Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3732.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77576\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.48059 | 0.559610 | 0.279805 | − | 0.960057i | \(-0.409730\pi\) | ||||
0.279805 | + | 0.960057i | \(0.409730\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.77576 | 1.74146 | 0.870728 | − | 0.491765i | \(-0.163648\pi\) | ||||
0.870728 | + | 0.491765i | \(0.163648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29517 | 0.526548 | 0.263274 | − | 0.964721i | \(-0.415198\pi\) | ||||
0.263274 | + | 0.964721i | \(0.415198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.48059 | 0.323091 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.29517 | −0.895605 | −0.447802 | − | 0.894133i | \(-0.647793\pi\) | ||||
−0.447802 | + | 0.894133i | \(0.647793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.55152 | 1.21659 | 0.608293 | − | 0.793713i | \(-0.291855\pi\) | ||||
0.608293 | + | 0.793713i | \(0.291855\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.77576 | 1.03736 | 0.518678 | − | 0.854969i | \(-0.326424\pi\) | ||||
0.518678 | + | 0.854969i | \(0.326424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.77576 | 1.00543 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.25635 | 0.535340 | 0.267670 | − | 0.963511i | \(-0.413746\pi\) | ||||
0.267670 | + | 0.963511i | \(0.413746\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.25635 | 0.820903 | 0.410452 | − | 0.911882i | \(-0.365371\pi\) | ||||
0.410452 | + | 0.911882i | \(0.365371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.25635 | 0.801585 | 0.400793 | − | 0.916169i | \(-0.368735\pi\) | ||||
0.400793 | + | 0.916169i | \(0.368735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.03210 | −0.734008 | −0.367004 | − | 0.930219i | \(-0.619616\pi\) | ||||
−0.367004 | + | 0.930219i | \(0.619616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.80786 | −0.686837 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.29517 | −0.452626 | −0.226313 | − | 0.974055i | \(-0.572667\pi\) | ||||
−0.226313 | + | 0.974055i | \(0.572667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.29517 | 0.304003 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.03210 | −0.655124 | −0.327562 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327562 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55152 | −0.582762 | −0.291381 | − | 0.956607i | \(-0.594115\pi\) | ||||
−0.291381 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.48059 | 0.186537 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.22424 | 0.516073 | 0.258037 | − | 0.966135i | \(-0.416924\pi\) | ||||
0.258037 | + | 0.966135i | \(0.416924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.29517 | −0.517078 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8079 | −1.52001 | −0.760007 | − | 0.649915i | \(-0.774804\pi\) | ||||
−0.760007 | + | 0.649915i | \(0.774804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8079 | −1.49905 | −0.749523 | − | 0.661978i | \(-0.769717\pi\) | ||||
−0.749523 | + | 0.661978i | \(0.769717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.55152 | 0.974536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.25635 | −0.141350 | −0.0706749 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706749 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0709 | −1.32496 | −0.662478 | − | 0.749081i | \(-0.730495\pi\) | ||||
−0.662478 | + | 0.749081i | \(0.730495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.55152 | 0.702396 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.5515 | 1.43646 | 0.718229 | − | 0.695807i | \(-0.244953\pi\) | ||||
0.718229 | + | 0.695807i | \(0.244953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.48059 | −0.155208 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.77576 | 0.598918 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.96118 | 0.706800 | 0.353400 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353400 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.77576 | 0.580485 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.33399 | −0.232241 | −0.116121 | − | 0.993235i | \(-0.537046\pi\) | ||||
−0.116121 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.25635 | 0.320857 | 0.160429 | − | 0.987047i | \(-0.448712\pi\) | ||||
0.160429 | + | 0.987047i | \(0.448712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.1419 | 1.94719 | 0.973593 | − | 0.228289i | \(-0.0733132\pi\) | ||||
0.973593 | + | 0.228289i | \(0.0733132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.8079 | 1.80147 | 0.900733 | − | 0.434373i | \(-0.143030\pi\) | ||||
0.900733 | + | 0.434373i | \(0.143030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.25635 | 0.309079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.55152 | 0.710387 | 0.355193 | − | 0.934793i | \(-0.384415\pi\) | ||||
0.355193 | + | 0.934793i | \(0.384415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.44176 | 0.407176 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.3594 | 2.03267 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.25635 | 0.473949 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.80786 | −0.249157 | −0.124579 | − | 0.992210i | \(-0.539758\pi\) | ||||
