Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6720,2,Mod(1,6720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6720, 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("6720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6720.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: | \(53.6594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 3360) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6720.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61213 | −0.486075 | −0.243037 | − | 0.970017i | \(-0.578144\pi\) | ||||
−0.243037 | + | 0.970017i | \(0.578144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.31265 | 1.75081 | 0.875407 | − | 0.483386i | \(-0.160593\pi\) | ||||
0.875407 | + | 0.483386i | \(0.160593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.92478 | 1.92204 | 0.961020 | − | 0.276477i | \(-0.0891671\pi\) | ||||
0.961020 | + | 0.276477i | \(0.0891671\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38787 | −0.547816 | −0.273908 | − | 0.961756i | \(-0.588316\pi\) | ||||
−0.273908 | + | 0.961756i | \(0.588316\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.70052 | −1.39716 | −0.698578 | − | 0.715534i | \(-0.746183\pi\) | ||||
−0.698578 | + | 0.715534i | \(0.746183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.92478 | −1.47159 | −0.735797 | − | 0.677202i | \(-0.763192\pi\) | ||||
−0.735797 | + | 0.677202i | \(0.763192\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.08840 | 1.63232 | 0.816162 | − | 0.577823i | \(-0.196098\pi\) | ||||
0.816162 | + | 0.577823i | \(0.196098\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61213 | 0.280635 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.92478 | 1.30283 | 0.651413 | − | 0.758724i | \(-0.274177\pi\) | ||||
0.651413 | + | 0.758724i | \(0.274177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.31265 | −1.01083 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.22425 | −0.191196 | −0.0955982 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955982 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.92478 | 0.903520 | 0.451760 | − | 0.892139i | \(-0.350796\pi\) | ||||
0.451760 | + | 0.892139i | \(0.350796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.70052 | 0.977372 | 0.488686 | − | 0.872460i | \(-0.337476\pi\) | ||||
0.488686 | + | 0.872460i | \(0.337476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.92478 | −1.10969 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.61213 | 0.496164 | 0.248082 | − | 0.968739i | \(-0.420200\pi\) | ||||
0.248082 | + | 0.968739i | \(0.420200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.61213 | 0.217379 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.38787 | 0.316282 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70052 | −0.601840 | −0.300920 | − | 0.953649i | \(-0.597294\pi\) | ||||
−0.300920 | + | 0.953649i | \(0.597294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.31265 | −0.782988 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.14903 | −1.11773 | −0.558866 | − | 0.829258i | \(-0.688763\pi\) | ||||
−0.558866 | + | 0.829258i | \(0.688763\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.70052 | 0.806648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.31265 | 0.986530 | 0.493265 | − | 0.869879i | \(-0.335803\pi\) | ||||
0.493265 | + | 0.869879i | \(0.335803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3127 | 1.20700 | 0.603502 | − | 0.797361i | \(-0.293771\pi\) | ||||
0.603502 | + | 0.797361i | \(0.293771\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.61213 | −0.183719 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.775746 | −0.0851492 | −0.0425746 | − | 0.999093i | \(-0.513556\pi\) | ||||
−0.0425746 | + | 0.999093i | \(0.513556\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.92478 | −0.859563 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.92478 | 0.849625 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.6253 | −1.55028 | −0.775139 | − | 0.631790i | \(-0.782320\pi\) | ||||
−0.775139 | + | 0.631790i | \(0.782320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.31265 | 0.661746 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.08840 | −0.942423 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.38787 | 0.244991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.31265 | −0.640953 | −0.320476 | − | 0.947257i | \(-0.603843\pi\) | ||||
−0.320476 | + | 0.947257i | \(0.603843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.61213 | −0.162025 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7005 | −1.03446 | −0.517229 | − | 0.855847i | \(-0.673037\pi\) | ||||
−0.517229 | + | 0.855847i | \(0.673037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.84955 | −0.943416 | −0.471708 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.92478 | −0.752187 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.16362 | 0.109464 | 0.0547321 | − | 0.998501i | \(-0.482570\pi\) | ||||
0.0547321 | + | 0.998501i | \(0.482570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.70052 | 0.624827 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.31265 | 0.583605 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.92478 | 0.726463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.40105 | −0.763732 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.22425 | 0.110387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.62530 | −0.765372 | −0.382686 | − | 0.923879i | \(-0.625001\pi\) | ||||
−0.382686 | + | 0.923879i | \(0.625001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.92478 | −0.521648 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.62530 | 0.753596 | 0.376798 | − | 0.926295i | \(-0.377025\pi\) | ||||
0.376798 | + | 0.926295i | \(0.377025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.38787 | −0.207055 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.23743 | 0.703771 | 0.351885 | − | 0.936043i | \(-0.385541\pi\) | ||||
