Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [308,2,Mod(1,308)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(308, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("308.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 308 = 2^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 308.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: | \(2.45939238226\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.85577\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 308.1 |
$q$-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 | ||||||||
\(3\) | −2.85577 | −1.64878 | −0.824391 | − | 0.566021i | \(-0.808482\pi\) | ||||
−0.824391 | + | 0.566021i | \(0.808482\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.15544 | −1.85837 | −0.929184 | − | 0.369618i | \(-0.879489\pi\) | ||||
−0.929184 | + | 0.369618i | \(0.879489\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.15544 | 1.71848 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.29966 | 1.46986 | 0.734931 | − | 0.678142i | \(-0.237214\pi\) | ||||
0.734931 | + | 0.678142i | \(0.237214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.8670 | 3.06404 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.41188 | 1.07004 | 0.535019 | − | 0.844840i | \(-0.320304\pi\) | ||||
0.535019 | + | 0.844840i | \(0.320304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.71155 | −1.31032 | −0.655159 | − | 0.755491i | \(-0.727398\pi\) | ||||
−0.655159 | + | 0.755491i | \(0.727398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.85577 | −0.623181 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.55611 | −0.741500 | −0.370750 | − | 0.928733i | \(-0.620899\pi\) | ||||
−0.370750 | + | 0.928733i | \(0.620899\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.2677 | 2.45353 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.15544 | −1.18461 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.599328 | −0.111292 | −0.0556462 | − | 0.998451i | \(-0.517722\pi\) | ||||
−0.0556462 | + | 0.998451i | \(0.517722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56732 | 0.820314 | 0.410157 | − | 0.912015i | \(-0.365474\pi\) | ||||
0.410157 | + | 0.912015i | \(0.365474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.85577 | −0.497126 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.15544 | −0.702397 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.15544 | 1.01195 | 0.505974 | − | 0.862549i | \(-0.331133\pi\) | ||||
0.505974 | + | 0.862549i | \(0.331133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.1346 | −2.42348 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.41188 | −0.689020 | −0.344510 | − | 0.938783i | \(-0.611955\pi\) | ||||
−0.344510 | + | 0.938783i | \(0.611955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.71155 | 0.566005 | 0.283003 | − | 0.959119i | \(-0.408669\pi\) | ||||
0.283003 | + | 0.959119i | \(0.408669\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21.4231 | −3.19357 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.01121 | 0.730960 | 0.365480 | − | 0.930819i | \(-0.380905\pi\) | ||||
0.365480 | + | 0.930819i | \(0.380905\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.5993 | −1.76426 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.31087 | 1.14159 | 0.570793 | − | 0.821094i | \(-0.306636\pi\) | ||||
0.570793 | + | 0.821094i | \(0.306636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.15544 | −0.560319 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.3109 | 2.16043 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.14423 | −0.669721 | −0.334861 | − | 0.942268i | \(-0.608689\pi\) | ||||
−0.334861 | + | 0.942268i | \(0.608689\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6105 | 1.74265 | 0.871325 | − | 0.490706i | \(-0.163261\pi\) | ||||
0.871325 | + | 0.490706i | \(0.163261\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.15544 | 0.649524 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −22.0224 | −2.73154 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.443892 | −0.0542300 | −0.0271150 | − | 0.999632i | \(-0.508632\pi\) | ||||
−0.0271150 | + | 0.999632i | \(0.508632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.1554 | 1.22257 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.75476 | 0.564287 | 0.282143 | − | 0.959372i | \(-0.408955\pi\) | ||||
0.282143 | + | 0.959372i | \(0.408955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.41188 | −0.984536 | −0.492268 | − | 0.870444i | \(-0.663832\pi\) | ||||
−0.492268 | + | 0.870444i | \(0.663832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −35.0336 | −4.04533 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.02242 | −0.902593 | −0.451296 | − | 0.892374i | \(-0.649038\pi\) | ||||
−0.451296 | + | 0.892374i | \(0.649038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.11222 | 0.234691 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.82376 | 0.968534 | 0.484267 | − | 0.874920i | \(-0.339086\pi\) | ||||
0.484267 | + | 0.874920i | \(0.339086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.3333 | −1.98852 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.71155 | 0.183497 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.57853 | 0.803322 | 0.401661 | − | 0.915788i | \(-0.368433\pi\) | ||||
0.401661 | + | 0.915788i | \(0.368433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.29966 | 0.555556 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.0432 | −1.35252 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.7340 | 2.43505 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8670 | 1.40798 | 0.703989 | − | 0.710211i | \(-0.251400\pi\) | ||||
0.703989 | + | 0.710211i | \(0.251400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.15544 | 0.518141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.70034 | −0.268693 | −0.134347 | − | 0.990934i | \(-0.542894\pi\) | ||||
−0.134347 | + | 0.990934i | \(0.542894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.41188 | 0.631781 | 0.315891 | − | 0.948796i | \(-0.397697\pi\) | ||||
0.315891 | + | 0.948796i | \(0.397697\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.8670 | 1.15810 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.31087 | 0.803442 | 0.401721 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401721 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1346 | −1.44964 | −0.724818 | − | 0.688941i | \(-0.758076\pi\) | ||||
