Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33568 | −0.944466 | −0.472233 | − | 0.881474i | \(-0.656552\pi\) | ||||
−0.472233 | + | 0.881474i | \(0.656552\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.215968 | −0.107984 | ||||||||
\(5\) | 1.69750 | 0.759143 | 0.379572 | − | 0.925162i | \(-0.376071\pi\) | ||||
0.379572 | + | 0.925162i | \(0.376071\pi\) | |||||||
\(6\) | 1.33568 | 0.545288 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.95982 | 1.04645 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.26731 | −0.716985 | ||||||||
\(11\) | 3.75523 | 1.13224 | 0.566122 | − | 0.824322i | \(-0.308443\pi\) | ||||
0.566122 | + | 0.824322i | \(0.308443\pi\) | |||||||
\(12\) | 0.215968 | 0.0623447 | ||||||||
\(13\) | 5.32280 | 1.47628 | 0.738139 | − | 0.674648i | \(-0.235705\pi\) | ||||
0.738139 | + | 0.674648i | \(0.235705\pi\) | |||||||
\(14\) | −1.33568 | −0.356975 | ||||||||
\(15\) | −1.69750 | −0.438292 | ||||||||
\(16\) | −3.52142 | −0.880355 | ||||||||
\(17\) | −2.49651 | −0.605493 | −0.302746 | − | 0.953071i | \(-0.597904\pi\) | ||||
−0.302746 | + | 0.953071i | \(0.597904\pi\) | |||||||
\(18\) | −1.33568 | −0.314822 | ||||||||
\(19\) | 7.37835 | 1.69271 | 0.846354 | − | 0.532620i | \(-0.178792\pi\) | ||||
0.846354 | + | 0.532620i | \(0.178792\pi\) | |||||||
\(20\) | −0.366605 | −0.0819755 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.01577 | −1.06937 | ||||||||
\(23\) | −5.92366 | −1.23517 | −0.617584 | − | 0.786505i | \(-0.711889\pi\) | ||||
−0.617584 | + | 0.786505i | \(0.711889\pi\) | |||||||
\(24\) | −2.95982 | −0.604170 | ||||||||
\(25\) | −2.11851 | −0.423702 | ||||||||
\(26\) | −7.10954 | −1.39429 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.215968 | −0.0408142 | ||||||||
\(29\) | −5.24120 | −0.973266 | −0.486633 | − | 0.873607i | \(-0.661775\pi\) | ||||
−0.486633 | + | 0.873607i | \(0.661775\pi\) | |||||||
\(30\) | 2.26731 | 0.413951 | ||||||||
\(31\) | 3.55339 | 0.638207 | 0.319104 | − | 0.947720i | \(-0.396618\pi\) | ||||
0.319104 | + | 0.947720i | \(0.396618\pi\) | |||||||
\(32\) | −1.21615 | −0.214988 | ||||||||
\(33\) | −3.75523 | −0.653701 | ||||||||
\(34\) | 3.33453 | 0.571867 | ||||||||
\(35\) | 1.69750 | 0.286929 | ||||||||
\(36\) | −0.215968 | −0.0359947 | ||||||||
\(37\) | −3.75035 | −0.616555 | −0.308277 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308277 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(38\) | −9.85509 | −1.59871 | ||||||||
\(39\) | −5.32280 | −0.852330 | ||||||||
\(40\) | 5.02428 | 0.794408 | ||||||||
\(41\) | 1.06302 | 0.166015 | 0.0830077 | − | 0.996549i | \(-0.473547\pi\) | ||||
0.0830077 | + | 0.996549i | \(0.473547\pi\) | |||||||
\(42\) | 1.33568 | 0.206099 | ||||||||
\(43\) | 4.38892 | 0.669304 | 0.334652 | − | 0.942342i | \(-0.391381\pi\) | ||||
0.334652 | + | 0.942342i | \(0.391381\pi\) | |||||||
\(44\) | −0.811010 | −0.122264 | ||||||||
\(45\) | 1.69750 | 0.253048 | ||||||||
\(46\) | 7.91210 | 1.16657 | ||||||||
\(47\) | 10.7838 | 1.57298 | 0.786489 | − | 0.617604i | \(-0.211896\pi\) | ||||
0.786489 | + | 0.617604i | \(0.211896\pi\) | |||||||
\(48\) | 3.52142 | 0.508273 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.82964 | 0.400172 | ||||||||
\(51\) | 2.49651 | 0.349581 | ||||||||
\(52\) | −1.14956 | −0.159415 | ||||||||
\(53\) | 12.9604 | 1.78025 | 0.890124 | − | 0.455718i | \(-0.150617\pi\) | ||||
0.890124 | + | 0.455718i | \(0.150617\pi\) | |||||||
\(54\) | 1.33568 | 0.181763 | ||||||||
\(55\) | 6.37448 | 0.859535 | ||||||||
\(56\) | 2.95982 | 0.395522 | ||||||||
\(57\) | −7.37835 | −0.977286 | ||||||||
\(58\) | 7.00054 | 0.919216 | ||||||||
\(59\) | 12.1700 | 1.58440 | 0.792201 | − | 0.610260i | \(-0.208935\pi\) | ||||
0.792201 | + | 0.610260i | \(0.208935\pi\) | |||||||
\(60\) | 0.366605 | 0.0473286 | ||||||||
\(61\) | 4.93871 | 0.632337 | 0.316169 | − | 0.948703i | \(-0.397603\pi\) | ||||
0.316169 | + | 0.948703i | \(0.397603\pi\) | |||||||
\(62\) | −4.74618 | −0.602765 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.66723 | 1.08340 | ||||||||
\(65\) | 9.03543 | 1.12071 | ||||||||
\(66\) | 5.01577 | 0.617398 | ||||||||
\(67\) | 12.8390 | 1.56853 | 0.784266 | − | 0.620425i | \(-0.213040\pi\) | ||||
0.784266 | + | 0.620425i | \(0.213040\pi\) | |||||||
\(68\) | 0.539167 | 0.0653836 | ||||||||
\(69\) | 5.92366 | 0.713125 | ||||||||
\(70\) | −2.26731 | −0.270995 | ||||||||
\(71\) | −8.68290 | −1.03047 | −0.515235 | − | 0.857049i | \(-0.672295\pi\) | ||||
−0.515235 | + | 0.857049i | \(0.672295\pi\) | |||||||
\(72\) | 2.95982 | 0.348818 | ||||||||
\(73\) | 3.19139 | 0.373524 | 0.186762 | − | 0.982405i | \(-0.440201\pi\) | ||||
0.186762 | + | 0.982405i | \(0.440201\pi\) | |||||||
\(74\) | 5.00926 | 0.582315 | ||||||||
\(75\) | 2.11851 | 0.244624 | ||||||||
\(76\) | −1.59349 | −0.182786 | ||||||||
\(77\) | 3.75523 | 0.427948 | ||||||||
\(78\) | 7.10954 | 0.804996 | ||||||||
\(79\) | −12.9595 | −1.45806 | −0.729031 | − | 0.684481i | \(-0.760029\pi\) | ||||
−0.729031 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(80\) | −5.97760 | −0.668316 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.41985 | −0.156796 | ||||||||
\(83\) | −6.28392 | −0.689750 | −0.344875 | − | 0.938649i | \(-0.612079\pi\) | ||||
−0.344875 | + | 0.938649i | \(0.612079\pi\) | |||||||
\(84\) | 0.215968 | 0.0235641 | ||||||||
\(85\) | −4.23782 | −0.459656 | ||||||||
\(86\) | −5.86218 | −0.632135 | ||||||||
\(87\) | 5.24120 | 0.561915 | ||||||||
\(88\) | 11.1148 | 1.18484 | ||||||||
\(89\) | 8.53964 | 0.905200 | 0.452600 | − | 0.891714i | \(-0.350496\pi\) | ||||
0.452600 | + | 0.891714i | \(0.350496\pi\) | |||||||
\(90\) | −2.26731 | −0.238995 | ||||||||
\(91\) | 5.32280 | 0.557981 | ||||||||
\(92\) | 1.27932 | 0.133379 | ||||||||
\(93\) | −3.55339 | −0.368469 | ||||||||
\(94\) | −14.4037 | −1.48562 | ||||||||
\(95\) | 12.5247 | 1.28501 | ||||||||
\(96\) | 1.21615 | 0.124123 | ||||||||
\(97\) | −1.20766 | −0.122619 | −0.0613097 | − | 0.998119i | \(-0.519528\pi\) | ||||
−0.0613097 | + | 0.998119i | \(0.519528\pi\) | |||||||
\(98\) | −1.33568 | −0.134924 | ||||||||
\(99\) | 3.75523 | 0.377414 | ||||||||
\(100\) | 0.457531 | 0.0457531 | ||||||||
\(101\) | 16.3275 | 1.62465 | 0.812324 | − | 0.583206i | \(-0.198202\pi\) | ||||
0.812324 | + | 0.583206i | \(0.198202\pi\) | |||||||
\(102\) | −3.33453 | −0.330168 | ||||||||
\(103\) | 7.41862 | 0.730978 | 0.365489 | − | 0.930816i | \(-0.380902\pi\) | ||||
0.365489 | + | 0.930816i | \(0.380902\pi\) | |||||||
\(104\) | 15.7545 | 1.54486 | ||||||||
\(105\) | −1.69750 | −0.165659 | ||||||||
\(106\) | −17.3109 | −1.68138 | ||||||||
\(107\) | −18.8442 | −1.82174 | −0.910871 | − | 0.412691i | \(-0.864589\pi\) | ||||
−0.910871 | + | 0.412691i | \(0.864589\pi\) | |||||||
\(108\) | 0.215968 | 0.0207816 | ||||||||
\(109\) | −5.17771 | −0.495935 | −0.247967 | − | 0.968768i | \(-0.579763\pi\) | ||||
−0.247967 | + | 0.968768i | \(0.579763\pi\) | |||||||
\(110\) | −8.51424 | −0.811801 | ||||||||
\(111\) | 3.75035 | 0.355968 | ||||||||
\(112\) | −3.52142 | −0.332743 | ||||||||
\(113\) | −4.09944 | −0.385643 | −0.192821 | − | 0.981234i | \(-0.561764\pi\) | ||||
