Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,2,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(8.81548438315\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 276) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.585786 | 0.261972 | 0.130986 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130986 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.41421 | 0.534522 | 0.267261 | − | 0.963624i | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.65685 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.24264 | −0.543920 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.24264 | 1.89099 | 0.945496 | − | 0.325634i | \(-0.105578\pi\) | ||||
0.945496 | + | 0.325634i | \(0.105578\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.82843 | 1.63940 | 0.819699 | − | 0.572795i | \(-0.194141\pi\) | ||||
0.819699 | + | 0.572795i | \(0.194141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.65685 | 0.984732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.828427 | 0.140030 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.17157 | −0.521403 | −0.260702 | − | 0.965419i | \(-0.583954\pi\) | ||||
−0.260702 | + | 0.965419i | \(0.583954\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.65685 | −0.905822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.41421 | 0.825660 | 0.412830 | − | 0.910808i | \(-0.364540\pi\) | ||||
0.412830 | + | 0.910808i | \(0.364540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.585786 | 0.0873239 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4853 | 1.52944 | 0.764718 | − | 0.644365i | \(-0.222878\pi\) | ||||
0.764718 | + | 0.644365i | \(0.222878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.24264 | 0.314033 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.58579 | 0.629906 | 0.314953 | − | 0.949107i | \(-0.398011\pi\) | ||||
0.314953 | + | 0.949107i | \(0.398011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.31371 | −0.446820 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.24264 | −1.09176 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.82843 | 1.14936 | 0.574682 | − | 0.818377i | \(-0.305126\pi\) | ||||
0.574682 | + | 0.818377i | \(0.305126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.17157 | 0.406078 | 0.203039 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203039 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.41421 | 0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.31371 | 0.411015 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.75736 | 0.947712 | 0.473856 | − | 0.880602i | \(-0.342862\pi\) | ||||
0.473856 | + | 0.880602i | \(0.342862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | −1.34269 | −0.671345 | − | 0.741145i | \(-0.734283\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.343146 | 0.0401622 | 0.0200811 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200811 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.07107 | 0.795557 | 0.397779 | − | 0.917481i | \(-0.369781\pi\) | ||||
0.397779 | + | 0.917481i | \(0.369781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.65685 | 1.05998 | 0.529989 | − | 0.848005i | \(-0.322196\pi\) | ||||
0.529989 | + | 0.848005i | \(0.322196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31371 | −0.142492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.82843 | −0.946507 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0711 | 1.38553 | 0.692765 | − | 0.721163i | \(-0.256392\pi\) | ||||
0.692765 | + | 0.721163i | \(0.256392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | 0.838628 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.17157 | −0.121486 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.82843 | 0.495386 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1421 | 1.63899 | 0.819493 | − | 0.573090i | \(-0.194255\pi\) | ||||
0.819493 | + | 0.573090i | \(0.194255\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | −0.568535 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.31371 | −0.528734 | −0.264367 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264367 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7279 | 1.25412 | 0.627060 | − | 0.778971i | \(-0.284258\pi\) | ||||
0.627060 | + | 0.778971i | \(0.284258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.828427 | −0.0808462 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.65685 | −0.546869 | −0.273434 | − | 0.961891i | \(-0.588160\pi\) | ||||
−0.273434 | + | 0.961891i | \(0.588160\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.17157 | 0.301032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.58579 | −0.807683 | −0.403841 | − | 0.914829i | \(-0.632325\pi\) | ||||
−0.403841 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.585786 | −0.0546249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65685 | 0.522976 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.17157 | −0.290738 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0000 | 1.90909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.4853 | −1.46283 | −0.731416 | − | 0.681931i | \(-0.761140\pi\) | ||||
−0.731416 | + | 0.681931i | \(0.761140\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.41421 | −0.476695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.65685 | −0.843723 | −0.421862 | − | 0.906660i | \(-0.638623\pi\) | ||||
−0.421862 | + | 0.906660i | \(0.638623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.6569 | 1.01078 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0711 | −1.11674 | −0.558368 | − | 0.829593i | \(-0.688572\pi\) | ||||
−0.558368 | + | 0.829593i | \(0.688572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.65685 | −0.819084 | −0.409542 | − | 0.912291i | \(-0.634311\pi\) | ||||
