Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(1,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, 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("1536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.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: | \(12.2650217505\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.585786 | −0.221406 | −0.110703 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110703 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41421 | −0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.65685 | −1.29777 | −0.648886 | − | 0.760886i | \(-0.724765\pi\) | ||||
−0.648886 | + | 0.760886i | \(0.724765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.585786 | 0.127829 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.82843 | −1.42383 | −0.711913 | − | 0.702268i | \(-0.752171\pi\) | ||||
−0.711913 | + | 0.702268i | \(0.752171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.41421 | 0.634004 | 0.317002 | − | 0.948425i | \(-0.397324\pi\) | ||||
0.317002 | + | 0.948425i | \(0.397324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.41421 | −1.33163 | −0.665816 | − | 0.746116i | \(-0.731916\pi\) | ||||
−0.665816 | + | 0.746116i | \(0.731916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.65685 | 0.272385 | 0.136193 | − | 0.990682i | \(-0.456513\pi\) | ||||
0.136193 | + | 0.990682i | \(0.456513\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.82843 | 0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.343146 | −0.0535904 | −0.0267952 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267952 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.65685 | 1.47266 | 0.736328 | − | 0.676625i | \(-0.236558\pi\) | ||||
0.736328 | + | 0.676625i | \(0.236558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.41421 | 0.508961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.48528 | 0.654246 | 0.327123 | − | 0.944982i | \(-0.393921\pi\) | ||||
0.327123 | + | 0.944982i | \(0.393921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.89949 | −1.08508 | −0.542540 | − | 0.840030i | \(-0.682537\pi\) | ||||
−0.542540 | + | 0.840030i | \(0.682537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.82843 | −0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.65685 | 0.749269 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65685 | 0.212138 | 0.106069 | − | 0.994359i | \(-0.466173\pi\) | ||||
0.106069 | + | 0.994359i | \(0.466173\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.585786 | −0.0738022 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.65685 | −1.19779 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.82843 | 0.822046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8284 | −1.75981 | −0.879905 | − | 0.475149i | \(-0.842394\pi\) | ||||
−0.879905 | + | 0.475149i | \(0.842394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.65685 | 1.13025 | 0.565125 | − | 0.825006i | \(-0.308828\pi\) | ||||
0.565125 | + | 0.825006i | \(0.308828\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.65685 | −0.768667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.17157 | 0.133513 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2426 | −1.60242 | −0.801211 | − | 0.598382i | \(-0.795811\pi\) | ||||
−0.801211 | + | 0.598382i | \(0.795811\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.3137 | 1.46137 | 0.730685 | − | 0.682715i | \(-0.239201\pi\) | ||||
0.730685 | + | 0.682715i | \(0.239201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26.1421 | −2.83551 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.41421 | −0.366042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.65685 | 0.173686 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.41421 | 0.768818 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.3137 | −1.98154 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.31371 | −0.945664 | −0.472832 | − | 0.881153i | \(-0.656768\pi\) | ||||
−0.472832 | + | 0.881153i | \(0.656768\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5563 | 1.34891 | 0.674454 | − | 0.738317i | \(-0.264379\pi\) | ||||
0.674454 | + | 0.738317i | \(0.264379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.07107 | 0.499667 | 0.249834 | − | 0.968289i | \(-0.419624\pi\) | ||||
0.249834 | + | 0.968289i | \(0.419624\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.31371 | −0.707043 | −0.353521 | − | 0.935426i | \(-0.615016\pi\) | ||||
−0.353521 | + | 0.935426i | \(0.615016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.8284 | −1.80344 | −0.901718 | − | 0.432324i | \(-0.857694\pi\) | ||||
−0.901718 | + | 0.432324i | \(0.857694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65685 | −0.157262 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.3137 | −2.17401 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.82843 | −0.261488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.48528 | 0.411165 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.343146 | 0.0309404 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.7279 | 1.66183 | 0.830917 | − | 0.556396i | \(-0.187816\pi\) | ||||
0.830917 | + | 0.556396i | \(0.187816\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.31371 | 0.287335 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41421 | −0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6569 | 1.33766 | 0.668828 | − | 0.743417i | \(-0.266796\pi\) | ||||
0.668828 | + | 0.743417i | \(0.266796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31371 | 0.281065 | 0.140533 | − | 0.990076i | \(-0.455119\pi\) | ||||
