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 | 1.2 | ||
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 | \(-0.413881\pi\) | ||||
0.267261 | + | 0.963624i | \(0.413881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.585786 | −0.176621 | −0.0883106 | − | 0.996093i | \(-0.528147\pi\) | ||||
−0.0883106 | + | 0.996093i | \(0.528147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41421 | −0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 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 | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.82843 | −0.867211 | −0.433606 | − | 0.901103i | \(-0.642759\pi\) | ||||
−0.433606 | + | 0.901103i | \(0.642759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.24264 | 1.02628 | 0.513142 | − | 0.858304i | \(-0.328481\pi\) | ||||
0.513142 | + | 0.858304i | \(0.328481\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.585786 | −0.0938009 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.89949 | 1.54604 | 0.773021 | − | 0.634381i | \(-0.218745\pi\) | ||||
0.773021 | + | 0.634381i | \(0.218745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0711 | 1.68832 | 0.844161 | − | 0.536090i | \(-0.180099\pi\) | ||||
0.844161 | + | 0.536090i | \(0.180099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.17157 | −0.462621 | −0.231311 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231311 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(48\) | 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 | \(-0.301968\pi\) | ||||
0.582772 | + | 0.812636i | \(0.301968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.17157 | −0.152526 | −0.0762629 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762629 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65685 | −0.212138 | −0.106069 | − | 0.994359i | \(-0.533827\pi\) | ||||
−0.106069 | + | 0.994359i | \(0.533827\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.41421 | 0.178174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.585786 | −0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3137 | −1.38219 | −0.691095 | − | 0.722764i | \(-0.742871\pi\) | ||||
−0.691095 | + | 0.722764i | \(0.742871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82843 | 0.581274 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8284 | −1.75981 | −0.879905 | − | 0.475149i | \(-0.842394\pi\) | ||||
−0.879905 | + | 0.475149i | \(0.842394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.6569 | −1.36433 | −0.682166 | − | 0.731198i | \(-0.738962\pi\) | ||||
−0.682166 | + | 0.731198i | \(0.738962\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.828427 | −0.0944080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6569 | −1.53652 | −0.768258 | − | 0.640140i | \(-0.778876\pi\) | ||||
−0.768258 | + | 0.640140i | \(0.778876\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.65685 | −0.840449 | −0.420224 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420224 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.07107 | 0.758098 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2426 | −1.29772 | −0.648859 | − | 0.760909i | \(-0.724753\pi\) | ||||
−0.648859 | + | 0.760909i | \(0.724753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.828427 | 0.0868428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.82843 | 0.500685 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8995 | 1.20821 | 0.604105 | − | 0.796904i | \(-0.293531\pi\) | ||||
0.604105 | + | 0.796904i | \(0.293531\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.585786 | −0.0588738 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.828427 | −0.0824316 | −0.0412158 | − | 0.999150i | \(-0.513123\pi\) | ||||
−0.0412158 | + | 0.999150i | \(0.513123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.31371 | 0.326509 | 0.163255 | − | 0.986584i | \(-0.447801\pi\) | ||||
0.163255 | + | 0.986584i | \(0.447801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421 | 0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6569 | −1.32026 | −0.660129 | − | 0.751152i | \(-0.729498\pi\) | ||||
−0.660129 | + | 0.751152i | \(0.729498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.14214 | 0.779875 | 0.389938 | − | 0.920841i | \(-0.372497\pi\) | ||||
0.389938 | + | 0.920841i | \(0.372497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.24264 | −0.592525 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.3137 | −1.44059 | −0.720296 | − | 0.693667i | \(-0.755994\pi\) | ||||
−0.720296 | + | 0.693667i | \(0.755994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.82843 | 0.450253 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.585786 | 0.0541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 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 | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0711 | −0.974753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.72792 | 0.587821 | 0.293911 | − | 0.955833i | \(-0.405043\pi\) | ||||
0.293911 | + | 0.955833i | \(0.405043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.41421 | 0.122628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6569 | 1.33766 | 0.668828 | − | 0.743417i | \(-0.266796\pi\) | ||||
0.668828 | + | 0.743417i | \(0.266796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.82843 | −0.239904 | −0.119952 | − | 0.992780i | \(-0.538274\pi\) | ||||
