Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(769,1536)]
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, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(12.2650217505\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.769 |
Dual form | 1536.2.d.f.769.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(517\) | \(1025\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.41421i | − 1.52688i | −0.645877 | − | 0.763441i | \(-0.723508\pi\) | ||||
0.645877 | − | 0.763441i | \(-0.276492\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.585786 | 0.221406 | 0.110703 | − | 0.993854i | \(-0.464690\pi\) | ||||
0.110703 | + | 0.993854i | \(0.464690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.82843i | − 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 5.65685i | − 1.29777i | −0.760886 | − | 0.648886i | \(-0.775235\pi\) | ||||
0.760886 | − | 0.648886i | \(-0.224765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.585786i | − 0.127829i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.82843 | 1.42383 | 0.711913 | − | 0.702268i | \(-0.247829\pi\) | ||||
0.711913 | + | 0.702268i | \(0.247829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.65685 | −1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.41421i | 0.634004i | 0.948425 | + | 0.317002i | \(0.102676\pi\) | ||||
−0.948425 | + | 0.317002i | \(0.897324\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | − 2.00000i | − 0.338062i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.65685i | − 0.272385i | −0.990682 | − | 0.136193i | \(-0.956513\pi\) | ||||
0.990682 | − | 0.136193i | \(-0.0434866\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.82843 | −0.452911 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.343146 | 0.0535904 | 0.0267952 | − | 0.999641i | \(-0.491470\pi\) | ||||
0.0267952 | + | 0.999641i | \(0.491470\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9.65685i | − 1.47266i | −0.676625 | − | 0.736328i | \(-0.736558\pi\) | ||||
0.676625 | − | 0.736328i | \(-0.263442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.41421i | 0.508961i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 7.65685i | 1.07217i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.89949i | 1.08508i | 0.840030 | + | 0.542540i | \(0.182537\pi\) | ||||
−0.840030 | + | 0.542540i | \(0.817463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.82843 | 0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.65685 | −0.749269 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4.00000i | − 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||||
0.965507 | − | 0.260378i | \(-0.0838471\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65685i | 0.212138i | 0.994359 | + | 0.106069i | \(0.0338265\pi\) | ||||
−0.994359 | + | 0.106069i | \(0.966173\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.585786 | −0.0738022 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.65685 | −1.19779 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000i | 0.977356i | 0.872464 | + | 0.488678i | \(0.162521\pi\) | ||||
−0.872464 | + | 0.488678i | \(0.837479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.82843i | − 0.822046i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.8284 | 1.75981 | 0.879905 | − | 0.475149i | \(-0.157606\pi\) | ||||
0.879905 | + | 0.475149i | \(0.157606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.65685 | −1.13025 | −0.565125 | − | 0.825006i | \(-0.691172\pi\) | ||||
−0.565125 | + | 0.825006i | \(0.691172\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.65685i | 0.768667i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.17157i | 0.133513i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 13.3137i | 1.46137i | 0.682715 | + | 0.730685i | \(0.260799\pi\) | ||||
−0.682715 | + | 0.730685i | \(0.739201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.1421i | 2.83551i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41421 | 0.366042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.65685i | − 0.173686i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.41421i | 0.768818i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 2.00000i | − 0.201008i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 13.5563i | − 1.34891i | −0.738317 | − | 0.674454i | \(-0.764379\pi\) | ||||
0.738317 | − | 0.674454i | \(-0.235621\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.07107 | −0.499667 | −0.249834 | − | 0.968289i | \(-0.580376\pi\) | ||||
−0.249834 | + | 0.968289i | \(0.580376\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.31371i | 0.707043i | 0.935426 | + | 0.353521i | \(0.115016\pi\) | ||||
−0.935426 | + | 0.353521i | \(0.884984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 18.8284i | − 1.80344i | −0.432324 | − | 0.901718i | \(-0.642306\pi\) | ||||
0.432324 | − | 0.901718i | \(-0.357694\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 23.3137i | − 2.17401i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82843i | 0.261488i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.48528 | −0.411165 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.343146i | − 0.0309404i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 4.00000i | 0.349482i | 0.984614 | + | 0.174741i | \(0.0559088\pi\) | ||||
