Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 45x^{6} + 67x^{5} - 166x^{4} - 83x^{3} + 152x^{2} + 51x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.94484\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | 1.94484 | 0.869760 | 0.434880 | − | 0.900488i | \(-0.356791\pi\) | ||||
0.434880 | + | 0.900488i | \(0.356791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.19705 | −1.20837 | −0.604185 | − | 0.796844i | \(-0.706501\pi\) | ||||
−0.604185 | + | 0.796844i | \(0.706501\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.785264 | −0.236766 | −0.118383 | − | 0.992968i | \(-0.537771\pi\) | ||||
−0.118383 | + | 0.992968i | \(0.537771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.88513 | −1.35489 | −0.677445 | − | 0.735573i | \(-0.736913\pi\) | ||||
−0.677445 | + | 0.735573i | \(0.736913\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.94484 | 0.502156 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.74809 | 0.666511 | 0.333255 | − | 0.942837i | \(-0.391853\pi\) | ||||
0.333255 | + | 0.942837i | \(0.391853\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.67411 | 0.384067 | 0.192034 | − | 0.981388i | \(-0.438492\pi\) | ||||
0.192034 | + | 0.981388i | \(0.438492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.19705 | −0.697653 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.23759 | −1.30063 | −0.650314 | − | 0.759665i | \(-0.725363\pi\) | ||||
−0.650314 | + | 0.759665i | \(0.725363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.21759 | −0.243518 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.902257 | −0.167545 | −0.0837724 | − | 0.996485i | \(-0.526697\pi\) | ||||
−0.0837724 | + | 0.996485i | \(0.526697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.13811 | 0.922832 | 0.461416 | − | 0.887184i | \(-0.347342\pi\) | ||||
0.461416 | + | 0.887184i | \(0.347342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.785264 | −0.136697 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.21775 | −1.05099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.279586 | 0.0459636 | 0.0229818 | − | 0.999736i | \(-0.492684\pi\) | ||||
0.0229818 | + | 0.999736i | \(0.492684\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.88513 | −0.782247 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.15508 | 0.180393 | 0.0901965 | − | 0.995924i | \(-0.471250\pi\) | ||||
0.0901965 | + | 0.995924i | \(0.471250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50592 | 0.687146 | 0.343573 | − | 0.939126i | \(-0.388363\pi\) | ||||
0.343573 | + | 0.939126i | \(0.388363\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.94484 | 0.289920 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.29789 | −1.21037 | −0.605186 | − | 0.796084i | \(-0.706901\pi\) | ||||
−0.605186 | + | 0.796084i | \(0.706901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.22111 | 0.460159 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.74809 | 0.384810 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.24888 | −0.858350 | −0.429175 | − | 0.903221i | \(-0.641196\pi\) | ||||
−0.429175 | + | 0.903221i | \(0.641196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.52721 | −0.205930 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.67411 | 0.221741 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.18041 | −1.19519 | −0.597594 | − | 0.801799i | \(-0.703877\pi\) | ||||
−0.597594 | + | 0.801799i | \(0.703877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.717810 | 0.0919061 | 0.0459531 | − | 0.998944i | \(-0.485368\pi\) | ||||
0.0459531 | + | 0.998944i | \(0.485368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.19705 | −0.402790 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.50080 | −1.17843 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0469 | −1.47176 | −0.735882 | − | 0.677110i | \(-0.763232\pi\) | ||||
−0.735882 | + | 0.677110i | \(0.763232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.23759 | −0.750918 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.7083 | −1.86423 | −0.932116 | − | 0.362160i | \(-0.882039\pi\) | ||||
−0.932116 | + | 0.362160i | \(0.882039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50452 | 0.293132 | 0.146566 | − | 0.989201i | \(-0.453178\pi\) | ||||
0.146566 | + | 0.989201i | \(0.453178\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.21759 | −0.140595 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.51053 | 0.286101 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2869 | −1.15737 | −0.578683 | − | 0.815552i | \(-0.696433\pi\) | ||||
−0.578683 | + | 0.815552i | \(0.696433\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.93675 | 0.541879 | 0.270939 | − | 0.962596i | \(-0.412666\pi\) | ||||
0.270939 | + | 0.962596i | \(0.412666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.34461 | 0.579704 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.902257 | −0.0967321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4270 | 1.63526 | 0.817629 | − | 0.575746i | \(-0.195288\pi\) | ||||
0.817629 | + | 0.575746i | \(0.195288\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.6180 | 1.63721 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.13811 | 0.532797 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.25588 | 0.334046 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.53933 | 0.156296 | 0.0781479 | − | 0.996942i | \(-0.475099\pi\) | ||||
0.0781479 | + | 0.996942i | \(0.475099\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.785264 | −0.0789220 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.637664 | −0.0634500 | −0.0317250 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317250 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.83309 | 0.476219 | 0.238109 | − | 0.971238i | \(-0.423472\pi\) | ||||
0.238109 | + | 0.971238i | \(0.423472\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.21775 | −0.606790 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.26070 | −0.895266 | −0.447633 | − | 0.894217i | \(-0.647733\pi\) | ||||
−0.447633 | + | 0.894217i | \(0.647733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.140018 | −0.0134112 | −0.00670562 | − | 0.999978i | \(-0.502134\pi\) | ||||
