Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.34 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | 1.38028 | 0.796903 | 0.398452 | − | 0.917189i | \(-0.369548\pi\) | ||||
0.398452 | + | 0.917189i | \(0.369548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.43256 | −1.53509 | −0.767544 | − | 0.640996i | \(-0.778521\pi\) | ||||
−0.767544 | + | 0.640996i | \(0.778521\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.30717 | 1.24999 | 0.624996 | − | 0.780628i | \(-0.285100\pi\) | ||||
0.624996 | + | 0.780628i | \(0.285100\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.09484 | −0.364945 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.715209 | −0.215644 | −0.107822 | − | 0.994170i | \(-0.534388\pi\) | ||||
−0.107822 | + | 0.994170i | \(0.534388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.15563 | 1.42992 | 0.714958 | − | 0.699168i | \(-0.246446\pi\) | ||||
0.714958 | + | 0.699168i | \(0.246446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.73789 | −1.22332 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.52677 | −0.370297 | −0.185148 | − | 0.982711i | \(-0.559277\pi\) | ||||
−0.185148 | + | 0.982711i | \(0.559277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.44406 | 1.70779 | 0.853893 | − | 0.520449i | \(-0.174235\pi\) | ||||
0.853893 | + | 0.520449i | \(0.174235\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56481 | 0.996123 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.93916 | −0.821372 | −0.410686 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410686 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.78248 | 1.35650 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65201 | −1.08773 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.20561 | −0.780961 | −0.390481 | − | 0.920611i | \(-0.627691\pi\) | ||||
−0.390481 | + | 0.920611i | \(0.627691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.78288 | 1.21824 | 0.609121 | − | 0.793078i | \(-0.291523\pi\) | ||||
0.609121 | + | 0.793078i | \(0.291523\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.987187 | −0.171847 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.3521 | −1.91885 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.07948 | −0.835061 | −0.417530 | − | 0.908663i | \(-0.637104\pi\) | ||||
−0.417530 | + | 0.908663i | \(0.637104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.11620 | 1.13950 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.57167 | 0.245453 | 0.122727 | − | 0.992441i | \(-0.460836\pi\) | ||||
0.122727 | + | 0.992441i | \(0.460836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.14412 | −0.174476 | −0.0872381 | − | 0.996187i | \(-0.527804\pi\) | ||||
−0.0872381 | + | 0.996187i | \(0.527804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.75809 | 0.560223 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.06761 | 0.593322 | 0.296661 | − | 0.954983i | \(-0.404127\pi\) | ||||
0.296661 | + | 0.954983i | \(0.404127\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.93737 | 0.562482 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.10737 | −0.295091 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.64581 | 0.500790 | 0.250395 | − | 0.968144i | \(-0.419439\pi\) | ||||
0.250395 | + | 0.968144i | \(0.419439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.45500 | 0.331032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.2749 | 1.36094 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.5592 | 1.63507 | 0.817536 | − | 0.575877i | \(-0.195339\pi\) | ||||
0.817536 | + | 0.575877i | \(0.195339\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.54003 | −0.709328 | −0.354664 | − | 0.934994i | \(-0.615405\pi\) | ||||
−0.354664 | + | 0.934994i | \(0.615405\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.62081 | −0.456179 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.6970 | −2.19505 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.31555 | −0.282890 | −0.141445 | − | 0.989946i | \(-0.545175\pi\) | ||||
−0.141445 | + | 0.989946i | \(0.545175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.43713 | −0.654554 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.03969 | 0.716780 | 0.358390 | − | 0.933572i | \(-0.383326\pi\) | ||||
0.358390 | + | 0.933572i | \(0.383326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.14485 | −0.719201 | −0.359600 | − | 0.933106i | \(-0.617087\pi\) | ||||
−0.359600 | + | 0.933106i | \(0.617087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.36170 | 1.08100 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.36532 | −0.269553 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9617 | 1.45830 | 0.729152 | − | 0.684351i | \(-0.239915\pi\) | ||||
0.729152 | + | 0.684351i | \(0.239915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.51682 | −0.501869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.06286 | 0.885014 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.24074 | 0.568438 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.80490 | −0.622351 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.5246 | −1.64560 | −0.822802 | − | 0.568328i | \(-0.807590\pi\) | ||||
−0.822802 | + | 0.568328i | \(0.807590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.0506 | 1.78738 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.36225 | 0.970820 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −25.5522 | −2.62160 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.13304 | 0.419647 | 0.209824 | − | 0.977739i | \(-0.432711\pi\) | ||||
0.209824 | + | 0.977739i | \(0.432711\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.783037 | 0.0786982 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.07921 | −0.306393 | −0.153197 | − | 0.988196i | \(-0.548957\pi\) | ||||
−0.153197 | + | 0.988196i | \(0.548957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9048 | −1.27155 | −0.635775 | − | 0.771874i | \(-0.719319\pi\) | ||||
−0.635775 | + | 0.771874i | \(0.719319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15.6690 | −1.52914 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.1027 | 1.75006 | 0.875029 | − | 0.484071i | \(-0.160842\pi\) | ||||
0.875029 | + | 0.484071i | \(0.160842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.37607 | −0.131804 | −0.0659018 | − | 0.997826i | \(-0.520992\pi\) | ||||
