Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2280,2,Mod(1,2280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2280.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: | \(18.2058916609\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2280.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.41421 | −1.02942 | −0.514712 | − | 0.857363i | \(-0.672101\pi\) | ||||
−0.514712 | + | 0.857363i | \(0.672101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | 0.946932 | 0.473466 | − | 0.880812i | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.07107 | 1.31306 | 0.656532 | − | 0.754298i | \(-0.272023\pi\) | ||||
0.656532 | + | 0.754298i | \(0.272023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.41421 | 0.594338 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24264 | −0.368688 | −0.184344 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184344 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.41421 | −0.546712 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.89949 | −1.54604 | −0.773021 | − | 0.634381i | \(-0.781255\pi\) | ||||
−0.773021 | + | 0.634381i | \(0.781255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.07107 | −0.468333 | −0.234167 | − | 0.972196i | \(-0.575236\pi\) | ||||
−0.234167 | + | 0.972196i | \(0.575236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.82843 | −1.28776 | −0.643879 | − | 0.765127i | \(-0.722676\pi\) | ||||
−0.643879 | + | 0.765127i | \(0.722676\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.82843 | −0.396059 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.48528 | −1.16554 | −0.582772 | − | 0.812636i | \(-0.698032\pi\) | ||||
−0.582772 | + | 0.812636i | \(0.698032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41421 | 0.460372 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.82843 | −0.888985 | −0.444493 | − | 0.895782i | \(-0.646616\pi\) | ||||
−0.444493 | + | 0.895782i | \(0.646616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.65685 | 1.23643 | 0.618217 | − | 0.786008i | \(-0.287855\pi\) | ||||
0.618217 | + | 0.786008i | \(0.287855\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.41421 | −0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.41421 | −0.423481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.828427 | −0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.17157 | −1.08847 | −0.544233 | − | 0.838934i | \(-0.683179\pi\) | ||||
−0.544233 | + | 0.838934i | \(0.683179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.343146 | −0.0401622 | −0.0200811 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200811 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.82843 | 0.550250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.34315 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542080\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.65685 | 0.401392 | 0.200696 | − | 0.979654i | \(-0.435680\pi\) | ||||
0.200696 | + | 0.979654i | \(0.435680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.07107 | −0.758098 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.75736 | −0.398279 | −0.199140 | − | 0.979971i | \(-0.563815\pi\) | ||||
−0.199140 | + | 0.979971i | \(0.563815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.82843 | −0.506157 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.828427 | −0.0859039 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.89949 | −0.802072 | −0.401036 | − | 0.916062i | \(-0.631350\pi\) | ||||
−0.401036 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.41421 | −0.343141 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.82843 | 0.480446 | 0.240223 | − | 0.970718i | \(-0.422779\pi\) | ||||
0.240223 | + | 0.970718i | \(0.422779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.3137 | −1.90304 | −0.951518 | − | 0.307593i | \(-0.900477\pi\) | ||||
−0.951518 | + | 0.307593i | \(0.900477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.41421 | −0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.34315 | −0.226520 | −0.113260 | − | 0.993565i | \(-0.536129\pi\) | ||||
−0.113260 | + | 0.993565i | \(0.536129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.1421 | −1.92927 | −0.964633 | − | 0.263595i | \(-0.915092\pi\) | ||||
−0.964633 | + | 0.263595i | \(0.915092\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24264 | 0.212862 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.31371 | 0.688016 | 0.344008 | − | 0.938967i | \(-0.388215\pi\) | ||||
0.344008 | + | 0.938967i | \(0.388215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.41421 | 0.315644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.89949 | 0.892607 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.65685 | 0.501965 | 0.250982 | − | 0.967992i | \(-0.419246\pi\) | ||||
0.250982 | + | 0.967992i | \(0.419246\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.07107 | 0.270392 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7279 | −1.63627 | −0.818133 | − | 0.575029i | \(-0.804991\pi\) | ||||
−0.818133 | + | 0.575029i | \(0.804991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41421 | −0.122628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.34315 | 0.371060 | 0.185530 | − | 0.982639i | \(-0.440600\pi\) | ||||
0.185530 | + | 0.982639i | \(0.440600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.82843 | 0.239904 | 0.119952 | − | 0.992780i | \(-0.461726\pi\) | ||||
0.119952 | + | 0.992780i | \(0.461726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.82843 | 0.743488 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.6569 | −0.974795 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.07107 | −0.587220 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6569 | −1.28266 | −0.641330 | − | 0.767265i | \(-0.721617\pi\) | ||||
