Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(1,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(12.2650217505\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.27133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.95687 | 1.76957 | 0.884784 | − | 0.466001i | \(-0.154306\pi\) | ||||
0.884784 | + | 0.466001i | \(0.154306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.63899 | 0.619480 | 0.309740 | − | 0.950821i | \(-0.399758\pi\) | ||||
0.309740 | + | 0.950821i | \(0.399758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.59587 | 1.55201 | 0.776007 | − | 0.630724i | \(-0.217242\pi\) | ||||
0.776007 | + | 0.630724i | \(0.217242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.95687 | −1.02166 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.63899 | −0.357657 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.91375 | 1.65013 | 0.825065 | − | 0.565037i | \(-0.191138\pi\) | ||||
0.825065 | + | 0.565037i | \(0.191138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6569 | 2.13137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.23486 | −1.34348 | −0.671740 | − | 0.740787i | \(-0.734453\pi\) | ||||
−0.671740 | + | 0.740787i | \(0.734453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63899 | −0.294371 | −0.147186 | − | 0.989109i | \(-0.547022\pi\) | ||||
−0.147186 | + | 0.989109i | \(0.547022\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.82843 | 0.840521 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.48528 | 1.09621 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.31788 | −0.381058 | −0.190529 | − | 0.981682i | \(-0.561020\pi\) | ||||
−0.190529 | + | 0.981682i | \(0.561020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.59587 | −0.896056 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.17157 | 0.495316 | 0.247658 | − | 0.968847i | \(-0.420339\pi\) | ||||
0.247658 | + | 0.968847i | \(0.420339\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.48528 | −0.683999 | −0.341999 | − | 0.939700i | \(-0.611104\pi\) | ||||
−0.341999 | + | 0.939700i | \(0.611104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.95687 | 0.589856 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.91375 | 1.15434 | 0.577169 | − | 0.816624i | \(-0.304157\pi\) | ||||
0.577169 | + | 0.816624i | \(0.304157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.31371 | −0.616244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.828427 | 0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.678892 | −0.0932530 | −0.0466265 | − | 0.998912i | \(-0.514847\pi\) | ||||
−0.0466265 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.1055 | −2.57618 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.65685 | −1.25722 | −0.628608 | − | 0.777723i | \(-0.716375\pi\) | ||||
−0.628608 | + | 0.777723i | \(0.716375\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.31788 | −0.296775 | −0.148387 | − | 0.988929i | \(-0.547408\pi\) | ||||
−0.148387 | + | 0.988929i | \(0.547408\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.63899 | 0.206493 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.1421 | 2.74639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6569 | 1.66845 | 0.834225 | − | 0.551424i | \(-0.185915\pi\) | ||||
0.834225 | + | 0.551424i | \(0.185915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.91375 | −0.952703 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27798 | −0.389025 | −0.194512 | − | 0.980900i | \(-0.562312\pi\) | ||||
−0.194512 | + | 0.980900i | \(0.562312\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.6569 | −1.23055 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.91375 | −0.901855 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.63899 | 0.184401 | 0.0922004 | − | 0.995740i | \(-0.470610\pi\) | ||||
0.0922004 | + | 0.995740i | \(0.470610\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.82843 | −0.969046 | −0.484523 | − | 0.874779i | \(-0.661007\pi\) | ||||
−0.484523 | + | 0.874779i | \(0.661007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.27798 | −0.355547 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.23486 | 0.775658 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.17157 | 0.961442 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.63899 | 0.169955 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.1917 | 1.14825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.6569 | 1.18357 | 0.591787 | − | 0.806094i | \(-0.298423\pi\) | ||||
0.591787 | + | 0.806094i | \(0.298423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.82843 | −0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.678892 | 0.0675523 | 0.0337762 | − | 0.999429i | \(-0.489247\pi\) | ||||
0.0337762 | + | 0.999429i | \(0.489247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4665 | 1.72102 | 0.860512 | − | 0.509430i | \(-0.170144\pi\) | ||||
0.860512 | + | 0.509430i | \(0.170144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.48528 | −0.632899 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.7876 | −1.60796 | −0.803980 | − | 0.594656i | \(-0.797288\pi\) | ||||
−0.803980 | + | 0.594656i | \(0.797288\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.31788 | 0.220004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.343146 | 0.0322804 | 0.0161402 | − | 0.999870i | \(-0.494862\pi\) | ||||
0.0161402 | + | 0.999870i | \(0.494862\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.3137 | 2.92002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.59587 | 0.517338 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.35778 | −0.124468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.17157 | −0.285971 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.3835 | 2.00204 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1885 | −1.25903 | −0.629513 | − | 0.776990i | \(-0.716746\pi\) | ||||
