Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.41 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.62887 | 1.51778 | 0.758891 | − | 0.651218i | \(-0.225742\pi\) | ||||
0.758891 | + | 0.651218i | \(0.225742\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.385949 | −0.172602 | −0.0863008 | − | 0.996269i | \(-0.527505\pi\) | ||||
−0.0863008 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.06025 | 0.400738 | 0.200369 | − | 0.979720i | \(-0.435786\pi\) | ||||
0.200369 | + | 0.979720i | \(0.435786\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.91098 | 1.30366 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.06623 | −0.924504 | −0.462252 | − | 0.886749i | \(-0.652959\pi\) | ||||
−0.462252 | + | 0.886749i | \(0.652959\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.43652 | −1.23047 | −0.615235 | − | 0.788344i | \(-0.710939\pi\) | ||||
−0.615235 | + | 0.788344i | \(0.710939\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.01461 | −0.261971 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.91886 | −0.707928 | −0.353964 | − | 0.935259i | \(-0.615166\pi\) | ||||
−0.353964 | + | 0.935259i | \(0.615166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.422058 | −0.0968267 | −0.0484134 | − | 0.998827i | \(-0.515416\pi\) | ||||
−0.0484134 | + | 0.998827i | \(0.515416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.78728 | 0.608233 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.921411 | −0.192128 | −0.0960638 | − | 0.995375i | \(-0.530625\pi\) | ||||
−0.0960638 | + | 0.995375i | \(0.530625\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.85104 | −0.970209 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.39486 | 0.460890 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.01261 | −1.48791 | −0.743953 | − | 0.668233i | \(-0.767051\pi\) | ||||
−0.743953 | + | 0.668233i | \(0.767051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.77228 | 1.21634 | 0.608169 | − | 0.793808i | \(-0.291904\pi\) | ||||
0.608169 | + | 0.793808i | \(0.291904\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.06074 | −1.40320 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.409204 | −0.0691681 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.94195 | 0.812452 | 0.406226 | − | 0.913773i | \(-0.366845\pi\) | ||||
0.406226 | + | 0.913773i | \(0.366845\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.6631 | −1.86758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.67152 | 1.19809 | 0.599045 | − | 0.800715i | \(-0.295547\pi\) | ||||
0.599045 | + | 0.800715i | \(0.295547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.55444 | 0.237049 | 0.118525 | − | 0.992951i | \(-0.462184\pi\) | ||||
0.118525 | + | 0.992951i | \(0.462184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50944 | −0.225014 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.43923 | −0.647528 | −0.323764 | − | 0.946138i | \(-0.604948\pi\) | ||||
−0.323764 | + | 0.946138i | \(0.604948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.87586 | −0.839409 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.67332 | −1.07448 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.11898 | −1.25259 | −0.626294 | − | 0.779587i | \(-0.715429\pi\) | ||||
−0.626294 | + | 0.779587i | \(0.715429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.18341 | 0.159571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.10954 | −0.146962 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.46728 | 0.191024 | 0.0955121 | − | 0.995428i | \(-0.469551\pi\) | ||||
0.0955121 | + | 0.995428i | \(0.469551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.75627 | 0.352904 | 0.176452 | − | 0.984309i | \(-0.443538\pi\) | ||||
0.176452 | + | 0.984309i | \(0.443538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.14664 | 0.522427 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.71227 | 0.212381 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8281 | −1.44503 | −0.722516 | − | 0.691354i | \(-0.757014\pi\) | ||||
−0.722516 | + | 0.691354i | \(0.757014\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.42228 | −0.291608 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.47433 | 1.00572 | 0.502859 | − | 0.864368i | \(-0.332281\pi\) | ||||
0.502859 | + | 0.864368i | \(0.332281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0133 | −1.64014 | −0.820068 | − | 0.572266i | \(-0.806064\pi\) | ||||
−0.820068 | + | 0.572266i | \(0.806064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7528 | −1.47256 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.25099 | −0.370484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.1827 | −1.14564 | −0.572822 | − | 0.819679i | \(-0.694152\pi\) | ||||
−0.572822 | + | 0.819679i | \(0.694152\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.43717 | −0.604130 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7930 | 1.51398 | 0.756989 | − | 0.653427i | \(-0.226669\pi\) | ||||
0.756989 | + | 0.653427i | \(0.226669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12653 | 0.122189 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.0642 | −2.25831 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.11756 | 0.224461 | 0.112230 | − | 0.993682i | \(-0.464201\pi\) | ||||
0.112230 | + | 0.993682i | \(0.464201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70384 | −0.493097 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.8035 | 1.84613 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.162893 | 0.0167124 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01462 | 0.103019 | 0.0515095 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515095 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.9920 | −1.20524 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3078 | 1.32417 | 0.662086 | − | 0.749428i | \(-0.269671\pi\) | ||||
0.662086 | + | 0.749428i | \(0.269671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9579 | −1.47384 | −0.736922 | − | 0.675977i | \(-0.763722\pi\) | ||||
−0.736922 | + | 0.675977i | \(0.763722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.07575 | −0.104982 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.42206 | −0.620844 | −0.310422 | − | 0.950599i | \(-0.600470\pi\) | ||||
−0.310422 | + | 0.950599i | \(0.600470\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2439 | −1.36432 | −0.682158 | − | 0.731204i | \(-0.738959\pi\) | ||||
