Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.56155 | −1.72410 | −0.862052 | − | 0.506819i | \(-0.830821\pi\) | ||||
−0.862052 | + | 0.506819i | \(0.830821\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.56155 | −0.710447 | −0.355223 | − | 0.934781i | \(-0.615595\pi\) | ||||
−0.355223 | + | 0.934781i | \(0.615595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.56155 | −0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.561553 | −0.136197 | −0.0680983 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680983 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.6847 | 2.54980 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.68466 | 1.18533 | 0.592667 | − | 0.805448i | \(-0.298075\pi\) | ||||
0.592667 | + | 0.805448i | \(0.298075\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43845 | 0.638504 | 0.319252 | − | 0.947670i | \(-0.396568\pi\) | ||||
0.319252 | + | 0.947670i | \(0.396568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.12311 | 0.920137 | 0.460068 | − | 0.887883i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.2462 | 1.78364 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.56155 | −0.771043 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.56155 | 1.05069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.24621 | 1.28784 | 0.643921 | − | 0.765092i | \(-0.277307\pi\) | ||||
0.643921 | + | 0.765092i | \(0.277307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.12311 | −0.455552 | −0.227776 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227776 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.8078 | 1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.43845 | 0.201423 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.56155 | −0.901299 | −0.450649 | − | 0.892701i | \(-0.648807\pi\) | ||||
−0.450649 | + | 0.892701i | \(0.648807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.8078 | 1.66743 | 0.833714 | − | 0.552196i | \(-0.186210\pi\) | ||||
0.833714 | + | 0.552196i | \(0.186210\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.87689 | 0.624422 | 0.312211 | − | 0.950013i | \(-0.398930\pi\) | ||||
0.312211 | + | 0.950013i | \(0.398930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.2462 | −2.04683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.56155 | −0.317722 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5616 | −1.29030 | −0.645150 | − | 0.764056i | \(-0.723205\pi\) | ||||
−0.645150 | + | 0.764056i | \(0.723205\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.5616 | −1.75300 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.8078 | 1.73312 | 0.866559 | − | 0.499075i | \(-0.166327\pi\) | ||||
0.866559 | + | 0.499075i | \(0.166327\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.2462 | 2.07935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.12311 | −0.576394 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0000 | −1.53670 | −0.768350 | − | 0.640030i | \(-0.778922\pi\) | ||||
−0.768350 | + | 0.640030i | \(0.778922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.561553 | −0.0609090 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.80776 | −0.944291 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.6847 | 1.22489 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.1231 | −1.36080 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12311 | −0.114034 | −0.0570170 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570170 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.2462 | −1.43180 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.12311 | 0.310761 | 0.155380 | − | 0.987855i | \(-0.450340\pi\) | ||||
0.155380 | + | 0.987855i | \(0.450340\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.6847 | 1.14031 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6847 | −1.12960 | −0.564799 | − | 0.825228i | \(-0.691046\pi\) | ||||
−0.564799 | + | 0.825228i | \(0.691046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4384 | −1.09560 | −0.547802 | − | 0.836608i | \(-0.684535\pi\) | ||||
−0.547802 | + | 0.836608i | \(0.684535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.87689 | −0.273063 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.24621 | −0.587594 | −0.293797 | − | 0.955868i | \(-0.594919\pi\) | ||||
−0.293797 | + | 0.955868i | \(0.594919\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.68466 | 0.530097 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.12311 | −0.843431 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.56155 | 0.234817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.1231 | −1.90461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3693 | 1.36381 | 0.681903 | − | 0.731442i | \(-0.261153\pi\) | ||||
0.681903 | + | 0.731442i | \(0.261153\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.12311 | 0.451064 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.56155 | 0.395537 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.43845 | −0.123802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.80776 | −0.239883 | −0.119942 | − | 0.992781i | \(-0.538271\pi\) | ||||
−0.119942 | + | 0.992781i | \(0.538271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.24621 | 0.190521 | 0.0952606 | − | 0.995452i | \(-0.469632\pi\) | ||||
0.0952606 | + | 0.995452i | \(0.469632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2462 | 0.856831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.43845 | 0.285547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −35.3693 | −2.91721 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.12311 | −0.255855 | −0.127927 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127927 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1231 | −1.06794 | −0.533972 | − | 0.845502i | \(-0.679301\pi\) | ||||
