Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 7x^{5} + 11x^{4} + 12x^{3} - 14x^{2} - 6x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.332704\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.61705 | 1.61759 | 0.808797 | − | 0.588088i | \(-0.200119\pi\) | ||||
0.808797 | + | 0.588088i | \(0.200119\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.72774 | −1.03099 | −0.515495 | − | 0.856893i | \(-0.672392\pi\) | ||||
−0.515495 | + | 0.856893i | \(0.672392\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.28246 | −1.29121 | −0.645605 | − | 0.763672i | \(-0.723395\pi\) | ||||
−0.645605 | + | 0.763672i | \(0.723395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0474194 | −0.0131518 | −0.00657589 | − | 0.999978i | \(-0.502093\pi\) | ||||
−0.00657589 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.61705 | 0.933918 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.70725 | 0.899140 | 0.449570 | − | 0.893245i | \(-0.351577\pi\) | ||||
0.449570 | + | 0.893245i | \(0.351577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.502366 | −0.115251 | −0.0576254 | − | 0.998338i | \(-0.518353\pi\) | ||||
−0.0576254 | + | 0.998338i | \(0.518353\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.72774 | −0.595242 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.97951 | −0.621270 | −0.310635 | − | 0.950529i | \(-0.600542\pi\) | ||||
−0.310635 | + | 0.950529i | \(0.600542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.08304 | 1.61661 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.25576 | −1.16167 | −0.580833 | − | 0.814023i | \(-0.697273\pi\) | ||||
−0.580833 | + | 0.814023i | \(0.697273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.93115 | −1.06527 | −0.532633 | − | 0.846346i | \(-0.678797\pi\) | ||||
−0.532633 | + | 0.846346i | \(0.678797\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.28246 | −0.745480 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.86637 | −1.66772 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.158358 | 0.0260339 | 0.0130170 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130170 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0474194 | −0.00759318 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.89424 | −0.608178 | −0.304089 | − | 0.952644i | \(-0.598352\pi\) | ||||
−0.304089 | + | 0.952644i | \(0.598352\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.94980 | −0.754838 | −0.377419 | − | 0.926043i | \(-0.623188\pi\) | ||||
−0.377419 | + | 0.926043i | \(0.623188\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.61705 | 0.539198 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.39628 | −1.22472 | −0.612362 | − | 0.790578i | \(-0.709780\pi\) | ||||
−0.612362 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.440569 | 0.0629384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.70725 | 0.519119 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.7084 | −1.47091 | −0.735453 | − | 0.677576i | \(-0.763031\pi\) | ||||
−0.735453 | + | 0.677576i | \(0.763031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.4899 | −2.08865 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.502366 | −0.0665401 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.54507 | 0.461529 | 0.230764 | − | 0.973010i | \(-0.425877\pi\) | ||||
0.230764 | + | 0.973010i | \(0.425877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62786 | 0.464500 | 0.232250 | − | 0.972656i | \(-0.425391\pi\) | ||||
0.232250 | + | 0.972656i | \(0.425391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.72774 | −0.343663 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.171518 | −0.0212742 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.477808 | −0.0583736 | −0.0291868 | − | 0.999574i | \(-0.509292\pi\) | ||||
−0.0291868 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.97951 | −0.358691 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.963732 | −0.114374 | −0.0571870 | − | 0.998363i | \(-0.518213\pi\) | ||||
−0.0571870 | + | 0.998363i | \(0.518213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5153 | −1.46481 | −0.732405 | − | 0.680870i | \(-0.761602\pi\) | ||||
−0.732405 | + | 0.680870i | \(0.761602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.08304 | 0.933349 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6814 | 1.33122 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.53153 | 0.172311 | 0.0861554 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861554 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.4089 | 1.47182 | 0.735911 | − | 0.677078i | \(-0.236754\pi\) | ||||
0.735911 | + | 0.677078i | \(0.236754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.4093 | 1.45444 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.25576 | −0.670688 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.01339 | 0.107419 | 0.0537095 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537095 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.129348 | 0.0135593 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.93115 | −0.615031 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.81708 | −0.186429 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.19560 | −0.121395 | −0.0606973 | − | 0.998156i | \(-0.519332\pi\) | ||||
−0.0606973 | + | 0.998156i | \(0.519332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.28246 | −0.430403 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.15983 | 0.214911 | 0.107456 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107456 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6082 | 1.34086 | 0.670428 | − | 0.741975i | \(-0.266111\pi\) | ||||
0.670428 | + | 0.741975i | \(0.266111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.86637 | −0.962859 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.76340 | 0.363821 | 0.181911 | − | 0.983315i | \(-0.441772\pi\) | ||||
0.181911 | + | 0.983315i | \(0.441772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9192 | −1.14165 | −0.570824 | − | 0.821072i | \(-0.693376\pi\) | ||||
−0.570824 | + | 0.821072i | \(0.693376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.158358 | 0.0150307 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.99961 | −0.564396 | −0.282198 | − | 0.959356i | \(-0.591063\pi\) | ||||