−0.0659018 | + | 0.997826i | \(0.520992\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.01108 | −0.665463 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9587 | 1.68941 | 0.844707 | − | 0.535228i | \(-0.179774\pi\) | ||||
0.844707 | + | 0.535228i | \(0.179774\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5214 | 1.26088 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.64457 | −0.521841 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.04929 | −0.462868 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4885 | −0.953498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.16934 | 0.195602 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.11848 | −0.547253 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.8271 | 1.84810 | 0.924052 | − | 0.382267i | \(-0.124857\pi\) | ||||
0.924052 | + | 0.382267i | \(0.124857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.57920 | −0.139041 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.81472 | 0.595404 | 0.297702 | − | 0.954659i | \(-0.403780\pi\) | ||||
0.297702 | + | 0.954659i | \(0.403780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.6188 | 2.13472 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.4009 | 1.66976 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4759 | −1.15133 | −0.575664 | − | 0.817686i | \(-0.695256\pi\) | ||||
−0.575664 | + | 0.817686i | \(0.695256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6302 | −0.986460 | −0.493230 | − | 0.869899i | \(-0.664184\pi\) | ||||
−0.493230 | + | 0.869899i | \(0.664184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.61443 | 0.472820 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.68736 | −0.308352 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4360 | 1.19884 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.43466 | 0.448243 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7126 | −1.28723 | −0.643614 | − | 0.765350i | \(-0.722566\pi\) | ||||
−0.643614 | + | 0.765350i | \(0.722566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.13637 | 0.499371 | 0.249685 | − | 0.968327i | \(-0.419673\pi\) | ||||
0.249685 | + | 0.968327i | \(0.419673\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67157 | 0.135138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.2827 | −1.87011 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.25511 | 0.499213 | 0.249606 | − | 0.968347i | \(-0.419699\pi\) | ||||
0.249606 | + | 0.968347i | \(0.419699\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.03222 | 0.399081 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.0275 | −1.02671 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.7242 | 1.93655 | 0.968274 | − | 0.249891i | \(-0.0803947\pi\) | ||||
0.968274 | + | 0.249891i | \(0.0803947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.38858 | 0.263801 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.736630 | 0.0570021 | 0.0285011 | − | 0.999594i | \(-0.490927\pi\) | ||||
0.0285011 | + | 0.999594i | \(0.490927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.5805 | 1.04466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.15003 | −0.623249 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.0400 | 0.915387 | 0.457694 | − | 0.889110i | \(-0.348676\pi\) | ||||
0.457694 | + | 0.889110i | \(0.348676\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4308 | 1.69561 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.3352 | 1.30299 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.6240 | 1.01831 | 0.509154 | − | 0.860676i | \(-0.329958\pi\) | ||||
0.509154 | + | 0.860676i | \(0.329958\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7372 | 0.872421 | 0.436210 | − | 0.899845i | \(-0.356320\pi\) | ||||
0.436210 | + | 0.899845i | \(0.356320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.64677 | −0.565266 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.4356 | 1.28189 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.09196 | 0.0798521 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.6921 | −1.35965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41855 | −0.102643 | −0.0513215 | − | 0.998682i | \(-0.516343\pi\) | ||||
−0.0513215 | + | 0.998682i | \(0.516343\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5267 | 0.973672 | 0.486836 | − | 0.873493i | \(-0.338151\pi\) | ||||
0.486836 | + | 0.873493i | \(0.338151\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.4268 | −1.74924 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.85311 | −0.488264 | −0.244132 | − | 0.969742i | \(-0.578503\pi\) | ||||
−0.244132 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9050 | 1.69458 | 0.847291 | − | 0.531129i | \(-0.178232\pi\) | ||||
0.847291 | + | 0.531129i | \(0.178232\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.19610 | −0.225436 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.9087 | −0.976196 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.39484 | −0.376792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.31274 | 0.299756 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.32406 | −0.368273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0715 | 0.762192 | 0.381096 | − | 0.924536i | \(-0.375547\pi\) | ||||
0.381096 | + | 0.924536i | \(0.375547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.33645 | 0.571204 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.92725 | 0.267836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.4321 | 1.52279 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.48160 | −0.573133 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.87148 | −0.529493 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.8141 | 1.05899 | 0.529494 | − | 0.848314i | \(-0.322382\pi\) | ||||
0.529494 | + | 0.848314i | \(0.322382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.42571 | −0.495047 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.9752 | −0.794822 | −0.397411 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397411 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.96277 | 0.460113 | 0.230056 | − | 0.973177i | \(-0.426109\pi\) | ||||
0.230056 | + | 0.973177i | \(0.426109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.26479 | −0.214808 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.3936 | −1.27052 | −0.635258 | − | 0.772300i | \(-0.719106\pi\) | ||||