−0.192821 | + | 0.981234i | \(0.561764\pi\) | |||||||
\(114\) | 9.85509 | 0.923013 | ||||||||
\(115\) | −10.0554 | −0.937670 | ||||||||
\(116\) | 1.13193 | 0.105097 | ||||||||
\(117\) | 5.32280 | 0.492093 | ||||||||
\(118\) | −16.2552 | −1.49641 | ||||||||
\(119\) | −2.49651 | −0.228855 | ||||||||
\(120\) | −5.02428 | −0.458652 | ||||||||
\(121\) | 3.10172 | 0.281975 | ||||||||
\(122\) | −6.59652 | −0.597221 | ||||||||
\(123\) | −1.06302 | −0.0958491 | ||||||||
\(124\) | −0.767419 | −0.0689163 | ||||||||
\(125\) | −12.0836 | −1.08079 | ||||||||
\(126\) | −1.33568 | −0.118992 | ||||||||
\(127\) | 6.02495 | 0.534628 | 0.267314 | − | 0.963610i | \(-0.413864\pi\) | ||||
0.267314 | + | 0.963610i | \(0.413864\pi\) | |||||||
\(128\) | −9.14431 | −0.808250 | ||||||||
\(129\) | −4.38892 | −0.386423 | ||||||||
\(130\) | −12.0684 | −1.05847 | ||||||||
\(131\) | −7.33967 | −0.641270 | −0.320635 | − | 0.947203i | \(-0.603896\pi\) | ||||
−0.320635 | + | 0.947203i | \(0.603896\pi\) | |||||||
\(132\) | 0.811010 | 0.0705894 | ||||||||
\(133\) | 7.37835 | 0.639784 | ||||||||
\(134\) | −17.1487 | −1.48143 | ||||||||
\(135\) | −1.69750 | −0.146097 | ||||||||
\(136\) | −7.38921 | −0.633620 | ||||||||
\(137\) | −8.68237 | −0.741785 | −0.370892 | − | 0.928676i | \(-0.620948\pi\) | ||||
−0.370892 | + | 0.928676i | \(0.620948\pi\) | |||||||
\(138\) | −7.91210 | −0.673522 | ||||||||
\(139\) | −4.14693 | −0.351738 | −0.175869 | − | 0.984414i | \(-0.556273\pi\) | ||||
−0.175869 | + | 0.984414i | \(0.556273\pi\) | |||||||
\(140\) | −0.366605 | −0.0309838 | ||||||||
\(141\) | −10.7838 | −0.908160 | ||||||||
\(142\) | 11.5975 | 0.973244 | ||||||||
\(143\) | 19.9883 | 1.67151 | ||||||||
\(144\) | −3.52142 | −0.293452 | ||||||||
\(145\) | −8.89691 | −0.738848 | ||||||||
\(146\) | −4.26267 | −0.352781 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.809958 | 0.0665781 | ||||||||
\(149\) | −20.5114 | −1.68036 | −0.840180 | − | 0.542307i | \(-0.817551\pi\) | ||||
−0.840180 | + | 0.542307i | \(0.817551\pi\) | |||||||
\(150\) | −2.82964 | −0.231039 | ||||||||
\(151\) | −15.1657 | −1.23417 | −0.617085 | − | 0.786897i | \(-0.711686\pi\) | ||||
−0.617085 | + | 0.786897i | \(0.711686\pi\) | |||||||
\(152\) | 21.8386 | 1.77134 | ||||||||
\(153\) | −2.49651 | −0.201831 | ||||||||
\(154\) | −5.01577 | −0.404182 | ||||||||
\(155\) | 6.03186 | 0.484491 | ||||||||
\(156\) | 1.14956 | 0.0920381 | ||||||||
\(157\) | 8.17014 | 0.652048 | 0.326024 | − | 0.945361i | \(-0.394291\pi\) | ||||
0.326024 | + | 0.945361i | \(0.394291\pi\) | |||||||
\(158\) | 17.3098 | 1.37709 | ||||||||
\(159\) | −12.9604 | −1.02783 | ||||||||
\(160\) | −2.06442 | −0.163207 | ||||||||
\(161\) | −5.92366 | −0.466850 | ||||||||
\(162\) | −1.33568 | −0.104941 | ||||||||
\(163\) | −11.6560 | −0.912968 | −0.456484 | − | 0.889732i | \(-0.650891\pi\) | ||||
−0.456484 | + | 0.889732i | \(0.650891\pi\) | |||||||
\(164\) | −0.229578 | −0.0179270 | ||||||||
\(165\) | −6.37448 | −0.496253 | ||||||||
\(166\) | 8.39329 | 0.651446 | ||||||||
\(167\) | −5.42683 | −0.419941 | −0.209970 | − | 0.977708i | \(-0.567337\pi\) | ||||
−0.209970 | + | 0.977708i | \(0.567337\pi\) | |||||||
\(168\) | −2.95982 | −0.228355 | ||||||||
\(169\) | 15.3322 | 1.17940 | ||||||||
\(170\) | 5.66035 | 0.434129 | ||||||||
\(171\) | 7.37835 | 0.564236 | ||||||||
\(172\) | −0.947868 | −0.0722743 | ||||||||
\(173\) | 18.3772 | 1.39719 | 0.698597 | − | 0.715515i | \(-0.253808\pi\) | ||||
0.698597 | + | 0.715515i | \(0.253808\pi\) | |||||||
\(174\) | −7.00054 | −0.530710 | ||||||||
\(175\) | −2.11851 | −0.160144 | ||||||||
\(176\) | −13.2237 | −0.996776 | ||||||||
\(177\) | −12.1700 | −0.914755 | ||||||||
\(178\) | −11.4062 | −0.854931 | ||||||||
\(179\) | 15.1027 | 1.12883 | 0.564416 | − | 0.825491i | \(-0.309101\pi\) | ||||
0.564416 | + | 0.825491i | \(0.309101\pi\) | |||||||
\(180\) | −0.366605 | −0.0273252 | ||||||||
\(181\) | −6.32077 | −0.469819 | −0.234910 | − | 0.972017i | \(-0.575479\pi\) | ||||
−0.234910 | + | 0.972017i | \(0.575479\pi\) | |||||||
\(182\) | −7.10954 | −0.526994 | ||||||||
\(183\) | −4.93871 | −0.365080 | ||||||||
\(184\) | −17.5330 | −1.29255 | ||||||||
\(185\) | −6.36621 | −0.468053 | ||||||||
\(186\) | 4.74618 | 0.348006 | ||||||||
\(187\) | −9.37496 | −0.685565 | ||||||||
\(188\) | −2.32896 | −0.169857 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −16.7290 | −1.21365 | ||||||||
\(191\) | 26.6769 | 1.93028 | 0.965138 | − | 0.261742i | \(-0.0842970\pi\) | ||||
0.965138 | + | 0.261742i | \(0.0842970\pi\) | |||||||
\(192\) | −8.66723 | −0.625504 | ||||||||
\(193\) | 13.0202 | 0.937215 | 0.468608 | − | 0.883406i | \(-0.344756\pi\) | ||||
0.468608 | + | 0.883406i | \(0.344756\pi\) | |||||||
\(194\) | 1.61305 | 0.115810 | ||||||||
\(195\) | −9.03543 | −0.647040 | ||||||||
\(196\) | −0.215968 | −0.0154263 | ||||||||
\(197\) | −14.4235 | −1.02763 | −0.513815 | − | 0.857901i | \(-0.671768\pi\) | ||||
−0.513815 | + | 0.857901i | \(0.671768\pi\) | |||||||
\(198\) | −5.01577 | −0.356455 | ||||||||
\(199\) | 2.51404 | 0.178216 | 0.0891078 | − | 0.996022i | \(-0.471598\pi\) | ||||
0.0891078 | + | 0.996022i | \(0.471598\pi\) | |||||||
\(200\) | −6.27039 | −0.443384 | ||||||||
\(201\) | −12.8390 | −0.905592 | ||||||||
\(202\) | −21.8083 | −1.53442 | ||||||||
\(203\) | −5.24120 | −0.367860 | ||||||||
\(204\) | −0.539167 | −0.0377493 | ||||||||
\(205\) | 1.80447 | 0.126030 | ||||||||
\(206\) | −9.90887 | −0.690384 | ||||||||
\(207\) | −5.92366 | −0.411723 | ||||||||
\(208\) | −18.7438 | −1.29965 | ||||||||
\(209\) | 27.7074 | 1.91656 | ||||||||
\(210\) | 2.26731 | 0.156459 | ||||||||
\(211\) | −5.58475 | −0.384470 | −0.192235 | − | 0.981349i | \(-0.561574\pi\) | ||||
−0.192235 | + | 0.981349i | \(0.561574\pi\) | |||||||
\(212\) | −2.79904 | −0.192239 | ||||||||
\(213\) | 8.68290 | 0.594942 | ||||||||
\(214\) | 25.1698 | 1.72057 | ||||||||
\(215\) | 7.45018 | 0.508098 | ||||||||
\(216\) | −2.95982 | −0.201390 | ||||||||
\(217\) | 3.55339 | 0.241220 | ||||||||
\(218\) | 6.91575 | 0.468393 | ||||||||
\(219\) | −3.19139 | −0.215654 | ||||||||
\(220\) | −1.37669 | −0.0928162 | ||||||||
\(221\) | −13.2884 | −0.893876 | ||||||||
\(222\) | −5.00926 | −0.336200 | ||||||||
\(223\) | 15.8619 | 1.06219 | 0.531095 | − | 0.847312i | \(-0.321781\pi\) | ||||
0.531095 | + | 0.847312i | \(0.321781\pi\) | |||||||
\(224\) | −1.21615 | −0.0812577 | ||||||||
\(225\) | −2.11851 | −0.141234 | ||||||||
\(226\) | 5.47552 | 0.364226 | ||||||||
\(227\) | 26.8776 | 1.78393 | 0.891964 | − | 0.452106i | \(-0.149327\pi\) | ||||
0.891964 | + | 0.452106i | \(0.149327\pi\) | |||||||
\(228\) | 1.59349 | 0.105531 | ||||||||
\(229\) | 15.2681 | 1.00895 | 0.504473 | − | 0.863427i | \(-0.331687\pi\) | ||||
0.504473 | + | 0.863427i | \(0.331687\pi\) | |||||||
\(230\) | 13.4308 | 0.885597 | ||||||||
\(231\) | −3.75523 | −0.247076 | ||||||||
\(232\) | −15.5130 | −1.01848 | ||||||||
\(233\) | 13.3056 | 0.871680 | 0.435840 | − | 0.900024i | \(-0.356451\pi\) | ||||
0.435840 | + | 0.900024i | \(0.356451\pi\) | |||||||
\(234\) | −7.10954 | −0.464765 | ||||||||
\(235\) | 18.3055 | 1.19412 | ||||||||
\(236\) | −2.62834 | −0.171090 | ||||||||
