Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1351,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3042.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(24.2904922949\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1014) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.3 | ||
Root | \(1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1351 |
Dual form | 3042.2.b.r.1351.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3042\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 4.04892i | 1.81073i | 0.424633 | + | 0.905365i | \(0.360403\pi\) | ||||
−0.424633 | + | 0.905365i | \(0.639597\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.692021i | 0.261560i | 0.991411 | + | 0.130780i | \(0.0417481\pi\) | ||||
−0.991411 | + | 0.130780i | \(0.958252\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.04892 | 1.28038 | ||||||||
\(11\) | 4.85086i | 1.46259i | 0.682062 | + | 0.731294i | \(0.261083\pi\) | ||||
−0.682062 | + | 0.731294i | \(0.738917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.692021 | 0.184951 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.38404 | 1.79089 | 0.895447 | − | 0.445169i | \(-0.146856\pi\) | ||||
0.895447 | + | 0.445169i | \(0.146856\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78017i | 0.408398i | 0.978929 | + | 0.204199i | \(0.0654590\pi\) | ||||
−0.978929 | + | 0.204199i | \(0.934541\pi\) | |||||||
\(20\) | − 4.04892i | − 0.905365i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.85086 | 1.03421 | ||||||||
\(23\) | 5.10992 | 1.06549 | 0.532746 | − | 0.846275i | \(-0.321160\pi\) | ||||
0.532746 | + | 0.846275i | \(0.321160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.3937 | −2.27875 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.692021i | − 0.130780i | ||||||||
\(29\) | 3.34481 | 0.621116 | 0.310558 | − | 0.950554i | \(-0.399484\pi\) | ||||
0.310558 | + | 0.950554i | \(0.399484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.972853i | − 0.174730i | −0.996176 | − | 0.0873648i | \(-0.972155\pi\) | ||||
0.996176 | − | 0.0873648i | \(-0.0278446\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 7.38404i | − 1.26635i | ||||||||
\(35\) | −2.80194 | −0.473614 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.28621i | 0.211451i | 0.994395 | + | 0.105726i | \(0.0337165\pi\) | ||||
−0.994395 | + | 0.105726i | \(0.966283\pi\) | |||||||
\(38\) | 1.78017 | 0.288781 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.04892 | −0.640190 | ||||||||
\(41\) | 1.50604i | 0.235204i | 0.993061 | + | 0.117602i | \(0.0375207\pi\) | ||||
−0.993061 | + | 0.117602i | \(0.962479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.31767 | 1.26843 | 0.634216 | − | 0.773156i | \(-0.281323\pi\) | ||||
0.634216 | + | 0.773156i | \(0.281323\pi\) | |||||||
\(44\) | − 4.85086i | − 0.731294i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 5.10992i | − 0.753416i | ||||||||
\(47\) | 7.20775i | 1.05136i | 0.850683 | + | 0.525679i | \(0.176189\pi\) | ||||
−0.850683 | + | 0.525679i | \(0.823811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.52111 | 0.931587 | ||||||||
\(50\) | 11.3937i | 1.61132i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.4765 | −1.85114 | −0.925570 | − | 0.378577i | \(-0.876414\pi\) | ||||
−0.925570 | + | 0.378577i | \(0.876414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.6407 | −2.64835 | ||||||||
\(56\) | −0.692021 | −0.0924753 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 3.34481i | − 0.439196i | ||||||||
\(59\) | − 1.30798i | − 0.170284i | −0.996369 | − | 0.0851422i | \(-0.972866\pi\) | ||||
0.996369 | − | 0.0851422i | \(-0.0271344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.396125 | −0.0507185 | −0.0253593 | − | 0.999678i | \(-0.508073\pi\) | ||||
−0.0253593 | + | 0.999678i | \(0.508073\pi\) | |||||||
\(62\) | −0.972853 | −0.123552 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.05429i | − 0.739650i | −0.929101 | − | 0.369825i | \(-0.879418\pi\) | ||||
0.929101 | − | 0.369825i | \(-0.120582\pi\) | |||||||
\(68\) | −7.38404 | −0.895447 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.80194i | 0.334896i | ||||||||
\(71\) | − 1.32975i | − 0.157812i | −0.996882 | − | 0.0789061i | \(-0.974857\pi\) | ||||
0.996882 | − | 0.0789061i | \(-0.0251427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 7.65279i | − 0.895692i | −0.894111 | − | 0.447846i | \(-0.852191\pi\) | ||||
0.894111 | − | 0.447846i | \(-0.147809\pi\) | |||||||
\(74\) | 1.28621 | 0.149519 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 1.78017i | − 0.204199i | ||||||||
\(77\) | −3.35690 | −0.382554 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.33944 | −0.938260 | −0.469130 | − | 0.883129i | \(-0.655432\pi\) | ||||
−0.469130 | + | 0.883129i | \(0.655432\pi\) | |||||||
\(80\) | 4.04892i | 0.452683i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.50604 | 0.166314 | ||||||||
\(83\) | 15.3274i | 1.68240i | 0.540727 | + | 0.841198i | \(0.318149\pi\) | ||||
−0.540727 | + | 0.841198i | \(0.681851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.8974i | 3.24283i | ||||||||
\(86\) | − 8.31767i | − 0.896917i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.85086 | −0.517103 | ||||||||
\(89\) | − 3.10992i | − 0.329650i | −0.986323 | − | 0.164825i | \(-0.947294\pi\) | ||||
0.986323 | − | 0.164825i | \(-0.0527060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.10992 | −0.532746 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.20775 | 0.743423 | ||||||||
\(95\) | −7.20775 | −0.739500 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.54288i | 0.867398i | 0.901058 | + | 0.433699i | \(0.142792\pi\) | ||||
−0.901058 | + | 0.433699i | \(0.857208\pi\) | |||||||
\(98\) | − 6.52111i | − 0.658731i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.3937 | 1.13937 | ||||||||
\(101\) | −11.9976 | −1.19381 | −0.596903 | − | 0.802313i | \(-0.703602\pi\) | ||||
−0.596903 | + | 0.802313i | \(0.703602\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3230 | 1.21423 | 0.607113 | − | 0.794616i | \(-0.292328\pi\) | ||||
0.607113 | + | 0.794616i | \(0.292328\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4765i | 1.30895i | ||||||||
\(107\) | −5.89977 | −0.570353 | −0.285176 | − | 0.958475i | \(-0.592052\pi\) | ||||
−0.285176 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 0.792249i | − 0.0758837i | −0.999280 | − | 0.0379418i | \(-0.987920\pi\) | ||||
0.999280 | − | 0.0379418i | \(-0.0120802\pi\) | |||||||
\(110\) | 19.6407i | 1.87267i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.692021i | 0.0653899i | ||||||||
\(113\) | −6.21983 | −0.585113 | −0.292556 | − | 0.956248i | \(-0.594506\pi\) | ||||
