Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1755,2,Mod(1,1755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1755, 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("1755.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1755 = 3^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1755.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: | \(14.0137455547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.12357.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.16027\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1755.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16027 | 0.820437 | 0.410218 | − | 0.911987i | \(-0.365452\pi\) | ||||
0.410218 | + | 0.911987i | \(0.365452\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.653767 | −0.326884 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26505 | −0.478145 | −0.239073 | − | 0.971002i | \(-0.576843\pi\) | ||||
−0.239073 | + | 0.971002i | \(0.576843\pi\) | |||||||
\(8\) | −3.07909 | −1.08862 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.16027 | 0.366910 | ||||||||
\(11\) | 2.81404 | 0.848465 | 0.424232 | − | 0.905553i | \(-0.360544\pi\) | ||||
0.424232 | + | 0.905553i | \(0.360544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −1.46781 | −0.392288 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.26505 | −0.566263 | ||||||||
\(17\) | −1.42533 | −0.345692 | −0.172846 | − | 0.984949i | \(-0.555296\pi\) | ||||
−0.172846 | + | 0.984949i | \(0.555296\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.05341 | 1.38875 | 0.694373 | − | 0.719615i | \(-0.255682\pi\) | ||||
0.694373 | + | 0.719615i | \(0.255682\pi\) | |||||||
\(20\) | −0.653767 | −0.146187 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.26505 | 0.696112 | ||||||||
\(23\) | 2.77156 | 0.577910 | 0.288955 | − | 0.957343i | \(-0.406692\pi\) | ||||
0.288955 | + | 0.957343i | \(0.406692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.16027 | 0.227548 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.827051 | 0.156298 | ||||||||
\(29\) | −1.23937 | −0.230145 | −0.115072 | − | 0.993357i | \(-0.536710\pi\) | ||||
−0.115072 | + | 0.993357i | \(0.536710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.653767 | 0.117420 | 0.0587100 | − | 0.998275i | \(-0.481301\pi\) | ||||
0.0587100 | + | 0.998275i | \(0.481301\pi\) | |||||||
\(32\) | 3.53011 | 0.624041 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.65377 | −0.283619 | ||||||||
\(35\) | −1.26505 | −0.213833 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.39964 | 0.723296 | 0.361648 | − | 0.932315i | \(-0.382214\pi\) | ||||
0.361648 | + | 0.932315i | \(0.382214\pi\) | |||||||
\(38\) | 7.02360 | 1.13938 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.07909 | −0.486847 | ||||||||
\(41\) | 2.50651 | 0.391450 | 0.195725 | − | 0.980659i | \(-0.437294\pi\) | ||||
0.195725 | + | 0.980659i | \(0.437294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.27598 | 0.957078 | 0.478539 | − | 0.878066i | \(-0.341167\pi\) | ||||
0.478539 | + | 0.878066i | \(0.341167\pi\) | |||||||
\(44\) | −1.83973 | −0.277349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.21576 | 0.474139 | ||||||||
\(47\) | 9.88012 | 1.44116 | 0.720582 | − | 0.693370i | \(-0.243875\pi\) | ||||
0.720582 | + | 0.693370i | \(0.243875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39964 | −0.771377 | ||||||||
\(50\) | 1.16027 | 0.164087 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.653767 | −0.0906612 | ||||||||
\(53\) | 8.18387 | 1.12414 | 0.562071 | − | 0.827089i | \(-0.310005\pi\) | ||||
0.562071 | + | 0.827089i | \(0.310005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.81404 | 0.379445 | ||||||||
\(56\) | 3.89522 | 0.520521 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.43800 | −0.188819 | ||||||||
\(59\) | −8.74379 | −1.13834 | −0.569172 | − | 0.822218i | \(-0.692736\pi\) | ||||
−0.569172 | + | 0.822218i | \(0.692736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.957519 | −0.122598 | −0.0612989 | − | 0.998119i | \(-0.519524\pi\) | ||||
−0.0612989 | + | 0.998119i | \(0.519524\pi\) | |||||||
\(62\) | 0.758548 | 0.0963357 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.62599 | 1.07825 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7565 | 1.31411 | 0.657056 | − | 0.753842i | \(-0.271802\pi\) | ||||
0.657056 | + | 0.753842i | \(0.271802\pi\) | |||||||
\(68\) | 0.931832 | 0.113001 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.46781 | −0.175437 | ||||||||
\(71\) | 9.63901 | 1.14394 | 0.571970 | − | 0.820275i | \(-0.306179\pi\) | ||||
0.571970 | + | 0.820275i | \(0.306179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09589 | −0.596428 | −0.298214 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298214 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(74\) | 5.10478 | 0.593419 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.95752 | −0.453959 | ||||||||
\(77\) | −3.55991 | −0.405690 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8801 | −1.22411 | −0.612055 | − | 0.790815i | \(-0.709657\pi\) | ||||
−0.612055 | + | 0.790815i | \(0.709657\pi\) | |||||||
\(80\) | −2.26505 | −0.253241 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.90823 | 0.321160 | ||||||||
\(83\) | 1.43119 | 0.157094 | 0.0785470 | − | 0.996910i | \(-0.474972\pi\) | ||||
0.0785470 | + | 0.996910i | \(0.474972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.42533 | −0.154598 | ||||||||
\(86\) | 7.28185 | 0.785222 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.66469 | −0.923659 | ||||||||
\(89\) | 5.90581 | 0.626015 | 0.313007 | − | 0.949751i | \(-0.398664\pi\) | ||||
0.313007 | + | 0.949751i | \(0.398664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.26505 | −0.132614 | ||||||||
\(92\) | −1.81195 | −0.188909 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.4636 | 1.18238 | ||||||||
\(95\) | 6.05341 | 0.621066 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8801 | 1.20624 | 0.603122 | − | 0.797649i | \(-0.293923\pi\) | ||||
0.603122 | + | 0.797649i | \(0.293923\pi\) | |||||||
\(98\) | −6.26505 | −0.632866 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.653767 | −0.0653767 | ||||||||
\(101\) | 14.1712 | 1.41009 | 0.705043 | − | 0.709164i | \(-0.250927\pi\) | ||||
0.705043 | + | 0.709164i | \(0.250927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4530 | −1.02997 | −0.514985 | − | 0.857199i | \(-0.672202\pi\) | ||||
−0.514985 | + | 0.857199i | \(0.672202\pi\) | |||||||
\(104\) | −3.07909 | −0.301930 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.49553 | 0.922287 | ||||||||
\(107\) | −14.8229 | −1.43298 | −0.716491 | − | 0.697596i | \(-0.754253\pi\) | ||||
