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 | 1.38 | ||
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 | ||||||||
\(3\) | 1.87831 | 1.08444 | 0.542220 | − | 0.840236i | \(-0.317584\pi\) | ||||
0.542220 | + | 0.840236i | \(0.317584\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.46462 | −0.655000 | −0.327500 | − | 0.944851i | \(-0.606206\pi\) | ||||
−0.327500 | + | 0.944851i | \(0.606206\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.498105 | −0.188266 | −0.0941330 | − | 0.995560i | \(-0.530008\pi\) | ||||
−0.0941330 | + | 0.995560i | \(0.530008\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.528033 | 0.176011 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.602542 | 0.181673 | 0.0908366 | − | 0.995866i | \(-0.471046\pi\) | ||||
0.0908366 | + | 0.995866i | \(0.471046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.48030 | 0.965262 | 0.482631 | − | 0.875824i | \(-0.339681\pi\) | ||||
0.482631 | + | 0.875824i | \(0.339681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.75101 | −0.710308 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.975945 | −0.236701 | −0.118351 | − | 0.992972i | \(-0.537761\pi\) | ||||
−0.118351 | + | 0.992972i | \(0.537761\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.95948 | 0.449535 | 0.224768 | − | 0.974412i | \(-0.427838\pi\) | ||||
0.224768 | + | 0.974412i | \(0.427838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.935593 | −0.204163 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.22486 | −1.29797 | −0.648987 | − | 0.760800i | \(-0.724807\pi\) | ||||
−0.648987 | + | 0.760800i | \(0.724807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.85487 | −0.570975 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.64311 | −0.893567 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.238672 | −0.0443202 | −0.0221601 | − | 0.999754i | \(-0.507054\pi\) | ||||
−0.0221601 | + | 0.999754i | \(0.507054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.95329 | −0.350822 | −0.175411 | − | 0.984495i | \(-0.556125\pi\) | ||||
−0.175411 | + | 0.984495i | \(0.556125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.13176 | 0.197014 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.729537 | 0.123314 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.114676 | 0.0188526 | 0.00942629 | − | 0.999956i | \(-0.496999\pi\) | ||||
0.00942629 | + | 0.999956i | \(0.496999\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.53707 | 1.04677 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.20599 | −0.344518 | −0.172259 | − | 0.985052i | \(-0.555107\pi\) | ||||
−0.172259 | + | 0.985052i | \(0.555107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.53861 | −0.692131 | −0.346066 | − | 0.938210i | \(-0.612483\pi\) | ||||
−0.346066 | + | 0.938210i | \(0.612483\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.773370 | −0.115287 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00260 | 0.583840 | 0.291920 | − | 0.956443i | \(-0.405706\pi\) | ||||
0.291920 | + | 0.956443i | \(0.405706\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.75189 | −0.964556 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.83312 | −0.256689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.59279 | 1.04295 | 0.521475 | − | 0.853266i | \(-0.325382\pi\) | ||||
0.521475 | + | 0.853266i | \(0.325382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.882497 | −0.118996 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.68050 | 0.487494 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.21604 | −0.288504 | −0.144252 | − | 0.989541i | \(-0.546078\pi\) | ||||
−0.144252 | + | 0.989541i | \(0.546078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3328 | −1.45102 | −0.725509 | − | 0.688212i | \(-0.758396\pi\) | ||||
−0.725509 | + | 0.688212i | \(0.758396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.263016 | −0.0331369 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.09734 | −0.632247 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.31589 | −1.13812 | −0.569059 | − | 0.822297i | \(-0.692692\pi\) | ||||
−0.569059 | + | 0.822297i | \(0.692692\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.6922 | −1.40758 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.58698 | −0.544374 | −0.272187 | − | 0.962244i | \(-0.587747\pi\) | ||||
−0.272187 | + | 0.962244i | \(0.587747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.26713 | 0.733512 | 0.366756 | − | 0.930317i | \(-0.380468\pi\) | ||||
0.366756 | + | 0.930317i | \(0.380468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.36233 | −0.619188 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.300129 | −0.0342029 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.09141 | 0.347811 | 0.173905 | − | 0.984762i | \(-0.444361\pi\) | ||||
0.173905 | + | 0.984762i | \(0.444361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3053 | −1.14503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.87490 | 0.315561 | 0.157781 | − | 0.987474i | \(-0.449566\pi\) | ||||
0.157781 | + | 0.987474i | \(0.449566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.42939 | 0.155039 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.448299 | −0.0480627 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.49258 | 0.900212 | 0.450106 | − | 0.892975i | \(-0.351386\pi\) | ||||
0.450106 | + | 0.892975i | \(0.351386\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73356 | −0.181726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.66888 | −0.380446 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.86990 | −0.294446 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8132 | 1.40252 | 0.701261 | − | 0.712904i | \(-0.252621\pi\) | ||||
0.701261 | + | 0.712904i | \(0.252621\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.318162 | 0.0319765 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.70228 | −0.268887 | −0.134443 | − | 0.990921i | \(-0.542925\pi\) | ||||
−0.134443 | + | 0.990921i | \(0.542925\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.79271 | 0.373707 | 0.186853 | − | 0.982388i | \(-0.440171\pi\) | ||||
0.186853 | + | 0.982388i | \(0.440171\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.37029 | 0.133727 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.04476 | −0.777716 | −0.388858 | − | 0.921298i | \(-0.627130\pi\) | ||||
