Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-3.24091\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.24091 | 1.87114 | 0.935571 | − | 0.353140i | \(-0.114886\pi\) | ||||
0.935571 | + | 0.353140i | \(0.114886\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.45353 | 0.650038 | 0.325019 | − | 0.945708i | \(-0.394629\pi\) | ||||
0.325019 | + | 0.945708i | \(0.394629\pi\) | |||||||
\(6\) | 3.24091 | 1.32310 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.50351 | 2.50117 | ||||||||
\(10\) | 1.45353 | 0.459646 | ||||||||
\(11\) | 4.18274 | 1.26114 | 0.630572 | − | 0.776131i | \(-0.282820\pi\) | ||||
0.630572 | + | 0.776131i | \(0.282820\pi\) | |||||||
\(12\) | 3.24091 | 0.935571 | ||||||||
\(13\) | −5.22423 | −1.44894 | −0.724470 | − | 0.689307i | \(-0.757915\pi\) | ||||
−0.724470 | + | 0.689307i | \(0.757915\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.71076 | 1.21631 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.04998 | −1.22480 | −0.612400 | − | 0.790548i | \(-0.709796\pi\) | ||||
−0.612400 | + | 0.790548i | \(0.709796\pi\) | |||||||
\(18\) | 7.50351 | 1.76859 | ||||||||
\(19\) | 4.31873 | 0.990784 | 0.495392 | − | 0.868670i | \(-0.335024\pi\) | ||||
0.495392 | + | 0.868670i | \(0.335024\pi\) | |||||||
\(20\) | 1.45353 | 0.325019 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.18274 | 0.891764 | ||||||||
\(23\) | −3.03034 | −0.631869 | −0.315934 | − | 0.948781i | \(-0.602318\pi\) | ||||
−0.315934 | + | 0.948781i | \(0.602318\pi\) | |||||||
\(24\) | 3.24091 | 0.661548 | ||||||||
\(25\) | −2.88726 | −0.577451 | ||||||||
\(26\) | −5.22423 | −1.02456 | ||||||||
\(27\) | 14.5955 | 2.80890 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.29501 | 0.426173 | 0.213086 | − | 0.977033i | \(-0.431648\pi\) | ||||
0.213086 | + | 0.977033i | \(0.431648\pi\) | |||||||
\(30\) | 4.71076 | 0.860063 | ||||||||
\(31\) | −7.50317 | −1.34761 | −0.673804 | − | 0.738910i | \(-0.735341\pi\) | ||||
−0.673804 | + | 0.738910i | \(0.735341\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 13.5559 | 2.35978 | ||||||||
\(34\) | −5.04998 | −0.866065 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.50351 | 1.25058 | ||||||||
\(37\) | 2.48890 | 0.409173 | 0.204586 | − | 0.978849i | \(-0.434415\pi\) | ||||
0.204586 | + | 0.978849i | \(0.434415\pi\) | |||||||
\(38\) | 4.31873 | 0.700590 | ||||||||
\(39\) | −16.9313 | −2.71117 | ||||||||
\(40\) | 1.45353 | 0.229823 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.36993 | 1.42890 | 0.714451 | − | 0.699686i | \(-0.246677\pi\) | ||||
0.714451 | + | 0.699686i | \(0.246677\pi\) | |||||||
\(44\) | 4.18274 | 0.630572 | ||||||||
\(45\) | 10.9066 | 1.62585 | ||||||||
\(46\) | −3.03034 | −0.446799 | ||||||||
\(47\) | 7.57920 | 1.10554 | 0.552770 | − | 0.833334i | \(-0.313571\pi\) | ||||
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(48\) | 3.24091 | 0.467785 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.88726 | −0.408320 | ||||||||
\(51\) | −16.3665 | −2.29177 | ||||||||
\(52\) | −5.22423 | −0.724470 | ||||||||
\(53\) | 1.22893 | 0.168806 | 0.0844031 | − | 0.996432i | \(-0.473102\pi\) | ||||
0.0844031 | + | 0.996432i | \(0.473102\pi\) | |||||||
\(54\) | 14.5955 | 1.98619 | ||||||||
\(55\) | 6.07973 | 0.819791 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.9966 | 1.85390 | ||||||||
\(58\) | 2.29501 | 0.301350 | ||||||||
\(59\) | 2.55484 | 0.332611 | 0.166306 | − | 0.986074i | \(-0.446816\pi\) | ||||
0.166306 | + | 0.986074i | \(0.446816\pi\) | |||||||
\(60\) | 4.71076 | 0.608156 | ||||||||
\(61\) | 10.3886 | 1.33013 | 0.665065 | − | 0.746786i | \(-0.268404\pi\) | ||||
0.665065 | + | 0.746786i | \(0.268404\pi\) | |||||||
\(62\) | −7.50317 | −0.952903 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.59356 | −0.941865 | ||||||||
\(66\) | 13.5559 | 1.66862 | ||||||||
\(67\) | −4.10815 | −0.501891 | −0.250945 | − | 0.968001i | \(-0.580741\pi\) | ||||
−0.250945 | + | 0.968001i | \(0.580741\pi\) | |||||||
\(68\) | −5.04998 | −0.612400 | ||||||||
\(69\) | −9.82105 | −1.18232 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.47279 | −1.00554 | −0.502768 | − | 0.864421i | \(-0.667685\pi\) | ||||
−0.502768 | + | 0.864421i | \(0.667685\pi\) | |||||||
\(72\) | 7.50351 | 0.884297 | ||||||||
\(73\) | −4.49215 | −0.525766 | −0.262883 | − | 0.964828i | \(-0.584673\pi\) | ||||
−0.262883 | + | 0.964828i | \(0.584673\pi\) | |||||||
\(74\) | 2.48890 | 0.289329 | ||||||||
\(75\) | −9.35734 | −1.08049 | ||||||||
\(76\) | 4.31873 | 0.495392 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −16.9313 | −1.91709 | ||||||||
\(79\) | −10.1084 | −1.13728 | −0.568640 | − | 0.822586i | \(-0.692530\pi\) | ||||
−0.568640 | + | 0.822586i | \(0.692530\pi\) | |||||||
\(80\) | 1.45353 | 0.162509 | ||||||||
\(81\) | 24.7921 | 2.75468 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | −2.86502 | −0.314476 | −0.157238 | − | 0.987561i | \(-0.550259\pi\) | ||||
−0.157238 | + | 0.987561i | \(0.550259\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.34029 | −0.796166 | ||||||||
\(86\) | 9.36993 | 1.01039 | ||||||||
\(87\) | 7.43793 | 0.797430 | ||||||||
\(88\) | 4.18274 | 0.445882 | ||||||||
\(89\) | −15.4950 | −1.64247 | −0.821233 | − | 0.570594i | \(-0.806713\pi\) | ||||
−0.821233 | + | 0.570594i | \(0.806713\pi\) | |||||||
\(90\) | 10.9066 | 1.14965 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.03034 | −0.315934 | ||||||||
\(93\) | −24.3171 | −2.52157 | ||||||||
\(94\) | 7.57920 | 0.781735 | ||||||||
\(95\) | 6.27739 | 0.644047 | ||||||||
\(96\) | 3.24091 | 0.330774 | ||||||||
\(97\) | −14.7885 | −1.50155 | −0.750775 | − | 0.660558i | \(-0.770320\pi\) | ||||
−0.750775 | + | 0.660558i | \(0.770320\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.3852 | 3.15434 | ||||||||
\(100\) | −2.88726 | −0.288726 | ||||||||
\(101\) | −3.63661 | −0.361856 | −0.180928 | − | 0.983496i | \(-0.557910\pi\) | ||||
−0.180928 | + | 0.983496i | \(0.557910\pi\) | |||||||
\(102\) | −16.3665 | −1.62053 | ||||||||
\(103\) | 13.7935 | 1.35911 | 0.679556 | − | 0.733624i | \(-0.262173\pi\) | ||||
0.679556 | + | 0.733624i | \(0.262173\pi\) | |||||||
\(104\) | −5.22423 | −0.512278 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.22893 | 0.119364 | ||||||||
\(107\) | 20.2757 | 1.96013 | 0.980065 | − | 0.198676i | \(-0.0636640\pi\) | ||||
0.980065 | + | 0.198676i | \(0.0636640\pi\) | |||||||
\(108\) | 14.5955 | 1.40445 | ||||||||
\(109\) | −8.86423 | −0.849039 | −0.424520 | − | 0.905419i | \(-0.639557\pi\) | ||||
−0.424520 | + | 0.905419i | \(0.639557\pi\) | |||||||
\(110\) | 6.07973 | 0.579680 | ||||||||
\(111\) | 8.06631 | 0.765620 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.33107 | −0.689649 | −0.344825 | − | 0.938667i | \(-0.612062\pi\) | ||||
−0.344825 | + | 0.938667i | \(0.612062\pi\) | |||||||
\(114\) | 13.9966 | 1.31090 | ||||||||
\(115\) | −4.40468 | −0.410738 | ||||||||
