Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.55466\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | −3.95805 | −1.77009 | −0.885046 | − | 0.465503i | \(-0.845873\pi\) | ||||
−0.885046 | + | 0.465503i | \(0.845873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.848723 | 0.255900 | 0.127950 | − | 0.991781i | \(-0.459160\pi\) | ||||
0.127950 | + | 0.991781i | \(0.459160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.85936 | −1.62509 | −0.812547 | − | 0.582895i | \(-0.801920\pi\) | ||||
−0.812547 | + | 0.582895i | \(0.801920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.75004 | −0.666982 | −0.333491 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333491 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.66613 | −1.75873 | −0.879365 | − | 0.476147i | \(-0.842033\pi\) | ||||
−0.879365 | + | 0.476147i | \(0.842033\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.70808 | −0.564675 | −0.282337 | − | 0.959315i | \(-0.591110\pi\) | ||||
−0.282337 | + | 0.959315i | \(0.591110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6661 | 2.13323 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.85936 | 1.08806 | 0.544028 | − | 0.839067i | \(-0.316899\pi\) | ||||
0.544028 | + | 0.839067i | \(0.316899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.80677 | −1.04293 | −0.521463 | − | 0.853274i | \(-0.674614\pi\) | ||||
−0.521463 | + | 0.853274i | \(0.674614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.95805 | 0.669032 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.35929 | −0.552263 | −0.276132 | − | 0.961120i | \(-0.589053\pi\) | ||||
−0.276132 | + | 0.961120i | \(0.589053\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.90131 | −0.296935 | −0.148468 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148468 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.35929 | −0.359788 | −0.179894 | − | 0.983686i | \(-0.557575\pi\) | ||||
−0.179894 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.55681 | −0.518814 | −0.259407 | − | 0.965768i | \(-0.583527\pi\) | ||||
−0.259407 | + | 0.965768i | \(0.583527\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.2186 | −1.40364 | −0.701820 | − | 0.712355i | \(-0.747629\pi\) | ||||
−0.701820 | + | 0.712355i | \(0.747629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.35929 | −0.452966 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.77545 | −0.751900 | −0.375950 | − | 0.926640i | \(-0.622684\pi\) | ||||
−0.375950 | + | 0.926640i | \(0.622684\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50008 | −0.704212 | −0.352106 | − | 0.935960i | \(-0.614534\pi\) | ||||
−0.352106 | + | 0.935960i | \(0.614534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.1916 | 2.87657 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4729 | −1.40164 | −0.700819 | − | 0.713339i | \(-0.747182\pi\) | ||||
−0.700819 | + | 0.713339i | \(0.747182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.45812 | 1.12247 | 0.561236 | − | 0.827656i | \(-0.310326\pi\) | ||||
0.561236 | + | 0.827656i | \(0.310326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.97282 | −0.933148 | −0.466574 | − | 0.884482i | \(-0.654512\pi\) | ||||
−0.466574 | + | 0.884482i | \(0.654512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.848723 | −0.0967210 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0780 | −1.13386 | −0.566932 | − | 0.823764i | \(-0.691870\pi\) | ||||
−0.566932 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.85936 | 1.08221 | 0.541103 | − | 0.840957i | \(-0.318007\pi\) | ||||
0.541103 | + | 0.840957i | \(0.318007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8848 | 1.18062 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.81741 | 0.192645 | 0.0963224 | − | 0.995350i | \(-0.469292\pi\) | ||||
0.0963224 | + | 0.995350i | \(0.469292\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.85936 | 0.614228 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30.3429 | 3.11312 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8322 | 1.60751 | 0.803757 | − | 0.594957i | \(-0.202831\pi\) | ||||
0.803757 | + | 0.594957i | \(0.202831\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.5822 | −1.45099 | −0.725493 | − | 0.688230i | \(-0.758388\pi\) | ||||
−0.725493 | + | 0.688230i | \(0.758388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.91195 | 0.582522 | 0.291261 | − | 0.956644i | \(-0.405925\pi\) | ||||
0.291261 | + | 0.956644i | \(0.405925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.6661 | 1.80452 | 0.902261 | − | 0.431189i | \(-0.141906\pi\) | ||||
0.902261 | + | 0.431189i | \(0.141906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.80677 | −0.556188 | −0.278094 | − | 0.960554i | \(-0.589703\pi\) | ||||
