Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2646.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.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: | \(21.1284163748\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.64575 | −0.736002 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.64575 | 0.520432 | ||||||||
\(11\) | 1.64575 | 0.496213 | 0.248106 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248106 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.645751 | 0.179099 | 0.0895496 | − | 0.995982i | \(-0.471457\pi\) | ||||
0.0895496 | + | 0.995982i | \(0.471457\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.64575 | 0.399153 | 0.199577 | − | 0.979882i | \(-0.436043\pi\) | ||||
0.199577 | + | 0.979882i | \(0.436043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.64575 | −0.368001 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.64575 | −0.350875 | ||||||||
\(23\) | −9.29150 | −1.93741 | −0.968706 | − | 0.248211i | \(-0.920158\pi\) | ||||
−0.968706 | + | 0.248211i | \(0.920158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | −0.645751 | −0.126642 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.64575 | −1.41978 | −0.709890 | − | 0.704312i | \(-0.751255\pi\) | ||||
−0.709890 | + | 0.704312i | \(0.751255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.645751 | 0.115980 | 0.0579902 | − | 0.998317i | \(-0.481531\pi\) | ||||
0.0579902 | + | 0.998317i | \(0.481531\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.64575 | −0.282244 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.93725 | 0.647281 | 0.323640 | − | 0.946180i | \(-0.395093\pi\) | ||||
0.323640 | + | 0.946180i | \(0.395093\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.64575 | 0.260216 | ||||||||
\(41\) | 4.93725 | 0.771070 | 0.385535 | − | 0.922693i | \(-0.374017\pi\) | ||||
0.385535 | + | 0.922693i | \(0.374017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | 0.762493 | 0.381246 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(44\) | 1.64575 | 0.248106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.29150 | 1.36996 | ||||||||
\(47\) | 10.9373 | 1.59536 | 0.797681 | − | 0.603079i | \(-0.206060\pi\) | ||||
0.797681 | + | 0.603079i | \(0.206060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.29150 | 0.324067 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.645751 | 0.0895496 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.70850 | −0.365214 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.64575 | 1.00394 | ||||||||
\(59\) | −13.6458 | −1.77653 | −0.888263 | − | 0.459336i | \(-0.848088\pi\) | ||||
−0.888263 | + | 0.459336i | \(0.848088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6458 | 1.61912 | 0.809561 | − | 0.587035i | \(-0.199705\pi\) | ||||
0.809561 | + | 0.587035i | \(0.199705\pi\) | |||||||
\(62\) | −0.645751 | −0.0820105 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.06275 | −0.131817 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.29150 | 1.01297 | 0.506484 | − | 0.862249i | \(-0.330945\pi\) | ||||
0.506484 | + | 0.862249i | \(0.330945\pi\) | |||||||
\(68\) | 1.64575 | 0.199577 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3542 | −1.22882 | −0.614412 | − | 0.788986i | \(-0.710607\pi\) | ||||
−0.614412 | + | 0.788986i | \(0.710607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5830 | −1.23865 | −0.619324 | − | 0.785136i | \(-0.712593\pi\) | ||||
−0.619324 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(74\) | −3.93725 | −0.457696 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.2288 | −1.71337 | −0.856684 | − | 0.515841i | \(-0.827480\pi\) | ||||
−0.856684 | + | 0.515841i | \(0.827480\pi\) | |||||||
\(80\) | −1.64575 | −0.184001 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.93725 | −0.545228 | ||||||||
\(83\) | 2.70850 | 0.297296 | 0.148648 | − | 0.988890i | \(-0.452508\pi\) | ||||
0.148648 | + | 0.988890i | \(0.452508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.70850 | −0.293778 | ||||||||
\(86\) | −5.00000 | −0.539164 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.64575 | −0.175438 | ||||||||
\(89\) | 10.9373 | 1.15935 | 0.579673 | − | 0.814849i | \(-0.303180\pi\) | ||||
0.579673 | + | 0.814849i | \(0.303180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.29150 | −0.968706 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.9373 | −1.12809 | ||||||||
\(95\) | −3.29150 | −0.337701 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.58301 | −0.769938 | −0.384969 | − | 0.922930i | \(-0.625788\pi\) | ||||
