Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5472,2,Mod(2737,5472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5472, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("5472.2737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5472.g (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: | \(43.6941399860\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + 48 x^{7} - 40 x^{6} + 32 x^{5} + 64 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2737.4 | ||
Root | \(0.340606 - 1.37258i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5472.2737 |
Dual form | 5472.2.g.b.2737.13 |
$q$-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 \(\left(\mathbb{Z}/5472\mathbb{Z}\right)^\times\).
\(n\) | \(1217\) | \(2053\) | \(3745\) | \(4447\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.13486i | − 0.954737i | −0.878703 | − | 0.477369i | \(-0.841591\pi\) | ||||
0.878703 | − | 0.477369i | \(-0.158409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.29464 | −1.24526 | −0.622629 | − | 0.782517i | \(-0.713936\pi\) | ||||
−0.622629 | + | 0.782517i | \(0.713936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.71210i | − 1.11924i | −0.828749 | − | 0.559620i | \(-0.810947\pi\) | ||||
0.828749 | − | 0.559620i | \(-0.189053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.32843i | 0.645792i | 0.946435 | + | 0.322896i | \(0.104656\pi\) | ||||
−0.946435 | + | 0.322896i | \(0.895344\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.48822 | 1.57362 | 0.786812 | − | 0.617192i | \(-0.211730\pi\) | ||||
0.786812 | + | 0.617192i | \(0.211730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.32651 | 1.52768 | 0.763842 | − | 0.645404i | \(-0.223311\pi\) | ||||
0.763842 | + | 0.645404i | \(0.223311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.442384 | 0.0884769 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.59857i | 0.482542i | 0.970458 | + | 0.241271i | \(0.0775643\pi\) | ||||
−0.970458 | + | 0.241271i | \(0.922436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.34204 | 0.241037 | 0.120518 | − | 0.992711i | \(-0.461544\pi\) | ||||
0.120518 | + | 0.992711i | \(0.461544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.03360i | 1.18889i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.72986i | − 0.613186i | −0.951841 | − | 0.306593i | \(-0.900811\pi\) | ||||
0.951841 | − | 0.306593i | \(-0.0991890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.52385 | −1.01885 | −0.509427 | − | 0.860514i | \(-0.670143\pi\) | ||||
−0.509427 | + | 0.860514i | \(0.670143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.97202i | 0.300729i | 0.988631 | + | 0.150365i | \(0.0480448\pi\) | ||||
−0.988631 | + | 0.150365i | \(0.951955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.45991 | 0.796410 | 0.398205 | − | 0.917297i | \(-0.369633\pi\) | ||||
0.398205 | + | 0.917297i | \(0.369633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.85468 | 0.550669 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.98640i | − 0.684935i | −0.939530 | − | 0.342467i | \(-0.888737\pi\) | ||||
0.939530 | − | 0.342467i | \(-0.111263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.92480 | −1.06858 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.67136i | 1.25910i | 0.776958 | + | 0.629552i | \(0.216762\pi\) | ||||
−0.776958 | + | 0.629552i | \(0.783238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15570i | 1.04423i | 0.852875 | + | 0.522115i | \(0.174857\pi\) | ||||
−0.852875 | + | 0.522115i | \(0.825143\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.97088 | 0.616561 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.524986i | 0.0641372i | 0.999486 | + | 0.0320686i | \(0.0102095\pi\) | ||||
−0.999486 | + | 0.0320686i | \(0.989790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.17489 | 0.851503 | 0.425751 | − | 0.904840i | \(-0.360010\pi\) | ||||
0.425751 | + | 0.904840i | \(0.360010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.33130 | −0.741022 | −0.370511 | − | 0.928828i | \(-0.620817\pi\) | ||||
−0.370511 | + | 0.928828i | \(0.620817\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.2300i | 1.39374i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.75644 | 0.985176 | 0.492588 | − | 0.870263i | \(-0.336051\pi\) | ||||
0.492588 | + | 0.870263i | \(0.336051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.74008i | − 0.849585i | −0.905291 | − | 0.424792i | \(-0.860347\pi\) | ||||
0.905291 | − | 0.424792i | \(-0.139653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.8514i | − 1.50240i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.04368 | 0.110630 | 0.0553148 | − | 0.998469i | \(-0.482384\pi\) | ||||
0.0553148 | + | 0.998469i | \(0.482384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 7.67136i | − 0.804178i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.13486 | 0.219032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.117594 | −0.0119398 | −0.00596992 | − | 0.999982i | \(-0.501900\pi\) | ||||
−0.00596992 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.6142i | 1.05615i | 0.849197 | + | 0.528077i | \(0.177087\pi\) | ||||