−0.635258 | + | 0.772300i | \(0.719106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.9623 | −0.910801 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.8907 | 1.16213 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1021 | 0.976876 | 0.488438 | − | 0.872599i | \(-0.337567\pi\) | ||||
0.488438 | + | 0.872599i | \(0.337567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5806 | −0.939222 | −0.469611 | − | 0.882873i | \(-0.655606\pi\) | ||||
−0.469611 | + | 0.882873i | \(0.655606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7216 | 0.687788 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.5153 | −0.863459 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.3789 | 2.44199 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1290 | 0.705271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.72647 | −0.298332 | −0.149166 | − | 0.988812i | \(-0.547659\pi\) | ||||
−0.149166 | + | 0.988812i | \(0.547659\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.81733 | 0.177124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.23367 | 0.452990 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.0945381 | 0.00589713 | 0.00294856 | − | 0.999996i | \(-0.499061\pi\) | ||||
0.00294856 | + | 0.999996i | \(0.499061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.7987 | −1.04382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.60445 | 0.285008 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6136 | 0.962774 | 0.481387 | − | 0.876508i | \(-0.340133\pi\) | ||||
0.481387 | + | 0.876508i | \(0.340133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.5145 | −0.768757 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4282 | −1.31139 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0602 | 0.735323 | 0.367662 | − | 0.929960i | \(-0.380158\pi\) | ||||
0.367662 | + | 0.929960i | \(0.380158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.82291 | −0.292971 | −0.146485 | − | 0.989213i | \(-0.546796\pi\) | ||||
−0.146485 | + | 0.989213i | \(0.546796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.5345 | 1.42437 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.85089 | −0.292520 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8417 | −0.651415 | −0.325707 | − | 0.945471i | \(-0.605602\pi\) | ||||
−0.325707 | + | 0.945471i | \(0.605602\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.42614 | −0.444592 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5903 | −0.691420 | −0.345710 | − | 0.938341i | \(-0.612362\pi\) | ||||
−0.345710 | + | 0.938341i | \(0.612362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.2298 | −0.726989 | −0.363494 | − | 0.931596i | \(-0.618416\pi\) | ||||
−0.363494 | + | 0.931596i | \(0.618416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −35.2691 | −2.08916 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.19777 | 0.306815 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6690 | −0.862880 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.70475 | 0.334418 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8915 | 0.694710 | 0.347355 | − | 0.937734i | \(-0.387080\pi\) | ||||
0.347355 | + | 0.937734i | \(0.387080\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −43.1103 | −2.50998 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.04237 | 0.234562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.3089 | −1.17449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.78379 | −0.218094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.25017 | −0.244166 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.0165 | 1.08888 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9784 | −1.31144 | −0.655722 | − | 0.755002i | \(-0.727636\pi\) | ||||
−0.655722 | + | 0.755002i | \(0.727636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.8122 | −1.01330 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1728 | 0.576848 | 0.288424 | − | 0.957503i | \(-0.406869\pi\) | ||||
0.288424 | + | 0.957503i | \(0.406869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0258 | 0.566692 | 0.283346 | − | 0.959018i | \(-0.408556\pi\) | ||||
0.283346 | + | 0.959018i | \(0.408556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.4287 | 0.700275 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.3486 | 1.19906 | 0.599528 | − | 0.800354i | \(-0.295355\pi\) | ||||
0.599528 | + | 0.800354i | \(0.295355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00789 | 0.168409 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.9868 | 1.39463 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3654 | −0.632387 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.9680 | 1.93967 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.89936 | −0.105035 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.4523 | 0.741648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.7276 | 1.30419 | 0.652093 | − | 0.758139i | \(-0.273891\pi\) | ||||
0.652093 | + | 0.758139i | \(0.273891\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.56120 | 0.304752 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.94827 | 0.434261 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0819 | 1.20288 | 0.601438 | − | 0.798919i | \(-0.294595\pi\) | ||||
0.601438 | + | 0.798919i | \(0.294595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.7880 | 1.34630 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.85118 | −0.262706 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.1286 | −0.546895 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.6633 | 1.00480 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.7902 | 1.27712 | 0.638562 | − | 0.769570i | \(-0.279529\pi\) | ||||
0.638562 | + | 0.769570i | \(0.279529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9757 | 1.28339 | 0.641695 | − | 0.766960i | \(-0.278232\pi\) | ||||
0.641695 | + | 0.766960i | \(0.278232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.1397 | −1.55536 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.63502 | 0.0870233 | 0.0435117 | − | 0.999053i | \(-0.486145\pi\) | ||||
0.0435117 | + | 0.999053i | \(0.486145\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.7316 | −1.10032 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.96942 | −0.368861 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.8539 | −0.678405 | −0.339202 | − | 0.940713i | \(-0.610157\pi\) | ||||
