Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4680,2,Mod(1,4680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4680.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: | \(37.3699881460\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.17741\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4680.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.09593 | 1.92608 | 0.963041 | − | 0.269356i | \(-0.0868108\pi\) | ||||
0.963041 | + | 0.269356i | \(0.0868108\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.25889 | 0.379569 | 0.189784 | − | 0.981826i | \(-0.439221\pi\) | ||||
0.189784 | + | 0.981826i | \(0.439221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.09593 | 1.72102 | 0.860508 | − | 0.509437i | \(-0.170146\pi\) | ||||
0.860508 | + | 0.509437i | \(0.170146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.35482 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.61371 | −1.17054 | −0.585269 | − | 0.810839i | \(-0.699011\pi\) | ||||
−0.585269 | + | 0.810839i | \(0.699011\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.35482 | 0.808670 | 0.404335 | − | 0.914611i | \(-0.367503\pi\) | ||||
0.404335 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.09593 | −0.861370 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.741113 | 0.121838 | 0.0609191 | − | 0.998143i | \(-0.480597\pi\) | ||||
0.0609191 | + | 0.998143i | \(0.480597\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.741113 | −0.115742 | −0.0578712 | − | 0.998324i | \(-0.518431\pi\) | ||||
−0.0578712 | + | 0.998324i | \(0.518431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.48223 | 0.836032 | 0.418016 | − | 0.908440i | \(-0.362726\pi\) | ||||
0.418016 | + | 0.908440i | \(0.362726\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.48223 | −0.799665 | −0.399832 | − | 0.916588i | \(-0.630932\pi\) | ||||
−0.399832 | + | 0.916588i | \(0.630932\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.9685 | 2.70979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.74111 | −0.925963 | −0.462982 | − | 0.886368i | \(-0.653220\pi\) | ||||
−0.462982 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.25889 | −0.169748 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.74111 | 0.607037 | 0.303519 | − | 0.952825i | \(-0.401839\pi\) | ||||
0.303519 | + | 0.952825i | \(0.401839\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.48223 | 0.425422 | 0.212711 | − | 0.977115i | \(-0.431771\pi\) | ||||
0.212711 | + | 0.977115i | \(0.431771\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4508 | −1.35895 | −0.679477 | − | 0.733697i | \(-0.737793\pi\) | ||||
−0.679477 | + | 0.733697i | \(0.737793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.83705 | −0.449092 | −0.224546 | − | 0.974463i | \(-0.572090\pi\) | ||||
−0.224546 | + | 0.974463i | \(0.572090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.41520 | 0.731080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9330 | −1.45507 | −0.727537 | − | 0.686069i | \(-0.759335\pi\) | ||||
−0.727537 | + | 0.686069i | \(0.759335\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.09593 | −0.769662 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.9685 | −1.69266 | −0.846330 | − | 0.532659i | \(-0.821193\pi\) | ||||
−0.846330 | + | 0.532659i | \(0.821193\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.09593 | −0.534199 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.35482 | −0.651991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0959 | 1.32969 | 0.664845 | − | 0.746981i | \(-0.268497\pi\) | ||||
0.664845 | + | 0.746981i | \(0.268497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.87259 | −0.683849 | −0.341924 | − | 0.939727i | \(-0.611079\pi\) | ||||
−0.341924 | + | 0.939727i | \(0.611079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19186 | −0.215971 | −0.107985 | − | 0.994152i | \(-0.534440\pi\) | ||||
−0.107985 | + | 0.994152i | \(0.534440\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9330 | 1.25028 | 0.625139 | − | 0.780513i | \(-0.285042\pi\) | ||||
0.625139 | + | 0.780513i | \(0.285042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8370 | 1.13378 | 0.566892 | − | 0.823792i | \(-0.308146\pi\) | ||||
0.566892 | + | 0.823792i | \(0.308146\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.35482 | 0.785955 | 0.392978 | − | 0.919548i | \(-0.371445\pi\) | ||||
0.392978 | + | 0.919548i | \(0.371445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.61371 | 0.523481 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 36.1604 | 3.31482 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.41520 | −0.855928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5467 | −1.27095 | −0.635475 | − | 0.772122i | \(-0.719196\pi\) | ||||
