Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −1.73205 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.73205 | 0.707107 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.73205 | −0.500000 | ||||||||
\(13\) | 2.26795 | 0.629016 | 0.314508 | − | 0.949255i | \(-0.398160\pi\) | ||||
0.314508 | + | 0.949255i | \(0.398160\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.73205 | 0.447214 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.73205 | −0.662620 | −0.331310 | − | 0.943522i | \(-0.607491\pi\) | ||||
−0.331310 | + | 0.943522i | \(0.607491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.73205 | 0.856191 | 0.428096 | − | 0.903733i | \(-0.359185\pi\) | ||||
0.428096 | + | 0.903733i | \(0.359185\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.73205 | 0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.00000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.26795 | −0.444781 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | −1.73205 | −0.316228 | ||||||||
\(31\) | 0.732051 | 0.131480 | 0.0657401 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657401 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.73205 | 0.468543 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000 | 0.986394 | 0.493197 | − | 0.869918i | \(-0.335828\pi\) | ||||
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | −3.73205 | −0.605419 | ||||||||
\(39\) | −3.92820 | −0.629016 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −4.19615 | −0.655329 | −0.327664 | − | 0.944794i | \(-0.606262\pi\) | ||||
−0.327664 | + | 0.944794i | \(0.606262\pi\) | |||||||
\(42\) | −1.73205 | −0.267261 | ||||||||
\(43\) | 8.73205 | 1.33163 | 0.665813 | − | 0.746119i | \(-0.268085\pi\) | ||||
0.665813 | + | 0.746119i | \(0.268085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.00000 | 0.737210 | ||||||||
\(47\) | −1.26795 | −0.184949 | −0.0924747 | − | 0.995715i | \(-0.529478\pi\) | ||||
−0.0924747 | + | 0.995715i | \(0.529478\pi\) | |||||||
\(48\) | −1.73205 | −0.250000 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 4.73205 | 0.662620 | ||||||||
\(52\) | 2.26795 | 0.314508 | ||||||||
\(53\) | 4.19615 | 0.576386 | 0.288193 | − | 0.957572i | \(-0.406946\pi\) | ||||
0.288193 | + | 0.957572i | \(0.406946\pi\) | |||||||
\(54\) | −5.19615 | −0.707107 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −6.46410 | −0.856191 | ||||||||
\(58\) | 8.00000 | 1.05045 | ||||||||
\(59\) | −12.4641 | −1.62269 | −0.811344 | − | 0.584569i | \(-0.801264\pi\) | ||||
−0.811344 | + | 0.584569i | \(0.801264\pi\) | |||||||
\(60\) | 1.73205 | 0.223607 | ||||||||
\(61\) | −10.9282 | −1.39921 | −0.699607 | − | 0.714528i | \(-0.746641\pi\) | ||||
−0.699607 | + | 0.714528i | \(0.746641\pi\) | |||||||
\(62\) | −0.732051 | −0.0929705 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.26795 | −0.281304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.66025 | 0.935849 | 0.467924 | − | 0.883768i | \(-0.345002\pi\) | ||||
0.467924 | + | 0.883768i | \(0.345002\pi\) | |||||||
\(68\) | −2.73205 | −0.331310 | ||||||||
\(69\) | 8.66025 | 1.04257 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −6.92820 | −0.822226 | −0.411113 | − | 0.911584i | \(-0.634860\pi\) | ||||
−0.411113 | + | 0.911584i | \(0.634860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1244 | 1.77017 | 0.885086 | − | 0.465428i | \(-0.154099\pi\) | ||||
0.885086 | + | 0.465428i | \(0.154099\pi\) | |||||||
\(74\) | −6.00000 | −0.697486 | ||||||||
\(75\) | −1.73205 | −0.200000 | ||||||||
\(76\) | 3.73205 | 0.428096 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.92820 | 0.444781 | ||||||||
\(79\) | 7.00000 | 0.787562 | 0.393781 | − | 0.919204i | \(-0.371167\pi\) | ||||
0.393781 | + | 0.919204i | \(0.371167\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 4.19615 | 0.463388 | ||||||||
\(83\) | −5.00000 | −0.548821 | −0.274411 | − | 0.961613i | \(-0.588483\pi\) | ||||
−0.274411 | + | 0.961613i | \(0.588483\pi\) | |||||||
\(84\) | 1.73205 | 0.188982 | ||||||||
\(85\) | 2.73205 | 0.296333 | ||||||||
\(86\) | −8.73205 | −0.941601 | ||||||||
\(87\) | 13.8564 | 1.48556 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.66025 | 0.387986 | 0.193993 | − | 0.981003i | \(-0.437856\pi\) | ||||
0.193993 | + | 0.981003i | \(0.437856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.26795 | −0.237746 | ||||||||
\(92\) | −5.00000 | −0.521286 | ||||||||
\(93\) | −1.26795 | −0.131480 | ||||||||
\(94\) | 1.26795 | 0.130779 | ||||||||
\(95\) | −3.73205 | −0.382900 | ||||||||
\(96\) | 1.73205 | 0.176777 | ||||||||
\(97\) | −2.92820 | −0.297314 | −0.148657 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148657 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 18.4641 | 1.83725 | 0.918623 | − | 0.395134i | \(-0.129302\pi\) | ||||
0.918623 | + | 0.395134i | \(0.129302\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | −7.26795 | −0.716132 | −0.358066 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358066 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(104\) | −2.26795 | −0.222391 | ||||||||
\(105\) | −1.73205 | −0.169031 | ||||||||
\(106\) | −4.19615 | −0.407566 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 5.19615 | 0.500000 | ||||||||
\(109\) | 18.0526 | 1.72912 | 0.864561 | − | 0.502528i | \(-0.167597\pi\) | ||||
0.864561 | + | 0.502528i | \(0.167597\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3923 | −0.986394 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 10.1244 | 0.952419 | 0.476210 | − | 0.879332i | \(-0.342010\pi\) | ||||
0.476210 | + | 0.879332i | \(0.342010\pi\) | |||||||
\(114\) | 6.46410 | 0.605419 | ||||||||
\(115\) | 5.00000 | 0.466252 | ||||||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.4641 | 1.14741 | ||||||||
\(119\) | 2.73205 | 0.250447 | ||||||||
\(120\) | −1.73205 | −0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.9282 | 0.989393 | ||||||||
\(123\) | 7.26795 | 0.655329 | ||||||||
\(124\) | 0.732051 | 0.0657401 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1244 | −1.60828 | −0.804138 | − | 0.594442i | \(-0.797373\pi\) | ||||
−0.804138 | + | 0.594442i | \(0.797373\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −15.1244 | −1.33163 | ||||||||
\(130\) | 2.26795 | 0.198912 | ||||||||
\(131\) | 2.80385 | 0.244973 | 0.122487 | − | 0.992470i | \(-0.460913\pi\) | ||||
0.122487 | + | 0.992470i | \(0.460913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.73205 | −0.323610 | ||||||||
\(134\) | −7.66025 | −0.661745 | ||||||||