−0.984614 | + | 0.174741i | \(0.944091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.31371i | − 0.287335i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.6569 | −1.33766 | −0.668828 | − | 0.743417i | \(-0.733204\pi\) | ||||
−0.668828 | + | 0.743417i | \(0.733204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.31371i | − 0.281065i | −0.990076 | − | 0.140533i | \(-0.955119\pi\) | ||||
0.990076 | − | 0.140533i | \(-0.0448815\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.48528i | − 0.377729i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.6569 | 0.968049 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.65685i | 0.549048i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.75736i | − 0.471661i | −0.971794 | − | 0.235831i | \(-0.924219\pi\) | ||||
0.971794 | − | 0.235831i | \(-0.0757811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.41421 | 0.603360 | 0.301680 | − | 0.953409i | \(-0.402453\pi\) | ||||
0.301680 | + | 0.953409i | \(0.402453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.65685 | 0.619020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.3137i | 2.03325i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 20.0000i | − 1.59617i | −0.602542 | − | 0.798087i | \(-0.705846\pi\) | ||||
0.602542 | − | 0.798087i | \(-0.294154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.89949 | 0.626471 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 17.6569i | − 1.38299i | −0.722380 | − | 0.691496i | \(-0.756952\pi\) | ||||
0.722380 | − | 0.691496i | \(-0.243048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 6.82843i | − 0.531592i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.3431 | −0.800377 | −0.400188 | − | 0.916433i | \(-0.631055\pi\) | ||||
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.65685i | 0.432590i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.72792i | − 0.511514i | −0.966741 | − | 0.255757i | \(-0.917675\pi\) | ||||
0.966741 | − | 0.255757i | \(-0.0823248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.89949 | −0.294774 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000i | 0.298974i | 0.988764 | + | 0.149487i | \(0.0477622\pi\) | ||||
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.65685 | 0.122478 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.65685 | −0.415900 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.3137i | − 1.11985i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.585786i | 0.0426097i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 9.65685i | 0.691542i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 17.0711i | − 1.21626i | −0.793836 | − | 0.608132i | \(-0.791919\pi\) | ||||
0.793836 | − | 0.608132i | \(-0.208081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.5563 | 1.24454 | 0.622268 | − | 0.782804i | \(-0.286211\pi\) | ||||
0.622268 | + | 0.782804i | \(0.286211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000i | 0.140372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 1.17157i | − 0.0818262i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.82843 | −0.474608 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.3137 | 0.782586 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.31371i | − 0.228125i | −0.993474 | − | 0.114063i | \(-0.963614\pi\) | ||||
0.993474 | − | 0.114063i | \(-0.0363864\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 14.8284i | − 1.01603i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.9706 | −2.24857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.34315 | −0.294832 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.65685i | 0.652550i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.6569i | 1.45680i | ||||||||
\(222\) | 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 | ||||||||
\(227\) | − 6.68629i | − 0.443785i | −0.975071 | − | 0.221892i | \(-0.928777\pi\) | ||||
0.975071 | − | 0.221892i | \(-0.0712234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 0.485281i | − 0.0320683i | −0.999871 | − | 0.0160341i | \(-0.994896\pi\) | ||||
0.999871 | − | 0.0160341i | \(-0.00510405\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.17157 | 0.0770838 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3137 | 0.872210 | 0.436105 | − | 0.899896i | \(-0.356358\pi\) | ||||
0.436105 | + | 0.899896i | \(0.356358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 15.3137i | − 0.998956i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.2426i | 0.925159i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.7279i | 1.45203i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.0000 | −1.01806 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.3137 | 0.843722 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 22.0000i | − 1.38863i | −0.719672 | − | 0.694314i | \(-0.755708\pi\) | ||||
0.719672 | − | 0.694314i | \(-0.244292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.6569i | 0.858599i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 0.970563i | − 0.0603078i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 3.41421i | − 0.211335i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.34315 | −0.144485 | −0.0722423 | − | 0.997387i | \(-0.523015\pi\) | ||||