−0.635475 | + | 0.772122i | \(0.719196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32.3837 | 2.80803 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4822 | −0.980993 | −0.490496 | − | 0.871443i | \(-0.663185\pi\) | ||||
−0.490496 | + | 0.871443i | \(0.663185\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.549248 | 0.0465866 | 0.0232933 | − | 0.999729i | \(-0.492585\pi\) | ||||
0.0232933 | + | 0.999729i | \(0.492585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.25889 | −0.105273 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.35482 | −0.361648 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4152 | 1.01709 | 0.508547 | − | 0.861035i | \(-0.330183\pi\) | ||||
0.508547 | + | 0.861035i | \(0.330183\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5178 | 1.01868 | 0.509341 | − | 0.860565i | \(-0.329889\pi\) | ||||
0.509341 | + | 0.860565i | \(0.329889\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9015 | −1.02965 | −0.514826 | − | 0.857295i | \(-0.672143\pi\) | ||||
−0.514826 | + | 0.857295i | \(0.672143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.6071 | −2.25455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.294435 | 0.0230620 | 0.0115310 | − | 0.999934i | \(-0.496329\pi\) | ||||
0.0115310 | + | 0.999934i | \(0.496329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.19186 | 0.479141 | 0.239570 | − | 0.970879i | \(-0.422993\pi\) | ||||
0.239570 | + | 0.970879i | \(0.422993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.2274 | 1.46183 | 0.730917 | − | 0.682467i | \(-0.239093\pi\) | ||||
0.730917 | + | 0.682467i | \(0.239093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.09593 | 0.385216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.64518 | 0.571428 | 0.285714 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285714 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.6782 | −1.83431 | −0.917157 | − | 0.398527i | \(-0.869522\pi\) | ||||
−0.917157 | + | 0.398527i | \(0.869522\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.741113 | −0.0544877 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.93298 | 0.653244 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5178 | 1.05047 | 0.525235 | − | 0.850957i | \(-0.323978\pi\) | ||||
0.525235 | + | 0.850957i | \(0.323978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.09593 | −0.366813 | −0.183407 | − | 0.983037i | \(-0.558712\pi\) | ||||
−0.183407 | + | 0.983037i | \(0.558712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.22741 | 0.372438 | 0.186219 | − | 0.982508i | \(-0.440377\pi\) | ||||
0.186219 | + | 0.982508i | \(0.440377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.4193 | −1.80192 | −0.900962 | − | 0.433897i | \(-0.857138\pi\) | ||||
−0.900962 | + | 0.433897i | \(0.857138\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.1919 | 1.55756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.741113 | 0.0517616 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7096 | 1.70108 | 0.850541 | − | 0.525909i | \(-0.176275\pi\) | ||||
0.850541 | + | 0.525909i | \(0.176275\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.48223 | −0.373885 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1919 | −0.691869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.09593 | −0.477324 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.39037 | 0.494896 | 0.247448 | − | 0.968901i | \(-0.420408\pi\) | ||||
0.247448 | + | 0.968901i | \(0.420408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.70964 | −0.312590 | −0.156295 | − | 0.987710i | \(-0.549955\pi\) | ||||
−0.156295 | + | 0.987710i | \(0.549955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.06446 | −0.202505 | −0.101253 | − | 0.994861i | \(-0.532285\pi\) | ||||
−0.101253 | + | 0.994861i | \(0.532285\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.8056 | −1.29751 | −0.648753 | − | 0.760999i | \(-0.724709\pi\) | ||||
−0.648753 | + | 0.760999i | \(0.724709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.48223 | 0.357621 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.29444 | 0.148415 | 0.0742073 | − | 0.997243i | \(-0.476357\pi\) | ||||
0.0742073 | + | 0.997243i | \(0.476357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.3482 | 1.89048 | 0.945241 | − | 0.326372i | \(-0.105826\pi\) | ||||
0.945241 | + | 0.326372i | \(0.105826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.9685 | −1.21185 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.35482 | −0.404347 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.5467 | 1.67561 | 0.837806 | − | 0.545968i | \(-0.183838\pi\) | ||||