−0.339202 | + | 0.940713i | \(0.610157\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4141 | 1.91653 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.4770 | −0.759845 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0926 | 1.10404 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2219 | 1.42097 | 0.710486 | − | 0.703711i | \(-0.248475\pi\) | ||||
0.710486 | + | 0.703711i | \(0.248475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.72072 | −0.0895770 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0573 | 0.625984 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.3061 | 0.844298 | 0.422149 | − | 0.906527i | \(-0.361276\pi\) | ||||
0.422149 | + | 0.906527i | \(0.361276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.44519 | −0.436108 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.6826 | −1.11671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.96706 | −0.357874 | −0.178937 | − | 0.983861i | \(-0.557266\pi\) | ||||
−0.178937 | + | 0.983861i | \(0.557266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.7471 | 1.47276 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.0321 | −1.43238 | −0.716188 | − | 0.697907i | \(-0.754115\pi\) | ||||
−0.716188 | + | 0.697907i | \(0.754115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.11910 | 0.413788 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.25262 | 0.0636743 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.1118 | 1.27322 | 0.636610 | − | 0.771186i | \(-0.280336\pi\) | ||||
0.636610 | + | 0.771186i | \(0.280336\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.01420 | 0.304151 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.40619 | 0.474480 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −44.4918 | −2.23863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0339 | −0.654154 | −0.327077 | − | 0.944998i | \(-0.606064\pi\) | ||||
−0.327077 | + | 0.944998i | \(0.606064\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33.9807 | 1.70116 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.2412 | −0.611296 | −0.305648 | − | 0.952145i | \(-0.598873\pi\) | ||||
−0.305648 | + | 0.952145i | \(0.598873\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.9700 | 1.74198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.5043 | 0.770414 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.63289 | 0.180076 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.12069 | −0.253202 | −0.126601 | − | 0.991954i | \(-0.540407\pi\) | ||||
−0.126601 | + | 0.991954i | \(0.540407\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.6005 | −0.917497 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.5355 | 2.04383 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.6763 | −1.35857 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0529 | −0.786113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.48489 | −0.0725419 | −0.0362709 | − | 0.999342i | \(-0.511548\pi\) | ||||
−0.0362709 | + | 0.999342i | \(0.511548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32660 | −0.0646545 | −0.0323272 | − | 0.999477i | \(-0.510292\pi\) | ||||
−0.0323272 | + | 0.999477i | \(0.510292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.45337 | −0.216530 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3553 | −0.502306 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.3218 | −0.886655 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.08957 | −0.245727 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.11034 | 0.0534832 | 0.0267416 | − | 0.999642i | \(-0.491487\pi\) | ||||
0.0267416 | + | 0.999642i | \(0.491487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7731 | −0.902179 | −0.451089 | − | 0.892479i | \(-0.648964\pi\) | ||||
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.9257 | 0.955363 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.3234 | −1.40273 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.77248 | −0.0845960 | −0.0422980 | − | 0.999105i | \(-0.513468\pi\) | ||||
−0.0422980 | + | 0.999105i | \(0.513468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.31078 | −0.205275 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5716 | −1.11992 | −0.559961 | − | 0.828519i | \(-0.689184\pi\) | ||||
−0.559961 | + | 0.828519i | \(0.689184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 53.2891 | 2.52615 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.6878 | −1.02580 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3934 | 0.537688 | 0.268844 | − | 0.963184i | \(-0.413358\pi\) | ||||
0.268844 | + | 0.963184i | \(0.413358\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12407 | −0.0529304 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.46989 | 0.397950 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −58.5271 | −2.74379 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.3769 | −1.74842 | −0.874209 | − | 0.485549i | \(-0.838620\pi\) | ||||
−0.874209 | + | 0.485549i | \(0.838620\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.62933 | 0.402783 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.6343 | 1.33363 | 0.666817 | − | 0.745221i | \(-0.267656\pi\) | ||||
0.666817 | + | 0.745221i | \(0.267656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.79462 | 0.0834032 | 0.0417016 | − | 0.999130i | \(-0.486722\pi\) | ||||
0.0417016 | + | 0.999130i | \(0.486722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32.1365 | −1.49029 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.7225 | 1.19029 | 0.595147 | − | 0.803617i | \(-0.297094\pi\) | ||||
0.595147 | + | 0.803617i | \(0.297094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.65792 | −0.353610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.63379 | 0.397824 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.818283 | 0.0376247 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 50.4892 | 2.31660 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.99156 | −0.182761 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.5167 | −1.12020 | −0.560099 | − | 0.828426i | \(-0.689237\pi\) | ||||
