Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 668) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.30278 | 1.24833 | 0.624166 | − | 0.781292i | \(-0.285439\pi\) | ||||
0.624166 | + | 0.781292i | \(0.285439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.30278 | 1.74808 | 0.874038 | − | 0.485858i | \(-0.161493\pi\) | ||||
0.874038 | + | 0.485858i | \(0.161493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.30278 | 0.315970 | 0.157985 | − | 0.987442i | \(-0.449500\pi\) | ||||
0.157985 | + | 0.987442i | \(0.449500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.30278 | −0.271647 | −0.135824 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135824 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.394449 | −0.0732473 | −0.0366236 | − | 0.999329i | \(-0.511660\pi\) | ||||
−0.0366236 | + | 0.999329i | \(0.511660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.605551 | −0.108760 | −0.0543801 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543801 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.90833 | 1.67481 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.60555 | 1.25034 | 0.625172 | − | 0.780487i | \(-0.285029\pi\) | ||||
0.625172 | + | 0.780487i | \(0.285029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.21110 | −1.28236 | −0.641179 | − | 0.767391i | \(-0.721555\pi\) | ||||
−0.641179 | + | 0.767391i | \(0.721555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.39445 | 0.365150 | 0.182575 | − | 0.983192i | \(-0.441557\pi\) | ||||
0.182575 | + | 0.983192i | \(0.441557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.60555 | 0.817654 | 0.408827 | − | 0.912612i | \(-0.365938\pi\) | ||||
0.408827 | + | 0.912612i | \(0.365938\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.90833 | 0.558332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.60555 | −0.357900 | −0.178950 | − | 0.983858i | \(-0.557270\pi\) | ||||
−0.178950 | + | 0.983858i | \(0.557270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.8167 | 1.79878 | 0.899388 | − | 0.437152i | \(-0.144013\pi\) | ||||
0.899388 | + | 0.437152i | \(0.144013\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.8167 | −1.89708 | −0.948539 | − | 0.316660i | \(-0.897439\pi\) | ||||
−0.948539 | + | 0.316660i | \(0.897439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.9083 | 2.34529 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.21110 | −0.758807 | −0.379403 | − | 0.925231i | \(-0.623871\pi\) | ||||
−0.379403 | + | 0.925231i | \(0.623871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.90833 | 0.819868 | 0.409934 | − | 0.912115i | \(-0.365552\pi\) | ||||
0.409934 | + | 0.912115i | \(0.365552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9083 | −1.62785 | −0.813923 | − | 0.580972i | \(-0.802672\pi\) | ||||
−0.813923 | + | 0.580972i | \(0.802672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6056 | 1.53074 | 0.765372 | − | 0.643588i | \(-0.222555\pi\) | ||||
0.765372 | + | 0.643588i | \(0.222555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.60555 | −0.615289 | −0.307645 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307645 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.90833 | 0.423918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.81665 | −0.828564 | −0.414282 | − | 0.910149i | \(-0.635967\pi\) | ||||
−0.414282 | + | 0.910149i | \(0.635967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.8167 | 2.18218 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5139 | −1.37213 | −0.686063 | − | 0.727542i | \(-0.740663\pi\) | ||||
−0.686063 | + | 0.727542i | \(0.740663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8167 | −1.07630 | −0.538149 | − | 0.842850i | \(-0.680876\pi\) | ||||
−0.538149 | + | 0.842850i | \(0.680876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.302776 | 0.0298334 | 0.0149167 | − | 0.999889i | \(-0.495252\pi\) | ||||
0.0149167 | + | 0.999889i | \(0.495252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.394449 | −0.0381328 | −0.0190664 | − | 0.999818i | \(-0.506069\pi\) | ||||
−0.0190664 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.4222 | 1.82709 | 0.913544 | − | 0.406741i | \(-0.133335\pi\) | ||||
0.913544 | + | 0.406741i | \(0.133335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.90833 | −0.364453 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.30278 | 0.394435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.211103 | −0.0187323 | −0.00936616 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936616 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0278 | −1.40035 | −0.700176 | − | 0.713970i | \(-0.746895\pi\) | ||||
−0.700176 | + | 0.713970i | \(0.746895\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.60555 | 0.572774 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.2111 | 1.47044 | 0.735222 | − | 0.677827i | \(-0.237078\pi\) | ||||
0.735222 | + | 0.677827i | \(0.237078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.90833 | −0.416319 | −0.208159 | − | 0.978095i | \(-0.566747\pi\) | ||||
