Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4788,2,Mod(1,4788)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4788, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4788.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4788.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(38.2323724878\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 532) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.69639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4788.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.42586 | −0.637663 | −0.318832 | − | 0.947811i | \(-0.603290\pi\) | ||||
−0.318832 | + | 0.947811i | \(0.603290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.27053 | 0.986103 | 0.493052 | − | 0.870000i | \(-0.335881\pi\) | ||||
0.493052 | + | 0.870000i | \(0.335881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.42586 | 0.950162 | 0.475081 | − | 0.879942i | \(-0.342419\pi\) | ||||
0.475081 | + | 0.879942i | \(0.342419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.27053 | −1.27829 | −0.639146 | − | 0.769085i | \(-0.720712\pi\) | ||||
−0.639146 | + | 0.769085i | \(0.720712\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.574141 | −0.119717 | −0.0598584 | − | 0.998207i | \(-0.519065\pi\) | ||||
−0.0598584 | + | 0.998207i | \(0.519065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96693 | −0.593385 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.122252 | 0.0227015 | 0.0113508 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113508 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12225 | 0.381168 | 0.190584 | − | 0.981671i | \(-0.438962\pi\) | ||||
0.190584 | + | 0.981671i | \(0.438962\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.42586 | 0.241014 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.96693 | −0.652159 | −0.326079 | − | 0.945342i | \(-0.605728\pi\) | ||||
−0.326079 | + | 0.945342i | \(0.605728\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.66332 | 0.728288 | 0.364144 | − | 0.931343i | \(-0.381362\pi\) | ||||
0.364144 | + | 0.931343i | \(0.381362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.9339 | −1.81990 | −0.909948 | − | 0.414723i | \(-0.863879\pi\) | ||||
−0.909948 | + | 0.414723i | \(0.863879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.11521 | −0.454400 | −0.227200 | − | 0.973848i | \(-0.572957\pi\) | ||||
−0.227200 | + | 0.973848i | \(0.572957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.08918 | 0.836413 | 0.418206 | − | 0.908352i | \(-0.362659\pi\) | ||||
0.418206 | + | 0.908352i | \(0.362659\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.66332 | −0.628802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.72242 | 0.224240 | 0.112120 | − | 0.993695i | \(-0.464236\pi\) | ||||
0.112120 | + | 0.993695i | \(0.464236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2114 | 1.56351 | 0.781757 | − | 0.623584i | \(-0.214324\pi\) | ||||
0.781757 | + | 0.623584i | \(0.214324\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.88479 | −0.605884 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.27053 | −0.643898 | −0.321949 | − | 0.946757i | \(-0.604338\pi\) | ||||
−0.321949 | + | 0.946757i | \(0.604338\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.81864 | 0.809224 | 0.404612 | − | 0.914488i | \(-0.367407\pi\) | ||||
0.404612 | + | 0.914488i | \(0.367407\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5481 | −1.35160 | −0.675802 | − | 0.737083i | \(-0.736203\pi\) | ||||
−0.675802 | + | 0.737083i | \(0.736203\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.27053 | −0.372712 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0821 | 1.24684 | 0.623419 | − | 0.781888i | \(-0.285743\pi\) | ||||
0.623419 | + | 0.781888i | \(0.285743\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.23746 | −0.574886 | −0.287443 | − | 0.957798i | \(-0.592805\pi\) | ||||
−0.287443 | + | 0.957798i | \(0.592805\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.51504 | 0.815120 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.45893 | 0.154646 | 0.0773232 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773232 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.42586 | −0.359128 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.42586 | 0.146290 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6563 | 1.79272 | 0.896362 | − | 0.443324i | \(-0.146201\pi\) | ||||
0.896362 | + | 0.443324i | \(0.146201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.0491 | −1.69645 | −0.848223 | − | 0.529640i | \(-0.822327\pi\) | ||||
−0.848223 | + | 0.529640i | \(0.822327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3597 | −1.11931 | −0.559653 | − | 0.828727i | \(-0.689066\pi\) | ||||
−0.559653 | + | 0.828727i | \(0.689066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8186 | −1.04588 | −0.522939 | − | 0.852370i | \(-0.675164\pi\) | ||||
