Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1287,2,Mod(1,1287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1287, 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("1287.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1287 = 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1287.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: | \(10.2767467401\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1287.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | 1.22474 | 0.612372 | − | 0.790569i | \(-0.290215\pi\) | ||||
0.612372 | + | 0.790569i | \(0.290215\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.732051 | −0.327383 | −0.163692 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163692 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.73205 | −0.612372 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.26795 | −0.400961 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.46410 | −0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −6.73205 | −1.63276 | −0.816381 | − | 0.577514i | \(-0.804023\pi\) | ||||
−0.816381 | + | 0.577514i | \(0.804023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.535898 | −0.122944 | −0.0614718 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614718 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(20\) | −0.732051 | −0.163692 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73205 | 0.369274 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | −1.73205 | −0.339683 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 4.19615 | 0.779206 | 0.389603 | − | 0.920983i | \(-0.372612\pi\) | ||||
0.389603 | + | 0.920983i | \(0.372612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.19615 | −1.47207 | −0.736036 | − | 0.676942i | \(-0.763305\pi\) | ||||
−0.736036 | + | 0.676942i | \(0.763305\pi\) | |||||||
\(32\) | −5.19615 | −0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.6603 | −1.99972 | ||||||||
\(35\) | 1.46410 | 0.247478 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −0.928203 | −0.150574 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.26795 | 0.200480 | ||||||||
\(41\) | 5.46410 | 0.853349 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.19615 | −0.944904 | −0.472452 | − | 0.881356i | \(-0.656631\pi\) | ||||
−0.472452 | + | 0.881356i | \(0.656631\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.46410 | 0.510754 | ||||||||
\(47\) | 1.46410 | 0.213561 | 0.106781 | − | 0.994283i | \(-0.465946\pi\) | ||||
0.106781 | + | 0.994283i | \(0.465946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −7.73205 | −1.09348 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.732051 | −0.0987097 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.26795 | 0.954328 | ||||||||
\(59\) | 13.4641 | 1.75288 | 0.876438 | − | 0.481514i | \(-0.159913\pi\) | ||||
0.876438 | + | 0.481514i | \(0.159913\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.92820 | 0.630992 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(62\) | −14.1962 | −1.80291 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.732051 | 0.0907997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1962 | −1.49000 | −0.744999 | − | 0.667066i | \(-0.767550\pi\) | ||||
−0.744999 | + | 0.667066i | \(0.767550\pi\) | |||||||
\(68\) | −6.73205 | −0.816381 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.53590 | 0.303098 | ||||||||
\(71\) | −6.92820 | −0.822226 | −0.411113 | − | 0.911584i | \(-0.634860\pi\) | ||||
−0.411113 | + | 0.911584i | \(0.634860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.92820 | 0.342720 | 0.171360 | − | 0.985208i | \(-0.445184\pi\) | ||||
0.171360 | + | 0.985208i | \(0.445184\pi\) | |||||||
\(74\) | −3.46410 | −0.402694 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.535898 | −0.0614718 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.66025 | −0.411811 | −0.205905 | − | 0.978572i | \(-0.566014\pi\) | ||||
−0.205905 | + | 0.978572i | \(0.566014\pi\) | |||||||
\(80\) | 3.66025 | 0.409229 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.46410 | 1.04514 | ||||||||
\(83\) | −13.8564 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.92820 | 0.534539 | ||||||||
\(86\) | −10.7321 | −1.15727 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.73205 | −0.184637 | ||||||||
\(89\) | 15.6603 | 1.65998 | 0.829992 | − | 0.557776i | \(-0.188345\pi\) | ||||
0.829992 | + | 0.557776i | \(0.188345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.53590 | 0.261558 | ||||||||
\(95\) | 0.392305 | 0.0402496 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92820 | 0.906522 | 0.453261 | − | 0.891378i | \(-0.350261\pi\) | ||||
0.453261 | + | 0.891378i | \(0.350261\pi\) | |||||||
\(98\) | −5.19615 | −0.524891 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.46410 | −0.446410 | ||||||||
\(101\) | −8.19615 | −0.815548 | −0.407774 | − | 0.913083i | \(-0.633695\pi\) | ||||
−0.407774 | + | 0.913083i | \(0.633695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.3205 | 1.90371 | 0.951853 | − | 0.306554i | \(-0.0991762\pi\) | ||||
0.951853 | + | 0.306554i | \(0.0991762\pi\) | |||||||
\(104\) | 1.73205 | 0.169842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.46410 | −0.336463 | ||||||||
\(107\) | 8.39230 | 0.811315 | 0.405657 | − | 0.914025i | \(-0.367043\pi\) | ||||
0.405657 | + | 0.914025i | \(0.367043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | −1.26795 | −0.120894 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0000 | 0.944911 | ||||||||
\(113\) | −10.0000 | −0.940721 | −0.470360 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470360 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.46410 | −0.136528 | ||||||||
\(116\) | 4.19615 | 0.389603 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.3205 | 2.14683 | ||||||||
\(119\) | 13.4641 | 1.23425 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.53590 | 0.772804 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.19615 | −0.736036 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1244 | 1.16460 | 0.582299 | − | 0.812975i | \(-0.302153\pi\) | ||||
0.582299 | + | 0.812975i | \(0.302153\pi\) | |||||||
\(128\) | 12.1244 | 1.07165 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.26795 | 0.111207 | ||||||||