−0.384969 | + | 0.922930i | \(0.625788\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29150 | −0.229150 | ||||||||
\(101\) | −13.6458 | −1.35780 | −0.678902 | − | 0.734229i | \(-0.737544\pi\) | ||||
−0.678902 | + | 0.734229i | \(0.737544\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.9373 | −1.17621 | −0.588106 | − | 0.808784i | \(-0.700126\pi\) | ||||
−0.588106 | + | 0.808784i | \(0.700126\pi\) | |||||||
\(104\) | −0.645751 | −0.0633211 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.64575 | −0.828113 | −0.414056 | − | 0.910251i | \(-0.635888\pi\) | ||||
−0.414056 | + | 0.910251i | \(0.635888\pi\) | |||||||
\(110\) | 2.70850 | 0.258245 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.64575 | −0.719252 | −0.359626 | − | 0.933097i | \(-0.617096\pi\) | ||||
−0.359626 | + | 0.933097i | \(0.617096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.2915 | 1.42594 | ||||||||
\(116\) | −7.64575 | −0.709890 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.6458 | 1.25619 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29150 | −0.753773 | ||||||||
\(122\) | −12.6458 | −1.14489 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.645751 | 0.0579902 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.64575 | 0.589715 | 0.294858 | − | 0.955541i | \(-0.404728\pi\) | ||||
0.294858 | + | 0.955541i | \(0.404728\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.06275 | 0.0932090 | ||||||||
\(131\) | −6.58301 | −0.575160 | −0.287580 | − | 0.957757i | \(-0.592851\pi\) | ||||
−0.287580 | + | 0.957757i | \(0.592851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.29150 | −0.716277 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.64575 | −0.141122 | ||||||||
\(137\) | 9.29150 | 0.793827 | 0.396913 | − | 0.917856i | \(-0.370081\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.5830 | −1.66101 | −0.830504 | − | 0.557012i | \(-0.811948\pi\) | ||||
−0.830504 | + | 0.557012i | \(0.811948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3542 | 0.868909 | ||||||||
\(143\) | 1.06275 | 0.0888713 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.5830 | 1.04496 | ||||||||
\(146\) | 10.5830 | 0.875856 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.93725 | 0.323640 | ||||||||
\(149\) | −7.06275 | −0.578603 | −0.289301 | − | 0.957238i | \(-0.593423\pi\) | ||||
−0.289301 | + | 0.957238i | \(0.593423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.22876 | 0.588268 | 0.294134 | − | 0.955764i | \(-0.404969\pi\) | ||||
0.294134 | + | 0.955764i | \(0.404969\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.06275 | −0.0853618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.00000 | −0.319235 | −0.159617 | − | 0.987179i | \(-0.551026\pi\) | ||||
−0.159617 | + | 0.987179i | \(0.551026\pi\) | |||||||
\(158\) | 15.2288 | 1.21153 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.64575 | 0.130108 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 4.93725 | 0.385535 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.70850 | −0.210220 | ||||||||
\(167\) | −12.5830 | −0.973702 | −0.486851 | − | 0.873485i | \(-0.661855\pi\) | ||||
−0.486851 | + | 0.873485i | \(0.661855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5830 | −0.967923 | ||||||||
\(170\) | 2.70850 | 0.207732 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.00000 | 0.381246 | ||||||||
\(173\) | −6.58301 | −0.500497 | −0.250248 | − | 0.968182i | \(-0.580512\pi\) | ||||
−0.250248 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.64575 | 0.124053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.9373 | −0.819782 | ||||||||
\(179\) | −1.06275 | −0.0794334 | −0.0397167 | − | 0.999211i | \(-0.512646\pi\) | ||||
−0.0397167 | + | 0.999211i | \(0.512646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2915 | −0.987950 | −0.493975 | − | 0.869476i | \(-0.664457\pi\) | ||||
−0.493975 | + | 0.869476i | \(0.664457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.29150 | 0.684979 | ||||||||
\(185\) | −6.47974 | −0.476400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.70850 | 0.198065 | ||||||||
\(188\) | 10.9373 | 0.797681 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.29150 | 0.238791 | ||||||||
\(191\) | −26.8118 | −1.94003 | −0.970015 | − | 0.243043i | \(-0.921854\pi\) | ||||
−0.970015 | + | 0.243043i | \(0.921854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.00000 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(194\) | 7.58301 | 0.544428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.2915 | −1.08947 | −0.544737 | − | 0.838607i | \(-0.683371\pi\) | ||||