−0.0722423 | + | 0.997387i | \(0.523015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.9706 | 1.65679 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.00000i | 0.122398i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.24264i | 0.136736i | 0.997660 | + | 0.0683681i | \(0.0217792\pi\) | ||||
−0.997660 | + | 0.0683681i | \(0.978221\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 13.3137i | − 0.802847i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4853i | 1.47118i | 0.677428 | + | 0.735589i | \(0.263094\pi\) | ||||
−0.677428 | + | 0.735589i | \(0.736906\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.41421 | 0.443877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.31371i | − 0.434755i | −0.976088 | − | 0.217377i | \(-0.930250\pi\) | ||||
0.976088 | − | 0.217377i | \(-0.0697502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.3137i | 1.14405i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.201010 | 0.0118653 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.31371i | 0.545979i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.10051i | − 0.473237i | −0.971603 | − | 0.236618i | \(-0.923961\pi\) | ||||
0.971603 | − | 0.236618i | \(-0.0760391\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.6569 | −0.795133 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 19.3137i | − 1.11694i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 5.65685i | − 0.326056i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5563 | −0.778792 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.65685 | 0.323911 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0000i | 0.913168i | 0.889680 | + | 0.456584i | \(0.150927\pi\) | ||||
−0.889680 | + | 0.456584i | \(0.849073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.07107i | 0.288483i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3137 | −0.641542 | −0.320771 | − | 0.947157i | \(-0.603942\pi\) | ||||
−0.320771 | + | 0.947157i | \(0.603942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.9706 | 0.959233 | 0.479616 | − | 0.877478i | \(-0.340776\pi\) | ||||
0.479616 | + | 0.877478i | \(0.340776\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.00000i | 0.112687i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9.07107i | − 0.509482i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) | ||||
0.967009 | − | 0.254741i | \(-0.0819902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82843 | −0.382319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.31371 | 0.408211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.3137i | 2.41004i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.8284i | 1.04441i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.8284 | −1.04121 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.62742 | 0.144854 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65685i | 0.0907951i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 6.00000i | − 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 14.8284i | − 0.803004i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.3137 | −1.25517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.68629i | 0.144208i | 0.997397 | + | 0.0721038i | \(0.0229713\pi\) | ||||
−0.997397 | + | 0.0721038i | \(0.977029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 23.3137i | − 1.24795i | −0.781443 | − | 0.623977i | \(-0.785516\pi\) | ||||
0.781443 | − | 0.623977i | \(-0.214484\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | − 50.6274i | − 2.68702i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.48528i | 0.237386i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.7990 | 1.25606 | 0.628031 | − | 0.778188i | \(-0.283861\pi\) | ||||
0.628031 | + | 0.778188i | \(0.283861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 7.00000i | − 0.367405i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706i | 1.72576i | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 4.62742i | 0.240244i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 32.2843i | − 1.67162i | −0.549022 | − | 0.835808i | \(-0.685000\pi\) | ||||
0.549022 | − | 0.835808i | \(-0.315000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.65685 | 0.497353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 29.6569i | − 1.52337i | −0.647947 | − | 0.761685i | \(-0.724372\pi\) | ||||
0.647947 | − | 0.761685i | \(-0.275628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 18.7279i | − 0.959461i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 9.65685i | 0.490885i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7574i | 0.697526i | 0.937211 | + | 0.348763i | \(0.113398\pi\) | ||||
−0.937211 | + | 0.348763i | \(0.886602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.2843 | −2.64413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.6274i | 2.44671i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.00000i | − 0.200754i | −0.994949 | − | 0.100377i | \(-0.967995\pi\) | ||||
0.994949 | − | 0.100377i | \(-0.0320049\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 20.9706i | 1.04462i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.41421i | − 0.169654i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.31371 | 0.164254 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3137 | 1.05390 | 0.526948 | − | 0.849898i | \(-0.323336\pi\) | ||||
