Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.23544108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 20x^{3} + 39x^{2} + 9x - 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.76376\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19175 | −0.450439 | −0.225220 | − | 0.974308i | \(-0.572310\pi\) | ||||
−0.225220 | + | 0.974308i | \(0.572310\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.64179 | 1.09804 | 0.549020 | − | 0.835809i | \(-0.315001\pi\) | ||||
0.549020 | + | 0.835809i | \(0.315001\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.86897 | 1.35041 | 0.675204 | − | 0.737631i | \(-0.264056\pi\) | ||||
0.675204 | + | 0.737631i | \(0.264056\pi\) | |||||||
\(14\) | 1.19175 | 0.318509 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.19175 | −0.774113 | −0.387057 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387057 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.27506 | 0.521935 | 0.260968 | − | 0.965348i | \(-0.415958\pi\) | ||||
0.260968 | + | 0.965348i | \(0.415958\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.64179 | −0.776431 | ||||||||
\(23\) | 2.86897 | 0.598221 | 0.299110 | − | 0.954219i | \(-0.403310\pi\) | ||||
0.299110 | + | 0.954219i | \(0.403310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.86897 | −0.954883 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.19175 | −0.225220 | ||||||||
\(29\) | −6.06072 | −1.12545 | −0.562723 | − | 0.826645i | \(-0.690246\pi\) | ||||
−0.562723 | + | 0.826645i | \(0.690246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.36672 | 0.963892 | 0.481946 | − | 0.876201i | \(-0.339930\pi\) | ||||
0.481946 | + | 0.876201i | \(0.339930\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.19175 | 0.547381 | ||||||||
\(35\) | 1.19175 | 0.201443 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −2.27506 | −0.369064 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.75471 | 1.36726 | 0.683628 | − | 0.729831i | \(-0.260401\pi\) | ||||
0.683628 | + | 0.729831i | \(0.260401\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.75471 | −1.03008 | −0.515042 | − | 0.857165i | \(-0.672224\pi\) | ||||
−0.515042 | + | 0.857165i | \(0.672224\pi\) | |||||||
\(44\) | 3.64179 | 0.549020 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.86897 | −0.423006 | ||||||||
\(47\) | −4.13955 | −0.603815 | −0.301907 | − | 0.953337i | \(-0.597623\pi\) | ||||
−0.301907 | + | 0.953337i | \(0.597623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57973 | −0.797105 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.86897 | 0.675204 | ||||||||
\(53\) | −5.88574 | −0.808469 | −0.404234 | − | 0.914655i | \(-0.632462\pi\) | ||||
−0.404234 | + | 0.914655i | \(0.632462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.64179 | −0.491058 | ||||||||
\(56\) | 1.19175 | 0.159254 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.06072 | 0.795811 | ||||||||
\(59\) | −7.28357 | −0.948240 | −0.474120 | − | 0.880460i | \(-0.657234\pi\) | ||||
−0.474120 | + | 0.880460i | \(0.657234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.5443 | 1.86221 | 0.931104 | − | 0.364755i | \(-0.118847\pi\) | ||||
0.931104 | + | 0.364755i | \(0.118847\pi\) | |||||||
\(62\) | −5.36672 | −0.681575 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.86897 | −0.603921 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.90007 | −0.598639 | −0.299320 | − | 0.954153i | \(-0.596760\pi\) | ||||
−0.299320 | + | 0.954153i | \(0.596760\pi\) | |||||||
\(68\) | −3.19175 | −0.387057 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.19175 | −0.142441 | ||||||||
\(71\) | −5.38798 | −0.639436 | −0.319718 | − | 0.947513i | \(-0.603588\pi\) | ||||
−0.319718 | + | 0.947513i | \(0.603588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8026 | 1.38139 | 0.690694 | − | 0.723147i | \(-0.257305\pi\) | ||||
0.690694 | + | 0.723147i | \(0.257305\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.27506 | 0.260968 | ||||||||
\(77\) | −4.34010 | −0.494600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.38798 | 0.831213 | 0.415606 | − | 0.909545i | \(-0.363569\pi\) | ||||
0.415606 | + | 0.909545i | \(0.363569\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.75471 | −0.966796 | ||||||||
\(83\) | −4.41461 | −0.484566 | −0.242283 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242283 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.19175 | 0.346194 | ||||||||
\(86\) | 6.75471 | 0.728379 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.64179 | −0.388216 | ||||||||
\(89\) | −9.63597 | −1.02141 | −0.510705 | − | 0.859756i | \(-0.670616\pi\) | ||||
−0.510705 | + | 0.859756i | \(0.670616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.80259 | −0.608277 | ||||||||
\(92\) | 2.86897 | 0.299110 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.13955 | 0.426962 | ||||||||
\(95\) | −2.27506 | −0.233416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8943 | 1.51228 | 0.756141 | − | 0.654409i | \(-0.227082\pi\) | ||||
0.756141 | + | 0.654409i | \(0.227082\pi\) | |||||||
\(98\) | 5.57973 | 0.563638 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.63194 | 0.759406 | 0.379703 | − | 0.925108i | \(-0.376026\pi\) | ||||
0.379703 | + | 0.925108i | \(0.376026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.13955 | −0.210816 | −0.105408 | − | 0.994429i | \(-0.533615\pi\) | ||||
−0.105408 | + | 0.994429i | \(0.533615\pi\) | |||||||
\(104\) | −4.86897 | −0.477441 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.88574 | 0.571674 | ||||||||
\(107\) | 14.9904 | 1.44918 | 0.724588 | − | 0.689182i | \(-0.242030\pi\) | ||||
0.724588 | + | 0.689182i | \(0.242030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.253804 | 0.0243101 | 0.0121550 | − | 0.999926i | \(-0.496131\pi\) | ||||
0.0121550 | + | 0.999926i | \(0.496131\pi\) | |||||||
\(110\) | 3.64179 | 0.347231 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.19175 | −0.112610 | ||||||||
\(113\) | 13.3443 | 1.25533 | 0.627663 | − | 0.778486i | \(-0.284012\pi\) | ||||
0.627663 | + | 0.778486i | \(0.284012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.86897 | −0.267532 | ||||||||
\(116\) | −6.06072 | −0.562723 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.28357 | 0.670507 | ||||||||
\(119\) | 3.80377 | 0.348691 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.26261 | 0.205692 | ||||||||