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.12311 | 0.411498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.8078 | 1.33294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.9309 | −2.04364 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.75379 | 0.294019 | 0.147010 | − | 0.989135i | \(-0.453035\pi\) | ||||
0.147010 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.2462 | 0.797666 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.3693 | 1.49884 | 0.749421 | − | 0.662093i | \(-0.230332\pi\) | ||||
0.749421 | + | 0.662093i | \(0.230332\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.43845 | −0.495265 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.56155 | −0.272359 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.87689 | −0.218726 | −0.109363 | − | 0.994002i | \(-0.534881\pi\) | ||||
−0.109363 | + | 0.994002i | \(0.534881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.56155 | −0.344821 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −32.8078 | −2.46598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2462 | 1.06481 | 0.532406 | − | 0.846489i | \(-0.321288\pi\) | ||||
0.532406 | + | 0.846489i | \(0.321288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.75379 | −0.576335 | −0.288167 | − | 0.957580i | \(-0.593046\pi\) | ||||
−0.288167 | + | 0.957580i | \(0.593046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4924 | −0.923466 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.12311 | 0.0825724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.24621 | 0.164259 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.56155 | 0.477283 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.31534 | −0.312247 | −0.156124 | − | 0.987738i | \(-0.549900\pi\) | ||||
−0.156124 | + | 0.987738i | \(0.549900\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.12311 | 0.656696 | 0.328348 | − | 0.944557i | \(-0.393508\pi\) | ||||
0.328348 | + | 0.944557i | \(0.393508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.56155 | 0.469883 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.2462 | 1.72747 | 0.863736 | − | 0.503945i | \(-0.168119\pi\) | ||||
0.863736 | + | 0.503945i | \(0.168119\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.43845 | 0.385521 | 0.192761 | − | 0.981246i | \(-0.438256\pi\) | ||||
0.192761 | + | 0.981246i | \(0.438256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.0540 | 1.90824 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.6847 | −1.10085 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.24621 | 0.575940 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.2462 | 1.40721 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0540 | 1.58710 | 0.793551 | − | 0.608504i | \(-0.208230\pi\) | ||||
0.793551 | + | 0.608504i | \(0.208230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.4924 | −1.40412 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.3693 | −1.58641 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −37.9309 | −2.56313 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.43845 | 0.0967604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3693 | −1.02921 | −0.514603 | − | 0.857429i | \(-0.672061\pi\) | ||||
−0.514603 | + | 0.857429i | \(0.672061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.31534 | −0.286419 | −0.143210 | − | 0.989692i | \(-0.545742\pi\) | ||||
−0.143210 | + | 0.989692i | \(0.545742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.7386 | 1.89910 | 0.949551 | − | 0.313612i | \(-0.101539\pi\) | ||||
0.949551 | + | 0.313612i | \(0.101539\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −46.7386 | −3.07518 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.4924 | −1.73558 | −0.867788 | − | 0.496934i | \(-0.834459\pi\) | ||||
−0.867788 | + | 0.496934i | \(0.834459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.12311 | −0.203729 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.1231 | 0.852437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.19224 | 0.206489 | 0.103244 | − | 0.994656i | \(-0.467078\pi\) | ||||
0.103244 | + | 0.994656i | \(0.467078\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.8617 | −1.92356 | −0.961782 | − | 0.273817i | \(-0.911714\pi\) | ||||
−0.961782 | + | 0.273817i | \(0.911714\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.8078 | 0.882146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.56155 | 0.162988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.8617 | 2.27265 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.75379 | 0.363176 | 0.181588 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181588 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.7386 | −1.42957 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.43845 | 0.0900791 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.3693 | −1.95676 | −0.978382 | − | 0.206805i | \(-0.933693\pi\) | ||||
−0.978382 | + | 0.206805i | \(0.933693\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.12311 | −0.318334 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2462 | 0.758021 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.36932 | 0.577737 | 0.288868 | − | 0.957369i | \(-0.406721\pi\) | ||||
0.288868 | + | 0.957369i | \(0.406721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.56155 | −0.403073 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.6155 | 1.56764 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.2462 | 1.47832 | 0.739159 | − | 0.673531i | \(-0.235223\pi\) | ||||
