Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1216) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.792287\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.37228 | −1.94699 | −0.973494 | − | 0.228714i | \(-0.926548\pi\) | ||||
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.52434 | −1.12892 | −0.564459 | − | 0.825461i | \(-0.690915\pi\) | ||||
−0.564459 | + | 0.825461i | \(0.690915\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.31662 | −1.25357 | −0.626783 | − | 0.779194i | \(-0.715629\pi\) | ||||
−0.626783 | + | 0.779194i | \(0.715629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.37228 | 2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.37228 | −0.715270 | −0.357635 | − | 0.933862i | \(-0.616417\pi\) | ||||
−0.357635 | + | 0.933862i | \(0.616417\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.84096 | 1.61999 | 0.809996 | − | 0.586436i | \(-0.199469\pi\) | ||||
0.809996 | + | 0.586436i | \(0.199469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.51278 | 2.19799 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1846 | 2.44068 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.792287 | −0.165203 | −0.0826016 | − | 0.996583i | \(-0.526323\pi\) | ||||
−0.0826016 | + | 0.996583i | \(0.526323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.37228 | 0.274456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −18.1168 | −3.48659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.67181 | −0.496144 | −0.248072 | − | 0.968742i | \(-0.579797\pi\) | ||||
−0.248072 | + | 0.968742i | \(0.579797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.37228 | 1.41517 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0974 | −1.65999 | −0.829997 | − | 0.557768i | \(-0.811658\pi\) | ||||
−0.829997 | + | 0.557768i | \(0.811658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.6974 | −3.15410 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.62772 | 0.553222 | 0.276611 | − | 0.960982i | \(-0.410789\pi\) | ||||
0.276611 | + | 0.960982i | \(0.410789\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −21.1345 | −3.15054 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.644810 | −0.0940552 | −0.0470276 | − | 0.998894i | \(-0.514975\pi\) | ||||
−0.0470276 | + | 0.998894i | \(0.514975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8614 | −2.36107 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.13592 | −0.842833 | −0.421416 | − | 0.906867i | \(-0.638467\pi\) | ||||
−0.421416 | + | 0.906867i | \(0.638467\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.98844 | 0.807481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.37228 | −0.446670 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.37228 | −0.178656 | −0.0893279 | − | 0.996002i | \(-0.528472\pi\) | ||||
−0.0893279 | + | 0.996002i | \(0.528472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.5012 | −1.85669 | −0.928345 | − | 0.371719i | \(-0.878768\pi\) | ||||
−0.928345 | + | 0.371719i | \(0.878768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −27.7677 | −3.49840 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.7446 | −1.82884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62772 | 0.321027 | 0.160513 | − | 0.987034i | \(-0.448685\pi\) | ||||
0.160513 | + | 0.987034i | \(0.448685\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.67181 | 0.321649 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.63325 | 0.787222 | 0.393611 | − | 0.919277i | \(-0.371226\pi\) | ||||
0.393611 | + | 0.919277i | \(0.371226\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.48913 | −0.993577 | −0.496788 | − | 0.867872i | \(-0.665488\pi\) | ||||
−0.496788 | + | 0.867872i | \(0.665488\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.62772 | −0.534363 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.86797 | 0.896638 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.294954 | −0.0331849 | −0.0165924 | − | 0.999862i | \(-0.505282\pi\) | ||||
−0.0165924 | + | 0.999862i | \(0.505282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.6217 | −1.36901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.01011 | 0.965985 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4891 | 1.64184 | 0.820922 | − | 0.571040i | \(-0.193460\pi\) | ||||
0.820922 | + | 0.571040i | \(0.193460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.3723 | −2.03077 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.6819 | −1.21136 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.52434 | −0.258992 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.74456 | −0.278668 | −0.139334 | − | 0.990245i | \(-0.544496\pi\) | ||||
−0.139334 | + | 0.990245i | \(0.544496\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −19.8614 | −1.99615 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564 | 1.37876 | 0.689382 | − | 0.724398i | \(-0.257882\pi\) | ||||
0.689382 | + | 0.724398i | \(0.257882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9769 | −1.18012 | −0.590058 | − | 0.807361i | \(-0.700895\pi\) | ||||
−0.590058 | + | 0.807361i | \(0.700895\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28.2337 | −2.75533 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3723 | 1.29275 | 0.646374 | − | 0.763021i | \(-0.276285\pi\) | ||||
0.646374 | + | 0.763021i | \(0.276285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.96143 | 0.379437 | 0.189718 | − | 0.981839i | \(-0.439243\pi\) | ||||
0.189718 | + | 0.981839i | \(0.439243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.0511 | 3.23199 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7446 | −1.38705 | −0.693526 | − | 0.720432i | \(-0.743944\pi\) | ||||
−0.693526 | + | 0.720432i | \(0.743944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 48.9022 | 4.52101 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.5831 | −1.52017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37228 | −0.488389 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.15759 | 0.819080 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2718 | 1.08895 | 0.544475 | − | 0.838777i | \(-0.316729\pi\) | ||||
