 | −0.0482739 | ||||||||
\(855\) | −0.286840 | −0.00980970 | ||||||||
\(856\) | −7.67997 | −0.262496 | ||||||||
\(857\) | −10.1668 | −0.347291 | −0.173645 | − | 0.984808i | \(-0.555555\pi\) | ||||
−0.173645 | + | 0.984808i | \(0.555555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.90568 | −0.235619 | −0.117809 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117809 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(860\) | −0.193142 | −0.00658609 | ||||||||
\(861\) | −11.4889 | −0.391540 | ||||||||
\(862\) | 21.4490 | 0.730557 | ||||||||
\(863\) | 49.7723 | 1.69427 | 0.847134 | − | 0.531379i | \(-0.178326\pi\) | ||||
0.847134 | + | 0.531379i | \(0.178326\pi\) | |||||||
\(864\) | 5.65567 | 0.192410 | ||||||||
\(865\) | −1.52872 | −0.0519779 | ||||||||
\(866\) | 7.85455 | 0.266908 | ||||||||
\(867\) | −2.45726 | −0.0834529 | ||||||||
\(868\) | −8.90089 | −0.302116 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.273833 | 0.00928381 | ||||||||
\(871\) | 11.3837 | 0.385723 | ||||||||
\(872\) | 11.1198 | 0.376563 | ||||||||
\(873\) | 1.51106 | 0.0511415 | ||||||||
\(874\) | −3.57498 | −0.120925 | ||||||||
\(875\) | 2.98412 | 0.100882 | ||||||||
\(876\) | −6.96297 | −0.235257 | ||||||||
\(877\) | 46.3334 | 1.56457 | 0.782284 | − | 0.622922i | \(-0.214054\pi\) | ||||
0.782284 | + | 0.622922i | \(0.214054\pi\) | |||||||
\(878\) | 0.650885 | 0.0219663 | ||||||||
\(879\) | −9.95681 | −0.335835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.6804 | 0.663051 | 0.331525 | − | 0.943446i | \(-0.392437\pi\) | ||||
0.331525 | + | 0.943446i | \(0.392437\pi\) | |||||||
\(882\) | −5.71502 | −0.192435 | ||||||||
\(883\) | 34.0283 | 1.14514 | 0.572572 | − | 0.819854i | \(-0.305946\pi\) | ||||
0.572572 | + | 0.819854i | \(0.305946\pi\) | |||||||
\(884\) | 5.46410 | 0.183778 | ||||||||
\(885\) | −0.216619 | −0.00728158 | ||||||||
\(886\) | −4.53815 | −0.152462 | ||||||||
\(887\) | 1.87463 | 0.0629438 | 0.0314719 | − | 0.999505i | \(-0.489981\pi\) | ||||
0.0314719 | + | 0.999505i | \(0.489981\pi\) | |||||||
\(888\) | 0.267949 | 0.00899179 | ||||||||
\(889\) | −4.07816 | −0.136777 | ||||||||
\(890\) | 1.13517 | 0.0380511 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.01450 | −0.234863 | ||||||||
\(893\) | 7.55068 | 0.252674 | ||||||||
\(894\) | −22.8250 | −0.763382 | ||||||||
\(895\) | −1.28320 | −0.0428927 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −7.14995 | −0.238730 | ||||||||
\(898\) | −37.3091 | −1.24502 | ||||||||
\(899\) | −5.65634 | −0.188649 | ||||||||
\(900\) | 4.67613 | 0.155871 | ||||||||
\(901\) | −3.59387 | −0.119729 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.917732 | 0.0305402 | ||||||||
\(904\) | 7.33180 | 0.243852 | ||||||||
\(905\) | 3.39771 | 0.112944 | ||||||||
\(906\) | 1.30340 | 0.0433025 | ||||||||
\(907\) | 56.5072 | 1.87629 | 0.938145 | − | 0.346242i | \(-0.112542\pi\) | ||||
0.938145 | + | 0.346242i | \(0.112542\pi\) | |||||||
\(908\) | −2.63089 | −0.0873092 | ||||||||
\(909\) | 6.52227 | 0.216330 | ||||||||
\(910\) | 0.420912 | 0.0139531 | ||||||||
\(911\) | 34.8858 | 1.15582 | 0.577909 | − | 0.816101i | \(-0.303869\pi\) | ||||
0.577909 | + | 0.816101i | \(0.303869\pi\) | |||||||
\(912\) | −1.43091 | −0.0473821 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21.3693 | 0.706834 | ||||||||
\(915\) | −0.607890 | −0.0200962 | ||||||||
\(916\) | −4.43961 | −0.146689 | ||||||||
\(917\) | −6.73636 | −0.222454 | ||||||||
\(918\) | 22.1098 | 0.729731 | ||||||||
\(919\) | 27.5658 | 0.909312 | 0.454656 | − | 0.890667i | \(-0.349762\pi\) | ||||
0.454656 | + | 0.890667i | \(0.349762\pi\) | |||||||
\(920\) | −1.07658 | −0.0354938 | ||||||||
\(921\) | 15.8270 | 0.521519 | ||||||||
\(922\) | −9.44157 | −0.310942 | ||||||||
\(923\) | 10.0724 | 0.331537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.919309 | 0.0302267 | ||||||||
\(926\) | 15.4976 | 0.509282 | ||||||||
\(927\) | −4.95906 | −0.162877 | ||||||||
\(928\) | −0.635480 | −0.0208606 | ||||||||
\(929\) | −56.1027 | −1.84067 | −0.920335 | − | 0.391131i | \(-0.872084\pi\) | ||||
