Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(7\) | 0.636672 | 0.240639 | 0.120320 | − | 0.992735i | \(-0.461608\pi\) | ||||
0.120320 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50466 | 0.453673 | 0.226837 | − | 0.973933i | \(-0.427162\pi\) | ||||
0.226837 | + | 0.973933i | \(0.427162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50466 | −0.972019 | −0.486010 | − | 0.873954i | \(-0.661548\pi\) | ||||
−0.486010 | + | 0.873954i | \(0.661548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.636672 | −0.154416 | −0.0772078 | − | 0.997015i | \(-0.524600\pi\) | ||||
−0.0772078 | + | 0.997015i | \(0.524600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.778008 | −0.178487 | −0.0892436 | − | 0.996010i | \(-0.528445\pi\) | ||||
−0.0892436 | + | 0.996010i | \(0.528445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.14134 | 0.769027 | 0.384513 | − | 0.923119i | \(-0.374369\pi\) | ||||
0.384513 | + | 0.923119i | \(0.374369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.14134 | 0.384595 | 0.192298 | − | 0.981337i | \(-0.438406\pi\) | ||||
0.192298 | + | 0.981337i | \(0.438406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.636672 | −0.107617 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.36333 | 0.224130 | 0.112065 | − | 0.993701i | \(-0.464254\pi\) | ||||
0.112065 | + | 0.993701i | \(0.464254\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.85866 | −0.290275 | −0.145137 | − | 0.989412i | \(-0.546362\pi\) | ||||
−0.145137 | + | 0.989412i | \(0.546362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.00933 | −1.06891 | −0.534456 | − | 0.845196i | \(-0.679484\pi\) | ||||
−0.534456 | + | 0.845196i | \(0.679484\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22199 | −0.469976 | −0.234988 | − | 0.971998i | \(-0.575505\pi\) | ||||
−0.234988 | + | 0.971998i | \(0.575505\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59465 | −0.942093 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.636672 | −0.0874536 | −0.0437268 | − | 0.999044i | \(-0.513923\pi\) | ||||
−0.0437268 | + | 0.999044i | \(0.513923\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50466 | −0.202889 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.1507 | −1.45169 | −0.725846 | − | 0.687857i | \(-0.758552\pi\) | ||||
−0.725846 | + | 0.687857i | \(0.758552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.7873 | 1.76529 | 0.882644 | − | 0.470043i | \(-0.155761\pi\) | ||||
0.882644 | + | 0.470043i | \(0.155761\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.50466 | 0.434700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.9287 | 1.70166 | 0.850829 | − | 0.525443i | \(-0.176100\pi\) | ||||
0.850829 | + | 0.525443i | \(0.176100\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.97070 | −1.06463 | −0.532313 | − | 0.846548i | \(-0.678677\pi\) | ||||
−0.532313 | + | 0.846548i | \(0.678677\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2406 | 1.78378 | 0.891892 | − | 0.452249i | \(-0.149378\pi\) | ||||
0.891892 | + | 0.452249i | \(0.149378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.957977 | 0.109172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5653 | −1.41371 | −0.706856 | − | 0.707358i | \(-0.749887\pi\) | ||||
−0.706856 | + | 0.707358i | \(0.749887\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.64600 | −1.05879 | −0.529393 | − | 0.848377i | \(-0.677580\pi\) | ||||
−0.529393 | + | 0.848377i | \(0.677580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.636672 | 0.0690567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.44398 | 0.259062 | 0.129531 | − | 0.991575i | \(-0.458653\pi\) | ||||
0.129531 | + | 0.991575i | \(0.458653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.23132 | −0.233906 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.778008 | 0.0798219 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.55602 | −0.767197 | −0.383599 | − | 0.923500i | \(-0.625315\pi\) | ||||
−0.383599 | + | 0.923500i | \(0.625315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8680 | −1.08141 | −0.540703 | − | 0.841214i | \(-0.681842\pi\) | ||||
−0.540703 | + | 0.841214i | \(0.681842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1893 | 1.69371 | 0.846856 | − | 0.531822i | \(-0.178493\pi\) | ||||
0.846856 | + | 0.531822i | \(0.178493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.9287 | 1.34654 | 0.673268 | − | 0.739399i | \(-0.264890\pi\) | ||||
0.673268 | + | 0.739399i | \(0.264890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5140 | −1.19862 | −0.599312 | − | 0.800516i | \(-0.704559\pi\) | ||||
−0.599312 | + | 0.800516i | \(0.704559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.47536 | 0.609151 | 0.304575 | − | 0.952488i | \(-0.401485\pi\) | ||||
