Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −1.48695 | −0.858492 | −0.429246 | − | 0.903188i | \(-0.641221\pi\) | ||||
−0.429246 | + | 0.903188i | \(0.641221\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.53428 | −1.33583 | −0.667916 | − | 0.744236i | \(-0.732814\pi\) | ||||
−0.667916 | + | 0.744236i | \(0.732814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.788974 | −0.262991 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.193476 | −0.0583351 | −0.0291675 | − | 0.999575i | \(-0.509286\pi\) | ||||
−0.0291675 | + | 0.999575i | \(0.509286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.78611 | −0.495379 | −0.247689 | − | 0.968839i | \(-0.579671\pi\) | ||||
−0.247689 | + | 0.968839i | \(0.579671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.48695 | 0.383929 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.112625 | 0.0273156 | 0.0136578 | − | 0.999907i | \(-0.495652\pi\) | ||||
0.0136578 | + | 0.999907i | \(0.495652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.44633 | −0.331812 | −0.165906 | − | 0.986142i | \(-0.553055\pi\) | ||||
−0.165906 | + | 0.986142i | \(0.553055\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.25531 | 1.14680 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.37160 | 1.53708 | 0.768542 | − | 0.639799i | \(-0.220982\pi\) | ||||
0.768542 | + | 0.639799i | \(0.220982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63402 | 1.08427 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.99452 | −0.370372 | −0.185186 | − | 0.982703i | \(-0.559289\pi\) | ||||
−0.185186 | + | 0.982703i | \(0.559289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.75759 | −0.495277 | −0.247639 | − | 0.968852i | \(-0.579655\pi\) | ||||
−0.247639 | + | 0.968852i | \(0.579655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.287689 | 0.0500802 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.53428 | 0.597403 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.38909 | −0.885961 | −0.442980 | − | 0.896531i | \(-0.646079\pi\) | ||||
−0.442980 | + | 0.896531i | \(0.646079\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.65587 | 0.425279 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.08586 | 1.41897 | 0.709487 | − | 0.704719i | \(-0.248927\pi\) | ||||
0.709487 | + | 0.704719i | \(0.248927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.95947 | 1.21381 | 0.606904 | − | 0.794775i | \(-0.292411\pi\) | ||||
0.606904 | + | 0.794775i | \(0.292411\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.788974 | 0.117613 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.63499 | −1.40541 | −0.702704 | − | 0.711483i | \(-0.748024\pi\) | ||||
−0.702704 | + | 0.711483i | \(0.748024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.49115 | 0.784449 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.167468 | −0.0234502 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.21869 | 0.167400 | 0.0836999 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0836999 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.193476 | 0.0260882 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.15063 | 0.284858 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.20935 | −0.548010 | −0.274005 | − | 0.961728i | \(-0.588348\pi\) | ||||
−0.274005 | + | 0.961728i | \(0.588348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.14882 | 0.787276 | 0.393638 | − | 0.919266i | \(-0.371216\pi\) | ||||
0.393638 | + | 0.919266i | \(0.371216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.78846 | 0.351313 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.78611 | 0.221540 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.98383 | 1.09755 | 0.548775 | − | 0.835970i | \(-0.315094\pi\) | ||||
0.548775 | + | 0.835970i | \(0.315094\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.9612 | −1.31957 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.09651 | −0.842201 | −0.421100 | − | 0.907014i | \(-0.638356\pi\) | ||||
−0.421100 | + | 0.907014i | \(0.638356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1077 | 1.30006 | 0.650029 | − | 0.759909i | \(-0.274757\pi\) | ||||
0.650029 | + | 0.759909i | \(0.274757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.48695 | −0.171698 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.683797 | 0.0779259 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.03284 | 0.566239 | 0.283119 | − | 0.959085i | \(-0.408631\pi\) | ||||
0.283119 | + | 0.959085i | \(0.408631\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.01060 | −0.667844 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.2788 | 1.45753 | 0.728767 | − | 0.684762i | \(-0.240094\pi\) | ||||
0.728767 | + | 0.684762i | \(0.240094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.112625 | −0.0122159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.96575 | 0.317962 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2676 | 1.72436 | 0.862179 | − | 0.506603i | \(-0.169099\pi\) | ||||
0.862179 | + | 0.506603i | \(0.169099\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.31263 | 0.661743 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.10040 | 0.425192 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.44633 | 0.148391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.48853 | −0.658810 | −0.329405 | − | 0.944189i | \(-0.606848\pi\) | ||||
−0.329405 | + | 0.944189i | \(0.606848\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.152647 | 0.0153416 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5189 | −1.34518 | −0.672590 | − | 0.740015i | \(-0.734818\pi\) | ||||
−0.672590 | + | 0.740015i | \(0.734818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.98880 | 0.393028 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.25531 | −0.512865 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.98727 | 0.675485 | 0.337742 | − | 0.941239i | \(-0.390337\pi\) | ||||
0.337742 | + | 0.941239i | \(0.390337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.01805 | −0.384860 | −0.192430 | − | 0.981311i | \(-0.561637\pi\) | ||||
−0.192430 | + | 0.981311i | \(0.561637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.01331 | 0.760590 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.47938 | −0.421384 | −0.210692 | − | 0.977552i | \(-0.567572\pi\) | ||||