0.739159 | + | 0.673531i | \(0.235223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1771 | 1.22567 | 0.612835 | − | 0.790211i | \(-0.290029\pi\) | ||||
0.612835 | + | 0.790211i | \(0.290029\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −29.9309 | −1.81150 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6155 | 1.17858 | 0.589291 | − | 0.807921i | \(-0.299407\pi\) | ||||
0.589291 | + | 0.807921i | \(0.299407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.2462 | 1.09237 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.2462 | 1.44641 | 0.723204 | − | 0.690635i | \(-0.242669\pi\) | ||||
0.723204 | + | 0.690635i | \(0.242669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | −0.356663 | −0.178331 | − | 0.983970i | \(-0.557070\pi\) | ||||
−0.178331 | + | 0.983970i | \(0.557070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.56155 | 0.151733 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.6155 | −2.22037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.87689 | 0.168647 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.93087 | −0.346485 | −0.173243 | − | 0.984879i | \(-0.555424\pi\) | ||||
−0.173243 | + | 0.984879i | \(0.555424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8078 | 0.745697 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.75379 | 0.333869 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.5616 | −0.842116 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.12311 | 0.525847 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.00000 | −0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.87689 | 0.279250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.75379 | −0.328386 | −0.164193 | − | 0.986428i | \(-0.552502\pi\) | ||||
−0.164193 | + | 0.986428i | \(0.552502\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −40.9848 | −2.33155 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.43845 | 0.308386 | 0.154193 | − | 0.988041i | \(-0.450722\pi\) | ||||
0.154193 | + | 0.988041i | \(0.450722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.1771 | −1.70571 | −0.852855 | − | 0.522148i | \(-0.825131\pi\) | ||||
−0.852855 | + | 0.522148i | \(0.825131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.2462 | −0.915370 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.43845 | −0.305454 | −0.152727 | − | 0.988268i | \(-0.548805\pi\) | ||||
−0.152727 | + | 0.988268i | \(0.548805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.7538 | −0.770064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 29.9309 | 1.67058 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.561553 | 0.0312456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.56155 | −0.142089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.3002 | 1.62030 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.2462 | 0.785419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8078 | −0.703978 | −0.351989 | − | 0.936004i | \(-0.614495\pi\) | ||||
−0.351989 | + | 0.936004i | \(0.614495\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.5616 | −0.577039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8769 | 0.810396 | 0.405198 | − | 0.914229i | \(-0.367203\pi\) | ||||
0.405198 | + | 0.914229i | \(0.367203\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0000 | 0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.4924 | −1.10973 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.0540 | −1.67676 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.5616 | −0.783968 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.0000 | −0.966291 | −0.483145 | − | 0.875540i | \(-0.660506\pi\) | ||||
−0.483145 | + | 0.875540i | \(0.660506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.68466 | 0.196673 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.4233 | −1.93862 | −0.969308 | − | 0.245849i | \(-0.920933\pi\) | ||||
−0.969308 | + | 0.245849i | \(0.920933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.56155 | −0.347274 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.93087 | −0.313019 | −0.156510 | − | 0.987676i | \(-0.550024\pi\) | ||||
−0.156510 | + | 0.987676i | \(0.550024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.8078 | −0.672233 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.8078 | 0.775074 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.1231 | −1.83341 | −0.916706 | − | 0.399563i | \(-0.869162\pi\) | ||||
−0.916706 | + | 0.399563i | \(0.869162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 29.3693 | 1.52891 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.9309 | 1.55393 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8078 | 1.28450 | 0.642249 | − | 0.766496i | \(-0.278002\pi\) | ||||
0.642249 | + | 0.766496i | \(0.278002\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.56155 | −0.132278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.80776 | −0.453623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31534 | 0.427130 | 0.213565 | − | 0.976929i | \(-0.431492\pi\) | ||||
0.213565 | + | 0.976929i | \(0.431492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.3693 | −2.01695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.7386 | −1.36628 | −0.683140 | − | 0.730287i | \(-0.739386\pi\) | ||||
−0.683140 | + | 0.730287i | \(0.739386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.2462 | 0.929913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.12311 | −0.362088 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.12311 | −0.361156 | −0.180578 | − | 0.983561i | \(-0.557797\pi\) | ||||