−0.641330 | + | 0.767265i | \(0.721617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.82843 | −0.392932 | −0.196466 | − | 0.980511i | \(-0.562947\pi\) | ||||
−0.196466 | + | 0.980511i | \(0.562947\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.82843 | 0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.828427 | −0.0665409 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.1421 | 1.92675 | 0.963376 | − | 0.268154i | \(-0.0864136\pi\) | ||||
0.963376 | + | 0.268154i | \(0.0864136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | 0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.17157 | −0.0923329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.55635 | 0.591859 | 0.295929 | − | 0.955210i | \(-0.404371\pi\) | ||||
0.295929 | + | 0.955210i | \(0.404371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.41421 | −0.265796 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.31371 | 0.411187 | 0.205594 | − | 0.978637i | \(-0.434088\pi\) | ||||
0.205594 | + | 0.978637i | \(0.434088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.3137 | 0.860165 | 0.430083 | − | 0.902790i | \(-0.358484\pi\) | ||||
0.430083 | + | 0.902790i | \(0.358484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.41421 | −0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.82843 | 0.513256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8284 | −1.40730 | −0.703651 | − | 0.710545i | \(-0.748448\pi\) | ||||
−0.703651 | + | 0.710545i | \(0.748448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.14214 | −0.605200 | −0.302600 | − | 0.953118i | \(-0.597855\pi\) | ||||
−0.302600 | + | 0.953118i | \(0.597855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.65685 | −0.713855 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.24264 | 0.164882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.65685 | −0.706179 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | 0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.2426 | −1.60942 | −0.804710 | − | 0.593667i | \(-0.797679\pi\) | ||||
−0.804710 | + | 0.593667i | \(0.797679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.07107 | −0.0770971 | −0.0385486 | − | 0.999257i | \(-0.512273\pi\) | ||||
−0.0385486 | + | 0.999257i | \(0.512273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.14214 | −0.437609 | −0.218805 | − | 0.975769i | \(-0.570216\pi\) | ||||
−0.218805 | + | 0.975769i | \(0.570216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8284 | −1.05116 | −0.525580 | − | 0.850744i | \(-0.676152\pi\) | ||||
−0.525580 | + | 0.850744i | \(0.676152\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3137 | −0.798007 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0000 | −0.701862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.89949 | 0.691411 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.41421 | −0.236166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.17157 | 0.628426 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.07107 | 0.209445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17157 | −0.0795315 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.343146 | 0.0231876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.65685 | 0.649590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3137 | −0.757622 | −0.378811 | − | 0.925474i | \(-0.623667\pi\) | ||||
−0.378811 | + | 0.925474i | \(0.623667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.343146 | 0.0227754 | 0.0113877 | − | 0.999935i | \(-0.496375\pi\) | ||||
0.0113877 | + | 0.999935i | \(0.496375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3431 | −0.683494 | −0.341747 | − | 0.939792i | \(-0.611019\pi\) | ||||
−0.341747 | + | 0.939792i | \(0.611019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.82843 | −0.317687 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.34315 | 0.284529 | 0.142264 | − | 0.989829i | \(-0.454562\pi\) | ||||
0.142264 | + | 0.989829i | \(0.454562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.82843 | 0.575903 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.2426 | −1.69750 | −0.848748 | − | 0.528798i | \(-0.822643\pi\) | ||||
−0.848748 | + | 0.528798i | \(0.822643\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6569 | 1.52387 | 0.761936 | − | 0.647652i | \(-0.224249\pi\) | ||||
0.761936 | + | 0.647652i | \(0.224249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.41421 | 0.217241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.65685 | −0.231744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2426 | −0.898988 | −0.449494 | − | 0.893283i | \(-0.648396\pi\) | ||||
−0.449494 | + | 0.893283i | \(0.648396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.82843 | 0.177123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.0000 | 0.748539 | 0.374270 | − | 0.927320i | \(-0.377893\pi\) | ||||
0.374270 | + | 0.927320i | \(0.377893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.17157 | 0.197072 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.07107 | 0.437688 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.00000 | −0.123325 | −0.0616626 | − | 0.998097i | \(-0.519640\pi\) | ||||
−0.0616626 | + | 0.998097i | \(0.519640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.48528 | 0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.75736 | 0.229947 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.3848 | −1.36482 | −0.682412 | − | 0.730968i | \(-0.739069\pi\) | ||||
