Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.344611 | 0.154115 | 0.0770574 | − | 0.997027i | \(-0.475448\pi\) | ||||
0.0770574 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72948 | 1.03165 | 0.515824 | − | 0.856695i | \(-0.327486\pi\) | ||||
0.515824 | + | 0.856695i | \(0.327486\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.712991 | −0.214975 | −0.107487 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107487 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.42474 | 1.78190 | 0.890952 | − | 0.454098i | \(-0.150038\pi\) | ||||
0.890952 | + | 0.454098i | \(0.150038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.344611 | −0.0889782 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.96822 | −1.44751 | −0.723753 | − | 0.690059i | \(-0.757585\pi\) | ||||
−0.723753 | + | 0.690059i | \(0.757585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12134 | 0.257254 | 0.128627 | − | 0.991693i | \(-0.458943\pi\) | ||||
0.128627 | + | 0.991693i | \(0.458943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.72948 | −0.595622 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47994 | 0.517103 | 0.258552 | − | 0.965997i | \(-0.416755\pi\) | ||||
0.258552 | + | 0.965997i | \(0.416755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88124 | −0.976249 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.35862 | 0.252290 | 0.126145 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126145 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.54555 | 0.636800 | 0.318400 | − | 0.947956i | \(-0.396854\pi\) | ||||
0.318400 | + | 0.947956i | \(0.396854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.712991 | 0.124116 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.940610 | 0.158992 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.77120 | 1.44198 | 0.720988 | − | 0.692947i | \(-0.243688\pi\) | ||||
0.720988 | + | 0.692947i | \(0.243688\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.42474 | −1.02878 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.02539 | 0.472486 | 0.236243 | − | 0.971694i | \(-0.424084\pi\) | ||||
0.236243 | + | 0.971694i | \(0.424084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.8201 | 1.95505 | 0.977527 | − | 0.210810i | \(-0.0676100\pi\) | ||||
0.977527 | + | 0.210810i | \(0.0676100\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.344611 | 0.0513716 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.01538 | −1.31503 | −0.657514 | − | 0.753442i | \(-0.728392\pi\) | ||||
−0.657514 | + | 0.753442i | \(0.728392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.450076 | 0.0642965 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.96822 | 0.835718 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.26873 | −0.723715 | −0.361858 | − | 0.932233i | \(-0.617857\pi\) | ||||
−0.361858 | + | 0.932233i | \(0.617857\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.245704 | −0.0331308 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.12134 | −0.148525 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.02996 | 1.17560 | 0.587800 | − | 0.809006i | \(-0.299994\pi\) | ||||
0.587800 | + | 0.809006i | \(0.299994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.78442 | 0.996693 | 0.498347 | − | 0.866978i | \(-0.333941\pi\) | ||||
0.498347 | + | 0.866978i | \(0.333941\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.72948 | 0.343882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.21404 | 0.274618 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5521 | −1.53349 | −0.766744 | − | 0.641953i | \(-0.778124\pi\) | ||||
−0.766744 | + | 0.641953i | \(0.778124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.47994 | −0.298550 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.01561 | 0.476565 | 0.238282 | − | 0.971196i | \(-0.423416\pi\) | ||||
0.238282 | + | 0.971196i | \(0.423416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.39756 | 0.982860 | 0.491430 | − | 0.870917i | \(-0.336474\pi\) | ||||
0.491430 | + | 0.870917i | \(0.336474\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.88124 | 0.563637 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.94610 | −0.221778 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.26540 | −0.142369 | −0.0711844 | − | 0.997463i | \(-0.522678\pi\) | ||||
−0.0711844 | + | 0.997463i | \(0.522678\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.6297 | −1.60582 | −0.802909 | − | 0.596102i | \(-0.796715\pi\) | ||||
−0.802909 | + | 0.596102i | \(0.796715\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.05672 | −0.223082 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.35862 | −0.145659 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.273555 | 0.0289967 | 0.0144984 | − | 0.999895i | \(-0.495385\pi\) | ||||
0.0144984 | + | 0.999895i | \(0.495385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5362 | 1.83830 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.54555 | −0.367657 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.386427 | 0.0396466 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.105936 | −0.0107562 | −0.00537808 | − | 0.999986i | \(-0.501712\pi\) | ||||
−0.00537808 | + | 0.999986i | \(0.501712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.712991 | −0.0716583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4179 | 1.13612 | 0.568062 | − | 0.822985i | \(-0.307693\pi\) | ||||
0.568062 | + | 0.822985i | \(0.307693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.63462 | 0.653728 | 0.326864 | − | 0.945071i | \(-0.394008\pi\) | ||||
0.326864 | + | 0.945071i | \(0.394008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.940610 | −0.0917941 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.41570 | 0.813576 | 0.406788 | − | 0.913523i | \(-0.366649\pi\) | ||||
0.406788 | + | 0.913523i | \(0.366649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.93390 | −0.376799 | −0.188400 | − | 0.982092i | \(-0.560330\pi\) | ||||
−0.188400 | + | 0.982092i | \(0.560330\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.77120 | −0.832526 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1560 | 1.14354 | 0.571772 | − | 0.820412i | \(-0.306256\pi\) | ||||
