Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1536,2,Mod(769,1536)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1536, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1536.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1536 = 2^{9} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1536.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.2650217505\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(0.500000 + 0.691860i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1536.769 |
Dual form | 1536.2.d.g.769.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1536\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(517\) | \(1025\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.95687i | − 1.76957i | −0.466001 | − | 0.884784i | \(-0.654306\pi\) | ||||
0.466001 | − | 0.884784i | \(-0.345694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.63899 | −0.619480 | −0.309740 | − | 0.950821i | \(-0.600242\pi\) | ||||
−0.309740 | + | 0.950821i | \(0.600242\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.82843i | 1.45583i | 0.685670 | + | 0.727913i | \(0.259509\pi\) | ||||
−0.685670 | + | 0.727913i | \(0.740491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.59587i | 1.55201i | 0.630724 | + | 0.776007i | \(0.282758\pi\) | ||||
−0.630724 | + | 0.776007i | \(0.717242\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 2.82843i | 0.648886i | 0.945905 | + | 0.324443i | \(0.105177\pi\) | ||||
−0.945905 | + | 0.324443i | \(0.894823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.63899i | 0.357657i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.91375 | −1.65013 | −0.825065 | − | 0.565037i | \(-0.808862\pi\) | ||||
−0.825065 | + | 0.565037i | \(0.808862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6569 | −2.13137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.23486i | − 1.34348i | −0.740787 | − | 0.671740i | \(-0.765547\pi\) | ||||
0.740787 | − | 0.671740i | \(-0.234453\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 6.48528i | 1.09621i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.31788i | 0.381058i | 0.981682 | + | 0.190529i | \(0.0610203\pi\) | ||||
−0.981682 | + | 0.190529i | \(0.938980\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.59587 | 0.896056 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.17157 | −0.495316 | −0.247658 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247658 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48528i | 0.683999i | 0.939700 | + | 0.341999i | \(0.111104\pi\) | ||||
−0.939700 | + | 0.341999i | \(0.888896\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.95687i | 0.589856i | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 0.828427i | 0.116003i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.678892i | 0.0932530i | 0.998912 | + | 0.0466265i | \(0.0148471\pi\) | ||||
−0.998912 | + | 0.0466265i | \(0.985153\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.1055 | 2.57618 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685i | 1.25722i | 0.777723 | + | 0.628608i | \(0.216375\pi\) | ||||
−0.777723 | + | 0.628608i | \(0.783625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.31788i | − 0.296775i | −0.988929 | − | 0.148387i | \(-0.952592\pi\) | ||||
0.988929 | − | 0.148387i | \(-0.0474082\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.63899 | 0.206493 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.1421 | 2.74639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6569i | 1.66845i | 0.551424 | + | 0.834225i | \(0.314085\pi\) | ||||
−0.551424 | + | 0.834225i | \(0.685915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.91375i | 0.952703i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.27798 | 0.389025 | 0.194512 | − | 0.980900i | \(-0.437688\pi\) | ||||
0.194512 | + | 0.980900i | \(0.437688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.6569i | 1.23055i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.91375i | − 0.901855i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | − 8.82843i | − 0.969046i | −0.874779 | − | 0.484523i | \(-0.838993\pi\) | ||||
0.874779 | − | 0.484523i | \(-0.161007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.27798i | 0.355547i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.23486 | −0.775658 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 9.17157i | − 0.961442i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.63899i | 0.169955i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 4.82843i | − 0.485275i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.678892i | − 0.0675523i | −0.999429 | − | 0.0337762i | \(-0.989247\pi\) | ||||
0.999429 | − | 0.0337762i | \(-0.0107533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.4665 | −1.72102 | −0.860512 | − | 0.509430i | \(-0.829856\pi\) | ||||
−0.860512 | + | 0.509430i | \(0.829856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.48528 | 0.632899 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 16.7876i | − 1.60796i | −0.594656 | − | 0.803980i | \(-0.702712\pi\) | ||||
0.594656 | − | 0.803980i | \(-0.297288\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 31.3137i | 2.92002i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 5.59587i | − 0.517338i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.35778 | 0.124468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.17157i | 0.285971i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.3835i | 2.00204i | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 7.31371i | 0.639002i | 0.947586 | + | 0.319501i | \(0.103515\pi\) | ||||