−0.00670562 | + | 0.999978i | \(0.502134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.279586 | 0.0265371 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1206 | −1.32836 | −0.664178 | − | 0.747574i | \(-0.731218\pi\) | ||||
−0.664178 | + | 0.747574i | \(0.731218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1311 | −1.13123 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.88513 | −0.451630 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.78579 | −0.805392 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3834 | −0.943942 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.15508 | 0.104150 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0922 | −1.08156 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0579 | −1.06996 | −0.534981 | − | 0.844864i | \(-0.679681\pi\) | ||||
−0.534981 | + | 0.844864i | \(0.679681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.50592 | 0.396724 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.67350 | −0.583066 | −0.291533 | − | 0.956561i | \(-0.594165\pi\) | ||||
−0.291533 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.35221 | −0.464095 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.94484 | 0.167385 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.73895 | 0.832054 | 0.416027 | − | 0.909352i | \(-0.363422\pi\) | ||||
0.416027 | + | 0.909352i | \(0.363422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.08219 | −0.600704 | −0.300352 | − | 0.953828i | \(-0.597104\pi\) | ||||
−0.300352 | + | 0.953828i | \(0.597104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.29789 | −0.698808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.83612 | 0.320792 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.75475 | −0.145724 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.22111 | 0.265673 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.98095 | 0.162285 | 0.0811427 | − | 0.996702i | \(-0.474143\pi\) | ||||
0.0811427 | + | 0.996702i | \(0.474143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.5517 | −1.75385 | −0.876925 | − | 0.480627i | \(-0.840409\pi\) | ||||
−0.876925 | + | 0.480627i | \(0.840409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.74809 | 0.222170 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.99281 | 0.802642 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.14846 | 0.490701 | 0.245350 | − | 0.969434i | \(-0.421097\pi\) | ||||
0.245350 | + | 0.969434i | \(0.421097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.24888 | −0.495569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.9419 | 1.57164 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.988706 | −0.0774414 | −0.0387207 | − | 0.999250i | \(-0.512328\pi\) | ||||
−0.0387207 | + | 0.999250i | \(0.512328\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.52721 | −0.118894 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8645 | 0.835729 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.67411 | 0.128022 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.748097 | 0.0568767 | 0.0284384 | − | 0.999596i | \(-0.490947\pi\) | ||||
0.0284384 | + | 0.999596i | \(0.490947\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.89269 | 0.294260 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.18041 | −0.690042 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.6260 | 1.46691 | 0.733457 | − | 0.679736i | \(-0.237905\pi\) | ||||
0.733457 | + | 0.679736i | \(0.237905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6840 | 0.794134 | 0.397067 | − | 0.917790i | \(-0.370028\pi\) | ||||
0.397067 | + | 0.917790i | \(0.370028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.717810 | 0.0530620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.543750 | 0.0399773 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.15798 | −0.157807 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.19705 | −0.232551 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.6633 | 1.85693 | 0.928465 | − | 0.371420i | \(-0.121129\pi\) | ||||
0.928465 | + | 0.371420i | \(0.121129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.10218 | 0.295281 | 0.147641 | − | 0.989041i | \(-0.452832\pi\) | ||||
0.147641 | + | 0.989041i | \(0.452832\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.50080 | −0.680366 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.58320 | −0.255292 | −0.127646 | − | 0.991820i | \(-0.540742\pi\) | ||||
−0.127646 | + | 0.991820i | \(0.540742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.22740 | 0.0870078 | 0.0435039 | − | 0.999053i | \(-0.486148\pi\) | ||||
0.0435039 | + | 0.999053i | \(0.486148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0469 | −0.849723 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.88456 | 0.202456 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.24645 | 0.156899 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.23759 | −0.433543 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.31462 | −0.0909341 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.24358 | −0.360983 | −0.180492 | − | 0.983577i | \(-0.557769\pi\) | ||||
−0.180492 | + | 0.983577i | \(0.557769\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.7083 | −1.07631 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.76329 | 0.597652 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.4268 | −1.11512 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.50452 | 0.169240 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.4248 | −0.903049 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.10636 | 0.0740872 | 0.0370436 | − | 0.999314i | \(-0.488206\pi\) | ||||
0.0370436 | + | 0.999314i | \(0.488206\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21759 | −0.0811727 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7395 | −1.17741 | −0.588707 | − | 0.808347i | \(-0.700363\pi\) | ||||
−0.588707 | + | 0.808347i | \(0.700363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.65487 | 0.241521 | 0.120760 | − | 0.992682i | \(-0.461467\pi\) | ||||
0.120760 | + | 0.992682i | \(0.461467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.51053 | 0.165181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.77622 | −0.640462 | −0.320231 | − | 0.947340i | \(-0.603760\pi\) | ||||
−0.320231 | + | 0.947340i | \(0.603760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.1381 | −1.05273 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.2869 | −0.668206 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.9111 | 1.02921 | 0.514603 | − | 0.857429i | \(-0.327939\pi\) | ||||