0.140533 | + | 0.990076i | \(0.455119\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.48528 | −0.377729 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.6569 | 0.968049 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.65685 | 0.549048 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.75736 | 0.471661 | 0.235831 | − | 0.971794i | \(-0.424219\pi\) | ||||
0.235831 | + | 0.971794i | \(0.424219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.41421 | −0.603360 | −0.301680 | − | 0.953409i | \(-0.597547\pi\) | ||||
−0.301680 | + | 0.953409i | \(0.597547\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.65685 | −0.619020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.3137 | −2.03325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | −1.59617 | −0.798087 | − | 0.602542i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602542i | \(0.794154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.89949 | 0.626471 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6569 | −1.38299 | −0.691496 | − | 0.722380i | \(-0.743048\pi\) | ||||
−0.691496 | + | 0.722380i | \(0.743048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.82843 | 0.531592 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3431 | 0.800377 | 0.400188 | − | 0.916433i | \(-0.368945\pi\) | ||||
0.400188 | + | 0.916433i | \(0.368945\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.65685 | −0.432590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.72792 | −0.511514 | −0.255757 | − | 0.966741i | \(-0.582325\pi\) | ||||
−0.255757 | + | 0.966741i | \(0.582325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.89949 | −0.294774 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.48528 | −0.630706 | −0.315353 | − | 0.948974i | \(-0.602123\pi\) | ||||
−0.315353 | + | 0.948974i | \(0.602123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.65685 | −0.122478 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.65685 | 0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.3137 | 1.11985 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.585786 | 0.0426097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9706 | −1.22795 | −0.613973 | − | 0.789327i | \(-0.710430\pi\) | ||||
−0.613973 | + | 0.789327i | \(0.710430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.3431 | −0.744516 | −0.372258 | − | 0.928129i | \(-0.621416\pi\) | ||||
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.65685 | 0.691542 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.0711 | 1.21626 | 0.608132 | − | 0.793836i | \(-0.291919\pi\) | ||||
0.608132 | + | 0.793836i | \(0.291919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5563 | −1.24454 | −0.622268 | − | 0.782804i | \(-0.713789\pi\) | ||||
−0.622268 | + | 0.782804i | \(0.713789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17157 | −0.0818262 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.82843 | −0.474608 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3137 | 0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.31371 | −0.228125 | −0.114063 | − | 0.993474i | \(-0.536386\pi\) | ||||
−0.114063 | + | 0.993474i | \(0.536386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.8284 | 1.01603 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 32.9706 | 2.24857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.34315 | 0.294832 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.65685 | −0.652550 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.6569 | 1.45680 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8995 | 0.796849 | 0.398425 | − | 0.917201i | \(-0.369557\pi\) | ||||
0.398425 | + | 0.917201i | \(0.369557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.68629 | −0.443785 | −0.221892 | − | 0.975071i | \(-0.571223\pi\) | ||||
−0.221892 | + | 0.975071i | \(0.571223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.485281 | 0.0320683 | 0.0160341 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160341 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.17157 | −0.0770838 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3137 | −0.872210 | −0.436105 | − | 0.899896i | \(-0.643642\pi\) | ||||
−0.436105 | + | 0.899896i | \(0.643642\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3137 | 0.998956 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.2426 | 0.925159 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9706 | 1.09773 | 0.548867 | − | 0.835910i | \(-0.315059\pi\) | ||||
0.548867 | + | 0.835910i | \(0.315059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.34315 | −0.408598 | −0.204299 | − | 0.978909i | \(-0.565491\pi\) | ||||
−0.204299 | + | 0.978909i | \(0.565491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.7279 | −1.45203 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000 | 1.01806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.3137 | −0.843722 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0000 | 1.38863 | 0.694314 | − | 0.719672i | \(-0.255708\pi\) | ||||
0.694314 | + | 0.719672i | \(0.255708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.6569 | 0.858599 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.1421 | 1.63708 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.3137 | 1.32951 | 0.664756 | − | 0.747060i | \(-0.268535\pi\) | ||||
0.664756 | + | 0.747060i | \(0.268535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.970563 | −0.0603078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.41421 | 0.211335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.34315 | 0.144485 | 0.0722423 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722423 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.9706 | −1.65679 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.24264 | 0.136736 | 0.0683681 | − | 0.997660i | \(-0.478221\pi\) | ||||
0.0683681 | + | 0.997660i | \(0.478221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5858 | 1.00751 | 0.503757 | − | 0.863845i | \(-0.331951\pi\) | ||||
