Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, 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("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.52892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 | ||||||||
\(5\) | 0.133492 | 0.0596994 | 0.0298497 | − | 0.999554i | \(-0.490497\pi\) | ||||
0.0298497 | + | 0.999554i | \(0.490497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.92434 | −1.48326 | −0.741631 | − | 0.670808i | \(-0.765948\pi\) | ||||
−0.741631 | + | 0.670808i | \(0.765948\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.05784 | −1.52499 | −0.762497 | − | 0.646991i | \(-0.776027\pi\) | ||||
−0.762497 | + | 0.646991i | \(0.776027\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.133492 | −0.0344675 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.92434 | −1.19433 | −0.597164 | − | 0.802119i | \(-0.703706\pi\) | ||||
−0.597164 | + | 0.802119i | \(0.703706\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.79085 | 1.55793 | 0.778964 | − | 0.627068i | \(-0.215745\pi\) | ||||
0.778964 | + | 0.627068i | \(0.215745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.92434 | 0.856362 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.05784 | −1.05463 | −0.527316 | − | 0.849669i | \(-0.676802\pi\) | ||||
−0.527316 | + | 0.849669i | \(0.676802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98218 | −0.996436 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.86651 | −0.717993 | −0.358996 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358996 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.13349 | 0.203581 | 0.101791 | − | 0.994806i | \(-0.467543\pi\) | ||||
0.101791 | + | 0.994806i | \(0.467543\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.05784 | 0.880456 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.523868 | −0.0885499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92434 | 1.13836 | 0.569178 | − | 0.822215i | \(-0.307262\pi\) | ||||
0.569178 | + | 0.822215i | \(0.307262\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.19133 | 0.810749 | 0.405375 | − | 0.914151i | \(-0.367141\pi\) | ||||
0.405375 | + | 0.914151i | \(0.367141\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9243 | −1.81845 | −0.909223 | − | 0.416310i | \(-0.863323\pi\) | ||||
−0.909223 | + | 0.416310i | \(0.863323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.133492 | 0.0198998 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.05784 | −1.32122 | −0.660611 | − | 0.750729i | \(-0.729703\pi\) | ||||
−0.660611 | + | 0.750729i | \(0.729703\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.40048 | 1.20007 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.92434 | 0.689546 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.59952 | −0.219712 | −0.109856 | − | 0.993948i | \(-0.535039\pi\) | ||||
−0.109856 | + | 0.993948i | \(0.535039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.675180 | −0.0910413 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.79085 | −0.899470 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.8487 | 1.54257 | 0.771284 | − | 0.636491i | \(-0.219615\pi\) | ||||
0.771284 | + | 0.636491i | \(0.219615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.79085 | 0.741443 | 0.370721 | − | 0.928744i | \(-0.379111\pi\) | ||||
0.370721 | + | 0.928744i | \(0.379111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.92434 | −0.494421 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.07566 | 0.497921 | 0.248960 | − | 0.968514i | \(-0.419911\pi\) | ||||
0.248960 | + | 0.968514i | \(0.419911\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.05784 | 0.608892 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.05784 | −0.125542 | −0.0627710 | − | 0.998028i | \(-0.519994\pi\) | ||||
−0.0627710 | + | 0.998028i | \(0.519994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.26698 | −0.382372 | −0.191186 | − | 0.981554i | \(-0.561233\pi\) | ||||
−0.191186 | + | 0.981554i | \(0.561233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.98218 | 0.575293 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.8487 | 2.26197 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.24916 | −0.815595 | −0.407797 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407797 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3248 | −1.24306 | −0.621530 | − | 0.783390i | \(-0.713489\pi\) | ||||
−0.621530 | + | 0.783390i | \(0.713489\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.657360 | −0.0713007 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.86651 | 0.414533 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.73302 | 0.819698 | 0.409849 | − | 0.912153i | \(-0.365581\pi\) | ||||
0.409849 | + | 0.912153i | \(0.365581\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.13349 | −0.117538 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.906524 | 0.0930074 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.13349 | 0.724296 | 0.362148 | − | 0.932121i | \(-0.382043\pi\) | ||||
0.362148 | + | 0.932121i | \(0.382043\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.05784 | −0.508332 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.71520 | 0.568683 | 0.284342 | − | 0.958723i | \(-0.408225\pi\) | ||||
0.284342 | + | 0.958723i | \(0.408225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.19133 | 0.610050 | 0.305025 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305025 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.523868 | 0.0511243 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.05784 | −0.875654 | −0.437827 | − | 0.899059i | \(-0.644252\pi\) | ||||
−0.437827 | + | 0.899059i | \(0.644252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7152 | 1.21789 | 0.608947 | − | 0.793211i | \(-0.291592\pi\) | ||||
0.608947 | + | 0.793211i | \(0.291592\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92434 | −0.657230 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.9243 | 1.78025 | 0.890126 | − | 0.455714i | \(-0.150616\pi\) | ||||