−0.716491 | + | 0.697596i | \(0.754253\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.1561 | −1.73904 | −0.869520 | − | 0.493898i | \(-0.835571\pi\) | ||||
−0.869520 | + | 0.493898i | \(0.835571\pi\) | |||||||
\(110\) | 3.26505 | 0.311311 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.86541 | 0.270756 | ||||||||
\(113\) | 9.10890 | 0.856893 | 0.428447 | − | 0.903567i | \(-0.359061\pi\) | ||||
0.428447 | + | 0.903567i | \(0.359061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.77156 | 0.258449 | ||||||||
\(116\) | 0.810257 | 0.0752305 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1452 | −0.933939 | ||||||||
\(119\) | 1.80311 | 0.165291 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.08118 | −0.280107 | ||||||||
\(122\) | −1.11098 | −0.100584 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.427412 | −0.0383827 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.66469 | 0.413925 | 0.206962 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206962 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(128\) | 2.94829 | 0.260595 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.16027 | 0.101763 | ||||||||
\(131\) | 6.48082 | 0.566232 | 0.283116 | − | 0.959086i | \(-0.408632\pi\) | ||||
0.283116 | + | 0.959086i | \(0.408632\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.65788 | −0.664023 | ||||||||
\(134\) | 12.4804 | 1.07814 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.38871 | 0.376329 | ||||||||
\(137\) | 15.2500 | 1.30289 | 0.651446 | − | 0.758695i | \(-0.274163\pi\) | ||||
0.651446 | + | 0.758695i | \(0.274163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.9339 | −1.69077 | −0.845384 | − | 0.534159i | \(-0.820628\pi\) | ||||
−0.845384 | + | 0.534159i | \(0.820628\pi\) | |||||||
\(140\) | 0.827051 | 0.0698985 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.1839 | 0.938530 | ||||||||
\(143\) | 2.81404 | 0.235322 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.23937 | −0.102924 | ||||||||
\(146\) | −5.91262 | −0.489332 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.87634 | −0.236434 | ||||||||
\(149\) | −4.90614 | −0.401927 | −0.200964 | − | 0.979599i | \(-0.564407\pi\) | ||||
−0.200964 | + | 0.979599i | \(0.564407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9835 | −1.30072 | −0.650359 | − | 0.759627i | \(-0.725381\pi\) | ||||
−0.650359 | + | 0.759627i | \(0.725381\pi\) | |||||||
\(152\) | −18.6390 | −1.51182 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.13047 | −0.332843 | ||||||||
\(155\) | 0.653767 | 0.0525119 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0260 | −1.03959 | −0.519793 | − | 0.854292i | \(-0.673991\pi\) | ||||
−0.519793 | + | 0.854292i | \(0.673991\pi\) | |||||||
\(158\) | −12.6239 | −1.00430 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.53011 | 0.279079 | ||||||||
\(161\) | −3.50617 | −0.276325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.39586 | 0.422636 | 0.211318 | − | 0.977417i | \(-0.432224\pi\) | ||||
0.211318 | + | 0.977417i | \(0.432224\pi\) | |||||||
\(164\) | −1.63867 | −0.127959 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.66058 | 0.128886 | ||||||||
\(167\) | −15.0732 | −1.16640 | −0.583201 | − | 0.812328i | \(-0.698200\pi\) | ||||
−0.583201 | + | 0.812328i | \(0.698200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.65377 | −0.126838 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.10303 | −0.312853 | ||||||||
\(173\) | 8.74762 | 0.665069 | 0.332535 | − | 0.943091i | \(-0.392096\pi\) | ||||
0.332535 | + | 0.943091i | \(0.392096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26505 | −0.0956291 | ||||||||
\(176\) | −6.37395 | −0.480455 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.85235 | 0.513605 | ||||||||
\(179\) | −11.3777 | −0.850412 | −0.425206 | − | 0.905097i | \(-0.639798\pi\) | ||||
−0.425206 | + | 0.905097i | \(0.639798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1136 | 0.974728 | 0.487364 | − | 0.873199i | \(-0.337959\pi\) | ||||
0.487364 | + | 0.873199i | \(0.337959\pi\) | |||||||
\(182\) | −1.46781 | −0.108801 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.53389 | −0.629127 | ||||||||
\(185\) | 4.39964 | 0.323468 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.01093 | −0.293308 | ||||||||
\(188\) | −6.45930 | −0.471093 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.02360 | 0.509546 | ||||||||
\(191\) | 18.8191 | 1.36170 | 0.680851 | − | 0.732422i | \(-0.261610\pi\) | ||||
0.680851 | + | 0.732422i | \(0.261610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.08530 | −0.438029 | −0.219015 | − | 0.975722i | \(-0.570284\pi\) | ||||
−0.219015 | + | 0.975722i | \(0.570284\pi\) | |||||||
\(194\) | 13.7842 | 0.989647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.53011 | 0.252151 | ||||||||
\(197\) | −2.71304 | −0.193296 | −0.0966481 | − | 0.995319i | \(-0.530812\pi\) | ||||
−0.0966481 | + | 0.995319i | \(0.530812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.66848 | 0.260051 | 0.130026 | − | 0.991511i | \(-0.458494\pi\) | ||||
0.130026 | + | 0.991511i | \(0.458494\pi\) | |||||||
\(200\) | −3.07909 | −0.217725 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.4425 | 1.15689 | ||||||||
\(203\) | 1.56787 | 0.110043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.50651 | 0.175062 | ||||||||
\(206\) | −12.1284 | −0.845024 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.26505 | −0.157053 | ||||||||
\(209\) | 17.0345 | 1.17830 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2199 | −0.978937 | −0.489469 | − | 0.872021i | \(-0.662809\pi\) | ||||
−0.489469 | + | 0.872021i | \(0.662809\pi\) | |||||||
\(212\) | −5.35035 | −0.367464 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.1986 | −1.17567 | ||||||||
\(215\) | 6.27598 | 0.428018 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.827051 | −0.0561439 | ||||||||
\(218\) | −21.0660 | −1.42677 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.83973 | −0.124034 | ||||||||
\(221\) | −1.42533 | −0.0958778 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.3756 | 1.43142 | 0.715710 | − | 0.698398i | \(-0.246103\pi\) | ||||
0.715710 | + | 0.698398i | \(0.246103\pi\) | |||||||
\(224\) | −4.46578 | −0.298382 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5688 | 0.703026 | ||||||||
\(227\) | −4.24523 | −0.281766 | −0.140883 | − | 0.990026i | \(-0.544994\pi\) | ||||
−0.140883 | + | 0.990026i | \(0.544994\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.91916 | −0.523313 | −0.261656 | − | 0.965161i | \(-0.584269\pi\) | ||||
−0.261656 | + | 0.965161i | \(0.584269\pi\) | |||||||