−0.119952 | + | 0.992780i | \(0.538274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.17157 | 0.267095 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.343146 | −0.0286953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.07107 | 0.587220 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00000 | 0.412393 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.34315 | −0.355804 | −0.177902 | − | 0.984048i | \(-0.556931\pi\) | ||||
−0.177902 | + | 0.984048i | \(0.556931\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.828427 | 0.0674164 | 0.0337082 | − | 0.999432i | \(-0.489268\pi\) | ||||
0.0337082 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82843 | −0.228665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.82843 | 0.387829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.14214 | −0.330578 | −0.165289 | − | 0.986245i | \(-0.552856\pi\) | ||||
−0.165289 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.48528 | −0.672927 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.82843 | −0.538155 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.5563 | −1.84508 | −0.922538 | − | 0.385907i | \(-0.873889\pi\) | ||||
−0.922538 | + | 0.385907i | \(0.873889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.585786 | −0.0456034 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3137 | −1.33977 | −0.669887 | − | 0.742463i | \(-0.733658\pi\) | ||||
−0.669887 | + | 0.742463i | \(0.733658\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3137 | −0.860165 | −0.430083 | − | 0.902790i | \(-0.641516\pi\) | ||||
−0.430083 | + | 0.902790i | \(0.641516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.41421 | 0.106904 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.17157 | 0.0880608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1716 | −0.984490 | −0.492245 | − | 0.870457i | \(-0.663824\pi\) | ||||
−0.492245 | + | 0.870457i | \(0.663824\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1421 | 1.49715 | 0.748577 | − | 0.663048i | \(-0.230738\pi\) | ||||
0.748577 | + | 0.663048i | \(0.230738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.65685 | 0.122478 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.24264 | −0.458968 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.65685 | 0.121161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.41421 | −0.102869 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7574 | −0.995448 | −0.497724 | − | 0.867336i | \(-0.665831\pi\) | ||||
−0.497724 | + | 0.867336i | \(0.665831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0711 | 0.940876 | 0.470438 | − | 0.882433i | \(-0.344096\pi\) | ||||
0.470438 | + | 0.882433i | \(0.344096\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.585786 | 0.0419490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.1421 | 1.57756 | 0.788781 | − | 0.614674i | \(-0.210713\pi\) | ||||
0.788781 | + | 0.614674i | \(0.210713\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.17157 | −0.650156 | −0.325078 | − | 0.945687i | \(-0.605390\pi\) | ||||
−0.325078 | + | 0.945687i | \(0.605390\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | −4.82843 | −0.335599 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.585786 | −0.0405197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.8284 | 1.01603 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.0711 | −0.755041 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.82843 | −0.463544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.6569 | 0.787697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.65685 | −0.111452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3137 | 0.757622 | 0.378811 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378811 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6569 | 0.773693 | 0.386846 | − | 0.922144i | \(-0.373564\pi\) | ||||
0.386846 | + | 0.922144i | \(0.373564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.6569 | −1.43113 | −0.715563 | − | 0.698549i | \(-0.753830\pi\) | ||||
−0.715563 | + | 0.698549i | \(0.753830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.828427 | 0.0545065 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.6569 | 1.02571 | 0.512857 | − | 0.858474i | \(-0.328587\pi\) | ||||
0.512857 | + | 0.858474i | \(0.328587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.17157 | 0.206891 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6569 | 0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.7574 | −1.14863 | −0.574314 | − | 0.818635i | \(-0.694731\pi\) | ||||
−0.574314 | + | 0.818635i | \(0.694731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.3431 | 0.795092 | 0.397546 | − | 0.917582i | \(-0.369862\pi\) | ||||
0.397546 | + | 0.917582i | \(0.369862\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.585786 | 0.0372727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.75736 | −0.363401 | −0.181701 | − | 0.983354i | \(-0.558160\pi\) | ||||
−0.181701 | + | 0.983354i | \(0.558160\pi\) | |||||||
\(252\) | 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 | ||||||||
\(259\) | 8.82843 | 0.548572 | ||||||||
\(260\) | 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 | ||||||||
\(267\) | 12.2426 | 0.749237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3848 | 0.877055 | 0.438528 | − | 0.898718i | \(-0.355500\pi\) | ||||
0.438528 | + | 0.898718i | \(0.355500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.82843 | −0.171815 | −0.0859074 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859074 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.828427 | −0.0501387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.585786 | −0.0353243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.6274 | −1.47972 | −0.739859 | − | 0.672762i | \(-0.765108\pi\) | ||||