\(131\) | 5.07180 | 0.443125 | 0.221562 | − | 0.975146i | \(-0.428884\pi\) | ||||
0.221562 | + | 0.975146i | \(0.428884\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.07180 | 0.0929366 | ||||||||
\(134\) | −21.1244 | −1.82487 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.6603 | 0.999859 | ||||||||
\(137\) | 14.5885 | 1.24638 | 0.623188 | − | 0.782072i | \(-0.285837\pi\) | ||||
0.623188 | + | 0.782072i | \(0.285837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.80385 | −0.831551 | −0.415776 | − | 0.909467i | \(-0.636490\pi\) | ||||
−0.415776 | + | 0.909467i | \(0.636490\pi\) | |||||||
\(140\) | 1.46410 | 0.123739 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.07180 | −0.255099 | ||||||||
\(146\) | 5.07180 | 0.419745 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −8.00000 | −0.655386 | −0.327693 | − | 0.944784i | \(-0.606271\pi\) | ||||
−0.327693 | + | 0.944784i | \(0.606271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.53590 | −0.369126 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(152\) | 0.928203 | 0.0752872 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.46410 | −0.279145 | ||||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3205 | −1.22271 | −0.611355 | − | 0.791357i | \(-0.709375\pi\) | ||||
−0.611355 | + | 0.791357i | \(0.709375\pi\) | |||||||
\(158\) | −6.33975 | −0.504363 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.80385 | 0.300721 | ||||||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2679 | −1.35253 | −0.676265 | − | 0.736658i | \(-0.736403\pi\) | ||||
−0.676265 | + | 0.736658i | \(0.736403\pi\) | |||||||
\(164\) | 5.46410 | 0.426675 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −24.0000 | −1.86276 | ||||||||
\(167\) | 9.85641 | 0.762712 | 0.381356 | − | 0.924428i | \(-0.375457\pi\) | ||||
0.381356 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 8.53590 | 0.654674 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.19615 | −0.472452 | ||||||||
\(173\) | −19.1244 | −1.45400 | −0.726999 | − | 0.686639i | \(-0.759085\pi\) | ||||
−0.726999 | + | 0.686639i | \(0.759085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.92820 | 0.674909 | ||||||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 27.1244 | 2.03306 | ||||||||
\(179\) | −7.85641 | −0.587215 | −0.293608 | − | 0.955926i | \(-0.594856\pi\) | ||||
−0.293608 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.39230 | 0.623795 | 0.311898 | − | 0.950116i | \(-0.399035\pi\) | ||||
0.311898 | + | 0.950116i | \(0.399035\pi\) | |||||||
\(182\) | 3.46410 | 0.256776 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.46410 | −0.255377 | ||||||||
\(185\) | 1.46410 | 0.107643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.73205 | −0.492296 | ||||||||
\(188\) | 1.46410 | 0.106781 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.679492 | 0.0492955 | ||||||||
\(191\) | 18.9282 | 1.36960 | 0.684798 | − | 0.728733i | \(-0.259890\pi\) | ||||
0.684798 | + | 0.728733i | \(0.259890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.92820 | −0.498703 | −0.249351 | − | 0.968413i | \(-0.580217\pi\) | ||||
−0.249351 | + | 0.968413i | \(0.580217\pi\) | |||||||
\(194\) | 15.4641 | 1.11026 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −8.00000 | −0.569976 | −0.284988 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284988 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5359 | 0.746870 | 0.373435 | − | 0.927656i | \(-0.378180\pi\) | ||||
0.373435 | + | 0.927656i | \(0.378180\pi\) | |||||||
\(200\) | 7.73205 | 0.546739 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.1962 | −0.998838 | ||||||||
\(203\) | −8.39230 | −0.589024 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | 33.4641 | 2.33155 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.00000 | 0.346688 | ||||||||
\(209\) | −0.535898 | −0.0370689 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2679 | 1.32646 | 0.663230 | − | 0.748415i | \(-0.269185\pi\) | ||||
0.663230 | + | 0.748415i | \(0.269185\pi\) | |||||||
\(212\) | −2.00000 | −0.137361 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.5359 | 0.993654 | ||||||||
\(215\) | 4.53590 | 0.309346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.3923 | 1.11278 | ||||||||
\(218\) | −13.8564 | −0.938474 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.732051 | −0.0493549 | ||||||||
\(221\) | 6.73205 | 0.452847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.5167 | −1.57479 | −0.787396 | − | 0.616447i | \(-0.788571\pi\) | ||||
−0.787396 | + | 0.616447i | \(0.788571\pi\) | |||||||
\(224\) | 10.3923 | 0.694365 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.3205 | −1.15214 | ||||||||
\(227\) | 10.3923 | 0.689761 | 0.344881 | − | 0.938647i | \(-0.387919\pi\) | ||||
0.344881 | + | 0.938647i | \(0.387919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4641 | −1.02190 | −0.510948 | − | 0.859611i | \(-0.670706\pi\) | ||||
−0.510948 | + | 0.859611i | \(0.670706\pi\) | |||||||
\(230\) | −2.53590 | −0.167212 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.26795 | −0.477164 | ||||||||
\(233\) | −4.19615 | −0.274899 | −0.137450 | − | 0.990509i | \(-0.543890\pi\) | ||||
−0.137450 | + | 0.990509i | \(0.543890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.07180 | −0.0699163 | ||||||||
\(236\) | 13.4641 | 0.876438 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.3205 | 1.51164 | ||||||||
\(239\) | −22.3923 | −1.44844 | −0.724219 | − | 0.689570i | \(-0.757799\pi\) | ||||
−0.724219 | + | 0.689570i | \(0.757799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7846 | −1.21002 | −0.605012 | − | 0.796217i | \(-0.706832\pi\) | ||||
−0.605012 | + | 0.796217i | \(0.706832\pi\) | |||||||
\(242\) | 1.73205 | 0.111340 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.92820 | 0.315496 | ||||||||
\(245\) | 2.19615 | 0.140307 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.535898 | 0.0340984 | ||||||||
\(248\) | 14.1962 | 0.901457 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 17.0718 | 1.07756 | 0.538781 | − | 0.842446i | \(-0.318885\pi\) | ||||