\(122\) | −14.5443 | −1.31678 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.36672 | 0.481946 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.21891 | −0.640575 | −0.320288 | − | 0.947320i | \(-0.603780\pi\) | ||||
−0.320288 | + | 0.947320i | \(0.603780\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.86897 | 0.427037 | ||||||||
\(131\) | 20.0506 | 1.75183 | 0.875913 | − | 0.482468i | \(-0.160260\pi\) | ||||
0.875913 | + | 0.482468i | \(0.160260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.71131 | −0.235100 | ||||||||
\(134\) | 4.90007 | 0.423302 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.19175 | 0.273690 | ||||||||
\(137\) | −9.52753 | −0.813992 | −0.406996 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406996 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.7323 | 1.75849 | 0.879244 | − | 0.476372i | \(-0.158048\pi\) | ||||
0.879244 | + | 0.476372i | \(0.158048\pi\) | |||||||
\(140\) | 1.19175 | 0.100721 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.38798 | 0.452149 | ||||||||
\(143\) | 17.7317 | 1.48280 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.06072 | 0.503315 | ||||||||
\(146\) | −11.8026 | −0.976789 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | 9.17758 | 0.751857 | 0.375928 | − | 0.926649i | \(-0.377324\pi\) | ||||
0.375928 | + | 0.926649i | \(0.377324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6024 | 1.43246 | 0.716232 | − | 0.697862i | \(-0.245865\pi\) | ||||
0.716232 | + | 0.697862i | \(0.245865\pi\) | |||||||
\(152\) | −2.27506 | −0.184532 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.34010 | 0.349735 | ||||||||
\(155\) | −5.36672 | −0.431066 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.89857 | 0.550566 | 0.275283 | − | 0.961363i | \(-0.411228\pi\) | ||||
0.275283 | + | 0.961363i | \(0.411228\pi\) | |||||||
\(158\) | −7.38798 | −0.587756 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.41909 | −0.269462 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8194 | −0.847438 | −0.423719 | − | 0.905794i | \(-0.639276\pi\) | ||||
−0.423719 | + | 0.905794i | \(0.639276\pi\) | |||||||
\(164\) | 8.75471 | 0.683628 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.41461 | 0.342640 | ||||||||
\(167\) | −2.86897 | −0.222007 | −0.111004 | − | 0.993820i | \(-0.535407\pi\) | ||||
−0.111004 | + | 0.993820i | \(0.535407\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7068 | 0.823602 | ||||||||
\(170\) | −3.19175 | −0.244796 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.75471 | −0.515042 | ||||||||
\(173\) | −18.3571 | −1.39567 | −0.697833 | − | 0.716260i | \(-0.745852\pi\) | ||||
−0.697833 | + | 0.716260i | \(0.745852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.19175 | −0.0900878 | ||||||||
\(176\) | 3.64179 | 0.274510 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.63597 | 0.722246 | ||||||||
\(179\) | 23.1259 | 1.72851 | 0.864256 | − | 0.503052i | \(-0.167790\pi\) | ||||
0.864256 | + | 0.503052i | \(0.167790\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9001 | 1.10751 | 0.553757 | − | 0.832678i | \(-0.313194\pi\) | ||||
0.553757 | + | 0.832678i | \(0.313194\pi\) | |||||||
\(182\) | 5.80259 | 0.430117 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.86897 | −0.211503 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.6237 | −0.850007 | ||||||||
\(188\) | −4.13955 | −0.301907 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.27506 | 0.165050 | ||||||||
\(191\) | −8.31766 | −0.601845 | −0.300922 | − | 0.953649i | \(-0.597295\pi\) | ||||
−0.300922 | + | 0.953649i | \(0.597295\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5445 | −1.55081 | −0.775405 | − | 0.631464i | \(-0.782454\pi\) | ||||
−0.775405 | + | 0.631464i | \(0.782454\pi\) | |||||||
\(194\) | −14.8943 | −1.06934 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.57973 | −0.398552 | ||||||||
\(197\) | 3.76904 | 0.268533 | 0.134266 | − | 0.990945i | \(-0.457132\pi\) | ||||
0.134266 | + | 0.990945i | \(0.457132\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.92914 | −0.420306 | −0.210153 | − | 0.977669i | \(-0.567396\pi\) | ||||
−0.210153 | + | 0.977669i | \(0.567396\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.63194 | −0.536981 | ||||||||
\(203\) | 7.22286 | 0.506945 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.75471 | −0.611455 | ||||||||
\(206\) | 2.13955 | 0.149069 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.86897 | 0.337602 | ||||||||
\(209\) | 8.28529 | 0.573105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.51059 | −0.241679 | −0.120840 | − | 0.992672i | \(-0.538559\pi\) | ||||
−0.120840 | + | 0.992672i | \(0.538559\pi\) | |||||||
\(212\) | −5.88574 | −0.404234 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.9904 | −1.02472 | ||||||||
\(215\) | 6.75471 | 0.460667 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.39579 | −0.434175 | ||||||||
\(218\) | −0.253804 | −0.0171898 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.64179 | −0.245529 | ||||||||
\(221\) | −15.5405 | −1.04537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8322 | 1.32806 | 0.664031 | − | 0.747705i | \(-0.268844\pi\) | ||||
0.664031 | + | 0.747705i | \(0.268844\pi\) | |||||||
\(224\) | 1.19175 | 0.0796271 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.3443 | −0.887649 | ||||||||
\(227\) | 12.9608 | 0.860238 | 0.430119 | − | 0.902772i | \(-0.358472\pi\) | ||||
0.430119 | + | 0.902772i | \(0.358472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2384 | −1.53564 | −0.767818 | − | 0.640668i | \(-0.778657\pi\) | ||||
−0.767818 | + | 0.640668i | \(0.778657\pi\) | |||||||
\(230\) | 2.86897 | 0.189174 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.06072 | 0.397905 | ||||||||
\(233\) | 8.88196 | 0.581876 | 0.290938 | − | 0.956742i | \(-0.406033\pi\) | ||||
0.290938 | + | 0.956742i | \(0.406033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.13955 | 0.270034 | ||||||||
\(236\) | −7.28357 | −0.474120 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.80377 | −0.246562 | ||||||||
\(239\) | 25.3778 | 1.64156 | 0.820778 | − | 0.571247i | \(-0.193540\pi\) | ||||
0.820778 | + | 0.571247i | \(0.193540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.2429 | −0.659801 | −0.329900 | − | 0.944016i | \(-0.607015\pi\) | ||||
−0.329900 | + | 0.944016i | \(0.607015\pi\) | |||||||
\(242\) | −2.26261 | −0.145446 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.5443 | 0.931104 | ||||||||