−0.682412 | + | 0.730968i | \(0.739069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.82843 | 0.171815 | 0.0859074 | − | 0.996303i | \(-0.472621\pi\) | ||||
0.0859074 | + | 0.996303i | \(0.472621\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843 | 0.292230 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.41421 | −0.205885 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.6274 | 1.23938 | 0.619691 | − | 0.784846i | \(-0.287258\pi\) | ||||
0.619691 | + | 0.784846i | \(0.287258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.828427 | 0.0495966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.38478 | 0.380884 | 0.190442 | − | 0.981698i | \(-0.439008\pi\) | ||||
0.190442 | + | 0.981698i | \(0.439008\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2426 | 0.965525 | 0.482762 | − | 0.875751i | \(-0.339633\pi\) | ||||
0.482762 | + | 0.875751i | \(0.339633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.0000 | 0.826394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.89949 | 0.463077 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.65685 | −0.564159 | −0.282080 | − | 0.959391i | \(-0.591024\pi\) | ||||
−0.282080 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.82843 | 0.397566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.41421 | 0.198113 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.82843 | 0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.34315 | 0.250335 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.82843 | −0.277386 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.65685 | −0.552950 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.85786 | 0.106034 | 0.0530170 | − | 0.998594i | \(-0.483116\pi\) | ||||
0.0530170 | + | 0.998594i | \(0.483116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3137 | 1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.2132 | 1.08948 | 0.544740 | − | 0.838605i | \(-0.316628\pi\) | ||||
0.544740 | + | 0.838605i | \(0.316628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7990 | −0.779965 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.41421 | 0.0796819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.14214 | −0.120314 | −0.0601572 | − | 0.998189i | \(-0.519160\pi\) | ||||
−0.0601572 | + | 0.998189i | \(0.519160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.1421 | −1.35170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34315 | 0.130782 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.82843 | 0.157378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.41421 | 0.189386 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.1421 | 1.11386 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.4853 | 0.688336 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1421 | 0.887252 | 0.443626 | − | 0.896212i | \(-0.353692\pi\) | ||||
0.443626 | + | 0.896212i | \(0.353692\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.24264 | −0.122896 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.2426 | 1.42953 | 0.714764 | − | 0.699366i | \(-0.246534\pi\) | ||||
0.714764 | + | 0.699366i | \(0.246534\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.31371 | −0.397226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.82843 | −0.153168 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.828427 | 0.0446010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.31371 | −0.0705236 | −0.0352618 | − | 0.999378i | \(-0.511227\pi\) | ||||
−0.0352618 | + | 0.999378i | \(0.511227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.41421 | −0.182237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.3137 | −1.56021 | −0.780106 | − | 0.625648i | \(-0.784835\pi\) | ||||
−0.780106 | + | 0.625648i | \(0.784835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.17157 | 0.486777 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | 0.211702 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.5563 | −0.926589 | −0.463294 | − | 0.886204i | \(-0.653333\pi\) | ||||
−0.463294 | + | 0.886204i | \(0.653333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.656854 | −0.0344759 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.343146 | 0.0179611 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.727922 | −0.0379972 | −0.0189986 | − | 0.999820i | \(-0.506048\pi\) | ||||
−0.0189986 | + | 0.999820i | \(0.506048\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.89949 | −0.515347 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.92893 | −0.151654 | −0.0758272 | − | 0.997121i | \(-0.524160\pi\) | ||||
−0.0758272 | + | 0.997121i | \(0.524160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.1421 | 1.24338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4853 | 1.36046 | 0.680229 | − | 0.733000i | \(-0.261880\pi\) | ||||
0.680229 | + | 0.733000i | \(0.261880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.65685 | −0.289809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6274 | 0.543036 | 0.271518 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271518 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.82843 | −0.246079 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.07107 | −0.156111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.02944 | −0.0521945 | −0.0260973 | − | 0.999659i | \(-0.508308\pi\) | ||||
−0.0260973 | + | 0.999659i | \(0.508308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.34315 | 0.118498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.7279 | 0.944699 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.34315 | 0.117896 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6274 | −1.43677 | −0.718384 | − | 0.695646i | \(-0.755118\pi\) | ||||