0.571772 | + | 0.820412i | \(0.306256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.854615 | 0.0796933 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.42474 | 0.593968 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.2902 | −1.49332 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4916 | −0.953786 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.02539 | −0.272790 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.40519 | −0.304569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2409 | −1.08620 | −0.543101 | − | 0.839667i | \(-0.682750\pi\) | ||||
−0.543101 | + | 0.839667i | \(0.682750\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.8201 | −1.12875 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.5682 | −1.01072 | −0.505358 | − | 0.862910i | \(-0.668640\pi\) | ||||
−0.505358 | + | 0.862910i | \(0.668640\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.06069 | 0.265395 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.344611 | −0.0296594 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.2770 | −1.73238 | −0.866191 | − | 0.499712i | \(-0.833439\pi\) | ||||
−0.866191 | + | 0.499712i | \(0.833439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.686829 | 0.0582561 | 0.0291280 | − | 0.999576i | \(-0.490727\pi\) | ||||
0.0291280 | + | 0.999576i | \(0.490727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.01538 | 0.759232 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.58078 | −0.383064 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.468196 | 0.0388815 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.450076 | −0.0371216 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.07076 | 0.251567 | 0.125783 | − | 0.992058i | \(-0.459856\pi\) | ||||
0.125783 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2823 | 0.918142 | 0.459071 | − | 0.888400i | \(-0.348182\pi\) | ||||
0.459071 | + | 0.888400i | \(0.348182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.96822 | −0.482502 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.22184 | 0.0981403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8937 | −1.34827 | −0.674134 | − | 0.738609i | \(-0.735483\pi\) | ||||
−0.674134 | + | 0.738609i | \(0.735483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.26873 | 0.417837 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.76896 | 0.533468 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.9112 | 1.08961 | 0.544806 | − | 0.838562i | \(-0.316603\pi\) | ||||
0.544806 | + | 0.838562i | \(0.316603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.245704 | 0.0191281 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.3646 | −0.956798 | −0.478399 | − | 0.878143i | \(-0.658783\pi\) | ||||
−0.478399 | + | 0.878143i | \(0.658783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.2773 | 2.17518 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.12134 | 0.0857512 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5946 | 1.18563 | 0.592817 | − | 0.805337i | \(-0.298016\pi\) | ||||
0.592817 | + | 0.805337i | \(0.298016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.3233 | −1.00714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.02996 | −0.678733 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6541 | −1.17004 | −0.585020 | − | 0.811019i | \(-0.698913\pi\) | ||||
−0.585020 | + | 0.811019i | \(0.698913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.78808 | −0.504554 | −0.252277 | − | 0.967655i | \(-0.581179\pi\) | ||||
−0.252277 | + | 0.967655i | \(0.581179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.78442 | −0.575441 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.02265 | 0.222230 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.25529 | 0.311177 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.72948 | −0.198541 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.54867 | 0.112058 | 0.0560291 | − | 0.998429i | \(-0.482156\pi\) | ||||
0.0560291 | + | 0.998429i | \(0.482156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.2987 | 1.38915 | 0.694574 | − | 0.719421i | \(-0.255593\pi\) | ||||
0.694574 | + | 0.719421i | \(0.255593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.21404 | −0.158551 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1837 | 1.36678 | 0.683391 | − | 0.730052i | \(-0.260504\pi\) | ||||
0.683391 | + | 0.730052i | \(0.260504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.04744 | 0.570468 | 0.285234 | − | 0.958458i | \(-0.407929\pi\) | ||||
0.285234 | + | 0.958458i | \(0.407929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.5521 | 0.885360 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.70833 | 0.260274 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04258 | 0.0728171 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.47994 | 0.172368 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.799507 | −0.0553030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3451 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.01561 | −0.275145 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.41796 | 0.301303 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.67753 | 0.656953 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.39756 | −0.567455 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.3443 | −2.57932 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.6754 | −0.714879 | −0.357439 | − | 0.933936i | \(-0.616350\pi\) | ||||
−0.357439 | + | 0.933936i | \(0.616350\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.88124 | −0.325416 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.7335 | 1.84073 | 0.920367 | − | 0.391056i | \(-0.127890\pi\) | ||||
0.920367 | + | 0.391056i | \(0.127890\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.99849 | 0.198146 | 0.0990728 | − | 0.995080i | \(-0.468412\pi\) | ||||
0.0990728 | + | 0.995080i | \(0.468412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.94610 | 0.128044 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.0232 | 1.11523 | 0.557614 | − | 0.830100i | \(-0.311717\pi\) | ||||
0.557614 | + | 0.830100i | \(0.311717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.10680 | −0.202665 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.26540 | 0.0821967 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5646 | −1.26553 | −0.632766 | − | 0.774343i | \(-0.718080\pi\) | ||||