−0.682158 | + | 0.731204i | \(0.738959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9918 | 1.23312 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.6439 | −1.84794 | −0.923970 | − | 0.382464i | \(-0.875075\pi\) | ||||
−0.923970 | + | 0.382464i | \(0.875075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.355618 | 0.0331615 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.3512 | −1.60412 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.09473 | −0.283694 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.59821 | −0.145292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.1675 | 1.81844 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.80200 | 0.340061 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9335 | 1.14766 | 0.573832 | − | 0.818973i | \(-0.305456\pi\) | ||||
0.573832 | + | 0.818973i | \(0.305456\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.08642 | 0.359789 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.47119 | −0.303280 | −0.151640 | − | 0.988436i | \(-0.548455\pi\) | ||||
−0.151640 | + | 0.988436i | \(0.548455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.447489 | −0.0388022 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.924292 | −0.0795504 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.485435 | 0.0414735 | 0.0207367 | − | 0.999785i | \(-0.493399\pi\) | ||||
0.0207367 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.43389 | −0.291259 | −0.145629 | − | 0.989339i | \(-0.546521\pi\) | ||||
−0.145629 | + | 0.989339i | \(0.546521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6702 | −0.982806 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6034 | 1.13757 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.09246 | 0.256815 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.4469 | −1.27404 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6436 | 1.03581 | 0.517903 | − | 0.855440i | \(-0.326713\pi\) | ||||
0.517903 | + | 0.855440i | \(0.326713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.80235 | −0.553568 | −0.276784 | − | 0.960932i | \(-0.589269\pi\) | ||||
−0.276784 | + | 0.960932i | \(0.589269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.4156 | −0.922897 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.61375 | −0.209942 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1570 | −1.36928 | −0.684641 | − | 0.728881i | \(-0.740041\pi\) | ||||
−0.684641 | + | 0.728881i | \(0.740041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.9727 | −1.90116 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.976931 | −0.0769929 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.85431 | −0.458545 | −0.229272 | − | 0.973362i | \(-0.573635\pi\) | ||||
−0.229272 | + | 0.973362i | \(0.573635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.11103 | 0.242194 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.83009 | 0.528528 | 0.264264 | − | 0.964450i | \(-0.414871\pi\) | ||||
0.264264 | + | 0.964450i | \(0.414871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.68273 | 0.514056 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.65066 | −0.126229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.75144 | 0.589331 | 0.294665 | − | 0.955600i | \(-0.404792\pi\) | ||||
0.294665 | + | 0.955600i | \(0.404792\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.14334 | −0.388800 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.85731 | 0.289933 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.8904 | 0.963471 | 0.481735 | − | 0.876317i | \(-0.340007\pi\) | ||||
0.481735 | + | 0.876317i | \(0.340007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.7202 | 1.46579 | 0.732897 | − | 0.680340i | \(-0.238168\pi\) | ||||
0.732897 | + | 0.680340i | \(0.238168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.24589 | 0.535632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.90734 | −0.140230 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94991 | 0.654482 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.53916 | 0.184696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8115 | 1.36115 | 0.680576 | − | 0.732678i | \(-0.261730\pi\) | ||||
0.680576 | + | 0.732678i | \(0.261730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8869 | −0.783659 | −0.391829 | − | 0.920038i | \(-0.628158\pi\) | ||||
−0.391829 | + | 0.920038i | \(0.628158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.50134 | 0.322348 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7351 | −0.764846 | −0.382423 | − | 0.923987i | \(-0.624910\pi\) | ||||
−0.382423 | + | 0.923987i | \(0.624910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.49440 | 0.176823 | 0.0884115 | − | 0.996084i | \(-0.471821\pi\) | ||||
0.0884115 | + | 0.996084i | \(0.471821\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −31.0946 | −2.19324 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.49541 | −0.596261 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.96081 | −0.206792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.60362 | −0.250469 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.29413 | 0.0895167 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3338 | 0.986776 | 0.493388 | − | 0.869809i | \(-0.335758\pi\) | ||||
0.493388 | + | 0.869809i | \(0.335758\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.2780 | 1.52646 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.599932 | −0.0409150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.18034 | 0.487433 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −36.8393 | −2.48937 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.9496 | 0.871084 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4907 | 0.769471 | 0.384736 | − | 0.923027i | \(-0.374293\pi\) | ||||
0.384736 | + | 0.923027i | \(0.374293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.9723 | −1.26482 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.6613 | 1.90232 | 0.951159 | − | 0.308703i | \(-0.0998949\pi\) | ||||
0.951159 | + | 0.308703i | \(0.0998949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7970 | 1.70471 | 0.852356 | − | 0.522962i | \(-0.175173\pi\) | ||||