−0.522939 | + | 0.852370i | \(0.675164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.2776 | −1.17598 | −0.587989 | − | 0.808869i | \(-0.700080\pi\) | ||||
−0.587989 | + | 0.808869i | \(0.700080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.696393 | 0.0655111 | 0.0327556 | − | 0.999463i | \(-0.489572\pi\) | ||||
0.0327556 | + | 0.999463i | \(0.489572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.818644 | 0.0763390 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.27053 | 0.483149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.303607 | −0.0276007 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3597 | 1.01604 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.68935 | −0.504848 | −0.252424 | − | 0.967617i | \(-0.581228\pi\) | ||||
−0.252424 | + | 0.967617i | \(0.581228\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2044 | 1.32841 | 0.664207 | − | 0.747549i | \(-0.268769\pi\) | ||||
0.664207 | + | 0.747549i | \(0.268769\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.70344 | −0.316406 | −0.158203 | − | 0.987407i | \(-0.550570\pi\) | ||||
−0.158203 | + | 0.987407i | \(0.550570\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6704 | −0.989867 | −0.494934 | − | 0.868931i | \(-0.664808\pi\) | ||||
−0.494934 | + | 0.868931i | \(0.664808\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2044 | 0.936958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.174313 | −0.0144759 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8186 | −1.54168 | −0.770842 | − | 0.637027i | \(-0.780164\pi\) | ||||
−0.770842 | + | 0.637027i | \(0.780164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.43290 | −0.360744 | −0.180372 | − | 0.983598i | \(-0.557730\pi\) | ||||
−0.180372 | + | 0.983598i | \(0.557730\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.02603 | −0.243057 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.82569 | −0.784175 | −0.392088 | − | 0.919928i | \(-0.628247\pi\) | ||||
−0.392088 | + | 0.919928i | \(0.628247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.574141 | 0.0452487 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9409 | −0.856957 | −0.428479 | − | 0.903552i | \(-0.640950\pi\) | ||||
−0.428479 | + | 0.903552i | \(0.640950\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7525 | 0.986818 | 0.493409 | − | 0.869797i | \(-0.335751\pi\) | ||||
0.493409 | + | 0.869797i | \(0.335751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.26349 | −0.0971917 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.5411 | −1.71377 | −0.856883 | − | 0.515511i | \(-0.827602\pi\) | ||||
−0.856883 | + | 0.515511i | \(0.827602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.96693 | 0.224279 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.41882 | −0.479765 | −0.239882 | − | 0.970802i | \(-0.577109\pi\) | ||||
−0.239882 | + | 0.970802i | \(0.577109\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.81160 | 0.729291 | 0.364645 | − | 0.931146i | \(-0.381190\pi\) | ||||
0.364645 | + | 0.931146i | \(0.381190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.65628 | 0.415858 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.2375 | −1.26053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2515 | −1.10356 | −0.551782 | − | 0.833989i | \(-0.686052\pi\) | ||||
−0.551782 | + | 0.833989i | \(0.686052\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7455 | −1.13338 | −0.566691 | − | 0.823930i | \(-0.691777\pi\) | ||||
−0.566691 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.8086 | −1.76754 | −0.883770 | − | 0.467922i | \(-0.845003\pi\) | ||||
−0.883770 | + | 0.467922i | \(0.845003\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.58823 | −0.183474 | −0.0917372 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917372 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.122252 | −0.00858038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.64924 | −0.464403 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.27053 | −0.226228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.7785 | 1.49930 | 0.749648 | − | 0.661837i | \(-0.230223\pi\) | ||||
0.749648 | + | 0.661837i | \(0.230223\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.0160 | 1.16048 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.12225 | −0.144068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.0561 | −1.21459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.90078 | −0.663005 | −0.331503 | − | 0.943454i | \(-0.607556\pi\) | ||||
−0.331503 | + | 0.943454i | \(0.607556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.71538 | −0.180226 | −0.0901131 | − | 0.995932i | \(-0.528723\pi\) | ||||
−0.0901131 | + | 0.995932i | \(0.528723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.29656 | −0.548252 | −0.274126 | − | 0.961694i | \(-0.588389\pi\) | ||||