\(245\) | 5.57973 | 0.356476 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0772 | 0.704825 | ||||||||
\(248\) | −5.36672 | −0.340787 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 10.2258 | 0.645449 | 0.322725 | − | 0.946493i | \(-0.395401\pi\) | ||||
0.322725 | + | 0.946493i | \(0.395401\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.4482 | 0.656870 | ||||||||
\(254\) | 7.21891 | 0.452955 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.0481 | −1.12581 | −0.562906 | − | 0.826521i | \(-0.690317\pi\) | ||||
−0.562906 | + | 0.826521i | \(0.690317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.19175 | −0.0740517 | ||||||||
\(260\) | −4.86897 | −0.301960 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.0506 | −1.23873 | ||||||||
\(263\) | −13.5658 | −0.836503 | −0.418252 | − | 0.908331i | \(-0.637357\pi\) | ||||
−0.418252 | + | 0.908331i | \(0.637357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.88574 | 0.361558 | ||||||||
\(266\) | 2.71131 | 0.166241 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.90007 | −0.299320 | ||||||||
\(269\) | 18.3629 | 1.11961 | 0.559804 | − | 0.828625i | \(-0.310876\pi\) | ||||
0.559804 | + | 0.828625i | \(0.310876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.279091 | −0.0169536 | −0.00847678 | − | 0.999964i | \(-0.502698\pi\) | ||||
−0.00847678 | + | 0.999964i | \(0.502698\pi\) | |||||||
\(272\) | −3.19175 | −0.193528 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.52753 | 0.575579 | ||||||||
\(275\) | 3.64179 | 0.219608 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9195 | 1.49727 | 0.748635 | − | 0.662982i | \(-0.230710\pi\) | ||||
0.748635 | + | 0.662982i | \(0.230710\pi\) | |||||||
\(278\) | −20.7323 | −1.24344 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.19175 | −0.0712207 | ||||||||
\(281\) | −2.25695 | −0.134638 | −0.0673191 | − | 0.997731i | \(-0.521445\pi\) | ||||
−0.0673191 | + | 0.997731i | \(0.521445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.31884 | 0.256728 | 0.128364 | − | 0.991727i | \(-0.459027\pi\) | ||||
0.128364 | + | 0.991727i | \(0.459027\pi\) | |||||||
\(284\) | −5.38798 | −0.319718 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.7317 | −1.04850 | ||||||||
\(287\) | −10.4334 | −0.615865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.81273 | −0.400749 | ||||||||
\(290\) | −6.06072 | −0.355897 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.8026 | 0.690694 | ||||||||
\(293\) | −7.43138 | −0.434146 | −0.217073 | − | 0.976155i | \(-0.569651\pi\) | ||||
−0.217073 | + | 0.976155i | \(0.569651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.28357 | 0.424066 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.17758 | −0.531643 | ||||||||
\(299\) | 13.9689 | 0.807842 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.04992 | 0.463990 | ||||||||
\(302\) | −17.6024 | −1.01291 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.27506 | 0.130484 | ||||||||
\(305\) | −14.5443 | −0.832804 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.28357 | 0.187403 | 0.0937017 | − | 0.995600i | \(-0.470130\pi\) | ||||
0.0937017 | + | 0.995600i | \(0.470130\pi\) | |||||||
\(308\) | −4.34010 | −0.247300 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.36672 | 0.304809 | ||||||||
\(311\) | 11.8438 | 0.671603 | 0.335801 | − | 0.941933i | \(-0.390993\pi\) | ||||
0.335801 | + | 0.941933i | \(0.390993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4653 | 0.874151 | 0.437076 | − | 0.899425i | \(-0.356014\pi\) | ||||
0.437076 | + | 0.899425i | \(0.356014\pi\) | |||||||
\(314\) | −6.89857 | −0.389309 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.38798 | 0.415606 | ||||||||
\(317\) | 16.4553 | 0.924223 | 0.462112 | − | 0.886822i | \(-0.347092\pi\) | ||||
0.462112 | + | 0.886822i | \(0.347092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.0718 | −1.23579 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.41909 | 0.190538 | ||||||||
\(323\) | −7.26143 | −0.404037 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.86897 | 0.270082 | ||||||||
\(326\) | 10.8194 | 0.599229 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.75471 | −0.483398 | ||||||||
\(329\) | 4.93330 | 0.271982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.4204 | 1.94688 | 0.973442 | − | 0.228935i | \(-0.0735243\pi\) | ||||
0.973442 | + | 0.228935i | \(0.0735243\pi\) | |||||||
\(332\) | −4.41461 | −0.242283 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.86897 | 0.156983 | ||||||||
\(335\) | 4.90007 | 0.267720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.80675 | −0.261840 | −0.130920 | − | 0.991393i | \(-0.541793\pi\) | ||||
−0.130920 | + | 0.991393i | \(0.541793\pi\) | |||||||
\(338\) | −10.7068 | −0.582374 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.19175 | 0.173097 | ||||||||
\(341\) | 19.5445 | 1.05839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9919 | 0.809486 | ||||||||
\(344\) | 6.75471 | 0.364189 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.3571 | 0.986885 | ||||||||
\(347\) | −18.5049 | −0.993397 | −0.496698 | − | 0.867923i | \(-0.665454\pi\) | ||||
−0.496698 | + | 0.867923i | \(0.665454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.7975 | −1.80914 | −0.904568 | − | 0.426328i | \(-0.859807\pi\) | ||||
−0.904568 | + | 0.426328i | \(0.859807\pi\) | |||||||
\(350\) | 1.19175 | 0.0637017 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.64179 | −0.194108 | ||||||||
\(353\) | 37.4657 | 1.99410 | 0.997049 | − | 0.0767613i | \(-0.0244579\pi\) | ||||
0.997049 | + | 0.0767613i | \(0.0244579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.38798 | 0.285964 | ||||||||
\(356\) | −9.63597 | −0.510705 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.1259 | −1.22224 | ||||||||
\(359\) | −14.6886 | −0.775233 | −0.387617 | − | 0.921821i | \(-0.626702\pi\) | ||||
−0.387617 | + | 0.921821i | \(0.626702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.8241 | −0.727584 | ||||||||
\(362\) | −14.9001 | −0.783130 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.80259 | −0.304138 | ||||||||
\(365\) | −11.8026 | −0.617776 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1175 | 0.841326 | 0.420663 | − | 0.907217i | \(-0.361797\pi\) | ||||
0.420663 | + | 0.907217i | \(0.361797\pi\) | |||||||
\(368\) | 2.86897 | 0.149555 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | 7.01433 | 0.364166 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.25002 | 0.168280 | 0.0841399 | − | 0.996454i | \(-0.473186\pi\) | ||||