−0.947586 | + | 0.319501i | \(0.896485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.63577i | − 0.401972i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.95687 | 0.340554 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1421 | 1.37912 | 0.689558 | − | 0.724231i | \(-0.257805\pi\) | ||||
0.689558 | + | 0.724231i | \(0.257805\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 8.00000i | − 0.678551i | −0.940687 | − | 0.339276i | \(-0.889818\pi\) | ||||
0.940687 | − | 0.339276i | \(-0.110182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 7.91375i | − 0.666458i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.0192 | −2.25946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.6274 | −2.37738 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.31371i | 0.355789i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.95687i | − 0.324160i | −0.986778 | − | 0.162080i | \(-0.948180\pi\) | ||||
0.986778 | − | 0.162080i | \(-0.0518202\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1885 | −1.15464 | −0.577322 | − | 0.816516i | \(-0.695902\pi\) | ||||
−0.577322 | + | 0.816516i | \(0.695902\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.828427 | 0.0669744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.48528i | 0.520910i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.1454i | 1.44816i | 0.689717 | + | 0.724080i | \(0.257735\pi\) | ||||
−0.689717 | + | 0.724080i | \(0.742265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.678892 | 0.0538397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9706 | 1.02222 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.1421i | − 0.794393i | −0.917734 | − | 0.397197i | \(-0.869983\pi\) | ||||
0.917734 | − | 0.397197i | \(-0.130017\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 19.1055i | − 1.48736i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.63577 | 0.358726 | 0.179363 | − | 0.983783i | \(-0.442596\pi\) | ||||
0.179363 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.3137 | −1.40875 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.82843i | − 0.216295i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8706i | 0.902507i | 0.892396 | + | 0.451253i | \(0.149023\pi\) | ||||
−0.892396 | + | 0.451253i | \(0.850977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.4665 | 1.32034 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 12.9706i | − 0.969465i | −0.874662 | − | 0.484733i | \(-0.838917\pi\) | ||||
0.874662 | − | 0.484733i | \(-0.161083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 16.7876i | − 1.24781i | −0.781499 | − | 0.623906i | \(-0.785545\pi\) | ||||
0.781499 | − | 0.623906i | \(-0.214455\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.31788 | −0.171343 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.17157 | 0.674307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.00000i | − 0.292509i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.63899i | − 0.119219i | ||||||||
\(190\) | 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 | ||||||||
\(195\) | − 22.1421i | − 1.58563i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5064i | 1.17603i | 0.808849 | + | 0.588016i | \(0.200091\pi\) | ||||
−0.808849 | + | 0.588016i | \(0.799909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.63899 | −0.116185 | −0.0580925 | − | 0.998311i | \(-0.518502\pi\) | ||||
−0.0580925 | + | 0.998311i | \(0.518502\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.6569 | 0.963280 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.8579i | 0.832259i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.5495i | 0.876496i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.91375 | 0.550044 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6569 | −0.944664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 8.00000i | − 0.550743i | −0.961338 | − | 0.275371i | \(-0.911199\pi\) | ||||
0.961338 | − | 0.275371i | \(-0.0888008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.27798i | − 0.224604i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.7477 | 1.21038 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.68629 | 0.182357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00000i | 0.270295i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 4.63577i | − 0.311835i | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 12.1421i | 0.805902i | 0.915222 | + | 0.402951i | \(0.132015\pi\) | ||||
−0.915222 | + | 0.402951i | \(0.867985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.4234i | 1.41570i | 0.706365 | + | 0.707848i | \(0.250334\pi\) | ||||
−0.706365 | + | 0.707848i | \(0.749666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.91375 | −0.520686 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.3137 | 1.39631 | 0.698154 | − | 0.715948i | \(-0.254005\pi\) | ||||
0.698154 | + | 0.715948i | \(0.254005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 31.3137i | − 2.04268i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.63899i | − 0.106464i | ||||||||