−0.282198 | + | 0.959356i | \(0.591063\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7770 | −1.00496 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0474194 | −0.00438393 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.1124 | −0.927003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.33944 | 0.667222 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.89424 | −0.351132 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1515 | 0.997421 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.12683 | −0.277461 | −0.138731 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138731 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.94980 | −0.435806 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0808 | 1.49236 | 0.746180 | − | 0.665745i | \(-0.231886\pi\) | ||||
0.746180 | + | 0.665745i | \(0.231886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37033 | 0.118822 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.61705 | 0.311306 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.91181 | −0.505080 | −0.252540 | − | 0.967586i | \(-0.581266\pi\) | ||||
−0.252540 | + | 0.967586i | \(0.581266\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.2110 | −1.62946 | −0.814729 | − | 0.579842i | \(-0.803114\pi\) | ||||
−0.814729 | + | 0.579842i | \(0.803114\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.39628 | −0.707094 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.203072 | 0.0169817 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.6274 | −1.87910 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.440569 | 0.0363375 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4216 | 1.01762 | 0.508810 | − | 0.860879i | \(-0.330086\pi\) | ||||
0.508810 | + | 0.860879i | \(0.330086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.4910 | 1.58615 | 0.793076 | − | 0.609123i | \(-0.208478\pi\) | ||||
0.793076 | + | 0.609123i | \(0.208478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.70725 | 0.299713 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.4533 | −1.72317 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.17743 | −0.732439 | −0.366219 | − | 0.930529i | \(-0.619348\pi\) | ||||
−0.366219 | + | 0.930529i | \(0.619348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.7084 | −0.849228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.12733 | 0.640523 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.11130 | −0.322022 | −0.161011 | − | 0.986953i | \(-0.551475\pi\) | ||||
−0.161011 | + | 0.986953i | \(0.551475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.4899 | −1.20588 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9978 | −0.999827 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.502366 | −0.0384169 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.79124 | 0.136185 | 0.0680925 | − | 0.997679i | \(-0.478309\pi\) | ||||
0.0680925 | + | 0.997679i | \(0.478309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.0484 | −1.66670 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.54507 | 0.266464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.69277 | −0.649728 | −0.324864 | − | 0.945761i | \(-0.605319\pi\) | ||||
−0.324864 | + | 0.945761i | \(0.605319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5836 | −0.861003 | −0.430501 | − | 0.902590i | \(-0.641663\pi\) | ||||
−0.430501 | + | 0.902590i | \(0.641663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.62786 | 0.268179 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.572789 | 0.0421123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.8761 | −1.16098 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.72774 | −0.198414 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.96251 | −0.286717 | −0.143359 | − | 0.989671i | \(-0.545790\pi\) | ||||
−0.143359 | + | 0.989671i | \(0.545790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81160 | 0.490310 | 0.245155 | − | 0.969484i | \(-0.421161\pi\) | ||||
0.245155 | + | 0.969484i | \(0.421161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.171518 | −0.0122827 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.39262 | −0.526702 | −0.263351 | − | 0.964700i | \(-0.584828\pi\) | ||||
−0.263351 | + | 0.964700i | \(0.584828\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2256 | 1.15020 | 0.575100 | − | 0.818083i | \(-0.304963\pi\) | ||||
0.575100 | + | 0.818083i | \(0.304963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.477808 | −0.0337020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.0641 | 1.19766 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.0856 | −0.983784 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.97951 | −0.207090 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.15136 | 0.148813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.20559 | −0.633739 | −0.316869 | − | 0.948469i | \(-0.602632\pi\) | ||||
−0.316869 | + | 0.948469i | \(0.602632\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.963732 | −0.0660338 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.9037 | −1.22102 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1786 | 1.09828 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.5153 | −0.845708 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.175796 | −0.0118253 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.77142 | 0.118623 | 0.0593114 | − | 0.998240i | \(-0.481109\pi\) | ||||
0.0593114 | + | 0.998240i | \(0.481109\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.08304 | 0.538869 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.39753 | −0.225502 | −0.112751 | − | 0.993623i | \(-0.535966\pi\) | ||||
−0.112751 | + | 0.993623i | \(0.535966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6919 | 0.772622 | 0.386311 | − | 0.922369i | \(-0.373749\pi\) | ||||
0.386311 | + | 0.922369i | \(0.373749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.6814 | 0.768582 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.2352 | 1.32565 | 0.662825 | − | 0.748775i | \(-0.269357\pi\) | ||||
0.662825 | + | 0.748775i | \(0.269357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.3698 | −1.98110 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.53153 | 0.0994837 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.35872 | −0.540680 | −0.270340 | − | 0.962765i | \(-0.587136\pi\) | ||||