−0.180578 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.19224 | −0.161438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 40.9848 | 2.06741 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.12311 | −0.257771 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8617 | −1.29796 | −0.648982 | − | 0.760804i | \(-0.724805\pi\) | ||||
−0.648982 | + | 0.760804i | \(0.724805\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.6847 | −0.584965 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7386 | −1.03564 | −0.517819 | − | 0.855490i | \(-0.673256\pi\) | ||||
−0.517819 | + | 0.855490i | \(0.673256\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1231 | −0.653708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.49242 | −0.222681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7386 | 1.22325 | 0.611623 | − | 0.791149i | \(-0.290517\pi\) | ||||
0.611623 | + | 0.791149i | \(0.290517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.19224 | 0.354767 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −58.4233 | −2.87482 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0000 | −0.687233 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.75379 | −0.281764 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.8769 | −1.11761 | −0.558805 | − | 0.829299i | \(-0.688740\pi\) | ||||
−0.558805 | + | 0.829299i | \(0.688740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3002 | −0.940634 | −0.470317 | − | 0.882498i | \(-0.655860\pi\) | ||||
−0.470317 | + | 0.882498i | \(0.655860\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.1231 | −0.540824 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.561553 | −0.0272393 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.2462 | −1.07657 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.2462 | −1.26718 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.4924 | −0.987085 | −0.493543 | − | 0.869722i | \(-0.664298\pi\) | ||||
−0.493543 | + | 0.869722i | \(0.664298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.80776 | −0.422300 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.68466 | −0.271934 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.3693 | −1.49718 | −0.748588 | − | 0.663036i | \(-0.769268\pi\) | ||||
−0.748588 | + | 0.663036i | \(0.769268\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.1771 | 2.34177 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.6155 | 0.551870 | 0.275935 | − | 0.961176i | \(-0.411012\pi\) | ||||
0.275935 | + | 0.961176i | \(0.411012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.00000 | 0.378387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7386 | 0.789945 | 0.394972 | − | 0.918693i | \(-0.370754\pi\) | ||||
0.394972 | + | 0.918693i | \(0.370754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.9848 | −1.55320 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.6155 | 1.57940 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.6847 | 0.547785 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.5616 | 0.774717 | 0.387358 | − | 0.921929i | \(-0.373388\pi\) | ||||
0.387358 | + | 0.921929i | \(0.373388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.807764 | 0.0377032 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2462 | −1.12926 | −0.564629 | − | 0.825345i | \(-0.690981\pi\) | ||||
−0.564629 | + | 0.825345i | \(0.690981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.8617 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.1231 | −0.608569 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.8617 | −1.38184 | −0.690918 | − | 0.722933i | \(-0.742794\pi\) | ||||
−0.690918 | + | 0.722933i | \(0.742794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.1771 | 2.22461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.3693 | 0.708181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | 0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.3693 | −1.07001 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.87689 | −0.131175 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 66.4233 | 3.02236 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.12311 | −0.0509976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.3693 | −1.24022 | −0.620111 | − | 0.784514i | \(-0.712912\pi\) | ||||
−0.620111 | + | 0.784514i | \(0.712912\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.61553 | −0.434829 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.87689 | −0.129832 | −0.0649162 | − | 0.997891i | \(-0.520678\pi\) | ||||
−0.0649162 | + | 0.997891i | \(0.520678\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.93087 | −0.0869620 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.2462 | −0.640320 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.4924 | −1.63691 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1231 | 1.30373 | 0.651865 | − | 0.758335i | \(-0.273987\pi\) | ||||
0.651865 | + | 0.758335i | \(0.273987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.6155 | −2.21666 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.4233 | 1.62403 | 0.812017 | − | 0.583634i | \(-0.198370\pi\) | ||||
0.812017 | + | 0.583634i | \(0.198370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.12311 | 0.138976 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.4924 | 0.732454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −67.5464 | −2.98808 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43845 | 0.0635090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4924 | 0.549416 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.36932 | 0.323477 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.12311 | 0.312069 | 0.156034 | − | 0.987752i | \(-0.450129\pi\) | ||||