−0.292556 | + | 0.956248i | \(0.594506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.6896i | 1.92932i | ||||||||
\(116\) | −3.34481 | −0.310558 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.30798 | −0.120409 | ||||||||
\(119\) | 5.10992i | 0.468425i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5308 | −1.13916 | ||||||||
\(122\) | 0.396125i | 0.0358634i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.972853i | 0.0873648i | ||||||||
\(125\) | − 25.8877i | − 2.31547i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00538 | 0.532891 | 0.266446 | − | 0.963850i | \(-0.414151\pi\) | ||||
0.266446 | + | 0.963850i | \(0.414151\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.81700 | −0.770345 | −0.385173 | − | 0.922845i | \(-0.625858\pi\) | ||||
−0.385173 | + | 0.922845i | \(0.625858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.23191 | −0.106821 | ||||||||
\(134\) | −6.05429 | −0.523011 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.38404i | 0.633176i | ||||||||
\(137\) | 15.7560i | 1.34613i | 0.739585 | + | 0.673063i | \(0.235022\pi\) | ||||
−0.739585 | + | 0.673063i | \(0.764978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.09783 | −0.517212 | −0.258606 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258606 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(140\) | 2.80194 | 0.236807 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.32975 | −0.111590 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5429i | 1.12467i | ||||||||
\(146\) | −7.65279 | −0.633350 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 1.28621i | − 0.105726i | ||||||||
\(149\) | − 2.55257i | − 0.209114i | −0.994519 | − | 0.104557i | \(-0.966657\pi\) | ||||
0.994519 | − | 0.104557i | \(-0.0333425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 17.7168i | − 1.44177i | −0.693054 | − | 0.720885i | \(-0.743735\pi\) | ||||
0.693054 | − | 0.720885i | \(-0.256265\pi\) | |||||||
\(152\) | −1.78017 | −0.144391 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.35690i | 0.270506i | ||||||||
\(155\) | 3.93900 | 0.316388 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.31767 | −0.504205 | −0.252102 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252102 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(158\) | 8.33944i | 0.663450i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.04892 | 0.320095 | ||||||||
\(161\) | 3.53617i | 0.278689i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.5918i | − 1.14292i | −0.820631 | − | 0.571459i | \(-0.806378\pi\) | ||||
0.820631 | − | 0.571459i | \(-0.193622\pi\) | |||||||
\(164\) | − 1.50604i | − 0.117602i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.3274 | 1.18963 | ||||||||
\(167\) | − 19.5013i | − 1.50905i | −0.656270 | − | 0.754526i | \(-0.727867\pi\) | ||||
0.656270 | − | 0.754526i | \(-0.272133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 29.8974 | 2.29302 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.31767 | −0.634216 | ||||||||
\(173\) | −9.29052 | −0.706345 | −0.353173 | − | 0.935558i | \(-0.614897\pi\) | ||||
−0.353173 | + | 0.935558i | \(0.614897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 7.88471i | − 0.596028i | ||||||||
\(176\) | 4.85086i | 0.365647i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.10992 | −0.233098 | ||||||||
\(179\) | 22.7928 | 1.70362 | 0.851808 | − | 0.523853i | \(-0.175506\pi\) | ||||
0.851808 | + | 0.523853i | \(0.175506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.537500 | −0.0399520 | −0.0199760 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199760 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.10992i | 0.376708i | ||||||||
\(185\) | −5.20775 | −0.382881 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.8189i | 2.61934i | ||||||||
\(188\) | − 7.20775i | − 0.525679i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.20775i | 0.522905i | ||||||||
\(191\) | 9.79954 | 0.709070 | 0.354535 | − | 0.935043i | \(-0.384639\pi\) | ||||
0.354535 | + | 0.935043i | \(0.384639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1957i | 1.02183i | 0.859632 | + | 0.510913i | \(0.170693\pi\) | ||||
−0.859632 | + | 0.510913i | \(0.829307\pi\) | |||||||
\(194\) | 8.54288 | 0.613343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.52111 | −0.465793 | ||||||||
\(197\) | 3.00969i | 0.214431i | 0.994236 | + | 0.107216i | \(0.0341935\pi\) | ||||
−0.994236 | + | 0.107216i | \(0.965806\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8944 | −0.914059 | −0.457030 | − | 0.889451i | \(-0.651087\pi\) | ||||
−0.457030 | + | 0.889451i | \(0.651087\pi\) | |||||||
\(200\) | − 11.3937i | − 0.805658i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.9976i | 0.844149i | ||||||||
\(203\) | 2.31468i | 0.162459i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.09783 | −0.425891 | ||||||||
\(206\) | − 12.3230i | − 0.858587i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.63533 | −0.597319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.79954 | 0.536943 | 0.268471 | − | 0.963288i | \(-0.413482\pi\) | ||||
0.268471 | + | 0.963288i | \(0.413482\pi\) | |||||||
\(212\) | 13.4765 | 0.925570 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.89977i | 0.403300i | ||||||||
\(215\) | 33.6775i | 2.29679i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.673235 | 0.0457022 | ||||||||
\(218\) | −0.792249 | −0.0536579 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.6407 | 1.32418 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 12.1957i | − 0.816682i | −0.912829 | − | 0.408341i | \(-0.866107\pi\) | ||||
0.912829 | − | 0.408341i | \(-0.133893\pi\) | |||||||
\(224\) | 0.692021 | 0.0462376 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.21983i | 0.413737i | ||||||||
\(227\) | − 6.74333i | − 0.447571i | −0.974638 | − | 0.223785i | \(-0.928159\pi\) | ||||
0.974638 | − | 0.223785i | \(-0.0718415\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.8237i | 1.30999i | 0.755634 | + | 0.654994i | \(0.227329\pi\) | ||||
−0.755634 | + | 0.654994i | \(0.772671\pi\) | |||||||
\(230\) | 20.6896 | 1.36423 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.34481i | 0.219598i | ||||||||
\(233\) | −30.0301 | −1.96734 | −0.983670 | − | 0.179983i | \(-0.942396\pi\) | ||||
−0.983670 | + | 0.179983i | \(0.942396\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1836 | −1.90373 | ||||||||
\(236\) | 1.30798i | 0.0851422i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.10992 | 0.331227 | ||||||||
\(239\) | − 22.0978i | − 1.42939i | −0.699436 | − | 0.714695i | \(-0.746565\pi\) | ||||