\(230\) | 3.21576 | 0.212041 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.81613 | 0.250541 | ||||||||
\(233\) | −0.657550 | −0.0430775 | −0.0215388 | − | 0.999768i | \(-0.506857\pi\) | ||||
−0.0215388 | + | 0.999768i | \(0.506857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.88012 | 0.644508 | ||||||||
\(236\) | 5.71640 | 0.372106 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.09210 | 0.135611 | ||||||||
\(239\) | −1.98227 | −0.128222 | −0.0641111 | − | 0.997943i | \(-0.520421\pi\) | ||||
−0.0641111 | + | 0.997943i | \(0.520421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.35716 | 0.0874222 | 0.0437111 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437111 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(242\) | −3.57501 | −0.229810 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.625995 | 0.0400752 | ||||||||
\(245\) | −5.39964 | −0.344970 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.05341 | 0.385169 | ||||||||
\(248\) | −2.01301 | −0.127826 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.16027 | 0.0733821 | ||||||||
\(251\) | 10.3668 | 0.654347 | 0.327174 | − | 0.944964i | \(-0.393904\pi\) | ||||
0.327174 | + | 0.944964i | \(0.393904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.79928 | 0.490336 | ||||||||
\(254\) | 5.41232 | 0.339599 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8312 | −0.864448 | ||||||||
\(257\) | 9.28070 | 0.578914 | 0.289457 | − | 0.957191i | \(-0.406525\pi\) | ||||
0.289457 | + | 0.957191i | \(0.406525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.56578 | −0.345841 | ||||||||
\(260\) | −0.653767 | −0.0405449 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.51952 | 0.464557 | ||||||||
\(263\) | −9.62094 | −0.593252 | −0.296626 | − | 0.954994i | \(-0.595862\pi\) | ||||
−0.296626 | + | 0.954994i | \(0.595862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.18387 | 0.502731 | ||||||||
\(266\) | −8.88523 | −0.544789 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.03222 | −0.429561 | ||||||||
\(269\) | 4.77628 | 0.291215 | 0.145608 | − | 0.989342i | \(-0.453486\pi\) | ||||
0.145608 | + | 0.989342i | \(0.453486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.3787 | −0.934188 | −0.467094 | − | 0.884208i | \(-0.654699\pi\) | ||||
−0.467094 | + | 0.884208i | \(0.654699\pi\) | |||||||
\(272\) | 3.22844 | 0.195753 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.6941 | 1.06894 | ||||||||
\(275\) | 2.81404 | 0.169693 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.33262 | 0.380490 | 0.190245 | − | 0.981737i | \(-0.439072\pi\) | ||||
0.190245 | + | 0.981737i | \(0.439072\pi\) | |||||||
\(278\) | −23.1287 | −1.38717 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.89522 | 0.232784 | ||||||||
\(281\) | 17.3928 | 1.03757 | 0.518785 | − | 0.854905i | \(-0.326385\pi\) | ||||
0.518785 | + | 0.854905i | \(0.326385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.6012 | −1.46239 | −0.731196 | − | 0.682167i | \(-0.761038\pi\) | ||||
−0.731196 | + | 0.682167i | \(0.761038\pi\) | |||||||
\(284\) | −6.30167 | −0.373935 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.26505 | 0.193067 | ||||||||
\(287\) | −3.17086 | −0.187170 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9684 | −0.880497 | ||||||||
\(290\) | −1.43800 | −0.0844424 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.33152 | 0.194963 | ||||||||
\(293\) | 19.7462 | 1.15358 | 0.576791 | − | 0.816892i | \(-0.304305\pi\) | ||||
0.576791 | + | 0.816892i | \(0.304305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.74379 | −0.509083 | ||||||||
\(296\) | −13.5469 | −0.787398 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.69247 | −0.329756 | ||||||||
\(299\) | 2.77156 | 0.160283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.93945 | −0.457622 | ||||||||
\(302\) | −18.5452 | −1.06716 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.7113 | −0.786396 | ||||||||
\(305\) | −0.957519 | −0.0548274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.1249 | −1.37688 | −0.688440 | − | 0.725293i | \(-0.741704\pi\) | ||||
−0.688440 | + | 0.725293i | \(0.741704\pi\) | |||||||
\(308\) | 2.32735 | 0.132613 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.758548 | 0.0430827 | ||||||||
\(311\) | −20.6794 | −1.17262 | −0.586311 | − | 0.810086i | \(-0.699420\pi\) | ||||
−0.586311 | + | 0.810086i | \(0.699420\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.27565 | −0.524290 | −0.262145 | − | 0.965028i | \(-0.584430\pi\) | ||||
−0.262145 | + | 0.965028i | \(0.584430\pi\) | |||||||
\(314\) | −15.1137 | −0.852914 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.11307 | 0.400141 | ||||||||
\(317\) | −25.8276 | −1.45062 | −0.725311 | − | 0.688421i | \(-0.758304\pi\) | ||||
−0.725311 | + | 0.688421i | \(0.758304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.48763 | −0.195270 | ||||||||
\(320\) | 8.62599 | 0.482208 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.06811 | −0.226707 | ||||||||
\(323\) | −8.62808 | −0.480079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 6.26066 | 0.346746 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.71776 | −0.426142 | ||||||||
\(329\) | −12.4989 | −0.689086 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.57225 | −0.141384 | −0.0706919 | − | 0.997498i | \(-0.522521\pi\) | ||||
−0.0706919 | + | 0.997498i | \(0.522521\pi\) | |||||||
\(332\) | −0.935668 | −0.0513515 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.4891 | −0.956958 | ||||||||
\(335\) | 10.7565 | 0.587688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0812 | 0.821524 | 0.410762 | − | 0.911743i | \(-0.365263\pi\) | ||||
0.410762 | + | 0.911743i | \(0.365263\pi\) | |||||||
\(338\) | 1.16027 | 0.0631105 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.931832 | 0.0505357 | ||||||||
\(341\) | 1.83973 | 0.0996268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.6862 | 0.846976 | ||||||||
\(344\) | −19.3243 | −1.04190 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.1496 | 0.545647 | ||||||||
\(347\) | −10.1438 | −0.544546 | −0.272273 | − | 0.962220i | \(-0.587775\pi\) | ||||
−0.272273 | + | 0.962220i | \(0.587775\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.88760 | 0.529271 | 0.264636 | − | 0.964348i | \(-0.414748\pi\) | ||||
0.264636 | + | 0.964348i | \(0.414748\pi\) | |||||||
\(350\) | −1.46781 | −0.0784576 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.93386 | 0.529477 | ||||||||
\(353\) | −24.0256 | −1.27875 | −0.639376 | − | 0.768894i | \(-0.720807\pi\) | ||||
−0.639376 | + | 0.768894i | \(0.720807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.63901 | 0.511585 | ||||||||