0.304575 | + | 0.952488i | \(0.401485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.405351 | −0.0371585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.73599 | −0.794180 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.60737 | −0.852516 | −0.426258 | − | 0.904602i | \(-0.640168\pi\) | ||||
−0.426258 | + | 0.904602i | \(0.640168\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.00933 | −0.0881855 | −0.0440927 | − | 0.999027i | \(-0.514040\pi\) | ||||
−0.0440927 | + | 0.999027i | \(0.514040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.495336 | −0.0429510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.2920 | −1.47736 | −0.738678 | − | 0.674059i | \(-0.764549\pi\) | ||||
−0.738678 | + | 0.674059i | \(0.764549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7160 | 1.50265 | 0.751326 | − | 0.659931i | \(-0.229415\pi\) | ||||
0.751326 | + | 0.659931i | \(0.229415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.27334 | −0.440979 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.14134 | −0.343919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.2406 | −1.24856 | −0.624281 | − | 0.781200i | \(-0.714608\pi\) | ||||
−0.624281 | + | 0.781200i | \(0.714608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.28267 | −0.348519 | −0.174259 | − | 0.984700i | \(-0.555753\pi\) | ||||
−0.174259 | + | 0.984700i | \(0.555753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.14134 | −0.171996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2020 | 0.894018 | 0.447009 | − | 0.894529i | \(-0.352489\pi\) | ||||
0.447009 | + | 0.894529i | \(0.352489\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.636672 | 0.0501768 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.83869 | 0.770626 | 0.385313 | − | 0.922786i | \(-0.374094\pi\) | ||||
0.385313 | + | 0.922786i | \(0.374094\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.6846 | −1.21371 | −0.606857 | − | 0.794811i | \(-0.707570\pi\) | ||||
−0.606857 | + | 0.794811i | \(0.707570\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.717328 | −0.0551791 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.8480 | −1.73710 | −0.868551 | − | 0.495599i | \(-0.834948\pi\) | ||||
−0.868551 | + | 0.495599i | \(0.834948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.636672 | 0.0481279 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.1893 | −1.58376 | −0.791881 | − | 0.610675i | \(-0.790898\pi\) | ||||
−0.791881 | + | 0.610675i | \(0.790898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.161312 | −0.0119902 | −0.00599511 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599511 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.36333 | −0.100234 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.957977 | −0.0700542 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.5140 | −1.33963 | −0.669813 | − | 0.742530i | \(-0.733626\pi\) | ||||
−0.669813 | + | 0.742530i | \(0.733626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.2827 | −1.60394 | −0.801971 | − | 0.597363i | \(-0.796215\pi\) | ||||
−0.801971 | + | 0.597363i | \(0.796215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5840 | 1.75154 | 0.875769 | − | 0.482731i | \(-0.160355\pi\) | ||||
0.875769 | + | 0.482731i | \(0.160355\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.73599 | 0.123061 | 0.0615304 | − | 0.998105i | \(-0.480402\pi\) | ||||
0.0615304 | + | 0.998105i | \(0.480402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.63667 | 0.185058 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.85866 | 0.129815 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.17064 | −0.0809749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.69735 | −0.254536 | −0.127268 | − | 0.991868i | \(-0.540621\pi\) | ||||
−0.127268 | + | 0.991868i | \(0.540621\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.00933 | 0.478032 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.36333 | 0.0925488 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23132 | 0.150095 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.443984 | 0.0297314 | 0.0148657 | − | 0.999889i | \(-0.495268\pi\) | ||||
0.0148657 | + | 0.999889i | \(0.495268\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.0187 | −1.46143 | −0.730715 | − | 0.682683i | \(-0.760813\pi\) | ||||
−0.730715 | + | 0.682683i | \(0.760813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.62395 | 0.305559 | 0.152780 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152780 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.83869 | −0.513530 | −0.256765 | − | 0.966474i | \(-0.582657\pi\) | ||||
−0.256765 | + | 0.966474i | \(0.582657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.22199 | 0.210180 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.1693 | 1.49870 | 0.749349 | − | 0.662175i | \(-0.230366\pi\) | ||||