−0.274126 | + | 0.961694i | \(0.588389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.7295 | −0.964959 | −0.482480 | − | 0.875907i | \(-0.660264\pi\) | ||||
−0.482480 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.44185 | 0.289754 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.9970 | −1.87566 | −0.937830 | − | 0.347095i | \(-0.887168\pi\) | ||||
−0.937830 | + | 0.347095i | \(0.887168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.31065 | −0.277673 | −0.138837 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138837 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.42586 | −0.0910948 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.42586 | −0.217982 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.4329 | 0.658519 | 0.329259 | − | 0.944239i | \(-0.393201\pi\) | ||||
0.329259 | + | 0.944239i | \(0.393201\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.87775 | −0.118053 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.7124 | −1.47914 | −0.739569 | − | 0.673081i | \(-0.764971\pi\) | ||||
−0.739569 | + | 0.673081i | \(0.764971\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.96693 | 0.246493 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.9409 | −1.90790 | −0.953949 | − | 0.299970i | \(-0.903023\pi\) | ||||
−0.953949 | + | 0.299970i | \(0.903023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.68231 | −0.533350 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.17131 | 0.559185 | 0.279592 | − | 0.960119i | \(-0.409801\pi\) | ||||
0.279592 | + | 0.960119i | \(0.409801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0420 | 1.21747 | 0.608733 | − | 0.793375i | \(-0.291678\pi\) | ||||
0.608733 | + | 0.793375i | \(0.291678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.70344 | −0.585139 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.45893 | −0.448164 | −0.224082 | − | 0.974570i | \(-0.571938\pi\) | ||||
−0.224082 | + | 0.974570i | \(0.571938\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2114 | −0.728473 | −0.364236 | − | 0.931307i | \(-0.618670\pi\) | ||||
−0.364236 | + | 0.931307i | \(0.618670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.02303 | −0.476920 | −0.238460 | − | 0.971152i | \(-0.576643\pi\) | ||||
−0.238460 | + | 0.971152i | \(0.576643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.66332 | −0.275267 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.7785 | 0.634031 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0331 | −0.819821 | −0.409910 | − | 0.912126i | \(-0.634440\pi\) | ||||
−0.409910 | + | 0.912126i | \(0.634440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.45593 | −0.142990 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.96693 | −0.113750 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9339 | 0.687856 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.4118 | −0.996995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0702 | 0.917174 | 0.458587 | − | 0.888649i | \(-0.348356\pi\) | ||||
0.458587 | + | 0.888649i | \(0.348356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.56710 | 0.0888620 | 0.0444310 | − | 0.999012i | \(-0.485853\pi\) | ||||
0.0444310 | + | 0.999012i | \(0.485853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.6232 | 1.67440 | 0.837201 | − | 0.546895i | \(-0.184190\pi\) | ||||
0.837201 | + | 0.546895i | \(0.184190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4890 | 1.26311 | 0.631554 | − | 0.775332i | \(-0.282417\pi\) | ||||
0.631554 | + | 0.775332i | \(0.282417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.399828 | 0.0223861 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.27053 | 0.293260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.1643 | −0.563812 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.11521 | 0.171747 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.3857 | 1.56022 | 0.780111 | − | 0.625641i | \(-0.215163\pi\) | ||||
0.780111 | + | 0.625641i | \(0.215163\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.51504 | 0.410590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.6272 | 1.61390 | 0.806950 | − | 0.590620i | \(-0.201117\pi\) | ||||
0.806950 | + | 0.590620i | \(0.201117\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.94090 | 0.375871 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.8607 | 1.76405 | 0.882026 | − | 0.471200i | \(-0.156179\pi\) | ||||
0.882026 | + | 0.471200i | \(0.156179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.5641 | −1.74312 | −0.871558 | − | 0.490292i | \(-0.836890\pi\) | ||||
−0.871558 | + | 0.490292i | \(0.836890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.6633 | 1.63204 | 0.816022 | − | 0.578021i | \(-0.196175\pi\) | ||||
0.816022 | + | 0.578021i | \(0.196175\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.72242 | −0.516013 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.67740 | 0.352420 | 0.176210 | − | 0.984353i | \(-0.443616\pi\) | ||||