−0.270340 | + | 0.962765i | \(0.587136\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.49687 | −0.482916 | −0.241458 | − | 0.970411i | \(-0.577626\pi\) | ||||
−0.241458 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.59356 | 0.101809 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0238219 | 0.00151575 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.4089 | 0.849757 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.63798 | −0.608344 | −0.304172 | − | 0.952617i | \(-0.598380\pi\) | ||||
−0.304172 | + | 0.952617i | \(0.598380\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7596 | 0.802190 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.4093 | 0.839723 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.0721 | 1.00255 | 0.501275 | − | 0.865288i | \(-0.332865\pi\) | ||||
0.501275 | + | 0.865288i | \(0.332865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.431960 | −0.0268407 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.25576 | −0.387222 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8779 | −0.855745 | −0.427872 | − | 0.903839i | \(-0.640737\pi\) | ||||
−0.427872 | + | 0.903839i | \(0.640737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.7327 | −2.37933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.01339 | 0.0620184 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.7466 | −0.716202 | −0.358101 | − | 0.933683i | \(-0.616576\pi\) | ||||
−0.358101 | + | 0.933683i | \(0.616576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0126 | −1.64090 | −0.820450 | − | 0.571718i | \(-0.806277\pi\) | ||||
−0.820450 | + | 0.571718i | \(0.806277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.129348 | 0.00782849 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −34.6153 | −2.08738 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.7942 | −1.66999 | −0.834997 | − | 0.550255i | \(-0.814531\pi\) | ||||
−0.834997 | + | 0.550255i | \(0.814531\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.93115 | −0.355089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0329 | 0.956443 | 0.478221 | − | 0.878239i | \(-0.341282\pi\) | ||||
0.478221 | + | 0.878239i | \(0.341282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.97967 | 0.593230 | 0.296615 | − | 0.954997i | \(-0.404142\pi\) | ||||
0.296615 | + | 0.954997i | \(0.404142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.81708 | −0.107635 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6225 | 0.627025 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.25630 | −0.191547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.19560 | −0.0700872 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.84400 | −0.399831 | −0.199915 | − | 0.979813i | \(-0.564067\pi\) | ||||
−0.199915 | + | 0.979813i | \(0.564067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8227 | 0.746566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.28246 | −0.248493 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.141287 | 0.00817081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5018 | 0.778230 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.15983 | 0.124079 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1222 | 0.751373 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.88679 | 0.107685 | 0.0538424 | − | 0.998549i | \(-0.482853\pi\) | ||||
0.0538424 | + | 0.998549i | \(0.482853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6082 | 0.774144 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8665 | −1.06982 | −0.534910 | − | 0.844909i | \(-0.679654\pi\) | ||||
−0.534910 | + | 0.844909i | \(0.679654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.2178 | 1.59497 | 0.797483 | − | 0.603341i | \(-0.206164\pi\) | ||||
0.797483 | + | 0.603341i | \(0.206164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.86637 | −0.555907 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.9184 | −1.00640 | −0.503198 | − | 0.864171i | \(-0.667843\pi\) | ||||
−0.503198 | + | 0.864171i | \(0.667843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.7900 | 1.49995 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.76340 | 0.210052 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.86240 | −0.103627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.383293 | −0.0212613 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.9192 | −0.659131 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.9029 | 1.26268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.98539 | −0.383952 | −0.191976 | − | 0.981400i | \(-0.561490\pi\) | ||||
−0.191976 | + | 0.981400i | \(0.561490\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.158358 | 0.00867797 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.72826 | −0.0944247 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8306 | 0.644455 | 0.322227 | − | 0.946662i | \(-0.395568\pi\) | ||||
0.322227 | + | 0.946662i | \(0.395568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.99961 | −0.325854 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3999 | 1.37548 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8924 | 0.966100 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7770 | −0.580216 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.1259 | −1.83197 | −0.915987 | − | 0.401208i | \(-0.868591\pi\) | ||||
−0.915987 | + | 0.401208i | \(0.868591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.2829 | 1.51395 | 0.756975 | − | 0.653444i | \(-0.226677\pi\) | ||||
0.756975 | + | 0.653444i | \(0.226677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0474194 | −0.00253106 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.561669 | −0.0298946 | −0.0149473 | − | 0.999888i | \(-0.504758\pi\) | ||||
−0.0149473 | + | 0.999888i | \(0.504758\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.48586 | −0.185010 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.1124 | −0.535206 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.11628 | 0.0589149 | 0.0294574 | − | 0.999566i | \(-0.490622\pi\) | ||||
0.0294574 | + | 0.999566i | \(0.490622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7476 | −0.986717 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.33944 | 0.385221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.2686 | −2.36947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.04257 | 0.315420 | 0.157710 | − | 0.987485i | \(-0.449589\pi\) | ||||