−0.208159 | + | 0.978095i | \(0.566747\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.18335 | −0.0982716 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.513878 | 0.0420985 | 0.0210493 | − | 0.999778i | \(-0.493299\pi\) | ||||
0.0210493 | + | 0.999778i | \(0.493299\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.48612 | 0.120939 | 0.0604694 | − | 0.998170i | \(-0.480740\pi\) | ||||
0.0604694 | + | 0.998170i | \(0.480740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.81665 | −0.145917 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8167 | −1.66135 | −0.830675 | − | 0.556758i | \(-0.812045\pi\) | ||||
−0.830675 | + | 0.556758i | \(0.812045\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.30278 | −0.339106 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6056 | −0.987343 | −0.493671 | − | 0.869648i | \(-0.664345\pi\) | ||||
−0.493671 | + | 0.869648i | \(0.664345\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.7250 | 2.05577 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.2111 | −1.53662 | −0.768311 | − | 0.640077i | \(-0.778902\pi\) | ||||
−0.768311 | + | 0.640077i | \(0.778902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2111 | 0.998665 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.90833 | 0.740583 | 0.370292 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370292 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.21110 | 0.535997 | 0.267999 | − | 0.963419i | \(-0.413638\pi\) | ||||
0.267999 | + | 0.963419i | \(0.413638\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.8167 | 1.67751 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.69722 | 0.556952 | 0.278476 | − | 0.960443i | \(-0.410171\pi\) | ||||
0.278476 | + | 0.960443i | \(0.410171\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.90833 | −0.353309 | −0.176655 | − | 0.984273i | \(-0.556528\pi\) | ||||
−0.176655 | + | 0.984273i | \(0.556528\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.30278 | −0.520301 | −0.260151 | − | 0.965568i | \(-0.583772\pi\) | ||||
−0.260151 | + | 0.965568i | \(0.583772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.3028 | −1.01390 | −0.506948 | − | 0.861976i | \(-0.669227\pi\) | ||||
−0.506948 | + | 0.861976i | \(0.669227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.30278 | −0.0914369 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.6333 | −1.72046 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.51388 | −0.310748 | −0.155374 | − | 0.987856i | \(-0.549658\pi\) | ||||
−0.155374 | + | 0.987856i | \(0.549658\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.18335 | 0.489900 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.21110 | 0.552339 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.5139 | 1.17282 | 0.586408 | − | 0.810016i | \(-0.300542\pi\) | ||||
0.586408 | + | 0.810016i | \(0.300542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.8167 | −1.51439 | −0.757197 | − | 0.653186i | \(-0.773432\pi\) | ||||
−0.757197 | + | 0.653186i | \(0.773432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3028 | 0.812990 | 0.406495 | − | 0.913653i | \(-0.366751\pi\) | ||||
0.406495 | + | 0.913653i | \(0.366751\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.90833 | 0.256043 | 0.128022 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128022 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.8167 | 1.09700 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9083 | −1.41713 | −0.708566 | − | 0.705645i | \(-0.750658\pi\) | ||||
−0.708566 | + | 0.705645i | \(0.750658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.30278 | 0.405997 | 0.202999 | − | 0.979179i | \(-0.434931\pi\) | ||||
0.202999 | + | 0.979179i | \(0.434931\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7250 | 0.749082 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6056 | 0.802072 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6056 | 1.11125 | 0.555626 | − | 0.831432i | \(-0.312479\pi\) | ||||
0.555626 | + | 0.831432i | \(0.312479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.11943 | 0.381720 | 0.190860 | − | 0.981617i | \(-0.438872\pi\) | ||||
0.190860 | + | 0.981617i | \(0.438872\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.1194 | 1.56085 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.21110 | 0.136342 | 0.0681712 | − | 0.997674i | \(-0.478284\pi\) | ||||
0.0681712 | + | 0.997674i | \(0.478284\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.81665 | −0.480173 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.69722 | −0.103482 | −0.0517408 | − | 0.998661i | \(-0.516477\pi\) | ||||
−0.0517408 | + | 0.998661i | \(0.516477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4222 | −0.876087 | −0.438043 | − | 0.898954i | \(-0.644328\pi\) | ||||
−0.438043 | + | 0.898954i | \(0.644328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.48612 | 0.449797 | 0.224899 | − | 0.974382i | \(-0.427795\pi\) | ||||