0.176210 | + | 0.984353i | \(0.443616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.4660 | 0.861868 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.19544 | 0.271200 | 0.135600 | − | 0.990764i | \(-0.456704\pi\) | ||||
0.135600 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.08918 | −0.316134 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.31769 | −0.0682275 | −0.0341137 | − | 0.999418i | \(-0.510861\pi\) | ||||
−0.0341137 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.418817 | 0.0215701 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6563 | −0.804209 | −0.402104 | − | 0.915594i | \(-0.631721\pi\) | ||||
−0.402104 | + | 0.915594i | \(0.631721\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.0631 | −1.48506 | −0.742529 | − | 0.669814i | \(-0.766374\pi\) | ||||
−0.742529 | + | 0.669814i | \(0.766374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.66332 | 0.237665 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7295 | −0.544006 | −0.272003 | − | 0.962296i | \(-0.587686\pi\) | ||||
−0.272003 | + | 0.962296i | \(0.587686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.02603 | 0.153033 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.8016 | −0.795063 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7997 | 0.542019 | 0.271010 | − | 0.962577i | \(-0.412642\pi\) | ||||
0.271010 | + | 0.962577i | \(0.412642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.66332 | 0.332750 | 0.166375 | − | 0.986063i | \(-0.446794\pi\) | ||||
0.166375 | + | 0.986063i | \(0.446794\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.27053 | 0.362171 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.9740 | −0.643096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.5481 | −1.26327 | −0.631636 | − | 0.775265i | \(-0.717616\pi\) | ||||
−0.631636 | + | 0.775265i | \(0.717616\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.72242 | −0.0847549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.46788 | 0.366584 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.2415 | −1.62395 | −0.811977 | − | 0.583690i | \(-0.801608\pi\) | ||||
−0.811977 | + | 0.583690i | \(0.801608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.95094 | 0.143820 | 0.0719099 | − | 0.997411i | \(-0.477091\pi\) | ||||
0.0719099 | + | 0.997411i | \(0.477091\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.6373 | 0.758520 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2114 | −0.590953 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.29656 | −0.206958 | −0.103479 | − | 0.994632i | \(-0.532997\pi\) | ||||
−0.103479 | + | 0.994632i | \(0.532997\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.96693 | 0.286752 | 0.143376 | − | 0.989668i | \(-0.454204\pi\) | ||||
0.143376 | + | 0.989668i | \(0.454204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.574141 | 0.0274649 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.5711 | 1.79317 | 0.896586 | − | 0.442869i | \(-0.146039\pi\) | ||||
0.896586 | + | 0.442869i | \(0.146039\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.2515 | 0.724623 | 0.362311 | − | 0.932057i | \(-0.381988\pi\) | ||||
0.362311 | + | 0.932057i | \(0.381988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.08023 | −0.0986124 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.7926 | 1.68916 | 0.844579 | − | 0.535431i | \(-0.179851\pi\) | ||||
0.844579 | + | 0.535431i | \(0.179851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.2515 | 0.718167 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.88479 | 0.229003 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6443 | 0.872145 | 0.436073 | − | 0.899912i | \(-0.356369\pi\) | ||||
0.436073 | + | 0.899912i | \(0.356369\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8306 | 0.551006 | 0.275503 | − | 0.961300i | \(-0.411156\pi\) | ||||
0.275503 | + | 0.961300i | \(0.411156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.752498 | 0.0349715 | 0.0174858 | − | 0.999847i | \(-0.494434\pi\) | ||||
0.0174858 | + | 0.999847i | \(0.494434\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8588 | 0.641307 | 0.320653 | − | 0.947197i | \(-0.396098\pi\) | ||||
0.320653 | + | 0.947197i | \(0.396098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.27053 | 0.243371 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.0301 | −1.79460 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.96693 | 0.136132 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.58118 | 0.346393 | 0.173197 | − | 0.984887i | \(-0.444590\pi\) | ||||
0.173197 | + | 0.984887i | \(0.444590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.5901 | −0.619657 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.1754 | −1.14315 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.6864 | −0.484245 | −0.242122 | − | 0.970246i | \(-0.577844\pi\) | ||||