−0.544737 | + | 0.838607i | \(0.683371\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9373 | 1.55509 | 0.777545 | − | 0.628827i | \(-0.216465\pi\) | ||||
0.777545 | + | 0.628827i | \(0.216465\pi\) | |||||||
\(200\) | 2.29150 | 0.162034 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.6458 | 0.960112 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.12549 | −0.567509 | ||||||||
\(206\) | 11.9373 | 0.831708 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.645751 | 0.0447748 | ||||||||
\(209\) | 3.29150 | 0.227678 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8745 | −1.16169 | −0.580845 | − | 0.814015i | \(-0.697278\pi\) | ||||
−0.580845 | + | 0.814015i | \(0.697278\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | −8.22876 | −0.561197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.64575 | 0.585564 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.70850 | −0.182607 | ||||||||
\(221\) | 1.06275 | 0.0714880 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8745 | 1.19697 | 0.598483 | − | 0.801136i | \(-0.295770\pi\) | ||||
0.598483 | + | 0.801136i | \(0.295770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.64575 | 0.508588 | ||||||||
\(227\) | −6.00000 | −0.398234 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.6458 | −0.967818 | −0.483909 | − | 0.875118i | \(-0.660784\pi\) | ||||
−0.483909 | + | 0.875118i | \(0.660784\pi\) | |||||||
\(230\) | −15.2915 | −1.00829 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.64575 | 0.501968 | ||||||||
\(233\) | 8.70850 | 0.570513 | 0.285256 | − | 0.958451i | \(-0.407921\pi\) | ||||
0.285256 | + | 0.958451i | \(0.407921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | −1.17419 | ||||||||
\(236\) | −13.6458 | −0.888263 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.93725 | −0.319364 | −0.159682 | − | 0.987168i | \(-0.551047\pi\) | ||||
−0.159682 | + | 0.987168i | \(0.551047\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | 0.322078 | 0.161039 | − | 0.986948i | \(-0.448515\pi\) | ||||
0.161039 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(242\) | 8.29150 | 0.532998 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6458 | 0.809561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.29150 | 0.0821763 | ||||||||
\(248\) | −0.645751 | −0.0410052 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.2915 | −0.961369 | ||||||||
\(254\) | −6.64575 | −0.416992 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8745 | 0.990225 | 0.495112 | − | 0.868829i | \(-0.335127\pi\) | ||||
0.495112 | + | 0.868829i | \(0.335127\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.06275 | −0.0659087 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.58301 | 0.406699 | ||||||||
\(263\) | −10.9373 | −0.674420 | −0.337210 | − | 0.941429i | \(-0.609483\pi\) | ||||
−0.337210 | + | 0.941429i | \(0.609483\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.87451 | 0.606586 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.29150 | 0.506484 | ||||||||
\(269\) | 27.2915 | 1.66399 | 0.831996 | − | 0.554781i | \(-0.187198\pi\) | ||||
0.831996 | + | 0.554781i | \(0.187198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.2288 | −1.28956 | −0.644778 | − | 0.764370i | \(-0.723050\pi\) | ||||
−0.644778 | + | 0.764370i | \(0.723050\pi\) | |||||||
\(272\) | 1.64575 | 0.0997883 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.29150 | −0.561320 | ||||||||
\(275\) | −3.77124 | −0.227415 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9373 | −1.07775 | −0.538873 | − | 0.842387i | \(-0.681150\pi\) | ||||
−0.538873 | + | 0.842387i | \(0.681150\pi\) | |||||||
\(278\) | 19.5830 | 1.17451 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5203 | 1.04517 | 0.522586 | − | 0.852587i | \(-0.324968\pi\) | ||||
0.522586 | + | 0.852587i | \(0.324968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.29150 | 0.492879 | 0.246439 | − | 0.969158i | \(-0.420739\pi\) | ||||
0.246439 | + | 0.969158i | \(0.420739\pi\) | |||||||
\(284\) | −10.3542 | −0.614412 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.06275 | −0.0628415 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2915 | −0.840677 | ||||||||
\(290\) | −12.5830 | −0.738900 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.5830 | −0.619324 | ||||||||
\(293\) | −22.9373 | −1.34001 | −0.670004 | − | 0.742357i | \(-0.733708\pi\) | ||||
−0.670004 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.4575 | 1.30753 | ||||||||
\(296\) | −3.93725 | −0.228848 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.06275 | 0.409134 | ||||||||