−0.388858 | + | 0.921298i | \(0.627130\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2748 | −1.36727 | −0.683637 | − | 0.729822i | \(-0.739603\pi\) | ||||
−0.683637 | + | 0.729822i | \(0.739603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.215396 | 0.0204445 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.2185 | −1.43163 | −0.715817 | − | 0.698288i | \(-0.753946\pi\) | ||||
−0.715817 | + | 0.698288i | \(0.753946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.11709 | 0.850173 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.83771 | 0.169897 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.486123 | 0.0445628 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6369 | −0.966995 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.14353 | −0.373610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5044 | 1.02899 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5573 | 1.02555 | 0.512774 | − | 0.858524i | \(-0.328618\pi\) | ||||
0.512774 | + | 0.858524i | \(0.328618\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.52490 | −0.750575 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.5891 | 1.79887 | 0.899437 | − | 0.437050i | \(-0.143977\pi\) | ||||
0.899437 | + | 0.437050i | \(0.143977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.976026 | −0.0846322 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.80041 | 0.585286 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.46955 | 0.552731 | 0.276365 | − | 0.961053i | \(-0.410870\pi\) | ||||
0.276365 | + | 0.961053i | \(0.410870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.44362 | −0.800997 | −0.400499 | − | 0.916297i | \(-0.631163\pi\) | ||||
−0.400499 | + | 0.916297i | \(0.631163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.51812 | 0.633140 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.09703 | 0.175362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.349565 | 0.0290298 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.6821 | −1.04600 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.2603 | −1.57787 | −0.788933 | − | 0.614479i | \(-0.789366\pi\) | ||||
−0.788933 | + | 0.614479i | \(0.789366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.39212 | 0.276046 | 0.138023 | − | 0.990429i | \(-0.455925\pi\) | ||||
0.138023 | + | 0.990429i | \(0.455925\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.515331 | −0.0416620 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.86084 | 0.229788 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.40878 | 0.272050 | 0.136025 | − | 0.990705i | \(-0.456567\pi\) | ||||
0.136025 | + | 0.990705i | \(0.456567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.2616 | 1.13102 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.10063 | 0.244364 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.5157 | −1.68524 | −0.842618 | − | 0.538511i | \(-0.818987\pi\) | ||||
−0.842618 | + | 0.538511i | \(0.818987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.65760 | −0.129044 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1544 | 1.01792 | 0.508958 | − | 0.860792i | \(-0.330031\pi\) | ||||
0.508958 | + | 0.860792i | \(0.330031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.887489 | −0.0682684 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.03467 | 0.0791231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.10497 | 0.236067 | 0.118033 | − | 0.993010i | \(-0.462341\pi\) | ||||
0.118033 | + | 0.993010i | \(0.462341\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.42203 | 0.107495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.16240 | −0.312865 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.81994 | −0.435003 | −0.217502 | − | 0.976060i | \(-0.569791\pi\) | ||||
−0.217502 | + | 0.976060i | \(0.569791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.5155 | −1.52491 | −0.762453 | − | 0.647044i | \(-0.776005\pi\) | ||||
−0.762453 | + | 0.647044i | \(0.776005\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.2865 | −1.57354 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.167957 | −0.0123484 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.588047 | −0.0430023 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.31276 | 0.168228 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.847720 | 0.0613389 | 0.0306694 | − | 0.999530i | \(-0.490236\pi\) | ||||
0.0306694 | + | 0.999530i | \(0.490236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7399 | −0.845059 | −0.422530 | − | 0.906349i | \(-0.638858\pi\) | ||||
−0.422530 | + | 0.906349i | \(0.638858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.57436 | −0.685634 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.30965 | −0.449544 | −0.224772 | − | 0.974411i | \(-0.572164\pi\) | ||||
−0.224772 | + | 0.974411i | \(0.572164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7268 | −1.32751 | −0.663753 | − | 0.747952i | \(-0.731037\pi\) | ||||
−0.663753 | + | 0.747952i | \(0.731037\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.4981 | −1.23422 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.118884 | 0.00834399 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.23095 | 0.225660 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.28693 | −0.228457 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.18067 | 0.0816685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.9126 | −1.78390 | −0.891949 | − | 0.452137i | \(-0.850662\pi\) | ||||
−0.891949 | + | 0.452137i | \(0.850662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.61575 | −0.590342 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.64736 | 0.453346 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.972945 | 0.0660478 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.7716 | 0.795450 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.39658 | −0.228479 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.48609 | −0.501306 | −0.250653 | − | 0.968077i | \(-0.580645\pi\) | ||||
−0.250653 | + | 0.968077i | \(0.580645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.50747 | −0.100498 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.3558 | −0.820086 | −0.410043 | − | 0.912066i | \(-0.634486\pi\) | ||||
−0.410043 | + | 0.912066i | \(0.634486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.69215 | 0.376148 | 0.188074 | − | 0.982155i | \(-0.439776\pi\) | ||||