\(135\) | −5.19615 | −0.447214 | ||||||||
\(136\) | 2.73205 | 0.234271 | ||||||||
\(137\) | −2.66025 | −0.227281 | −0.113640 | − | 0.993522i | \(-0.536251\pi\) | ||||
−0.113640 | + | 0.993522i | \(0.536251\pi\) | |||||||
\(138\) | −8.66025 | −0.737210 | ||||||||
\(139\) | 6.80385 | 0.577095 | 0.288547 | − | 0.957466i | \(-0.406828\pi\) | ||||
0.288547 | + | 0.957466i | \(0.406828\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 2.19615 | 0.184949 | ||||||||
\(142\) | 6.92820 | 0.581402 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | −15.1244 | −1.25170 | ||||||||
\(147\) | −1.73205 | −0.142857 | ||||||||
\(148\) | 6.00000 | 0.493197 | ||||||||
\(149\) | −12.5359 | −1.02698 | −0.513490 | − | 0.858095i | \(-0.671648\pi\) | ||||
−0.513490 | + | 0.858095i | \(0.671648\pi\) | |||||||
\(150\) | 1.73205 | 0.141421 | ||||||||
\(151\) | −8.85641 | −0.720724 | −0.360362 | − | 0.932813i | \(-0.617347\pi\) | ||||
−0.360362 | + | 0.932813i | \(0.617347\pi\) | |||||||
\(152\) | −3.73205 | −0.302709 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.732051 | −0.0587997 | ||||||||
\(156\) | −3.92820 | −0.314508 | ||||||||
\(157\) | 15.3923 | 1.22844 | 0.614220 | − | 0.789135i | \(-0.289471\pi\) | ||||
0.614220 | + | 0.789135i | \(0.289471\pi\) | |||||||
\(158\) | −7.00000 | −0.556890 | ||||||||
\(159\) | −7.26795 | −0.576386 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.00000 | 0.394055 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 10.0000 | 0.783260 | 0.391630 | − | 0.920123i | \(-0.371911\pi\) | ||||
0.391630 | + | 0.920123i | \(0.371911\pi\) | |||||||
\(164\) | −4.19615 | −0.327664 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.00000 | 0.388075 | ||||||||
\(167\) | 17.6603 | 1.36659 | 0.683296 | − | 0.730142i | \(-0.260546\pi\) | ||||
0.683296 | + | 0.730142i | \(0.260546\pi\) | |||||||
\(168\) | −1.73205 | −0.133631 | ||||||||
\(169\) | −7.85641 | −0.604339 | ||||||||
\(170\) | −2.73205 | −0.209539 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.73205 | 0.665813 | ||||||||
\(173\) | 19.8564 | 1.50965 | 0.754827 | − | 0.655924i | \(-0.227721\pi\) | ||||
0.754827 | + | 0.655924i | \(0.227721\pi\) | |||||||
\(174\) | −13.8564 | −1.05045 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.5885 | 1.62269 | ||||||||
\(178\) | −3.66025 | −0.274348 | ||||||||
\(179\) | −5.80385 | −0.433800 | −0.216900 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216900 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.33975 | −0.396900 | −0.198450 | − | 0.980111i | \(-0.563591\pi\) | ||||
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(182\) | 2.26795 | 0.168112 | ||||||||
\(183\) | 18.9282 | 1.39921 | ||||||||
\(184\) | 5.00000 | 0.368605 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 1.26795 | 0.0929705 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.26795 | −0.0924747 | ||||||||
\(189\) | −5.19615 | −0.377964 | ||||||||
\(190\) | 3.73205 | 0.270751 | ||||||||
\(191\) | 8.66025 | 0.626634 | 0.313317 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313317 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(192\) | −1.73205 | −0.125000 | ||||||||
\(193\) | 9.39230 | 0.676073 | 0.338036 | − | 0.941133i | \(-0.390237\pi\) | ||||
0.338036 | + | 0.941133i | \(0.390237\pi\) | |||||||
\(194\) | 2.92820 | 0.210233 | ||||||||
\(195\) | 3.92820 | 0.281304 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.53590 | 0.180675 | 0.0903376 | − | 0.995911i | \(-0.471205\pi\) | ||||
0.0903376 | + | 0.995911i | \(0.471205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −13.2679 | −0.935849 | ||||||||
\(202\) | −18.4641 | −1.29913 | ||||||||
\(203\) | 8.00000 | 0.561490 | ||||||||
\(204\) | 4.73205 | 0.331310 | ||||||||
\(205\) | 4.19615 | 0.293072 | ||||||||
\(206\) | 7.26795 | 0.506382 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.26795 | 0.157254 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.73205 | 0.119523 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 4.19615 | 0.288193 | ||||||||
\(213\) | 12.0000 | 0.822226 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | −8.73205 | −0.595521 | ||||||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | −0.732051 | −0.0496948 | ||||||||
\(218\) | −18.0526 | −1.22267 | ||||||||
\(219\) | −26.1962 | −1.77017 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.19615 | −0.416798 | ||||||||
\(222\) | 10.3923 | 0.697486 | ||||||||
\(223\) | −14.7321 | −0.986531 | −0.493266 | − | 0.869879i | \(-0.664197\pi\) | ||||
−0.493266 | + | 0.869879i | \(0.664197\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.1244 | −0.673462 | ||||||||
\(227\) | 17.3205 | 1.14960 | 0.574801 | − | 0.818293i | \(-0.305079\pi\) | ||||
0.574801 | + | 0.818293i | \(0.305079\pi\) | |||||||
\(228\) | −6.46410 | −0.428096 | ||||||||
\(229\) | −21.8564 | −1.44431 | −0.722156 | − | 0.691730i | \(-0.756849\pi\) | ||||
−0.722156 | + | 0.691730i | \(0.756849\pi\) | |||||||
\(230\) | −5.00000 | −0.329690 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00000 | 0.525226 | ||||||||
\(233\) | −12.4641 | −0.816550 | −0.408275 | − | 0.912859i | \(-0.633870\pi\) | ||||
−0.408275 | + | 0.912859i | \(0.633870\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26795 | 0.0827119 | ||||||||
\(236\) | −12.4641 | −0.811344 | ||||||||
\(237\) | −12.1244 | −0.787562 | ||||||||
\(238\) | −2.73205 | −0.177093 | ||||||||
\(239\) | −2.46410 | −0.159389 | −0.0796947 | − | 0.996819i | \(-0.525395\pi\) | ||||
−0.0796947 | + | 0.996819i | \(0.525395\pi\) | |||||||
\(240\) | 1.73205 | 0.111803 | ||||||||
\(241\) | −10.5359 | −0.678677 | −0.339338 | − | 0.940664i | \(-0.610203\pi\) | ||||
−0.339338 | + | 0.940664i | \(0.610203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.9282 | −0.699607 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −7.26795 | −0.463388 | ||||||||
\(247\) | 8.46410 | 0.538558 | ||||||||
\(248\) | −0.732051 | −0.0464853 | ||||||||
\(249\) | 8.66025 | 0.548821 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.3923 | 0.908434 | 0.454217 | − | 0.890891i | \(-0.349919\pi\) | ||||
0.454217 | + | 0.890891i | \(0.349919\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 18.1244 | 1.13722 | ||||||||
\(255\) | −4.73205 | −0.296333 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.19615 | −0.136992 | −0.0684961 | − | 0.997651i | \(-0.521820\pi\) | ||||
−0.0684961 | + | 0.997651i | \(0.521820\pi\) | |||||||
\(258\) | 15.1244 | 0.941601 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | −2.26795 | −0.140652 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.80385 | −0.173222 | ||||||||