0.538781 | + | 0.842446i | \(0.318885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 22.7321 | 1.42634 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −17.3205 | −1.08042 | −0.540212 | − | 0.841529i | \(-0.681656\pi\) | ||||
−0.540212 | + | 0.841529i | \(0.681656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0.732051 | 0.0453999 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.78461 | 0.542715 | ||||||||
\(263\) | −9.46410 | −0.583582 | −0.291791 | − | 0.956482i | \(-0.594251\pi\) | ||||
−0.291791 | + | 0.956482i | \(0.594251\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.46410 | 0.0899390 | ||||||||
\(266\) | 1.85641 | 0.113824 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.1962 | −0.744999 | ||||||||
\(269\) | 17.3205 | 1.05605 | 0.528025 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528025 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.32051 | 0.566181 | 0.283090 | − | 0.959093i | \(-0.408640\pi\) | ||||
0.283090 | + | 0.959093i | \(0.408640\pi\) | |||||||
\(272\) | 33.6603 | 2.04095 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.2679 | 1.52649 | ||||||||
\(275\) | −4.46410 | −0.269195 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | −16.9808 | −1.01844 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.53590 | −0.151549 | ||||||||
\(281\) | −23.3205 | −1.39118 | −0.695592 | − | 0.718437i | \(-0.744858\pi\) | ||||
−0.695592 | + | 0.718437i | \(0.744858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.80385 | 0.582778 | 0.291389 | − | 0.956605i | \(-0.405883\pi\) | ||||
0.291389 | + | 0.956605i | \(0.405883\pi\) | |||||||
\(284\) | −6.92820 | −0.411113 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.73205 | −0.102418 | ||||||||
\(287\) | −10.9282 | −0.645071 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.3205 | 1.66591 | ||||||||
\(290\) | −5.32051 | −0.312431 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.92820 | 0.171360 | ||||||||
\(293\) | −13.0718 | −0.763663 | −0.381831 | − | 0.924232i | \(-0.624706\pi\) | ||||
−0.381831 | + | 0.924232i | \(0.624706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.85641 | −0.573862 | ||||||||
\(296\) | 3.46410 | 0.201347 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.8564 | −0.802680 | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.3923 | 0.714281 | ||||||||
\(302\) | −7.85641 | −0.452085 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.67949 | 0.153679 | ||||||||
\(305\) | −3.60770 | −0.206576 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.5359 | −1.17205 | −0.586023 | − | 0.810295i | \(-0.699307\pi\) | ||||
−0.586023 | + | 0.810295i | \(0.699307\pi\) | |||||||
\(308\) | −2.00000 | −0.113961 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.3923 | 0.590243 | ||||||||
\(311\) | 3.07180 | 0.174186 | 0.0870928 | − | 0.996200i | \(-0.472242\pi\) | ||||
0.0870928 | + | 0.996200i | \(0.472242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.46410 | −0.534943 | −0.267471 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267471 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(314\) | −26.5359 | −1.49751 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.66025 | −0.205905 | ||||||||
\(317\) | −17.1244 | −0.961800 | −0.480900 | − | 0.876776i | \(-0.659690\pi\) | ||||
−0.480900 | + | 0.876776i | \(0.659690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.19615 | 0.234939 | ||||||||
\(320\) | −0.732051 | −0.0409229 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.92820 | −0.386094 | ||||||||
\(323\) | 3.60770 | 0.200738 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.46410 | 0.247624 | ||||||||
\(326\) | −29.9090 | −1.65650 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.46410 | −0.522568 | ||||||||
\(329\) | −2.92820 | −0.161437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5167 | 1.29259 | 0.646296 | − | 0.763087i | \(-0.276317\pi\) | ||||
0.646296 | + | 0.763087i | \(0.276317\pi\) | |||||||
\(332\) | −13.8564 | −0.760469 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.0718 | 0.934127 | ||||||||
\(335\) | 8.92820 | 0.487800 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.32051 | 0.507720 | 0.253860 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(338\) | 1.73205 | 0.0942111 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.92820 | 0.267269 | ||||||||
\(341\) | −8.19615 | −0.443847 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 10.7321 | 0.578633 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.1244 | −1.78078 | ||||||||
\(347\) | 4.39230 | 0.235791 | 0.117896 | − | 0.993026i | \(-0.462385\pi\) | ||||
0.117896 | + | 0.993026i | \(0.462385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.85641 | −0.206429 | −0.103214 | − | 0.994659i | \(-0.532913\pi\) | ||||
−0.103214 | + | 0.994659i | \(0.532913\pi\) | |||||||
\(350\) | 15.4641 | 0.826591 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.19615 | −0.276956 | ||||||||
\(353\) | −22.9808 | −1.22314 | −0.611571 | − | 0.791189i | \(-0.709462\pi\) | ||||
−0.611571 | + | 0.791189i | \(0.709462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.07180 | 0.269183 | ||||||||
\(356\) | 15.6603 | 0.829992 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.6077 | −0.719189 | ||||||||
\(359\) | 16.5359 | 0.872731 | 0.436366 | − | 0.899769i | \(-0.356265\pi\) | ||||
0.436366 | + | 0.899769i | \(0.356265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7128 | −0.984885 | ||||||||
\(362\) | 14.5359 | 0.763990 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −2.14359 | −0.112201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.9282 | 1.61444 | 0.807220 | − | 0.590251i | \(-0.200971\pi\) | ||||
0.807220 | + | 0.590251i | \(0.200971\pi\) | |||||||
\(368\) | −10.0000 | −0.521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.53590 | 0.131835 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2487 | −0.841326 | −0.420663 | − | 0.907217i | \(-0.638203\pi\) | ||||
−0.420663 | + | 0.907217i | \(0.638203\pi\) | |||||||
\(374\) | −11.6603 | −0.602937 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.53590 | −0.130779 | ||||||||
\(377\) | −4.19615 | −0.216113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1962 | 0.626474 | 0.313237 | − | 0.949675i | \(-0.398587\pi\) | ||||
0.313237 | + | 0.949675i | \(0.398587\pi\) | |||||||