−0.278094 | + | 0.960554i | \(0.589703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.9161 | 1.87355 | 0.936774 | − | 0.349934i | \(-0.113796\pi\) | ||||
0.936774 | + | 0.349934i | \(0.113796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.7187 | 0.999526 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.75004 | 0.252096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2797 | −0.934515 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −22.4268 | −2.00591 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.359285 | 0.0318814 | 0.0159407 | − | 0.999873i | \(-0.494926\pi\) | ||||
0.0159407 | + | 0.999873i | \(0.494926\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.94327 | 0.519266 | 0.259633 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259633 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.66613 | 0.664738 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9730 | −1.10836 | −0.554178 | − | 0.832398i | \(-0.686967\pi\) | ||||
−0.554178 | + | 0.832398i | \(0.686967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.61354 | 0.476134 | 0.238067 | − | 0.971249i | \(-0.423486\pi\) | ||||
0.238067 | + | 0.971249i | \(0.423486\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.97298 | −0.415861 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.1916 | −1.92596 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.80263 | 0.639216 | 0.319608 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319608 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.499925 | 0.0406833 | 0.0203416 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203416 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.9835 | 1.84608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1915 | −1.61145 | −0.805727 | − | 0.592287i | \(-0.798225\pi\) | ||||
−0.805727 | + | 0.592287i | \(0.798225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.70808 | 0.213427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.25425 | 0.724849 | 0.362425 | − | 0.932013i | \(-0.381949\pi\) | ||||
0.362425 | + | 0.932013i | \(0.381949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.5296 | 1.97554 | 0.987771 | − | 0.155911i | \(-0.0498313\pi\) | ||||
0.987771 | + | 0.155911i | \(0.0498313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.3321 | 1.64093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.70808 | −0.205892 | −0.102946 | − | 0.994687i | \(-0.532827\pi\) | ||||
−0.102946 | + | 0.994687i | \(0.532827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.6661 | −0.806284 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.16621 | −0.610371 | −0.305185 | − | 0.952293i | \(-0.598718\pi\) | ||||
−0.305185 | + | 0.952293i | \(0.598718\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.39489 | −0.400999 | −0.200500 | − | 0.979694i | \(-0.564257\pi\) | ||||
−0.200500 | + | 0.979694i | \(0.564257\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.2962 | 0.977557 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.33402 | −0.170680 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.8428 | −1.21870 | −0.609352 | − | 0.792900i | \(-0.708570\pi\) | ||||
−0.609352 | + | 0.792900i | \(0.708570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6135 | 1.12389 | 0.561944 | − | 0.827176i | \(-0.310054\pi\) | ||||
0.561944 | + | 0.827176i | \(0.310054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.80263 | 0.270926 | 0.135463 | − | 0.990782i | \(-0.456748\pi\) | ||||
0.135463 | + | 0.990782i | \(0.456748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3594 | −1.15969 | −0.579845 | − | 0.814727i | \(-0.696887\pi\) | ||||
−0.579845 | + | 0.814727i | \(0.696887\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.85936 | −0.411247 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.52549 | 0.525603 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.50642 | −0.450059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.11346 | 0.145497 | 0.0727484 | − | 0.997350i | \(-0.476823\pi\) | ||||
0.0727484 | + | 0.997350i | \(0.476823\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.33816 | 0.636857 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.80677 | 0.394189 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.1135 | 1.08391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.35929 | 0.358884 | 0.179442 | − | 0.983769i | \(-0.442571\pi\) | ||||
0.179442 | + | 0.983769i | \(0.442571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.80263 | 0.517879 | 0.258939 | − | 0.965894i | \(-0.416627\pi\) | ||||
0.258939 | + | 0.965894i | \(0.416627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4999 | −0.693855 | −0.346927 | − | 0.937892i | \(-0.612775\pi\) | ||||
−0.346927 | + | 0.937892i | \(0.612775\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.0297 | −1.77077 | −0.885387 | − | 0.464854i | \(-0.846107\pi\) | ||||