0.544475 | + | 0.838777i | \(0.316729\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.2337 | −1.07712 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.37228 | −0.382008 | −0.191004 | − | 0.981589i | \(-0.561174\pi\) | ||||
−0.191004 | + | 0.981589i | \(0.561174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.31662 | −0.287588 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.7330 | 3.93607 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | −0.427179 | −0.213589 | − | 0.976924i | \(-0.568515\pi\) | ||||
−0.213589 | + | 0.976924i | \(0.568515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.62772 | 0.307699 | 0.153850 | − | 0.988094i | \(-0.450833\pi\) | ||||
0.153850 | + | 0.988094i | \(0.450833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.17448 | 0.183124 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.74456 | 0.560105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.4891 | −1.11256 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.69882 | −0.384942 | −0.192471 | − | 0.981303i | \(-0.561650\pi\) | ||||
−0.192471 | + | 0.981303i | \(0.561650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7359 | −1.28057 | −0.640286 | − | 0.768137i | \(-0.721184\pi\) | ||||
−0.640286 | + | 0.768137i | \(0.721184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 41.8614 | 3.38429 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.74456 | −0.702380 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6101 | −1.48525 | −0.742625 | − | 0.669708i | \(-0.766419\pi\) | ||||
−0.742625 | + | 0.669708i | \(0.766419\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.6920 | 1.64099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.62772 | 0.207093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7446 | 0.841579 | 0.420790 | − | 0.907158i | \(-0.361753\pi\) | ||||
0.420790 | + | 0.907158i | \(0.361753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.1947 | −1.57216 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.33830 | −0.490472 | −0.245236 | − | 0.969463i | \(-0.578865\pi\) | ||||
−0.245236 | + | 0.969463i | \(0.578865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.1168 | 1.62437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.37228 | 0.640244 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1460 | 1.15153 | 0.575766 | − | 0.817615i | \(-0.304704\pi\) | ||||
0.575766 | + | 0.817615i | \(0.304704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.55134 | −0.344049 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.62772 | 0.347841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.21782 | −0.610826 | −0.305413 | − | 0.952220i | \(-0.598795\pi\) | ||||
−0.305413 | + | 0.952220i | \(0.598795\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 48.9022 | 3.61495 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.4891 | 1.87400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8614 | −0.867392 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 60.0868 | 4.37067 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.07568 | −0.511978 | −0.255989 | − | 0.966680i | \(-0.582401\pi\) | ||||
−0.255989 | + | 0.966680i | \(0.582401\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.25544 | 0.234332 | 0.117166 | − | 0.993112i | \(-0.462619\pi\) | ||||
0.117166 | + | 0.993112i | \(0.462619\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 49.7228 | 3.56072 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.33830 | 0.451585 | 0.225792 | − | 0.974175i | \(-0.427503\pi\) | ||||
0.225792 | + | 0.974175i | \(0.427503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.147477 | 0.0104544 | 0.00522718 | − | 0.999986i | \(-0.498336\pi\) | ||||
0.00522718 | + | 0.999986i | \(0.498336\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.86141 | −0.625035 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.86141 | 0.621949 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.63325 | −0.461043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.37228 | −0.164094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.62772 | −0.180900 | −0.0904498 | − | 0.995901i | \(-0.528830\pi\) | ||||
−0.0904498 | + | 0.995901i | \(0.528830\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.3692 | −1.53271 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.15759 | −0.624542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4891 | −0.779933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.6277 | 1.93448 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.2048 | 1.96453 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | −0.463947 | −0.231973 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231973 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4891 | 0.765942 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1168 | −0.936968 | −0.468484 | − | 0.883472i | \(-0.655200\pi\) | ||||
−0.468484 | + | 0.883472i | \(0.655200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6217 | −0.834065 | −0.417032 | − | 0.908892i | \(-0.636930\pi\) | ||||
−0.417032 | + | 0.908892i | \(0.636930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.5330 | −1.74574 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8832 | 0.712979 | 0.356490 | − | 0.934299i | \(-0.383974\pi\) | ||||
0.356490 | + | 0.934299i | \(0.383974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.62772 | 0.106181 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.994667 | 0.0646105 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4680 | −1.12991 | −0.564955 | − | 0.825122i | \(-0.691106\pi\) | ||||