\(299\) | −6.00000 | −0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.22876 | −0.415968 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −20.8118 | −1.19168 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5830 | −0.775223 | −0.387612 | − | 0.921823i | \(-0.626700\pi\) | ||||
−0.387612 | + | 0.921823i | \(0.626700\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.06275 | 0.0603599 | ||||||||
\(311\) | −23.5203 | −1.33371 | −0.666856 | − | 0.745187i | \(-0.732360\pi\) | ||||
−0.666856 | + | 0.745187i | \(0.732360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.2915 | 1.31651 | 0.658257 | − | 0.752793i | \(-0.271294\pi\) | ||||
0.658257 | + | 0.752793i | \(0.271294\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.2288 | −0.856684 | ||||||||
\(317\) | 20.8118 | 1.16890 | 0.584452 | − | 0.811428i | \(-0.301309\pi\) | ||||
0.584452 | + | 0.811428i | \(0.301309\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.5830 | −0.704513 | ||||||||
\(320\) | −1.64575 | −0.0920003 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.29150 | 0.183144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.47974 | −0.0820813 | ||||||||
\(326\) | 1.00000 | 0.0553849 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.93725 | −0.272614 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.125492 | −0.00689767 | −0.00344884 | − | 0.999994i | \(-0.501098\pi\) | ||||
−0.00344884 | + | 0.999994i | \(0.501098\pi\) | |||||||
\(332\) | 2.70850 | 0.148648 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.5830 | 0.688511 | ||||||||
\(335\) | −13.6458 | −0.745547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.41699 | −0.512976 | −0.256488 | − | 0.966547i | \(-0.582565\pi\) | ||||
−0.256488 | + | 0.966547i | \(0.582565\pi\) | |||||||
\(338\) | 12.5830 | 0.684425 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.70850 | −0.146889 | ||||||||
\(341\) | 1.06275 | 0.0575509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.00000 | −0.269582 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.58301 | 0.353905 | ||||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.2288 | 1.35046 | 0.675232 | − | 0.737605i | \(-0.264043\pi\) | ||||
0.675232 | + | 0.737605i | \(0.264043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.64575 | −0.0877188 | ||||||||
\(353\) | 12.0000 | 0.638696 | 0.319348 | − | 0.947638i | \(-0.396536\pi\) | ||||
0.319348 | + | 0.947638i | \(0.396536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.0405 | 0.904417 | ||||||||
\(356\) | 10.9373 | 0.579673 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.06275 | 0.0561679 | ||||||||
\(359\) | 31.1660 | 1.64488 | 0.822440 | − | 0.568853i | \(-0.192612\pi\) | ||||
0.822440 | + | 0.568853i | \(0.192612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 13.2915 | 0.698586 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.4170 | 0.911647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.87451 | −0.0978485 | −0.0489243 | − | 0.998802i | \(-0.515579\pi\) | ||||
−0.0489243 | + | 0.998802i | \(0.515579\pi\) | |||||||
\(368\) | −9.29150 | −0.484353 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.47974 | 0.336866 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5830 | −0.858635 | −0.429318 | − | 0.903154i | \(-0.641246\pi\) | ||||
−0.429318 | + | 0.903154i | \(0.641246\pi\) | |||||||
\(374\) | −2.70850 | −0.140053 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.9373 | −0.564046 | ||||||||
\(377\) | −4.93725 | −0.254282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.41699 | 0.226886 | 0.113443 | − | 0.993545i | \(-0.463812\pi\) | ||||
0.113443 | + | 0.993545i | \(0.463812\pi\) | |||||||
\(380\) | −3.29150 | −0.168851 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.8118 | 1.37181 | ||||||||
\(383\) | 0.583005 | 0.0297902 | 0.0148951 | − | 0.999889i | \(-0.495259\pi\) | ||||
0.0148951 | + | 0.999889i | \(0.495259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.00000 | 0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.58301 | −0.384969 | ||||||||
\(389\) | −8.70850 | −0.441538 | −0.220769 | − | 0.975326i | \(-0.570857\pi\) | ||||
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.2915 | −0.773325 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.2915 | 0.770375 | ||||||||
\(395\) | 25.0627 | 1.26104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.3542 | −0.569853 | −0.284927 | − | 0.958549i | \(-0.591969\pi\) | ||||
−0.284927 | + | 0.958549i | \(0.591969\pi\) | |||||||
\(398\) | −21.9373 | −1.09962 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29150 | −0.114575 | ||||||||