0.156034 | + | 0.987752i | \(0.450129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9309 | −0.609154 | −0.304577 | − | 0.952488i | \(-0.598515\pi\) | ||||
−0.304577 | + | 0.952488i | \(0.598515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.6847 | 0.509960 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.87689 | −0.125319 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.31534 | 0.405015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 45.6155 | 1.97955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.1231 | −0.914943 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6847 | −0.505172 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.4924 | −1.57476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −55.2311 | −2.37897 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8769 | 0.725594 | 0.362797 | − | 0.931868i | \(-0.381822\pi\) | ||||
0.362797 | + | 0.931868i | \(0.381822\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.8617 | 0.852349 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.4384 | −0.489969 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.7538 | −0.930125 | −0.465062 | − | 0.885278i | \(-0.653968\pi\) | ||||
−0.465062 | + | 0.885278i | \(0.653968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.3693 | 0.741304 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43845 | −0.146483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.3693 | 0.993764 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.87689 | −0.122117 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.3693 | −1.24442 | −0.622209 | − | 0.782851i | \(-0.713765\pi\) | ||||
−0.622209 | + | 0.782851i | \(0.713765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12311 | 0.216684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.75379 | −0.242925 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.7386 | 1.29548 | 0.647739 | − | 0.761862i | \(-0.275715\pi\) | ||||
0.647739 | + | 0.761862i | \(0.275715\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.24621 | −0.262780 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.9309 | 1.34097 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.876894 | −0.0367613 | −0.0183807 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183807 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.3693 | 1.14537 | 0.572685 | − | 0.819775i | \(-0.305902\pi\) | ||||
0.572685 | + | 0.819775i | \(0.305902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.0540 | 0.461786 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.68466 | 0.237067 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4233 | 1.18328 | 0.591639 | − | 0.806203i | \(-0.298481\pi\) | ||||
0.591639 | + | 0.806203i | \(0.298481\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.3693 | −0.971196 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.8617 | 2.64943 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.2462 | 1.08701 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.12311 | −0.377194 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7538 | −0.650228 | −0.325114 | − | 0.945675i | \(-0.605403\pi\) | ||||
−0.325114 | + | 0.945675i | \(0.605403\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.12311 | −0.211094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.1080 | −2.55478 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.24621 | −0.338631 | −0.169316 | − | 0.985562i | \(-0.554156\pi\) | ||||
−0.169316 | + | 0.985562i | \(0.554156\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.56155 | 0.105013 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.9309 | −0.570153 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.61553 | −0.392880 | −0.196440 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196440 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.7386 | −1.98809 | −0.994045 | − | 0.108969i | \(-0.965245\pi\) | ||||
−0.994045 | + | 0.108969i | \(0.965245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.6155 | −1.53182 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.12311 | 0.370295 | 0.185148 | − | 0.982711i | \(-0.440724\pi\) | ||||
0.185148 | + | 0.982711i | \(0.440724\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.1771 | 1.62806 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.3693 | 1.67089 | 0.835445 | − | 0.549573i | \(-0.185210\pi\) | ||||
0.835445 | + | 0.549573i | \(0.185210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.1231 | −0.851766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.9848 | 0.925335 | 0.462668 | − | 0.886532i | \(-0.346892\pi\) | ||||
0.462668 | + | 0.886532i | \(0.346892\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.24621 | −0.0902829 | −0.0451414 | − | 0.998981i | \(-0.514374\pi\) | ||||
−0.0451414 | + | 0.998981i | \(0.514374\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.17708 | −0.328135 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.6155 | 1.82755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.2462 | −0.409194 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.630683 | −0.0251470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.7386 | 1.06445 | 0.532224 | − | 0.846604i | \(-0.321356\pi\) | ||||
0.532224 | + | 0.846604i | \(0.321356\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.0540 | −2.34718 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.3693 | 0.609913 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.3693 | −1.40138 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.4924 | 1.12714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.12311 | −0.281346 | −0.140673 | − | 0.990056i | \(-0.544927\pi\) | ||||