0.514603 | + | 0.857429i | \(0.327939\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.5185 | 1.70821 | 0.854105 | − | 0.520101i | \(-0.174106\pi\) | ||||
0.854105 | + | 0.520101i | \(0.174106\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.26455 | 0.400227 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.17824 | −0.520369 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.93675 | 0.312854 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.6017 | 1.48973 | 0.744865 | − | 0.667216i | \(-0.232514\pi\) | ||||
0.744865 | + | 0.667216i | \(0.232514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.89816 | 0.307945 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.34461 | 0.334692 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.0027 | 1.49725 | 0.748623 | − | 0.662996i | \(-0.230715\pi\) | ||||
0.748623 | + | 0.662996i | \(0.230715\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.893848 | −0.0555410 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.902257 | −0.0558483 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.9455 | −1.22989 | −0.614946 | − | 0.788569i | \(-0.710822\pi\) | ||||
−0.614946 | + | 0.788569i | \(0.710822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.1531 | −0.746558 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.4270 | 0.944116 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7796 | 0.901129 | 0.450564 | − | 0.892744i | \(-0.351223\pi\) | ||||
0.450564 | + | 0.892744i | \(0.351223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.89192 | 0.479400 | 0.239700 | − | 0.970847i | \(-0.422951\pi\) | ||||
0.239700 | + | 0.970847i | \(0.422951\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.6180 | 0.945243 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.956130 | 0.0576568 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.44295 | −0.507287 | −0.253644 | − | 0.967298i | \(-0.581629\pi\) | ||||
−0.253644 | + | 0.967298i | \(0.581629\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.13811 | 0.307611 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.38998 | −0.202229 | −0.101114 | − | 0.994875i | \(-0.532241\pi\) | ||||
−0.101114 | + | 0.994875i | \(0.532241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.5355 | 0.685715 | 0.342858 | − | 0.939387i | \(-0.388605\pi\) | ||||
0.342858 | + | 0.939387i | \(0.388605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.25588 | 0.192862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.69284 | −0.217982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.44797 | −0.555763 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.53933 | 0.0902374 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.92981 | −0.463265 | −0.231632 | − | 0.972803i | \(-0.574407\pi\) | ||||
−0.231632 | + | 0.972803i | \(0.574407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8545 | −1.03953 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.785264 | −0.0455657 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.4714 | 1.76221 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.4056 | −0.830326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.637664 | −0.0366329 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.39603 | 0.0799362 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.6509 | −1.29275 | −0.646377 | − | 0.763018i | \(-0.723717\pi\) | ||||
−0.646377 | + | 0.763018i | \(0.723717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.83309 | 0.274945 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.1604 | 0.916370 | 0.458185 | − | 0.888857i | \(-0.348500\pi\) | ||||
0.458185 | + | 0.888857i | \(0.348500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.80949 | −0.215325 | −0.107663 | − | 0.994187i | \(-0.534337\pi\) | ||||
−0.107663 | + | 0.994187i | \(0.534337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.21775 | −0.350331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.77439 | −0.380488 | −0.190244 | − | 0.981737i | \(-0.560928\pi\) | ||||
−0.190244 | + | 0.981737i | \(0.560928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.708510 | 0.0396689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.26070 | −0.516882 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.60061 | 0.255985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.94808 | 0.329940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.140018 | −0.00774299 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.5287 | 1.46258 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0240 | −1.48538 | −0.742688 | − | 0.669638i | \(-0.766449\pi\) | ||||
−0.742688 | + | 0.669638i | \(0.766449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.279586 | 0.0153212 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.4293 | −1.28008 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.9667 | 1.46897 | 0.734485 | − | 0.678625i | \(-0.237424\pi\) | ||||
0.734485 | + | 0.678625i | \(0.237424\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.1206 | −0.766927 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.03477 | −0.218495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0813 | 0.652328 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.1311 | −0.653118 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.71182 | 0.199261 | 0.0996305 | − | 0.995025i | \(-0.468234\pi\) | ||||
0.0996305 | + | 0.995025i | \(0.468234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.5718 | −1.90412 | −0.952058 | − | 0.305917i | \(-0.901037\pi\) | ||||
−0.952058 | + | 0.305917i | \(0.901037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.88513 | −0.260749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.37584 | 0.392576 | 0.196288 | − | 0.980546i | \(-0.437111\pi\) | ||||
0.196288 | + | 0.980546i | \(0.437111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.5501 | −1.62143 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.78579 | −0.464993 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.08145 | −0.162633 | −0.0813163 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813163 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1974 | −0.852492 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3834 | −0.544985 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.87090 | 0.254955 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9058 | 0.934674 | 0.467337 | − | 0.884079i | \(-0.345213\pi\) | ||||