−0.124579 | + | 0.992210i | \(0.539758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.25635 | 0.462795 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.29517 | 0.200530 | 0.100265 | − | 0.994961i | \(-0.468031\pi\) | ||||
0.100265 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.39820 | 0.294661 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.1419 | −1.20822 | −0.604110 | − | 0.796901i | \(-0.706471\pi\) | ||||
−0.604110 | + | 0.796901i | \(0.706471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.92235 | −0.671965 | −0.335982 | − | 0.941868i | \(-0.609068\pi\) | ||||
−0.335982 | + | 0.941868i | \(0.609068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.03210 | −0.423779 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.77576 | −0.482993 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.80786 | −0.396546 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0642 | −1.47988 | −0.739939 | − | 0.672674i | \(-0.765146\pi\) | ||||
−0.739939 | + | 0.672674i | \(0.765146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.0321 | −1.87433 | −0.937163 | − | 0.348892i | \(-0.886558\pi\) | ||||
−0.937163 | + | 0.348892i | \(0.886558\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.29517 | −0.262983 | −0.131492 | − | 0.991317i | \(-0.541977\pi\) | ||||
−0.131492 | + | 0.991317i | \(0.541977\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.29517 | −0.261324 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.35938 | −0.501189 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.21752 | −0.643646 | −0.321823 | − | 0.946800i | \(-0.604296\pi\) | ||||
−0.321823 | + | 0.946800i | \(0.604296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.743655 | 0.0575457 | 0.0287729 | − | 0.999586i | \(-0.490840\pi\) | ||||
0.0287729 | + | 0.999586i | \(0.490840\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.29517 | 0.175516 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.25635 | 0.323604 | 0.161802 | − | 0.986823i | \(-0.448269\pi\) | ||||
0.161802 | + | 0.986823i | \(0.448269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.03210 | −0.378236 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.76904 | 0.730172 | 0.365086 | − | 0.930974i | \(-0.381040\pi\) | ||||
0.365086 | + | 0.930974i | \(0.381040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.8467 | 1.40086 | 0.700432 | − | 0.713720i | \(-0.252991\pi\) | ||||
0.700432 | + | 0.713720i | \(0.252991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.55152 | −0.336458 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.3273 | 1.26710 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.48059 | 0.107697 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.2175 | −1.31133 | −0.655663 | − | 0.755054i | \(-0.727611\pi\) | ||||
−0.655663 | + | 0.755054i | \(0.727611\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.84669 | −0.701547 | −0.350774 | − | 0.936460i | \(-0.614081\pi\) | ||||
−0.350774 | + | 0.936460i | \(0.614081\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.59034 | −0.467177 | −0.233588 | − | 0.972336i | \(-0.575047\pi\) | ||||
−0.233588 | + | 0.972336i | \(0.575047\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.22424 | 0.297955 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.70009 | 0.680813 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.29517 | −0.298535 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2563 | 0.916961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.80786 | −0.193301 | −0.0966505 | − | 0.995318i | \(-0.530813\pi\) | ||||
−0.0966505 | + | 0.995318i | \(0.530813\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.8079 | −0.877580 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.55152 | 0.580515 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.8079 | −0.865475 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8855 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.7369 | 1.24361 | 0.621807 | − | 0.783171i | \(-0.286399\pi\) | ||||
0.621807 | + | 0.783171i | \(0.286399\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.55152 | 0.562648 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.448485 | 0.0293812 | 0.0146906 | − | 0.999892i | \(-0.495324\pi\) | ||||
0.0146906 | + | 0.999892i | \(0.495324\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.25635 | −0.0816084 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.9545 | 1.61417 | 0.807085 | − | 0.590436i | \(-0.201044\pi\) | ||||
0.807085 | + | 0.590436i | \(0.201044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.78248 | 0.372482 | 0.186241 | − | 0.982504i | \(-0.440369\pi\) | ||||
0.186241 | + | 0.982504i | \(0.440369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.29517 | −0.146038 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0709 | −0.764964 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.33399 | 0.589157 | 0.294578 | − | 0.955627i | \(-0.404821\pi\) | ||||