−0.724818 | + | 0.688941i | \(0.758076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.5785 | −1.66848 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8894 | −1.49475 | −0.747375 | − | 0.664403i | \(-0.768686\pi\) | ||||
−0.747375 | + | 0.664403i | \(0.768686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.7772 | 1.37798 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.3221 | 2.52593 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.41188 | 0.404436 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.5993 | 1.13604 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −30.2003 | −2.70119 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1122 | 1.34099 | 0.670496 | − | 0.741913i | \(-0.266081\pi\) | ||||
0.670496 | + | 0.741913i | \(0.266081\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5993 | −0.933219 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.68913 | −0.322321 | −0.161160 | − | 0.986928i | \(-0.551524\pi\) | ||||
−0.161160 | + | 0.986928i | \(0.551524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.71155 | −0.495254 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.5785 | 2.20145 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.04322 | 0.260000 | 0.130000 | − | 0.991514i | \(-0.458502\pi\) | ||||
0.130000 | + | 0.991514i | \(0.458502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9102 | 0.925391 | 0.462696 | − | 0.886517i | \(-0.346882\pi\) | ||||
0.462696 | + | 0.886517i | \(0.346882\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.3109 | −1.20519 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.29966 | 0.443180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.49047 | 0.206822 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.85577 | −0.235540 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.19866 | 0.589737 | 0.294868 | − | 0.955538i | \(-0.404724\pi\) | ||||
0.294868 | + | 0.955538i | \(0.404724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.02242 | −0.652855 | −0.326428 | − | 0.945222i | \(-0.605845\pi\) | ||||
−0.326428 | + | 0.945222i | \(0.605845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.7452 | 1.83884 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.9792 | −1.52445 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.84456 | 0.306830 | 0.153415 | − | 0.988162i | \(-0.450973\pi\) | ||||
0.153415 | + | 0.988162i | \(0.450973\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.7340 | −1.88223 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.55611 | −0.280261 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0224 | −1.09832 | −0.549160 | − | 0.835717i | \(-0.685052\pi\) | ||||
−0.549160 | + | 0.835717i | \(0.685052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.8670 | 0.923843 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.1122 | 1.47895 | 0.739474 | − | 0.673185i | \(-0.235074\pi\) | ||||
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0864 | 1.16050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29.4455 | −2.25175 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3221 | 1.46903 | 0.734515 | − | 0.678592i | \(-0.237410\pi\) | ||||
0.734515 | + | 0.678592i | \(0.237410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2677 | 0.927347 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6907 | 1.10422 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.73235 | 0.503199 | 0.251600 | − | 0.967831i | \(-0.419043\pi\) | ||||
0.251600 | + | 0.967831i | \(0.419043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.64255 | −0.568066 | −0.284033 | − | 0.958814i | \(-0.591673\pi\) | ||||
−0.284033 | + | 0.958814i | \(0.591673\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.8686 | −2.87325 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.5785 | −1.88057 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.41188 | 0.322629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.15544 | −0.447742 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.84456 | −0.133468 | −0.0667340 | − | 0.997771i | \(-0.521258\pi\) | ||||
−0.0667340 | + | 0.997771i | \(0.521258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6217 | −1.05250 | −0.526248 | − | 0.850331i | \(-0.676402\pi\) | ||||
−0.526248 | + | 0.850331i | \(0.676402\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 62.8910 | 4.50372 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.2099 | −0.723758 | −0.361879 | − | 0.932225i | \(-0.617865\pi\) | ||||
−0.361879 | + | 0.932225i | \(0.617865\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.26765 | 0.0894134 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.599328 | −0.0420646 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.3333 | 1.28045 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.3333 | −1.27425 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.71155 | −0.395076 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3109 | 1.12289 | 0.561443 | − | 0.827515i | \(-0.310246\pi\) | ||||
0.561443 | + | 0.827515i | \(0.310246\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5785 | −0.930385 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.4231 | −1.05185 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.56732 | 0.310050 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0224 | 1.62328 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.3815 | 1.57281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0802 | −0.875915 | −0.437958 | − | 0.898996i | \(-0.644298\pi\) | ||||
−0.437958 | + | 0.898996i | \(0.644298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 63.2451 | 4.21634 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.6217 | −1.10322 | −0.551612 | − | 0.834101i | \(-0.685987\pi\) | ||||
−0.551612 | + | 0.834101i | \(0.685987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1779 | 1.46555 | 0.732777 | − | 0.680469i | \(-0.238224\pi\) | ||||
0.732777 | + | 0.680469i | \(0.238224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.85577 | −0.187896 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5993 | −0.825409 | −0.412705 | − | 0.910865i | \(-0.635416\pi\) | ||||
−0.412705 | + | 0.910865i | \(0.635416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.8238 | −1.35839 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.9102 | 1.48818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.2244 | 0.920102 | 0.460051 | − | 0.887892i | \(-0.347831\pi\) | ||||