0.699436 | − | 0.714695i | \(-0.253435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 10.1274i | − 0.652362i | −0.945307 | − | 0.326181i | \(-0.894238\pi\) | ||||
0.945307 | − | 0.326181i | \(-0.105762\pi\) | |||||||
\(242\) | 12.5308i | 0.805510i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.396125 | 0.0253593 | ||||||||
\(245\) | 26.4034i | 1.68685i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.972853 | 0.0617762 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −25.8877 | −1.63728 | ||||||||
\(251\) | 5.54719 | 0.350135 | 0.175068 | − | 0.984556i | \(-0.443986\pi\) | ||||
0.175068 | + | 0.984556i | \(0.443986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.7875i | 1.55837i | ||||||||
\(254\) | − 6.00538i | − 0.376811i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.7995 | −0.860792 | −0.430396 | − | 0.902640i | \(-0.641626\pi\) | ||||
−0.430396 | + | 0.902640i | \(0.641626\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.890084 | −0.0553071 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.81700i | 0.544716i | ||||||||
\(263\) | 22.4698 | 1.38555 | 0.692773 | − | 0.721155i | \(-0.256389\pi\) | ||||
0.692773 | + | 0.721155i | \(0.256389\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 54.5652i | − 3.35192i | ||||||||
\(266\) | 1.23191i | 0.0755335i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.05429i | 0.369825i | ||||||||
\(269\) | 26.0140 | 1.58610 | 0.793051 | − | 0.609156i | \(-0.208491\pi\) | ||||
0.793051 | + | 0.609156i | \(0.208491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 2.88471i | − 0.175233i | −0.996154 | − | 0.0876167i | \(-0.972075\pi\) | ||||
0.996154 | − | 0.0876167i | \(-0.0279251\pi\) | |||||||
\(272\) | 7.38404 | 0.447723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7560 | 0.951855 | ||||||||
\(275\) | − 55.2693i | − 3.33287i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.46250 | 0.0878731 | 0.0439366 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439366 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(278\) | 6.09783i | 0.365724i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − 2.80194i | − 0.167448i | ||||||||
\(281\) | 5.68233i | 0.338980i | 0.985532 | + | 0.169490i | \(0.0542120\pi\) | ||||
−0.985532 | + | 0.169490i | \(0.945788\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.2078 | 1.49845 | 0.749223 | − | 0.662318i | \(-0.230427\pi\) | ||||
0.749223 | + | 0.662318i | \(0.230427\pi\) | |||||||
\(284\) | 1.32975i | 0.0789061i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.04221 | −0.0615199 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.5241 | 2.20730 | ||||||||
\(290\) | 13.5429 | 0.795265 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.65279i | 0.447846i | ||||||||
\(293\) | − 7.14914i | − 0.417658i | −0.977952 | − | 0.208829i | \(-0.933035\pi\) | ||||
0.977952 | − | 0.208829i | \(-0.0669651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.29590 | 0.308339 | ||||||||
\(296\) | −1.28621 | −0.0747593 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.55257 | −0.147866 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.75600i | 0.331771i | ||||||||
\(302\) | −17.7168 | −1.01949 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.78017i | 0.102100i | ||||||||
\(305\) | − 1.60388i | − 0.0918376i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.9952i | 1.02704i | 0.858077 | + | 0.513521i | \(0.171659\pi\) | ||||
−0.858077 | + | 0.513521i | \(0.828341\pi\) | |||||||
\(308\) | 3.35690 | 0.191277 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 3.93900i | − 0.223720i | ||||||||
\(311\) | 3.32975 | 0.188813 | 0.0944064 | − | 0.995534i | \(-0.469905\pi\) | ||||
0.0944064 | + | 0.995534i | \(0.469905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.8834 | −1.01083 | −0.505414 | − | 0.862877i | \(-0.668660\pi\) | ||||
−0.505414 | + | 0.862877i | \(0.668660\pi\) | |||||||
\(314\) | 6.31767i | 0.356527i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.33944 | 0.469130 | ||||||||
\(317\) | − 4.39373i | − 0.246777i | −0.992358 | − | 0.123388i | \(-0.960624\pi\) | ||||
0.992358 | − | 0.123388i | \(-0.0393761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.2252i | 0.908437i | ||||||||
\(320\) | − 4.04892i | − 0.226341i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.53617 | 0.197063 | ||||||||
\(323\) | 13.1448i | 0.731398i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.5918 | −0.808165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.50604 | −0.0831572 | ||||||||
\(329\) | −4.98792 | −0.274993 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 25.6775i | − 1.41137i | −0.708528 | − | 0.705683i | \(-0.750640\pi\) | ||||
0.708528 | − | 0.705683i | \(-0.249360\pi\) | |||||||
\(332\) | − 15.3274i | − 0.841198i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.5013 | −1.06706 | ||||||||
\(335\) | 24.5133 | 1.33931 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.6504 | 1.34279 | 0.671396 | − | 0.741098i | \(-0.265695\pi\) | ||||
0.671396 | + | 0.741098i | \(0.265695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 29.8974i | − 1.62141i | ||||||||
\(341\) | 4.71917 | 0.255557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.35690i | 0.505225i | ||||||||
\(344\) | 8.31767i | 0.448459i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.29052i | 0.499461i | ||||||||
\(347\) | −14.2959 | −0.767444 | −0.383722 | − | 0.923449i | \(-0.625358\pi\) | ||||
−0.383722 | + | 0.923449i | \(0.625358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 11.0616i | − 0.592113i | −0.955170 | − | 0.296057i | \(-0.904328\pi\) | ||||
0.955170 | − | 0.296057i | \(-0.0956717\pi\) | |||||||
\(350\) | −7.88471 | −0.421455 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.85086 | 0.258551 | ||||||||
\(353\) | 10.5047i | 0.559109i | 0.960130 | + | 0.279555i | \(0.0901868\pi\) | ||||
−0.960130 | + | 0.279555i | \(0.909813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.38404 | 0.285755 | ||||||||
\(356\) | 3.10992i | 0.164825i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 22.7928i | − 1.20464i | ||||||||
\(359\) | 5.10992i | 0.269691i | 0.990867 | + | 0.134846i | \(0.0430538\pi\) | ||||
−0.990867 | + | 0.134846i | \(0.956946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8310 | 0.833211 | ||||||||
\(362\) | 0.537500i | 0.0282504i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9855 | 1.62186 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.44803 | −0.440983 | −0.220492 | − | 0.975389i | \(-0.570766\pi\) | ||||
−0.220492 | + | 0.975389i | \(0.570766\pi\) | |||||||
\(368\) | 5.10992 | 0.266373 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.20775i | 0.270738i | ||||||||