0.852356 | + | 0.522962i | \(0.175173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.54644 | −0.562314 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5583 | −0.822719 | −0.411360 | − | 0.911473i | \(-0.634946\pi\) | ||||
−0.411360 | + | 0.911473i | \(0.634946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.71331 | 0.111764 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.7691 | −1.73884 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.1629 | −1.82171 | −0.910854 | − | 0.412730i | \(-0.864575\pi\) | ||||
−0.910854 | + | 0.412730i | \(0.864575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.9306 | −0.704100 | −0.352050 | − | 0.935981i | \(-0.614515\pi\) | ||||
−0.352050 | + | 0.935981i | \(0.614515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.4782 | −1.37783 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.26778 | 0.144883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.87247 | 0.119142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 36.2601 | 2.29789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5941 | 1.36301 | 0.681505 | − | 0.731814i | \(-0.261326\pi\) | ||||
0.681505 | + | 0.731814i | \(0.261326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82526 | 0.177623 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.96151 | 0.185457 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0167 | −0.811962 | −0.405981 | − | 0.913882i | \(-0.633070\pi\) | ||||
−0.405981 | + | 0.913882i | \(0.633070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.23973 | 0.325581 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −31.3372 | −1.93972 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6538 | 1.21190 | 0.605952 | − | 0.795501i | \(-0.292792\pi\) | ||||
0.605952 | + | 0.795501i | \(0.292792\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.51946 | 0.216199 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.56679 | 0.340682 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1920 | 0.926272 | 0.463136 | − | 0.886287i | \(-0.346724\pi\) | ||||
0.463136 | + | 0.886287i | \(0.346724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16377 | 0.131440 | 0.0657199 | − | 0.997838i | \(-0.479066\pi\) | ||||
0.0657199 | + | 0.997838i | \(0.479066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.3658 | −0.748413 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.8744 | 0.896962 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.4628 | −0.628649 | −0.314325 | − | 0.949316i | \(-0.601778\pi\) | ||||
−0.314325 | + | 0.949316i | \(0.601778\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.4863 | 1.58569 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.7212 | −0.699227 | −0.349613 | − | 0.936894i | \(-0.613687\pi\) | ||||
−0.349613 | + | 0.936894i | \(0.613687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8020 | −0.879887 | −0.439944 | − | 0.898025i | \(-0.645002\pi\) | ||||
−0.439944 | + | 0.898025i | \(0.645002\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.428225 | 0.0253658 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.13376 | 0.480121 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.48025 | −0.498838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.66731 | 0.156360 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.91494 | 0.403975 | 0.201987 | − | 0.979388i | \(-0.435260\pi\) | ||||
0.201987 | + | 0.979388i | \(0.435260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.566297 | −0.0329711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.34319 | −0.426095 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.08786 | 0.236407 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.64810 | 0.0949947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.9844 | 2.00980 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.06378 | −0.0609118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00843 | 0.399992 | 0.199996 | − | 0.979797i | \(-0.435907\pi\) | ||||
0.199996 | + | 0.979797i | \(0.435907\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.3224 | −2.23697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9854 | −1.07656 | −0.538282 | − | 0.842764i | \(-0.680927\pi\) | ||||
−0.538282 | + | 0.842764i | \(0.680927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.91551 | −0.277841 | −0.138921 | − | 0.990304i | \(-0.544363\pi\) | ||||
−0.138921 | + | 0.990304i | \(0.544363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.60039 | −0.0901717 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.6581 | −1.55343 | −0.776716 | − | 0.629851i | \(-0.783116\pi\) | ||||
−0.776716 | + | 0.629851i | \(0.783116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.5685 | 1.37557 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.8828 | −0.942305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23193 | 0.0685463 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.5218 | 1.19381 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −37.4454 | −2.07073 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.70671 | −0.259489 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.0884 | 1.15912 | 0.579562 | − | 0.814928i | \(-0.303224\pi\) | ||||
0.579562 | + | 0.814928i | \(0.303224\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.3279 | 1.05916 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.56504 | 0.249415 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.7334 | 1.51073 | 0.755366 | − | 0.655303i | \(-0.227459\pi\) | ||||
0.755366 | + | 0.655303i | \(0.227459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −51.6413 | −2.80477 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.7654 | −1.12451 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.6517 | −0.737122 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.934874 | 0.0503319 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.2013 | −0.923414 | −0.461707 | − | 0.887032i | \(-0.652763\pi\) | ||||
−0.461707 | + | 0.887032i | \(0.652763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0824 | 0.860871 | 0.430435 | − | 0.902621i | \(-0.358360\pi\) | ||||
0.430435 | + | 0.902621i | \(0.358360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6248 | −0.567112 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.7167 | 1.42199 | 0.710993 | − | 0.703199i | \(-0.248246\pi\) | ||||