\(380\) | 0.392305 | 0.0201248 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.7846 | 1.67741 | ||||||||
\(383\) | −24.3923 | −1.24639 | −0.623194 | − | 0.782067i | \(-0.714165\pi\) | ||||
−0.623194 | + | 0.782067i | \(0.714165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.46410 | 0.0746175 | ||||||||
\(386\) | −12.0000 | −0.610784 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.92820 | 0.453261 | ||||||||
\(389\) | −8.53590 | −0.432787 | −0.216394 | − | 0.976306i | \(-0.569429\pi\) | ||||
−0.216394 | + | 0.976306i | \(0.569429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4641 | −0.680909 | ||||||||
\(392\) | 5.19615 | 0.262445 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.8564 | −0.698076 | ||||||||
\(395\) | 2.67949 | 0.134820 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9282 | 1.25111 | 0.625555 | − | 0.780180i | \(-0.284872\pi\) | ||||
0.625555 | + | 0.780180i | \(0.284872\pi\) | |||||||
\(398\) | 18.2487 | 0.914725 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.3205 | 1.11603 | ||||||||
\(401\) | −26.1962 | −1.30817 | −0.654087 | − | 0.756420i | \(-0.726947\pi\) | ||||
−0.654087 | + | 0.756420i | \(0.726947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.19615 | 0.408279 | ||||||||
\(404\) | −8.19615 | −0.407774 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.5359 | −0.721405 | ||||||||
\(407\) | −2.00000 | −0.0991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7128 | −1.37031 | −0.685155 | − | 0.728397i | \(-0.740266\pi\) | ||||
−0.685155 | + | 0.728397i | \(0.740266\pi\) | |||||||
\(410\) | −6.92820 | −0.342160 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.3205 | 0.951853 | ||||||||
\(413\) | −26.9282 | −1.32505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1436 | 0.497929 | ||||||||
\(416\) | 5.19615 | 0.254762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.928203 | −0.0453999 | ||||||||
\(419\) | −26.0000 | −1.27018 | −0.635092 | − | 0.772437i | \(-0.719038\pi\) | ||||
−0.635092 | + | 0.772437i | \(0.719038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.92820 | 0.435134 | 0.217567 | − | 0.976045i | \(-0.430188\pi\) | ||||
0.217567 | + | 0.976045i | \(0.430188\pi\) | |||||||
\(422\) | 33.3731 | 1.62458 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.46410 | 0.168232 | ||||||||
\(425\) | 30.0526 | 1.45776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.85641 | −0.476985 | ||||||||
\(428\) | 8.39230 | 0.405657 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.85641 | 0.378870 | ||||||||
\(431\) | 12.7846 | 0.615813 | 0.307906 | − | 0.951417i | \(-0.400372\pi\) | ||||
0.307906 | + | 0.951417i | \(0.400372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 28.3923 | 1.36287 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | −1.07180 | −0.0512710 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.9090 | −1.42748 | −0.713739 | − | 0.700412i | \(-0.753000\pi\) | ||||
−0.713739 | + | 0.700412i | \(0.753000\pi\) | |||||||
\(440\) | 1.26795 | 0.0604471 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.6603 | 0.554622 | ||||||||
\(443\) | 4.78461 | 0.227324 | 0.113662 | − | 0.993519i | \(-0.463742\pi\) | ||||
0.113662 | + | 0.993519i | \(0.463742\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4641 | −0.543451 | ||||||||
\(446\) | −40.7321 | −1.92872 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | 2.19615 | 0.103643 | 0.0518214 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518214 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.46410 | 0.257294 | ||||||||
\(452\) | −10.0000 | −0.470360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | −1.46410 | −0.0686381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.7846 | −1.44004 | −0.720022 | − | 0.693952i | \(-0.755868\pi\) | ||||
−0.720022 | + | 0.693952i | \(0.755868\pi\) | |||||||
\(458\) | −26.7846 | −1.25156 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.46410 | −0.0682641 | ||||||||
\(461\) | 17.4641 | 0.813384 | 0.406692 | − | 0.913565i | \(-0.366682\pi\) | ||||
0.406692 | + | 0.913565i | \(0.366682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5167 | 0.907016 | 0.453508 | − | 0.891252i | \(-0.350172\pi\) | ||||
0.453508 | + | 0.891252i | \(0.350172\pi\) | |||||||
\(464\) | −20.9808 | −0.974007 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.26795 | −0.336681 | ||||||||
\(467\) | 32.9282 | 1.52374 | 0.761868 | − | 0.647733i | \(-0.224283\pi\) | ||||
0.761868 | + | 0.647733i | \(0.224283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.3923 | 1.12633 | ||||||||
\(470\) | −1.85641 | −0.0856296 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.3205 | −1.07341 | ||||||||
\(473\) | −6.19615 | −0.284899 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.39230 | 0.109766 | ||||||||
\(476\) | 13.4641 | 0.617126 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38.7846 | −1.77397 | ||||||||
\(479\) | −20.5359 | −0.938309 | −0.469155 | − | 0.883116i | \(-0.655441\pi\) | ||||
−0.469155 | + | 0.883116i | \(0.655441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | 0.0911922 | ||||||||
\(482\) | −32.5359 | −1.48197 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.53590 | −0.296780 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6603 | −1.16278 | −0.581389 | − | 0.813626i | \(-0.697490\pi\) | ||||
−0.581389 | + | 0.813626i | \(0.697490\pi\) | |||||||
\(488\) | −8.53590 | −0.386402 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.80385 | 0.171840 | ||||||||
\(491\) | −9.46410 | −0.427109 | −0.213554 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213554 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.2487 | −1.27226 | ||||||||
\(494\) | 0.928203 | 0.0417618 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.9808 | 1.84009 | ||||||||
\(497\) | 13.8564 | 0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.1962 | −1.26223 | −0.631117 | − | 0.775688i | \(-0.717403\pi\) | ||||
−0.631117 | + | 0.775688i | \(0.717403\pi\) | |||||||
\(500\) | 6.92820 | 0.309839 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.5692 | 1.31974 | ||||||||
\(503\) | 14.5359 | 0.648124 | 0.324062 | − | 0.946036i | \(-0.394951\pi\) | ||||