0.460051 | + | 0.887892i | \(0.347831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.101008 | −0.00650648 | −0.00325324 | − | 0.999995i | \(-0.501036\pi\) | ||||
−0.00325324 | + | 0.999995i | \(0.501036\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.4343 | 0.797661 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.15544 | −0.265481 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2693 | −1.92599 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.1987 | −1.59690 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.9680 | −1.63908 | −0.819542 | − | 0.573018i | \(-0.805772\pi\) | ||||
−0.819542 | + | 0.573018i | \(0.805772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55611 | −0.223571 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 52.3557 | 3.27864 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.57691 | 0.160743 | 0.0803716 | − | 0.996765i | \(-0.474389\pi\) | ||||
0.0803716 | + | 0.996765i | \(0.474389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.15544 | 0.382480 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.08980 | −0.191254 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.3109 | 1.25242 | 0.626211 | − | 0.779654i | \(-0.284605\pi\) | ||||
0.626211 | + | 0.779654i | \(0.284605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.5353 | −2.12149 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.6425 | −1.32450 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82376 | 0.172168 | 0.0860839 | − | 0.996288i | \(-0.472565\pi\) | ||||
0.0860839 | + | 0.996288i | \(0.472565\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.82376 | 0.293023 | 0.146511 | − | 0.989209i | \(-0.453196\pi\) | ||||
0.146511 | + | 0.989209i | \(0.453196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.1346 | −0.915990 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2677 | 0.739767 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7340 | 0.825194 | 0.412597 | − | 0.910914i | \(-0.364622\pi\) | ||||
0.412597 | + | 0.910914i | \(0.364622\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.5465 | 1.40969 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.9102 | −1.24740 | −0.623699 | − | 0.781665i | \(-0.714371\pi\) | ||||
−0.623699 | + | 0.781665i | \(0.714371\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.19866 | −0.309028 | −0.154514 | − | 0.987991i | \(-0.549381\pi\) | ||||
−0.154514 | + | 0.987991i | \(0.549381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −67.7788 | −4.01487 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.41188 | −0.260425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.46469 | 0.144982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.6009 | −2.32145 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.8574 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.3765 | 1.24459 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.15544 | −0.357175 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.8462 | −1.08990 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.71155 | 0.213930 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.71155 | 0.443017 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −56.5577 | −3.23849 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.6217 | −1.86182 | −0.930911 | − | 0.365247i | \(-0.880985\pi\) | ||||
−0.930911 | + | 0.365247i | \(0.880985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.3109 | −1.04167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.0560 | −1.42080 | −0.710399 | − | 0.703799i | \(-0.751485\pi\) | ||||
−0.710399 | + | 0.703799i | \(0.751485\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8894 | −1.12422 | −0.562108 | − | 0.827064i | \(-0.690009\pi\) | ||||
−0.562108 | + | 0.827064i | \(0.690009\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −21.4231 | −1.20705 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.04322 | −0.507918 | −0.253959 | − | 0.967215i | \(-0.581733\pi\) | ||||
−0.253959 | + | 0.967215i | \(0.581733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.599328 | −0.0335559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.7340 | −1.32470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.1987 | −1.40209 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 65.0144 | 3.60635 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 43.2211 | 2.39013 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.01121 | 0.276277 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.8894 | 1.64287 | 0.821435 | − | 0.570302i | \(-0.193174\pi\) | ||||
0.821435 | + | 0.570302i | \(0.193174\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.7340 | 1.73901 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.84456 | 0.100779 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.97758 | 0.216673 | 0.108336 | − | 0.994114i | \(-0.465448\pi\) | ||||
0.108336 | + | 0.994114i | \(0.465448\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 45.3765 | 2.46451 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.56732 | 0.247334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −42.2003 | −2.27199 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.82376 | −0.151587 | −0.0757937 | − | 0.997124i | \(-0.524149\pi\) | ||||
−0.0757937 | + | 0.997124i | \(0.524149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7868 | −0.684460 | −0.342230 | − | 0.939616i | \(-0.611182\pi\) | ||||
−0.342230 | + | 0.939616i | \(0.611182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.6217 | −1.74122 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.9758 | 1.80835 | 0.904176 | − | 0.427161i | \(-0.140486\pi\) | ||||
0.904176 | + | 0.427161i | \(0.140486\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7581 | −1.04865 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.5993 | −0.666827 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1346 | −0.587664 | −0.293832 | − | 0.955857i | \(-0.594931\pi\) | ||||
−0.293832 | + | 0.955857i | \(0.594931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.6217 | 0.716934 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.85577 | −0.149889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.9550 | 1.82963 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.3653 | 1.27186 | 0.635929 | − | 0.771747i | \(-0.280617\pi\) | ||||