0.710993 | + | 0.703199i | \(0.248246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.27066 | −0.173588 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.13567 | −0.430585 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.5985 | −1.29826 | −0.649130 | − | 0.760678i | \(-0.724867\pi\) | ||||
−0.649130 | + | 0.760678i | \(0.724867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8219 | −0.990625 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.20149 | −0.220521 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.40843 | 0.283090 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.6065 | −1.44105 | −0.720524 | − | 0.693430i | \(-0.756099\pi\) | ||||
−0.720524 | + | 0.693430i | \(0.756099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.0032 | 1.56190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.66844 | −0.501960 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.8027 | 1.59490 | 0.797452 | − | 0.603382i | \(-0.206181\pi\) | ||||
0.797452 | + | 0.603382i | \(0.206181\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.99497 | 0.516138 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.5481 | 1.83082 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2838 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.0006 | 1.74190 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.743755 | 0.0380041 | 0.0190020 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190020 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.25471 | 0.0639462 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.07937 | 0.309032 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.43706 | −0.427776 | −0.213888 | − | 0.976858i | \(-0.568613\pi\) | ||||
−0.213888 | + | 0.976858i | \(0.568613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.68947 | 0.136012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.12533 | −0.460312 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.93001 | 0.197740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4329 | 1.27644 | 0.638219 | − | 0.769855i | \(-0.279671\pi\) | ||||
0.638219 | + | 0.769855i | \(0.279671\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.17639 | −0.0588933 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4850 | −1.12285 | −0.561425 | − | 0.827528i | \(-0.689747\pi\) | ||||
−0.561425 | + | 0.827528i | \(0.689747\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.0454 | −1.49667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.09847 | 0.104274 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.1532 | −0.751115 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5185 | 1.01457 | 0.507287 | − | 0.861777i | \(-0.330648\pi\) | ||||
0.507287 | + | 0.861777i | \(0.330648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.27615 | 0.0629477 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55570 | 0.0765508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.32339 | −0.261315 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.02727 | −0.442067 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.2145 | 1.47607 | 0.738037 | − | 0.674761i | \(-0.235753\pi\) | ||||
0.738037 | + | 0.674761i | \(0.235753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1839 | 1.51981 | 0.759905 | − | 0.650034i | \(-0.225245\pi\) | ||||
0.759905 | + | 0.650034i | \(0.225245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.3617 | −0.844156 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.1595 | 0.686838 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.92235 | 0.141422 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 35.7617 | 1.72659 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.03702 | 0.146288 | 0.0731441 | − | 0.997321i | \(-0.476697\pi\) | ||||
0.0731441 | + | 0.997321i | \(0.476697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.7544 | −1.52602 | −0.763010 | − | 0.646387i | \(-0.776279\pi\) | ||||
−0.763010 | + | 0.646387i | \(0.776279\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.12968 | 0.389789 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.388889 | 0.0186031 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0020 | −0.954643 | −0.477321 | − | 0.878729i | \(-0.658392\pi\) | ||||
−0.477321 | + | 0.878729i | \(0.658392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.9804 | −1.09430 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.8403 | −1.65531 | −0.827657 | − | 0.561234i | \(-0.810327\pi\) | ||||
−0.827657 | + | 0.561234i | \(0.810327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.817268 | −0.0387422 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 33.2385 | 1.57213 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.947307 | 0.0447062 | 0.0223531 | − | 0.999750i | \(-0.492884\pi\) | ||||
0.0223531 | + | 0.999750i | \(0.492884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.5227 | −1.10764 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.8825 | −0.840195 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.81544 | 0.0851092 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.6267 | −1.76010 | −0.880052 | − | 0.474878i | \(-0.842492\pi\) | ||||
−0.880052 | + | 0.474878i | \(0.842492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.99025 | −0.326277 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.853835 | 0.0397671 | 0.0198835 | − | 0.999802i | \(-0.493670\pi\) | ||||
0.0198835 | + | 0.999802i | \(0.493670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3267 | 0.526397 | 0.263199 | − | 0.964742i | \(-0.415223\pi\) | ||||
0.263199 | + | 0.964742i | \(0.415223\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.87123 | −0.318646 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −41.3143 | −1.91180 | −0.955899 | − | 0.293696i | \(-0.905115\pi\) | ||||
−0.955899 | + | 0.293696i | \(0.905115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.5408 | −0.579080 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −45.1037 | −2.07827 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.76626 | −0.219153 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.04742 | 0.0939422 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.6642 | −1.63295 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.2435 | 1.10772 | 0.553858 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553858 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.9251 | −0.999698 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.56823 | −0.116858 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.391591 | −0.0177812 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.2489 | −0.781621 | −0.390811 | − | 0.920471i | \(-0.627805\pi\) | ||||