−0.242122 | + | 0.970246i | \(0.577844\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1643 | 0.639225 | 0.319612 | − | 0.947548i | \(-0.396447\pi\) | ||||
0.319612 | + | 0.947548i | \(0.396447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.644331 | −0.0290192 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.81864 | −0.305858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.9108 | −1.07040 | −0.535198 | − | 0.844727i | \(-0.679763\pi\) | ||||
−0.535198 | + | 0.844727i | \(0.679763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.4388 | 1.66932 | 0.834658 | − | 0.550769i | \(-0.185665\pi\) | ||||
0.834658 | + | 0.550769i | \(0.185665\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.3096 | 1.08176 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.3126 | −1.38790 | −0.693952 | − | 0.720021i | \(-0.744132\pi\) | ||||
−0.693952 | + | 0.720021i | \(0.744132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.5481 | 0.510858 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.1973 | 0.713740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1884 | −0.448085 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.8346 | −0.956593 | −0.478296 | − | 0.878199i | \(-0.658746\pi\) | ||||
−0.478296 | + | 0.878199i | \(0.658746\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.37380 | 0.409888 | 0.204944 | − | 0.978774i | \(-0.434299\pi\) | ||||
0.204944 | + | 0.978774i | \(0.434299\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.1854 | −0.487244 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6704 | −0.985668 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.9759 | 0.691992 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.4259 | 0.666918 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.27053 | 0.140872 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.4608 | −1.30961 | −0.654807 | − | 0.755796i | \(-0.727250\pi\) | ||||
−0.654807 | + | 0.755796i | \(0.727250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.5061 | 0.749878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.2675 | 1.46517 | 0.732587 | − | 0.680673i | \(-0.238313\pi\) | ||||
0.732587 | + | 0.680673i | \(0.238313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.122252 | −0.00520809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0821 | −0.471260 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.44889 | 0.0613915 | 0.0306957 | − | 0.999529i | \(-0.490228\pi\) | ||||
0.0306957 | + | 0.999529i | \(0.490228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.8837 | −1.72920 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8707 | 0.458146 | 0.229073 | − | 0.973409i | \(-0.426431\pi\) | ||||
0.229073 | + | 0.973409i | \(0.426431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.992958 | −0.0417740 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.0772 | −1.05129 | −0.525646 | − | 0.850703i | \(-0.676176\pi\) | ||||
−0.525646 | + | 0.850703i | \(0.676176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.6042 | −0.485621 | −0.242811 | − | 0.970074i | \(-0.578069\pi\) | ||||
−0.242811 | + | 0.970074i | \(0.578069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.70344 | 0.0710382 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.5782 | 1.10646 | 0.553232 | − | 0.833027i | \(-0.313394\pi\) | ||||
0.553232 | + | 0.833027i | \(0.313394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.23746 | 0.217286 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.9149 | 0.824789 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.5552 | 0.683304 | 0.341652 | − | 0.939826i | \(-0.389014\pi\) | ||||
0.341652 | + | 0.939826i | \(0.389014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.12225 | −0.0874459 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.6864 | −1.09588 | −0.547939 | − | 0.836519i | \(-0.684587\pi\) | ||||
−0.547939 | + | 0.836519i | \(0.684587\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.51504 | −0.308086 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.6603 | 0.803299 | 0.401649 | − | 0.915793i | \(-0.368437\pi\) | ||||
0.401649 | + | 0.915793i | \(0.368437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.1854 | −0.945752 | −0.472876 | − | 0.881129i | \(-0.656784\pi\) | ||||
−0.472876 | + | 0.881129i | \(0.656784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.432901 | 0.0175999 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.441848 | 0.0179341 | 0.00896704 | − | 0.999960i | \(-0.497146\pi\) | ||||
0.00896704 | + | 0.999960i | \(0.497146\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.6723 | −0.431754 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3478 | −1.14496 | −0.572478 | − | 0.819920i | \(-0.694018\pi\) | ||||