0.837806 | + | 0.545968i | \(0.183838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.06702 | −0.444300 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.6452 | −0.975920 | −0.487960 | − | 0.872866i | \(-0.662259\pi\) | ||||
−0.487960 | + | 0.872866i | \(0.662259\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.77666 | 0.234670 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.87259 | −0.423782 | −0.211891 | − | 0.977293i | \(-0.567962\pi\) | ||||
−0.211891 | + | 0.977293i | \(0.567962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.74111 | 0.414103 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.31927 | −0.446264 | −0.223132 | − | 0.974788i | \(-0.571628\pi\) | ||||
−0.223132 | + | 0.974788i | \(0.571628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9015 | 1.75564 | 0.877821 | − | 0.478989i | \(-0.158997\pi\) | ||||
0.877821 | + | 0.478989i | \(0.158997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.25889 | 0.0759137 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.92890 | −0.236065 | −0.118032 | − | 0.993010i | \(-0.537659\pi\) | ||||
−0.118032 | + | 0.993010i | \(0.537659\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3837 | −0.619441 | −0.309721 | − | 0.950828i | \(-0.600236\pi\) | ||||
−0.309721 | + | 0.950828i | \(0.600236\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4193 | −0.797693 | −0.398847 | − | 0.917018i | \(-0.630589\pi\) | ||||
−0.398847 | + | 0.917018i | \(0.630589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.77666 | −0.222929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.3523 | 1.96190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.70964 | 0.391981 | 0.195991 | − | 0.980606i | \(-0.437208\pi\) | ||||
0.195991 | + | 0.980606i | \(0.437208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.61371 | 0.324649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.9371 | 1.61026 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.74111 | −0.271475 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.9685 | 1.82454 | 0.912270 | − | 0.409589i | \(-0.134328\pi\) | ||||
0.912270 | + | 0.409589i | \(0.134328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.55332 | −0.201490 | −0.100745 | − | 0.994912i | \(-0.532123\pi\) | ||||
−0.100745 | + | 0.994912i | \(0.532123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.19186 | −0.236938 | −0.118469 | − | 0.992958i | \(-0.537799\pi\) | ||||
−0.118469 | + | 0.992958i | \(0.537799\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.03555 | −0.170493 | −0.0852467 | − | 0.996360i | \(-0.527168\pi\) | ||||
−0.0852467 | + | 0.996360i | \(0.527168\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.48223 | 0.306946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 45.0934 | 2.50906 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.9371 | −1.54022 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.28372 | 0.455315 | 0.227657 | − | 0.973741i | \(-0.426893\pi\) | ||||
0.227657 | + | 0.973741i | \(0.426893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.48223 | −0.190254 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3837 | −0.783532 | −0.391766 | − | 0.920065i | \(-0.628136\pi\) | ||||
−0.391766 | + | 0.920065i | \(0.628136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.51777 | −0.136345 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 60.9908 | 3.29319 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.74111 | −0.147151 | −0.0735753 | − | 0.997290i | \(-0.523441\pi\) | ||||
−0.0735753 | + | 0.997290i | \(0.523441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.28372 | 0.443418 | 0.221709 | − | 0.975113i | \(-0.428837\pi\) | ||||
0.221709 | + | 0.975113i | \(0.428837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.8030 | −1.90560 | −0.952801 | − | 0.303596i | \(-0.901813\pi\) | ||||
−0.952801 | + | 0.303596i | \(0.901813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4508 | 0.607743 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.96445 | 0.156458 | 0.0782289 | − | 0.996935i | \(-0.475074\pi\) | ||||
0.0782289 | + | 0.996935i | \(0.475074\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.3837 | 1.12546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.83705 | 0.200840 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3482 | 1.21877 | 0.609383 | − | 0.792876i | \(-0.291417\pi\) | ||||
0.609383 | + | 0.792876i | \(0.291417\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.3523 | −1.78348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.4193 | 1.62683 | 0.813414 | − | 0.581685i | \(-0.197606\pi\) | ||||