0.467337 | + | 0.884079i | \(0.345213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.15508 | 0.0601310 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.9780 | 1.03720 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.74741 | 0.245812 | 0.122906 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122906 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0922 | −0.624440 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.40764 | 0.227005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.8092 | 1.83940 | 0.919699 | − | 0.392625i | \(-0.128433\pi\) | ||||
0.919699 | + | 0.392625i | \(0.128433\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0579 | −0.617743 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.8974 | 0.863415 | 0.431707 | − | 0.902014i | \(-0.357911\pi\) | ||||
0.431707 | + | 0.902014i | \(0.357911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.88258 | 0.248839 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.50592 | 0.229049 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.81225 | −0.497501 | −0.248750 | − | 0.968568i | \(-0.580020\pi\) | ||||
−0.248750 | + | 0.968568i | \(0.580020\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1415 | −0.866883 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.67350 | −0.336633 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.0064 | −1.00663 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.5614 | 0.730818 | 0.365409 | − | 0.930847i | \(-0.380929\pi\) | ||||
0.365409 | + | 0.930847i | \(0.380929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.35221 | −0.267946 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.4361 | −1.02053 | −0.510266 | − | 0.860017i | \(-0.670453\pi\) | ||||
−0.510266 | + | 0.860017i | \(0.670453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.1003 | −1.25034 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.94484 | 0.0966400 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.219549 | −0.0108826 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4146 | −0.712758 | −0.356379 | − | 0.934341i | \(-0.615989\pi\) | ||||
−0.356379 | + | 0.934341i | \(0.615989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.73895 | 0.480387 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3502 | 1.44423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.60120 | 0.471304 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.08219 | −0.346816 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.8259 | −0.528881 | −0.264441 | − | 0.964402i | \(-0.585187\pi\) | ||||
−0.264441 | + | 0.964402i | \(0.585187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.79642 | 0.379974 | 0.189987 | − | 0.981787i | \(-0.439155\pi\) | ||||
0.189987 | + | 0.981787i | \(0.439155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.29789 | −0.403457 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.34605 | −0.162307 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.29487 | −0.111057 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.83612 | 0.185209 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.95879 | −0.0943518 | −0.0471759 | − | 0.998887i | \(-0.515022\pi\) | ||||
−0.0471759 | + | 0.998887i | \(0.515022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.77815 | 0.325737 | 0.162869 | − | 0.986648i | \(-0.447925\pi\) | ||||
0.162869 | + | 0.986648i | \(0.447925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.75475 | −0.0841337 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.4424 | −0.499529 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.60884 | −0.0767858 | −0.0383929 | − | 0.999263i | \(-0.512224\pi\) | ||||
−0.0383929 | + | 0.999263i | \(0.512224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.22111 | 0.153386 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1166 | −0.623189 | −0.311594 | − | 0.950215i | \(-0.600863\pi\) | ||||
−0.311594 | + | 0.950215i | \(0.600863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0030 | 1.42228 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.98095 | 0.0936955 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.2340 | 0.954900 | 0.477450 | − | 0.878659i | \(-0.341561\pi\) | ||||
0.477450 | + | 0.878659i | \(0.341561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.907042 | −0.0427110 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.5517 | −1.01259 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.3745 | 1.42398 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.8087 | −1.53473 | −0.767364 | − | 0.641212i | \(-0.778432\pi\) | ||||
−0.767364 | + | 0.641212i | \(0.778432\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.74809 | 0.128270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.330968 | 0.0154147 | 0.00770735 | − | 0.999970i | \(-0.497547\pi\) | ||||
0.00770735 | + | 0.999970i | \(0.497547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.7776 | −1.05857 | −0.529283 | − | 0.848445i | \(-0.677539\pi\) | ||||
−0.529283 | + | 0.848445i | \(0.677539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.99281 | 0.463405 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.0969 | −1.11507 | −0.557535 | − | 0.830153i | \(-0.688253\pi\) | ||||
−0.557535 | + | 0.830153i | \(0.688253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.5145 | 1.77844 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.14846 | 0.283306 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.53833 | −0.162693 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.03838 | −0.0935273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.24888 | −0.286117 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.21205 | −0.0553800 | −0.0276900 | − | 0.999617i | \(-0.508815\pi\) | ||||
−0.0276900 | + | 0.999617i | \(0.508815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36581 | −0.0622756 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.9419 | 0.907387 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.99376 | 0.135940 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.1030 | 0.548437 | 0.274219 | − | 0.961667i | \(-0.411581\pi\) | ||||