−0.849197 | + | 0.528077i | \(0.822913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4190 | −1.22368 | −0.611840 | − | 0.790982i | \(-0.709570\pi\) | ||||
−0.611840 | + | 0.790982i | \(0.709570\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.5439i | − 1.59936i | −0.600430 | − | 0.799678i | \(-0.705004\pi\) | ||||
0.600430 | − | 0.799678i | \(-0.294996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 17.4437i | − 1.67080i | −0.549641 | − | 0.835401i | \(-0.685235\pi\) | ||||
0.549641 | − | 0.835401i | \(-0.314765\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3193 | 1.34705 | 0.673523 | − | 0.739166i | \(-0.264780\pi\) | ||||
0.673523 | + | 0.739166i | \(0.264780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 15.6411i | − 1.45854i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.3764 | −1.95957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.77968 | −0.252698 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 11.6187i | − 1.03921i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.63985 | −0.234248 | −0.117124 | − | 0.993117i | \(-0.537368\pi\) | ||||
−0.117124 | + | 0.993117i | \(0.537368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.3670i | − 1.34263i | −0.741174 | − | 0.671313i | \(-0.765731\pi\) | ||||
0.741174 | − | 0.671313i | \(-0.234269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.29464i | − 0.285682i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.91853 | 0.420218 | 0.210109 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210109 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 9.80377i | − 0.831545i | −0.909469 | − | 0.415773i | \(-0.863511\pi\) | ||||
0.909469 | − | 0.415773i | \(-0.136489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.64338 | 0.722796 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.54758 | 0.460701 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.724147i | 0.0593244i | 0.999560 | + | 0.0296622i | \(0.00944316\pi\) | ||||
−0.999560 | + | 0.0296622i | \(0.990557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7252 | 1.27970 | 0.639850 | − | 0.768500i | \(-0.278997\pi\) | ||||
0.639850 | + | 0.768500i | \(0.278997\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.86505i | − 0.230127i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.141127i | 0.0112632i | 0.999984 | + | 0.00563160i | \(0.00179260\pi\) | ||||
−0.999984 | + | 0.00563160i | \(0.998207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.1383 | −1.90236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.41859i | − 0.659395i | −0.944087 | − | 0.329697i | \(-0.893053\pi\) | ||||
0.944087 | − | 0.329697i | \(-0.106947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.16538 | 0.399709 | 0.199854 | − | 0.979826i | \(-0.435953\pi\) | ||||
0.199854 | + | 0.979826i | \(0.435953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.57839 | 0.582953 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.13988i | 0.238721i | 0.992851 | + | 0.119360i | \(0.0380844\pi\) | ||||
−0.992851 | + | 0.119360i | \(0.961916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.45750 | −0.110177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 18.1898i | − 1.35957i | −0.733410 | − | 0.679786i | \(-0.762073\pi\) | ||||
0.733410 | − | 0.679786i | \(-0.237927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 14.0798i | − 1.04654i | −0.852166 | − | 0.523271i | \(-0.824712\pi\) | ||||
0.852166 | − | 0.523271i | \(-0.175288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.96273 | −0.585431 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 24.0849i | − 1.76126i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.87409 | 0.352677 | 0.176338 | − | 0.984330i | \(-0.443575\pi\) | ||||
0.176338 | + | 0.984330i | \(0.443575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.99845 | −0.719704 | −0.359852 | − | 0.933009i | \(-0.617173\pi\) | ||||
−0.359852 | + | 0.933009i | \(0.617173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 19.2209i | − 1.36943i | −0.728810 | − | 0.684716i | \(-0.759926\pi\) | ||||
0.728810 | − | 0.684716i | \(-0.240074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7323 | 0.831683 | 0.415842 | − | 0.909437i | \(-0.363487\pi\) | ||||
0.415842 | + | 0.909437i | \(0.363487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.56137i | − 0.600890i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.9275i | 0.972737i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.71210 | 0.256771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 0.399383i | − 0.0274947i | −0.999906 | − | 0.0137473i | \(-0.995624\pi\) | ||||
0.999906 | − | 0.0137473i | \(-0.00437605\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.20997 | 0.287118 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.42153 | −0.300153 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.1074i | 1.01623i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2548 | 1.28939 | 0.644697 | − | 0.764438i | \(-0.276983\pi\) | ||||