−0.739859 | + | 0.672762i | \(0.765108\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.82843 | −0.289070 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.3848 | −1.81260 | −0.906302 | − | 0.422631i | \(-0.861107\pi\) | ||||
−0.906302 | + | 0.422631i | \(0.861107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.75736 | 0.461127 | 0.230564 | − | 0.973057i | \(-0.425943\pi\) | ||||
0.230564 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −11.8995 | −0.697561 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.65685 | 0.0967945 | 0.0483972 | − | 0.998828i | \(-0.484589\pi\) | ||||
0.0483972 | + | 0.998828i | \(0.484589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.17157 | 0.0682116 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.585786 | 0.0339908 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.82843 | −0.163572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6569 | 0.902446 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.828427 | 0.0475919 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.65685 | 0.0948712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.1421 | 1.72030 | 0.860151 | − | 0.510039i | \(-0.170369\pi\) | ||||
0.860151 | + | 0.510039i | \(0.170369\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.31371 | −0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2132 | −1.31630 | −0.658150 | − | 0.752887i | \(-0.728661\pi\) | ||||
−0.658150 | + | 0.752887i | \(0.728661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.7990 | 1.45825 | 0.729123 | − | 0.684383i | \(-0.239928\pi\) | ||||
0.729123 | + | 0.684383i | \(0.239928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.41421 | −0.0796819 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.1421 | 1.46829 | 0.734144 | − | 0.678993i | \(-0.237584\pi\) | ||||
0.734144 | + | 0.678993i | \(0.237584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.14214 | 0.231915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.6569 | 0.762251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.82843 | −0.157378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.585786 | 0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.14214 | −0.450261 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.48528 | −0.247282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1421 | −0.667392 | −0.333696 | − | 0.942681i | \(-0.608296\pi\) | ||||
−0.333696 | + | 0.942681i | \(0.608296\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.24264 | 0.342095 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.3137 | 0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7574 | 0.967305 | 0.483652 | − | 0.875260i | \(-0.339310\pi\) | ||||
0.483652 | + | 0.875260i | \(0.339310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3137 | 0.831726 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.82843 | 0.153168 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.82843 | −0.259954 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.3137 | 1.14418 | 0.572090 | − | 0.820191i | \(-0.306133\pi\) | ||||
0.572090 | + | 0.820191i | \(0.306133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.585786 | −0.0312670 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.68629 | −0.355875 | −0.177938 | − | 0.984042i | \(-0.556943\pi\) | ||||
−0.177938 | + | 0.984042i | \(0.556943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.8284 | 0.787011 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | 0.211702 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5563 | 0.715477 | 0.357738 | − | 0.933822i | \(-0.383548\pi\) | ||||
0.357738 | + | 0.933822i | \(0.383548\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.6569 | 0.559340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.6569 | 0.610148 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7279 | 1.29079 | 0.645394 | − | 0.763850i | \(-0.276693\pi\) | ||||
0.645394 | + | 0.763850i | \(0.276693\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.89949 | 0.515347 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | 0.623009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0711 | −0.883906 | −0.441953 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441953 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.14214 | −0.213331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.51472 | 0.488738 | 0.244369 | − | 0.969682i | \(-0.421419\pi\) | ||||
0.244369 | + | 0.969682i | \(0.421419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.65685 | 0.289809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.6274 | −1.76938 | −0.884689 | − | 0.466181i | \(-0.845629\pi\) | ||||
−0.884689 | + | 0.466181i | \(0.845629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.828427 | 0.0422206 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0711 | 0.562774 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.9706 | −1.77308 | −0.886539 | − | 0.462654i | \(-0.846897\pi\) | ||||
−0.886539 | + | 0.462654i | \(0.846897\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.6569 | 0.690657 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.72792 | −0.339379 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.6569 | 0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6274 | 0.834506 | 0.417253 | − | 0.908790i | \(-0.362993\pi\) | ||||
0.417253 | + | 0.908790i | \(0.362993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.41421 | −0.0707992 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3848 | 0.918092 | 0.459046 | − | 0.888413i | \(-0.348191\pi\) | ||||