0.274219 | + | 0.961667i | \(0.411581\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.988706 | −0.0447108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.65281 | −0.119720 | −0.0598598 | − | 0.998207i | \(-0.519065\pi\) | ||||
−0.0598598 | + | 0.998207i | \(0.519065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.47949 | −0.111670 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.52721 | −0.0686432 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.2202 | 2.25268 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.8523 | −1.42590 | −0.712952 | − | 0.701213i | \(-0.752642\pi\) | ||||
−0.712952 | + | 0.701213i | \(0.752642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.6781 | −0.565290 | −0.282645 | − | 0.959225i | \(-0.591212\pi\) | ||||
−0.282645 | + | 0.959225i | \(0.591212\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.24016 | −0.0551862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.8645 | 0.482508 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.9221 | 0.572764 | 0.286382 | − | 0.958116i | \(-0.407547\pi\) | ||||
0.286382 | + | 0.958116i | \(0.407547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00708 | −0.354212 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.67411 | 0.0739138 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.39960 | 0.414196 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.51603 | 0.286575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.748097 | 0.0328378 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.3920 | 0.893390 | 0.446695 | − | 0.894686i | \(-0.352601\pi\) | ||||
0.446695 | + | 0.894686i | \(0.352601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.653312 | −0.0285673 | −0.0142837 | − | 0.999898i | \(-0.504547\pi\) | ||||
−0.0142837 | + | 0.999898i | \(0.504547\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.89269 | 0.169891 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.1200 | 0.615077 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.9076 | 0.691634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.18041 | −0.398396 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.64271 | −0.244413 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0106 | −0.778666 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.6260 | 0.846924 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.52942 | −0.108950 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.8468 | 0.939268 | 0.469634 | − | 0.882861i | \(-0.344386\pi\) | ||||
0.469634 | + | 0.882861i | \(0.344386\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.6840 | 0.458493 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.272312 | −0.0116646 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.3863 | −1.72679 | −0.863397 | − | 0.504525i | \(-0.831668\pi\) | ||||
−0.863397 | + | 0.504525i | \(0.831668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.717810 | 0.0306354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.51048 | −0.0643485 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.8877 | 1.39853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.543750 | 0.0230809 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0593 | 0.638084 | 0.319042 | − | 0.947741i | \(-0.396639\pi\) | ||||
0.319042 | + | 0.947741i | \(0.396639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0120 | −0.931007 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.15798 | −0.0911100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5299 | −0.865232 | −0.432616 | − | 0.901578i | \(-0.642409\pi\) | ||||
−0.432616 | + | 0.901578i | \(0.642409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.4624 | −1.15535 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.19705 | −0.134263 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.59982 | 0.276679 | 0.138339 | − | 0.990385i | \(-0.455824\pi\) | ||||
0.138339 | + | 0.990385i | \(0.455824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.4955 | −0.648469 | −0.324234 | − | 0.945977i | \(-0.605107\pi\) | ||||
−0.324234 | + | 0.945977i | \(0.605107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.6633 | 1.07210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.59483 | 0.316726 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.56245 | 0.314829 | 0.157415 | − | 0.987533i | \(-0.449684\pi\) | ||||
0.157415 | + | 0.987533i | \(0.449684\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.10218 | 0.170481 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.7830 | −0.654790 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.90702 | 0.203228 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.50080 | −0.392810 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.7031 | 1.68000 | 0.839999 | − | 0.542588i | \(-0.182555\pi\) | ||||
0.839999 | + | 0.542588i | \(0.182555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.60176 | 0.354429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.58320 | −0.147393 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.6194 | 1.29845 | 0.649227 | − | 0.760595i | \(-0.275092\pi\) | ||||
0.649227 | + | 0.760595i | \(0.275092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.0870 | −0.700497 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.22740 | 0.0502340 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.82585 | −0.0746023 | −0.0373011 | − | 0.999304i | \(-0.511876\pi\) | ||||
−0.0373011 | + | 0.999304i | \(0.511876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1032 | 1.47268 | 0.736340 | − | 0.676611i | \(-0.236552\pi\) | ||||
0.736340 | + | 0.676611i | \(0.236552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.0469 | −0.490588 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.1940 | −0.821003 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.38030 | 0.380735 | 0.190367 | − | 0.981713i | \(-0.439032\pi\) | ||||
0.190367 | + | 0.981713i | \(0.439032\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.88456 | 0.116888 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.5362 | 1.63992 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.2542 | −1.26234 | −0.631172 | − | 0.775643i | \(-0.717426\pi\) | ||||