−0.632766 | + | 0.774343i | \(0.718080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.6987 | 1.20449 | 0.602245 | − | 0.798311i | \(-0.294273\pi\) | ||||
0.602245 | + | 0.798311i | \(0.294273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.155101 | 0.00990905 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.20434 | 0.458401 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.6297 | 0.927119 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.722458 | 0.0456011 | 0.0228006 | − | 0.999740i | \(-0.492742\pi\) | ||||
0.0228006 | + | 0.999740i | \(0.492742\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.76817 | −0.111164 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.05672 | 0.128797 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.73334 | 0.607149 | 0.303575 | − | 0.952808i | \(-0.401820\pi\) | ||||
0.303575 | + | 0.952808i | \(0.401820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.9408 | 1.48761 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.35862 | 0.0840965 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8101 | 0.974896 | 0.487448 | − | 0.873152i | \(-0.337928\pi\) | ||||
0.487448 | + | 0.873152i | \(0.337928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81566 | −0.111535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.273555 | −0.0167413 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.54823 | 0.460224 | 0.230112 | − | 0.973164i | \(-0.426091\pi\) | ||||
0.230112 | + | 0.973164i | \(0.426091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.83611 | 0.172282 | 0.0861408 | − | 0.996283i | \(-0.472547\pi\) | ||||
0.0861408 | + | 0.996283i | \(0.472547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.5362 | −1.06134 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.48028 | 0.209869 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.975302 | 0.0586002 | 0.0293001 | − | 0.999571i | \(-0.490672\pi\) | ||||
0.0293001 | + | 0.999571i | \(0.490672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.54555 | 0.212267 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.6666 | 1.41183 | 0.705915 | − | 0.708296i | \(-0.250536\pi\) | ||||
0.705915 | + | 0.708296i | \(0.250536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.46571 | −0.265459 | −0.132729 | − | 0.991152i | \(-0.542374\pi\) | ||||
−0.132729 | + | 0.991152i | \(0.542374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.386427 | −0.0228900 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.25774 | 0.487439 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.6197 | 1.09528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.105936 | 0.00621007 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1854 | 1.17924 | 0.589621 | − | 0.807680i | \(-0.299277\pi\) | ||||
0.589621 | + | 0.807680i | \(0.299277\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.11182 | 0.181177 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.712991 | 0.0413719 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9330 | 0.921429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.9924 | 2.01693 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4179 | −0.655942 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.68260 | 0.153605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.34238 | −0.247833 | −0.123916 | − | 0.992293i | \(-0.539545\pi\) | ||||
−0.123916 | + | 0.992293i | \(0.539545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.63462 | −0.377430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9026 | 0.845047 | 0.422523 | − | 0.906352i | \(-0.361144\pi\) | ||||
0.422523 | + | 0.906352i | \(0.361144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.43464 | 0.363708 | 0.181854 | − | 0.983326i | \(-0.441790\pi\) | ||||
0.181854 | + | 0.983326i | \(0.441790\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.940610 | 0.0529974 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9271 | 1.23155 | 0.615775 | − | 0.787922i | \(-0.288843\pi\) | ||||
0.615775 | + | 0.787922i | \(0.288843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.968684 | −0.0542359 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.41570 | −0.469718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.69242 | −0.372376 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.3607 | −1.73958 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.93390 | 0.217545 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.6073 | −1.35665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.36105 | 0.459565 | 0.229782 | − | 0.973242i | \(-0.426199\pi\) | ||||
0.229782 | + | 0.973242i | \(0.426199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.77120 | 0.480659 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.32561 | −0.236333 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7567 | 1.78437 | 0.892187 | − | 0.451666i | \(-0.149170\pi\) | ||||
0.892187 | + | 0.451666i | \(0.149170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.1560 | −0.660226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.52795 | −0.136896 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8779 | −0.965316 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.854615 | −0.0460109 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8361 | 1.06486 | 0.532430 | − | 0.846474i | \(-0.321279\pi\) | ||||
0.532430 | + | 0.846474i | \(0.321279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.38519 | −0.0741478 | −0.0370739 | − | 0.999313i | \(-0.511804\pi\) | ||||
−0.0370739 | + | 0.999313i | \(0.511804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.42474 | −0.342928 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.44035 | −0.396010 | −0.198005 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198005 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.38382 | 0.0734457 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.2902 | 0.862167 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.1414 | −1.22136 | −0.610679 | − | 0.791878i | \(-0.709103\pi\) | ||||
−0.610679 | + | 0.791878i | \(0.709103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7426 | −0.933821 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4916 | 0.550669 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.89389 | 0.151473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.7366 | −1.03024 | −0.515121 | − | 0.857118i | \(-0.672253\pi\) | ||||