0.459046 | + | 0.888413i | \(0.348191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.82843 | −0.140894 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.65685 | −0.181264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.82843 | −0.238750 | −0.119375 | − | 0.992849i | \(-0.538089\pi\) | ||||
−0.119375 | + | 0.992849i | \(0.538089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.6569 | −0.772296 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.65685 | −0.0815285 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.65685 | 0.375860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.82843 | 0.138509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.55635 | −0.0760326 | −0.0380163 | − | 0.999277i | \(-0.512104\pi\) | ||||
−0.0380163 | + | 0.999277i | \(0.512104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6274 | −0.810371 | −0.405185 | − | 0.914235i | \(-0.632793\pi\) | ||||
−0.405185 | + | 0.914235i | \(0.632793\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.17157 | −0.154207 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.82843 | −0.137199 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.34315 | −0.113393 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.343146 | 0.0165672 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.14214 | 0.295856 | 0.147928 | − | 0.988998i | \(-0.452740\pi\) | ||||
0.147928 | + | 0.988998i | \(0.452740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2426 | −0.684458 | −0.342229 | − | 0.939617i | \(-0.611182\pi\) | ||||
−0.342229 | + | 0.939617i | \(0.611182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.07107 | −0.339032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.82843 | −0.230975 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.68629 | 0.223664 | 0.111832 | − | 0.993727i | \(-0.464328\pi\) | ||||
0.111832 | + | 0.993727i | \(0.464328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | −0.238095 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4558 | 1.11442 | 0.557210 | − | 0.830371i | \(-0.311872\pi\) | ||||
0.557210 | + | 0.830371i | \(0.311872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2426 | 0.580357 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.34315 | 0.205424 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3848 | −0.678860 | −0.339430 | − | 0.940631i | \(-0.610234\pi\) | ||||
−0.339430 | + | 0.940631i | \(0.610234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.79899 | −0.273064 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.828427 | −0.0389229 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.828427 | −0.0388373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.1421 | 0.755097 | 0.377549 | − | 0.925990i | \(-0.376767\pi\) | ||||
0.377549 | + | 0.925990i | \(0.376767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.82843 | 0.132020 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.68629 | 0.311412 | 0.155706 | − | 0.987803i | \(-0.450235\pi\) | ||||
0.155706 | + | 0.987803i | \(0.450235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.7279 | 1.14920 | 0.574602 | − | 0.818433i | \(-0.305157\pi\) | ||||
0.574602 | + | 0.818433i | \(0.305157\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.82843 | −0.223913 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.8284 | −0.778727 | −0.389363 | − | 0.921084i | \(-0.627305\pi\) | ||||
−0.389363 | + | 0.921084i | \(0.627305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.14214 | 0.190860 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.48528 | −0.298194 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.48528 | 0.388514 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.75736 | 0.263060 | 0.131530 | − | 0.991312i | \(-0.458011\pi\) | ||||
0.131530 | + | 0.991312i | \(0.458011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.65685 | 0.166738 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.82843 | 0.310704 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8995 | −0.540328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7990 | 1.07844 | 0.539218 | − | 0.842166i | \(-0.318720\pi\) | ||||
0.539218 | + | 0.842166i | \(0.318720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.5563 | 1.06525 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.3848 | −0.558917 | −0.279459 | − | 0.960158i | \(-0.590155\pi\) | ||||
−0.279459 | + | 0.960158i | \(0.590155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.585786 | 0.0263291 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.9706 | −0.940658 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.85786 | 0.0831694 | 0.0415847 | − | 0.999135i | \(-0.486759\pi\) | ||||
0.0415847 | + | 0.999135i | \(0.486759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.3137 | 0.773519 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.68629 | −0.298127 | −0.149064 | − | 0.988828i | \(-0.547626\pi\) | ||||
−0.149064 | + | 0.988828i | \(0.547626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.828427 | 0.0368645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6569 | 0.562111 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.92893 | −0.218471 | −0.109236 | − | 0.994016i | \(-0.534840\pi\) | ||||
−0.109236 | + | 0.994016i | \(0.534840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.4853 | −0.729266 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.31371 | −0.146019 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.85786 | 0.0817088 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.3137 | 0.496617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.55635 | 0.331050 | 0.165525 | − | 0.986206i | \(-0.447068\pi\) | ||||