0.351885 | + | 0.936043i | \(0.385541\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3879 | −0.881088 | −0.440544 | − | 0.897731i | \(-0.645214\pi\) | ||||
−0.440544 | + | 0.897731i | \(0.645214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.70052 | −0.564286 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.1768 | −0.851026 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.92478 | 0.658117 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.7005 | 1.36816 | 0.684080 | − | 0.729407i | \(-0.260204\pi\) | ||||
0.684080 | + | 0.729407i | \(0.260204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.22425 | 0.587901 | 0.293951 | − | 0.955821i | \(-0.405030\pi\) | ||||
0.293951 | + | 0.955821i | \(0.405030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.92478 | 0.640680 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.08840 | −0.729998 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.31265 | −0.184570 | −0.0922848 | − | 0.995733i | \(-0.529417\pi\) | ||||
−0.0922848 | + | 0.995733i | \(0.529417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.61213 | −0.286460 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.70052 | −0.528075 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.07522 | 0.162544 | 0.0812720 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812720 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.61213 | −0.125504 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.9248 | −1.38706 | −0.693530 | − | 0.720427i | \(-0.743946\pi\) | ||||
−0.693530 | + | 0.720427i | \(0.743946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.8496 | 2.06535 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.38787 | −0.182605 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.22425 | −0.0930783 | −0.0465391 | − | 0.998916i | \(-0.514819\pi\) | ||||
−0.0465391 | + | 0.998916i | \(0.514819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.6121 | −1.31639 | −0.658196 | − | 0.752847i | \(-0.728680\pi\) | ||||
−0.658196 | + | 0.752847i | \(0.728680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.07522 | 0.600227 | 0.300113 | − | 0.953904i | \(-0.402976\pi\) | ||||
0.300113 | + | 0.953904i | \(0.402976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.70052 | 0.347473 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.92478 | −0.582641 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.7757 | −0.934255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.31265 | −0.601482 | −0.300741 | − | 0.953706i | \(-0.597234\pi\) | ||||
−0.300741 | + | 0.953706i | \(0.597234\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.84955 | −0.708986 | −0.354493 | − | 0.935059i | \(-0.615347\pi\) | ||||
−0.354493 | + | 0.935059i | \(0.615347\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.31265 | 0.452058 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2374 | 1.44186 | 0.720929 | − | 0.693009i | \(-0.243716\pi\) | ||||
0.720929 | + | 0.693009i | \(0.243716\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5369 | 1.66849 | 0.834243 | − | 0.551396i | \(-0.185905\pi\) | ||||
0.834243 | + | 0.551396i | \(0.185905\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.14903 | 0.645323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.92478 | −0.556210 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22425 | 0.0855056 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.70052 | −0.465719 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.84955 | 0.266279 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.40105 | −0.647195 | −0.323597 | − | 0.946195i | \(-0.604892\pi\) | ||||
−0.323597 | + | 0.946195i | \(0.604892\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.31265 | −0.569573 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.92478 | −0.404066 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.08840 | 0.616961 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.3127 | −0.696864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 50.0263 | 3.36514 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.4749 | 1.90682 | 0.953409 | − | 0.301682i | \(-0.0975480\pi\) | ||||
0.953409 | + | 0.301682i | \(0.0975480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.4749 | 1.62445 | 0.812227 | − | 0.583342i | \(-0.198255\pi\) | ||||
0.812227 | + | 0.583342i | \(0.198255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.9986 | 1.78412 | 0.892058 | − | 0.451920i | \(-0.149261\pi\) | ||||
0.892058 | + | 0.451920i | \(0.149261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.61213 | 0.106070 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4617 | 0.750880 | 0.375440 | − | 0.926847i | \(-0.377492\pi\) | ||||
0.375440 | + | 0.926847i | \(0.377492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70052 | −0.437094 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | −0.259828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.31265 | 0.537701 | 0.268850 | − | 0.963182i | \(-0.413356\pi\) | ||||
0.268850 | + | 0.963182i | \(0.413356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.22425 | 0.336524 | 0.168262 | − | 0.985742i | \(-0.446185\pi\) | ||||
0.168262 | + | 0.985742i | \(0.446185\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0738 | −0.959123 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.775746 | 0.0491609 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8496 | −0.747937 | −0.373969 | − | 0.927441i | \(-0.622003\pi\) | ||||
−0.373969 | + | 0.927441i | \(0.622003\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8021 | 0.679122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.92478 | 0.496269 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.850969 | 0.0530820 | 0.0265410 | − | 0.999648i | \(-0.491551\pi\) | ||||