−0.409542 | + | 0.912291i | \(0.634311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4853 | −0.883020 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.0000 | −2.67597 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.17157 | 0.429476 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.24264 | −0.511417 | −0.255709 | − | 0.966754i | \(-0.582309\pi\) | ||||
−0.255709 | + | 0.966754i | \(0.582309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.34315 | −0.190682 | −0.0953412 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953412 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.24264 | −0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.686292 | 0.0551243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.82843 | −0.704585 | −0.352293 | − | 0.935890i | \(-0.614598\pi\) | ||||
−0.352293 | + | 0.935890i | \(0.614598\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.58579 | −0.363677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.41421 | −0.111456 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8284 | −0.848148 | −0.424074 | − | 0.905628i | \(-0.639400\pi\) | ||||
−0.424074 | + | 0.905628i | \(0.639400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.31371 | 0.257972 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.34315 | −0.181318 | −0.0906590 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906590 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.24264 | 0.630330 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4853 | 1.70952 | 0.854762 | − | 0.519020i | \(-0.173703\pi\) | ||||
0.854762 | + | 0.519020i | \(0.173703\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.58579 | −0.497839 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.82843 | −0.663585 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.48528 | 0.185759 | 0.0928793 | − | 0.995677i | \(-0.470393\pi\) | ||||
0.0928793 | + | 0.995677i | \(0.470393\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3137 | −1.28692 | −0.643459 | − | 0.765481i | \(-0.722501\pi\) | ||||
−0.643459 | + | 0.765481i | \(0.722501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.17157 | −0.234449 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.85786 | −0.136593 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6863 | 0.927714 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.41421 | −0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.82843 | 0.494088 | 0.247044 | − | 0.969004i | \(-0.420541\pi\) | ||||
0.247044 | + | 0.969004i | \(0.420541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.3137 | −0.814379 | −0.407189 | − | 0.913344i | \(-0.633491\pi\) | ||||
−0.407189 | + | 0.913344i | \(0.633491\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.31371 | −0.237300 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.17157 | −0.225965 | −0.112983 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112983 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7574 | −0.833457 | −0.416729 | − | 0.909031i | \(-0.636823\pi\) | ||||
−0.416729 | + | 0.909031i | \(0.636823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.75736 | −0.547162 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.4853 | 0.876295 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17157 | −0.0818262 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −46.6274 | −3.22529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4853 | −1.13489 | −0.567447 | − | 0.823410i | \(-0.692069\pi\) | ||||
−0.567447 | + | 0.823410i | \(0.692069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.3137 | 0.775203 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.17157 | 0.216299 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.65685 | 0.112475 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.343146 | −0.0231876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6863 | −0.853372 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0000 | −0.803579 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.17157 | −0.343249 | −0.171625 | − | 0.985162i | \(-0.554902\pi\) | ||||
−0.171625 | + | 0.985162i | \(0.554902\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.97056 | 0.460628 | 0.230314 | − | 0.973116i | \(-0.426025\pi\) | ||||
0.230314 | + | 0.973116i | \(0.426025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.34315 | −0.284529 | −0.142264 | − | 0.989829i | \(-0.545438\pi\) | ||||
−0.142264 | + | 0.989829i | \(0.545438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.14214 | 0.400669 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.07107 | −0.459315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6569 | −1.40087 | −0.700433 | − | 0.713718i | \(-0.747010\pi\) | ||||
−0.700433 | + | 0.713718i | \(0.747010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7990 | 1.14653 | 0.573267 | − | 0.819369i | \(-0.305676\pi\) | ||||
0.573267 | + | 0.819369i | \(0.305676\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.92893 | −0.187123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 46.6274 | 2.96683 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.65685 | −0.611978 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.4558 | 1.85924 | 0.929618 | − | 0.368524i | \(-0.120137\pi\) | ||||
0.929618 | + | 0.368524i | \(0.120137\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65685 | 0.355643 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.31371 | 0.0822676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.68629 | −0.417079 | −0.208540 | − | 0.978014i | \(-0.566871\pi\) | ||||
−0.208540 | + | 0.978014i | \(0.566871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.48528 | −0.278702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.82843 | 0.546466 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.7990 | −1.46751 | −0.733754 | − | 0.679415i | \(-0.762234\pi\) | ||||
−0.733754 | + | 0.679415i | \(0.762234\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68629 | 0.165018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.0711 | −0.799936 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.8284 | 1.75770 | 0.878850 | − | 0.477098i | \(-0.158311\pi\) | ||||