−0.564955 | + | 0.825122i | \(0.691106\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −66.9783 | −4.29666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0974 | −0.645096 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.84096 | 0.371652 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.9783 | 1.70968 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.8614 | 1.12740 | 0.563701 | − | 0.825979i | \(-0.309377\pi\) | ||||
0.563701 | + | 0.825979i | \(0.309377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.87953 | 0.118165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 42.5639 | 2.66545 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.2337 | −1.01263 | −0.506315 | − | 0.862349i | \(-0.668993\pi\) | ||||
−0.506315 | + | 0.862349i | \(0.668993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.4891 | 2.08091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.3692 | −1.38462 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.9600 | −1.16912 | −0.584561 | − | 0.811349i | \(-0.698733\pi\) | ||||
−0.584561 | + | 0.811349i | \(0.698733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4891 | 0.951489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −52.2337 | −3.19665 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.87953 | 0.114597 | 0.0572984 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572984 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.37686 | 0.144384 | 0.0721920 | − | 0.997391i | \(-0.477001\pi\) | ||||
0.0721920 | + | 0.997391i | \(0.477001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 65.3288 | 3.95388 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.25544 | −0.196310 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.3807 | 0.984224 | 0.492112 | − | 0.870532i | \(-0.336225\pi\) | ||||
0.492112 | + | 0.870532i | \(0.336225\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 29.0024 | 1.73633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.23369 | −0.371871 | −0.185935 | − | 0.982562i | \(-0.559531\pi\) | ||||
−0.185935 | + | 0.982562i | \(0.559531\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6277 | −1.04786 | −0.523930 | − | 0.851762i | \(-0.675534\pi\) | ||||
−0.523930 | + | 0.851762i | \(0.675534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.51278 | 0.504253 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.25544 | 0.542563 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.84630 | −0.283124 | −0.141562 | − | 0.989929i | \(-0.545212\pi\) | ||||
−0.141562 | + | 0.989929i | \(0.545212\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | 0.201688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 42.9783 | 2.49385 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.62772 | −0.267628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0318 | −0.693500 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −46.7277 | −2.68444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.6060 | 2.09605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2554 | −0.870674 | −0.435337 | − | 0.900268i | \(-0.643371\pi\) | ||||
−0.435337 | + | 0.900268i | \(0.643371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.3894 | 2.29767 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2164 | −1.31648 | −0.658240 | − | 0.752808i | \(-0.728699\pi\) | ||||
−0.658240 | + | 0.752808i | \(0.728699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.88316 | −0.219489 | −0.109744 | − | 0.993960i | \(-0.535003\pi\) | ||||
−0.109744 | + | 0.993960i | \(0.535003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 70.0951 | 3.94941 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5769 | 1.21188 | 0.605940 | − | 0.795511i | \(-0.292797\pi\) | ||||
0.605940 | + | 0.795511i | \(0.292797\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.33830 | 0.354876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −45.0951 | −2.51696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000 | 0.278207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.01544 | 0.444617 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3591 | −0.738758 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.13859 | 0.117904 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.8614 | 0.596997 | 0.298498 | − | 0.954410i | \(-0.403514\pi\) | ||||
0.298498 | + | 0.954410i | \(0.403514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −84.5379 | −4.63265 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.63325 | −0.362413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2554 | −0.722070 | −0.361035 | − | 0.932552i | \(-0.617576\pi\) | ||||
−0.361035 | + | 0.932552i | \(0.617576\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 49.7228 | 2.70057 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.21782 | −0.445020 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.94987 | 0.537243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.74456 | −0.363115 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 37.1168 | 1.99254 | 0.996268 | − | 0.0863104i | \(-0.0275077\pi\) | ||||
0.996268 | + | 0.0863104i | \(0.0275077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2116 | 0.707201 | 0.353600 | − | 0.935397i | \(-0.384957\pi\) | ||||
0.353600 | + | 0.935397i | \(0.384957\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −105.820 | −5.64824 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.88316 | 0.206680 | 0.103340 | − | 0.994646i | \(-0.467047\pi\) | ||||
0.103340 | + | 0.994646i | \(0.467047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.7446 | −0.888709 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 55.9230 | 2.95976 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.5831 | 0.875224 | 0.437612 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437612 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.1168 | 0.950888 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.4294 | 1.12167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.05401 | 0.211618 | 0.105809 | − | 0.994386i | \(-0.466257\pi\) | ||||