−0.390811 | + | 0.920471i | \(0.627805\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.3902 | −0.695971 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.32041 | 0.0595892 | 0.0297946 | − | 0.999556i | \(-0.490515\pi\) | ||||
0.0297946 | + | 0.999556i | \(0.490515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.3877 | 1.05333 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.62829 | 0.208026 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.98495 | 0.403030 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.79336 | −0.214580 | −0.107290 | − | 0.994228i | \(-0.534217\pi\) | ||||
−0.107290 | + | 0.994228i | \(0.534217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.9554 | 0.802190 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.3724 | −0.551657 | −0.275829 | − | 0.961207i | \(-0.588952\pi\) | ||||
−0.275829 | + | 0.961207i | \(0.588952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.13611 | −0.228554 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.5681 | 0.780225 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.2590 | 1.69580 | 0.847901 | − | 0.530155i | \(-0.177866\pi\) | ||||
0.847901 | + | 0.530155i | \(0.177866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8577 | −0.657266 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01077 | −0.0446265 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.77298 | 0.254388 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6117 | 0.598642 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.3776 | 0.894475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.4874 | −0.678514 | −0.339257 | − | 0.940694i | \(-0.610176\pi\) | ||||
−0.339257 | + | 0.940694i | \(0.610176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0329 | 1.13834 | 0.569170 | − | 0.822220i | \(-0.307265\pi\) | ||||
0.569170 | + | 0.822220i | \(0.307265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.5212 | −0.590113 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7673 | −0.861079 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1510 | −0.963087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.73852 | 0.249031 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.0349 | −1.47421 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.47859 | 0.107159 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 33.8871 | 1.46234 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.0168 | 0.776037 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8172 | 1.53990 | 0.769952 | − | 0.638102i | \(-0.220280\pi\) | ||||
0.769952 | + | 0.638102i | \(0.220280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 51.8420 | 2.22475 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.49741 | 0.235483 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.76624 | 0.332060 | 0.166030 | − | 0.986121i | \(-0.446905\pi\) | ||||
0.166030 | + | 0.986121i | \(0.446905\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.7797 | 0.460067 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.38179 | 0.144069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7963 | −0.459104 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.01416 | −0.212839 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.1611 | 1.61694 | 0.808470 | − | 0.588538i | \(-0.200296\pi\) | ||||
0.808470 | + | 0.588538i | \(0.200296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.89629 | −0.291682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.5282 | 0.993361 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.95868 | −0.251129 | −0.125564 | − | 0.992085i | \(-0.540074\pi\) | ||||
−0.125564 | + | 0.992085i | \(0.540074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.58153 | 0.318957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.76478 | −0.242098 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.1828 | 1.68455 | 0.842275 | − | 0.539048i | \(-0.181216\pi\) | ||||
0.842275 | + | 0.539048i | \(0.181216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1336 | 0.884416 | 0.442208 | − | 0.896913i | \(-0.354195\pi\) | ||||
0.442208 | + | 0.896913i | \(0.354195\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 49.4530 | 2.06593 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.46981 | 0.186404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8944 | 0.828213 | 0.414107 | − | 0.910228i | \(-0.364094\pi\) | ||||
0.414107 | + | 0.910228i | \(0.364094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.6204 | −1.18942 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.6241 | 0.606710 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.9609 | 1.15802 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.69666 | 0.276873 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.59029 | 0.230736 | 0.115368 | − | 0.993323i | \(-0.463195\pi\) | ||||
0.115368 | + | 0.993323i | \(0.463195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.85830 | −0.117774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.2213 | −1.16087 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9966 | 0.697967 | 0.348984 | − | 0.937129i | \(-0.386527\pi\) | ||||
0.348984 | + | 0.937129i | \(0.386527\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.19441 | 0.0489660 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.55745 | 0.268379 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.0485 | 1.51376 | 0.756881 | − | 0.653553i | \(-0.226722\pi\) | ||||
0.756881 | + | 0.653553i | \(0.226722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.79139 | −0.277027 | −0.138513 | − | 0.990361i | \(-0.544232\pi\) | ||||
−0.138513 | + | 0.990361i | \(0.544232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −46.2595 | −1.88383 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.616827 | 0.0250776 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.5147 | 0.954432 | 0.477216 | − | 0.878786i | \(-0.341646\pi\) | ||||
