Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, 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("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.202932.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 12x + 33 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.49111\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.49111 | 0.666845 | 0.333422 | − | 0.942778i | \(-0.391796\pi\) | ||||
0.333422 | + | 0.942778i | \(0.391796\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.49111 | 0.471531 | ||||||||
\(11\) | 0.794368 | 0.239511 | 0.119755 | − | 0.992803i | \(-0.461789\pi\) | ||||
0.119755 | + | 0.992803i | \(0.461789\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.49111 | −0.385003 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.49111 | −1.08925 | −0.544627 | − | 0.838678i | \(-0.683329\pi\) | ||||
−0.544627 | + | 0.838678i | \(0.683329\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.49111 | 0.333422 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.794368 | 0.169360 | ||||||||
\(23\) | 3.15514 | 0.657892 | 0.328946 | − | 0.944349i | \(-0.393307\pi\) | ||||
0.328946 | + | 0.944349i | \(0.393307\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.77659 | −0.555318 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.23498 | −1.15781 | −0.578904 | − | 0.815396i | \(-0.696519\pi\) | ||||
−0.578904 | + | 0.815396i | \(0.696519\pi\) | |||||||
\(30\) | −1.49111 | −0.272238 | ||||||||
\(31\) | −9.01157 | −1.61853 | −0.809263 | − | 0.587446i | \(-0.800133\pi\) | ||||
−0.809263 | + | 0.587446i | \(0.800133\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.794368 | −0.138282 | ||||||||
\(34\) | −4.49111 | −0.770219 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.49111 | −0.409536 | −0.204768 | − | 0.978811i | \(-0.565644\pi\) | ||||
−0.204768 | + | 0.978811i | \(0.565644\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 1.49111 | 0.235765 | ||||||||
\(41\) | 4.18449 | 0.653508 | 0.326754 | − | 0.945110i | \(-0.394045\pi\) | ||||
0.326754 | + | 0.945110i | \(0.394045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.94951 | −0.754793 | −0.377396 | − | 0.926052i | \(-0.623181\pi\) | ||||
−0.377396 | + | 0.926052i | \(0.623181\pi\) | |||||||
\(44\) | 0.794368 | 0.119755 | ||||||||
\(45\) | 1.49111 | 0.222282 | ||||||||
\(46\) | 3.15514 | 0.465200 | ||||||||
\(47\) | −11.9106 | −1.73734 | −0.868669 | − | 0.495394i | \(-0.835024\pi\) | ||||
−0.868669 | + | 0.495394i | \(0.835024\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.77659 | −0.392669 | ||||||||
\(51\) | 4.49111 | 0.628881 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | −5.42284 | −0.744884 | −0.372442 | − | 0.928055i | \(-0.621479\pi\) | ||||
−0.372442 | + | 0.928055i | \(0.621479\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 1.18449 | 0.159717 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −6.23498 | −0.818694 | ||||||||
\(59\) | −11.8093 | −1.53744 | −0.768720 | − | 0.639585i | \(-0.779106\pi\) | ||||
−0.768720 | + | 0.639585i | \(0.779106\pi\) | |||||||
\(60\) | −1.49111 | −0.192502 | ||||||||
\(61\) | 12.5825 | 1.61103 | 0.805514 | − | 0.592577i | \(-0.201889\pi\) | ||||
0.805514 | + | 0.592577i | \(0.201889\pi\) | |||||||
\(62\) | −9.01157 | −1.14447 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.98222 | −0.369899 | ||||||||
\(66\) | −0.794368 | −0.0977799 | ||||||||
\(67\) | 16.0231 | 1.95754 | 0.978769 | − | 0.204964i | \(-0.0657078\pi\) | ||||
0.978769 | + | 0.204964i | \(0.0657078\pi\) | |||||||
\(68\) | −4.49111 | −0.544627 | ||||||||
\(69\) | −3.15514 | −0.379834 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47333 | 0.174852 | 0.0874262 | − | 0.996171i | \(-0.472136\pi\) | ||||
0.0874262 | + | 0.996171i | \(0.472136\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.23498 | 0.144544 | 0.0722720 | − | 0.997385i | \(-0.476975\pi\) | ||||
0.0722720 | + | 0.997385i | \(0.476975\pi\) | |||||||
\(74\) | −2.49111 | −0.289586 | ||||||||
\(75\) | 2.77659 | 0.320613 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −2.33597 | −0.262817 | −0.131409 | − | 0.991328i | \(-0.541950\pi\) | ||||
−0.131409 | + | 0.991328i | \(0.541950\pi\) | |||||||
\(80\) | 1.49111 | 0.166711 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.18449 | 0.462100 | ||||||||
\(83\) | 1.57096 | 0.172435 | 0.0862174 | − | 0.996276i | \(-0.472522\pi\) | ||||
0.0862174 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.69674 | −0.726364 | ||||||||
\(86\) | −4.94951 | −0.533719 | ||||||||
\(87\) | 6.23498 | 0.668460 | ||||||||
\(88\) | 0.794368 | 0.0846799 | ||||||||
\(89\) | −2.28548 | −0.242260 | −0.121130 | − | 0.992637i | \(-0.538652\pi\) | ||||
−0.121130 | + | 0.992637i | \(0.538652\pi\) | |||||||
\(90\) | 1.49111 | 0.157177 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.15514 | 0.328946 | ||||||||
\(93\) | 9.01157 | 0.934457 | ||||||||
\(94\) | −11.9106 | −1.22848 | ||||||||
\(95\) | −1.49111 | −0.152985 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −17.2971 | −1.75625 | −0.878125 | − | 0.478432i | \(-0.841205\pi\) | ||||
−0.878125 | + | 0.478432i | \(0.841205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.794368 | 0.0798370 | ||||||||
\(100\) | −2.77659 | −0.277659 | ||||||||
\(101\) | −3.85188 | −0.383277 | −0.191638 | − | 0.981466i | \(-0.561380\pi\) | ||||
−0.191638 | + | 0.981466i | \(0.561380\pi\) | |||||||
\(102\) | 4.49111 | 0.444686 | ||||||||
\(103\) | 1.79437 | 0.176804 | 0.0884021 | − | 0.996085i | \(-0.471824\pi\) | ||||
0.0884021 | + | 0.996085i | \(0.471824\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.42284 | −0.526713 | ||||||||
\(107\) | 11.5027 | 1.11201 | 0.556003 | − | 0.831180i | \(-0.312334\pi\) | ||||
0.556003 | + | 0.831180i | \(0.312334\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 3.47333 | 0.332685 | 0.166342 | − | 0.986068i | \(-0.446804\pi\) | ||||
0.166342 | + | 0.986068i | \(0.446804\pi\) | |||||||
\(110\) | 1.18449 | 0.112937 | ||||||||
\(111\) | 2.49111 | 0.236446 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.87421 | −0.364455 | −0.182228 | − | 0.983256i | \(-0.558331\pi\) | ||||
−0.182228 | + | 0.983256i | \(0.558331\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 4.70466 | 0.438712 | ||||||||
\(116\) | −6.23498 | −0.578904 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | −11.8093 | −1.08713 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.49111 | −0.136119 | ||||||||
\(121\) | −10.3690 | −0.942635 | ||||||||
\(122\) | 12.5825 | 1.13917 | ||||||||
\(123\) | −4.18449 | −0.377303 | ||||||||
\(124\) | −9.01157 | −0.809263 | ||||||||
\(125\) | −11.5958 | −1.03716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.55938 | −0.138373 | −0.0691865 | − | 0.997604i | \(-0.522040\pi\) | ||||