0.105809 | + | 0.994386i | \(0.466257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3505 | 1.05655 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9436 | −0.773753 | −0.386876 | − | 0.922132i | \(-0.626446\pi\) | ||||
−0.386876 | + | 0.922132i | \(0.626446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.8820 | −1.59474 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.6060 | −0.803748 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.3505 | 1.86720 | 0.933601 | − | 0.358315i | \(-0.116649\pi\) | ||||
0.933601 | + | 0.358315i | \(0.116649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −41.3841 | −2.12017 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.2434 | −1.28988 | −0.644938 | − | 0.764235i | \(-0.723117\pi\) | ||||
−0.644938 | + | 0.764235i | \(0.723117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.8614 | −1.01223 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 30.3723 | 1.54391 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.3036 | −1.23224 | −0.616121 | − | 0.787651i | \(-0.711297\pi\) | ||||
−0.616121 | + | 0.787651i | \(0.711297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.96143 | −0.200338 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7446 | 0.743765 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.744563 | 0.0374630 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.644810 | 0.0323621 | 0.0161810 | − | 0.999869i | \(-0.494849\pi\) | ||||
0.0161810 | + | 0.999869i | \(0.494849\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.1846 | 0.559930 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.7228 | 1.78391 | 0.891956 | − | 0.452122i | \(-0.149333\pi\) | ||||
0.891956 | + | 0.452122i | \(0.149333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.2337 | 1.00791 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −90.8213 | −4.51294 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.9538 | 1.18734 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.8614 | 0.831712 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.55134 | 0.223957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1947 | 0.991319 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.2337 | −0.599086 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.233688 | 0.0114164 | 0.00570820 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570820 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3971 | 0.994093 | 0.497046 | − | 0.867724i | \(-0.334418\pi\) | ||||
0.497046 | + | 0.867724i | \(0.334418\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.39853 | −0.262486 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.86141 | 0.332827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.0951 | 2.32748 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 46.7277 | 2.25603 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.7793 | −1.04907 | −0.524535 | − | 0.851389i | \(-0.675761\pi\) | ||||
−0.524535 | + | 0.851389i | \(0.675761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.48913 | −0.0715628 | −0.0357814 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357814 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.7446 | −1.09052 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.792287 | −0.0379002 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.92820 | 0.330665 | 0.165333 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165333 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.4891 | 1.59472 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.3505 | 1.96462 | 0.982312 | − | 0.187254i | \(-0.0599587\pi\) | ||||
0.982312 | + | 0.187254i | \(0.0599587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −39.0998 | −1.85351 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.8457 | 0.749478 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.4891 | 1.76922 | 0.884611 | − | 0.466330i | \(-0.154424\pi\) | ||||
0.884611 | + | 0.466330i | \(0.154424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 53.0660 | 2.49326 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 48.9022 | 2.29257 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −90.5842 | −4.22811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.86797 | 0.366448 | 0.183224 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183224 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.5268 | 1.46517 | 0.732587 | − | 0.680674i | \(-0.238313\pi\) | ||||
0.732587 | + | 0.680674i | \(0.238313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.4891 | 1.36753 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8832 | 0.503612 | 0.251806 | − | 0.967778i | \(-0.418975\pi\) | ||||
0.251806 | + | 0.967778i | \(0.418975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.71516 | −0.402429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.7586 | 2.89176 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.60597 | −0.395703 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.37228 | 0.0629646 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −51.3716 | −2.35214 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4179 | 1.25275 | 0.626377 | − | 0.779520i | \(-0.284537\pi\) | ||||
0.626377 | + | 0.779520i | \(0.284537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.9783 | −2.68918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.86141 | −0.403208 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.92820 | 0.314594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.6641 | −1.02701 | −0.513505 | − | 0.858087i | \(-0.671653\pi\) | ||||
−0.513505 | + | 0.858087i | \(0.671653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.2337 | −1.63854 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9783 | 1.39803 | 0.699014 | − | 0.715108i | \(-0.253622\pi\) | ||||
0.699014 | + | 0.715108i | \(0.253622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.3591 | −0.601662 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 50.1369 | 2.25349 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.0000 | −0.986835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.37228 | −0.195730 | −0.0978651 | − | 0.995200i | \(-0.531201\pi\) | ||||