−0.885387 | + | 0.464854i | \(0.846107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0780 | 0.918348 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.3849 | −0.671740 | −0.335870 | − | 0.941908i | \(-0.609030\pi\) | ||||
−0.335870 | + | 0.941908i | \(0.609030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1915 | −1.17182 | −0.585908 | − | 0.810378i | \(-0.699262\pi\) | ||||
−0.585908 | + | 0.810378i | \(0.699262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.95805 | −0.252870 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.9186 | 2.85810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.1644 | −1.84084 | −0.920422 | − | 0.390927i | \(-0.872155\pi\) | ||||
−0.920422 | + | 0.390927i | \(0.872155\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.29841 | −0.144500 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.8700 | 0.678052 | 0.339026 | − | 0.940777i | \(-0.389903\pi\) | ||||
0.339026 | + | 0.940777i | \(0.389903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.35929 | 0.208736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.6455 | −0.779752 | −0.389876 | − | 0.920867i | \(-0.627482\pi\) | ||||
−0.389876 | + | 0.920867i | \(0.627482\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.4459 | 2.48457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.2590 | 1.35715 | 0.678577 | − | 0.734529i | \(-0.262597\pi\) | ||||
0.678577 | + | 0.734529i | \(0.262597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.0510 | 1.52174 | 0.760869 | − | 0.648905i | \(-0.224773\pi\) | ||||
0.760869 | + | 0.648905i | \(0.224773\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.05259 | 0.545892 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3051 | 1.22001 | 0.610007 | − | 0.792396i | \(-0.291167\pi\) | ||||
0.610007 | + | 0.792396i | \(0.291167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.94327 | 0.593166 | 0.296583 | − | 0.955007i | \(-0.404153\pi\) | ||||
0.296583 | + | 0.955007i | \(0.404153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7187 | 0.934381 | 0.467191 | − | 0.884157i | \(-0.345266\pi\) | ||||
0.467191 | + | 0.884157i | \(0.345266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.90131 | 0.112231 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.43729 | −0.555135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.1958 | −1.41353 | −0.706766 | − | 0.707448i | \(-0.749847\pi\) | ||||
−0.706766 | + | 0.707448i | \(0.749847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.8595 | 1.33093 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.8676 | 0.917649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.35929 | 0.135987 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.7696 | 1.24652 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.6661 | 1.00826 | 0.504130 | − | 0.863628i | \(-0.331813\pi\) | ||||
0.504130 | + | 0.863628i | \(0.331813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8050 | 1.46327 | 0.731634 | − | 0.681698i | \(-0.238758\pi\) | ||||
0.731634 | + | 0.681698i | \(0.238758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8594 | 1.46166 | 0.730829 | − | 0.682561i | \(-0.239134\pi\) | ||||
0.730829 | + | 0.682561i | \(0.239134\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.329730 | −0.0185195 | −0.00925973 | − | 0.999957i | \(-0.502948\pi\) | ||||
−0.00925973 | + | 0.999957i | \(0.502948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.97298 | 0.278433 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0821 | 1.17304 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −62.4967 | −3.46669 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.55681 | 0.196093 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6135 | −1.40785 | −0.703924 | − | 0.710276i | \(-0.748570\pi\) | ||||
−0.703924 | + | 0.710276i | \(0.748570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 45.4103 | 2.48103 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.71872 | −0.474939 | −0.237470 | − | 0.971395i | \(-0.576318\pi\) | ||||
−0.237470 | + | 0.971395i | \(0.576318\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.92834 | −0.266885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5066 | 0.939802 | 0.469901 | − | 0.882719i | \(-0.344290\pi\) | ||||
0.469901 | + | 0.882719i | \(0.344290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.71872 | −0.520231 | −0.260116 | − | 0.965577i | \(-0.583761\pi\) | ||||
−0.260116 | + | 0.965577i | \(0.583761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.682517 | 0.0363267 | 0.0181634 | − | 0.999835i | \(-0.494218\pi\) | ||||