0.644697 | + | 0.764438i | \(0.276983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0414i | 1.33019i | 0.746758 | + | 0.665096i | \(0.231609\pi\) | ||||
−0.746758 | + | 0.665096i | \(0.768391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2013i | 1.20277i | 0.798958 | + | 0.601387i | \(0.205385\pi\) | ||||
−0.798958 | + | 0.601387i | \(0.794615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.2376 | −0.932739 | −0.466369 | − | 0.884590i | \(-0.654438\pi\) | ||||
−0.466369 | + | 0.884590i | \(0.654438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 11.6561i | − 0.760362i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.31368 | 0.537767 | 0.268884 | − | 0.963173i | \(-0.413345\pi\) | ||||
0.268884 | + | 0.963173i | \(0.413345\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1776 | −1.68625 | −0.843125 | − | 0.537718i | \(-0.819287\pi\) | ||||
−0.843125 | + | 0.537718i | \(0.819287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 8.22920i | − 0.525744i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.32843 | −0.148155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 29.4740i | − 1.86038i | −0.367075 | − | 0.930191i | \(-0.619641\pi\) | ||||
0.367075 | − | 0.930191i | \(-0.380359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 27.1967i | − 1.70984i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.28195 | −0.0799657 | −0.0399828 | − | 0.999200i | \(-0.512730\pi\) | ||||
−0.0399828 | + | 0.999200i | \(0.512730\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.2886i | 0.763575i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.2736 | −1.80509 | −0.902544 | − | 0.430597i | \(-0.858303\pi\) | ||||
−0.902544 | + | 0.430597i | \(0.858303\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6453 | −0.653933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1850i | 0.864875i | 0.901664 | + | 0.432437i | \(0.142346\pi\) | ||||
−0.901664 | + | 0.432437i | \(0.857654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.3185 | −1.59874 | −0.799369 | − | 0.600840i | \(-0.794833\pi\) | ||||
−0.799369 | + | 0.600840i | \(0.794833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.64217i | − 0.0990269i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.58863i | 0.215620i | 0.994172 | + | 0.107810i | \(0.0343838\pi\) | ||||
−0.994172 | + | 0.107810i | \(0.965616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.42597 | 0.264031 | 0.132016 | − | 0.991248i | \(-0.457855\pi\) | ||||
0.132016 | + | 0.991248i | \(0.457855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 0.493151i | − 0.0293148i | −0.999893 | − | 0.0146574i | \(-0.995334\pi\) | ||||
0.999893 | − | 0.0146574i | \(-0.00466576\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.4938 | 1.26874 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.0970 | 1.47630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 12.7228i | − 0.743275i | −0.928378 | − | 0.371637i | \(-0.878796\pi\) | ||||
0.928378 | − | 0.371637i | \(-0.121204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.6470 | 1.20211 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.0593i | 0.986565i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 6.49709i | − 0.374486i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.4113 | 0.996966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.2166i | 0.583092i | 0.956557 | + | 0.291546i | \(0.0941697\pi\) | ||||
−0.956557 | + | 0.291546i | \(0.905830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.184934 | 0.0104867 | 0.00524333 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524333 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0733 | −1.07809 | −0.539044 | − | 0.842278i | \(-0.681214\pi\) | ||||
−0.539044 | + | 0.842278i | \(0.681214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 0.911635i | − 0.0512025i | −0.999672 | − | 0.0256013i | \(-0.991850\pi\) | ||||
0.999672 | − | 0.0256013i | \(-0.00815002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.64615 | 0.540081 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.48822i | 0.361014i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.03006i | 0.0571376i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.9885 | −0.991736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2.45230i | − 0.134791i | −0.997726 | − | 0.0673953i | \(-0.978531\pi\) | ||||
0.997726 | − | 0.0673953i | \(-0.0214689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.12077 | 0.0612342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.1467 | 1.91456 | 0.957282 | − | 0.289156i | \(-0.0933746\pi\) | ||||
0.957282 | + | 0.289156i | \(0.0933746\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.98177i | − 0.269778i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.3627 | 0.559533 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.30643i | 0.284864i | 0.989805 | + | 0.142432i | \(0.0454922\pi\) | ||||
−0.989805 | + | 0.142432i | \(0.954508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 26.8913i | − 1.43946i | −0.694255 | − | 0.719729i | \(-0.744266\pi\) | ||||