−0.515121 | + | 0.857118i | \(0.672253\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.02539 | 0.157495 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.3809 | −0.746619 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.2414 | −0.789172 | −0.394586 | − | 0.918859i | \(-0.629112\pi\) | ||||
−0.394586 | + | 0.918859i | \(0.629112\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.40519 | 0.175843 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.72879 | 0.449556 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.52495 | −0.335164 | −0.167582 | − | 0.985858i | \(-0.553596\pi\) | ||||
−0.167582 | + | 0.985858i | \(0.553596\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2409 | 0.627119 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.99961 | 0.255468 | 0.127734 | − | 0.991808i | \(-0.459230\pi\) | ||||
0.127734 | + | 0.991808i | \(0.459230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.670646 | −0.0341793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.8201 | 0.651685 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.3083 | −1.02967 | −0.514836 | − | 0.857289i | \(-0.672147\pi\) | ||||
−0.514836 | + | 0.857289i | \(0.672147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8008 | −0.748511 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5682 | 0.583538 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.436072 | −0.0219411 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.23966 | −0.162594 | −0.0812970 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812970 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.06069 | −0.153226 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.9754 | 1.39702 | 0.698511 | − | 0.715599i | \(-0.253846\pi\) | ||||
0.698511 | + | 0.715599i | \(0.253846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.7793 | 1.13472 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.344611 | 0.0171239 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.25378 | −0.309989 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.6848 | 0.874459 | 0.437229 | − | 0.899350i | \(-0.355960\pi\) | ||||
0.437229 | + | 0.899350i | \(0.355960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.2770 | 1.00019 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.6471 | 1.21281 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.04155 | −0.247480 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.686829 | −0.0336342 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4621 | −1.24391 | −0.621953 | − | 0.783054i | \(-0.713661\pi\) | ||||
−0.621953 | + | 0.783054i | \(0.713661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.6786 | −1.25150 | −0.625748 | − | 0.780025i | \(-0.715206\pi\) | ||||
−0.625748 | + | 0.780025i | \(0.715206\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.01538 | −0.438343 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.1324 | 1.41313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.2474 | 1.02824 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.58078 | 0.221162 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.1431 | 0.873921 | 0.436961 | − | 0.899481i | \(-0.356055\pi\) | ||||
0.436961 | + | 0.899481i | \(0.356055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.31062 | 0.159098 | 0.0795491 | − | 0.996831i | \(-0.474652\pi\) | ||||
0.0795491 | + | 0.996831i | \(0.474652\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.468196 | −0.0224483 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.78086 | 0.133027 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.2782 | 1.11101 | 0.555503 | − | 0.831515i | \(-0.312526\pi\) | ||||
0.555503 | + | 0.831515i | \(0.312526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.450076 | 0.0214322 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.9935 | 1.42503 | 0.712517 | − | 0.701655i | \(-0.247555\pi\) | ||||
0.712517 | + | 0.701655i | \(0.247555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0942700 | 0.00446883 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.07076 | −0.145242 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9309 | 0.799019 | 0.399509 | − | 0.916729i | \(-0.369180\pi\) | ||||
0.399509 | + | 0.916729i | \(0.369180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.15707 | −0.101573 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.2823 | −0.530089 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.04318 | 0.283309 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0052 | −0.655135 | −0.327568 | − | 0.944828i | \(-0.606229\pi\) | ||||
−0.327568 | + | 0.944828i | \(0.606229\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.96822 | 0.278573 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1453 | −0.565663 | −0.282832 | − | 0.959170i | \(-0.591274\pi\) | ||||
−0.282832 | + | 0.959170i | \(0.591274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.4655 | −1.22995 | −0.614977 | − | 0.788545i | \(-0.710835\pi\) | ||||
−0.614977 | + | 0.788545i | \(0.710835\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.22184 | −0.0566613 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8836 | 0.642458 | 0.321229 | − | 0.947002i | \(-0.395904\pi\) | ||||
0.321229 | + | 0.947002i | \(0.395904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.2609 | −1.58202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.8937 | 0.778423 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.14065 | −0.420287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.47355 | −0.251144 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.26873 | −0.241238 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5052 | −0.845525 | −0.422762 | − | 0.906241i | \(-0.638939\pi\) | ||||
−0.422762 | + | 0.906241i | \(0.638939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.3527 | 2.56946 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.76896 | −0.307998 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0365067 | −0.00165768 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.61242 | 0.209009 | 0.104504 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104504 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.9112 | −0.629088 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.71153 | 0.257758 | 0.128879 | − | 0.991660i | \(-0.458862\pi\) | ||||