0.0265410 | + | 0.999648i | \(0.491551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.92478 | 0.492422 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.92478 | −0.490531 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.8773 | 1.53400 | 0.767001 | − | 0.641646i | \(-0.221748\pi\) | ||||
0.767001 | + | 0.641646i | \(0.221748\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.61213 | −0.221891 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6253 | 0.895054 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.2981 | 1.72536 | 0.862682 | − | 0.505747i | \(-0.168783\pi\) | ||||
0.862682 | + | 0.505747i | \(0.168783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.08840 | −0.0661154 | −0.0330577 | − | 0.999453i | \(-0.510525\pi\) | ||||
−0.0330577 | + | 0.999453i | \(0.510525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.31265 | −0.382059 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.61213 | −0.0972149 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0752 | 0.725530 | 0.362765 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362765 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.08840 | 0.544108 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.22425 | −0.0730329 | −0.0365164 | − | 0.999333i | \(-0.511626\pi\) | ||||
−0.0365164 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.55149 | 0.330002 | 0.165001 | − | 0.986293i | \(-0.447237\pi\) | ||||
0.165001 | + | 0.986293i | \(0.447237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.38787 | −0.141445 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22425 | −0.0722654 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.8021 | 2.69424 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.31265 | 0.370054 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.37470 | 0.0803108 | 0.0401554 | − | 0.999193i | \(-0.487215\pi\) | ||||
0.0401554 | + | 0.999193i | \(0.487215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.61213 | 0.0935451 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −42.2981 | −2.44616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.92478 | 0.341498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0000 | −0.574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.70052 | 0.269151 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0738 | −0.632016 | −0.316008 | − | 0.948757i | \(-0.602343\pi\) | ||||
−0.316008 | + | 0.948757i | \(0.602343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.44851 | −0.365661 | −0.182831 | − | 0.983144i | \(-0.558526\pi\) | ||||
−0.182831 | + | 0.983144i | \(0.558526\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0884 | 1.30503 | 0.652517 | − | 0.757774i | \(-0.273713\pi\) | ||||
0.652517 | + | 0.757774i | \(0.273713\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.6385 | −1.21534 | −0.607669 | − | 0.794190i | \(-0.707895\pi\) | ||||
−0.607669 | + | 0.794190i | \(0.707895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7757 | 0.715304 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.7005 | 0.597245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.9234 | −1.05292 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.31265 | 0.350163 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.84955 | 0.544682 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.70052 | 0.369412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.4010 | 1.83589 | 0.917944 | − | 0.396710i | \(-0.129848\pi\) | ||||
0.917944 | + | 0.396710i | \(0.129848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.92478 | 0.434275 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.14903 | 0.499865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40105 | −0.185267 | −0.0926334 | − | 0.995700i | \(-0.529528\pi\) | ||||
−0.0926334 | + | 0.995700i | \(0.529528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.16362 | −0.0631991 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6516 | −0.793431 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.70052 | −0.360744 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.92478 | 0.318059 | 0.159029 | − | 0.987274i | \(-0.449164\pi\) | ||||
0.159029 | + | 0.987274i | \(0.449164\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1016 | −0.968955 | −0.484477 | − | 0.874804i | \(-0.660990\pi\) | ||||
−0.484477 | + | 0.874804i | \(0.660990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.31265 | −0.336944 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.02776 | −0.374050 | −0.187025 | − | 0.982355i | \(-0.559885\pi\) | ||||
−0.187025 | + | 0.982355i | \(0.559885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.31265 | −0.441190 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.92478 | −0.419424 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.7137 | −0.723781 | −0.361891 | − | 0.932221i | \(-0.617869\pi\) | ||||
−0.361891 | + | 0.932221i | \(0.617869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2981 | −0.699898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.40105 | 0.440941 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.3127 | −0.539789 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.6253 | 1.70303 | 0.851513 | − | 0.524333i | \(-0.175685\pi\) | ||||
0.851513 | + | 0.524333i | \(0.175685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.22425 | −0.0637321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.61213 | 0.187532 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5975 | −0.704054 | −0.352027 | − | 0.935990i | \(-0.614507\pi\) | ||||
−0.352027 | + | 0.935990i | \(0.614507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −50.0263 | −2.57649 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0263 | 0.925951 | 0.462976 | − | 0.886371i | \(-0.346782\pi\) | ||||
0.462976 | + | 0.886371i | \(0.346782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.62530 | 0.441888 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.3733 | −1.24542 | −0.622708 | − | 0.782454i | \(-0.713968\pi\) | ||||