\(263\) | 14.1244 | 0.870945 | 0.435473 | − | 0.900202i | \(-0.356581\pi\) | ||||
0.435473 | + | 0.900202i | \(0.356581\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.19615 | −0.257768 | ||||||||
\(266\) | 3.73205 | 0.228827 | ||||||||
\(267\) | −6.33975 | −0.387986 | ||||||||
\(268\) | 7.66025 | 0.467924 | ||||||||
\(269\) | −18.2679 | −1.11382 | −0.556908 | − | 0.830574i | \(-0.688013\pi\) | ||||
−0.556908 | + | 0.830574i | \(0.688013\pi\) | |||||||
\(270\) | 5.19615 | 0.316228 | ||||||||
\(271\) | −14.5359 | −0.882993 | −0.441496 | − | 0.897263i | \(-0.645552\pi\) | ||||
−0.441496 | + | 0.897263i | \(0.645552\pi\) | |||||||
\(272\) | −2.73205 | −0.165655 | ||||||||
\(273\) | 3.92820 | 0.237746 | ||||||||
\(274\) | 2.66025 | 0.160712 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.66025 | 0.521286 | ||||||||
\(277\) | −12.1962 | −0.732796 | −0.366398 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366398 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(278\) | −6.80385 | −0.408068 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −4.26795 | −0.254605 | −0.127302 | − | 0.991864i | \(-0.540632\pi\) | ||||
−0.127302 | + | 0.991864i | \(0.540632\pi\) | |||||||
\(282\) | −2.19615 | −0.130779 | ||||||||
\(283\) | 15.7846 | 0.938298 | 0.469149 | − | 0.883119i | \(-0.344561\pi\) | ||||
0.469149 | + | 0.883119i | \(0.344561\pi\) | |||||||
\(284\) | −6.92820 | −0.411113 | ||||||||
\(285\) | 6.46410 | 0.382900 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.19615 | 0.247691 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.53590 | −0.560935 | ||||||||
\(290\) | −8.00000 | −0.469776 | ||||||||
\(291\) | 5.07180 | 0.297314 | ||||||||
\(292\) | 15.1244 | 0.885086 | ||||||||
\(293\) | −8.26795 | −0.483019 | −0.241509 | − | 0.970398i | \(-0.577642\pi\) | ||||
−0.241509 | + | 0.970398i | \(0.577642\pi\) | |||||||
\(294\) | 1.73205 | 0.101015 | ||||||||
\(295\) | 12.4641 | 0.725688 | ||||||||
\(296\) | −6.00000 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.5359 | 0.726185 | ||||||||
\(299\) | −11.3397 | −0.655794 | ||||||||
\(300\) | −1.73205 | −0.100000 | ||||||||
\(301\) | −8.73205 | −0.503307 | ||||||||
\(302\) | 8.85641 | 0.509629 | ||||||||
\(303\) | −31.9808 | −1.83725 | ||||||||
\(304\) | 3.73205 | 0.214048 | ||||||||
\(305\) | 10.9282 | 0.625747 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9282 | 1.19444 | 0.597218 | − | 0.802079i | \(-0.296273\pi\) | ||||
0.597218 | + | 0.802079i | \(0.296273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5885 | 0.716132 | ||||||||
\(310\) | 0.732051 | 0.0415777 | ||||||||
\(311\) | 9.26795 | 0.525537 | 0.262769 | − | 0.964859i | \(-0.415364\pi\) | ||||
0.262769 | + | 0.964859i | \(0.415364\pi\) | |||||||
\(312\) | 3.92820 | 0.222391 | ||||||||
\(313\) | −26.3923 | −1.49178 | −0.745891 | − | 0.666068i | \(-0.767976\pi\) | ||||
−0.745891 | + | 0.666068i | \(0.767976\pi\) | |||||||
\(314\) | −15.3923 | −0.868638 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00000 | 0.393781 | ||||||||
\(317\) | −19.1244 | −1.07413 | −0.537065 | − | 0.843541i | \(-0.680467\pi\) | ||||
−0.537065 | + | 0.843541i | \(0.680467\pi\) | |||||||
\(318\) | 7.26795 | 0.407566 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.46410 | 0.193347 | ||||||||
\(322\) | −5.00000 | −0.278639 | ||||||||
\(323\) | −10.1962 | −0.567329 | ||||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 2.26795 | 0.125803 | ||||||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | −31.2679 | −1.72912 | ||||||||
\(328\) | 4.19615 | 0.231694 | ||||||||
\(329\) | 1.26795 | 0.0699043 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.05256 | −0.222749 | −0.111374 | − | 0.993779i | \(-0.535525\pi\) | ||||
−0.111374 | + | 0.993779i | \(0.535525\pi\) | |||||||
\(332\) | −5.00000 | −0.274411 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.6603 | −0.966326 | ||||||||
\(335\) | −7.66025 | −0.418524 | ||||||||
\(336\) | 1.73205 | 0.0944911 | ||||||||
\(337\) | −11.3923 | −0.620578 | −0.310289 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310289 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(338\) | 7.85641 | 0.427332 | ||||||||
\(339\) | −17.5359 | −0.952419 | ||||||||
\(340\) | 2.73205 | 0.148166 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −8.73205 | −0.470801 | ||||||||
\(345\) | −8.66025 | −0.466252 | ||||||||
\(346\) | −19.8564 | −1.06749 | ||||||||
\(347\) | 8.53590 | 0.458231 | 0.229116 | − | 0.973399i | \(-0.426417\pi\) | ||||
0.229116 | + | 0.973399i | \(0.426417\pi\) | |||||||
\(348\) | 13.8564 | 0.742781 | ||||||||
\(349\) | 6.46410 | 0.346015 | 0.173008 | − | 0.984920i | \(-0.444651\pi\) | ||||
0.173008 | + | 0.984920i | \(0.444651\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 11.7846 | 0.629016 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.80385 | 0.0960091 | 0.0480046 | − | 0.998847i | \(-0.484714\pi\) | ||||
0.0480046 | + | 0.998847i | \(0.484714\pi\) | |||||||
\(354\) | −21.5885 | −1.14741 | ||||||||
\(355\) | 6.92820 | 0.367711 | ||||||||
\(356\) | 3.66025 | 0.193993 | ||||||||
\(357\) | −4.73205 | −0.250447 | ||||||||
\(358\) | 5.80385 | 0.306743 | ||||||||
\(359\) | 33.7128 | 1.77929 | 0.889647 | − | 0.456649i | \(-0.150950\pi\) | ||||
0.889647 | + | 0.456649i | \(0.150950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.07180 | −0.266937 | ||||||||
\(362\) | 5.33975 | 0.280651 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.26795 | −0.118873 | ||||||||
\(365\) | −15.1244 | −0.791645 | ||||||||
\(366\) | −18.9282 | −0.989393 | ||||||||
\(367\) | −20.7321 | −1.08220 | −0.541102 | − | 0.840957i | \(-0.681993\pi\) | ||||
−0.541102 | + | 0.840957i | \(0.681993\pi\) | |||||||
\(368\) | −5.00000 | −0.260643 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −4.19615 | −0.217853 | ||||||||
\(372\) | −1.26795 | −0.0657401 | ||||||||
\(373\) | 13.3205 | 0.689710 | 0.344855 | − | 0.938656i | \(-0.387928\pi\) | ||||
0.344855 | + | 0.938656i | \(0.387928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.73205 | 0.0894427 | ||||||||
\(376\) | 1.26795 | 0.0653895 | ||||||||
\(377\) | −18.1436 | −0.934443 | ||||||||
\(378\) | 5.19615 | 0.267261 | ||||||||
\(379\) | 34.7846 | 1.78677 | 0.893383 | − | 0.449297i | \(-0.148325\pi\) | ||||
0.893383 | + | 0.449297i | \(0.148325\pi\) | |||||||
\(380\) | −3.73205 | −0.191450 | ||||||||
\(381\) | 31.3923 | 1.60828 | ||||||||