−0.560099 | + | 0.828426i | \(0.689237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1879 | −1.19407 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.9815 | −0.818188 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.1869 | −0.644195 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.10226 | 0.0499482 | 0.0249741 | − | 0.999688i | \(-0.492050\pi\) | ||||
0.0249741 | + | 0.999688i | \(0.492050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.1262 | 1.54324 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1395 | 1.04427 | 0.522136 | − | 0.852862i | \(-0.325135\pi\) | ||||
0.522136 | + | 0.852862i | \(0.325135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.42100 | 0.289187 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.68782 | −0.120809 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.9743 | 0.895969 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.4595 | −1.22926 | −0.614628 | − | 0.788817i | \(-0.710694\pi\) | ||||
−0.614628 | + | 0.788817i | \(0.710694\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.01675 | 0.0454252 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2079 | 0.678086 | 0.339043 | − | 0.940771i | \(-0.389897\pi\) | ||||
0.339043 | + | 0.940771i | \(0.389897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5696 | 0.470341 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.7449 | 0.832491 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.6588 | 0.960011 | 0.480005 | − | 0.877266i | \(-0.340635\pi\) | ||||
0.480005 | + | 0.877266i | \(0.340635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.3221 | −0.898996 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −42.0739 | −1.85761 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.2966 | 1.95194 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.90919 | −0.127946 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.6186 | 0.729475 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3182 | −1.02159 | −0.510795 | − | 0.859703i | \(-0.670649\pi\) | ||||
−0.510795 | + | 0.859703i | \(0.670649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9308 | −0.521698 | −0.260849 | − | 0.965380i | \(-0.584002\pi\) | ||||
−0.260849 | + | 0.965380i | \(0.584002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.9607 | 1.35124 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.3559 | −0.451111 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.48300 | −0.325348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.7503 | −0.596712 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.10294 | 0.350977 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −62.1388 | −2.68649 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.8049 | 0.811492 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.81604 | −0.121296 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0986 | −1.29404 | −0.647021 | − | 0.762472i | \(-0.723985\pi\) | ||||
−0.647021 | + | 0.762472i | \(0.723985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.2006 | 0.695235 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.72344 | 0.202330 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1630 | −0.477296 | −0.238648 | − | 0.971106i | \(-0.576704\pi\) | ||||
−0.238648 | + | 0.971106i | \(0.576704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.06542 | 0.258866 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.3068 | −1.33371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.8665 | 1.82287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0660 | 1.02154 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1492 | −0.684264 | −0.342132 | − | 0.939652i | \(-0.611149\pi\) | ||||
−0.342132 | + | 0.939652i | \(0.611149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.89865 | −0.249486 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.50721 | 0.0636344 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.34711 | 0.0989191 | 0.0494595 | − | 0.998776i | \(-0.484250\pi\) | ||||
0.0494595 | + | 0.998776i | \(0.484250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −61.6444 | −2.59340 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.9379 | −0.627333 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.18458 | 0.385038 | 0.192519 | − | 0.981293i | \(-0.438334\pi\) | ||||
0.192519 | + | 0.981293i | \(0.438334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.8042 | −1.03802 | −0.519012 | − | 0.854767i | \(-0.673700\pi\) | ||||
−0.519012 | + | 0.854767i | \(0.673700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.95800 | −0.0817965 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.7173 | −1.11419 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8202 | −1.11654 | −0.558269 | − | 0.829660i | \(-0.688534\pi\) | ||||
−0.558269 | + | 0.829660i | \(0.688534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.6706 | 0.775922 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.6653 | 1.10626 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.60752 | −0.107992 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.3753 | 0.801072 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.2607 | −1.49664 | −0.748319 | − | 0.663339i | \(-0.769139\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.4922 | 2.08049 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.45918 | −0.389099 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5126 | −0.554895 | −0.277448 | − | 0.960741i | \(-0.589489\pi\) | ||||
−0.277448 | + | 0.960741i | \(0.589489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.3320 | 0.710543 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.9956 | 1.35042 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.2268 | 1.07160 | 0.535800 | − | 0.844345i | \(-0.320010\pi\) | ||||
0.535800 | + | 0.844345i | \(0.320010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9506 | −0.691428 | −0.345714 | − | 0.938340i | \(-0.612363\pi\) | ||||
−0.345714 | + | 0.938340i | \(0.612363\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.53515 | 0.103239 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.0023 | 1.46370 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.2591 | −1.51230 | −0.756149 | − | 0.654399i | \(-0.772922\pi\) | ||||
−0.756149 | + | 0.654399i | \(0.772922\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.1978 | −0.777934 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.9711 | 0.848400 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4194 | −0.582393 | −0.291197 | − | 0.956663i | \(-0.594053\pi\) | ||||