0.128879 | + | 0.991660i | \(0.458862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.10855 | −0.365191 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.245704 | −0.0110436 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.9605 | 0.491647 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1365 | −0.453773 | −0.226887 | − | 0.973921i | \(-0.572855\pi\) | ||||
−0.226887 | + | 0.973921i | \(0.572855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.3646 | 0.552408 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.93474 | 0.175094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.2773 | −1.25584 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.1486 | −0.848746 | −0.424373 | − | 0.905487i | \(-0.639506\pi\) | ||||
−0.424373 | + | 0.905487i | \(0.639506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.9210 | 1.01397 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12134 | −0.0495085 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.28636 | 0.100749 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.42788 | 0.282698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.5946 | −0.684526 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.0158 | −1.49026 | −0.745129 | − | 0.666920i | \(-0.767612\pi\) | ||||
−0.745129 | + | 0.666920i | \(0.767612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0719 | 1.27123 | 0.635613 | − | 0.772008i | \(-0.280747\pi\) | ||||
0.635613 | + | 0.772008i | \(0.280747\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.3233 | 0.581475 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.1607 | −0.921773 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8499 | −0.732604 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.02996 | 0.391867 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.4373 | 0.841924 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.90014 | 0.125384 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.6541 | 0.675522 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.320900 | −0.0138221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1986 | −0.954394 | −0.477197 | − | 0.878796i | \(-0.658347\pi\) | ||||
−0.477197 | + | 0.878796i | \(0.658347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.78808 | 0.291304 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.35567 | −0.0580703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3015 | 0.996298 | 0.498149 | − | 0.867091i | \(-0.334013\pi\) | ||||
0.498149 | + | 0.867091i | \(0.334013\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.78442 | 0.332231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.52348 | 0.0649024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.45389 | −0.146874 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.02265 | −0.128304 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.5058 | 0.487515 | 0.243757 | − | 0.969836i | \(-0.421620\pi\) | ||||
0.243757 | + | 0.969836i | \(0.421620\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 82.3662 | 3.48372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.25529 | −0.179658 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.72703 | 0.0727857 | 0.0363928 | − | 0.999338i | \(-0.488413\pi\) | ||||
0.0363928 | + | 0.999338i | \(0.488413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.18911 | 0.176237 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.72948 | 0.114627 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.1662 | 0.426189 | 0.213094 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213094 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.2680 | −0.555248 | −0.277624 | − | 0.960690i | \(-0.589547\pi\) | ||||
−0.277624 | + | 0.960690i | \(0.589547\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.54867 | −0.0646968 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.1052 | −0.504822 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.0954 | 1.41941 | 0.709705 | − | 0.704499i | \(-0.248828\pi\) | ||||
0.709705 | + | 0.704499i | \(0.248828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.2987 | −0.802025 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.9315 | −1.65664 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.75655 | 0.155581 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.21404 | 0.0915392 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.0120 | −1.52765 | −0.763824 | − | 0.645424i | \(-0.776681\pi\) | ||||
−0.763824 | + | 0.645424i | \(0.776681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.97578 | 0.163819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.1837 | −0.789112 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8805 | 0.487874 | 0.243937 | − | 0.969791i | \(-0.421561\pi\) | ||||
0.243937 | + | 0.969791i | \(0.421561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.61377 | −0.230142 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.04744 | −0.329360 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.09978 | 0.0857947 | 0.0428973 | − | 0.999079i | \(-0.486341\pi\) | ||||
0.0428973 | + | 0.999079i | \(0.486341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3572 | 0.748805 | 0.374403 | − | 0.927266i | \(-0.377848\pi\) | ||||
0.374403 | + | 0.927266i | \(0.377848\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.5521 | −0.511163 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.61554 | −0.146992 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.34608 | 0.0546357 | 0.0273178 | − | 0.999627i | \(-0.491303\pi\) | ||||
0.0273178 | + | 0.999627i | \(0.491303\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.70833 | −0.150269 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −57.9215 | −2.34325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.540113 | −0.0218149 | −0.0109075 | − | 0.999941i | \(-0.503472\pi\) | ||||
−0.0109075 | + | 0.999941i | \(0.503472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.04258 | −0.0420409 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.6285 | −1.23306 | −0.616529 | − | 0.787332i | \(-0.711462\pi\) | ||||