0.813414 | + | 0.581685i | \(0.197606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.35482 | −0.224285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8370 | −1.22443 | −0.612213 | − | 0.790693i | \(-0.709721\pi\) | ||||
−0.612213 | + | 0.790693i | \(0.709721\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.32591 | 0.221044 | 0.110522 | − | 0.993874i | \(-0.464748\pi\) | ||||
0.110522 | + | 0.993874i | \(0.464748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.41520 | −0.326949 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.4837 | 1.74839 | 0.874197 | − | 0.485571i | \(-0.161388\pi\) | ||||
0.874197 | + | 0.485571i | \(0.161388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.8345 | −2.01452 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9330 | 0.650729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2233 | −0.513095 | −0.256547 | − | 0.966532i | \(-0.582585\pi\) | ||||
−0.256547 | + | 0.966532i | \(0.582585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.29036 | −0.0644376 | −0.0322188 | − | 0.999481i | \(-0.510257\pi\) | ||||
−0.0322188 | + | 0.999481i | \(0.510257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.932977 | 0.0462460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.19186 | 0.207274 | 0.103637 | − | 0.994615i | \(-0.466952\pi\) | ||||
0.103637 | + | 0.994615i | \(0.466952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.3837 | 1.00302 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.3193 | 1.72546 | 0.862730 | − | 0.505665i | \(-0.168753\pi\) | ||||
0.862730 | + | 0.505665i | \(0.168753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.10001 | 0.199822 | 0.0999110 | − | 0.994996i | \(-0.468144\pi\) | ||||
0.0999110 | + | 0.994996i | \(0.468144\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.09593 | 0.344203 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.1604 | 1.16920 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.0934 | 1.01603 | 0.508016 | − | 0.861348i | \(-0.330379\pi\) | ||||
0.508016 | + | 0.861348i | \(0.330379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.9371 | −1.43868 | −0.719341 | − | 0.694657i | \(-0.755556\pi\) | ||||
−0.719341 | + | 0.694657i | \(0.755556\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.6741 | −1.70652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.96853 | 0.0939526 | 0.0469763 | − | 0.998896i | \(-0.485041\pi\) | ||||
0.0469763 | + | 0.998896i | \(0.485041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.6426 | 1.40836 | 0.704182 | − | 0.710020i | \(-0.251314\pi\) | ||||
0.704182 | + | 0.710020i | \(0.251314\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.9685 | 0.756981 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45075 | −0.257237 | −0.128618 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128618 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.932977 | −0.0439322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.09593 | 0.238901 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3589 | −0.812015 | −0.406007 | − | 0.913870i | \(-0.633079\pi\) | ||||
−0.406007 | + | 0.913870i | \(0.633079\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6426 | 0.542251 | 0.271125 | − | 0.962544i | \(-0.412604\pi\) | ||||
0.271125 | + | 0.962544i | \(0.412604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −41.4167 | −1.92480 | −0.962399 | − | 0.271640i | \(-0.912434\pi\) | ||||
−0.962399 | + | 0.271640i | \(0.912434\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.4152 | −1.03725 | −0.518626 | − | 0.855001i | \(-0.673556\pi\) | ||||
−0.518626 | + | 0.855001i | \(0.673556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7452 | 0.819397 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.90150 | 0.317331 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.35482 | 0.291579 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.7137 | −1.26627 | −0.633136 | − | 0.774041i | \(-0.718233\pi\) | ||||
−0.633136 | + | 0.774041i | \(0.718233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.741113 | −0.0337918 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0959 | −0.594656 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0685 | 1.36254 | 0.681268 | − | 0.732034i | \(-0.261429\pi\) | ||||
0.681268 | + | 0.732034i | \(0.261429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3904 | 0.784816 | 0.392408 | − | 0.919791i | \(-0.371642\pi\) | ||||
0.392408 | + | 0.919791i | \(0.371642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.9015 | 1.39173 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −58.3523 | −2.61746 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8726 | −0.755321 | −0.377661 | − | 0.925944i | \(-0.623271\pi\) | ||||