−0.0691865 | + | 0.997604i | \(0.522040\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.94951 | 0.435780 | ||||||||
\(130\) | −2.98222 | −0.261558 | ||||||||
\(131\) | 8.91058 | 0.778521 | 0.389261 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389261 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(132\) | −0.794368 | −0.0691408 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.0231 | 1.38419 | ||||||||
\(135\) | −1.49111 | −0.128334 | ||||||||
\(136\) | −4.49111 | −0.385110 | ||||||||
\(137\) | 9.85188 | 0.841703 | 0.420852 | − | 0.907130i | \(-0.361731\pi\) | ||||
0.420852 | + | 0.907130i | \(0.361731\pi\) | |||||||
\(138\) | −3.15514 | −0.268583 | ||||||||
\(139\) | −21.4195 | −1.81678 | −0.908388 | − | 0.418128i | \(-0.862686\pi\) | ||||
−0.908388 | + | 0.418128i | \(0.862686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.9106 | 1.00305 | ||||||||
\(142\) | 1.47333 | 0.123639 | ||||||||
\(143\) | −1.58874 | −0.132857 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.29705 | −0.772078 | ||||||||
\(146\) | 1.23498 | 0.102208 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.49111 | −0.204768 | ||||||||
\(149\) | 17.4051 | 1.42588 | 0.712939 | − | 0.701226i | \(-0.247364\pi\) | ||||
0.712939 | + | 0.701226i | \(0.247364\pi\) | |||||||
\(150\) | 2.77659 | 0.226708 | ||||||||
\(151\) | 2.88744 | 0.234976 | 0.117488 | − | 0.993074i | \(-0.462516\pi\) | ||||
0.117488 | + | 0.993074i | \(0.462516\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −4.49111 | −0.363085 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.4373 | −1.07931 | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | 9.91058 | 0.790951 | 0.395475 | − | 0.918477i | \(-0.370580\pi\) | ||||
0.395475 | + | 0.918477i | \(0.370580\pi\) | |||||||
\(158\) | −2.33597 | −0.185840 | ||||||||
\(159\) | 5.42284 | 0.430059 | ||||||||
\(160\) | 1.49111 | 0.117883 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.02935 | 0.707233 | 0.353617 | − | 0.935390i | \(-0.384952\pi\) | ||||
0.353617 | + | 0.935390i | \(0.384952\pi\) | |||||||
\(164\) | 4.18449 | 0.326754 | ||||||||
\(165\) | −1.18449 | −0.0922124 | ||||||||
\(166\) | 1.57096 | 0.121930 | ||||||||
\(167\) | 1.47333 | 0.114010 | 0.0570049 | − | 0.998374i | \(-0.481845\pi\) | ||||
0.0570049 | + | 0.998374i | \(0.481845\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −6.69674 | −0.513617 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −4.94951 | −0.377396 | ||||||||
\(173\) | −16.0691 | −1.22171 | −0.610855 | − | 0.791742i | \(-0.709174\pi\) | ||||
−0.610855 | + | 0.791742i | \(0.709174\pi\) | |||||||
\(174\) | 6.23498 | 0.472673 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.794368 | 0.0598777 | ||||||||
\(177\) | 11.8093 | 0.887642 | ||||||||
\(178\) | −2.28548 | −0.171304 | ||||||||
\(179\) | −0.505526 | −0.0377848 | −0.0188924 | − | 0.999822i | \(-0.506014\pi\) | ||||
−0.0188924 | + | 0.999822i | \(0.506014\pi\) | |||||||
\(180\) | 1.49111 | 0.111141 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.5825 | −0.930127 | ||||||||
\(184\) | 3.15514 | 0.232600 | ||||||||
\(185\) | −3.71452 | −0.273097 | ||||||||
\(186\) | 9.01157 | 0.660761 | ||||||||
\(187\) | −3.56759 | −0.260888 | ||||||||
\(188\) | −11.9106 | −0.868669 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.49111 | −0.108177 | ||||||||
\(191\) | −26.5825 | −1.92344 | −0.961722 | − | 0.274026i | \(-0.911644\pi\) | ||||
−0.961722 | + | 0.274026i | \(0.911644\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.77204 | −0.343499 | −0.171749 | − | 0.985141i | \(-0.554942\pi\) | ||||
−0.171749 | + | 0.985141i | \(0.554942\pi\) | |||||||
\(194\) | −17.2971 | −1.24186 | ||||||||
\(195\) | 2.98222 | 0.213561 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0152 | 1.14104 | 0.570519 | − | 0.821284i | \(-0.306742\pi\) | ||||
0.570519 | + | 0.821284i | \(0.306742\pi\) | |||||||
\(198\) | 0.794368 | 0.0564532 | ||||||||
\(199\) | 10.8341 | 0.768009 | 0.384005 | − | 0.923331i | \(-0.374545\pi\) | ||||
0.384005 | + | 0.923331i | \(0.374545\pi\) | |||||||
\(200\) | −2.77659 | −0.196334 | ||||||||
\(201\) | −16.0231 | −1.13019 | ||||||||
\(202\) | −3.85188 | −0.271017 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.49111 | 0.314441 | ||||||||
\(205\) | 6.23954 | 0.435788 | ||||||||
\(206\) | 1.79437 | 0.125020 | ||||||||
\(207\) | 3.15514 | 0.219297 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −0.794368 | −0.0549476 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.24992 | 0.292577 | 0.146288 | − | 0.989242i | \(-0.453267\pi\) | ||||
0.146288 | + | 0.989242i | \(0.453267\pi\) | |||||||
\(212\) | −5.42284 | −0.372442 | ||||||||
\(213\) | −1.47333 | −0.100951 | ||||||||
\(214\) | 11.5027 | 0.786307 | ||||||||
\(215\) | −7.38026 | −0.503330 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.47333 | 0.235244 | ||||||||
\(219\) | −1.23498 | −0.0834525 | ||||||||
\(220\) | 1.18449 | 0.0798583 | ||||||||
\(221\) | 8.98222 | 0.604210 | ||||||||
\(222\) | 2.49111 | 0.167192 | ||||||||
\(223\) | 15.0807 | 1.00988 | 0.504938 | − | 0.863156i | \(-0.331515\pi\) | ||||
0.504938 | + | 0.863156i | \(0.331515\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.77659 | −0.185106 | ||||||||
\(226\) | −3.87421 | −0.257709 | ||||||||
\(227\) | −5.19241 | −0.344632 | −0.172316 | − | 0.985042i | \(-0.555125\pi\) | ||||
−0.172316 | + | 0.985042i | \(0.555125\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 10.7802 | 0.712379 | 0.356189 | − | 0.934414i | \(-0.384076\pi\) | ||||
0.356189 | + | 0.934414i | \(0.384076\pi\) | |||||||
\(230\) | 4.70466 | 0.310216 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.23498 | −0.409347 | ||||||||
\(233\) | 1.58874 | 0.104082 | 0.0520408 | − | 0.998645i | \(-0.483427\pi\) | ||||
0.0520408 | + | 0.998645i | \(0.483427\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −17.7600 | −1.15853 | ||||||||
\(236\) | −11.8093 | −0.768720 | ||||||||
\(237\) | 2.33597 | 0.151738 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.41126 | −0.285341 | −0.142670 | − | 0.989770i | \(-0.545569\pi\) | ||||
−0.142670 | + | 0.989770i | \(0.545569\pi\) | |||||||
\(240\) | −1.49111 | −0.0962508 | ||||||||
\(241\) | 3.84486 | 0.247669 | 0.123835 | − | 0.992303i | \(-0.460481\pi\) | ||||
0.123835 | + | 0.992303i | \(0.460481\pi\) | |||||||
\(242\) | −10.3690 | −0.666543 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.5825 | 0.805514 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.18449 | −0.266793 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | −9.01157 | −0.572235 | ||||||||
\(249\) | −1.57096 | −0.0995553 | ||||||||
\(250\) | −11.5958 | −0.733380 | ||||||||