\(382\) | −8.66025 | −0.443097 | ||||||||
\(383\) | 8.33975 | 0.426141 | 0.213071 | − | 0.977037i | \(-0.431654\pi\) | ||||
0.213071 | + | 0.977037i | \(0.431654\pi\) | |||||||
\(384\) | 1.73205 | 0.0883883 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.39230 | −0.478056 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.92820 | −0.148657 | ||||||||
\(389\) | 1.12436 | 0.0570071 | 0.0285035 | − | 0.999594i | \(-0.490926\pi\) | ||||
0.0285035 | + | 0.999594i | \(0.490926\pi\) | |||||||
\(390\) | −3.92820 | −0.198912 | ||||||||
\(391\) | 13.6603 | 0.690829 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −4.85641 | −0.244973 | ||||||||
\(394\) | −2.53590 | −0.127757 | ||||||||
\(395\) | −7.00000 | −0.352208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.7846 | −1.44466 | −0.722329 | − | 0.691549i | \(-0.756928\pi\) | ||||
−0.722329 | + | 0.691549i | \(0.756928\pi\) | |||||||
\(398\) | 4.00000 | 0.200502 | ||||||||
\(399\) | 6.46410 | 0.323610 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −25.4641 | −1.27162 | −0.635808 | − | 0.771847i | \(-0.719333\pi\) | ||||
−0.635808 | + | 0.771847i | \(0.719333\pi\) | |||||||
\(402\) | 13.2679 | 0.661745 | ||||||||
\(403\) | 1.66025 | 0.0827031 | ||||||||
\(404\) | 18.4641 | 0.918623 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | −8.00000 | −0.397033 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.73205 | −0.234271 | ||||||||
\(409\) | 19.7128 | 0.974736 | 0.487368 | − | 0.873197i | \(-0.337957\pi\) | ||||
0.487368 | + | 0.873197i | \(0.337957\pi\) | |||||||
\(410\) | −4.19615 | −0.207233 | ||||||||
\(411\) | 4.60770 | 0.227281 | ||||||||
\(412\) | −7.26795 | −0.358066 | ||||||||
\(413\) | 12.4641 | 0.613318 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.00000 | 0.245440 | ||||||||
\(416\) | −2.26795 | −0.111195 | ||||||||
\(417\) | −11.7846 | −0.577095 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.07180 | 0.101214 | 0.0506069 | − | 0.998719i | \(-0.483884\pi\) | ||||
0.0506069 | + | 0.998719i | \(0.483884\pi\) | |||||||
\(420\) | −1.73205 | −0.0845154 | ||||||||
\(421\) | −28.3923 | −1.38376 | −0.691878 | − | 0.722014i | \(-0.743216\pi\) | ||||
−0.691878 | + | 0.722014i | \(0.743216\pi\) | |||||||
\(422\) | −8.00000 | −0.389434 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19615 | −0.203783 | ||||||||
\(425\) | −2.73205 | −0.132524 | ||||||||
\(426\) | −12.0000 | −0.581402 | ||||||||
\(427\) | 10.9282 | 0.528853 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.73205 | 0.421097 | ||||||||
\(431\) | 27.5359 | 1.32636 | 0.663179 | − | 0.748461i | \(-0.269207\pi\) | ||||
0.663179 | + | 0.748461i | \(0.269207\pi\) | |||||||
\(432\) | 5.19615 | 0.250000 | ||||||||
\(433\) | 18.0526 | 0.867551 | 0.433775 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433775 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(434\) | 0.732051 | 0.0351396 | ||||||||
\(435\) | −13.8564 | −0.664364 | ||||||||
\(436\) | 18.0526 | 0.864561 | ||||||||
\(437\) | −18.6603 | −0.892641 | ||||||||
\(438\) | 26.1962 | 1.25170 | ||||||||
\(439\) | 11.2679 | 0.537790 | 0.268895 | − | 0.963170i | \(-0.413342\pi\) | ||||
0.268895 | + | 0.963170i | \(0.413342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.19615 | 0.294721 | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | −10.3923 | −0.493197 | ||||||||
\(445\) | −3.66025 | −0.173513 | ||||||||
\(446\) | 14.7321 | 0.697583 | ||||||||
\(447\) | 21.7128 | 1.02698 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 10.6077 | 0.500608 | 0.250304 | − | 0.968167i | \(-0.419469\pi\) | ||||
0.250304 | + | 0.968167i | \(0.419469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.1244 | 0.476210 | ||||||||
\(453\) | 15.3397 | 0.720724 | ||||||||
\(454\) | −17.3205 | −0.812892 | ||||||||
\(455\) | 2.26795 | 0.106323 | ||||||||
\(456\) | 6.46410 | 0.302709 | ||||||||
\(457\) | −17.3923 | −0.813578 | −0.406789 | − | 0.913522i | \(-0.633352\pi\) | ||||
−0.406789 | + | 0.913522i | \(0.633352\pi\) | |||||||
\(458\) | 21.8564 | 1.02128 | ||||||||
\(459\) | −14.1962 | −0.662620 | ||||||||
\(460\) | 5.00000 | 0.233126 | ||||||||
\(461\) | −17.4641 | −0.813384 | −0.406692 | − | 0.913565i | \(-0.633318\pi\) | ||||
−0.406692 | + | 0.913565i | \(0.633318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.1769 | −1.68128 | −0.840642 | − | 0.541591i | \(-0.817822\pi\) | ||||
−0.840642 | + | 0.541591i | \(0.817822\pi\) | |||||||
\(464\) | −8.00000 | −0.371391 | ||||||||
\(465\) | 1.26795 | 0.0587997 | ||||||||
\(466\) | 12.4641 | 0.577388 | ||||||||
\(467\) | −17.5885 | −0.813897 | −0.406948 | − | 0.913451i | \(-0.633407\pi\) | ||||
−0.406948 | + | 0.913451i | \(0.633407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.66025 | −0.353718 | ||||||||
\(470\) | −1.26795 | −0.0584861 | ||||||||
\(471\) | −26.6603 | −1.22844 | ||||||||
\(472\) | 12.4641 | 0.573707 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.1244 | 0.556890 | ||||||||
\(475\) | 3.73205 | 0.171238 | ||||||||
\(476\) | 2.73205 | 0.125223 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.46410 | 0.112705 | ||||||||
\(479\) | 22.9808 | 1.05002 | 0.525009 | − | 0.851097i | \(-0.324062\pi\) | ||||
0.525009 | + | 0.851097i | \(0.324062\pi\) | |||||||
\(480\) | −1.73205 | −0.0790569 | ||||||||
\(481\) | 13.6077 | 0.620457 | ||||||||
\(482\) | 10.5359 | 0.479897 | ||||||||
\(483\) | −8.66025 | −0.394055 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.92820 | 0.132963 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.39230 | −0.153720 | −0.0768600 | − | 0.997042i | \(-0.524489\pi\) | ||||
−0.0768600 | + | 0.997042i | \(0.524489\pi\) | |||||||
\(488\) | 10.9282 | 0.494697 | ||||||||
\(489\) | −17.3205 | −0.783260 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 7.66025 | 0.345702 | 0.172851 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172851 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(492\) | 7.26795 | 0.327664 | ||||||||
\(493\) | 21.8564 | 0.984363 | ||||||||
\(494\) | −8.46410 | −0.380818 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.732051 | 0.0328701 | ||||||||
\(497\) | 6.92820 | 0.310772 | ||||||||
\(498\) | −8.66025 | −0.388075 | ||||||||
\(499\) | −22.0000 | −0.984855 | −0.492428 | − | 0.870353i | \(-0.663890\pi\) | ||||
−0.492428 | + | 0.870353i | \(0.663890\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −30.5885 | −1.36659 | ||||||||
\(502\) | −14.3923 | −0.642360 | ||||||||
\(503\) | −7.80385 | −0.347956 | −0.173978 | − | 0.984750i | \(-0.555662\pi\) | ||||