\(238\) | 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 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.0688i | 1.09049i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.8275 | −1.00708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.82843 | −0.559479 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.8284i | 1.31468i | 0.753595 | + | 0.657339i | \(0.228318\pi\) | ||||
−0.753595 | + | 0.657339i | \(0.771682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 38.2110i | − 2.40230i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 3.79899i | − 0.236058i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.23486i | 0.447826i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8275 | 0.975965 | 0.487983 | − | 0.872853i | \(-0.337733\pi\) | ||||
0.487983 | + | 0.872853i | \(0.337733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68629 | 0.165018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000i | 0.611990i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.23486i | 0.441117i | 0.975374 | + | 0.220558i | \(0.0707880\pi\) | ||||
−0.975374 | + | 0.220558i | \(0.929212\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − 51.4558i | − 3.10290i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8674i | 0.893295i | 0.894710 | + | 0.446648i | \(0.147382\pi\) | ||||
−0.894710 | + | 0.446648i | \(0.852618\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.63899 | 0.0981238 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.343146 | −0.0204704 | −0.0102352 | − | 0.999948i | \(-0.503258\pi\) | ||||
−0.0102352 | + | 0.999948i | \(0.503258\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 28.9706i | − 1.72212i | −0.508502 | − | 0.861061i | \(-0.669801\pi\) | ||||
0.508502 | − | 0.861061i | \(-0.330199\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 11.1917i | − 0.662941i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.19818 | 0.306839 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 11.6569i | − 0.683337i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.678892i | 0.0396613i | 0.999803 | + | 0.0198307i | \(0.00631271\pi\) | ||||
−0.999803 | + | 0.0198307i | \(0.993687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.2110 | 2.22473 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.82843 | −0.280174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 44.2843i | − 2.56103i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 7.35134i | − 0.423724i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.678892 | −0.0390013 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.17157 | −0.525163 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6569i | 1.23602i | 0.786169 | + | 0.618011i | \(0.212061\pi\) | ||||
−0.786169 | + | 0.618011i | \(0.787939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.4665i | 0.993634i | ||||||||
\(310\) | 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 | \(-0.566272\pi\) | ||||
−0.206698 | + | 0.978405i | \(0.566272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6.48528i | − 0.365404i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 21.7046i | − 1.21905i | −0.792767 | − | 0.609525i | \(-0.791360\pi\) | ||||
0.792767 | − | 0.609525i | \(-0.208640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.9330 | 1.95587 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.34315i | − 0.130376i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 59.6343i | − 3.30792i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.7876 | −0.928356 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9706 | −0.715090 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3431i | 0.568511i | 0.958749 | + | 0.284255i | \(0.0917463\pi\) | ||||
−0.958749 | + | 0.284255i | \(0.908254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.31788i | − 0.127019i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 0.343146i | − 0.0186371i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.91375i | − 0.428554i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5431 | 1.00123 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.3137 | 1.68587 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.828427i | 0.0444723i | 0.999753 | + | 0.0222361i | \(0.00707857\pi\) | ||||
−0.999753 | + | 0.0222361i | \(0.992921\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.23808i | 0.226859i | 0.993546 | + | 0.113430i | \(0.0361836\pi\) | ||||
−0.993546 | + | 0.113430i | \(0.963816\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | − 12.9706i | − 0.688406i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.35778i | − 0.0718616i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.9330 | −1.84369 | −0.921846 | − | 0.387556i | \(-0.873319\pi\) | ||||
−0.921846 | + | 0.387556i | \(0.873319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3137i | 0.646302i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8275i | 0.828449i | ||||||||
\(366\) | 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 | ||||||||
\(371\) | − 1.11270i | − 0.0577684i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0656i | 1.03896i | 0.854484 | + | 0.519478i | \(0.173874\pi\) | ||||
−0.854484 | + | 0.519478i | \(0.826126\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.3835 | 1.15588 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.4853 | 2.08510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 0.485281i | − 0.0249272i | −0.999922 | − | 0.0124636i | \(-0.996033\pi\) | ||||
0.999922 | − | 0.0124636i | \(-0.00396739\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1885i | 0.726899i | ||||||||