\(251\) | −18.9185 | −1.19413 | −0.597063 | − | 0.802195i | \(-0.703666\pi\) | ||||
−0.597063 | + | 0.802195i | \(0.703666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50634 | 0.157572 | ||||||||
\(254\) | −1.55938 | −0.0978444 | ||||||||
\(255\) | 6.69674 | 0.419366 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.9399 | 1.18144 | 0.590720 | − | 0.806876i | \(-0.298844\pi\) | ||||
0.590720 | + | 0.806876i | \(0.298844\pi\) | |||||||
\(258\) | 4.94951 | 0.308143 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.98222 | −0.184950 | ||||||||
\(261\) | −6.23498 | −0.385936 | ||||||||
\(262\) | 8.91058 | 0.550498 | ||||||||
\(263\) | 30.9806 | 1.91034 | 0.955172 | − | 0.296052i | \(-0.0956701\pi\) | ||||
0.955172 | + | 0.296052i | \(0.0956701\pi\) | |||||||
\(264\) | −0.794368 | −0.0488899 | ||||||||
\(265\) | −8.08605 | −0.496722 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.28548 | 0.139869 | ||||||||
\(268\) | 16.0231 | 0.978769 | ||||||||
\(269\) | −5.92471 | −0.361236 | −0.180618 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180618 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(270\) | −1.49111 | −0.0907461 | ||||||||
\(271\) | 13.0798 | 0.794544 | 0.397272 | − | 0.917701i | \(-0.369957\pi\) | ||||
0.397272 | + | 0.917701i | \(0.369957\pi\) | |||||||
\(272\) | −4.49111 | −0.272314 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.85188 | 0.595174 | ||||||||
\(275\) | −2.20563 | −0.133005 | ||||||||
\(276\) | −3.15514 | −0.189917 | ||||||||
\(277\) | −12.2316 | −0.734927 | −0.367463 | − | 0.930038i | \(-0.619774\pi\) | ||||
−0.367463 | + | 0.930038i | \(0.619774\pi\) | |||||||
\(278\) | −21.4195 | −1.28465 | ||||||||
\(279\) | −9.01157 | −0.539509 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.150585 | −0.00898313 | −0.00449156 | − | 0.999990i | \(-0.501430\pi\) | ||||
−0.00449156 | + | 0.999990i | \(0.501430\pi\) | |||||||
\(282\) | 11.9106 | 0.709265 | ||||||||
\(283\) | −24.4017 | −1.45053 | −0.725265 | − | 0.688470i | \(-0.758283\pi\) | ||||
−0.725265 | + | 0.688470i | \(0.758283\pi\) | |||||||
\(284\) | 1.47333 | 0.0874262 | ||||||||
\(285\) | 1.49111 | 0.0883258 | ||||||||
\(286\) | −1.58874 | −0.0939439 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 3.17008 | 0.186475 | ||||||||
\(290\) | −9.29705 | −0.545942 | ||||||||
\(291\) | 17.2971 | 1.01397 | ||||||||
\(292\) | 1.23498 | 0.0722720 | ||||||||
\(293\) | −12.6694 | −0.740154 | −0.370077 | − | 0.929001i | \(-0.620669\pi\) | ||||
−0.370077 | + | 0.929001i | \(0.620669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.6090 | −1.02523 | ||||||||
\(296\) | −2.49111 | −0.144793 | ||||||||
\(297\) | −0.794368 | −0.0460939 | ||||||||
\(298\) | 17.4051 | 1.00825 | ||||||||
\(299\) | −6.31028 | −0.364933 | ||||||||
\(300\) | 2.77659 | 0.160306 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.88744 | 0.166153 | ||||||||
\(303\) | 3.85188 | 0.221285 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 18.7619 | 1.07431 | ||||||||
\(306\) | −4.49111 | −0.256740 | ||||||||
\(307\) | 19.8031 | 1.13022 | 0.565111 | − | 0.825015i | \(-0.308833\pi\) | ||||
0.565111 | + | 0.825015i | \(0.308833\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.79437 | −0.102078 | ||||||||
\(310\) | −13.4373 | −0.763185 | ||||||||
\(311\) | 23.3918 | 1.32643 | 0.663215 | − | 0.748429i | \(-0.269192\pi\) | ||||
0.663215 | + | 0.748429i | \(0.269192\pi\) | |||||||
\(312\) | 2.00000 | 0.113228 | ||||||||
\(313\) | 27.6045 | 1.56030 | 0.780149 | − | 0.625594i | \(-0.215143\pi\) | ||||
0.780149 | + | 0.625594i | \(0.215143\pi\) | |||||||
\(314\) | 9.91058 | 0.559287 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.33597 | −0.131409 | ||||||||
\(317\) | −21.4883 | −1.20690 | −0.603451 | − | 0.797400i | \(-0.706208\pi\) | ||||
−0.603451 | + | 0.797400i | \(0.706208\pi\) | |||||||
\(318\) | 5.42284 | 0.304098 | ||||||||
\(319\) | −4.95287 | −0.277307 | ||||||||
\(320\) | 1.49111 | 0.0833556 | ||||||||
\(321\) | −11.5027 | −0.642017 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.49111 | 0.249892 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.55318 | 0.308035 | ||||||||
\(326\) | 9.02935 | 0.500090 | ||||||||
\(327\) | −3.47333 | −0.192076 | ||||||||
\(328\) | 4.18449 | 0.231050 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.18449 | −0.0652040 | ||||||||
\(331\) | −15.7377 | −0.865020 | −0.432510 | − | 0.901629i | \(-0.642372\pi\) | ||||
−0.432510 | + | 0.901629i | \(0.642372\pi\) | |||||||
\(332\) | 1.57096 | 0.0862174 | ||||||||
\(333\) | −2.49111 | −0.136512 | ||||||||
\(334\) | 1.47333 | 0.0806171 | ||||||||
\(335\) | 23.8923 | 1.30537 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.7670 | −1.73046 | −0.865230 | − | 0.501375i | \(-0.832828\pi\) | ||||
−0.865230 | + | 0.501375i | \(0.832828\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 3.87421 | 0.210418 | ||||||||
\(340\) | −6.69674 | −0.363182 | ||||||||
\(341\) | −7.15850 | −0.387655 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.94951 | −0.266859 | ||||||||
\(345\) | −4.70466 | −0.253290 | ||||||||
\(346\) | −16.0691 | −0.863879 | ||||||||
\(347\) | −12.3769 | −0.664427 | −0.332213 | − | 0.943204i | \(-0.607795\pi\) | ||||
−0.332213 | + | 0.943204i | \(0.607795\pi\) | |||||||
\(348\) | 6.23498 | 0.334230 | ||||||||
\(349\) | −29.2610 | −1.56630 | −0.783152 | − | 0.621830i | \(-0.786389\pi\) | ||||
−0.783152 | + | 0.621830i | \(0.786389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0.794368 | 0.0423399 | ||||||||
\(353\) | −21.8423 | −1.16255 | −0.581274 | − | 0.813708i | \(-0.697446\pi\) | ||||
−0.581274 | + | 0.813708i | \(0.697446\pi\) | |||||||
\(354\) | 11.8093 | 0.627657 | ||||||||
\(355\) | 2.19690 | 0.116599 | ||||||||
\(356\) | −2.28548 | −0.121130 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.505526 | −0.0267179 | ||||||||
\(359\) | −24.2209 | −1.27833 | −0.639164 | − | 0.769070i | \(-0.720720\pi\) | ||||
−0.639164 | + | 0.769070i | \(0.720720\pi\) | |||||||
\(360\) | 1.49111 | 0.0785884 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 10.3690 | 0.544230 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.84150 | 0.0963884 | ||||||||
\(366\) | −12.5825 | −0.657699 | ||||||||
\(367\) | 17.4373 | 0.910217 | 0.455109 | − | 0.890436i | \(-0.349600\pi\) | ||||
0.455109 | + | 0.890436i | \(0.349600\pi\) | |||||||
\(368\) | 3.15514 | 0.164473 | ||||||||
\(369\) | 4.18449 | 0.217836 | ||||||||
\(370\) | −3.71452 | −0.193109 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.01157 | 0.467228 | ||||||||
\(373\) | −10.7374 | −0.555960 | −0.277980 | − | 0.960587i | \(-0.589665\pi\) | ||||
−0.277980 | + | 0.960587i | \(0.589665\pi\) | |||||||
\(374\) | −3.56759 | −0.184476 | ||||||||