0.0841399 | + | 0.996454i | \(0.473186\pi\) | |||||||
\(374\) | 11.6237 | 0.601046 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.13955 | 0.213481 | ||||||||
\(377\) | −29.5094 | −1.51981 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.7639 | −1.73434 | −0.867168 | − | 0.498016i | \(-0.834062\pi\) | ||||
−0.867168 | + | 0.498016i | \(0.834062\pi\) | |||||||
\(380\) | −2.27506 | −0.116708 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.31766 | 0.425569 | ||||||||
\(383\) | 14.3859 | 0.735087 | 0.367544 | − | 0.930006i | \(-0.380199\pi\) | ||||
0.367544 | + | 0.930006i | \(0.380199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.34010 | 0.221192 | ||||||||
\(386\) | 21.5445 | 1.09659 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.8943 | 0.756141 | ||||||||
\(389\) | 25.5445 | 1.29516 | 0.647578 | − | 0.761999i | \(-0.275782\pi\) | ||||
0.647578 | + | 0.761999i | \(0.275782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.15702 | −0.463090 | ||||||||
\(392\) | 5.57973 | 0.281819 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.76904 | −0.189881 | ||||||||
\(395\) | −7.38798 | −0.371730 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.81219 | −0.241517 | −0.120759 | − | 0.992682i | \(-0.538533\pi\) | ||||
−0.120759 | + | 0.992682i | \(0.538533\pi\) | |||||||
\(398\) | 5.92914 | 0.297201 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 8.45191 | 0.422068 | 0.211034 | − | 0.977479i | \(-0.432317\pi\) | ||||
0.211034 | + | 0.977479i | \(0.432317\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.1304 | 1.30165 | ||||||||
\(404\) | 7.63194 | 0.379703 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.22286 | −0.358464 | ||||||||
\(407\) | 3.64179 | 0.180517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.51209 | −0.272555 | −0.136278 | − | 0.990671i | \(-0.543514\pi\) | ||||
−0.136278 | + | 0.990671i | \(0.543514\pi\) | |||||||
\(410\) | 8.75471 | 0.432364 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.13955 | −0.105408 | ||||||||
\(413\) | 8.68020 | 0.427125 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.41461 | 0.216705 | ||||||||
\(416\) | −4.86897 | −0.238721 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.28529 | −0.405247 | ||||||||
\(419\) | 0.853529 | 0.0416976 | 0.0208488 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208488 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5275 | 1.14666 | 0.573331 | − | 0.819324i | \(-0.305651\pi\) | ||||
0.573331 | + | 0.819324i | \(0.305651\pi\) | |||||||
\(422\) | 3.51059 | 0.170893 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.88574 | 0.285837 | ||||||||
\(425\) | −3.19175 | −0.154823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.3332 | −0.838811 | ||||||||
\(428\) | 14.9904 | 0.724588 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.75471 | −0.325741 | ||||||||
\(431\) | 34.1849 | 1.64663 | 0.823315 | − | 0.567585i | \(-0.192122\pi\) | ||||
0.823315 | + | 0.567585i | \(0.192122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.747535 | −0.0359242 | −0.0179621 | − | 0.999839i | \(-0.505718\pi\) | ||||
−0.0179621 | + | 0.999839i | \(0.505718\pi\) | |||||||
\(434\) | 6.39579 | 0.307008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.253804 | 0.0121550 | ||||||||
\(437\) | 6.52707 | 0.312232 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4504 | 0.689682 | 0.344841 | − | 0.938661i | \(-0.387933\pi\) | ||||
0.344841 | + | 0.938661i | \(0.387933\pi\) | |||||||
\(440\) | 3.64179 | 0.173615 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.5405 | 0.739187 | ||||||||
\(443\) | 34.8974 | 1.65803 | 0.829013 | − | 0.559230i | \(-0.188903\pi\) | ||||
0.829013 | + | 0.559230i | \(0.188903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.63597 | 0.456789 | ||||||||
\(446\) | −19.8322 | −0.939082 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.19175 | −0.0563049 | ||||||||
\(449\) | 7.54564 | 0.356101 | 0.178050 | − | 0.984021i | \(-0.443021\pi\) | ||||
0.178050 | + | 0.984021i | \(0.443021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.8828 | 1.50130 | ||||||||
\(452\) | 13.3443 | 0.627663 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.9608 | −0.608280 | ||||||||
\(455\) | 5.80259 | 0.272030 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.70645 | −0.266936 | −0.133468 | − | 0.991053i | \(-0.542611\pi\) | ||||
−0.133468 | + | 0.991053i | \(0.542611\pi\) | |||||||
\(458\) | 23.2384 | 1.08586 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.86897 | −0.133766 | ||||||||
\(461\) | −18.0324 | −0.839851 | −0.419926 | − | 0.907559i | \(-0.637944\pi\) | ||||
−0.419926 | + | 0.907559i | \(0.637944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.3869 | −1.17983 | −0.589914 | − | 0.807466i | \(-0.700839\pi\) | ||||
−0.589914 | + | 0.807466i | \(0.700839\pi\) | |||||||
\(464\) | −6.06072 | −0.281362 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.88196 | −0.411449 | ||||||||
\(467\) | −23.6153 | −1.09279 | −0.546393 | − | 0.837529i | \(-0.684000\pi\) | ||||
−0.546393 | + | 0.837529i | \(0.684000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.83966 | 0.269651 | ||||||||
\(470\) | −4.13955 | −0.190943 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.28357 | 0.335254 | ||||||||
\(473\) | −24.5992 | −1.13107 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.27506 | 0.104387 | ||||||||
\(476\) | 3.80377 | 0.174345 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.3778 | −1.16076 | ||||||||
\(479\) | 34.7981 | 1.58997 | 0.794983 | − | 0.606632i | \(-0.207480\pi\) | ||||
0.794983 | + | 0.606632i | \(0.207480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.86897 | 0.222006 | ||||||||
\(482\) | 10.2429 | 0.466550 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.26261 | 0.102846 | ||||||||
\(485\) | −14.8943 | −0.676313 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.65612 | −0.392246 | −0.196123 | − | 0.980579i | \(-0.562835\pi\) | ||||
−0.196123 | + | 0.980579i | \(0.562835\pi\) | |||||||
\(488\) | −14.5443 | −0.658390 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.57973 | −0.252067 | ||||||||
\(491\) | −12.0632 | −0.544407 | −0.272203 | − | 0.962240i | \(-0.587752\pi\) | ||||
−0.272203 | + | 0.962240i | \(0.587752\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3443 | 0.871223 | ||||||||