−0.210692 | + | 0.977552i | \(0.567572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.37160 | −0.687405 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.40920 | 0.130280 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.398049 | −0.0364891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9626 | −0.996597 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.5102 | −1.21818 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.8211 | −1.22643 | −0.613213 | − | 0.789918i | \(-0.710123\pi\) | ||||
−0.613213 | + | 0.789918i | \(0.710123\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.8353 | −1.04204 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.38722 | 0.121202 | 0.0606012 | − | 0.998162i | \(-0.480698\pi\) | ||||
0.0606012 | + | 0.998162i | \(0.480698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.11175 | 0.443245 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.63402 | −0.484899 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4983 | 1.66585 | 0.832926 | − | 0.553385i | \(-0.186664\pi\) | ||||
0.832926 | + | 0.553385i | \(0.186664\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9114 | 1.51922 | 0.759611 | − | 0.650378i | \(-0.225389\pi\) | ||||
0.759611 | + | 0.650378i | \(0.225389\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.3268 | 1.20653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.345569 | 0.0288980 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99452 | 0.165636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.16507 | −0.673444 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.3947 | −1.17926 | −0.589629 | − | 0.807674i | \(-0.700726\pi\) | ||||
−0.589629 | + | 0.807674i | \(0.700726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.5542 | −1.42854 | −0.714269 | − | 0.699872i | \(-0.753241\pi\) | ||||
−0.714269 | + | 0.699872i | \(0.753241\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0888583 | −0.00718377 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.75759 | 0.221495 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.777288 | −0.0620343 | −0.0310172 | − | 0.999519i | \(-0.509875\pi\) | ||||
−0.0310172 | + | 0.999519i | \(0.509875\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.81213 | −0.143711 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.0533 | −2.05329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.1267 | −1.18481 | −0.592405 | − | 0.805640i | \(-0.701822\pi\) | ||||
−0.592405 | + | 0.805640i | \(0.701822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.287689 | −0.0223966 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.0767 | −1.32143 | −0.660717 | − | 0.750635i | \(-0.729748\pi\) | ||||
−0.660717 | + | 0.750635i | \(0.729748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.80980 | −0.754600 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14112 | 0.0872637 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.50041 | 0.418189 | 0.209094 | − | 0.977895i | \(-0.432948\pi\) | ||||
0.209094 | + | 0.977895i | \(0.432948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.53428 | −0.267167 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.25909 | 0.470462 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.0063 | 1.71957 | 0.859787 | − | 0.510652i | \(-0.170596\pi\) | ||||
0.859787 | + | 0.510652i | \(0.170596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5892 | −1.08441 | −0.542204 | − | 0.840247i | \(-0.682410\pi\) | ||||
−0.542204 | + | 0.840247i | \(0.682410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.14300 | −0.675870 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.38909 | 0.396214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0217902 | −0.00159346 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.9122 | −1.44840 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.7289 | 1.35518 | 0.677588 | − | 0.735442i | \(-0.263025\pi\) | ||||
0.677588 | + | 0.735442i | \(0.263025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.04939 | 0.363463 | 0.181731 | − | 0.983348i | \(-0.441830\pi\) | ||||
0.181731 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.65587 | −0.190190 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.5642 | 1.18015 | 0.590075 | − | 0.807348i | \(-0.299098\pi\) | ||||
0.590075 | + | 0.807348i | \(0.299098\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.77860 | −0.267858 | −0.133929 | − | 0.990991i | \(-0.542759\pi\) | ||||
−0.133929 | + | 0.990991i | \(0.542759\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.3585 | −0.942238 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.04918 | 0.494756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.08586 | −0.634584 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.81600 | −0.404240 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.279830 | 0.0193563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0139 | −1.72203 | −0.861013 | − | 0.508583i | \(-0.830169\pi\) | ||||
−0.861013 | + | 0.508583i | \(0.830169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.5522 | 0.723022 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.95947 | −0.542831 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.74609 | 0.661608 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.5166 | −1.11609 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.201161 | −0.0135316 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.64801 | 0.311254 | 0.155627 | − | 0.987816i | \(-0.450260\pi\) | ||||
0.155627 | + | 0.987816i | \(0.450260\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.788974 | −0.0525983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.26965 | 0.615248 | 0.307624 | − | 0.951508i | \(-0.400466\pi\) | ||||
0.307624 | + | 0.951508i | \(0.400466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.5492 | −1.22577 | −0.612883 | − | 0.790174i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790174i | \(0.709990\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.01677 | −0.0668988 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0707 | −1.18385 | −0.591925 | − | 0.805993i | \(-0.701632\pi\) | ||||
−0.591925 | + | 0.805993i | \(0.701632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.63499 | 0.628517 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.48359 | −0.486111 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1329 | 1.23761 | 0.618804 | − | 0.785546i | \(-0.287618\pi\) | ||||