0.503757 | + | 0.863845i | \(0.331951\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.65685 | −0.100277 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.3137 | −0.802847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4853 | −1.47118 | −0.735589 | − | 0.677428i | \(-0.763094\pi\) | ||||
−0.735589 | + | 0.677428i | \(0.763094\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.41421 | −0.443877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.31371 | 0.434755 | 0.217377 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217377 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.3137 | 1.14405 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.201010 | 0.0118653 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.31371 | 0.545979 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.10051 | 0.473237 | 0.236618 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236618 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6569 | 0.795133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.65685 | −0.326056 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5563 | −0.778792 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.65685 | 0.323911 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000 | 0.913168 | 0.456584 | − | 0.889680i | \(-0.349073\pi\) | ||||
0.456584 | + | 0.889680i | \(0.349073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.07107 | −0.288483 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3137 | 0.641542 | 0.320771 | − | 0.947157i | \(-0.396058\pi\) | ||||
0.320771 | + | 0.947157i | \(0.396058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.9706 | −0.959233 | −0.479616 | − | 0.877478i | \(-0.659224\pi\) | ||||
−0.479616 | + | 0.877478i | \(0.659224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.07107 | −0.509482 | −0.254741 | − | 0.967009i | \(-0.581990\pi\) | ||||
−0.254741 | + | 0.967009i | \(0.581990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82843 | −0.382319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.31371 | 0.408211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.3137 | 2.41004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.8284 | −1.04441 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.8284 | 1.04121 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.62742 | −0.144854 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65685 | 0.0907951 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.3137 | 1.49231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9706 | −0.706552 | −0.353276 | − | 0.935519i | \(-0.614932\pi\) | ||||
−0.353276 | + | 0.935519i | \(0.614932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.8284 | 0.803004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.3137 | 1.25517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.68629 | −0.144208 | −0.0721038 | − | 0.997397i | \(-0.522971\pi\) | ||||
−0.0721038 | + | 0.997397i | \(0.522971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.3137 | −1.24795 | −0.623977 | − | 0.781443i | \(-0.714484\pi\) | ||||
−0.623977 | + | 0.781443i | \(0.714484\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82843 | 0.150970 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.31371 | 0.495719 | 0.247859 | − | 0.968796i | \(-0.420273\pi\) | ||||
0.247859 | + | 0.968796i | \(0.420273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −50.6274 | −2.68702 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.48528 | −0.237386 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.7990 | −1.25606 | −0.628031 | − | 0.778188i | \(-0.716139\pi\) | ||||
−0.628031 | + | 0.778188i | \(0.716139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706 | 1.72576 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.72792 | −0.142396 | −0.0711982 | − | 0.997462i | \(-0.522682\pi\) | ||||
−0.0711982 | + | 0.997462i | \(0.522682\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.343146 | −0.0178635 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.62742 | 0.240244 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.2843 | 1.67162 | 0.835808 | − | 0.549022i | \(-0.185000\pi\) | ||||
0.835808 | + | 0.549022i | \(0.185000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.65685 | −0.497353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6569 | 1.52337 | 0.761685 | − | 0.647947i | \(-0.224372\pi\) | ||||
0.761685 | + | 0.647947i | \(0.224372\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.7279 | −0.959461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.31371 | −0.169323 | −0.0846613 | − | 0.996410i | \(-0.526981\pi\) | ||||
−0.0846613 | + | 0.996410i | \(0.526981\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.65685 | 0.490885 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.7574 | −0.697526 | −0.348763 | − | 0.937211i | \(-0.613398\pi\) | ||||
−0.348763 | + | 0.937211i | \(0.613398\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.2843 | 2.64413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −48.6274 | −2.44671 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.31371 | −0.165893 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.3431 | −1.01589 | −0.507944 | − | 0.861390i | \(-0.669594\pi\) | ||||
−0.507944 | + | 0.861390i | \(0.669594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.9706 | 1.04462 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.41421 | 0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.31371 | −0.164254 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3137 | −1.05390 | −0.526948 | − | 0.849898i | \(-0.676664\pi\) | ||||