−0.629513 | + | 0.776990i | \(0.716746\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.48528 | 0.394907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.31371 | 0.639002 | 0.319501 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319501 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.63577 | 0.401972 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.95687 | −0.340554 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1421 | −1.37912 | −0.689558 | − | 0.724231i | \(-0.742195\pi\) | ||||
−0.689558 | + | 0.724231i | \(0.742195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.91375 | −0.666458 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.0192 | −2.25946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.6274 | −2.37738 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.31371 | 0.355789 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.95687 | 0.324160 | 0.162080 | − | 0.986778i | \(-0.448180\pi\) | ||||
0.162080 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1885 | 1.15464 | 0.577322 | − | 0.816516i | \(-0.304098\pi\) | ||||
0.577322 | + | 0.816516i | \(0.304098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.828427 | −0.0669744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.48528 | −0.520910 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1454 | 1.44816 | 0.724080 | − | 0.689717i | \(-0.242265\pi\) | ||||
0.724080 | + | 0.689717i | \(0.242265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.678892 | 0.0538397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9706 | 1.02222 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1421 | −0.794393 | −0.397197 | − | 0.917734i | \(-0.630017\pi\) | ||||
−0.397197 | + | 0.917734i | \(0.630017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.1055 | 1.48736 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.63577 | −0.358726 | −0.179363 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179363 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.3137 | 1.40875 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8706 | 0.902507 | 0.451253 | − | 0.892396i | \(-0.350977\pi\) | ||||
0.451253 | + | 0.892396i | \(0.350977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.4665 | 1.32034 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9706 | −0.969465 | −0.484733 | − | 0.874662i | \(-0.661083\pi\) | ||||
−0.484733 | + | 0.874662i | \(0.661083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7876 | 1.24781 | 0.623906 | − | 0.781499i | \(-0.285545\pi\) | ||||
0.623906 | + | 0.781499i | \(0.285545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.31788 | 0.171343 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.17157 | −0.674307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.63899 | −0.119219 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7477 | −1.28418 | −0.642089 | − | 0.766630i | \(-0.721932\pi\) | ||||
−0.642089 | + | 0.766630i | \(0.721932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.1421 | −1.58563 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.5064 | −1.17603 | −0.588016 | − | 0.808849i | \(-0.700091\pi\) | ||||
−0.588016 | + | 0.808849i | \(0.700091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.63899 | 0.116185 | 0.0580925 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580925 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.6569 | −0.963280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.8579 | −0.832259 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5495 | 0.876496 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.91375 | 0.550044 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6569 | −0.944664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.27798 | 0.224604 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.7477 | −1.21038 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.68629 | −0.182357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.63577 | −0.311835 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1885 | 0.950133 | 0.475066 | − | 0.879950i | \(-0.342424\pi\) | ||||
0.475066 | + | 0.879950i | \(0.342424\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6569 | 0.710457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1421 | 0.805902 | 0.402951 | − | 0.915222i | \(-0.367985\pi\) | ||||
0.402951 | + | 0.915222i | \(0.367985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.4234 | −1.41570 | −0.707848 | − | 0.706365i | \(-0.750334\pi\) | ||||
−0.707848 | + | 0.706365i | \(0.750334\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.91375 | 0.520686 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.3137 | −1.39631 | −0.698154 | − | 0.715948i | \(-0.745995\pi\) | ||||
−0.698154 | + | 0.715948i | \(0.745995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.3137 | 2.04268 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.63899 | −0.106464 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.63577 | −0.299863 | −0.149931 | − | 0.988696i | \(-0.547905\pi\) | ||||
−0.149931 | + | 0.988696i | \(0.547905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9706 | −1.09317 | −0.546585 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546585 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.0688 | −1.09049 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.8275 | 1.00708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.82843 | 0.559479 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.8284 | −1.31468 | −0.657339 | − | 0.753595i | \(-0.728318\pi\) | ||||
−0.657339 | + | 0.753595i | \(0.728318\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.2110 | −2.40230 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.27798 | 0.205275 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.6569 | −1.22616 | −0.613080 | − | 0.790020i | \(-0.710070\pi\) | ||||
−0.613080 | + | 0.790020i | \(0.710070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.79899 | −0.236058 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.23486 | −0.447826 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.8275 | −0.975965 | −0.487983 | − | 0.872853i | \(-0.662267\pi\) | ||||