\(371\) | − 9.32603i | − 0.484183i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.69096 | 0.398223 | 0.199111 | − | 0.979977i | \(-0.436194\pi\) | ||||
0.199111 | + | 0.979977i | \(0.436194\pi\) | |||||||
\(374\) | 35.8189 | 1.85215 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.20775 | −0.371711 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 11.4034i | − 0.585754i | −0.956150 | − | 0.292877i | \(-0.905387\pi\) | ||||
0.956150 | − | 0.292877i | \(-0.0946127\pi\) | |||||||
\(380\) | 7.20775 | 0.369750 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 9.79954i | − 0.501388i | ||||||||
\(383\) | − 20.6703i | − 1.05620i | −0.849182 | − | 0.528100i | \(-0.822905\pi\) | ||||
0.849182 | − | 0.528100i | \(-0.177095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 13.5918i | − 0.692702i | ||||||||
\(386\) | 14.1957 | 0.722541 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 8.54288i | − 0.433699i | ||||||||
\(389\) | 17.4776 | 0.886148 | 0.443074 | − | 0.896485i | \(-0.353888\pi\) | ||||
0.443074 | + | 0.896485i | \(0.353888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.7318 | 1.90818 | ||||||||
\(392\) | 6.52111i | 0.329366i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.00969 | 0.151626 | ||||||||
\(395\) | − 33.7657i | − 1.69894i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3599i | 0.971645i | 0.874058 | + | 0.485822i | \(0.161480\pi\) | ||||
−0.874058 | + | 0.485822i | \(0.838520\pi\) | |||||||
\(398\) | 12.8944i | 0.646338i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.3937 | −0.569687 | ||||||||
\(401\) | − 14.4832i | − 0.723257i | −0.932322 | − | 0.361628i | \(-0.882221\pi\) | ||||
0.932322 | − | 0.361628i | \(-0.117779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.9976 | 0.596903 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.31468 | 0.114876 | ||||||||
\(407\) | −6.23921 | −0.309266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 18.8984i | − 0.934468i | −0.884134 | − | 0.467234i | \(-0.845251\pi\) | ||||
0.884134 | − | 0.467234i | \(-0.154749\pi\) | |||||||
\(410\) | 6.09783i | 0.301151i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.3230 | −0.607113 | ||||||||
\(413\) | 0.905149 | 0.0445395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −62.0592 | −3.04637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.63533i | 0.422368i | ||||||||
\(419\) | 21.7603 | 1.06306 | 0.531531 | − | 0.847039i | \(-0.321617\pi\) | ||||
0.531531 | + | 0.847039i | \(0.321617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5918i | 1.00358i | 0.864989 | + | 0.501791i | \(0.167325\pi\) | ||||
−0.864989 | + | 0.501791i | \(0.832675\pi\) | |||||||
\(422\) | − 7.79954i | − 0.379676i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 13.4765i | − 0.654477i | ||||||||
\(425\) | −84.1318 | −4.08099 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.274127i | − 0.0132659i | ||||||||
\(428\) | 5.89977 | 0.285176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.6775 | 1.62408 | ||||||||
\(431\) | − 34.5133i | − 1.66245i | −0.555937 | − | 0.831224i | \(-0.687640\pi\) | ||||
0.555937 | − | 0.831224i | \(-0.312360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.12631 | 0.102184 | 0.0510920 | − | 0.998694i | \(-0.483730\pi\) | ||||
0.0510920 | + | 0.998694i | \(0.483730\pi\) | |||||||
\(434\) | − 0.673235i | − 0.0323163i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.792249i | 0.0379418i | ||||||||
\(437\) | 9.09651i | 0.435145i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.8321 | −1.04199 | −0.520994 | − | 0.853560i | \(-0.674439\pi\) | ||||
−0.520994 | + | 0.853560i | \(0.674439\pi\) | |||||||
\(440\) | − 19.6407i | − 0.936334i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.54048 | 0.358259 | 0.179130 | − | 0.983825i | \(-0.442672\pi\) | ||||
0.179130 | + | 0.983825i | \(0.442672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.5918 | 0.596908 | ||||||||
\(446\) | −12.1957 | −0.577482 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 0.692021i | − 0.0326949i | ||||||||
\(449\) | 19.7560i | 0.932343i | 0.884694 | + | 0.466172i | \(0.154367\pi\) | ||||
−0.884694 | + | 0.466172i | \(0.845633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.30559 | −0.344007 | ||||||||
\(452\) | 6.21983 | 0.292556 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.74333 | −0.316480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8582i | 1.11604i | 0.829828 | + | 0.558019i | \(0.188438\pi\) | ||||
−0.829828 | + | 0.558019i | \(0.811562\pi\) | |||||||
\(458\) | 19.8237 | 0.926301 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 20.6896i | − 0.964659i | ||||||||
\(461\) | 17.5773i | 0.818657i | 0.912387 | + | 0.409329i | \(0.134237\pi\) | ||||
−0.912387 | + | 0.409329i | \(0.865763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 23.8431i | − 1.10808i | −0.832489 | − | 0.554041i | \(-0.813085\pi\) | ||||
0.832489 | − | 0.554041i | \(-0.186915\pi\) | |||||||
\(464\) | 3.34481 | 0.155279 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.0301i | 1.39112i | ||||||||
\(467\) | 8.61058 | 0.398450 | 0.199225 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199225 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.18970 | 0.193462 | ||||||||
\(470\) | 29.1836i | 1.34614i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.30798 | 0.0602046 | ||||||||
\(473\) | 40.3478i | 1.85519i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 20.2828i | − 0.930636i | ||||||||
\(476\) | − 5.10992i | − 0.234213i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.0978 | −1.01073 | ||||||||
\(479\) | 6.58104i | 0.300695i | 0.988633 | + | 0.150348i | \(0.0480393\pi\) | ||||
−0.988633 | + | 0.150348i | \(0.951961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.1274 | −0.461289 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.5308 | 0.569582 | ||||||||
\(485\) | −34.5894 | −1.57062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.2760i | − 1.05474i | −0.849636 | − | 0.527369i | \(-0.823178\pi\) | ||||
0.849636 | − | 0.527369i | \(-0.176822\pi\) | |||||||
\(488\) | − 0.396125i | − 0.0179317i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 26.4034 | 1.19278 | ||||||||
\(491\) | −15.5405 | −0.701332 | −0.350666 | − | 0.936501i | \(-0.614045\pi\) | ||||
−0.350666 | + | 0.936501i | \(0.614045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.6983 | 1.11235 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 0.972853i | − 0.0436824i | ||||||||
\(497\) | 0.920215 | 0.0412773 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.53617i | 0.426898i | 0.976954 | + | 0.213449i | \(0.0684697\pi\) | ||||