\(356\) | −3.86103 | −0.204634 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.2013 | −0.697709 | ||||||||
\(359\) | −10.5948 | −0.559171 | −0.279585 | − | 0.960121i | \(-0.590197\pi\) | ||||
−0.279585 | + | 0.960121i | \(0.590197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6437 | 0.928617 | ||||||||
\(362\) | 15.2154 | 0.799702 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.827051 | 0.0433492 | ||||||||
\(365\) | −5.09589 | −0.266731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.44481 | 0.179818 | 0.0899088 | − | 0.995950i | \(-0.471342\pi\) | ||||
0.0899088 | + | 0.995950i | \(0.471342\pi\) | |||||||
\(368\) | −6.27773 | −0.327249 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.10478 | 0.265385 | ||||||||
\(371\) | −10.3530 | −0.537503 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.9726 | −0.619916 | −0.309958 | − | 0.950750i | \(-0.600315\pi\) | ||||
−0.309958 | + | 0.950750i | \(0.600315\pi\) | |||||||
\(374\) | −4.65377 | −0.240641 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −30.4218 | −1.56889 | ||||||||
\(377\) | −1.23937 | −0.0638306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1877 | −0.728771 | −0.364386 | − | 0.931248i | \(-0.618721\pi\) | ||||
−0.364386 | + | 0.931248i | \(0.618721\pi\) | |||||||
\(380\) | −3.95752 | −0.203016 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.8353 | 1.11719 | ||||||||
\(383\) | −19.0968 | −0.975802 | −0.487901 | − | 0.872899i | \(-0.662237\pi\) | ||||
−0.487901 | + | 0.872899i | \(0.662237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.55991 | −0.181430 | ||||||||
\(386\) | −7.06060 | −0.359375 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.76684 | −0.394301 | ||||||||
\(389\) | 27.3794 | 1.38819 | 0.694096 | − | 0.719882i | \(-0.255804\pi\) | ||||
0.694096 | + | 0.719882i | \(0.255804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.95038 | −0.199779 | ||||||||
\(392\) | 16.6260 | 0.839740 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.14787 | −0.158587 | ||||||||
\(395\) | −10.8801 | −0.547438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0181 | 0.552981 | 0.276490 | − | 0.961017i | \(-0.410829\pi\) | ||||
0.276490 | + | 0.961017i | \(0.410829\pi\) | |||||||
\(398\) | 4.25643 | 0.213356 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.26505 | −0.113253 | ||||||||
\(401\) | −1.33058 | −0.0664462 | −0.0332231 | − | 0.999448i | \(-0.510577\pi\) | ||||
−0.0332231 | + | 0.999448i | \(0.510577\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.653767 | 0.0325665 | ||||||||
\(404\) | −9.26467 | −0.460934 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.81915 | 0.0902829 | ||||||||
\(407\) | 12.3808 | 0.613692 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.6691 | 0.824236 | 0.412118 | − | 0.911130i | \(-0.364789\pi\) | ||||
0.412118 | + | 0.911130i | \(0.364789\pi\) | |||||||
\(410\) | 2.90823 | 0.143627 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.83386 | 0.336680 | ||||||||
\(413\) | 11.0614 | 0.544294 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.43119 | 0.0702546 | ||||||||
\(416\) | 3.53011 | 0.173078 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.7647 | 0.966723 | ||||||||
\(419\) | −22.0593 | −1.07767 | −0.538833 | − | 0.842413i | \(-0.681135\pi\) | ||||
−0.538833 | + | 0.842413i | \(0.681135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2907 | 0.891434 | 0.445717 | − | 0.895174i | \(-0.352949\pi\) | ||||
0.445717 | + | 0.895174i | \(0.352949\pi\) | |||||||
\(422\) | −16.4989 | −0.803156 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.1989 | −1.22377 | ||||||||
\(425\) | −1.42533 | −0.0691385 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.21131 | 0.0586196 | ||||||||
\(428\) | 9.69071 | 0.468418 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.28185 | 0.351162 | ||||||||
\(431\) | −5.83939 | −0.281274 | −0.140637 | − | 0.990061i | \(-0.544915\pi\) | ||||
−0.140637 | + | 0.990061i | \(0.544915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.49174 | 0.456144 | 0.228072 | − | 0.973644i | \(-0.426758\pi\) | ||||
0.228072 | + | 0.973644i | \(0.426758\pi\) | |||||||
\(434\) | −0.959604 | −0.0460625 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.8699 | 0.568463 | ||||||||
\(437\) | 16.7774 | 0.802571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1568 | 0.818848 | 0.409424 | − | 0.912344i | \(-0.365730\pi\) | ||||
0.409424 | + | 0.912344i | \(0.365730\pi\) | |||||||
\(440\) | −8.66469 | −0.413073 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.65377 | −0.0786617 | ||||||||
\(443\) | −2.21610 | −0.105290 | −0.0526450 | − | 0.998613i | \(-0.516765\pi\) | ||||
−0.0526450 | + | 0.998613i | \(0.516765\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.90581 | 0.279962 | ||||||||
\(446\) | 24.8016 | 1.17439 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.9123 | −0.515560 | ||||||||
\(449\) | −31.1619 | −1.47062 | −0.735311 | − | 0.677730i | \(-0.762964\pi\) | ||||
−0.735311 | + | 0.677730i | \(0.762964\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.05341 | 0.332132 | ||||||||
\(452\) | −5.95510 | −0.280104 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.92563 | −0.231171 | ||||||||
\(455\) | −1.26505 | −0.0593066 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.1812 | 1.36504 | 0.682519 | − | 0.730868i | \(-0.260884\pi\) | ||||
0.682519 | + | 0.730868i | \(0.260884\pi\) | |||||||
\(458\) | −9.18838 | −0.429345 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.81195 | −0.0844828 | ||||||||
\(461\) | 24.6927 | 1.15006 | 0.575028 | − | 0.818134i | \(-0.304991\pi\) | ||||
0.575028 | + | 0.818134i | \(0.304991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.2844 | 1.68628 | 0.843140 | − | 0.537694i | \(-0.180704\pi\) | ||||
0.843140 | + | 0.537694i | \(0.180704\pi\) | |||||||
\(464\) | 2.80723 | 0.130322 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.762937 | −0.0353424 | ||||||||
\(467\) | 8.19803 | 0.379360 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.6075 | −0.628336 | ||||||||
\(470\) | 11.4636 | 0.528778 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.9229 | 1.23923 | ||||||||
\(473\) | 17.6609 | 0.812047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.05341 | 0.277749 | ||||||||
\(476\) | −1.17882 | −0.0540310 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.29997 | −0.105198 | ||||||||
\(479\) | −12.6946 | −0.580029 | −0.290014 | − | 0.957022i | \(-0.593660\pi\) | ||||
−0.290014 | + | 0.957022i | \(0.593660\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.39964 | 0.200606 | ||||||||
\(482\) | 1.57467 | 0.0717244 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.01437 | 0.0915625 | ||||||||