0.878850 | + | 0.477098i | \(0.158311\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1716 | −0.800116 | −0.400058 | − | 0.916490i | \(-0.631010\pi\) | ||||
−0.400058 | + | 0.916490i | \(0.631010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.00000 | −0.484182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.3431 | 1.58855 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.6274 | −1.96039 | −0.980196 | − | 0.198031i | \(-0.936545\pi\) | ||||
−0.980196 | + | 0.198031i | \(0.936545\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.17157 | 0.0701402 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9289 | 0.651965 | 0.325983 | − | 0.945376i | \(-0.394305\pi\) | ||||
0.325983 | + | 0.945376i | \(0.394305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.10051 | 0.124862 | 0.0624310 | − | 0.998049i | \(-0.480115\pi\) | ||||
0.0624310 | + | 0.998049i | \(0.480115\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.82843 | −0.286011 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.82843 | −0.166957 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.1421 | −0.946269 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.2426 | −1.06575 | −0.532873 | − | 0.846195i | \(-0.678888\pi\) | ||||
−0.532873 | + | 0.846195i | \(0.678888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.17157 | 0.301101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.65685 | 0.441334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.31371 | 0.305265 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.85786 | 0.106381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4558 | 1.68113 | 0.840567 | − | 0.541708i | \(-0.182222\pi\) | ||||
0.840567 | + | 0.541708i | \(0.182222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.7279 | −0.724066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.17157 | −0.179843 | −0.0899217 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899217 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6569 | −0.884978 | −0.442489 | − | 0.896774i | \(-0.645904\pi\) | ||||
−0.442489 | + | 0.896774i | \(0.645904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.828427 | 0.0466766 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.17157 | −0.178133 | −0.0890666 | − | 0.996026i | \(-0.528388\pi\) | ||||
−0.0890666 | + | 0.996026i | \(0.528388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −49.9411 | −2.79617 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.65685 | 0.315735 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.4853 | −1.02855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.3431 | −1.46125 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.65685 | −0.202225 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8284 | 0.817518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1421 | 1.43690 | 0.718451 | − | 0.695578i | \(-0.244852\pi\) | ||||
0.718451 | + | 0.695578i | \(0.244852\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.17157 | −0.173801 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.54416 | 0.248274 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8284 | 0.698809 | 0.349404 | − | 0.936972i | \(-0.386384\pi\) | ||||
0.349404 | + | 0.936972i | \(0.386384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.58579 | 0.466316 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.62742 | −0.358895 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.585786 | 0.0315377 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.8284 | 0.688666 | 0.344333 | − | 0.938848i | \(-0.388105\pi\) | ||||
0.344333 | + | 0.938848i | \(0.388105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.3137 | −1.03384 | −0.516920 | − | 0.856034i | \(-0.672921\pi\) | ||||
−0.516920 | + | 0.856034i | \(0.672921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.65685 | −0.301941 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.1421 | −0.646261 | −0.323130 | − | 0.946354i | \(-0.604735\pi\) | ||||
−0.323130 | + | 0.946354i | \(0.604735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.62742 | −0.351747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.17157 | 0.167857 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.1716 | −1.32850 | −0.664252 | − | 0.747508i | \(-0.731250\pi\) | ||||
−0.664252 | + | 0.747508i | \(0.731250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.9411 | 2.57585 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.0000 | −1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.201010 | 0.0105214 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.7574 | 0.613729 | 0.306865 | − | 0.951753i | \(-0.400720\pi\) | ||||
0.306865 | + | 0.951753i | \(0.400720\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.48528 | 0.336699 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1716 | −0.578442 | −0.289221 | − | 0.957262i | \(-0.593396\pi\) | ||||
−0.289221 | + | 0.957262i | \(0.593396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 49.9411 | 2.57210 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.72792 | 0.448323 | 0.224162 | − | 0.974552i | \(-0.428036\pi\) | ||||
0.224162 | + | 0.974552i | \(0.428036\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.4853 | 0.844567 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.7990 | 1.42046 | 0.710231 | − | 0.703969i | \(-0.248590\pi\) | ||||
0.710231 | + | 0.703969i | \(0.248590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.68629 | −0.238836 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.41421 | 0.275220 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.7279 | 0.746735 | 0.373368 | − | 0.927683i | \(-0.378203\pi\) | ||||