\(375\) | 11.5958 | 0.598802 | ||||||||
\(376\) | −11.9106 | −0.614242 | ||||||||
\(377\) | 12.4700 | 0.642236 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.5887 | −0.595273 | −0.297637 | − | 0.954679i | \(-0.596198\pi\) | ||||
−0.297637 | + | 0.954679i | \(0.596198\pi\) | |||||||
\(380\) | −1.49111 | −0.0764924 | ||||||||
\(381\) | 1.55938 | 0.0798896 | ||||||||
\(382\) | −26.5825 | −1.36008 | ||||||||
\(383\) | −5.69704 | −0.291105 | −0.145552 | − | 0.989351i | \(-0.546496\pi\) | ||||
−0.145552 | + | 0.989351i | \(0.546496\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.77204 | −0.242890 | ||||||||
\(387\) | −4.94951 | −0.251598 | ||||||||
\(388\) | −17.2971 | −0.878125 | ||||||||
\(389\) | −1.35793 | −0.0688497 | −0.0344249 | − | 0.999407i | \(-0.510960\pi\) | ||||
−0.0344249 | + | 0.999407i | \(0.510960\pi\) | |||||||
\(390\) | 2.98222 | 0.151011 | ||||||||
\(391\) | −14.1701 | −0.716611 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.91058 | −0.449480 | ||||||||
\(394\) | 16.0152 | 0.806836 | ||||||||
\(395\) | −3.48319 | −0.175258 | ||||||||
\(396\) | 0.794368 | 0.0399185 | ||||||||
\(397\) | −28.3334 | −1.42201 | −0.711007 | − | 0.703185i | \(-0.751761\pi\) | ||||
−0.711007 | + | 0.703185i | \(0.751761\pi\) | |||||||
\(398\) | 10.8341 | 0.543064 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.77659 | −0.138829 | ||||||||
\(401\) | −33.9577 | −1.69577 | −0.847884 | − | 0.530182i | \(-0.822123\pi\) | ||||
−0.847884 | + | 0.530182i | \(0.822123\pi\) | |||||||
\(402\) | −16.0231 | −0.799162 | ||||||||
\(403\) | 18.0231 | 0.897797 | ||||||||
\(404\) | −3.85188 | −0.191638 | ||||||||
\(405\) | 1.49111 | 0.0740939 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.97886 | −0.0980883 | ||||||||
\(408\) | 4.49111 | 0.222343 | ||||||||
\(409\) | −14.6251 | −0.723165 | −0.361582 | − | 0.932340i | \(-0.617763\pi\) | ||||
−0.361582 | + | 0.932340i | \(0.617763\pi\) | |||||||
\(410\) | 6.23954 | 0.308149 | ||||||||
\(411\) | −9.85188 | −0.485957 | ||||||||
\(412\) | 1.79437 | 0.0884021 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.15514 | 0.155067 | ||||||||
\(415\) | 2.34247 | 0.114987 | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 21.4195 | 1.04892 | ||||||||
\(418\) | −0.794368 | −0.0388538 | ||||||||
\(419\) | 1.52211 | 0.0743602 | 0.0371801 | − | 0.999309i | \(-0.488162\pi\) | ||||
0.0371801 | + | 0.999309i | \(0.488162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.7129 | −1.74054 | −0.870269 | − | 0.492576i | \(-0.836055\pi\) | ||||
−0.870269 | + | 0.492576i | \(0.836055\pi\) | |||||||
\(422\) | 4.24992 | 0.206883 | ||||||||
\(423\) | −11.9106 | −0.579112 | ||||||||
\(424\) | −5.42284 | −0.263356 | ||||||||
\(425\) | 12.4700 | 0.604882 | ||||||||
\(426\) | −1.47333 | −0.0713832 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.5027 | 0.556003 | ||||||||
\(429\) | 1.58874 | 0.0767049 | ||||||||
\(430\) | −7.38026 | −0.355908 | ||||||||
\(431\) | 39.9664 | 1.92512 | 0.962558 | − | 0.271076i | \(-0.0873794\pi\) | ||||
0.962558 | + | 0.271076i | \(0.0873794\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −15.5568 | −0.747614 | −0.373807 | − | 0.927507i | \(-0.621948\pi\) | ||||
−0.373807 | + | 0.927507i | \(0.621948\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.29705 | 0.445759 | ||||||||
\(436\) | 3.47333 | 0.166342 | ||||||||
\(437\) | −3.15514 | −0.150931 | ||||||||
\(438\) | −1.23498 | −0.0590098 | ||||||||
\(439\) | 18.6395 | 0.889616 | 0.444808 | − | 0.895626i | \(-0.353272\pi\) | ||||
0.444808 | + | 0.895626i | \(0.353272\pi\) | |||||||
\(440\) | 1.18449 | 0.0564683 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.98222 | 0.427241 | ||||||||
\(443\) | 25.5929 | 1.21596 | 0.607978 | − | 0.793954i | \(-0.291981\pi\) | ||||
0.607978 | + | 0.793954i | \(0.291981\pi\) | |||||||
\(444\) | 2.49111 | 0.118223 | ||||||||
\(445\) | −3.40790 | −0.161550 | ||||||||
\(446\) | 15.0807 | 0.714090 | ||||||||
\(447\) | −17.4051 | −0.823231 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.49477 | −0.212121 | −0.106061 | − | 0.994360i | \(-0.533824\pi\) | ||||
−0.106061 | + | 0.994360i | \(0.533824\pi\) | |||||||
\(450\) | −2.77659 | −0.130890 | ||||||||
\(451\) | 3.32402 | 0.156522 | ||||||||
\(452\) | −3.87421 | −0.182228 | ||||||||
\(453\) | −2.88744 | −0.135664 | ||||||||
\(454\) | −5.19241 | −0.243692 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −31.1633 | −1.45776 | −0.728880 | − | 0.684642i | \(-0.759959\pi\) | ||||
−0.728880 | + | 0.684642i | \(0.759959\pi\) | |||||||
\(458\) | 10.7802 | 0.503728 | ||||||||
\(459\) | 4.49111 | 0.209627 | ||||||||
\(460\) | 4.70466 | 0.219356 | ||||||||
\(461\) | 22.4815 | 1.04707 | 0.523535 | − | 0.852004i | \(-0.324613\pi\) | ||||
0.523535 | + | 0.852004i | \(0.324613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.16590 | 0.0541838 | 0.0270919 | − | 0.999633i | \(-0.491375\pi\) | ||||
0.0270919 | + | 0.999633i | \(0.491375\pi\) | |||||||
\(464\) | −6.23498 | −0.289452 | ||||||||
\(465\) | 13.4373 | 0.623138 | ||||||||
\(466\) | 1.58874 | 0.0735967 | ||||||||
\(467\) | 23.0984 | 1.06887 | 0.534434 | − | 0.845210i | \(-0.320525\pi\) | ||||
0.534434 | + | 0.845210i | \(0.320525\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −17.7600 | −0.819208 | ||||||||
\(471\) | −9.91058 | −0.456656 | ||||||||
\(472\) | −11.8093 | −0.543567 | ||||||||
\(473\) | −3.93173 | −0.180781 | ||||||||
\(474\) | 2.33597 | 0.107295 | ||||||||
\(475\) | 2.77659 | 0.127399 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.42284 | −0.248295 | ||||||||
\(478\) | −4.41126 | −0.201767 | ||||||||
\(479\) | −7.15349 | −0.326851 | −0.163426 | − | 0.986556i | \(-0.552254\pi\) | ||||
−0.163426 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(480\) | −1.49111 | −0.0680596 | ||||||||
\(481\) | 4.98222 | 0.227170 | ||||||||
\(482\) | 3.84486 | 0.175129 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.3690 | −0.471317 | ||||||||
\(485\) | −25.7918 | −1.17115 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −9.76867 | −0.442661 | −0.221330 | − | 0.975199i | \(-0.571040\pi\) | ||||
−0.221330 | + | 0.975199i | \(0.571040\pi\) | |||||||
\(488\) | 12.5825 | 0.569584 | ||||||||
\(489\) | −9.02935 | −0.408321 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.03556 | 0.407769 | 0.203884 | − | 0.978995i | \(-0.434643\pi\) | ||||
0.203884 | + | 0.978995i | \(0.434643\pi\) | |||||||
\(492\) | −4.18449 | −0.188651 | ||||||||
\(493\) | 28.0020 | 1.26115 | ||||||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | 1.18449 | 0.0532389 | ||||||||
\(496\) | −9.01157 | −0.404632 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.57096 | −0.0703962 | ||||||||