−0.291197 | + | 0.956663i | \(0.594053\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.44638 | −0.300267 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.0114 | 1.08744 | 0.543719 | − | 0.839267i | \(-0.317016\pi\) | ||||
0.543719 | + | 0.839267i | \(0.317016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4323 | 0.740855 | 0.370427 | − | 0.928861i | \(-0.379211\pi\) | ||||
0.370427 | + | 0.928861i | \(0.379211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.2642 | 0.893431 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.3425 | −2.05699 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.9104 | −0.516414 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.34868 | −0.293478 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.75520 | 0.309220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.25049 | −0.0895906 | −0.0447953 | − | 0.998996i | \(-0.514264\pi\) | ||||
−0.0447953 | + | 0.998996i | \(0.514264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.2817 | 0.607393 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −71.4902 | −2.83700 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.2996 | 0.804301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.61247 | −0.261585 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.7234 | 0.660533 | 0.330267 | − | 0.943888i | \(-0.392861\pi\) | ||||
0.330267 | + | 0.943888i | \(0.392861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.08542 | 0.121677 | 0.0608386 | − | 0.998148i | \(-0.480622\pi\) | ||||
0.0608386 | + | 0.998148i | \(0.480622\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.42070 | 0.213440 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.4215 | −1.51050 | −0.755252 | − | 0.655435i | \(-0.772485\pi\) | ||||
−0.755252 | + | 0.655435i | \(0.772485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.98248 | −0.352593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.9626 | 1.21352 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.35524 | −0.131301 | −0.0656503 | − | 0.997843i | \(-0.520912\pi\) | ||||
−0.0656503 | + | 0.997843i | \(0.520912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.3919 | −0.913998 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.72761 | 0.262469 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.8296 | −0.850359 | −0.425179 | − | 0.905109i | \(-0.639789\pi\) | ||||
−0.425179 | + | 0.905109i | \(0.639789\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.8057 | −1.39268 | −0.696340 | − | 0.717712i | \(-0.745189\pi\) | ||||
−0.696340 | + | 0.717712i | \(0.745189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.8648 | −0.421954 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −84.5055 | −3.27698 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.5666 | 0.641460 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.8278 | 0.843910 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.96228 | 0.152962 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.1693 | −1.66406 | −0.832028 | − | 0.554734i | \(-0.812820\pi\) | ||||
−0.832028 | + | 0.554734i | \(0.812820\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −38.3346 | −1.47550 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.38497 | 0.245394 | 0.122697 | − | 0.992444i | \(-0.460846\pi\) | ||||
0.122697 | + | 0.992444i | \(0.460846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6687 | 0.524556 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.5291 | −0.633396 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5133 | −0.746656 | −0.373328 | − | 0.927699i | \(-0.621783\pi\) | ||||
−0.373328 | + | 0.927699i | \(0.621783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.2570 | 1.76739 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.61055 | 0.366665 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.7964 | 0.716088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9634 | −0.645319 | −0.322659 | − | 0.946515i | \(-0.604577\pi\) | ||||
−0.322659 | + | 0.946515i | \(0.604577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.58964 | 0.0983721 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.9214 | 1.51430 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.39958 | −0.0908905 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.7685 | −1.01248 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.32280 | −0.0877311 | −0.0438655 | − | 0.999037i | \(-0.513967\pi\) | ||||
−0.0438655 | + | 0.999037i | \(0.513967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.8120 | −1.42610 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.2719 | −0.725820 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.1835 | −0.382989 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.4777 | −1.36995 | −0.684974 | − | 0.728568i | \(-0.740186\pi\) | ||||
−0.684974 | + | 0.728568i | \(0.740186\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.1909 | −0.532202 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.7189 | −1.00063 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.6571 | 0.473348 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.8451 | 0.778475 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.31384 | −0.310054 | −0.155027 | − | 0.987910i | \(-0.549546\pi\) | ||||
−0.155027 | + | 0.987910i | \(0.549546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.6785 | −1.58943 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1253 | −0.748469 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.5244 | −1.05937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7570 | 1.02945 | 0.514725 | − | 0.857356i | \(-0.327894\pi\) | ||||
0.514725 | + | 0.857356i | \(0.327894\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.3492 | 1.04997 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.74681 | 0.0646080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.2015 | 1.66955 | 0.834777 | − | 0.550588i | \(-0.185597\pi\) | ||||
0.834777 | + | 0.550588i | \(0.185597\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18.6548 | −0.688093 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.65610 | 0.0610034 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7131 | 0.725159 | 0.362580 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362580 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 52.9734 | 1.94603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.33662 | 0.0857224 | 0.0428612 | − | 0.999081i | \(-0.486353\pi\) | ||||