\(401\) | −26.8118 | −1.33892 | −0.669458 | − | 0.742850i | \(-0.733473\pi\) | ||||
−0.669458 | + | 0.742850i | \(0.733473\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.416995 | 0.0207720 | ||||||||
\(404\) | −13.6458 | −0.678902 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.47974 | 0.321189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.8745 | −0.834391 | −0.417195 | − | 0.908817i | \(-0.636987\pi\) | ||||
−0.417195 | + | 0.908817i | \(0.636987\pi\) | |||||||
\(410\) | 8.12549 | 0.401289 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.9373 | −0.588106 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.45751 | −0.218811 | ||||||||
\(416\) | −0.645751 | −0.0316606 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.29150 | −0.160993 | ||||||||
\(419\) | −13.0627 | −0.638157 | −0.319078 | − | 0.947728i | \(-0.603373\pi\) | ||||
−0.319078 | + | 0.947728i | \(0.603373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.2915 | −1.23263 | −0.616316 | − | 0.787499i | \(-0.711376\pi\) | ||||
−0.616316 | + | 0.787499i | \(0.711376\pi\) | |||||||
\(422\) | 16.8745 | 0.821438 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | −3.77124 | −0.182932 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.22876 | 0.396826 | ||||||||
\(431\) | 8.81176 | 0.424448 | 0.212224 | − | 0.977221i | \(-0.431929\pi\) | ||||
0.212224 | + | 0.977221i | \(0.431929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.64575 | −0.414056 | ||||||||
\(437\) | −18.5830 | −0.888946 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.1660 | −0.819289 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(440\) | 2.70850 | 0.129123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.06275 | −0.0505497 | ||||||||
\(443\) | 8.70850 | 0.413753 | 0.206877 | − | 0.978367i | \(-0.433670\pi\) | ||||
0.206877 | + | 0.978367i | \(0.433670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.0000 | −0.853282 | ||||||||
\(446\) | −17.8745 | −0.846382 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.64575 | −0.360825 | −0.180413 | − | 0.983591i | \(-0.557743\pi\) | ||||
−0.180413 | + | 0.983591i | \(0.557743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.12549 | 0.382614 | ||||||||
\(452\) | −7.64575 | −0.359626 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.29150 | 0.107192 | 0.0535960 | − | 0.998563i | \(-0.482932\pi\) | ||||
0.0535960 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(458\) | 14.6458 | 0.684351 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.2915 | 0.712970 | ||||||||
\(461\) | 2.22876 | 0.103804 | 0.0519018 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0519018 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2915 | 1.36129 | 0.680646 | − | 0.732613i | \(-0.261699\pi\) | ||||
0.680646 | + | 0.732613i | \(0.261699\pi\) | |||||||
\(464\) | −7.64575 | −0.354945 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.70850 | −0.403413 | ||||||||
\(467\) | 26.2288 | 1.21372 | 0.606861 | − | 0.794808i | \(-0.292428\pi\) | ||||
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.0000 | 0.830278 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.6458 | 0.628097 | ||||||||
\(473\) | 8.22876 | 0.378359 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.58301 | −0.210283 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.93725 | 0.225825 | ||||||||
\(479\) | 1.64575 | 0.0751963 | 0.0375981 | − | 0.999293i | \(-0.488029\pi\) | ||||
0.0375981 | + | 0.999293i | \(0.488029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.54249 | 0.115927 | ||||||||
\(482\) | −5.00000 | −0.227744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.29150 | −0.376886 | ||||||||
\(485\) | 12.4797 | 0.566676 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.87451 | −0.356828 | −0.178414 | − | 0.983956i | \(-0.557097\pi\) | ||||
−0.178414 | + | 0.983956i | \(0.557097\pi\) | |||||||
\(488\) | −12.6458 | −0.572446 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.7490 | 1.70359 | 0.851795 | − | 0.523876i | \(-0.175514\pi\) | ||||
0.851795 | + | 0.523876i | \(0.175514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.5830 | −0.566710 | ||||||||
\(494\) | −1.29150 | −0.0581075 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.645751 | 0.0289951 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1660 | 1.61901 | 0.809506 | − | 0.587111i | \(-0.199735\pi\) | ||||
0.809506 | + | 0.587111i | \(0.199735\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.0000 | −0.803379 | ||||||||
\(503\) | 27.8745 | 1.24286 | 0.621431 | − | 0.783469i | \(-0.286551\pi\) | ||||