−0.140673 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.4924 | 0.571525 | 0.285763 | − | 0.958300i | \(-0.407753\pi\) | ||||
0.285763 | + | 0.958300i | \(0.407753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.12311 | 0.201722 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6847 | 0.695256 | 0.347628 | − | 0.937633i | \(-0.386987\pi\) | ||||
0.347628 | + | 0.937633i | \(0.386987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.2311 | −2.01099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 59.8617 | 2.34617 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −45.3693 | −1.77544 | −0.887719 | − | 0.460385i | \(-0.847711\pi\) | ||||
−0.887719 | + | 0.460385i | \(0.847711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.7386 | 2.05753 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1922 | 1.05926 | 0.529630 | − | 0.848229i | \(-0.322331\pi\) | ||||
0.529630 | + | 0.848229i | \(0.322331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.9309 | −0.775221 | −0.387610 | − | 0.921823i | \(-0.626699\pi\) | ||||
−0.387610 | + | 0.921823i | \(0.626699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.68466 | −0.143100 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.56155 | 0.176889 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5464 | 0.756840 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.3693 | 1.52211 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5076 | −0.753082 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.4924 | −1.40668 | −0.703340 | − | 0.710854i | \(-0.748309\pi\) | ||||
−0.703340 | + | 0.710854i | \(0.748309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.43845 | −0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.1922 | −0.583885 | −0.291943 | − | 0.956436i | \(-0.594302\pi\) | ||||
−0.291943 | + | 0.956436i | \(0.594302\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.12311 | 0.196607 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0540 | 0.423589 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.2462 | 1.31039 | 0.655197 | − | 0.755458i | \(-0.272585\pi\) | ||||
0.655197 | + | 0.755458i | \(0.272585\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.80776 | −0.107279 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −73.6155 | −2.80861 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.8078 | 0.640325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1080 | −1.29753 | −0.648764 | − | 0.760990i | \(-0.724714\pi\) | ||||
−0.648764 | + | 0.760990i | \(0.724714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 64.9848 | 2.46857 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.24621 | 0.0852036 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.63068 | −0.175400 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 67.8617 | 2.56677 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.1231 | −0.420114 | −0.210057 | − | 0.977689i | \(-0.567365\pi\) | ||||
−0.210057 | + | 0.977689i | \(0.567365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.12311 | −0.0423587 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.2462 | −0.535784 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2462 | −0.684286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.1231 | 1.09067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.2462 | 0.383187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.17708 | −0.305379 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.4233 | 1.28377 | 0.641886 | − | 0.766800i | \(-0.278152\pi\) | ||||
0.641886 | + | 0.766800i | \(0.278152\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −72.9848 | −2.71810 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 76.4924 | 2.84478 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.43845 | 0.127701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6847 | 0.507536 | 0.253768 | − | 0.967265i | \(-0.418330\pi\) | ||||
0.253768 | + | 0.967265i | \(0.418330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.12311 | 0.0415396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.38447 | 0.161944 | 0.0809721 | − | 0.996716i | \(-0.474198\pi\) | ||||
0.0809721 | + | 0.996716i | \(0.474198\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.3693 | −1.30462 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.2462 | 1.55616 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1231 | 0.629884 | 0.314942 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314942 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.56155 | −0.241045 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.3693 | 1.29757 | 0.648787 | − | 0.760970i | \(-0.275277\pi\) | ||||
0.648787 | + | 0.760970i | \(0.275277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.12311 | −0.114422 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −49.8617 | −1.82435 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 53.3002 | 1.94755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.3693 | −1.14468 | −0.572341 | − | 0.820015i | \(-0.693965\pi\) | ||||
−0.572341 | + | 0.820015i | \(0.693965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.7386 | −0.537106 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.1231 | −0.477599 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7386 | 0.462994 | 0.231497 | − | 0.972836i | \(-0.425638\pi\) | ||||
0.231497 | + | 0.972836i | \(0.425638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 58.2462 | 2.11420 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3153 | 0.663931 | 0.331965 | − | 0.943292i | \(-0.392288\pi\) | ||||