−0.631172 | + | 0.775643i | \(0.717426\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.24645 | 0.0905855 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.0094 | −0.402962 | −0.201481 | − | 0.979492i | \(-0.564575\pi\) | ||||
−0.201481 | + | 0.979492i | \(0.564575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.03107 | −0.322796 | −0.161398 | − | 0.986889i | \(-0.551600\pi\) | ||||
−0.161398 | + | 0.986889i | \(0.551600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.23759 | −0.250306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.3208 | −1.97600 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.4295 | −0.697181 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.31462 | −0.0525008 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.768328 | 0.0306352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.1105 | 0.442302 | 0.221151 | − | 0.975240i | \(-0.429019\pi\) | ||||
0.221151 | + | 0.975240i | \(0.429019\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.24358 | −0.208414 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23.4506 | −0.930610 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7355 | −0.623465 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.7083 | −0.621411 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.7769 | 1.88707 | 0.943537 | − | 0.331268i | \(-0.107476\pi\) | ||||
0.943537 | + | 0.331268i | \(0.107476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.0665 | −0.949092 | −0.474546 | − | 0.880231i | \(-0.657388\pi\) | ||||
−0.474546 | + | 0.880231i | \(0.657388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.76329 | 0.345054 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.2896 | −1.62326 | −0.811631 | − | 0.584170i | \(-0.801420\pi\) | ||||
−0.811631 | + | 0.584170i | \(0.801420\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.20905 | 0.282980 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.4268 | −0.643816 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.6726 | −0.652449 | −0.326225 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326225 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9789 | −0.507127 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.50452 | 0.0977108 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.8476 | 1.24061 | 0.620303 | − | 0.784362i | \(-0.287010\pi\) | ||||
0.620303 | + | 0.784362i | \(0.287010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.0798 | 1.59782 | 0.798909 | − | 0.601452i | \(-0.205411\pi\) | ||||
0.798909 | + | 0.601452i | \(0.205411\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.4248 | −0.521376 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.4092 | −0.403652 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.62791 | 0.217914 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.10636 | 0.0427742 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.563670 | −0.0217602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.5600 | −1.75621 | −0.878105 | − | 0.478469i | \(-0.841192\pi\) | ||||
−0.878105 | + | 0.478469i | \(0.841192\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.21759 | −0.0468651 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.1339 | −0.389478 | −0.194739 | − | 0.980855i | \(-0.562386\pi\) | ||||
−0.194739 | + | 0.980855i | \(0.562386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.92133 | −0.188863 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7395 | −0.679780 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0786 | 0.462173 | 0.231086 | − | 0.972933i | \(-0.425772\pi\) | ||||
0.231086 | + | 0.972933i | \(0.425772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.9407 | 0.723687 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.65487 | 0.139442 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.5266 | 1.16297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.9988 | 0.456457 | 0.228228 | − | 0.973608i | \(-0.426707\pi\) | ||||
0.228228 | + | 0.973608i | \(0.426707\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.51053 | 0.0953670 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13.7737 | −0.522468 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.17427 | 0.120234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.77622 | −0.369771 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.9550 | 0.942537 | 0.471269 | − | 0.881990i | \(-0.343796\pi\) | ||||
0.471269 | + | 0.881990i | \(0.343796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.468057 | 0.0176531 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.1381 | −0.607795 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.03864 | 0.0766710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.9420 | −1.01183 | −0.505914 | − | 0.862584i | \(-0.668845\pi\) | ||||
−0.505914 | + | 0.862584i | \(0.668845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.2869 | −0.385789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.0494 | −1.20026 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.46064 | 0.279012 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.9111 | 0.594212 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.0824 | −0.935416 | −0.467708 | − | 0.883883i | \(-0.654920\pi\) | ||||
−0.467708 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4516 | −0.575449 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.5185 | 0.986235 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.09858 | 0.0408002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.0283 | −1.70709 | −0.853547 | − | 0.521015i | \(-0.825553\pi\) | ||||
−0.853547 | + | 0.521015i | \(0.825553\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.3827 | 0.457990 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.71867 | −0.322032 | −0.161016 | − | 0.986952i | \(-0.551477\pi\) | ||||
−0.161016 | + | 0.986952i | \(0.551477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.26455 | 0.231071 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.46001 | 0.348464 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.73695 | −0.174252 | −0.0871258 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871258 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.17824 | −0.300435 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.4489 | 0.896942 | 0.448471 | − | 0.893797i | \(-0.351969\pi\) | ||||