0.749349 | + | 0.662175i | \(0.230366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.60737 | 0.103540 | 0.0517698 | − | 0.998659i | \(-0.483514\pi\) | ||||
0.0517698 | + | 0.998659i | \(0.483514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.59465 | 0.421317 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.72666 | 0.173493 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.99067 | −0.188769 | −0.0943847 | − | 0.995536i | \(-0.530088\pi\) | ||||
−0.0943847 | + | 0.995536i | \(0.530088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.50466 | 0.0945974 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.9486 | −0.745336 | −0.372668 | − | 0.927965i | \(-0.621557\pi\) | ||||
−0.372668 | + | 0.927965i | \(0.621557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.867993 | 0.0539344 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.5033 | 1.57260 | 0.786302 | − | 0.617843i | \(-0.211993\pi\) | ||||
0.786302 | + | 0.617843i | \(0.211993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.636672 | 0.0391104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.33063 | −0.446957 | −0.223478 | − | 0.974709i | \(-0.571741\pi\) | ||||
−0.223478 | + | 0.974709i | \(0.571741\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5267 | 0.882435 | 0.441217 | − | 0.897400i | \(-0.354547\pi\) | ||||
0.441217 | + | 0.897400i | \(0.354547\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50466 | 0.0907347 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.72666 | 0.163829 | 0.0819145 | − | 0.996639i | \(-0.473897\pi\) | ||||
0.0819145 | + | 0.996639i | \(0.473897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.3620 | 1.39366 | 0.696830 | − | 0.717236i | \(-0.254593\pi\) | ||||
0.696830 | + | 0.717236i | \(0.254593\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2113 | −1.08255 | −0.541276 | − | 0.840845i | \(-0.682059\pi\) | ||||
−0.541276 | + | 0.840845i | \(0.682059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.18336 | −0.0698515 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5946 | −0.976156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.26063 | −0.190488 | −0.0952439 | − | 0.995454i | \(-0.530363\pi\) | ||||
−0.0952439 | + | 0.995454i | \(0.530363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1507 | 0.649217 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.50466 | −0.202680 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.46264 | −0.257222 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.7873 | −0.789461 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.9580 | 1.65272 | 0.826360 | − | 0.563143i | \(-0.190408\pi\) | ||||
0.826360 | + | 0.563143i | \(0.190408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3854 | 0.702310 | 0.351155 | − | 0.936317i | \(-0.385789\pi\) | ||||
0.351155 | + | 0.936317i | \(0.385789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2886 | −1.59897 | −0.799483 | − | 0.600688i | \(-0.794893\pi\) | ||||
−0.799483 | + | 0.600688i | \(0.794893\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.4206 | 1.09077 | 0.545385 | − | 0.838185i | \(-0.316383\pi\) | ||||
0.545385 | + | 0.838185i | \(0.316383\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.23132 | 0.348887 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.495336 | 0.0275612 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50466 | −0.194404 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.05135 | −0.113095 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9707 | 1.37251 | 0.686257 | − | 0.727359i | \(-0.259253\pi\) | ||||
0.686257 | + | 0.727359i | \(0.259253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.9287 | −0.761005 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8387 | −1.29858 | −0.649288 | − | 0.760543i | \(-0.724933\pi\) | ||||
−0.649288 | + | 0.760543i | \(0.724933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.22199 | 0.174481 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.65533 | −0.467344 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8773 | −1.17107 | −0.585533 | − | 0.810649i | \(-0.699115\pi\) | ||||
−0.585533 | + | 0.810649i | \(0.699115\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.9860 | −1.91534 | −0.957670 | − | 0.287869i | \(-0.907053\pi\) | ||||
−0.957670 | + | 0.287869i | \(0.907053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.97070 | 0.476115 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.9486 | −1.15841 | −0.579203 | − | 0.815184i | \(-0.696636\pi\) | ||||
−0.579203 | + | 0.815184i | \(0.696636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3947 | −0.968142 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2406 | −0.797732 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.79798 | 0.146054 | 0.0730268 | − | 0.997330i | \(-0.476734\pi\) | ||||