−0.976954 | + | 0.213449i | \(0.931530\pi\) | |||||||
\(500\) | 25.8877i | 1.15773i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 5.54719i | − 0.247583i | ||||||||
\(503\) | 13.8345 | 0.616848 | 0.308424 | − | 0.951249i | \(-0.400198\pi\) | ||||
0.308424 | + | 0.951249i | \(0.400198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 48.5773i | − 2.16166i | ||||||||
\(506\) | 24.7875 | 1.10194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00538 | −0.266446 | ||||||||
\(509\) | 40.9638i | 1.81569i | 0.419310 | + | 0.907843i | \(0.362272\pi\) | ||||
−0.419310 | + | 0.907843i | \(0.637728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.29590 | 0.234277 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.7995i | 0.608672i | ||||||||
\(515\) | 49.8950i | 2.19864i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.9638 | −1.53770 | ||||||||
\(518\) | 0.890084i | 0.0391080i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.3672 | −1.59327 | −0.796637 | − | 0.604457i | \(-0.793390\pi\) | ||||
−0.796637 | + | 0.604457i | \(0.793390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.03013 | −0.263679 | −0.131840 | − | 0.991271i | \(-0.542088\pi\) | ||||
−0.131840 | + | 0.991271i | \(0.542088\pi\) | |||||||
\(524\) | 8.81700 | 0.385173 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − 22.4698i | − 0.979730i | ||||||||
\(527\) | − 7.18359i | − 0.312922i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.11124 | 0.135271 | ||||||||
\(530\) | −54.5652 | −2.37016 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.23191 | 0.0534103 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 23.8877i | − 1.03275i | ||||||||
\(536\) | 6.05429 | 0.261506 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 26.0140i | − 1.12154i | ||||||||
\(539\) | 31.6329i | 1.36253i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.92154i | 0.340574i | 0.985395 | + | 0.170287i | \(0.0544694\pi\) | ||||
−0.985395 | + | 0.170287i | \(0.945531\pi\) | |||||||
\(542\) | −2.88471 | −0.123909 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 7.38404i | − 0.316588i | ||||||||
\(545\) | 3.20775 | 0.137405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4155 | 0.787390 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(548\) | − 15.7560i | − 0.673063i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −55.2693 | −2.35669 | ||||||||
\(551\) | 5.95433i | 0.253663i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 5.77107i | − 0.245411i | ||||||||
\(554\) | − 1.46250i | − 0.0621357i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.09783 | 0.258606 | ||||||||
\(557\) | − 23.9758i | − 1.01589i | −0.861390 | − | 0.507944i | \(-0.830406\pi\) | ||||
0.861390 | − | 0.507944i | \(-0.169594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.80194 | −0.118403 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.68233 | 0.239695 | ||||||||
\(563\) | −2.29291 | −0.0966348 | −0.0483174 | − | 0.998832i | \(-0.515386\pi\) | ||||
−0.0483174 | + | 0.998832i | \(0.515386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 25.1836i | − 1.05948i | ||||||||
\(566\) | − 25.2078i | − 1.05956i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.32975 | 0.0557950 | ||||||||
\(569\) | −44.3430 | −1.85896 | −0.929478 | − | 0.368878i | \(-0.879742\pi\) | ||||
−0.929478 | + | 0.368878i | \(0.879742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.2707 | 0.639058 | 0.319529 | − | 0.947577i | \(-0.396475\pi\) | ||||
0.319529 | + | 0.947577i | \(0.396475\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.04221i | 0.0435011i | ||||||||
\(575\) | −58.2210 | −2.42798 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.77048i | 0.365120i | 0.983195 | + | 0.182560i | \(0.0584383\pi\) | ||||
−0.983195 | + | 0.182560i | \(0.941562\pi\) | |||||||
\(578\) | − 37.5241i | − 1.56080i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 13.5429i | − 0.562337i | ||||||||
\(581\) | −10.6069 | −0.440047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 65.3726i | − 2.70745i | ||||||||
\(584\) | 7.65279 | 0.316675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.14914 | −0.295328 | ||||||||
\(587\) | 38.1430i | 1.57433i | 0.616742 | + | 0.787166i | \(0.288452\pi\) | ||||
−0.616742 | + | 0.787166i | \(0.711548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.73184 | 0.0713593 | ||||||||
\(590\) | − 5.29590i | − 0.218029i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.28621i | 0.0528628i | ||||||||
\(593\) | − 37.9517i | − 1.55849i | −0.626720 | − | 0.779244i | \(-0.715603\pi\) | ||||
0.626720 | − | 0.779244i | \(-0.284397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.6896 | −0.848192 | ||||||||
\(596\) | 2.55257i | 0.104557i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.57971 | 0.146263 | 0.0731315 | − | 0.997322i | \(-0.476701\pi\) | ||||
0.0731315 | + | 0.997322i | \(0.476701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.71678 | −0.233192 | −0.116596 | − | 0.993179i | \(-0.537198\pi\) | ||||
−0.116596 | + | 0.993179i | \(0.537198\pi\) | |||||||
\(602\) | 5.75600 | 0.234597 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.7168i | 0.720885i | ||||||||
\(605\) | − 50.7362i | − 2.06272i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4286 | 0.910351 | 0.455175 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455175 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(608\) | 1.78017 | 0.0721953 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.60388 | −0.0649390 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 39.9603i | − 1.61398i | −0.590564 | − | 0.806991i | \(-0.701095\pi\) | ||||
0.590564 | − | 0.806991i | \(-0.298905\pi\) | |||||||
\(614\) | 17.9952 | 0.726228 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − 3.35690i | − 0.135253i | ||||||||
\(617\) | − 31.4470i | − 1.26601i | −0.774149 | − | 0.633003i | \(-0.781822\pi\) | ||||
0.774149 | − | 0.633003i | \(-0.218178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.3685i | 1.18042i | 0.807250 | + | 0.590210i | \(0.200955\pi\) | ||||
−0.807250 | + | 0.590210i | \(0.799045\pi\) | |||||||
\(620\) | −3.93900 | −0.158194 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 3.32975i | − 0.133511i | ||||||||
\(623\) | 2.15213 | 0.0862232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 47.8485 | 1.91394 | ||||||||
\(626\) | 17.8834i | 0.714764i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.31767 | 0.252102 | ||||||||
\(629\) | 9.49742i | 0.378687i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 21.6799i | − 0.863065i | −0.902097 | − | 0.431532i | \(-0.857973\pi\) | ||||
0.902097 | − | 0.431532i | \(-0.142027\pi\) | |||||||