−0.526948 | + | 0.849898i | \(0.676664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.6569 | −0.772296 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.34315 | −0.115299 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.4558 | 2.23134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.31371 | −0.162273 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.3137 | −1.04124 | −0.520621 | − | 0.853788i | \(-0.674300\pi\) | ||||
−0.520621 | + | 0.853788i | \(0.674300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.14214 | −0.299349 | −0.149675 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149675 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.48528 | 0.218082 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −50.9706 | −2.47244 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.970563 | −0.0469688 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65685 | −0.273115 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.1127 | 1.30597 | 0.652986 | − | 0.757370i | \(-0.273516\pi\) | ||||
0.652986 | + | 0.757370i | \(0.273516\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.6274 | 1.37575 | 0.687873 | − | 0.725831i | \(-0.258545\pi\) | ||||
0.687873 | + | 0.725831i | \(0.258545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.6569 | −0.558903 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 38.6274 | 1.84780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.89949 | −0.186113 | −0.0930564 | − | 0.995661i | \(-0.529664\pi\) | ||||
−0.0930564 | + | 0.995661i | \(0.529664\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.65685 | −0.316993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.9411 | −1.89766 | −0.948830 | − | 0.315787i | \(-0.897731\pi\) | ||||
−0.948830 | + | 0.315787i | \(0.897731\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.82843 | 0.323698 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.75736 | −0.272314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.65685 | 0.172578 | 0.0862888 | − | 0.996270i | \(-0.472499\pi\) | ||||
0.0862888 | + | 0.996270i | \(0.472499\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.686292 | 0.0323162 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.41421 | 0.348350 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.65685 | 0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.31371 | 0.248565 | 0.124282 | − | 0.992247i | \(-0.460337\pi\) | ||||
0.124282 | + | 0.992247i | \(0.460337\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.65685 | 0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.0711 | −1.16768 | −0.583838 | − | 0.811870i | \(-0.698450\pi\) | ||||
−0.583838 | + | 0.811870i | \(0.698450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.5563 | −1.55950 | −0.779748 | − | 0.626094i | \(-0.784653\pi\) | ||||
−0.779748 | + | 0.626094i | \(0.784653\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.3137 | 1.17390 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.3137 | −0.616085 | −0.308042 | − | 0.951373i | \(-0.599674\pi\) | ||||
−0.308042 | + | 0.951373i | \(0.599674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.68629 | −0.216393 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0000 | 0.921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.3137 | −0.888045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.6569 | −1.72781 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.89949 | −0.361693 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.4853 | −0.570467 | −0.285234 | − | 0.958458i | \(-0.592071\pi\) | ||||
−0.285234 | + | 0.958458i | \(0.592071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.68629 | −0.213676 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.7990 | −1.44392 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.5563 | −1.15807 | −0.579034 | − | 0.815303i | \(-0.696570\pi\) | ||||
−0.579034 | + | 0.815303i | \(0.696570\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.6569 | 0.798471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3137 | 1.05213 | 0.526066 | − | 0.850443i | \(-0.323666\pi\) | ||||
0.526066 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.1421 | −1.17738 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.82843 | −0.306915 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.68629 | 0.389633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.686292 | −0.0307226 | −0.0153613 | − | 0.999882i | \(-0.504890\pi\) | ||||
−0.0153613 | + | 0.999882i | \(0.504890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.3431 | −0.462098 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4853 | −0.556691 | −0.278346 | − | 0.960481i | \(-0.589786\pi\) | ||||
−0.278346 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 46.2843 | 2.05962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.2132 | −0.851610 | −0.425805 | − | 0.904815i | \(-0.640009\pi\) | ||||
−0.425805 | + | 0.904815i | \(0.640009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.65685 | −0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.65685 | 0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3137 | 0.762933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.97056 | −0.394525 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.72792 | 0.295323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.9706 | 1.00636 | 0.503179 | − | 0.864182i | \(-0.332164\pi\) | ||||
0.503179 | + | 0.864182i | \(0.332164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.6569 | −1.64662 | −0.823310 | − | 0.567593i | \(-0.807875\pi\) | ||||
−0.823310 | + | 0.567593i | \(0.807875\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.89949 | 0.170188 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.7696 | 2.47292 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.970563 | 0.0420397 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.9706 | −1.07957 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.00000 | −0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.3137 | 0.573462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8284 | −0.465550 | −0.232775 | − | 0.972531i | \(-0.574781\pi\) | ||||