0.165525 | + | 0.986206i | \(0.447068\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7990 | 1.04066 | 0.520329 | − | 0.853966i | \(-0.325809\pi\) | ||||
0.520329 | + | 0.853966i | \(0.325809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.41421 | −0.0617213 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.6569 | 0.594902 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.17157 | −0.0508419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.79899 | 0.251182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6569 | 0.590437 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.1716 | 0.568395 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.92893 | 0.126158 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3137 | −0.572401 | −0.286201 | − | 0.958170i | \(-0.592392\pi\) | ||||
−0.286201 | + | 0.958170i | \(0.592392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.1421 | −0.864382 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.14214 | −0.348771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.48528 | −0.362804 | −0.181402 | − | 0.983409i | \(-0.558064\pi\) | ||||
−0.181402 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.65685 | −0.0707128 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.07107 | −0.301238 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.3137 | −0.821302 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.24264 | 0.264985 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3431 | 0.522996 | 0.261498 | − | 0.965204i | \(-0.415784\pi\) | ||||
0.261498 | + | 0.965204i | \(0.415784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.48528 | 0.274298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.65685 | −0.0699524 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6569 | 0.491278 | 0.245639 | − | 0.969361i | \(-0.421002\pi\) | ||||
0.245639 | + | 0.969361i | \(0.421002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3137 | 0.644253 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.41421 | 0.0593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.1838 | 1.43306 | 0.716529 | − | 0.697557i | \(-0.245730\pi\) | ||||
0.716529 | + | 0.697557i | \(0.245730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.1421 | 1.09401 | 0.547007 | − | 0.837128i | \(-0.315767\pi\) | ||||
0.547007 | + | 0.837128i | \(0.315767\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.7574 | 0.574722 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.82843 | −0.201359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.4853 | −1.10260 | −0.551298 | − | 0.834308i | \(-0.685867\pi\) | ||||
−0.551298 | + | 0.834308i | \(0.685867\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0711 | −0.543215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.8284 | −0.449239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.97056 | −0.205860 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.585786 | −0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.4558 | −0.968126 | −0.484063 | − | 0.875033i | \(-0.660840\pi\) | ||||
−0.484063 | + | 0.875033i | \(0.660840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.82843 | −0.198952 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.1421 | −0.910806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.627417 | −0.0257649 | −0.0128825 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128825 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | 0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.17157 | 0.375367 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9706 | −0.693398 | −0.346699 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346699 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.7990 | 1.86818 | 0.934090 | − | 0.357038i | \(-0.116213\pi\) | ||||
0.934090 | + | 0.357038i | \(0.116213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3137 | −0.460730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6569 | 0.433263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.4558 | −0.708511 | −0.354255 | − | 0.935149i | \(-0.615266\pi\) | ||||
−0.354255 | + | 0.935149i | \(0.615266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0000 | 0.405220 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85786 | −0.0751611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.17157 | −0.289657 | −0.144829 | − | 0.989457i | \(-0.546263\pi\) | ||||
−0.144829 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.89949 | 0.399186 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.1127 | 1.89669 | 0.948343 | − | 0.317247i | \(-0.102758\pi\) | ||||
0.948343 | + | 0.317247i | \(0.102758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4853 | 0.823373 | 0.411686 | − | 0.911326i | \(-0.364940\pi\) | ||||
0.411686 | + | 0.911326i | \(0.364940\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.82843 | 0.193758 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.3137 | −0.693659 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.585786 | 0.0233941 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.6569 | −0.704025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2843 | 0.807504 | 0.403752 | − | 0.914868i | \(-0.367706\pi\) | ||||
0.403752 | + | 0.914868i | \(0.367706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.65685 | 0.224485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.92893 | −0.116049 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.8284 | −0.586604 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.0711 | 1.22723 | 0.613617 | − | 0.789604i | \(-0.289714\pi\) | ||||