\(494\) | −11.0772 | −0.498387 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.36672 | 0.240973 | ||||||||
\(497\) | 6.42113 | 0.288027 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14647 | 0.0513231 | 0.0256616 | − | 0.999671i | \(-0.491831\pi\) | ||||
0.0256616 | + | 0.999671i | \(0.491831\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.2258 | −0.456402 | ||||||||
\(503\) | −6.98795 | −0.311577 | −0.155789 | − | 0.987790i | \(-0.549792\pi\) | ||||
−0.155789 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.63194 | −0.339617 | ||||||||
\(506\) | −10.4482 | −0.464477 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.21891 | −0.320288 | ||||||||
\(509\) | 27.9592 | 1.23927 | 0.619634 | − | 0.784891i | \(-0.287281\pi\) | ||||
0.619634 | + | 0.784891i | \(0.287281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0657 | −0.622232 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0481 | 0.796069 | ||||||||
\(515\) | 2.13955 | 0.0942796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0753 | −0.663013 | ||||||||
\(518\) | 1.19175 | 0.0523625 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.86897 | 0.213518 | ||||||||
\(521\) | −29.5052 | −1.29265 | −0.646323 | − | 0.763064i | \(-0.723694\pi\) | ||||
−0.646323 | + | 0.763064i | \(0.723694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0588 | 0.571022 | 0.285511 | − | 0.958375i | \(-0.407837\pi\) | ||||
0.285511 | + | 0.958375i | \(0.407837\pi\) | |||||||
\(524\) | 20.0506 | 0.875913 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5658 | 0.591497 | ||||||||
\(527\) | −17.1292 | −0.746162 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7690 | −0.642132 | ||||||||
\(530\) | −5.88574 | −0.255660 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.71131 | −0.117550 | ||||||||
\(533\) | 42.6264 | 1.84635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.9904 | −0.648091 | ||||||||
\(536\) | 4.90007 | 0.211651 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.3629 | −0.791683 | ||||||||
\(539\) | −20.3202 | −0.875253 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.5134 | −1.01092 | −0.505461 | − | 0.862850i | \(-0.668678\pi\) | ||||
−0.505461 | + | 0.862850i | \(0.668678\pi\) | |||||||
\(542\) | 0.279091 | 0.0119880 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.19175 | 0.136845 | ||||||||
\(545\) | −0.253804 | −0.0108718 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.5166 | −1.43307 | −0.716533 | − | 0.697553i | \(-0.754272\pi\) | ||||
−0.716533 | + | 0.697553i | \(0.754272\pi\) | |||||||
\(548\) | −9.52753 | −0.406996 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.64179 | −0.155286 | ||||||||
\(551\) | −13.7885 | −0.587410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.80463 | −0.374411 | ||||||||
\(554\) | −24.9195 | −1.05873 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.7323 | 0.879244 | ||||||||
\(557\) | 11.6308 | 0.492815 | 0.246407 | − | 0.969166i | \(-0.420750\pi\) | ||||
0.246407 | + | 0.969166i | \(0.420750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.8884 | −1.39103 | ||||||||
\(560\) | 1.19175 | 0.0503606 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.25695 | 0.0952036 | ||||||||
\(563\) | −2.37336 | −0.100025 | −0.0500125 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500125 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.3443 | −0.561398 | ||||||||
\(566\) | −4.31884 | −0.181534 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.38798 | 0.226075 | ||||||||
\(569\) | −3.83093 | −0.160601 | −0.0803005 | − | 0.996771i | \(-0.525588\pi\) | ||||
−0.0803005 | + | 0.996771i | \(0.525588\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.85678 | 0.161401 | 0.0807007 | − | 0.996738i | \(-0.474284\pi\) | ||||
0.0807007 | + | 0.996738i | \(0.474284\pi\) | |||||||
\(572\) | 17.7317 | 0.741401 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.4334 | 0.435483 | ||||||||
\(575\) | 2.86897 | 0.119644 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.2565 | −0.635136 | −0.317568 | − | 0.948235i | \(-0.602866\pi\) | ||||
−0.317568 | + | 0.948235i | \(0.602866\pi\) | |||||||
\(578\) | 6.81273 | 0.283372 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.06072 | 0.251658 | ||||||||
\(581\) | 5.26111 | 0.218268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.4346 | −0.887731 | ||||||||
\(584\) | −11.8026 | −0.488395 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.43138 | 0.306988 | ||||||||
\(587\) | −20.0442 | −0.827312 | −0.413656 | − | 0.910433i | \(-0.635748\pi\) | ||||
−0.413656 | + | 0.910433i | \(0.635748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2096 | 0.503089 | ||||||||
\(590\) | −7.28357 | −0.299860 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −38.0414 | −1.56217 | −0.781087 | − | 0.624422i | \(-0.785334\pi\) | ||||
−0.781087 | + | 0.624422i | \(0.785334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.80377 | −0.155939 | ||||||||
\(596\) | 9.17758 | 0.375928 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.9689 | −0.571230 | ||||||||
\(599\) | −0.900073 | −0.0367760 | −0.0183880 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183880 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.8298 | 0.727291 | 0.363645 | − | 0.931537i | \(-0.381532\pi\) | ||||
0.363645 | + | 0.931537i | \(0.381532\pi\) | |||||||
\(602\) | −8.04992 | −0.328090 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.6024 | 0.716232 | ||||||||
\(605\) | −2.26261 | −0.0919881 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.6109 | −1.56717 | −0.783585 | − | 0.621285i | \(-0.786611\pi\) | ||||
−0.783585 | + | 0.621285i | \(0.786611\pi\) | |||||||
\(608\) | −2.27506 | −0.0922659 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.5443 | 0.588882 | ||||||||
\(611\) | −20.1553 | −0.815396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.7108 | 0.553773 | 0.276886 | − | 0.960903i | \(-0.410697\pi\) | ||||
0.276886 | + | 0.960903i | \(0.410697\pi\) | |||||||
\(614\) | −3.28357 | −0.132514 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.34010 | 0.174868 | ||||||||
\(617\) | 23.0875 | 0.929468 | 0.464734 | − | 0.885450i | \(-0.346150\pi\) | ||||
0.464734 | + | 0.885450i | \(0.346150\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4872 | 1.14500 | 0.572499 | − | 0.819905i | \(-0.305974\pi\) | ||||
0.572499 | + | 0.819905i | \(0.305974\pi\) | |||||||