−0.377661 | + | 0.925944i | \(0.623271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.6178 | 0.919301 | 0.459651 | − | 0.888100i | \(-0.347975\pi\) | ||||
0.459651 | + | 0.888100i | \(0.347975\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.87259 | 0.305826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.6426 | −0.693347 | −0.346673 | − | 0.937986i | \(-0.612689\pi\) | ||||
−0.346673 | + | 0.937986i | \(0.612689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.5533 | −0.864988 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.19186 | 0.0965851 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.90150 | −0.303528 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.19186 | 0.0960273 | 0.0480137 | − | 0.998847i | \(-0.484711\pi\) | ||||
0.0480137 | + | 0.998847i | \(0.484711\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4193 | −1.28642 | −0.643208 | − | 0.765692i | \(-0.722397\pi\) | ||||
−0.643208 | + | 0.765692i | \(0.722397\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.1919 | −0.618207 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.51370 | 0.370161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.741113 | 0.0321012 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9330 | −0.559141 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.8792 | 1.02855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7385 | −0.977607 | −0.488803 | − | 0.872394i | \(-0.662566\pi\) | ||||
−0.488803 | + | 0.872394i | \(0.662566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.8370 | −0.507043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.9015 | −1.15023 | −0.575113 | − | 0.818074i | \(-0.695042\pi\) | ||||
−0.575113 | + | 0.818074i | \(0.695042\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.6741 | 1.17896 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −65.9056 | −2.80259 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.3837 | −1.62637 | −0.813185 | − | 0.582005i | \(-0.802269\pi\) | ||||
−0.813185 | + | 0.582005i | \(0.802269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.48223 | −0.231873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5441 | −0.865831 | −0.432916 | − | 0.901434i | \(-0.642515\pi\) | ||||
−0.432916 | + | 0.901434i | \(0.642515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.35482 | −0.351490 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.5756 | 1.95255 | 0.976275 | − | 0.216533i | \(-0.0694750\pi\) | ||||
0.976275 | + | 0.216533i | \(0.0694750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.06702 | 0.128351 | 0.0641754 | − | 0.997939i | \(-0.479558\pi\) | ||||
0.0641754 | + | 0.997939i | \(0.479558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.61371 | −0.234108 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.84112 | 0.284800 | 0.142400 | − | 0.989809i | \(-0.454518\pi\) | ||||
0.142400 | + | 0.989809i | \(0.454518\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3837 | 0.845660 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.48630 | −0.351467 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.67409 | 0.316744 | 0.158372 | − | 0.987380i | \(-0.449376\pi\) | ||||
0.158372 | + | 0.987380i | \(0.449376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.7096 | −0.523692 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.4548 | −1.00424 | −0.502120 | − | 0.864798i | \(-0.667446\pi\) | ||||
−0.502120 | + | 0.864798i | \(0.667446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.1604 | −1.48243 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.8660 | −1.05685 | −0.528427 | − | 0.848979i | \(-0.677218\pi\) | ||||
−0.528427 | + | 0.848979i | \(0.677218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9330 | 0.445965 | 0.222983 | − | 0.974822i | \(-0.428421\pi\) | ||||
0.222983 | + | 0.974822i | \(0.428421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.41520 | 0.382782 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0355 | 0.853807 | 0.426903 | − | 0.904297i | \(-0.359604\pi\) | ||||
0.426903 | + | 0.904297i | \(0.359604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.48223 | 0.221787 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7767 | −1.36423 | −0.682113 | − | 0.731247i | \(-0.738939\pi\) | ||||
−0.682113 | + | 0.731247i | \(0.738939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1289 | 0.810360 | 0.405180 | − | 0.914237i | \(-0.367209\pi\) | ||||
0.405180 | + | 0.914237i | \(0.367209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.7741 | −1.11634 | −0.558168 | − | 0.829728i | \(-0.688495\pi\) | ||||