−0.173978 | + | 0.984750i | \(0.555662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.4641 | −0.821642 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.6077 | 0.604339 | ||||||||
\(508\) | −18.1244 | −0.804138 | ||||||||
\(509\) | −15.3397 | −0.679922 | −0.339961 | − | 0.940439i | \(-0.610414\pi\) | ||||
−0.339961 | + | 0.940439i | \(0.610414\pi\) | |||||||
\(510\) | 4.73205 | 0.209539 | ||||||||
\(511\) | −15.1244 | −0.669062 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 19.3923 | 0.856191 | ||||||||
\(514\) | 2.19615 | 0.0968681 | ||||||||
\(515\) | 7.26795 | 0.320264 | ||||||||
\(516\) | −15.1244 | −0.665813 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.00000 | 0.263625 | ||||||||
\(519\) | −34.3923 | −1.50965 | ||||||||
\(520\) | 2.26795 | 0.0994562 | ||||||||
\(521\) | −4.00000 | −0.175243 | −0.0876216 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876216 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.60770 | 0.114027 | 0.0570133 | − | 0.998373i | \(-0.481842\pi\) | ||||
0.0570133 | + | 0.998373i | \(0.481842\pi\) | |||||||
\(524\) | 2.80385 | 0.122487 | ||||||||
\(525\) | 1.73205 | 0.0755929 | ||||||||
\(526\) | −14.1244 | −0.615851 | ||||||||
\(527\) | −2.00000 | −0.0871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | 0.0869565 | ||||||||
\(530\) | 4.19615 | 0.182269 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.73205 | −0.161805 | ||||||||
\(533\) | −9.51666 | −0.412212 | ||||||||
\(534\) | 6.33975 | 0.274348 | ||||||||
\(535\) | 2.00000 | 0.0864675 | ||||||||
\(536\) | −7.66025 | −0.330873 | ||||||||
\(537\) | 10.0526 | 0.433800 | ||||||||
\(538\) | 18.2679 | 0.787587 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.19615 | −0.223607 | ||||||||
\(541\) | −9.60770 | −0.413067 | −0.206534 | − | 0.978440i | \(-0.566218\pi\) | ||||
−0.206534 | + | 0.978440i | \(0.566218\pi\) | |||||||
\(542\) | 14.5359 | 0.624370 | ||||||||
\(543\) | 9.24871 | 0.396900 | ||||||||
\(544\) | 2.73205 | 0.117136 | ||||||||
\(545\) | −18.0526 | −0.773287 | ||||||||
\(546\) | −3.92820 | −0.168112 | ||||||||
\(547\) | −37.5167 | −1.60410 | −0.802048 | − | 0.597259i | \(-0.796256\pi\) | ||||
−0.802048 | + | 0.597259i | \(0.796256\pi\) | |||||||
\(548\) | −2.66025 | −0.113640 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.8564 | −1.27193 | ||||||||
\(552\) | −8.66025 | −0.368605 | ||||||||
\(553\) | −7.00000 | −0.297670 | ||||||||
\(554\) | 12.1962 | 0.518165 | ||||||||
\(555\) | 10.3923 | 0.441129 | ||||||||
\(556\) | 6.80385 | 0.288547 | ||||||||
\(557\) | −27.3731 | −1.15983 | −0.579917 | − | 0.814676i | \(-0.696915\pi\) | ||||
−0.579917 | + | 0.814676i | \(0.696915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.8038 | 0.837614 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.26795 | 0.180033 | ||||||||
\(563\) | 1.53590 | 0.0647304 | 0.0323652 | − | 0.999476i | \(-0.489696\pi\) | ||||
0.0323652 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(564\) | 2.19615 | 0.0924747 | ||||||||
\(565\) | −10.1244 | −0.425935 | ||||||||
\(566\) | −15.7846 | −0.663477 | ||||||||
\(567\) | 9.00000 | 0.377964 | ||||||||
\(568\) | 6.92820 | 0.290701 | ||||||||
\(569\) | −38.1244 | −1.59826 | −0.799128 | − | 0.601161i | \(-0.794705\pi\) | ||||
−0.799128 | + | 0.601161i | \(0.794705\pi\) | |||||||
\(570\) | −6.46410 | −0.270751 | ||||||||
\(571\) | −13.4641 | −0.563455 | −0.281728 | − | 0.959494i | \(-0.590907\pi\) | ||||
−0.281728 | + | 0.959494i | \(0.590907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | −4.19615 | −0.175144 | ||||||||
\(575\) | −5.00000 | −0.208514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4449 | 0.767870 | 0.383935 | − | 0.923360i | \(-0.374569\pi\) | ||||
0.383935 | + | 0.923360i | \(0.374569\pi\) | |||||||
\(578\) | 9.53590 | 0.396641 | ||||||||
\(579\) | −16.2679 | −0.676073 | ||||||||
\(580\) | 8.00000 | 0.332182 | ||||||||
\(581\) | 5.00000 | 0.207435 | ||||||||
\(582\) | −5.07180 | −0.210233 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.1244 | −0.625850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.26795 | 0.341546 | ||||||||
\(587\) | 14.5167 | 0.599167 | 0.299583 | − | 0.954070i | \(-0.403152\pi\) | ||||
0.299583 | + | 0.954070i | \(0.403152\pi\) | |||||||
\(588\) | −1.73205 | −0.0714286 | ||||||||
\(589\) | 2.73205 | 0.112572 | ||||||||
\(590\) | −12.4641 | −0.513139 | ||||||||
\(591\) | −4.39230 | −0.180675 | ||||||||
\(592\) | 6.00000 | 0.246598 | ||||||||
\(593\) | 29.8564 | 1.22606 | 0.613028 | − | 0.790061i | \(-0.289951\pi\) | ||||
0.613028 | + | 0.790061i | \(0.289951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.73205 | −0.112003 | ||||||||
\(596\) | −12.5359 | −0.513490 | ||||||||
\(597\) | 6.92820 | 0.283552 | ||||||||
\(598\) | 11.3397 | 0.463717 | ||||||||
\(599\) | −31.9808 | −1.30670 | −0.653349 | − | 0.757057i | \(-0.726637\pi\) | ||||
−0.653349 | + | 0.757057i | \(0.726637\pi\) | |||||||
\(600\) | 1.73205 | 0.0707107 | ||||||||
\(601\) | −3.66025 | −0.149305 | −0.0746524 | − | 0.997210i | \(-0.523785\pi\) | ||||
−0.0746524 | + | 0.997210i | \(0.523785\pi\) | |||||||
\(602\) | 8.73205 | 0.355892 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.85641 | −0.360362 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 31.9808 | 1.29913 | ||||||||
\(607\) | 0.248711 | 0.0100949 | 0.00504744 | − | 0.999987i | \(-0.498393\pi\) | ||||
0.00504744 | + | 0.999987i | \(0.498393\pi\) | |||||||
\(608\) | −3.73205 | −0.151355 | ||||||||
\(609\) | −13.8564 | −0.561490 | ||||||||
\(610\) | −10.9282 | −0.442470 | ||||||||
\(611\) | −2.87564 | −0.116336 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2679 | −1.50524 | −0.752619 | − | 0.658456i | \(-0.771210\pi\) | ||||
−0.752619 | + | 0.658456i | \(0.771210\pi\) | |||||||
\(614\) | −20.9282 | −0.844594 | ||||||||
\(615\) | −7.26795 | −0.293072 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6077 | 0.547825 | 0.273913 | − | 0.961755i | \(-0.411682\pi\) | ||||
0.273913 | + | 0.961755i | \(0.411682\pi\) | |||||||
\(618\) | −12.5885 | −0.506382 | ||||||||
\(619\) | 32.7128 | 1.31484 | 0.657419 | − | 0.753525i | \(-0.271648\pi\) | ||||
0.657419 | + | 0.753525i | \(0.271648\pi\) | |||||||
\(620\) | −0.732051 | −0.0293999 | ||||||||
\(621\) | −25.9808 | −1.04257 | ||||||||
\(622\) | −9.26795 | −0.371611 | ||||||||
\(623\) | −3.66025 | −0.146645 | ||||||||
\(624\) | −3.92820 | −0.157254 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.3923 | 1.05485 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3923 | 0.614220 | ||||||||