0.224899 | + | 0.974382i | \(0.427795\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4222 | −0.800702 | −0.400351 | − | 0.916362i | \(-0.631112\pi\) | ||||
−0.400351 | + | 0.916362i | \(0.631112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.4222 | 1.09509 | 0.547543 | − | 0.836777i | \(-0.315563\pi\) | ||||
0.547543 | + | 0.836777i | \(0.315563\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.1194 | −1.60081 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3028 | −0.900163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.4500 | 2.41331 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.21110 | −0.474860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.90833 | 0.455828 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.4500 | −2.54520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9361 | −1.19489 | −0.597443 | − | 0.801912i | \(-0.703816\pi\) | ||||
−0.597443 | + | 0.801912i | \(0.703816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.21110 | 0.465609 | 0.232804 | − | 0.972524i | \(-0.425210\pi\) | ||||
0.232804 | + | 0.972524i | \(0.425210\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.51388 | −0.424710 | −0.212355 | − | 0.977193i | \(-0.568113\pi\) | ||||
−0.212355 | + | 0.977193i | \(0.568113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.5416 | 1.43456 | 0.717281 | − | 0.696784i | \(-0.245387\pi\) | ||||
0.717281 | + | 0.696784i | \(0.245387\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.60555 | 0.144977 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.2111 | 1.39846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.5139 | 1.02070 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.8167 | 1.69384 | 0.846918 | − | 0.531723i | \(-0.178455\pi\) | ||||
0.846918 | + | 0.531723i | \(0.178455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.6333 | −1.01805 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3944 | 1.11096 | 0.555478 | − | 0.831531i | \(-0.312535\pi\) | ||||
0.555478 | + | 0.831531i | \(0.312535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.2111 | −0.551348 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.0917 | −0.595432 | −0.297716 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297716 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.4500 | 1.52289 | 0.761446 | − | 0.648229i | \(-0.224490\pi\) | ||||
0.761446 | + | 0.648229i | \(0.224490\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.8167 | 1.37408 | 0.687041 | − | 0.726619i | \(-0.258909\pi\) | ||||
0.687041 | + | 0.726619i | \(0.258909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7250 | 1.09997 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.8167 | −1.20422 | −0.602108 | − | 0.798414i | \(-0.705673\pi\) | ||||
−0.602108 | + | 0.798414i | \(0.705673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.7250 | −2.18399 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.81665 | −0.147028 | −0.0735141 | − | 0.997294i | \(-0.523421\pi\) | ||||
−0.0735141 | + | 0.997294i | \(0.523421\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.60555 | −0.446778 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.5139 | −1.78706 | −0.893530 | − | 0.449003i | \(-0.851779\pi\) | ||||
−0.893530 | + | 0.449003i | \(0.851779\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.48612 | −0.128042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0278 | 1.85062 | 0.925311 | − | 0.379210i | \(-0.123804\pi\) | ||||
0.925311 | + | 0.379210i | \(0.123804\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8444 | −1.52498 | −0.762489 | − | 0.647001i | \(-0.776023\pi\) | ||||
−0.762489 | + | 0.647001i | \(0.776023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.8167 | −0.852638 | −0.426319 | − | 0.904573i | \(-0.640190\pi\) | ||||
−0.426319 | + | 0.904573i | \(0.640190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.69722 | −0.0858323 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.8167 | 2.05371 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.1194 | −1.11014 | −0.555071 | − | 0.831803i | \(-0.687309\pi\) | ||||
−0.555071 | + | 0.831803i | \(0.687309\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3028 | 1.26356 | 0.631780 | − | 0.775148i | \(-0.282325\pi\) | ||||
0.631780 | + | 0.775148i | \(0.282325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.81665 | −0.190121 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9083 | 1.47887 | 0.739436 | − | 0.673227i | \(-0.235092\pi\) | ||||
0.739436 | + | 0.673227i | \(0.235092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.6333 | 2.24547 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.8167 | −0.825497 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.21110 | −0.108019 | −0.0540097 | − | 0.998540i | \(-0.517200\pi\) | ||||
−0.0540097 | + | 0.998540i | \(0.517200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.39445 | 0.262909 | 0.131455 | − | 0.991322i | \(-0.458035\pi\) | ||||
0.131455 | + | 0.991322i | \(0.458035\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.21110 | 0.252776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −48.9361 | −2.36818 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.0278 | 0.916535 | 0.458267 | − | 0.888814i | \(-0.348470\pi\) | ||||