\(382\) | 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 | ||||||||
\(387\) | − 4.48528i | − 0.228000i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.95687i | 0.200621i | 0.994956 | + | 0.100311i | \(0.0319837\pi\) | ||||
−0.994956 | + | 0.100311i | \(0.968016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.55596 | 0.331549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31371 | 0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.48528i | − 0.326310i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.1454i | 0.910691i | 0.890315 | + | 0.455345i | \(0.150484\pi\) | ||||
−0.890315 | + | 0.455345i | \(0.849516\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 9.17157i | − 0.456869i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.95687i | − 0.196619i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.1917 | −0.554753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.65685 | 0.180820 | 0.0904099 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904099 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 16.1421i | − 0.796233i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 15.8275i | − 0.778820i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −34.9330 | −1.71479 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 15.1716i | − 0.741180i | −0.928797 | − | 0.370590i | \(-0.879156\pi\) | ||||
0.928797 | − | 0.370590i | \(-0.120844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4234i | 1.04411i | 0.852912 | + | 0.522055i | \(0.174835\pi\) | ||||
−0.852912 | + | 0.522055i | \(0.825165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.91375 | −0.384780 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.82843 | 0.428242 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.79899i | 0.183846i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 27.0192i | 1.30450i | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 28.6274i | 1.37258i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 22.3835i | − 1.07075i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.8499 | −1.90193 | −0.950967 | − | 0.309292i | \(-0.899908\pi\) | ||||
−0.950967 | + | 0.309292i | \(0.899908\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.31371 | 0.205415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 18.4853i | − 0.878262i | −0.898423 | − | 0.439131i | \(-0.855286\pi\) | ||||
0.898423 | − | 0.439131i | \(-0.144714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.5687i | 1.87574i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 15.3137i | − 0.721094i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.1885i | 0.666634i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −36.2908 | −1.70134 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6569 | 1.10662 | 0.553310 | − | 0.832975i | \(-0.313364\pi\) | ||||
0.553310 | + | 0.832975i | \(0.313364\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 0.828427i | − 0.0386677i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 32.8963i | − 1.53213i | −0.642761 | − | 0.766067i | \(-0.722211\pi\) | ||||
0.642761 | − | 0.766067i | \(-0.277789\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − 37.7990i | − 1.74913i | −0.484910 | − | 0.874564i | \(-0.661147\pi\) | ||||
0.484910 | − | 0.874564i | \(-0.338853\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 22.3835i | − 1.03357i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.1454 | 0.836095 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.6569 | −0.995783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 30.1421i | − 1.38302i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 0.678892i | − 0.0310843i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | − 12.9706i | − 0.590181i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 46.1247i | − 2.09442i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.7445 | 0.940022 | 0.470011 | − | 0.882661i | \(-0.344250\pi\) | ||||
0.470011 | + | 0.882661i | \(0.344250\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1421 | −0.458643 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.65685i | 0.0747728i | 0.999301 | + | 0.0373864i | \(0.0119032\pi\) | ||||
−0.999301 | + | 0.0373864i | \(0.988097\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.99355i | 0.269936i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.1055 | −0.858727 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.37258 | −0.240993 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.3431i | 1.35835i | 0.733978 | + | 0.679173i | \(0.237661\pi\) | ||||
−0.733978 | + | 0.679173i | \(0.762339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 4.63577i | − 0.207111i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.5495 | −0.559555 | −0.279778 | − | 0.960065i | \(-0.590261\pi\) | ||||
−0.279778 | + | 0.960065i | \(0.590261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.68629 | −0.119538 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.3137i | 0.813340i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.59264i | 0.380862i | 0.981701 | + | 0.190431i | \(0.0609886\pi\) | ||||
−0.981701 | + | 0.190431i | \(0.939011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.55596 | 0.290019 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 69.1127i | 3.04547i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.2110i | 1.68052i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8706 | 0.521063 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.1716 | −0.664679 | −0.332339 | − | 0.943160i | \(-0.607838\pi\) | ||||