−0.0978651 | + | 0.995200i | \(0.531201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.3745 | 0.954943 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.4795 | 0.511848 | 0.255924 | − | 0.966697i | \(-0.417620\pi\) | ||||
0.255924 | + | 0.966697i | \(0.417620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.9783 | −1.55651 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −71.2119 | −3.16263 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.8102 | −1.67591 | −0.837953 | − | 0.545742i | \(-0.816248\pi\) | ||||
−0.837953 | + | 0.545742i | \(0.816248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1552 | 1.24551 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.1168 | −0.799878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.2337 | 1.33226 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.52967 | 0.0672749 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −51.0767 | −2.24202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.76631 | 0.252627 | 0.126313 | − | 0.991990i | \(-0.459686\pi\) | ||||
0.126313 | + | 0.991990i | \(0.459686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.3723 | −1.10945 | −0.554726 | − | 0.832033i | \(-0.687177\pi\) | ||||
−0.554726 | + | 0.832033i | \(0.687177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.3484 | 0.669859 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3205 | 0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3723 | −0.972708 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.4891 | −0.498586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.7562 | −1.45941 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −77.4891 | −3.34390 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.48913 | −0.408726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6039 | −1.01481 | −0.507405 | − | 0.861707i | \(-0.669395\pi\) | ||||
−0.507405 | + | 0.861707i | \(0.669395\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.7128 | 1.18927 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.51087 | −0.107357 | −0.0536786 | − | 0.998558i | \(-0.517095\pi\) | ||||
−0.0536786 | + | 0.998558i | \(0.517095\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −121.408 | −5.18158 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.67181 | −0.113823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.978251 | 0.0415994 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −85.9565 | −3.64865 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.1885 | 1.06727 | 0.533635 | − | 0.845715i | \(-0.320826\pi\) | ||||
0.533635 | + | 0.845715i | \(0.320826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.1894 | 0.896215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | 1.68880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.4891 | −0.568499 | −0.284249 | − | 0.958750i | \(-0.591744\pi\) | ||||
−0.284249 | + | 0.958750i | \(0.591744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.2203 | 1.56587 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −119.326 | −5.01124 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9783 | 1.13099 | 0.565494 | − | 0.824753i | \(-0.308686\pi\) | ||||
0.565494 | + | 0.824753i | \(0.308686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.9783 | 1.79858 | 0.899292 | − | 0.437349i | \(-0.144083\pi\) | ||||
0.899292 | + | 0.437349i | \(0.144083\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.8612 | 0.996815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.08724 | −0.0453411 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.4674 | 1.39327 | 0.696633 | − | 0.717428i | \(-0.254681\pi\) | ||||
0.696633 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.9783 | −0.456241 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.5330 | 1.10077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5561 | 0.602853 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −123.446 | −5.10385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.8614 | −1.31506 | −0.657530 | − | 0.753428i | \(-0.728399\pi\) | ||||
−0.657530 | + | 0.753428i | \(0.728399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.46410 | 0.142736 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.3745 | −0.879230 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.97825 | 0.204432 | 0.102216 | − | 0.994762i | \(-0.467407\pi\) | ||||
0.102216 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 41.8614 | 1.71615 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.497333 | −0.0203545 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.6897 | 1.62168 | 0.810838 | − | 0.585270i | \(-0.199012\pi\) | ||||
0.810838 | + | 0.585270i | \(0.199012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.4674 | 0.916463 | 0.458232 | − | 0.888833i | \(-0.348483\pi\) | ||||
0.458232 | + | 0.888833i | \(0.348483\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.0000 | 0.895909 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.5615 | 0.551351 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.8048 | −1.57504 | −0.787520 | − | 0.616289i | \(-0.788635\pi\) | ||||
−0.787520 | + | 0.616289i | \(0.788635\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.8832 | −1.21093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.76631 | −0.152369 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.5552 | 0.749439 | 0.374719 | − | 0.927138i | \(-0.377739\pi\) | ||||
0.374719 | + | 0.927138i | \(0.377739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.8397 | 1.64414 | 0.822071 | − | 0.569384i | \(-0.192818\pi\) | ||||