0.188074 | + | 0.982155i | \(0.439776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.563734 | −0.0370910 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8469 | −0.710606 | −0.355303 | − | 0.934751i | \(-0.615622\pi\) | ||||
−0.355303 | + | 0.934751i | \(0.615622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.86231 | −0.382415 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.80661 | 0.377180 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.09267 | 0.200048 | 0.100024 | − | 0.994985i | \(-0.468108\pi\) | ||||
0.100024 | + | 0.994985i | \(0.468108\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.39728 | 0.154422 | 0.0772112 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772112 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.42713 | −0.348151 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.88899 | 0.631784 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.81958 | 0.433920 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.39994 | 0.342208 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2555 | −1.15228 | −0.576139 | − | 0.817352i | \(-0.695441\pi\) | ||||
−0.576139 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.75074 | −0.235807 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.68484 | 0.168131 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.00317 | −0.187333 | −0.0936664 | − | 0.995604i | \(-0.529859\pi\) | ||||
−0.0936664 | + | 0.995604i | \(0.529859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0571206 | −0.00354930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.126026 | −0.00780084 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2256 | −1.00051 | −0.500256 | − | 0.865878i | \(-0.666761\pi\) | ||||
−0.500256 | + | 0.865878i | \(0.666761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1206 | −0.683132 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.9517 | 0.976226 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1857 | 1.10880 | 0.554400 | − | 0.832250i | \(-0.312948\pi\) | ||||
0.554400 | + | 0.832250i | \(0.312948\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7670 | 1.20076 | 0.600380 | − | 0.799715i | \(-0.295016\pi\) | ||||
0.600380 | + | 0.799715i | \(0.295016\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.25615 | −0.197071 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.72018 | −0.103731 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4874 | −1.47130 | −0.735652 | − | 0.677359i | \(-0.763124\pi\) | ||||
−0.735652 | + | 0.677359i | \(0.763124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.03140 | −0.0617485 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.40921 | −0.0840666 | −0.0420333 | − | 0.999116i | \(-0.513384\pi\) | ||||
−0.0420333 | + | 0.999116i | \(0.513384\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7300 | −1.64838 | −0.824188 | − | 0.566317i | \(-0.808368\pi\) | ||||
−0.824188 | + | 0.566317i | \(0.808368\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.39055 | −0.319309 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.09882 | 0.0648611 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0475 | −0.943972 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.9455 | 1.52095 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.4625 | 1.60438 | 0.802188 | − | 0.597072i | \(-0.203669\pi\) | ||||
0.802188 | + | 0.597072i | \(0.203669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.24567 | 0.188970 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.79767 | −0.162337 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.6644 | −1.25289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.26070 | 0.130305 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.07570 | −0.291592 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5983 | 0.950417 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.0884198 | −0.00504638 | −0.00252319 | − | 0.999997i | \(-0.500803\pi\) | ||||
−0.00252319 | + | 0.999997i | \(0.500803\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.12387 | 0.405263 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8893 | 1.12782 | 0.563908 | − | 0.825838i | \(-0.309297\pi\) | ||||
0.563908 | + | 0.825838i | \(0.309297\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.05293 | −0.455179 | −0.227589 | − | 0.973757i | \(-0.573084\pi\) | ||||
−0.227589 | + | 0.973757i | \(0.573084\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.385219 | 0.0217046 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.1117 | 1.18575 | 0.592876 | − | 0.805294i | \(-0.297992\pi\) | ||||
0.592876 | + | 0.805294i | \(0.297992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.143810 | −0.00805180 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.1105 | −0.843387 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.91234 | −0.106406 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.93583 | −0.551141 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.8124 | −1.48273 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99372 | −0.109917 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.586105 | −0.0322152 | −0.0161076 | − | 0.999870i | \(-0.505127\pi\) | ||||
−0.0161076 | + | 0.999870i | \(0.505127\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0605526 | 0.00331826 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.6443 | 0.745467 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8242 | −0.916474 | −0.458237 | − | 0.888830i | \(-0.651519\pi\) | ||||
−0.458237 | + | 0.888830i | \(0.651519\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5850 | −1.55252 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17694 | −0.0637350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.84988 | 0.369859 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.1247 | 0.921962 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.49786 | −0.187775 | −0.0938876 | − | 0.995583i | \(-0.529929\pi\) | ||||
−0.0938876 | + | 0.995583i | \(0.529929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.897813 | 0.0480588 | 0.0240294 | − | 0.999711i | \(-0.492350\pi\) | ||||
0.0240294 | + | 0.999711i | \(0.492350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.1594 | −0.862527 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.56450 | 0.136495 | 0.0682473 | − | 0.997668i | \(-0.478259\pi\) | ||||