−0.232775 | + | 0.972531i | \(0.574781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.48528 | 0.364138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −64.2843 | −2.75364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.97056 | 0.212526 | 0.106263 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106263 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.65685 | 0.0707128 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.34315 | 0.354787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.65685 | −0.240120 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.07107 | 0.0453826 | 0.0226913 | − | 0.999743i | \(-0.492777\pi\) | ||||
0.0226913 | + | 0.999743i | \(0.492777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.3137 | −1.15525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3137 | −0.646545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.6274 | −0.700762 | −0.350381 | − | 0.936607i | \(-0.613948\pi\) | ||||
−0.350381 | + | 0.936607i | \(0.613948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.4853 | 0.861822 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.585786 | −0.0246007 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9706 | −0.627599 | −0.313799 | − | 0.949489i | \(-0.601602\pi\) | ||||
−0.313799 | + | 0.949489i | \(0.601602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9706 | 0.708955 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −45.4558 | −1.89564 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.2843 | −1.17749 | −0.588745 | − | 0.808319i | \(-0.700378\pi\) | ||||
−0.588745 | + | 0.808319i | \(0.700378\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.3431 | 0.429846 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.79899 | −0.323557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.7990 | 0.654327 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.65685 | −0.399262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.3137 | 1.29246 | 0.646228 | − | 0.763145i | \(-0.276346\pi\) | ||||
0.646228 | + | 0.763145i | \(0.276346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.9411 | 1.72815 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.0711 | −0.702210 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.00000 | −0.0821302 | −0.0410651 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410651 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.3137 | 0.627801 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.5563 | 0.718534 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5147 | −0.470479 | −0.235239 | − | 0.971937i | \(-0.575587\pi\) | ||||
−0.235239 | + | 0.971937i | \(0.575587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.65685 | −0.230748 | −0.115374 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115374 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.8995 | −0.971653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.89949 | −0.158276 | −0.0791378 | − | 0.996864i | \(-0.525217\pi\) | ||||
−0.0791378 | + | 0.996864i | \(0.525217\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6863 | −0.513232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6274 | −0.429237 | −0.214619 | − | 0.976698i | \(-0.568851\pi\) | ||||
−0.214619 | + | 0.976698i | \(0.568851\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.17157 | 0.0472424 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9411 | 0.963833 | 0.481917 | − | 0.876217i | \(-0.339941\pi\) | ||||
0.481917 | + | 0.876217i | \(0.339941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.82843 | 0.274015 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.17157 | −0.0469381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.3137 | −0.451826 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.6863 | −0.505836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.9289 | −0.753549 | −0.376774 | − | 0.926305i | \(-0.622967\pi\) | ||||
−0.376774 | + | 0.926305i | \(0.622967\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.31371 | 0.131708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.9411 | 2.53743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.8284 | 0.746009 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.8284 | −0.586604 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.02944 | 0.356641 | 0.178321 | − | 0.983972i | \(-0.442934\pi\) | ||||
0.178321 | + | 0.983972i | \(0.442934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.2843 | 1.27317 | 0.636584 | − | 0.771208i | \(-0.280347\pi\) | ||||
0.636584 | + | 0.771208i | \(0.280347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.9706 | −1.29821 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8284 | 0.897478 | 0.448739 | − | 0.893663i | \(-0.351873\pi\) | ||||
0.448739 | + | 0.893663i | \(0.351873\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.34315 | −0.170221 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5858 | 0.805584 | 0.402792 | − | 0.915292i | \(-0.368040\pi\) | ||||
0.402792 | + | 0.915292i | \(0.368040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6569 | 0.533617 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.65685 | 0.376750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.3137 | 1.53144 | 0.765722 | − | 0.643171i | \(-0.222382\pi\) | ||||
0.765722 | + | 0.643171i | \(0.222382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.3137 | 1.52913 | 0.764563 | − | 0.644549i | \(-0.222955\pi\) | ||||