0.635929 | + | 0.771747i | \(0.280617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.7452 | −1.18407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.31087 | 0.431479 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.1122 | 1.09315 | 0.546575 | − | 0.837410i | \(-0.315931\pi\) | ||||
0.546575 | + | 0.837410i | \(0.315931\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 86.2451 | 4.45368 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.17624 | −0.163585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0914 | 0.518361 | 0.259181 | − | 0.965829i | \(-0.416548\pi\) | ||||
0.259181 | + | 0.965829i | \(0.416548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.1571 | −2.21100 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.4359 | 1.91289 | 0.956443 | − | 0.291919i | \(-0.0942939\pi\) | ||||
0.956443 | + | 0.291919i | \(0.0942939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.15544 | −0.211781 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.1346 | 0.972668 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.3541 | 0.879887 | 0.439944 | − | 0.898025i | \(-0.354998\pi\) | ||||
0.439944 | + | 0.898025i | \(0.354998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.6891 | −0.793433 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5353 | 0.531436 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.3367 | 1.67735 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0448 | −0.905644 | −0.452822 | − | 0.891601i | \(-0.649583\pi\) | ||||
−0.452822 | + | 0.891601i | \(0.649583\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.3109 | 0.816565 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.57691 | 0.128685 | 0.0643424 | − | 0.997928i | \(-0.479505\pi\) | ||||
0.0643424 | + | 0.997928i | \(0.479505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.2052 | 1.20575 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.77718 | −0.436142 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.15544 | 0.305114 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0336 | −1.23783 | −0.618917 | − | 0.785457i | \(-0.712428\pi\) | ||||
−0.618917 | + | 0.785457i | \(0.712428\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.69074 | −0.428683 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.14423 | −0.253131 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.6666 | −1.79989 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.1571 | −1.52577 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.56570 | 0.174196 | 0.0870979 | − | 0.996200i | \(-0.472241\pi\) | ||||
0.0870979 | + | 0.996200i | \(0.472241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.31087 | 0.210099 | 0.105050 | − | 0.994467i | \(-0.466500\pi\) | ||||
0.105050 | + | 0.994467i | \(0.466500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.8350 | 1.25614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 54.1234 | 2.62537 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.6105 | 0.658660 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.1346 | −0.730707 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5577 | 0.701221 | 0.350610 | − | 0.936521i | \(-0.385974\pi\) | ||||
0.350610 | + | 0.936521i | \(0.385974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.357452 | −0.0171780 | −0.00858902 | − | 0.999963i | \(-0.502734\pi\) | ||||
−0.00858902 | + | 0.999963i | \(0.502734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.11222 | −0.341005 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3109 | 0.971601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.2885 | −0.681951 | −0.340975 | − | 0.940072i | \(-0.610757\pi\) | ||||
−0.340975 | + | 0.940072i | \(0.610757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.15544 | 0.245497 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.95678 | 0.425549 | 0.212775 | − | 0.977101i | \(-0.431750\pi\) | ||||
0.212775 | + | 0.977101i | \(0.431750\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.4921 | −1.49287 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.5577 | −0.972347 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.379870 | 0.0179272 | 0.00896359 | − | 0.999960i | \(-0.497147\pi\) | ||||
0.00896359 | + | 0.999960i | \(0.497147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.41188 | −0.207747 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.9102 | 1.07642 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.0224 | −1.03243 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.3557 | −1.23287 | −0.616434 | − | 0.787407i | \(-0.711423\pi\) | ||||
−0.616434 | + | 0.787407i | \(0.711423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.1571 | −1.26758 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.4343 | 1.79006 | 0.895032 | − | 0.446002i | \(-0.147153\pi\) | ||||
0.895032 | + | 0.446002i | \(0.147153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.64255 | −0.0763357 | −0.0381678 | − | 0.999271i | \(-0.512152\pi\) | ||||
−0.0381678 | + | 0.999271i | \(0.512152\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 54.2003 | 2.51348 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.65712 | 0.261780 | 0.130890 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130890 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.443892 | −0.0204970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.9792 | −0.505895 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.71155 | 0.170657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −70.0673 | −3.21491 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 42.8462 | 1.96179 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.8238 | 1.49976 | 0.749878 | − | 0.661576i | \(-0.230112\pi\) | ||||
0.749878 | + | 0.661576i | \(0.230112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.6217 | 1.48742 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1554 | 0.462088 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −57.6234 | −2.61654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.53033 | −0.295918 | −0.147959 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147959 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.0448 | 1.81089 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.4455 | 1.41912 | 0.709558 | − | 0.704647i | \(-0.248895\pi\) | ||||
0.709558 | + | 0.704647i | \(0.248895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64416 | −0.119087 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −21.4231 | −0.962896 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.75476 | 0.213280 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.6699 | 1.05961 | 0.529806 | − | 0.848119i | \(-0.322265\pi\) | ||||