0.294578 | + | 0.955627i | \(0.404821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8079 | −1.55966 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.192140 | −0.0119853 | −0.00599267 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599267 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.82130 | 0.299581 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.55152 | 0.405529 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.25635 | −0.447445 | −0.223723 | − | 0.974653i | \(-0.571821\pi\) | ||||
−0.223723 | + | 0.974653i | \(0.571821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.5515 | 0.829339 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9224 | −0.787890 | −0.393945 | − | 0.919134i | \(-0.628890\pi\) | ||||
−0.393945 | + | 0.919134i | \(0.628890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.6224 | −1.43496 | −0.717481 | − | 0.696578i | \(-0.754705\pi\) | ||||
−0.717481 | + | 0.696578i | \(0.754705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.48059 | −0.0896092 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.96118 | −0.418256 | −0.209128 | − | 0.977888i | \(-0.567063\pi\) | ||||
−0.209128 | + | 0.977888i | \(0.567063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.77576 | 0.345786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4097 | 0.799953 | 0.399977 | − | 0.916525i | \(-0.369018\pi\) | ||||
0.399977 | + | 0.916525i | \(0.369018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.40966 | −0.559346 | −0.279673 | − | 0.960095i | \(-0.590226\pi\) | ||||
−0.279673 | + | 0.960095i | \(0.590226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.78248 | 0.459385 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.96118 | 0.408071 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1030 | −0.999170 | −0.499585 | − | 0.866265i | \(-0.666514\pi\) | ||||
−0.499585 | + | 0.866265i | \(0.666514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.77576 | 0.335143 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.29517 | 0.248396 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.78248 | 0.448575 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.33399 | −0.134084 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3594 | 1.04782 | 0.523912 | − | 0.851772i | \(-0.324472\pi\) | ||||
0.523912 | + | 0.851772i | \(0.324472\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.25635 | 0.185247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.6157 | 1.56594 | 0.782972 | − | 0.622057i | \(-0.213703\pi\) | ||||
0.782972 | + | 0.622057i | \(0.213703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2952 | −1.20367 | −0.601837 | − | 0.798619i | \(-0.705564\pi\) | ||||
−0.601837 | + | 0.798619i | \(0.705564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.372819 | 0.0209396 | 0.0104698 | − | 0.999945i | \(-0.496667\pi\) | ||||
0.0104698 | + | 0.999945i | \(0.496667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.8400 | 2.11863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.1419 | 1.12421 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.88551 | 0.383120 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.8079 | 1.04008 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.45047 | −0.410758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.39820 | 0.516572 | 0.258286 | − | 0.966069i | \(-0.416842\pi\) | ||||
0.258286 | + | 0.966069i | \(0.416842\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.25635 | 0.178447 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.58836 | −0.304417 | −0.152209 | − | 0.988348i | \(-0.548639\pi\) | ||||
−0.152209 | + | 0.988348i | \(0.548639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.55152 | 0.410142 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.3594 | 1.80651 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4826 | −0.943970 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.89697 | 0.370249 | 0.185124 | − | 0.982715i | \(-0.440731\pi\) | ||||
0.185124 | + | 0.982715i | \(0.440731\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3340 | 0.713752 | 0.356876 | − | 0.934152i | \(-0.383842\pi\) | ||||
0.356876 | + | 0.934152i | \(0.383842\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.3594 | 1.93521 | 0.967607 | − | 0.252461i | \(-0.0812398\pi\) | ||||
0.967607 | + | 0.252461i | \(0.0812398\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.44176 | 0.235083 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.03210 | −0.160028 | −0.0800141 | − | 0.996794i | \(-0.525497\pi\) | ||||
−0.0800141 | + | 0.996794i | \(0.525497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7322 | −0.722747 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.3594 | 1.17356 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1807 | 1.10562 | 0.552811 | − | 0.833307i | \(-0.313555\pi\) | ||||
0.552811 | + | 0.833307i | \(0.313555\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.25635 | 0.273634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.87879 | −0.253294 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.1787 | −1.14837 | −0.574185 | − | 0.818726i | \(-0.694681\pi\) | ||||
−0.574185 | + | 0.818726i | \(0.694681\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.55152 | −0.337420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8400 | −0.916377 | −0.458189 | − | 0.888855i | \(-0.651502\pi\) | ||||