0.0181634 | + | 0.999835i | \(0.494218\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.4357 | −1.98688 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.55252 | 0.398607 | 0.199303 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199303 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.7696 | 2.09313 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.5568 | 1.65176 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.6915 | 1.28889 | 0.644444 | − | 0.764651i | \(-0.277089\pi\) | ||||
0.644444 | + | 0.764651i | \(0.277089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.2186 | 0.530526 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.1390 | −1.81943 | −0.909715 | − | 0.415233i | \(-0.863700\pi\) | ||||
−0.909715 | + | 0.415233i | \(0.863700\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.3321 | −1.76819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.35944 | −0.275296 | −0.137648 | − | 0.990481i | \(-0.543954\pi\) | ||||
−0.137648 | + | 0.990481i | \(0.543954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6348 | 1.20768 | 0.603841 | − | 0.797105i | \(-0.293636\pi\) | ||||
0.603841 | + | 0.797105i | \(0.293636\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.35929 | 0.171205 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8950 | 0.653801 | 0.326900 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326900 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.44733 | 0.376628 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.8892 | 2.00704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.3324 | 1.32159 | 0.660793 | − | 0.750568i | \(-0.270220\pi\) | ||||
0.660793 | + | 0.750568i | \(0.270220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.6917 | −1.43279 | −0.716397 | − | 0.697692i | \(-0.754210\pi\) | ||||
−0.716397 | + | 0.697692i | \(0.754210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.0240 | 1.69485 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.85110 | −0.141324 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.5239 | −1.11373 | −0.556867 | − | 0.830602i | \(-0.687997\pi\) | ||||
−0.556867 | + | 0.830602i | \(0.687997\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.77545 | 0.284191 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.0238 | −1.91560 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.6856 | −1.84106 | −0.920532 | − | 0.390667i | \(-0.872244\pi\) | ||||
−0.920532 | + | 0.390667i | \(0.872244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.69155 | 0.131178 | 0.0655890 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655890 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.3323 | −1.42282 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.50008 | 0.266167 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.70808 | 0.130444 | 0.0652219 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652219 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.964393 | 0.0463458 | 0.0231729 | − | 0.999731i | \(-0.492623\pi\) | ||||
0.0231729 | + | 0.999731i | \(0.492623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.7605 | 0.993111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.4373 | 0.975419 | 0.487709 | − | 0.873006i | \(-0.337833\pi\) | ||||
0.487709 | + | 0.873006i | \(0.337833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.8156 | 1.46410 | 0.732048 | − | 0.681253i | \(-0.238565\pi\) | ||||
0.732048 | + | 0.681253i | \(0.238565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.19338 | −0.340999 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.3535 | −1.10212 | −0.551061 | − | 0.834465i | \(-0.685777\pi\) | ||||
−0.551061 | + | 0.834465i | \(0.685777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.61369 | −0.0759857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.1916 | −1.08724 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6644 | −0.873082 | −0.436541 | − | 0.899684i | \(-0.643797\pi\) | ||||
−0.436541 | + | 0.899684i | \(0.643797\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.7802 | 1.24728 | 0.623639 | − | 0.781713i | \(-0.285654\pi\) | ||||
0.623639 | + | 0.781713i | \(0.285654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.71872 | −0.265772 | −0.132886 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132886 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.7128 | 1.83769 | 0.918845 | − | 0.394618i | \(-0.129123\pi\) | ||||
0.918845 | + | 0.394618i | \(0.129123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.4729 | 0.529769 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.00238 | −0.0920695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −81.7679 | −3.75177 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.8323 | 0.494942 | 0.247471 | − | 0.968895i | \(-0.420400\pi\) | ||||
0.247471 | + | 0.968895i | \(0.420400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.6833 | 0.897480 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −62.6645 | −2.84545 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5781 | −1.43094 | −0.715470 | − | 0.698644i | \(-0.753787\pi\) | ||||