\(237\) | 12.9595 | 0.841812 | ||||||||
\(238\) | 3.33453 | 0.216146 | ||||||||
\(239\) | −18.3294 | −1.18563 | −0.592814 | − | 0.805340i | \(-0.701983\pi\) | ||||
−0.592814 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(240\) | 5.97760 | 0.385852 | ||||||||
\(241\) | −7.63094 | −0.491552 | −0.245776 | − | 0.969327i | \(-0.579043\pi\) | ||||
−0.245776 | + | 0.969327i | \(0.579043\pi\) | |||||||
\(242\) | −4.14290 | −0.266316 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.06661 | −0.0682824 | ||||||||
\(245\) | 1.69750 | 0.108449 | ||||||||
\(246\) | 1.41985 | 0.0905262 | ||||||||
\(247\) | 39.2734 | 2.49891 | ||||||||
\(248\) | 10.5174 | 0.667854 | ||||||||
\(249\) | 6.28392 | 0.398227 | ||||||||
\(250\) | 16.1398 | 1.02077 | ||||||||
\(251\) | 13.5907 | 0.857839 | 0.428919 | − | 0.903343i | \(-0.358894\pi\) | ||||
0.428919 | + | 0.903343i | \(0.358894\pi\) | |||||||
\(252\) | −0.215968 | −0.0136047 | ||||||||
\(253\) | −22.2447 | −1.39851 | ||||||||
\(254\) | −8.04738 | −0.504938 | ||||||||
\(255\) | 4.23782 | 0.265382 | ||||||||
\(256\) | −5.12063 | −0.320039 | ||||||||
\(257\) | 0.642134 | 0.0400552 | 0.0200276 | − | 0.999799i | \(-0.493625\pi\) | ||||
0.0200276 | + | 0.999799i | \(0.493625\pi\) | |||||||
\(258\) | 5.86218 | 0.364963 | ||||||||
\(259\) | −3.75035 | −0.233036 | ||||||||
\(260\) | −1.95137 | −0.121019 | ||||||||
\(261\) | −5.24120 | −0.324422 | ||||||||
\(262\) | 9.80342 | 0.605657 | ||||||||
\(263\) | −0.825121 | −0.0508791 | −0.0254396 | − | 0.999676i | \(-0.508099\pi\) | ||||
−0.0254396 | + | 0.999676i | \(0.508099\pi\) | |||||||
\(264\) | −11.1148 | −0.684068 | ||||||||
\(265\) | 22.0002 | 1.35146 | ||||||||
\(266\) | −9.85509 | −0.604254 | ||||||||
\(267\) | −8.53964 | −0.522618 | ||||||||
\(268\) | −2.77282 | −0.169377 | ||||||||
\(269\) | −18.9954 | −1.15817 | −0.579084 | − | 0.815268i | \(-0.696590\pi\) | ||||
−0.579084 | + | 0.815268i | \(0.696590\pi\) | |||||||
\(270\) | 2.26731 | 0.137984 | ||||||||
\(271\) | −11.4377 | −0.694791 | −0.347396 | − | 0.937719i | \(-0.612934\pi\) | ||||
−0.347396 | + | 0.937719i | \(0.612934\pi\) | |||||||
\(272\) | 8.79126 | 0.533049 | ||||||||
\(273\) | −5.32280 | −0.322150 | ||||||||
\(274\) | 11.5968 | 0.700590 | ||||||||
\(275\) | −7.95548 | −0.479733 | ||||||||
\(276\) | −1.27932 | −0.0770062 | ||||||||
\(277\) | 16.8365 | 1.01161 | 0.505804 | − | 0.862649i | \(-0.331196\pi\) | ||||
0.505804 | + | 0.862649i | \(0.331196\pi\) | |||||||
\(278\) | 5.53895 | 0.332204 | ||||||||
\(279\) | 3.55339 | 0.212736 | ||||||||
\(280\) | 5.02428 | 0.300258 | ||||||||
\(281\) | −9.22285 | −0.550189 | −0.275094 | − | 0.961417i | \(-0.588709\pi\) | ||||
−0.275094 | + | 0.961417i | \(0.588709\pi\) | |||||||
\(282\) | 14.4037 | 0.857726 | ||||||||
\(283\) | 25.6717 | 1.52602 | 0.763012 | − | 0.646384i | \(-0.223720\pi\) | ||||
0.763012 | + | 0.646384i | \(0.223720\pi\) | |||||||
\(284\) | 1.87523 | 0.111274 | ||||||||
\(285\) | −12.5247 | −0.741900 | ||||||||
\(286\) | −26.6979 | −1.57868 | ||||||||
\(287\) | 1.06302 | 0.0627480 | ||||||||
\(288\) | −1.21615 | −0.0716626 | ||||||||
\(289\) | −10.7674 | −0.633379 | ||||||||
\(290\) | 11.8834 | 0.697817 | ||||||||
\(291\) | 1.20766 | 0.0707944 | ||||||||
\(292\) | −0.689240 | −0.0403347 | ||||||||
\(293\) | −30.9067 | −1.80559 | −0.902795 | − | 0.430070i | \(-0.858489\pi\) | ||||
−0.902795 | + | 0.430070i | \(0.858489\pi\) | |||||||
\(294\) | 1.33568 | 0.0778982 | ||||||||
\(295\) | 20.6586 | 1.20279 | ||||||||
\(296\) | −11.1004 | −0.645195 | ||||||||
\(297\) | −3.75523 | −0.217900 | ||||||||
\(298\) | 27.3966 | 1.58704 | ||||||||
\(299\) | −31.5305 | −1.82345 | ||||||||
\(300\) | −0.457531 | −0.0264155 | ||||||||
\(301\) | 4.38892 | 0.252973 | ||||||||
\(302\) | 20.2565 | 1.16563 | ||||||||
\(303\) | −16.3275 | −0.937991 | ||||||||
\(304\) | −25.9823 | −1.49019 | ||||||||
\(305\) | 8.38344 | 0.480034 | ||||||||
\(306\) | 3.33453 | 0.190622 | ||||||||
\(307\) | −20.8554 | −1.19028 | −0.595140 | − | 0.803622i | \(-0.702903\pi\) | ||||
−0.595140 | + | 0.803622i | \(0.702903\pi\) | |||||||
\(308\) | −0.811010 | −0.0462116 | ||||||||
\(309\) | −7.41862 | −0.422030 | ||||||||
\(310\) | −8.05661 | −0.457585 | ||||||||
\(311\) | −17.0656 | −0.967700 | −0.483850 | − | 0.875151i | \(-0.660762\pi\) | ||||
−0.483850 | + | 0.875151i | \(0.660762\pi\) | |||||||
\(312\) | −15.7545 | −0.891923 | ||||||||
\(313\) | −7.13261 | −0.403159 | −0.201580 | − | 0.979472i | \(-0.564607\pi\) | ||||
−0.201580 | + | 0.979472i | \(0.564607\pi\) | |||||||
\(314\) | −10.9127 | −0.615837 | ||||||||
\(315\) | 1.69750 | 0.0956431 | ||||||||
\(316\) | 2.79885 | 0.157448 | ||||||||
\(317\) | −20.0951 | −1.12865 | −0.564326 | − | 0.825552i | \(-0.690864\pi\) | ||||
−0.564326 | + | 0.825552i | \(0.690864\pi\) | |||||||
\(318\) | 17.3109 | 0.970748 | ||||||||
\(319\) | −19.6819 | −1.10197 | ||||||||
\(320\) | 14.7126 | 0.822459 | ||||||||
\(321\) | 18.8442 | 1.05178 | ||||||||
\(322\) | 7.91210 | 0.440924 | ||||||||
\(323\) | −18.4201 | −1.02492 | ||||||||
\(324\) | −0.215968 | −0.0119982 | ||||||||
\(325\) | −11.2764 | −0.625501 | ||||||||
\(326\) | 15.5686 | 0.862267 | ||||||||
\(327\) | 5.17771 | 0.286328 | ||||||||
\(328\) | 3.14634 | 0.173727 | ||||||||
\(329\) | 10.7838 | 0.594530 | ||||||||
\(330\) | 8.51424 | 0.468694 | ||||||||
\(331\) | −8.46792 | −0.465439 | −0.232719 | − | 0.972544i | \(-0.574762\pi\) | ||||
−0.232719 | + | 0.972544i | \(0.574762\pi\) | |||||||
\(332\) | 1.35713 | 0.0744821 | ||||||||
\(333\) | −3.75035 | −0.205518 | ||||||||
\(334\) | 7.24849 | 0.396620 | ||||||||
\(335\) | 21.7941 | 1.19074 | ||||||||
\(336\) | 3.52142 | 0.192109 | ||||||||
\(337\) | 22.2680 | 1.21302 | 0.606508 | − | 0.795077i | \(-0.292570\pi\) | ||||
0.606508 | + | 0.795077i | \(0.292570\pi\) | |||||||
\(338\) | −20.4788 | −1.11390 | ||||||||
\(339\) | 4.09944 | 0.222651 | ||||||||
\(340\) | 0.915234 | 0.0496355 | ||||||||
\(341\) | 13.3438 | 0.722606 | ||||||||
\(342\) | −9.85509 | −0.532902 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.9904 | 0.700396 | ||||||||
\(345\) | 10.0554 | 0.541364 | ||||||||
\(346\) | −24.5460 | −1.31960 | ||||||||
\(347\) | −9.10153 | −0.488595 | −0.244298 | − | 0.969700i | \(-0.578557\pi\) | ||||
−0.244298 | + | 0.969700i | \(0.578557\pi\) | |||||||
\(348\) | −1.13193 | −0.0606780 | ||||||||
\(349\) | 3.77629 | 0.202140 | 0.101070 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101070 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(350\) | 2.82964 | 0.151251 | ||||||||
\(351\) | −5.32280 | −0.284110 | ||||||||
\(352\) | −4.56693 | −0.243418 | ||||||||
\(353\) | 0.491194 | 0.0261436 | 0.0130718 | − | 0.999915i | \(-0.495839\pi\) | ||||
0.0130718 | + | 0.999915i | \(0.495839\pi\) | |||||||
\(354\) | 16.2552 | 0.863955 | ||||||||
\(355\) | −14.7392 | −0.782275 | ||||||||
\(356\) | −1.84429 | −0.0977473 | ||||||||
\(357\) | 2.49651 | 0.132129 | ||||||||
\(358\) | −20.1724 | −1.06614 | ||||||||
\(359\) | 16.7852 | 0.885889 | 0.442944 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442944 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(360\) | 5.02428 | 0.264803 | ||||||||