0.890126 | + | 0.455714i | \(0.150616\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.675180 | −0.0629609 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.3248 | 1.77150 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.5817 | 1.32561 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.19133 | −0.468086 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.33254 | −0.119186 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.24916 | −0.643259 | −0.321630 | − | 0.946866i | \(-0.604231\pi\) | ||||
−0.321630 | + | 0.946866i | \(0.604231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.9243 | 1.04988 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.96436 | 0.870590 | 0.435295 | − | 0.900288i | \(-0.356644\pi\) | ||||
0.435295 | + | 0.900288i | \(0.356644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −26.6496 | −2.31082 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.133492 | −0.0114892 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.45831 | −0.808078 | −0.404039 | − | 0.914742i | \(-0.632394\pi\) | ||||
−0.404039 | + | 0.914742i | \(0.632394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.40048 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.05784 | 0.762807 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.516148 | −0.0428637 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.40048 | −0.692860 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.71520 | −0.304361 | −0.152180 | − | 0.988353i | \(-0.548629\pi\) | ||||
−0.152180 | + | 0.988353i | \(0.548629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.32482 | 0.270570 | 0.135285 | − | 0.990807i | \(-0.456805\pi\) | ||||
0.135285 | + | 0.990807i | \(0.456805\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.92434 | −0.398110 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.151312 | 0.0121537 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.32482 | 0.185541 | 0.0927704 | − | 0.995688i | \(-0.470428\pi\) | ||||
0.0927704 | + | 0.995688i | \(0.470428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.59952 | 0.126851 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.8487 | 1.56430 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.86651 | 0.537826 | 0.268913 | − | 0.963164i | \(-0.413336\pi\) | ||||
0.268913 | + | 0.963164i | \(0.413336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.675180 | 0.0525627 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.8130 | 1.68794 | 0.843972 | − | 0.536387i | \(-0.180211\pi\) | ||||
0.843972 | + | 0.536387i | \(0.180211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.79085 | 0.519309 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.58170 | −0.272312 | −0.136156 | − | 0.990687i | \(-0.543475\pi\) | ||||
−0.136156 | + | 0.990687i | \(0.543475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.5518 | 1.47798 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.8487 | −0.890602 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.20915 | −0.0903760 | −0.0451880 | − | 0.998979i | \(-0.514389\pi\) | ||||
−0.0451880 | + | 0.998979i | \(0.514389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.9243 | 1.40664 | 0.703318 | − | 0.710876i | \(-0.251701\pi\) | ||||
0.703318 | + | 0.710876i | \(0.251701\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.79085 | −0.428072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.924344 | 0.0679591 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.9065 | 1.82135 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.92434 | 0.285454 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.84869 | 0.567911 | 0.283956 | − | 0.958837i | \(-0.408353\pi\) | ||||
0.283956 | + | 0.958837i | \(0.408353\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.11567 | −0.512197 | −0.256099 | − | 0.966651i | \(-0.582437\pi\) | ||||
−0.256099 | + | 0.966651i | \(0.582437\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.4304 | −1.66935 | −0.834673 | − | 0.550746i | \(-0.814343\pi\) | ||||
−0.834673 | + | 0.550746i | \(0.814343\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6574 | −0.968145 | −0.484072 | − | 0.875028i | \(-0.660843\pi\) | ||||
−0.484072 | + | 0.875028i | \(0.660843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.07566 | −0.287475 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.1735 | 1.06497 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.693000 | 0.0484012 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.05784 | −0.351544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.3470 | −2.37583 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.2492 | −1.32517 | −0.662584 | − | 0.748988i | \(-0.730540\pi\) | ||||
−0.662584 | + | 0.748988i | \(0.730540\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.05784 | 0.0724817 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.59180 | −0.108560 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.44821 | −0.301964 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.26698 | 0.220762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.98218 | −0.332145 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0222 | 1.52804 | 0.764018 | − | 0.645194i | \(-0.223224\pi\) | ||||
0.764018 | + | 0.645194i | \(0.223224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.11567 | −0.536299 | −0.268149 | − | 0.963377i | \(-0.586412\pi\) | ||||
−0.268149 | + | 0.963377i | \(0.586412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.8487 | −1.30595 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.53397 | 0.428054 | 0.214027 | − | 0.976828i | \(-0.431342\pi\) | ||||
0.214027 | + | 0.976828i | \(0.431342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.20915 | −0.0788761 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.24916 | 0.470884 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3248 | −0.732542 | −0.366271 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366271 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5995 | 0.747191 | 0.373596 | − | 0.927592i | \(-0.378125\pi\) | ||||