0.157710 | + | 0.987485i | \(0.449589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.89424 | −0.202726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.2096 | 1.51649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.5233 | 1.52866 | 0.764328 | − | 0.644828i | \(-0.223071\pi\) | ||||
0.764328 | + | 0.644828i | \(0.223071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.1515 | 0.575861 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.296644 | 0.0152780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.8528 | 1.58480 | 0.792401 | − | 0.610000i | \(-0.208831\pi\) | ||||
0.792401 | + | 0.610000i | \(0.208831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.12683 | −0.160192 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.1831 | 0.571427 | 0.285714 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285714 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 42.2523 | 2.15338 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.94980 | −0.251613 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.2164 | 1.22782 | 0.613911 | − | 0.789375i | \(-0.289595\pi\) | ||||
0.613911 | + | 0.789375i | \(0.289595\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0458 | −0.558609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.0808 | 0.861614 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.53962 | 0.278729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.297814 | 0.0149469 | 0.00747343 | − | 0.999972i | \(-0.497621\pi\) | ||||
0.00747343 | + | 0.999972i | \(0.497621\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.37033 | 0.0686021 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.84713 | 0.0922413 | 0.0461207 | − | 0.998936i | \(-0.485314\pi\) | ||||
0.0461207 | + | 0.998936i | \(0.485314\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.281252 | 0.0140101 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.61705 | 0.179733 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.678162 | −0.0336152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.7688 | −1.42252 | −0.711262 | − | 0.702927i | \(-0.751876\pi\) | ||||
−0.711262 | + | 0.702927i | \(0.751876\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.91181 | −0.291608 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.67003 | −0.475831 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.5008 | 2.38081 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.2110 | −0.940768 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6216 | 1.54482 | 0.772408 | − | 0.635127i | \(-0.219052\pi\) | ||||
0.772408 | + | 0.635127i | \(0.219052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.86687 | −0.237197 | −0.118598 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118598 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.39628 | −0.408241 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.9658 | 1.45356 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.89587 | −0.478895 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.203072 | 0.00980439 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.5696 | 0.942635 | 0.471317 | − | 0.881964i | \(-0.343779\pi\) | ||||
0.471317 | + | 0.881964i | \(0.343779\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.2099 | −0.971224 | −0.485612 | − | 0.874174i | \(-0.661403\pi\) | ||||
−0.485612 | + | 0.874174i | \(0.661403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.6274 | −1.08490 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.49681 | 0.0716019 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6452 | −1.17625 | −0.588126 | − | 0.808769i | \(-0.700134\pi\) | ||||
−0.588126 | + | 0.808769i | \(0.700134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.440569 | 0.0209795 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1398 | −1.24194 | −0.620969 | − | 0.783835i | \(-0.713261\pi\) | ||||
−0.620969 | + | 0.783835i | \(0.713261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.66548 | 0.173760 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4216 | 0.587523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.704072 | −0.0332272 | −0.0166136 | − | 0.999862i | \(-0.505289\pi\) | ||||
−0.0166136 | + | 0.999862i | \(0.505289\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6769 | 0.785285 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.4910 | 0.915765 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.467857 | 0.0219335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.5289 | 1.89586 | 0.947931 | − | 0.318476i | \(-0.103171\pi\) | ||||
0.947931 | + | 0.318476i | \(0.103171\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.70725 | 0.173040 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.2707 | −0.711228 | −0.355614 | − | 0.934633i | \(-0.615728\pi\) | ||||
−0.355614 | + | 0.934633i | \(0.615728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1528 | −1.02953 | −0.514763 | − | 0.857333i | \(-0.672120\pi\) | ||||
−0.514763 | + | 0.857333i | \(0.672120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.4533 | −0.994871 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.2118 | −0.935291 | −0.467646 | − | 0.883916i | \(-0.654898\pi\) | ||||
−0.467646 | + | 0.883916i | \(0.654898\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30334 | 0.0601825 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.17743 | −0.422874 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.1973 | 0.974654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.06065 | −0.186315 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.7084 | −0.490302 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2890 | −1.47532 | −0.737661 | − | 0.675171i | \(-0.764070\pi\) | ||||
−0.737661 | + | 0.675171i | \(0.764070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.00750925 | −0.000342392 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.12733 | 0.369806 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.32454 | −0.196367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.6362 | −1.52420 | −0.762101 | − | 0.647458i | \(-0.775832\pi\) | ||||