0.0730268 | + | 0.997330i | \(0.476734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.405351 | −0.0210448 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.8853 | 1.90985 | 0.954925 | − | 0.296847i | \(-0.0959352\pi\) | ||||
0.954925 | + | 0.296847i | \(0.0959352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.5140 | −0.747509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9253 | −1.48579 | −0.742896 | − | 0.669407i | \(-0.766548\pi\) | ||||
−0.742896 | + | 0.669407i | \(0.766548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.1927 | −1.23619 | −0.618094 | − | 0.786104i | \(-0.712095\pi\) | ||||
−0.618094 | + | 0.786104i | \(0.712095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.957977 | −0.0488230 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.6867 | −1.25167 | −0.625833 | − | 0.779957i | \(-0.715241\pi\) | ||||
−0.625833 | + | 0.779957i | \(0.715241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.636672 | −0.0321979 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.5653 | 0.632231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.65872 | −0.284003 | −0.142001 | − | 0.989866i | \(-0.545354\pi\) | ||||
−0.142001 | + | 0.989866i | \(0.545354\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.8387 | −1.29032 | −0.645161 | − | 0.764046i | \(-0.723210\pi\) | ||||
−0.645161 | + | 0.764046i | \(0.723210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.50466 | −0.373834 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.05135 | 0.101682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.9800 | −1.28463 | −0.642315 | − | 0.766441i | \(-0.722026\pi\) | ||||
−0.642315 | + | 0.766441i | \(0.722026\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.09931 | −0.349334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.64600 | 0.473504 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.96731 | 0.0961092 | 0.0480546 | − | 0.998845i | \(-0.484698\pi\) | ||||
0.0480546 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.14473 | −0.0557905 | −0.0278953 | − | 0.999611i | \(-0.508880\pi\) | ||||
−0.0278953 | + | 0.999611i | \(0.508880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.636672 | −0.0308831 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.77801 | 0.424798 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4720 | −0.937932 | −0.468966 | − | 0.883216i | \(-0.655373\pi\) | ||||
−0.468966 | + | 0.883216i | \(0.655373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.1834 | −0.537438 | −0.268719 | − | 0.963219i | \(-0.586600\pi\) | ||||
−0.268719 | + | 0.963219i | \(0.586600\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.778008 | −0.0372172 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2733 | −0.633502 | −0.316751 | − | 0.948509i | \(-0.602592\pi\) | ||||
−0.316751 | + | 0.948509i | \(0.602592\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.8994 | −0.707890 | −0.353945 | − | 0.935266i | \(-0.615160\pi\) | ||||
−0.353945 | + | 0.935266i | \(0.615160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.44398 | −0.115856 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1693 | 1.09343 | 0.546714 | − | 0.837319i | \(-0.315879\pi\) | ||||
0.546714 | + | 0.837319i | \(0.315879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.79667 | −0.131690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.23132 | 0.104606 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9380 | 0.511658 | 0.255829 | − | 0.966722i | \(-0.417652\pi\) | ||||
0.255829 | + | 0.966722i | \(0.417652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2920 | 0.619070 | 0.309535 | − | 0.950888i | \(-0.399827\pi\) | ||||
0.309535 | + | 0.950888i | \(0.399827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.436726 | 0.0202964 | 0.0101482 | − | 0.999949i | \(-0.496770\pi\) | ||||
0.0101482 | + | 0.999949i | \(0.496770\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.1180 | 1.34742 | 0.673709 | − | 0.738996i | \(-0.264700\pi\) | ||||
0.673709 | + | 0.738996i | \(0.264700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.86799 | 0.409486 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5467 | −0.484937 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.778008 | −0.0356974 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.1541 | −0.463951 | −0.231975 | − | 0.972722i | \(-0.574519\pi\) | ||||
−0.231975 | + | 0.972722i | \(0.574519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.77801 | −0.217858 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.55602 | 0.343101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5980 | 0.842758 | 0.421379 | − | 0.906885i | \(-0.361546\pi\) | ||||