0.324062 | + | 0.946036i | \(0.394951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 3.46410 | 0.153998 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.1244 | 0.582299 | ||||||||
\(509\) | 24.3397 | 1.07884 | 0.539420 | − | 0.842037i | \(-0.318643\pi\) | ||||
0.539420 | + | 0.842037i | \(0.318643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.85641 | −0.259072 | ||||||||
\(512\) | 8.66025 | 0.382733 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −30.0000 | −1.32324 | ||||||||
\(515\) | −14.1436 | −0.623241 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.46410 | 0.0643911 | ||||||||
\(518\) | 6.92820 | 0.304408 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.26795 | −0.0556033 | ||||||||
\(521\) | 27.0718 | 1.18604 | 0.593018 | − | 0.805189i | \(-0.297936\pi\) | ||||
0.593018 | + | 0.805189i | \(0.297936\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7321 | −1.08146 | −0.540729 | − | 0.841197i | \(-0.681851\pi\) | ||||
−0.540729 | + | 0.841197i | \(0.681851\pi\) | |||||||
\(524\) | 5.07180 | 0.221562 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.3923 | −0.714738 | ||||||||
\(527\) | 55.1769 | 2.40354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 2.53590 | 0.110152 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.07180 | 0.0464683 | ||||||||
\(533\) | −5.46410 | −0.236677 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.14359 | −0.265611 | ||||||||
\(536\) | 21.1244 | 0.912433 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.0000 | 1.29339 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7846 | 1.15156 | 0.575780 | − | 0.817605i | \(-0.304698\pi\) | ||||
0.575780 | + | 0.817605i | \(0.304698\pi\) | |||||||
\(542\) | 16.1436 | 0.693427 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 34.9808 | 1.49979 | ||||||||
\(545\) | 5.85641 | 0.250861 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.9808 | −1.66670 | −0.833349 | − | 0.552748i | \(-0.813579\pi\) | ||||
−0.833349 | + | 0.552748i | \(0.813579\pi\) | |||||||
\(548\) | 14.5885 | 0.623188 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.73205 | −0.329696 | ||||||||
\(551\) | −2.24871 | −0.0957983 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.32051 | 0.311300 | ||||||||
\(554\) | −17.3205 | −0.735878 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.80385 | −0.415776 | ||||||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.19615 | 0.262069 | ||||||||
\(560\) | −7.32051 | −0.309348 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.3923 | −1.70385 | ||||||||
\(563\) | −15.7128 | −0.662216 | −0.331108 | − | 0.943593i | \(-0.607422\pi\) | ||||
−0.331108 | + | 0.943593i | \(0.607422\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.32051 | 0.307976 | ||||||||
\(566\) | 16.9808 | 0.713755 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | 1.66025 | 0.0696015 | 0.0348007 | − | 0.999394i | \(-0.488920\pi\) | ||||
0.0348007 | + | 0.999394i | \(0.488920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5885 | −0.610508 | −0.305254 | − | 0.952271i | \(-0.598741\pi\) | ||||
−0.305254 | + | 0.952271i | \(0.598741\pi\) | |||||||
\(572\) | −1.00000 | −0.0418121 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.9282 | −0.790048 | ||||||||
\(575\) | −8.92820 | −0.372332 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.92820 | 0.205164 | 0.102582 | − | 0.994725i | \(-0.467290\pi\) | ||||
0.102582 | + | 0.994725i | \(0.467290\pi\) | |||||||
\(578\) | 49.0526 | 2.04032 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.07180 | −0.127549 | ||||||||
\(581\) | 27.7128 | 1.14972 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | −0.0828315 | ||||||||
\(584\) | −5.07180 | −0.209872 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.6410 | −0.935292 | ||||||||
\(587\) | −9.46410 | −0.390625 | −0.195313 | − | 0.980741i | \(-0.562572\pi\) | ||||
−0.195313 | + | 0.980741i | \(0.562572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.39230 | 0.180982 | ||||||||
\(590\) | −17.0718 | −0.702835 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | −36.0000 | −1.47834 | −0.739171 | − | 0.673517i | \(-0.764783\pi\) | ||||
−0.739171 | + | 0.673517i | \(0.764783\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.85641 | −0.404073 | ||||||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.46410 | −0.141658 | ||||||||
\(599\) | −27.7128 | −1.13231 | −0.566157 | − | 0.824297i | \(-0.691571\pi\) | ||||
−0.566157 | + | 0.824297i | \(0.691571\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.8564 | 1.13629 | 0.568143 | − | 0.822930i | \(-0.307662\pi\) | ||||
0.568143 | + | 0.822930i | \(0.307662\pi\) | |||||||
\(602\) | 21.4641 | 0.874811 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.53590 | −0.184563 | ||||||||
\(605\) | −0.732051 | −0.0297621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.1962 | 1.38798 | 0.693990 | − | 0.719985i | \(-0.255851\pi\) | ||||
0.693990 | + | 0.719985i | \(0.255851\pi\) | |||||||
\(608\) | 2.78461 | 0.112931 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.24871 | −0.253003 | ||||||||
\(611\) | −1.46410 | −0.0592312 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.8564 | 0.721213 | 0.360607 | − | 0.932718i | \(-0.382570\pi\) | ||||
0.360607 | + | 0.932718i | \(0.382570\pi\) | |||||||
\(614\) | −35.5692 | −1.43546 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.46410 | 0.139573 | ||||||||
\(617\) | −23.6603 | −0.952526 | −0.476263 | − | 0.879303i | \(-0.658009\pi\) | ||||
−0.476263 | + | 0.879303i | \(0.658009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5885 | −1.14907 | −0.574534 | − | 0.818481i | \(-0.694817\pi\) | ||||
−0.574534 | + | 0.818481i | \(0.694817\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.32051 | 0.213333 | ||||||||
\(623\) | −31.3205 | −1.25483 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | −16.3923 | −0.655168 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.3205 | −0.611355 | ||||||||
\(629\) | 13.4641 | 0.536849 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.33975 | −0.252381 | −0.126191 | − | 0.992006i | \(-0.540275\pi\) | ||||
−0.126191 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(632\) | 6.33975 | 0.252182 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.6603 | −1.17796 | ||||||||