−0.487983 | + | 0.872853i | \(0.662267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.68629 | −0.165018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.23486 | 0.441117 | 0.220558 | − | 0.975374i | \(-0.429212\pi\) | ||||
0.220558 | + | 0.975374i | \(0.429212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4665 | −1.06101 | −0.530507 | − | 0.847681i | \(-0.677998\pi\) | ||||
−0.530507 | + | 0.847681i | \(0.677998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.17157 | −0.555089 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −51.4558 | −3.10290 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8674 | −0.893295 | −0.446648 | − | 0.894710i | \(-0.647382\pi\) | ||||
−0.446648 | + | 0.894710i | \(0.647382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.63899 | −0.0981238 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.343146 | 0.0204704 | 0.0102352 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102352 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.9706 | 1.72212 | 0.861061 | − | 0.508502i | \(-0.169801\pi\) | ||||
0.861061 | + | 0.508502i | \(0.169801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.1917 | −0.662941 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.19818 | 0.306839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6569 | −0.683337 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.678892 | −0.0396613 | −0.0198307 | − | 0.999803i | \(-0.506313\pi\) | ||||
−0.0198307 | + | 0.999803i | \(0.506313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.2110 | −2.22473 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.82843 | 0.280174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.2843 | 2.56103 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.35134 | −0.423724 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.678892 | −0.0390013 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.17157 | −0.525163 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6569 | 1.23602 | 0.618011 | − | 0.786169i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786169i | \(0.287939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4665 | −0.993634 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.31371 | 0.413395 | 0.206698 | − | 0.978405i | \(-0.433728\pi\) | ||||
0.206698 | + | 0.978405i | \(0.433728\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.48528 | 0.365404 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.7046 | −1.21905 | −0.609525 | − | 0.792767i | \(-0.708640\pi\) | ||||
−0.609525 | + | 0.792767i | \(0.708640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.9330 | 1.95587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.34315 | −0.130376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 59.6343 | 3.30792 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.7876 | 0.928356 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.9706 | 0.715090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3431 | −0.568511 | −0.284255 | − | 0.958749i | \(-0.591746\pi\) | ||||
−0.284255 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.31788 | −0.127019 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 54.0385 | 2.95244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.0000 | −1.08947 | −0.544735 | − | 0.838608i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.343146 | −0.0186371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.91375 | 0.428554 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5431 | −1.00123 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.3137 | −1.68587 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.828427 | −0.0444723 | −0.0222361 | − | 0.999753i | \(-0.507079\pi\) | ||||
−0.0222361 | + | 0.999753i | \(0.507079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.23808 | 0.226859 | 0.113430 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113430 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.59587 | −0.298685 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.31371 | 0.0699216 | 0.0349608 | − | 0.999389i | \(-0.488869\pi\) | ||||
0.0349608 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.9706 | −0.688406 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.35778 | 0.0718616 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.9330 | 1.84369 | 0.921846 | − | 0.387556i | \(-0.126681\pi\) | ||||
0.921846 | + | 0.387556i | \(0.126681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.3137 | −0.646302 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8275 | 0.828449 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0225 | −1.25396 | −0.626981 | − | 0.779035i | \(-0.715710\pi\) | ||||
−0.626981 | + | 0.779035i | \(0.715710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.17157 | 0.165105 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.11270 | −0.0577684 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0656 | −1.03896 | −0.519478 | − | 0.854484i | \(-0.673874\pi\) | ||||
−0.519478 | + | 0.854484i | \(0.673874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.3835 | −1.15588 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.4853 | −2.08510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.485281 | 0.0249272 | 0.0124636 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124636 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1885 | 0.726899 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1917 | −0.571871 | −0.285935 | − | 0.958249i | \(-0.592304\pi\) | ||||
−0.285935 | + | 0.958249i | \(0.592304\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.3137 | −1.59589 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.48528 | −0.228000 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.95687 | −0.200621 | −0.100311 | − | 0.994956i | \(-0.531984\pi\) | ||||
−0.100311 | + | 0.994956i | \(0.531984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.55596 | −0.331549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.31371 | −0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.48528 | 0.326310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.1454 | 0.910691 | 0.455345 | − | 0.890315i | \(-0.349516\pi\) | ||||