0.421379 | + | 0.906885i | \(0.361546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.0080 | −1.57989 | −0.789945 | − | 0.613178i | \(-0.789891\pi\) | ||||
−0.789945 | + | 0.613178i | \(0.789891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.63667 | −0.118750 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.71139 | −0.256191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.40535 | −0.376275 | −0.188138 | − | 0.982143i | \(-0.560245\pi\) | ||||
−0.188138 | + | 0.982143i | \(0.560245\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.5806 | 1.67564 | 0.837818 | − | 0.545949i | \(-0.183831\pi\) | ||||
0.837818 | + | 0.545949i | \(0.183831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.8680 | 0.483619 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.2427 | 1.51778 | 0.758891 | − | 0.651218i | \(-0.225742\pi\) | ||||
0.758891 | + | 0.651218i | \(0.225742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.70329 | 0.429248 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.1893 | −0.757451 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.84802 | −0.213216 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.572602 | −0.0250862 | −0.0125431 | − | 0.999921i | \(-0.503993\pi\) | ||||
−0.0125431 | + | 0.999921i | \(0.503993\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3760 | 0.584894 | 0.292447 | − | 0.956282i | \(-0.405531\pi\) | ||||
0.292447 | + | 0.956282i | \(0.405531\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.36333 | −0.0593875 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.51399 | 0.282152 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.9287 | −0.602189 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.92273 | −0.427402 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.4040 | −1.56513 | −0.782566 | − | 0.622568i | \(-0.786089\pi\) | ||||
−0.782566 | + | 0.622568i | \(0.786089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5140 | 0.536041 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5840 | −0.623567 | −0.311783 | − | 0.950153i | \(-0.600926\pi\) | ||||
−0.311783 | + | 0.950153i | \(0.600926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.22199 | −0.137261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.00000 | −0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −46.4100 | −1.96645 | −0.983227 | − | 0.182387i | \(-0.941618\pi\) | ||||
−0.983227 | + | 0.182387i | \(0.941618\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.5653 | 1.03900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.36333 | −0.394617 | −0.197309 | − | 0.980341i | \(-0.563220\pi\) | ||||
−0.197309 | + | 0.980341i | \(0.563220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.47536 | −0.272420 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.282672 | 0.0118502 | 0.00592512 | − | 0.999982i | \(-0.498114\pi\) | ||||
0.00592512 | + | 0.999982i | \(0.498114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.1073 | −1.00886 | −0.504430 | − | 0.863453i | \(-0.668297\pi\) | ||||
−0.504430 | + | 0.863453i | \(0.668297\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.4227 | 0.933469 | 0.466734 | − | 0.884398i | \(-0.345430\pi\) | ||||
0.466734 | + | 0.884398i | \(0.345430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.14134 | −0.254786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.957977 | −0.0396754 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.1893 | −0.792027 | −0.396014 | − | 0.918245i | \(-0.629607\pi\) | ||||
−0.396014 | + | 0.918245i | \(0.629607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.66598 | −0.0686454 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.04202 | −0.371311 | −0.185656 | − | 0.982615i | \(-0.559441\pi\) | ||||
−0.185656 | + | 0.982615i | \(0.559441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.405351 | 0.0166178 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.3386 | −1.89335 | −0.946673 | − | 0.322196i | \(-0.895579\pi\) | ||||
−0.946673 | + | 0.322196i | \(0.895579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.6974 | −0.721890 | −0.360945 | − | 0.932587i | \(-0.617546\pi\) | ||||
−0.360945 | + | 0.932587i | \(0.617546\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.73599 | 0.355168 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.5327 | 1.72635 | 0.863174 | − | 0.504907i | \(-0.168473\pi\) | ||||
0.863174 | + | 0.504907i | \(0.168473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.2920 | 0.456825 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.5747 | −1.27529 | −0.637645 | − | 0.770331i | \(-0.720091\pi\) | ||||
−0.637645 | + | 0.770331i | \(0.720091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.2393 | −1.82127 | −0.910633 | − | 0.413215i | \(-0.864406\pi\) | ||||