0.458267 | + | 0.888814i | \(0.348470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3305 | 0.496454 | 0.248227 | − | 0.968702i | \(-0.420152\pi\) | ||||
0.248227 | + | 0.968702i | \(0.420152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.60555 | −0.124640 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.78890 | −0.371744 | −0.185872 | − | 0.982574i | \(-0.559511\pi\) | ||||
−0.185872 | + | 0.982574i | \(0.559511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7250 | −1.55481 | −0.777405 | − | 0.629000i | \(-0.783465\pi\) | ||||
−0.777405 | + | 0.629000i | \(0.783465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.4500 | −1.11163 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.0278 | −1.88903 | −0.944513 | − | 0.328473i | \(-0.893466\pi\) | ||||
−0.944513 | + | 0.328473i | \(0.893466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 62.4500 | 2.92770 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1194 | 1.50248 | 0.751242 | − | 0.660027i | \(-0.229455\pi\) | ||||
0.751242 | + | 0.660027i | \(0.229455\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.3028 | 1.17847 | 0.589234 | − | 0.807963i | \(-0.299430\pi\) | ||||
0.589234 | + | 0.807963i | \(0.299430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2111 | 0.753394 | 0.376697 | − | 0.926337i | \(-0.377060\pi\) | ||||
0.376697 | + | 0.926337i | \(0.377060\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.1194 | −0.560820 | −0.280410 | − | 0.959880i | \(-0.590470\pi\) | ||||
−0.280410 | + | 0.959880i | \(0.590470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.5139 | −0.947243 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.6333 | 1.81089 | 0.905446 | − | 0.424461i | \(-0.139537\pi\) | ||||
0.905446 | + | 0.424461i | \(0.139537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 47.9361 | 2.18570 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40.5416 | −1.84090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.18335 | 0.416137 | 0.208069 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208069 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.6333 | 1.92401 | 0.962007 | − | 0.273024i | \(-0.0880240\pi\) | ||||
0.962007 | + | 0.273024i | \(0.0880240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.513878 | −0.0231439 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.8167 | 1.02347 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.3305 | 1.80544 | 0.902721 | − | 0.430226i | \(-0.141566\pi\) | ||||
0.902721 | + | 0.430226i | \(0.141566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.5139 | 0.825493 | 0.412747 | − | 0.910846i | \(-0.364570\pi\) | ||||
0.412747 | + | 0.910846i | \(0.364570\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.4500 | −1.44400 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.0917 | −0.624602 | −0.312301 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312301 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.9361 | −2.03209 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.908327 | 0.0400257 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1833 | 0.971870 | 0.485935 | − | 0.873995i | \(-0.338479\pi\) | ||||
0.485935 | + | 0.873995i | \(0.338479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8167 | 0.560433 | 0.280217 | − | 0.959937i | \(-0.409594\pi\) | ||||
0.280217 | + | 0.959937i | \(0.409594\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.788897 | −0.0343649 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3028 | −0.926208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −51.7527 | −2.24166 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.18335 | −0.0511605 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.3944 | −1.22077 | −0.610386 | − | 0.792104i | \(-0.708986\pi\) | ||||
−0.610386 | + | 0.792104i | \(0.708986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.3583 | 1.76835 | 0.884176 | − | 0.467153i | \(-0.154720\pi\) | ||||
0.884176 | + | 0.467153i | \(0.154720\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.788897 | −0.0336082 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.9361 | 1.91088 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8167 | 0.458316 | 0.229158 | − | 0.973389i | \(-0.426403\pi\) | ||||
0.229158 | + | 0.973389i | \(0.426403\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0917 | 0.638310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.48612 | −0.231212 | −0.115606 | − | 0.993295i | \(-0.536881\pi\) | ||||
−0.115606 | + | 0.993295i | \(0.536881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.2666 | 2.45129 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7889 | −0.913438 | −0.456719 | − | 0.889611i | \(-0.650976\pi\) | ||||
−0.456719 | + | 0.889611i | \(0.650976\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.5416 | 1.65477 | 0.827383 | − | 0.561638i | \(-0.189829\pi\) | ||||