0.455345 | + | 0.890315i | \(0.349516\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.63577 | −0.232079 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.1421 | 1.20560 | 0.602800 | − | 0.797892i | \(-0.294052\pi\) | ||||
0.602800 | + | 0.797892i | \(0.294052\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.17157 | −0.456869 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.95687 | 0.196619 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.1917 | 0.554753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.65685 | −0.180820 | −0.0904099 | − | 0.995905i | \(-0.528818\pi\) | ||||
−0.0904099 | + | 0.995905i | \(0.528818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.1421 | 0.796233 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.8275 | −0.778820 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.9330 | −1.71479 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.1716 | −0.741180 | −0.370590 | − | 0.928797i | \(-0.620844\pi\) | ||||
−0.370590 | + | 0.928797i | \(0.620844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.4234 | −1.04411 | −0.522055 | − | 0.852912i | \(-0.674835\pi\) | ||||
−0.522055 | + | 0.852912i | \(0.674835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.91375 | 0.384780 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.82843 | −0.428242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.79899 | −0.183846 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.0192 | 1.30450 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.4697 | −0.696982 | −0.348491 | − | 0.937312i | \(-0.613306\pi\) | ||||
−0.348491 | + | 0.937312i | \(0.613306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.6274 | 1.18352 | 0.591759 | − | 0.806115i | \(-0.298434\pi\) | ||||
0.591759 | + | 0.806115i | \(0.298434\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.6274 | 1.37258 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.3835 | 1.07075 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 39.8499 | 1.90193 | 0.950967 | − | 0.309292i | \(-0.100092\pi\) | ||||
0.950967 | + | 0.309292i | \(0.100092\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.31371 | −0.205415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.4853 | 0.878262 | 0.439131 | − | 0.898423i | \(-0.355286\pi\) | ||||
0.439131 | + | 0.898423i | \(0.355286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.5687 | 1.87574 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.95687 | −0.187154 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5147 | 0.826571 | 0.413285 | − | 0.910602i | \(-0.364381\pi\) | ||||
0.413285 | + | 0.910602i | \(0.364381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.3137 | −0.721094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1885 | −0.666634 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.2908 | 1.70134 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6569 | −1.10662 | −0.553310 | − | 0.832975i | \(-0.686636\pi\) | ||||
−0.553310 | + | 0.832975i | \(0.686636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.828427 | 0.0386677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.8963 | −1.53213 | −0.766067 | − | 0.642761i | \(-0.777789\pi\) | ||||
−0.766067 | + | 0.642761i | \(0.777789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9105 | 0.507055 | 0.253528 | − | 0.967328i | \(-0.418409\pi\) | ||||
0.253528 | + | 0.967328i | \(0.418409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.48528 | 0.300748 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.7990 | −1.74913 | −0.874564 | − | 0.484910i | \(-0.838853\pi\) | ||||
−0.874564 | + | 0.484910i | \(0.838853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.3835 | 1.03357 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.1454 | −0.836095 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.6569 | 0.995783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.1421 | 1.38302 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.678892 | −0.0310843 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.2174 | −1.47205 | −0.736025 | − | 0.676954i | \(-0.763300\pi\) | ||||
−0.736025 | + | 0.676954i | \(0.763300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.9706 | −0.591407 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.9706 | −0.590181 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.1247 | 2.09442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7445 | −0.940022 | −0.470011 | − | 0.882661i | \(-0.655750\pi\) | ||||
−0.470011 | + | 0.882661i | \(0.655750\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.1421 | 0.458643 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.65685 | −0.0747728 | −0.0373864 | − | 0.999301i | \(-0.511903\pi\) | ||||
−0.0373864 | + | 0.999301i | \(0.511903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.99355 | 0.269936 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.1055 | −0.858727 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.37258 | −0.240993 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3431 | 1.35835 | 0.679173 | − | 0.733978i | \(-0.262339\pi\) | ||||
0.679173 | + | 0.733978i | \(0.262339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.63577 | 0.207111 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.5495 | 0.559555 | 0.279778 | − | 0.960065i | \(-0.409739\pi\) | ||||
0.279778 | + | 0.960065i | \(0.409739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.68629 | 0.119538 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.3137 | −0.813340 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.59264 | 0.380862 | 0.190431 | − | 0.981701i | \(-0.439011\pi\) | ||||
0.190431 | + | 0.981701i | \(0.439011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.55596 | 0.290019 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 69.1127 | 3.04547 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −38.2110 | −1.68052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.8706 | −0.521063 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.1716 | 0.664679 | 0.332339 | − | 0.943160i | \(-0.392162\pi\) | ||||