0.373368 | + | 0.927683i | \(0.378203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.24264 | 0.113415 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.65685 | 0.487124 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.14214 | 0.208413 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.6274 | −0.834506 | −0.417253 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417253 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.6569 | −0.583573 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8995 | −0.793983 | −0.396991 | − | 0.917822i | \(-0.629946\pi\) | ||||
−0.396991 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.62742 | 0.330135 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.9411 | 0.889309 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.34315 | 0.313648 | 0.156824 | − | 0.987627i | \(-0.449874\pi\) | ||||
0.156824 | + | 0.987627i | \(0.449874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0711 | 0.644748 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.4853 | 0.614361 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.65685 | 0.277684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.65685 | 0.472898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3137 | −1.52977 | −0.764887 | − | 0.644164i | \(-0.777205\pi\) | ||||
−0.764887 | + | 0.644164i | \(0.777205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.3137 | 1.42866 | 0.714331 | − | 0.699808i | \(-0.246731\pi\) | ||||
0.714331 | + | 0.699808i | \(0.246731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.4853 | 0.509812 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4437 | 0.506591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.48528 | 0.217058 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 32.0000 | 1.54497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.00000 | 0.192673 | 0.0963366 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963366 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.97056 | 0.142756 | 0.0713781 | − | 0.997449i | \(-0.477260\pi\) | ||||
0.0713781 | + | 0.997449i | \(0.477260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.17157 | −0.247958 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.24264 | −0.394299 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.34315 | 0.111832 | 0.0559161 | − | 0.998435i | \(-0.482192\pi\) | ||||
0.0559161 | + | 0.998435i | \(0.482192\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.2843 | −1.91396 | −0.956982 | − | 0.290148i | \(-0.906295\pi\) | ||||
−0.956982 | + | 0.290148i | \(0.906295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.65685 | 0.362970 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.24264 | 0.295267 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.6569 | 1.87152 | 0.935761 | − | 0.352634i | \(-0.114714\pi\) | ||||
0.935761 | + | 0.352634i | \(0.114714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3137 | 0.532742 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.34315 | 0.110091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.68629 | 0.219697 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.1716 | −1.45814 | −0.729072 | − | 0.684437i | \(-0.760048\pi\) | ||||
−0.729072 | + | 0.684437i | \(0.760048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.24264 | 0.104678 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4558 | 1.09245 | 0.546224 | − | 0.837639i | \(-0.316065\pi\) | ||||
0.546224 | + | 0.837639i | \(0.316065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.97056 | 0.231002 | 0.115501 | − | 0.993307i | \(-0.463153\pi\) | ||||
0.115501 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.686292 | −0.0318260 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.1127 | −1.62482 | −0.812411 | − | 0.583085i | \(-0.801845\pi\) | ||||
−0.812411 | + | 0.583085i | \(0.801845\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9706 | 0.506574 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.82843 | 0.406792 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.6274 | −1.40825 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.3848 | −1.76121 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.58579 | 0.209969 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.62742 | −0.120050 | −0.0600249 | − | 0.998197i | \(-0.519118\pi\) | ||||
−0.0600249 | + | 0.998197i | \(0.519118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.9411 | −0.818045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.41421 | 0.0643489 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.45584 | 0.429368 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3431 | 0.649950 | 0.324975 | − | 0.945723i | \(-0.394644\pi\) | ||||
0.324975 | + | 0.945723i | \(0.394644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.8284 | 0.489678 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.142136 | −0.00641449 | −0.00320725 | − | 0.999995i | \(-0.501021\pi\) | ||||
−0.00320725 | + | 0.999995i | \(0.501021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7990 | −0.891702 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.31371 | −0.148940 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0000 | −0.717698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.4853 | 1.09611 | 0.548056 | − | 0.836442i | \(-0.315368\pi\) | ||||
0.548056 | + | 0.836442i | \(0.315368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.34315 | 0.104684 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.686292 | −0.0306002 | −0.0153001 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0153001 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.11270 | −0.138513 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.0000 | −0.843820 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.4853 | −0.996643 | −0.498321 | − | 0.866992i | \(-0.666050\pi\) | ||||
−0.498321 | + | 0.866992i | \(0.666050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.485281 | 0.0214676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.24264 | −0.363921 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.45584 | 0.328544 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −59.3137 | −2.60861 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.4853 | −0.986994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.24264 | −0.273495 | −0.136748 | − | 0.990606i | \(-0.543665\pi\) | ||||
