Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.681212\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.95163 | 1.70412 | 0.852061 | − | 0.523442i | \(-0.175352\pi\) | ||||
0.852061 | + | 0.523442i | \(0.175352\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.13486 | 0.954737 | 0.477369 | − | 0.878703i | \(-0.341591\pi\) | ||||
0.477369 | + | 0.878703i | \(0.341591\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.29464 | 1.24526 | 0.622629 | − | 0.782517i | \(-0.286064\pi\) | ||||
0.622629 | + | 0.782517i | \(0.286064\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.71210 | 1.90403 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.71210 | 1.11924 | 0.559620 | − | 0.828749i | \(-0.310947\pi\) | ||||
0.559620 | + | 0.828749i | \(0.310947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.32843 | −0.645792 | −0.322896 | − | 0.946435i | \(-0.604656\pi\) | ||||
−0.322896 | + | 0.946435i | \(0.604656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.30130 | 1.62699 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.48822 | −1.57362 | −0.786812 | − | 0.617192i | \(-0.788270\pi\) | ||||
−0.786812 | + | 0.617192i | \(0.788270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.72456 | 2.12207 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 8.00510 | 1.54058 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.59857 | 0.482542 | 0.241271 | − | 0.970458i | \(-0.422436\pi\) | ||||
0.241271 | + | 0.970458i | \(0.422436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.34204 | 0.241037 | 0.120518 | − | 0.992711i | \(-0.461544\pi\) | ||||
0.120518 | + | 0.992711i | \(0.461544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.9567 | 1.90732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.03360 | 1.18889 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.72986 | −0.613186 | −0.306593 | − | 0.951841i | \(-0.599189\pi\) | ||||
−0.306593 | + | 0.951841i | \(0.599189\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.87267 | −1.10051 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.52385 | −1.01885 | −0.509427 | − | 0.860514i | \(-0.670143\pi\) | ||||
−0.509427 | + | 0.860514i | \(0.670143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.97202 | 0.300729 | 0.150365 | − | 0.988631i | \(-0.451955\pi\) | ||||
0.150365 | + | 0.988631i | \(0.451955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.1945 | 1.81785 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.45991 | −0.796410 | −0.398205 | − | 0.917297i | \(-0.630367\pi\) | ||||
−0.398205 | + | 0.917297i | \(0.630367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.85468 | 0.550669 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.1508 | −2.68165 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.98640 | 0.684935 | 0.342467 | − | 0.939530i | \(-0.388737\pi\) | ||||
0.342467 | + | 0.939530i | \(0.388737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.92480 | 1.06858 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.95163 | −0.390952 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.67136 | −1.25910 | −0.629552 | − | 0.776958i | \(-0.716762\pi\) | ||||
−0.629552 | + | 0.776958i | \(0.716762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.15570 | −1.04423 | −0.522115 | − | 0.852875i | \(-0.674857\pi\) | ||||
−0.522115 | + | 0.852875i | \(0.674857\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.8193 | 2.37101 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.97088 | −0.616561 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.524986 | −0.0641372 | −0.0320686 | − | 0.999486i | \(-0.510210\pi\) | ||||
−0.0320686 | + | 0.999486i | \(0.510210\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.6251 | 2.60336 | ||||||||
\(70\) | 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 | \(-0.379183\pi\) | ||||
0.370511 | + | 0.928828i | \(0.379183\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.30575 | −0.150775 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.2300 | 1.39374 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.75644 | 0.985176 | 0.492588 | − | 0.870263i | \(-0.336051\pi\) | ||||
0.492588 | + | 0.870263i | \(0.336051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.49178 | 0.721309 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.74008 | −0.849585 | −0.424792 | − | 0.905291i | \(-0.639653\pi\) | ||||
−0.424792 | + | 0.905291i | \(0.639653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8514 | −1.50240 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.67001 | 0.822311 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.04368 | 0.110630 | 0.0553148 | − | 0.998469i | \(-0.482384\pi\) | ||||
0.0553148 | + | 0.998469i | \(0.482384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.67136 | −0.804178 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.96119 | 0.410756 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 21.2039 | 2.13107 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.6142 | −1.05615 | −0.528077 | − | 0.849197i | \(-0.677087\pi\) | ||||
−0.528077 | + | 0.849197i | \(0.677087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4190 | 1.22368 | 0.611840 | − | 0.790982i | \(-0.290430\pi\) | ||||
0.611840 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.7605 | 2.02602 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5439 | 1.59936 | 0.799678 | − | 0.600430i | \(-0.205004\pi\) | ||||
0.799678 | + | 0.600430i | \(0.205004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4437 | 1.67080 | 0.835401 | − | 0.549641i | \(-0.185235\pi\) | ||||
0.835401 | + | 0.549641i | \(0.185235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0092 | −1.04494 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3193 | −1.34705 | −0.673523 | − | 0.739166i | \(-0.735220\pi\) | ||||