\(361\) | 35.4400 | 1.86526 | ||||||||
\(362\) | 8.44250 | 0.443728 | ||||||||
\(363\) | −3.10172 | −0.162798 | ||||||||
\(364\) | −1.14956 | −0.0602531 | ||||||||
\(365\) | 5.41738 | 0.283558 | ||||||||
\(366\) | 6.59652 | 0.344806 | ||||||||
\(367\) | 12.9189 | 0.674360 | 0.337180 | − | 0.941440i | \(-0.390527\pi\) | ||||
0.337180 | + | 0.941440i | \(0.390527\pi\) | |||||||
\(368\) | 20.8597 | 1.08739 | ||||||||
\(369\) | 1.06302 | 0.0553385 | ||||||||
\(370\) | 8.50320 | 0.442060 | ||||||||
\(371\) | 12.9604 | 0.672871 | ||||||||
\(372\) | 0.767419 | 0.0397888 | ||||||||
\(373\) | 4.10925 | 0.212769 | 0.106385 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106385 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(374\) | 12.5219 | 0.647493 | ||||||||
\(375\) | 12.0836 | 0.623996 | ||||||||
\(376\) | 31.9181 | 1.64605 | ||||||||
\(377\) | −27.8978 | −1.43681 | ||||||||
\(378\) | 1.33568 | 0.0686998 | ||||||||
\(379\) | 8.73671 | 0.448775 | 0.224387 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224387 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(380\) | −2.70494 | −0.138761 | ||||||||
\(381\) | −6.02495 | −0.308667 | ||||||||
\(382\) | −35.6318 | −1.82308 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 9.14431 | 0.466643 | ||||||||
\(385\) | 6.37448 | 0.324874 | ||||||||
\(386\) | −17.3908 | −0.885168 | ||||||||
\(387\) | 4.38892 | 0.223101 | ||||||||
\(388\) | 0.260817 | 0.0132410 | ||||||||
\(389\) | −13.4081 | −0.679819 | −0.339909 | − | 0.940458i | \(-0.610396\pi\) | ||||
−0.339909 | + | 0.940458i | \(0.610396\pi\) | |||||||
\(390\) | 12.0684 | 0.611108 | ||||||||
\(391\) | 14.7885 | 0.747886 | ||||||||
\(392\) | 2.95982 | 0.149493 | ||||||||
\(393\) | 7.33967 | 0.370237 | ||||||||
\(394\) | 19.2651 | 0.970561 | ||||||||
\(395\) | −21.9988 | −1.10688 | ||||||||
\(396\) | −0.811010 | −0.0407548 | ||||||||
\(397\) | −16.3886 | −0.822519 | −0.411259 | − | 0.911518i | \(-0.634911\pi\) | ||||
−0.411259 | + | 0.911518i | \(0.634911\pi\) | |||||||
\(398\) | −3.35794 | −0.168319 | ||||||||
\(399\) | −7.37835 | −0.369379 | ||||||||
\(400\) | 7.46016 | 0.373008 | ||||||||
\(401\) | 27.3698 | 1.36678 | 0.683392 | − | 0.730052i | \(-0.260504\pi\) | ||||
0.683392 | + | 0.730052i | \(0.260504\pi\) | |||||||
\(402\) | 17.1487 | 0.855301 | ||||||||
\(403\) | 18.9140 | 0.942171 | ||||||||
\(404\) | −3.52623 | −0.175436 | ||||||||
\(405\) | 1.69750 | 0.0843492 | ||||||||
\(406\) | 7.00054 | 0.347431 | ||||||||
\(407\) | −14.0834 | −0.698090 | ||||||||
\(408\) | 7.38921 | 0.365821 | ||||||||
\(409\) | −10.9155 | −0.539738 | −0.269869 | − | 0.962897i | \(-0.586980\pi\) | ||||
−0.269869 | + | 0.962897i | \(0.586980\pi\) | |||||||
\(410\) | −2.41019 | −0.119031 | ||||||||
\(411\) | 8.68237 | 0.428270 | ||||||||
\(412\) | −1.60219 | −0.0789341 | ||||||||
\(413\) | 12.1700 | 0.598848 | ||||||||
\(414\) | 7.91210 | 0.388858 | ||||||||
\(415\) | −10.6669 | −0.523619 | ||||||||
\(416\) | −6.47334 | −0.317382 | ||||||||
\(417\) | 4.14693 | 0.203076 | ||||||||
\(418\) | −37.0081 | −1.81012 | ||||||||
\(419\) | 30.2530 | 1.47795 | 0.738977 | − | 0.673730i | \(-0.235309\pi\) | ||||
0.738977 | + | 0.673730i | \(0.235309\pi\) | |||||||
\(420\) | 0.366605 | 0.0178885 | ||||||||
\(421\) | 5.90060 | 0.287577 | 0.143789 | − | 0.989608i | \(-0.454071\pi\) | ||||
0.143789 | + | 0.989608i | \(0.454071\pi\) | |||||||
\(422\) | 7.45942 | 0.363119 | ||||||||
\(423\) | 10.7838 | 0.524326 | ||||||||
\(424\) | 38.3604 | 1.86295 | ||||||||
\(425\) | 5.28888 | 0.256548 | ||||||||
\(426\) | −11.5975 | −0.561903 | ||||||||
\(427\) | 4.93871 | 0.239001 | ||||||||
\(428\) | 4.06976 | 0.196719 | ||||||||
\(429\) | −19.9883 | −0.965045 | ||||||||
\(430\) | −9.95103 | −0.479881 | ||||||||
\(431\) | −1.01165 | −0.0487294 | −0.0243647 | − | 0.999703i | \(-0.507756\pi\) | ||||
−0.0243647 | + | 0.999703i | \(0.507756\pi\) | |||||||
\(432\) | 3.52142 | 0.169424 | ||||||||
\(433\) | 31.7253 | 1.52462 | 0.762311 | − | 0.647211i | \(-0.224065\pi\) | ||||
0.762311 | + | 0.647211i | \(0.224065\pi\) | |||||||
\(434\) | −4.74618 | −0.227824 | ||||||||
\(435\) | 8.89691 | 0.426574 | ||||||||
\(436\) | 1.11822 | 0.0535531 | ||||||||
\(437\) | −43.7068 | −2.09078 | ||||||||
\(438\) | 4.26267 | 0.203678 | ||||||||
\(439\) | 21.5617 | 1.02909 | 0.514543 | − | 0.857465i | \(-0.327962\pi\) | ||||
0.514543 | + | 0.857465i | \(0.327962\pi\) | |||||||
\(440\) | 18.8673 | 0.899463 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 17.7490 | 0.844235 | ||||||||
\(443\) | −35.5429 | −1.68869 | −0.844346 | − | 0.535798i | \(-0.820011\pi\) | ||||
−0.844346 | + | 0.535798i | \(0.820011\pi\) | |||||||
\(444\) | −0.809958 | −0.0384389 | ||||||||
\(445\) | 14.4960 | 0.687177 | ||||||||
\(446\) | −21.1863 | −1.00320 | ||||||||
\(447\) | 20.5114 | 0.970157 | ||||||||
\(448\) | 8.66723 | 0.409488 | ||||||||
\(449\) | −31.2291 | −1.47379 | −0.736896 | − | 0.676006i | \(-0.763709\pi\) | ||||
−0.736896 | + | 0.676006i | \(0.763709\pi\) | |||||||
\(450\) | 2.82964 | 0.133391 | ||||||||
\(451\) | 3.99187 | 0.187970 | ||||||||
\(452\) | 0.885349 | 0.0416433 | ||||||||
\(453\) | 15.1657 | 0.712548 | ||||||||
\(454\) | −35.8998 | −1.68486 | ||||||||
\(455\) | 9.03543 | 0.423587 | ||||||||
\(456\) | −21.8386 | −1.02268 | ||||||||
\(457\) | 14.8037 | 0.692487 | 0.346243 | − | 0.938145i | \(-0.387457\pi\) | ||||
0.346243 | + | 0.938145i | \(0.387457\pi\) | |||||||
\(458\) | −20.3933 | −0.952915 | ||||||||
\(459\) | 2.49651 | 0.116527 | ||||||||
\(460\) | 2.17165 | 0.101254 | ||||||||
\(461\) | −26.9870 | −1.25691 | −0.628455 | − | 0.777846i | \(-0.716312\pi\) | ||||
−0.628455 | + | 0.777846i | \(0.716312\pi\) | |||||||
\(462\) | 5.01577 | 0.233355 | ||||||||
\(463\) | 20.7330 | 0.963545 | 0.481772 | − | 0.876296i | \(-0.339993\pi\) | ||||
0.481772 | + | 0.876296i | \(0.339993\pi\) | |||||||
\(464\) | 18.4565 | 0.856820 | ||||||||
\(465\) | −6.03186 | −0.279721 | ||||||||
\(466\) | −17.7720 | −0.823272 | ||||||||
\(467\) | −26.8341 | −1.24174 | −0.620868 | − | 0.783915i | \(-0.713220\pi\) | ||||
−0.620868 | + | 0.783915i | \(0.713220\pi\) | |||||||
\(468\) | −1.14956 | −0.0531382 | ||||||||
\(469\) | 12.8390 | 0.592849 | ||||||||
\(470\) | −24.4502 | −1.12780 | ||||||||
\(471\) | −8.17014 | −0.376460 | ||||||||
\(472\) | 36.0210 | 1.65800 | ||||||||
\(473\) | 16.4814 | 0.757816 | ||||||||
\(474\) | −17.3098 | −0.795063 | ||||||||
\(475\) | −15.6311 | −0.717203 | ||||||||
\(476\) | 0.539167 | 0.0247127 | ||||||||
\(477\) | 12.9604 | 0.593416 | ||||||||
\(478\) | 24.4821 | 1.11978 | ||||||||
\(479\) | 24.6417 | 1.12591 | 0.562954 | − | 0.826488i | \(-0.309665\pi\) | ||||
0.562954 | + | 0.826488i | \(0.309665\pi\) | |||||||
\(480\) | 2.06442 | 0.0942273 | ||||||||
\(481\) | −19.9624 | −0.910206 | ||||||||
\(482\) | 10.1925 | 0.464254 | ||||||||
\(483\) | 5.92366 | 0.269536 | ||||||||
\(484\) | −0.669874 | −0.0304488 | ||||||||
\(485\) | −2.05000 | −0.0930858 | ||||||||
\(486\) | 1.33568 | 0.0605875 | ||||||||
\(487\) | 18.0099 | 0.816108 | 0.408054 | − | 0.912958i | \(-0.366208\pi\) | ||||