0.0428612 | + | 0.999081i | \(0.486353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 53.9346 | 1.97601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.82751 | −0.322982 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 59.8688 | 2.18756 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.52384 | −0.237742 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.0635 | −0.766579 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.4457 | −1.28830 | −0.644148 | − | 0.764901i | \(-0.722788\pi\) | ||||
−0.644148 | + | 0.764901i | \(0.722788\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.88869 | 0.141150 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.7618 | −0.970116 | −0.485058 | − | 0.874482i | \(-0.661201\pi\) | ||||
−0.485058 | + | 0.874482i | \(0.661201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.55090 | −0.164753 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.73775 | −0.207449 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.7508 | 2.33801 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.18115 | 0.0425934 | 0.0212967 | − | 0.999773i | \(-0.493221\pi\) | ||||
0.0212967 | + | 0.999773i | \(0.493221\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.130489 | 0.00469944 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.27705 | 0.225770 | 0.112885 | − | 0.993608i | \(-0.463991\pi\) | ||||
0.112885 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 46.0048 | 1.65254 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.1868 | −0.831823 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6996 | 0.419181 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.31964 | −0.154569 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.7701 | 0.849475 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.4711 | −0.766335 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1036 | −0.431447 | −0.215724 | − | 0.976454i | \(-0.569211\pi\) | ||||
−0.215724 | + | 0.976454i | \(0.569211\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.5510 | 0.767237 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 59.3926 | 2.11176 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.5623 | −1.01428 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.2734 | −0.612625 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −53.8903 | −1.90889 | −0.954446 | − | 0.298383i | \(-0.903553\pi\) | ||||
−0.954446 | + | 0.298383i | \(0.903553\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.21031 | −0.219705 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.9969 | 0.600556 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.39486 | 0.155091 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.7176 | 1.57609 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.6464 | 0.585981 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.4573 | 0.648923 | 0.324461 | − | 0.945899i | \(-0.394817\pi\) | ||||
0.324461 | + | 0.945899i | \(0.394817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.7375 | 1.74652 | 0.873260 | − | 0.487254i | \(-0.162002\pi\) | ||||
0.873260 | + | 0.487254i | \(0.162002\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.65694 | −0.233469 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −84.8673 | −2.97277 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.51688 | −0.297968 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.6676 | −0.652297 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4080 | 1.41025 | 0.705125 | − | 0.709083i | \(-0.250891\pi\) | ||||
0.705125 | + | 0.709083i | \(0.250891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5688 | 0.995845 | 0.497923 | − | 0.867221i | \(-0.334096\pi\) | ||||
0.497923 | + | 0.867221i | \(0.334096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.69557 | −0.233110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.8368 | 0.550698 | 0.275349 | − | 0.961344i | \(-0.411207\pi\) | ||||
0.275349 | + | 0.961344i | \(0.411207\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5314 | 0.956204 | 0.478102 | − | 0.878304i | \(-0.341325\pi\) | ||||
0.478102 | + | 0.878304i | \(0.341325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9645 | −0.519114 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.01147 | −0.208285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.52853 | −0.0875033 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −38.3369 | −1.32512 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.77127 | −0.0956750 | −0.0478375 | − | 0.998855i | \(-0.515233\pi\) | ||||
−0.0478375 | + | 0.998855i | \(0.515233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3129 | −0.390099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.9978 | −0.550994 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.6161 | −1.60364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.6872 | −1.19187 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8806 | −0.579340 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0089 | 0.685896 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.26328 | 0.111733 | 0.0558664 | − | 0.998438i | \(-0.482208\pi\) | ||||
0.0558664 | + | 0.998438i | \(0.482208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.9755 | 0.956742 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.70878 | 0.0925301 | 0.0462650 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462650 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1510 | 1.30170 | 0.650848 | − | 0.759208i | \(-0.274414\pi\) | ||||
0.650848 | + | 0.759208i | \(0.274414\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.17436 | 0.244502 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.41001 | −0.116078 | −0.0580391 | − | 0.998314i | \(-0.518485\pi\) | ||||
−0.0580391 | + | 0.998314i | \(0.518485\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −41.3282 | −1.40520 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.2472 | −0.687632 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.27032 | −0.314474 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9381 | −0.404508 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.52501 | −0.153148 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.2348 | −0.684063 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6335 | 0.629210 | 0.314605 | − | 0.949223i | \(-0.398128\pi\) | ||||