0.0682473 | + | 0.997668i | \(0.478259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.71820 | 0.356565 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.913087 | 0.0483257 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.5733 | 0.980259 | 0.490130 | − | 0.871650i | \(-0.336949\pi\) | ||||
0.490130 | + | 0.871650i | \(0.336949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1604 | −0.797918 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.9794 | −1.04865 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.17899 | −0.480450 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.41854 | −0.282846 | −0.141423 | − | 0.989949i | \(-0.545168\pi\) | ||||
−0.141423 | + | 0.989949i | \(0.545168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.16484 | −0.0606390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.78201 | −0.196352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.81215 | 0.249164 | 0.124582 | − | 0.992209i | \(-0.460241\pi\) | ||||
0.124582 | + | 0.992209i | \(0.460241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.6089 | 1.11588 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.830650 | −0.0427807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7484 | 1.01441 | 0.507204 | − | 0.861826i | \(-0.330679\pi\) | ||||
0.507204 | + | 0.861826i | \(0.330679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.7082 | 1.11214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.3952 | −1.55312 | −0.776561 | − | 0.630043i | \(-0.783037\pi\) | ||||
−0.776561 | + | 0.630043i | \(0.783037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.439576 | 0.0224029 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.39653 | −0.121823 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.6896 | 1.75883 | 0.879417 | − | 0.476051i | \(-0.157932\pi\) | ||||
0.879417 | + | 0.476051i | \(0.157932\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.07512 | 0.307232 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38.6725 | 1.95077 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.52775 | −0.227816 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.18192 | 0.360450 | 0.180225 | − | 0.983625i | \(-0.442317\pi\) | ||||
0.180225 | + | 0.983625i | \(0.442317\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.83328 | −0.0917786 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.4454 | 0.521621 | 0.260810 | − | 0.965390i | \(-0.416010\pi\) | ||||
0.260810 | + | 0.965390i | \(0.416010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.79806 | −0.338635 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.0934 | 0.749995 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0690969 | 0.00342501 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1123 | −0.549466 | −0.274733 | − | 0.961520i | \(-0.588590\pi\) | ||||
−0.274733 | + | 0.961520i | \(0.588590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.1518 | 0.599403 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.10382 | 0.0543154 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.21065 | −0.206693 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.7380 | −0.868634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.1323 | 1.61862 | 0.809309 | − | 0.587383i | \(-0.199842\pi\) | ||||
0.809309 | + | 0.587383i | \(0.199842\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.0960 | 1.75921 | 0.879605 | − | 0.475704i | \(-0.157807\pi\) | ||||
0.879605 | + | 0.475704i | \(0.157807\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.11351 | 0.102762 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.78620 | 0.135151 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.64493 | 0.273177 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.93886 | 0.190170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.8845 | −1.58399 | −0.791996 | − | 0.610526i | \(-0.790958\pi\) | ||||
−0.791996 | + | 0.610526i | \(0.790958\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5043 | 0.552860 | 0.276430 | − | 0.961034i | \(-0.410849\pi\) | ||||
0.276430 | + | 0.961034i | \(0.410849\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.656589 | 0.0314810 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.1975 | −0.583485 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5543 | 0.981004 | 0.490502 | − | 0.871440i | \(-0.336813\pi\) | ||||
0.490502 | + | 0.871440i | \(0.336813\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.56522 | −0.169772 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.3136 | 1.48775 | 0.743877 | − | 0.668317i | \(-0.232985\pi\) | ||||
0.743877 | + | 0.668317i | \(0.232985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4384 | −0.589639 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.1767 | −1.71110 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3467 | −1.29057 | −0.645286 | − | 0.763941i | \(-0.723262\pi\) | ||||
−0.645286 | + | 0.763941i | \(0.723262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.32920 | −0.0625897 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.37143 | 0.299356 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.53901 | 0.119031 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.3735 | 1.65470 | 0.827350 | − | 0.561686i | \(-0.189847\pi\) | ||||
0.827350 | + | 0.561686i | \(0.189847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.53142 | 0.211509 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86418 | 0.133398 | 0.0666991 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0666991 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.335522 | −0.0155930 | −0.00779651 | − | 0.999970i | \(-0.502482\pi\) | ||||
−0.00779651 | + | 0.999970i | \(0.502482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.37354 | 0.249192 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.19806 | −0.240538 | −0.120269 | − | 0.992741i | \(-0.538376\pi\) | ||||
−0.120269 | + | 0.992741i | \(0.538376\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.64029 | 0.214269 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.40273 | 0.295022 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.73470 | −0.125742 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.59407 | −0.256673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.00924 | 0.183571 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.45623 | 0.0665370 | 0.0332685 | − | 0.999446i | \(-0.489408\pi\) | ||||