0.526948 | + | 0.849898i | \(0.323336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.6569i | 0.772296i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.34315i | − 0.115299i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.4558 | 2.23134 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.31371 | −0.162273 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 21.3137i | − 1.04124i | −0.853788 | − | 0.520621i | \(-0.825700\pi\) | ||||
0.853788 | − | 0.520621i | \(-0.174300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.14214i | 0.299349i | 0.988735 | + | 0.149675i | \(0.0478226\pi\) | ||||
−0.988735 | + | 0.149675i | \(0.952177\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.48528 | −0.218082 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 50.9706 | 2.47244 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.970563i | 0.0469688i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 5.65685i | − 0.273115i | ||||||||
\(430\) | 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 | ||||||||
\(435\) | − 11.6569i | − 0.558903i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 38.6274i | − 1.84780i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.89949 | 0.186113 | 0.0930564 | − | 0.995661i | \(-0.470336\pi\) | ||||
0.0930564 | + | 0.995661i | \(0.470336\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.65685 | 0.316993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.9411i | 1.89766i | 0.315787 | + | 0.948830i | \(0.397731\pi\) | ||||
−0.315787 | + | 0.948830i | \(0.602269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.82843i | 0.323698i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 0.686292i | 0.0323162i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 7.41421i | − 0.348350i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.65685 | −0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.31371 | −0.248565 | −0.124282 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124282 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 7.65685i | − 0.357391i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 25.0711i | − 1.16768i | −0.811870 | − | 0.583838i | \(-0.801550\pi\) | ||||
0.811870 | − | 0.583838i | \(-0.198450\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − 13.3137i | − 0.616085i | −0.951373 | − | 0.308042i | \(-0.900326\pi\) | ||||
0.951373 | − | 0.308042i | \(-0.0996739\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.68629i | 0.216393i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0000 | −0.921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.3137 | 0.888045 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.6569i | 1.72781i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.89949i | − 0.361693i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | − 4.00000i | − 0.182006i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.7990i | 1.44392i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.5563 | 1.15807 | 0.579034 | − | 0.815303i | \(-0.303430\pi\) | ||||
0.579034 | + | 0.815303i | \(0.303430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6569 | −0.798471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 23.3137i | − 1.05213i | −0.850443 | − | 0.526066i | \(-0.823666\pi\) | ||||
0.850443 | − | 0.526066i | \(-0.176334\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 26.1421i | − 1.17738i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.82843 | −0.306915 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.68629 | 0.389633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 0.686292i | − 0.0307226i | −0.999882 | − | 0.0153613i | \(-0.995110\pi\) | ||||
0.999882 | − | 0.0153613i | \(-0.00488985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3431i | 0.462098i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4853 | 0.556691 | 0.278346 | − | 0.960481i | \(-0.410214\pi\) | ||||
0.278346 | + | 0.960481i | \(0.410214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.2843 | −2.05962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 5.00000i | − 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 19.2132i | − 0.851610i | −0.904815 | − | 0.425805i | \(-0.859991\pi\) | ||||
0.904815 | − | 0.425805i | \(-0.140009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.65685 | −0.250244 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.65685 | 0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.3137i | 0.762933i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.97056i | 0.394525i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.72792 | −0.295323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9706 | −1.00636 | −0.503179 | − | 0.864182i | \(-0.667836\pi\) | ||||
−0.503179 | + | 0.864182i | \(0.667836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.6569i | 1.64662i | 0.567593 | + | 0.823310i | \(0.307875\pi\) | ||||