0.314605 | + | 0.949223i | \(0.398128\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.4136 | 0.553617 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.7308 | 1.27118 | 0.635592 | − | 0.772025i | \(-0.280756\pi\) | ||||
0.635592 | + | 0.772025i | \(0.280756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.9761 | −0.436681 | −0.218340 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218340 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −59.5042 | −2.00021 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.7085 | −1.60190 | −0.800948 | − | 0.598734i | \(-0.795671\pi\) | ||||
−0.800948 | + | 0.598734i | \(0.795671\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.8786 | 2.31012 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.23047 | 0.108225 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.2795 | 1.01327 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.7653 | −1.56319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.0319 | −0.935957 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.5261 | −0.951399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.56632 | −0.185441 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.22268 | −0.173800 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.2887 | −1.33924 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.5414 | 1.34615 | 0.673077 | − | 0.739572i | \(-0.264972\pi\) | ||||
0.673077 | + | 0.739572i | \(0.264972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.37124 | 0.111817 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.0323 | −1.02815 | −0.514073 | − | 0.857747i | \(-0.671864\pi\) | ||||
−0.514073 | + | 0.857747i | \(0.671864\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.76663 | −0.190848 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.2480 | 0.867733 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.5374 | 0.744251 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.2321 | 1.62402 | 0.812009 | − | 0.583644i | \(-0.198374\pi\) | ||||
0.812009 | + | 0.583644i | \(0.198374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.7165 | −1.04509 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.1384 | 1.02493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.4515 | −1.13276 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1287 | 0.464047 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.5816 | −1.52829 | −0.764146 | − | 0.645043i | \(-0.776839\pi\) | ||||
−0.764146 | + | 0.645043i | \(0.776839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.3100 | 0.960598 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.0413 | 0.459692 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.74823 | −0.122580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.6760 | −1.16548 | −0.582742 | − | 0.812657i | \(-0.698020\pi\) | ||||
−0.582742 | + | 0.812657i | \(0.698020\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8384 | 0.451598 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.4784 | 1.38476 | 0.692379 | − | 0.721534i | \(-0.256563\pi\) | ||||
0.692379 | + | 0.721534i | \(0.256563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.19105 | −0.201608 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64.1619 | 2.08719 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.4930 | 1.18586 | 0.592932 | − | 0.805252i | \(-0.297970\pi\) | ||||
0.592932 | + | 0.805252i | \(0.297970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.6806 | −1.02840 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.4669 | 0.955531 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.3087 | 1.33812 | 0.669061 | − | 0.743208i | \(-0.266697\pi\) | ||||
0.669061 | + | 0.743208i | \(0.266697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.86928 | 0.157566 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.15172 | 0.134206 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.5672 | −1.43915 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0075 | 0.484112 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.8195 | −0.638676 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.4312 | −1.49467 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5504 | 0.725172 | 0.362586 | − | 0.931950i | \(-0.381894\pi\) | ||||
0.362586 | + | 0.931950i | \(0.381894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.6874 | −0.503951 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.4442 | −1.07328 | −0.536638 | − | 0.843813i | \(-0.680306\pi\) | ||||
−0.536638 | + | 0.843813i | \(0.680306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.4630 | −1.23307 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 48.2655 | 1.54573 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1927 | −1.12591 | −0.562957 | − | 0.826486i | \(-0.690336\pi\) | ||||
−0.562957 | + | 0.826486i | \(0.690336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1033 | 0.354864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.50657 | 0.0481011 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.33888 | 0.202179 | 0.101089 | − | 0.994877i | \(-0.467767\pi\) | ||||
0.101089 | + | 0.994877i | \(0.467767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.5237 | 0.749528 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.5679 | 0.591021 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.50686 | 0.143310 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.1283 | −1.02059 | −0.510294 | − | 0.860000i | \(-0.670463\pi\) | ||||
−0.510294 | + | 0.860000i | \(0.670463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.7506 | 1.03931 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −82.0555 | −2.60133 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.6952 | 0.465402 | 0.232701 | − | 0.972548i | \(-0.425244\pi\) | ||||
0.232701 | + | 0.972548i | \(0.425244\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.7092 | 0.908320 |
(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 | 6008.2.a.e.1.34 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.34 | ✓ | 50 | 1.1 | even | 1 | trivial |