\(485\) | 11.8801 | 0.539449 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1140 | 0.548936 | 0.274468 | − | 0.961596i | \(-0.411498\pi\) | ||||
0.274468 | + | 0.961596i | \(0.411498\pi\) | |||||||
\(488\) | 2.94829 | 0.133463 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.26505 | −0.283026 | ||||||||
\(491\) | −37.7496 | −1.70362 | −0.851808 | − | 0.523854i | \(-0.824494\pi\) | ||||
−0.851808 | + | 0.523854i | \(0.824494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.76650 | 0.0795592 | ||||||||
\(494\) | 7.02360 | 0.316007 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.48082 | −0.0664907 | ||||||||
\(497\) | −12.1939 | −0.546969 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9688 | 0.491030 | 0.245515 | − | 0.969393i | \(-0.421043\pi\) | ||||
0.245515 | + | 0.969393i | \(0.421043\pi\) | |||||||
\(500\) | −0.653767 | −0.0292374 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0283 | 0.536850 | ||||||||
\(503\) | −4.15582 | −0.185299 | −0.0926495 | − | 0.995699i | \(-0.529534\pi\) | ||||
−0.0926495 | + | 0.995699i | \(0.529534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.1712 | 0.630610 | ||||||||
\(506\) | 9.04929 | 0.402290 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.04962 | −0.135305 | ||||||||
\(509\) | 0.895219 | 0.0396799 | 0.0198399 | − | 0.999803i | \(-0.493684\pi\) | ||||
0.0198399 | + | 0.999803i | \(0.493684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.44657 | 0.285180 | ||||||||
\(512\) | −21.9445 | −0.969819 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.7681 | 0.474963 | ||||||||
\(515\) | −10.4530 | −0.460616 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.8031 | 1.22278 | ||||||||
\(518\) | −6.45782 | −0.283740 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.07909 | −0.135027 | ||||||||
\(521\) | 41.6448 | 1.82449 | 0.912246 | − | 0.409642i | \(-0.134346\pi\) | ||||
0.912246 | + | 0.409642i | \(0.134346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.0731 | −1.53364 | −0.766820 | − | 0.641862i | \(-0.778162\pi\) | ||||
−0.766820 | + | 0.641862i | \(0.778162\pi\) | |||||||
\(524\) | −4.23695 | −0.185092 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.1629 | −0.486726 | ||||||||
\(527\) | −0.931832 | −0.0405912 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3185 | −0.666020 | ||||||||
\(530\) | 9.49553 | 0.412459 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.00647 | 0.217058 | ||||||||
\(533\) | 2.50651 | 0.108569 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.8229 | −0.640849 | ||||||||
\(536\) | −33.1202 | −1.43057 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.54179 | 0.238924 | ||||||||
\(539\) | −15.1948 | −0.654486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3444 | −0.487735 | −0.243868 | − | 0.969809i | \(-0.578416\pi\) | ||||
−0.243868 | + | 0.969809i | \(0.578416\pi\) | |||||||
\(542\) | −17.8435 | −0.766442 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.03156 | −0.215726 | ||||||||
\(545\) | −18.1561 | −0.777722 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.3170 | 1.38177 | 0.690887 | − | 0.722962i | \(-0.257220\pi\) | ||||
0.690887 | + | 0.722962i | \(0.257220\pi\) | |||||||
\(548\) | −9.96992 | −0.425894 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.26505 | 0.139222 | ||||||||
\(551\) | −7.50239 | −0.319612 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7639 | 0.585302 | ||||||||
\(554\) | 7.34756 | 0.312168 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0321 | 0.552684 | ||||||||
\(557\) | 41.1683 | 1.74436 | 0.872178 | − | 0.489188i | \(-0.162707\pi\) | ||||
0.872178 | + | 0.489188i | \(0.162707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.27598 | 0.265446 | ||||||||
\(560\) | 2.86541 | 0.121086 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.1804 | 0.851260 | ||||||||
\(563\) | 36.2940 | 1.52961 | 0.764805 | − | 0.644262i | \(-0.222835\pi\) | ||||
0.764805 | + | 0.644262i | \(0.222835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.10890 | 0.383214 | ||||||||
\(566\) | −28.5442 | −1.19980 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.6794 | −1.24532 | ||||||||
\(569\) | −16.7700 | −0.703036 | −0.351518 | − | 0.936181i | \(-0.614334\pi\) | ||||
−0.351518 | + | 0.936181i | \(0.614334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2366 | −0.888725 | −0.444362 | − | 0.895847i | \(-0.646570\pi\) | ||||
−0.444362 | + | 0.895847i | \(0.646570\pi\) | |||||||
\(572\) | −1.83973 | −0.0769229 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.67907 | −0.153561 | ||||||||
\(575\) | 2.77156 | 0.115582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4640 | −1.35149 | −0.675746 | − | 0.737134i | \(-0.736179\pi\) | ||||
−0.675746 | + | 0.737134i | \(0.736179\pi\) | |||||||
\(578\) | −17.3675 | −0.722392 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.810257 | 0.0336441 | ||||||||
\(581\) | −1.81054 | −0.0751138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.0298 | 0.953795 | ||||||||
\(584\) | 15.6907 | 0.649286 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.9109 | 0.946441 | ||||||||
\(587\) | 12.3701 | 0.510569 | 0.255285 | − | 0.966866i | \(-0.417831\pi\) | ||||
0.255285 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.95752 | 0.163067 | ||||||||
\(590\) | −10.1452 | −0.417670 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.96542 | −0.409576 | ||||||||
\(593\) | 36.0294 | 1.47955 | 0.739775 | − | 0.672854i | \(-0.234932\pi\) | ||||
0.739775 | + | 0.672854i | \(0.234932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.80311 | 0.0739205 | ||||||||
\(596\) | 3.20748 | 0.131383 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.21576 | 0.131502 | ||||||||
\(599\) | 30.2656 | 1.23662 | 0.618310 | − | 0.785935i | \(-0.287818\pi\) | ||||
0.618310 | + | 0.785935i | \(0.287818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7110 | −1.08956 | −0.544781 | − | 0.838578i | \(-0.683387\pi\) | ||||
−0.544781 | + | 0.838578i | \(0.683387\pi\) | |||||||
\(602\) | −9.21193 | −0.375450 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4495 | 0.425183 | ||||||||
\(605\) | −3.08118 | −0.125268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.11543 | 0.0452737 | 0.0226369 | − | 0.999744i | \(-0.492794\pi\) | ||||
0.0226369 | + | 0.999744i | \(0.492794\pi\) | |||||||
\(608\) | 21.3692 | 0.866634 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.11098 | −0.0449824 | ||||||||
\(611\) | 9.88012 | 0.399707 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.6446 | −1.56084 | −0.780421 | − | 0.625255i | \(-0.784995\pi\) | ||||