0.618804 | + | 0.785546i | \(0.287618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.6502 | −0.750454 | −0.375227 | − | 0.926933i | \(-0.622435\pi\) | ||||
−0.375227 | + | 0.926933i | \(0.622435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.96460 | −0.510929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.49115 | −0.350816 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.58332 | 0.164373 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.7449 | −1.25128 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.1082 | 1.20610 | 0.603050 | − | 0.797703i | \(-0.293952\pi\) | ||||
0.603050 | + | 0.797703i | \(0.293952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.42622 | −0.0896660 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.167468 | 0.0104873 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.1419 | −0.944527 | −0.472263 | − | 0.881458i | \(-0.656563\pi\) | ||||
−0.472263 | + | 0.881458i | \(0.656563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.0466 | 1.18350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.57362 | 0.0974048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.07163 | 0.374393 | 0.187196 | − | 0.982323i | \(-0.440060\pi\) | ||||
0.187196 | + | 0.982323i | \(0.440060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.21869 | −0.0748635 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.1891 | −1.48035 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.96215 | −0.546432 | −0.273216 | − | 0.961953i | \(-0.588087\pi\) | ||||
−0.273216 | + | 0.961953i | \(0.588087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.54580 | −0.458375 | −0.229187 | − | 0.973382i | \(-0.573607\pi\) | ||||
−0.229187 | + | 0.973382i | \(0.573607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.38658 | −0.568101 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.193476 | −0.0116670 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.84641 | −0.471445 | −0.235722 | − | 0.971820i | \(-0.575746\pi\) | ||||
−0.235722 | + | 0.971820i | \(0.575746\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.17567 | 0.130254 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.57281 | 0.571066 | 0.285533 | − | 0.958369i | \(-0.407829\pi\) | ||||
0.285533 | + | 0.958369i | \(0.407829\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.3180 | −0.851117 | −0.425559 | − | 0.904931i | \(-0.639922\pi\) | ||||
−0.425559 | + | 0.904931i | \(0.639922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.15063 | −0.127392 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32.1120 | −1.89551 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9873 | −0.999254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.64812 | 0.565583 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.431624 | −0.0252158 | −0.0126079 | − | 0.999921i | \(-0.504013\pi\) | ||||
−0.0126079 | + | 0.999921i | \(0.504013\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.20935 | 0.245078 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.09005 | −0.0632509 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.1665 | −0.761439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.1310 | −1.62144 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.1019 | 1.15483 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.14882 | −0.352080 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.5282 | 1.74234 | 0.871169 | − | 0.490983i | \(-0.163362\pi\) | ||||
0.871169 | + | 0.490983i | \(0.163362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.93116 | −0.337412 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.45876 | 0.196128 | 0.0980642 | − | 0.995180i | \(-0.468735\pi\) | ||||
0.0980642 | + | 0.995180i | \(0.468735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.74163 | −0.154966 | −0.0774829 | − | 0.996994i | \(-0.524688\pi\) | ||||
−0.0774829 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.78846 | −0.157112 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.42548 | −0.248560 | −0.124280 | − | 0.992247i | \(-0.539662\pi\) | ||||
−0.124280 | + | 0.992247i | \(0.539662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.385890 | 0.0216057 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3897 | −0.579898 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.162894 | −0.00906364 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.78611 | −0.0990758 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.97465 | 0.330399 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.0528 | 1.87739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.28540 | −0.180582 | −0.0902910 | − | 0.995915i | \(-0.528780\pi\) | ||||
−0.0902910 | + | 0.995915i | \(0.528780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.25185 | 0.233000 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.98383 | −0.490839 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.70217 | −0.0927231 | −0.0463616 | − | 0.998925i | \(-0.514763\pi\) | ||||
−0.0463616 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.66062 | 0.361755 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.533526 | 0.0288921 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.33271 | 0.287939 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.9612 | 0.590132 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1025 | 1.07916 | 0.539579 | − | 0.841935i | \(-0.318583\pi\) | ||||
0.539579 | + | 0.841935i | \(0.318583\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2275 | −0.922165 | −0.461082 | − | 0.887357i | \(-0.652539\pi\) | ||||
−0.461082 | + | 0.887357i | \(0.652539\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0630 | −0.537123 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.0409 | −1.33279 | −0.666397 | − | 0.745597i | \(-0.732164\pi\) | ||||
−0.666397 | + | 0.745597i | \(0.732164\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.09651 | 0.376644 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.591880 | 0.0313256 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.3525 | 1.12694 | 0.563471 | − | 0.826136i | \(-0.309466\pi\) | ||||