−0.718384 | + | 0.695646i | \(0.755118\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.41421 | 0.0707992 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3848 | −0.918092 | −0.459046 | − | 0.888413i | \(-0.651809\pi\) | ||||
−0.459046 | + | 0.888413i | \(0.651809\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.82843 | 0.140894 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.65685 | 0.379536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.828427 | 0.0409631 | 0.0204815 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204815 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.34315 | −0.214232 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.65685 | 0.475183 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.65685 | −0.179508 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.82843 | −0.138509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.5563 | 1.44392 | 0.721961 | − | 0.691934i | \(-0.243241\pi\) | ||||
0.721961 | + | 0.691934i | \(0.243241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.6274 | 1.39521 | 0.697607 | − | 0.716480i | \(-0.254248\pi\) | ||||
0.697607 | + | 0.716480i | \(0.254248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.82843 | −0.429253 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82843 | 0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.6569 | −0.660901 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.6569 | 0.562798 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.1421 | −1.06655 | −0.533275 | − | 0.845942i | \(-0.679039\pi\) | ||||
−0.533275 | + | 0.845942i | \(0.679039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.75736 | −0.276681 | −0.138341 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138341 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.07107 | 0.339032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.828427 | 0.0396290 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.3137 | 1.30361 | 0.651806 | − | 0.758386i | \(-0.274012\pi\) | ||||
0.651806 | + | 0.758386i | \(0.274012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.4558 | −1.30447 | −0.652233 | − | 0.758018i | \(-0.726168\pi\) | ||||
−0.652233 | + | 0.758018i | \(0.726168\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.75736 | 0.178116 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.6569 | 0.740544 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.3848 | 1.05640 | 0.528201 | − | 0.849119i | \(-0.322867\pi\) | ||||
0.528201 | + | 0.849119i | \(0.322867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.7990 | 1.59153 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.82843 | 0.226859 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.82843 | 0.226360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1421 | −0.567985 | −0.283993 | − | 0.958826i | \(-0.591659\pi\) | ||||
−0.283993 | + | 0.958826i | \(0.591659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.82843 | −0.132020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.3137 | 1.36528 | 0.682638 | − | 0.730757i | \(-0.260833\pi\) | ||||
0.682638 | + | 0.730757i | \(0.260833\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.727922 | −0.0338294 | −0.0169147 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169147 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.828427 | 0.0384174 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.1716 | −0.516959 | −0.258479 | − | 0.966017i | \(-0.583221\pi\) | ||||
−0.258479 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.1421 | −1.11241 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.4853 | 0.482114 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | −0.388514 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2426 | 0.650763 | 0.325381 | − | 0.945583i | \(-0.394507\pi\) | ||||
0.325381 | + | 0.945583i | \(0.394507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.65685 | −0.349123 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.17157 | 0.0533084 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.89949 | 0.358698 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7990 | −0.715921 | −0.357960 | − | 0.933737i | \(-0.616528\pi\) | ||||
−0.357960 | + | 0.933737i | \(0.616528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.55635 | −0.341710 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.3848 | 1.10047 | 0.550235 | − | 0.835010i | \(-0.314538\pi\) | ||||
0.550235 | + | 0.835010i | \(0.314538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.41421 | 0.153457 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.9706 | 0.581809 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1421 | 1.34935 | 0.674674 | − | 0.738116i | \(-0.264284\pi\) | ||||
0.674674 | + | 0.738116i | \(0.264284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.31371 | −0.237399 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −29.3137 | −1.30703 | −0.653517 | − | 0.756912i | \(-0.726707\pi\) | ||||
−0.653517 | + | 0.756912i | \(0.726707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.82843 | −0.214862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.34315 | 0.0596512 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0711 | −0.845310 | −0.422655 | − | 0.906291i | \(-0.638902\pi\) | ||||
−0.422655 | + | 0.906291i | \(0.638902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.485281 | 0.0214676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.3137 | 0.851064 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.1421 | 1.32565 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.3137 | −0.496617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.5563 | −1.03202 | −0.516011 | − | 0.856582i | \(-0.672584\pi\) | ||||