\(620\) | −5.36672 | −0.215533 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.8438 | −0.474895 | ||||||||
\(623\) | 11.4837 | 0.460083 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.4653 | −0.618118 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.89857 | 0.275283 | ||||||||
\(629\) | −3.19175 | −0.127263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.84975 | 0.232875 | 0.116437 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116437 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(632\) | −7.38798 | −0.293878 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.4553 | −0.653525 | ||||||||
\(635\) | 7.21891 | 0.286474 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.1675 | −1.07642 | ||||||||
\(638\) | 22.0718 | 0.873832 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 16.5884 | 0.655203 | 0.327601 | − | 0.944816i | \(-0.393760\pi\) | ||||
0.327601 | + | 0.944816i | \(0.393760\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.3695 | −0.921603 | −0.460801 | − | 0.887503i | \(-0.652438\pi\) | ||||
−0.460801 | + | 0.887503i | \(0.652438\pi\) | |||||||
\(644\) | −3.41909 | −0.134731 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.26143 | 0.285697 | ||||||||
\(647\) | −25.8618 | −1.01673 | −0.508366 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508366 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.5252 | −1.04121 | ||||||||
\(650\) | −4.86897 | −0.190977 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.8194 | −0.423719 | ||||||||
\(653\) | −34.9853 | −1.36908 | −0.684540 | − | 0.728976i | \(-0.739997\pi\) | ||||
−0.684540 | + | 0.728976i | \(0.739997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.0506 | −0.783441 | ||||||||
\(656\) | 8.75471 | 0.341814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.93330 | −0.192320 | ||||||||
\(659\) | 21.3274 | 0.830796 | 0.415398 | − | 0.909640i | \(-0.363642\pi\) | ||||
0.415398 | + | 0.909640i | \(0.363642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.8420 | −0.538390 | −0.269195 | − | 0.963086i | \(-0.586758\pi\) | ||||
−0.269195 | + | 0.963086i | \(0.586758\pi\) | |||||||
\(662\) | −35.4204 | −1.37665 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.41461 | 0.171320 | ||||||||
\(665\) | 2.71131 | 0.105140 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3880 | −0.673265 | ||||||||
\(668\) | −2.86897 | −0.111004 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.90007 | −0.189306 | ||||||||
\(671\) | 52.9672 | 2.04478 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.5866 | −1.33322 | −0.666608 | − | 0.745409i | \(-0.732254\pi\) | ||||
−0.666608 | + | 0.745409i | \(0.732254\pi\) | |||||||
\(674\) | 4.80675 | 0.185149 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.7068 | 0.411801 | ||||||||
\(677\) | −32.0401 | −1.23140 | −0.615700 | − | 0.787981i | \(-0.711127\pi\) | ||||
−0.615700 | + | 0.787981i | \(0.711127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.7502 | −0.681191 | ||||||||
\(680\) | −3.19175 | −0.122398 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −19.5445 | −0.748396 | ||||||||
\(683\) | 25.2036 | 0.964391 | 0.482195 | − | 0.876064i | \(-0.339840\pi\) | ||||
0.482195 | + | 0.876064i | \(0.339840\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.52753 | 0.364028 | ||||||||
\(686\) | −14.9919 | −0.572393 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.75471 | −0.257521 | ||||||||
\(689\) | −28.6575 | −1.09176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5818 | −0.821009 | −0.410505 | − | 0.911859i | \(-0.634647\pi\) | ||||
−0.410505 | + | 0.911859i | \(0.634647\pi\) | |||||||
\(692\) | −18.3571 | −0.697833 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5049 | 0.702438 | ||||||||
\(695\) | −20.7323 | −0.786420 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.9428 | −1.05841 | ||||||||
\(698\) | 33.7975 | 1.27925 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.19175 | −0.0450439 | ||||||||
\(701\) | −14.0622 | −0.531123 | −0.265561 | − | 0.964094i | \(-0.585557\pi\) | ||||
−0.265561 | + | 0.964094i | \(0.585557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.27506 | 0.0858056 | ||||||||
\(704\) | 3.64179 | 0.137255 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.4657 | −1.41004 | ||||||||
\(707\) | −9.09536 | −0.342066 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.83300 | −0.143951 | −0.0719756 | − | 0.997406i | \(-0.522930\pi\) | ||||
−0.0719756 | + | 0.997406i | \(0.522930\pi\) | |||||||
\(710\) | −5.38798 | −0.202207 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.63597 | 0.361123 | ||||||||
\(713\) | 15.3969 | 0.576620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.7317 | −0.663129 | ||||||||
\(716\) | 23.1259 | 0.864256 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.6886 | 0.548173 | ||||||||
\(719\) | 40.5298 | 1.51151 | 0.755754 | − | 0.654856i | \(-0.227271\pi\) | ||||
0.755754 | + | 0.654856i | \(0.227271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54980 | 0.0949596 | ||||||||
\(722\) | 13.8241 | 0.514479 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.9001 | 0.553757 | ||||||||
\(725\) | −6.06072 | −0.225089 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.5871 | 1.09732 | 0.548662 | − | 0.836044i | \(-0.315137\pi\) | ||||
0.548662 | + | 0.836044i | \(0.315137\pi\) | |||||||
\(728\) | 5.80259 | 0.215058 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.8026 | 0.436833 | ||||||||
\(731\) | 21.5593 | 0.797401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.5400 | −1.12802 | −0.564010 | − | 0.825768i | \(-0.690742\pi\) | ||||
−0.564010 | + | 0.825768i | \(0.690742\pi\) | |||||||
\(734\) | −16.1175 | −0.594907 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.86897 | −0.105751 | ||||||||
\(737\) | −17.8450 | −0.657330 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.49357 | −0.0549419 | −0.0274709 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274709 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.01433 | −0.257504 | ||||||||
\(743\) | 25.2442 | 0.926120 | 0.463060 | − | 0.886327i | \(-0.346751\pi\) | ||||
0.463060 | + | 0.886327i | \(0.346751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.17758 | −0.336240 | ||||||||
\(746\) | −3.25002 | −0.118992 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.6237 | −0.425004 | ||||||||
\(749\) | −17.8648 | −0.652766 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.44304 | 0.308091 | 0.154045 | − | 0.988064i | \(-0.450770\pi\) | ||||