−0.673523 | + | 0.739166i | \(0.735220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.6411 | 1.45854 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3002 | −1.22961 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.3764 | −1.95957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.77968 | 0.252698 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.2560 | −1.73625 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6187 | −1.03921 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.63985 | −0.234248 | −0.117124 | − | 0.993117i | \(-0.537368\pi\) | ||||
−0.117124 | + | 0.993117i | \(0.537368\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.82065 | 0.512480 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3670 | −1.34263 | −0.671313 | − | 0.741174i | \(-0.734269\pi\) | ||||
−0.671313 | + | 0.741174i | \(0.734269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.29464 | −0.285682 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.0898 | 1.47085 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.91853 | 0.420218 | 0.210109 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210109 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.80377 | −0.831545 | −0.415773 | − | 0.909469i | \(-0.636489\pi\) | ||||
−0.415773 | + | 0.909469i | \(0.636489\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.1156 | −1.35718 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.64338 | −0.722796 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.54758 | 0.460701 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.3776 | 0.938407 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.724147 | −0.0593244 | −0.0296622 | − | 0.999560i | \(-0.509443\pi\) | ||||
−0.0296622 | + | 0.999560i | \(0.509443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7252 | −1.27970 | −0.639850 | − | 0.768500i | \(-0.721003\pi\) | ||||
−0.639850 | + | 0.768500i | \(0.721003\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.0614 | −2.99623 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.86505 | 0.230127 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.141127 | −0.0112632 | −0.00563160 | − | 0.999984i | \(-0.501793\pi\) | ||||
−0.00563160 | + | 0.999984i | \(0.501793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7180 | 1.16721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.1383 | 1.90236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.41859 | 0.659395 | 0.329697 | − | 0.944087i | \(-0.393053\pi\) | ||||
0.329697 | + | 0.944087i | \(0.393053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.3911 | 1.82099 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | −5.71210 | −0.436815 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.13988 | 0.238721 | 0.119360 | − | 0.992851i | \(-0.461916\pi\) | ||||
0.119360 | + | 0.992851i | \(0.461916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.45750 | −0.110177 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.5463 | −2.14567 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.1898 | −1.35957 | −0.679786 | − | 0.733410i | \(-0.737927\pi\) | ||||
−0.679786 | + | 0.733410i | \(0.737927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0798 | −1.04654 | −0.523271 | − | 0.852166i | \(-0.675288\pi\) | ||||
−0.523271 | + | 0.852166i | \(0.675288\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0726 | −1.77950 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.96273 | −0.585431 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.0849 | −1.76126 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 26.3740 | 1.91842 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.87409 | −0.352677 | −0.176338 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176338 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.99845 | −0.719704 | −0.359852 | − | 0.933009i | \(-0.617173\pi\) | ||||
−0.359852 | + | 0.933009i | \(0.617173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.6722 | −1.05070 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.2209 | 1.36943 | 0.684716 | − | 0.728810i | \(-0.259926\pi\) | ||||
0.684716 | + | 0.728810i | \(0.259926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7323 | −0.831683 | −0.415842 | − | 0.909437i | \(-0.636513\pi\) | ||||
−0.415842 | + | 0.909437i | \(0.636513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.54956 | −0.109298 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.56137 | 0.600890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9275 | −0.972737 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 41.8498 | 2.90876 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.71210 | −0.256771 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.399383 | 0.0274947 | 0.0137473 | − | 0.999906i | \(-0.495624\pi\) | ||||
0.0137473 | + | 0.999906i | \(0.495624\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.1776 | 1.45106 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.20997 | 0.287118 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.42153 | 0.300153 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.6876 | 1.26279 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.1074 | 1.01623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2548 | 1.28939 | 0.644697 | − | 0.764438i | \(-0.276983\pi\) | ||||
0.644697 | + | 0.764438i | \(0.276983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.52694 | −0.168463 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0414 | 1.33019 | 0.665096 | − | 0.746758i | \(-0.268391\pi\) | ||||
0.665096 | + | 0.746758i | \(0.268391\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.2013 | 1.20277 | 0.601387 | − | 0.798958i | \(-0.294615\pi\) | ||||
0.601387 | + | 0.798958i | \(0.294615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 36.0985 | 2.37511 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.2376 | −0.932739 | −0.466369 | − | 0.884590i | \(-0.654438\pi\) | ||||
−0.466369 | + | 0.884590i | \(0.654438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6561 | −0.760362 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.8457 | 1.67886 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.31368 | −0.537767 | −0.268884 | − | 0.963173i | \(-0.586655\pi\) | ||||