\(632\) | − 8.33944i | − 0.331725i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.39373 | −0.174497 | ||||||||
\(635\) | 24.3153i | 0.964922i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.2252 | 0.642362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.04892 | −0.160048 | ||||||||
\(641\) | 14.0108 | 0.553391 | 0.276696 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276696 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7875i | 1.21414i | 0.794649 | + | 0.607070i | \(0.207655\pi\) | ||||
−0.794649 | + | 0.607070i | \(0.792345\pi\) | |||||||
\(644\) | − 3.53617i | − 0.139345i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.1448 | 0.517177 | ||||||||
\(647\) | −16.6025 | −0.652713 | −0.326357 | − | 0.945247i | \(-0.605821\pi\) | ||||
−0.326357 | + | 0.945247i | \(0.605821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.34481 | 0.249056 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.5918i | 0.571459i | ||||||||
\(653\) | −28.5459 | −1.11709 | −0.558543 | − | 0.829476i | \(-0.688639\pi\) | ||||
−0.558543 | + | 0.829476i | \(0.688639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 35.6993i | − 1.39489i | ||||||||
\(656\) | 1.50604i | 0.0588010i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.98792i | 0.194449i | ||||||||
\(659\) | −27.7187 | −1.07977 | −0.539884 | − | 0.841740i | \(-0.681532\pi\) | ||||
−0.539884 | + | 0.841740i | \(0.681532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 10.8009i | − 0.420105i | −0.977690 | − | 0.210053i | \(-0.932636\pi\) | ||||
0.977690 | − | 0.210053i | \(-0.0673635\pi\) | |||||||
\(662\) | −25.6775 | −0.997986 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3274 | −0.594817 | ||||||||
\(665\) | − 4.98792i | − 0.193423i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.0917 | 0.661794 | ||||||||
\(668\) | 19.5013i | 0.754526i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 24.5133i | − 0.947033i | ||||||||
\(671\) | − 1.92154i | − 0.0741803i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3260 | −0.629322 | −0.314661 | − | 0.949204i | \(-0.601891\pi\) | ||||
−0.314661 | + | 0.949204i | \(0.601891\pi\) | |||||||
\(674\) | − 24.6504i | − 0.949498i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.4252 | −1.59210 | −0.796050 | − | 0.605231i | \(-0.793081\pi\) | ||||
−0.796050 | + | 0.605231i | \(0.793081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.91185 | −0.226876 | ||||||||
\(680\) | −29.8974 | −1.14651 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 4.71917i | − 0.180706i | ||||||||
\(683\) | 31.2325i | 1.19508i | 0.801840 | + | 0.597539i | \(0.203855\pi\) | ||||
−0.801840 | + | 0.597539i | \(0.796145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.7948 | −2.43747 | ||||||||
\(686\) | 9.35690 | 0.357248 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.31767 | 0.317108 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9638i | 0.949666i | 0.880076 | + | 0.474833i | \(0.157492\pi\) | ||||
−0.880076 | + | 0.474833i | \(0.842508\pi\) | |||||||
\(692\) | 9.29052 | 0.353173 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2959i | 0.542665i | ||||||||
\(695\) | − 24.6896i | − 0.936531i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1207i | 0.421225i | ||||||||
\(698\) | −11.0616 | −0.418687 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.88471i | 0.298014i | ||||||||
\(701\) | 8.17151 | 0.308634 | 0.154317 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154317 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.28967 | −0.0863564 | ||||||||
\(704\) | − 4.85086i | − 0.182823i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5047 | 0.395350 | ||||||||
\(707\) | − 8.30260i | − 0.312251i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.7982i | 1.38199i | 0.722861 | + | 0.690993i | \(0.242826\pi\) | ||||
−0.722861 | + | 0.690993i | \(0.757174\pi\) | |||||||
\(710\) | − 5.38404i | − 0.202060i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.10992 | 0.116549 | ||||||||
\(713\) | − 4.97120i | − 0.186173i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.7928 | −0.851808 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.10992 | 0.190700 | ||||||||
\(719\) | 35.2223 | 1.31357 | 0.656786 | − | 0.754077i | \(-0.271916\pi\) | ||||
0.656786 | + | 0.754077i | \(0.271916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.52781i | 0.317592i | ||||||||
\(722\) | − 15.8310i | − 0.589169i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.537500 | 0.0199760 | ||||||||
\(725\) | −38.1099 | −1.41537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.6872 | −1.50901 | −0.754503 | − | 0.656297i | \(-0.772122\pi\) | ||||
−0.754503 | + | 0.656297i | \(0.772122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − 30.9855i | − 1.14683i | ||||||||
\(731\) | 61.4180 | 2.27163 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.1400i | 1.00244i | 0.865320 | + | 0.501220i | \(0.167115\pi\) | ||||
−0.865320 | + | 0.501220i | \(0.832885\pi\) | |||||||
\(734\) | 8.44803i | 0.311822i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 5.10992i | − 0.188354i | ||||||||
\(737\) | 29.3685 | 1.08180 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 3.72587i | − 0.137058i | −0.997649 | − | 0.0685292i | \(-0.978169\pi\) | ||||
0.997649 | − | 0.0685292i | \(-0.0218306\pi\) | |||||||
\(740\) | 5.20775 | 0.191441 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.32603 | −0.342369 | ||||||||
\(743\) | − 21.8586i | − 0.801915i | −0.916097 | − | 0.400958i | \(-0.868677\pi\) | ||||
0.916097 | − | 0.400958i | \(-0.131323\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.3351 | 0.378650 | ||||||||
\(746\) | − 7.69096i | − 0.281586i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 35.8189i | − 1.30967i | ||||||||
\(749\) | − 4.08277i | − 0.149181i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.3642 | −1.94729 | −0.973644 | − | 0.228075i | \(-0.926757\pi\) | ||||
−0.973644 | + | 0.228075i | \(0.926757\pi\) | |||||||
\(752\) | 7.20775i | 0.262840i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 71.7338 | 2.61066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.63533 | −0.168474 | −0.0842370 | − | 0.996446i | \(-0.526845\pi\) | ||||
−0.0842370 | + | 0.996446i | \(0.526845\pi\) | |||||||
\(758\) | −11.4034 | −0.414191 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − 7.20775i | − 0.261453i | ||||||||
\(761\) | 11.5603i | 0.419062i | 0.977802 | + | 0.209531i | \(0.0671937\pi\) | ||||
−0.977802 | + | 0.209531i | \(0.932806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.548253 | 0.0198481 | ||||||||