0.563471 | + | 0.826136i | \(0.309466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9081 | −0.889901 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.3008 | 0.855571 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.1077 | −0.581404 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.3382 | 1.53144 | 0.765721 | − | 0.643173i | \(-0.222382\pi\) | ||||
0.765721 | + | 0.643173i | \(0.222382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.16851 | −0.373178 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.30719 | −0.223618 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3750 | −0.847866 | −0.423933 | − | 0.905694i | \(-0.639351\pi\) | ||||
−0.423933 | + | 0.905694i | \(0.639351\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.48695 | 0.0767859 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.56243 | 0.183475 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1622 | 0.624729 | 0.312365 | − | 0.949962i | \(-0.398879\pi\) | ||||
0.312365 | + | 0.949962i | \(0.398879\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.5513 | 1.05288 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.7095 | 1.72247 | 0.861237 | − | 0.508204i | \(-0.169690\pi\) | ||||
0.861237 | + | 0.508204i | \(0.169690\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.683797 | −0.0348495 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.27982 | −0.319221 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.2394 | −1.07688 | −0.538441 | − | 0.842663i | \(-0.680987\pi\) | ||||
−0.538441 | + | 0.842663i | \(0.680987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.830227 | 0.0419864 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.06274 | −0.104051 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.03284 | −0.253230 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.7491 | 1.64363 | 0.821814 | − | 0.569756i | \(-0.192962\pi\) | ||||
0.821814 | + | 0.569756i | \(0.192962\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.60093 | −0.380522 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.92537 | 0.245350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.01060 | 0.298669 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.04266 | 0.0516826 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.0172 | −1.03924 | −0.519618 | − | 0.854399i | \(-0.673926\pi\) | ||||
−0.519618 | + | 0.854399i | \(0.673926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.9930 | −1.43012 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8770 | 0.732050 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.2788 | −0.651829 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.6333 | −1.30424 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.3818 | −1.87507 | −0.937536 | − | 0.347889i | \(-0.886899\pi\) | ||||
−0.937536 | + | 0.347889i | \(0.886899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.3134 | 1.37991 | 0.689955 | − | 0.723853i | \(-0.257631\pi\) | ||||
0.689955 | + | 0.723853i | \(0.257631\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.60176 | 0.369610 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.112625 | 0.00546312 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7317 | −1.05167 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.513845 | −0.0248087 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.6760 | −1.86296 | −0.931480 | − | 0.363793i | \(-0.881482\pi\) | ||||
−0.931480 | + | 0.363793i | \(0.881482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.4278 | 1.17393 | 0.586963 | − | 0.809613i | \(-0.300323\pi\) | ||||
0.586963 | + | 0.809613i | \(0.300323\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.96575 | −0.142197 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.6618 | −0.510023 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8409 | −0.899226 | −0.449613 | − | 0.893223i | \(-0.648438\pi\) | ||||
−0.449613 | + | 0.893223i | \(0.648438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.33237 | −0.206304 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2871 | −0.821333 | −0.410666 | − | 0.911786i | \(-0.634704\pi\) | ||||
−0.410666 | + | 0.911786i | \(0.634704\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.2676 | −0.771157 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.4042 | 1.01238 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.9137 | −0.892594 | −0.446297 | − | 0.894885i | \(-0.647258\pi\) | ||||
−0.446297 | + | 0.894885i | \(0.647258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.75789 | −0.0827760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.1022 | 1.22639 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.31263 | −0.295941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.8322 | −1.34871 | −0.674357 | − | 0.738406i | \(-0.735579\pi\) | ||||
−0.674357 | + | 0.738406i | \(0.735579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.634533 | 0.0296174 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.8142 | −1.85433 | −0.927167 | − | 0.374649i | \(-0.877763\pi\) | ||||
−0.927167 | + | 0.374649i | \(0.877763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.38144 | 0.203623 | 0.101811 | − | 0.994804i | \(-0.467536\pi\) | ||||
0.101811 | + | 0.994804i | \(0.467536\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.10040 | −0.190151 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.6136 | −0.537414 | −0.268707 | − | 0.963222i | \(-0.586596\pi\) | ||||
−0.268707 | + | 0.963222i | \(0.586596\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.7514 | −1.46614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.15579 | 0.0532560 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.53996 | −0.0708076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.44633 | −0.0663623 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.961515 | −0.0440247 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6284 | 0.485624 | 0.242812 | − | 0.970073i | \(-0.421930\pi\) | ||||
0.242812 | + | 0.970073i | \(0.421930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.62552 | 0.438886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.7400 | 1.76273 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.48853 | 0.294629 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.50656 | 0.0682686 | 0.0341343 | − | 0.999417i | \(-0.489133\pi\) | ||||