0.332339 | + | 0.943160i | \(0.392162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1716 | −0.575953 | −0.287976 | − | 0.957638i | \(-0.592982\pi\) | ||||
−0.287976 | + | 0.957638i | \(0.592982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.4665 | −0.762300 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.35778 | 0.0591460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.6274 | 1.72293 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.65685 | −0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.7477 | 0.768738 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.8275 | 0.684282 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.9706 | 0.559721 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.8284 | 0.897144 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2316 | 0.439892 | 0.219946 | − | 0.975512i | \(-0.429412\pi\) | ||||
0.219946 | + | 0.975512i | \(0.429412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.7876 | −0.720425 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −66.4264 | −2.84539 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.79899 | 0.333461 | 0.166730 | − | 0.986003i | \(-0.446679\pi\) | ||||
0.166730 | + | 0.986003i | \(0.446679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.31788 | −0.0989248 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.4633 | −0.871764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.68629 | 0.114233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.17157 | 0.389312 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6981 | −1.17361 | −0.586804 | − | 0.809729i | \(-0.699614\pi\) | ||||
−0.586804 | + | 0.809729i | \(0.699614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.0990 | −1.06158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.82843 | −0.203494 | −0.101747 | − | 0.994810i | \(-0.532443\pi\) | ||||
−0.101747 | + | 0.994810i | \(0.532443\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.35778 | 0.0571224 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.63899 | 0.0688312 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.4558 | −1.15101 | −0.575504 | − | 0.817799i | \(-0.695194\pi\) | ||||
−0.575504 | + | 0.817799i | \(0.695194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.686292 | −0.0287204 | −0.0143602 | − | 0.999897i | \(-0.504571\pi\) | ||||
−0.0143602 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.7477 | 0.741421 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 84.3357 | 3.51704 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | 0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.4697 | −0.600305 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.27798 | 0.135760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.1421 | 0.915465 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.9706 | −1.19574 | −0.597872 | − | 0.801592i | \(-0.703987\pi\) | ||||
−0.597872 | + | 0.801592i | \(0.703987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.63577 | −0.191013 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.5064 | 0.678982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.9706 | 1.27181 | 0.635904 | − | 0.771768i | \(-0.280627\pi\) | ||||
0.635904 | + | 0.771768i | \(0.280627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.37258 | −0.220254 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.63899 | −0.0670794 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.1247 | −1.88460 | −0.942302 | − | 0.334763i | \(-0.891344\pi\) | ||||
−0.942302 | + | 0.334763i | \(0.891344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.3137 | −1.11415 | −0.557075 | − | 0.830462i | \(-0.688076\pi\) | ||||
−0.557075 | + | 0.830462i | \(0.688076\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.6569 | 0.556150 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 48.7238 | 1.98090 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.19496 | 0.332623 | 0.166311 | − | 0.986073i | \(-0.446814\pi\) | ||||
0.166311 | + | 0.986073i | \(0.446814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.8579 | 0.480505 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.2843 | 1.79155 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.8931 | −1.44971 | −0.724854 | − | 0.688903i | \(-0.758093\pi\) | ||||
−0.724854 | + | 0.688903i | \(0.758093\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.5495 | −0.506045 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9411 | 0.963833 | 0.481917 | − | 0.876217i | \(-0.339941\pi\) | ||||
0.481917 | + | 0.876217i | \(0.339941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000 | 1.12542 | 0.562708 | − | 0.826656i | \(-0.309760\pi\) | ||||
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.91375 | −0.317568 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3899 | 0.656648 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 35.2843 | 1.41137 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.6569 | 0.545402 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.92020 | 0.0765633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.4729 | −0.456730 | −0.228365 | − | 0.973576i | \(-0.573338\pi\) | ||||
−0.228365 | + | 0.973576i | \(0.573338\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | 0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −56.1421 | −2.22793 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1389 | −0.956419 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.27798 | −0.129675 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.1716 | 1.07321 | 0.536606 | − | 0.843833i | \(-0.319706\pi\) | ||||
0.536606 | + | 0.843833i | \(0.319706\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4853 | −0.807861 | −0.403930 | − | 0.914790i | \(-0.632356\pi\) | ||||