−0.567593 | + | 0.823310i | \(0.692125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.89949i | 0.170188i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.7696 | 2.47292 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000i | 0.173585i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.970563i | − 0.0420397i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.9706 | 1.07957 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | 0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 13.3137i | − 0.573462i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 10.8284i | − 0.465550i | −0.972531 | − | 0.232775i | \(-0.925219\pi\) | ||||
0.972531 | − | 0.232775i | \(-0.0747806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.48528 | 0.364138 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −64.2843 | −2.75364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.97056i | 0.212526i | 0.994338 | + | 0.106263i | \(0.0338885\pi\) | ||||
−0.994338 | + | 0.106263i | \(0.966111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.65685i | − 0.0707128i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.3137 | 0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.34315 | −0.354787 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.65685i | 0.240120i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.07107i | 0.0453826i | 0.999743 | + | 0.0226913i | \(0.00722349\pi\) | ||||
−0.999743 | + | 0.0226913i | \(0.992777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.3137 | −1.15525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3137 | −0.646545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 16.6274i | − 0.700762i | −0.936607 | − | 0.350381i | \(-0.886052\pi\) | ||||
0.936607 | − | 0.350381i | \(-0.113948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 20.4853i | − 0.861822i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.585786 | 0.0246007 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.9706 | 0.627599 | 0.313799 | − | 0.949489i | \(-0.398398\pi\) | ||||
0.313799 | + | 0.949489i | \(0.398398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 20.0000i | − 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9706i | 0.708955i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 10.3431i | 0.429846i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.79899i | 0.323557i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.7990 | −0.654327 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.65685 | 0.399262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 31.3137i | − 1.29246i | −0.763145 | − | 0.646228i | \(-0.776346\pi\) | ||||
0.763145 | − | 0.646228i | \(-0.223654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.9411i | 1.72815i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 15.3137i | 0.627801i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 17.5563i | − 0.718534i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.5147 | 0.470479 | 0.235239 | − | 0.971937i | \(-0.424413\pi\) | ||||
0.235239 | + | 0.971937i | \(0.424413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.65685 | 0.230748 | 0.115374 | − | 0.993322i | \(-0.463193\pi\) | ||||
0.115374 | + | 0.993322i | \(0.463193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.00000i | − 0.325785i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23.8995i | − 0.971653i | ||||||||
\(606\) | 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 | ||||||||
\(611\) | − 12.6863i | − 0.513232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6274i | 0.429237i | 0.976698 | + | 0.214619i | \(0.0688509\pi\) | ||||
−0.976698 | + | 0.214619i | \(0.931149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.17157 | −0.0472424 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.9411 | −0.963833 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.82843i | 0.274015i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.17157 | −0.0469381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 11.3137i | − 0.451826i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.6863i | 0.505836i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9289 | 0.753549 | 0.376774 | − | 0.926305i | \(-0.377033\pi\) | ||||
0.376774 | + | 0.926305i | \(0.377033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.31371 | −0.131708 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 63.9411i | − 2.53743i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.8284i | 0.746009i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 32.2843i | 1.27317i | 0.771208 | + | 0.636584i | \(0.219653\pi\) | ||||
−0.771208 | + | 0.636584i | \(0.780347\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.9706i | 1.29821i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.8284 | −0.897478 | −0.448739 | − | 0.893663i | \(-0.648127\pi\) | ||||
−0.448739 | + | 0.893663i | \(0.648127\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.34315i | 0.170221i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5858i | 0.805584i | 0.915292 | + | 0.402792i | \(0.131960\pi\) | ||||
−0.915292 | + | 0.402792i | \(0.868040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.6569 | 0.533617 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.65685 | 0.376750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.3137i | 1.53144i | 0.643171 | + | 0.765722i | \(0.277618\pi\) | ||||