0.529806 | + | 0.848119i | \(0.322265\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −54.5801 | −2.43846 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.57355 | 0.248512 | 0.124256 | − | 0.992250i | \(-0.460346\pi\) | ||||
0.124256 | + | 0.992250i | \(0.460346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.2211 | 0.499331 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −43.0834 | −1.91340 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.82215 | −0.435359 | −0.217679 | − | 0.976020i | \(-0.569849\pi\) | ||||
−0.217679 | + | 0.976020i | \(0.569849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.41188 | −0.372120 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.1571 | 1.55222 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.6442 | −1.17408 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.01121 | 0.220393 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −55.1795 | −2.42211 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.1363 | 1.75840 | 0.879201 | − | 0.476452i | \(-0.158077\pi\) | ||||
0.879201 | + | 0.476452i | \(0.158077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.2244 | −0.796899 | −0.398449 | − | 0.917190i | \(-0.630452\pi\) | ||||
−0.398449 | + | 0.917190i | \(0.630452\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −35.0336 | −1.52899 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1505 | 0.877768 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.3541 | −0.450178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.5207 | −1.15090 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.3815 | −1.01276 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.5353 | −1.49309 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.2261 | −0.829665 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.68913 | −0.0726212 | −0.0363106 | − | 0.999341i | \(-0.511561\pi\) | ||||
−0.0363106 | + | 0.999341i | \(0.511561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.8254 | 0.936617 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 62.8910 | 2.69396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.0706 | −1.07194 | −0.535971 | − | 0.844236i | \(-0.680054\pi\) | ||||
−0.535971 | + | 0.844236i | \(0.680054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 70.1683 | 2.99471 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.42309 | 0.145829 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.02242 | −0.341148 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 73.0465 | 3.10065 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.0448 | 1.10356 | 0.551778 | − | 0.833991i | \(-0.313950\pi\) | ||||
0.551778 | + | 0.833991i | \(0.313950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.6699 | 0.831950 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5993 | −0.531944 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.4455 | −1.57814 | −0.789070 | − | 0.614303i | \(-0.789437\pi\) | ||||
−0.789070 | + | 0.614303i | \(0.789437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 66.0274 | 2.77779 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.11222 | 0.0887048 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.97758 | −0.334438 | −0.167219 | − | 0.985920i | \(-0.553479\pi\) | ||||
−0.167219 | + | 0.985920i | \(0.553479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.19866 | 0.384952 | 0.192476 | − | 0.981302i | \(-0.438348\pi\) | ||||
0.192476 | + | 0.981302i | \(0.438348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.26765 | 0.220059 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −43.6251 | −1.81929 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.75476 | −0.114682 | −0.0573412 | − | 0.998355i | \(-0.518262\pi\) | ||||
−0.0573412 | + | 0.998355i | \(0.518262\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.7564 | 1.73534 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.82376 | 0.366071 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.31087 | 0.344201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −113.535 | −4.69410 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.20987 | 0.256309 | 0.128154 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.0864 | −1.07487 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.1346 | 0.704825 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.2356 | −1.03630 | −0.518152 | − | 0.855289i | \(-0.673380\pi\) | ||||
−0.518152 | + | 0.855289i | \(0.673380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.3333 | −0.751592 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.1571 | 1.19332 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6442 | −0.598344 | −0.299172 | − | 0.954199i | \(-0.596710\pi\) | ||||
−0.299172 | + | 0.954199i | \(0.596710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.87657 | −0.402874 | −0.201437 | − | 0.979501i | \(-0.564561\pi\) | ||||
−0.201437 | + | 0.979501i | \(0.564561\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.28845 | −0.0931931 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.15544 | −0.168943 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.1571 | 1.91405 | 0.957023 | − | 0.290012i | \(-0.0936595\pi\) | ||||
0.957023 | + | 0.290012i | \(0.0936595\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.71155 | 0.0693553 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.5577 | 1.07441 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.10886 | 0.246734 | 0.123367 | − | 0.992361i | \(-0.460631\pi\) | ||||
0.123367 | + | 0.992361i | \(0.460631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −52.3557 | −2.11119 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3815 | −1.18285 | −0.591427 | − | 0.806359i | \(-0.701435\pi\) | ||||
−0.591427 | + | 0.806359i | \(0.701435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.4551 | −0.701580 | −0.350790 | − | 0.936454i | \(-0.614087\pi\) | ||||
−0.350790 | + | 0.936454i | \(0.614087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.8894 | 0.878391 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.57853 | 0.303627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 64.1571 | 2.56628 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.3109 | 0.651394 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.1571 | 1.08282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.6234 | −1.97547 | −0.987737 | − | 0.156124i | \(-0.950100\pi\) | ||||