−0.558168 | + | 0.829728i | \(0.688495\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −81.3745 | −3.26020 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.25889 | 0.209686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.6741 | −1.34054 | −0.670272 | − | 0.742115i | \(-0.733823\pi\) | ||||
−0.670272 | + | 0.742115i | \(0.733823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.9685 | −0.751560 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3837 | 1.43707 | 0.718535 | − | 0.695490i | \(-0.244813\pi\) | ||||
0.718535 | + | 0.695490i | \(0.244813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.0041 | 0.986064 | 0.493032 | − | 0.870011i | \(-0.335888\pi\) | ||||
0.493032 | + | 0.870011i | \(0.335888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.7700 | −1.36695 | −0.683475 | − | 0.729974i | \(-0.739532\pi\) | ||||
−0.683475 | + | 0.729974i | \(0.739532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.03555 | 0.197663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.3208 | −1.57787 | −0.788937 | − | 0.614474i | \(-0.789368\pi\) | ||||
−0.788937 | + | 0.614474i | \(0.789368\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5467 | 0.568386 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.4837 | −0.875842 | −0.437921 | − | 0.899013i | \(-0.644285\pi\) | ||||
−0.437921 | + | 0.899013i | \(0.644285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.6401 | −1.93077 | −0.965387 | − | 0.260821i | \(-0.916007\pi\) | ||||
−0.965387 | + | 0.260821i | \(0.916007\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −32.3837 | −1.25579 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.4467 | −0.946579 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.96853 | 0.230412 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6030 | −0.755640 | −0.377820 | − | 0.925879i | \(-0.623326\pi\) | ||||
−0.377820 | + | 0.925879i | \(0.623326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.7989 | −1.18370 | −0.591850 | − | 0.806048i | \(-0.701602\pi\) | ||||
−0.591850 | + | 0.806048i | \(0.701602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.7360 | 2.56109 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.3126 | 1.15988 | 0.579940 | − | 0.814659i | \(-0.303076\pi\) | ||||
0.579940 | + | 0.814659i | \(0.303076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.4822 | 0.438713 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.74111 | 0.256816 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.4126 | −1.46129 | −0.730643 | − | 0.682760i | \(-0.760780\pi\) | ||||
−0.730643 | + | 0.682760i | \(0.760780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.549248 | −0.0208342 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.25889 | −0.199195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 52.3497 | 1.97722 | 0.988610 | − | 0.150498i | \(-0.0480878\pi\) | ||||
0.988610 | + | 0.150498i | \(0.0480878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.70964 | 0.177627 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.0223 | −1.31715 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.60963 | −0.173118 | −0.0865592 | − | 0.996247i | \(-0.527587\pi\) | ||||
−0.0865592 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.2274 | 0.420470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.25889 | 0.0470797 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.7452 | 1.25848 | 0.629242 | − | 0.777210i | \(-0.283366\pi\) | ||||
0.629242 | + | 0.777210i | \(0.283366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.1696 | −0.415977 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.35482 | 0.161734 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5533 | 0.576841 | 0.288420 | − | 0.957504i | \(-0.406870\pi\) | ||||
0.288420 | + | 0.957504i | \(0.406870\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.9015 | 1.43882 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.5441 | 1.27592 | 0.637958 | − | 0.770071i | \(-0.279779\pi\) | ||||
0.637958 | + | 0.770071i | \(0.279779\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.38373 | 0.161477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.8370 | −1.46543 | −0.732715 | − | 0.680536i | \(-0.761747\pi\) | ||||
−0.732715 | + | 0.680536i | \(0.761747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.8030 | −1.68035 | −0.840175 | − | 0.542316i | \(-0.817548\pi\) | ||||
−0.840175 | + | 0.542316i | \(0.817548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.4152 | −0.454858 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 65.9056 | 2.40814 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8974 | 0.580105 | 0.290053 | − | 0.957011i | \(-0.406327\pi\) | ||||