−0.268884 | + | 0.963173i | \(0.586655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1776 | −1.68625 | −0.843125 | − | 0.537718i | \(-0.819287\pi\) | ||||
−0.843125 | + | 0.537718i | \(0.819287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.85401 | −0.311385 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.22920 | 0.525744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.32843 | 0.148155 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.8458 | −1.44780 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.4740 | 1.86038 | 0.930191 | − | 0.367075i | \(-0.119641\pi\) | ||||
0.930191 | + | 0.367075i | \(0.119641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.1967 | 1.70984 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −40.8842 | −2.56027 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.28195 | 0.0799657 | 0.0399828 | − | 0.999200i | \(-0.487270\pi\) | ||||
0.0399828 | + | 0.999200i | \(0.487270\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2886 | −0.763575 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.8433 | 0.918777 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 3.08055 | 0.188526 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1850 | 0.864875 | 0.432437 | − | 0.901664i | \(-0.357654\pi\) | ||||
0.432437 | + | 0.901664i | \(0.357654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.3185 | −1.59874 | −0.799369 | − | 0.600840i | \(-0.794833\pi\) | ||||
−0.799369 | + | 0.600840i | \(0.794833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.6430 | −1.37042 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.64217 | −0.0990269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.58863 | 0.215620 | 0.107810 | − | 0.994172i | \(-0.465616\pi\) | ||||
0.107810 | + | 0.994172i | \(0.465616\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.66584 | 0.458942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.42597 | 0.264031 | 0.132016 | − | 0.991248i | \(-0.457855\pi\) | ||||
0.132016 | + | 0.991248i | \(0.457855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.493151 | −0.0293148 | −0.0146574 | − | 0.999893i | \(-0.504666\pi\) | ||||
−0.0146574 | + | 0.999893i | \(0.504666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.30130 | −0.373257 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.4938 | −1.26874 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.0970 | 1.47630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.347093 | −0.0203469 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.7228 | 0.743275 | 0.371637 | − | 0.928378i | \(-0.378796\pi\) | ||||
0.371637 | + | 0.928378i | \(0.378796\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.6470 | −1.20211 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.7157 | 1.72428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.0593 | −0.986565 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.49709 | 0.374486 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.3292 | −1.79981 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.4113 | −0.996966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2166 | −0.583092 | −0.291546 | − | 0.956557i | \(-0.594170\pi\) | ||||
−0.291546 | + | 0.956557i | \(0.594170\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.6562 | 2.08530 | ||||||||
\(310\) | 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 | \(-0.318786\pi\) | ||||
0.539044 | + | 0.842278i | \(0.318786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 40.1766 | 2.26369 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.911635 | −0.0512025 | −0.0256013 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256013 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.64615 | 0.540081 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 48.8313 | 2.72550 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.48822 | 0.361014 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.03006 | 0.0571376 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 51.4872 | 2.84725 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.9885 | −0.991736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.45230 | −0.134791 | −0.0673953 | − | 0.997726i | \(-0.521469\pi\) | ||||
−0.0673953 | + | 0.997726i | \(0.521469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.3054 | −1.16753 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −42.2652 | −2.29553 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.98177 | 0.269778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3627 | −0.559533 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 46.1666 | 2.48552 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.30643 | −0.284864 | −0.142432 | − | 0.989805i | \(-0.545492\pi\) | ||||
−0.142432 | + | 0.989805i | \(0.545492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.8913 | 1.43946 | 0.719729 | − | 0.694255i | \(-0.244266\pi\) | ||||
0.719729 | + | 0.694255i | \(0.244266\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.6394 | −0.994895 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.21383 | −0.171055 | −0.0855275 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855275 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.3174 | 0.812961 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −63.0951 | −3.33935 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 8.20457 | 0.430628 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5164 | 0.707481 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3509 | −0.749111 | −0.374555 | − | 0.927205i | \(-0.622205\pi\) | ||||
−0.374555 | + | 0.927205i | \(0.622205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.2649 | −1.93993 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4284 | 0.852921 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.08701 | −0.470508 | −0.235254 | − | 0.971934i | \(-0.575592\pi\) | ||||