−0.622708 | + | 0.782454i | \(0.713968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.61213 | 0.0821616 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.92478 | 0.301173 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.2995 | 0.978522 | 0.489261 | − | 0.872137i | \(-0.337266\pi\) | ||||
0.489261 | + | 0.872137i | \(0.337266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −53.1002 | −2.68539 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.62530 | −0.435089 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.2652 | 1.46878 | 0.734389 | − | 0.678729i | \(-0.237469\pi\) | ||||
0.734389 | + | 0.678729i | \(0.237469\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.38787 | 0.119543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.8496 | 1.89012 | 0.945058 | − | 0.326902i | \(-0.106005\pi\) | ||||
0.945058 | + | 0.326902i | \(0.106005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57.3719 | 2.85790 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7757 | −0.633270 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.6516 | −1.81231 | −0.906154 | − | 0.422949i | \(-0.860995\pi\) | ||||
−0.906154 | + | 0.422949i | \(0.860995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.23743 | −0.406322 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.775746 | 0.0380799 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3879 | 0.508696 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.07381 | 0.345578 | 0.172789 | − | 0.984959i | \(-0.444722\pi\) | ||||
0.172789 | + | 0.984959i | \(0.444722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4485 | −0.606703 | −0.303352 | − | 0.952879i | \(-0.598106\pi\) | ||||
−0.303352 | + | 0.952879i | \(0.598106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.70052 | 0.325791 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.92478 | 0.384408 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.70052 | −0.227474 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1768 | 0.491340 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.7612 | 1.48171 | 0.740856 | − | 0.671663i | \(-0.234420\pi\) | ||||
0.740856 | + | 0.671663i | \(0.234420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.1622 | −1.64173 | −0.820865 | − | 0.571122i | \(-0.806508\pi\) | ||||
−0.820865 | + | 0.571122i | \(0.806508\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.92478 | −0.379964 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.0000 | 0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.68735 | 0.175988 | 0.0879938 | − | 0.996121i | \(-0.471954\pi\) | ||||
0.0879938 | + | 0.996121i | \(0.471954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.3733 | 1.34806 | 0.674028 | − | 0.738706i | \(-0.264563\pi\) | ||||
0.674028 | + | 0.738706i | \(0.264563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.6253 | 0.693306 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.7005 | −0.789908 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4010 | −0.538049 | −0.269024 | − | 0.963133i | \(-0.586701\pi\) | ||||
−0.269024 | + | 0.963133i | \(0.586701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.97365 | 0.0929357 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.22425 | −0.339425 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.31265 | −0.295942 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6253 | 1.24548 | 0.622740 | − | 0.782429i | \(-0.286020\pi\) | ||||
0.622740 | + | 0.782429i | \(0.286020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.92478 | −0.369897 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.4010 | 1.46249 | 0.731246 | − | 0.682114i | \(-0.238939\pi\) | ||||
0.731246 | + | 0.682114i | \(0.238939\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.0263 | −1.39544 | −0.697721 | − | 0.716369i | \(-0.745803\pi\) | ||||
−0.697721 | + | 0.716369i | \(0.745803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.08840 | 0.421464 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.37470 | −0.156162 | −0.0780812 | − | 0.996947i | \(-0.524879\pi\) | ||||
−0.0780812 | + | 0.996947i | \(0.524879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.14903 | −0.422463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.31265 | 0.106561 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.55149 | −0.439178 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.38787 | −0.109563 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.61213 | 0.165388 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −23.6991 | −1.08284 | −0.541420 | − | 0.840752i | \(-0.682113\pi\) | ||||
−0.541420 | + | 0.840752i | \(0.682113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.0263 | 2.28101 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.70052 | 0.304884 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.31265 | 0.286643 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7757 | −0.578924 | −0.289462 | − | 0.957189i | \(-0.593476\pi\) | ||||
−0.289462 | + | 0.957189i | \(0.593476\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.07522 | −0.0938448 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.0870 | 1.71884 | 0.859421 | − | 0.511269i | \(-0.170824\pi\) | ||||
0.859421 | + | 0.511269i | \(0.170824\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −62.8021 | −2.82846 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.61213 | 0.0724597 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.31265 | 0.372873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.47486 | −0.379387 | −0.189693 | − | 0.981843i | \(-0.560749\pi\) | ||||
−0.189693 | + | 0.981843i | \(0.560749\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.9248 | 0.800820 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.8773 | −1.82263 | −0.911315 | − | 0.411710i | \(-0.864932\pi\) | ||||