−0.403930 | + | 0.914790i | \(0.632356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.7477 | 0.698815 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.19818 | 0.204362 | 0.102181 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102181 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.6274 | 1.83029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.68629 | 0.105284 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.2284 | −0.517668 | −0.258834 | − | 0.965922i | \(-0.583338\pi\) | ||||
−0.258834 | + | 0.965922i | \(0.583338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.9394 | 1.13076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.65685 | −0.0645419 | −0.0322709 | − | 0.999479i | \(-0.510274\pi\) | ||||
−0.0322709 | + | 0.999479i | \(0.510274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.23808 | −0.164842 | −0.0824211 | − | 0.996598i | \(-0.526265\pi\) | ||||
−0.0824211 | + | 0.996598i | \(0.526265\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.63577 | 0.180038 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.3431 | 0.711317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57.2548 | −2.21692 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.1885 | −0.548559 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1917 | 0.432052 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6863 | 0.566115 | 0.283057 | − | 0.959103i | \(-0.408651\pi\) | ||||
0.283057 | + | 0.959103i | \(0.408651\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.6569 | −0.410183 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.59909 | −0.0998911 | −0.0499456 | − | 0.998752i | \(-0.515905\pi\) | ||||
−0.0499456 | + | 0.998752i | \(0.515905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1055 | 0.733201 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.1421 | −0.465288 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.51472 | 0.211015 | 0.105507 | − | 0.994419i | \(-0.466353\pi\) | ||||
0.105507 | + | 0.994419i | \(0.466353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.8724 | −2.44044 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.4234 | 0.817352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.79899 | −0.144730 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8284 | −1.47710 | −0.738551 | − | 0.674197i | \(-0.764490\pi\) | ||||
−0.738551 | + | 0.674197i | \(0.764490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.91375 | −0.300618 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 31.6550 | 1.20074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.62742 | −0.0995205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.3137 | 0.806158 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9761 | −1.16995 | −0.584976 | − | 0.811051i | \(-0.698896\pi\) | ||||
−0.584976 | + | 0.811051i | \(0.698896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.55596 | −0.247263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.3137 | −1.17934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11270 | 0.0418473 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0591 | 0.978671 | 0.489336 | − | 0.872096i | \(-0.337239\pi\) | ||||
0.489336 | + | 0.872096i | \(0.337239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.63899 | 0.0614670 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.9706 | −0.485751 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −106.912 | −3.99827 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.63577 | 0.173126 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.9330 | −1.30278 | −0.651390 | − | 0.758743i | \(-0.725814\pi\) | ||||
−0.651390 | + | 0.758743i | \(0.725814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.6274 | 1.06614 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9706 | 0.631142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −77.1008 | −2.86345 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5784 | −1.13409 | −0.567045 | − | 0.823687i | \(-0.691914\pi\) | ||||
−0.567045 | + | 0.823687i | \(0.691914\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.71573 | 0.137431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7078 | −0.690988 | −0.345494 | − | 0.938421i | \(-0.612289\pi\) | ||||
−0.345494 | + | 0.938421i | \(0.612289\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.0688 | 0.629592 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −65.9411 | −2.42897 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.8275 | −0.581438 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.5752 | −1.23175 | −0.615877 | − | 0.787842i | \(-0.711198\pi\) | ||||
−0.615877 | + | 0.787842i | \(0.711198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.6569 | 0.573623 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.82843 | −0.323015 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.55596 | 0.239550 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.63899 | 0.0598076 | 0.0299038 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299038 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8284 | 0.759030 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.1421 | 2.04322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.960099 | 0.0348954 | 0.0174477 | − | 0.999848i | \(-0.494446\pi\) | ||||
0.0174477 | + | 0.999848i | \(0.494446\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.2110 | 1.38697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.7696 | 1.11540 | 0.557698 | − | 0.830044i | \(-0.311685\pi\) | ||||
0.557698 | + | 0.830044i | \(0.311685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.5147 | −0.996100 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.27798 | −0.118516 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.0385 | −1.95122 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0000 | 0.432731 | 0.216366 | − | 0.976312i | \(-0.430580\pi\) | ||||
0.216366 | + | 0.976312i | \(0.430580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.6569 | 0.707924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.87707 | −0.211384 | −0.105692 | − | 0.994399i | \(-0.533706\pi\) | ||||