\(635\) | −9.60770 | −0.381270 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | 0.118864 | ||||||||
\(638\) | 7.26795 | 0.287741 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.87564 | −0.350841 | ||||||||
\(641\) | −19.8564 | −0.784281 | −0.392140 | − | 0.919905i | \(-0.628265\pi\) | ||||
−0.392140 | + | 0.919905i | \(0.628265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.0526 | 1.18516 | 0.592579 | − | 0.805513i | \(-0.298110\pi\) | ||||
0.592579 | + | 0.805513i | \(0.298110\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.24871 | 0.245852 | ||||||||
\(647\) | −5.07180 | −0.199393 | −0.0996965 | − | 0.995018i | \(-0.531787\pi\) | ||||
−0.0996965 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.4641 | 0.528512 | ||||||||
\(650\) | 7.73205 | 0.303276 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.2679 | −0.676265 | ||||||||
\(653\) | −37.3205 | −1.46046 | −0.730232 | − | 0.683199i | \(-0.760588\pi\) | ||||
−0.730232 | + | 0.683199i | \(0.760588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.71281 | −0.145072 | ||||||||
\(656\) | −27.3205 | −1.06669 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.07180 | −0.197719 | ||||||||
\(659\) | 25.0718 | 0.976659 | 0.488329 | − | 0.872659i | \(-0.337607\pi\) | ||||
0.488329 | + | 0.872659i | \(0.337607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.53590 | −0.176426 | −0.0882130 | − | 0.996102i | \(-0.528116\pi\) | ||||
−0.0882130 | + | 0.996102i | \(0.528116\pi\) | |||||||
\(662\) | 40.7321 | 1.58310 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.0000 | 0.931381 | ||||||||
\(665\) | −0.784610 | −0.0304259 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.39230 | 0.324951 | ||||||||
\(668\) | 9.85641 | 0.381356 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.4641 | 0.597430 | ||||||||
\(671\) | 4.92820 | 0.190251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.4641 | −0.904475 | −0.452237 | − | 0.891898i | \(-0.649374\pi\) | ||||
−0.452237 | + | 0.891898i | \(0.649374\pi\) | |||||||
\(674\) | 16.1436 | 0.621828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 40.3013 | 1.54890 | 0.774452 | − | 0.632633i | \(-0.218026\pi\) | ||||
0.774452 | + | 0.632633i | \(0.218026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8564 | −0.685266 | ||||||||
\(680\) | −8.53590 | −0.327337 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.1962 | −0.543599 | ||||||||
\(683\) | 24.7846 | 0.948357 | 0.474178 | − | 0.880429i | \(-0.342745\pi\) | ||||
0.474178 | + | 0.880429i | \(0.342745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6795 | −0.408042 | ||||||||
\(686\) | 34.6410 | 1.32260 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.9808 | 1.18113 | ||||||||
\(689\) | 2.00000 | 0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.4449 | 1.00601 | 0.503005 | − | 0.864283i | \(-0.332228\pi\) | ||||
0.503005 | + | 0.864283i | \(0.332228\pi\) | |||||||
\(692\) | −19.1244 | −0.726999 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.60770 | 0.288784 | ||||||||
\(695\) | 7.17691 | 0.272236 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.7846 | −1.39332 | ||||||||
\(698\) | −6.67949 | −0.252822 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.92820 | 0.337454 | ||||||||
\(701\) | 5.94744 | 0.224632 | 0.112316 | − | 0.993673i | \(-0.464173\pi\) | ||||
0.112316 | + | 0.993673i | \(0.464173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07180 | 0.0404236 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.8038 | −1.49804 | ||||||||
\(707\) | 16.3923 | 0.616496 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.53590 | −0.170349 | −0.0851746 | − | 0.996366i | \(-0.527145\pi\) | ||||
−0.0851746 | + | 0.996366i | \(0.527145\pi\) | |||||||
\(710\) | 8.78461 | 0.329681 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −27.1244 | −1.01653 | ||||||||
\(713\) | −16.3923 | −0.613897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.732051 | 0.0273771 | ||||||||
\(716\) | −7.85641 | −0.293608 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.6410 | 1.06887 | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.6410 | −1.43907 | ||||||||
\(722\) | −32.4115 | −1.20623 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.39230 | 0.311898 | ||||||||
\(725\) | −18.7321 | −0.695691 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.3205 | 1.45832 | 0.729158 | − | 0.684345i | \(-0.239912\pi\) | ||||
0.729158 | + | 0.684345i | \(0.239912\pi\) | |||||||
\(728\) | −3.46410 | −0.128388 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.71281 | −0.137417 | ||||||||
\(731\) | 41.7128 | 1.54280 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9282 | −0.846873 | −0.423436 | − | 0.905926i | \(-0.639176\pi\) | ||||
−0.423436 | + | 0.905926i | \(0.639176\pi\) | |||||||
\(734\) | 53.5692 | 1.97728 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.3923 | −0.383065 | ||||||||
\(737\) | −12.1962 | −0.449251 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.00000 | −0.0735712 | −0.0367856 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367856 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(740\) | 1.46410 | 0.0538214 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.92820 | 0.254342 | ||||||||
\(743\) | −37.8564 | −1.38882 | −0.694408 | − | 0.719581i | \(-0.744334\pi\) | ||||
−0.694408 | + | 0.719581i | \(0.744334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.85641 | 0.214562 | ||||||||
\(746\) | −28.1436 | −1.03041 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.73205 | −0.246148 | ||||||||
\(749\) | −16.7846 | −0.613296 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.21539 | −0.117331 | −0.0586656 | − | 0.998278i | \(-0.518685\pi\) | ||||
−0.0586656 | + | 0.998278i | \(0.518685\pi\) | |||||||
\(752\) | −7.32051 | −0.266951 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.26795 | −0.264683 | ||||||||
\(755\) | 3.32051 | 0.120846 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.46410 | −0.343979 | −0.171989 | − | 0.985099i | \(-0.555019\pi\) | ||||
−0.171989 | + | 0.985099i | \(0.555019\pi\) | |||||||
\(758\) | 21.1244 | 0.767271 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.679492 | −0.0246478 | ||||||||