0.827383 | + | 0.561638i | \(0.189829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.21110 | −0.217318 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.48612 | −0.270021 | −0.135010 | − | 0.990844i | \(-0.543107\pi\) | ||||
−0.135010 | + | 0.990844i | \(0.543107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.5139 | −0.768085 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0917 | 1.32457 | 0.662283 | − | 0.749254i | \(-0.269588\pi\) | ||||
0.662283 | + | 0.749254i | \(0.269588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.21110 | −0.0499026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.6056 | 1.46214 | 0.731072 | − | 0.682300i | \(-0.239020\pi\) | ||||
0.731072 | + | 0.682300i | \(0.239020\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9083 | 0.529190 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.9083 | 1.50803 | 0.754017 | − | 0.656855i | \(-0.228114\pi\) | ||||
0.754017 | + | 0.656855i | \(0.228114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.5416 | −1.20503 | −0.602514 | − | 0.798108i | \(-0.705834\pi\) | ||||
−0.602514 | + | 0.798108i | \(0.705834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.0000 | −1.34164 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7250 | −0.760024 | −0.380012 | − | 0.924982i | \(-0.624080\pi\) | ||||
−0.380012 | + | 0.924982i | \(0.624080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.3305 | 1.42932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.33053 | 0.0537397 | 0.0268698 | − | 0.999639i | \(-0.491446\pi\) | ||||
0.0268698 | + | 0.999639i | \(0.491446\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.4500 | −1.06484 | −0.532418 | − | 0.846482i | \(-0.678716\pi\) | ||||
−0.532418 | + | 0.846482i | \(0.678716\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0278 | −0.443243 | −0.221621 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221621 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.8167 | −1.03432 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.90833 | 0.395071 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9361 | 0.514977 | 0.257489 | − | 0.966281i | \(-0.417105\pi\) | ||||
0.257489 | + | 0.966281i | \(0.417105\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.633308 | −0.0251320 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.6333 | 0.976007 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.69722 | 0.304022 | 0.152011 | − | 0.988379i | \(-0.451425\pi\) | ||||
0.152011 | + | 0.988379i | \(0.451425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.51388 | 0.217446 | 0.108723 | − | 0.994072i | \(-0.465324\pi\) | ||||
0.108723 | + | 0.994072i | \(0.465324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.9361 | −0.429942 | −0.214971 | − | 0.976620i | \(-0.568966\pi\) | ||||
−0.214971 | + | 0.976620i | \(0.568966\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.1194 | −0.474270 | −0.237135 | − | 0.971477i | \(-0.576208\pi\) | ||||
−0.237135 | + | 0.971477i | \(0.576208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −48.0833 | −1.87877 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.81665 | −0.0707668 | −0.0353834 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353834 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8806 | −0.500996 | −0.250498 | − | 0.968117i | \(-0.580594\pi\) | ||||
−0.250498 | + | 0.968117i | \(0.580594\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.8167 | 0.768457 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.513878 | 0.0198974 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.63331 | −0.0629594 | −0.0314797 | − | 0.999504i | \(-0.510022\pi\) | ||||
−0.0314797 | + | 0.999504i | \(0.510022\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.81665 | −0.300418 | −0.150209 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150209 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.6333 | −1.71287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.54163 | −0.173781 | −0.0868904 | − | 0.996218i | \(-0.527693\pi\) | ||||
−0.0868904 | + | 0.996218i | \(0.527693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.6333 | 1.97281 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.4222 | −0.625636 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4500 | 0.854037 | 0.427018 | − | 0.904243i | \(-0.359564\pi\) | ||||
0.427018 | + | 0.904243i | \(0.359564\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.7250 | −0.558550 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.6972 | −0.405186 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.0278 | 1.05859 | 0.529297 | − | 0.848437i | \(-0.322456\pi\) | ||||
0.529297 | + | 0.848437i | \(0.322456\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2111 | 0.573698 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.7250 | −1.34358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1472 | −0.418641 | −0.209321 | − | 0.977847i | \(-0.567125\pi\) | ||||