0.0341343 | + | 0.999417i | \(0.489133\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.4926 | 1.01715 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.0549 | −1.62714 | −0.813568 | − | 0.581470i | \(-0.802478\pi\) | ||||
−0.813568 | + | 0.581470i | \(0.802478\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.224633 | −0.0101169 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.152647 | −0.00686099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.0811 | 1.12504 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.62024 | 0.162064 | 0.0810322 | − | 0.996711i | \(-0.474178\pi\) | ||||
0.0810322 | + | 0.996711i | \(0.474178\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.3922 | 1.13444 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.4027 | 0.642183 | 0.321091 | − | 0.947048i | \(-0.395950\pi\) | ||||
0.321091 | + | 0.947048i | \(0.395950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5189 | 0.601583 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.5867 | 0.647818 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.4384 | 0.462676 | 0.231338 | − | 0.972873i | \(-0.425690\pi\) | ||||
0.231338 | + | 0.972873i | \(0.425690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.2577 | −1.73666 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.14868 | −0.359773 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.98880 | −0.175768 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.86414 | 0.0819846 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.17885 | −0.359012 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0504 | −0.659371 | −0.329686 | − | 0.944091i | \(-0.606943\pi\) | ||||
−0.329686 | + | 0.944091i | \(0.606943\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.23145 | 0.403663 | 0.201832 | − | 0.979420i | \(-0.435311\pi\) | ||||
0.201832 | + | 0.979420i | \(0.435311\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.25531 | 0.229360 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.310574 | −0.0135288 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.3405 | 1.36263 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.32107 | 0.144122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.2284 | −0.702929 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.98727 | −0.302086 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.2093 | −1.47624 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.06240 | −0.0457609 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.6894 | −0.975493 | −0.487747 | − | 0.872985i | \(-0.662181\pi\) | ||||
−0.487747 | + | 0.872985i | \(0.662181\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.6935 | 0.930956 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.01805 | 0.172114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.94368 | 0.168619 | 0.0843097 | − | 0.996440i | \(-0.473131\pi\) | ||||
0.0843097 | + | 0.996440i | \(0.473131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.85126 | −0.207047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.88474 | 0.122894 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.7875 | −0.756400 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.01331 | −0.340146 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.9761 | 1.48199 | 0.740993 | − | 0.671513i | \(-0.234355\pi\) | ||||
0.740993 | + | 0.671513i | \(0.234355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2165 | −0.601295 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0324010 | 0.00136797 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.6779 | −1.08219 | −0.541096 | − | 0.840961i | \(-0.681991\pi\) | ||||
−0.541096 | + | 0.840961i | \(0.681991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.47938 | 0.188449 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.2431 | 0.892128 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2230 | −1.30893 | −0.654467 | − | 0.756090i | \(-0.727107\pi\) | ||||
−0.654467 | + | 0.756090i | \(0.727107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.98990 | 0.166972 | 0.0834861 | − | 0.996509i | \(-0.473395\pi\) | ||||
0.0834861 | + | 0.996509i | \(0.473395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.8490 | −1.16341 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.37160 | 0.307417 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.20979 | 0.175256 | 0.0876279 | − | 0.996153i | \(-0.472071\pi\) | ||||
0.0876279 | + | 0.996153i | \(0.472071\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.50819 | −0.312030 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.9309 | −1.94702 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.235787 | −0.00976529 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.40920 | −0.0582632 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.3113 | −0.879610 | −0.439805 | − | 0.898093i | \(-0.644952\pi\) | ||||
−0.439805 | + | 0.898093i | \(0.644952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.98839 | 0.164339 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.6302 | −1.01315 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.8757 | −1.18578 | −0.592892 | − | 0.805282i | \(-0.702014\pi\) | ||||
−0.592892 | + | 0.805282i | \(0.702014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.398049 | 0.0163184 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.61860 | 0.229954 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.18410 | −0.130099 | −0.0650494 | − | 0.997882i | \(-0.520721\pi\) | ||||
−0.0650494 | + | 0.997882i | \(0.520721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4009 | 1.19929 | 0.599644 | − | 0.800267i | \(-0.295309\pi\) | ||||
0.599644 | + | 0.800267i | \(0.295309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.08802 | −0.288646 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9626 | 0.445692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0583 | −0.611199 | −0.305600 | − | 0.952160i | \(-0.598857\pi\) | ||||
−0.305600 | + | 0.952160i | \(0.598857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.4818 | −0.424744 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.2092 | 0.696209 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.903071 | −0.0364747 | −0.0182374 | − | 0.999834i | \(-0.505805\pi\) | ||||