−0.643171 | + | 0.765722i | \(0.722382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 39.3137i | − 1.52913i | −0.644549 | − | 0.764563i | \(-0.722955\pi\) | ||||
0.644549 | − | 0.764563i | \(-0.277045\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.6569 | 0.841083 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.3137 | −0.438727 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.3137i | 0.902710i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 11.8995i | − 0.460061i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 6.65685i | − 0.256222i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.2132i | 1.35335i | 0.736280 | + | 0.676677i | \(0.236580\pi\) | ||||
−0.736280 | + | 0.676677i | \(0.763420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.45584 | −0.209376 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.68629 | −0.256219 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 2.68629i | − 0.102788i | −0.998678 | − | 0.0513940i | \(-0.983634\pi\) | ||||
0.998678 | − | 0.0513940i | \(-0.0163664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 53.4558i | 2.04244i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.485281 | −0.0185146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.3431 | 0.851206 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.34315i | 0.241305i | 0.992695 | + | 0.120652i | \(0.0384986\pi\) | ||||
−0.992695 | + | 0.120652i | \(0.961501\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.17157i | − 0.0445044i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3137 | −0.429153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.62742 | −0.0995205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 13.3137i | − 0.503571i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.58579i | 0.173203i | 0.996243 | + | 0.0866014i | \(0.0276006\pi\) | ||||
−0.996243 | + | 0.0866014i | \(0.972399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.37258 | −0.353494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3137 | −0.576748 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 7.94113i | − 0.298657i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.1127i | 1.16846i | 0.811587 | + | 0.584231i | \(0.198604\pi\) | ||||
−0.811587 | + | 0.584231i | \(0.801396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.2426 | 0.534141 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −50.6274 | −1.89601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 19.3137i | − 0.722292i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 16.9706i | − 0.633777i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 6.34315i | 0.235904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 22.7279i | − 0.844094i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2426 | −0.824934 | −0.412467 | − | 0.910973i | \(-0.635333\pi\) | ||||
−0.412467 | + | 0.910973i | \(0.635333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.9411i | 2.73481i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5147i | 0.868536i | 0.900784 | + | 0.434268i | \(0.142993\pi\) | ||||
−0.900784 | + | 0.434268i | \(0.857007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.7279 | 0.838332 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0000 | −0.589368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.6274i | 0.390936i | 0.980710 | + | 0.195468i | \(0.0626226\pi\) | ||||
−0.980710 | + | 0.195468i | \(0.937377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.0000i | 0.587775i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.0000 | 1.46746 | 0.733729 | − | 0.679442i | \(-0.237778\pi\) | ||||
0.733729 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6569 | −0.720171 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 13.3137i | − 0.487123i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.28427i | 0.156544i | ||||||||
\(750\) | 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 | ||||||||
\(755\) | − 25.3137i | − 0.921260i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 32.4853i | − 1.18070i | −0.807148 | − | 0.590349i | \(-0.798990\pi\) | ||||
0.807148 | − | 0.590349i | \(-0.201010\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.6569 | 0.495712 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.6569 | −1.29256 | −0.646280 | − | 0.763100i | \(-0.723676\pi\) | ||||
−0.646280 | + | 0.763100i | \(0.723676\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11.0294i | − 0.399292i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 26.1421i | − 0.945171i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 21.3137i | − 0.767594i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.72792i | 0.241987i | 0.992653 | + | 0.120993i | \(0.0386079\pi\) | ||||
−0.992653 | + | 0.120993i | \(0.961392\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.3553 | 1.77290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.970563 | −0.0348187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.94113i | − 0.0695480i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.6569i | 1.06121i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.41421 | −0.122014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −68.2843 | −2.43717 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 21.6569i | − 0.771983i | −0.922502 | − | 0.385992i | \(-0.873859\pi\) | ||||