\(116\) | 2.29501 | 0.213086 | ||||||||
\(117\) | −39.2000 | −3.62404 | ||||||||
\(118\) | 2.55484 | 0.235192 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.71076 | 0.430031 | ||||||||
\(121\) | 6.49533 | 0.590485 | ||||||||
\(122\) | 10.3886 | 0.940544 | ||||||||
\(123\) | −3.24091 | −0.292223 | ||||||||
\(124\) | −7.50317 | −0.673804 | ||||||||
\(125\) | −11.4643 | −1.02540 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.797302 | −0.0707491 | −0.0353746 | − | 0.999374i | \(-0.511262\pi\) | ||||
−0.0353746 | + | 0.999374i | \(0.511262\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 30.3671 | 2.67368 | ||||||||
\(130\) | −7.59356 | −0.665999 | ||||||||
\(131\) | −9.27577 | −0.810428 | −0.405214 | − | 0.914222i | \(-0.632803\pi\) | ||||
−0.405214 | + | 0.914222i | \(0.632803\pi\) | |||||||
\(132\) | 13.5559 | 1.17989 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.10815 | −0.354890 | ||||||||
\(135\) | 21.2149 | 1.82589 | ||||||||
\(136\) | −5.04998 | −0.433032 | ||||||||
\(137\) | −5.22892 | −0.446737 | −0.223368 | − | 0.974734i | \(-0.571705\pi\) | ||||
−0.223368 | + | 0.974734i | \(0.571705\pi\) | |||||||
\(138\) | −9.82105 | −0.836024 | ||||||||
\(139\) | −12.9221 | −1.09604 | −0.548021 | − | 0.836465i | \(-0.684618\pi\) | ||||
−0.548021 | + | 0.836465i | \(0.684618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.5635 | 2.06862 | ||||||||
\(142\) | −8.47279 | −0.711021 | ||||||||
\(143\) | −21.8516 | −1.82732 | ||||||||
\(144\) | 7.50351 | 0.625292 | ||||||||
\(145\) | 3.33586 | 0.277028 | ||||||||
\(146\) | −4.49215 | −0.371773 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.48890 | 0.204586 | ||||||||
\(149\) | −8.42101 | −0.689876 | −0.344938 | − | 0.938625i | \(-0.612100\pi\) | ||||
−0.344938 | + | 0.938625i | \(0.612100\pi\) | |||||||
\(150\) | −9.35734 | −0.764024 | ||||||||
\(151\) | −2.37428 | −0.193216 | −0.0966079 | − | 0.995323i | \(-0.530799\pi\) | ||||
−0.0966079 | + | 0.995323i | \(0.530799\pi\) | |||||||
\(152\) | 4.31873 | 0.350295 | ||||||||
\(153\) | −37.8926 | −3.06343 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9061 | −0.875996 | ||||||||
\(156\) | −16.9313 | −1.35559 | ||||||||
\(157\) | −23.3643 | −1.86468 | −0.932339 | − | 0.361586i | \(-0.882235\pi\) | ||||
−0.932339 | + | 0.361586i | \(0.882235\pi\) | |||||||
\(158\) | −10.1084 | −0.804179 | ||||||||
\(159\) | 3.98285 | 0.315860 | ||||||||
\(160\) | 1.45353 | 0.114911 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.7921 | 1.94785 | ||||||||
\(163\) | 19.3371 | 1.51460 | 0.757301 | − | 0.653066i | \(-0.226518\pi\) | ||||
0.757301 | + | 0.653066i | \(0.226518\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 19.7039 | 1.53395 | ||||||||
\(166\) | −2.86502 | −0.222368 | ||||||||
\(167\) | −2.00988 | −0.155529 | −0.0777646 | − | 0.996972i | \(-0.524778\pi\) | ||||
−0.0777646 | + | 0.996972i | \(0.524778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.2925 | 1.09943 | ||||||||
\(170\) | −7.34029 | −0.562975 | ||||||||
\(171\) | 32.4056 | 2.47812 | ||||||||
\(172\) | 9.36993 | 0.714451 | ||||||||
\(173\) | −10.8809 | −0.827258 | −0.413629 | − | 0.910446i | \(-0.635739\pi\) | ||||
−0.413629 | + | 0.910446i | \(0.635739\pi\) | |||||||
\(174\) | 7.43793 | 0.563868 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.18274 | 0.315286 | ||||||||
\(177\) | 8.28000 | 0.622363 | ||||||||
\(178\) | −15.4950 | −1.16140 | ||||||||
\(179\) | 6.59120 | 0.492649 | 0.246325 | − | 0.969187i | \(-0.420777\pi\) | ||||
0.246325 | + | 0.969187i | \(0.420777\pi\) | |||||||
\(180\) | 10.9066 | 0.812927 | ||||||||
\(181\) | −10.3441 | −0.768875 | −0.384437 | − | 0.923151i | \(-0.625604\pi\) | ||||
−0.384437 | + | 0.923151i | \(0.625604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.6687 | 2.48886 | ||||||||
\(184\) | −3.03034 | −0.223399 | ||||||||
\(185\) | 3.61769 | 0.265978 | ||||||||
\(186\) | −24.3171 | −1.78302 | ||||||||
\(187\) | −21.1228 | −1.54465 | ||||||||
\(188\) | 7.57920 | 0.552770 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.27739 | 0.455410 | ||||||||
\(191\) | −4.11146 | −0.297495 | −0.148747 | − | 0.988875i | \(-0.547524\pi\) | ||||
−0.148747 | + | 0.988875i | \(0.547524\pi\) | |||||||
\(192\) | 3.24091 | 0.233893 | ||||||||
\(193\) | 17.4496 | 1.25605 | 0.628026 | − | 0.778192i | \(-0.283863\pi\) | ||||
0.628026 | + | 0.778192i | \(0.283863\pi\) | |||||||
\(194\) | −14.7885 | −1.06176 | ||||||||
\(195\) | −24.6101 | −1.76236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.9669 | −1.56508 | −0.782538 | − | 0.622603i | \(-0.786075\pi\) | ||||
−0.782538 | + | 0.622603i | \(0.786075\pi\) | |||||||
\(198\) | 31.3852 | 2.23045 | ||||||||
\(199\) | 9.23644 | 0.654754 | 0.327377 | − | 0.944894i | \(-0.393835\pi\) | ||||
0.327377 | + | 0.944894i | \(0.393835\pi\) | |||||||
\(200\) | −2.88726 | −0.204160 | ||||||||
\(201\) | −13.3142 | −0.939108 | ||||||||
\(202\) | −3.63661 | −0.255871 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.3665 | −1.14589 | ||||||||
\(205\) | −1.45353 | −0.101519 | ||||||||
\(206\) | 13.7935 | 0.961037 | ||||||||
\(207\) | −22.7382 | −1.58041 | ||||||||
\(208\) | −5.22423 | −0.362235 | ||||||||
\(209\) | 18.0641 | 1.24952 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.8202 | 1.57101 | 0.785505 | − | 0.618856i | \(-0.212403\pi\) | ||||
0.785505 | + | 0.618856i | \(0.212403\pi\) | |||||||
\(212\) | 1.22893 | 0.0844031 | ||||||||
\(213\) | −27.4596 | −1.88150 | ||||||||
\(214\) | 20.2757 | 1.38602 | ||||||||
\(215\) | 13.6195 | 0.928840 | ||||||||
\(216\) | 14.5955 | 0.993097 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.86423 | −0.600361 | ||||||||
\(219\) | −14.5587 | −0.983783 | ||||||||
\(220\) | 6.07973 | 0.409896 | ||||||||
\(221\) | 26.3822 | 1.77466 | ||||||||
\(222\) | 8.06631 | 0.541375 | ||||||||
\(223\) | 18.1731 | 1.21696 | 0.608479 | − | 0.793570i | \(-0.291780\pi\) | ||||
0.608479 | + | 0.793570i | \(0.291780\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.6646 | −1.44430 | ||||||||
\(226\) | −7.33107 | −0.487656 | ||||||||
\(227\) | 11.2158 | 0.744417 | 0.372208 | − | 0.928149i | \(-0.378601\pi\) | ||||
0.372208 | + | 0.928149i | \(0.378601\pi\) | |||||||
\(228\) | 13.9966 | 0.926948 | ||||||||
\(229\) | 7.14061 | 0.471865 | 0.235932 | − | 0.971769i | \(-0.424186\pi\) | ||||
0.235932 | + | 0.971769i | \(0.424186\pi\) | |||||||
\(230\) | −4.40468 | −0.290436 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.29501 | 0.150675 | ||||||||
\(233\) | 12.4071 | 0.812819 | 0.406409 | − | 0.913691i | \(-0.366781\pi\) | ||||
0.406409 | + | 0.913691i | \(0.366781\pi\) | |||||||
\(234\) | −39.2000 | −2.56259 | ||||||||
\(235\) | 11.0166 | 0.718643 | ||||||||
\(236\) | 2.55484 | 0.166306 | ||||||||
\(237\) | −32.7603 | −2.12801 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.9128 | 1.22336 | 0.611682 | − | 0.791103i | \(-0.290493\pi\) | ||||
0.611682 | + | 0.791103i | \(0.290493\pi\) | |||||||