−0.332339 | + | 0.943160i | \(0.607838\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.1716i | 0.575953i | 0.957638 | + | 0.287976i | \(0.0929824\pi\) | ||||
−0.957638 | + | 0.287976i | \(0.907018\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 17.4665i | − 0.762300i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.35778 | 0.0591460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.6274 | 1.72293 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 9.65685i | − 0.419072i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17.7477i | − 0.768738i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.8275 | −0.684282 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.9706 | −0.559721 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 20.8284i | − 0.897144i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2316i | 0.439892i | 0.975512 | + | 0.219946i | \(0.0705882\pi\) | ||||
−0.975512 | + | 0.219946i | \(0.929412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.7876 | −0.720425 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −66.4264 | −2.84539 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.79899i | 0.333461i | 0.986003 | + | 0.166730i | \(0.0533209\pi\) | ||||
−0.986003 | + | 0.166730i | \(0.946679\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.31788i | 0.0989248i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.4633 | 0.871764 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.68629 | −0.114233 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 9.17157i | − 0.389312i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 27.6981i | − 1.17361i | −0.809729 | − | 0.586804i | \(-0.800386\pi\) | ||||
0.809729 | − | 0.586804i | \(-0.199614\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.0990 | −1.06158 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.82843i | − 0.203494i | −0.994810 | − | 0.101747i | \(-0.967557\pi\) | ||||
0.994810 | − | 0.101747i | \(-0.0324432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.35778i | − 0.0571224i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.63899 | −0.0688312 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.4558 | 1.15101 | 0.575504 | − | 0.817799i | \(-0.304806\pi\) | ||||
0.575504 | + | 0.817799i | \(0.304806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.686292i | 0.0287204i | 0.999897 | + | 0.0143602i | \(0.00457115\pi\) | ||||
−0.999897 | + | 0.0143602i | \(0.995429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.7477i | 0.741421i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 4.00000i | 0.166234i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4697i | 0.600305i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.27798 | −0.135760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.1421 | −0.915465 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9706i | 1.19574i | 0.801592 | + | 0.597872i | \(0.203987\pi\) | ||||
−0.801592 | + | 0.597872i | \(0.796013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 4.63577i | − 0.191013i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 5.37258i | − 0.220254i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.63899i | 0.0670794i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.1247 | 1.88460 | 0.942302 | − | 0.334763i | \(-0.108656\pi\) | ||||
0.942302 | + | 0.334763i | \(0.108656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.3137 | 1.11415 | 0.557075 | − | 0.830462i | \(-0.311924\pi\) | ||||
0.557075 | + | 0.830462i | \(0.311924\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 13.6569i | − 0.556150i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 48.7238i | 1.98090i | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 44.2843i | 1.79155i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.8931i | 1.44971i | 0.688903 | + | 0.724854i | \(0.258093\pi\) | ||||
−0.688903 | + | 0.724854i | \(0.741907\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.5495 | 0.506045 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.9411 | −0.963833 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 28.0000i | − 1.12542i | −0.826656 | − | 0.562708i | \(-0.809760\pi\) | ||||
0.826656 | − | 0.562708i | \(-0.190240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7.91375i | − 0.317568i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.3899 | 0.656648 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 35.2843 | 1.41137 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.6569i | 0.545402i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.92020i | − 0.0765633i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.4729 | 0.456730 | 0.228365 | − | 0.973576i | \(-0.426662\pi\) | ||||
0.228365 | + | 0.973576i | \(0.426662\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.00000 | −0.317971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.1421i | 2.22793i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 24.1389i | − 0.956419i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − 20.4853i | − 0.807861i | −0.914790 | − | 0.403930i | \(-0.867644\pi\) | ||||
0.914790 | − | 0.403930i | \(-0.132356\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 17.7477i | − 0.698815i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.19818 | −0.204362 | −0.102181 | − | 0.994766i | \(-0.532582\pi\) | ||||