−0.235254 | + | 0.971934i | \(0.575592\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.2941 | −1.77094 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.05060 | −0.311622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2006 | 0.934900 | 0.467450 | − | 0.884020i | \(-0.345173\pi\) | ||||
0.467450 | + | 0.884020i | \(0.345173\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.79184 | −0.399188 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.4154 | 1.14537 | 0.572686 | − | 0.819775i | \(-0.305901\pi\) | ||||
0.572686 | + | 0.819775i | \(0.305901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.1094 | 1.33066 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.2643 | 0.572599 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.9213 | 1.77058 | 0.885291 | − | 0.465038i | \(-0.153959\pi\) | ||||
0.885291 | + | 0.465038i | \(0.153959\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.5360 | −2.40400 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −45.3578 | −2.28800 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.6937 | 0.940584 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.3443 | −1.57313 | −0.786563 | − | 0.617510i | \(-0.788142\pi\) | ||||
−0.786563 | + | 0.617510i | \(0.788142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.72456 | −0.486837 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.64321 | 0.0820579 | 0.0410290 | − | 0.999158i | \(-0.486936\pi\) | ||||
0.0410290 | + | 0.999158i | \(0.486936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.12484 | −0.155659 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.8590 | 0.688660 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8456 | −0.686302 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.46645 | 0.121958 | 0.0609791 | − | 0.998139i | \(-0.480578\pi\) | ||||
0.0609791 | + | 0.998139i | \(0.480578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5177 | 0.716104 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.8637 | −1.56791 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.5240 | −0.811130 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −28.9371 | −1.41705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.25063 | 0.207657 | 0.103828 | − | 0.994595i | \(-0.466891\pi\) | ||||
0.103828 | + | 0.994595i | \(0.466891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4900 | 1.53473 | 0.767364 | − | 0.641212i | \(-0.221568\pi\) | ||||
0.767364 | + | 0.641212i | \(0.221568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.1875 | −1.51639 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.87029 | 0.139229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.8701 | −1.30034 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.5120 | −1.23173 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0564 | 1.01425 | 0.507125 | − | 0.861872i | \(-0.330708\pi\) | ||||
0.507125 | + | 0.861872i | \(0.330708\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.53125 | −0.361929 | −0.180964 | − | 0.983490i | \(-0.557922\pi\) | ||||
−0.180964 | + | 0.983490i | \(0.557922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.3744 | 0.785091 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.32651 | −0.350475 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.823995 | 0.0393271 | 0.0196636 | − | 0.999807i | \(-0.493740\pi\) | ||||
0.0196636 | + | 0.999807i | \(0.493740\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.0183 | 1.04849 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.58526 | 0.407898 | 0.203949 | − | 0.978982i | \(-0.434622\pi\) | ||||
0.203949 | + | 0.978982i | \(0.434622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.22810 | 0.105622 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.13741 | −0.101096 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.49451 | 0.117723 | 0.0588615 | − | 0.998266i | \(-0.481253\pi\) | ||||
0.0588615 | + | 0.998266i | \(0.481253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.2172 | −1.14034 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.4150 | −2.18076 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.3773 | −0.767778 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5004 | −0.678301 | −0.339150 | − | 0.940732i | \(-0.610140\pi\) | ||||
−0.339150 | + | 0.940732i | \(0.610140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −51.9389 | −2.42430 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1930 | 1.08020 | 0.540102 | − | 0.841600i | \(-0.318386\pi\) | ||||
0.540102 | + | 0.841600i | \(0.318386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0637 | −1.21128 | −0.605642 | − | 0.795737i | \(-0.707084\pi\) | ||||
−0.605642 | + | 0.795737i | \(0.707084\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.45657 | 0.392164 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1953 | 0.564332 | 0.282166 | − | 0.959366i | \(-0.408947\pi\) | ||||
0.282166 | + | 0.959366i | \(0.408947\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.72964 | −0.0798674 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.416556 | −0.0191939 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.32031 | 0.336588 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.442384 | 0.0202980 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.4828 | 1.30414 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.1883 | −0.831045 | −0.415523 | − | 0.909583i | \(-0.636401\pi\) | ||||
−0.415523 | + | 0.909583i | \(0.636401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68475 | 0.395990 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 71.2471 | 3.24186 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.251046 | −0.0113994 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.13693 | −0.0968334 | −0.0484167 | − | 0.998827i | \(-0.515418\pi\) | ||||
−0.0484167 | + | 0.998827i | \(0.515418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.8485 | 1.12369 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.32773 | 0.105049 | 0.0525244 | − | 0.998620i | \(-0.483273\pi\) | ||||