0.373596 | + | 0.927592i | \(0.378125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.12140 | 0.0716433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.3248 | 0.717681 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1157 | −0.638496 | −0.319248 | − | 0.947671i | \(-0.603430\pi\) | ||||
−0.319248 | + | 0.947671i | \(0.603430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.5817 | 1.60831 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.657360 | 0.0411655 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.19133 | 0.0743130 | 0.0371565 | − | 0.999309i | \(-0.488170\pi\) | ||||
0.0371565 | + | 0.999309i | \(0.488170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.1735 | −1.68848 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.86651 | −0.239331 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.9065 | 1.28915 | 0.644576 | − | 0.764540i | \(-0.277034\pi\) | ||||
0.644576 | + | 0.764540i | \(0.277034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.213524 | −0.0131166 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.73302 | −0.473253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.84869 | −0.356601 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.0979 | −1.40309 | −0.701547 | − | 0.712623i | \(-0.747507\pi\) | ||||
−0.701547 | + | 0.712623i | \(0.747507\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.1990 | 1.51956 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.80867 | 0.288925 | 0.144463 | − | 0.989510i | \(-0.453855\pi\) | ||||
0.144463 | + | 0.989510i | \(0.453855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.13349 | 0.0678604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.60962 | −0.334642 | −0.167321 | − | 0.985902i | \(-0.553512\pi\) | ||||
−0.167321 | + | 0.985902i | \(0.553512\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8887 | 1.53892 | 0.769462 | − | 0.638693i | \(-0.220525\pi\) | ||||
0.769462 | + | 0.638693i | \(0.220525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.906524 | −0.0536978 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.3726 | −1.20255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24916 | 0.426421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.13349 | −0.418173 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.4482 | −1.48670 | −0.743350 | − | 0.668902i | \(-0.766764\pi\) | ||||
−0.743350 | + | 0.668902i | \(0.766764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.58170 | 0.0920904 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.05784 | 0.293485 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 46.7952 | 2.69723 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.71520 | −0.328329 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.773032 | 0.0442637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.458312 | −0.0261572 | −0.0130786 | − | 0.999914i | \(-0.504163\pi\) | ||||
−0.0130786 | + | 0.999914i | \(0.504163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.19133 | −0.352212 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.7909 | 1.29235 | 0.646175 | − | 0.763189i | \(-0.276367\pi\) | ||||
0.646175 | + | 0.763189i | \(0.276367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.5639 | 1.61453 | 0.807263 | − | 0.590192i | \(-0.200948\pi\) | ||||
0.807263 | + | 0.590192i | \(0.200948\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.523868 | −0.0295166 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.9465 | −1.34497 | −0.672486 | − | 0.740110i | \(-0.734773\pi\) | ||||
−0.672486 | + | 0.740110i | \(0.734773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.5562 | 1.09493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.05784 | 0.505559 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.4405 | −1.86068 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.7152 | −0.703152 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 35.5461 | 1.95972 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.1335 | 1.38146 | 0.690731 | − | 0.723112i | \(-0.257289\pi\) | ||||
0.690731 | + | 0.723112i | \(0.257289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.92434 | 0.379452 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.544067 | 0.0297256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9644 | 1.57779 | 0.788895 | − | 0.614529i | \(-0.210654\pi\) | ||||
0.788895 | + | 0.614529i | \(0.210654\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.9243 | −1.02783 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.73302 | −0.310460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.49595 | −0.296753 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.675180 | 0.0363505 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.67518 | 0.250977 | 0.125488 | − | 0.992095i | \(-0.459950\pi\) | ||||
0.125488 | + | 0.992095i | \(0.459950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.5161 | 1.47291 | 0.736453 | − | 0.676489i | \(-0.236499\pi\) | ||||
0.736453 | + | 0.676489i | \(0.236499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5060 | 0.665630 | 0.332815 | − | 0.942992i | \(-0.392002\pi\) | ||||
0.332815 | + | 0.942992i | \(0.392002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.141213 | −0.00749478 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.3248 | −1.02278 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.7909 | 0.569519 | 0.284760 | − | 0.958599i | \(-0.408086\pi\) | ||||
0.284760 | + | 0.958599i | \(0.408086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.1157 | 1.42714 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5817 | −0.765341 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.436116 | −0.0228274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.92434 | 0.413647 | 0.206824 | − | 0.978378i | \(-0.433687\pi\) | ||||
0.206824 | + | 0.978378i | \(0.433687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.19133 | 0.270250 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.27708 | 0.325890 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.3726 | −1.72797 | −0.863983 | − | 0.503521i | \(-0.832037\pi\) | ||||