−0.572478 | + | 0.819920i | \(0.694018\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.7455 | −1.27802 | −0.639012 | − | 0.769197i | \(-0.720657\pi\) | ||||
−0.639012 | + | 0.769197i | \(0.720657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.2535 | 0.894442 | 0.447221 | − | 0.894424i | \(-0.352414\pi\) | ||||
0.447221 | + | 0.894424i | \(0.352414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.45893 | −0.0584509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.36271 | −0.0545085 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.9078 | 0.833649 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.4719 | −0.775165 | −0.387583 | − | 0.921835i | \(-0.626690\pi\) | ||||
−0.387583 | + | 0.921835i | \(0.626690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.11221 | 0.321923 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.42586 | 0.135737 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2345 | −1.58917 | −0.794583 | − | 0.607156i | \(-0.792310\pi\) | ||||
−0.794583 | + | 0.607156i | \(0.792310\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1011 | −0.674403 | −0.337201 | − | 0.941433i | \(-0.609480\pi\) | ||||
−0.337201 | + | 0.941433i | \(0.609480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.37380 | 0.211266 | 0.105633 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105633 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.63325 | 0.221124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.6183 | 0.454659 | 0.227330 | − | 0.973818i | \(-0.427001\pi\) | ||||
0.227330 | + | 0.973818i | \(0.427001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.6793 | −0.847081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.8718 | 1.63109 | 0.815546 | − | 0.578692i | \(-0.196437\pi\) | ||||
0.815546 | + | 0.578692i | \(0.196437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.71942 | 0.261355 | 0.130678 | − | 0.991425i | \(-0.458285\pi\) | ||||
0.130678 | + | 0.991425i | \(0.458285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.42586 | −0.0552924 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0701896 | −0.00271775 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.9379 | 1.54179 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.5280 | 1.67788 | 0.838941 | − | 0.544222i | \(-0.183175\pi\) | ||||
0.838941 | + | 0.544222i | \(0.183175\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1033 | −0.695765 | −0.347882 | − | 0.937538i | \(-0.613099\pi\) | ||||
−0.347882 | + | 0.937538i | \(0.613099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.6563 | −0.677586 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.3456 | −1.04635 | −0.523176 | − | 0.852225i | \(-0.675253\pi\) | ||||
−0.523176 | + | 0.852225i | \(0.675253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.28058 | 0.201760 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.8607 | 0.794728 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.8316 | −1.17289 | −0.586445 | − | 0.809989i | \(-0.699473\pi\) | ||||
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.6403 | 0.631202 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.5782 | −0.930965 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.23042 | 0.310859 | 0.155429 | − | 0.987847i | \(-0.450324\pi\) | ||||
0.155429 | + | 0.987847i | \(0.450324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.96693 | 0.149615 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.0491 | 0.641196 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6183 | −0.586558 | −0.293279 | − | 0.956027i | \(-0.594746\pi\) | ||||
−0.293279 | + | 0.956027i | \(0.594746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.21847 | −0.0456321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.9759 | −0.597464 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.3567 | −0.610002 | −0.305001 | − | 0.952352i | \(-0.598657\pi\) | ||||
−0.305001 | + | 0.952352i | \(0.598657\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3597 | 0.423058 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.362711 | −0.0134708 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.6183 | −0.653427 | −0.326713 | − | 0.945123i | \(-0.605941\pi\) | ||||
−0.326713 | + | 0.945123i | \(0.605941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 62.8978 | 2.32636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.8837 | −1.58395 | −0.791973 | − | 0.610556i | \(-0.790946\pi\) | ||||
−0.791973 | + | 0.610556i | \(0.790946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.2375 | −0.634950 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.4259 | 0.714592 | 0.357296 | − | 0.933991i | \(-0.383699\pi\) | ||||
0.357296 | + | 0.933991i | \(0.383699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −51.7305 | −1.89781 | −0.948904 | − | 0.315564i | \(-0.897806\pi\) | ||||