0.764563 | + | 0.644549i | \(0.222955\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.6569 | −0.841083 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3137 | 0.438727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3137 | −0.902710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.8995 | −0.460061 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.31371 | −0.127924 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.62742 | −0.332562 | −0.166281 | − | 0.986078i | \(-0.553176\pi\) | ||||
−0.166281 | + | 0.986078i | \(0.553176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.65685 | −0.256222 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.2132 | −1.35335 | −0.676677 | − | 0.736280i | \(-0.736580\pi\) | ||||
−0.676677 | + | 0.736280i | \(0.736580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.45584 | 0.209376 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.68629 | 0.256219 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.68629 | 0.102788 | 0.0513940 | − | 0.998678i | \(-0.483634\pi\) | ||||
0.0513940 | + | 0.998678i | \(0.483634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.4558 | 2.04244 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.485281 | −0.0185146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.3431 | 0.851206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.34315 | 0.241305 | 0.120652 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120652 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.17157 | 0.0445044 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.3137 | 0.429153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.62742 | 0.0995205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.3137 | 0.503571 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.58579 | 0.173203 | 0.0866014 | − | 0.996243i | \(-0.472399\pi\) | ||||
0.0866014 | + | 0.996243i | \(0.472399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.37258 | −0.353494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3137 | −0.576748 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.94113 | −0.298657 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.1127 | −1.16846 | −0.584231 | − | 0.811587i | \(-0.698604\pi\) | ||||
−0.584231 | + | 0.811587i | \(0.698604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.2426 | −0.534141 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.6274 | 1.89601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.3137 | 0.722292 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.9706 | −0.633777 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.8284 | −1.14971 | −0.574853 | − | 0.818257i | \(-0.694941\pi\) | ||||
−0.574853 | + | 0.818257i | \(0.694941\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.97056 | −0.110630 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.34315 | 0.235904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.7279 | 0.844094 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2426 | 0.824934 | 0.412467 | − | 0.910973i | \(-0.364667\pi\) | ||||
0.412467 | + | 0.910973i | \(0.364667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −73.9411 | −2.73481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5147 | 0.868536 | 0.434268 | − | 0.900784i | \(-0.357007\pi\) | ||||
0.434268 | + | 0.900784i | \(0.357007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.7279 | 0.838332 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6274 | 0.390936 | 0.195468 | − | 0.980710i | \(-0.437377\pi\) | ||||
0.195468 | + | 0.980710i | \(0.437377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.0000 | −0.587775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.0000 | −1.46746 | −0.733729 | − | 0.679442i | \(-0.762222\pi\) | ||||
−0.733729 | + | 0.679442i | \(0.762222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.6569 | 0.720171 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.3137 | 0.487123 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.28427 | 0.156544 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.27208 | −0.192381 | −0.0961904 | − | 0.995363i | \(-0.530666\pi\) | ||||
−0.0961904 | + | 0.995363i | \(0.530666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0000 | −0.801725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.3137 | −0.921260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4853 | 1.18070 | 0.590349 | − | 0.807148i | \(-0.298990\pi\) | ||||
0.590349 | + | 0.807148i | \(0.298990\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.6569 | −0.495712 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6569 | 1.29256 | 0.646280 | − | 0.763100i | \(-0.276324\pi\) | ||||
0.646280 | + | 0.763100i | \(0.276324\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.0294 | 0.399292 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.1421 | −0.945171 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3137 | −0.408514 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.34315 | −0.0844960 | −0.0422480 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422480 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3137 | −0.767594 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.72792 | −0.241987 | −0.120993 | − | 0.992653i | \(-0.538608\pi\) | ||||
−0.120993 | + | 0.992653i | \(0.538608\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.3553 | −1.77290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.970563 | 0.0348187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.94113 | 0.0695480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.6569 | 1.06121 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.41421 | −0.122014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −68.2843 | −2.43717 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.6569 | −0.771983 | −0.385992 | − | 0.922502i | \(-0.626141\pi\) | ||||