0.822071 | + | 0.569384i | \(0.192818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.2337 | −0.652487 | −0.326244 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326244 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.3537 | 0.575996 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.3716 | −2.05816 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.9783 | −1.19913 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.4868 | −2.01304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8651 | 1.50738 | 0.753692 | − | 0.657227i | \(-0.228271\pi\) | ||||
0.753692 | + | 0.657227i | \(0.228271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.86141 | 0.352209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.9783 | −1.22933 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.3639 | 0.925709 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 55.5354 | 2.19695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.9783 | −0.433615 | −0.216807 | − | 0.976214i | \(-0.569564\pi\) | ||||
−0.216807 | + | 0.976214i | \(0.569564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.3723 | 1.43438 | 0.717191 | − | 0.696876i | \(-0.245427\pi\) | ||||
0.717191 | + | 0.696876i | \(0.245427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.8820 | 1.21598 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.5831 | 0.651950 | 0.325975 | − | 0.945378i | \(-0.394307\pi\) | ||||
0.325975 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.25544 | 0.127787 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.7446 | 1.51852 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.3956 | −1.38514 | −0.692569 | − | 0.721352i | \(-0.743521\pi\) | ||||
−0.692569 | + | 0.721352i | \(0.743521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.0371 | 0.431256 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −71.0733 | −2.77284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.8614 | −1.82546 | −0.912731 | − | 0.408562i | \(-0.866030\pi\) | ||||
−0.912731 | + | 0.408562i | \(0.866030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5947 | −0.412085 | −0.206043 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206043 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −98.4868 | −3.82491 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.37228 | 0.324663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.11684 | 0.0819645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.3639 | 0.903299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.4010 | 1.32803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.7446 | 0.645455 | 0.322728 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322728 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.8614 | −0.956916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.84096 | 0.224486 | 0.112243 | − | 0.993681i | \(-0.464196\pi\) | ||||
0.112243 | + | 0.993681i | \(0.464196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.10268 | 0.349329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.6060 | 1.82426 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6217 | 0.482250 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.5639 | 1.62391 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35.8397 | −1.36538 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.8614 | 0.679480 | 0.339740 | − | 0.940519i | \(-0.389661\pi\) | ||||
0.339740 | + | 0.940519i | \(0.389661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 65.8728 | 2.50230 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.15759 | −0.347367 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.7011 | −1.38816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7128 | 1.04670 | 0.523349 | − | 0.852118i | \(-0.324682\pi\) | ||||
0.523349 | + | 0.852118i | \(0.324682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0974 | −0.380829 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.48913 | −0.206732 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.9565 | −1.72837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.7330 | 1.71754 | 0.858770 | − | 0.512361i | \(-0.171229\pi\) | ||||
0.858770 | + | 0.512361i | \(0.171229\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.46943 | −0.0926110 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.74456 | −0.102785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.9783 | 1.30811 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 58.9070 | 2.19992 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5369 | −1.51177 | −0.755885 | − | 0.654704i | \(-0.772793\pi\) | ||||
−0.755885 | + | 0.654704i | \(0.772793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.7228 | 1.47935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.9783 | −1.00333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.66648 | −0.136170 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0039 | 0.519375 | 0.259688 | − | 0.965693i | \(-0.416380\pi\) | ||||
0.259688 | + | 0.965693i | \(0.416380\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 117.935 | 4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.1386 | 0.670880 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1894 | −0.782647 | −0.391324 | − | 0.920253i | \(-0.627983\pi\) | ||||
−0.391324 | + | 0.920253i | \(0.627983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.0511 | 1.25599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.23369 | −0.229621 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6060 | −0.463718 | −0.231859 | − | 0.972749i | \(-0.574481\pi\) | ||||
−0.231859 | + | 0.972749i | \(0.574481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.6974 | −0.723601 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.63325 | 0.243350 | 0.121675 | − | 0.992570i | \(-0.461173\pi\) | ||||
0.121675 | + | 0.992570i | \(0.461173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.8614 | 0.434568 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −66.9783 | −2.45061 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.3508 | −1.62054 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.50744 | −0.346932 | −0.173466 | − | 0.984840i | \(-0.555497\pi\) | ||||