0.448471 | + | 0.893797i | \(0.351969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.85263 | 0.141149 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.93675 | 0.180626 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.6069 | 1.08181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8796 | 0.944360 | 0.472180 | − | 0.881502i | \(-0.343467\pi\) | ||||
0.472180 | + | 0.881502i | \(0.343467\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.6017 | 0.860096 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.9146 | −1.52543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.7756 | 1.66374 | 0.831872 | − | 0.554968i | \(-0.187270\pi\) | ||||
0.831872 | + | 0.554968i | \(0.187270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.89816 | 0.177792 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.9566 | −0.433426 | −0.216713 | − | 0.976235i | \(-0.569534\pi\) | ||||
−0.216713 | + | 0.976235i | \(0.569534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.447643 | 0.0162058 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.34461 | 0.193235 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44.8475 | 1.61935 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.0375 | −1.69622 | −0.848108 | − | 0.529823i | \(-0.822258\pi\) | ||||
−0.848108 | + | 0.529823i | \(0.822258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0027 | 0.864436 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.5761 | 0.991843 | 0.495922 | − | 0.868367i | \(-0.334830\pi\) | ||||
0.495922 | + | 0.868367i | \(0.334830\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.25611 | −0.224726 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.893848 | −0.0320666 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.93373 | 0.0692831 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.3352 | 0.441387 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.902257 | −0.0322440 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.9578 | 0.426792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.3548 | 1.47414 | 0.737069 | − | 0.675817i | \(-0.236209\pi\) | ||||
0.737069 | + | 0.675817i | \(0.236209\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.9455 | −0.710079 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.1443 | 1.60515 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.50659 | −0.124523 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.1531 | −0.431026 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.1923 | −1.84875 | −0.924374 | − | 0.381489i | \(-0.875412\pi\) | ||||
−0.924374 | + | 0.381489i | \(0.875412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.8034 | −0.806726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4270 | 0.545086 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.96671 | −0.0694038 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 38.7838 | 1.36695 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7796 | 0.520267 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.72641 | 0.271646 | 0.135823 | − | 0.990733i | \(-0.456632\pi\) | ||||
0.135823 | + | 0.990733i | \(0.456632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0077 | 0.526993 | 0.263496 | − | 0.964660i | \(-0.415124\pi\) | ||||
0.263496 | + | 0.964660i | \(0.415124\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.89192 | 0.276782 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.92288 | −0.0673554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.54340 | 0.263910 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.6180 | 0.545737 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.08701 | 0.282239 | 0.141119 | − | 0.989993i | \(-0.454930\pi\) | ||||
0.141119 | + | 0.989993i | \(0.454930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.51032 | 0.0526465 | 0.0263233 | − | 0.999653i | \(-0.491620\pi\) | ||||
0.0263233 | + | 0.999653i | \(0.491620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.956130 | 0.0332882 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.2284 | 1.50320 | 0.751599 | − | 0.659621i | \(-0.229283\pi\) | ||||
0.751599 | + | 0.659621i | \(0.229283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1690 | 0.353185 | 0.176593 | − | 0.984284i | \(-0.443493\pi\) | ||||
0.176593 | + | 0.984284i | \(0.443493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.44295 | −0.292883 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.85192 | 0.306701 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.94484 | −0.0673040 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.13811 | 0.177599 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.9084 | 1.27422 | 0.637110 | − | 0.770773i | \(-0.280130\pi\) | ||||
0.637110 | + | 0.770773i | \(0.280130\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1859 | −0.971929 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.38998 | −0.116757 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.1297 | 0.726883 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.1961 | 1.14063 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.5355 | 0.395898 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.74394 | −0.0597815 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.95854 | 0.169777 | 0.0848886 | − | 0.996390i | \(-0.472947\pi\) | ||||
0.0848886 | + | 0.996390i | \(0.472947\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.25588 | 0.111349 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2261 | 0.554272 | 0.277136 | − | 0.960831i | \(-0.410615\pi\) | ||||
0.277136 | + | 0.960831i | \(0.410615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7556 | 0.401097 | 0.200549 | − | 0.979684i | \(-0.435728\pi\) | ||||
0.200549 | + | 0.979684i | \(0.435728\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.69284 | −0.125852 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.1048 | −1.16094 | −0.580470 | − | 0.814282i | \(-0.697131\pi\) | ||||
−0.580470 | + | 0.814282i | \(0.697131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.45493 | 0.0494691 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.44797 | −0.320870 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.07793 | 0.274025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.8507 | 1.99408 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.53933 | 0.0520986 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.6594 | 1.30693 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.5036 | 0.793662 | 0.396831 | − | 0.917892i | \(-0.370110\pi\) | ||||