−0.0182374 | + | 0.999834i | \(0.505805\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13.5102 | 0.544786 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.3753 | −0.699503 | −0.349751 | − | 0.936843i | \(-0.613734\pi\) | ||||
−0.349751 | + | 0.936843i | \(0.613734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.6595 | −1.07154 | −0.535768 | − | 0.844366i | \(-0.679978\pi\) | ||||
−0.535768 | + | 0.844366i | \(0.679978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 41.5317 | 1.66661 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −57.4942 | −2.30346 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.416094 | −0.0166172 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.606947 | −0.0242006 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.4043 | 1.52885 | 0.764425 | − | 0.644712i | \(-0.223023\pi\) | ||||
0.764425 | + | 0.644712i | \(0.223023\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.1944 | 1.47835 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8211 | 0.548474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.80781 | −0.388600 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.59896 | 0.221492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.3895 | −1.39780 | −0.698901 | − | 0.715219i | \(-0.746327\pi\) | ||||
−0.698901 | + | 0.715219i | \(0.746327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2717 | 0.760000 | 0.380000 | − | 0.924986i | \(-0.375924\pi\) | ||||
0.380000 | + | 0.924986i | \(0.375924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.8353 | 0.466016 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.813647 | 0.0319878 | 0.0159939 | − | 0.999872i | \(-0.494909\pi\) | ||||
0.0159939 | + | 0.999872i | \(0.494909\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.814406 | 0.0319682 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.4920 | −0.567985 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.9370 | −0.701931 | −0.350965 | − | 0.936388i | \(-0.614147\pi\) | ||||
−0.350965 | + | 0.936388i | \(0.614147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.38722 | −0.0542034 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.76369 | −0.341904 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.3867 | −0.755198 | −0.377599 | − | 0.925969i | \(-0.623250\pi\) | ||||
−0.377599 | + | 0.925969i | \(0.623250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3116 | 1.17898 | 0.589491 | − | 0.807775i | \(-0.299328\pi\) | ||||
0.589491 | + | 0.807775i | \(0.299328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.299117 | 0.0116167 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.11175 | −0.198225 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.7028 | −0.569294 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.91137 | −0.267209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.18965 | −0.0459258 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9797 | 1.54110 | 0.770552 | − | 0.637377i | \(-0.219981\pi\) | ||||
0.770552 | + | 0.637377i | \(0.219981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.63402 | 0.216854 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.2058 | 0.776570 | 0.388285 | − | 0.921539i | \(-0.373068\pi\) | ||||
0.388285 | + | 0.921539i | \(0.373068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.9323 | 0.880060 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.7835 | −0.528185 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.0610 | 1.60942 | 0.804709 | − | 0.593670i | \(-0.202321\pi\) | ||||
0.804709 | + | 0.593670i | \(0.202321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.4983 | −0.744992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.5818 | 1.05231 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.17672 | −0.0829263 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9484 | −0.416496 | −0.208248 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208248 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.539499 | −0.0204939 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.9114 | −0.679417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.02330 | 0.0387601 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.8702 | 1.01633 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8360 | 0.560349 | 0.280175 | − | 0.959949i | \(-0.409608\pi\) | ||||
0.280175 | + | 0.959949i | \(0.409608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.79442 | 0.293972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.3268 | −0.539577 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7796 | 1.79694 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2554 | 0.460262 | 0.230131 | − | 0.973160i | \(-0.426085\pi\) | ||||
0.230131 | + | 0.973160i | \(0.426085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.97078 | −0.148916 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.3278 | −0.761283 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.345569 | −0.0129236 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.4498 | −1.06248 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4270 | 0.873678 | 0.436839 | − | 0.899540i | \(-0.356098\pi\) | ||||
0.436839 | + | 0.899540i | \(0.356098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0975 | −0.525020 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.3232 | 0.644258 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.99452 | −0.0740745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9929 | −1.40908 | −0.704540 | − | 0.709664i | \(-0.748847\pi\) | ||||
−0.704540 | + | 0.709664i | \(0.748847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8748 | 1.10647 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.896436 | 0.0331559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.5719 | 1.24001 | 0.620003 | − | 0.784600i | \(-0.287131\pi\) | ||||
0.620003 | + | 0.784600i | \(0.287131\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.16507 | 0.301173 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.73815 | −0.0640257 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1897 | −0.411620 | −0.205810 | − | 0.978592i | \(-0.565983\pi\) | ||||
−0.205810 | + | 0.978592i | \(0.565983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.84127 | −0.141112 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.5552 | 1.01090 | 0.505450 | − | 0.862856i | \(-0.331326\pi\) | ||||