0.477216 | + | 0.878786i | \(0.341646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.3334 | −0.904994 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.6947 | 0.796763 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.4466 | −1.39129 | −0.695643 | − | 0.718388i | \(-0.744880\pi\) | ||||
−0.695643 | + | 0.718388i | \(0.744880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.78361 | −0.313865 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.77501 | 0.111718 | 0.0558589 | − | 0.998439i | \(-0.482210\pi\) | ||||
0.0558589 | + | 0.998439i | \(0.482210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.8593 | −1.44131 | −0.720653 | − | 0.693295i | \(-0.756158\pi\) | ||||
−0.720653 | + | 0.693295i | \(0.756158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.20665 | −0.0885497 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.24515 | 0.0899500 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7878 | 0.911514 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.40210 | 0.135867 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.4249 | −0.575157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2138 | −1.16298 | −0.581491 | − | 0.813553i | \(-0.697530\pi\) | ||||
−0.581491 | + | 0.813553i | \(0.697530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.6816 | 1.49771 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.99168 | −0.198089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.0684 | 1.03287 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.1430 | 1.31112 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.769270 | −0.0303843 | −0.0151922 | − | 0.999885i | \(-0.504836\pi\) | ||||
−0.0151922 | + | 0.999885i | \(0.504836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.0795 | −1.22566 | −0.612829 | − | 0.790216i | \(-0.709968\pi\) | ||||
−0.612829 | + | 0.790216i | \(0.709968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.57715 | −0.0621001 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1262 | 0.948498 | 0.474249 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474249 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.49904 | −0.176603 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.8762 | 0.739817 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.6172 | −0.767681 | −0.383841 | − | 0.923399i | \(-0.625399\pi\) | ||||
−0.383841 | + | 0.923399i | \(0.625399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.33970 | 0.0523465 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −54.8059 | −2.13818 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.2915 | −0.517761 | −0.258881 | − | 0.965909i | \(-0.583354\pi\) | ||||
−0.258881 | + | 0.965909i | \(0.583354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.7632 | 1.54661 | 0.773306 | − | 0.634034i | \(-0.218602\pi\) | ||||
0.773306 | + | 0.634034i | \(0.218602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.0429 | 1.32211 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.172708 | 0.00669732 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.38291 | 0.285868 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.2075 | 1.16789 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.45137 | −0.326262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3955 | −1.05602 | −0.528009 | − | 0.849238i | \(-0.677061\pi\) | ||||
−0.528009 | + | 0.849238i | \(0.677061\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.6176 | −0.447160 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.2926 | 1.12580 | 0.562902 | − | 0.826523i | \(-0.309685\pi\) | ||||
0.562902 | + | 0.826523i | \(0.309685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.07575 | 0.0412836 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 75.3470 | 2.88730 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.05739 | 0.270043 | 0.135022 | − | 0.990843i | \(-0.456890\pi\) | ||||
0.135022 | + | 0.990843i | \(0.456890\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.187353 | −0.00715839 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.8170 | 2.58738 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.4566 | 1.54127 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −49.9069 | −1.89855 | −0.949275 | − | 0.314448i | \(-0.898181\pi\) | ||||
−0.949275 | + | 0.314448i | \(0.898181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.7146 | −0.482986 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.32531 | 0.0502717 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.3921 | −0.848161 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.0141 | −1.24871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.71795 | −0.178195 | −0.0890973 | − | 0.996023i | \(-0.528398\pi\) | ||||
−0.0890973 | + | 0.996023i | \(0.528398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.08579 | −0.0786671 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.50409 | 0.169634 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.1096 | 0.530647 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7207 | 0.515292 | 0.257646 | − | 0.966239i | \(-0.417053\pi\) | ||||
0.257646 | + | 0.966239i | \(0.417053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.8244 | −1.49353 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.24006 | −0.233692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.25022 | −0.196347 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −74.0368 | −2.76495 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.45561 | −0.0542850 | −0.0271425 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271425 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.8592 | −0.590626 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.7351 | −1.06867 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.8695 | 1.44358 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8028 | 1.36494 | 0.682471 | − | 0.730913i | \(-0.260906\pi\) | ||||
0.682471 | + | 0.730913i | \(0.260906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.1520 | −1.48711 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.53718 | −0.167814 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.4744 | −1.64270 | −0.821350 | − | 0.570425i | \(-0.806778\pi\) | ||||
−0.821350 | + | 0.570425i | \(0.806778\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.96171 | 0.219901 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.2677 | 1.33594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.5303 | −0.681650 | −0.340825 | − | 0.940127i | \(-0.610706\pi\) | ||||