−0.715470 | + | 0.698644i | \(0.753787\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.5361 | −0.971912 | −0.485956 | − | 0.873983i | \(-0.661528\pi\) | ||||
−0.485956 | + | 0.873983i | \(0.661528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.1135 | −0.725714 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.45812 | −0.424255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.2425 | 1.57767 | 0.788834 | − | 0.614606i | \(-0.210685\pi\) | ||||
0.788834 | + | 0.614606i | \(0.210685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.1915 | 0.721942 | 0.360971 | − | 0.932577i | \(-0.382445\pi\) | ||||
0.360971 | + | 0.932577i | \(0.382445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.7171 | 2.56838 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6957 | 0.828672 | 0.414336 | − | 0.910124i | \(-0.364014\pi\) | ||||
0.414336 | + | 0.910124i | \(0.364014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.97282 | 0.352697 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.3998 | −1.03112 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.01874 | −0.132764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3698 | −0.454308 | −0.227154 | − | 0.973859i | \(-0.572942\pi\) | ||||
−0.227154 | + | 0.973859i | \(0.572942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.6137 | 1.03255 | 0.516277 | − | 0.856421i | \(-0.327317\pi\) | ||||
0.516277 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.9688 | 0.695613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.6663 | −0.681143 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.1405 | 0.482548 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −73.8814 | −3.19417 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.848723 | 0.0365571 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9730 | −1.03068 | −0.515339 | − | 0.856986i | \(-0.672334\pi\) | ||||
−0.515339 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.9835 | 0.984503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.9458 | −1.66520 | −0.832601 | − | 0.553873i | \(-0.813149\pi\) | ||||
−0.832601 | + | 0.553873i | \(0.813149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44.9186 | −1.91360 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0780 | 0.428560 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.9161 | −0.674386 | −0.337193 | − | 0.941435i | \(-0.609478\pi\) | ||||
−0.337193 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8239 | 0.584689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4103 | −1.23949 | −0.619747 | − | 0.784801i | \(-0.712765\pi\) | ||||
−0.619747 | + | 0.784801i | \(0.712765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −78.8288 | −3.31635 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5295 | −0.609108 | −0.304554 | − | 0.952495i | \(-0.598507\pi\) | ||||
−0.304554 | + | 0.952495i | \(0.598507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.55091 | −0.399693 | −0.199847 | − | 0.979827i | \(-0.564044\pi\) | ||||
−0.199847 | + | 0.979827i | \(0.564044\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.8848 | −1.20458 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.0510 | 1.29267 | 0.646335 | − | 0.763054i | \(-0.276301\pi\) | ||||
0.646335 | + | 0.763054i | \(0.276301\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.85936 | −0.409035 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.67280 | −0.359191 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.7483 | −0.484903 | −0.242452 | − | 0.970163i | \(-0.577952\pi\) | ||||
−0.242452 | + | 0.970163i | \(0.577952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.5155 | 1.83423 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.6514 | −1.50509 | −0.752545 | − | 0.658540i | \(-0.771174\pi\) | ||||
−0.752545 | + | 0.658540i | \(0.771174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8848 | −0.446232 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.6453 | 0.720967 | 0.360484 | − | 0.932766i | \(-0.382612\pi\) | ||||
0.360484 | + | 0.932766i | \(0.382612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6407 | 0.474835 | 0.237417 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237417 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.6874 | 1.65418 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.0508 | −1.70679 | −0.853395 | − | 0.521264i | \(-0.825461\pi\) | ||||
−0.853395 | + | 0.521264i | \(0.825461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.8406 | 0.843121 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.1934 | −0.855993 | −0.427996 | − | 0.903780i | \(-0.640780\pi\) | ||||
−0.427996 | + | 0.903780i | \(0.640780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2245 | 0.572659 | 0.286329 | − | 0.958131i | \(-0.407565\pi\) | ||||