0.331965 | + | 0.943292i | \(0.392288\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52.1771 | 1.88894 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.8078 | −1.18462 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.1771 | 1.37670 | 0.688350 | − | 0.725378i | \(-0.258335\pi\) | ||||
0.688350 | + | 0.725378i | \(0.258335\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 80.3542 | 2.89388 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.1771 | −0.725719 | −0.362860 | − | 0.931844i | \(-0.618200\pi\) | ||||
−0.362860 | + | 0.931844i | \(0.618200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.12311 | 0.184027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.1231 | 0.470789 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.24621 | −0.295451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.94602 | −0.176757 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.0540 | −1.24954 | −0.624770 | − | 0.780809i | \(-0.714807\pi\) | ||||
−0.624770 | + | 0.780809i | \(0.714807\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.4924 | 1.01307 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4924 | −0.443619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 16.8078 | 0.596110 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.8078 | −0.878736 | −0.439368 | − | 0.898307i | \(-0.644798\pi\) | ||||
−0.439368 | + | 0.898307i | \(0.644798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.75379 | 0.0620446 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.6155 | −1.25841 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −59.2311 | −2.09022 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.9309 | −0.913943 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −62.1080 | −2.18630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.9309 | 1.40389 | 0.701947 | − | 0.712229i | \(-0.252314\pi\) | ||||
0.701947 | + | 0.712229i | \(0.252314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.0388 | −1.68687 | −0.843436 | − | 0.537230i | \(-0.819471\pi\) | ||||
−0.843436 | + | 0.537230i | \(0.819471\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −51.6847 | −1.81266 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.75379 | 0.131489 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.6155 | 1.45416 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.87689 | −0.170205 | −0.0851024 | − | 0.996372i | \(-0.527122\pi\) | ||||
−0.0851024 | + | 0.996372i | \(0.527122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.4233 | −0.711911 | −0.355956 | − | 0.934503i | \(-0.615845\pi\) | ||||
−0.355956 | + | 0.934503i | \(0.615845\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.2462 | 0.356727 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.0540 | −1.35804 | −0.679020 | − | 0.734120i | \(-0.737595\pi\) | ||||
−0.679020 | + | 0.734120i | \(0.737595\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.4384 | −1.50868 | −0.754340 | − | 0.656484i | \(-0.772043\pi\) | ||||
−0.754340 | + | 0.656484i | \(0.772043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.2462 | −1.74302 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.75379 | −0.268653 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.3693 | 0.670303 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.36932 | −0.254721 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.2311 | −1.21631 | −0.608156 | − | 0.793818i | \(-0.708090\pi\) | ||||
−0.608156 | + | 0.793818i | \(0.708090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.1771 | −0.592313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −62.1080 | −2.13911 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.43845 | −0.221489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.8078 | −0.783684 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3693 | 0.527474 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.38447 | 0.218857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.7386 | 1.53182 | 0.765911 | − | 0.642947i | \(-0.222288\pi\) | ||||
0.765911 | + | 0.642947i | \(0.222288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.56155 | −0.121803 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.9848 | −0.853466 | −0.426733 | − | 0.904378i | \(-0.640336\pi\) | ||||
−0.426733 | + | 0.904378i | \(0.640336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.26137 | −0.179515 | −0.0897577 | − | 0.995964i | \(-0.528609\pi\) | ||||
−0.0897577 | + | 0.995964i | \(0.528609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 96.3542 | 3.28374 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.4773 | −1.68423 | −0.842113 | − | 0.539301i | \(-0.818688\pi\) | ||||
−0.842113 | + | 0.539301i | \(0.818688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.87689 | −0.0978173 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.7386 | 1.45148 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.4924 | 0.695158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.0540 | 0.916689 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.56155 | −0.154209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.8078 | 0.837699 | 0.418849 | − | 0.908056i | \(-0.362434\pi\) | ||||
0.418849 | + | 0.908056i | \(0.362434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.1922 | 0.512421 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.4924 | −0.892552 | −0.446276 | − | 0.894895i | \(-0.647250\pi\) | ||||
−0.446276 | + | 0.894895i | \(0.647250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7538 | 0.664768 | 0.332384 | − | 0.943144i | \(-0.392147\pi\) | ||||