−0.340825 | + | 0.940127i | \(0.610706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.92249 | 0.180832 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.1551 | −1.25303 | −0.626515 | − | 0.779409i | \(-0.715519\pi\) | ||||
−0.626515 | + | 0.779409i | \(0.715519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.87979 | −0.178782 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.9442 | 1.97371 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.80902 | −0.248796 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 56.7682 | 2.06875 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.62536 | 0.0955466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.5644 | −0.856463 | −0.428231 | − | 0.903669i | \(-0.640863\pi\) | ||||
−0.428231 | + | 0.903669i | \(0.640863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.42726 | 0.269593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.8766 | 1.98928 | 0.994638 | − | 0.103417i | \(-0.0329777\pi\) | ||||
0.994638 | + | 0.103417i | \(0.0329777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1021 | −0.546734 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.40584 | 0.159293 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.50964 | −0.235050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.01166 | 0.324969 | 0.162484 | − | 0.986711i | \(-0.448049\pi\) | ||||
0.162484 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.2194 | −1.23238 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.4863 | −0.880712 | −0.440356 | − | 0.897823i | \(-0.645148\pi\) | ||||
−0.440356 | + | 0.897823i | \(0.645148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.8526 | −1.18010 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.7746 | 0.494160 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.23783 | −0.116007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.9843 | −0.929791 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.1891 | −0.685761 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.62174 | 0.236340 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3100 | −0.438804 | −0.219402 | − | 0.975635i | \(-0.570411\pi\) | ||||
−0.219402 | + | 0.975635i | \(0.570411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 51.6674 | 1.83941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.8275 | −0.740541 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.2283 | −0.434238 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.25221 | 0.328142 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.1894 | 1.91949 | 0.959744 | − | 0.280877i | \(-0.0906253\pi\) | ||||
0.959744 | + | 0.280877i | \(0.0906253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.9575 | 0.458403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.28172 | 0.292620 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.9681 | 1.51631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.377045 | 0.0132891 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.9378 | 1.40588 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.73276 | −0.271869 | −0.135935 | − | 0.990718i | \(-0.543404\pi\) | ||||
−0.135935 | + | 0.990718i | \(0.543404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8591 | −0.521774 | −0.260887 | − | 0.965369i | \(-0.584015\pi\) | ||||
−0.260887 | + | 0.965369i | \(0.584015\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.68829 | 0.199497 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.25946 | 0.0791455 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.656062 | −0.0229527 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.3966 | −0.642831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.73848 | −0.339875 | −0.169938 | − | 0.985455i | \(-0.554357\pi\) | ||||
−0.169938 | + | 0.985455i | \(0.554357\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.3051 | 0.638075 | 0.319038 | − | 0.947742i | \(-0.396640\pi\) | ||||
0.319038 | + | 0.947742i | \(0.396640\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 39.1030 | 1.36139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.4200 | −1.12735 | −0.563677 | − | 0.825995i | \(-0.690614\pi\) | ||||
−0.563677 | + | 0.825995i | \(0.690614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7075 | −0.406617 | −0.203309 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203309 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.5054 | −0.954152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.1508 | 0.594241 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.63606 | −0.0912247 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.2186 | 0.560598 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.03241 | 0.311833 | 0.155917 | − | 0.987770i | \(-0.450167\pi\) | ||||
0.155917 | + | 0.987770i | \(0.450167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.2020 | 1.21386 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.8135 | −1.06127 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.57919 | −0.0887269 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.69451 | −0.0582240 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.9126 | −1.33548 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.55357 | −0.156094 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.0552 | −1.88506 | −0.942528 | − | 0.334128i | \(-0.891558\pi\) | ||||
−0.942528 | + | 0.334128i | \(0.891558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.637070 | 0.0217874 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.95859 | 0.340179 | 0.170089 | − | 0.985429i | \(-0.445594\pi\) | ||||
0.170089 | + | 0.985429i | \(0.445594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.52496 | 0.0861506 | 0.0430753 | − | 0.999072i | \(-0.486284\pi\) | ||||
0.0430753 | + | 0.999072i | \(0.486284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.3826 | 0.728718 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.27195 | −0.213500 | −0.106750 | − | 0.994286i | \(-0.534044\pi\) | ||||
−0.106750 | + | 0.994286i | \(0.534044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.99166 | −0.101719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.2935 | −0.757128 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2226 | 1.05915 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.4756 | 1.77807 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.96815 | 0.134302 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.03108 | 0.136276 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.7100 | 1.00324 | 0.501618 | − | 0.865089i | \(-0.332738\pi\) | ||||