0.408054 | + | 0.912958i | \(0.366208\pi\) | |||||||
\(488\) | 14.6177 | 0.661711 | ||||||||
\(489\) | 11.6560 | 0.527102 | ||||||||
\(490\) | −2.26731 | −0.102426 | ||||||||
\(491\) | −19.2469 | −0.868601 | −0.434301 | − | 0.900768i | \(-0.643004\pi\) | ||||
−0.434301 | + | 0.900768i | \(0.643004\pi\) | |||||||
\(492\) | 0.229578 | 0.0103502 | ||||||||
\(493\) | 13.0847 | 0.589305 | ||||||||
\(494\) | −52.4566 | −2.36013 | ||||||||
\(495\) | 6.37448 | 0.286512 | ||||||||
\(496\) | −12.5130 | −0.561849 | ||||||||
\(497\) | −8.68290 | −0.389481 | ||||||||
\(498\) | −8.39329 | −0.376112 | ||||||||
\(499\) | 16.4691 | 0.737260 | 0.368630 | − | 0.929576i | \(-0.379827\pi\) | ||||
0.368630 | + | 0.929576i | \(0.379827\pi\) | |||||||
\(500\) | 2.60968 | 0.116709 | ||||||||
\(501\) | 5.42683 | 0.242453 | ||||||||
\(502\) | −18.1528 | −0.810199 | ||||||||
\(503\) | 3.03448 | 0.135301 | 0.0676504 | − | 0.997709i | \(-0.478450\pi\) | ||||
0.0676504 | + | 0.997709i | \(0.478450\pi\) | |||||||
\(504\) | 2.95982 | 0.131841 | ||||||||
\(505\) | 27.7159 | 1.23334 | ||||||||
\(506\) | 29.7117 | 1.32085 | ||||||||
\(507\) | −15.3322 | −0.680926 | ||||||||
\(508\) | −1.30120 | −0.0577313 | ||||||||
\(509\) | 23.0428 | 1.02135 | 0.510677 | − | 0.859773i | \(-0.329395\pi\) | ||||
0.510677 | + | 0.859773i | \(0.329395\pi\) | |||||||
\(510\) | −5.66035 | −0.250645 | ||||||||
\(511\) | 3.19139 | 0.141179 | ||||||||
\(512\) | 25.1281 | 1.11052 | ||||||||
\(513\) | −7.37835 | −0.325762 | ||||||||
\(514\) | −0.857684 | −0.0378308 | ||||||||
\(515\) | 12.5931 | 0.554917 | ||||||||
\(516\) | 0.947868 | 0.0417276 | ||||||||
\(517\) | 40.4956 | 1.78099 | ||||||||
\(518\) | 5.00926 | 0.220094 | ||||||||
\(519\) | −18.3772 | −0.806670 | ||||||||
\(520\) | 26.7432 | 1.17277 | ||||||||
\(521\) | −22.8920 | −1.00291 | −0.501457 | − | 0.865182i | \(-0.667203\pi\) | ||||
−0.501457 | + | 0.865182i | \(0.667203\pi\) | |||||||
\(522\) | 7.00054 | 0.306405 | ||||||||
\(523\) | −20.1557 | −0.881347 | −0.440674 | − | 0.897667i | \(-0.645260\pi\) | ||||
−0.440674 | + | 0.897667i | \(0.645260\pi\) | |||||||
\(524\) | 1.58514 | 0.0692470 | ||||||||
\(525\) | 2.11851 | 0.0924593 | ||||||||
\(526\) | 1.10209 | 0.0480536 | ||||||||
\(527\) | −8.87107 | −0.386430 | ||||||||
\(528\) | 13.2237 | 0.575489 | ||||||||
\(529\) | 12.0898 | 0.525642 | ||||||||
\(530\) | −29.3852 | −1.27641 | ||||||||
\(531\) | 12.1700 | 0.528134 | ||||||||
\(532\) | −1.59349 | −0.0690865 | ||||||||
\(533\) | 5.65823 | 0.245085 | ||||||||
\(534\) | 11.4062 | 0.493595 | ||||||||
\(535\) | −31.9880 | −1.38296 | ||||||||
\(536\) | 38.0011 | 1.64140 | ||||||||
\(537\) | −15.1027 | −0.651731 | ||||||||
\(538\) | 25.3717 | 1.09385 | ||||||||
\(539\) | 3.75523 | 0.161749 | ||||||||
\(540\) | 0.366605 | 0.0157762 | ||||||||
\(541\) | 22.4002 | 0.963062 | 0.481531 | − | 0.876429i | \(-0.340081\pi\) | ||||
0.481531 | + | 0.876429i | \(0.340081\pi\) | |||||||
\(542\) | 15.2771 | 0.656206 | ||||||||
\(543\) | 6.32077 | 0.271250 | ||||||||
\(544\) | 3.03614 | 0.130174 | ||||||||
\(545\) | −8.78914 | −0.376485 | ||||||||
\(546\) | 7.10954 | 0.304260 | ||||||||
\(547\) | −31.9766 | −1.36722 | −0.683610 | − | 0.729847i | \(-0.739591\pi\) | ||||
−0.683610 | + | 0.729847i | \(0.739591\pi\) | |||||||
\(548\) | 1.87512 | 0.0801010 | ||||||||
\(549\) | 4.93871 | 0.210779 | ||||||||
\(550\) | 10.6259 | 0.453092 | ||||||||
\(551\) | −38.6714 | −1.64746 | ||||||||
\(552\) | 17.5330 | 0.746252 | ||||||||
\(553\) | −12.9595 | −0.551096 | ||||||||
\(554\) | −22.4881 | −0.955429 | ||||||||
\(555\) | 6.36621 | 0.270231 | ||||||||
\(556\) | 0.895605 | 0.0379821 | ||||||||
\(557\) | −1.77205 | −0.0750841 | −0.0375421 | − | 0.999295i | \(-0.511953\pi\) | ||||
−0.0375421 | + | 0.999295i | \(0.511953\pi\) | |||||||
\(558\) | −4.74618 | −0.200922 | ||||||||
\(559\) | 23.3613 | 0.988080 | ||||||||
\(560\) | −5.97760 | −0.252600 | ||||||||
\(561\) | 9.37496 | 0.395811 | ||||||||
\(562\) | 12.3187 | 0.519635 | ||||||||
\(563\) | −33.1272 | −1.39615 | −0.698073 | − | 0.716027i | \(-0.745959\pi\) | ||||
−0.698073 | + | 0.716027i | \(0.745959\pi\) | |||||||
\(564\) | 2.32896 | 0.0980669 | ||||||||
\(565\) | −6.95878 | −0.292758 | ||||||||
\(566\) | −34.2891 | −1.44128 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −25.6998 | −1.07834 | ||||||||
\(569\) | −41.5393 | −1.74142 | −0.870710 | − | 0.491798i | \(-0.836340\pi\) | ||||
−0.870710 | + | 0.491798i | \(0.836340\pi\) | |||||||
\(570\) | 16.7290 | 0.700699 | ||||||||
\(571\) | −32.2555 | −1.34985 | −0.674926 | − | 0.737885i | \(-0.735824\pi\) | ||||
−0.674926 | + | 0.737885i | \(0.735824\pi\) | |||||||
\(572\) | −4.31684 | −0.180496 | ||||||||
\(573\) | −26.6769 | −1.11445 | ||||||||
\(574\) | −1.41985 | −0.0592633 | ||||||||
\(575\) | 12.5493 | 0.523343 | ||||||||
\(576\) | 8.66723 | 0.361135 | ||||||||
\(577\) | 33.6431 | 1.40058 | 0.700289 | − | 0.713859i | \(-0.253054\pi\) | ||||
0.700289 | + | 0.713859i | \(0.253054\pi\) | |||||||
\(578\) | 14.3818 | 0.598204 | ||||||||
\(579\) | −13.0202 | −0.541101 | ||||||||
\(580\) | 1.92145 | 0.0797839 | ||||||||
\(581\) | −6.28392 | −0.260701 | ||||||||
\(582\) | −1.61305 | −0.0668629 | ||||||||
\(583\) | 48.6693 | 2.01567 | ||||||||
\(584\) | 9.44594 | 0.390876 | ||||||||
\(585\) | 9.03543 | 0.373569 | ||||||||
\(586\) | 41.2814 | 1.70532 | ||||||||
\(587\) | −40.6368 | −1.67726 | −0.838631 | − | 0.544700i | \(-0.816643\pi\) | ||||
−0.838631 | + | 0.544700i | \(0.816643\pi\) | |||||||
\(588\) | 0.215968 | 0.00890638 | ||||||||
\(589\) | 26.2181 | 1.08030 | ||||||||
\(590\) | −27.5932 | −1.13599 | ||||||||
\(591\) | 14.4235 | 0.593302 | ||||||||
\(592\) | 13.2066 | 0.542787 | ||||||||
\(593\) | 7.77946 | 0.319464 | 0.159732 | − | 0.987160i | \(-0.448937\pi\) | ||||
0.159732 | + | 0.987160i | \(0.448937\pi\) | |||||||
\(594\) | 5.01577 | 0.205799 | ||||||||
\(595\) | −4.23782 | −0.173734 | ||||||||
\(596\) | 4.42982 | 0.181452 | ||||||||
\(597\) | −2.51404 | −0.102893 | ||||||||
\(598\) | 42.1145 | 1.72219 | ||||||||
\(599\) | −19.5135 | −0.797300 | −0.398650 | − | 0.917103i | \(-0.630521\pi\) | ||||
−0.398650 | + | 0.917103i | \(0.630521\pi\) | |||||||
\(600\) | 6.27039 | 0.255988 | ||||||||
\(601\) | 10.6220 | 0.433281 | 0.216640 | − | 0.976251i | \(-0.430490\pi\) | ||||
0.216640 | + | 0.976251i | \(0.430490\pi\) | |||||||
\(602\) | −5.86218 | −0.238925 | ||||||||
\(603\) | 12.8390 | 0.522844 | ||||||||
\(604\) | 3.27532 | 0.133271 | ||||||||
\(605\) | 5.26516 | 0.214059 | ||||||||
\(606\) | 21.8083 | 0.885900 | ||||||||
\(607\) | −28.0475 | −1.13841 | −0.569207 | − | 0.822194i | \(-0.692750\pi\) | ||||
−0.569207 | + | 0.822194i | \(0.692750\pi\) | |||||||
\(608\) | −8.97321 | −0.363912 | ||||||||
\(609\) | 5.24120 | 0.212384 | ||||||||
\(610\) | −11.1976 | −0.453376 | ||||||||
\(611\) | 57.4000 | 2.32215 | ||||||||
\(612\) | 0.539167 | 0.0217945 | ||||||||
\(613\) | −16.2849 | −0.657743 | −0.328871 | − | 0.944375i | \(-0.606668\pi\) | ||||
−0.328871 | + | 0.944375i | \(0.606668\pi\) | |||||||
\(614\) | 27.8560 | 1.12418 | ||||||||
\(615\) | −1.80447 | −0.0727632 | ||||||||
\(616\) | 11.1148 | 0.447827 | ||||||||