\(240\) | 4.71076 | 0.304078 | ||||||||
\(241\) | 23.3723 | 1.50554 | 0.752772 | − | 0.658282i | \(-0.228716\pi\) | ||||
0.752772 | + | 0.658282i | \(0.228716\pi\) | |||||||
\(242\) | 6.49533 | 0.417536 | ||||||||
\(243\) | 36.5627 | 2.34550 | ||||||||
\(244\) | 10.3886 | 0.665065 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.24091 | −0.206633 | ||||||||
\(247\) | −22.5620 | −1.43559 | ||||||||
\(248\) | −7.50317 | −0.476452 | ||||||||
\(249\) | −9.28526 | −0.588430 | ||||||||
\(250\) | −11.4643 | −0.725069 | ||||||||
\(251\) | −3.44847 | −0.217666 | −0.108833 | − | 0.994060i | \(-0.534711\pi\) | ||||
−0.108833 | + | 0.994060i | \(0.534711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.6751 | −0.796878 | ||||||||
\(254\) | −0.797302 | −0.0500272 | ||||||||
\(255\) | −23.7892 | −1.48974 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.0084 | 1.62236 | 0.811180 | − | 0.584797i | \(-0.198826\pi\) | ||||
0.811180 | + | 0.584797i | \(0.198826\pi\) | |||||||
\(258\) | 30.3671 | 1.89057 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.59356 | −0.470933 | ||||||||
\(261\) | 17.2206 | 1.06593 | ||||||||
\(262\) | −9.27577 | −0.573059 | ||||||||
\(263\) | −0.875593 | −0.0539914 | −0.0269957 | − | 0.999636i | \(-0.508594\pi\) | ||||
−0.0269957 | + | 0.999636i | \(0.508594\pi\) | |||||||
\(264\) | 13.5559 | 0.834308 | ||||||||
\(265\) | 1.78628 | 0.109730 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −50.2179 | −3.07328 | ||||||||
\(268\) | −4.10815 | −0.250945 | ||||||||
\(269\) | −27.9132 | −1.70190 | −0.850949 | − | 0.525248i | \(-0.823972\pi\) | ||||
−0.850949 | + | 0.525248i | \(0.823972\pi\) | |||||||
\(270\) | 21.2149 | 1.29110 | ||||||||
\(271\) | 9.10994 | 0.553389 | 0.276695 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276695 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(272\) | −5.04998 | −0.306200 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.22892 | −0.315890 | ||||||||
\(275\) | −12.0766 | −0.728249 | ||||||||
\(276\) | −9.82105 | −0.591158 | ||||||||
\(277\) | −0.0967641 | −0.00581399 | −0.00290699 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290699 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(278\) | −12.9221 | −0.775018 | ||||||||
\(279\) | −56.3001 | −3.37060 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4020 | 0.978462 | 0.489231 | − | 0.872154i | \(-0.337278\pi\) | ||||
0.489231 | + | 0.872154i | \(0.337278\pi\) | |||||||
\(282\) | 24.5635 | 1.46274 | ||||||||
\(283\) | −2.48341 | −0.147623 | −0.0738116 | − | 0.997272i | \(-0.523516\pi\) | ||||
−0.0738116 | + | 0.997272i | \(0.523516\pi\) | |||||||
\(284\) | −8.47279 | −0.502768 | ||||||||
\(285\) | 20.3445 | 1.20510 | ||||||||
\(286\) | −21.8516 | −1.29211 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.50351 | 0.442149 | ||||||||
\(289\) | 8.50231 | 0.500136 | ||||||||
\(290\) | 3.33586 | 0.195889 | ||||||||
\(291\) | −47.9284 | −2.80961 | ||||||||
\(292\) | −4.49215 | −0.262883 | ||||||||
\(293\) | −9.32569 | −0.544813 | −0.272406 | − | 0.962182i | \(-0.587820\pi\) | ||||
−0.272406 | + | 0.962182i | \(0.587820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.71353 | 0.216210 | ||||||||
\(296\) | 2.48890 | 0.144664 | ||||||||
\(297\) | 61.0491 | 3.54243 | ||||||||
\(298\) | −8.42101 | −0.487816 | ||||||||
\(299\) | 15.8312 | 0.915540 | ||||||||
\(300\) | −9.35734 | −0.540246 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.37428 | −0.136624 | ||||||||
\(303\) | −11.7859 | −0.677084 | ||||||||
\(304\) | 4.31873 | 0.247696 | ||||||||
\(305\) | 15.1002 | 0.864634 | ||||||||
\(306\) | −37.8926 | −2.16618 | ||||||||
\(307\) | 15.8969 | 0.907286 | 0.453643 | − | 0.891184i | \(-0.350124\pi\) | ||||
0.453643 | + | 0.891184i | \(0.350124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.7034 | 2.54309 | ||||||||
\(310\) | −10.9061 | −0.619423 | ||||||||
\(311\) | 16.9719 | 0.962387 | 0.481194 | − | 0.876614i | \(-0.340203\pi\) | ||||
0.481194 | + | 0.876614i | \(0.340203\pi\) | |||||||
\(312\) | −16.9313 | −0.958544 | ||||||||
\(313\) | −31.6976 | −1.79165 | −0.895827 | − | 0.444404i | \(-0.853416\pi\) | ||||
−0.895827 | + | 0.444404i | \(0.853416\pi\) | |||||||
\(314\) | −23.3643 | −1.31853 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.1084 | −0.568640 | ||||||||
\(317\) | 16.7818 | 0.942557 | 0.471279 | − | 0.881984i | \(-0.343793\pi\) | ||||
0.471279 | + | 0.881984i | \(0.343793\pi\) | |||||||
\(318\) | 3.98285 | 0.223347 | ||||||||
\(319\) | 9.59944 | 0.537466 | ||||||||
\(320\) | 1.45353 | 0.0812547 | ||||||||
\(321\) | 65.7119 | 3.66768 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.8095 | −1.21351 | ||||||||
\(324\) | 24.7921 | 1.37734 | ||||||||
\(325\) | 15.0837 | 0.836692 | ||||||||
\(326\) | 19.3371 | 1.07099 | ||||||||
\(327\) | −28.7282 | −1.58867 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 19.7039 | 1.08466 | ||||||||
\(331\) | −20.5312 | −1.12850 | −0.564248 | − | 0.825605i | \(-0.690834\pi\) | ||||
−0.564248 | + | 0.825605i | \(0.690834\pi\) | |||||||
\(332\) | −2.86502 | −0.157238 | ||||||||
\(333\) | 18.6755 | 1.02341 | ||||||||
\(334\) | −2.00988 | −0.109976 | ||||||||
\(335\) | −5.97131 | −0.326248 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.71983 | −0.148158 | −0.0740792 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740792 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(338\) | 14.2925 | 0.777412 | ||||||||
\(339\) | −23.7594 | −1.29043 | ||||||||
\(340\) | −7.34029 | −0.398083 | ||||||||
\(341\) | −31.3838 | −1.69953 | ||||||||
\(342\) | 32.4056 | 1.75229 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.36993 | 0.505193 | ||||||||
\(345\) | −14.2752 | −0.768550 | ||||||||
\(346\) | −10.8809 | −0.584960 | ||||||||
\(347\) | 12.9347 | 0.694368 | 0.347184 | − | 0.937797i | \(-0.387138\pi\) | ||||
0.347184 | + | 0.937797i | \(0.387138\pi\) | |||||||
\(348\) | 7.43793 | 0.398715 | ||||||||
\(349\) | 19.9087 | 1.06569 | 0.532843 | − | 0.846214i | \(-0.321124\pi\) | ||||
0.532843 | + | 0.846214i | \(0.321124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −76.2501 | −4.06993 | ||||||||
\(352\) | 4.18274 | 0.222941 | ||||||||
\(353\) | 0.487930 | 0.0259699 | 0.0129849 | − | 0.999916i | \(-0.495867\pi\) | ||||
0.0129849 | + | 0.999916i | \(0.495867\pi\) | |||||||
\(354\) | 8.28000 | 0.440077 | ||||||||
\(355\) | −12.3154 | −0.653636 | ||||||||
\(356\) | −15.4950 | −0.821233 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.59120 | 0.348356 | ||||||||
\(359\) | −7.91222 | −0.417591 | −0.208795 | − | 0.977959i | \(-0.566954\pi\) | ||||
−0.208795 | + | 0.977959i | \(0.566954\pi\) | |||||||
\(360\) | 10.9066 | 0.574826 | ||||||||
\(361\) | −0.348598 | −0.0183473 | ||||||||
\(362\) | −10.3441 | −0.543676 | ||||||||
\(363\) | 21.0508 | 1.10488 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.52946 | −0.341768 | ||||||||