−0.910633 | + | 0.413215i | \(0.864406\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.4906 | 1.18533 | 0.592664 | − | 0.805450i | \(-0.298076\pi\) | ||||
0.592664 | + | 0.805450i | \(0.298076\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.55602 | 0.0623405 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.867993 | −0.0346091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.6447 | 1.73747 | 0.868734 | − | 0.495280i | \(-0.164934\pi\) | ||||
0.868734 | + | 0.495280i | \(0.164934\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.60737 | 0.381257 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.1120 | 0.915732 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.3527 | −1.11986 | −0.559932 | − | 0.828539i | \(-0.689173\pi\) | ||||
−0.559932 | + | 0.828539i | \(0.689173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.1086 | 0.871880 | 0.435940 | − | 0.899976i | \(-0.356416\pi\) | ||||
0.435940 | + | 0.899976i | \(0.356416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.42062 | −0.370363 | −0.185181 | − | 0.982704i | \(-0.559287\pi\) | ||||
−0.185181 | + | 0.982704i | \(0.559287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.7780 | −0.658594 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.76868 | −0.147480 | −0.0737399 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737399 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.00933 | 0.0394377 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9393 | −0.659862 | −0.329931 | − | 0.944005i | \(-0.607026\pi\) | ||||
−0.329931 | + | 0.944005i | \(0.607026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.6960 | 1.38841 | 0.694207 | − | 0.719775i | \(-0.255755\pi\) | ||||
0.694207 | + | 0.719775i | \(0.255755\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.495336 | 0.0192083 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.14134 | 0.160353 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7453 | 0.800864 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.53265 | 0.0976265 | 0.0488133 | − | 0.998808i | \(-0.484456\pi\) | ||||
0.0488133 | + | 0.998808i | \(0.484456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.3633 | −1.20539 | −0.602695 | − | 0.797971i | \(-0.705907\pi\) | ||||
−0.602695 | + | 0.797971i | \(0.705907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.81070 | −0.184618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.7873 | 0.910197 | 0.455099 | − | 0.890441i | \(-0.349604\pi\) | ||||
0.455099 | + | 0.890441i | \(0.349604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.2920 | 0.660693 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.23132 | 0.0850066 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6613 | −0.862075 | −0.431038 | − | 0.902334i | \(-0.641852\pi\) | ||||
−0.431038 | + | 0.902334i | \(0.641852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.7160 | −0.672007 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.18336 | 0.0448229 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2593 | 0.500797 | 0.250399 | − | 0.968143i | \(-0.419438\pi\) | ||||
0.250399 | + | 0.968143i | \(0.419438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06068 | −0.0400043 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.91934 | −0.260229 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.6940 | −1.52829 | −0.764147 | − | 0.645042i | \(-0.776840\pi\) | ||||
−0.764147 | + | 0.645042i | \(0.776840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.14134 | 0.0801937 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.27334 | 0.197212 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.79073 | −0.178664 | −0.0893320 | − | 0.996002i | \(-0.528473\pi\) | ||||
−0.0893320 | + | 0.996002i | \(0.528473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9439 | 0.407574 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.14134 | 0.153805 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.9473 | −0.665630 | −0.332815 | − | 0.942992i | \(-0.607998\pi\) | ||||
−0.332815 | + | 0.942992i | \(0.607998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.46264 | 0.165057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.9287 | −0.662211 | −0.331105 | − | 0.943594i | \(-0.607422\pi\) | ||||
−0.331105 | + | 0.943594i | \(0.607422\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.9580 | 0.771997 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5853 | 0.610101 | 0.305050 | − | 0.952336i | \(-0.401327\pi\) | ||||
0.305050 | + | 0.952336i | \(0.401327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.90663 | −0.106634 | −0.0533169 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533169 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.2406 | 0.558374 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.86799 | 0.324029 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8994 | −0.689648 | −0.344824 | − | 0.938667i | \(-0.612061\pi\) | ||||