\(629\) | −16.3923 | −0.653604 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.3205 | −1.56532 | −0.782662 | − | 0.622446i | \(-0.786139\pi\) | ||||
−0.782662 | + | 0.622446i | \(0.786139\pi\) | |||||||
\(632\) | −7.00000 | −0.278445 | ||||||||
\(633\) | −13.8564 | −0.550743 | ||||||||
\(634\) | 19.1244 | 0.759525 | ||||||||
\(635\) | 18.1244 | 0.719243 | ||||||||
\(636\) | −7.26795 | −0.288193 | ||||||||
\(637\) | 2.26795 | 0.0898594 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.5359 | −1.56157 | −0.780787 | − | 0.624797i | \(-0.785182\pi\) | ||||
−0.780787 | + | 0.624797i | \(0.785182\pi\) | |||||||
\(642\) | −3.46410 | −0.136717 | ||||||||
\(643\) | 23.1769 | 0.914008 | 0.457004 | − | 0.889465i | \(-0.348922\pi\) | ||||
0.457004 | + | 0.889465i | \(0.348922\pi\) | |||||||
\(644\) | 5.00000 | 0.197028 | ||||||||
\(645\) | 15.1244 | 0.595521 | ||||||||
\(646\) | 10.1962 | 0.401162 | ||||||||
\(647\) | −21.8038 | −0.857198 | −0.428599 | − | 0.903495i | \(-0.640993\pi\) | ||||
−0.428599 | + | 0.903495i | \(0.640993\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.26795 | −0.0889563 | ||||||||
\(651\) | 1.26795 | 0.0496948 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −2.19615 | −0.0859421 | −0.0429710 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429710 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(654\) | 31.2679 | 1.22267 | ||||||||
\(655\) | −2.80385 | −0.109555 | ||||||||
\(656\) | −4.19615 | −0.163832 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.26795 | −0.0494298 | ||||||||
\(659\) | 32.4449 | 1.26387 | 0.631936 | − | 0.775020i | \(-0.282260\pi\) | ||||
0.631936 | + | 0.775020i | \(0.282260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.33975 | 0.129901 | 0.0649505 | − | 0.997888i | \(-0.479311\pi\) | ||||
0.0649505 | + | 0.997888i | \(0.479311\pi\) | |||||||
\(662\) | 4.05256 | 0.157507 | ||||||||
\(663\) | 10.7321 | 0.416798 | ||||||||
\(664\) | 5.00000 | 0.194038 | ||||||||
\(665\) | 3.73205 | 0.144723 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.0000 | 1.54881 | ||||||||
\(668\) | 17.6603 | 0.683296 | ||||||||
\(669\) | 25.5167 | 0.986531 | ||||||||
\(670\) | 7.66025 | 0.295941 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.73205 | −0.0668153 | ||||||||
\(673\) | −47.1051 | −1.81577 | −0.907884 | − | 0.419221i | \(-0.862303\pi\) | ||||
−0.907884 | + | 0.419221i | \(0.862303\pi\) | |||||||
\(674\) | 11.3923 | 0.438815 | ||||||||
\(675\) | 5.19615 | 0.200000 | ||||||||
\(676\) | −7.85641 | −0.302169 | ||||||||
\(677\) | −45.9808 | −1.76718 | −0.883592 | − | 0.468257i | \(-0.844882\pi\) | ||||
−0.883592 | + | 0.468257i | \(0.844882\pi\) | |||||||
\(678\) | 17.5359 | 0.673462 | ||||||||
\(679\) | 2.92820 | 0.112374 | ||||||||
\(680\) | −2.73205 | −0.104769 | ||||||||
\(681\) | −30.0000 | −1.14960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.9282 | −1.48955 | −0.744773 | − | 0.667318i | \(-0.767442\pi\) | ||||
−0.744773 | + | 0.667318i | \(0.767442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.66025 | 0.101643 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 37.8564 | 1.44431 | ||||||||
\(688\) | 8.73205 | 0.332906 | ||||||||
\(689\) | 9.51666 | 0.362556 | ||||||||
\(690\) | 8.66025 | 0.329690 | ||||||||
\(691\) | 1.85641 | 0.0706210 | 0.0353105 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353105 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(692\) | 19.8564 | 0.754827 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.53590 | −0.324018 | ||||||||
\(695\) | −6.80385 | −0.258085 | ||||||||
\(696\) | −13.8564 | −0.525226 | ||||||||
\(697\) | 11.4641 | 0.434234 | ||||||||
\(698\) | −6.46410 | −0.244670 | ||||||||
\(699\) | 21.5885 | 0.816550 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −47.9090 | −1.80950 | −0.904748 | − | 0.425947i | \(-0.859941\pi\) | ||||
−0.904748 | + | 0.425947i | \(0.859941\pi\) | |||||||
\(702\) | −11.7846 | −0.444781 | ||||||||
\(703\) | 22.3923 | 0.844542 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.19615 | −0.0827119 | ||||||||
\(706\) | −1.80385 | −0.0678887 | ||||||||
\(707\) | −18.4641 | −0.694414 | ||||||||
\(708\) | 21.5885 | 0.811344 | ||||||||
\(709\) | 1.32051 | 0.0495927 | 0.0247964 | − | 0.999693i | \(-0.492106\pi\) | ||||
0.0247964 | + | 0.999693i | \(0.492106\pi\) | |||||||
\(710\) | −6.92820 | −0.260011 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.66025 | −0.137174 | ||||||||
\(713\) | −3.66025 | −0.137078 | ||||||||
\(714\) | 4.73205 | 0.177093 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.80385 | −0.216900 | ||||||||
\(717\) | 4.26795 | 0.159389 | ||||||||
\(718\) | −33.7128 | −1.25815 | ||||||||
\(719\) | −34.9282 | −1.30260 | −0.651301 | − | 0.758819i | \(-0.725777\pi\) | ||||
−0.651301 | + | 0.758819i | \(0.725777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.26795 | 0.270673 | ||||||||
\(722\) | 5.07180 | 0.188753 | ||||||||
\(723\) | 18.2487 | 0.678677 | ||||||||
\(724\) | −5.33975 | −0.198450 | ||||||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.3205 | −0.568206 | −0.284103 | − | 0.958794i | \(-0.591696\pi\) | ||||
−0.284103 | + | 0.958794i | \(0.591696\pi\) | |||||||
\(728\) | 2.26795 | 0.0840558 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 15.1244 | 0.559778 | ||||||||
\(731\) | −23.8564 | −0.882361 | ||||||||
\(732\) | 18.9282 | 0.699607 | ||||||||
\(733\) | 23.5885 | 0.871260 | 0.435630 | − | 0.900126i | \(-0.356526\pi\) | ||||
0.435630 | + | 0.900126i | \(0.356526\pi\) | |||||||
\(734\) | 20.7321 | 0.765234 | ||||||||
\(735\) | 1.73205 | 0.0638877 | ||||||||
\(736\) | 5.00000 | 0.184302 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.9808 | −0.992503 | −0.496252 | − | 0.868179i | \(-0.665291\pi\) | ||||
−0.496252 | + | 0.868179i | \(0.665291\pi\) | |||||||
\(740\) | −6.00000 | −0.220564 | ||||||||
\(741\) | −14.6603 | −0.538558 | ||||||||
\(742\) | 4.19615 | 0.154046 | ||||||||
\(743\) | −12.5359 | −0.459898 | −0.229949 | − | 0.973203i | \(-0.573856\pi\) | ||||
−0.229949 | + | 0.973203i | \(0.573856\pi\) | |||||||
\(744\) | 1.26795 | 0.0464853 | ||||||||
\(745\) | 12.5359 | 0.459280 | ||||||||
\(746\) | −13.3205 | −0.487698 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.00000 | 0.0730784 | ||||||||
\(750\) | −1.73205 | −0.0632456 | ||||||||
\(751\) | −42.3731 | −1.54622 | −0.773108 | − | 0.634275i | \(-0.781299\pi\) | ||||
−0.773108 | + | 0.634275i | \(0.781299\pi\) | |||||||
\(752\) | −1.26795 | −0.0462373 | ||||||||