−0.516011 | + | 0.856582i | \(0.672584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.7990 | −0.690842 | −0.345421 | − | 0.938448i | \(-0.612264\pi\) | ||||
−0.345421 | + | 0.938448i | \(0.612264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.41421 | 0.0617213 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.34315 | 0.102069 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.82843 | −0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.7990 | −1.46400 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.34315 | 0.101303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.8284 | 0.812507 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.0711 | 0.735303 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.31371 | 0.400428 | 0.200214 | − | 0.979752i | \(-0.435836\pi\) | ||||
0.200214 | + | 0.979752i | \(0.435836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.14214 | 0.349412 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.1421 | 0.862794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.48528 | 0.362804 | 0.181402 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181402 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.65685 | 0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.07107 | 0.301238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.31371 | 0.140913 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.24264 | −0.0951948 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6569 | 1.00237 | 0.501187 | − | 0.865339i | \(-0.332897\pi\) | ||||
0.501187 | + | 0.865339i | \(0.332897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.4853 | −0.443480 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.65685 | 0.407713 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.343146 | 0.0144619 | 0.00723093 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723093 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.31371 | −0.307690 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.41421 | −0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.1838 | −1.76844 | −0.884218 | − | 0.467075i | \(-0.845308\pi\) | ||||
−0.884218 | + | 0.467075i | \(0.845308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.14214 | −0.0896456 | −0.0448228 | − | 0.998995i | \(-0.514272\pi\) | ||||
−0.0448228 | + | 0.998995i | \(0.514272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.2426 | 0.929200 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.828427 | 0.0345478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.51472 | −0.396103 | −0.198051 | − | 0.980192i | \(-0.563461\pi\) | ||||
−0.198051 | + | 0.980192i | \(0.563461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.07107 | 0.0445121 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.17157 | −0.214553 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.9706 | 1.19984 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.41421 | −0.141160 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.4558 | 1.13322 | 0.566612 | − | 0.823985i | \(-0.308254\pi\) | ||||
0.566612 | + | 0.823985i | \(0.308254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.828427 | 0.0341347 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.14214 | 0.252654 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.6274 | 1.83263 | 0.916314 | − | 0.400460i | \(-0.131150\pi\) | ||||
0.916314 | + | 0.400460i | \(0.131150\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.8284 | 0.606887 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9706 | 0.693398 | 0.346699 | − | 0.937976i | \(-0.387302\pi\) | ||||
0.346699 | + | 0.937976i | \(0.387302\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.20101 | 0.252944 | 0.126472 | − | 0.991970i | \(-0.459635\pi\) | ||||
0.126472 | + | 0.991970i | \(0.459635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | 0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.656854 | −0.0267049 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.4558 | 1.35793 | 0.678965 | − | 0.734170i | \(-0.262429\pi\) | ||||
0.678965 | + | 0.734170i | \(0.262429\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.1421 | −1.21942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.8284 | −0.518135 | −0.259068 | − | 0.965859i | \(-0.583415\pi\) | ||||
−0.259068 | + | 0.965859i | \(0.583415\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.89949 | −0.399186 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1127 | −0.608414 | −0.304207 | − | 0.952606i | \(-0.598392\pi\) | ||||
−0.304207 | + | 0.952606i | \(0.598392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.51472 | 0.141268 | 0.0706342 | − | 0.997502i | \(-0.477498\pi\) | ||||
0.0706342 | + | 0.997502i | \(0.477498\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.828427 | −0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.31371 | 0.212889 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.41421 | 0.136351 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.34315 | −0.252918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.2843 | −1.44445 | −0.722227 | − | 0.691656i | \(-0.756881\pi\) | ||||
−0.722227 | + | 0.691656i | \(0.756881\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65685 | −0.224485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.0711 | −0.676380 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.17157 | −0.362822 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9289 | 0.668653 | 0.334326 | − | 0.942457i | \(-0.391491\pi\) | ||||
0.334326 | + | 0.942457i | \(0.391491\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.9289 | −1.14085 | −0.570423 | − | 0.821351i | \(-0.693221\pi\) | ||||