0.613617 | + | 0.789604i | \(0.289714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.0711 | −1.69856 | −0.849279 | − | 0.527945i | \(-0.822963\pi\) | ||||
−0.849279 | + | 0.527945i | \(0.822963\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0711 | 0.435923 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.68629 | 0.105609 | 0.0528045 | − | 0.998605i | \(-0.483184\pi\) | ||||
0.0528045 | + | 0.998605i | \(0.483184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.686292 | 0.0269393 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.82843 | 0.267627 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.1421 | −0.709957 | −0.354978 | − | 0.934875i | \(-0.615512\pi\) | ||||
−0.354978 | + | 0.934875i | \(0.615512\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.72792 | −0.262882 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.6569 | −0.454777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.97056 | −0.193626 | −0.0968128 | − | 0.995303i | \(-0.530865\pi\) | ||||
−0.0968128 | + | 0.995303i | \(0.530865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1127 | 0.510025 | 0.255012 | − | 0.966938i | \(-0.417920\pi\) | ||||
0.255012 | + | 0.966938i | \(0.417920\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.65685 | 0.0643469 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.41421 | −0.0548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.1421 | 1.32199 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.3137 | −0.437413 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.970563 | 0.0374682 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.75736 | 0.221930 | 0.110965 | − | 0.993824i | \(-0.464606\pi\) | ||||
0.110965 | + | 0.993824i | \(0.464606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.8284 | 1.33857 | 0.669283 | − | 0.743008i | \(-0.266602\pi\) | ||||
0.669283 | + | 0.743008i | \(0.266602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8284 | 0.645816 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.6569 | −0.446692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.6863 | 0.485427 | 0.242714 | − | 0.970098i | \(-0.421962\pi\) | ||||
0.242714 | + | 0.970098i | \(0.421962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.6569 | −0.598218 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.6569 | 0.826261 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.97056 | 0.189363 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.7990 | 1.81836 | 0.909180 | − | 0.416404i | \(-0.136710\pi\) | ||||
0.909180 | + | 0.416404i | \(0.136710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.828427 | −0.0314693 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.82843 | 0.107288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.0000 | −1.06058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.6569 | −0.592197 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.9706 | −0.414352 | −0.207176 | − | 0.978304i | \(-0.566427\pi\) | ||||
−0.207176 | + | 0.978304i | \(0.566427\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.24264 | 0.235446 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.17157 | −0.119448 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.17157 | −0.0440615 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.0000 | −0.751116 | −0.375558 | − | 0.926799i | \(-0.622549\pi\) | ||||
−0.375558 | + | 0.926799i | \(0.622549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6569 | −0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.3137 | 0.873105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.343146 | 0.0128329 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.7574 | 0.663161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.2426 | 0.381986 | 0.190993 | − | 0.981591i | \(-0.438829\pi\) | ||||
0.190993 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.68629 | 0.174527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.3431 | −0.459047 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.07107 | −0.262613 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2426 | 0.899110 | 0.449555 | − | 0.893253i | \(-0.351583\pi\) | ||||
0.449555 | + | 0.893253i | \(0.351583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.3137 | −1.15818 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6863 | −0.394707 | −0.197354 | − | 0.980332i | \(-0.563235\pi\) | ||||
−0.197354 | + | 0.980332i | \(0.563235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.00000 | −0.184428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.62742 | 0.244124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.31371 | 0.269039 | 0.134520 | − | 0.990911i | \(-0.457051\pi\) | ||||
0.134520 | + | 0.990911i | \(0.457051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.585786 | −0.0215194 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.2548 | 1.51349 | 0.756747 | − | 0.653708i | \(-0.226788\pi\) | ||||
0.756747 | + | 0.653708i | \(0.226788\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.34315 | 0.159121 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.65685 | −0.280150 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.3137 | −0.705708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.1421 | −1.61077 | −0.805385 | − | 0.592752i | \(-0.798041\pi\) | ||||
−0.805385 | + | 0.592752i | \(0.798041\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.75736 | 0.209810 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.828427 | −0.0301496 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4853 | −0.962624 | −0.481312 | − | 0.876549i | \(-0.659840\pi\) | ||||