0.290053 | + | 0.957011i | \(0.406327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.5178 | −0.455568 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.4904 | −0.490316 | −0.245158 | − | 0.969483i | \(-0.578840\pi\) | ||||
−0.245158 | + | 0.969483i | \(0.578840\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.1289 | 1.59967 | 0.799836 | − | 0.600219i | \(-0.204920\pi\) | ||||
0.799836 | + | 0.600219i | \(0.204920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60.3208 | 2.18376 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.00000 | −0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.9645 | 0.467510 | 0.233755 | − | 0.972296i | \(-0.424899\pi\) | ||||
0.233755 | + | 0.972296i | \(0.424899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.5756 | 0.883923 | 0.441961 | − | 0.897034i | \(-0.354283\pi\) | ||||
0.441961 | + | 0.897034i | \(0.354283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.70964 | −0.168740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.4152 | −0.515817 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.9015 | 0.460474 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2274 | −0.899260 | −0.449630 | − | 0.893215i | \(-0.648444\pi\) | ||||
−0.449630 | + | 0.893215i | \(0.648444\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.5756 | 1.51381 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.74111 | −0.168362 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.6071 | −1.15500 | −0.577501 | − | 0.816390i | \(-0.695972\pi\) | ||||
−0.577501 | + | 0.816390i | \(0.695972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.9015 | −1.37624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.83041 | −0.170461 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.6071 | 1.00827 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.3482 | −0.961511 | −0.480755 | − | 0.876855i | \(-0.659638\pi\) | ||||
−0.480755 | + | 0.876855i | \(0.659638\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5467 | −0.861951 | −0.430975 | − | 0.902364i | \(-0.641830\pi\) | ||||
−0.430975 | + | 0.902364i | \(0.641830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.294435 | −0.0103136 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.8386 | 1.21885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.10257 | −0.212981 | −0.106491 | − | 0.994314i | \(-0.533961\pi\) | ||||
−0.106491 | + | 0.994314i | \(0.533961\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.6385 | −0.649699 | −0.324849 | − | 0.945766i | \(-0.605314\pi\) | ||||
−0.324849 | + | 0.945766i | \(0.605314\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.44668 | 0.154626 | 0.0773131 | − | 0.997007i | \(-0.475366\pi\) | ||||
0.0773131 | + | 0.997007i | \(0.475366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3837 | −0.499568 | −0.249784 | − | 0.968302i | \(-0.580360\pi\) | ||||
−0.249784 | + | 0.968302i | \(0.580360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 134.599 | 4.66359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.19186 | −0.214278 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.0263 | 1.58901 | 0.794503 | − | 0.607260i | \(-0.207731\pi\) | ||||
0.794503 | + | 0.607260i | \(0.207731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0355 | −0.346053 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −47.9792 | −1.64859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.16039 | −0.142616 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1248 | −0.586343 | −0.293172 | − | 0.956060i | \(-0.594711\pi\) | ||||
−0.293172 | + | 0.956060i | \(0.594711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.1670 | −0.723052 | −0.361526 | − | 0.932362i | \(-0.617744\pi\) | ||||
−0.361526 | + | 0.932362i | \(0.617744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.64262 | 0.0560453 | 0.0280227 | − | 0.999607i | \(-0.491079\pi\) | ||||
0.0280227 | + | 0.999607i | \(0.491079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.5045 | 1.65111 | 0.825556 | − | 0.564320i | \(-0.190862\pi\) | ||||
0.825556 | + | 0.564320i | \(0.190862\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.2274 | −0.653752 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.2812 | −0.552300 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.48223 | −0.117991 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.09593 | −0.172274 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.41928 | 0.250531 | 0.125266 | − | 0.992123i | \(-0.460022\pi\) | ||||
0.125266 | + | 0.992123i | \(0.460022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1563 | 0.712774 | 0.356387 | − | 0.934338i | \(-0.384008\pi\) | ||||