−0.102181 | + | 0.994766i | \(0.532582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.6274 | −1.83029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 2.68629i | − 0.105284i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 13.2284i | − 0.517668i | −0.965922 | − | 0.258834i | \(-0.916662\pi\) | ||||
0.965922 | − | 0.258834i | \(-0.0833382\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.9394 | 1.13076 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.65685i | − 0.0645419i | −0.999479 | − | 0.0322709i | \(-0.989726\pi\) | ||||
0.999479 | − | 0.0322709i | \(-0.0102739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.23808i | 0.164842i | 0.996598 | + | 0.0824211i | \(0.0262653\pi\) | ||||
−0.996598 | + | 0.0824211i | \(0.973735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.63577 | −0.180038 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.3431 | −0.711317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.2548i | 2.21692i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 14.1885i | − 0.548559i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 10.6569i | − 0.410183i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.59909i | 0.0998911i | 0.998752 | + | 0.0499456i | \(0.0159048\pi\) | ||||
−0.998752 | + | 0.0499456i | \(0.984095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.1055 | −0.733201 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1421 | 0.465288 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.51472i | − 0.211015i | −0.994419 | − | 0.105507i | \(-0.966353\pi\) | ||||
0.994419 | − | 0.105507i | \(-0.0336467\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 63.8724i | − 2.44044i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.4234 | 0.817352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.79899 | −0.144730 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 38.8284i | − 1.47710i | −0.674197 | − | 0.738551i | \(-0.735510\pi\) | ||||
0.674197 | − | 0.738551i | \(-0.264490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.91375i | 0.300618i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.6550 | −1.20074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.62742 | 0.0995205 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 21.3137i | − 0.806158i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 30.9761i | − 1.16995i | −0.811051 | − | 0.584976i | \(-0.801104\pi\) | ||||
0.811051 | − | 0.584976i | \(-0.198896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.55596 | −0.247263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −31.3137 | −1.17934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11270i | 0.0418473i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 26.0591i | − 0.978671i | −0.872096 | − | 0.489336i | \(-0.837239\pi\) | ||||
0.872096 | − | 0.489336i | \(-0.162761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.63899 | −0.0614670 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9706 | 0.485751 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 106.912i | 3.99827i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.63577i | 0.173126i | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 16.9706i | 0.631142i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 77.1008i | 2.86345i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.5784 | 1.13409 | 0.567045 | − | 0.823687i | \(-0.308086\pi\) | ||||
0.567045 | + | 0.823687i | \(0.308086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.71573i | − 0.137431i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18.7078i | − 0.690988i | −0.938421 | − | 0.345494i | \(-0.887711\pi\) | ||||
0.938421 | − | 0.345494i | \(-0.112289\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.0688 | 0.629592 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −65.9411 | −2.42897 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8275i | 0.581438i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.5752 | 1.23175 | 0.615877 | − | 0.787842i | \(-0.288802\pi\) | ||||
0.615877 | + | 0.787842i | \(0.288802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.6569 | −0.573623 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.82843i | 0.323015i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.55596i | 0.239550i | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 56.1421i | 2.04322i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.960099i | − 0.0348954i | −0.999848 | − | 0.0174477i | \(-0.994446\pi\) | ||||
0.999848 | − | 0.0174477i | \(-0.00555405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −38.2110 | −1.38697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7696 | −1.11540 | −0.557698 | − | 0.830044i | \(-0.688315\pi\) | ||||
−0.557698 | + | 0.830044i | \(0.688315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5147i | 0.996100i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.27798i | − 0.118516i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 19.6569i | 0.707924i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.87707i | 0.211384i | 0.994399 | + | 0.105692i | \(0.0337057\pi\) | ||||