−0.481312 | + | 0.876549i | \(0.659840\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.82843 | −0.102665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.6569 | −1.43756 | −0.718780 | − | 0.695238i | \(-0.755299\pi\) | ||||
−0.718780 | + | 0.695238i | \(0.755299\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5147 | 0.416861 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.82843 | 0.102262 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.686292 | −0.0247805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.2843 | −1.23632 | −0.618161 | − | 0.786051i | \(-0.712122\pi\) | ||||
−0.618161 | + | 0.786051i | \(0.712122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.45584 | 0.196233 | 0.0981165 | − | 0.995175i | \(-0.468718\pi\) | ||||
0.0981165 | + | 0.995175i | \(0.468718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.82843 | −0.173442 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.82843 | −0.316718 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.89949 | 0.354686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.68629 | 0.310820 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.07107 | 0.252699 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.14214 | 0.147839 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.82843 | −0.243407 | −0.121704 | − | 0.992566i | \(-0.538836\pi\) | ||||
−0.121704 | + | 0.992566i | \(0.538836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.00000 | 0.0712019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.6569 | −0.770029 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.970563 | −0.0344657 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.48528 | 0.300942 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.68629 | 0.165997 | 0.0829985 | − | 0.996550i | \(-0.473550\pi\) | ||||
0.0829985 | + | 0.996550i | \(0.473550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.97056 | 0.317356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.2426 | −0.432572 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.82843 | 0.240970 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.82843 | 0.240670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.3848 | −0.506368 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.3137 | −1.87441 | −0.937205 | − | 0.348779i | \(-0.886596\pi\) | ||||
−0.937205 | + | 0.348779i | \(0.886596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.9706 | 1.86005 | 0.930024 | − | 0.367499i | \(-0.119786\pi\) | ||||
0.930024 | + | 0.367499i | \(0.119786\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.82843 | 0.0991973 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.5563 | 0.825143 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.0711 | 0.387328 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.828427 | 0.0289476 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.7990 | −0.760790 | −0.380395 | − | 0.924824i | \(-0.624212\pi\) | ||||
−0.380395 | + | 0.924824i | \(0.624212\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.8701 | −1.77322 | −0.886609 | − | 0.462519i | \(-0.846946\pi\) | ||||
−0.886609 | + | 0.462519i | \(0.846946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.585786 | 0.0203945 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.65685 | 0.266255 | 0.133127 | − | 0.991099i | \(-0.457498\pi\) | ||||
0.133127 | + | 0.991099i | \(0.457498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.544156 | −0.0188993 | −0.00944966 | − | 0.999955i | \(-0.503008\pi\) | ||||
−0.00944966 | + | 0.999955i | \(0.503008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.6274 | 0.854316 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.1421 | 0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3137 | 0.599166 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.82843 | 0.166895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.1421 | 1.17872 | 0.589359 | − | 0.807871i | \(-0.299380\pi\) | ||||
0.589359 | + | 0.807871i | \(0.299380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.3848 | 1.04651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6569 | 0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.0711 | −0.517848 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.75736 | −0.266232 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.1421 | −1.03326 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.17157 | 0.108593 | 0.0542963 | − | 0.998525i | \(-0.482708\pi\) | ||||
0.0542963 | + | 0.998525i | \(0.482708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.4558 | −0.869555 | −0.434778 | − | 0.900538i | \(-0.643173\pi\) | ||||
−0.434778 | + | 0.900538i | \(0.643173\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −57.2548 | −1.94898 | −0.974489 | − | 0.224437i | \(-0.927946\pi\) | ||||
−0.974489 | + | 0.224437i | \(0.927946\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | −6.62742 | −0.224561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.8995 | 0.402737 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.41421 | −0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.04163 | 0.0689410 | 0.0344705 | − | 0.999406i | \(-0.489026\pi\) | ||||
0.0344705 | + | 0.999406i | \(0.489026\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.65685 | −0.0558843 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.5147 | −0.590086 | −0.295043 | − | 0.955484i | \(-0.595334\pi\) | ||||