−0.136748 | + | 0.990606i | \(0.543665\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.21320 | −0.0530497 | −0.0265248 | − | 0.999648i | \(-0.508444\pi\) | ||||
−0.0265248 | + | 0.999648i | \(0.508444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.58579 | 0.287427 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.62742 | −0.114452 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.82843 | 0.383121 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.3137 | −0.490051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.31371 | −0.143264 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.48528 | −0.107248 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.2843 | 1.21829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.2843 | 1.04406 | 0.522031 | − | 0.852926i | \(-0.325174\pi\) | ||||
0.522031 | + | 0.852926i | \(0.325174\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.3137 | 0.743002 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.14214 | 0.0917590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.1421 | −1.28878 | −0.644392 | − | 0.764695i | \(-0.722890\pi\) | ||||
−0.644392 | + | 0.764695i | \(0.722890\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.17157 | 0.135359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 72.7696 | 3.10009 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0000 | 0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.85786 | 0.0788620 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.7574 | 0.921889 | 0.460944 | − | 0.887429i | \(-0.347511\pi\) | ||||
0.460944 | + | 0.887429i | \(0.347511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.6274 | 1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6863 | −0.535616 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.8284 | −1.13068 | −0.565342 | − | 0.824857i | \(-0.691256\pi\) | ||||
−0.565342 | + | 0.824857i | \(0.691256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.02944 | −0.211590 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41421 | 0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.2426 | 0.764771 | 0.382386 | − | 0.924003i | \(-0.375103\pi\) | ||||
0.382386 | + | 0.924003i | \(0.375103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.727922 | −0.0304626 | −0.0152313 | − | 0.999884i | \(-0.504848\pi\) | ||||
−0.0152313 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.82843 | −0.285262 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.65685 | 0.194204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.37258 | −0.0571414 | −0.0285707 | − | 0.999592i | \(-0.509096\pi\) | ||||
−0.0285707 | + | 0.999592i | \(0.509096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3137 | 0.470182 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6569 | 0.566582 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.9411 | −1.07437 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.31371 | 0.137005 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3431 | 0.922200 | 0.461100 | − | 0.887348i | \(-0.347455\pi\) | ||||
0.461100 | + | 0.887348i | \(0.347455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.65685 | 0.397904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.17157 | 0.130461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.6569 | −1.79277 | −0.896386 | − | 0.443274i | \(-0.853817\pi\) | ||||
−0.896386 | + | 0.443274i | \(0.853817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85786 | −0.0761650 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.7574 | 0.481197 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.2843 | 0.501922 | 0.250961 | − | 0.967997i | \(-0.419253\pi\) | ||||
0.250961 | + | 0.967997i | \(0.419253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6863 | 0.517485 | 0.258742 | − | 0.965946i | \(-0.416692\pi\) | ||||
0.258742 | + | 0.965946i | \(0.416692\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.75736 | 0.315904 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.3015 | 0.500128 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3431 | 0.419815 | 0.209908 | − | 0.977721i | \(-0.432684\pi\) | ||||
0.209908 | + | 0.977721i | \(0.432684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4853 | −0.505929 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.3137 | 2.39958 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4853 | 0.746613 | 0.373307 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373307 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.17157 | 0.0472424 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.8995 | −0.479056 | −0.239528 | − | 0.970890i | \(-0.576993\pi\) | ||||
−0.239528 | + | 0.970890i | \(0.576993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.242641 | 0.00975255 | 0.00487628 | − | 0.999988i | \(-0.498448\pi\) | ||||
0.00487628 | + | 0.999988i | \(0.498448\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.4853 | 0.740597 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 46.6274 | 1.86212 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.11270 | 0.283602 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.24264 | 0.168897 | 0.0844484 | − | 0.996428i | \(-0.473087\pi\) | ||||
0.0844484 | + | 0.996428i | \(0.473087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.4853 | 0.655231 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.65685 | −0.383221 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.2843 | −1.12066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3137 | −0.447563 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.6985 | 1.56800 | 0.783998 | − | 0.620763i | \(-0.213177\pi\) | ||||