\(499\) | 23.9405 | 1.07172 | 0.535861 | − | 0.844306i | \(-0.319987\pi\) | ||||
0.535861 | + | 0.844306i | \(0.319987\pi\) | |||||||
\(500\) | −11.5958 | −0.518578 | ||||||||
\(501\) | −1.47333 | −0.0658236 | ||||||||
\(502\) | −18.9185 | −0.844374 | ||||||||
\(503\) | 37.5044 | 1.67224 | 0.836119 | − | 0.548548i | \(-0.184819\pi\) | ||||
0.836119 | + | 0.548548i | \(0.184819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.74358 | −0.255586 | ||||||||
\(506\) | 2.50634 | 0.111420 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | −1.55938 | −0.0691865 | ||||||||
\(509\) | 4.10517 | 0.181958 | 0.0909791 | − | 0.995853i | \(-0.471000\pi\) | ||||
0.0909791 | + | 0.995853i | \(0.471000\pi\) | |||||||
\(510\) | 6.69674 | 0.296537 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 18.9399 | 0.835405 | ||||||||
\(515\) | 2.67560 | 0.117901 | ||||||||
\(516\) | 4.94951 | 0.217890 | ||||||||
\(517\) | −9.46138 | −0.416111 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0691 | 0.705355 | ||||||||
\(520\) | −2.98222 | −0.130779 | ||||||||
\(521\) | 9.14191 | 0.400514 | 0.200257 | − | 0.979743i | \(-0.435822\pi\) | ||||
0.200257 | + | 0.979743i | \(0.435822\pi\) | |||||||
\(522\) | −6.23498 | −0.272898 | ||||||||
\(523\) | 34.5106 | 1.50904 | 0.754522 | − | 0.656275i | \(-0.227869\pi\) | ||||
0.754522 | + | 0.656275i | \(0.227869\pi\) | |||||||
\(524\) | 8.91058 | 0.389261 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.9806 | 1.35082 | ||||||||
\(527\) | 40.4720 | 1.76299 | ||||||||
\(528\) | −0.794368 | −0.0345704 | ||||||||
\(529\) | −13.0451 | −0.567178 | ||||||||
\(530\) | −8.08605 | −0.351236 | ||||||||
\(531\) | −11.8093 | −0.512480 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.36898 | −0.362501 | ||||||||
\(534\) | 2.28548 | 0.0989023 | ||||||||
\(535\) | 17.1518 | 0.741536 | ||||||||
\(536\) | 16.0231 | 0.692095 | ||||||||
\(537\) | 0.505526 | 0.0218150 | ||||||||
\(538\) | −5.92471 | −0.255432 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.49111 | −0.0641672 | ||||||||
\(541\) | 19.6483 | 0.844744 | 0.422372 | − | 0.906422i | \(-0.361198\pi\) | ||||
0.422372 | + | 0.906422i | \(0.361198\pi\) | |||||||
\(542\) | 13.0798 | 0.561827 | ||||||||
\(543\) | 14.0000 | 0.600798 | ||||||||
\(544\) | −4.49111 | −0.192555 | ||||||||
\(545\) | 5.17912 | 0.221849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3582 | 1.12700 | 0.563498 | − | 0.826117i | \(-0.309455\pi\) | ||||
0.563498 | + | 0.826117i | \(0.309455\pi\) | |||||||
\(548\) | 9.85188 | 0.420852 | ||||||||
\(549\) | 12.5825 | 0.537009 | ||||||||
\(550\) | −2.20563 | −0.0940485 | ||||||||
\(551\) | 6.23498 | 0.265619 | ||||||||
\(552\) | −3.15514 | −0.134292 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.2316 | −0.519672 | ||||||||
\(555\) | 3.71452 | 0.157673 | ||||||||
\(556\) | −21.4195 | −0.908388 | ||||||||
\(557\) | −25.7430 | −1.09077 | −0.545384 | − | 0.838186i | \(-0.683616\pi\) | ||||
−0.545384 | + | 0.838186i | \(0.683616\pi\) | |||||||
\(558\) | −9.01157 | −0.381490 | ||||||||
\(559\) | 9.89901 | 0.418684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.56759 | 0.150624 | ||||||||
\(562\) | −0.150585 | −0.00635203 | ||||||||
\(563\) | −19.2383 | −0.810800 | −0.405400 | − | 0.914139i | \(-0.632868\pi\) | ||||
−0.405400 | + | 0.914139i | \(0.632868\pi\) | |||||||
\(564\) | 11.9106 | 0.501526 | ||||||||
\(565\) | −5.77688 | −0.243035 | ||||||||
\(566\) | −24.4017 | −1.02568 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.47333 | 0.0618196 | ||||||||
\(569\) | −2.20198 | −0.0923117 | −0.0461558 | − | 0.998934i | \(-0.514697\pi\) | ||||
−0.0461558 | + | 0.998934i | \(0.514697\pi\) | |||||||
\(570\) | 1.49111 | 0.0624558 | ||||||||
\(571\) | −11.7224 | −0.490569 | −0.245284 | − | 0.969451i | \(-0.578881\pi\) | ||||
−0.245284 | + | 0.969451i | \(0.578881\pi\) | |||||||
\(572\) | −1.58874 | −0.0664284 | ||||||||
\(573\) | 26.5825 | 1.11050 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.76052 | −0.365339 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 14.5532 | 0.605857 | 0.302928 | − | 0.953013i | \(-0.402036\pi\) | ||||
0.302928 | + | 0.953013i | \(0.402036\pi\) | |||||||
\(578\) | 3.17008 | 0.131858 | ||||||||
\(579\) | 4.77204 | 0.198319 | ||||||||
\(580\) | −9.29705 | −0.386039 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.2971 | 0.716986 | ||||||||
\(583\) | −4.30773 | −0.178408 | ||||||||
\(584\) | 1.23498 | 0.0511040 | ||||||||
\(585\) | −2.98222 | −0.123300 | ||||||||
\(586\) | −12.6694 | −0.523368 | ||||||||
\(587\) | −0.509703 | −0.0210377 | −0.0105189 | − | 0.999945i | \(-0.503348\pi\) | ||||
−0.0105189 | + | 0.999945i | \(0.503348\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.01157 | 0.371315 | ||||||||
\(590\) | −17.6090 | −0.724950 | ||||||||
\(591\) | −16.0152 | −0.658778 | ||||||||
\(592\) | −2.49111 | −0.102384 | ||||||||
\(593\) | −29.2545 | −1.20134 | −0.600669 | − | 0.799498i | \(-0.705099\pi\) | ||||
−0.600669 | + | 0.799498i | \(0.705099\pi\) | |||||||
\(594\) | −0.794368 | −0.0325933 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.4051 | 0.712939 | ||||||||
\(597\) | −10.8341 | −0.443410 | ||||||||
\(598\) | −6.31028 | −0.258046 | ||||||||
\(599\) | −10.6864 | −0.436633 | −0.218316 | − | 0.975878i | \(-0.570056\pi\) | ||||
−0.218316 | + | 0.975878i | \(0.570056\pi\) | |||||||
\(600\) | 2.77659 | 0.113354 | ||||||||
\(601\) | 24.0541 | 0.981189 | 0.490595 | − | 0.871388i | \(-0.336780\pi\) | ||||
0.490595 | + | 0.871388i | \(0.336780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.0231 | 0.652513 | ||||||||
\(604\) | 2.88744 | 0.117488 | ||||||||
\(605\) | −15.4613 | −0.628591 | ||||||||
\(606\) | 3.85188 | 0.156472 | ||||||||
\(607\) | −5.56304 | −0.225797 | −0.112898 | − | 0.993607i | \(-0.536013\pi\) | ||||
−0.112898 | + | 0.993607i | \(0.536013\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.7619 | 0.759649 | ||||||||
\(611\) | 23.8212 | 0.963701 | ||||||||
\(612\) | −4.49111 | −0.181542 | ||||||||
\(613\) | −11.3975 | −0.460341 | −0.230171 | − | 0.973150i | \(-0.573928\pi\) | ||||
−0.230171 | + | 0.973150i | \(0.573928\pi\) | |||||||
\(614\) | 19.8031 | 0.799188 | ||||||||
\(615\) | −6.23954 | −0.251602 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5205 | 0.946898 | 0.473449 | − | 0.880821i | \(-0.343009\pi\) | ||||
0.473449 | + | 0.880821i | \(0.343009\pi\) | |||||||
\(618\) | −1.79437 | −0.0721801 | ||||||||
\(619\) | 42.4393 | 1.70578 | 0.852889 | − | 0.522092i | \(-0.174848\pi\) | ||||
0.852889 | + | 0.522092i | \(0.174848\pi\) | |||||||
\(620\) | −13.4373 | −0.539653 | ||||||||
\(621\) | −3.15514 | −0.126611 | ||||||||
\(622\) | 23.3918 | 0.937927 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −3.40761 | −0.136304 | ||||||||