0.0332685 | + | 0.999446i | \(0.489408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.399107 | 0.0181977 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.82394 | 0.264998 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.2312 | −0.918652 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.6526 | 0.618658 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −40.4130 | −1.82754 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.5999 | −0.929660 | −0.464830 | − | 0.885400i | \(-0.653885\pi\) | ||||
−0.464830 | + | 0.885400i | \(0.653885\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.232930 | 0.0104907 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.465987 | −0.0209446 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.28480 | 0.102487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5332 | −0.963958 | −0.481979 | − | 0.876183i | \(-0.660082\pi\) | ||||
−0.481979 | + | 0.876183i | \(0.660082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.7079 | 1.10387 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.8753 | −1.82254 | −0.911270 | − | 0.411810i | \(-0.864897\pi\) | ||||
−0.911270 | + | 0.411810i | \(0.864897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.95782 | 0.176121 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.66698 | −0.0740330 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2908 | −0.899372 | −0.449686 | − | 0.893187i | \(-0.648464\pi\) | ||||
−0.449686 | + | 0.893187i | \(0.648464\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.12169 | −0.138095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.09808 | −0.401690 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.55490 | −0.244778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.41174 | 0.106068 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.83209 | 0.256000 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2044 | 0.666117 | 0.333059 | − | 0.942906i | \(-0.391919\pi\) | ||||
0.333059 | + | 0.942906i | \(0.391919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.8582 | 0.955793 | 0.477896 | − | 0.878416i | \(-0.341399\pi\) | ||||
0.477896 | + | 0.878416i | \(0.341399\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.67100 | 0.116572 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.90631 | 0.0830401 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.7489 | 0.684736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.17014 | −0.0507798 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.67753 | −0.332551 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.7826 | 0.509404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.9316 | −0.471735 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.06830 | −0.175234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3644 | 1.00452 | 0.502258 | − | 0.864718i | \(-0.332503\pi\) | ||||
0.502258 | + | 0.864718i | \(0.332503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.5344 | −1.65367 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.9072 | 0.895565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2811 | 0.696130 | 0.348065 | − | 0.937470i | \(-0.386839\pi\) | ||||
0.348065 | + | 0.937470i | \(0.386839\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.98410 | −0.255395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.467672 | −0.0199235 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.53985 | −0.0654809 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.315475 | −0.0133911 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6940 | 0.453120 | 0.226560 | − | 0.973997i | \(-0.427252\pi\) | ||||
0.226560 | + | 0.973997i | \(0.427252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7957 | −0.668088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10453 | −0.0466334 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.76883 | −0.116692 | −0.0583461 | − | 0.998296i | \(-0.518583\pi\) | ||||
−0.0583461 | + | 0.998296i | \(0.518583\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.2894 | 0.937721 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.13311 | 0.215570 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.5177 | 1.69859 | 0.849296 | − | 0.527917i | \(-0.177027\pi\) | ||||
0.849296 | + | 0.527917i | \(0.177027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9082 | −0.749436 | −0.374718 | − | 0.927139i | \(-0.622260\pi\) | ||||
−0.374718 | + | 0.927139i | \(0.622260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.59228 | 0.0665184 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.7712 | 0.741110 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4904 | 1.35259 | 0.676296 | − | 0.736630i | \(-0.263584\pi\) | ||||
0.676296 | + | 0.736630i | \(0.263584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0512 | −0.916416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.43200 | −0.0594095 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.57497 | 0.189476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.69156 | −0.111282 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.16993 | −0.254660 | −0.127330 | − | 0.991860i | \(-0.540641\pi\) | ||||
−0.127330 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.82744 | −0.157707 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.8515 | −0.487504 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.13388 | 0.334018 | 0.167009 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167009 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.711987 | −0.0291886 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.1746 | −1.43960 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.9323 | 1.42730 | 0.713648 | − | 0.700504i | \(-0.247041\pi\) | ||||
0.713648 | + | 0.700504i | \(0.247041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.1604 | 0.903940 | 0.451970 | − | 0.892033i | \(-0.350721\pi\) | ||||
0.451970 | + | 0.892033i | \(0.350721\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.91910 | −0.200321 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.5791 | 0.633382 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.7350 | −1.00396 | −0.501981 | − | 0.864878i | \(-0.667395\pi\) | ||||