−0.385992 | + | 0.922502i | \(0.626141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.34315 | −0.0834182 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.51472 | −0.124969 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.68629 | −0.166415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.9706 | 0.956547 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.4142 | 1.25444 | 0.627218 | − | 0.778844i | \(-0.284194\pi\) | ||||
0.627218 | + | 0.778844i | \(0.284194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3431 | −1.21497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3137 | −0.681566 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6569 | 0.481341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.24264 | −0.0789447 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.02944 | −0.176826 | −0.0884128 | − | 0.996084i | \(-0.528179\pi\) | ||||
−0.0884128 | + | 0.996084i | \(0.528179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.3431 | 0.644115 | 0.322057 | − | 0.946720i | \(-0.395626\pi\) | ||||
0.322057 | + | 0.946720i | \(0.395626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5858 | −0.581689 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.2843 | −2.11167 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6274 | −1.91117 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.65685 | 0.0578952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.87006 | 0.309567 | 0.154784 | − | 0.987948i | \(-0.450532\pi\) | ||||
0.154784 | + | 0.987948i | \(0.450532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.2132 | −1.36689 | −0.683443 | − | 0.730004i | \(-0.739518\pi\) | ||||
−0.683443 | + | 0.730004i | \(0.739518\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.3137 | 0.463524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.9411 | 1.04115 | 0.520577 | − | 0.853814i | \(-0.325717\pi\) | ||||
0.520577 | + | 0.853814i | \(0.325717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.7696 | −1.83276 | −0.916381 | − | 0.400307i | \(-0.868904\pi\) | ||||
−0.916381 | + | 0.400307i | \(0.868904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.4853 | 0.849385 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50.9706 | 1.76603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.3137 | 1.22208 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.41421 | 0.256273 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.4853 | −0.983421 | −0.491711 | − | 0.870759i | \(-0.663628\pi\) | ||||
−0.491711 | + | 0.870759i | \(0.663628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.3431 | −0.598040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.00000 | 0.0688837 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.0711 | −0.587263 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.10051 | 0.140895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.31371 | −0.251006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.3137 | −0.387829 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.6274 | 1.18562 | 0.592810 | − | 0.805342i | \(-0.298018\pi\) | ||||
0.592810 | + | 0.805342i | \(0.298018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3137 | −0.660515 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.5980 | 1.42096 | 0.710480 | − | 0.703717i | \(-0.248478\pi\) | ||||
0.710480 | + | 0.703717i | \(0.248478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.9706 | −1.53438 | −0.767188 | − | 0.641422i | \(-0.778345\pi\) | ||||
−0.767188 | + | 0.641422i | \(0.778345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.201010 | −0.00685041 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.0294 | −0.511608 | −0.255804 | − | 0.966729i | \(-0.582340\pi\) | ||||
−0.255804 | + | 0.966729i | \(0.582340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.9706 | −0.781023 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.6274 | −1.41374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.4853 | 0.966297 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6274 | −0.766701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.31371 | −0.315221 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.31371 | −0.112024 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.3137 | −0.787248 | −0.393624 | − | 0.919272i | \(-0.628779\pi\) | ||||
−0.393624 | + | 0.919272i | \(0.628779\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.10051 | −0.273223 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.3137 | 1.52666 | 0.763329 | − | 0.646010i | \(-0.223564\pi\) | ||||
0.763329 | + | 0.646010i | \(0.223564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.3431 | −1.02113 | −0.510564 | − | 0.859840i | \(-0.670563\pi\) | ||||
−0.510564 | + | 0.859840i | \(0.670563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.6569 | −0.459070 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.6569 | 0.995780 | 0.497890 | − | 0.867240i | \(-0.334108\pi\) | ||||
0.497890 | + | 0.867240i | \(0.334108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9706 | −0.367941 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00000 | −0.0670025 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.3726 | −0.849061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6569 | 0.456498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.3137 | −0.644866 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.3137 | −0.844259 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.4853 | 2.01506 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | 0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.9706 | −0.963014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51.5980 | −1.71328 | −0.856641 | − | 0.515912i | \(-0.827453\pi\) | ||||