0.0525244 | + | 0.998620i | \(0.483273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.8601 | −0.759341 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.2673 | 2.03461 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.6387 | 1.06034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9382 | 0.758260 | 0.379130 | − | 0.925343i | \(-0.376223\pi\) | ||||
0.379130 | + | 0.925343i | \(0.376223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.2463 | 0.681153 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | −22.3686 | −0.993424 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8145 | −0.878261 | −0.439131 | − | 0.898423i | \(-0.644713\pi\) | ||||
−0.439131 | + | 0.898423i | \(0.644713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8594 | 0.922764 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00510 | −0.353434 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.5128 | 1.16829 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.2677 | −0.891374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.26775 | 0.406809 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0978 | 1.58147 | 0.790737 | − | 0.612156i | \(-0.209698\pi\) | ||||
0.790737 | + | 0.612156i | \(0.209698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.19475 | −0.183424 | −0.0917119 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917119 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.30199 | −0.187754 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.70743 | −0.379301 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.6778 | 1.33382 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −55.2438 | −2.39738 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.1903 | 0.657967 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 35.3188 | 1.52696 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −53.6896 | −2.31688 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14.3090 | 0.616331 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.12211 | 0.263210 | 0.131605 | − | 0.991302i | \(-0.457987\pi\) | ||||
0.131605 | + | 0.991302i | \(0.457987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.5582 | −1.78343 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.2398 | 1.59518 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.88879 | −0.209029 | −0.104515 | − | 0.994523i | \(-0.533329\pi\) | ||||
−0.104515 | + | 0.994523i | \(0.533329\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.5862 | −1.98825 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.59857 | −0.110703 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.8493 | 1.22680 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.5030 | −0.997647 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.5987 | −1.21176 | −0.605882 | − | 0.795554i | \(-0.707180\pi\) | ||||
−0.605882 | + | 0.795554i | \(0.707180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.59171 | −0.194209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −71.0897 | −3.00141 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.83345 | 0.414431 | 0.207215 | − | 0.978295i | \(-0.433560\pi\) | ||||
0.207215 | + | 0.978295i | \(0.433560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.5697 | −1.28608 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.3881 | 0.898216 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3543 | 0.434075 | 0.217037 | − | 0.976163i | \(-0.430361\pi\) | ||||
0.217037 | + | 0.976163i | \(0.430361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.7988 | 1.53998 | 0.769991 | − | 0.638055i | \(-0.220261\pi\) | ||||
0.769991 | + | 0.638055i | \(0.220261\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.3865 | −0.601005 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −29.5117 | −1.22646 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.5008 | −1.05795 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.5100 | 0.766606 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.3941 | −1.17395 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.18047 | 0.296370 | 0.148185 | − | 0.988960i | \(-0.452657\pi\) | ||||
0.148185 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.34204 | −0.0552976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 56.7329 | 2.33368 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.7687 | −1.01713 | −0.508564 | − | 0.861024i | \(-0.669823\pi\) | ||||
−0.508564 | + | 0.861024i | \(0.669823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −45.6355 | −1.87087 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.6295 | −1.41729 | ||||||||
\(598\) | 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 | \(-0.513639\pi\) | ||||
−0.0428359 | + | 0.999082i | \(0.513639\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.99877 | −0.122119 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.93422 | 0.241260 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.2877 | 0.458152 | 0.229076 | − | 0.973409i | \(-0.426430\pi\) | ||||
0.229076 | + | 0.973409i | \(0.426430\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.2700 | 1.02399 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7130 | 0.514315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.4983 | −1.27220 | −0.636102 | − | 0.771605i | \(-0.719454\pi\) | ||||
−0.636102 | + | 0.771605i | \(0.719454\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −41.1087 | −1.65766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4563 | 0.461214 | 0.230607 | − | 0.973047i | \(-0.425929\pi\) | ||||
0.230607 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.6816 | −1.51455 | −0.757276 | − | 0.653095i | \(-0.773470\pi\) | ||||