\(366\) | 33.6687 | 1.75989 | ||||||||
\(367\) | −14.4797 | −0.755835 | −0.377918 | − | 0.925839i | \(-0.623360\pi\) | ||||
−0.377918 | + | 0.925839i | \(0.623360\pi\) | |||||||
\(368\) | −3.03034 | −0.157967 | ||||||||
\(369\) | −7.50351 | −0.390617 | ||||||||
\(370\) | 3.61769 | 0.188075 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −24.3171 | −1.26078 | ||||||||
\(373\) | 18.9631 | 0.981874 | 0.490937 | − | 0.871195i | \(-0.336655\pi\) | ||||
0.490937 | + | 0.871195i | \(0.336655\pi\) | |||||||
\(374\) | −21.1228 | −1.09223 | ||||||||
\(375\) | −37.1549 | −1.91867 | ||||||||
\(376\) | 7.57920 | 0.390868 | ||||||||
\(377\) | −11.9897 | −0.617499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3181 | −1.45461 | −0.727303 | − | 0.686317i | \(-0.759226\pi\) | ||||
−0.727303 | + | 0.686317i | \(0.759226\pi\) | |||||||
\(380\) | 6.27739 | 0.322023 | ||||||||
\(381\) | −2.58399 | −0.132382 | ||||||||
\(382\) | −4.11146 | −0.210361 | ||||||||
\(383\) | −13.0221 | −0.665400 | −0.332700 | − | 0.943033i | \(-0.607960\pi\) | ||||
−0.332700 | + | 0.943033i | \(0.607960\pi\) | |||||||
\(384\) | 3.24091 | 0.165387 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.4496 | 0.888163 | ||||||||
\(387\) | 70.3074 | 3.57392 | ||||||||
\(388\) | −14.7885 | −0.750775 | ||||||||
\(389\) | −35.3836 | −1.79402 | −0.897009 | − | 0.442012i | \(-0.854265\pi\) | ||||
−0.897009 | + | 0.442012i | \(0.854265\pi\) | |||||||
\(390\) | −24.6101 | −1.24618 | ||||||||
\(391\) | 15.3031 | 0.773913 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −30.0620 | −1.51642 | ||||||||
\(394\) | −21.9669 | −1.10668 | ||||||||
\(395\) | −14.6928 | −0.739275 | ||||||||
\(396\) | 31.3852 | 1.57717 | ||||||||
\(397\) | −20.0384 | −1.00570 | −0.502850 | − | 0.864374i | \(-0.667715\pi\) | ||||
−0.502850 | + | 0.864374i | \(0.667715\pi\) | |||||||
\(398\) | 9.23644 | 0.462981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.88726 | −0.144363 | ||||||||
\(401\) | −14.8916 | −0.743652 | −0.371826 | − | 0.928302i | \(-0.621268\pi\) | ||||
−0.371826 | + | 0.928302i | \(0.621268\pi\) | |||||||
\(402\) | −13.3142 | −0.664050 | ||||||||
\(403\) | 39.1982 | 1.95260 | ||||||||
\(404\) | −3.63661 | −0.180928 | ||||||||
\(405\) | 36.0361 | 1.79065 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4104 | 0.516026 | ||||||||
\(408\) | −16.3665 | −0.810265 | ||||||||
\(409\) | 22.5833 | 1.11667 | 0.558336 | − | 0.829615i | \(-0.311440\pi\) | ||||
0.558336 | + | 0.829615i | \(0.311440\pi\) | |||||||
\(410\) | −1.45353 | −0.0717846 | ||||||||
\(411\) | −16.9465 | −0.835907 | ||||||||
\(412\) | 13.7935 | 0.679556 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −22.7382 | −1.11752 | ||||||||
\(415\) | −4.16438 | −0.204421 | ||||||||
\(416\) | −5.22423 | −0.256139 | ||||||||
\(417\) | −41.8795 | −2.05085 | ||||||||
\(418\) | 18.0641 | 0.883545 | ||||||||
\(419\) | 19.4523 | 0.950305 | 0.475153 | − | 0.879903i | \(-0.342393\pi\) | ||||
0.475153 | + | 0.879903i | \(0.342393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7322 | −0.718005 | −0.359003 | − | 0.933337i | \(-0.616883\pi\) | ||||
−0.359003 | + | 0.933337i | \(0.616883\pi\) | |||||||
\(422\) | 22.8202 | 1.11087 | ||||||||
\(423\) | 56.8706 | 2.76514 | ||||||||
\(424\) | 1.22893 | 0.0596820 | ||||||||
\(425\) | 14.5806 | 0.707262 | ||||||||
\(426\) | −27.4596 | −1.33042 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 20.2757 | 0.980065 | ||||||||
\(429\) | −70.8191 | −3.41918 | ||||||||
\(430\) | 13.6195 | 0.656789 | ||||||||
\(431\) | 8.85046 | 0.426311 | 0.213156 | − | 0.977018i | \(-0.431626\pi\) | ||||
0.213156 | + | 0.977018i | \(0.431626\pi\) | |||||||
\(432\) | 14.5955 | 0.702225 | ||||||||
\(433\) | 2.99616 | 0.143986 | 0.0719931 | − | 0.997405i | \(-0.477064\pi\) | ||||
0.0719931 | + | 0.997405i | \(0.477064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.8112 | 0.518359 | ||||||||
\(436\) | −8.86423 | −0.424520 | ||||||||
\(437\) | −13.0872 | −0.626045 | ||||||||
\(438\) | −14.5587 | −0.695640 | ||||||||
\(439\) | −11.2325 | −0.536096 | −0.268048 | − | 0.963406i | \(-0.586379\pi\) | ||||
−0.268048 | + | 0.963406i | \(0.586379\pi\) | |||||||
\(440\) | 6.07973 | 0.289840 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.3822 | 1.25488 | ||||||||
\(443\) | −30.2403 | −1.43676 | −0.718381 | − | 0.695650i | \(-0.755116\pi\) | ||||
−0.718381 | + | 0.695650i | \(0.755116\pi\) | |||||||
\(444\) | 8.06631 | 0.382810 | ||||||||
\(445\) | −22.5224 | −1.06766 | ||||||||
\(446\) | 18.1731 | 0.860520 | ||||||||
\(447\) | −27.2918 | −1.29086 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5454 | −0.922403 | −0.461202 | − | 0.887295i | \(-0.652582\pi\) | ||||
−0.461202 | + | 0.887295i | \(0.652582\pi\) | |||||||
\(450\) | −21.6646 | −1.02128 | ||||||||
\(451\) | −4.18274 | −0.196958 | ||||||||
\(452\) | −7.33107 | −0.344825 | ||||||||
\(453\) | −7.69482 | −0.361534 | ||||||||
\(454\) | 11.2158 | 0.526382 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.9966 | 0.655451 | ||||||||
\(457\) | 27.1077 | 1.26804 | 0.634022 | − | 0.773315i | \(-0.281403\pi\) | ||||
0.634022 | + | 0.773315i | \(0.281403\pi\) | |||||||
\(458\) | 7.14061 | 0.333659 | ||||||||
\(459\) | −73.7069 | −3.44034 | ||||||||
\(460\) | −4.40468 | −0.205369 | ||||||||
\(461\) | −9.69624 | −0.451599 | −0.225800 | − | 0.974174i | \(-0.572499\pi\) | ||||
−0.225800 | + | 0.974174i | \(0.572499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3349 | 1.13094 | 0.565468 | − | 0.824770i | \(-0.308695\pi\) | ||||
0.565468 | + | 0.824770i | \(0.308695\pi\) | |||||||
\(464\) | 2.29501 | 0.106543 | ||||||||
\(465\) | −35.3456 | −1.63911 | ||||||||
\(466\) | 12.4071 | 0.574750 | ||||||||
\(467\) | −21.6468 | −1.00170 | −0.500848 | − | 0.865535i | \(-0.666979\pi\) | ||||
−0.500848 | + | 0.865535i | \(0.666979\pi\) | |||||||
\(468\) | −39.2000 | −1.81202 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.0166 | 0.508157 | ||||||||
\(471\) | −75.7218 | −3.48908 | ||||||||
\(472\) | 2.55484 | 0.117596 | ||||||||
\(473\) | 39.1920 | 1.80205 | ||||||||
\(474\) | −32.7603 | −1.50473 | ||||||||
\(475\) | −12.4693 | −0.572129 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.22128 | 0.422213 | ||||||||
\(478\) | 18.9128 | 0.865050 | ||||||||
\(479\) | −5.40224 | −0.246834 | −0.123417 | − | 0.992355i | \(-0.539385\pi\) | ||||
−0.123417 | + | 0.992355i | \(0.539385\pi\) | |||||||
\(480\) | 4.71076 | 0.215016 | ||||||||
\(481\) | −13.0026 | −0.592867 | ||||||||
\(482\) | 23.3723 | 1.06458 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.49533 | 0.295242 | ||||||||
\(485\) | −21.4956 | −0.976064 | ||||||||
\(486\) | 36.5627 | 1.65852 | ||||||||
\(487\) | −0.808632 | −0.0366426 | −0.0183213 | − | 0.999832i | \(-0.505832\pi\) | ||||
−0.0183213 | + | 0.999832i | \(0.505832\pi\) | |||||||
\(488\) | 10.3886 | 0.470272 | ||||||||