0.621431 | + | 0.783469i | \(0.286551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.4575 | 0.999346 | ||||||||
\(506\) | 15.2915 | 0.679790 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.64575 | 0.294858 | ||||||||
\(509\) | −39.8745 | −1.76741 | −0.883703 | − | 0.468048i | \(-0.844958\pi\) | ||||
−0.883703 | + | 0.468048i | \(0.844958\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.8745 | −0.700195 | ||||||||
\(515\) | 19.6458 | 0.865695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.06275 | 0.0466045 | ||||||||
\(521\) | 39.8745 | 1.74693 | 0.873467 | − | 0.486883i | \(-0.161866\pi\) | ||||
0.873467 | + | 0.486883i | \(0.161866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.00000 | −0.0437269 | −0.0218635 | − | 0.999761i | \(-0.506960\pi\) | ||||
−0.0218635 | + | 0.999761i | \(0.506960\pi\) | |||||||
\(524\) | −6.58301 | −0.287580 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9373 | 0.476887 | ||||||||
\(527\) | 1.06275 | 0.0462939 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 63.3320 | 2.75357 | ||||||||
\(530\) | −9.87451 | −0.428921 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.18824 | 0.138098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.87451 | −0.426912 | ||||||||
\(536\) | −8.29150 | −0.358138 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.2915 | −1.17662 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.1660 | −1.76987 | −0.884933 | − | 0.465719i | \(-0.845796\pi\) | ||||
−0.884933 | + | 0.465719i | \(0.845796\pi\) | |||||||
\(542\) | 21.2288 | 0.911853 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.64575 | −0.0705610 | ||||||||
\(545\) | 14.2288 | 0.609493 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.70850 | 0.329592 | 0.164796 | − | 0.986328i | \(-0.447303\pi\) | ||||
0.164796 | + | 0.986328i | \(0.447303\pi\) | |||||||
\(548\) | 9.29150 | 0.396913 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.77124 | 0.160806 | ||||||||
\(551\) | −15.2915 | −0.651440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 17.9373 | 0.762081 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.5830 | −0.830504 | ||||||||
\(557\) | 32.2288 | 1.36558 | 0.682788 | − | 0.730616i | \(-0.260767\pi\) | ||||
0.682788 | + | 0.730616i | \(0.260767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.22876 | 0.136562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.5203 | −0.739048 | ||||||||
\(563\) | 34.4575 | 1.45221 | 0.726106 | − | 0.687583i | \(-0.241328\pi\) | ||||
0.726106 | + | 0.687583i | \(0.241328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.5830 | 0.529371 | ||||||||
\(566\) | −8.29150 | −0.348518 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.3542 | 0.434455 | ||||||||
\(569\) | 1.06275 | 0.0445526 | 0.0222763 | − | 0.999752i | \(-0.492909\pi\) | ||||
0.0222763 | + | 0.999752i | \(0.492909\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.29150 | −0.0540477 | −0.0270239 | − | 0.999635i | \(-0.508603\pi\) | ||||
−0.0270239 | + | 0.999635i | \(0.508603\pi\) | |||||||
\(572\) | 1.06275 | 0.0444356 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.2915 | 0.887917 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7085 | −0.903737 | −0.451868 | − | 0.892085i | \(-0.649242\pi\) | ||||
−0.451868 | + | 0.892085i | \(0.649242\pi\) | |||||||
\(578\) | 14.2915 | 0.594448 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.5830 | 0.522481 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.87451 | −0.408960 | ||||||||
\(584\) | 10.5830 | 0.437928 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.9373 | 0.947529 | ||||||||
\(587\) | −38.2288 | −1.57787 | −0.788935 | − | 0.614477i | \(-0.789367\pi\) | ||||
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29150 | 0.0532154 | ||||||||
\(590\) | −22.4575 | −0.924561 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.93725 | 0.161820 | ||||||||
\(593\) | −25.0627 | −1.02920 | −0.514602 | − | 0.857429i | \(-0.672060\pi\) | ||||
−0.514602 | + | 0.857429i | \(0.672060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.06275 | −0.289301 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.00000 | 0.245358 | ||||||||
\(599\) | 21.8745 | 0.893768 | 0.446884 | − | 0.894592i | \(-0.352534\pi\) | ||||
0.446884 | + | 0.894592i | \(0.352534\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.87451 | −0.198835 | −0.0994177 | − | 0.995046i | \(-0.531698\pi\) | ||||
−0.0994177 | + | 0.995046i | \(0.531698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.22876 | 0.294134 | ||||||||