−0.863983 | + | 0.503521i | \(0.832037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.33254 | 0.0688121 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0501 | 0.721706 | 0.360853 | − | 0.932623i | \(-0.382486\pi\) | ||||
0.360853 | + | 0.932623i | \(0.382486\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.24916 | 0.371386 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2313 | −0.624992 | −0.312496 | − | 0.949919i | \(-0.601165\pi\) | ||||
−0.312496 | + | 0.949919i | \(0.601165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.64964 | 0.135038 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.9243 | −0.606148 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.4805 | −1.44402 | −0.722010 | − | 0.691883i | \(-0.756781\pi\) | ||||
−0.722010 | + | 0.691883i | \(0.756781\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9065 | 1.25958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.96436 | −0.502635 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.967705 | −0.0486905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.2135 | 1.36581 | 0.682904 | − | 0.730508i | \(-0.260717\pi\) | ||||
0.682904 | + | 0.730508i | \(0.260717\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.6496 | 1.33415 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2391 | 0.910815 | 0.455408 | − | 0.890283i | \(-0.349494\pi\) | ||||
0.455408 | + | 0.890283i | \(0.349494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.133492 | 0.00663327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.0222 | −1.73599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.0323 | −1.38611 | −0.693054 | − | 0.720886i | \(-0.743735\pi\) | ||||
−0.693054 | + | 0.720886i | \(0.743735\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.45831 | 0.466544 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −46.4983 | −2.28803 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.51177 | −0.0742100 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.40048 | 0.166522 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.6974 | −0.766867 | −0.383433 | − | 0.923568i | \(-0.625258\pi\) | ||||
−0.383433 | + | 0.923568i | \(0.625258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5239 | 0.561639 | 0.280819 | − | 0.959761i | \(-0.409394\pi\) | ||||
0.280819 | + | 0.959761i | \(0.409394\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.05784 | −0.440407 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.5340 | 1.19007 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.7253 | −1.09975 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.3248 | −1.12352 | −0.561759 | − | 0.827301i | \(-0.689875\pi\) | ||||
−0.561759 | + | 0.827301i | \(0.689875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.23134 | −0.251402 | −0.125701 | − | 0.992068i | \(-0.540118\pi\) | ||||
−0.125701 | + | 0.992068i | \(0.540118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.516148 | 0.0247474 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.3470 | −1.64304 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7730 | 1.13462 | 0.567312 | − | 0.823503i | \(-0.307983\pi\) | ||||
0.567312 | + | 0.823503i | \(0.307983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.40048 | 0.400023 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.1157 | −0.480610 | −0.240305 | − | 0.970697i | \(-0.577247\pi\) | ||||
−0.240305 | + | 0.970697i | \(0.577247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03230 | 0.0489355 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.71520 | 0.175723 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.53397 | 0.308357 | 0.154179 | − | 0.988043i | \(-0.450727\pi\) | ||||
0.154179 | + | 0.988043i | \(0.450727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.2569 | −1.23639 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.32482 | −0.156214 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.0800 | −1.54742 | −0.773709 | − | 0.633541i | \(-0.781601\pi\) | ||||
−0.773709 | + | 0.633541i | \(0.781601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.92434 | 0.229849 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.551788 | −0.0256993 | −0.0128497 | − | 0.999917i | \(-0.504090\pi\) | ||||
−0.0128497 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.34264 | 0.108872 | 0.0544359 | − | 0.998517i | \(-0.482664\pi\) | ||||
0.0544359 | + | 0.998517i | \(0.482664\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.151312 | −0.00701693 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.1735 | 0.702146 | 0.351073 | − | 0.936348i | \(-0.385817\pi\) | ||||
0.351073 | + | 0.936348i | \(0.385817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.9943 | −0.738547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.32482 | −0.107122 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 60.3114 | 2.77312 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.8332 | −1.55238 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.59952 | −0.0732372 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.58170 | −0.0722699 | −0.0361350 | − | 0.999347i | \(-0.511505\pi\) | ||||
−0.0361350 | + | 0.999347i | \(0.511505\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.8487 | −0.903147 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.952264 | 0.0432401 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.2091 | 0.779821 | 0.389910 | − | 0.920853i | \(-0.372506\pi\) | ||||
0.389910 | + | 0.920853i | \(0.372506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.86651 | −0.310514 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7075 | −1.06990 | −0.534952 | − | 0.844883i | \(-0.679670\pi\) | ||||
−0.534952 | + | 0.844883i | \(0.679670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.0400 | 0.857519 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.675180 | −0.0303471 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.15131 | 0.186212 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.11567 | −0.273775 | −0.136888 | − | 0.990587i | \(-0.543710\pi\) | ||||