0.286329 | + | 0.958131i | \(0.407565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.82390 | −0.354663 | −0.177331 | − | 0.984151i | \(-0.556746\pi\) | ||||
−0.177331 | + | 0.984151i | \(0.556746\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.81741 | −0.0728129 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 35.4357 | 1.41743 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.23816 | 0.368350 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1406 | −0.483311 | −0.241656 | − | 0.970362i | \(-0.577690\pi\) | ||||
−0.241656 | + | 0.970362i | \(0.577690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.42207 | −0.0564331 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.85936 | −0.232156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.30270 | 0.209444 | 0.104722 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104722 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.5409 | 1.48047 | 0.740234 | − | 0.672350i | \(-0.234715\pi\) | ||||
0.740234 | + | 0.672350i | \(0.234715\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6076 | 1.79302 | 0.896511 | − | 0.443022i | \(-0.146094\pi\) | ||||
0.896511 | + | 0.443022i | \(0.146094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.90176 | −0.192411 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.5652 | 1.11784 | 0.558922 | − | 0.829220i | \(-0.311215\pi\) | ||||
0.558922 | + | 0.829220i | \(0.311215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.5237 | −0.919148 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.2436 | 0.476944 | 0.238472 | − | 0.971149i | \(-0.423354\pi\) | ||||
0.238472 | + | 0.971149i | \(0.423354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9728 | −1.16581 | −0.582904 | − | 0.812541i | \(-0.698084\pi\) | ||||
−0.582904 | + | 0.812541i | \(0.698084\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −30.3429 | −1.17665 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.8676 | −0.614398 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.66804 | −0.180208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.38661 | 0.130544 | 0.0652722 | − | 0.997867i | \(-0.479208\pi\) | ||||
0.0652722 | + | 0.997867i | \(0.479208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.9792 | −0.729429 | −0.364714 | − | 0.931119i | \(-0.618833\pi\) | ||||
−0.364714 | + | 0.931119i | \(0.618833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8322 | −0.607583 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.5555 | −1.89619 | −0.948094 | − | 0.317990i | \(-0.896992\pi\) | ||||
−0.948094 | + | 0.317990i | \(0.896992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.3476 | 1.96189 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 59.8747 | 2.28105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.5593 | 1.08645 | 0.543224 | − | 0.839588i | \(-0.317203\pi\) | ||||
0.543224 | + | 0.839588i | \(0.317203\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.2186 | −0.842801 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.22869 | 0.198051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1913 | 0.649307 | 0.324654 | − | 0.945833i | \(-0.394752\pi\) | ||||
0.324654 | + | 0.945833i | \(0.394752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7527 | 0.971282 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5822 | 0.548421 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.8578 | −1.75978 | −0.879890 | − | 0.475178i | \(-0.842384\pi\) | ||||
−0.879890 | + | 0.475178i | \(0.842384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.7252 | 0.588914 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.6833 | 0.736112 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.3265 | −1.80227 | −0.901137 | − | 0.433534i | \(-0.857267\pi\) | ||||
−0.901137 | + | 0.433534i | \(0.857267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.91195 | −0.220173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.4967 | 2.32107 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2814 | 0.566757 | 0.283378 | − | 0.959008i | \(-0.408545\pi\) | ||||
0.283378 | + | 0.959008i | \(0.408545\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.48812 | 0.239972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.07816 | −0.335309 | −0.167655 | − | 0.985846i | \(-0.553619\pi\) | ||||
−0.167655 | + | 0.985846i | \(0.553619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.73732 | −0.358679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.7814 | 0.727669 | 0.363834 | − | 0.931464i | \(-0.381467\pi\) | ||||
0.363834 | + | 0.931464i | \(0.381467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.1554 | −0.592685 | −0.296342 | − | 0.955082i | \(-0.595767\pi\) | ||||