\(489\) | 62.6700 | 2.83403 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.24205 | 0.326829 | 0.163415 | − | 0.986557i | \(-0.447749\pi\) | ||||
0.163415 | + | 0.986557i | \(0.447749\pi\) | |||||||
\(492\) | −3.24091 | −0.146112 | ||||||||
\(493\) | −11.5898 | −0.521977 | ||||||||
\(494\) | −22.5620 | −1.01511 | ||||||||
\(495\) | 45.6193 | 2.05044 | ||||||||
\(496\) | −7.50317 | −0.336902 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.28526 | −0.416083 | ||||||||
\(499\) | −7.70718 | −0.345021 | −0.172510 | − | 0.985008i | \(-0.555188\pi\) | ||||
−0.172510 | + | 0.985008i | \(0.555188\pi\) | |||||||
\(500\) | −11.4643 | −0.512701 | ||||||||
\(501\) | −6.51384 | −0.291017 | ||||||||
\(502\) | −3.44847 | −0.153913 | ||||||||
\(503\) | −4.34375 | −0.193678 | −0.0968391 | − | 0.995300i | \(-0.530873\pi\) | ||||
−0.0968391 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.28591 | −0.235220 | ||||||||
\(506\) | −12.6751 | −0.563478 | ||||||||
\(507\) | 46.3209 | 2.05718 | ||||||||
\(508\) | −0.797302 | −0.0353746 | ||||||||
\(509\) | −22.1583 | −0.982148 | −0.491074 | − | 0.871118i | \(-0.663395\pi\) | ||||
−0.491074 | + | 0.871118i | \(0.663395\pi\) | |||||||
\(510\) | −23.7892 | −1.05341 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 63.0339 | 2.78301 | ||||||||
\(514\) | 26.0084 | 1.14718 | ||||||||
\(515\) | 20.0492 | 0.883474 | ||||||||
\(516\) | 30.3671 | 1.33684 | ||||||||
\(517\) | 31.7018 | 1.39425 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.2640 | −1.54792 | ||||||||
\(520\) | −7.59356 | −0.333000 | ||||||||
\(521\) | −35.9075 | −1.57314 | −0.786569 | − | 0.617503i | \(-0.788144\pi\) | ||||
−0.786569 | + | 0.617503i | \(0.788144\pi\) | |||||||
\(522\) | 17.2206 | 0.753727 | ||||||||
\(523\) | 35.7784 | 1.56448 | 0.782241 | − | 0.622976i | \(-0.214076\pi\) | ||||
0.782241 | + | 0.622976i | \(0.214076\pi\) | |||||||
\(524\) | −9.27577 | −0.405214 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.875593 | −0.0381777 | ||||||||
\(527\) | 37.8909 | 1.65055 | ||||||||
\(528\) | 13.5559 | 0.589945 | ||||||||
\(529\) | −13.8171 | −0.600742 | ||||||||
\(530\) | 1.78628 | 0.0775911 | ||||||||
\(531\) | 19.1702 | 0.831918 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.22423 | 0.226286 | ||||||||
\(534\) | −50.2179 | −2.17314 | ||||||||
\(535\) | 29.4714 | 1.27416 | ||||||||
\(536\) | −4.10815 | −0.177445 | ||||||||
\(537\) | 21.3615 | 0.921816 | ||||||||
\(538\) | −27.9132 | −1.20342 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 21.2149 | 0.912946 | ||||||||
\(541\) | 13.7164 | 0.589716 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(542\) | 9.10994 | 0.391305 | ||||||||
\(543\) | −33.5245 | −1.43867 | ||||||||
\(544\) | −5.04998 | −0.216516 | ||||||||
\(545\) | −12.8844 | −0.551907 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.7038 | 1.52658 | 0.763292 | − | 0.646054i | \(-0.223582\pi\) | ||||
0.763292 | + | 0.646054i | \(0.223582\pi\) | |||||||
\(548\) | −5.22892 | −0.223368 | ||||||||
\(549\) | 77.9513 | 3.32688 | ||||||||
\(550\) | −12.0766 | −0.514950 | ||||||||
\(551\) | 9.91153 | 0.422245 | ||||||||
\(552\) | −9.82105 | −0.418012 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.0967641 | −0.00411111 | ||||||||
\(555\) | 11.7246 | 0.497682 | ||||||||
\(556\) | −12.9221 | −0.548021 | ||||||||
\(557\) | 3.47414 | 0.147204 | 0.0736020 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0736020 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(558\) | −56.3001 | −2.38337 | ||||||||
\(559\) | −48.9506 | −2.07039 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −68.4570 | −2.89026 | ||||||||
\(562\) | 16.4020 | 0.691877 | ||||||||
\(563\) | −35.2600 | −1.48603 | −0.743015 | − | 0.669274i | \(-0.766605\pi\) | ||||
−0.743015 | + | 0.669274i | \(0.766605\pi\) | |||||||
\(564\) | 24.5635 | 1.03431 | ||||||||
\(565\) | −10.6559 | −0.448298 | ||||||||
\(566\) | −2.48341 | −0.104385 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.47279 | −0.355511 | ||||||||
\(569\) | 25.4642 | 1.06752 | 0.533758 | − | 0.845637i | \(-0.320779\pi\) | ||||
0.533758 | + | 0.845637i | \(0.320779\pi\) | |||||||
\(570\) | 20.3445 | 0.852136 | ||||||||
\(571\) | 2.68312 | 0.112285 | 0.0561425 | − | 0.998423i | \(-0.482120\pi\) | ||||
0.0561425 | + | 0.998423i | \(0.482120\pi\) | |||||||
\(572\) | −21.8516 | −0.913661 | ||||||||
\(573\) | −13.3249 | −0.556655 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.74936 | 0.364873 | ||||||||
\(576\) | 7.50351 | 0.312646 | ||||||||
\(577\) | 16.3197 | 0.679396 | 0.339698 | − | 0.940535i | \(-0.389675\pi\) | ||||
0.339698 | + | 0.940535i | \(0.389675\pi\) | |||||||
\(578\) | 8.50231 | 0.353650 | ||||||||
\(579\) | 56.5527 | 2.35025 | ||||||||
\(580\) | 3.33586 | 0.138514 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −47.9284 | −1.98670 | ||||||||
\(583\) | 5.14029 | 0.212889 | ||||||||
\(584\) | −4.49215 | −0.185886 | ||||||||
\(585\) | −56.9784 | −2.35576 | ||||||||
\(586\) | −9.32569 | −0.385241 | ||||||||
\(587\) | 3.21883 | 0.132855 | 0.0664277 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664277 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.4041 | −1.33519 | ||||||||
\(590\) | 3.71353 | 0.152884 | ||||||||
\(591\) | −71.1927 | −2.92848 | ||||||||
\(592\) | 2.48890 | 0.102293 | ||||||||
\(593\) | 3.30169 | 0.135584 | 0.0677920 | − | 0.997699i | \(-0.478405\pi\) | ||||
0.0677920 | + | 0.997699i | \(0.478405\pi\) | |||||||
\(594\) | 61.0491 | 2.50488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.42101 | −0.344938 | ||||||||
\(597\) | 29.9345 | 1.22514 | ||||||||
\(598\) | 15.8312 | 0.647384 | ||||||||
\(599\) | 24.7427 | 1.01096 | 0.505480 | − | 0.862838i | \(-0.331315\pi\) | ||||
0.505480 | + | 0.862838i | \(0.331315\pi\) | |||||||
\(600\) | −9.35734 | −0.382012 | ||||||||
\(601\) | −19.4774 | −0.794500 | −0.397250 | − | 0.917710i | \(-0.630035\pi\) | ||||
−0.397250 | + | 0.917710i | \(0.630035\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.8256 | −1.25531 | ||||||||
\(604\) | −2.37428 | −0.0966079 | ||||||||
\(605\) | 9.44115 | 0.383837 | ||||||||
\(606\) | −11.7859 | −0.478771 | ||||||||
\(607\) | 24.1581 | 0.980547 | 0.490274 | − | 0.871569i | \(-0.336897\pi\) | ||||
0.490274 | + | 0.871569i | \(0.336897\pi\) | |||||||
\(608\) | 4.31873 | 0.175148 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.1002 | 0.611389 | ||||||||
\(611\) | −39.5955 | −1.60186 | ||||||||
\(612\) | −37.8926 | −1.53172 | ||||||||
\(613\) | −13.3981 | −0.541144 | −0.270572 | − | 0.962700i | \(-0.587213\pi\) | ||||
−0.270572 | + | 0.962700i | \(0.587213\pi\) | |||||||
\(614\) | 15.8969 | 0.641548 | ||||||||
\(615\) | −4.71076 | −0.189956 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.9785 | 1.73025 | 0.865125 | − | 0.501557i | \(-0.167239\pi\) | ||||
0.865125 | + | 0.501557i | \(0.167239\pi\) | |||||||
\(618\) | 44.7034 | 1.79824 | ||||||||