\(761\) | −54.6410 | −1.98074 | −0.990368 | − | 0.138463i | \(-0.955784\pi\) | ||||
−0.990368 | + | 0.138463i | \(0.955784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0000 | 0.579239 | ||||||||
\(764\) | 18.9282 | 0.684798 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.2487 | −1.52651 | ||||||||
\(767\) | −13.4641 | −0.486161 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.1436 | 0.582153 | 0.291076 | − | 0.956700i | \(-0.405987\pi\) | ||||
0.291076 | + | 0.956700i | \(0.405987\pi\) | |||||||
\(770\) | 2.53590 | 0.0913874 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.92820 | −0.249351 | ||||||||
\(773\) | 49.5167 | 1.78099 | 0.890495 | − | 0.454993i | \(-0.150358\pi\) | ||||
0.890495 | + | 0.454993i | \(0.150358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.5885 | 1.31430 | ||||||||
\(776\) | −15.4641 | −0.555129 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.7846 | −0.530054 | ||||||||
\(779\) | −2.92820 | −0.104914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.92820 | −0.247911 | ||||||||
\(782\) | −23.3205 | −0.833940 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.0000 | 0.535714 | ||||||||
\(785\) | 11.2154 | 0.400294 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.9282 | −1.31635 | −0.658174 | − | 0.752866i | \(-0.728671\pi\) | ||||
−0.658174 | + | 0.752866i | \(0.728671\pi\) | |||||||
\(788\) | −8.00000 | −0.284988 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.64102 | 0.165120 | ||||||||
\(791\) | 20.0000 | 0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92820 | −0.175006 | ||||||||
\(794\) | 43.1769 | 1.53229 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.5359 | 0.373435 | ||||||||
\(797\) | 50.3923 | 1.78499 | 0.892494 | − | 0.451060i | \(-0.148954\pi\) | ||||
0.892494 | + | 0.451060i | \(0.148954\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.85641 | −0.348695 | ||||||||
\(800\) | 23.1962 | 0.820108 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −45.3731 | −1.60218 | ||||||||
\(803\) | 2.92820 | 0.103334 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.92820 | 0.103206 | ||||||||
\(806\) | 14.1962 | 0.500038 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.1962 | 0.499419 | ||||||||
\(809\) | −42.8372 | −1.50607 | −0.753037 | − | 0.657978i | \(-0.771412\pi\) | ||||
−0.753037 | + | 0.657978i | \(0.771412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.3923 | 0.786300 | 0.393150 | − | 0.919474i | \(-0.371385\pi\) | ||||
0.393150 | + | 0.919474i | \(0.371385\pi\) | |||||||
\(812\) | −8.39230 | −0.294512 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.46410 | −0.121417 | ||||||||
\(815\) | 12.6410 | 0.442795 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.32051 | 0.116170 | ||||||||
\(818\) | −48.0000 | −1.67828 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | 12.6795 | 0.442517 | 0.221259 | − | 0.975215i | \(-0.428983\pi\) | ||||
0.221259 | + | 0.975215i | \(0.428983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.6077 | 0.404619 | 0.202309 | − | 0.979322i | \(-0.435155\pi\) | ||||
0.202309 | + | 0.979322i | \(0.435155\pi\) | |||||||
\(824\) | −33.4641 | −1.16578 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −46.6410 | −1.62285 | ||||||||
\(827\) | −20.2487 | −0.704117 | −0.352058 | − | 0.935978i | \(-0.614518\pi\) | ||||
−0.352058 | + | 0.935978i | \(0.614518\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.8564 | −1.66212 | −0.831061 | − | 0.556182i | \(-0.812266\pi\) | ||||
−0.831061 | + | 0.556182i | \(0.812266\pi\) | |||||||
\(830\) | 17.5692 | 0.609837 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 20.1962 | 0.699755 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.21539 | −0.249699 | ||||||||
\(836\) | −0.535898 | −0.0185344 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45.0333 | −1.55565 | ||||||||
\(839\) | −23.7128 | −0.818657 | −0.409329 | − | 0.912387i | \(-0.634237\pi\) | ||||
−0.409329 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3923 | −0.392838 | ||||||||
\(842\) | 15.4641 | 0.532928 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.2679 | 0.663230 | ||||||||
\(845\) | −0.732051 | −0.0251833 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 10.0000 | 0.343401 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 52.0526 | 1.78539 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1436 | −0.415789 | −0.207894 | − | 0.978151i | \(-0.566661\pi\) | ||||
−0.207894 | + | 0.978151i | \(0.566661\pi\) | |||||||
\(854\) | −17.0718 | −0.584185 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.5359 | −0.496827 | ||||||||
\(857\) | −31.8038 | −1.08640 | −0.543199 | − | 0.839604i | \(-0.682787\pi\) | ||||
−0.543199 | + | 0.839604i | \(0.682787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9615 | 1.70467 | 0.852333 | − | 0.523000i | \(-0.175187\pi\) | ||||
0.852333 | + | 0.523000i | \(0.175187\pi\) | |||||||
\(860\) | 4.53590 | 0.154673 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.1436 | 0.754214 | ||||||||
\(863\) | −11.3205 | −0.385355 | −0.192677 | − | 0.981262i | \(-0.561717\pi\) | ||||
−0.192677 | + | 0.981262i | \(0.561717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | −10.3923 | −0.353145 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.3923 | 0.556391 | ||||||||
\(869\) | −3.66025 | −0.124166 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.1962 | 0.413251 | ||||||||
\(872\) | 13.8564 | 0.469237 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.85641 | −0.0627939 | ||||||||
\(875\) | −13.8564 | −0.468432 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8564 | 0.535433 | 0.267716 | − | 0.963498i | \(-0.413731\pi\) | ||||
0.267716 | + | 0.963498i | \(0.413731\pi\) | |||||||
\(878\) | −51.8038 | −1.74830 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.66025 | 0.123387 | ||||||||
\(881\) | 28.6410 | 0.964940 | 0.482470 | − | 0.875912i | \(-0.339740\pi\) | ||||
0.482470 | + | 0.875912i | \(0.339740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.24871 | −0.0756752 | −0.0378376 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378376 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(884\) | 6.73205 | 0.226423 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.28719 | 0.278413 | ||||||||