0.694255 | − | 0.719729i | \(-0.255734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.21383 | 0.171055 | 0.0855275 | − | 0.996336i | \(-0.472742\pi\) | ||||
0.0855275 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 15.3174i | − 0.812961i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.6827 | −0.827699 | −0.413850 | − | 0.910345i | \(-0.635816\pi\) | ||||
−0.413850 | + | 0.910345i | \(0.635816\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5164i | 0.707481i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3509 | −0.749111 | −0.374555 | − | 0.927205i | \(-0.622205\pi\) | ||||
−0.374555 | + | 0.927205i | \(0.622205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4284i | 0.852921i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 9.08701i | − 0.470508i | −0.971934 | − | 0.235254i | \(-0.924408\pi\) | ||||
0.971934 | − | 0.235254i | \(-0.0755921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.05060 | −0.311622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2006i | 0.934900i | 0.884020 | + | 0.467450i | \(0.154827\pi\) | ||||
−0.884020 | + | 0.467450i | \(0.845173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.4154 | −1.14537 | −0.572686 | − | 0.819775i | \(-0.694099\pi\) | ||||
−0.572686 | + | 0.819775i | \(0.694099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.1094 | 1.33066 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 34.9213i | − 1.77058i | −0.465038 | − | 0.885291i | \(-0.653959\pi\) | ||||
0.465038 | − | 0.885291i | \(-0.346041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 47.5360 | 2.40400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 18.6937i | − 0.940584i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3443i | 1.57313i | 0.617510 | + | 0.786563i | \(0.288142\pi\) | ||||
−0.617510 | + | 0.786563i | \(0.711858\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.64321 | −0.0820579 | −0.0410290 | − | 0.999158i | \(-0.513064\pi\) | ||||
−0.0410290 | + | 0.999158i | \(0.513064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12484i | 0.155659i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8456 | −0.686302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.46645 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 31.8637i | − 1.56791i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.5240 | −0.811130 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.25063i | 0.207657i | 0.994595 | + | 0.103828i | \(0.0331093\pi\) | ||||
−0.994595 | + | 0.103828i | \(0.966891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4900i | 1.53473i | 0.641212 | + | 0.767364i | \(0.278432\pi\) | ||||
−0.641212 | + | 0.767364i | \(0.721568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.87029 | 0.139229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 26.8701i | − 1.30034i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0564 | −1.01425 | −0.507125 | − | 0.861872i | \(-0.669292\pi\) | ||||
−0.507125 | + | 0.861872i | \(0.669292\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.53125 | −0.361929 | −0.180964 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180964 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.32651i | 0.350475i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.823995 | −0.0393271 | −0.0196636 | − | 0.999807i | \(-0.506260\pi\) | ||||
−0.0196636 | + | 0.999807i | \(0.506260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.58526i | − 0.407898i | −0.978982 | − | 0.203949i | \(-0.934622\pi\) | ||||
0.978982 | − | 0.203949i | \(-0.0653777\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.22810i | − 0.105622i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.49451 | −0.117723 | −0.0588615 | − | 0.998266i | \(-0.518747\pi\) | ||||
−0.0588615 | + | 0.998266i | \(0.518747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.2172i | 1.14034i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.3773 | −0.767778 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5004 | 0.678301 | 0.339150 | − | 0.940732i | \(-0.389860\pi\) | ||||
0.339150 | + | 0.940732i | \(0.389860\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1930i | 1.08020i | 0.841600 | + | 0.540102i | \(0.181614\pi\) | ||||
−0.841600 | + | 0.540102i | \(0.818386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0637 | −1.21128 | −0.605642 | − | 0.795737i | \(-0.707084\pi\) | ||||
−0.605642 | + | 0.795737i | \(0.707084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1953i | 0.564332i | 0.959366 | + | 0.282166i | \(0.0910529\pi\) | ||||
−0.959366 | + | 0.282166i | \(0.908947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1.72964i | − 0.0798674i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.32031 | 0.336588 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.442384i | 0.0202980i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1883 | 0.831045 | 0.415523 | − | 0.909583i | \(-0.363599\pi\) | ||||
0.415523 | + | 0.909583i | \(0.363599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68475 | 0.395990 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.251046i | 0.0113994i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.13693 | 0.0968334 | 0.0484167 | − | 0.998827i | \(-0.484582\pi\) | ||||