−0.173466 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −60.2337 | −2.19504 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.7228 | 1.44566 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.8502 | −0.685121 | −0.342561 | − | 0.939496i | \(-0.611294\pi\) | ||||
−0.342561 | + | 0.939496i | \(0.611294\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.33830 | −0.230066 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0000 | 0.398750 | 0.199375 | − | 0.979923i | \(-0.436109\pi\) | ||||
0.199375 | + | 0.979923i | \(0.436109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.1386 | −0.475649 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −105.672 | −3.82059 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.01544 | −0.289421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.4674 | 1.35111 | 0.675554 | − | 0.737310i | \(-0.263904\pi\) | ||||
0.675554 | + | 0.737310i | \(0.263904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.7446 | 1.97158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.1561 | 0.868836 | 0.434418 | − | 0.900711i | \(-0.356954\pi\) | ||||
0.434418 | + | 0.900711i | \(0.356954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.75372 | 0.170759 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −112.935 | −4.05151 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7359 | −0.563076 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 48.4048 | 1.72985 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.9783 | 1.67673 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.6060 | −0.698877 | −0.349439 | − | 0.936959i | \(-0.613628\pi\) | ||||
−0.349439 | + | 0.936959i | \(0.613628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 63.9384 | 2.27627 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.9022 | 1.73876 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −84.7011 | −3.00782 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −52.2337 | −1.85254 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.6487 | −0.518883 | −0.259442 | − | 0.965759i | \(-0.583539\pi\) | ||||
−0.259442 | + | 0.965759i | \(0.583539\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.22405 | −0.114059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 129.679 | 4.58199 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1386 | 0.710676 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.63325 | −0.233791 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.33830 | −0.223119 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.9783 | 1.33524 | 0.667622 | − | 0.744500i | \(-0.267312\pi\) | ||||
0.667622 | + | 0.744500i | \(0.267312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.8614 | 1.01346 | 0.506731 | − | 0.862105i | \(-0.330854\pi\) | ||||
0.506731 | + | 0.862105i | \(0.330854\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.01544 | −0.281114 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.1229 | −0.950074 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.62772 | 0.126918 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −162.190 | −5.66738 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0680 | −0.944680 | −0.472340 | − | 0.881416i | \(-0.656591\pi\) | ||||
−0.472340 | + | 0.881416i | \(0.656591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.37063 | −0.256924 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.9783 | 0.382214 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.3505 | 1.40313 | 0.701563 | − | 0.712608i | \(-0.252486\pi\) | ||||
0.701563 | + | 0.712608i | \(0.252486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.26172 | 0.113284 | 0.0566421 | − | 0.998395i | \(-0.481961\pi\) | ||||
0.0566421 | + | 0.998395i | \(0.481961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −55.2405 | −1.91627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0000 | 0.692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.7586 | −2.16925 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.80240 | 0.338416 | 0.169208 | − | 0.985580i | \(-0.445879\pi\) | ||||
0.169208 | + | 0.985580i | \(0.445879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.8614 | −0.753842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.0217 | 0.724028 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.3060 | −1.83378 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.8178 | 0.612228 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 59.4456 | 2.04017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3894 | 1.38291 | 0.691453 | − | 0.722421i | \(-0.256971\pi\) | ||||
0.691453 | + | 0.722421i | \(0.256971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.1345 | −0.722783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2337 | −0.759488 | −0.379744 | − | 0.925092i | \(-0.623988\pi\) | ||||
−0.379744 | + | 0.925092i | \(0.623988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.60597 | −0.293632 | −0.146816 | − | 0.989164i | \(-0.546903\pi\) | ||||
−0.146816 | + | 0.989164i | \(0.546903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.76439 | 0.0941009 | 0.0470504 | − | 0.998893i | \(-0.485018\pi\) | ||||
0.0470504 | + | 0.998893i | \(0.485018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.2337 | −1.29998 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.9783 | −0.916229 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.699713 | 0.0237361 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3484 | 0.520061 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.9783 | −0.777696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.3723 | −1.02677 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.38219 | −0.0466734 | −0.0233367 | − | 0.999728i | \(-0.507429\pi\) | ||||
−0.0233367 | + | 0.999728i | \(0.507429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.3431 | 0.551238 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.37228 | −0.147306 | −0.0736530 | − | 0.997284i | \(-0.523466\pi\) | ||||