−0.856641 | + | 0.515912i | \(0.827453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5563 | 0.449636 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.6863 | −0.950419 | −0.475210 | − | 0.879873i | \(-0.657628\pi\) | ||||
−0.475210 | + | 0.879873i | \(0.657628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.6274 | −0.881239 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.65685 | −0.187010 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.34315 | −0.0773775 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3553 | 0.572500 | 0.286250 | − | 0.958155i | \(-0.407591\pi\) | ||||
0.286250 | + | 0.958155i | \(0.407591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | −0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.9411 | 1.38051 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0294 | 0.362646 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.07107 | 0.166556 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.5980 | 0.971078 | 0.485539 | − | 0.874215i | \(-0.338623\pi\) | ||||
0.485539 | + | 0.874215i | \(0.338623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.6569 | 1.23415 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.3137 | −0.370394 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 52.2843 | 1.70988 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.6274 | 1.19657 | 0.598283 | − | 0.801285i | \(-0.295850\pi\) | ||||
0.598283 | + | 0.801285i | \(0.295850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9706 | 0.553813 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.3848 | −0.664525 | −0.332262 | − | 0.943187i | \(-0.607812\pi\) | ||||
−0.332262 | + | 0.943187i | \(0.607812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.34315 | 0.0763033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6274 | 1.12524 | 0.562620 | − | 0.826716i | \(-0.309793\pi\) | ||||
0.562620 | + | 0.826716i | \(0.309793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3137 | −0.886640 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.07107 | 0.294150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.9706 | 1.00323 | 0.501617 | − | 0.865090i | \(-0.332739\pi\) | ||||
0.501617 | + | 0.865090i | \(0.332739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −57.9411 | −1.87493 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.82843 | 0.220732 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.17157 | −0.296166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.31371 | −0.235681 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.3137 | −1.13679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.75736 | −0.0565129 | −0.0282564 | − | 0.999601i | \(-0.508995\pi\) | ||||
−0.0282564 | + | 0.999601i | \(0.508995\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.3137 | −1.39144 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.3137 | −0.940722 | −0.470361 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470361 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.94113 | −0.0622296 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.8284 | 0.602992 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.2843 | −0.968880 | −0.484440 | − | 0.874825i | \(-0.660977\pi\) | ||||
−0.484440 | + | 0.874825i | \(0.660977\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.8284 | −0.601145 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.28427 | 0.136647 | 0.0683235 | − | 0.997663i | \(-0.478235\pi\) | ||||
0.0683235 | + | 0.997663i | \(0.478235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58.2843 | 1.85709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.62742 | 0.0836316 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65.9411 | −2.09681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8995 | −0.378000 | −0.189000 | − | 0.981977i | \(-0.560525\pi\) | ||||
−0.189000 | + | 0.981977i | \(0.560525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59.9411 | −1.90026 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.9706 | 0.410782 | 0.205391 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205391 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.65685 | −0.0524205 |
(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 | 1536.2.a.e.1.2 | yes | 2 | |
3.2 | odd | 2 | 4608.2.a.a.1.1 | 2 | |||
4.3 | odd | 2 | 1536.2.a.l.1.2 | yes | 2 | ||
8.3 | odd | 2 | 1536.2.a.b.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 1536.2.a.g.1.1 | yes | 2 | ||
12.11 | even | 2 | 4608.2.a.e.1.1 | 2 | |||
16.3 | odd | 4 | 1536.2.d.a.769.3 | 4 | |||
16.5 | even | 4 | 1536.2.d.f.769.4 | 4 | |||
16.11 | odd | 4 | 1536.2.d.a.769.2 | 4 | |||
16.13 | even | 4 | 1536.2.d.f.769.1 | 4 | |||
24.5 | odd | 2 | 4608.2.a.n.1.2 | 2 | |||
24.11 | even | 2 | 4608.2.a.r.1.2 | 2 | |||
48.5 | odd | 4 | 4608.2.d.o.2305.1 | 4 | |||
48.11 | even | 4 | 4608.2.d.c.2305.1 | 4 | |||
48.29 | odd | 4 | 4608.2.d.o.2305.4 | 4 | |||
48.35 | even | 4 | 4608.2.d.c.2305.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.b.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
1536.2.a.e.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1536.2.a.g.1.1 | yes | 2 | 8.5 | even | 2 | ||
1536.2.a.l.1.2 | yes | 2 | 4.3 | odd | 2 | ||
1536.2.d.a.769.2 | 4 | 16.11 | odd | 4 | |||
1536.2.d.a.769.3 | 4 | 16.3 | odd | 4 | |||
1536.2.d.f.769.1 | 4 | 16.13 | even | 4 | |||
1536.2.d.f.769.4 | 4 | 16.5 | even | 4 | |||
4608.2.a.a.1.1 | 2 | 3.2 | odd | 2 | |||
4608.2.a.e.1.1 | 2 | 12.11 | even | 2 | |||
4608.2.a.n.1.2 | 2 | 24.5 | odd | 2 | |||
4608.2.a.r.1.2 | 2 | 24.11 | even | 2 | |||
4608.2.d.c.2305.1 | 4 | 48.11 | even | 4 | |||
4608.2.d.c.2305.4 | 4 | 48.35 | even | 4 | |||
4608.2.d.o.2305.1 | 4 | 48.5 | odd | 4 | |||
4608.2.d.o.2305.4 | 4 | 48.29 | odd | 4 |