0.922502 | − | 0.385992i | \(-0.126141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.34315i | 0.0834182i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.51472 | 0.124969 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.68629 | 0.166415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 26.9706i | − 0.956547i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.4142i | 1.25444i | 0.778844 | + | 0.627218i | \(0.215806\pi\) | ||||
−0.778844 | + | 0.627218i | \(0.784194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.3431 | −1.21497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19.3137i | − 0.681566i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 13.6569i | − 0.481341i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.24264 | 0.0789447 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.02944 | 0.176826 | 0.0884128 | − | 0.996084i | \(-0.471821\pi\) | ||||
0.0884128 | + | 0.996084i | \(0.471821\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 18.3431i | − 0.644115i | −0.946720 | − | 0.322057i | \(-0.895626\pi\) | ||||
0.946720 | − | 0.322057i | \(-0.104374\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 16.5858i | − 0.581689i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.2843 | −2.11167 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −54.6274 | −1.91117 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.65685i | 0.0578952i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 8.87006i | − 0.309567i | −0.987948 | − | 0.154784i | \(-0.950532\pi\) | ||||
0.987948 | − | 0.154784i | \(-0.0494680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.2132 | 1.36689 | 0.683443 | − | 0.730004i | \(-0.260482\pi\) | ||||
0.683443 | + | 0.730004i | \(0.260482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.3137 | −0.463524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 29.9411i | − 1.04115i | −0.853814 | − | 0.520577i | \(-0.825717\pi\) | ||||
0.853814 | − | 0.520577i | \(-0.174283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 52.7696i | − 1.83276i | −0.400307 | − | 0.916381i | \(-0.631096\pi\) | ||||
0.400307 | − | 0.916381i | \(-0.368904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.4853 | 0.849385 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50.9706 | 1.76603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.3137i | 1.22208i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7.41421i | − 0.256273i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.4853 | 0.983421 | 0.491711 | − | 0.870759i | \(-0.336372\pi\) | ||||
0.491711 | + | 0.870759i | \(0.336372\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3431 | 0.598040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.00000i | − 0.0688837i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 17.0711i | − 0.587263i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.10051 | 0.140895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.31371 | −0.251006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 11.3137i | − 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 34.6274i | − 1.18562i | −0.805342 | − | 0.592810i | \(-0.798018\pi\) | ||||
0.805342 | − | 0.592810i | \(-0.201982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.3137 | 0.660515 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.5980 | −1.42096 | −0.710480 | − | 0.703717i | \(-0.751522\pi\) | ||||
−0.710480 | + | 0.703717i | \(0.751522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.9706i | 1.53438i | 0.641422 | + | 0.767188i | \(0.278345\pi\) | ||||
−0.641422 | + | 0.767188i | \(0.721655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 0.201010i | − 0.00685041i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | − 41.6274i | − 1.41374i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 28.4853i | − 0.966297i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6274 | 0.766701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.31371 | 0.315221 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.31371i | 0.112024i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 23.3137i | − 0.787248i | −0.919272 | − | 0.393624i | \(-0.871221\pi\) | ||||
0.919272 | − | 0.393624i | \(-0.128779\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 30.3431i | − 1.02113i | −0.859840 | − | 0.510564i | \(-0.829437\pi\) | ||||
0.859840 | − | 0.510564i | \(-0.170563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.6569i | 0.459070i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.6569 | −0.995780 | −0.497890 | − | 0.867240i | \(-0.665892\pi\) | ||||
−0.497890 | + | 0.867240i | \(0.665892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9706 | 0.367941 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000i | 0.0670025i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 25.3726i | − 0.849061i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6569 | 0.456498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.3137 | −0.644866 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 25.3137i | − 0.844259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 60.4853i | − 2.01506i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65685 | −0.188248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.9706 | 0.963014 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.5980i | 1.71328i | 0.515912 | + | 0.856641i | \(0.327453\pi\) | ||||