0.154045 | + | 0.988064i | \(0.450770\pi\) | |||||||
\(752\) | −4.13955 | −0.150954 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 29.5094 | 1.07467 | ||||||||
\(755\) | −17.6024 | −0.640617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.8169 | 1.30179 | 0.650894 | − | 0.759168i | \(-0.274394\pi\) | ||||
0.650894 | + | 0.759168i | \(0.274394\pi\) | |||||||
\(758\) | 33.7639 | 1.22636 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.27506 | 0.0825252 | ||||||||
\(761\) | −27.0428 | −0.980299 | −0.490150 | − | 0.871638i | \(-0.663058\pi\) | ||||
−0.490150 | + | 0.871638i | \(0.663058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.302471 | −0.0109502 | ||||||||
\(764\) | −8.31766 | −0.300922 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.3859 | −0.519785 | ||||||||
\(767\) | −35.4635 | −1.28051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.3051 | −1.52556 | −0.762780 | − | 0.646658i | \(-0.776166\pi\) | ||||
−0.762780 | + | 0.646658i | \(0.776166\pi\) | |||||||
\(770\) | −4.34010 | −0.156406 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.5445 | −0.775405 | ||||||||
\(773\) | −11.5566 | −0.415661 | −0.207830 | − | 0.978165i | \(-0.566640\pi\) | ||||
−0.207830 | + | 0.978165i | \(0.566640\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.36672 | 0.192778 | ||||||||
\(776\) | −14.8943 | −0.534672 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.5445 | −0.915813 | ||||||||
\(779\) | 19.9175 | 0.713618 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6219 | −0.702126 | ||||||||
\(782\) | 9.15702 | 0.327454 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.57973 | −0.199276 | ||||||||
\(785\) | −6.89857 | −0.246221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9099 | 1.20876 | 0.604379 | − | 0.796697i | \(-0.293421\pi\) | ||||
0.604379 | + | 0.796697i | \(0.293421\pi\) | |||||||
\(788\) | 3.76904 | 0.134266 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.38798 | 0.262853 | ||||||||
\(791\) | −15.9031 | −0.565448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 70.8157 | 2.51474 | ||||||||
\(794\) | 4.81219 | 0.170778 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.92914 | −0.210153 | ||||||||
\(797\) | 20.6886 | 0.732827 | 0.366413 | − | 0.930452i | \(-0.380586\pi\) | ||||
0.366413 | + | 0.930452i | \(0.380586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2124 | 0.467421 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.45191 | −0.298447 | ||||||||
\(803\) | 42.9825 | 1.51682 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41909 | 0.120507 | ||||||||
\(806\) | −26.1304 | −0.920404 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.63194 | −0.268491 | ||||||||
\(809\) | 44.3868 | 1.56056 | 0.780278 | − | 0.625433i | \(-0.215078\pi\) | ||||
0.780278 | + | 0.625433i | \(0.215078\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.4929 | −1.45701 | −0.728506 | − | 0.685039i | \(-0.759785\pi\) | ||||
−0.728506 | + | 0.685039i | \(0.759785\pi\) | |||||||
\(812\) | 7.22286 | 0.253473 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.64179 | −0.127645 | ||||||||
\(815\) | 10.8194 | 0.378986 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.3674 | −0.537636 | ||||||||
\(818\) | 5.51209 | 0.192726 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.75471 | −0.305728 | ||||||||
\(821\) | −21.9624 | −0.766494 | −0.383247 | − | 0.923646i | \(-0.625194\pi\) | ||||
−0.383247 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.5911 | 1.10120 | 0.550598 | − | 0.834770i | \(-0.314400\pi\) | ||||
0.550598 | + | 0.834770i | \(0.314400\pi\) | |||||||
\(824\) | 2.13955 | 0.0745346 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.68020 | −0.302023 | ||||||||
\(827\) | −5.42271 | −0.188566 | −0.0942831 | − | 0.995545i | \(-0.530056\pi\) | ||||
−0.0942831 | + | 0.995545i | \(0.530056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −54.0226 | −1.87628 | −0.938141 | − | 0.346252i | \(-0.887454\pi\) | ||||
−0.938141 | + | 0.346252i | \(0.887454\pi\) | |||||||
\(830\) | −4.41461 | −0.153233 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.86897 | 0.168801 | ||||||||
\(833\) | 17.8091 | 0.617049 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.86897 | 0.0992846 | ||||||||
\(836\) | 8.28529 | 0.286553 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.853529 | −0.0294847 | ||||||||
\(839\) | 22.4803 | 0.776108 | 0.388054 | − | 0.921637i | \(-0.373147\pi\) | ||||
0.388054 | + | 0.921637i | \(0.373147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.73227 | 0.266630 | ||||||||
\(842\) | −23.5275 | −0.810812 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.51059 | −0.120840 | ||||||||
\(845\) | −10.7068 | −0.368326 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.69646 | −0.0926516 | ||||||||
\(848\) | −5.88574 | −0.202117 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.19175 | 0.109476 | ||||||||
\(851\) | 2.86897 | 0.0983469 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.4482 | 0.837089 | 0.418545 | − | 0.908196i | \(-0.362540\pi\) | ||||
0.418545 | + | 0.908196i | \(0.362540\pi\) | |||||||
\(854\) | 17.3332 | 0.593129 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.9904 | −0.512361 | ||||||||
\(857\) | −19.1295 | −0.653452 | −0.326726 | − | 0.945119i | \(-0.605946\pi\) | ||||
−0.326726 | + | 0.945119i | \(0.605946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5662 | −0.394634 | −0.197317 | − | 0.980340i | \(-0.563223\pi\) | ||||
−0.197317 | + | 0.980340i | \(0.563223\pi\) | |||||||
\(860\) | 6.75471 | 0.230334 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.1849 | −1.16434 | ||||||||
\(863\) | −14.2397 | −0.484726 | −0.242363 | − | 0.970186i | \(-0.577922\pi\) | ||||
−0.242363 | + | 0.970186i | \(0.577922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.3571 | 0.624161 | ||||||||
\(866\) | 0.747535 | 0.0254023 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.39579 | −0.217087 | ||||||||
\(869\) | 26.9055 | 0.912705 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.8583 | −0.808407 | ||||||||
\(872\) | −0.253804 | −0.00859490 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.52707 | −0.220782 | ||||||||
\(875\) | 1.19175 | 0.0402885 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.8021 | −1.24272 | −0.621358 | − | 0.783526i | \(-0.713419\pi\) | ||||