−0.911315 | + | 0.411710i | \(0.864932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.8496 | −1.19243 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.2981 | −1.07699 | −0.538496 | − | 0.842628i | \(-0.681007\pi\) | ||||
−0.538496 | + | 0.842628i | \(0.681007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3127 | 0.456205 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.38787 | 0.105427 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8021 | −0.475076 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.22425 | 0.0537388 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.17679 | 0.182989 | 0.0914943 | − | 0.995806i | \(-0.470836\pi\) | ||||
0.0914943 | + | 0.995806i | \(0.470836\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6253 | −0.552066 | −0.276033 | − | 0.961148i | \(-0.589020\pi\) | ||||
−0.276033 | + | 0.961148i | \(0.589020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 72.0235 | 3.13739 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8970 | 0.952044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.72829 | −0.334749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.7005 | 0.462624 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.6121 | 0.760019 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.61213 | −0.0694392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.29806 | 0.184788 | 0.0923941 | − | 0.995723i | \(-0.470548\pi\) | ||||
0.0923941 | + | 0.995723i | \(0.470548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.07522 | −0.346541 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.84955 | 0.421909 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.9511 | −0.853049 | −0.426524 | − | 0.904476i | \(-0.640262\pi\) | ||||
−0.426524 | + | 0.904476i | \(0.640262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.70052 | −0.200613 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9234 | 0.806162 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.92478 | 0.336388 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0606 | 0.426283 | 0.213141 | − | 0.977021i | \(-0.431631\pi\) | ||||
0.213141 | + | 0.977021i | \(0.431631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.4010 | 1.58190 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7757 | 0.539392 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.2506 | −0.558446 | −0.279223 | − | 0.960226i | \(-0.590077\pi\) | ||||
−0.279223 | + | 0.960226i | \(0.590077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.16362 | −0.0489538 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.2981 | −0.683250 | −0.341625 | − | 0.939836i | \(-0.610977\pi\) | ||||
−0.341625 | + | 0.939836i | \(0.610977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.7757 | 1.37162 | 0.685811 | − | 0.727780i | \(-0.259448\pi\) | ||||
0.685811 | + | 0.727780i | \(0.259448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.31265 | 0.347266 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.70052 | −0.279431 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.91160 | −0.370995 | −0.185497 | − | 0.982645i | \(-0.559390\pi\) | ||||
−0.185497 | + | 0.982645i | \(0.559390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.84955 | 0.409334 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.775746 | −0.0321834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.82321 | −0.241173 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.31265 | −0.260996 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.25060 | −0.216716 | −0.108358 | − | 0.994112i | \(-0.534559\pi\) | ||||
−0.108358 | + | 0.994112i | \(0.534559\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.7019 | −0.894213 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.2374 | −0.832457 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.2228 | −0.912583 | −0.456291 | − | 0.889830i | \(-0.650823\pi\) | ||||
−0.456291 | + | 0.889830i | \(0.650823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.92478 | −0.324884 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.5369 | −0.963301 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9380 | 1.34581 | 0.672904 | − | 0.739730i | \(-0.265047\pi\) | ||||
0.672904 | + | 0.739730i | \(0.265047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0738 | 0.696455 | 0.348228 | − | 0.937410i | \(-0.386784\pi\) | ||||
0.348228 | + | 0.937410i | \(0.386784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.14903 | −0.372577 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.40105 | 0.341551 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.32724 | −0.256815 | −0.128407 | − | 0.991722i | \(-0.540986\pi\) | ||||
−0.128407 | + | 0.991722i | \(0.540986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.92478 | 0.321128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.2981 | 1.71120 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.3258 | −1.02290 | −0.511450 | − | 0.859313i | \(-0.670892\pi\) | ||||
−0.511450 | + | 0.859313i | \(0.670892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.22425 | −0.0493667 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.78892 | −0.233053 | −0.116527 | − | 0.993188i | \(-0.537176\pi\) | ||||
−0.116527 | + | 0.993188i | \(0.537176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7889 | −0.956157 | −0.478079 | − | 0.878317i | \(-0.658667\pi\) | ||||
−0.478079 | + | 0.878317i | \(0.658667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.70052 | 0.268883 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6253 | −0.585950 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.84955 | −0.153736 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.8021 | 2.50408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.6516 | 1.69794 | 0.848968 | − | 0.528445i | \(-0.177225\pi\) | ||||