\(617\) | −0.624218 | −0.0251301 | −0.0125650 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125650 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(618\) | 9.90887 | 0.398593 | ||||||||
\(619\) | 2.50764 | 0.100791 | 0.0503953 | − | 0.998729i | \(-0.483952\pi\) | ||||
0.0503953 | + | 0.998729i | \(0.483952\pi\) | |||||||
\(620\) | −1.30269 | −0.0523173 | ||||||||
\(621\) | 5.92366 | 0.237708 | ||||||||
\(622\) | 22.7941 | 0.913960 | ||||||||
\(623\) | 8.53964 | 0.342134 | ||||||||
\(624\) | 18.7438 | 0.750353 | ||||||||
\(625\) | −9.91939 | −0.396775 | ||||||||
\(626\) | 9.52687 | 0.380770 | ||||||||
\(627\) | −27.7074 | −1.10653 | ||||||||
\(628\) | −1.76449 | −0.0704109 | ||||||||
\(629\) | 9.36280 | 0.373319 | ||||||||
\(630\) | −2.26731 | −0.0903316 | ||||||||
\(631\) | −40.3774 | −1.60740 | −0.803699 | − | 0.595037i | \(-0.797138\pi\) | ||||
−0.803699 | + | 0.595037i | \(0.797138\pi\) | |||||||
\(632\) | −38.3579 | −1.52579 | ||||||||
\(633\) | 5.58475 | 0.221974 | ||||||||
\(634\) | 26.8405 | 1.06597 | ||||||||
\(635\) | 10.2273 | 0.405859 | ||||||||
\(636\) | 2.79904 | 0.110989 | ||||||||
\(637\) | 5.32280 | 0.210897 | ||||||||
\(638\) | 26.2886 | 1.04078 | ||||||||
\(639\) | −8.68290 | −0.343490 | ||||||||
\(640\) | −15.5224 | −0.613578 | ||||||||
\(641\) | 13.2862 | 0.524773 | 0.262386 | − | 0.964963i | \(-0.415491\pi\) | ||||
0.262386 | + | 0.964963i | \(0.415491\pi\) | |||||||
\(642\) | −25.1698 | −0.993374 | ||||||||
\(643\) | −17.4125 | −0.686682 | −0.343341 | − | 0.939211i | \(-0.611559\pi\) | ||||
−0.343341 | + | 0.939211i | \(0.611559\pi\) | |||||||
\(644\) | 1.27932 | 0.0504124 | ||||||||
\(645\) | −7.45018 | −0.293351 | ||||||||
\(646\) | 24.6033 | 0.968005 | ||||||||
\(647\) | 18.5961 | 0.731088 | 0.365544 | − | 0.930794i | \(-0.380883\pi\) | ||||
0.365544 | + | 0.930794i | \(0.380883\pi\) | |||||||
\(648\) | 2.95982 | 0.116273 | ||||||||
\(649\) | 45.7012 | 1.79393 | ||||||||
\(650\) | 15.0616 | 0.590765 | ||||||||
\(651\) | −3.55339 | −0.139268 | ||||||||
\(652\) | 2.51733 | 0.0985861 | ||||||||
\(653\) | 33.8070 | 1.32297 | 0.661485 | − | 0.749958i | \(-0.269926\pi\) | ||||
0.661485 | + | 0.749958i | \(0.269926\pi\) | |||||||
\(654\) | −6.91575 | −0.270427 | ||||||||
\(655\) | −12.4591 | −0.486816 | ||||||||
\(656\) | −3.74333 | −0.146153 | ||||||||
\(657\) | 3.19139 | 0.124508 | ||||||||
\(658\) | −14.4037 | −0.561513 | ||||||||
\(659\) | −33.3206 | −1.29798 | −0.648992 | − | 0.760795i | \(-0.724809\pi\) | ||||
−0.648992 | + | 0.760795i | \(0.724809\pi\) | |||||||
\(660\) | 1.37669 | 0.0535874 | ||||||||
\(661\) | 12.2738 | 0.477396 | 0.238698 | − | 0.971094i | \(-0.423279\pi\) | ||||
0.238698 | + | 0.971094i | \(0.423279\pi\) | |||||||
\(662\) | 11.3104 | 0.439591 | ||||||||
\(663\) | 13.2884 | 0.516079 | ||||||||
\(664\) | −18.5993 | −0.721791 | ||||||||
\(665\) | 12.5247 | 0.485688 | ||||||||
\(666\) | 5.00926 | 0.194105 | ||||||||
\(667\) | 31.0471 | 1.20215 | ||||||||
\(668\) | 1.17202 | 0.0453469 | ||||||||
\(669\) | −15.8619 | −0.613256 | ||||||||
\(670\) | −29.1099 | −1.12461 | ||||||||
\(671\) | 18.5460 | 0.715959 | ||||||||
\(672\) | 1.21615 | 0.0469142 | ||||||||
\(673\) | 41.9057 | 1.61535 | 0.807673 | − | 0.589631i | \(-0.200727\pi\) | ||||
0.807673 | + | 0.589631i | \(0.200727\pi\) | |||||||
\(674\) | −29.7429 | −1.14565 | ||||||||
\(675\) | 2.11851 | 0.0815414 | ||||||||
\(676\) | −3.31126 | −0.127356 | ||||||||
\(677\) | 12.0934 | 0.464788 | 0.232394 | − | 0.972622i | \(-0.425344\pi\) | ||||
0.232394 | + | 0.972622i | \(0.425344\pi\) | |||||||
\(678\) | −5.47552 | −0.210286 | ||||||||
\(679\) | −1.20766 | −0.0463458 | ||||||||
\(680\) | −12.5432 | −0.481008 | ||||||||
\(681\) | −26.8776 | −1.02995 | ||||||||
\(682\) | −17.8230 | −0.682476 | ||||||||
\(683\) | 4.74954 | 0.181736 | 0.0908680 | − | 0.995863i | \(-0.471036\pi\) | ||||
0.0908680 | + | 0.995863i | \(0.471036\pi\) | |||||||
\(684\) | −1.59349 | −0.0609286 | ||||||||
\(685\) | −14.7383 | −0.563121 | ||||||||
\(686\) | −1.33568 | −0.0509964 | ||||||||
\(687\) | −15.2681 | −0.582515 | ||||||||
\(688\) | −15.4552 | −0.589226 | ||||||||
\(689\) | 68.9856 | 2.62814 | ||||||||
\(690\) | −13.4308 | −0.511300 | ||||||||
\(691\) | 37.1894 | 1.41475 | 0.707376 | − | 0.706837i | \(-0.249879\pi\) | ||||
0.707376 | + | 0.706837i | \(0.249879\pi\) | |||||||
\(692\) | −3.96890 | −0.150875 | ||||||||
\(693\) | 3.75523 | 0.142649 | ||||||||
\(694\) | 12.1567 | 0.461462 | ||||||||
\(695\) | −7.03939 | −0.267019 | ||||||||
\(696\) | 15.5130 | 0.588018 | ||||||||
\(697\) | −2.65384 | −0.100521 | ||||||||
\(698\) | −5.04390 | −0.190914 | ||||||||
\(699\) | −13.3056 | −0.503265 | ||||||||
\(700\) | 0.457531 | 0.0172930 | ||||||||
\(701\) | −16.9795 | −0.641308 | −0.320654 | − | 0.947196i | \(-0.603903\pi\) | ||||
−0.320654 | + | 0.947196i | \(0.603903\pi\) | |||||||
\(702\) | 7.10954 | 0.268332 | ||||||||
\(703\) | −27.6714 | −1.04365 | ||||||||
\(704\) | 32.5474 | 1.22668 | ||||||||
\(705\) | −18.3055 | −0.689423 | ||||||||
\(706\) | −0.656077 | −0.0246918 | ||||||||
\(707\) | 16.3275 | 0.614059 | ||||||||
\(708\) | 2.62834 | 0.0987790 | ||||||||
\(709\) | −3.88506 | −0.145906 | −0.0729532 | − | 0.997335i | \(-0.523242\pi\) | ||||
−0.0729532 | + | 0.997335i | \(0.523242\pi\) | |||||||
\(710\) | 19.6868 | 0.738832 | ||||||||
\(711\) | −12.9595 | −0.486021 | ||||||||
\(712\) | 25.2758 | 0.947250 | ||||||||
\(713\) | −21.0491 | −0.788294 | ||||||||
\(714\) | −3.33453 | −0.124792 | ||||||||
\(715\) | 33.9301 | 1.26891 | ||||||||
\(716\) | −3.26171 | −0.121896 | ||||||||
\(717\) | 18.3294 | 0.684522 | ||||||||
\(718\) | −22.4196 | −0.836692 | ||||||||
\(719\) | −11.0565 | −0.412338 | −0.206169 | − | 0.978516i | \(-0.566100\pi\) | ||||
−0.206169 | + | 0.978516i | \(0.566100\pi\) | |||||||
\(720\) | −5.97760 | −0.222772 | ||||||||
\(721\) | 7.41862 | 0.276284 | ||||||||
\(722\) | −47.3364 | −1.76168 | ||||||||
\(723\) | 7.63094 | 0.283798 | ||||||||
\(724\) | 1.36509 | 0.0507330 | ||||||||
\(725\) | 11.1035 | 0.412374 | ||||||||
\(726\) | 4.14290 | 0.153757 | ||||||||
\(727\) | 13.0931 | 0.485597 | 0.242799 | − | 0.970077i | \(-0.421935\pi\) | ||||
0.242799 | + | 0.970077i | \(0.421935\pi\) | |||||||
\(728\) | 15.7545 | 0.583901 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.23586 | −0.267811 | ||||||||
\(731\) | −10.9570 | −0.405259 | ||||||||
\(732\) | 1.06661 | 0.0394229 | ||||||||
\(733\) | −0.249606 | −0.00921942 | −0.00460971 | − | 0.999989i | \(-0.501467\pi\) | ||||
−0.00460971 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(734\) | −17.2554 | −0.636910 | ||||||||
\(735\) | −1.69750 | −0.0626131 | ||||||||
\(736\) | 7.20409 | 0.265546 | ||||||||
\(737\) | 48.2133 | 1.77596 | ||||||||
\(738\) | −1.41985 | −0.0522653 | ||||||||
\(739\) | 30.4472 | 1.12002 | 0.560010 | − | 0.828486i | \(-0.310797\pi\) | ||||
0.560010 | + | 0.828486i | \(0.310797\pi\) | |||||||
\(740\) | 1.37490 | 0.0505423 | ||||||||
\(741\) | −39.2734 | −1.44275 | ||||||||
\(742\) | −17.3109 | −0.635504 | ||||||||
\(743\) | −13.0890 | −0.480190 | −0.240095 | − | 0.970749i | \(-0.577179\pi\) | ||||