\(626\) | 27.6045 | 1.10330 | ||||||||
\(627\) | 0.794368 | 0.0317240 | ||||||||
\(628\) | 9.91058 | 0.395475 | ||||||||
\(629\) | 11.1879 | 0.446089 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5730 | −1.33652 | −0.668259 | − | 0.743928i | \(-0.732960\pi\) | ||||
−0.668259 | + | 0.743928i | \(0.732960\pi\) | |||||||
\(632\) | −2.33597 | −0.0929200 | ||||||||
\(633\) | −4.24992 | −0.168919 | ||||||||
\(634\) | −21.4883 | −0.853408 | ||||||||
\(635\) | −2.32521 | −0.0922733 | ||||||||
\(636\) | 5.42284 | 0.215030 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.95287 | −0.196086 | ||||||||
\(639\) | 1.47333 | 0.0582841 | ||||||||
\(640\) | 1.49111 | 0.0589413 | ||||||||
\(641\) | 2.35659 | 0.0930798 | 0.0465399 | − | 0.998916i | \(-0.485181\pi\) | ||||
0.0465399 | + | 0.998916i | \(0.485181\pi\) | |||||||
\(642\) | −11.5027 | −0.453975 | ||||||||
\(643\) | 30.4488 | 1.20078 | 0.600392 | − | 0.799706i | \(-0.295011\pi\) | ||||
0.600392 | + | 0.799706i | \(0.295011\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.38026 | 0.290597 | ||||||||
\(646\) | 4.49111 | 0.176700 | ||||||||
\(647\) | 28.4336 | 1.11784 | 0.558920 | − | 0.829222i | \(-0.311216\pi\) | ||||
0.558920 | + | 0.829222i | \(0.311216\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −9.38093 | −0.368234 | ||||||||
\(650\) | 5.55318 | 0.217814 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.02935 | 0.353617 | ||||||||
\(653\) | 41.0008 | 1.60449 | 0.802243 | − | 0.596998i | \(-0.203640\pi\) | ||||
0.802243 | + | 0.596998i | \(0.203640\pi\) | |||||||
\(654\) | −3.47333 | −0.135818 | ||||||||
\(655\) | 13.2867 | 0.519153 | ||||||||
\(656\) | 4.18449 | 0.163377 | ||||||||
\(657\) | 1.23498 | 0.0481813 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.41298 | −0.366678 | −0.183339 | − | 0.983050i | \(-0.558691\pi\) | ||||
−0.183339 | + | 0.983050i | \(0.558691\pi\) | |||||||
\(660\) | −1.18449 | −0.0461062 | ||||||||
\(661\) | −24.4200 | −0.949828 | −0.474914 | − | 0.880032i | \(-0.657521\pi\) | ||||
−0.474914 | + | 0.880032i | \(0.657521\pi\) | |||||||
\(662\) | −15.7377 | −0.611662 | ||||||||
\(663\) | −8.98222 | −0.348841 | ||||||||
\(664\) | 1.57096 | 0.0609649 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.49111 | −0.0965286 | ||||||||
\(667\) | −19.6722 | −0.761712 | ||||||||
\(668\) | 1.47333 | 0.0570049 | ||||||||
\(669\) | −15.0807 | −0.583052 | ||||||||
\(670\) | 23.8923 | 0.923039 | ||||||||
\(671\) | 9.99515 | 0.385859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.30743 | −0.127492 | −0.0637461 | − | 0.997966i | \(-0.520305\pi\) | ||||
−0.0637461 | + | 0.997966i | \(0.520305\pi\) | |||||||
\(674\) | −31.7670 | −1.22362 | ||||||||
\(675\) | 2.77659 | 0.106871 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −6.27420 | −0.241137 | −0.120568 | − | 0.992705i | \(-0.538472\pi\) | ||||
−0.120568 | + | 0.992705i | \(0.538472\pi\) | |||||||
\(678\) | 3.87421 | 0.148788 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.69674 | −0.256808 | ||||||||
\(681\) | 5.19241 | 0.198973 | ||||||||
\(682\) | −7.15850 | −0.274113 | ||||||||
\(683\) | −34.2406 | −1.31018 | −0.655091 | − | 0.755550i | \(-0.727370\pi\) | ||||
−0.655091 | + | 0.755550i | \(0.727370\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 14.6902 | 0.561285 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7802 | −0.411292 | ||||||||
\(688\) | −4.94951 | −0.188698 | ||||||||
\(689\) | 10.8457 | 0.413187 | ||||||||
\(690\) | −4.70466 | −0.179103 | ||||||||
\(691\) | 20.3834 | 0.775421 | 0.387710 | − | 0.921781i | \(-0.373266\pi\) | ||||
0.387710 | + | 0.921781i | \(0.373266\pi\) | |||||||
\(692\) | −16.0691 | −0.610855 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.3769 | −0.469821 | ||||||||
\(695\) | −31.9388 | −1.21151 | ||||||||
\(696\) | 6.23498 | 0.236336 | ||||||||
\(697\) | −18.7930 | −0.711836 | ||||||||
\(698\) | −29.2610 | −1.10754 | ||||||||
\(699\) | −1.58874 | −0.0600915 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.3620 | 0.844600 | 0.422300 | − | 0.906456i | \(-0.361223\pi\) | ||||
0.422300 | + | 0.906456i | \(0.361223\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | 2.49111 | 0.0939540 | ||||||||
\(704\) | 0.794368 | 0.0299389 | ||||||||
\(705\) | 17.7600 | 0.668880 | ||||||||
\(706\) | −21.8423 | −0.822046 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 11.8093 | 0.443821 | ||||||||
\(709\) | −18.3466 | −0.689023 | −0.344511 | − | 0.938782i | \(-0.611955\pi\) | ||||
−0.344511 | + | 0.938782i | \(0.611955\pi\) | |||||||
\(710\) | 2.19690 | 0.0824482 | ||||||||
\(711\) | −2.33597 | −0.0876058 | ||||||||
\(712\) | −2.28548 | −0.0856519 | ||||||||
\(713\) | −28.4328 | −1.06482 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.36898 | −0.0885948 | ||||||||
\(716\) | −0.505526 | −0.0188924 | ||||||||
\(717\) | 4.41126 | 0.164742 | ||||||||
\(718\) | −24.2209 | −0.903915 | ||||||||
\(719\) | 0.852403 | 0.0317893 | 0.0158946 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158946 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(720\) | 1.49111 | 0.0555704 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −3.84486 | −0.142992 | ||||||||
\(724\) | −14.0000 | −0.520306 | ||||||||
\(725\) | 17.3120 | 0.642951 | ||||||||
\(726\) | 10.3690 | 0.384829 | ||||||||
\(727\) | −35.9487 | −1.33326 | −0.666631 | − | 0.745388i | \(-0.732264\pi\) | ||||
−0.666631 | + | 0.745388i | \(0.732264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.84150 | 0.0681569 | ||||||||
\(731\) | 22.2288 | 0.822161 | ||||||||
\(732\) | −12.5825 | −0.465064 | ||||||||
\(733\) | −35.0037 | −1.29289 | −0.646446 | − | 0.762960i | \(-0.723745\pi\) | ||||
−0.646446 | + | 0.762960i | \(0.723745\pi\) | |||||||
\(734\) | 17.4373 | 0.643621 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.15514 | 0.116300 | ||||||||
\(737\) | 12.7283 | 0.468852 | ||||||||
\(738\) | 4.18449 | 0.154033 | ||||||||
\(739\) | 5.49648 | 0.202191 | 0.101096 | − | 0.994877i | \(-0.467765\pi\) | ||||
0.101096 | + | 0.994877i | \(0.467765\pi\) | |||||||
\(740\) | −3.71452 | −0.136549 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2871 | 0.377398 | 0.188699 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188699 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(744\) | 9.01157 | 0.330380 | ||||||||
\(745\) | 25.9529 | 0.950840 | ||||||||
\(746\) | −10.7374 | −0.393123 | ||||||||
\(747\) | 1.57096 | 0.0574783 | ||||||||
\(748\) | −3.56759 | −0.130444 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.5958 | 0.423417 | ||||||||
\(751\) | 19.4621 | 0.710180 | 0.355090 | − | 0.934832i | \(-0.384450\pi\) | ||||
0.355090 | + | 0.934832i | \(0.384450\pi\) | |||||||
\(752\) | −11.9106 | −0.434334 | ||||||||