−0.0736530 | + | 0.997284i | \(0.523466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.8832 | −0.635469 | −0.317734 | − | 0.948180i | \(-0.602922\pi\) | ||||
−0.317734 | + | 0.948180i | \(0.602922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.6819 | −0.392684 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0333 | −1.51207 | −0.756035 | − | 0.654531i | \(-0.772866\pi\) | ||||
−0.756035 | + | 0.654531i | \(0.772866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.7011 | −1.36507 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −85.3505 | −2.85935 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.644810 | −0.0215777 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.0049 | −1.93889 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.6060 | 0.521068 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.25544 | −0.308686 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.6796 | −1.02209 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.5746 | 1.35024 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7446 | 0.689573 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.8614 | −1.55601 | −0.778004 | − | 0.628260i | \(-0.783768\pi\) | ||||
−0.778004 | + | 0.628260i | \(0.783768\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 116.010 | 3.84780 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.6126 | 1.57747 | 0.788737 | − | 0.614730i | \(-0.210735\pi\) | ||||
0.788737 | + | 0.614730i | \(0.210735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.9783 | 0.628088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −123.446 | −4.08099 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5012 | 0.478872 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.71516 | 0.287486 | 0.143743 | − | 0.989615i | \(-0.454086\pi\) | ||||
0.143743 | + | 0.989615i | \(0.454086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.4456 | 1.69519 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.7446 | 1.27529 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8564 | −0.455596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −100.274 | −3.29342 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8832 | −0.914817 | −0.457408 | − | 0.889257i | \(-0.651222\pi\) | ||||
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 78.2921 | 2.56317 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9422 | 0.979215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.9783 | 0.717998 | 0.358999 | − | 0.933338i | \(-0.383118\pi\) | ||||
0.358999 | + | 0.933338i | \(0.383118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.0951 | 0.427342 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8896 | 0.354992 | 0.177496 | − | 0.984122i | \(-0.443200\pi\) | ||||
0.177496 | + | 0.984122i | \(0.443200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −151.679 | −4.93413 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.2119 | −1.40420 | −0.702100 | − | 0.712079i | \(-0.747754\pi\) | ||||
−0.702100 | + | 0.712079i | \(0.747754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.5847 | −1.60959 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.7634 | −2.35951 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.2337 | −0.849793 | −0.424896 | − | 0.905242i | \(-0.639689\pi\) | ||||
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.8614 | 0.577982 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.3745 | −0.690940 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.5831 | 0.535497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 111.957 | 3.60775 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.21782 | −0.264541 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.1307 | 1.77288 | 0.886441 | − | 0.462841i | \(-0.153170\pi\) | ||||
0.886441 | + | 0.462841i | \(0.153170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.8614 | −0.541666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0318 | −0.385721 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.0303 | −0.865663 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.4891 | 0.879455 | 0.439728 | − | 0.898131i | \(-0.355075\pi\) | ||||
0.439728 | + | 0.898131i | \(0.355075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.7446 | −1.17436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1662 | 1.05892 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.6612 | 1.67963 | 0.839816 | − | 0.542871i | \(-0.182663\pi\) | ||||
0.839816 | + | 0.542871i | \(0.182663\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.21194 | −0.229559 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.87419 | −0.0913941 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.92287 | 0.251678 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.6277 | −1.16235 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.372281 | −0.0118021 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.8164 | 1.03931 | 0.519653 | − | 0.854378i | \(-0.326061\pi\) | ||||
0.519653 | + | 0.854378i | \(0.326061\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 182.932 | 5.78772 |
(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 | 4864.2.a.bi.1.1 | 4 | ||
4.3 | odd | 2 | 4864.2.a.bl.1.3 | 4 | |||
8.3 | odd | 2 | inner | 4864.2.a.bi.1.2 | 4 | ||
8.5 | even | 2 | 4864.2.a.bl.1.4 | 4 | |||
16.3 | odd | 4 | 1216.2.c.h.609.8 | yes | 8 | ||
16.5 | even | 4 | 1216.2.c.h.609.7 | yes | 8 | ||
16.11 | odd | 4 | 1216.2.c.h.609.1 | ✓ | 8 | ||
16.13 | even | 4 | 1216.2.c.h.609.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.h.609.1 | ✓ | 8 | 16.11 | odd | 4 | ||
1216.2.c.h.609.2 | yes | 8 | 16.13 | even | 4 | ||
1216.2.c.h.609.7 | yes | 8 | 16.5 | even | 4 | ||
1216.2.c.h.609.8 | yes | 8 | 16.3 | odd | 4 | ||
4864.2.a.bi.1.1 | 4 | 1.1 | even | 1 | trivial | ||
4864.2.a.bi.1.2 | 4 | 8.3 | odd | 2 | inner | ||
4864.2.a.bl.1.3 | 4 | 4.3 | odd | 2 | |||
4864.2.a.bl.1.4 | 4 | 8.5 | even | 2 |