−0.105692 | + | 0.994399i | \(0.533706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.4665 | −0.627415 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.79899 | 0.136288 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.97056 | 0.321404 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8275 | 0.566352 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.23486 | 0.258553 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 71.7990 | 2.56262 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7696 | 0.740355 | 0.370177 | − | 0.928961i | \(-0.379297\pi\) | ||||
0.370177 | + | 0.928961i | \(0.379297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.8275 | 0.563474 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.562413 | 0.0199971 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.9706 | −0.460598 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.68629 | 0.0952729 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2284 | 0.468574 | 0.234287 | − | 0.972167i | \(-0.424724\pi\) | ||||
0.234287 | + | 0.972167i | \(0.424724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.55596 | −0.231933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3137 | −0.681566 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.3229 | 1.80889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.23486 | −0.254679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.4558 | 1.66846 | 0.834229 | − | 0.551418i | \(-0.185913\pi\) | ||||
0.834229 | + | 0.551418i | \(0.185913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.45584 | 0.0511216 | 0.0255608 | − | 0.999673i | \(-0.491863\pi\) | ||||
0.0255608 | + | 0.999673i | \(0.491863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.4665 | 0.612576 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.1312 | −1.40573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.6863 | −0.443837 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.17157 | 0.320481 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.03668 | −0.0710805 | −0.0355403 | − | 0.999368i | \(-0.511315\pi\) | ||||
−0.0355403 | + | 0.999368i | \(0.511315\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1885 | −0.494580 | −0.247290 | − | 0.968941i | \(-0.579540\pi\) | ||||
−0.247290 | + | 0.968941i | \(0.579540\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 51.4558 | 1.79146 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.9411 | −0.484780 | −0.242390 | − | 0.970179i | \(-0.577931\pi\) | ||||
−0.242390 | + | 0.970179i | \(0.577931\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.59587 | 0.194352 | 0.0971762 | − | 0.995267i | \(-0.469019\pi\) | ||||
0.0971762 | + | 0.995267i | \(0.469019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8674 | 0.515744 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.57359 | 0.123818 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.3431 | −0.634791 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.63899 | 0.0566518 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.2174 | −1.11227 | −0.556134 | − | 0.831092i | \(-0.687716\pi\) | ||||
−0.556134 | + | 0.831092i | \(0.687716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3431 | 0.804936 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.343146 | −0.0118186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.4650 | 2.49287 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1821 | 0.693464 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.9706 | −0.994267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.3431 | −0.628795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1454 | 0.621286 | 0.310643 | − | 0.950527i | \(-0.399456\pi\) | ||||
0.310643 | + | 0.950527i | \(0.399456\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.1917 | 0.382749 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.5147 | 0.461654 | 0.230827 | − | 0.972995i | \(-0.425857\pi\) | ||||
0.230827 | + | 0.972995i | \(0.425857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4558 | 1.00502 | 0.502510 | − | 0.864571i | \(-0.332410\pi\) | ||||
0.502510 | + | 0.864571i | \(0.332410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.19818 | −0.177153 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.63577 | 0.157803 | 0.0789017 | − | 0.996882i | \(-0.474859\pi\) | ||||
0.0789017 | + | 0.996882i | \(0.474859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 46.9706 | 1.59705 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.3137 | 0.554043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.91375 | −0.268456 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.4219 | 2.58946 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.6569 | 0.394525 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.6863 | 1.24022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.2765 | 1.96786 | 0.983929 | − | 0.178558i | \(-0.0571432\pi\) | ||||
0.983929 | + | 0.178558i | \(0.0571432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.678892 | 0.0228985 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.02944 | −0.169446 | −0.0847230 | − | 0.996405i | \(-0.527001\pi\) | ||||
−0.0847230 | + | 0.996405i | \(0.527001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.7696 | 1.64123 | 0.820613 | − | 0.571484i | \(-0.193632\pi\) | ||||
0.820613 | + | 0.571484i | \(0.193632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.2110 | 1.28445 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8275 | −0.531435 | −0.265718 | − | 0.964051i | \(-0.585609\pi\) | ||||
−0.265718 | + | 0.964051i | \(0.585609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2548 | −0.779942 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.82843 | −0.161758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.3835 | 0.749034 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.3229 | −1.71553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.2843 | −1.47861 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8579 | 0.395482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.562413 | 0.0187367 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.35134 | 0.244637 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 66.4264 | 2.20809 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.7990 | −0.524597 | −0.262298 | − | 0.964987i | \(-0.584480\pi\) | ||||