\(753\) | 18.9185 | 0.689429 | ||||||||
\(754\) | 12.4700 | 0.454129 | ||||||||
\(755\) | 4.30549 | 0.156693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.9230 | −1.45103 | −0.725513 | − | 0.688209i | \(-0.758397\pi\) | ||||
−0.725513 | + | 0.688209i | \(0.758397\pi\) | |||||||
\(758\) | −11.5887 | −0.420922 | ||||||||
\(759\) | −2.50634 | −0.0909744 | ||||||||
\(760\) | −1.49111 | −0.0540883 | ||||||||
\(761\) | 37.7029 | 1.36673 | 0.683365 | − | 0.730077i | \(-0.260516\pi\) | ||||
0.683365 | + | 0.730077i | \(0.260516\pi\) | |||||||
\(762\) | 1.55938 | 0.0564905 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26.5825 | −0.961722 | ||||||||
\(765\) | −6.69674 | −0.242121 | ||||||||
\(766\) | −5.69704 | −0.205842 | ||||||||
\(767\) | 23.6186 | 0.852819 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 8.86711 | 0.319756 | 0.159878 | − | 0.987137i | \(-0.448890\pi\) | ||||
0.159878 | + | 0.987137i | \(0.448890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9399 | −0.682105 | ||||||||
\(772\) | −4.77204 | −0.171749 | ||||||||
\(773\) | 35.2043 | 1.26621 | 0.633105 | − | 0.774066i | \(-0.281780\pi\) | ||||
0.633105 | + | 0.774066i | \(0.281780\pi\) | |||||||
\(774\) | −4.94951 | −0.177906 | ||||||||
\(775\) | 25.0214 | 0.898796 | ||||||||
\(776\) | −17.2971 | −0.620928 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.35793 | −0.0486841 | ||||||||
\(779\) | −4.18449 | −0.149925 | ||||||||
\(780\) | 2.98222 | 0.106781 | ||||||||
\(781\) | 1.17037 | 0.0418790 | ||||||||
\(782\) | −14.1701 | −0.506721 | ||||||||
\(783\) | 6.23498 | 0.222820 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.7778 | 0.527442 | ||||||||
\(786\) | −8.91058 | −0.317830 | ||||||||
\(787\) | −17.1775 | −0.612311 | −0.306155 | − | 0.951982i | \(-0.599043\pi\) | ||||
−0.306155 | + | 0.951982i | \(0.599043\pi\) | |||||||
\(788\) | 16.0152 | 0.570519 | ||||||||
\(789\) | −30.9806 | −1.10294 | ||||||||
\(790\) | −3.48319 | −0.123926 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.794368 | 0.0282266 | ||||||||
\(793\) | −25.1651 | −0.893637 | ||||||||
\(794\) | −28.3334 | −1.00552 | ||||||||
\(795\) | 8.08605 | 0.286783 | ||||||||
\(796\) | 10.8341 | 0.384005 | ||||||||
\(797\) | 39.7758 | 1.40893 | 0.704465 | − | 0.709739i | \(-0.251187\pi\) | ||||
0.704465 | + | 0.709739i | \(0.251187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.4918 | 1.89240 | ||||||||
\(800\) | −2.77659 | −0.0981672 | ||||||||
\(801\) | −2.28548 | −0.0807534 | ||||||||
\(802\) | −33.9577 | −1.19909 | ||||||||
\(803\) | 0.981031 | 0.0346198 | ||||||||
\(804\) | −16.0231 | −0.565093 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.0231 | 0.634838 | ||||||||
\(807\) | 5.92471 | 0.208560 | ||||||||
\(808\) | −3.85188 | −0.135509 | ||||||||
\(809\) | 33.0968 | 1.16362 | 0.581811 | − | 0.813324i | \(-0.302345\pi\) | ||||
0.581811 | + | 0.813324i | \(0.302345\pi\) | |||||||
\(810\) | 1.49111 | 0.0523923 | ||||||||
\(811\) | −40.7994 | −1.43266 | −0.716330 | − | 0.697762i | \(-0.754179\pi\) | ||||
−0.716330 | + | 0.697762i | \(0.754179\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0798 | −0.458730 | ||||||||
\(814\) | −1.97886 | −0.0693589 | ||||||||
\(815\) | 13.4638 | 0.471615 | ||||||||
\(816\) | 4.49111 | 0.157220 | ||||||||
\(817\) | 4.94951 | 0.173161 | ||||||||
\(818\) | −14.6251 | −0.511355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.23954 | 0.217894 | ||||||||
\(821\) | −22.7873 | −0.795281 | −0.397641 | − | 0.917541i | \(-0.630171\pi\) | ||||
−0.397641 | + | 0.917541i | \(0.630171\pi\) | |||||||
\(822\) | −9.85188 | −0.343624 | ||||||||
\(823\) | −27.2189 | −0.948792 | −0.474396 | − | 0.880312i | \(-0.657333\pi\) | ||||
−0.474396 | + | 0.880312i | \(0.657333\pi\) | |||||||
\(824\) | 1.79437 | 0.0625098 | ||||||||
\(825\) | 2.20563 | 0.0767903 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.9995 | 1.53001 | 0.765005 | − | 0.644024i | \(-0.222736\pi\) | ||||
0.765005 | + | 0.644024i | \(0.222736\pi\) | |||||||
\(828\) | 3.15514 | 0.109649 | ||||||||
\(829\) | 10.9755 | 0.381195 | 0.190597 | − | 0.981668i | \(-0.438958\pi\) | ||||
0.190597 | + | 0.981668i | \(0.438958\pi\) | |||||||
\(830\) | 2.34247 | 0.0813083 | ||||||||
\(831\) | 12.2316 | 0.424310 | ||||||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.4195 | 0.741696 | ||||||||
\(835\) | 2.19690 | 0.0760269 | ||||||||
\(836\) | −0.794368 | −0.0274738 | ||||||||
\(837\) | 9.01157 | 0.311486 | ||||||||
\(838\) | 1.52211 | 0.0525806 | ||||||||
\(839\) | 39.4965 | 1.36357 | 0.681785 | − | 0.731553i | \(-0.261204\pi\) | ||||
0.681785 | + | 0.731553i | \(0.261204\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.87503 | 0.340518 | ||||||||
\(842\) | −35.7129 | −1.23075 | ||||||||
\(843\) | 0.150585 | 0.00518641 | ||||||||
\(844\) | 4.24992 | 0.146288 | ||||||||
\(845\) | −13.4200 | −0.461662 | ||||||||
\(846\) | −11.9106 | −0.409494 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.42284 | −0.186221 | ||||||||
\(849\) | 24.4017 | 0.837464 | ||||||||
\(850\) | 12.4700 | 0.427716 | ||||||||
\(851\) | −7.85980 | −0.269430 | ||||||||
\(852\) | −1.47333 | −0.0504755 | ||||||||
\(853\) | 25.7492 | 0.881637 | 0.440819 | − | 0.897596i | \(-0.354688\pi\) | ||||
0.440819 | + | 0.897596i | \(0.354688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.49111 | −0.0509949 | ||||||||
\(856\) | 11.5027 | 0.393154 | ||||||||
\(857\) | −33.1492 | −1.13236 | −0.566178 | − | 0.824283i | \(-0.691579\pi\) | ||||
−0.566178 | + | 0.824283i | \(0.691579\pi\) | |||||||
\(858\) | 1.58874 | 0.0542385 | ||||||||
\(859\) | −14.7630 | −0.503707 | −0.251853 | − | 0.967765i | \(-0.581040\pi\) | ||||
−0.251853 | + | 0.967765i | \(0.581040\pi\) | |||||||
\(860\) | −7.38026 | −0.251665 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.9664 | 1.36126 | ||||||||
\(863\) | 49.1439 | 1.67288 | 0.836439 | − | 0.548060i | \(-0.184633\pi\) | ||||
0.836439 | + | 0.548060i | \(0.184633\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −23.9608 | −0.814691 | ||||||||
\(866\) | −15.5568 | −0.528643 | ||||||||
\(867\) | −3.17008 | −0.107661 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.85562 | −0.0629476 | ||||||||
\(870\) | 9.29705 | 0.315200 | ||||||||
\(871\) | −32.0463 | −1.08585 | ||||||||
\(872\) | 3.47333 | 0.117622 | ||||||||
\(873\) | −17.2971 | −0.585416 | ||||||||
\(874\) | −3.15514 | −0.106724 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.23498 | −0.0417262 | ||||||||
\(877\) | 21.4186 | 0.723256 | 0.361628 | − | 0.932322i | \(-0.382221\pi\) | ||||
0.361628 | + | 0.932322i | \(0.382221\pi\) | |||||||
\(878\) | 18.6395 | 0.629053 | ||||||||
\(879\) | 12.6694 | 0.427328 | ||||||||
\(880\) | 1.18449 | 0.0399292 | ||||||||