−0.987737 | + | 0.156124i | \(0.950100\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −46.5801 | −1.85139 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −62.7979 | −2.49206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.29966 | 0.209980 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.5129 | 0.969715 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1554 | 0.875087 | 0.437544 | − | 0.899197i | \(-0.355849\pi\) | ||||
0.437544 | + | 0.899197i | \(0.355849\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.07685 | 0.0819029 | 0.0409514 | − | 0.999161i | \(-0.486961\pi\) | ||||
0.0409514 | + | 0.999161i | \(0.486961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 44.0448 | 1.73426 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.67953 | 0.144657 | 0.0723287 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723287 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.14423 | −0.201929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.0432 | −0.511204 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.0016 | −1.36972 | −0.684860 | − | 0.728675i | \(-0.740136\pi\) | ||||
−0.684860 | + | 0.728675i | \(0.740136\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.3299 | 0.598990 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −43.3669 | −1.69190 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 48.0673 | 1.87243 | 0.936217 | − | 0.351422i | \(-0.114302\pi\) | ||||
0.936217 | + | 0.351422i | \(0.114302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.3989 | −1.61023 | −0.805116 | − | 0.593118i | \(-0.797897\pi\) | ||||
−0.805116 | + | 0.593118i | \(0.797897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −66.7722 | −2.59322 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.7340 | 0.920364 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.13128 | 0.0825233 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.3541 | 1.44419 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.6105 | 0.525429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9360 | 0.691381 | 0.345691 | − | 0.938349i | \(-0.387645\pi\) | ||||
0.345691 | + | 0.938349i | \(0.387645\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −75.5128 | −2.90649 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.6363 | 0.716252 | 0.358126 | − | 0.933673i | \(-0.383416\pi\) | ||||
0.358126 | + | 0.933673i | \(0.383416\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8670 | 0.532166 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.4679 | 1.81897 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.19866 | −0.0458653 | −0.0229327 | − | 0.999737i | \(-0.507300\pi\) | ||||
−0.0229327 | + | 0.999737i | \(0.507300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.6459 | −0.483175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −63.3349 | −2.41638 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.0448 | 1.67797 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.7884 | −1.81796 | −0.908978 | − | 0.416844i | \(-0.863136\pi\) | ||||
−0.908978 | + | 0.416844i | \(0.863136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.15544 | 0.195839 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45.3367 | −1.71972 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.4647 | −0.737278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.9808 | 1.36092 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.51289 | −0.245988 | −0.122994 | − | 0.992407i | \(-0.539250\pi\) | ||||
−0.122994 | + | 0.992407i | \(0.539250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.1571 | −1.32597 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 59.4679 | 2.23969 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.70034 | −0.101557 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.1554 | −0.756953 | −0.378477 | − | 0.925611i | \(-0.623552\pi\) | ||||
−0.378477 | + | 0.925611i | \(0.623552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.3591 | −1.55109 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.2419 | −0.608263 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.0224 | −0.823592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.6217 | −1.51705 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.6795 | −1.03227 | −0.516136 | − | 0.856507i | \(-0.672630\pi\) | ||||
−0.516136 | + | 0.856507i | \(0.672630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.41188 | 0.238791 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.288455 | 0.0107278 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.35235 | −0.273059 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3429 | 0.531948 | 0.265974 | − | 0.963980i | \(-0.414306\pi\) | ||||
0.265974 | + | 0.963980i | \(0.414306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.8462 | −1.54986 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3749 | 0.605647 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.16826 | −0.227830 | −0.113915 | − | 0.993491i | \(-0.536339\pi\) | ||||
−0.113915 | + | 0.993491i | \(0.536339\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.8670 | 0.437720 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.443892 | −0.0163510 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3367 | −0.932024 | −0.466012 | − | 0.884778i | \(-0.654310\pi\) | ||||
−0.466012 | + | 0.884778i | \(0.654310\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 86.4421 | 3.17553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.2435 | 1.21959 | 0.609793 | − | 0.792561i | \(-0.291253\pi\) | ||||
0.609793 | + | 0.792561i | \(0.291253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.9136 | −1.09595 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.4903 | 1.66440 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.31087 | 0.303673 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7548 | 0.465428 | 0.232714 | − | 0.972545i | \(-0.425239\pi\) | ||||
0.232714 | + | 0.972545i | \(0.425239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 74.1587 | 2.70249 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.3367 | 1.21324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4679 | −0.780265 | −0.390133 | − | 0.920759i | \(-0.627571\pi\) | ||||
−0.390133 | + | 0.920759i | \(0.627571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.1554 | 0.368619 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.1458 | −1.45529 | −0.727643 | − | 0.685956i | \(-0.759384\pi\) | ||||