−0.295043 | + | 0.955484i | \(0.595334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.2426 | −1.48888 | −0.744442 | − | 0.667687i | \(-0.767284\pi\) | ||||
−0.744442 | + | 0.667687i | \(0.767284\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.17157 | −0.0393820 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.3431 | −0.347289 | −0.173644 | − | 0.984808i | \(-0.555554\pi\) | ||||
−0.173644 | + | 0.984808i | \(0.555554\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.585786 | −0.0196246 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.17157 | −0.106133 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1716 | 0.440277 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.82843 | 0.0944384 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.1421 | 1.13870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0000 | −0.799556 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.6569 | −0.521027 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.1421 | −0.669547 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7696 | −0.689642 | −0.344821 | − | 0.938669i | \(-0.612060\pi\) | ||||
−0.344821 | + | 0.938669i | \(0.612060\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.828427 | −0.0274772 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6274 | 1.14726 | 0.573629 | − | 0.819115i | \(-0.305535\pi\) | ||||
0.573629 | + | 0.819115i | \(0.305535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.48528 | 0.148441 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.65685 | −0.0547739 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.51472 | 0.314204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.5980 | −1.70206 | −0.851030 | − | 0.525117i | \(-0.824022\pi\) | ||||
−0.851030 | + | 0.525117i | \(0.824022\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.1421 | −0.993217 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.68629 | −0.285913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.24264 | 0.205257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.31371 | 0.108836 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.2010 | −0.465920 | −0.232960 | − | 0.972486i | \(-0.574841\pi\) | ||||
−0.232960 | + | 0.972486i | \(0.574841\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.2132 | 0.759966 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.65685 | −0.0541849 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7990 | −0.973491 | −0.486745 | − | 0.873544i | \(-0.661816\pi\) | ||||
−0.486745 | + | 0.873544i | \(0.661816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.7990 | −0.841918 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.75736 | 0.252883 | 0.126441 | − | 0.991974i | \(-0.459644\pi\) | ||||
0.126441 | + | 0.991974i | \(0.459644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7990 | −1.55655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.41421 | 0.0460044 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.2843 | 1.24407 | 0.622036 | − | 0.782989i | \(-0.286306\pi\) | ||||
0.622036 | + | 0.782989i | \(0.286306\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.82843 | −0.221660 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.1421 | −0.847717 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.9706 | 1.19759 | 0.598797 | − | 0.800901i | \(-0.295646\pi\) | ||||
0.598797 | + | 0.800901i | \(0.295646\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7574 | 0.445178 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.14214 | −0.133896 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.1421 | 0.715007 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.6569 | −0.440086 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.0711 | −0.420773 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.4142 | −0.560003 | −0.280002 | − | 0.960000i | \(-0.590335\pi\) | ||||
−0.280002 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(968\) | 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 | ||||||||
\(975\) | −0.585786 | −0.0187602 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.51472 | 0.112446 | 0.0562229 | − | 0.998418i | \(-0.482094\pi\) | ||||
0.0562229 | + | 0.998418i | \(0.482094\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.17157 | 0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.14214 | 0.259958 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.9411 | −1.65666 | −0.828332 | − | 0.560237i | \(-0.810710\pi\) | ||||
−0.828332 | + | 0.560237i | \(0.810710\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.1421 | −0.705507 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.48528 | 0.142768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.4558 | −1.69980 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.6569 | −0.687953 | −0.343976 | − | 0.938978i | \(-0.611774\pi\) | ||||
−0.343976 | + | 0.938978i | \(0.611774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.1421 | 0.385319 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.17157 | 0.290758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.4558 | −0.742854 | −0.371427 | − | 0.928462i | \(-0.621131\pi\) | ||||
−0.371427 | + | 0.928462i | \(0.621131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.24264 | −0.197508 |
(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.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6840.2.a.bb.1.2 | 2 | |||
4.3 | odd | 2 | 4560.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.k.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4560.2.a.bn.1.1 | 2 | 4.3 | odd | 2 | |||
6840.2.a.bb.1.2 | 2 | 3.2 | odd | 2 |