−0.994399 | + | 0.105692i | \(0.966294\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.4665 | 0.627415 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.79899 | −0.136288 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 8.97056i | − 0.321404i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8275i | 0.566352i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.23486 | 0.258553 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 71.7990 | 2.56262 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7696i | 0.740355i | 0.928961 | + | 0.370177i | \(0.120703\pi\) | ||||
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 15.8275i | − 0.563474i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.562413 | −0.0199971 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.9706 | 0.460598 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.68629i | − 0.0952729i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2284i | 0.468574i | 0.972167 | + | 0.234287i | \(0.0752756\pi\) | ||||
−0.972167 | + | 0.234287i | \(0.924724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.55596 | −0.231933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0000 | 0.353333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19.3137i | − 0.681566i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 51.3229i | − 1.80889i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.23486 | 0.254679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −47.4558 | −1.66846 | −0.834229 | − | 0.551418i | \(-0.814087\pi\) | ||||
−0.834229 | + | 0.551418i | \(0.814087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.45584i | − 0.0511216i | −0.999673 | − | 0.0255608i | \(-0.991863\pi\) | ||||
0.999673 | − | 0.0255608i | \(-0.00813714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.4665i | 0.612576i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.1312 | −1.40573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.6863 | −0.443837 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.17157i | 0.320481i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.03668i | 0.0710805i | 0.999368 | + | 0.0355403i | \(0.0113152\pi\) | ||||
−0.999368 | + | 0.0355403i | \(0.988685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1885 | 0.494580 | 0.247290 | − | 0.968941i | \(-0.420460\pi\) | ||||
0.247290 | + | 0.968941i | \(0.420460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −51.4558 | −1.79146 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.9411i | 0.484780i | 0.970179 | + | 0.242390i | \(0.0779314\pi\) | ||||
−0.970179 | + | 0.242390i | \(0.922069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.59587i | 0.194352i | 0.995267 | + | 0.0971762i | \(0.0309810\pi\) | ||||
−0.995267 | + | 0.0971762i | \(0.969019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.8674 | 0.515744 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.57359 | 0.123818 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 18.3431i | − 0.634791i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.63899i | − 0.0566518i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.2174 | 1.11227 | 0.556134 | − | 0.831092i | \(-0.312284\pi\) | ||||
0.556134 | + | 0.831092i | \(0.312284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3431 | −0.804936 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.343146i | 0.0118186i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.4650i | 2.49287i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1821 | 0.693464 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.9706 | −0.994267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 18.3431i | − 0.628795i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 18.1454i | − 0.621286i | −0.950527 | − | 0.310643i | \(-0.899456\pi\) | ||||
0.950527 | − | 0.310643i | \(-0.100544\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.1917 | −0.382749 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5147 | −0.461654 | −0.230827 | − | 0.972995i | \(-0.574143\pi\) | ||||
−0.230827 | + | 0.972995i | \(0.574143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 29.4558i | − 1.00502i | −0.864571 | − | 0.502510i | \(-0.832410\pi\) | ||||
0.864571 | − | 0.502510i | \(-0.167590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 5.19818i | − 0.177153i | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 16.3137i | 0.554043i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.91375i | 0.268456i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −76.4219 | −2.58946 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.6569 | −0.394525 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 36.6863i | − 1.24022i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.2765i | 1.96786i | 0.178558 | + | 0.983929i | \(0.442857\pi\) | ||||
−0.178558 | + | 0.983929i | \(0.557143\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 48.7696i | 1.64123i | 0.571484 | + | 0.820613i | \(0.306368\pi\) | ||||
−0.571484 | + | 0.820613i | \(0.693632\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 38.2110i | − 1.28445i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8275 | 0.531435 | 0.265718 | − | 0.964051i | \(-0.414391\pi\) | ||||