0.332384 | + | 0.943144i | \(0.392147\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.8078 | −1.10282 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −70.1080 | −2.35135 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.0000 | 0.938035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.12311 | 0.104511 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2462 | 0.476198 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.3002 | 1.24542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.6155 | 0.587511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.68466 | 0.122754 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.3693 | −0.777682 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.75379 | −0.257745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.4233 | −1.40864 | −0.704321 | − | 0.709881i | \(-0.748748\pi\) | ||||
−0.704321 | + | 0.709881i | \(0.748748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.1231 | 0.368930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.7386 | 0.753365 | 0.376682 | − | 0.926343i | \(-0.377065\pi\) | ||||
0.376682 | + | 0.926343i | \(0.377065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.0000 | 1.85333 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.4924 | −0.412987 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 72.9848 | 2.41017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.8078 | 0.686385 | 0.343192 | − | 0.939265i | \(-0.388492\pi\) | ||||
0.343192 | + | 0.939265i | \(0.388492\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.7386 | 0.485654 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.4924 | −0.674516 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12311 | 0.0369275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 56.9848 | 1.87163 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.05398 | −0.165816 | −0.0829078 | − | 0.996557i | \(-0.526421\pi\) | ||||
−0.0829078 | + | 0.996557i | \(0.526421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8078 | −0.452531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.9309 | −0.456076 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.24621 | 0.0734590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0540 | 0.557129 | 0.278565 | − | 0.960418i | \(-0.410141\pi\) | ||||
0.278565 | + | 0.960418i | \(0.410141\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 77.3002 | 2.52260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3153 | −0.466667 | −0.233333 | − | 0.972397i | \(-0.574963\pi\) | ||||
−0.233333 | + | 0.972397i | \(0.574963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.8769 | 1.52652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.56155 | 0.213447 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.3693 | −1.08436 | −0.542179 | − | 0.840263i | \(-0.682400\pi\) | ||||
−0.542179 | + | 0.840263i | \(0.682400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.9309 | −1.23129 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9309 | 0.451739 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.2311 | 1.65954 | 0.829768 | − | 0.558108i | \(-0.188473\pi\) | ||||
0.829768 | + | 0.558108i | \(0.188473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.31534 | −0.139641 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.2311 | 1.13886 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8078 | 0.413584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.6155 | −1.34104 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.12311 | 0.293683 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.1231 | −1.25811 | −0.629057 | − | 0.777359i | \(-0.716559\pi\) | ||||
−0.629057 | + | 0.777359i | \(0.716559\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.43845 | −0.0462096 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9848 | 0.416704 | 0.208352 | − | 0.978054i | \(-0.433190\pi\) | ||||
0.208352 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2462 | −0.328478 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.56155 | 0.210138 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.12311 | 0.163903 | 0.0819513 | − | 0.996636i | \(-0.473885\pi\) | ||||
0.0819513 | + | 0.996636i | \(0.473885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.0000 | 1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.7386 | −1.30068 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6155 | −0.944589 | −0.472294 | − | 0.881441i | \(-0.656574\pi\) | ||||
−0.472294 | + | 0.881441i | \(0.656574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2462 | 0.772549 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.4924 | −1.16157 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3693 | −0.361523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1231 | −0.670998 | −0.335499 | − | 0.942041i | \(-0.608905\pi\) | ||||
−0.335499 | + | 0.942041i | \(0.608905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.8078 | 1.04112 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.43845 | 0.172410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.24621 | −0.261160 | −0.130580 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130580 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.61553 | −0.0511130 |
(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 | 6080.2.a.bc.1.1 | 2 | ||
4.3 | odd | 2 | 6080.2.a.bi.1.2 | 2 | |||
8.3 | odd | 2 | 3040.2.a.e.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 3040.2.a.h.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.e.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
3040.2.a.h.1.2 | yes | 2 | 8.5 | even | 2 | ||
6080.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6080.2.a.bi.1.2 | 2 | 4.3 | odd | 2 |