0.783998 | + | 0.620763i | \(0.213177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.72792 | 0.344196 | 0.172098 | − | 0.985080i | \(-0.444945\pi\) | ||||
0.172098 | + | 0.985080i | \(0.444945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.17157 | −0.124881 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.7990 | −1.17152 | −0.585760 | − | 0.810485i | \(-0.699204\pi\) | ||||
−0.585760 | + | 0.810485i | \(0.699204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −49.9411 | −1.96036 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.65685 | −0.0649372 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.9706 | −0.585843 | −0.292922 | − | 0.956136i | \(-0.594628\pi\) | ||||
−0.292922 | + | 0.956136i | \(0.594628\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.343146 | 0.0133874 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.7990 | 1.55035 | 0.775174 | − | 0.631747i | \(-0.217662\pi\) | ||||
0.775174 | + | 0.631747i | \(0.217662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.1421 | −0.783438 | −0.391719 | − | 0.920085i | \(-0.628120\pi\) | ||||
−0.391719 | + | 0.920085i | \(0.628120\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.6863 | 0.492695 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.82843 | 0.264795 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.82843 | −0.341838 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.0000 | 0.463947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.9411 | −0.692609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.686292 | 0.0264546 | 0.0132273 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132273 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.6985 | 1.67947 | 0.839735 | − | 0.542997i | \(-0.182711\pi\) | ||||
0.839735 | + | 0.542997i | \(0.182711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.8284 | 0.876075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.17157 | 0.198175 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.6274 | −1.01887 | −0.509435 | − | 0.860509i | \(-0.670146\pi\) | ||||
−0.509435 | + | 0.860509i | \(0.670146\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.65685 | −0.292553 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.97056 | −0.265944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.9411 | 0.988278 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4558 | −0.968386 | −0.484193 | − | 0.874961i | \(-0.660887\pi\) | ||||
−0.484193 | + | 0.874961i | \(0.660887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.00000 | −0.303895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.65685 | −0.214577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.48528 | 0.169892 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.34315 | 0.164273 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.2132 | 1.78322 | 0.891609 | − | 0.452806i | \(-0.149577\pi\) | ||||
0.891609 | + | 0.452806i | \(0.149577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.1421 | −0.985969 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.14214 | −0.231326 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.51472 | −0.282620 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.31371 | −0.199561 | −0.0997803 | − | 0.995009i | \(-0.531814\pi\) | ||||
−0.0997803 | + | 0.995009i | \(0.531814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.07107 | 0.265186 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.17157 | −0.0438757 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.7452 | −0.701029 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.6569 | 0.808790 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.1421 | 0.751175 | 0.375587 | − | 0.926787i | \(-0.377441\pi\) | ||||
0.375587 | + | 0.926787i | \(0.377441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.7990 | −0.661952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.1127 | −1.52689 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0416 | −0.891655 | −0.445827 | − | 0.895119i | \(-0.647090\pi\) | ||||
−0.445827 | + | 0.895119i | \(0.647090\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.1421 | −0.449093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.9706 | 0.405207 | 0.202603 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202603 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.92893 | 0.108035 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43.8823 | −1.61642 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.6863 | −0.908100 | −0.454050 | − | 0.890976i | \(-0.650021\pi\) | ||||
−0.454050 | + | 0.890976i | \(0.650021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.6274 | −1.71290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.4558 | 0.640393 | 0.320196 | − | 0.947351i | \(-0.396251\pi\) | ||||
0.320196 | + | 0.947351i | \(0.396251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.65685 | −0.133977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.65685 | 0.353326 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.69848 | 0.207941 | 0.103970 | − | 0.994580i | \(-0.466845\pi\) | ||||
0.103970 | + | 0.994580i | \(0.466845\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.4558 | −1.07343 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.37258 | −0.0499534 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3137 | 0.774660 | 0.387330 | − | 0.921941i | \(-0.373397\pi\) | ||||
0.387330 | + | 0.921941i | \(0.373397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.65685 | −0.205331 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.1716 | −1.27497 | −0.637484 | − | 0.770463i | \(-0.720025\pi\) | ||||
−0.637484 | + | 0.770463i | \(0.720025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.17157 | 0.187224 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.31371 | −0.0474972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.9411 | 1.80327 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.6569 | 0.708844 | 0.354422 | − | 0.935086i | \(-0.384678\pi\) | ||||