−0.948904 | + | 0.315564i | \(0.897806\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.8327 | 0.983075 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.8186 | 0.395305 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.9428 | 0.873685 | 0.436843 | − | 0.899538i | \(-0.356097\pi\) | ||||
0.436843 | + | 0.899538i | \(0.356097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.32069 | 0.230033 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.48901 | −0.0904645 | −0.0452322 | − | 0.998976i | \(-0.514403\pi\) | ||||
−0.0452322 | + | 0.998976i | \(0.514403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.14528 | 0.150266 | 0.0751332 | − | 0.997174i | \(-0.476062\pi\) | ||||
0.0751332 | + | 0.997174i | \(0.476062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2776 | 0.444478 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.90078 | 0.213065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0442 | −0.398263 | −0.199131 | − | 0.979973i | \(-0.563812\pi\) | ||||
−0.199131 | + | 0.979973i | \(0.563812\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.3426 | 1.52296 | 0.761479 | − | 0.648189i | \(-0.224473\pi\) | ||||
0.761479 | + | 0.648189i | \(0.224473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.29656 | −0.226179 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.66332 | −0.167081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3006 | 0.797979 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0100 | 0.500040 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.5711 | 1.76702 | 0.883510 | − | 0.468412i | \(-0.155174\pi\) | ||||
0.883510 | + | 0.468412i | \(0.155174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.696393 | −0.0247609 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.8346 | 1.48559 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.8276 | −1.37534 | −0.687672 | − | 0.726022i | \(-0.741367\pi\) | ||||
−0.687672 | + | 0.726022i | \(0.741367\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4188 | 0.580856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.7685 | −1.33282 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.818644 | −0.0288534 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.4920 | −0.474354 | −0.237177 | − | 0.971466i | \(-0.576222\pi\) | ||||
−0.237177 | + | 0.971466i | \(0.576222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5552 | 0.862248 | 0.431124 | − | 0.902293i | \(-0.358117\pi\) | ||||
0.431124 | + | 0.902293i | \(0.358117\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.6002 | 0.546450 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9339 | 0.417513 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.9339 | 1.32390 | 0.661950 | − | 0.749548i | \(-0.269729\pi\) | ||||
0.661950 | + | 0.749548i | \(0.269729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0141 | −0.349069 | −0.174535 | − | 0.984651i | \(-0.555842\pi\) | ||||
−0.174535 | + | 0.984651i | \(0.555842\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.7685 | 1.24379 | 0.621896 | − | 0.783100i | \(-0.286363\pi\) | ||||
0.621896 | + | 0.783100i | \(0.286363\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6753 | 0.891739 | 0.445869 | − | 0.895098i | \(-0.352895\pi\) | ||||
0.445869 | + | 0.895098i | \(0.352895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.27053 | −0.182613 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1833 | −0.629258 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.7856 | 1.47712 | 0.738561 | − | 0.674187i | \(-0.235506\pi\) | ||||
0.738561 | + | 0.674187i | \(0.235506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9851 | −0.999485 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.80156 | 0.0619756 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.303607 | 0.0104321 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.27758 | 0.0780743 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.8447 | 0.610990 | 0.305495 | − | 0.952194i | \(-0.401178\pi\) | ||||
0.305495 | + | 0.952194i | \(0.401178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37.8116 | −1.29162 | −0.645810 | − | 0.763498i | \(-0.723480\pi\) | ||||
−0.645810 | + | 0.763498i | \(0.723480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.8558 | 0.779828 | 0.389914 | − | 0.920851i | \(-0.372505\pi\) | ||||
0.389914 | + | 0.920851i | \(0.372505\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.3177 | −0.453339 | −0.226670 | − | 0.973972i | \(-0.572784\pi\) | ||||
−0.226670 | + | 0.973972i | \(0.572784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.1404 | 1.09281 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.2445 | 1.22951 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0561 | −0.611808 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3597 | −0.384028 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5571 | −1.13314 | −0.566571 | − | 0.824013i | \(-0.691730\pi\) | ||||