−0.515912 | + | 0.856641i | \(0.672547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5563i | 0.449636i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 5.65685i | − 0.187010i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.34315i | 0.0773775i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.3553 | −0.572500 | −0.286250 | − | 0.958155i | \(-0.592409\pi\) | ||||
−0.286250 | + | 0.958155i | \(0.592409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.0000 | 0.527218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 41.9411i | − 1.38051i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0294i | 0.362646i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 37.6569i | 1.23415i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.3137i | 0.370394i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −52.2843 | −1.70988 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.6274 | −1.19657 | −0.598283 | − | 0.801285i | \(-0.704150\pi\) | ||||
−0.598283 | + | 0.801285i | \(0.704150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 16.9706i | − 0.553813i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 20.3848i | − 0.664525i | −0.943187 | − | 0.332262i | \(-0.892188\pi\) | ||||
0.943187 | − | 0.332262i | \(-0.107812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.34315 | 0.0763033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.6274i | 1.12524i | 0.826716 | + | 0.562620i | \(0.190207\pi\) | ||||
−0.826716 | + | 0.562620i | \(0.809793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.3137i | 0.886640i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.07107 | −0.294150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.9706 | −1.00323 | −0.501617 | − | 0.865090i | \(-0.667261\pi\) | ||||
−0.501617 | + | 0.865090i | \(0.667261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.9411i | 1.87493i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.82843i | 0.220732i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.17157 | −0.296166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 7.31371i | − 0.235681i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.3137i | 1.13679i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.75736 | 0.0565129 | 0.0282564 | − | 0.999601i | \(-0.491005\pi\) | ||||
0.0282564 | + | 0.999601i | \(0.491005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.3137 | 1.39144 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.3137i | 0.940722i | 0.882474 | + | 0.470361i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470361i | \(0.844124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.94113i | − 0.0622296i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 4.00000i | − 0.127841i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8284i | 0.601145i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.28427 | −0.136647 | −0.0683235 | − | 0.997663i | \(-0.521765\pi\) | ||||
−0.0683235 | + | 0.997663i | \(0.521765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58.2843 | −1.85709 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.62742i | − 0.0836316i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 65.9411i | − 2.09681i | ||||||||
\(990\) | 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 | ||||||||
\(995\) | − 59.9411i | − 1.90026i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 12.9706i | − 0.410782i | −0.978680 | − | 0.205391i | \(-0.934153\pi\) | ||||
0.978680 | − | 0.205391i | \(-0.0658466\pi\) | |||||||
\(998\) | 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.d.f.769.1 | 4 | ||
3.2 | odd | 2 | 4608.2.d.o.2305.4 | 4 | |||
4.3 | odd | 2 | 1536.2.d.a.769.3 | 4 | |||
8.3 | odd | 2 | 1536.2.d.a.769.2 | 4 | |||
8.5 | even | 2 | inner | 1536.2.d.f.769.4 | 4 | ||
12.11 | even | 2 | 4608.2.d.c.2305.4 | 4 | |||
16.3 | odd | 4 | 1536.2.a.b.1.1 | ✓ | 2 | ||
16.5 | even | 4 | 1536.2.a.e.1.2 | yes | 2 | ||
16.11 | odd | 4 | 1536.2.a.l.1.2 | yes | 2 | ||
16.13 | even | 4 | 1536.2.a.g.1.1 | yes | 2 | ||
24.5 | odd | 2 | 4608.2.d.o.2305.1 | 4 | |||
24.11 | even | 2 | 4608.2.d.c.2305.1 | 4 | |||
48.5 | odd | 4 | 4608.2.a.a.1.1 | 2 | |||
48.11 | even | 4 | 4608.2.a.e.1.1 | 2 | |||
48.29 | odd | 4 | 4608.2.a.n.1.2 | 2 | |||
48.35 | even | 4 | 4608.2.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.b.1.1 | ✓ | 2 | 16.3 | odd | 4 | ||
1536.2.a.e.1.2 | yes | 2 | 16.5 | even | 4 | ||
1536.2.a.g.1.1 | yes | 2 | 16.13 | even | 4 | ||
1536.2.a.l.1.2 | yes | 2 | 16.11 | odd | 4 | ||
1536.2.d.a.769.2 | 4 | 8.3 | odd | 2 | |||
1536.2.d.a.769.3 | 4 | 4.3 | odd | 2 | |||
1536.2.d.f.769.1 | 4 | 1.1 | even | 1 | trivial | ||
1536.2.d.f.769.4 | 4 | 8.5 | even | 2 | inner | ||
4608.2.a.a.1.1 | 2 | 48.5 | odd | 4 | |||
4608.2.a.e.1.1 | 2 | 48.11 | even | 4 | |||
4608.2.a.n.1.2 | 2 | 48.29 | odd | 4 | |||
4608.2.a.r.1.2 | 2 | 48.35 | even | 4 | |||
4608.2.d.c.2305.1 | 4 | 24.11 | even | 2 | |||
4608.2.d.c.2305.4 | 4 | 12.11 | even | 2 | |||
4608.2.d.o.2305.1 | 4 | 24.5 | odd | 2 | |||
4608.2.d.o.2305.4 | 4 | 3.2 | odd | 2 |