\(881\) | −38.2184 | −1.28761 | −0.643805 | − | 0.765189i | \(-0.722645\pi\) | ||||
−0.643805 | + | 0.765189i | \(0.722645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3667 | 0.719045 | 0.359523 | − | 0.933136i | \(-0.382940\pi\) | ||||
0.359523 | + | 0.933136i | \(0.382940\pi\) | |||||||
\(884\) | 8.98222 | 0.302105 | ||||||||
\(885\) | 17.6090 | 0.591919 | ||||||||
\(886\) | 25.5929 | 0.859811 | ||||||||
\(887\) | −2.83126 | −0.0950644 | −0.0475322 | − | 0.998870i | \(-0.515136\pi\) | ||||
−0.0475322 | + | 0.998870i | \(0.515136\pi\) | |||||||
\(888\) | 2.49111 | 0.0835962 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.40790 | −0.114233 | ||||||||
\(891\) | 0.794368 | 0.0266123 | ||||||||
\(892\) | 15.0807 | 0.504938 | ||||||||
\(893\) | 11.9106 | 0.398573 | ||||||||
\(894\) | −17.4051 | −0.582112 | ||||||||
\(895\) | −0.753795 | −0.0251966 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.31028 | 0.210694 | ||||||||
\(898\) | −4.49477 | −0.149992 | ||||||||
\(899\) | 56.1870 | 1.87394 | ||||||||
\(900\) | −2.77659 | −0.0925530 | ||||||||
\(901\) | 24.3546 | 0.811368 | ||||||||
\(902\) | 3.32402 | 0.110678 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.87421 | −0.128854 | ||||||||
\(905\) | −20.8755 | −0.693927 | ||||||||
\(906\) | −2.88744 | −0.0959287 | ||||||||
\(907\) | −8.02480 | −0.266459 | −0.133230 | − | 0.991085i | \(-0.542535\pi\) | ||||
−0.133230 | + | 0.991085i | \(0.542535\pi\) | |||||||
\(908\) | −5.19241 | −0.172316 | ||||||||
\(909\) | −3.85188 | −0.127759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.7253 | −0.587265 | −0.293632 | − | 0.955918i | \(-0.594864\pi\) | ||||
−0.293632 | + | 0.955918i | \(0.594864\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 1.24792 | 0.0413000 | ||||||||
\(914\) | −31.1633 | −1.03079 | ||||||||
\(915\) | −18.7619 | −0.620251 | ||||||||
\(916\) | 10.7802 | 0.356189 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.49111 | 0.148229 | ||||||||
\(919\) | −12.8445 | −0.423700 | −0.211850 | − | 0.977302i | \(-0.567949\pi\) | ||||
−0.211850 | + | 0.977302i | \(0.567949\pi\) | |||||||
\(920\) | 4.70466 | 0.155108 | ||||||||
\(921\) | −19.8031 | −0.652534 | ||||||||
\(922\) | 22.4815 | 0.740390 | ||||||||
\(923\) | −2.94666 | −0.0969906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.91679 | 0.227423 | ||||||||
\(926\) | 1.16590 | 0.0383138 | ||||||||
\(927\) | 1.79437 | 0.0589348 | ||||||||
\(928\) | −6.23498 | −0.204673 | ||||||||
\(929\) | −10.8552 | −0.356149 | −0.178075 | − | 0.984017i | \(-0.556987\pi\) | ||||
−0.178075 | + | 0.984017i | \(0.556987\pi\) | |||||||
\(930\) | 13.4373 | 0.440625 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.58874 | 0.0520408 | ||||||||
\(933\) | −23.3918 | −0.765814 | ||||||||
\(934\) | 23.0984 | 0.755804 | ||||||||
\(935\) | −5.31968 | −0.173972 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 20.9520 | 0.684473 | 0.342237 | − | 0.939614i | \(-0.388816\pi\) | ||||
0.342237 | + | 0.939614i | \(0.388816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.6045 | −0.900838 | ||||||||
\(940\) | −17.7600 | −0.579267 | ||||||||
\(941\) | 13.5893 | 0.442997 | 0.221499 | − | 0.975161i | \(-0.428905\pi\) | ||||
0.221499 | + | 0.975161i | \(0.428905\pi\) | |||||||
\(942\) | −9.91058 | −0.322904 | ||||||||
\(943\) | 13.2026 | 0.429937 | ||||||||
\(944\) | −11.8093 | −0.384360 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.93173 | −0.127831 | ||||||||
\(947\) | 57.8118 | 1.87863 | 0.939316 | − | 0.343053i | \(-0.111461\pi\) | ||||
0.939316 | + | 0.343053i | \(0.111461\pi\) | |||||||
\(948\) | 2.33597 | 0.0758689 | ||||||||
\(949\) | −2.46997 | −0.0801786 | ||||||||
\(950\) | 2.77659 | 0.0900844 | ||||||||
\(951\) | 21.4883 | 0.696805 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7129 | −0.444203 | −0.222102 | − | 0.975024i | \(-0.571292\pi\) | ||||
−0.222102 | + | 0.975024i | \(0.571292\pi\) | |||||||
\(954\) | −5.42284 | −0.175571 | ||||||||
\(955\) | −39.6375 | −1.28264 | ||||||||
\(956\) | −4.41126 | −0.142670 | ||||||||
\(957\) | 4.95287 | 0.160104 | ||||||||
\(958\) | −7.15349 | −0.231119 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.49111 | −0.0481254 | ||||||||
\(961\) | 50.2085 | 1.61963 | ||||||||
\(962\) | 4.98222 | 0.160633 | ||||||||
\(963\) | 11.5027 | 0.370669 | ||||||||
\(964\) | 3.84486 | 0.123835 | ||||||||
\(965\) | −7.11563 | −0.229060 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.29900 | −0.0739307 | −0.0369654 | − | 0.999317i | \(-0.511769\pi\) | ||||
−0.0369654 | + | 0.999317i | \(0.511769\pi\) | |||||||
\(968\) | −10.3690 | −0.333272 | ||||||||
\(969\) | −4.49111 | −0.144275 | ||||||||
\(970\) | −25.7918 | −0.828125 | ||||||||
\(971\) | 41.2755 | 1.32459 | 0.662297 | − | 0.749241i | \(-0.269582\pi\) | ||||
0.662297 | + | 0.749241i | \(0.269582\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.76867 | −0.313008 | ||||||||
\(975\) | −5.55318 | −0.177844 | ||||||||
\(976\) | 12.5825 | 0.402757 | ||||||||
\(977\) | 41.2445 | 1.31953 | 0.659765 | − | 0.751472i | \(-0.270656\pi\) | ||||
0.659765 | + | 0.751472i | \(0.270656\pi\) | |||||||
\(978\) | −9.02935 | −0.288727 | ||||||||
\(979\) | −1.81551 | −0.0580239 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.47333 | 0.110895 | ||||||||
\(982\) | 9.03556 | 0.288336 | ||||||||
\(983\) | 18.3623 | 0.585665 | 0.292832 | − | 0.956164i | \(-0.405402\pi\) | ||||
0.292832 | + | 0.956164i | \(0.405402\pi\) | |||||||
\(984\) | −4.18449 | −0.133397 | ||||||||
\(985\) | 23.8805 | 0.760895 | ||||||||
\(986\) | 28.0020 | 0.891765 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.00000 | 0.0636285 | ||||||||
\(989\) | −15.6164 | −0.496572 | ||||||||
\(990\) | 1.18449 | 0.0376456 | ||||||||
\(991\) | −54.7673 | −1.73974 | −0.869870 | − | 0.493280i | \(-0.835798\pi\) | ||||
−0.869870 | + | 0.493280i | \(0.835798\pi\) | |||||||
\(992\) | −9.01157 | −0.286118 | ||||||||
\(993\) | 15.7377 | 0.499420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.1548 | 0.512143 | ||||||||
\(996\) | −1.57096 | −0.0497777 | ||||||||
\(997\) | −32.5941 | −1.03227 | −0.516133 | − | 0.856509i | \(-0.672629\pi\) | ||||
−0.516133 | + | 0.856509i | \(0.672629\pi\) | |||||||
\(998\) | 23.9405 | 0.757822 | ||||||||
\(999\) | 2.49111 | 0.0788153 |
(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 | 5586.2.a.ca.1.3 | 4 | ||
7.3 | odd | 6 | 798.2.j.k.457.3 | ✓ | 8 | ||
7.5 | odd | 6 | 798.2.j.k.571.3 | yes | 8 | ||
7.6 | odd | 2 | 5586.2.a.cb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.j.k.457.3 | ✓ | 8 | 7.3 | odd | 6 | ||
798.2.j.k.571.3 | yes | 8 | 7.5 | odd | 6 | ||
5586.2.a.ca.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5586.2.a.cb.1.2 | 4 | 7.6 | odd | 2 |