0.354422 | + | 0.935086i | \(0.384678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.68629 | 0.240801 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.8701 | −1.61386 | −0.806932 | − | 0.590644i | \(-0.798874\pi\) | ||||
−0.806932 | + | 0.590644i | \(0.798874\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.45584 | −0.195980 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.48528 | 0.160909 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.4853 | −0.590647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 64.0000 | 2.29010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.82843 | −0.315502 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.17157 | −0.184581 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.5269 | −1.58721 | −0.793606 | − | 0.608431i | \(-0.791799\pi\) | ||||
−0.793606 | + | 0.608431i | \(0.791799\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.7990 | 0.847266 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1421 | −0.431725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.9411 | 0.637108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.68629 | −0.0952729 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.100505 | −0.00356007 | −0.00178004 | − | 0.999998i | \(-0.500567\pi\) | ||||
−0.00178004 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.5147 | −0.831891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.0711 | 0.461843 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.94113 | −0.0685008 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.828427 | −0.0291982 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.8284 | −1.01481 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.8284 | 1.71672 | 0.858358 | − | 0.513051i | \(-0.171485\pi\) | ||||
0.858358 | + | 0.513051i | \(0.171485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.8284 | 0.380238 | 0.190119 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190119 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.1716 | 0.461947 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.34315 | −0.222191 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.6274 | 1.56132 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.00000 | 0.279543 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3137 | 0.883455 | 0.441727 | − | 0.897149i | \(-0.354366\pi\) | ||||
0.441727 | + | 0.897149i | \(0.354366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.20101 | −0.146438 | −0.0732190 | − | 0.997316i | \(-0.523327\pi\) | ||||
−0.0732190 | + | 0.997316i | \(0.523327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −26.3431 | −0.917151 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7696 | −0.861322 | −0.430661 | − | 0.902514i | \(-0.641719\pi\) | ||||
−0.430661 | + | 0.902514i | \(0.641719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0294 | −0.660920 | −0.330460 | − | 0.943820i | \(-0.607204\pi\) | ||||
−0.330460 | + | 0.943820i | \(0.607204\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.6274 | 1.13183 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.2132 | 0.388514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.37258 | −0.0475002 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.17157 | −0.0404955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17157 | 0.0404472 | 0.0202236 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202236 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.9289 | −0.376412 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.1299 | 0.382882 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6985 | 1.02045 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.10051 | −0.0720891 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.17157 | 0.108720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.9411 | −1.64147 | −0.820736 | − | 0.571307i | \(-0.806437\pi\) | ||||
−0.820736 | + | 0.571307i | \(0.806437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.82843 | 0.165129 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.97056 | 0.238110 | 0.119055 | − | 0.992888i | \(-0.462014\pi\) | ||||
0.119055 | + | 0.992888i | \(0.462014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | 0.272956 | 0.136478 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136478 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.82843 | 0.0963925 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.4853 | 0.901569 | 0.450785 | − | 0.892633i | \(-0.351144\pi\) | ||||
0.450785 | + | 0.892633i | \(0.351144\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.1716 | 0.447847 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.0000 | −1.35691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.8823 | 1.48689 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.1421 | 0.546329 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.00000 | −0.270449 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.97056 | 0.100309 | 0.0501544 | − | 0.998741i | \(-0.484029\pi\) | ||||
0.0501544 | + | 0.998741i | \(0.484029\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.2426 | 0.615309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.7574 | −1.40684 | −0.703421 | − | 0.710774i | \(-0.748345\pi\) | ||||
−0.703421 | + | 0.710774i | \(0.748345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7990 | −1.07012 | −0.535061 | − | 0.844814i | \(-0.679711\pi\) | ||||
−0.535061 | + | 0.844814i | \(0.679711\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.17157 | −0.173841 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.79899 | 0.329018 | 0.164509 | − | 0.986376i | \(-0.447396\pi\) | ||||