−0.136888 | + | 0.990587i | \(0.543710\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.8130 | −0.974535 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.7075 | −1.59212 | −0.796059 | − | 0.605219i | \(-0.793085\pi\) | ||||
−0.796059 | + | 0.605219i | \(0.793085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.762933 | 0.0339501 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.2135 | −1.51649 | −0.758244 | − | 0.651971i | \(-0.773942\pi\) | ||||
−0.758244 | + | 0.651971i | \(0.773942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8208 | 0.567157 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.79085 | −0.299823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.826492 | 0.0364196 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.8130 | 2.01486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.58170 | 0.157219 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4704 | 1.68542 | 0.842710 | − | 0.538368i | \(-0.180959\pi\) | ||||
0.842710 | + | 0.538368i | \(0.180959\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.44049 | 0.237896 | 0.118948 | − | 0.992900i | \(-0.462048\pi\) | ||||
0.118948 | + | 0.992900i | \(0.462048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.5518 | −0.853310 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.58170 | −0.243143 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.58170 | 0.112248 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.8487 | 0.514189 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.20915 | −0.0522760 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.20915 | 0.0521786 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −42.4882 | −1.83010 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.3369 | 1.60524 | 0.802620 | − | 0.596491i | \(-0.203439\pi\) | ||||
0.802620 | + | 0.596491i | \(0.203439\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9243 | −0.812121 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.69738 | 0.0727076 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2391 | −0.822603 | −0.411301 | − | 0.911499i | \(-0.634926\pi\) | ||||
−0.411301 | + | 0.911499i | \(0.634926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.79085 | 0.247148 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.2569 | −1.11858 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.4482 | 1.20974 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.924344 | −0.0392362 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.7952 | 1.77092 | 0.885460 | − | 0.464715i | \(-0.153843\pi\) | ||||
0.885460 | + | 0.464715i | \(0.153843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.9065 | −1.05155 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.0121 | 1.30700 | 0.653502 | − | 0.756925i | \(-0.273299\pi\) | ||||
0.653502 | + | 0.756925i | \(0.273299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.52625 | 0.106280 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.92434 | −0.164807 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.8130 | −1.50136 | −0.750681 | − | 0.660665i | \(-0.770274\pi\) | ||||
−0.750681 | + | 0.660665i | \(0.770274\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.2091 | −1.05497 | −0.527485 | − | 0.849564i | \(-0.676865\pi\) | ||||
−0.527485 | + | 0.849564i | \(0.676865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.84869 | −0.327884 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.1990 | 1.05087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.8988 | 1.53612 | 0.768059 | − | 0.640380i | \(-0.221223\pi\) | ||||
0.768059 | + | 0.640380i | \(0.221223\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.11567 | 0.295717 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.4425 | 1.84379 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.09013 | 0.335059 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.26698 | 0.0935684 | 0.0467842 | − | 0.998905i | \(-0.485103\pi\) | ||||
0.0467842 | + | 0.998905i | \(0.485103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.69738 | 0.317165 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.4304 | 0.963798 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.49395 | −0.143479 | −0.0717397 | − | 0.997423i | \(-0.522855\pi\) | ||||
−0.0717397 | + | 0.997423i | \(0.522855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.57971 | 0.105758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.6574 | 0.558959 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.1990 | 0.702734 | 0.351367 | − | 0.936238i | \(-0.385717\pi\) | ||||
0.351367 | + | 0.936238i | \(0.385717\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.51615 | −0.102636 | −0.0513179 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513179 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.07566 | 0.165974 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.94654 | 0.0791381 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.04774 | −0.204881 | −0.102441 | − | 0.994739i | \(-0.532665\pi\) | ||||
−0.102441 | + | 0.994739i | \(0.532665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1735 | −0.614862 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.25688 | −0.131544 | −0.0657722 | − | 0.997835i | \(-0.520951\pi\) | ||||
−0.0657722 | + | 0.997835i | \(0.520951\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.693000 | −0.0279445 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.2391 | −0.975828 | −0.487914 | − | 0.872892i | \(-0.662242\pi\) | ||||
−0.487914 | + | 0.872892i | \(0.662242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.90215 | 0.357808 | 0.178904 | − | 0.983867i | \(-0.442745\pi\) | ||||
0.178904 | + | 0.983867i | \(0.442745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.05784 | 0.202964 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.3470 | −1.21583 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7330 | 0.989321 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 34.3470 | 1.37169 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.0979 | −1.35957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2969 | −0.808007 | −0.404003 | − | 0.914757i | \(-0.632382\pi\) | ||||