−0.780421 | + | 0.625255i | \(0.784995\pi\) | |||||||
\(614\) | −27.9914 | −1.12964 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9613 | 0.441643 | ||||||||
\(617\) | −34.0379 | −1.37032 | −0.685158 | − | 0.728395i | \(-0.740267\pi\) | ||||
−0.685158 | + | 0.728395i | \(0.740267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.2665 | −1.21651 | −0.608256 | − | 0.793741i | \(-0.708131\pi\) | ||||
−0.608256 | + | 0.793741i | \(0.708131\pi\) | |||||||
\(620\) | −0.427412 | −0.0171653 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −23.9937 | −0.962061 | ||||||||
\(623\) | −7.47117 | −0.299326 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.7623 | −0.430147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.51595 | 0.339823 | ||||||||
\(629\) | −6.27092 | −0.250038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.44426 | 0.137114 | 0.0685569 | − | 0.997647i | \(-0.478161\pi\) | ||||
0.0685569 | + | 0.997647i | \(0.478161\pi\) | |||||||
\(632\) | 33.5009 | 1.33259 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.9671 | −1.19014 | ||||||||
\(635\) | 4.66469 | 0.185113 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.39964 | −0.213941 | ||||||||
\(638\) | −4.04660 | −0.160206 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.94829 | 0.116541 | ||||||||
\(641\) | −25.0135 | −0.987974 | −0.493987 | − | 0.869469i | \(-0.664461\pi\) | ||||
−0.493987 | + | 0.869469i | \(0.664461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7996 | 0.701948 | 0.350974 | − | 0.936385i | \(-0.385851\pi\) | ||||
0.350974 | + | 0.936385i | \(0.385851\pi\) | |||||||
\(644\) | 2.29222 | 0.0903261 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0109 | −0.393875 | ||||||||
\(647\) | 36.6601 | 1.44126 | 0.720629 | − | 0.693321i | \(-0.243853\pi\) | ||||
0.720629 | + | 0.693321i | \(0.243853\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.6054 | −0.965845 | ||||||||
\(650\) | 1.16027 | 0.0455096 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.52763 | −0.138153 | ||||||||
\(653\) | −18.1192 | −0.709057 | −0.354529 | − | 0.935045i | \(-0.615359\pi\) | ||||
−0.354529 | + | 0.935045i | \(0.615359\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.48082 | 0.253227 | ||||||||
\(656\) | −5.67737 | −0.221664 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.5021 | −0.565351 | ||||||||
\(659\) | −8.26297 | −0.321880 | −0.160940 | − | 0.986964i | \(-0.551452\pi\) | ||||
−0.160940 | + | 0.986964i | \(0.551452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0331 | −1.16815 | −0.584076 | − | 0.811699i | \(-0.698543\pi\) | ||||
−0.584076 | + | 0.811699i | \(0.698543\pi\) | |||||||
\(662\) | −2.98452 | −0.115997 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.40678 | −0.171016 | ||||||||
\(665\) | −7.65788 | −0.296960 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.43498 | −0.133003 | ||||||||
\(668\) | 9.85438 | 0.381277 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.4804 | 0.482161 | ||||||||
\(671\) | −2.69450 | −0.104020 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.1463 | 1.39334 | 0.696668 | − | 0.717394i | \(-0.254665\pi\) | ||||
0.696668 | + | 0.717394i | \(0.254665\pi\) | |||||||
\(674\) | 17.4983 | 0.674009 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.653767 | −0.0251449 | ||||||||
\(677\) | 4.27098 | 0.164147 | 0.0820735 | − | 0.996626i | \(-0.473846\pi\) | ||||
0.0820735 | + | 0.996626i | \(0.473846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0290 | −0.576760 | ||||||||
\(680\) | 4.38871 | 0.168299 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.13459 | 0.0817375 | ||||||||
\(683\) | 7.91443 | 0.302837 | 0.151419 | − | 0.988470i | \(-0.451616\pi\) | ||||
0.151419 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.2500 | 0.582671 | ||||||||
\(686\) | 18.2003 | 0.694890 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.2154 | −0.541958 | ||||||||
\(689\) | 8.18387 | 0.311781 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.5914 | −1.23984 | −0.619918 | − | 0.784667i | \(-0.712834\pi\) | ||||
−0.619918 | + | 0.784667i | \(0.712834\pi\) | |||||||
\(692\) | −5.71891 | −0.217400 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.7695 | −0.446765 | ||||||||
\(695\) | −19.9339 | −0.756135 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.57259 | −0.135321 | ||||||||
\(698\) | 11.4723 | 0.434233 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.827051 | 0.0312596 | ||||||||
\(701\) | 29.5797 | 1.11721 | 0.558606 | − | 0.829433i | \(-0.311337\pi\) | ||||
0.558606 | + | 0.829433i | \(0.311337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 26.6328 | 1.00448 | ||||||||
\(704\) | 24.2739 | 0.914857 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.8762 | −1.04914 | ||||||||
\(707\) | −17.9273 | −0.674227 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.5817 | 0.697851 | 0.348925 | − | 0.937151i | \(-0.386547\pi\) | ||||
0.348925 | + | 0.937151i | \(0.386547\pi\) | |||||||
\(710\) | 11.1839 | 0.419723 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18.1845 | −0.681495 | ||||||||
\(713\) | 1.81195 | 0.0678582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.81404 | 0.105239 | ||||||||
\(716\) | 7.43839 | 0.277986 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.2928 | −0.458764 | ||||||||
\(719\) | 9.75410 | 0.363766 | 0.181883 | − | 0.983320i | \(-0.441781\pi\) | ||||
0.181883 | + | 0.983320i | \(0.441781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2237 | 0.492475 | ||||||||
\(722\) | 20.4715 | 0.761872 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.57326 | −0.318623 | ||||||||
\(725\) | −1.23937 | −0.0460289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.8851 | −1.29382 | −0.646909 | − | 0.762567i | \(-0.723939\pi\) | ||||
−0.646909 | + | 0.762567i | \(0.723939\pi\) | |||||||
\(728\) | 3.89522 | 0.144366 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.91262 | −0.218836 | ||||||||
\(731\) | −8.94532 | −0.330855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0790 | 0.483085 | 0.241543 | − | 0.970390i | \(-0.422347\pi\) | ||||
0.241543 | + | 0.970390i | \(0.422347\pi\) | |||||||
\(734\) | 3.99692 | 0.147529 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.78390 | 0.360639 | ||||||||
\(737\) | 30.2691 | 1.11498 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5102 | −0.607339 | −0.303669 | − | 0.952777i | \(-0.598212\pi\) | ||||
−0.303669 | + | 0.952777i | \(0.598212\pi\) | |||||||
\(740\) | −2.87634 | −0.105736 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0124 | −0.440987 | ||||||||
\(743\) | 49.4943 | 1.81577 | 0.907885 | − | 0.419218i | \(-0.137696\pi\) | ||||