\(619\) | 13.1401 | 0.528145 | 0.264073 | − | 0.964503i | \(-0.414934\pi\) | ||||
0.264073 | + | 0.964503i | \(0.414934\pi\) | |||||||
\(620\) | −10.9061 | −0.437998 | ||||||||
\(621\) | −44.2292 | −1.77486 | ||||||||
\(622\) | 16.9719 | 0.680511 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −16.9313 | −0.677793 | ||||||||
\(625\) | −2.22748 | −0.0890990 | ||||||||
\(626\) | −31.6976 | −1.26689 | ||||||||
\(627\) | 58.5442 | 2.33803 | ||||||||
\(628\) | −23.3643 | −0.932339 | ||||||||
\(629\) | −12.5689 | −0.501155 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7634 | 1.02562 | 0.512812 | − | 0.858501i | \(-0.328604\pi\) | ||||
0.512812 | + | 0.858501i | \(0.328604\pi\) | |||||||
\(632\) | −10.1084 | −0.402089 | ||||||||
\(633\) | 73.9584 | 2.93958 | ||||||||
\(634\) | 16.7818 | 0.666489 | ||||||||
\(635\) | −1.15890 | −0.0459896 | ||||||||
\(636\) | 3.98285 | 0.157930 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.59944 | 0.380046 | ||||||||
\(639\) | −63.5757 | −2.51502 | ||||||||
\(640\) | 1.45353 | 0.0574557 | ||||||||
\(641\) | 43.8275 | 1.73108 | 0.865542 | − | 0.500837i | \(-0.166974\pi\) | ||||
0.865542 | + | 0.500837i | \(0.166974\pi\) | |||||||
\(642\) | 65.7119 | 2.59344 | ||||||||
\(643\) | 45.7881 | 1.80571 | 0.902853 | − | 0.429949i | \(-0.141468\pi\) | ||||
0.902853 | + | 0.429949i | \(0.141468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.1395 | 1.73799 | ||||||||
\(646\) | −21.8095 | −0.858083 | ||||||||
\(647\) | −12.6013 | −0.495410 | −0.247705 | − | 0.968836i | \(-0.579676\pi\) | ||||
−0.247705 | + | 0.968836i | \(0.579676\pi\) | |||||||
\(648\) | 24.7921 | 0.973927 | ||||||||
\(649\) | 10.6862 | 0.419471 | ||||||||
\(650\) | 15.0837 | 0.591630 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.3371 | 0.757301 | ||||||||
\(653\) | 41.4853 | 1.62344 | 0.811722 | − | 0.584044i | \(-0.198531\pi\) | ||||
0.811722 | + | 0.584044i | \(0.198531\pi\) | |||||||
\(654\) | −28.7282 | −1.12336 | ||||||||
\(655\) | −13.4826 | −0.526808 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −33.7069 | −1.31503 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.3880 | 0.794206 | 0.397103 | − | 0.917774i | \(-0.370016\pi\) | ||||
0.397103 | + | 0.917774i | \(0.370016\pi\) | |||||||
\(660\) | 19.7039 | 0.766973 | ||||||||
\(661\) | −39.5463 | −1.53817 | −0.769086 | − | 0.639145i | \(-0.779288\pi\) | ||||
−0.769086 | + | 0.639145i | \(0.779288\pi\) | |||||||
\(662\) | −20.5312 | −0.797968 | ||||||||
\(663\) | 85.5025 | 3.32064 | ||||||||
\(664\) | −2.86502 | −0.111184 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.6755 | 0.723661 | ||||||||
\(667\) | −6.95466 | −0.269285 | ||||||||
\(668\) | −2.00988 | −0.0777646 | ||||||||
\(669\) | 58.8973 | 2.27710 | ||||||||
\(670\) | −5.97131 | −0.230692 | ||||||||
\(671\) | 43.4530 | 1.67749 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9729 | −0.731352 | −0.365676 | − | 0.930742i | \(-0.619162\pi\) | ||||
−0.365676 | + | 0.930742i | \(0.619162\pi\) | |||||||
\(674\) | −2.71983 | −0.104764 | ||||||||
\(675\) | −42.1409 | −1.62200 | ||||||||
\(676\) | 14.2925 | 0.549713 | ||||||||
\(677\) | 11.6773 | 0.448794 | 0.224397 | − | 0.974498i | \(-0.427959\pi\) | ||||
0.224397 | + | 0.974498i | \(0.427959\pi\) | |||||||
\(678\) | −23.7594 | −0.912473 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.34029 | −0.281487 | ||||||||
\(681\) | 36.3493 | 1.39291 | ||||||||
\(682\) | −31.3838 | −1.20175 | ||||||||
\(683\) | 15.6257 | 0.597899 | 0.298949 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298949 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(684\) | 32.4056 | 1.23906 | ||||||||
\(685\) | −7.60038 | −0.290396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.1421 | 0.882925 | ||||||||
\(688\) | 9.36993 | 0.357225 | ||||||||
\(689\) | −6.42020 | −0.244590 | ||||||||
\(690\) | −14.2752 | −0.543447 | ||||||||
\(691\) | −14.3995 | −0.547784 | −0.273892 | − | 0.961760i | \(-0.588311\pi\) | ||||
−0.273892 | + | 0.961760i | \(0.588311\pi\) | |||||||
\(692\) | −10.8809 | −0.413629 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.9347 | 0.490993 | ||||||||
\(695\) | −18.7827 | −0.712468 | ||||||||
\(696\) | 7.43793 | 0.281934 | ||||||||
\(697\) | 5.04998 | 0.191282 | ||||||||
\(698\) | 19.9087 | 0.753554 | ||||||||
\(699\) | 40.2105 | 1.52090 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2708 | 0.463462 | 0.231731 | − | 0.972780i | \(-0.425561\pi\) | ||||
0.231731 | + | 0.972780i | \(0.425561\pi\) | |||||||
\(702\) | −76.2501 | −2.87787 | ||||||||
\(703\) | 10.7489 | 0.405402 | ||||||||
\(704\) | 4.18274 | 0.157643 | ||||||||
\(705\) | 35.7038 | 1.34468 | ||||||||
\(706\) | 0.487930 | 0.0183635 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.28000 | 0.311182 | ||||||||
\(709\) | 17.7056 | 0.664948 | 0.332474 | − | 0.943112i | \(-0.392117\pi\) | ||||
0.332474 | + | 0.943112i | \(0.392117\pi\) | |||||||
\(710\) | −12.3154 | −0.462190 | ||||||||
\(711\) | −75.8483 | −2.84453 | ||||||||
\(712\) | −15.4950 | −0.580699 | ||||||||
\(713\) | 22.7371 | 0.851512 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7619 | −1.18783 | ||||||||
\(716\) | 6.59120 | 0.246325 | ||||||||
\(717\) | 61.2946 | 2.28909 | ||||||||
\(718\) | −7.91222 | −0.295281 | ||||||||
\(719\) | 48.6849 | 1.81564 | 0.907819 | − | 0.419362i | \(-0.137746\pi\) | ||||
0.907819 | + | 0.419362i | \(0.137746\pi\) | |||||||
\(720\) | 10.9066 | 0.406464 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.348598 | −0.0129735 | ||||||||
\(723\) | 75.7476 | 2.81708 | ||||||||
\(724\) | −10.3441 | −0.384437 | ||||||||
\(725\) | −6.62629 | −0.246094 | ||||||||
\(726\) | 21.0508 | 0.781268 | ||||||||
\(727\) | −48.2554 | −1.78970 | −0.894848 | − | 0.446372i | \(-0.852716\pi\) | ||||
−0.894848 | + | 0.446372i | \(0.852716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.1200 | 1.63407 | ||||||||
\(730\) | −6.52946 | −0.241666 | ||||||||
\(731\) | −47.3180 | −1.75012 | ||||||||
\(732\) | 33.6687 | 1.24443 | ||||||||
\(733\) | −23.1361 | −0.854550 | −0.427275 | − | 0.904122i | \(-0.640526\pi\) | ||||
−0.427275 | + | 0.904122i | \(0.640526\pi\) | |||||||
\(734\) | −14.4797 | −0.534456 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.03034 | −0.111700 | ||||||||
\(737\) | −17.1833 | −0.632956 | ||||||||
\(738\) | −7.50351 | −0.276208 | ||||||||
\(739\) | 1.81517 | 0.0667721 | 0.0333861 | − | 0.999443i | \(-0.489371\pi\) | ||||
0.0333861 | + | 0.999443i | \(0.489371\pi\) | |||||||
\(740\) | 3.61769 | 0.132989 | ||||||||
\(741\) | −73.1215 | −2.68618 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.27732 | 0.120233 | 0.0601165 | − | 0.998191i | \(-0.480853\pi\) | ||||
0.0601165 | + | 0.998191i | \(0.480853\pi\) | |||||||
\(744\) | −24.3171 | −0.891508 | ||||||||
\(745\) | −12.2402 | −0.448446 | ||||||||
\(746\) | 18.9631 | 0.694290 | ||||||||
\(747\) | −21.4977 | −0.786559 | ||||||||