−0.757276 | + | 0.653095i | \(0.773470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 58.6495 | 2.35352 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.43855 | 0.137763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.5924 | −0.903695 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.9567 | −0.437570 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.2002 | 0.964925 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.99670 | 0.278534 | 0.139267 | − | 0.990255i | \(-0.455525\pi\) | ||||
0.139267 | + | 0.990255i | \(0.455525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.17883 | 0.0468543 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.63569 | −0.223646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.97538 | −0.355617 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.9837 | 1.62129 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.20749 | −0.245181 | −0.122591 | − | 0.992457i | \(-0.539120\pi\) | ||||
−0.122591 | + | 0.992457i | \(0.539120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.4008 | 1.15945 | 0.579726 | − | 0.814811i | \(-0.303159\pi\) | ||||
0.579726 | + | 0.814811i | \(0.303159\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4263 | 0.489284 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 13.0507 | 0.511498 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.9447 | 1.36749 | 0.683745 | − | 0.729721i | \(-0.260350\pi\) | ||||
0.683745 | + | 0.729721i | \(0.260350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.8064 | −1.28185 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1650 | 1.41093 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.8768 | 1.47547 | 0.737736 | − | 0.675090i | \(-0.235895\pi\) | ||||
0.737736 | + | 0.675090i | \(0.235895\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.77264 | −0.263425 | −0.131713 | − | 0.991288i | \(-0.542048\pi\) | ||||
−0.131713 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44.5914 | 1.73179 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.03360 | −0.272751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.0385 | 0.737172 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 56.8329 | 2.19729 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −3.54133 | −0.136306 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.2956 | −1.08749 | −0.543744 | − | 0.839251i | \(-0.682994\pi\) | ||||
−0.543744 | + | 0.839251i | \(0.682994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.387430 | −0.0148682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 59.1546 | 2.26681 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.4333 | −1.31755 | −0.658777 | − | 0.752339i | \(-0.728926\pi\) | ||||
−0.658777 | + | 0.752339i | \(0.728926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.5004 | 0.401198 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 53.7234 | 2.04967 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.6105 | −0.442325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.19928 | 0.0836646 | 0.0418323 | − | 0.999125i | \(-0.486680\pi\) | ||||
0.0418323 | + | 0.999125i | \(0.486680\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 69.8592 | 2.65373 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9297 | −0.793907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.3282 | 1.60329 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42.0242 | −1.58950 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0608 | −1.36200 | −0.680999 | − | 0.732285i | \(-0.738454\pi\) | ||||
−0.680999 | + | 0.732285i | \(0.738454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.72986 | 0.140675 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.4045 | −1.29575 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −34.9701 | −1.31518 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7299 | −0.402970 | −0.201485 | − | 0.979492i | \(-0.564577\pi\) | ||||
−0.201485 | + | 0.979492i | \(0.564577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.0176 | 1.87581 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.83244 | 0.368228 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.4524 | −0.690080 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.5389 | −0.916421 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.1037 | −1.08539 | −0.542693 | − | 0.839931i | \(-0.682595\pi\) | ||||
−0.542693 | + | 0.839931i | \(0.682595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.9162 | 1.52380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −77.2666 | −2.87358 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.14957 | −0.0426938 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.5850 | −1.50521 | −0.752607 | − | 0.658470i | \(-0.771204\pi\) | ||||
−0.752607 | + | 0.658470i | \(0.771204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.8025 | −1.25195 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.7949 | −0.473235 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.6206 | −0.687766 | −0.343883 | − | 0.939012i | \(-0.611742\pi\) | ||||
−0.343883 | + | 0.939012i | \(0.611742\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 24.2895 | 0.895933 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.94880 | −0.0717849 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.89939 | 0.290584 | 0.145292 | − | 0.989389i | \(-0.453588\pi\) | ||||
0.145292 | + | 0.989389i | \(0.453588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.87267 | 0.252474 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | −44.2121 | −1.61764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 54.5061 | 1.99161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0914 | −0.514204 | −0.257102 | − | 0.966384i | \(-0.582768\pi\) | ||||
−0.257102 | + | 0.966384i | \(0.582768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 86.9962 | 3.17032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.5711 | −1.22178 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.2311 | 1.82568 | 0.912840 | − | 0.408318i | \(-0.133884\pi\) | ||||
0.912840 | + | 0.408318i | \(0.133884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80.2746 | 2.91378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.7483 | −0.860875 | −0.430437 | − | 0.902620i | \(-0.641641\pi\) | ||||