−0.458189 | + | 0.888855i | \(0.651502\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.80786 | −0.143851 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.2175 | −1.03307 | −0.516534 | − | 0.856267i | \(-0.672778\pi\) | ||||
−0.516534 | + | 0.856267i | \(0.672778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.25635 | 0.267195 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6545 | −0.945823 | −0.472911 | − | 0.881110i | \(-0.656797\pi\) | ||||
−0.472911 | + | 0.881110i | \(0.656797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8855 | −0.651648 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.29517 | 0.115776 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.6292 | −1.08554 | −0.542768 | − | 0.839882i | \(-0.682624\pi\) | ||||
−0.542768 | + | 0.839882i | \(0.682624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.39820 | 0.170123 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.0274 | 1.64931 | 0.824654 | − | 0.565638i | \(-0.191370\pi\) | ||||
0.824654 | + | 0.565638i | \(0.191370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.77576 | −0.287711 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8079 | 0.932271 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.0274 | 1.53420 | 0.767102 | − | 0.641525i | \(-0.221698\pi\) | ||||
0.767102 | + | 0.641525i | \(0.221698\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.1419 | −0.697566 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.45047 | −0.366614 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.92235 | −0.387959 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7437 | 0.817981 | 0.408991 | − | 0.912539i | \(-0.365881\pi\) | ||||
0.408991 | + | 0.912539i | \(0.365881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.6934 | 1.15474 | 0.577372 | − | 0.816481i | \(-0.304078\pi\) | ||||
0.577372 | + | 0.816481i | \(0.304078\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.03210 | −0.244669 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.73892 | −0.326119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.77576 | −0.278856 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.8855 | 1.48770 | 0.743851 | − | 0.668345i | \(-0.232997\pi\) | ||||
0.743851 | + | 0.668345i | \(0.232997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1419 | −0.967956 | −0.483978 | − | 0.875080i | \(-0.660808\pi\) | ||||
−0.483978 | + | 0.875080i | \(0.660808\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.85814 | −0.471579 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.2429 | 1.68205 | 0.841026 | − | 0.540995i | \(-0.181952\pi\) | ||||
0.841026 | + | 0.540995i | \(0.181952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.80786 | −0.228946 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.8467 | −0.657876 | −0.328938 | − | 0.944352i | \(-0.606691\pi\) | ||||
−0.328938 | + | 0.944352i | \(0.606691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.0642 | −0.854408 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4350 | −1.15316 | −0.576580 | − | 0.817040i | \(-0.695613\pi\) | ||||
−0.576580 | + | 0.817040i | \(0.695613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.3594 | 1.42957 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.0321 | −1.08214 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.4370 | 0.675336 | 0.337668 | − | 0.941265i | \(-0.390362\pi\) | ||||
0.337668 | + | 0.941265i | \(0.390362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | 0.140028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.6157 | 1.84509 | 0.922544 | − | 0.385892i | \(-0.126106\pi\) | ||||
0.922544 | + | 0.385892i | \(0.126106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.9176 | −1.57629 | −0.788143 | − | 0.615493i | \(-0.788957\pi\) | ||||
−0.788143 | + | 0.615493i | \(0.788957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.4739 | 1.27134 | 0.635669 | − | 0.771961i | \(-0.280724\pi\) | ||||
0.635669 | + | 0.771961i | \(0.280724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.25436 | 0.288800 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.29517 | −0.151833 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.3594 | 1.39593 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.29517 | −0.150875 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.26307 | 0.0577110 | 0.0288555 | − | 0.999584i | \(-0.490814\pi\) | ||||
0.0288555 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.25635 | −0.148477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.35938 | −0.289362 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4303 | −1.01641 | −0.508207 | − | 0.861235i | \(-0.669692\pi\) | ||||
−0.508207 | + | 0.861235i | \(0.669692\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.21752 | −0.371609 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0000 | 0.992846 | 0.496423 | − | 0.868081i | \(-0.334646\pi\) | ||||
0.496423 | + | 0.868081i | \(0.334646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.6545 | 0.885196 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.9632 | −0.850614 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.70009 | −0.0761066 | −0.0380533 | − | 0.999276i | \(-0.512116\pi\) | ||||