0.265718 | + | 0.964051i | \(0.414391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2548 | 0.779942 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.82843i | 0.161758i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.3835i | 0.749034i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.3229 | −1.71553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.2843 | −1.47861 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8579i | 0.395482i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.562413i | − 0.0187367i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.35134 | −0.244637 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −66.4264 | −2.20809 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.7990i | 0.524597i | 0.964987 | + | 0.262298i | \(0.0844805\pi\) | ||||
−0.964987 | + | 0.262298i | \(0.915520\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.678892i | 0.0225174i | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 9.17157i | 0.303203i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 11.9871i | − 0.395849i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.91697 | 0.162196 | 0.0810980 | − | 0.996706i | \(-0.474157\pi\) | ||||
0.0810980 | + | 0.996706i | \(0.474157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.6569 | 0.713618 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.3431i | 0.603772i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 24.7013i | − 0.812175i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | − 12.2010i | − 0.399872i | ||||||||
\(932\) | 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 | \(-0.269019\pi\) | ||||
0.663620 | + | 0.748070i | \(0.269019\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.31371i | 0.238674i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.7972i | 1.72114i | 0.509334 | + | 0.860569i | \(0.329892\pi\) | ||||
−0.509334 | + | 0.860569i | \(0.670108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.0990 | 0.817337 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.48528 | −0.210966 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.9706i | 0.941417i | 0.882289 | + | 0.470708i | \(0.156002\pi\) | ||||
−0.882289 | + | 0.470708i | \(0.843998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 22.3835i | − 0.726598i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.7046 | −0.703819 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7990 | −0.965284 | −0.482642 | − | 0.875818i | \(-0.660323\pi\) | ||||
−0.482642 | + | 0.875818i | \(0.660323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.2254i | 2.27244i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 34.9330i | − 1.12922i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.4568 | −0.854335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3137 | −0.913345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.8275i | 0.509505i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.1279 | −1.38690 | −0.693450 | − | 0.720504i | \(-0.743910\pi\) | ||||
−0.693450 | + | 0.720504i | \(0.743910\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.34315 | −0.0752727 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 15.4558i | − 0.496002i | −0.968760 | − | 0.248001i | \(-0.920226\pi\) | ||||
0.968760 | − | 0.248001i | \(-0.0797736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.1119i | 0.420349i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 48.2843i | − 1.54317i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.7876i | 0.535987i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.2110 | −1.21874 | −0.609370 | − | 0.792886i | \(-0.708578\pi\) | ||||
−0.609370 | + | 0.792886i | \(0.708578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.3137 | 2.08107 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.9706i | 0.412858i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 35.4954i | − 1.12869i | ||||||||
\(990\) | 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 | ||||||||
\(995\) | 6.48528i | 0.205597i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.3371i | − 0.929116i | −0.885543 | − | 0.464558i | \(-0.846213\pi\) | ||||
0.885543 | − | 0.464558i | \(-0.153787\pi\) | |||||||
\(998\) | 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.d.g.769.1 | 8 | ||
3.2 | odd | 2 | 4608.2.d.p.2305.7 | 8 | |||
4.3 | odd | 2 | inner | 1536.2.d.g.769.5 | 8 | ||
8.3 | odd | 2 | inner | 1536.2.d.g.769.4 | 8 | ||
8.5 | even | 2 | inner | 1536.2.d.g.769.8 | 8 | ||
12.11 | even | 2 | 4608.2.d.p.2305.8 | 8 | |||
16.3 | odd | 4 | 1536.2.a.m.1.1 | ✓ | 4 | ||
16.5 | even | 4 | 1536.2.a.m.1.4 | yes | 4 | ||
16.11 | odd | 4 | 1536.2.a.n.1.4 | yes | 4 | ||
16.13 | even | 4 | 1536.2.a.n.1.1 | yes | 4 | ||
24.5 | odd | 2 | 4608.2.d.p.2305.1 | 8 | |||
24.11 | even | 2 | 4608.2.d.p.2305.2 | 8 | |||
48.5 | odd | 4 | 4608.2.a.ba.1.1 | 4 | |||
48.11 | even | 4 | 4608.2.a.t.1.1 | 4 | |||
48.29 | odd | 4 | 4608.2.a.t.1.4 | 4 | |||
48.35 | even | 4 | 4608.2.a.ba.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1536.2.a.m.1.1 | ✓ | 4 | 16.3 | odd | 4 | ||
1536.2.a.m.1.4 | yes | 4 | 16.5 | even | 4 | ||
1536.2.a.n.1.1 | yes | 4 | 16.13 | even | 4 | ||
1536.2.a.n.1.4 | yes | 4 | 16.11 | odd | 4 | ||
1536.2.d.g.769.1 | 8 | 1.1 | even | 1 | trivial | ||
1536.2.d.g.769.4 | 8 | 8.3 | odd | 2 | inner | ||
1536.2.d.g.769.5 | 8 | 4.3 | odd | 2 | inner | ||
1536.2.d.g.769.8 | 8 | 8.5 | even | 2 | inner | ||
4608.2.a.t.1.1 | 4 | 48.11 | even | 4 | |||
4608.2.a.t.1.4 | 4 | 48.29 | odd | 4 | |||
4608.2.a.ba.1.1 | 4 | 48.5 | odd | 4 | |||
4608.2.a.ba.1.4 | 4 | 48.35 | even | 4 | |||
4608.2.d.p.2305.1 | 8 | 24.5 | odd | 2 | |||
4608.2.d.p.2305.2 | 8 | 24.11 | even | 2 | |||
4608.2.d.p.2305.7 | 8 | 3.2 | odd | 2 | |||
4608.2.d.p.2305.8 | 8 | 12.11 | even | 2 |