−0.296342 | + | 0.955082i | \(0.595767\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.8832 | −1.13147 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.6661 | −0.682046 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4100 | 0.781261 | 0.390630 | − | 0.920548i | \(-0.372257\pi\) | ||||
0.390630 | + | 0.920548i | \(0.372257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.97872 | −0.0720132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49164 | −0.235943 | −0.117971 | − | 0.993017i | \(-0.537639\pi\) | ||||
−0.117971 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.5704 | −1.83318 | −0.916588 | − | 0.399833i | \(-0.869068\pi\) | ||||
−0.916588 | + | 0.399833i | \(0.869068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.80677 | 0.210219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.8405 | 1.22191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.1290 | −0.761931 | −0.380965 | − | 0.924589i | \(-0.624408\pi\) | ||||
−0.380965 | + | 0.924589i | \(0.624408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.3116 | −0.982329 | −0.491165 | − | 0.871067i | \(-0.663429\pi\) | ||||
−0.491165 | + | 0.871067i | \(0.663429\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −61.9358 | −2.22480 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.5757 | 0.522230 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.02733 | 0.287240 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 79.9188 | 2.85242 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7694 | −0.811642 | −0.405821 | − | 0.913953i | \(-0.633014\pi\) | ||||
−0.405821 | + | 0.913953i | \(0.633014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.9161 | −0.708135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.2269 | 1.14441 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.9041 | 1.73227 | 0.866137 | − | 0.499807i | \(-0.166596\pi\) | ||||
0.866137 | + | 0.499807i | \(0.166596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.78135 | 0.346039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.76672 | −0.238792 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7187 | −0.377785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.24597 | −0.254755 | −0.127377 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127377 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.3832 | −1.87454 | −0.937270 | − | 0.348605i | \(-0.886655\pi\) | ||||
−0.937270 | + | 0.348605i | \(0.886655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.6288 | −1.28305 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0866 | 0.632770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.99395 | 0.313891 | 0.156945 | − | 0.987607i | \(-0.449835\pi\) | ||||
0.156945 | + | 0.987607i | \(0.449835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.6645 | −1.69634 | −0.848169 | − | 0.529725i | \(-0.822295\pi\) | ||||
−0.848169 | + | 0.529725i | \(0.822295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.3046 | −0.914702 | −0.457351 | − | 0.889286i | \(-0.651202\pi\) | ||||
−0.457351 | + | 0.889286i | \(0.651202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.8052 | 0.930982 | 0.465491 | − | 0.885053i | \(-0.345878\pi\) | ||||
0.465491 | + | 0.885053i | \(0.345878\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.75004 | −0.0952832 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −101.047 | −3.49689 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.85936 | 0.0641923 | 0.0320961 | − | 0.999485i | \(-0.489782\pi\) | ||||
0.0320961 | + | 0.999485i | \(0.489782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.33211 | 0.183866 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −84.4335 | −2.90460 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2797 | 0.353214 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.09723 | 0.311849 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8323 | 0.370892 | 0.185446 | − | 0.982654i | \(-0.440627\pi\) | ||||
0.185446 | + | 0.982654i | \(0.440627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.598610 | 0.0204481 | 0.0102241 | − | 0.999948i | \(-0.496746\pi\) | ||||
0.0102241 | + | 0.999948i | \(0.496746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4391 | 0.629132 | 0.314566 | − | 0.949236i | \(-0.398141\pi\) | ||||
0.314566 | + | 0.949236i | \(0.398141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −50.2761 | −1.71142 | −0.855710 | − | 0.517456i | \(-0.826879\pi\) | ||||
−0.855710 | + | 0.517456i | \(0.826879\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.7187 | 0.364447 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.55344 | −0.290156 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.2239 | 2.27779 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.4268 | 0.758164 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.66789 | 0.123856 | 0.0619279 | − | 0.998081i | \(-0.480275\pi\) | ||||