\(764\) | −9.79954 | −0.354535 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.6703 | −0.746847 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.7439i | 0.531679i | 0.964017 | + | 0.265840i | \(0.0856492\pi\) | ||||
−0.964017 | + | 0.265840i | \(0.914351\pi\) | |||||||
\(770\) | −13.5918 | −0.489814 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 14.1957i | − 0.510913i | ||||||||
\(773\) | 6.42268i | 0.231008i | 0.993307 | + | 0.115504i | \(0.0368483\pi\) | ||||
−0.993307 | + | 0.115504i | \(0.963152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.0844i | 0.398164i | ||||||||
\(776\) | −8.54288 | −0.306671 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 17.4776i | − 0.626601i | ||||||||
\(779\) | −2.68100 | −0.0960570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.45042 | 0.230814 | ||||||||
\(782\) | − 37.7318i | − 1.34929i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.52111 | 0.232897 | ||||||||
\(785\) | − 25.5797i | − 0.912979i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 43.4336i | − 1.54824i | −0.633040 | − | 0.774119i | \(-0.718193\pi\) | ||||
0.633040 | − | 0.774119i | \(-0.281807\pi\) | |||||||
\(788\) | − 3.00969i | − 0.107216i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.7657 | −1.20133 | ||||||||
\(791\) | − 4.30426i | − 0.153042i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 19.3599 | 0.687056 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8944 | 0.457030 | ||||||||
\(797\) | 21.0164 | 0.744439 | 0.372219 | − | 0.928145i | \(-0.378597\pi\) | ||||
0.372219 | + | 0.928145i | \(0.378597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.2223i | 1.88287i | ||||||||
\(800\) | 11.3937i | 0.402829i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.4832 | −0.511420 | ||||||||
\(803\) | 37.1226 | 1.31003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.3177 | −0.504631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 11.9976i | − 0.422074i | ||||||||
\(809\) | 8.32245 | 0.292602 | 0.146301 | − | 0.989240i | \(-0.453263\pi\) | ||||
0.146301 | + | 0.989240i | \(0.453263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.4638i | 0.507894i | 0.967218 | + | 0.253947i | \(0.0817288\pi\) | ||||
−0.967218 | + | 0.253947i | \(0.918271\pi\) | |||||||
\(812\) | − 2.31468i | − 0.0812295i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.23921i | 0.218684i | ||||||||
\(815\) | 59.0810 | 2.06952 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.8068i | 0.518026i | ||||||||
\(818\) | −18.8984 | −0.660769 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.09783 | 0.212946 | ||||||||
\(821\) | − 38.4161i | − 1.34073i | −0.742031 | − | 0.670365i | \(-0.766137\pi\) | ||||
0.742031 | − | 0.670365i | \(-0.233863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.9748 | 1.42829 | 0.714145 | − | 0.699997i | \(-0.246816\pi\) | ||||
0.714145 | + | 0.699997i | \(0.246816\pi\) | |||||||
\(824\) | 12.3230i | 0.429294i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 0.905149i | − 0.0314942i | ||||||||
\(827\) | − 3.51035i | − 0.122067i | −0.998136 | − | 0.0610335i | \(-0.980560\pi\) | ||||
0.998136 | − | 0.0610335i | \(-0.0194396\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2185 | 0.459098 | 0.229549 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229549 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(830\) | 62.0592i | 2.15411i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 48.1521 | 1.66837 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 78.9590 | 2.73249 | ||||||||
\(836\) | 8.63533 | 0.298659 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 21.7603i | − 0.751698i | ||||||||
\(839\) | − 55.8491i | − 1.92812i | −0.265678 | − | 0.964062i | \(-0.585596\pi\) | ||||
0.265678 | − | 0.964062i | \(-0.414404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.8122 | −0.614214 | ||||||||
\(842\) | 20.5918 | 0.709640 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.79954 | −0.268471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 8.67158i | − 0.297959i | ||||||||
\(848\) | −13.4765 | −0.462785 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 84.1318i | 2.88570i | ||||||||
\(851\) | 6.57242i | 0.225300i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.8103i | 0.746770i | 0.927676 | + | 0.373385i | \(0.121803\pi\) | ||||
−0.927676 | + | 0.373385i | \(0.878197\pi\) | |||||||
\(854\) | −0.274127 | −0.00938042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − 5.89977i | − 0.201650i | ||||||||
\(857\) | 28.8961 | 0.987070 | 0.493535 | − | 0.869726i | \(-0.335704\pi\) | ||||
0.493535 | + | 0.869726i | \(0.335704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.2755 | −0.589431 | −0.294715 | − | 0.955585i | \(-0.595225\pi\) | ||||
−0.294715 | + | 0.955585i | \(0.595225\pi\) | |||||||
\(860\) | − 33.6775i | − 1.14839i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.5133 | −1.17553 | ||||||||
\(863\) | 44.7741i | 1.52413i | 0.647503 | + | 0.762063i | \(0.275813\pi\) | ||||
−0.647503 | + | 0.762063i | \(0.724187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 37.6165i | − 1.27900i | ||||||||
\(866\) | − 2.12631i | − 0.0722549i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.673235 | −0.0228511 | ||||||||
\(869\) | − 40.4534i | − 1.37229i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.792249 | 0.0268289 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.09651 | 0.307694 | ||||||||
\(875\) | 17.9148 | 0.605632 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 40.2741i | − 1.35996i | −0.733230 | − | 0.679980i | \(-0.761988\pi\) | ||||
0.733230 | − | 0.679980i | \(-0.238012\pi\) | |||||||
\(878\) | 21.8321i | 0.736797i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.6407 | −0.662088 | ||||||||
\(881\) | 9.40821 | 0.316971 | 0.158485 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158485 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.2271 | 1.72393 | 0.861965 | − | 0.506968i | \(-0.169234\pi\) | ||||
0.861965 | + | 0.506968i | \(0.169234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 7.54048i | − 0.253328i | ||||||||
\(887\) | 39.9215 | 1.34043 | 0.670217 | − | 0.742165i | \(-0.266201\pi\) | ||||
0.670217 | + | 0.742165i | \(0.266201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.15585i | 0.139383i | ||||||||
\(890\) | − 12.5918i | − 0.422078i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.1957i | 0.408341i | ||||||||
\(893\) | −12.8310 | −0.429373 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 92.2863i | 3.08479i | ||||||||
\(896\) | −0.692021 | −0.0231188 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.7560 | 0.659266 | ||||||||