0.0484167 | + | 0.998827i | \(0.484582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.32773i | − 0.105049i | −0.998620 | − | 0.0525244i | \(-0.983273\pi\) | ||||
0.998620 | − | 0.0525244i | \(-0.0167267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.8601i | 0.759341i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.6387 | −1.06034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16.9382i | − 0.758260i | −0.925343 | − | 0.379130i | \(-0.876223\pi\) | ||||
0.925343 | − | 0.379130i | \(-0.123777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.22413 | 0.366696 | 0.183348 | − | 0.983048i | \(-0.441307\pi\) | ||||
0.183348 | + | 0.983048i | \(0.441307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6598 | 1.00835 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 19.8145i | − 0.878261i | −0.898423 | − | 0.439131i | \(-0.855287\pi\) | ||||
0.898423 | − | 0.439131i | \(-0.144713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8594 | 0.922764 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.5128i | 1.16829i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 20.2677i | − 0.891374i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0978 | 1.58147 | 0.790737 | − | 0.612156i | \(-0.209698\pi\) | ||||
0.790737 | + | 0.612156i | \(0.209698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.19475i | − 0.183424i | −0.995786 | − | 0.0917119i | \(-0.970766\pi\) | ||||
0.995786 | − | 0.0917119i | \(-0.0292339\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.70743 | 0.379301 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.6778 | 1.33382 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 15.1903i | − 0.657967i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.3188 | −1.52696 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 14.3090i | − 0.616331i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 6.12211i | − 0.263210i | −0.991302 | − | 0.131605i | \(-0.957987\pi\) | ||||
0.991302 | − | 0.131605i | \(-0.0420131\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −37.2398 | −1.59518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.88879i | 0.209029i | 0.994523 | + | 0.104515i | \(0.0333289\pi\) | ||||
−0.994523 | + | 0.104515i | \(0.966671\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.59857 | −0.110703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.8493 | −1.22680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 28.5987i | − 1.21176i | −0.795554 | − | 0.605882i | \(-0.792820\pi\) | ||||
0.795554 | − | 0.605882i | \(-0.207180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.59171 | −0.194209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.83345i | 0.414431i | 0.978295 | + | 0.207215i | \(0.0664401\pi\) | ||||
−0.978295 | + | 0.207215i | \(0.933560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 30.5697i | − 1.28608i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3543 | 0.434075 | 0.217037 | − | 0.976163i | \(-0.430361\pi\) | ||||
0.217037 | + | 0.976163i | \(0.430361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.7988i | 1.53998i | 0.638055 | + | 0.769991i | \(0.279739\pi\) | ||||
−0.638055 | + | 0.769991i | \(0.720261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.24113 | 0.135165 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.22871 | −0.342566 | −0.171283 | − | 0.985222i | \(-0.554791\pi\) | ||||
−0.171283 | + | 0.985222i | \(0.554791\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.5008i | 1.05795i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5100 | −0.766606 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7.18047i | − 0.296370i | −0.988960 | − | 0.148185i | \(-0.952657\pi\) | ||||
0.988960 | − | 0.148185i | \(-0.0473431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.34204i | 0.0552976i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.7687 | 1.01713 | 0.508564 | − | 0.861024i | \(-0.330177\pi\) | ||||
0.508564 | + | 0.861024i | \(0.330177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.6355i | 1.87087i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.9307 | 1.71324 | 0.856621 | − | 0.515946i | \(-0.172560\pi\) | ||||
0.856621 | + | 0.515946i | \(0.172560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.10027 | 0.0856718 | 0.0428359 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428359 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.93422i | 0.241260i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.2877 | 0.458152 | 0.229076 | − | 0.973409i | \(-0.426430\pi\) | ||||
0.229076 | + | 0.973409i | \(0.426430\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7130i | 0.514315i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 31.4983i | − 1.27220i | −0.771605 | − | 0.636102i | \(-0.780546\pi\) | ||||
0.771605 | − | 0.636102i | \(-0.219454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4563 | 0.461214 | 0.230607 | − | 0.973047i | \(-0.425929\pi\) | ||||
0.230607 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 37.6816i | − 1.51455i | −0.653095 | − | 0.757276i | \(-0.726530\pi\) | ||||