\(605\) | 13.6458 | 0.554779 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.5830 | 1.07897 | 0.539485 | − | 0.841995i | \(-0.318619\pi\) | ||||
0.539485 | + | 0.841995i | \(0.318619\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.8118 | 0.842644 | ||||||||
\(611\) | 7.06275 | 0.285728 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.3948 | 1.06607 | 0.533037 | − | 0.846092i | \(-0.321051\pi\) | ||||
0.533037 | + | 0.846092i | \(0.321051\pi\) | |||||||
\(614\) | 13.5830 | 0.548165 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.5203 | 1.42999 | 0.714996 | − | 0.699129i | \(-0.246429\pi\) | ||||
0.714996 | + | 0.699129i | \(0.246429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29150 | 0.0921033 | 0.0460516 | − | 0.998939i | \(-0.485336\pi\) | ||||
0.0460516 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(620\) | −1.06275 | −0.0426809 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.5203 | 0.943076 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | −23.2915 | −0.930916 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.00000 | −0.159617 | ||||||||
\(629\) | 6.47974 | 0.258364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9373 | 0.873308 | 0.436654 | − | 0.899629i | \(-0.356163\pi\) | ||||
0.436654 | + | 0.899629i | \(0.356163\pi\) | |||||||
\(632\) | 15.2288 | 0.605767 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.8118 | −0.826541 | ||||||||
\(635\) | −10.9373 | −0.434032 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.5830 | 0.498166 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.64575 | 0.0650540 | ||||||||
\(641\) | −8.22876 | −0.325016 | −0.162508 | − | 0.986707i | \(-0.551958\pi\) | ||||
−0.162508 | + | 0.986707i | \(0.551958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.8745 | −1.37532 | −0.687658 | − | 0.726035i | \(-0.741361\pi\) | ||||
−0.687658 | + | 0.726035i | \(0.741361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.29150 | −0.129502 | ||||||||
\(647\) | 21.8745 | 0.859976 | 0.429988 | − | 0.902835i | \(-0.358518\pi\) | ||||
0.429988 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.4575 | −0.881534 | ||||||||
\(650\) | 1.47974 | 0.0580402 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8340 | 0.423319 | ||||||||
\(656\) | 4.93725 | 0.192767 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.22876 | −0.0868200 | −0.0434100 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434100 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1660 | 1.52338 | 0.761691 | − | 0.647941i | \(-0.224370\pi\) | ||||
0.761691 | + | 0.647941i | \(0.224370\pi\) | |||||||
\(662\) | 0.125492 | 0.00487739 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.70850 | −0.105110 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 71.0405 | 2.75070 | ||||||||
\(668\) | −12.5830 | −0.486851 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.6458 | 0.527181 | ||||||||
\(671\) | 20.8118 | 0.803429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.7490 | −1.84059 | −0.920295 | − | 0.391226i | \(-0.872051\pi\) | ||||
−0.920295 | + | 0.391226i | \(0.872051\pi\) | |||||||
\(674\) | 9.41699 | 0.362729 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.5830 | −0.483962 | ||||||||
\(677\) | 14.1255 | 0.542887 | 0.271443 | − | 0.962454i | \(-0.412499\pi\) | ||||
0.271443 | + | 0.962454i | \(0.412499\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.70850 | 0.103866 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.06275 | −0.0406947 | ||||||||
\(683\) | −20.8118 | −0.796340 | −0.398170 | − | 0.917312i | \(-0.630355\pi\) | ||||
−0.398170 | + | 0.917312i | \(0.630355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2915 | −0.584258 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.00000 | 0.190623 | ||||||||
\(689\) | −3.87451 | −0.147607 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.7490 | 0.941497 | 0.470748 | − | 0.882267i | \(-0.343984\pi\) | ||||
0.470748 | + | 0.882267i | \(0.343984\pi\) | |||||||
\(692\) | −6.58301 | −0.250248 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 32.2288 | 1.22251 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.12549 | 0.307775 | ||||||||
\(698\) | −25.2288 | −0.954923 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.41699 | 0.204597 | 0.102299 | − | 0.994754i | \(-0.467380\pi\) | ||||
0.102299 | + | 0.994754i | \(0.467380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.87451 | 0.296993 | ||||||||