\(753\) | −24.9282 | −0.908434 | ||||||||
\(754\) | 18.1436 | 0.660751 | ||||||||
\(755\) | 8.85641 | 0.322318 | ||||||||
\(756\) | −5.19615 | −0.188982 | ||||||||
\(757\) | −25.9090 | −0.941677 | −0.470839 | − | 0.882219i | \(-0.656049\pi\) | ||||
−0.470839 | + | 0.882219i | \(0.656049\pi\) | |||||||
\(758\) | −34.7846 | −1.26343 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.73205 | 0.135376 | ||||||||
\(761\) | 40.4449 | 1.46613 | 0.733063 | − | 0.680161i | \(-0.238090\pi\) | ||||
0.733063 | + | 0.680161i | \(0.238090\pi\) | |||||||
\(762\) | −31.3923 | −1.13722 | ||||||||
\(763\) | −18.0526 | −0.653547 | ||||||||
\(764\) | 8.66025 | 0.313317 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.33975 | −0.301327 | ||||||||
\(767\) | −28.2679 | −1.02070 | ||||||||
\(768\) | −1.73205 | −0.0625000 | ||||||||
\(769\) | −34.7846 | −1.25437 | −0.627183 | − | 0.778872i | \(-0.715792\pi\) | ||||
−0.627183 | + | 0.778872i | \(0.715792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.80385 | 0.136992 | ||||||||
\(772\) | 9.39230 | 0.338036 | ||||||||
\(773\) | 27.5359 | 0.990397 | 0.495199 | − | 0.868780i | \(-0.335095\pi\) | ||||
0.495199 | + | 0.868780i | \(0.335095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.732051 | 0.0262960 | ||||||||
\(776\) | 2.92820 | 0.105116 | ||||||||
\(777\) | 10.3923 | 0.372822 | ||||||||
\(778\) | −1.12436 | −0.0403101 | ||||||||
\(779\) | −15.6603 | −0.561087 | ||||||||
\(780\) | 3.92820 | 0.140652 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −13.6603 | −0.488490 | ||||||||
\(783\) | −41.5692 | −1.48556 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −15.3923 | −0.549375 | ||||||||
\(786\) | 4.85641 | 0.173222 | ||||||||
\(787\) | −46.4974 | −1.65745 | −0.828727 | − | 0.559653i | \(-0.810934\pi\) | ||||
−0.828727 | + | 0.559653i | \(0.810934\pi\) | |||||||
\(788\) | 2.53590 | 0.0903376 | ||||||||
\(789\) | −24.4641 | −0.870945 | ||||||||
\(790\) | 7.00000 | 0.249049 | ||||||||
\(791\) | −10.1244 | −0.359981 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.7846 | −0.880127 | ||||||||
\(794\) | 28.7846 | 1.02153 | ||||||||
\(795\) | 7.26795 | 0.257768 | ||||||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | 34.1769 | 1.21061 | 0.605304 | − | 0.795994i | \(-0.293051\pi\) | ||||
0.605304 | + | 0.795994i | \(0.293051\pi\) | |||||||
\(798\) | −6.46410 | −0.228827 | ||||||||
\(799\) | 3.46410 | 0.122551 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.4641 | 0.899169 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −13.2679 | −0.467924 | ||||||||
\(805\) | −5.00000 | −0.176227 | ||||||||
\(806\) | −1.66025 | −0.0584800 | ||||||||
\(807\) | 31.6410 | 1.11382 | ||||||||
\(808\) | −18.4641 | −0.649565 | ||||||||
\(809\) | 9.21539 | 0.323996 | 0.161998 | − | 0.986791i | \(-0.448206\pi\) | ||||
0.161998 | + | 0.986791i | \(0.448206\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | 30.5359 | 1.07226 | 0.536130 | − | 0.844135i | \(-0.319886\pi\) | ||||
0.536130 | + | 0.844135i | \(0.319886\pi\) | |||||||
\(812\) | 8.00000 | 0.280745 | ||||||||
\(813\) | 25.1769 | 0.882993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0000 | −0.350285 | ||||||||
\(816\) | 4.73205 | 0.165655 | ||||||||
\(817\) | 32.5885 | 1.14013 | ||||||||
\(818\) | −19.7128 | −0.689242 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.19615 | 0.146536 | ||||||||
\(821\) | −43.8564 | −1.53060 | −0.765300 | − | 0.643674i | \(-0.777409\pi\) | ||||
−0.765300 | + | 0.643674i | \(0.777409\pi\) | |||||||
\(822\) | −4.60770 | −0.160712 | ||||||||
\(823\) | 42.7846 | 1.49138 | 0.745689 | − | 0.666294i | \(-0.232121\pi\) | ||||
0.745689 | + | 0.666294i | \(0.232121\pi\) | |||||||
\(824\) | 7.26795 | 0.253191 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.4641 | −0.433682 | ||||||||
\(827\) | −19.9090 | −0.692303 | −0.346151 | − | 0.938179i | \(-0.612512\pi\) | ||||
−0.346151 | + | 0.938179i | \(0.612512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.124356 | −0.00431905 | −0.00215953 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215953 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(830\) | −5.00000 | −0.173553 | ||||||||
\(831\) | 21.1244 | 0.732796 | ||||||||
\(832\) | 2.26795 | 0.0786270 | ||||||||
\(833\) | −2.73205 | −0.0946600 | ||||||||
\(834\) | 11.7846 | 0.408068 | ||||||||
\(835\) | −17.6603 | −0.611158 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.80385 | 0.131480 | ||||||||
\(838\) | −2.07180 | −0.0715690 | ||||||||
\(839\) | 12.1962 | 0.421058 | 0.210529 | − | 0.977588i | \(-0.432481\pi\) | ||||
0.210529 | + | 0.977588i | \(0.432481\pi\) | |||||||
\(840\) | 1.73205 | 0.0597614 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 28.3923 | 0.978463 | ||||||||
\(843\) | 7.39230 | 0.254605 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 7.85641 | 0.270269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.19615 | 0.144096 | ||||||||
\(849\) | −27.3397 | −0.938298 | ||||||||
\(850\) | 2.73205 | 0.0937086 | ||||||||
\(851\) | −30.0000 | −1.02839 | ||||||||
\(852\) | 12.0000 | 0.411113 | ||||||||
\(853\) | −43.8372 | −1.50096 | −0.750478 | − | 0.660895i | \(-0.770177\pi\) | ||||
−0.750478 | + | 0.660895i | \(0.770177\pi\) | |||||||
\(854\) | −10.9282 | −0.373955 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 15.6077 | 0.533149 | 0.266574 | − | 0.963814i | \(-0.414108\pi\) | ||||
0.266574 | + | 0.963814i | \(0.414108\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.14359 | 0.141378 | 0.0706888 | − | 0.997498i | \(-0.477480\pi\) | ||||
0.0706888 | + | 0.997498i | \(0.477480\pi\) | |||||||
\(860\) | −8.73205 | −0.297760 | ||||||||
\(861\) | −7.26795 | −0.247691 | ||||||||
\(862\) | −27.5359 | −0.937876 | ||||||||
\(863\) | −10.1436 | −0.345292 | −0.172646 | − | 0.984984i | \(-0.555232\pi\) | ||||
−0.172646 | + | 0.984984i | \(0.555232\pi\) | |||||||
\(864\) | −5.19615 | −0.176777 | ||||||||
\(865\) | −19.8564 | −0.675138 | ||||||||
\(866\) | −18.0526 | −0.613451 | ||||||||
\(867\) | 16.5167 | 0.560935 | ||||||||
\(868\) | −0.732051 | −0.0248474 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 13.8564 | 0.469776 | ||||||||
\(871\) | 17.3731 | 0.588664 | ||||||||
\(872\) | −18.0526 | −0.611337 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.6603 | 0.631193 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −26.1962 | −0.885086 | ||||||||
\(877\) | −9.94744 | −0.335901 | −0.167951 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167951 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(878\) | −11.2679 | −0.380275 | ||||||||