0.653095 | − | 0.757276i | \(-0.273470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.43855 | −0.137763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.5924 | −0.903695 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 24.2002i | − 0.964925i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.99670 | −0.278534 | −0.139267 | − | 0.990255i | \(-0.544475\pi\) | ||||
−0.139267 | + | 0.990255i | \(0.544475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.63569i | 0.223646i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.97538i | 0.355617i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.20749 | 0.245181 | 0.122591 | − | 0.992457i | \(-0.460880\pi\) | ||||
0.122591 | + | 0.992457i | \(0.460880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 29.4008i | − 1.15945i | −0.814811 | − | 0.579726i | \(-0.803159\pi\) | ||||
0.814811 | − | 0.579726i | \(-0.196841\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.62285 | 0.221057 | 0.110529 | − | 0.993873i | \(-0.464746\pi\) | ||||
0.110529 | + | 0.993873i | \(0.464746\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.9011 | 1.40924 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.9447i | 1.36749i | 0.729721 | + | 0.683745i | \(0.239650\pi\) | ||||
−0.729721 | + | 0.683745i | \(0.760350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.8064 | −1.28185 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.8768i | 1.47547i | 0.675090 | + | 0.737736i | \(0.264105\pi\) | ||||
−0.675090 | + | 0.737736i | \(0.735895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.77264i | − 0.263425i | −0.991288 | − | 0.131713i | \(-0.957952\pi\) | ||||
0.991288 | − | 0.131713i | \(-0.0420476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.03360 | −0.272751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.0385i | 0.737172i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.2748 | 1.16874 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6355 | 0.949630 | 0.474815 | − | 0.880086i | \(-0.342515\pi\) | ||||
0.474815 | + | 0.880086i | \(0.342515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.2956i | 1.08749i | 0.839251 | + | 0.543744i | \(0.182994\pi\) | ||||
−0.839251 | + | 0.543744i | \(0.817006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.387430 | 0.0148682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.4333i | 1.31755i | 0.752339 | + | 0.658777i | \(0.228926\pi\) | ||||
−0.752339 | + | 0.658777i | \(0.771074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.5004i | − 0.401198i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.6105 | 0.442325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.19928i | − 0.0836646i | −0.999125 | − | 0.0418323i | \(-0.986680\pi\) | ||||
0.999125 | − | 0.0418323i | \(-0.0133195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9297 | −0.793907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −42.3282 | −1.60329 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 36.0608i | − 1.36200i | −0.732285 | − | 0.680999i | \(-0.761546\pi\) | ||||
0.732285 | − | 0.680999i | \(-0.238454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.72986 | 0.140675 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 34.9701i | − 1.31518i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10.7299i | − 0.402970i | −0.979492 | − | 0.201485i | \(-0.935423\pi\) | ||||
0.979492 | − | 0.201485i | \(-0.0645768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.83244 | 0.368228 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 18.4524i | − 0.690080i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.1037 | 1.08539 | 0.542693 | − | 0.839931i | \(-0.317405\pi\) | ||||
0.542693 | + | 0.839931i | \(0.317405\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.9162 | 1.52380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.14957i | 0.0426938i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.5850 | 1.50521 | 0.752607 | − | 0.658470i | \(-0.228796\pi\) | ||||
0.752607 | + | 0.658470i | \(0.228796\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7949i | 0.473235i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.6206i | 0.687766i | 0.939012 | + | 0.343883i | \(0.111742\pi\) | ||||
−0.939012 | + | 0.343883i | \(0.888258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.94880 | 0.0717849 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 7.89939i | − 0.290584i | −0.989389 | − | 0.145292i | \(-0.953588\pi\) | ||||
0.989389 | − | 0.145292i | \(-0.0464121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.4064 | −0.528521 | −0.264261 | − | 0.964451i | \(-0.585128\pi\) | ||||
−0.264261 | + | 0.964451i | \(0.585128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.54595 | 0.0566392 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.5061i | 1.99161i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0914 | −0.514204 | −0.257102 | − | 0.966384i | \(-0.582768\pi\) | ||||
−0.257102 | + | 0.966384i | \(0.582768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 33.5711i | − 1.22178i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.2311i | 1.82568i | 0.408318 | + | 0.912840i | \(0.366116\pi\) | ||||