0.848968 | + | 0.528445i | \(0.177225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.40105 | 0.373658 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.62530 | 0.342285 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.31265 | 0.250116 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.31265 | 0.328843 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1768 | −0.638945 | −0.319472 | − | 0.947596i | \(-0.603506\pi\) | ||||
−0.319472 | + | 0.947596i | \(0.603506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.0263 | 1.65736 | 0.828679 | − | 0.559725i | \(-0.189093\pi\) | ||||
0.828679 | + | 0.559725i | \(0.189093\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.92478 | 0.233288 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.52373 | −0.177846 | −0.0889231 | − | 0.996038i | \(-0.528343\pi\) | ||||
−0.0889231 | + | 0.996038i | \(0.528343\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8970 | 0.506252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.08840 | −0.356202 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.0870 | 0.942596 | 0.471298 | − | 0.881974i | \(-0.343786\pi\) | ||||
0.471298 | + | 0.881974i | \(0.343786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.62530 | −0.337018 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3127 | 0.402335 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4617 | 0.524393 | 0.262196 | − | 0.965015i | \(-0.415553\pi\) | ||||
0.262196 | + | 0.965015i | \(0.415553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.6531 | 1.54233 | 0.771163 | − | 0.636638i | \(-0.219675\pi\) | ||||
0.771163 | + | 0.636638i | \(0.219675\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −50.0263 | −1.94286 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.38787 | 0.0925977 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.1002 | 2.05605 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.4749 | −1.10090 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.57784 | 0.292539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.4749 | 1.17472 | 0.587360 | − | 0.809326i | \(-0.300167\pi\) | ||||
0.587360 | + | 0.809326i | \(0.300167\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.0263 | 0.923408 | 0.461704 | − | 0.887034i | \(-0.347238\pi\) | ||||
0.461704 | + | 0.887034i | \(0.347238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.31265 | −0.242257 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.4749 | −0.937878 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.8773 | 1.41107 | 0.705536 | − | 0.708674i | \(-0.250706\pi\) | ||||
0.705536 | + | 0.708674i | \(0.250706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.23743 | −0.314736 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.9986 | −1.03006 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.8021 | 0.868691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.1900 | 1.41477 | 0.707387 | − | 0.706827i | \(-0.249874\pi\) | ||||
0.707387 | + | 0.706827i | \(0.249874\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.61213 | −0.0612396 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3879 | 0.394034 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.70194 | −0.367487 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.4617 | −0.433521 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.3733 | −0.542871 | −0.271436 | − | 0.962457i | \(-0.587498\pi\) | ||||
−0.271436 | + | 0.962457i | \(0.587498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9234 | −0.713708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.70052 | 0.252356 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000 | 0.376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1504 | −0.681654 | −0.340827 | − | 0.940126i | \(-0.610707\pi\) | ||||
−0.340827 | + | 0.940126i | \(0.610707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00000 | 0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −60.8970 | −2.28061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.1768 | 0.380590 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.31265 | −0.310442 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.7757 | −0.774805 | −0.387402 | − | 0.921911i | \(-0.626628\pi\) | ||||
−0.387402 | + | 0.921911i | \(0.626628\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.22425 | −0.194292 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.92478 | −0.294319 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.0738 | −0.855760 | −0.427880 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427880 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.9525 | 1.73660 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.9380 | −1.88144 | −0.940718 | − | 0.339189i | \(-0.889847\pi\) | ||||
−0.940718 | + | 0.339189i | \(0.889847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.7494 | 0.543301 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.6253 | 1.05300 | 0.526499 | − | 0.850176i | \(-0.323504\pi\) | ||||
0.526499 | + | 0.850176i | \(0.323504\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0738 | 0.553750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.9248 | −1.53807 | −0.769035 | − | 0.639206i | \(-0.779263\pi\) | ||||
−0.769035 | + | 0.639206i | \(0.779263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.7005 | −0.611860 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.775746 | −0.0283831 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.7005 | −0.390989 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.6991 | 1.01075 | 0.505377 | − | 0.862898i | \(-0.331353\pi\) | ||||
0.505377 | + | 0.862898i | \(0.331353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.8496 | 0.431822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.22425 | −0.262918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.74798 | 0.208914 | 0.104457 | − | 0.994529i | \(-0.466690\pi\) | ||||