−0.621358 | + | 0.783526i | \(0.713419\pi\) | |||||||
\(878\) | −14.4504 | −0.487679 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.64179 | −0.122765 | ||||||||
\(881\) | −5.78645 | −0.194951 | −0.0974753 | − | 0.995238i | \(-0.531077\pi\) | ||||
−0.0974753 | + | 0.995238i | \(0.531077\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.30279 | 0.279411 | 0.139706 | − | 0.990193i | \(-0.455384\pi\) | ||||
0.139706 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(884\) | −15.5405 | −0.522684 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.8974 | −1.17240 | ||||||||
\(887\) | −40.2125 | −1.35020 | −0.675101 | − | 0.737725i | \(-0.735900\pi\) | ||||
−0.675101 | + | 0.737725i | \(0.735900\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.60314 | 0.288540 | ||||||||
\(890\) | −9.63597 | −0.322998 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.8322 | 0.664031 | ||||||||
\(893\) | −9.41772 | −0.315152 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.1259 | −0.773014 | ||||||||
\(896\) | 1.19175 | 0.0398136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.54564 | −0.251801 | ||||||||
\(899\) | −32.5262 | −1.08481 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7858 | 0.625846 | ||||||||
\(902\) | −31.8828 | −1.06158 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.3443 | −0.443824 | ||||||||
\(905\) | −14.9001 | −0.495295 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9432 | 0.595795 | 0.297898 | − | 0.954598i | \(-0.403715\pi\) | ||||
0.297898 | + | 0.954598i | \(0.403715\pi\) | |||||||
\(908\) | 12.9608 | 0.430119 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.80259 | −0.192354 | ||||||||
\(911\) | −10.0090 | −0.331612 | −0.165806 | − | 0.986158i | \(-0.553023\pi\) | ||||
−0.165806 | + | 0.986158i | \(0.553023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.0771 | −0.532073 | ||||||||
\(914\) | 5.70645 | 0.188752 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.2384 | −0.767818 | ||||||||
\(917\) | −23.8953 | −0.789091 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.4439 | 1.76295 | 0.881476 | − | 0.472228i | \(-0.156550\pi\) | ||||
0.881476 | + | 0.472228i | \(0.156550\pi\) | |||||||
\(920\) | 2.86897 | 0.0945870 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0324 | 0.593865 | ||||||||
\(923\) | −26.2339 | −0.863499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 25.3869 | 0.834265 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.06072 | 0.198953 | ||||||||
\(929\) | −17.5723 | −0.576528 | −0.288264 | − | 0.957551i | \(-0.593078\pi\) | ||||
−0.288264 | + | 0.957551i | \(0.593078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.6942 | −0.416037 | ||||||||
\(932\) | 8.88196 | 0.290938 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23.6153 | 0.772717 | ||||||||
\(935\) | 11.6237 | 0.380135 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.5641 | −1.06382 | −0.531912 | − | 0.846800i | \(-0.678526\pi\) | ||||
−0.531912 | + | 0.846800i | \(0.678526\pi\) | |||||||
\(938\) | −5.83966 | −0.190672 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.13955 | 0.135017 | ||||||||
\(941\) | −17.0656 | −0.556323 | −0.278161 | − | 0.960534i | \(-0.589725\pi\) | ||||
−0.278161 | + | 0.960534i | \(0.589725\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.1169 | 0.817920 | ||||||||
\(944\) | −7.28357 | −0.237060 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.5992 | 0.799789 | ||||||||
\(947\) | 25.2036 | 0.819009 | 0.409504 | − | 0.912308i | \(-0.365702\pi\) | ||||
0.409504 | + | 0.912308i | \(0.365702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.4664 | 1.86544 | ||||||||
\(950\) | −2.27506 | −0.0738128 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.80377 | −0.123281 | ||||||||
\(953\) | −21.7560 | −0.704747 | −0.352374 | − | 0.935859i | \(-0.614625\pi\) | ||||
−0.352374 | + | 0.935859i | \(0.614625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.31766 | 0.269153 | ||||||||
\(956\) | 25.3778 | 0.820778 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.7981 | −1.12428 | ||||||||
\(959\) | 11.3544 | 0.366654 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.19827 | −0.0709119 | ||||||||
\(962\) | −4.86897 | −0.156982 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.2429 | −0.329900 | ||||||||
\(965\) | 21.5445 | 0.693544 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3654 | −0.397644 | −0.198822 | − | 0.980036i | \(-0.563712\pi\) | ||||
−0.198822 | + | 0.980036i | \(0.563712\pi\) | |||||||
\(968\) | −2.26261 | −0.0727230 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.8943 | 0.478226 | ||||||||
\(971\) | −50.2114 | −1.61136 | −0.805680 | − | 0.592351i | \(-0.798200\pi\) | ||||
−0.805680 | + | 0.592351i | \(0.798200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.7077 | −0.792092 | ||||||||
\(974\) | 8.65612 | 0.277360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.5443 | 0.465552 | ||||||||
\(977\) | −8.06724 | −0.258094 | −0.129047 | − | 0.991638i | \(-0.541192\pi\) | ||||
−0.129047 | + | 0.991638i | \(0.541192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.0921 | −1.12155 | ||||||||
\(980\) | 5.57973 | 0.178238 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.0632 | 0.384954 | ||||||||
\(983\) | 42.2151 | 1.34645 | 0.673227 | − | 0.739436i | \(-0.264908\pi\) | ||||
0.673227 | + | 0.739436i | \(0.264908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.76904 | −0.120092 | ||||||||
\(986\) | −19.3443 | −0.616048 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.0772 | 0.352413 | ||||||||
\(989\) | −19.3790 | −0.616217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.9294 | −0.537780 | −0.268890 | − | 0.963171i | \(-0.586657\pi\) | ||||
−0.268890 | + | 0.963171i | \(0.586657\pi\) | |||||||
\(992\) | −5.36672 | −0.170394 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.42113 | −0.203666 | ||||||||
\(995\) | 5.92914 | 0.187966 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.75699 | −0.277337 | −0.138668 | − | 0.990339i | \(-0.544282\pi\) | ||||
−0.138668 | + | 0.990339i | \(0.544282\pi\) | |||||||
\(998\) | −1.14647 | −0.0362909 | ||||||||
\(999\) | 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 | 3330.2.a.bk.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 3330.2.a.bl.1.2 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3330.2.a.bk.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
3330.2.a.bl.1.2 | yes | 5 | 3.2 | odd | 2 |