0.396831 | + | 0.917892i | \(0.370110\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.92981 | −0.267466 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4073 | 1.19290 | 0.596451 | − | 0.802650i | \(-0.296577\pi\) | ||||
0.596451 | + | 0.802650i | \(0.296577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.4104 | 1.49453 | 0.747265 | − | 0.664526i | \(-0.231367\pi\) | ||||
0.747265 | + | 0.664526i | \(0.231367\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.8545 | −0.600171 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.959427 | 0.0322144 | 0.0161072 | − | 0.999870i | \(-0.494873\pi\) | ||||
0.0161072 | + | 0.999870i | \(0.494873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.5495 | 1.29291 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.785264 | −0.0263073 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.8916 | −0.464864 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.1694 | 1.27586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 30.4714 | 1.01741 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.63589 | −0.154616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.1725 | −0.572100 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.4056 | −0.479389 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7786 | 0.690705 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.753739 | 0.0250275 | 0.0125137 | − | 0.999922i | \(-0.496017\pi\) | ||||
0.0125137 | + | 0.999922i | \(0.496017\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.637664 | −0.0211500 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.87062 | −0.227634 | −0.113817 | − | 0.993502i | \(-0.536308\pi\) | ||||
−0.113817 | + | 0.993502i | \(0.536308\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.87666 | −0.128299 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.39603 | 0.0461512 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.3355 | 0.704560 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.1883 | −1.58958 | −0.794792 | − | 0.606881i | \(-0.792420\pi\) | ||||
−0.794792 | + | 0.606881i | \(0.792420\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.6509 | −0.746372 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 76.7370 | 2.52583 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.340421 | −0.0111930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.83309 | 0.158740 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.0774 | −0.691528 | −0.345764 | − | 0.938322i | \(-0.612380\pi\) | ||||
−0.345764 | + | 0.938322i | \(0.612380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.39249 | 0.176732 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.1604 | 0.529066 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.19693 | −0.137254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1319 | 0.723019 | 0.361509 | − | 0.932368i | \(-0.382262\pi\) | ||||
0.361509 | + | 0.932368i | \(0.382262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.80949 | −0.124318 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.58967 | −0.182218 | −0.0911091 | − | 0.995841i | \(-0.529041\pi\) | ||||
−0.0911091 | + | 0.995841i | \(0.529041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.20491 | −0.234624 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.21775 | −0.202263 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.824122 | 0.0267804 | 0.0133902 | − | 0.999910i | \(-0.495738\pi\) | ||||
0.0133902 | + | 0.999910i | \(0.495738\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2349 | −0.397162 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.77439 | −0.219675 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.76121 | −0.283804 | −0.141902 | − | 0.989881i | \(-0.545322\pi\) | ||||
−0.141902 | + | 0.989881i | \(0.545322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.9110 | 1.61508 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.708510 | 0.0229029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.1359 | −1.00543 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.59983 | −0.148382 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.26070 | −0.298422 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.97808 | 0.256824 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.1756 | −0.680963 | −0.340481 | − | 0.940251i | \(-0.610590\pi\) | ||||
−0.340481 | + | 0.940251i | \(0.610590\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.60061 | 0.147793 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9748 | 0.769388 | 0.384694 | − | 0.923044i | \(-0.374307\pi\) | ||||
0.384694 | + | 0.923044i | \(0.374307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.6421 | 0.725872 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.94808 | 0.190491 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.56075 | −0.273883 | −0.136941 | − | 0.990579i | \(-0.543727\pi\) | ||||
−0.136941 | + | 0.990579i | \(0.543727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1143 | −0.387173 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.140018 | −0.00447042 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.5757 | 0.815738 | 0.407869 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407869 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.96875 | −0.222043 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.5287 | 0.844419 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.1061 | −0.893721 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.5988 | −1.13083 | −0.565416 | − | 0.824806i | \(-0.691284\pi\) | ||||
−0.565416 | + | 0.824806i | \(0.691284\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.0240 | −0.857582 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.38709 | 0.0756759 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.21830 | −0.291946 | −0.145973 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145973 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.279586 | 0.00884570 |
(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 | 4008.2.a.i.1.8 | ✓ | 9 | |
4.3 | odd | 2 | 8016.2.a.ba.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.i.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial | |
8016.2.a.ba.1.8 | 9 | 4.3 | odd | 2 |