0.104457 | + | 0.994529i | \(0.466690\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.8021 | −0.392091 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.67276 | 0.133137 | 0.0665687 | − | 0.997782i | \(-0.478795\pi\) | ||||
0.0665687 | + | 0.997782i | \(0.478795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.84955 | −0.356578 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.92478 | −0.286521 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.5012 | −1.82349 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.9234 | −0.898759 | −0.449380 | − | 0.893341i | \(-0.648355\pi\) | ||||
−0.449380 | + | 0.893341i | \(0.648355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.850969 | −0.0306469 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.72829 | 0.206032 | 0.103016 | − | 0.994680i | \(-0.467151\pi\) | ||||
0.103016 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.08840 | 0.326465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.92478 | −0.284300 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.92336 | 0.104740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.4010 | −0.479527 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.92478 | 0.283208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.31265 | 0.0825420 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 48.4749 | 1.72794 | 0.863971 | − | 0.503542i | \(-0.167970\pi\) | ||||
0.863971 | + | 0.503542i | \(0.167970\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.8773 | −0.885656 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.16362 | 0.0413735 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.6728 | −1.05371 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.61213 | 0.128109 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.22425 | −0.0433653 | −0.0216826 | − | 0.999765i | \(-0.506902\pi\) | ||||
−0.0216826 | + | 0.999765i | \(0.506902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53.1002 | 1.87855 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6253 | −0.516760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.6253 | −0.586694 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.70052 | 0.236162 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.2981 | −0.996139 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.72829 | 0.201396 | 0.100698 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100698 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.1900 | −1.02500 | −0.512499 | − | 0.858688i | \(-0.671280\pi\) | ||||
−0.512499 | + | 0.858688i | \(0.671280\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.08840 | 0.0381717 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.07522 | −0.0726919 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1476 | −0.494962 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.31265 | 0.220582 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.6239 | 0.964080 | 0.482040 | − | 0.876149i | \(-0.339896\pi\) | ||||
0.482040 | + | 0.876149i | \(0.339896\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.3272 | −0.778279 | −0.389139 | − | 0.921179i | \(-0.627228\pi\) | ||||
−0.389139 | + | 0.921179i | \(0.627228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.61213 | 0.0561271 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1016 | −0.559906 | −0.279953 | − | 0.960014i | \(-0.590319\pi\) | ||||
−0.279953 | + | 0.960014i | \(0.590319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.2228 | −1.46646 | −0.733230 | − | 0.679981i | \(-0.761988\pi\) | ||||
−0.733230 | + | 0.679981i | \(0.761988\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0752 | −0.418885 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.92478 | 0.274577 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.9248 | 0.620312 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.08840 | −0.314141 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.7757 | −0.993449 | −0.496725 | − | 0.867908i | \(-0.665464\pi\) | ||||
−0.496725 | + | 0.867908i | \(0.665464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.8021 | 1.16559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.22425 | 0.0421655 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.8496 | −0.923653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.40105 | −0.288663 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.55149 | −0.190527 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53.1002 | −1.82025 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.7137 | 1.49673 | 0.748364 | − | 0.663288i | \(-0.230840\pi\) | ||||
0.748364 | + | 0.663288i | \(0.230840\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.38787 | 0.0816635 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.1016 | 0.345063 | 0.172532 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172532 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0132 | −1.19463 | −0.597317 | − | 0.802005i | \(-0.703767\pi\) | ||||
−0.597317 | + | 0.802005i | \(0.703767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.22425 | 0.0417225 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.9986 | −1.12328 | −0.561642 | − | 0.827380i | \(-0.689830\pi\) | ||||
−0.561642 | + | 0.827380i | \(0.689830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.22425 | 0.0416259 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −45.8021 | −1.55552 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.44851 | −0.218751 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.7546 | −1.95694 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.31265 | −0.213651 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.37328 | −0.0801401 | −0.0400701 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400701 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.37470 | −0.0463675 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.07381 | 0.0361775 | 0.0180888 | − | 0.999836i | \(-0.494242\pi\) | ||||