−0.762101 | + | 0.647458i | \(0.775832\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.11130 | −0.185919 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.820863 | −0.0370450 | −0.0185225 | − | 0.999828i | \(-0.505896\pi\) | ||||
−0.0185225 | + | 0.999828i | \(0.505896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.1917 | −1.04450 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.4899 | −0.696217 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.62881 | 0.117918 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.5903 | 1.54847 | 0.774237 | − | 0.632896i | \(-0.218134\pi\) | ||||
0.774237 | + | 0.632896i | \(0.218134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.2747 | 1.26071 | 0.630354 | − | 0.776308i | \(-0.282910\pi\) | ||||
0.630354 | + | 0.776308i | \(0.282910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.81222 | 0.347639 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9978 | −0.577250 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.01436 | −0.310906 | −0.155453 | − | 0.987843i | \(-0.549684\pi\) | ||||
−0.155453 | + | 0.987843i | \(0.549684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.1386 | 1.51020 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.502366 | −0.0221800 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.2215 | 2.16896 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.9567 | 1.58137 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79124 | 0.0786265 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4917 | 1.02919 | 0.514594 | − | 0.857434i | \(-0.327943\pi\) | ||||
0.514594 | + | 0.857434i | \(0.327943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.3081 | −0.581924 | −0.290962 | − | 0.956735i | \(-0.593975\pi\) | ||||
−0.290962 | + | 0.956735i | \(0.593975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −22.0484 | −0.962273 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.9882 | −0.957823 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.1225 | −0.614023 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.54507 | 0.153843 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.184662 | 0.00799862 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6124 | 0.588515 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.69277 | −0.375121 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.88672 | −0.0812666 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.93696 | −0.0832765 | −0.0416383 | − | 0.999133i | \(-0.513258\pi\) | ||||
−0.0416383 | + | 0.999133i | \(0.513258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.5836 | −0.497100 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.1122 | −1.84672 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2239 | 0.779200 | 0.389600 | − | 0.920984i | \(-0.372613\pi\) | ||||
0.389600 | + | 0.920984i | \(0.372613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.62786 | 0.154833 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.14268 | 0.133883 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.17762 | −0.177651 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.572789 | 0.0243135 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50775 | 0.190999 | 0.0954997 | − | 0.995429i | \(-0.469555\pi\) | ||||
0.0954997 | + | 0.995429i | \(0.469555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.234717 | 0.00992746 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.8761 | −0.670291 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.26172 | 0.137465 | 0.0687325 | − | 0.997635i | \(-0.478104\pi\) | ||||
0.0687325 | + | 0.997635i | \(0.478104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.7009 | −0.912963 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.72774 | −0.114554 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.6572 | 0.782151 | 0.391075 | − | 0.920359i | \(-0.372103\pi\) | ||||
0.391075 | + | 0.920359i | \(0.372103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.26021 | 0.178284 | 0.0891422 | − | 0.996019i | \(-0.471587\pi\) | ||||
0.0891422 | + | 0.996019i | \(0.471587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.96251 | −0.165536 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.0835 | −1.00435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.98097 | 0.415513 | 0.207757 | − | 0.978181i | \(-0.433384\pi\) | ||||
0.207757 | + | 0.978181i | \(0.433384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.81160 | 0.283080 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.5761 | −1.51743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.8581 | 1.89925 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.171518 | −0.00709141 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.1902 | −1.49373 | −0.746864 | − | 0.664977i | \(-0.768441\pi\) | ||||
−0.746864 | + | 0.664977i | \(0.768441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.97961 | 0.122773 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.39262 | −0.304092 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.81631 | −0.115652 | −0.0578261 | − | 0.998327i | \(-0.518417\pi\) | ||||
−0.0578261 | + | 0.998327i | \(0.518417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.5771 | −1.49951 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.2256 | 0.664069 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4462 | 0.508537 | 0.254269 | − | 0.967134i | \(-0.418165\pi\) | ||||
0.254269 | + | 0.967134i | \(0.418165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.462497 | 0.0188657 | 0.00943283 | − | 0.999956i | \(-0.496997\pi\) | ||||
0.00943283 | + | 0.999956i | \(0.496997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.477808 | −0.0194579 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.5471 | 1.07929 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5665 | −0.428883 | −0.214441 | − | 0.976737i | \(-0.568793\pi\) | ||||
−0.214441 | + | 0.976737i | \(0.568793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.0641 | 0.691472 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.398147 | 0.0161073 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −48.6267 | −1.96401 | −0.982007 | − | 0.188846i | \(-0.939525\pi\) | ||||