−0.0380533 | + | 0.999276i | \(0.512116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.743655 | 0.0332240 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.19214 | 0.320682 | 0.160341 | − | 0.987062i | \(-0.448741\pi\) | ||||
0.160341 | + | 0.987062i | \(0.448741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.1399 | −0.892684 | −0.446342 | − | 0.894862i | \(-0.647274\pi\) | ||||
−0.446342 | + | 0.894862i | \(0.647274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.9632 | −0.838881 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.29517 | 0.101334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.0642 | −1.27824 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.25635 | 0.186833 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.1030 | −1.27503 | −0.637513 | − | 0.770439i | \(-0.720037\pi\) | ||||
−0.637513 | + | 0.770439i | \(0.720037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.1419 | −1.58037 | −0.790186 | − | 0.612866i | \(-0.790016\pi\) | ||||
−0.790186 | + | 0.612866i | \(0.790016\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3273 | 0.754788 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.55152 | −0.197892 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.03210 | −0.218375 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.25635 | −0.227678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.76904 | 0.421565 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.7690 | −1.19610 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.80786 | 0.378679 | 0.189340 | − | 0.981912i | \(-0.439365\pi\) | ||||
0.189340 | + | 0.981912i | \(0.439365\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.8467 | 0.808789 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.07567 | 0.0887490 | 0.0443745 | − | 0.999015i | \(-0.485871\pi\) | ||||
0.0443745 | + | 0.999015i | \(0.485871\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.55152 | −0.194254 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.0368 | 0.640591 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.86013 | −0.0791007 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.2175 | −0.602416 | −0.301208 | − | 0.953559i | \(-0.597390\pi\) | ||||
−0.301208 | + | 0.953559i | \(0.597390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.25635 | −0.222320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.3273 | 0.731558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.9109 | 1.59775 | 0.798877 | − | 0.601495i | \(-0.205428\pi\) | ||||
0.798877 | + | 0.601495i | \(0.205428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.48059 | 0.0621788 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.2563 | −1.43610 | −0.718050 | − | 0.695991i | \(-0.754965\pi\) | ||||
−0.718050 | + | 0.695991i | \(0.754965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37282 | −0.266694 | −0.133347 | − | 0.991069i | \(-0.542573\pi\) | ||||
−0.133347 | + | 0.991069i | \(0.542573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1672 | −1.71381 | −0.856907 | − | 0.515471i | \(-0.827617\pi\) | ||||
−0.856907 | + | 0.515471i | \(0.827617\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.2175 | −0.757094 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.8721 | −0.741458 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.0321 | −0.788229 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.6593 | 1.01780 | 0.508899 | − | 0.860826i | \(-0.330053\pi\) | ||||
0.508899 | + | 0.860826i | \(0.330053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.2563 | 0.546218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.84669 | −0.405039 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4350 | 0.921297 | 0.460648 | − | 0.887583i | \(-0.347617\pi\) | ||||
0.460648 | + | 0.887583i | \(0.347617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.59034 | −0.269725 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.9885 | 0.898427 | 0.449214 | − | 0.893424i | \(-0.351704\pi\) | ||||
0.449214 | + | 0.893424i | \(0.351704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.3982 | −0.424151 | −0.212076 | − | 0.977253i | \(-0.568022\pi\) | ||||
−0.212076 | + | 0.977253i | \(0.568022\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.22424 | 0.172024 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.47387 | 0.384532 | 0.192266 | − | 0.981343i | \(-0.438416\pi\) | ||||
0.192266 | + | 0.981343i | \(0.438416\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.70009 | 0.393068 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.03210 | 0.203577 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.10303 | 0.206109 | 0.103055 | − | 0.994676i | \(-0.467138\pi\) | ||||
0.103055 | + | 0.994676i | \(0.467138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.4739 | 1.66967 | 0.834837 | − | 0.550496i | \(-0.185562\pi\) | ||||
0.834837 | + | 0.550496i | \(0.185562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.8721 | 1.16047 | 0.580233 | − | 0.814450i | \(-0.302961\pi\) | ||||
0.580233 | + | 0.814450i | \(0.302961\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.29517 | −0.172359 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.0642 | 0.803855 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.2563 | 0.529407 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.76904 | 0.389517 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6660 | −0.743082 | −0.371541 | − | 0.928417i | \(-0.621170\pi\) | ||||