−0.344824 | + | 0.938667i | \(0.612061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.28267 | 0.155862 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.34467 | 0.121564 | 0.0607821 | − | 0.998151i | \(-0.480641\pi\) | ||||
0.0607821 | + | 0.998151i | \(0.480641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.5946 | −0.855305 | −0.427653 | − | 0.903943i | \(-0.640659\pi\) | ||||
−0.427653 | + | 0.903943i | \(0.640659\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.96731 | −0.288436 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.0793 | 1.41107 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.8340 | 1.61675 | 0.808377 | − | 0.588665i | \(-0.200346\pi\) | ||||
0.808377 | + | 0.588665i | \(0.200346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.9160 | 0.716327 | 0.358164 | − | 0.933659i | \(-0.383403\pi\) | ||||
0.358164 | + | 0.933659i | \(0.383403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.14134 | 0.0769191 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.44606 | 0.0518103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4979 | −0.482992 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2020 | −0.399817 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.2207 | 1.18419 | 0.592095 | − | 0.805868i | \(-0.298301\pi\) | ||||
0.592095 | + | 0.805868i | \(0.298301\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.12268 | 0.146586 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.3200 | −1.71589 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.8633 | 0.845281 | 0.422640 | − | 0.906297i | \(-0.361103\pi\) | ||||
0.422640 | + | 0.906297i | \(0.361103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.05135 | 0.0725716 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.9321 | 0.809255 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.636672 | −0.0224397 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.1693 | 1.23649 | 0.618244 | − | 0.785986i | \(-0.287844\pi\) | ||||
0.618244 | + | 0.785986i | \(0.287844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.0480 | 1.02001 | 0.510006 | − | 0.860171i | \(-0.329643\pi\) | ||||
0.510006 | + | 0.860171i | \(0.329643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.83869 | −0.344634 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.45331 | 0.190787 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.6027 | −1.34724 | −0.673621 | − | 0.739077i | \(-0.735262\pi\) | ||||
−0.673621 | + | 0.739077i | \(0.735262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4040 | −0.571809 | −0.285904 | − | 0.958258i | \(-0.592294\pi\) | ||||
−0.285904 | + | 0.958258i | \(0.592294\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.2393 | −0.947204 | −0.473602 | − | 0.880739i | \(-0.657047\pi\) | ||||
−0.473602 | + | 0.880739i | \(0.657047\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1107 | 1.08052 | 0.540260 | − | 0.841498i | \(-0.318326\pi\) | ||||
0.540260 | + | 0.841498i | \(0.318326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.19863 | 0.145474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.6846 | 0.542789 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.71733 | −0.128336 | −0.0641682 | − | 0.997939i | \(-0.520439\pi\) | ||||
−0.0641682 | + | 0.997939i | \(0.520439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8493 | −0.408598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.717328 | 0.0246768 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.56196 | −0.191111 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.36333 | 0.0467343 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.17064 | 0.313997 | 0.156998 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156998 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.9907 | 0.512072 | 0.256036 | − | 0.966667i | \(-0.417584\pi\) | ||||
0.256036 | + | 0.966667i | \(0.417584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.98935 | −0.238474 | −0.119237 | − | 0.992866i | \(-0.538045\pi\) | ||||
−0.119237 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.2080 | −0.721927 | −0.360964 | − | 0.932580i | \(-0.617552\pi\) | ||||
−0.360964 | + | 0.932580i | \(0.617552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.8480 | 0.776856 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9066 | −0.641363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.8153 | −1.65404 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.636672 | −0.0215234 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3760 | 0.991959 | 0.495979 | − | 0.868334i | \(-0.334809\pi\) | ||||