0.356387 | + | 0.934338i | \(0.384008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.8304 | 0.835610 | 0.417805 | − | 0.908537i | \(-0.362800\pi\) | ||||
0.417805 | + | 0.908537i | \(0.362800\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.7071 | 0.896736 | 0.448368 | − | 0.893849i | \(-0.352005\pi\) | ||||
0.448368 | + | 0.893849i | \(0.352005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.8386 | −1.16583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.64518 | −0.255550 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.70964 | −0.290483 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.8345 | −1.59360 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.6782 | 0.820330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.8304 | 0.558844 | 0.279422 | − | 0.960168i | \(-0.409857\pi\) | ||||
0.279422 | + | 0.960168i | \(0.409857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6385 | −0.882574 | −0.441287 | − | 0.897366i | \(-0.645478\pi\) | ||||
−0.441287 | + | 0.897366i | \(0.645478\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.03555 | 0.166652 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −74.1289 | −2.44795 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.8974 | −1.05220 | −0.526100 | − | 0.850423i | \(-0.676346\pi\) | ||||
−0.526100 | + | 0.850423i | \(0.676346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.4508 | 0.376906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.741113 | 0.0243676 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.4508 | 0.441305 | 0.220652 | − | 0.975353i | \(-0.429181\pi\) | ||||
0.220652 | + | 0.975353i | \(0.429181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 120.542 | 3.95059 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.93298 | −0.292140 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.8081 | −0.647104 | −0.323552 | − | 0.946210i | \(-0.604877\pi\) | ||||
−0.323552 | + | 0.946210i | \(0.604877\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −58.0974 | −1.89392 | −0.946961 | − | 0.321348i | \(-0.895864\pi\) | ||||
−0.946961 | + | 0.321348i | \(0.895864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.16039 | 0.135481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.8660 | −0.970513 | −0.485257 | − | 0.874372i | \(-0.661274\pi\) | ||||
−0.485257 | + | 0.874372i | \(0.661274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.83705 | 0.124556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.6715 | −1.47945 | −0.739723 | − | 0.672912i | \(-0.765043\pi\) | ||||
−0.739723 | + | 0.672912i | \(0.765043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.5178 | −0.469784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −58.5126 | −1.88947 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.09593 | 0.164044 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.7741 | −0.764523 | −0.382262 | − | 0.924054i | \(-0.624855\pi\) | ||||
−0.382262 | + | 0.924054i | \(0.624855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.12741 | 0.292912 | 0.146456 | − | 0.989217i | \(-0.453213\pi\) | ||||
0.146456 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.79893 | 0.0897297 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.4548 | −1.03832 | −0.519161 | − | 0.854677i | \(-0.673755\pi\) | ||||
−0.519161 | + | 0.854677i | \(0.673755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.1026 | −0.642481 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8030 | 0.695408 | 0.347704 | − | 0.937604i | \(-0.386961\pi\) | ||||
0.347704 | + | 0.937604i | \(0.386961\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.22741 | −0.166559 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.7756 | −0.978607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0396 | 0.763644 | 0.381822 | − | 0.924236i | \(-0.375297\pi\) | ||||
0.381822 | + | 0.924236i | \(0.375297\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.4193 | 0.805845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.3837 | 1.34231 | 0.671153 | − | 0.741319i | \(-0.265799\pi\) | ||||
0.671153 | + | 0.741319i | \(0.265799\pi\) | |||||||
\(998\) | 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 | 4680.2.a.bg.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 4680.2.a.bj.1.3 | yes | 3 | ||
4.3 | odd | 2 | 9360.2.a.cz.1.1 | 3 | |||
12.11 | even | 2 | 9360.2.a.de.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4680.2.a.bg.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4680.2.a.bj.1.3 | yes | 3 | 3.2 | odd | 2 | ||
9360.2.a.cz.1.1 | 3 | 4.3 | odd | 2 | |||
9360.2.a.de.1.1 | 3 | 12.11 | even | 2 |