−0.240095 | + | 0.970749i | \(0.577179\pi\) | |||||||
\(744\) | −10.5174 | −0.385586 | ||||||||
\(745\) | −34.8180 | −1.27563 | ||||||||
\(746\) | −5.48863 | −0.200953 | ||||||||
\(747\) | −6.28392 | −0.229917 | ||||||||
\(748\) | 2.02470 | 0.0740302 | ||||||||
\(749\) | −18.8442 | −0.688554 | ||||||||
\(750\) | −16.1398 | −0.589343 | ||||||||
\(751\) | −11.8460 | −0.432267 | −0.216134 | − | 0.976364i | \(-0.569345\pi\) | ||||
−0.216134 | + | 0.976364i | \(0.569345\pi\) | |||||||
\(752\) | −37.9743 | −1.38478 | ||||||||
\(753\) | −13.5907 | −0.495273 | ||||||||
\(754\) | 37.2625 | 1.35702 | ||||||||
\(755\) | −25.7438 | −0.936912 | ||||||||
\(756\) | 0.215968 | 0.00785469 | ||||||||
\(757\) | 43.1212 | 1.56727 | 0.783634 | − | 0.621223i | \(-0.213364\pi\) | ||||
0.783634 | + | 0.621223i | \(0.213364\pi\) | |||||||
\(758\) | −11.6694 | −0.423852 | ||||||||
\(759\) | 22.2447 | 0.807431 | ||||||||
\(760\) | 37.0709 | 1.34470 | ||||||||
\(761\) | 34.2917 | 1.24307 | 0.621537 | − | 0.783385i | \(-0.286508\pi\) | ||||
0.621537 | + | 0.783385i | \(0.286508\pi\) | |||||||
\(762\) | 8.04738 | 0.291526 | ||||||||
\(763\) | −5.17771 | −0.187446 | ||||||||
\(764\) | −5.76137 | −0.208439 | ||||||||
\(765\) | −4.23782 | −0.153219 | ||||||||
\(766\) | 1.33568 | 0.0482600 | ||||||||
\(767\) | 64.7786 | 2.33902 | ||||||||
\(768\) | 5.12063 | 0.184775 | ||||||||
\(769\) | −3.46281 | −0.124872 | −0.0624361 | − | 0.998049i | \(-0.519887\pi\) | ||||
−0.0624361 | + | 0.998049i | \(0.519887\pi\) | |||||||
\(770\) | −8.51424 | −0.306832 | ||||||||
\(771\) | −0.642134 | −0.0231259 | ||||||||
\(772\) | −2.81195 | −0.101204 | ||||||||
\(773\) | 36.8435 | 1.32517 | 0.662584 | − | 0.748987i | \(-0.269460\pi\) | ||||
0.662584 | + | 0.748987i | \(0.269460\pi\) | |||||||
\(774\) | −5.86218 | −0.210712 | ||||||||
\(775\) | −7.52788 | −0.270409 | ||||||||
\(776\) | −3.57446 | −0.128316 | ||||||||
\(777\) | 3.75035 | 0.134543 | ||||||||
\(778\) | 17.9089 | 0.642066 | ||||||||
\(779\) | 7.84331 | 0.281016 | ||||||||
\(780\) | 1.95137 | 0.0698701 | ||||||||
\(781\) | −32.6062 | −1.16674 | ||||||||
\(782\) | −19.7526 | −0.706353 | ||||||||
\(783\) | 5.24120 | 0.187305 | ||||||||
\(784\) | −3.52142 | −0.125765 | ||||||||
\(785\) | 13.8688 | 0.494998 | ||||||||
\(786\) | −9.80342 | −0.349676 | ||||||||
\(787\) | −14.4079 | −0.513588 | −0.256794 | − | 0.966466i | \(-0.582666\pi\) | ||||
−0.256794 | + | 0.966466i | \(0.582666\pi\) | |||||||
\(788\) | 3.11501 | 0.110968 | ||||||||
\(789\) | 0.825121 | 0.0293751 | ||||||||
\(790\) | 29.3832 | 1.04541 | ||||||||
\(791\) | −4.09944 | −0.145759 | ||||||||
\(792\) | 11.1148 | 0.394947 | ||||||||
\(793\) | 26.2878 | 0.933506 | ||||||||
\(794\) | 21.8898 | 0.776841 | ||||||||
\(795\) | −22.0002 | −0.780268 | ||||||||
\(796\) | −0.542953 | −0.0192445 | ||||||||
\(797\) | −6.27037 | −0.222108 | −0.111054 | − | 0.993814i | \(-0.535423\pi\) | ||||
−0.111054 | + | 0.993814i | \(0.535423\pi\) | |||||||
\(798\) | 9.85509 | 0.348866 | ||||||||
\(799\) | −26.9219 | −0.952427 | ||||||||
\(800\) | 2.57643 | 0.0910906 | ||||||||
\(801\) | 8.53964 | 0.301733 | ||||||||
\(802\) | −36.5572 | −1.29088 | ||||||||
\(803\) | 11.9844 | 0.422920 | ||||||||
\(804\) | 2.77282 | 0.0977896 | ||||||||
\(805\) | −10.0554 | −0.354406 | ||||||||
\(806\) | −25.2629 | −0.889849 | ||||||||
\(807\) | 18.9954 | 0.668668 | ||||||||
\(808\) | 48.3264 | 1.70012 | ||||||||
\(809\) | 20.4750 | 0.719864 | 0.359932 | − | 0.932979i | \(-0.382800\pi\) | ||||
0.359932 | + | 0.932979i | \(0.382800\pi\) | |||||||
\(810\) | −2.26731 | −0.0796650 | ||||||||
\(811\) | −23.8349 | −0.836956 | −0.418478 | − | 0.908227i | \(-0.637436\pi\) | ||||
−0.418478 | + | 0.908227i | \(0.637436\pi\) | |||||||
\(812\) | 1.13193 | 0.0397231 | ||||||||
\(813\) | 11.4377 | 0.401138 | ||||||||
\(814\) | 18.8109 | 0.659322 | ||||||||
\(815\) | −19.7860 | −0.693073 | ||||||||
\(816\) | −8.79126 | −0.307756 | ||||||||
\(817\) | 32.3830 | 1.13294 | ||||||||
\(818\) | 14.5796 | 0.509764 | ||||||||
\(819\) | 5.32280 | 0.185994 | ||||||||
\(820\) | −0.389708 | −0.0136092 | ||||||||
\(821\) | 35.7441 | 1.24748 | 0.623739 | − | 0.781633i | \(-0.285613\pi\) | ||||
0.623739 | + | 0.781633i | \(0.285613\pi\) | |||||||
\(822\) | −11.5968 | −0.404486 | ||||||||
\(823\) | 10.3709 | 0.361507 | 0.180753 | − | 0.983528i | \(-0.442146\pi\) | ||||
0.180753 | + | 0.983528i | \(0.442146\pi\) | |||||||
\(824\) | 21.9577 | 0.764934 | ||||||||
\(825\) | 7.95548 | 0.276974 | ||||||||
\(826\) | −16.2552 | −0.565591 | ||||||||
\(827\) | −2.86561 | −0.0996469 | −0.0498234 | − | 0.998758i | \(-0.515866\pi\) | ||||
−0.0498234 | + | 0.998758i | \(0.515866\pi\) | |||||||
\(828\) | 1.27932 | 0.0444596 | ||||||||
\(829\) | 30.2709 | 1.05135 | 0.525676 | − | 0.850685i | \(-0.323812\pi\) | ||||
0.525676 | + | 0.850685i | \(0.323812\pi\) | |||||||
\(830\) | 14.2476 | 0.494540 | ||||||||
\(831\) | −16.8365 | −0.584052 | ||||||||
\(832\) | 46.1339 | 1.59941 | ||||||||
\(833\) | −2.49651 | −0.0864990 | ||||||||
\(834\) | −5.53895 | −0.191798 | ||||||||
\(835\) | −9.21202 | −0.318795 | ||||||||
\(836\) | −5.98391 | −0.206958 | ||||||||
\(837\) | −3.55339 | −0.122823 | ||||||||
\(838\) | −40.4082 | −1.39588 | ||||||||
\(839\) | 16.7672 | 0.578867 | 0.289433 | − | 0.957198i | \(-0.406533\pi\) | ||||
0.289433 | + | 0.957198i | \(0.406533\pi\) | |||||||
\(840\) | −5.02428 | −0.173354 | ||||||||
\(841\) | −1.52985 | −0.0527534 | ||||||||
\(842\) | −7.88129 | −0.271607 | ||||||||
\(843\) | 9.22285 | 0.317652 | ||||||||
\(844\) | 1.20613 | 0.0415167 | ||||||||
\(845\) | 26.0263 | 0.895332 | ||||||||
\(846\) | −14.4037 | −0.495208 | ||||||||
\(847\) | 3.10172 | 0.106576 | ||||||||
\(848\) | −45.6390 | −1.56725 | ||||||||
\(849\) | −25.6717 | −0.881051 | ||||||||
\(850\) | −7.06423 | −0.242301 | ||||||||
\(851\) | 22.2158 | 0.761549 | ||||||||
\(852\) | −1.87523 | −0.0642444 | ||||||||
\(853\) | 23.4945 | 0.804438 | 0.402219 | − | 0.915544i | \(-0.368239\pi\) | ||||
0.402219 | + | 0.915544i | \(0.368239\pi\) | |||||||
\(854\) | −6.59652 | −0.225728 | ||||||||
\(855\) | 12.5247 | 0.428336 | ||||||||
\(856\) | −55.7755 | −1.90637 | ||||||||
\(857\) | −25.6041 | −0.874621 | −0.437311 | − | 0.899311i | \(-0.644069\pi\) | ||||
−0.437311 | + | 0.899311i | \(0.644069\pi\) | |||||||
\(858\) | 26.6979 | 0.911452 | ||||||||
\(859\) | −31.5902 | −1.07784 | −0.538922 | − | 0.842356i | \(-0.681168\pi\) | ||||
−0.538922 | + | 0.842356i | \(0.681168\pi\) | |||||||
\(860\) | −1.60900 | −0.0548665 | ||||||||
\(861\) | −1.06302 | −0.0362275 | ||||||||
\(862\) | 1.35123 | 0.0460232 | ||||||||
\(863\) | 41.3966 | 1.40916 | 0.704578 | − | 0.709626i | \(-0.251136\pi\) | ||||
0.704578 | + | 0.709626i | \(0.251136\pi\) | |||||||
\(864\) | 1.21615 | 0.0413744 | ||||||||
\(865\) | 31.1953 | 1.06067 | ||||||||
\(866\) | −42.3748 | −1.43995 | ||||||||
\(867\) | 10.7674 | 0.365681 | ||||||||
\(868\) | −0.767419 | −0.0260479 | ||||||||
\(869\) | −48.6660 | −1.65088 | ||||||||
\(870\) | −11.8834 | −0.402885 | ||||||||
\(871\) | 68.3393 | 2.31559 | ||||||||
\(872\) | −15.3251 | −0.518972 | ||||||||
\(873\) | −1.20766 | −0.0408732 | ||||||||