−0.209321 | + | 0.977847i | \(0.567125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.788897 | 0.0295444 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.1194 | 1.79455 | 0.897276 | − | 0.441470i | \(-0.145543\pi\) | ||||
0.897276 | + | 0.441470i | \(0.145543\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.00000 | 0.0372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.57779 | −0.0585978 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.72498 | −0.138152 | −0.0690759 | − | 0.997611i | \(-0.522005\pi\) | ||||
−0.0690759 | + | 0.997611i | \(0.522005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.11943 | 0.115376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.9361 | 1.57943 | 0.789715 | − | 0.613474i | \(-0.210229\pi\) | ||||
0.789715 | + | 0.613474i | \(0.210229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.8806 | −0.986152 | −0.493076 | − | 0.869986i | \(-0.664128\pi\) | ||||
−0.493076 | + | 0.869986i | \(0.664128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.54163 | 0.0564811 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.30278 | −0.0476024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.3944 | −0.598242 | −0.299121 | − | 0.954215i | \(-0.596693\pi\) | ||||
−0.299121 | + | 0.954215i | \(0.596693\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.45837 | 0.162257 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.72498 | −0.353460 | −0.176730 | − | 0.984259i | \(-0.556552\pi\) | ||||
−0.176730 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.30278 | 0.264725 | 0.132363 | − | 0.991201i | \(-0.457744\pi\) | ||||
0.132363 | + | 0.991201i | \(0.457744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.60555 | 0.239137 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 87.0833 | 3.14439 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.81665 | 0.245815 | 0.122907 | − | 0.992418i | \(-0.460778\pi\) | ||||
0.122907 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.39445 | −0.122090 | −0.0610449 | − | 0.998135i | \(-0.519443\pi\) | ||||
−0.0610449 | + | 0.998135i | \(0.519443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.42221 | −0.0870082 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.4222 | −0.588387 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.4500 | −2.22893 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4500 | −0.764609 | −0.382304 | − | 0.924036i | \(-0.624869\pi\) | ||||
−0.382304 | + | 0.924036i | \(0.624869\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 64.1472 | 2.28081 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −93.3860 | −3.31624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.63331 | 0.234964 | 0.117482 | − | 0.993075i | \(-0.462518\pi\) | ||||
0.117482 | + | 0.993075i | \(0.462518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.30278 | 0.258354 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.9083 | −0.454959 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.72498 | 0.306754 | 0.153377 | − | 0.988168i | \(-0.450985\pi\) | ||||
0.153377 | + | 0.988168i | \(0.450985\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8444 | 0.696831 | 0.348416 | − | 0.937340i | \(-0.386720\pi\) | ||||
0.348416 | + | 0.937340i | \(0.386720\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.8167 | −1.32466 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.78890 | 0.167542 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7250 | 0.618606 | 0.309303 | − | 0.950964i | \(-0.399904\pi\) | ||||
0.309303 | + | 0.950964i | \(0.399904\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.6972 | −0.616886 | −0.308443 | − | 0.951243i | \(-0.599808\pi\) | ||||
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.5416 | −1.93137 | −0.965686 | − | 0.259713i | \(-0.916372\pi\) | ||||
−0.965686 | + | 0.259713i | \(0.916372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.8722 | −1.94052 | −0.970260 | − | 0.242064i | \(-0.922176\pi\) | ||||
−0.970260 | + | 0.242064i | \(0.922176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.09167 | 0.176416 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00000 | 0.103819 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.6056 | −1.64353 | −0.821763 | − | 0.569829i | \(-0.807009\pi\) | ||||
−0.821763 | + | 0.569829i | \(0.807009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8444 | −0.994635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 80.1749 | 2.75810 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.3305 | −1.24833 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.90833 | −0.339653 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.27502 | 0.283331 | 0.141666 | − | 0.989915i | \(-0.454754\pi\) | ||||
0.141666 | + | 0.989915i | \(0.454754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5416 | 0.974964 | 0.487482 | − | 0.873133i | \(-0.337916\pi\) | ||||
0.487482 | + | 0.873133i | \(0.337916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.6056 | −1.65840 | −0.829200 | − | 0.558952i | \(-0.811204\pi\) | ||||
−0.829200 | + | 0.558952i | \(0.811204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.51388 | −0.221735 | −0.110867 | − | 0.993835i | \(-0.535363\pi\) | ||||