\(887\) | 58.6410 | 1.96897 | 0.984486 | − | 0.175461i | \(-0.0561417\pi\) | ||||
0.984486 | + | 0.175461i | \(0.0561417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.2487 | −0.880354 | ||||||||
\(890\) | −19.8564 | −0.665588 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.5167 | −0.787396 | ||||||||
\(893\) | −0.784610 | −0.0262560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.75129 | 0.192244 | ||||||||
\(896\) | −24.2487 | −0.810093 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.80385 | 0.126936 | ||||||||
\(899\) | −34.3923 | −1.14705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4641 | 0.448554 | ||||||||
\(902\) | 9.46410 | 0.315120 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.3205 | 0.576072 | ||||||||
\(905\) | −6.14359 | −0.204220 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.92820 | −0.0972294 | −0.0486147 | − | 0.998818i | \(-0.515481\pi\) | ||||
−0.0486147 | + | 0.998818i | \(0.515481\pi\) | |||||||
\(908\) | 10.3923 | 0.344881 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.53590 | −0.0840642 | ||||||||
\(911\) | −29.8564 | −0.989187 | −0.494593 | − | 0.869124i | \(-0.664683\pi\) | ||||
−0.494593 | + | 0.869124i | \(0.664683\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8564 | −0.458580 | ||||||||
\(914\) | −53.3205 | −1.76369 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.4641 | −0.510948 | ||||||||
\(917\) | −10.1436 | −0.334971 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1244 | 0.828776 | 0.414388 | − | 0.910100i | \(-0.363996\pi\) | ||||
0.414388 | + | 0.910100i | \(0.363996\pi\) | |||||||
\(920\) | 2.53590 | 0.0836061 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.2487 | 0.996188 | ||||||||
\(923\) | 6.92820 | 0.228045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.92820 | 0.293558 | ||||||||
\(926\) | 33.8038 | 1.11086 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.8038 | −0.715746 | ||||||||
\(929\) | 26.8756 | 0.881761 | 0.440881 | − | 0.897566i | \(-0.354666\pi\) | ||||
0.440881 | + | 0.897566i | \(0.354666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60770 | 0.0526901 | ||||||||
\(932\) | −4.19615 | −0.137450 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 57.0333 | 1.86619 | ||||||||
\(935\) | 4.92820 | 0.161169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.0333 | −1.86320 | −0.931599 | − | 0.363488i | \(-0.881586\pi\) | ||||
−0.931599 | + | 0.363488i | \(0.881586\pi\) | |||||||
\(938\) | 42.2487 | 1.37947 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.07180 | −0.0349582 | ||||||||
\(941\) | −4.39230 | −0.143185 | −0.0715925 | − | 0.997434i | \(-0.522808\pi\) | ||||
−0.0715925 | + | 0.997434i | \(0.522808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9282 | 0.355871 | ||||||||
\(944\) | −67.3205 | −2.19110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.7321 | −0.348929 | ||||||||
\(947\) | −35.3205 | −1.14776 | −0.573881 | − | 0.818939i | \(-0.694563\pi\) | ||||
−0.573881 | + | 0.818939i | \(0.694563\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.92820 | −0.0950535 | ||||||||
\(950\) | 4.14359 | 0.134436 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.3205 | −0.755822 | ||||||||
\(953\) | −10.7321 | −0.347645 | −0.173823 | − | 0.984777i | \(-0.555612\pi\) | ||||
−0.173823 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.8564 | −0.448383 | ||||||||
\(956\) | −22.3923 | −0.724219 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.5692 | −1.14919 | ||||||||
\(959\) | −29.1769 | −0.942172 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.1769 | 1.16700 | ||||||||
\(962\) | 3.46410 | 0.111687 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.7846 | −0.605012 | ||||||||
\(965\) | 5.07180 | 0.163267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9282 | 1.31616 | 0.658081 | − | 0.752947i | \(-0.271368\pi\) | ||||
0.658081 | + | 0.752947i | \(0.271368\pi\) | |||||||
\(968\) | −1.73205 | −0.0556702 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.3205 | −0.363480 | ||||||||
\(971\) | 23.8564 | 0.765589 | 0.382794 | − | 0.923834i | \(-0.374962\pi\) | ||||
0.382794 | + | 0.923834i | \(0.374962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6077 | 0.628594 | ||||||||
\(974\) | −44.4449 | −1.42411 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.6410 | −0.788740 | ||||||||
\(977\) | 0.339746 | 0.0108694 | 0.00543472 | − | 0.999985i | \(-0.498270\pi\) | ||||
0.00543472 | + | 0.999985i | \(0.498270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6603 | 0.500504 | ||||||||
\(980\) | 2.19615 | 0.0701535 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.3923 | −0.523099 | ||||||||
\(983\) | 46.9282 | 1.49678 | 0.748389 | − | 0.663260i | \(-0.230828\pi\) | ||||
0.748389 | + | 0.663260i | \(0.230828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.85641 | 0.186601 | ||||||||
\(986\) | −48.9282 | −1.55819 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.535898 | 0.0170492 | ||||||||
\(989\) | −12.3923 | −0.394052 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.1769 | 1.81628 | 0.908142 | − | 0.418662i | \(-0.137501\pi\) | ||||
0.908142 | + | 0.418662i | \(0.137501\pi\) | |||||||
\(992\) | 42.5885 | 1.35218 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.0000 | 0.761234 | ||||||||
\(995\) | −7.71281 | −0.244513 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.67949 | 0.211542 | 0.105771 | − | 0.994391i | \(-0.466269\pi\) | ||||
0.105771 | + | 0.994391i | \(0.466269\pi\) | |||||||
\(998\) | −48.8372 | −1.54591 | ||||||||
\(999\) | 0 | 0 |
(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 | 1287.2.a.f.1.2 | 2 | ||
3.2 | odd | 2 | 429.2.a.d.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 6864.2.a.bk.1.2 | 2 | |||
33.32 | even | 2 | 4719.2.a.n.1.2 | 2 | |||
39.38 | odd | 2 | 5577.2.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.a.d.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1287.2.a.f.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4719.2.a.n.1.2 | 2 | 33.32 | even | 2 | |||
5577.2.a.h.1.2 | 2 | 39.38 | odd | 2 | |||
6864.2.a.bk.1.2 | 2 | 12.11 | even | 2 |