−0.616529 | + | 0.787332i | \(0.711462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.4834 | 0.702718 | 0.351359 | − | 0.936241i | \(-0.385720\pi\) | ||||
0.351359 | + | 0.936241i | \(0.385720\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.47994 | −0.0995166 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.746663 | 0.0299144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2328 | 0.929310 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.799507 | 0.0319292 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.3485 | −2.08727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0691 | 1.35627 | 0.678134 | − | 0.734938i | \(-0.262789\pi\) | ||||
0.678134 | + | 0.734938i | \(0.262789\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.3451 | 0.649659 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.21834 | −0.167400 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.89162 | 0.114570 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.01561 | 0.158855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.3734 | 1.83164 | 0.915820 | − | 0.401589i | \(-0.131542\pi\) | ||||
0.915820 | + | 0.401589i | \(0.131542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.2735 | −0.838946 | −0.419473 | − | 0.907768i | \(-0.637785\pi\) | ||||
−0.419473 | + | 0.907768i | \(0.637785\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.41796 | −0.173957 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.69695 | 0.223970 | 0.111985 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111985 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.43828 | −0.252724 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.67753 | −0.379292 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.03281 | 0.196949 | 0.0984746 | − | 0.995140i | \(-0.468604\pi\) | ||||
0.0984746 | + | 0.995140i | \(0.468604\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.98652 | −0.155766 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.39756 | 0.327620 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.44130 | 0.0561449 | 0.0280725 | − | 0.999606i | \(-0.491063\pi\) | ||||
0.0280725 | + | 0.999606i | \(0.491063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.7236 | 1.70065 | 0.850325 | − | 0.526259i | \(-0.176406\pi\) | ||||
0.850325 | + | 0.526259i | \(0.176406\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 38.3443 | 1.48917 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.05475 | 0.0409013 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.36930 | 0.130460 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.6754 | 0.412735 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.55022 | −0.214264 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6739 | 0.796922 | 0.398461 | − | 0.917185i | \(-0.369544\pi\) | ||||
0.398461 | + | 0.917185i | \(0.369544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.88124 | 0.187879 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.8278 | −0.685177 | −0.342588 | − | 0.939486i | \(-0.611304\pi\) | ||||
−0.342588 | + | 0.939486i | \(0.611304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.289150 | −0.0110966 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.7335 | −1.06275 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.7317 | −1.21418 | −0.607090 | − | 0.794633i | \(-0.707663\pi\) | ||||
−0.607090 | + | 0.794633i | \(0.707663\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.98769 | −0.266986 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.99849 | −0.114399 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.8502 | −1.28959 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2469 | 0.618060 | 0.309030 | − | 0.951052i | \(-0.399996\pi\) | ||||
0.309030 | + | 0.951052i | \(0.399996\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.94610 | −0.0739261 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.236689 | 0.00897812 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0562 | −0.683927 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.0232 | −0.643877 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.0334 | −0.643343 | −0.321671 | − | 0.946851i | \(-0.604245\pi\) | ||||
−0.321671 | + | 0.946851i | \(0.604245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.83552 | 0.370954 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.10680 | 0.117009 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.1650 | 1.17208 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.3174 | 1.73949 | 0.869743 | − | 0.493506i | \(-0.164285\pi\) | ||||
0.869743 | + | 0.493506i | \(0.164285\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.26540 | −0.0474563 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.79276 | 0.329292 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.57859 | −0.0590359 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.5646 | 0.730655 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.2054 | 1.61129 | 0.805645 | − | 0.592398i | \(-0.201819\pi\) | ||||
0.805645 | + | 0.592398i | \(0.201819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1091 | 0.674417 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.6987 | −0.695413 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.63176 | −0.246297 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7377 | 0.398239 | 0.199119 | − | 0.979975i | \(-0.436192\pi\) | ||||
0.199119 | + | 0.979975i | \(0.436192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −76.5135 | −2.82995 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3161 | −1.23056 | −0.615279 | − | 0.788309i | \(-0.710957\pi\) | ||||
−0.615279 | + | 0.788309i | \(0.710957\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.155101 | −0.00572099 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.94956 | 0.329661 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.76650 | −0.0649818 | −0.0324909 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324909 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.20434 | −0.264658 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.5339 | −1.19355 | −0.596777 | − | 0.802407i | \(-0.703552\pi\) | ||||