−0.408318 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.7483 | −0.860875 | −0.430437 | − | 0.902620i | \(-0.641641\pi\) | ||||
−0.430437 | + | 0.902620i | \(0.641641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.4707i | 2.08058i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.5191 | −0.813119 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.4035 | −1.70942 | −0.854708 | − | 0.519109i | \(-0.826264\pi\) | ||||
−0.854708 | + | 0.519109i | \(0.826264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 11.8508i | − 0.426242i | −0.977026 | − | 0.213121i | \(-0.931637\pi\) | ||||
0.977026 | − | 0.213121i | \(-0.0683628\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.593696 | 0.0213262 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.52385i | − 0.233741i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 26.6339i | − 0.953036i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.301287 | 0.0107534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 26.3903i | − 0.940713i | −0.882477 | − | 0.470356i | \(-0.844125\pi\) | ||||
0.882477 | − | 0.470356i | \(-0.155875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.1770 | −1.67742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.9900 | −0.674356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.1893i | − 0.502610i | −0.967908 | − | 0.251305i | \(-0.919140\pi\) | ||||
0.967908 | − | 0.251305i | \(-0.0808597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.4251 | 1.25325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.5024i | 0.829382i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.5317i | 1.81625i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9998 | 1.05474 | 0.527368 | − | 0.849637i | \(-0.323179\pi\) | ||||
0.527368 | + | 0.849637i | \(0.323179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.8833i | 1.40049i | 0.713901 | + | 0.700246i | \(0.246927\pi\) | ||||
−0.713901 | + | 0.700246i | \(0.753073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.9725 | −0.629549 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.97202 | −0.0689921 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 56.4395i | − 1.96975i | −0.173256 | − | 0.984877i | \(-0.555429\pi\) | ||||
0.173256 | − | 0.984877i | \(-0.444571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.7360 | 1.45482 | 0.727412 | − | 0.686201i | \(-0.240723\pi\) | ||||
0.727412 | + | 0.686201i | \(0.240723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4248i | 0.605921i | 0.953003 | + | 0.302960i | \(0.0979750\pi\) | ||||
−0.953003 | + | 0.302960i | \(0.902025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 52.2723i | − 1.81549i | −0.419519 | − | 0.907747i | \(-0.637801\pi\) | ||||
0.419519 | − | 0.907747i | \(-0.362199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.0100 | 0.866547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 11.0273i | − 0.381617i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.8429 | 1.41005 | 0.705027 | − | 0.709180i | \(-0.250935\pi\) | ||||
0.705027 | + | 0.709180i | \(0.250935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2474 | 0.767153 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 16.1788i | − 0.556567i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.15805 | 0.314674 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 27.3269i | − 0.936754i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 42.8153i | − 1.46597i | −0.680245 | − | 0.732984i | \(-0.738127\pi\) | ||||
0.680245 | − | 0.732984i | \(-0.261873\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2947 | −0.795732 | −0.397866 | − | 0.917444i | \(-0.630249\pi\) | ||||
−0.397866 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 17.5879i | − 0.600091i | −0.953925 | − | 0.300045i | \(-0.902998\pi\) | ||||
0.953925 | − | 0.300045i | \(-0.0970018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.8886 | −0.404692 | −0.202346 | − | 0.979314i | \(-0.564857\pi\) | ||||
−0.202346 | + | 0.979314i | \(0.564857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.70319 | 0.227915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 32.5048i | − 1.10265i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22239 | −0.0414193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 38.2795i | 1.29408i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6698i | 0.968111i | 0.875037 | + | 0.484056i | \(0.160837\pi\) | ||||
−0.875037 | + | 0.484056i | \(0.839163\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2297 | 1.49014 | 0.745069 | − | 0.666988i | \(-0.232417\pi\) | ||||
0.745069 | + | 0.666988i | \(0.232417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.5869i | 0.894719i | 0.894354 | + | 0.447359i | \(0.147636\pi\) | ||||
−0.894354 | + | 0.447359i | \(0.852364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.4124 | 0.551074 | 0.275537 | − | 0.961290i | \(-0.411144\pi\) | ||||