−0.920335 | + | 0.391131i | \(0.872084\pi\) | |||||||
\(930\) | −3.83546 | −0.125770 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | −15.4482 | −0.506023 | ||||||||
\(933\) | 36.8970 | 1.20795 | ||||||||
\(934\) | 5.81733 | 0.190349 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.33133 | 0.0435158 | ||||||||
\(937\) | 29.4082 | 0.960725 | 0.480363 | − | 0.877070i | \(-0.340505\pi\) | ||||
0.480363 | + | 0.877070i | \(0.340505\pi\) | |||||||
\(938\) | −8.14454 | −0.265929 | ||||||||
\(939\) | −24.7570 | −0.807915 | ||||||||
\(940\) | 2.27383 | 0.0741643 | ||||||||
\(941\) | −50.0127 | −1.63037 | −0.815184 | − | 0.579202i | \(-0.803364\pi\) | ||||
−0.815184 | + | 0.579202i | \(0.803364\pi\) | |||||||
\(942\) | −20.7264 | −0.675301 | ||||||||
\(943\) | 28.7038 | 0.934724 | ||||||||
\(944\) | 0.502705 | 0.0163616 | ||||||||
\(945\) | 1.70316 | 0.0554039 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.5117 | 0.666542 | 0.333271 | − | 0.942831i | \(-0.391848\pi\) | ||||
0.333271 | + | 0.942831i | \(0.391848\pi\) | |||||||
\(948\) | −8.20429 | −0.266463 | ||||||||
\(949\) | −6.80145 | −0.220784 | ||||||||
\(950\) | −4.90931 | −0.159279 | ||||||||
\(951\) | −16.9237 | −0.548788 | ||||||||
\(952\) | −3.90931 | −0.126702 | ||||||||
\(953\) | −12.2473 | −0.396729 | −0.198364 | − | 0.980128i | \(-0.563563\pi\) | ||||
−0.198364 | + | 0.980128i | \(0.563563\pi\) | |||||||
\(954\) | −0.875644 | −0.0283500 | ||||||||
\(955\) | 0.149282 | 0.00483066 | ||||||||
\(956\) | −13.1489 | −0.425264 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.8407 | −0.802567 | ||||||||
\(959\) | −21.0107 | −0.678470 | ||||||||
\(960\) | −0.430908 | −0.0139075 | ||||||||
\(961\) | 48.2259 | 1.55567 | ||||||||
\(962\) | 0.261733 | 0.00843862 | ||||||||
\(963\) | −7.31519 | −0.235729 | ||||||||
\(964\) | −16.1545 | −0.520303 | ||||||||
\(965\) | −5.81261 | −0.187114 | ||||||||
\(966\) | 5.11546 | 0.164587 | ||||||||
\(967\) | 14.7363 | 0.473889 | 0.236945 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236945 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.59387 | −0.179701 | ||||||||
\(970\) | −0.477735 | −0.0153391 | ||||||||
\(971\) | 16.1716 | 0.518970 | 0.259485 | − | 0.965747i | \(-0.416447\pi\) | ||||
0.259485 | + | 0.965747i | \(0.416447\pi\) | |||||||
\(972\) | 9.47587 | 0.303939 | ||||||||
\(973\) | −1.30272 | −0.0417633 | ||||||||
\(974\) | 10.5918 | 0.339384 | ||||||||
\(975\) | −9.81863 | −0.314448 | ||||||||
\(976\) | 1.41072 | 0.0451561 | ||||||||
\(977\) | 13.4473 | 0.430216 | 0.215108 | − | 0.976590i | \(-0.430990\pi\) | ||||
0.215108 | + | 0.976590i | \(0.430990\pi\) | |||||||
\(978\) | 21.0864 | 0.674268 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.80686 | 0.0577180 | ||||||||
\(981\) | 10.5916 | 0.338164 | ||||||||
\(982\) | −38.6077 | −1.23202 | ||||||||
\(983\) | 22.9399 | 0.731669 | 0.365834 | − | 0.930680i | \(-0.380784\pi\) | ||||
0.365834 | + | 0.930680i | \(0.380784\pi\) | |||||||
\(984\) | 11.4889 | 0.366252 | ||||||||
\(985\) | −6.91396 | −0.220297 | ||||||||
\(986\) | −2.48429 | −0.0791159 | ||||||||
\(987\) | −10.8043 | −0.343905 | ||||||||
\(988\) | −1.39771 | −0.0444672 | ||||||||
\(989\) | −2.29286 | −0.0729087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.97222 | −0.316778 | −0.158389 | − | 0.987377i | \(-0.550630\pi\) | ||||
−0.158389 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(992\) | 8.90089 | 0.282604 | ||||||||
\(993\) | −30.2490 | −0.959925 | ||||||||
\(994\) | −7.20634 | −0.228571 | ||||||||
\(995\) | 7.39642 | 0.234482 | ||||||||
\(996\) | 21.3423 | 0.676256 | ||||||||
\(997\) | −47.9311 | −1.51799 | −0.758997 | − | 0.651094i | \(-0.774310\pi\) | ||||
−0.758997 | + | 0.651094i | \(0.774310\pi\) | |||||||
\(998\) | −4.54198 | −0.143774 | ||||||||
\(999\) | 1.05907 | 0.0335075 |
(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.bq.1.4 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bt.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bq.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bt.1.4 | yes | 4 | 11.10 | odd | 2 |