0.505450 | + | 0.862856i | \(0.331326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3947 | 0.527380 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.4766 | −0.383319 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.6950 | −0.902335 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.2253 | −0.592068 | −0.296034 | − | 0.955177i | \(-0.595664\pi\) | ||||
−0.296034 | + | 0.955177i | \(0.595664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.4130 | −1.03543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.5542 | 0.638861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.51887 | 0.164241 | 0.0821206 | − | 0.996622i | \(-0.473831\pi\) | ||||
0.0821206 | + | 0.996622i | \(0.473831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.12073 | 0.0769775 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.0959 | 0.619727 | 0.309864 | − | 0.950781i | \(-0.399717\pi\) | ||||
0.309864 | + | 0.950781i | \(0.399717\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2009 | 0.514108 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0888583 | 0.00321268 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.51837 | 0.271473 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.2230 | 1.41442 | 0.707209 | − | 0.707005i | \(-0.249954\pi\) | ||||
0.707209 | + | 0.707005i | \(0.249954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.5153 | 0.810869 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.9671 | −1.04188 | −0.520938 | − | 0.853595i | \(-0.674418\pi\) | ||||
−0.520938 | + | 0.853595i | \(0.674418\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.75759 | −0.0990555 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.3213 | −1.01602 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.1412 | −0.470832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37300 | 0.0491298 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.2371 | −0.401583 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.777288 | 0.0277426 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.9282 | 1.95798 | 0.978990 | − | 0.203911i | \(-0.0653652\pi\) | ||||
0.978990 | + | 0.203911i | \(0.0653652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.02822 | −0.321413 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.8314 | 0.562899 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9825 | −0.390000 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.81213 | 0.0642697 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.6568 | −1.08592 | −0.542959 | − | 0.839759i | \(-0.682696\pi\) | ||||
−0.542959 | + | 0.839759i | \(0.682696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.08514 | −0.0383896 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8347 | −0.453492 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.14907 | −0.0758390 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.0533 | 0.918258 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.3263 | 0.469108 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.4876 | −1.31799 | −0.658997 | − | 0.752146i | \(-0.729019\pi\) | ||||
−0.658997 | + | 0.752146i | \(0.729019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9039 | 0.944723 | 0.472361 | − | 0.881405i | \(-0.343402\pi\) | ||||
0.472361 | + | 0.881405i | \(0.343402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2202 | 0.393511 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.1267 | 0.529864 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.5121 | −0.402756 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.98050 | −0.174033 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.6042 | −1.90570 | −0.952849 | − | 0.303444i | \(-0.901864\pi\) | ||||
−0.952849 | + | 0.303444i | \(0.901864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.6787 | −1.90598 | −0.952990 | − | 0.303000i | \(-0.902012\pi\) | ||||
−0.952990 | + | 0.303000i | \(0.902012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.287689 | 0.0100160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.35326 | 0.255698 | 0.127849 | − | 0.991794i | \(-0.459193\pi\) | ||||
0.127849 | + | 0.991794i | \(0.459193\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.0723 | 1.46123 | 0.730616 | − | 0.682788i | \(-0.239233\pi\) | ||||
0.730616 | + | 0.682788i | \(0.239233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.6672 | 0.404732 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.618441 | 0.0214277 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.0767 | 0.590963 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.5363 | −0.537013 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.5945 | 1.78124 | 0.890621 | − | 0.454747i | \(-0.150270\pi\) | ||||
0.890621 | + | 0.454747i | \(0.150270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0219 | −0.862824 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.2343 | −0.490256 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.80980 | 0.337467 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.7448 | 1.33129 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.2902 | 0.730678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.7262 | −1.36180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.5634 | 1.66278 | 0.831389 | − | 0.555691i | \(-0.187546\pi\) | ||||
0.831389 | + | 0.555691i | \(0.187546\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14112 | −0.0390255 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.0291 | −1.23073 | −0.615365 | − | 0.788242i | \(-0.710991\pi\) | ||||
−0.615365 | + | 0.788242i | \(0.710991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.9646 | 1.39769 | 0.698846 | − | 0.715272i | \(-0.253697\pi\) | ||||
0.698846 | + | 0.715272i | \(0.253697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 47.7490 | 1.62728 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.6228 | −1.00837 | −0.504186 | − | 0.863595i | \(-0.668207\pi\) | ||||
−0.504186 | + | 0.863595i | \(0.668207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.50041 | −0.187020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.2593 | 0.857851 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.973732 | −0.0330316 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0462 | −0.543703 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.11928 | 0.173261 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.53428 | 0.119481 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.8356 | −0.534730 | −0.267365 | − | 0.963595i | \(-0.586153\pi\) | ||||