−0.371541 | + | 0.928417i | \(0.621170\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.80786 | −0.111602 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.80786 | 0.190494 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.8079 | −0.506671 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0254 | 1.02794 | 0.513970 | − | 0.857808i | \(-0.328174\pi\) | ||||
0.513970 | + | 0.857808i | \(0.328174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3206 | 0.446439 | 0.223219 | − | 0.974768i | \(-0.428343\pi\) | ||||
0.223219 | + | 0.974768i | \(0.428343\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.7322 | 0.421926 | 0.210963 | − | 0.977494i | \(-0.432340\pi\) | ||||
0.210963 | + | 0.977494i | \(0.432340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0642 | −1.14087 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.55152 | 0.335160 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | −0.352197 | −0.176099 | − | 0.984373i | \(-0.556348\pi\) | ||||
−0.176099 | + | 0.984373i | \(0.556348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.8079 | −0.499682 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6914 | −1.00079 | −0.500397 | − | 0.865796i | \(-0.666813\pi\) | ||||
−0.500397 | + | 0.865796i | \(0.666813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6660 | 0.492651 | 0.246325 | − | 0.969187i | \(-0.420777\pi\) | ||||
0.246325 | + | 0.969187i | \(0.420777\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.00000 | −0.116510 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.1399 | −1.08958 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8855 | 0.420858 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.2884 | −1.01485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2817 | 1.05163 | 0.525817 | − | 0.850598i | \(-0.323760\pi\) | ||||
0.525817 | + | 0.850598i | \(0.323760\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.4097 | −0.976573 | −0.488286 | − | 0.872684i | \(-0.662378\pi\) | ||||
−0.488286 | + | 0.872684i | \(0.662378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3066 | 0.395532 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.7369 | 0.718001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.55625 | −0.365660 | −0.182830 | − | 0.983145i | \(-0.558526\pi\) | ||||
−0.182830 | + | 0.983145i | \(0.558526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000 | 0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.29517 | 0.125536 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0575 | 0.991273 | 0.495637 | − | 0.868530i | \(-0.334935\pi\) | ||||
0.495637 | + | 0.868530i | \(0.334935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.55152 | 0.324845 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7690 | 0.597295 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.448485 | 0.0169633 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.4992 | −1.86956 | −0.934780 | − | 0.355226i | \(-0.884404\pi\) | ||||
−0.934780 | + | 0.355226i | \(0.884404\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.47387 | 0.281882 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.45568 | −0.129964 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.33399 | 0.275434 | 0.137717 | − | 0.990472i | \(-0.456024\pi\) | ||||
0.137717 | + | 0.990472i | \(0.456024\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.25635 | −0.0471166 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.8079 | −0.929062 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.9545 | 0.931941 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9497 | −1.15423 | −0.577115 | − | 0.816663i | \(-0.695821\pi\) | ||||
−0.577115 | + | 0.816663i | \(0.695821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.82130 | 0.179555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.78248 | 0.215053 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.6660 | −0.988987 | −0.494494 | − | 0.869181i | \(-0.664646\pi\) | ||||
−0.494494 | + | 0.869181i | \(0.664646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7690 | 0.583239 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.6934 | −1.02288 | −0.511439 | − | 0.859320i | \(-0.670887\pi\) | ||||
−0.511439 | + | 0.859320i | \(0.670887\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.3982 | 0.898719 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.91761 | −0.0705405 | −0.0352703 | − | 0.999378i | \(-0.511229\pi\) | ||||
−0.0352703 | + | 0.999378i | \(0.511229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.29517 | −0.0843152 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.2884 | 1.84490 | 0.922452 | − | 0.386112i | \(-0.126182\pi\) | ||||
0.922452 | + | 0.386112i | \(0.126182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.0709 | −0.441652 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.8218 | 1.08966 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.4758 | 0.491741 | 0.245870 | − | 0.969303i | \(-0.420926\pi\) | ||||