−0.982007 | + | 0.188846i | \(0.939525\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.0856 | −0.567988 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.72932 | 0.0696197 | 0.0348098 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348098 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.2593 | 1.93971 | 0.969853 | − | 0.243692i | \(-0.0783587\pi\) | ||||
0.969853 | + | 0.243692i | \(0.0783587\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.97951 | −0.119564 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.76426 | −0.110748 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.0796737 | −0.00318695 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.15136 | 0.0859172 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.587073 | 0.0234081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.15911 | −0.125762 | −0.0628812 | − | 0.998021i | \(-0.520029\pi\) | ||||
−0.0628812 | + | 0.998021i | \(0.520029\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.20559 | −0.365889 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.3099 | −0.448819 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0208915 | −0.000827752 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.963732 | −0.0381246 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.2179 | 1.19353 | 0.596767 | − | 0.802415i | \(-0.296452\pi\) | ||||
0.596767 | + | 0.802415i | \(0.296452\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1151 | 1.22706 | 0.613531 | − | 0.789671i | \(-0.289749\pi\) | ||||
0.613531 | + | 0.789671i | \(0.289749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.9037 | −0.704957 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.7860 | 0.935125 | 0.467563 | − | 0.883960i | \(-0.345132\pi\) | ||||
0.467563 | + | 0.883960i | \(0.345132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.1816 | −0.595930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.1786 | 0.634091 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.4018 | −1.85497 | −0.927487 | − | 0.373855i | \(-0.878036\pi\) | ||||
−0.927487 | + | 0.373855i | \(0.878036\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 61.7822 | 2.41403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.5153 | −0.488270 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.52732 | 0.215314 | 0.107657 | − | 0.994188i | \(-0.465665\pi\) | ||||
0.107657 | + | 0.994188i | \(0.465665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.39078 | −0.326363 | −0.163182 | − | 0.986596i | \(-0.552176\pi\) | ||||
−0.163182 | + | 0.986596i | \(0.552176\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.175796 | −0.00682733 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.95653 | 0.192206 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.6391 | 0.721708 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.77142 | 0.0684869 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.5362 | −0.599767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2165 | −1.01057 | −0.505286 | − | 0.862952i | \(-0.668613\pi\) | ||||
−0.505286 | + | 0.862952i | \(0.668613\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.08304 | 0.311116 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.4778 | 1.40196 | 0.700978 | − | 0.713183i | \(-0.252747\pi\) | ||||
0.700978 | + | 0.713183i | \(0.252747\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.26128 | 0.125156 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.39753 | −0.130194 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.8618 | −1.29569 | −0.647843 | − | 0.761774i | \(-0.724329\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.3833 | −0.817014 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.6919 | 0.446074 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.507784 | 0.0193450 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0531 | 0.496562 | 0.248281 | − | 0.968688i | \(-0.420134\pi\) | ||||
0.248281 | + | 0.968688i | \(0.420134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.6814 | 0.443741 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −69.4872 | −2.63580 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.4369 | −0.546837 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.2352 | 0.765364 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.42917 | 0.280596 | 0.140298 | − | 0.990109i | \(-0.455194\pi\) | ||||
0.140298 | + | 0.990109i | \(0.455194\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0795538 | −0.00300043 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.3698 | −1.14379 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.89146 | −0.221571 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6979 | −0.627104 | −0.313552 | − | 0.949571i | \(-0.601519\pi\) | ||||
−0.313552 | + | 0.949571i | \(0.601519\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53153 | 0.0574369 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.6719 | 0.661818 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.734520 | 0.0274695 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.35872 | −0.312162 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5510 | −0.952892 | −0.476446 | − | 0.879204i | \(-0.658075\pi\) | ||||
−0.476446 | + | 0.879204i | \(0.658075\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.1196 | −1.38241 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.49687 | −0.278811 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −50.5655 | −1.87796 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2347 | 0.898814 | 0.449407 | − | 0.893327i | \(-0.351635\pi\) | ||||
0.449407 | + | 0.893327i | \(0.351635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.3502 | −0.678705 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.0374 | −1.51575 | −0.757875 | − | 0.652400i | \(-0.773762\pi\) | ||||
−0.757875 | + | 0.652400i | \(0.773762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.59356 | 0.0587793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.04619 | 0.0753725 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.7107 | 1.16650 | 0.583248 | − | 0.812294i | \(-0.301782\pi\) | ||||
0.583248 | + | 0.812294i | \(0.301782\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0238219 | 0.000875120 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.7721 | −1.16560 | −0.582802 | − | 0.812614i | \(-0.698044\pi\) | ||||