−0.404003 | + | 0.914757i | \(0.632382\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.2492 | 0.765086 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.967705 | −0.0384022 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.05784 | −0.0418473 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.7253 | −0.621112 | −0.310556 | − | 0.950555i | \(-0.600515\pi\) | ||||
−0.310556 | + | 0.950555i | \(0.600515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.66746 | −0.0657582 | −0.0328791 | − | 0.999459i | \(-0.510468\pi\) | ||||
−0.0328791 | + | 0.999459i | \(0.510468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.59180 | 0.0626772 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.4304 | 1.47154 | 0.735770 | − | 0.677231i | \(-0.236820\pi\) | ||||
0.735770 | + | 0.677231i | \(0.236820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −59.9287 | −2.35241 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44821 | 0.174339 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −46.6140 | −1.82415 | −0.912073 | − | 0.410027i | \(-0.865519\pi\) | ||||
−0.912073 | + | 0.410027i | \(0.865519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.33016 | 0.0519737 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.26698 | −0.127457 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.46603 | 0.135017 | 0.0675087 | − | 0.997719i | \(-0.478495\pi\) | ||||
0.0675087 | + | 0.997719i | \(0.478495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.9543 | −0.737235 | −0.368618 | − | 0.929581i | \(-0.620169\pi\) | ||||
−0.368618 | + | 0.929581i | \(0.620169\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.55751 | −0.137954 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5562 | 0.757218 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0000 | −0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.2892 | −1.13070 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.9321 | 0.537042 | 0.268521 | − | 0.963274i | \(-0.413465\pi\) | ||||
0.268521 | + | 0.963274i | \(0.413465\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.98218 | 0.191764 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.68528 | −0.103204 | −0.0516018 | − | 0.998668i | \(-0.516433\pi\) | ||||
−0.0516018 | + | 0.998668i | \(0.516433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.9943 | −1.07432 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0222 | −0.882212 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.26698 | 0.0867437 | 0.0433719 | − | 0.999059i | \(-0.486190\pi\) | ||||
0.0433719 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.26261 | −0.0482418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.11567 | 0.309632 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49395 | −0.0948744 | −0.0474372 | − | 0.998874i | \(-0.515105\pi\) | ||||
−0.0474372 | + | 0.998874i | \(0.515105\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.8487 | 0.753989 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.453936 | −0.0172188 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.5639 | −0.968301 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.53397 | −0.247137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.8487 | −1.42953 | −0.714763 | − | 0.699367i | \(-0.753465\pi\) | ||||
−0.714763 | + | 0.699367i | \(0.753465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.0222 | 1.77348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.20915 | 0.0455391 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.4284 | −0.843507 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4049 | −0.616097 | −0.308049 | − | 0.951371i | \(-0.599676\pi\) | ||||
−0.308049 | + | 0.951371i | \(0.599676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.24916 | −0.271865 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.73302 | −0.214703 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.3248 | 0.422933 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0800 | −0.599684 | −0.299842 | − | 0.953989i | \(-0.596934\pi\) | ||||
−0.299842 | + | 0.953989i | \(0.596934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.2969 | −0.904864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.5995 | −0.431391 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.2636 | 0.715434 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.6695 | −1.65670 | −0.828349 | − | 0.560212i | \(-0.810720\pi\) | ||||
−0.828349 | + | 0.560212i | \(0.810720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.7196 | 2.17182 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9422 | −1.03207 | −0.516034 | − | 0.856568i | \(-0.672592\pi\) | ||||
−0.516034 | + | 0.856568i | \(0.672592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.12140 | −0.0413633 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.6140 | −0.759326 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.4660 | 0.421785 | 0.210892 | − | 0.977509i | \(-0.432363\pi\) | ||||
0.210892 | + | 0.977509i | \(0.432363\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.3147 | −0.708588 | −0.354294 | − | 0.935134i | \(-0.615279\pi\) | ||||
−0.354294 | + | 0.935134i | \(0.615279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.495949 | −0.0181702 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.3248 | −0.414353 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.5461 | 1.29882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.97446 | −0.363973 | −0.181987 | − | 0.983301i | \(-0.558253\pi\) | ||||
−0.181987 | + | 0.983301i | \(0.558253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1157 | 0.368636 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.443837 | 0.0161529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2313 | −0.808012 | −0.404006 | − | 0.914756i | \(-0.632383\pi\) | ||||
−0.404006 | + | 0.914756i | \(0.632383\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.5817 | −0.928557 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.26698 | −0.299678 | −0.149839 | − | 0.988710i | \(-0.547876\pi\) | ||||