−0.570423 | + | 0.821351i | \(0.693221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.07107 | −0.120923 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.3137 | 0.995185 | 0.497592 | − | 0.867411i | \(-0.334218\pi\) | ||||
0.497592 | + | 0.867411i | \(0.334218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.3137 | 0.915143 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.17157 | 0.0459176 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.1421 | 0.396892 | 0.198446 | − | 0.980112i | \(-0.436410\pi\) | ||||
0.198446 | + | 0.980112i | \(0.436410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7279 | 0.731760 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.343146 | −0.0133874 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9706 | 1.12853 | 0.564266 | − | 0.825593i | \(-0.309159\pi\) | ||||
0.564266 | + | 0.825593i | \(0.309159\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.1127 | −1.91026 | −0.955131 | − | 0.296183i | \(-0.904286\pi\) | ||||
−0.955131 | + | 0.296183i | \(0.904286\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.65685 | −0.375041 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.41421 | 0.0548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.85786 | 0.226817 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.3137 | 0.437413 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.9706 | −1.27281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.2426 | 0.549013 | 0.274507 | − | 0.961585i | \(-0.411485\pi\) | ||||
0.274507 | + | 0.961585i | \(0.411485\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1716 | 1.12115 | 0.560577 | − | 0.828102i | \(-0.310579\pi\) | ||||
0.560577 | + | 0.828102i | \(0.310579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.1716 | 0.428726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.343146 | −0.0131494 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3137 | 1.35124 | 0.675621 | − | 0.737249i | \(-0.263876\pi\) | ||||
0.675621 | + | 0.737249i | \(0.263876\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.34315 | −0.165943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.3431 | 0.394616 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.9706 | −1.10369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.20101 | 0.311981 | 0.155991 | − | 0.987759i | \(-0.450143\pi\) | ||||
0.155991 | + | 0.987759i | \(0.450143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.82843 | 0.183417 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.82843 | −0.107288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.34315 | −0.164273 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.9706 | 0.867586 | 0.433793 | − | 0.901013i | \(-0.357175\pi\) | ||||
0.433793 | + | 0.901013i | \(0.357175\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.24264 | −0.0845828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.82843 | −0.332498 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.82843 | −0.256809 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0000 | −0.751116 | −0.375558 | − | 0.926799i | \(-0.622549\pi\) | ||||
−0.375558 | + | 0.926799i | \(0.622549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34315 | −0.0878748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.686292 | 0.0257018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6569 | 0.435942 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.2426 | 0.980049 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.75736 | 0.0655384 | 0.0327692 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327692 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3137 | 1.01722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.6569 | −0.879808 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.07107 | 0.262613 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.7574 | 0.584408 | 0.292204 | − | 0.956356i | \(-0.405611\pi\) | ||||
0.292204 | + | 0.956356i | \(0.405611\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.68629 | −0.321274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3137 | −1.23047 | −0.615235 | − | 0.788344i | \(-0.710939\pi\) | ||||
−0.615235 | + | 0.788344i | \(0.710939\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.00000 | −0.184428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.6274 | −1.42286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3137 | −0.563324 | −0.281662 | − | 0.959514i | \(-0.590886\pi\) | ||||
−0.281662 | + | 0.959514i | \(0.590886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.41421 | −0.125424 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.2548 | −1.80698 | −0.903492 | − | 0.428604i | \(-0.859005\pi\) | ||||
−0.903492 | + | 0.428604i | \(0.859005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.6569 | 0.573623 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.65685 | 0.133797 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.31371 | 0.121080 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8579 | −0.578662 | −0.289331 | − | 0.957229i | \(-0.593433\pi\) | ||||
−0.289331 | + | 0.957229i | \(0.593433\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.2426 | 0.519031 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.82843 | 0.175724 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.51472 | −0.345818 | −0.172909 | − | 0.984938i | \(-0.555317\pi\) | ||||
−0.172909 | + | 0.984938i | \(0.555317\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.82843 | 0.102665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.3431 | −1.02744 | −0.513719 | − | 0.857958i | \(-0.671733\pi\) | ||||