0.164509 | + | 0.986376i | \(0.447396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.3137 | −0.781917 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.65685 | −0.189512 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 86.4264 | 2.89215 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.45584 | 0.0486635 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.65685 | 0.188877 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.3431 | 0.344963 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2843 | −0.342619 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.65685 | −0.254804 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.1421 | −0.337136 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.0711 | 0.367609 | 0.183804 | − | 0.982963i | \(-0.441159\pi\) | ||||
0.183804 | + | 0.982963i | \(0.441159\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.31371 | −0.176245 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.9411 | −1.52210 | −0.761049 | − | 0.648695i | \(-0.775315\pi\) | ||||
−0.761049 | + | 0.648695i | \(0.775315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.6274 | −1.80790 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.85786 | −0.0614191 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.6569 | −0.450989 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0416 | −0.793060 | −0.396530 | − | 0.918022i | \(-0.629786\pi\) | ||||
−0.396530 | + | 0.918022i | \(0.629786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.4558 | −0.970603 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −64.0000 | −2.10659 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.7696 | 0.485620 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.7279 | 0.418040 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.97056 | −0.0974610 | −0.0487305 | − | 0.998812i | \(-0.515518\pi\) | ||||
−0.0487305 | + | 0.998812i | \(0.515518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.2132 | −1.35071 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.17157 | 0.103833 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.43146 | 0.243035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0000 | 0.588034 | 0.294017 | − | 0.955800i | \(-0.405008\pi\) | ||||
0.294017 | + | 0.955800i | \(0.405008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.6569 | 0.510942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0416 | −0.979329 | −0.489665 | − | 0.871911i | \(-0.662881\pi\) | ||||
−0.489665 | + | 0.871911i | \(0.662881\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000 | 0.0651290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.828427 | −0.0269487 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.7990 | 0.968337 | 0.484169 | − | 0.874975i | \(-0.339122\pi\) | ||||
0.484169 | + | 0.874975i | \(0.339122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.94113 | 0.0630116 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.17157 | 0.102845 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.8995 | 0.515035 | 0.257518 | − | 0.966274i | \(-0.417095\pi\) | ||||
0.257518 | + | 0.966274i | \(0.417095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.00000 | 0.129437 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.9411 | 1.61437 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.4853 | −0.596921 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.65685 | −0.182290 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.62742 | −0.213344 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.4558 | −1.46176 | −0.730881 | − | 0.682505i | \(-0.760890\pi\) | ||||
−0.730881 | + | 0.682505i | \(0.760890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.4853 | 0.593833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.45584 | 0.303452 | 0.151726 | − | 0.988423i | \(-0.451517\pi\) | ||||
0.151726 | + | 0.988423i | \(0.451517\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6569 | −0.437819 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.3431 | 0.843656 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.786797 | 0.0251719 | 0.0125859 | − | 0.999921i | \(-0.495994\pi\) | ||||
0.0125859 | + | 0.999921i | \(0.495994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.9411 | −2.36317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.65685 | 0.116754 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0000 | −0.637901 | −0.318950 | − | 0.947771i | \(-0.603330\pi\) | ||||
−0.318950 | + | 0.947771i | \(0.603330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.85786 | −0.0591965 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.8284 | −0.471994 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.41421 | −0.172162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.7696 | −1.93041 | −0.965204 | − | 0.261497i | \(-0.915784\pi\) | ||||
−0.965204 | + | 0.261497i | \(0.915784\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.1421 | −0.829596 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.88730 | −0.218342 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3137 | −0.865034 | −0.432517 | − | 0.901626i | \(-0.642374\pi\) | ||||
−0.432517 | + | 0.901626i | \(0.642374\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.17157 | 0.100344 |
(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 | 1104.2.a.l.1.1 | 2 | ||
3.2 | odd | 2 | 3312.2.a.s.1.2 | 2 | |||
4.3 | odd | 2 | 276.2.a.b.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 4416.2.a.bc.1.2 | 2 | |||
8.5 | even | 2 | 4416.2.a.bi.1.2 | 2 | |||
12.11 | even | 2 | 828.2.a.e.1.2 | 2 | |||
20.3 | even | 4 | 6900.2.f.l.6349.4 | 4 | |||
20.7 | even | 4 | 6900.2.f.l.6349.1 | 4 | |||
20.19 | odd | 2 | 6900.2.a.m.1.2 | 2 | |||
92.91 | even | 2 | 6348.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
828.2.a.e.1.2 | 2 | 12.11 | even | 2 | |||
1104.2.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3312.2.a.s.1.2 | 2 | 3.2 | odd | 2 | |||
4416.2.a.bc.1.2 | 2 | 8.3 | odd | 2 | |||
4416.2.a.bi.1.2 | 2 | 8.5 | even | 2 | |||
6348.2.a.h.1.2 | 2 | 92.91 | even | 2 | |||
6900.2.a.m.1.2 | 2 | 20.19 | odd | 2 | |||
6900.2.f.l.6349.1 | 4 | 20.7 | even | 4 | |||
6900.2.f.l.6349.4 | 4 | 20.3 | even | 4 |