\(748\) | −21.1228 | −0.772325 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −37.1549 | −1.35671 | ||||||||
\(751\) | −40.2715 | −1.46953 | −0.734765 | − | 0.678322i | \(-0.762707\pi\) | ||||
−0.734765 | + | 0.678322i | \(0.762707\pi\) | |||||||
\(752\) | 7.57920 | 0.276385 | ||||||||
\(753\) | −11.1762 | −0.407283 | ||||||||
\(754\) | −11.9897 | −0.436638 | ||||||||
\(755\) | −3.45108 | −0.125598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1294 | 0.477195 | 0.238597 | − | 0.971119i | \(-0.423312\pi\) | ||||
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(758\) | −28.3181 | −1.02856 | ||||||||
\(759\) | −41.0789 | −1.49107 | ||||||||
\(760\) | 6.27739 | 0.227705 | ||||||||
\(761\) | 2.72300 | 0.0987088 | 0.0493544 | − | 0.998781i | \(-0.484284\pi\) | ||||
0.0493544 | + | 0.998781i | \(0.484284\pi\) | |||||||
\(762\) | −2.58399 | −0.0936079 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.11146 | −0.148747 | ||||||||
\(765\) | −55.0779 | −1.99135 | ||||||||
\(766\) | −13.0221 | −0.470509 | ||||||||
\(767\) | −13.3470 | −0.481934 | ||||||||
\(768\) | 3.24091 | 0.116946 | ||||||||
\(769\) | 11.1411 | 0.401758 | 0.200879 | − | 0.979616i | \(-0.435620\pi\) | ||||
0.200879 | + | 0.979616i | \(0.435620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 84.2909 | 3.03566 | ||||||||
\(772\) | 17.4496 | 0.628026 | ||||||||
\(773\) | 28.6395 | 1.03009 | 0.515045 | − | 0.857163i | \(-0.327775\pi\) | ||||
0.515045 | + | 0.857163i | \(0.327775\pi\) | |||||||
\(774\) | 70.3074 | 2.52715 | ||||||||
\(775\) | 21.6636 | 0.778178 | ||||||||
\(776\) | −14.7885 | −0.530878 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.3836 | −1.26856 | ||||||||
\(779\) | −4.31873 | −0.154734 | ||||||||
\(780\) | −24.6101 | −0.881181 | ||||||||
\(781\) | −35.4395 | −1.26813 | ||||||||
\(782\) | 15.3031 | 0.547239 | ||||||||
\(783\) | 33.4968 | 1.19708 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.9607 | −1.21211 | ||||||||
\(786\) | −30.0620 | −1.07227 | ||||||||
\(787\) | 39.7506 | 1.41696 | 0.708479 | − | 0.705732i | \(-0.249382\pi\) | ||||
0.708479 | + | 0.705732i | \(0.249382\pi\) | |||||||
\(788\) | −21.9669 | −0.782538 | ||||||||
\(789\) | −2.83772 | −0.101025 | ||||||||
\(790\) | −14.6928 | −0.522746 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 31.3852 | 1.11523 | ||||||||
\(793\) | −54.2726 | −1.92728 | ||||||||
\(794\) | −20.0384 | −0.711137 | ||||||||
\(795\) | 5.78918 | 0.205321 | ||||||||
\(796\) | 9.23644 | 0.327377 | ||||||||
\(797\) | 54.7109 | 1.93796 | 0.968981 | − | 0.247137i | \(-0.0794898\pi\) | ||||
0.968981 | + | 0.247137i | \(0.0794898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.2748 | −1.35407 | ||||||||
\(800\) | −2.88726 | −0.102080 | ||||||||
\(801\) | −116.267 | −4.10808 | ||||||||
\(802\) | −14.8916 | −0.525841 | ||||||||
\(803\) | −18.7895 | −0.663067 | ||||||||
\(804\) | −13.3142 | −0.469554 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 39.1982 | 1.38070 | ||||||||
\(807\) | −90.4642 | −3.18449 | ||||||||
\(808\) | −3.63661 | −0.127935 | ||||||||
\(809\) | −19.5057 | −0.685784 | −0.342892 | − | 0.939375i | \(-0.611406\pi\) | ||||
−0.342892 | + | 0.939375i | \(0.611406\pi\) | |||||||
\(810\) | 36.0361 | 1.26618 | ||||||||
\(811\) | −31.6037 | −1.10976 | −0.554879 | − | 0.831931i | \(-0.687235\pi\) | ||||
−0.554879 | + | 0.831931i | \(0.687235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.5245 | 1.03547 | ||||||||
\(814\) | 10.4104 | 0.364885 | ||||||||
\(815\) | 28.1071 | 0.984548 | ||||||||
\(816\) | −16.3665 | −0.572944 | ||||||||
\(817\) | 40.4662 | 1.41573 | ||||||||
\(818\) | 22.5833 | 0.789606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.45353 | −0.0507594 | ||||||||
\(821\) | 11.9842 | 0.418250 | 0.209125 | − | 0.977889i | \(-0.432938\pi\) | ||||
0.209125 | + | 0.977889i | \(0.432938\pi\) | |||||||
\(822\) | −16.9465 | −0.591076 | ||||||||
\(823\) | −7.39458 | −0.257759 | −0.128879 | − | 0.991660i | \(-0.541138\pi\) | ||||
−0.128879 | + | 0.991660i | \(0.541138\pi\) | |||||||
\(824\) | 13.7935 | 0.480519 | ||||||||
\(825\) | −39.1393 | −1.36266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.5511 | 0.923272 | 0.461636 | − | 0.887069i | \(-0.347263\pi\) | ||||
0.461636 | + | 0.887069i | \(0.347263\pi\) | |||||||
\(828\) | −22.7382 | −0.790206 | ||||||||
\(829\) | 13.9729 | 0.485300 | 0.242650 | − | 0.970114i | \(-0.421983\pi\) | ||||
0.242650 | + | 0.970114i | \(0.421983\pi\) | |||||||
\(830\) | −4.16438 | −0.144548 | ||||||||
\(831\) | −0.313604 | −0.0108788 | ||||||||
\(832\) | −5.22423 | −0.181117 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −41.8795 | −1.45017 | ||||||||
\(835\) | −2.92142 | −0.101100 | ||||||||
\(836\) | 18.0641 | 0.624761 | ||||||||
\(837\) | −109.512 | −3.78530 | ||||||||
\(838\) | 19.4523 | 0.671967 | ||||||||
\(839\) | 9.50824 | 0.328261 | 0.164130 | − | 0.986439i | \(-0.447518\pi\) | ||||
0.164130 | + | 0.986439i | \(0.447518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7329 | −0.818377 | ||||||||
\(842\) | −14.7322 | −0.507707 | ||||||||
\(843\) | 53.1575 | 1.83084 | ||||||||
\(844\) | 22.8202 | 0.785505 | ||||||||
\(845\) | 20.7746 | 0.714668 | ||||||||
\(846\) | 56.8706 | 1.95525 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.22893 | 0.0422016 | ||||||||
\(849\) | −8.04850 | −0.276224 | ||||||||
\(850\) | 14.5806 | 0.500110 | ||||||||
\(851\) | −7.54221 | −0.258544 | ||||||||
\(852\) | −27.4596 | −0.940750 | ||||||||
\(853\) | −39.8656 | −1.36497 | −0.682485 | − | 0.730899i | \(-0.739101\pi\) | ||||
−0.682485 | + | 0.730899i | \(0.739101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47.1025 | 1.61087 | ||||||||
\(856\) | 20.2757 | 0.693011 | ||||||||
\(857\) | 12.5114 | 0.427381 | 0.213691 | − | 0.976901i | \(-0.431452\pi\) | ||||
0.213691 | + | 0.976901i | \(0.431452\pi\) | |||||||
\(858\) | −70.8191 | −2.41772 | ||||||||
\(859\) | −1.99659 | −0.0681227 | −0.0340613 | − | 0.999420i | \(-0.510844\pi\) | ||||
−0.0340613 | + | 0.999420i | \(0.510844\pi\) | |||||||
\(860\) | 13.6195 | 0.464420 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.85046 | 0.301448 | ||||||||
\(863\) | −16.5835 | −0.564510 | −0.282255 | − | 0.959339i | \(-0.591082\pi\) | ||||
−0.282255 | + | 0.959339i | \(0.591082\pi\) | |||||||
\(864\) | 14.5955 | 0.496548 | ||||||||
\(865\) | −15.8157 | −0.537749 | ||||||||
\(866\) | 2.99616 | 0.101814 | ||||||||
\(867\) | 27.5553 | 0.935825 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.2807 | −1.43427 | ||||||||
\(870\) | 10.8112 | 0.366535 | ||||||||
\(871\) | 21.4619 | 0.727209 | ||||||||
\(872\) | −8.86423 | −0.300181 | ||||||||
\(873\) | −110.966 | −3.75563 | ||||||||
\(874\) | −13.0872 | −0.442681 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.5587 | −0.491891 | ||||||||
\(877\) | −33.8770 | −1.14395 | −0.571973 | − | 0.820272i | \(-0.693822\pi\) | ||||
−0.571973 | + | 0.820272i | \(0.693822\pi\) | |||||||