−0.566571 | + | 0.824013i | \(0.691730\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.5641 | 1.77093 | 0.885465 | − | 0.464707i | \(-0.153840\pi\) | ||||
0.885465 | + | 0.464707i | \(0.153840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.68445 | −0.191297 | −0.0956484 | − | 0.995415i | \(-0.530492\pi\) | ||||
−0.0956484 | + | 0.995415i | \(0.530492\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.3898 | −0.886082 | −0.443041 | − | 0.896501i | \(-0.646100\pi\) | ||||
−0.443041 | + | 0.896501i | \(0.646100\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.68935 | 0.190815 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.11521 | 0.104247 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.15233 | 0.305929 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.259449 | 0.00865309 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.0932 | −1.06918 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.9900 | −0.465042 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.211430 | 0.00702041 | 0.00351021 | − | 0.999994i | \(-0.498883\pi\) | ||||
0.00351021 | + | 0.999994i | \(0.498883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3787 | 0.708308 | 0.354154 | − | 0.935187i | \(-0.384769\pi\) | ||||
0.354154 | + | 0.935187i | \(0.384769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.1293 | −0.566897 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.2044 | −0.502093 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.8186 | −0.554796 | −0.277398 | − | 0.960755i | \(-0.589472\pi\) | ||||
−0.277398 | + | 0.960755i | \(0.589472\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3597 | 0.768894 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.7696 | 0.386981 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.3497 | 1.15979 | 0.579893 | − | 0.814693i | \(-0.303095\pi\) | ||||
0.579893 | + | 0.814693i | \(0.303095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.5782 | 0.803793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.78153 | 0.156206 | 0.0781029 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781029 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6373 | 0.444563 | 0.222281 | − | 0.974983i | \(-0.428650\pi\) | ||||
0.222281 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.67740 | −0.0871883 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.3638 | 1.92906 | 0.964531 | − | 0.263968i | \(-0.0850313\pi\) | ||||
0.964531 | + | 0.263968i | \(0.0850313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.5622 | −1.28424 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.4790 | 1.69996 | 0.849980 | − | 0.526815i | \(-0.176614\pi\) | ||||
0.849980 | + | 0.526815i | \(0.176614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.7465 | 0.703702 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.70344 | 0.119590 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4960 | −0.854711 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4508 | 0.722717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.9900 | 0.707149 | 0.353575 | − | 0.935406i | \(-0.384966\pi\) | ||||
0.353575 | + | 0.935406i | \(0.384966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.9309 | 1.31353 | 0.656767 | − | 0.754094i | \(-0.271924\pi\) | ||||
0.656767 | + | 0.754094i | \(0.271924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6704 | 0.374135 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.56924 | −0.274154 | −0.137077 | − | 0.990560i | \(-0.543771\pi\) | ||||
−0.137077 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.77149 | 0.152497 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.2654 | −1.12479 | −0.562396 | − | 0.826868i | \(-0.690120\pi\) | ||||
−0.562396 | + | 0.826868i | \(0.690120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.3736 | 1.12710 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.85172 | 0.217872 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.78367 | 0.0566600 | 0.0283300 | − | 0.999599i | \(-0.490981\pi\) | ||||
0.0283300 | + | 0.999599i | \(0.490981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.69044 | 0.116995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.4299 | −1.18542 | −0.592708 | − | 0.805417i | \(-0.701941\pi\) | ||||
−0.592708 | + | 0.805417i | \(0.701941\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4788.2.a.o.1.2 | 3 | ||
3.2 | odd | 2 | 532.2.a.e.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 2128.2.a.r.1.1 | 3 | |||
21.20 | even | 2 | 3724.2.a.i.1.1 | 3 | |||
24.5 | odd | 2 | 8512.2.a.bn.1.1 | 3 | |||
24.11 | even | 2 | 8512.2.a.bl.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
532.2.a.e.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
2128.2.a.r.1.1 | 3 | 12.11 | even | 2 | |||
3724.2.a.i.1.1 | 3 | 21.20 | even | 2 | |||
4788.2.a.o.1.2 | 3 | 1.1 | even | 1 | trivial | ||
8512.2.a.bl.1.3 | 3 | 24.11 | even | 2 | |||
8512.2.a.bn.1.1 | 3 | 24.5 | odd | 2 |