0.907885 | + | 0.419218i | \(0.137696\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.90614 | −0.179747 | ||||||||
\(746\) | −13.8914 | −0.508602 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.62221 | 0.0958776 | ||||||||
\(749\) | 18.7517 | 0.685174 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.6331 | −1.15431 | −0.577155 | − | 0.816635i | \(-0.695837\pi\) | ||||
−0.577155 | + | 0.816635i | \(0.695837\pi\) | |||||||
\(752\) | −22.3790 | −0.816078 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.43800 | −0.0523690 | ||||||||
\(755\) | −15.9835 | −0.581699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.80575 | 0.0656312 | 0.0328156 | − | 0.999461i | \(-0.489553\pi\) | ||||
0.0328156 | + | 0.999461i | \(0.489553\pi\) | |||||||
\(758\) | −16.4616 | −0.597910 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.6390 | −0.676108 | ||||||||
\(761\) | −36.2291 | −1.31330 | −0.656651 | − | 0.754194i | \(-0.728028\pi\) | ||||
−0.656651 | + | 0.754194i | \(0.728028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.9684 | 0.831514 | ||||||||
\(764\) | −12.3033 | −0.445118 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.1575 | −0.800584 | ||||||||
\(767\) | −8.74379 | −0.315720 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.1502 | 1.84452 | 0.922261 | − | 0.386567i | \(-0.126339\pi\) | ||||
0.922261 | + | 0.386567i | \(0.126339\pi\) | |||||||
\(770\) | −4.13047 | −0.148852 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.97837 | 0.143185 | ||||||||
\(773\) | −32.5307 | −1.17005 | −0.585023 | − | 0.811016i | \(-0.698915\pi\) | ||||
−0.585023 | + | 0.811016i | \(0.698915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.653767 | 0.0234840 | ||||||||
\(776\) | −36.5800 | −1.31315 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.7676 | 1.13892 | ||||||||
\(779\) | 15.1729 | 0.543625 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.1245 | 0.970593 | ||||||||
\(782\) | −4.58351 | −0.163906 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.2305 | 0.436803 | ||||||||
\(785\) | −13.0260 | −0.464917 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.4269 | 1.58365 | 0.791824 | − | 0.610749i | \(-0.209132\pi\) | ||||
0.791824 | + | 0.610749i | \(0.209132\pi\) | |||||||
\(788\) | 1.77370 | 0.0631854 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.6239 | −0.449139 | ||||||||
\(791\) | −11.5232 | −0.409719 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.957519 | −0.0340025 | ||||||||
\(794\) | 12.7840 | 0.453686 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.39833 | −0.0850065 | ||||||||
\(797\) | −11.7800 | −0.417269 | −0.208635 | − | 0.977994i | \(-0.566902\pi\) | ||||
−0.208635 | + | 0.977994i | \(0.566902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0824 | −0.498200 | ||||||||
\(800\) | 3.53011 | 0.124808 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.54384 | −0.0545149 | ||||||||
\(803\) | −14.3400 | −0.506049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.50617 | −0.123576 | ||||||||
\(806\) | 0.758548 | 0.0267187 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.6344 | −1.53505 | ||||||||
\(809\) | 27.9603 | 0.983032 | 0.491516 | − | 0.870869i | \(-0.336443\pi\) | ||||
0.491516 | + | 0.870869i | \(0.336443\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6760 | 0.901608 | 0.450804 | − | 0.892623i | \(-0.351137\pi\) | ||||
0.450804 | + | 0.892623i | \(0.351137\pi\) | |||||||
\(812\) | −1.02502 | −0.0359711 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.3651 | 0.503495 | ||||||||
\(815\) | 5.39586 | 0.189009 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.9911 | 1.32914 | ||||||||
\(818\) | 19.3408 | 0.676234 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.63867 | −0.0572249 | ||||||||
\(821\) | 44.8582 | 1.56556 | 0.782780 | − | 0.622298i | \(-0.213801\pi\) | ||||
0.782780 | + | 0.622298i | \(0.213801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9798 | −0.487305 | −0.243652 | − | 0.969863i | \(-0.578346\pi\) | ||||
−0.243652 | + | 0.969863i | \(0.578346\pi\) | |||||||
\(824\) | 32.1859 | 1.12125 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.8342 | 0.446559 | ||||||||
\(827\) | 38.0478 | 1.32305 | 0.661526 | − | 0.749922i | \(-0.269909\pi\) | ||||
0.661526 | + | 0.749922i | \(0.269909\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.8983 | −1.10787 | −0.553937 | − | 0.832559i | \(-0.686875\pi\) | ||||
−0.553937 | + | 0.832559i | \(0.686875\pi\) | |||||||
\(830\) | 1.66058 | 0.0576394 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.62599 | 0.299053 | ||||||||
\(833\) | 7.69625 | 0.266659 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0732 | −0.521630 | ||||||||
\(836\) | −11.1366 | −0.385168 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.5948 | −0.884157 | ||||||||
\(839\) | 4.74170 | 0.163702 | 0.0818509 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818509 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4640 | −0.947033 | ||||||||
\(842\) | 21.2222 | 0.731365 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.29649 | 0.319998 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.89786 | 0.133932 | ||||||||
\(848\) | −18.5369 | −0.636560 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.65377 | −0.0567238 | ||||||||
\(851\) | 12.1939 | 0.418000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.4163 | −1.62350 | −0.811752 | − | 0.584002i | \(-0.801486\pi\) | ||||
−0.811752 | + | 0.584002i | \(0.801486\pi\) | |||||||
\(854\) | 1.40545 | 0.0480936 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.6410 | 1.55998 | ||||||||
\(857\) | −6.78726 | −0.231848 | −0.115924 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115924 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.73973 | −0.0934784 | −0.0467392 | − | 0.998907i | \(-0.514883\pi\) | ||||
−0.0467392 | + | 0.998907i | \(0.514883\pi\) | |||||||
\(860\) | −4.10303 | −0.139912 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.77529 | −0.230767 | ||||||||
\(863\) | −16.4176 | −0.558861 | −0.279430 | − | 0.960166i | \(-0.590146\pi\) | ||||
−0.279430 | + | 0.960166i | \(0.590146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.74762 | 0.297428 | ||||||||
\(866\) | 11.0130 | 0.374237 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.540699 | 0.0183525 | ||||||||
\(869\) | −30.6171 | −1.03861 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.7565 | 0.364469 | ||||||||
\(872\) | 55.9043 | 1.89316 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.4663 | 0.658458 | ||||||||
\(875\) | −1.26505 | −0.0427666 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.85625 | 0.299054 | 0.149527 | − | 0.988758i | \(-0.452225\pi\) | ||||