−0.501981 | + | 0.864878i | \(0.667395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.223300 | 0.00904856 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.9303 | 0.563559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6945 | 0.957013 | 0.478506 | − | 0.878084i | \(-0.341178\pi\) | ||||
0.478506 | + | 0.878084i | \(0.341178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.06872 | 0.244714 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.640308 | −0.0257778 | −0.0128889 | − | 0.999917i | \(-0.504103\pi\) | ||||
−0.0128889 | + | 0.999917i | \(0.504103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8745 | −1.36153 | −0.680766 | − | 0.732501i | \(-0.738353\pi\) | ||||
−0.680766 | + | 0.732501i | \(0.738353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9027 | 1.15983 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.23020 | −0.169479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.57532 | −0.103013 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.21766 | 0.0885646 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.111917 | −0.00446243 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6706 | 0.504410 | 0.252205 | − | 0.967674i | \(-0.418844\pi\) | ||||
0.252205 | + | 0.967674i | \(0.418844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −48.6718 | −1.93453 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9271 | −0.671733 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.4986 | −0.931050 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.42208 | −0.0958158 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.6854 | 0.777528 | 0.388764 | − | 0.921337i | \(-0.372902\pi\) | ||||
0.388764 | + | 0.921337i | \(0.372902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.5123 | 1.55821 | 0.779106 | − | 0.626892i | \(-0.215673\pi\) | ||||
0.779106 | + | 0.626892i | \(0.215673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4858 | 0.491627 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0648 | −1.14266 | −0.571328 | − | 0.820722i | \(-0.693572\pi\) | ||||
−0.571328 | + | 0.820722i | \(0.693572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.33526 | −0.0524134 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.82749 | 0.0716249 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.6203 | 1.66786 | 0.833930 | − | 0.551870i | \(-0.186086\pi\) | ||||
0.833930 | + | 0.551870i | \(0.186086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.1552 | −1.17826 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.30925 | 0.129106 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.2649 | −1.33477 | −0.667385 | − | 0.744713i | \(-0.732586\pi\) | ||||
−0.667385 | + | 0.744713i | \(0.732586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.4331 | 1.92272 | 0.961361 | − | 0.275289i | \(-0.0887737\pi\) | ||||
0.961361 | + | 0.275289i | \(0.0887737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.37982 | −0.247772 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.42951 | 0.0554341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.48570 | 0.0575265 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0612 | −0.543636 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.82850 | −0.263611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3737 | 0.592612 | 0.296306 | − | 0.955093i | \(-0.404245\pi\) | ||||
0.296306 | + | 0.955093i | \(0.404245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.2555 | 0.510204 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.5481 | 1.67369 | 0.836844 | − | 0.547441i | \(-0.184398\pi\) | ||||
0.836844 | + | 0.547441i | \(0.184398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.88044 | −0.264047 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.2081 | −0.889335 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3400 | −0.663498 | −0.331749 | − | 0.943368i | \(-0.607639\pi\) | ||||
−0.331749 | + | 0.943368i | \(0.607639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.47546 | −0.362039 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.6916 | 0.407910 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.4252 | 1.00672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8687 | 0.869966 | 0.434983 | − | 0.900439i | \(-0.356754\pi\) | ||||
0.434983 | + | 0.900439i | \(0.356754\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.158478 | −0.00602008 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.8314 | 0.524653 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.15293 | 0.0815480 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3739 | −0.770610 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2294 | 0.801822 | 0.400911 | − | 0.916117i | \(-0.368694\pi\) | ||||
0.400911 | + | 0.916117i | \(0.368694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.224705 | 0.00847490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.0112 | −0.414706 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.34602 | 0.0506222 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.50721 | 0.281939 | 0.140970 | − | 0.990014i | \(-0.454978\pi\) | ||||
0.140970 | + | 0.990014i | \(0.454978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.63236 | 0.0612185 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.1590 | 0.455358 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.07136 | −0.114862 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.80897 | 0.216940 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.2603 | 0.457232 | 0.228616 | − | 0.973517i | \(-0.426580\pi\) | ||||
0.228616 | + | 0.973517i | \(0.426580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.88917 | −0.0703563 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.50283 | 0.167462 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.681378 | 0.0253057 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.5974 | 1.24606 | 0.623029 | − | 0.782198i | \(-0.285902\pi\) | ||||
0.623029 | + | 0.782198i | \(0.285902\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7220 | 0.767482 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.42943 | 0.163828 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.39520 | 0.273148 | 0.136574 | − | 0.990630i | \(-0.456391\pi\) | ||||
0.136574 | + | 0.990630i | \(0.456391\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.5745 | 0.685132 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.61321 | −0.206765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.78108 | 0.323017 | 0.161509 | − | 0.986871i | \(-0.448364\pi\) | ||||