−0.727643 | + | 0.685956i | \(0.759384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1346 | −0.547911 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −94.5161 | −3.41724 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.2627 | −0.984398 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.145844 | 0.00525927 | 0.00262964 | − | 0.999997i | \(-0.499163\pi\) | ||||
0.00262964 | + | 0.999997i | \(0.499163\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.35907 | −0.265030 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.4713 | −0.736301 | −0.368150 | − | 0.929766i | \(-0.620009\pi\) | ||||
−0.368150 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 56.0303 | 2.01267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.5785 | −0.630626 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.1987 | 0.902836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.75476 | 0.170139 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.68913 | 0.131839 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.9758 | −0.570202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.75638 | 0.205193 | 0.102596 | − | 0.994723i | \(-0.467285\pi\) | ||||
0.102596 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −58.0032 | −2.06497 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.8894 | −0.564962 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.1313 | 2.56146 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 98.6250 | 3.49787 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.0432 | 1.17045 | 0.585225 | − | 0.810871i | \(-0.301006\pi\) | ||||
0.585225 | + | 0.810871i | \(0.301006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.1089 | 0.782155 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.0706 | 1.38049 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.41188 | −0.296849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.7772 | 0.520827 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.06402 | −0.283867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.4679 | −1.03604 | −0.518019 | − | 0.855369i | \(-0.673330\pi\) | ||||
−0.518019 | + | 0.855369i | \(0.673330\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.5095 | −0.474384 | −0.237192 | − | 0.971463i | \(-0.576227\pi\) | ||||
−0.237192 | + | 0.971463i | \(0.576227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.7756 | −0.483130 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58.2693 | 2.04108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.1987 | −0.741647 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3221 | 0.954711 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5960 | −0.753705 | −0.376852 | − | 0.926273i | \(-0.622994\pi\) | ||||
−0.376852 | + | 0.926273i | \(0.622994\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.64591 | 0.301377 | 0.150689 | − | 0.988581i | \(-0.451851\pi\) | ||||
0.150689 | + | 0.988581i | \(0.451851\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.0336 | −1.21971 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.1089 | −0.351519 | −0.175760 | − | 0.984433i | \(-0.556238\pi\) | ||||
−0.175760 | + | 0.984433i | \(0.556238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.4663 | 0.710824 | 0.355412 | − | 0.934710i | \(-0.384341\pi\) | ||||
0.355412 | + | 0.934710i | \(0.384341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39.2211 | −1.36056 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.41188 | 0.152863 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −79.4196 | −2.74843 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −28.1138 | −0.971756 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.6795 | −0.955604 | −0.477802 | − | 0.878468i | \(-0.658566\pi\) | ||||
−0.477802 | + | 0.878468i | \(0.658566\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6408 | −0.987614 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 59.7148 | 2.05669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −62.6907 | −2.15663 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.8462 | 0.509520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.8894 | −0.750359 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.1009 | −1.88662 | −0.943309 | − | 0.331915i | \(-0.892305\pi\) | ||||
−0.943309 | + | 0.331915i | \(0.892305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 122.359 | 4.18459 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.5689 | −1.48829 | −0.744143 | − | 0.668020i | \(-0.767142\pi\) | ||||
−0.744143 | + | 0.668020i | \(0.767142\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.45510 | 0.322604 | 0.161302 | − | 0.986905i | \(-0.448431\pi\) | ||||
0.161302 | + | 0.986905i | \(0.448431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.5993 | 0.429384 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.77557 | −0.332764 | −0.166382 | − | 0.986061i | \(-0.553209\pi\) | ||||
−0.166382 | + | 0.986061i | \(0.553209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.2917 | −2.73000 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.03860 | −0.239043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.02242 | −0.272142 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.35248 | −0.0797106 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 71.4903 | 2.41958 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.2003 | −1.02096 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.44551 | 0.116347 | 0.0581733 | − | 0.998307i | \(-0.481472\pi\) | ||||
0.0581733 | + | 0.998307i | \(0.481472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.9966 | 1.72007 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.7805 | −0.396897 | −0.198448 | − | 0.980111i | \(-0.563590\pi\) | ||||
−0.198448 | + | 0.980111i | \(0.563590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0448 | 0.539952 | 0.269976 | − | 0.962867i | \(-0.412984\pi\) | ||||
0.269976 | + | 0.962867i | \(0.412984\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −61.0465 | −2.05205 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.2885 | 1.55421 | 0.777107 | − | 0.629368i | \(-0.216686\pi\) | ||||