0.0180888 | + | 0.999836i | \(0.494242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.9511 | 1.20985 | 0.604926 | − | 0.796282i | \(-0.293203\pi\) | ||||
0.604926 | + | 0.796282i | \(0.293203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.3996 | −1.82656 | −0.913280 | − | 0.407331i | \(-0.866459\pi\) | ||||
−0.913280 | + | 0.407331i | \(0.866459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.62530 | −0.289283 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61213 | −0.0540083 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6121 | 0.588708 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.2981 | 1.41229 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −72.0235 | −2.40212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.6253 | 0.953647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.92478 | −0.197164 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.07522 | −0.268429 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.44992 | 0.0481439 | 0.0240719 | − | 0.999710i | \(-0.492337\pi\) | ||||
0.0240719 | + | 0.999710i | \(0.492337\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0000 | 0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.5633 | −1.64210 | −0.821052 | − | 0.570854i | \(-0.806612\pi\) | ||||
−0.821052 | + | 0.570854i | \(0.806612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.25060 | 0.0413889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.70052 | −0.155395 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.62530 | 0.284833 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.4485 | 1.13635 | 0.568176 | − | 0.822907i | \(-0.307649\pi\) | ||||
0.568176 | + | 0.822907i | \(0.307649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0738 | 0.364894 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 52.4749 | 1.72723 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.92478 | 0.260565 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.32724 | −0.141972 | −0.0709860 | − | 0.997477i | \(-0.522615\pi\) | ||||
−0.0709860 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38787 | −0.0782594 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.44851 | 0.211115 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7757 | 0.417812 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.5369 | −1.61830 | −0.809150 | − | 0.587602i | \(-0.800072\pi\) | ||||
−0.809150 | + | 0.587602i | \(0.800072\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.0884 | −0.753461 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.5012 | −1.58109 | −0.790547 | − | 0.612401i | \(-0.790204\pi\) | ||||
−0.790547 | + | 0.612401i | \(0.790204\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.20314 | 0.267131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.57925 | 0.0838145 | 0.0419073 | − | 0.999122i | \(-0.486657\pi\) | ||||
0.0419073 | + | 0.999122i | \(0.486657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.1002 | 2.11324 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.6385 | 0.701676 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.9394 | −0.581113 | −0.290557 | − | 0.956858i | \(-0.593840\pi\) | ||||
−0.290557 | + | 0.956858i | \(0.593840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.31265 | 0.268991 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.7757 | −0.412981 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.23743 | 0.266000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.5990 | 1.66448 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.7005 | −0.344820 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.84955 | 0.317068 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6516 | 0.985691 | 0.492845 | − | 0.870117i | \(-0.335957\pi\) | ||||
0.492845 | + | 0.870117i | \(0.335957\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.9234 | 0.607906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.3536 | −0.909910 | −0.454955 | − | 0.890514i | \(-0.650345\pi\) | ||||
−0.454955 | + | 0.890514i | \(0.650345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3879 | −0.333020 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.31265 | −0.202167 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.68594 | −0.0859307 | −0.0429653 | − | 0.999077i | \(-0.513681\pi\) | ||||
−0.0429653 | + | 0.999077i | \(0.513681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5778 | 0.753551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.84955 | −0.314472 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.8007 | 1.39702 | 0.698512 | − | 0.715598i | \(-0.253846\pi\) | ||||
0.698512 | + | 0.715598i | \(0.253846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.2374 | −0.644818 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.70052 | −0.213280 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.6991 | −1.26236 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5515 | 0.684606 | 0.342303 | − | 0.939590i | \(-0.388793\pi\) | ||||
0.342303 | + | 0.939590i | \(0.388793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.4010 | −1.05995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.5369 | −0.746170 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.1622 | 0.828565 | 0.414283 | − | 0.910148i | \(-0.364032\pi\) | ||||
0.414283 | + | 0.910148i | \(0.364032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.92478 | −0.250729 |
(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 | 6720.2.a.da.1.2 | 3 | ||
4.3 | odd | 2 | 6720.2.a.db.1.2 | 3 | |||
8.3 | odd | 2 | 3360.2.a.bi.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 3360.2.a.bj.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bi.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
3360.2.a.bj.1.2 | yes | 3 | 8.5 | even | 2 | ||
6720.2.a.da.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6720.2.a.db.1.2 | 3 | 4.3 | odd | 2 |