−0.582802 | + | 0.812614i | \(0.698044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 44.9297 | 1.64610 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4089 | 0.490607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.2656 | −0.375096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.5750 | 0.860264 | 0.430132 | − | 0.902766i | \(-0.358467\pi\) | ||||
0.430132 | + | 0.902766i | \(0.358467\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.63798 | −0.351227 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 70.4997 | 2.56575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.9217 | 0.760411 | 0.380206 | − | 0.924902i | \(-0.375853\pi\) | ||||
0.380206 | + | 0.924902i | \(0.375853\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7596 | 0.463145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.74661 | −0.244564 | −0.122282 | − | 0.992495i | \(-0.539021\pi\) | ||||
−0.122282 | + | 0.992495i | \(0.539021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5124 | 1.17703 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.4093 | 0.484814 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.168105 | −0.00606993 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1193 | 0.400974 | 0.200487 | − | 0.979696i | \(-0.435748\pi\) | ||||
0.200487 | + | 0.979696i | \(0.435748\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0721 | 0.578822 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.9830 | −1.54599 | −0.772995 | − | 0.634412i | \(-0.781242\pi\) | ||||
−0.772995 | + | 0.634412i | \(0.781242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.9417 | −1.72212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.431960 | −0.0154965 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.95633 | 0.0700930 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.12714 | 0.147681 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.25576 | −0.223563 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.1952 | −1.18479 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.90798 | 0.139304 | 0.0696522 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696522 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.8779 | −0.494065 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.3654 | 0.581886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.172031 | −0.00610901 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.7327 | −1.37371 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.2466 | 0.717171 | 0.358586 | − | 0.933497i | \(-0.383259\pi\) | ||||
0.358586 | + | 0.933497i | \(0.383259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.1271 | −1.10120 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.01339 | 0.0358063 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 53.5964 | 1.89138 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.3969 | 1.03611 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.7466 | −0.413499 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.8278 | −0.978372 | −0.489186 | − | 0.872179i | \(-0.662706\pi\) | ||||
−0.489186 | + | 0.872179i | \(0.662706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0208 | 1.01906 | 0.509529 | − | 0.860453i | \(-0.329820\pi\) | ||||
0.509529 | + | 0.860453i | \(0.329820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.0126 | −0.947374 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.8708 | −0.520900 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.48662 | 0.0869957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.129348 | 0.00451978 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.3461 | −1.54769 | −0.773845 | − | 0.633374i | \(-0.781669\pi\) | ||||
−0.773845 | + | 0.633374i | \(0.781669\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.6252 | 0.893239 | 0.446620 | − | 0.894724i | \(-0.352628\pi\) | ||||
0.446620 | + | 0.894724i | \(0.352628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.6153 | −1.20515 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.0006 | 0.486848 | 0.243424 | − | 0.969920i | \(-0.421729\pi\) | ||||
0.243424 | + | 0.969920i | \(0.421729\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6296 | −0.438643 | −0.219321 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219321 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.7942 | −0.964171 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.63330 | 0.0565904 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.61705 | 0.125173 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.93115 | −0.205010 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.8724 | 1.30750 | 0.653750 | − | 0.756710i | \(-0.273195\pi\) | ||||
0.653750 | + | 0.756710i | \(0.273195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1345 | 0.349466 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0329 | 0.552202 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.0135 | −1.61731 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0201 | −0.687898 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.97967 | 0.342501 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.471829 | −0.0161741 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.1052 | 1.06502 | 0.532512 | − | 0.846423i | \(-0.321248\pi\) | ||||
0.532512 | + | 0.846423i | \(0.321248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.81708 | −0.0621430 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.6667 | 1.62826 | 0.814131 | − | 0.580681i | \(-0.197214\pi\) | ||||
0.814131 | + | 0.580681i | \(0.197214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.93685 | −0.236682 | −0.118341 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118341 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.6225 | 0.362013 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.3736 | −1.51050 | −0.755248 | − | 0.655439i | \(-0.772484\pi\) | ||||
−0.755248 | + | 0.655439i | \(0.772484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.47898 | 0.220292 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.25630 | −0.110590 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.55872 | −0.222489 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0226574 | 0.000767717 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.19560 | −0.0404649 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.4184 | −1.02833 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.2810 | −0.516003 | −0.258002 | − | 0.966144i | \(-0.583064\pi\) | ||||