0.245870 | + | 0.969303i | \(0.420926\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.33399 | 0.340150 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.1030 | −0.876040 | −0.438020 | − | 0.898965i | \(-0.644320\pi\) | ||||
−0.438020 | + | 0.898965i | \(0.644320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.8079 | −0.900468 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.2175 | 1.02288 | 0.511442 | − | 0.859318i | \(-0.329111\pi\) | ||||
0.511442 | + | 0.859318i | \(0.329111\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.8467 | 1.00812 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.03210 | 0.181699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.9612 | −1.18861 | −0.594305 | − | 0.804240i | \(-0.702573\pi\) | ||||
−0.594305 | + | 0.804240i | \(0.702573\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.192140 | −0.00691974 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.88353 | −0.319518 | −0.159759 | − | 0.987156i | \(-0.551072\pi\) | ||||
−0.159759 | + | 0.987156i | \(0.551072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.82130 | 0.172963 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.0642 | 0.432245 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −73.9751 | −2.64704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.55152 | 0.234132 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.8788 | −0.459079 | −0.229540 | − | 0.973299i | \(-0.573722\pi\) | ||||
−0.229540 | + | 0.973299i | \(0.573722\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.25635 | −0.258333 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1807 | 0.397539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.55152 | 0.161629 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.78050 | −0.0984902 | −0.0492451 | − | 0.998787i | \(-0.515682\pi\) | ||||
−0.0492451 | + | 0.998787i | \(0.515682\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.0963 | −0.534069 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5515 | 0.478819 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −73.9751 | −2.61052 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.9224 | −0.454888 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.14186 | 0.286252 | 0.143126 | − | 0.989704i | \(-0.454285\pi\) | ||||
0.143126 | + | 0.989704i | \(0.454285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7255 | −0.657540 | −0.328770 | − | 0.944410i | \(-0.606634\pi\) | ||||
−0.328770 | + | 0.944410i | \(0.606634\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.6224 | −0.828475 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0642 | 0.422073 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.48059 | −0.0517359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.5401 | −0.821554 | −0.410777 | − | 0.911736i | \(-0.634742\pi\) | ||||
−0.410777 | + | 0.911736i | \(0.634742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.7576 | 1.80416 | 0.902078 | − | 0.431573i | \(-0.142041\pi\) | ||||
0.902078 | + | 0.431573i | \(0.142041\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.5333 | −1.30516 | −0.652581 | − | 0.757719i | \(-0.726314\pi\) | ||||
−0.652581 | + | 0.757719i | \(0.726314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.8835 | 1.31575 | 0.657875 | − | 0.753127i | \(-0.271456\pi\) | ||||
0.657875 | + | 0.753127i | \(0.271456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.96118 | −0.241480 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.4236 | −0.499747 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.77576 | 0.199639 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.0891094 | −0.00307640 | −0.00153820 | − | 0.999999i | \(-0.500490\pi\) | ||||
−0.00153820 | + | 0.999999i | \(0.500490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.9224 | 0.480081 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4097 | 0.461853 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.1050 | 1.13750 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.40966 | −0.322939 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.9866 | −0.479453 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2583 | −0.659393 | −0.329696 | − | 0.944087i | \(-0.606946\pi\) | ||||
−0.329696 | + | 0.944087i | \(0.606946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.84470 | 0.0630138 | 0.0315069 | − | 0.999504i | \(-0.489969\pi\) | ||||
0.0315069 | + | 0.999504i | \(0.489969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.3848 | 1.68499 | 0.842493 | − | 0.538707i | \(-0.181087\pi\) | ||||
0.842493 | + | 0.538707i | \(0.181087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.78248 | 0.265226 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.1720 | 0.993026 | 0.496513 | − | 0.868029i | \(-0.334614\pi\) | ||||
0.496513 | + | 0.868029i | \(0.334614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.25635 | −0.246155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.22424 | −0.143133 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.96118 | 0.235600 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.1419 | 0.747677 | 0.373839 | − | 0.927494i | \(-0.378041\pi\) | ||||
0.373839 | + | 0.927494i | \(0.378041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.1030 | −0.576871 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.1145 | −0.542911 | −0.271455 | − | 0.962451i | \(-0.587505\pi\) | ||||