−0.513719 | + | 0.857958i | \(0.671733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4853 | 1.03124 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.82843 | −0.102262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.3137 | −0.841809 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2843 | 0.803591 | 0.401796 | − | 0.915729i | \(-0.368386\pi\) | ||||
0.401796 | + | 0.915729i | \(0.368386\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.4558 | −1.63493 | −0.817467 | − | 0.575976i | \(-0.804622\pi\) | ||||
−0.817467 | + | 0.575976i | \(0.804622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.828427 | 0.0297580 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.17157 | −0.113780 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.89949 | −0.354686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.3137 | 1.12049 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.07107 | −0.252699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.1421 | −0.861670 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.17157 | −0.0417621 | −0.0208810 | − | 0.999782i | \(-0.506647\pi\) | ||||
−0.0208810 | + | 0.999782i | \(0.506647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.00000 | 0.0712019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.3431 | −0.367760 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.9706 | 1.17082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.48528 | −0.300942 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.3137 | 0.967501 | 0.483751 | − | 0.875206i | \(-0.339274\pi\) | ||||
0.483751 | + | 0.875206i | \(0.339274\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.9706 | −0.883395 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.75736 | −0.132760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.17157 | 0.0413439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.17157 | 0.0412925 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.3848 | 0.787981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.6863 | −1.07887 | −0.539436 | − | 0.842026i | \(-0.681363\pi\) | ||||
−0.539436 | + | 0.842026i | \(0.681363\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0294 | 0.668214 | 0.334107 | − | 0.942535i | \(-0.391565\pi\) | ||||
0.334107 | + | 0.942535i | \(0.391565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.82843 | −0.0991973 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.55635 | −0.264687 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.07107 | −0.107443 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.82843 | −0.168719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7990 | 0.621189 | 0.310595 | − | 0.950543i | \(-0.399472\pi\) | ||||
0.310595 | + | 0.950543i | \(0.399472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.87006 | 0.100044 | 0.0500220 | − | 0.998748i | \(-0.484071\pi\) | ||||
0.0500220 | + | 0.998748i | \(0.484071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.41421 | 0.118868 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.65685 | −0.127161 | −0.0635806 | − | 0.997977i | \(-0.520252\pi\) | ||||
−0.0635806 | + | 0.997977i | \(0.520252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.4558 | −1.78714 | −0.893568 | − | 0.448929i | \(-0.851806\pi\) | ||||
−0.893568 | + | 0.448929i | \(0.851806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.6274 | −0.715557 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.1421 | −0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.31371 | −0.183888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.828427 | −0.0286346 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.85786 | 0.202236 | 0.101118 | − | 0.994874i | \(-0.467758\pi\) | ||||
0.101118 | + | 0.994874i | \(0.467758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.38478 | −0.219903 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.34315 | 0.0462056 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.928932 | −0.0319185 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.2426 | −0.557446 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.85786 | −0.0636868 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.82843 | 0.302280 | 0.151140 | − | 0.988512i | \(-0.451706\pi\) | ||||
0.151140 | + | 0.988512i | \(0.451706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4558 | 0.869555 | 0.434778 | − | 0.900538i | \(-0.356827\pi\) | ||||
0.434778 | + | 0.900538i | \(0.356827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | −0.272956 | −0.136478 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136478 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.0000 | −0.477119 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.2548 | 1.13201 | 0.566004 | − | 0.824403i | \(-0.308489\pi\) | ||||
0.566004 | + | 0.824403i | \(0.308489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3137 | −0.384678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.00000 | 0.305656 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.6274 | 1.30884 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.89949 | −0.267357 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.41421 | 0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.0416 | −1.55472 | −0.777358 | − | 0.629059i | \(-0.783440\pi\) | ||||
−0.777358 | + | 0.629059i | \(0.783440\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.65685 | 0.325718 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.4853 | −1.16184 | −0.580919 | − | 0.813961i | \(-0.697307\pi\) | ||||
−0.580919 | + | 0.813961i | \(0.697307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7574 | −1.20333 | −0.601665 | − | 0.798748i | \(-0.705496\pi\) | ||||