0.501618 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.1785 | 0.613146 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.83415 | 0.263939 | 0.131970 | − | 0.991254i | \(-0.457870\pi\) | ||||
0.131970 | + | 0.991254i | \(0.457870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7670 | −1.10270 | −0.551349 | − | 0.834275i | \(-0.685887\pi\) | ||||
−0.551349 | + | 0.834275i | \(0.685887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.48872 | −0.0500429 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.7445 | −1.20018 | −0.600092 | − | 0.799931i | \(-0.704869\pi\) | ||||
−0.600092 | + | 0.799931i | \(0.704869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.7128 | 0.459914 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.6716 | 0.558521 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.87361 | 0.0626980 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.97502 | −0.166297 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.7465 | 0.358814 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −54.2637 | −1.80980 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.6170 | 0.886742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.33264 | 0.144181 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.61100 | −0.252998 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.3106 | −1.60413 | −0.802063 | − | 0.597239i | \(-0.796264\pi\) | ||||
−0.802063 | + | 0.597239i | \(0.796264\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 52.0464 | 1.72627 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.3628 | −1.46981 | −0.734903 | − | 0.678172i | \(-0.762772\pi\) | ||||
−0.734903 | + | 0.678172i | \(0.762772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.2926 | −1.39968 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.79654 | −0.0924508 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.68035 | −0.121536 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7212 | −0.914438 | −0.457219 | − | 0.889354i | \(-0.651154\pi\) | ||||
−0.457219 | + | 0.889354i | \(0.651154\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.4243 | 0.607100 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.5966 | −1.23751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9736 | −0.788248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −58.5000 | −1.92139 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.2627 | −0.467943 | −0.233972 | − | 0.972243i | \(-0.575172\pi\) | ||||
−0.233972 | + | 0.972243i | \(0.575172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.47995 | 0.0812772 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.9103 | −1.63399 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.45421 | −0.112965 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54.7211 | 1.78766 | 0.893831 | − | 0.448404i | \(-0.148007\pi\) | ||||
0.893831 | + | 0.448404i | \(0.148007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9223 | −0.421702 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.7531 | −0.643932 | −0.321966 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321966 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.06863 | −0.230186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.979984 | −0.0318789 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.5516 | −0.537856 | −0.268928 | − | 0.963160i | \(-0.586669\pi\) | ||||
−0.268928 | + | 0.963160i | \(0.586669\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.1704 | 2.01814 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.7096 | −2.35777 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.4666 | 1.40802 | 0.704011 | − | 0.710189i | \(-0.251391\pi\) | ||||
0.704011 | + | 0.710189i | \(0.251391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.26027 | −0.234937 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 64.5876 | 2.08782 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.514684 | 0.0166200 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8638 | 0.479478 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.1166 | −0.809370 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.20180 | 0.135261 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.4228 | 1.75012 | 0.875059 | − | 0.484015i | \(-0.160822\pi\) | ||||
0.875059 | + | 0.484015i | \(0.160822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.23859 | 0.104038 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6010 | −0.500660 | −0.250330 | − | 0.968161i | \(-0.580539\pi\) | ||||
−0.250330 | + | 0.968161i | \(0.580539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.64080 | −0.116719 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 56.5780 | 1.81195 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.6341 | −1.04406 | −0.522029 | − | 0.852928i | \(-0.674825\pi\) | ||||
−0.522029 | + | 0.852928i | \(0.674825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.49292 | −0.207515 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55.7076 | −1.77861 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.6891 | 0.627984 | 0.313992 | − | 0.949426i | \(-0.398333\pi\) | ||||
0.313992 | + | 0.949426i | \(0.398333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.14321 | 0.132014 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.3733 | −0.393848 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.43227 | −0.0455437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.6329 | −1.06838 | −0.534192 | − | 0.845363i | \(-0.679384\pi\) | ||||
−0.534192 | + | 0.845363i | \(0.679384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 55.4388 | 1.75930 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.962709 | −0.0305199 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5851 | 0.430244 | 0.215122 | − | 0.976587i | \(-0.430985\pi\) | ||||
0.215122 | + | 0.976587i | \(0.430985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.8353 | 0.374451 |
(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 | 6008.2.a.b.1.41 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.41 | ✓ | 44 | 1.1 | even | 1 | trivial |