0.275537 | + | 0.961290i | \(0.411144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.69735 | 0.291700 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.45991i | 0.182709i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.8327 | −1.29803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.48737i | 0.116310i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 32.3529i | − 1.07783i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.0583 | −0.999172 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3380i | 1.57183i | 0.618333 | + | 0.785916i | \(0.287808\pi\) | ||||
−0.618333 | + | 0.785916i | \(0.712192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.30896 | 0.175894 | 0.0879469 | − | 0.996125i | \(-0.471969\pi\) | ||||
0.0879469 | + | 0.996125i | \(0.471969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.7320 | −0.950889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.6290i | 1.67192i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.2513 | −1.62465 | −0.812326 | − | 0.583204i | \(-0.801799\pi\) | ||||
−0.812326 | + | 0.583204i | \(0.801799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.7063i | 0.549893i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1.65003i | − 0.0542528i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.2990 | 0.961270 | 0.480635 | − | 0.876921i | \(-0.340406\pi\) | ||||
0.480635 | + | 0.876921i | \(0.340406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.85468i | 0.126332i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.4179 | −1.68154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.35345 | −0.207558 | −0.103779 | − | 0.994600i | \(-0.533093\pi\) | ||||
−0.103779 | + | 0.994600i | \(0.533093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.07523i | − 0.0676505i | −0.999428 | − | 0.0338253i | \(-0.989231\pi\) | ||||
0.999428 | − | 0.0338253i | \(-0.0107690\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7970 | −1.55649 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.3618i | 0.434201i | 0.976149 | + | 0.217101i | \(0.0696600\pi\) | ||||
−0.976149 | + | 0.217101i | \(0.930340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 14.7420i | − 0.478546i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.6796 | 1.70646 | 0.853231 | − | 0.521534i | \(-0.174640\pi\) | ||||
0.853231 | + | 0.521534i | \(0.174640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 10.4055i | − 0.336714i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.2048 | −0.523281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1989 | −0.941901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.3453i | 0.687128i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.17519 | 0.230739 | 0.115369 | − | 0.993323i | \(-0.463195\pi\) | ||||
0.115369 | + | 0.993323i | \(0.463195\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.6991i | 0.471718i | 0.971787 | + | 0.235859i | \(0.0757903\pi\) | ||||
−0.971787 | + | 0.235859i | \(0.924210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.3000i | 1.03549i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.5470 | −0.625365 | −0.312682 | − | 0.949858i | \(-0.601228\pi\) | ||||
−0.312682 | + | 0.949858i | \(0.601228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.87424i | − 0.123821i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.0339 | 0.766562 | 0.383281 | − | 0.923632i | \(-0.374794\pi\) | ||||
0.383281 | + | 0.923632i | \(0.374794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.0339 | −1.30745 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.4480i | 0.459419i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5419 | −1.60552 | −0.802758 | − | 0.596305i | \(-0.796635\pi\) | ||||
−0.802758 | + | 0.596305i | \(0.796635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 25.0469i | − 0.794039i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 21.9225i | − 0.694293i | −0.937811 | − | 0.347147i | \(-0.887151\pi\) | ||||
0.937811 | − | 0.347147i | \(-0.112849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5472.2.g.b.2737.4 | 16 | ||
3.2 | odd | 2 | 608.2.c.b.305.2 | 16 | |||
4.3 | odd | 2 | 1368.2.g.b.685.13 | 16 | |||
8.3 | odd | 2 | 1368.2.g.b.685.14 | 16 | |||
8.5 | even | 2 | inner | 5472.2.g.b.2737.13 | 16 | ||
12.11 | even | 2 | 152.2.c.b.77.4 | yes | 16 | ||
24.5 | odd | 2 | 608.2.c.b.305.15 | 16 | |||
24.11 | even | 2 | 152.2.c.b.77.3 | ✓ | 16 | ||
48.5 | odd | 4 | 4864.2.a.bn.1.1 | 8 | |||
48.11 | even | 4 | 4864.2.a.bo.1.8 | 8 | |||
48.29 | odd | 4 | 4864.2.a.bp.1.8 | 8 | |||
48.35 | even | 4 | 4864.2.a.bq.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.3 | ✓ | 16 | 24.11 | even | 2 | ||
152.2.c.b.77.4 | yes | 16 | 12.11 | even | 2 | ||
608.2.c.b.305.2 | 16 | 3.2 | odd | 2 | |||
608.2.c.b.305.15 | 16 | 24.5 | odd | 2 | |||
1368.2.g.b.685.13 | 16 | 4.3 | odd | 2 | |||
1368.2.g.b.685.14 | 16 | 8.3 | odd | 2 | |||
4864.2.a.bn.1.1 | 8 | 48.5 | odd | 4 | |||
4864.2.a.bo.1.8 | 8 | 48.11 | even | 4 | |||
4864.2.a.bp.1.8 | 8 | 48.29 | odd | 4 | |||
4864.2.a.bq.1.1 | 8 | 48.35 | even | 4 | |||
5472.2.g.b.2737.4 | 16 | 1.1 | even | 1 | trivial | ||
5472.2.g.b.2737.13 | 16 | 8.5 | even | 2 | inner |