0.777107 | + | 0.629368i | \(0.216686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.1122 | 0.506847 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.11222 | 0.0707619 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.6217 | −0.957790 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.9758 | −0.935129 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 53.8204 | 1.79701 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.73732 | −0.0912948 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.6666 | 1.22154 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.5993 | −0.352724 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.7581 | 1.05568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.37489 | −0.278084 | −0.139042 | − | 0.990286i | \(-0.544402\pi\) | ||||
−0.139042 | + | 0.990286i | \(0.544402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.9214 | −0.461744 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2469 | −1.20091 | −0.600456 | − | 0.799658i | \(-0.705014\pi\) | ||||
−0.600456 | + | 0.799658i | \(0.705014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.82376 | 0.292024 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 161.516 | 5.33955 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.68913 | −0.121826 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.60269 | 0.184816 | 0.0924078 | − | 0.995721i | \(-0.470544\pi\) | ||||
0.0924078 | + | 0.995721i | \(0.470544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 93.1603 | 3.06974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.1987 | 0.829424 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 75.5128 | 2.48284 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.0560 | 1.08570 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.7980 | 0.846404 | 0.423202 | − | 0.906035i | \(-0.360906\pi\) | ||||
0.423202 | + | 0.906035i | \(0.360906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.71155 | −0.187188 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 71.5544 | 2.34258 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.3333 | −0.599563 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.8124 | 1.98666 | 0.993328 | − | 0.115326i | \(-0.0367913\pi\) | ||||
0.993328 | + | 0.115326i | \(0.0367913\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.7996 | 1.85358 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.2771 | 1.37819 | 0.689097 | − | 0.724669i | \(-0.258007\pi\) | ||||
0.689097 | + | 0.724669i | \(0.258007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6891 | 0.510908 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 25.5785 | 0.832070 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.4405 | −0.956689 | −0.478344 | − | 0.878172i | \(-0.658763\pi\) | ||||
−0.478344 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.5801 | −1.44713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.8254 | 0.837445 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.5801 | −0.796229 | −0.398114 | − | 0.917336i | \(-0.630335\pi\) | ||||
−0.398114 | + | 0.917336i | \(0.630335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.66497 | 0.248032 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.71155 | 0.0553264 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.04322 | 0.0982707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.1396 | −0.327084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.8462 | 1.38070 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.7597 | 1.95593 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6442 | −0.406609 | −0.203304 | − | 0.979116i | \(-0.565168\pi\) | ||||
−0.203304 | + | 0.979116i | \(0.565168\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 71.9616 | 2.31174 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.6795 | −1.27338 | −0.636688 | − | 0.771121i | \(-0.719696\pi\) | ||||
−0.636688 | + | 0.771121i | \(0.719696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.9102 | 0.349765 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −185.666 | −5.94609 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1745 | 1.50925 | 0.754623 | − | 0.656159i | \(-0.227820\pi\) | ||||
0.754623 | + | 0.656159i | \(0.227820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.57853 | 0.242211 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −78.0257 | −2.49117 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.6795 | −1.64832 | −0.824161 | − | 0.566356i | \(-0.808353\pi\) | ||||
−0.824161 | + | 0.566356i | \(0.808353\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.9326 | 0.794419 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.3109 | −0.455520 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.1987 | −0.419693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.2211 | 1.75416 | 0.877078 | − | 0.480349i | \(-0.159490\pi\) | ||||
0.877078 | + | 0.480349i | \(0.159490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −85.3573 | −2.70873 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.4264 | 1.34501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5432 | −1.47404 | −0.737018 | − | 0.675873i | \(-0.763767\pi\) | ||||
−0.737018 | + | 0.675873i | \(0.763767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.8894 | −1.19877 |
(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 | 308.2.a.c.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 2772.2.a.s.1.3 | 3 | |||
4.3 | odd | 2 | 1232.2.a.r.1.3 | 3 | |||
5.2 | odd | 4 | 7700.2.e.p.1849.6 | 6 | |||
5.3 | odd | 4 | 7700.2.e.p.1849.1 | 6 | |||
5.4 | even | 2 | 7700.2.a.y.1.3 | 3 | |||
7.2 | even | 3 | 2156.2.i.m.1145.3 | 6 | |||
7.3 | odd | 6 | 2156.2.i.k.177.1 | 6 | |||
7.4 | even | 3 | 2156.2.i.m.177.3 | 6 | |||
7.5 | odd | 6 | 2156.2.i.k.1145.1 | 6 | |||
7.6 | odd | 2 | 2156.2.a.j.1.3 | 3 | |||
8.3 | odd | 2 | 4928.2.a.bx.1.1 | 3 | |||
8.5 | even | 2 | 4928.2.a.ca.1.3 | 3 | |||
11.10 | odd | 2 | 3388.2.a.o.1.1 | 3 | |||
28.27 | even | 2 | 8624.2.a.cj.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.a.c.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1232.2.a.r.1.3 | 3 | 4.3 | odd | 2 | |||
2156.2.a.j.1.3 | 3 | 7.6 | odd | 2 | |||
2156.2.i.k.177.1 | 6 | 7.3 | odd | 6 | |||
2156.2.i.k.1145.1 | 6 | 7.5 | odd | 6 | |||
2156.2.i.m.177.3 | 6 | 7.4 | even | 3 | |||
2156.2.i.m.1145.3 | 6 | 7.2 | even | 3 | |||
2772.2.a.s.1.3 | 3 | 3.2 | odd | 2 | |||
3388.2.a.o.1.1 | 3 | 11.10 | odd | 2 | |||
4928.2.a.bx.1.1 | 3 | 8.3 | odd | 2 | |||
4928.2.a.ca.1.3 | 3 | 8.5 | even | 2 | |||
7700.2.a.y.1.3 | 3 | 5.4 | even | 2 | |||
7700.2.e.p.1849.1 | 6 | 5.3 | odd | 4 | |||
7700.2.e.p.1849.6 | 6 | 5.2 | odd | 4 | |||
8624.2.a.cj.1.1 | 3 | 28.27 | even | 2 |