\(874\) | 58.3782 | 1.97467 | ||||||||
\(875\) | −12.0836 | −0.408502 | ||||||||
\(876\) | 0.689240 | 0.0232873 | ||||||||
\(877\) | 12.6263 | 0.426361 | 0.213181 | − | 0.977013i | \(-0.431618\pi\) | ||||
0.213181 | + | 0.977013i | \(0.431618\pi\) | |||||||
\(878\) | −28.7995 | −0.971936 | ||||||||
\(879\) | 30.9067 | 1.04246 | ||||||||
\(880\) | −22.4472 | −0.756696 | ||||||||
\(881\) | 30.2927 | 1.02059 | 0.510294 | − | 0.860000i | \(-0.329536\pi\) | ||||
0.510294 | + | 0.860000i | \(0.329536\pi\) | |||||||
\(882\) | −1.33568 | −0.0449746 | ||||||||
\(883\) | 40.5711 | 1.36533 | 0.682663 | − | 0.730733i | \(-0.260822\pi\) | ||||
0.682663 | + | 0.730733i | \(0.260822\pi\) | |||||||
\(884\) | 2.86988 | 0.0965244 | ||||||||
\(885\) | −20.6586 | −0.694430 | ||||||||
\(886\) | 47.4738 | 1.59491 | ||||||||
\(887\) | −23.1901 | −0.778646 | −0.389323 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389323 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(888\) | 11.1004 | 0.372504 | ||||||||
\(889\) | 6.02495 | 0.202070 | ||||||||
\(890\) | −19.3620 | −0.649015 | ||||||||
\(891\) | 3.75523 | 0.125805 | ||||||||
\(892\) | −3.42566 | −0.114700 | ||||||||
\(893\) | 79.5666 | 2.66260 | ||||||||
\(894\) | −27.3966 | −0.916280 | ||||||||
\(895\) | 25.6368 | 0.856945 | ||||||||
\(896\) | −9.14431 | −0.305490 | ||||||||
\(897\) | 31.5305 | 1.05277 | ||||||||
\(898\) | 41.7120 | 1.39195 | ||||||||
\(899\) | −18.6240 | −0.621145 | ||||||||
\(900\) | 0.457531 | 0.0152510 | ||||||||
\(901\) | −32.3558 | −1.07793 | ||||||||
\(902\) | −5.33185 | −0.177531 | ||||||||
\(903\) | −4.38892 | −0.146054 | ||||||||
\(904\) | −12.1336 | −0.403557 | ||||||||
\(905\) | −10.7295 | −0.356660 | ||||||||
\(906\) | −20.2565 | −0.672977 | ||||||||
\(907\) | −49.3629 | −1.63907 | −0.819534 | − | 0.573031i | \(-0.805768\pi\) | ||||
−0.819534 | + | 0.573031i | \(0.805768\pi\) | |||||||
\(908\) | −5.80471 | −0.192636 | ||||||||
\(909\) | 16.3275 | 0.541549 | ||||||||
\(910\) | −12.0684 | −0.400064 | ||||||||
\(911\) | 18.8909 | 0.625884 | 0.312942 | − | 0.949772i | \(-0.398686\pi\) | ||||
0.312942 | + | 0.949772i | \(0.398686\pi\) | |||||||
\(912\) | 25.9823 | 0.860359 | ||||||||
\(913\) | −23.5976 | −0.780965 | ||||||||
\(914\) | −19.7729 | −0.654030 | ||||||||
\(915\) | −8.38344 | −0.277148 | ||||||||
\(916\) | −3.29743 | −0.108950 | ||||||||
\(917\) | −7.33967 | −0.242377 | ||||||||
\(918\) | −3.33453 | −0.110056 | ||||||||
\(919\) | 7.76030 | 0.255989 | 0.127994 | − | 0.991775i | \(-0.459146\pi\) | ||||
0.127994 | + | 0.991775i | \(0.459146\pi\) | |||||||
\(920\) | −29.7621 | −0.981228 | ||||||||
\(921\) | 20.8554 | 0.687208 | ||||||||
\(922\) | 36.0459 | 1.18711 | ||||||||
\(923\) | −46.2173 | −1.52126 | ||||||||
\(924\) | 0.811010 | 0.0266803 | ||||||||
\(925\) | 7.94516 | 0.261235 | ||||||||
\(926\) | −27.6926 | −0.910035 | ||||||||
\(927\) | 7.41862 | 0.243659 | ||||||||
\(928\) | 6.37411 | 0.209240 | ||||||||
\(929\) | −38.2558 | −1.25513 | −0.627566 | − | 0.778564i | \(-0.715949\pi\) | ||||
−0.627566 | + | 0.778564i | \(0.715949\pi\) | |||||||
\(930\) | 8.05661 | 0.264187 | ||||||||
\(931\) | 7.37835 | 0.241816 | ||||||||
\(932\) | −2.87359 | −0.0941276 | ||||||||
\(933\) | 17.0656 | 0.558702 | ||||||||
\(934\) | 35.8417 | 1.17278 | ||||||||
\(935\) | −15.9140 | −0.520442 | ||||||||
\(936\) | 15.7545 | 0.514952 | ||||||||
\(937\) | −13.5973 | −0.444205 | −0.222103 | − | 0.975023i | \(-0.571292\pi\) | ||||
−0.222103 | + | 0.975023i | \(0.571292\pi\) | |||||||
\(938\) | −17.1487 | −0.559926 | ||||||||
\(939\) | 7.13261 | 0.232764 | ||||||||
\(940\) | −3.95340 | −0.128946 | ||||||||
\(941\) | 40.9053 | 1.33348 | 0.666738 | − | 0.745292i | \(-0.267690\pi\) | ||||
0.666738 | + | 0.745292i | \(0.267690\pi\) | |||||||
\(942\) | 10.9127 | 0.355554 | ||||||||
\(943\) | −6.29696 | −0.205057 | ||||||||
\(944\) | −42.8558 | −1.39484 | ||||||||
\(945\) | −1.69750 | −0.0552195 | ||||||||
\(946\) | −22.0138 | −0.715731 | ||||||||
\(947\) | 4.79280 | 0.155745 | 0.0778726 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778726 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(948\) | −2.79885 | −0.0909024 | ||||||||
\(949\) | 16.9871 | 0.551426 | ||||||||
\(950\) | 20.8781 | 0.677374 | ||||||||
\(951\) | 20.0951 | 0.651627 | ||||||||
\(952\) | −7.38921 | −0.239486 | ||||||||
\(953\) | −37.5412 | −1.21608 | −0.608040 | − | 0.793907i | \(-0.708044\pi\) | ||||
−0.608040 | + | 0.793907i | \(0.708044\pi\) | |||||||
\(954\) | −17.3109 | −0.560461 | ||||||||
\(955\) | 45.2840 | 1.46536 | ||||||||
\(956\) | 3.95856 | 0.128029 | ||||||||
\(957\) | 19.6819 | 0.636225 | ||||||||
\(958\) | −32.9134 | −1.06338 | ||||||||
\(959\) | −8.68237 | −0.280368 | ||||||||
\(960\) | −14.7126 | −0.474847 | ||||||||
\(961\) | −18.3734 | −0.592692 | ||||||||
\(962\) | 26.6633 | 0.859659 | ||||||||
\(963\) | −18.8442 | −0.607247 | ||||||||
\(964\) | 1.64804 | 0.0530798 | ||||||||
\(965\) | 22.1018 | 0.711481 | ||||||||
\(966\) | −7.91210 | −0.254568 | ||||||||
\(967\) | 31.0487 | 0.998458 | 0.499229 | − | 0.866470i | \(-0.333617\pi\) | ||||
0.499229 | + | 0.866470i | \(0.333617\pi\) | |||||||
\(968\) | 9.18053 | 0.295074 | ||||||||
\(969\) | 18.4201 | 0.591740 | ||||||||
\(970\) | 2.73814 | 0.0879163 | ||||||||
\(971\) | −36.0446 | −1.15673 | −0.578363 | − | 0.815779i | \(-0.696308\pi\) | ||||
−0.578363 | + | 0.815779i | \(0.696308\pi\) | |||||||
\(972\) | 0.215968 | 0.00692719 | ||||||||
\(973\) | −4.14693 | −0.132944 | ||||||||
\(974\) | −24.0554 | −0.770786 | ||||||||
\(975\) | 11.2764 | 0.361133 | ||||||||
\(976\) | −17.3913 | −0.556681 | ||||||||
\(977\) | −13.4368 | −0.429883 | −0.214941 | − | 0.976627i | \(-0.568956\pi\) | ||||
−0.214941 | + | 0.976627i | \(0.568956\pi\) | |||||||
\(978\) | −15.5686 | −0.497830 | ||||||||
\(979\) | 32.0683 | 1.02491 | ||||||||
\(980\) | −0.366605 | −0.0117108 | ||||||||
\(981\) | −5.17771 | −0.165312 | ||||||||
\(982\) | 25.7077 | 0.820364 | ||||||||
\(983\) | −55.3856 | −1.76653 | −0.883263 | − | 0.468879i | \(-0.844658\pi\) | ||||
−0.883263 | + | 0.468879i | \(0.844658\pi\) | |||||||
\(984\) | −3.14634 | −0.100302 | ||||||||
\(985\) | −24.4838 | −0.780118 | ||||||||
\(986\) | −17.4769 | −0.556579 | ||||||||
\(987\) | −10.7838 | −0.343252 | ||||||||
\(988\) | −8.48182 | −0.269843 | ||||||||
\(989\) | −25.9985 | −0.826704 | ||||||||
\(990\) | −8.51424 | −0.270600 | ||||||||
\(991\) | −34.1703 | −1.08546 | −0.542728 | − | 0.839909i | \(-0.682608\pi\) | ||||
−0.542728 | + | 0.839909i | \(0.682608\pi\) | |||||||
\(992\) | −4.32147 | −0.137207 | ||||||||
\(993\) | 8.46792 | 0.268721 | ||||||||
\(994\) | 11.5975 | 0.367852 | ||||||||
\(995\) | 4.26757 | 0.135291 | ||||||||
\(996\) | −1.35713 | −0.0430023 | ||||||||
\(997\) | 44.0089 | 1.39378 | 0.696888 | − | 0.717180i | \(-0.254567\pi\) | ||||
0.696888 | + | 0.717180i | \(0.254567\pi\) | |||||||
\(998\) | −21.9975 | −0.696317 | ||||||||
\(999\) | 3.75035 | 0.118656 |
(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 | 8043.2.a.t.1.16 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.16 | ✓ | 52 | 1.1 | even | 1 | trivial |