0.0619279 | + | 0.998081i | \(0.480275\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.7122 | −0.798885 | −0.399443 | − | 0.916758i | \(-0.630796\pi\) | ||||
−0.399443 | + | 0.916758i | \(0.630796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.9374 | −0.469030 | −0.234515 | − | 0.972113i | \(-0.575350\pi\) | ||||
−0.234515 | + | 0.972113i | \(0.575350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.64087 | 0.222978 | 0.111489 | − | 0.993766i | \(-0.464438\pi\) | ||||
0.111489 | + | 0.993766i | \(0.464438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.359285 | −0.0120500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.2669 | 0.912454 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.3222 | 1.08041 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.0240 | −1.13476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.1017 | 0.936202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.3532 | 0.709806 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.2778 | 1.07177 | 0.535883 | − | 0.844292i | \(-0.319979\pi\) | ||||
0.535883 | + | 0.844292i | \(0.319979\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7168 | 0.586984 | 0.293492 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293492 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.36787 | 0.276936 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.94327 | −0.196264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.7071 | 1.80462 | 0.902310 | − | 0.431088i | \(-0.141870\pi\) | ||||
0.902310 | + | 0.431088i | \(0.141870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −55.4185 | −1.82412 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.8306 | −1.17810 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.4264 | −0.440505 | −0.220252 | − | 0.975443i | \(-0.570688\pi\) | ||||
−0.220252 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.66613 | −0.251247 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.23816 | 0.302120 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.1647 | −1.41013 | −0.705065 | − | 0.709142i | \(-0.749082\pi\) | ||||
−0.705065 | + | 0.709142i | \(0.749082\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.1735 | −1.63561 | −0.817804 | − | 0.575496i | \(-0.804809\pi\) | ||||
−0.817804 | + | 0.575496i | \(0.804809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.14892 | 0.167672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.7421 | −1.61640 | −0.808200 | − | 0.588908i | \(-0.799558\pi\) | ||||
−0.808200 | + | 0.588908i | \(0.799558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.7157 | 1.51645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.8595 | 0.675706 | 0.337853 | − | 0.941199i | \(-0.390299\pi\) | ||||
0.337853 | + | 0.941199i | \(0.390299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.6647 | 2.15722 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.9730 | 0.418919 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.71857 | 0.0876958 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −61.7991 | −1.98938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.2068 | 1.42160 | 0.710798 | − | 0.703396i | \(-0.248334\pi\) | ||||
0.710798 | + | 0.703396i | \(0.248334\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.3680 | −1.13501 | −0.567507 | − | 0.823369i | \(-0.692092\pi\) | ||||
−0.567507 | + | 0.823369i | \(0.692092\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.61354 | −0.179962 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.94580 | −0.222216 | −0.111108 | − | 0.993808i | \(-0.535440\pi\) | ||||
−0.111108 | + | 0.993808i | \(0.535440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.54248 | 0.0492977 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.4433 | −0.875307 | −0.437653 | − | 0.899144i | \(-0.644190\pi\) | ||||
−0.437653 | + | 0.899144i | \(0.644190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.0510 | −0.479564 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.38914 | 0.203163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9102 | 0.632468 | 0.316234 | − | 0.948681i | \(-0.397582\pi\) | ||||
0.316234 | + | 0.948681i | \(0.397582\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64.7514 | 2.05276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.6645 | −0.907814 | −0.453907 | − | 0.891049i | \(-0.649970\pi\) | ||||
−0.453907 | + | 0.891049i | \(0.649970\pi\) | |||||||
\(998\) | 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 | 6048.2.a.bl.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 6048.2.a.bq.1.4 | yes | 4 | ||
4.3 | odd | 2 | 6048.2.a.bn.1.1 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bu.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bl.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bn.1.1 | yes | 4 | 4.3 | odd | 2 | ||
6048.2.a.bq.1.4 | yes | 4 | 3.2 | odd | 2 | ||
6048.2.a.bu.1.4 | yes | 4 | 12.11 | even | 2 |