−0.258002 | + | 0.966144i | \(0.583064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.84400 | −0.230842 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.33130 | 0.314379 | 0.157190 | − | 0.987568i | \(-0.449757\pi\) | ||||
0.157190 | + | 0.987568i | \(0.449757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6940 | 0.494492 | 0.247246 | − | 0.968953i | \(-0.420474\pi\) | ||||
0.247246 | + | 0.968953i | \(0.420474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.8227 | 0.431030 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.8669 | −1.20429 | −0.602147 | − | 0.798385i | \(-0.705688\pi\) | ||||
−0.602147 | + | 0.798385i | \(0.705688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.52918 | 0.286060 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.28246 | −0.143468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.21801 | 0.141150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.4422 | −1.05100 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.141287 | 0.00471742 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.1038 | 1.23748 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6986 | −1.32255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.5018 | 0.449311 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.8985 | −1.39275 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0185 | −0.332658 | −0.166329 | − | 0.986070i | \(-0.553191\pi\) | ||||
−0.166329 | + | 0.986070i | \(0.553191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.15983 | 0.0716371 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.0288 | −1.49187 | −0.745936 | − | 0.666018i | \(-0.767997\pi\) | ||||
−0.745936 | + | 0.666018i | \(0.767997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −57.4232 | −1.90043 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.1222 | 0.433805 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.5921 | −1.53861 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.14537 | 0.202717 | 0.101359 | − | 0.994850i | \(-0.467681\pi\) | ||||
0.101359 | + | 0.994850i | \(0.467681\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.88679 | 0.0621718 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0456996 | 0.00150422 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.28002 | 0.0420866 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.6082 | 0.446952 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0472 | −0.788964 | −0.394482 | − | 0.918904i | \(-0.629076\pi\) | ||||
−0.394482 | + | 0.918904i | \(0.629076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.221327 | −0.00725370 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8665 | −0.617661 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −57.4247 | −1.87799 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.2412 | 0.334567 | 0.167283 | − | 0.985909i | \(-0.446501\pi\) | ||||
0.167283 | + | 0.985909i | \(0.446501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.2178 | 0.920854 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.37486 | 0.0774183 | 0.0387092 | − | 0.999251i | \(-0.487675\pi\) | ||||
0.0387092 | + | 0.999251i | \(0.487675\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6029 | 0.377843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.86637 | −0.320953 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.4904 | 0.340891 | 0.170445 | − | 0.985367i | \(-0.445479\pi\) | ||||
0.170445 | + | 0.985367i | \(0.445479\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.593470 | 0.0192648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.9184 | −0.581043 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4610 | 1.40784 | 0.703920 | − | 0.710279i | \(-0.251431\pi\) | ||||
0.703920 | + | 0.710279i | \(0.251431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.3326 | −0.463792 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.7900 | 0.865998 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.1259 | 0.520732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.17852 | 0.134791 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.76340 | 0.121274 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.6379 | 0.793122 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.9457 | −0.480623 | −0.240311 | − | 0.970696i | \(-0.577250\pi\) | ||||
−0.240311 | + | 0.970696i | \(0.577250\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.86240 | −0.0598288 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.84860 | −0.251873 | −0.125937 | − | 0.992038i | \(-0.540194\pi\) | ||||
−0.125937 | + | 0.992038i | \(0.540194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.4027 | 1.67995 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.383293 | −0.0122752 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.6046 | −1.39503 | −0.697517 | − | 0.716568i | \(-0.745712\pi\) | ||||
−0.697517 | + | 0.716568i | \(0.745712\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.33979 | −0.138700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9192 | −0.380549 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.1287 | −1.56696 | −0.783481 | − | 0.621416i | \(-0.786558\pi\) | ||||
−0.783481 | + | 0.621416i | \(0.786558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.7395 | −0.851990 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.9029 | 0.729007 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.7480 | 0.468959 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.17577 | 0.132648 | 0.0663239 | − | 0.997798i | \(-0.478873\pi\) | ||||
0.0663239 | + | 0.997798i | \(0.478873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.98539 | −0.221675 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 58.6887 | 1.86056 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.40338 | −0.139456 | −0.0697282 | − | 0.997566i | \(-0.522213\pi\) | ||||
−0.0697282 | + | 0.997566i | \(0.522213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.158358 | 0.00501023 |
(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 | 8016.2.a.w.1.7 | 7 | ||
4.3 | odd | 2 | 4008.2.a.g.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.g.1.7 | ✓ | 7 | 4.3 | odd | 2 | ||
8016.2.a.w.1.7 | 7 | 1.1 | even | 1 | trivial |