0.161509 | + | 0.986871i | \(0.448364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.8093 | 0.470560 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3641 | −0.600342 | −0.300171 | − | 0.953885i | \(-0.597044\pi\) | ||||
−0.300171 | + | 0.953885i | \(0.597044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.2091 | 1.03350 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.51804 | 0.0555422 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00713 | 0.146418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34.2895 | −1.24958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.96818 | −0.180810 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.0818 | −1.63853 | −0.819263 | − | 0.573418i | \(-0.805617\pi\) | ||||
−0.819263 | + | 0.573418i | \(0.805617\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.04504 | −0.255719 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.6919 | 0.895080 | 0.447540 | − | 0.894264i | \(-0.352300\pi\) | ||||
0.447540 | + | 0.894264i | \(0.352300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.11033 | 0.257411 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.754766 | 0.0272886 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.71249 | −0.278482 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.9969 | −1.65869 | −0.829346 | − | 0.558736i | \(-0.811287\pi\) | ||||
−0.829346 | + | 0.558736i | \(0.811287\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.64088 | −0.203151 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.5026 | −0.917266 | −0.458633 | − | 0.888626i | \(-0.651661\pi\) | ||||
−0.458633 | + | 0.888626i | \(0.651661\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.57641 | 0.200311 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.107290 | −0.00384900 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.32260 | −0.154873 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.76385 | −0.0988982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.10818 | 0.0396031 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.99258 | −0.178193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.2584 | −1.43506 | −0.717528 | − | 0.696530i | \(-0.754726\pi\) | ||||
−0.717528 | + | 0.696530i | \(0.754726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.4766 | −1.08499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.58040 | 0.269528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.4416 | −1.40061 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.8879 | −0.740816 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.5588 | 1.18871 | 0.594357 | − | 0.804201i | \(-0.297407\pi\) | ||||
0.594357 | + | 0.804201i | \(0.297407\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.90632 | −0.138196 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.48436 | 0.158447 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.77621 | 0.133259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.54127 | −0.160059 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.1583 | 1.20243 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.7743 | −1.08197 | −0.540983 | − | 0.841034i | \(-0.681948\pi\) | ||||
−0.540983 | + | 0.841034i | \(0.681948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.3081 | −0.432195 | −0.216097 | − | 0.976372i | \(-0.569333\pi\) | ||||
−0.216097 | + | 0.976372i | \(0.569333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.1285 | 1.30215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 31.5124 | 1.10383 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.89331 | −0.311138 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.915374 | −0.0319858 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58104 | 0.0551785 | 0.0275893 | − | 0.999619i | \(-0.491217\pi\) | ||||
0.0275893 | + | 0.999619i | \(0.491217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.92788 | −0.0672016 | −0.0336008 | − | 0.999435i | \(-0.510697\pi\) | ||||
−0.0336008 | + | 0.999435i | \(0.510697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.23103 | −0.112490 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.3693 | −0.360575 | −0.180287 | − | 0.983614i | \(-0.557703\pi\) | ||||
−0.180287 | + | 0.983614i | \(0.557703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.8729 | 1.45431 | 0.727154 | − | 0.686475i | \(-0.240843\pi\) | ||||
0.727154 | + | 0.686475i | \(0.240843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.9948 | −1.59554 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.58947 | 0.228312 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.2662 | −0.666735 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.06936 | 0.313483 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.3683 | −1.49724 | −0.748620 | − | 0.662999i | \(-0.769283\pi\) | ||||
−0.748620 | + | 0.662999i | \(0.769283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9430 | −0.998036 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.64693 | −0.0911652 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.29984 | 0.0447158 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.29831 | 0.182052 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.0854 | −1.78756 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.713841 | −0.0244702 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.6270 | −0.808972 | −0.404486 | − | 0.914544i | \(-0.632550\pi\) | ||||
−0.404486 | + | 0.914544i | \(0.632550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.51540 | −0.0518256 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.0946 | 1.19881 | 0.599405 | − | 0.800446i | \(-0.295404\pi\) | ||||
0.599405 | + | 0.800446i | \(0.295404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.17267 | 0.176489 | 0.0882446 | − | 0.996099i | \(-0.471874\pi\) | ||||
0.0882446 | + | 0.996099i | \(0.471874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.06391 | 0.0703380 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.3885 | −1.88545 | −0.942723 | − | 0.333575i | \(-0.891745\pi\) | ||||
−0.942723 | + | 0.333575i | \(0.891745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.54762 | −0.154624 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.1422 | −1.02368 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.86270 | 0.0631879 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.4221 | −1.09858 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.29384 | 0.246859 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.73042 | −0.193724 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7533 | 0.768323 | 0.384161 | − | 0.923266i | \(-0.374491\pi\) | ||||