−0.596777 | + | 0.802407i | \(0.703552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.05822 | 0.0387701 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.6297 | −0.535272 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.9705 | 0.839324 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.28617 | 0.229386 | 0.114693 | − | 0.993401i | \(-0.463412\pi\) | ||||
0.114693 | + | 0.993401i | \(0.463412\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.722458 | −0.0263278 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.88801 | 0.141499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.0233 | −1.05487 | −0.527436 | − | 0.849595i | \(-0.676846\pi\) | ||||
−0.527436 | + | 0.849595i | \(0.676846\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.76817 | 0.0641807 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3405 | −0.954842 | −0.477421 | − | 0.878675i | \(-0.658428\pi\) | ||||
−0.477421 | + | 0.878675i | \(0.658428\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7375 | −0.388724 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.05672 | −0.0743607 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.0152 | 2.09481 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.44239 | −0.304440 | −0.152220 | − | 0.988347i | \(-0.548642\pi\) | ||||
−0.152220 | + | 0.988347i | \(0.548642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.73334 | −0.350538 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.6881 | −0.492326 | −0.246163 | − | 0.969228i | \(-0.579170\pi\) | ||||
−0.246163 | + | 0.969228i | \(0.579170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3067 | −0.621675 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.9408 | −0.858873 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.39250 | 0.121549 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.86309 | −0.102449 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.35862 | −0.0485532 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.82177 | −0.207788 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9696 | 0.676194 | 0.338097 | − | 0.941111i | \(-0.390217\pi\) | ||||
0.338097 | + | 0.941111i | \(0.390217\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.8101 | −0.562856 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.1797 | 1.17974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.0129 | 1.77601 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.81566 | 0.0643949 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.2355 | −0.362560 | −0.181280 | − | 0.983432i | \(-0.558024\pi\) | ||||
−0.181280 | + | 0.983432i | \(0.558024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.8058 | 1.90351 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.273555 | 0.00966558 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.98738 | −0.211290 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.33266 | 0.0822154 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.54823 | −0.265710 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.2622 | 1.06396 | 0.531981 | − | 0.846757i | \(-0.321448\pi\) | ||||
0.531981 | + | 0.846757i | \(0.321448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.57459 | −0.160636 | −0.0803178 | − | 0.996769i | \(-0.525594\pi\) | ||||
−0.0803178 | + | 0.996769i | \(0.525594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.83611 | −0.0994668 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.79397 | 0.167925 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.3758 | 0.502945 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.5362 | 0.612765 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.9805 | 1.22083 | 0.610414 | − | 0.792083i | \(-0.291003\pi\) | ||||
0.610414 | + | 0.792083i | \(0.291003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.4259 | −1.47887 | −0.739437 | − | 0.673226i | \(-0.764908\pi\) | ||||
−0.739437 | + | 0.673226i | \(0.764908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.48028 | −0.121168 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.0267 | −1.18323 | −0.591613 | − | 0.806222i | \(-0.701509\pi\) | ||||
−0.591613 | + | 0.806222i | \(0.701509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.9270 | −0.900480 | −0.450240 | − | 0.892908i | \(-0.648662\pi\) | ||||
−0.450240 | + | 0.892908i | \(0.648662\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.975302 | −0.0338329 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.68615 | −0.0930697 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.26096 | −0.147457 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.54555 | −0.122552 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.7262 | −1.44055 | −0.720275 | − | 0.693689i | \(-0.755984\pi\) | ||||
−0.720275 | + | 0.693689i | \(0.755984\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1541 | −0.936350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.6666 | −0.815121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.74469 | 0.335227 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.6368 | −0.983971 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.46571 | 0.153263 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.7521 | 0.745651 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.4001 | 0.869682 | 0.434841 | − | 0.900507i | \(-0.356805\pi\) | ||||
0.434841 | + | 0.900507i | \(0.356805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.386427 | 0.0132155 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.5988 | −0.396207 | −0.198103 | − | 0.980181i | \(-0.563478\pi\) | ||||
−0.198103 | + | 0.980181i | \(0.563478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4999 | 0.597088 | 0.298544 | − | 0.954396i | \(-0.403499\pi\) | ||||
0.298544 | + | 0.954396i | \(0.403499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.25774 | −0.281423 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.8457 | 0.913839 | 0.456920 | − | 0.889508i | \(-0.348953\pi\) | ||||
0.456920 | + | 0.889508i | \(0.348953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.37406 | 0.182724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6197 | −0.632358 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.902220 | 0.0306057 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −80.6443 | −2.73253 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.105936 | −0.00358538 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.29440 | −0.314208 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.1483 | 1.69339 | 0.846693 | − | 0.532081i | \(-0.178590\pi\) | ||||