−0.149839 | + | 0.988710i | \(0.547876\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −49.8988 | −1.80646 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.657360 | −0.0237669 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5138 | −0.523380 | −0.261690 | − | 0.965152i | \(-0.584280\pi\) | ||||
−0.261690 | + | 0.965152i | \(0.584280\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.19133 | −0.0429046 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.1157 | −0.867380 | −0.433690 | − | 0.901062i | \(-0.642789\pi\) | ||||
−0.433690 | + | 0.901062i | \(0.642789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.64726 | −0.202856 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.1735 | 0.974844 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.2535 | 1.26309 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.35036 | 0.191451 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.86651 | 0.138178 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.310345 | 0.0110767 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.0979 | 1.25110 | 0.625552 | − | 0.780183i | \(-0.284874\pi\) | ||||
0.625552 | + | 0.780183i | \(0.284874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9065 | −0.744292 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −74.2656 | −2.64058 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.213524 | 0.00757290 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.0323 | −1.59513 | −0.797563 | − | 0.603236i | \(-0.793878\pi\) | ||||
−0.797563 | + | 0.603236i | \(0.793878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.6039 | 1.57797 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.73302 | 0.273233 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.5239 | 0.583115 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.64964 | 0.0933875 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.84869 | 0.205884 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.8208 | 1.68129 | 0.840644 | − | 0.541588i | \(-0.182177\pi\) | ||||
0.840644 | + | 0.541588i | \(0.182177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.56388 | −0.230489 | −0.115245 | − | 0.993337i | \(-0.536765\pi\) | ||||
−0.115245 | + | 0.993337i | \(0.536765\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.0979 | 0.810077 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.916623 | 0.0321079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −80.9765 | −2.83301 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.81305 | 0.133076 | 0.0665381 | − | 0.997784i | \(-0.478805\pi\) | ||||
0.0665381 | + | 0.997784i | \(0.478805\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3470 | −0.360674 | −0.180337 | − | 0.983605i | \(-0.557719\pi\) | ||||
−0.180337 | + | 0.983605i | \(0.557719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.1990 | −0.877318 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.6496 | 1.20489 | 0.602443 | − | 0.798162i | \(-0.294194\pi\) | ||||
0.602443 | + | 0.798162i | \(0.294194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.1056 | −0.524638 | −0.262319 | − | 0.964981i | \(-0.584487\pi\) | ||||
−0.262319 | + | 0.964981i | \(0.584487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.80867 | −0.166811 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −41.3668 | −1.43328 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.91187 | 0.100769 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.13349 | −0.0391792 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.8964 | 1.55000 | 0.774998 | − | 0.631963i | \(-0.217751\pi\) | ||||
0.774998 | + | 0.631963i | \(0.217751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0501 | −0.484487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.60962 | 0.193206 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −57.2236 | −1.96623 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.8887 | −0.888498 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.0222 | −1.20055 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.9543 | −0.648982 | −0.324491 | − | 0.945889i | \(-0.605193\pi\) | ||||
−0.324491 | + | 0.945889i | \(0.605193\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.906524 | 0.0310025 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.2391 | −0.827991 | −0.413995 | − | 0.910279i | \(-0.635867\pi\) | ||||
−0.413995 | + | 0.910279i | \(0.635867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.1913 | 0.484202 | 0.242101 | − | 0.970251i | \(-0.422163\pi\) | ||||
0.242101 | + | 0.970251i | \(0.422163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.3726 | 0.694295 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.7075 | −1.07934 | −0.539668 | − | 0.841878i | \(-0.681450\pi\) | ||||
−0.539668 | + | 0.841878i | \(0.681450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.478129 | −0.0162569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.24916 | −0.246195 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.6651 | 1.24378 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.13349 | 0.241432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.22935 | 0.176784 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.7374 | 1.37560 | 0.687802 | − | 0.725898i | \(-0.258576\pi\) | ||||
0.687802 | + | 0.725898i | \(0.258576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.4482 | 0.858347 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3904 | −0.686969 | −0.343485 | − | 0.939158i | \(-0.611607\pi\) | ||||
−0.343485 | + | 0.939158i | \(0.611607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.93444 | −0.132405 | −0.0662023 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662023 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.58170 | −0.0531684 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.3147 | −0.514218 | −0.257109 | − | 0.966382i | \(-0.582770\pi\) | ||||