−0.601665 | + | 0.798748i | \(0.705496\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.82843 | −0.229535 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.6569 | −0.727166 | −0.363583 | − | 0.931562i | \(-0.618447\pi\) | ||||
−0.363583 | + | 0.931562i | \(0.618447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.41421 | −0.114380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.82843 | −0.295432 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.8284 | 0.629365 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.82843 | −0.0944384 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.85786 | 0.195371 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0000 | −0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.34315 | −0.144531 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.14214 | 0.270654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7696 | 1.75218 | 0.876092 | − | 0.482144i | \(-0.160142\pi\) | ||||
0.876092 | + | 0.482144i | \(0.160142\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.82843 | 0.160149 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6274 | −0.352102 | −0.176051 | − | 0.984381i | \(-0.556332\pi\) | ||||
−0.176051 | + | 0.984381i | \(0.556332\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.4853 | −0.413203 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.65685 | 0.319246 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.4853 | 0.874621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5980 | 0.910373 | 0.455187 | − | 0.890396i | \(-0.349573\pi\) | ||||
0.455187 | + | 0.890396i | \(0.349573\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.85786 | −0.0612187 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.3137 | −1.03070 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.24264 | −0.0737376 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.3137 | −0.634345 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.7990 | −1.76509 | −0.882544 | − | 0.470230i | \(-0.844171\pi\) | ||||
−0.882544 | + | 0.470230i | \(0.844171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.2132 | −0.629012 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.65685 | 0.315813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.79899 | 0.320119 | 0.160060 | − | 0.987107i | \(-0.448831\pi\) | ||||
0.160060 | + | 0.987107i | \(0.448831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.7990 | 0.450313 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.2426 | 0.529495 | 0.264747 | − | 0.964318i | \(-0.414711\pi\) | ||||
0.264747 | + | 0.964318i | \(0.414711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.20101 | −0.267062 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.41421 | −0.0460044 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.2843 | −0.594159 | −0.297079 | − | 0.954853i | \(-0.596013\pi\) | ||||
−0.297079 | + | 0.954853i | \(0.596013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.17157 | −0.0380309 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.14214 | 0.0694635 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.02944 | 0.0981331 | 0.0490665 | − | 0.998796i | \(-0.484375\pi\) | ||||
0.0490665 | + | 0.998796i | \(0.484375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.2426 | 0.719755 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.1421 | 0.780404 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.14214 | −0.198340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.34315 | −0.0755068 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.07107 | 0.0344789 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5858 | −0.469047 | −0.234524 | − | 0.972110i | \(-0.575353\pi\) | ||||
−0.234524 | + | 0.972110i | \(0.575353\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.82843 | −0.0908622 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0000 | 1.41203 | 0.706014 | − | 0.708198i | \(-0.250492\pi\) | ||||
0.706014 | + | 0.708198i | \(0.250492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | −0.128234 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.41421 | −0.109342 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.4853 | 0.655382 | 0.327691 | − | 0.944785i | \(-0.393729\pi\) | ||||
0.327691 | + | 0.944785i | \(0.393729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.8284 | 0.409998 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.1421 | −0.643089 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9411 | 0.508443 | 0.254221 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254221 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.14214 | 0.195705 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.4853 | −0.397411 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.54416 | −0.0808995 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.3431 | −0.328561 | −0.164280 | − | 0.986414i | \(-0.552530\pi\) | ||||
−0.164280 | + | 0.986414i | \(0.552530\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.1421 | −0.512255 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.8284 | 0.470093 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.4558 | 0.869535 | 0.434768 | − | 0.900543i | \(-0.356830\pi\) | ||||
0.434768 | + | 0.900543i | \(0.356830\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.24264 | 0.0709540 |
(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 | 2280.2.a.k.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 6840.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.k.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4560.2.a.bn.1.2 | 2 | 4.3 | odd | 2 | |||
6840.2.a.bb.1.1 | 2 | 3.2 | odd | 2 |