−0.271455 | + | 0.962451i | \(0.587505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −59.1672 | −1.99114 | −0.995568 | − | 0.0940444i | \(-0.970020\pi\) | ||||
−0.995568 | + | 0.0940444i | \(0.970020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.5654 | −1.16059 | −0.580297 | − | 0.814405i | \(-0.697063\pi\) | ||||
−0.580297 | + | 0.814405i | \(0.697063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.15728 | −0.139431 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.77576 | 0.193495 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.5495 | −0.386490 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.29517 | 0.143412 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.8400 | 1.26203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.88551 | −0.329334 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.78248 | 0.258985 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.74167 | −0.157445 | −0.0787223 | − | 0.996897i | \(-0.525084\pi\) | ||||
−0.0787223 | + | 0.996897i | \(0.525084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.33399 | −0.0774137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.450469 | −0.0149247 | −0.00746235 | − | 0.999972i | \(-0.502375\pi\) | ||||
−0.00746235 | + | 0.999972i | \(0.502375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −69.7188 | −2.30735 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.39820 | 0.112218 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.5515 | −0.644945 | −0.322472 | − | 0.946579i | \(-0.604514\pi\) | ||||
−0.322472 | + | 0.946579i | \(0.604514\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.3594 | 0.604962 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.8079 | 0.421576 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.25635 | 0.106952 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.6934 | −0.842972 | −0.421486 | − | 0.906835i | \(-0.638491\pi\) | ||||
−0.421486 | + | 0.906835i | \(0.638491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0349 | −0.361653 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.6157 | 0.904098 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.6545 | −1.16478 | −0.582392 | − | 0.812908i | \(-0.697883\pi\) | ||||
−0.582392 | + | 0.812908i | \(0.697883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.2952 | −0.694942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.26979 | −0.171790 | −0.0858951 | − | 0.996304i | \(-0.527375\pi\) | ||||
−0.0858951 | + | 0.996304i | \(0.527375\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.5769 | −0.735205 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.9042 | 1.29671 | 0.648356 | − | 0.761338i | \(-0.275457\pi\) | ||||
0.648356 | + | 0.761338i | \(0.275457\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8079 | 0.415761 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.372819 | 0.0120895 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2563 | 0.980099 | 0.490050 | − | 0.871695i | \(-0.336979\pi\) | ||||
0.490050 | + | 0.871695i | \(0.336979\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.8400 | 1.22319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.9383 | −0.676132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.35938 | 0.0761089 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.1419 | 0.649062 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3915 | 0.945166 | 0.472583 | − | 0.881286i | \(-0.343322\pi\) | ||||
0.472583 | + | 0.881286i | \(0.343322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.88551 | 0.221194 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.4739 | −0.432397 | −0.216198 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216198 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.7297 | −0.376038 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.6934 | −1.01396 | −0.506980 | − | 0.861958i | \(-0.669238\pi\) | ||||
−0.506980 | + | 0.861958i | \(0.669238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78.2703 | 2.50153 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.8079 | 0.600489 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9311 | 0.444332 | 0.222166 | − | 0.975009i | \(-0.428687\pi\) | ||||
0.222166 | + | 0.975009i | \(0.428687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.45047 | −0.237151 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22.5769 | −0.717904 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.6296 | 1.60830 | 0.804152 | − | 0.594424i | \(-0.202620\pi\) | ||||
0.804152 | + | 0.594424i | \(0.202620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.39820 | 0.298243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.4002 | −1.21615 | −0.608073 | − | 0.793881i | \(-0.708057\pi\) | ||||
−0.608073 | + | 0.793881i | \(0.708057\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.25635 | 0.103026 |
(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 | 7800.2.a.bs.1.2 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bh.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bh.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.bs.1.2 | yes | 3 | 1.1 | even | 1 | trivial |