0.384161 | + | 0.923266i | \(0.374491\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.5829 | 1.73985 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.8757 | −0.972848 | −0.486424 | − | 0.873723i | \(-0.661699\pi\) | ||||
−0.486424 | + | 0.873723i | \(0.661699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1280 | 0.711013 | 0.355507 | − | 0.934674i | \(-0.384308\pi\) | ||||
0.355507 | + | 0.934674i | \(0.384308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.09635 | 0.204927 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.3497 | 1.01904 | 0.509522 | − | 0.860458i | \(-0.329822\pi\) | ||||
0.509522 | + | 0.860458i | \(0.329822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.75676 | −0.193076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.20936 | −0.208021 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.84302 | 0.262457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.52403 | 0.284927 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40.6924 | −1.35868 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.466196 | 0.0155485 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.41015 | −0.246868 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.24629 | 0.141308 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.0475 | 0.998813 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.5499 | 1.97732 | 0.988660 | − | 0.150169i | \(-0.0479819\pi\) | ||||
0.988660 | + | 0.150169i | \(0.0479819\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.42689 | −0.0473270 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8283 | −0.491283 | −0.245642 | − | 0.969361i | \(-0.578999\pi\) | ||||
−0.245642 | + | 0.969361i | \(0.578999\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.73225 | 0.0573290 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.1767 | 1.03067 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2555 | −0.338667 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.0890 | −1.48735 | −0.743674 | − | 0.668542i | \(-0.766919\pi\) | ||||
−0.743674 | + | 0.668542i | \(0.766919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.166079 | −0.00547250 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.9641 | −0.525464 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.327385 | −0.0107644 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00267 | 0.0657765 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.36673 | 0.176077 | 0.0880383 | − | 0.996117i | \(-0.471940\pi\) | ||||
0.0880383 | + | 0.996117i | \(0.471940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.2302 | −0.433602 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.3581 | 1.22305 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.861269 | 0.0281665 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.517479 | −0.0169053 | −0.00845265 | − | 0.999964i | \(-0.502691\pi\) | ||||
−0.00845265 | + | 0.999964i | \(0.502691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.1259 | −0.493614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.9991 | 0.684552 | 0.342276 | − | 0.939599i | \(-0.388802\pi\) | ||||
0.342276 | + | 0.939599i | \(0.388802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.7320 | 0.447176 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.38732 | −0.110189 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.4674 | −0.762587 | −0.381293 | − | 0.924454i | \(-0.624521\pi\) | ||||
−0.381293 | + | 0.924454i | \(0.624521\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.8115 | 0.708031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.6543 | 1.28588 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.5154 | 0.373019 | 0.186510 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186510 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.24159 | −0.0401770 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.270119 | −0.00873170 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.22251 | −0.104060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.1846 | −0.876924 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.24790 | −0.136887 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.1946 | 0.553514 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.9435 | 1.47744 | 0.738722 | − | 0.674010i | \(-0.235429\pi\) | ||||
0.738722 | + | 0.674010i | \(0.235429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.59197 | −0.115391 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.3784 | 0.782340 | 0.391170 | − | 0.920318i | \(-0.372070\pi\) | ||||
0.391170 | + | 0.920318i | \(0.372070\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.70391 | 0.150800 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.6625 | −0.597679 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.75204 | −0.216017 | −0.108008 | − | 0.994150i | \(-0.534447\pi\) | ||||
−0.108008 | + | 0.994150i | \(0.534447\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.11714 | 0.163544 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.53754 | −0.240655 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.2737 | 0.519051 | 0.259525 | − | 0.965736i | \(-0.416434\pi\) | ||||
0.259525 | + | 0.965736i | \(0.416434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.24127 | 0.294451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.74481 | −0.119199 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.2522 | 0.898368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7447 | −0.976637 | −0.488319 | − | 0.872665i | \(-0.662390\pi\) | ||||
−0.488319 | + | 0.872665i | \(0.662390\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.10088 | −0.0349355 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.4277 | 0.869516 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.8157 | −1.89438 | −0.947191 | − | 0.320670i | \(-0.896092\pi\) | ||||
−0.947191 | + | 0.320670i | \(0.896092\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.532452 | −0.0168460 |
(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.1.38 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.38 | ✓ | 44 | 1.1 | even | 1 | trivial |