−0.262298 | + | 0.964987i | \(0.584480\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.678892 | 0.0225174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.92020 | 0.0636190 | 0.0318095 | − | 0.999494i | \(-0.489873\pi\) | ||||
0.0318095 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.6274 | 1.41076 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.17157 | 0.303203 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9871 | 0.395849 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.91697 | −0.162196 | −0.0810980 | − | 0.996706i | \(-0.525843\pi\) | ||||
−0.0810980 | + | 0.996706i | \(0.525843\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.6569 | −0.713618 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.3431 | −0.603772 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.7013 | −0.812175 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.4665 | 0.573675 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.7990 | 0.715202 | 0.357601 | − | 0.933875i | \(-0.383595\pi\) | ||||
0.357601 | + | 0.933875i | \(0.383595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.2010 | −0.399872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.8275 | 0.517615 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6274 | −1.32724 | −0.663620 | − | 0.748070i | \(-0.730981\pi\) | ||||
−0.663620 | + | 0.748070i | \(0.730981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.31371 | −0.238674 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.7972 | 1.72114 | 0.860569 | − | 0.509334i | \(-0.170108\pi\) | ||||
0.860569 | + | 0.509334i | \(0.170108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0990 | 0.817337 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.48528 | −0.210966 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.9706 | 0.941417 | 0.470708 | − | 0.882289i | \(-0.343998\pi\) | ||||
0.470708 | + | 0.882289i | \(0.343998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.3835 | 0.726598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7046 | 0.703819 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.7990 | 0.965284 | 0.482642 | − | 0.875818i | \(-0.339677\pi\) | ||||
0.482642 | + | 0.875818i | \(0.339677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −70.2254 | −2.27244 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.9330 | −1.12922 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.4568 | −0.854335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3137 | −0.913345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.8275 | −0.509505 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1279 | 1.38690 | 0.693450 | − | 0.720504i | \(-0.256090\pi\) | ||||
0.693450 | + | 0.720504i | \(0.256090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.34315 | 0.0752727 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.4558 | 0.496002 | 0.248001 | − | 0.968760i | \(-0.420226\pi\) | ||||
0.248001 | + | 0.968760i | \(0.420226\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1119 | 0.420349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −59.6343 | −1.90983 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.7696 | −1.36832 | −0.684160 | − | 0.729332i | \(-0.739831\pi\) | ||||
−0.684160 | + | 0.729332i | \(0.739831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.2843 | −1.54317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.7876 | −0.535987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.2110 | 1.21874 | 0.609370 | − | 0.792886i | \(-0.291422\pi\) | ||||
0.609370 | + | 0.792886i | \(0.291422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65.3137 | −2.08107 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.9706 | −0.412858 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.4954 | −1.12869 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.4059 | 1.47413 | 0.737066 | − | 0.675821i | \(-0.236211\pi\) | ||||
0.737066 | + | 0.675821i | \(0.236211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3431 | 0.328230 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.48528 | 0.205597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3371 | 0.929116 | 0.464558 | − | 0.885543i | \(-0.346213\pi\) | ||||
0.464558 | + | 0.885543i | \(0.346213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.31788 | 0.0733346 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1536.2.a.m.1.4 | yes | 4 | |
3.2 | odd | 2 | 4608.2.a.ba.1.1 | 4 | |||
4.3 | odd | 2 | 1536.2.a.n.1.4 | yes | 4 | ||
8.3 | odd | 2 | inner | 1536.2.a.m.1.1 | ✓ | 4 | |
8.5 | even | 2 | 1536.2.a.n.1.1 | yes | 4 | ||
12.11 | even | 2 | 4608.2.a.t.1.1 | 4 | |||
16.3 | odd | 4 | 1536.2.d.g.769.5 | 8 | |||
16.5 | even | 4 | 1536.2.d.g.769.8 | 8 | |||
16.11 | odd | 4 | 1536.2.d.g.769.4 | 8 | |||
16.13 | even | 4 | 1536.2.d.g.769.1 | 8 | |||
24.5 | odd | 2 | 4608.2.a.t.1.4 | 4 | |||
24.11 | even | 2 | 4608.2.a.ba.1.4 | 4 | |||
48.5 | odd | 4 | 4608.2.d.p.2305.1 | 8 | |||
48.11 | even | 4 | 4608.2.d.p.2305.2 | 8 | |||
48.29 | odd | 4 | 4608.2.d.p.2305.7 | 8 | |||
48.35 | even | 4 | 4608.2.d.p.2305.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.m.1.1 | ✓ | 4 | 8.3 | odd | 2 | inner | |
1536.2.a.m.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1536.2.a.n.1.1 | yes | 4 | 8.5 | even | 2 | ||
1536.2.a.n.1.4 | yes | 4 | 4.3 | odd | 2 | ||
1536.2.d.g.769.1 | 8 | 16.13 | even | 4 | |||
1536.2.d.g.769.4 | 8 | 16.11 | odd | 4 | |||
1536.2.d.g.769.5 | 8 | 16.3 | odd | 4 | |||
1536.2.d.g.769.8 | 8 | 16.5 | even | 4 | |||
4608.2.a.t.1.1 | 4 | 12.11 | even | 2 | |||
4608.2.a.t.1.4 | 4 | 24.5 | odd | 2 | |||
4608.2.a.ba.1.1 | 4 | 3.2 | odd | 2 | |||
4608.2.a.ba.1.4 | 4 | 24.11 | even | 2 | |||
4608.2.d.p.2305.1 | 8 | 48.5 | odd | 4 | |||
4608.2.d.p.2305.2 | 8 | 48.11 | even | 4 | |||
4608.2.d.p.2305.7 | 8 | 48.29 | odd | 4 | |||
4608.2.d.p.2305.8 | 8 | 48.35 | even | 4 |