−0.257109 | + | 0.966382i | \(0.582770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.4482 | 0.954122 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.05784 | −0.169444 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.5104 | −2.05837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.161411 | −0.00539539 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.38266 | −0.146170 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.87661 | 0.262408 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −46.7952 | −1.55725 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.52625 | 0.0839753 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.5784 | −1.67943 | −0.839713 | − | 0.543030i | \(-0.817277\pi\) | ||||
−0.839713 | + | 0.543030i | \(0.817277\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.71520 | 0.189561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3470 | 0.342812 | 0.171406 | − | 0.985200i | \(-0.445169\pi\) | ||||
0.171406 | + | 0.985200i | \(0.445169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.2791 | 1.89566 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.773032 | −0.0255556 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.1036 | −1.29131 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.95226 | 0.0973862 | 0.0486931 | − | 0.998814i | \(-0.484494\pi\) | ||||
0.0486931 | + | 0.998814i | \(0.484494\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.458312 | 0.0151019 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.4983 | −1.13430 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.19133 | 0.203350 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.35474 | 0.274110 | 0.137055 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137055 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57.0464 | 1.86962 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.7909 | −0.746139 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.32482 | 0.108733 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3648 | 0.665290 | 0.332645 | − | 0.943052i | \(-0.392059\pi\) | ||||
0.332645 | + | 0.943052i | \(0.392059\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.5639 | −0.932147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.5138 | −0.342739 | −0.171370 | − | 0.985207i | \(-0.554819\pi\) | ||||
−0.171370 | + | 0.985207i | \(0.554819\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.2569 | −0.855042 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.523868 | 0.0170414 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.5817 | −1.09126 | −0.545629 | − | 0.838027i | \(-0.683709\pi\) | ||||
−0.545629 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.9465 | 0.776520 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.9765 | 1.91043 | 0.955217 | − | 0.295905i | \(-0.0956212\pi\) | ||||
0.955217 | + | 0.295905i | \(0.0956212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.04774 | 0.0339040 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.5562 | −0.632161 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.1177 | 1.19859 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7152 | −0.958555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.05784 | −0.291885 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.949885 | −0.0305779 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.9509 | 1.89573 | 0.947867 | − | 0.318667i | \(-0.103235\pi\) | ||||
0.947867 | + | 0.318667i | \(0.103235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.4405 | 1.07426 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.1601 | 1.67390 | 0.836948 | − | 0.547282i | \(-0.184338\pi\) | ||||
0.836948 | + | 0.547282i | \(0.184338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.3446 | 0.427809 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.5538 | −0.753552 | −0.376776 | − | 0.926304i | \(-0.622967\pi\) | ||||
−0.376776 | + | 0.926304i | \(0.622967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.1123 | −1.25004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7152 | 0.405965 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.453936 | −0.0144783 | −0.00723916 | − | 0.999974i | \(-0.502304\pi\) | ||||
−0.00723916 | + | 0.999974i | \(0.502304\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.12777 | −0.0996590 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.5461 | −1.13144 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.3114 | 1.91779 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.72292 | −0.0547303 | −0.0273651 | − | 0.999626i | \(-0.508712\pi\) | ||||
−0.0273651 | + | 0.999626i | \(0.508712\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.1335 | −0.797587 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.82315 | −0.0577977 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.3248 | −0.390331 | −0.195165 | − | 0.980770i | \(-0.562524\pi\) | ||||
−0.195165 | + | 0.980770i | \(0.562524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.92434 | −0.219077 |
(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 | 4056.2.a.z.1.2 | 3 | ||
4.3 | odd | 2 | 8112.2.a.ck.1.2 | 3 | |||
13.3 | even | 3 | 312.2.q.e.217.2 | ✓ | 6 | ||
13.5 | odd | 4 | 4056.2.c.m.337.3 | 6 | |||
13.8 | odd | 4 | 4056.2.c.m.337.4 | 6 | |||
13.9 | even | 3 | 312.2.q.e.289.2 | yes | 6 | ||
13.12 | even | 2 | 4056.2.a.y.1.2 | 3 | |||
39.29 | odd | 6 | 936.2.t.h.217.2 | 6 | |||
39.35 | odd | 6 | 936.2.t.h.289.2 | 6 | |||
52.3 | odd | 6 | 624.2.q.j.529.2 | 6 | |||
52.35 | odd | 6 | 624.2.q.j.289.2 | 6 | |||
52.51 | odd | 2 | 8112.2.a.cl.1.2 | 3 | |||
156.35 | even | 6 | 1872.2.t.u.289.2 | 6 | |||
156.107 | even | 6 | 1872.2.t.u.1153.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.q.e.217.2 | ✓ | 6 | 13.3 | even | 3 | ||
312.2.q.e.289.2 | yes | 6 | 13.9 | even | 3 | ||
624.2.q.j.289.2 | 6 | 52.35 | odd | 6 | |||
624.2.q.j.529.2 | 6 | 52.3 | odd | 6 | |||
936.2.t.h.217.2 | 6 | 39.29 | odd | 6 | |||
936.2.t.h.289.2 | 6 | 39.35 | odd | 6 | |||
1872.2.t.u.289.2 | 6 | 156.35 | even | 6 | |||
1872.2.t.u.1153.2 | 6 | 156.107 | even | 6 | |||
4056.2.a.y.1.2 | 3 | 13.12 | even | 2 | |||
4056.2.a.z.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4056.2.c.m.337.3 | 6 | 13.5 | odd | 4 | |||
4056.2.c.m.337.4 | 6 | 13.8 | odd | 4 | |||
8112.2.a.ck.1.2 | 3 | 4.3 | odd | 2 | |||
8112.2.a.cl.1.2 | 3 | 52.51 | odd | 2 |