−0.430437 | + | 0.902620i | \(0.641641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.4707 | 2.08058 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −79.1207 | −2.86062 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 3.78383 | 0.136271 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.8508 | 0.426242 | 0.213121 | − | 0.977026i | \(-0.431637\pi\) | ||||
0.213121 | + | 0.977026i | \(0.431637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.593696 | −0.0213262 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.2713 | −1.30123 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.52385 | 0.233741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.6339 | 0.953036 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.8018 | 0.743396 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.301287 | −0.0107534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.3903 | 0.940713 | 0.470356 | − | 0.882477i | \(-0.344125\pi\) | ||||
0.470356 | + | 0.882477i | \(0.344125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −86.4048 | −3.07609 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.1770 | −1.67742 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.9900 | 0.674356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.4208 | 1.11438 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.1893 | −0.502610 | −0.251305 | − | 0.967908i | \(-0.580860\pi\) | ||||
−0.251305 | + | 0.967908i | \(0.580860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.4251 | 1.25325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.96159 | 0.210643 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.5024 | 0.829382 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.5317 | 1.81625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.8688 | 1.47385 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9998 | 1.05474 | 0.527368 | − | 0.849637i | \(-0.323179\pi\) | ||||
0.527368 | + | 0.849637i | \(0.323179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.8833 | 1.40049 | 0.700246 | − | 0.713901i | \(-0.253073\pi\) | ||||
0.700246 | + | 0.713901i | \(0.253073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −77.6825 | −2.72445 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.9725 | 0.629549 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.97202 | −0.0689921 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −43.8196 | −1.53118 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.4395 | 1.96975 | 0.984877 | − | 0.173256i | \(-0.0554287\pi\) | ||||
0.984877 | + | 0.173256i | \(0.0554287\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.7360 | −1.45482 | −0.727412 | − | 0.686201i | \(-0.759277\pi\) | ||||
−0.727412 | + | 0.686201i | \(0.759277\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.84709 | −0.168754 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.4248 | −0.605921 | −0.302960 | − | 0.953003i | \(-0.597975\pi\) | ||||
−0.302960 | + | 0.953003i | \(0.597975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.2723 | 1.81549 | 0.907747 | − | 0.419519i | \(-0.137801\pi\) | ||||
0.907747 | + | 0.419519i | \(0.137801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5923 | 0.367443 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.0100 | −0.866547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0273 | 0.381617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7431 | 0.371337 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 13.0638 | 0.449941 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.1788 | −0.556567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.15805 | 0.314674 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.45560 | −0.0499560 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.3269 | −0.936754 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.8153 | −1.46597 | −0.732984 | − | 0.680245i | \(-0.761873\pi\) | ||||
−0.732984 | + | 0.680245i | \(0.761873\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.1945 | −0.417044 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2947 | −0.795732 | −0.397866 | − | 0.917444i | \(-0.630249\pi\) | ||||
−0.397866 | + | 0.917444i | \(0.630249\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.5879 | −0.600091 | −0.300045 | − | 0.953925i | \(-0.597002\pi\) | ||||
−0.300045 | + | 0.953925i | \(0.597002\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −63.4415 | −2.16208 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.8886 | 0.404692 | 0.202346 | − | 0.979314i | \(-0.435143\pi\) | ||||
0.202346 | + | 0.979314i | \(0.435143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.70319 | 0.227915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 74.0770 | 2.51579 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.5048 | 1.10265 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.22239 | 0.0414193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.671707 | −0.0227338 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.2795 | −1.29408 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.6698 | −0.968111 | −0.484056 | − | 0.875037i | \(-0.660837\pi\) | ||||
−0.484056 | + | 0.875037i | \(0.660837\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.5530 | 1.26663 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.2297 | −1.49014 | −0.745069 | − | 0.666988i | \(-0.767583\pi\) | ||||
−0.745069 | + | 0.666988i | \(0.767583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.5869 | −0.894719 | −0.447359 | − | 0.894354i | \(-0.647636\pi\) | ||||