\(879\) | 14.3205 | 0.483019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −53.4256 | −1.79996 | −0.899978 | − | 0.435936i | \(-0.856417\pi\) | ||||
−0.899978 | + | 0.435936i | \(0.856417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.6410 | −1.09846 | −0.549229 | − | 0.835672i | \(-0.685078\pi\) | ||||
−0.549229 | + | 0.835672i | \(0.685078\pi\) | |||||||
\(884\) | −6.19615 | −0.208399 | ||||||||
\(885\) | −21.5885 | −0.725688 | ||||||||
\(886\) | −4.00000 | −0.134383 | ||||||||
\(887\) | −2.33975 | −0.0785610 | −0.0392805 | − | 0.999228i | \(-0.512507\pi\) | ||||
−0.0392805 | + | 0.999228i | \(0.512507\pi\) | |||||||
\(888\) | 10.3923 | 0.348743 | ||||||||
\(889\) | 18.1244 | 0.607871 | ||||||||
\(890\) | 3.66025 | 0.122692 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.7321 | −0.493266 | ||||||||
\(893\) | −4.73205 | −0.158352 | ||||||||
\(894\) | −21.7128 | −0.726185 | ||||||||
\(895\) | 5.80385 | 0.194001 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 19.6410 | 0.655794 | ||||||||
\(898\) | −10.6077 | −0.353983 | ||||||||
\(899\) | −5.85641 | −0.195322 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4641 | −0.381925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.1244 | 0.503307 | ||||||||
\(904\) | −10.1244 | −0.336731 | ||||||||
\(905\) | 5.33975 | 0.177499 | ||||||||
\(906\) | −15.3397 | −0.509629 | ||||||||
\(907\) | 36.0000 | 1.19536 | 0.597680 | − | 0.801735i | \(-0.296089\pi\) | ||||
0.597680 | + | 0.801735i | \(0.296089\pi\) | |||||||
\(908\) | 17.3205 | 0.574801 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.26795 | −0.0751818 | ||||||||
\(911\) | 29.9808 | 0.993307 | 0.496653 | − | 0.867949i | \(-0.334562\pi\) | ||||
0.496653 | + | 0.867949i | \(0.334562\pi\) | |||||||
\(912\) | −6.46410 | −0.214048 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.3923 | 0.575286 | ||||||||
\(915\) | −18.9282 | −0.625747 | ||||||||
\(916\) | −21.8564 | −0.722156 | ||||||||
\(917\) | −2.80385 | −0.0925912 | ||||||||
\(918\) | 14.1962 | 0.468543 | ||||||||
\(919\) | −12.1436 | −0.400580 | −0.200290 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200290 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(920\) | −5.00000 | −0.164845 | ||||||||
\(921\) | −36.2487 | −1.19444 | ||||||||
\(922\) | 17.4641 | 0.575150 | ||||||||
\(923\) | −15.7128 | −0.517194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 36.1769 | 1.18885 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.00000 | 0.262613 | ||||||||
\(929\) | −47.3205 | −1.55254 | −0.776268 | − | 0.630403i | \(-0.782890\pi\) | ||||
−0.776268 | + | 0.630403i | \(0.782890\pi\) | |||||||
\(930\) | −1.26795 | −0.0415777 | ||||||||
\(931\) | 3.73205 | 0.122313 | ||||||||
\(932\) | −12.4641 | −0.408275 | ||||||||
\(933\) | −16.0526 | −0.525537 | ||||||||
\(934\) | 17.5885 | 0.575512 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5359 | −0.344193 | −0.172096 | − | 0.985080i | \(-0.555054\pi\) | ||||
−0.172096 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(938\) | 7.66025 | 0.250116 | ||||||||
\(939\) | 45.7128 | 1.49178 | ||||||||
\(940\) | 1.26795 | 0.0413559 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 26.6603 | 0.868638 | ||||||||
\(943\) | 20.9808 | 0.683228 | ||||||||
\(944\) | −12.4641 | −0.405672 | ||||||||
\(945\) | 5.19615 | 0.169031 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −60.0526 | −1.95145 | −0.975723 | − | 0.219008i | \(-0.929718\pi\) | ||||
−0.975723 | + | 0.219008i | \(0.929718\pi\) | |||||||
\(948\) | −12.1244 | −0.393781 | ||||||||
\(949\) | 34.3013 | 1.11347 | ||||||||
\(950\) | −3.73205 | −0.121084 | ||||||||
\(951\) | 33.1244 | 1.07413 | ||||||||
\(952\) | −2.73205 | −0.0885463 | ||||||||
\(953\) | 2.60770 | 0.0844715 | 0.0422358 | − | 0.999108i | \(-0.486552\pi\) | ||||
0.0422358 | + | 0.999108i | \(0.486552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.66025 | −0.280239 | ||||||||
\(956\) | −2.46410 | −0.0796947 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.9808 | −0.742475 | ||||||||
\(959\) | 2.66025 | 0.0859041 | ||||||||
\(960\) | 1.73205 | 0.0559017 | ||||||||
\(961\) | −30.4641 | −0.982713 | ||||||||
\(962\) | −13.6077 | −0.438730 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.5359 | −0.339338 | ||||||||
\(965\) | −9.39230 | −0.302349 | ||||||||
\(966\) | 8.66025 | 0.278639 | ||||||||
\(967\) | −12.7846 | −0.411125 | −0.205563 | − | 0.978644i | \(-0.565902\pi\) | ||||
−0.205563 | + | 0.978644i | \(0.565902\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6603 | 0.567329 | ||||||||
\(970\) | −2.92820 | −0.0940189 | ||||||||
\(971\) | −4.71281 | −0.151241 | −0.0756207 | − | 0.997137i | \(-0.524094\pi\) | ||||
−0.0756207 | + | 0.997137i | \(0.524094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.80385 | −0.218121 | ||||||||
\(974\) | 3.39230 | 0.108696 | ||||||||
\(975\) | −3.92820 | −0.125803 | ||||||||
\(976\) | −10.9282 | −0.349803 | ||||||||
\(977\) | −17.7321 | −0.567299 | −0.283649 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283649 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(978\) | 17.3205 | 0.553849 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.66025 | −0.244449 | ||||||||
\(983\) | 58.3923 | 1.86243 | 0.931213 | − | 0.364476i | \(-0.118752\pi\) | ||||
0.931213 | + | 0.364476i | \(0.118752\pi\) | |||||||
\(984\) | −7.26795 | −0.231694 | ||||||||
\(985\) | −2.53590 | −0.0808004 | ||||||||
\(986\) | −21.8564 | −0.696050 | ||||||||
\(987\) | −2.19615 | −0.0699043 | ||||||||
\(988\) | 8.46410 | 0.269279 | ||||||||
\(989\) | −43.6603 | −1.38832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1244 | −0.829868 | −0.414934 | − | 0.909852i | \(-0.636195\pi\) | ||||
−0.414934 | + | 0.909852i | \(0.636195\pi\) | |||||||
\(992\) | −0.732051 | −0.0232426 | ||||||||
\(993\) | 7.01924 | 0.222749 | ||||||||
\(994\) | −6.92820 | −0.219749 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 8.66025 | 0.274411 | ||||||||
\(997\) | −21.3397 | −0.675837 | −0.337918 | − | 0.941175i | \(-0.609723\pi\) | ||||
−0.337918 | + | 0.941175i | \(0.609723\pi\) | |||||||
\(998\) | 22.0000 | 0.696398 | ||||||||
\(999\) | 31.1769 | 0.986394 |
(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 | 8470.2.a.bm.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.bz.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bm.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.bz.1.1 | yes | 2 | 11.10 | odd | 2 |