0.495979 | + | 0.868334i | \(0.334809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.1820 | −1.32008 | −0.660038 | − | 0.751232i | \(-0.729460\pi\) | ||||
−0.660038 | + | 0.751232i | \(0.729460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.13795 | 0.0382950 | 0.0191475 | − | 0.999817i | \(-0.493905\pi\) | ||||
0.0191475 | + | 0.999817i | \(0.493905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1520 | 0.643061 | 0.321530 | − | 0.946899i | \(-0.395803\pi\) | ||||
0.321530 | + | 0.946899i | \(0.395803\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.11674 | −0.205149 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.50674 | 0.0838847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.1893 | 0.708280 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.86799 | 0.295764 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.405351 | 0.0135042 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.161312 | 0.00536219 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4406 | 0.711923 | 0.355962 | − | 0.934501i | \(-0.384153\pi\) | ||||
0.355962 | + | 0.934501i | \(0.384153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.9346 | 1.32309 | 0.661546 | − | 0.749904i | \(-0.269900\pi\) | ||||
0.661546 | + | 0.749904i | \(0.269900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.5140 | −0.480343 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.642611 | −0.0212209 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4066 | −1.56380 | −0.781899 | − | 0.623405i | \(-0.785749\pi\) | ||||
−0.781899 | + | 0.623405i | \(0.785749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.4393 | 1.03484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.36333 | 0.0448260 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.9053 | 1.34206 | 0.671030 | − | 0.741430i | \(-0.265852\pi\) | ||||
0.671030 | + | 0.741430i | \(0.265852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.13069 | 0.168152 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.957977 | 0.0313292 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.6120 | −0.836707 | −0.418354 | − | 0.908284i | \(-0.637393\pi\) | ||||
−0.418354 | + | 0.908284i | \(0.637393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.21266 | 0.202527 | 0.101264 | − | 0.994860i | \(-0.467711\pi\) | ||||
0.101264 | + | 0.994860i | \(0.467711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.85866 | −0.0605264 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.7987 | −1.22829 | −0.614147 | − | 0.789192i | \(-0.710500\pi\) | ||||
−0.614147 | + | 0.789192i | \(0.710500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.4134 | −1.73387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.32262 | −0.0752372 | −0.0376186 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376186 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.5140 | 0.599099 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.0093 | −0.355510 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4147 | −0.852086 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.2827 | 0.717305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.14473 | 0.294075 | 0.147037 | − | 0.989131i | \(-0.453026\pi\) | ||||
0.147037 | + | 0.989131i | \(0.453026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.7453 | 1.24340 | 0.621698 | − | 0.783257i | \(-0.286443\pi\) | ||||
0.621698 | + | 0.783257i | \(0.286443\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2793 | 0.361597 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.8794 | 1.05190 | 0.525952 | − | 0.850514i | \(-0.323709\pi\) | ||||
0.525952 | + | 0.850514i | \(0.323709\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.67738 | 0.117529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.13408 | −0.0680665 | −0.0340333 | − | 0.999421i | \(-0.510835\pi\) | ||||
−0.0340333 | + | 0.999421i | \(0.510835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.5840 | −0.783311 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.00933 | −0.222884 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.3586 | 1.85382 | 0.926911 | − | 0.375280i | \(-0.122454\pi\) | ||||
0.926911 | + | 0.375280i | \(0.122454\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.73599 | −0.0550344 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4347 | 0.362139 | 0.181070 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181070 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(998\) | 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 | 8280.2.a.bk.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bp.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bk.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
8280.2.a.bp.1.2 | yes | 3 | 3.2 | odd | 2 |