0.149527 | + | 0.988758i | \(0.452225\pi\) | |||||||
\(878\) | 19.9065 | 0.671813 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.37395 | −0.214866 | ||||||||
\(881\) | −4.18037 | −0.140840 | −0.0704202 | − | 0.997517i | \(-0.522434\pi\) | ||||
−0.0704202 | + | 0.997517i | \(0.522434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.21879 | 0.209279 | 0.104639 | − | 0.994510i | \(-0.466631\pi\) | ||||
0.104639 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(884\) | 0.931832 | 0.0313409 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.57128 | −0.0863838 | ||||||||
\(887\) | −16.2949 | −0.547130 | −0.273565 | − | 0.961854i | \(-0.588203\pi\) | ||||
−0.273565 | + | 0.961854i | \(0.588203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.90109 | −0.197916 | ||||||||
\(890\) | 6.85235 | 0.229691 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.9747 | −0.467908 | ||||||||
\(893\) | 59.8084 | 2.00141 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.3777 | −0.380316 | ||||||||
\(896\) | −3.72975 | −0.124602 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.1563 | −1.20655 | ||||||||
\(899\) | −0.810257 | −0.0270236 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.6647 | −0.388607 | ||||||||
\(902\) | 8.18387 | 0.272493 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.0472 | −0.932834 | ||||||||
\(905\) | 13.1136 | 0.435912 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0236556 | −0.000785472 0 | −0.000392736 | − | 1.00000i | \(-0.500125\pi\) | ||||
−0.000392736 | 1.00000i | \(0.500125\pi\) | ||||||||
\(908\) | 2.77540 | 0.0921047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.46781 | −0.0486573 | ||||||||
\(911\) | 33.7724 | 1.11893 | 0.559465 | − | 0.828854i | \(-0.311007\pi\) | ||||
0.559465 | + | 0.828854i | \(0.311007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.02744 | 0.133289 | ||||||||
\(914\) | 33.8581 | 1.11993 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.17728 | 0.171062 | ||||||||
\(917\) | −8.19858 | −0.270741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.0482 | 0.991197 | 0.495599 | − | 0.868552i | \(-0.334949\pi\) | ||||
0.495599 | + | 0.868552i | \(0.334949\pi\) | |||||||
\(920\) | −8.53389 | −0.281354 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.6503 | 0.943548 | ||||||||
\(923\) | 9.63901 | 0.317272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.39964 | 0.144659 | ||||||||
\(926\) | 42.0998 | 1.38349 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.37510 | −0.143620 | ||||||||
\(929\) | 14.4372 | 0.473669 | 0.236834 | − | 0.971550i | \(-0.423890\pi\) | ||||
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.6862 | −1.07125 | ||||||||
\(932\) | 0.429885 | 0.0140813 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.51195 | 0.311241 | ||||||||
\(935\) | −4.01093 | −0.131171 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0678 | −0.786260 | −0.393130 | − | 0.919483i | \(-0.628608\pi\) | ||||
−0.393130 | + | 0.919483i | \(0.628608\pi\) | |||||||
\(938\) | −15.7884 | −0.515510 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.45930 | −0.210679 | ||||||||
\(941\) | −31.1287 | −1.01477 | −0.507383 | − | 0.861721i | \(-0.669387\pi\) | ||||
−0.507383 | + | 0.861721i | \(0.669387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.94693 | 0.226223 | ||||||||
\(944\) | 19.8051 | 0.644603 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.4914 | 0.666233 | ||||||||
\(947\) | −10.2949 | −0.334540 | −0.167270 | − | 0.985911i | \(-0.553495\pi\) | ||||
−0.167270 | + | 0.985911i | \(0.553495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.09589 | −0.165419 | ||||||||
\(950\) | 7.02360 | 0.227876 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.55196 | −0.179940 | ||||||||
\(953\) | 40.4483 | 1.31025 | 0.655125 | − | 0.755521i | \(-0.272616\pi\) | ||||
0.655125 | + | 0.755521i | \(0.272616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8191 | 0.608972 | ||||||||
\(956\) | 1.29594 | 0.0419137 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.7291 | −0.475877 | ||||||||
\(959\) | −19.2920 | −0.622972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5726 | −0.986213 | ||||||||
\(962\) | 5.10478 | 0.164585 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.887266 | −0.0285769 | ||||||||
\(965\) | −6.08530 | −0.195893 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.9049 | −0.607940 | −0.303970 | − | 0.952682i | \(-0.598312\pi\) | ||||
−0.303970 | + | 0.952682i | \(0.598312\pi\) | |||||||
\(968\) | 9.48724 | 0.304931 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.7842 | 0.442583 | ||||||||
\(971\) | −22.3318 | −0.716660 | −0.358330 | − | 0.933595i | \(-0.616654\pi\) | ||||
−0.358330 | + | 0.933595i | \(0.616654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.2174 | 0.808433 | ||||||||
\(974\) | 14.0555 | 0.450367 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.16883 | 0.0694226 | ||||||||
\(977\) | 51.0252 | 1.63244 | 0.816220 | − | 0.577741i | \(-0.196066\pi\) | ||||
0.816220 | + | 0.577741i | \(0.196066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.6192 | 0.531151 | ||||||||
\(980\) | 3.53011 | 0.112765 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −43.7998 | −1.39771 | ||||||||
\(983\) | −60.9224 | −1.94312 | −0.971562 | − | 0.236785i | \(-0.923906\pi\) | ||||
−0.971562 | + | 0.236785i | \(0.923906\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.71304 | −0.0864447 | ||||||||
\(986\) | 2.04962 | 0.0652733 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.95752 | −0.125905 | ||||||||
\(989\) | 17.3942 | 0.553105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8267 | 0.343922 | 0.171961 | − | 0.985104i | \(-0.444990\pi\) | ||||
0.171961 | + | 0.985104i | \(0.444990\pi\) | |||||||
\(992\) | 2.30787 | 0.0732749 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.1482 | −0.448754 | ||||||||
\(995\) | 3.66848 | 0.116298 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.8396 | −0.691668 | −0.345834 | − | 0.938296i | \(-0.612404\pi\) | ||||
−0.345834 | + | 0.938296i | \(0.612404\pi\) | |||||||
\(998\) | 12.7268 | 0.402859 | ||||||||
\(999\) | 0 | 0 |
(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 | 1755.2.a.q.1.3 | yes | 4 | |
3.2 | odd | 2 | 1755.2.a.o.1.2 | ✓ | 4 | ||
5.4 | even | 2 | 8775.2.a.bj.1.2 | 4 | |||
15.14 | odd | 2 | 8775.2.a.br.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1755.2.a.o.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
1755.2.a.q.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
8775.2.a.bj.1.2 | 4 | 5.4 | even | 2 | |||
8775.2.a.br.1.3 | 4 | 15.14 | odd | 2 |