\(878\) | −11.2325 | −0.379077 | ||||||||
\(879\) | −30.2238 | −1.01942 | ||||||||
\(880\) | 6.07973 | 0.204948 | ||||||||
\(881\) | −35.6178 | −1.19999 | −0.599997 | − | 0.800002i | \(-0.704832\pi\) | ||||
−0.599997 | + | 0.800002i | \(0.704832\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.66968 | 0.190800 | 0.0953999 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0953999 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(884\) | 26.3822 | 0.887331 | ||||||||
\(885\) | 12.0352 | 0.404559 | ||||||||
\(886\) | −30.2403 | −1.01594 | ||||||||
\(887\) | −27.1241 | −0.910738 | −0.455369 | − | 0.890303i | \(-0.650493\pi\) | ||||
−0.455369 | + | 0.890303i | \(0.650493\pi\) | |||||||
\(888\) | 8.06631 | 0.270688 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −22.5224 | −0.754953 | ||||||||
\(891\) | 103.699 | 3.47405 | ||||||||
\(892\) | 18.1731 | 0.608479 | ||||||||
\(893\) | 32.7325 | 1.09535 | ||||||||
\(894\) | −27.2918 | −0.912773 | ||||||||
\(895\) | 9.58049 | 0.320240 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 51.3074 | 1.71310 | ||||||||
\(898\) | −19.5454 | −0.652238 | ||||||||
\(899\) | −17.2199 | −0.574314 | ||||||||
\(900\) | −21.6646 | −0.722152 | ||||||||
\(901\) | −6.20607 | −0.206754 | ||||||||
\(902\) | −4.18274 | −0.139270 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.33107 | −0.243828 | ||||||||
\(905\) | −15.0355 | −0.499797 | ||||||||
\(906\) | −7.69482 | −0.255643 | ||||||||
\(907\) | −5.03235 | −0.167096 | −0.0835482 | − | 0.996504i | \(-0.526625\pi\) | ||||
−0.0835482 | + | 0.996504i | \(0.526625\pi\) | |||||||
\(908\) | 11.2158 | 0.372208 | ||||||||
\(909\) | −27.2873 | −0.905063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0700 | 1.79142 | 0.895710 | − | 0.444639i | \(-0.146668\pi\) | ||||
0.895710 | + | 0.444639i | \(0.146668\pi\) | |||||||
\(912\) | 13.9966 | 0.463474 | ||||||||
\(913\) | −11.9836 | −0.396600 | ||||||||
\(914\) | 27.1077 | 0.896642 | ||||||||
\(915\) | 48.9384 | 1.61785 | ||||||||
\(916\) | 7.14061 | 0.235932 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −73.7069 | −2.43269 | ||||||||
\(919\) | −55.6099 | −1.83440 | −0.917200 | − | 0.398427i | \(-0.869556\pi\) | ||||
−0.917200 | + | 0.398427i | \(0.869556\pi\) | |||||||
\(920\) | −4.40468 | −0.145218 | ||||||||
\(921\) | 51.5205 | 1.69766 | ||||||||
\(922\) | −9.69624 | −0.319329 | ||||||||
\(923\) | 44.2638 | 1.45696 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.18609 | −0.236277 | ||||||||
\(926\) | 24.3349 | 0.799693 | ||||||||
\(927\) | 103.499 | 3.39937 | ||||||||
\(928\) | 2.29501 | 0.0753374 | ||||||||
\(929\) | 9.62188 | 0.315684 | 0.157842 | − | 0.987464i | \(-0.449546\pi\) | ||||
0.157842 | + | 0.987464i | \(0.449546\pi\) | |||||||
\(930\) | −35.3456 | −1.15903 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.4071 | 0.406409 | ||||||||
\(933\) | 55.0044 | 1.80076 | ||||||||
\(934\) | −21.6468 | −0.708306 | ||||||||
\(935\) | −30.7025 | −1.00408 | ||||||||
\(936\) | −39.2000 | −1.28129 | ||||||||
\(937\) | 6.63826 | 0.216863 | 0.108431 | − | 0.994104i | \(-0.465417\pi\) | ||||
0.108431 | + | 0.994104i | \(0.465417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −102.729 | −3.35244 | ||||||||
\(940\) | 11.0166 | 0.359321 | ||||||||
\(941\) | −13.9901 | −0.456065 | −0.228032 | − | 0.973654i | \(-0.573229\pi\) | ||||
−0.228032 | + | 0.973654i | \(0.573229\pi\) | |||||||
\(942\) | −75.7218 | −2.46715 | ||||||||
\(943\) | 3.03034 | 0.0986813 | ||||||||
\(944\) | 2.55484 | 0.0831529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.1920 | 1.27424 | ||||||||
\(947\) | 13.8264 | 0.449299 | 0.224649 | − | 0.974440i | \(-0.427876\pi\) | ||||
0.224649 | + | 0.974440i | \(0.427876\pi\) | |||||||
\(948\) | −32.7603 | −1.06401 | ||||||||
\(949\) | 23.4680 | 0.761804 | ||||||||
\(950\) | −12.4693 | −0.404557 | ||||||||
\(951\) | 54.3882 | 1.76366 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.27602 | −0.106121 | −0.0530604 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530604 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(954\) | 9.22128 | 0.298550 | ||||||||
\(955\) | −5.97613 | −0.193383 | ||||||||
\(956\) | 18.9128 | 0.611682 | ||||||||
\(957\) | 31.1109 | 1.00567 | ||||||||
\(958\) | −5.40224 | −0.174538 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.71076 | 0.152039 | ||||||||
\(961\) | 25.2975 | 0.816049 | ||||||||
\(962\) | −13.0026 | −0.419220 | ||||||||
\(963\) | 152.139 | 4.90262 | ||||||||
\(964\) | 23.3723 | 0.752772 | ||||||||
\(965\) | 25.3635 | 0.816481 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8513 | −0.927795 | −0.463898 | − | 0.885889i | \(-0.653549\pi\) | ||||
−0.463898 | + | 0.885889i | \(0.653549\pi\) | |||||||
\(968\) | 6.49533 | 0.208768 | ||||||||
\(969\) | −70.6826 | −2.27065 | ||||||||
\(970\) | −21.4956 | −0.690181 | ||||||||
\(971\) | −23.7272 | −0.761442 | −0.380721 | − | 0.924690i | \(-0.624324\pi\) | ||||
−0.380721 | + | 0.924690i | \(0.624324\pi\) | |||||||
\(972\) | 36.5627 | 1.17275 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.808632 | −0.0259102 | ||||||||
\(975\) | 48.8849 | 1.56557 | ||||||||
\(976\) | 10.3886 | 0.332532 | ||||||||
\(977\) | 0.886915 | 0.0283749 | 0.0141875 | − | 0.999899i | \(-0.495484\pi\) | ||||
0.0141875 | + | 0.999899i | \(0.495484\pi\) | |||||||
\(978\) | 62.6700 | 2.00396 | ||||||||
\(979\) | −64.8115 | −2.07139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66.5128 | −2.12359 | ||||||||
\(982\) | 7.24205 | 0.231103 | ||||||||
\(983\) | 10.3852 | 0.331235 | 0.165618 | − | 0.986190i | \(-0.447038\pi\) | ||||
0.165618 | + | 0.986190i | \(0.447038\pi\) | |||||||
\(984\) | −3.24091 | −0.103316 | ||||||||
\(985\) | −31.9295 | −1.01736 | ||||||||
\(986\) | −11.5898 | −0.369093 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.5620 | −0.717793 | ||||||||
\(989\) | −28.3940 | −0.902878 | ||||||||
\(990\) | 45.6193 | 1.44988 | ||||||||
\(991\) | −21.9812 | −0.698255 | −0.349128 | − | 0.937075i | \(-0.613522\pi\) | ||||
−0.349128 | + | 0.937075i | \(0.613522\pi\) | |||||||
\(992\) | −7.50317 | −0.238226 | ||||||||
\(993\) | −66.5398 | −2.11158 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.4254 | 0.425615 | ||||||||
\(996\) | −9.28526 | −0.294215 | ||||||||
\(997\) | −24.1310 | −0.764236 | −0.382118 | − | 0.924114i | \(-0.624805\pi\) | ||||
−0.382118 | + | 0.924114i | \(0.624805\pi\) | |||||||
\(998\) | −7.70718 | −0.243967 | ||||||||
\(999\) | 36.3267 | 1.14933 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4018.2.a.bt.1.10 | 10 | ||
7.2 | even | 3 | 574.2.e.h.165.1 | ✓ | 20 | ||
7.4 | even | 3 | 574.2.e.h.247.1 | yes | 20 | ||
7.6 | odd | 2 | 4018.2.a.bu.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.h.165.1 | ✓ | 20 | 7.2 | even | 3 | ||
574.2.e.h.247.1 | yes | 20 | 7.4 | even | 3 | ||
4018.2.a.bt.1.10 | 10 | 1.1 | even | 1 | trivial | ||
4018.2.a.bu.1.1 | 10 | 7.6 | odd | 2 |