\(899\) | − 3.25401i | − 0.108527i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −99.5111 | −3.31519 | ||||||||
\(902\) | 7.30559i | 0.243249i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 6.21983i | − 0.206869i | ||||||||
\(905\) | − 2.17629i | − 0.0723424i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.8310 | 1.15654 | 0.578272 | − | 0.815844i | \(-0.303727\pi\) | ||||
0.578272 | + | 0.815844i | \(0.303727\pi\) | |||||||
\(908\) | 6.74333i | 0.223785i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.2125 | −0.437751 | −0.218875 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218875 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74.3508 | −2.46065 | ||||||||
\(914\) | 23.8582 | 0.789157 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 19.8237i | − 0.654994i | ||||||||
\(917\) | − 6.10156i | − 0.201491i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0175 | 0.693302 | 0.346651 | − | 0.937994i | \(-0.387319\pi\) | ||||
0.346651 | + | 0.937994i | \(0.387319\pi\) | |||||||
\(920\) | −20.6896 | −0.682117 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.5773 | 0.578878 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 14.6547i | − 0.481844i | ||||||||
\(926\) | −23.8431 | −0.783532 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 3.34481i | − 0.109799i | ||||||||
\(929\) | 26.9965i | 0.885728i | 0.896589 | + | 0.442864i | \(0.146038\pi\) | ||||
−0.896589 | + | 0.442864i | \(0.853962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6087i | 0.380459i | ||||||||
\(932\) | 30.0301 | 0.983670 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 8.61058i | − 0.281747i | ||||||||
\(935\) | −145.028 | −4.74292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1745 | 0.757078 | 0.378539 | − | 0.925585i | \(-0.376427\pi\) | ||||
0.378539 | + | 0.925585i | \(0.376427\pi\) | |||||||
\(938\) | − 4.18970i | − 0.136799i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.1836 | 0.951864 | ||||||||
\(941\) | − 7.54048i | − 0.245813i | −0.992418 | − | 0.122906i | \(-0.960779\pi\) | ||||
0.992418 | − | 0.122906i | \(-0.0392215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.69574i | 0.250608i | ||||||||
\(944\) | − 1.30798i | − 0.0425711i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.3478 | 1.31182 | ||||||||
\(947\) | 20.6601i | 0.671363i | 0.941976 | + | 0.335681i | \(0.108967\pi\) | ||||
−0.941976 | + | 0.335681i | \(0.891033\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20.2828 | −0.658059 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.10992 | −0.165613 | ||||||||
\(953\) | −30.2935 | −0.981303 | −0.490651 | − | 0.871356i | \(-0.663241\pi\) | ||||
−0.490651 | + | 0.871356i | \(0.663241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.6775i | 1.28394i | ||||||||
\(956\) | 22.0978i | 0.714695i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.58104 | 0.212624 | ||||||||
\(959\) | −10.9035 | −0.352092 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0536 | 0.969470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.1274i | 0.326181i | ||||||||
\(965\) | −57.4771 | −1.85025 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 20.7289i | − 0.666595i | −0.942822 | − | 0.333298i | \(-0.891839\pi\) | ||||
0.942822 | − | 0.333298i | \(-0.108161\pi\) | |||||||
\(968\) | − 12.5308i | − 0.402755i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.5894i | 1.11060i | ||||||||
\(971\) | 39.1094 | 1.25508 | 0.627541 | − | 0.778584i | \(-0.284062\pi\) | ||||
0.627541 | + | 0.778584i | \(0.284062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.21983i | − 0.135282i | ||||||||
\(974\) | −23.2760 | −0.745813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396125 | −0.0126796 | ||||||||
\(977\) | − 7.27545i | − 0.232762i | −0.993205 | − | 0.116381i | \(-0.962871\pi\) | ||||
0.993205 | − | 0.116381i | \(-0.0371294\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0858 | 0.482143 | ||||||||
\(980\) | − 26.4034i | − 0.843426i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.5405i | 0.495917i | ||||||||
\(983\) | 53.4857i | 1.70593i | 0.521969 | + | 0.852965i | \(0.325198\pi\) | ||||
−0.521969 | + | 0.852965i | \(0.674802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.1860 | −0.388278 | ||||||||
\(986\) | − 24.6983i | − 0.786553i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.5026 | 1.35150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0575 | 0.510085 | 0.255042 | − | 0.966930i | \(-0.417911\pi\) | ||||
0.255042 | + | 0.966930i | \(0.417911\pi\) | |||||||
\(992\) | −0.972853 | −0.0308881 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − 0.920215i | − 0.0291874i | ||||||||
\(995\) | − 52.2083i | − 1.65512i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4263 | 0.710247 | 0.355123 | − | 0.934819i | \(-0.384439\pi\) | ||||
0.355123 | + | 0.934819i | \(0.384439\pi\) | |||||||
\(998\) | 9.53617 | 0.301862 | ||||||||
\(999\) | 0 | 0 |
(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 | 3042.2.b.r.1351.3 | 6 | ||
3.2 | odd | 2 | 1014.2.b.g.337.4 | 6 | |||
13.5 | odd | 4 | 3042.2.a.bd.1.3 | 3 | |||
13.8 | odd | 4 | 3042.2.a.be.1.1 | 3 | |||
13.12 | even | 2 | inner | 3042.2.b.r.1351.4 | 6 | ||
39.2 | even | 12 | 1014.2.e.k.529.1 | 6 | |||
39.5 | even | 4 | 1014.2.a.o.1.1 | yes | 3 | ||
39.8 | even | 4 | 1014.2.a.m.1.3 | ✓ | 3 | ||
39.11 | even | 12 | 1014.2.e.m.529.3 | 6 | |||
39.17 | odd | 6 | 1014.2.i.g.361.3 | 12 | |||
39.20 | even | 12 | 1014.2.e.m.991.3 | 6 | |||
39.23 | odd | 6 | 1014.2.i.g.823.6 | 12 | |||
39.29 | odd | 6 | 1014.2.i.g.823.1 | 12 | |||
39.32 | even | 12 | 1014.2.e.k.991.1 | 6 | |||
39.35 | odd | 6 | 1014.2.i.g.361.4 | 12 | |||
39.38 | odd | 2 | 1014.2.b.g.337.3 | 6 | |||
156.47 | odd | 4 | 8112.2.a.ce.1.3 | 3 | |||
156.83 | odd | 4 | 8112.2.a.bz.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.3 | ✓ | 3 | 39.8 | even | 4 | ||
1014.2.a.o.1.1 | yes | 3 | 39.5 | even | 4 | ||
1014.2.b.g.337.3 | 6 | 39.38 | odd | 2 | |||
1014.2.b.g.337.4 | 6 | 3.2 | odd | 2 | |||
1014.2.e.k.529.1 | 6 | 39.2 | even | 12 | |||
1014.2.e.k.991.1 | 6 | 39.32 | even | 12 | |||
1014.2.e.m.529.3 | 6 | 39.11 | even | 12 | |||
1014.2.e.m.991.3 | 6 | 39.20 | even | 12 | |||
1014.2.i.g.361.3 | 12 | 39.17 | odd | 6 | |||
1014.2.i.g.361.4 | 12 | 39.35 | odd | 6 | |||
1014.2.i.g.823.1 | 12 | 39.29 | odd | 6 | |||
1014.2.i.g.823.6 | 12 | 39.23 | odd | 6 | |||
3042.2.a.bd.1.3 | 3 | 13.5 | odd | 4 | |||
3042.2.a.be.1.1 | 3 | 13.8 | odd | 4 | |||
3042.2.b.r.1351.3 | 6 | 1.1 | even | 1 | trivial | ||
3042.2.b.r.1351.4 | 6 | 13.12 | even | 2 | inner | ||
8112.2.a.bz.1.1 | 3 | 156.83 | odd | 4 | |||
8112.2.a.ce.1.3 | 3 | 156.47 | odd | 4 |