−0.447359 | + | 0.894354i | \(0.647636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.9422 | −2.04855 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 24.0981 | 0.807317 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.45991 | 0.182709 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.8327 | −1.29803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50.3527 | −1.68123 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.48737 | 0.116310 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.3529 | −1.07783 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.1770 | 0.638170 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.0583 | −0.999172 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3380 | 1.57183 | 0.785916 | − | 0.618333i | \(-0.212192\pi\) | ||||
0.785916 | + | 0.618333i | \(0.212192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −60.6294 | −2.01095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.30896 | −0.175894 | −0.0879469 | − | 0.996125i | \(-0.528031\pi\) | ||||
−0.0879469 | + | 0.996125i | \(0.528031\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.7320 | −0.950889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −51.3915 | −1.69895 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −50.6290 | −1.67192 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.2513 | 1.62465 | 0.812326 | − | 0.583204i | \(-0.198201\pi\) | ||||
0.812326 | + | 0.583204i | \(0.198201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.1556 | −0.993661 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.7063 | −0.549893 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.65003 | 0.0542528 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 70.9385 | 2.32993 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.2990 | −0.961270 | −0.480635 | − | 0.876921i | \(-0.659594\pi\) | ||||
−0.480635 | + | 0.876921i | \(0.659594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.85468 | −0.126332 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.545857 | 0.0178706 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51.4179 | −1.68154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.35345 | 0.207558 | 0.103779 | − | 0.994600i | \(-0.466907\pi\) | ||||
0.103779 | + | 0.994600i | \(0.466907\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 56.2973 | 1.83719 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.07523 | −0.0676505 | −0.0338253 | − | 0.999428i | \(-0.510769\pi\) | ||||
−0.0338253 | + | 0.999428i | \(0.510769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7970 | −1.55649 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 56.3047 | 1.83159 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.3618 | 0.434201 | 0.217101 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217101 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.7420 | −0.478546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.69081 | −0.0872554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.6796 | 1.70646 | 0.853231 | − | 0.521534i | \(-0.174640\pi\) | ||||
0.853231 | + | 0.521534i | \(0.174640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.4055 | −0.336714 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.4718 | 0.920364 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.2048 | 0.523281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1989 | −0.941901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 94.5002 | 3.04522 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.3453 | −0.687128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.17519 | −0.230739 | −0.115369 | − | 0.993323i | \(-0.536805\pi\) | ||||
−0.115369 | + | 0.993323i | \(0.536805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.1508 | 0.615213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6991 | −0.471718 | −0.235859 | − | 0.971787i | \(-0.575790\pi\) | ||||
−0.235859 | + | 0.971787i | \(0.575790\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.3000 | −1.03549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.04036 | 0.0973695 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.5470 | 0.625365 | 0.312682 | − | 0.949858i | \(-0.398772\pi\) | ||||
0.312682 | + | 0.949858i | \(0.398772\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.87424 | 0.123821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 99.6401 | 3.18126 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | −53.0952 | −1.69004 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.4480 | 0.459419 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5419 | −1.60552 | −0.802758 | − | 0.596305i | \(-0.796635\pi\) | ||||
−0.802758 | + | 0.596305i | \(0.796635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.23827 | −0.229700 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.0469 | −0.794039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.9225 | −0.694293 | −0.347147 | − | 0.937811i | \(-0.612849\pi\) | ||||
−0.347147 | + | 0.937811i | \(0.612849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.8580 | −0.944664 |
(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 | 4864.2.a.bp.1.8 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bq.1.1 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bo.1.8 | 8 | |||
8.5 | even | 2 | 4864.2.a.bn.1.1 | 8 | |||
16.3 | odd | 4 | 152.2.c.b.77.3 | ✓ | 16 | ||
16.5 | even | 4 | 608.2.c.b.305.2 | 16 | |||
16.11 | odd | 4 | 152.2.c.b.77.4 | yes | 16 | ||
16.13 | even | 4 | 608.2.c.b.305.15 | 16 | |||
48.5 | odd | 4 | 5472.2.g.b.2737.4 | 16 | |||
48.11 | even | 4 | 1368.2.g.b.685.13 | 16 | |||
48.29 | odd | 4 | 5472.2.g.b.2737.13 | 16 | |||
48.35 | even | 4 | 1368.2.g.b.685.14 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.3 | ✓ | 16 | 16.3 | odd | 4 | ||
152.2.c.b.77.4 | yes | 16 | 16.11 | odd | 4 | ||
608.2.c.b.305.2 | 16 | 16.5 | even | 4 | |||
608.2.c.b.305.15 | 16 | 16.13 | even | 4 | |||
1368.2.g.b.685.13 | 16 | 48.11 | even | 4 | |||
1368.2.g.b.685.14 | 16 | 48.35 | even | 4 | |||
4864.2.a.bn.1.1 | 8 | 8.5 | even | 2 | |||
4864.2.a.bo.1.8 | 8 | 8.3 | odd | 2 | |||
4864.2.a.bp.1.8 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bq.1.1 | 8 | 4.3 | odd | 2 | |||
5472.2.g.b.2737.4 | 16 | 48.5 | odd | 4 | |||
5472.2.g.b.2737.13 | 16 | 48.29 | odd | 4 |