0.846693 | + | 0.532081i | \(0.178590\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.1854 | −0.680836 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.651404 | −0.0219464 | −0.0109732 | − | 0.999940i | \(-0.503493\pi\) | ||||
−0.0109732 | + | 0.999940i | \(0.503493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.1415 | −1.85566 | −0.927829 | − | 0.373006i | \(-0.878327\pi\) | ||||
−0.927829 | + | 0.373006i | \(0.878327\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.11182 | −0.104603 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.78991 | 0.261560 | 0.130780 | − | 0.991411i | \(-0.458252\pi\) | ||||
0.130780 | + | 0.991411i | \(0.458252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.4113 | −1.12058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.712991 | −0.0238861 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.1093 | −0.338296 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.39456 | −0.180320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.9330 | −0.531987 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.81706 | 0.160658 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.4449 | 1.04758 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −34.9924 | −1.16447 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.33925 | −0.0777592 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.3796 | −1.07515 | −0.537574 | − | 0.843216i | \(-0.680659\pi\) | ||||
−0.537574 | + | 0.843216i | \(0.680659\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4179 | 0.378708 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.11484 | −0.268857 | −0.134428 | − | 0.990923i | \(-0.542920\pi\) | ||||
−0.134428 | + | 0.990923i | \(0.542920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4308 | 0.345210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.68260 | −0.0886840 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.5752 | −1.04270 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.5173 | −1.50148 | −0.750738 | − | 0.660600i | \(-0.770302\pi\) | ||||
−0.750738 | + | 0.660600i | \(0.770302\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.34238 | 0.143086 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.7993 | 0.849193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.8144 | −1.40773 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.63462 | 0.217909 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53.3233 | 1.74948 | 0.874741 | − | 0.484591i | \(-0.161031\pi\) | ||||
0.874741 | + | 0.484591i | \(0.161031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.504689 | 0.0165405 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.9026 | −0.487888 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.46642 | 0.0479570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.8542 | 0.746613 | 0.373306 | − | 0.927708i | \(-0.378224\pi\) | ||||
0.373306 | + | 0.927708i | \(0.378224\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.43464 | −0.209987 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.8691 | −1.07150 | −0.535751 | − | 0.844376i | \(-0.679972\pi\) | ||||
−0.535751 | + | 0.844376i | \(0.679972\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.50278 | 0.244324 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.940610 | −0.0305980 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.0958 | −1.49791 | −0.748956 | − | 0.662619i | \(-0.769445\pi\) | ||||
−0.748956 | + | 0.662619i | \(0.769445\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.9522 | 1.75136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.9271 | −0.711036 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.9711 | 1.06804 | 0.534020 | − | 0.845472i | \(-0.320681\pi\) | ||||
0.534020 | + | 0.845472i | \(0.320681\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.533690 | 0.0172698 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.968684 | 0.0313131 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −55.3458 | −1.78721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4291 | −0.594486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.41570 | 0.271192 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.65054 | 0.214088 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8857 | −0.928902 | −0.464451 | − | 0.885599i | \(-0.653748\pi\) | ||||
−0.464451 | + | 0.885599i | \(0.653748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.69242 | 0.214992 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.4882 | −1.29933 | −0.649664 | − | 0.760222i | \(-0.725090\pi\) | ||||
−0.649664 | + | 0.760222i | \(0.725090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.87469 | 0.0600998 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 31.3607 | 1.00435 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0252 | −0.960592 | −0.480296 | − | 0.877106i | \(-0.659471\pi\) | ||||
−0.480296 | + | 0.877106i | \(0.659471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.195042 | −0.00623357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.93390 | −0.125600 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.5180 | −1.73886 | −0.869428 | − | 0.494060i | \(-0.835512\pi\) | ||||
−0.869428 | + | 0.494060i | \(0.835512\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.61092 | 0.210641 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.6073 | 0.783260 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.7932 | 1.01097 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.08348 | −0.0979500 | −0.0489750 | − | 0.998800i | \(-0.515595\pi\) | ||||
−0.0489750 | + | 0.998800i | \(0.515595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.36105 | −0.265330 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.77324 | 0.0879176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.8492 | 1.29371 | 0.646853 | − | 0.762615i | \(-0.276085\pi\) | ||||
0.646853 | + | 0.762615i | \(0.276085\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.77120 | −0.277509 |
(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 | 6036.2.a.i.1.14 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.14 | ✓ | 26 | 1.1 | even | 1 | trivial |