−0.267365 | + | 0.963595i | \(0.586153\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.641805 | 0.0216475 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.64366 | 0.257522 | 0.128761 | − | 0.991676i | \(-0.458900\pi\) | ||||
0.128761 | + | 0.991676i | \(0.458900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −55.2861 | −1.86052 | −0.930262 | − | 0.366896i | \(-0.880421\pi\) | ||||
−0.930262 | + | 0.366896i | \(0.880421\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.25909 | −0.210397 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.2402 | −0.713176 | −0.356588 | − | 0.934262i | \(-0.616060\pi\) | ||||
−0.356588 | + | 0.934262i | \(0.616060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.8477 | 1.63830 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.16290 | 0.0389587 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.9354 | 0.466331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.0063 | −0.769017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.5780 | 0.653689 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.50005 | 0.183437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.137255 | 0.00457263 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 41.8295 | 1.39200 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5892 | 0.484962 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.3924 | −1.14198 | −0.570991 | − | 0.820957i | \(-0.693441\pi\) | ||||
−0.570991 | + | 0.820957i | \(0.693441\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6661 | 0.353771 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.0166 | −1.02763 | −0.513814 | − | 0.857902i | \(-0.671768\pi\) | ||||
−0.513814 | + | 0.857902i | \(0.671768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.56912 | −0.0850253 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.14300 | 0.302258 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.90284 | −0.161906 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.6511 | 1.04407 | 0.522037 | − | 0.852923i | \(-0.325172\pi\) | ||||
0.522037 | + | 0.852923i | \(0.325172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.3940 | −1.49578 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.6752 | 0.417208 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.38909 | −0.177192 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.14706 | −0.103363 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.4108 | 1.39145 | 0.695726 | − | 0.718307i | \(-0.255083\pi\) | ||||
0.695726 | + | 0.718307i | \(0.255083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.94203 | −0.260290 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.14301 | −0.168375 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0217902 | 0.000712616 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.0283 | −0.425615 | −0.212807 | − | 0.977094i | \(-0.568261\pi\) | ||||
−0.212807 | + | 0.977094i | \(0.568261\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.07667 | 0.133037 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.8993 | −1.03989 | −0.519944 | − | 0.854201i | \(-0.674047\pi\) | ||||
−0.519944 | + | 0.854201i | \(0.674047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 66.9773 | 2.18108 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.9122 | 0.647745 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.1351 | −1.20673 | −0.603364 | − | 0.797466i | \(-0.706174\pi\) | ||||
−0.603364 | + | 0.797466i | \(0.706174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.8396 | −0.644021 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.58048 | 0.213387 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.3835 | 0.433533 | 0.216767 | − | 0.976223i | \(-0.430449\pi\) | ||||
0.216767 | + | 0.976223i | \(0.430449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.7289 | −0.606053 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.573800 | −0.0185483 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −68.9125 | −2.22530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3957 | −0.754700 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.51278 | −0.177647 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.04939 | −0.162546 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −57.5577 | −1.85093 | −0.925466 | − | 0.378831i | \(-0.876326\pi\) | ||||
−0.925466 | + | 0.378831i | \(0.876326\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.242215 | 0.00778106 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.4756 | 1.29892 | 0.649462 | − | 0.760394i | \(-0.274994\pi\) | ||||
0.649462 | + | 0.760394i | \(0.274994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −63.3038 | −2.02943 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.65587 | 0.0850558 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.6625 | −1.36489 | −0.682447 | − | 0.730935i | \(-0.739084\pi\) | ||||
−0.682447 | + | 0.730935i | \(0.739084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.14738 | −0.100591 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.17014 | 0.101215 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.5482 | −1.19760 | −0.598801 | − | 0.800898i | \(-0.704356\pi\) | ||||
−0.598801 | + | 0.800898i | \(0.704356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.5642 | −0.527780 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −50.6348 | −1.61172 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 58.6740 | 1.86573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.7458 | −1.51669 | −0.758347 | − | 0.651851i | \(-0.773993\pi\) | ||||
−0.758347 | + | 0.651851i | \(0.773993\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.88524 | 0.155028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.77860 | 0.119790 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.8594 | −0.628952 | −0.314476 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314476 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −30.3622 | −0.960619 |
(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 | 8020.2.a.c.1.9 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.9 | ✓ | 28 | 1.1 | even | 1 | trivial |