−0.110867 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.6333 | −2.06159 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.1472 | −1.32645 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.90833 | −0.334963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.48612 | 0.0501828 | 0.0250914 | − | 0.999685i | \(-0.492012\pi\) | ||||
0.0250914 | + | 0.999685i | \(0.492012\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2111 | 0.984147 | 0.492074 | − | 0.870554i | \(-0.336239\pi\) | ||||
0.492074 | + | 0.870554i | \(0.336239\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9361 | 0.637250 | 0.318625 | − | 0.947881i | \(-0.396779\pi\) | ||||
0.318625 | + | 0.947881i | \(0.396779\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.8167 | 0.363188 | 0.181594 | − | 0.983374i | \(-0.441874\pi\) | ||||
0.181594 | + | 0.983374i | \(0.441874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.697224 | −0.0233842 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.2111 | 0.375165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.7250 | 0.993597 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.238859 | 0.00796639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.39445 | −0.113085 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.6333 | 0.719115 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.6333 | 1.28280 | 0.641399 | − | 0.767208i | \(-0.278354\pi\) | ||||
0.641399 | + | 0.767208i | \(0.278354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8167 | −0.954738 | −0.477369 | − | 0.878703i | \(-0.658410\pi\) | ||||
−0.477369 | + | 0.878703i | \(0.658410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52.9361 | −1.74810 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.9083 | −0.359833 | −0.179916 | − | 0.983682i | \(-0.557583\pi\) | ||||
−0.179916 | + | 0.983682i | \(0.557583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.5416 | 1.43319 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.4222 | 1.00028 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5139 | −1.09955 | −0.549777 | − | 0.835311i | \(-0.685287\pi\) | ||||
−0.549777 | + | 0.835311i | \(0.685287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.81665 | 0.256180 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.4500 | 0.439391 | 0.219696 | − | 0.975568i | \(-0.429494\pi\) | ||||
0.219696 | + | 0.975568i | \(0.429494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.76114 | −0.285605 | −0.142803 | − | 0.989751i | \(-0.545611\pi\) | ||||
−0.142803 | + | 0.989751i | \(0.545611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6972 | 0.348350 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.9083 | −0.809412 | −0.404706 | − | 0.914447i | \(-0.632626\pi\) | ||||
−0.404706 | + | 0.914447i | \(0.632626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −87.6611 | −2.84560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.3583 | 1.08058 | 0.540290 | − | 0.841479i | \(-0.318314\pi\) | ||||
0.540290 | + | 0.841479i | \(0.318314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.0917 | 0.747229 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.8444 | 1.83560 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6333 | −0.988171 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.7250 | −0.474014 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.5139 | −1.39931 | −0.699656 | − | 0.714480i | \(-0.746663\pi\) | ||||
−0.699656 | + | 0.714480i | \(0.746663\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.4777 | 1.65200 | 0.825999 | − | 0.563671i | \(-0.190611\pi\) | ||||
0.825999 | + | 0.563671i | \(0.190611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.2111 | −0.519704 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.5694 | −1.52188 | −0.760940 | − | 0.648822i | \(-0.775262\pi\) | ||||
−0.760940 | + | 0.648822i | \(0.775262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.2666 | −1.76273 | −0.881366 | − | 0.472435i | \(-0.843375\pi\) | ||||
−0.881366 | + | 0.472435i | \(0.843375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.9083 | −0.698057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.11943 | −0.0991921 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6333 | 0.750737 | 0.375368 | − | 0.926876i | \(-0.377516\pi\) | ||||
0.375368 | + | 0.926876i | \(0.377516\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.9083 | −1.36029 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2111 | −1.24183 | −0.620914 | − | 0.783879i | \(-0.713238\pi\) | ||||
−0.620914 | + | 0.783879i | \(0.713238\pi\) | |||||||
\(998\) | 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 | 6012.2.a.a.1.2 | 2 | ||
3.2 | odd | 2 | 668.2.a.a.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 2672.2.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.a.a.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2672.2.a.c.1.1 | 2 | 12.11 | even | 2 | |||
6012.2.a.a.1.2 | 2 | 1.1 | even | 1 | trivial |