\(704\) | 1.64575 | 0.0620266 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.0000 | −0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.81176 | −0.368488 | −0.184244 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184244 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(710\) | −17.0405 | −0.639519 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.9373 | −0.409891 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.74902 | −0.0654095 | ||||||||
\(716\) | −1.06275 | −0.0397167 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.1660 | −1.16311 | ||||||||
\(719\) | −7.06275 | −0.263396 | −0.131698 | − | 0.991290i | \(-0.542043\pi\) | ||||
−0.131698 | + | 0.991290i | \(0.542043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2915 | −0.493975 | ||||||||
\(725\) | 17.5203 | 0.650686 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2288 | 0.935683 | 0.467841 | − | 0.883812i | \(-0.345032\pi\) | ||||
0.467841 | + | 0.883812i | \(0.345032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.4170 | −0.644632 | ||||||||
\(731\) | 8.22876 | 0.304352 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.77124 | 0.323973 | 0.161987 | − | 0.986793i | \(-0.448210\pi\) | ||||
0.161987 | + | 0.986793i | \(0.448210\pi\) | |||||||
\(734\) | 1.87451 | 0.0691893 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.29150 | 0.342489 | ||||||||
\(737\) | 13.6458 | 0.502648 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.4575 | 0.789327 | 0.394664 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(740\) | −6.47974 | −0.238200 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0627 | 0.479226 | 0.239613 | − | 0.970869i | \(-0.422979\pi\) | ||||
0.239613 | + | 0.970869i | \(0.422979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.6235 | 0.425853 | ||||||||
\(746\) | 16.5830 | 0.607147 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.70850 | 0.0990325 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.457513 | 0.0166949 | 0.00834745 | − | 0.999965i | \(-0.497343\pi\) | ||||
0.00834745 | + | 0.999965i | \(0.497343\pi\) | |||||||
\(752\) | 10.9373 | 0.398841 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.93725 | 0.179804 | ||||||||
\(755\) | −11.8967 | −0.432967 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.9778 | −1.48936 | −0.744681 | − | 0.667420i | \(-0.767398\pi\) | ||||
−0.744681 | + | 0.667420i | \(0.767398\pi\) | |||||||
\(758\) | −4.41699 | −0.160432 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.29150 | 0.119395 | ||||||||
\(761\) | 18.5830 | 0.673633 | 0.336817 | − | 0.941570i | \(-0.390650\pi\) | ||||
0.336817 | + | 0.941570i | \(0.390650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −26.8118 | −0.970015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.583005 | −0.0210648 | ||||||||
\(767\) | −8.81176 | −0.318174 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4170 | 0.700195 | 0.350097 | − | 0.936713i | \(-0.386148\pi\) | ||||
0.350097 | + | 0.936713i | \(0.386148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | −0.251936 | ||||||||
\(773\) | −38.3320 | −1.37871 | −0.689353 | − | 0.724425i | \(-0.742105\pi\) | ||||
−0.689353 | + | 0.724425i | \(0.742105\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.47974 | −0.0531539 | ||||||||
\(776\) | 7.58301 | 0.272214 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.70850 | 0.312215 | ||||||||
\(779\) | 9.87451 | 0.353791 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0405 | −0.609758 | ||||||||
\(782\) | 15.2915 | 0.546823 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.58301 | 0.234958 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.2915 | −0.794606 | −0.397303 | − | 0.917687i | \(-0.630054\pi\) | ||||
−0.397303 | + | 0.917687i | \(0.630054\pi\) | |||||||
\(788\) | −15.2915 | −0.544737 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −25.0627 | −0.891692 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.16601 | 0.289984 | ||||||||
\(794\) | 11.3542 | 0.402947 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.9373 | 0.777545 | ||||||||
\(797\) | −32.8118 | −1.16225 | −0.581126 | − | 0.813814i | \(-0.697388\pi\) | ||||
−0.581126 | + | 0.813814i | \(0.697388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 2.29150 | 0.0810169 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.8118 | 0.946756 | ||||||||
\(803\) | −17.4170 | −0.614632 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.416995 | −0.0146880 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.6458 | 0.480056 | ||||||||
\(809\) | −36.5830 | −1.28619 | −0.643095 | − | 0.765786i | \(-0.722350\pi\) | ||||
−0.643095 | + | 0.765786i | \(0.722350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7085 | −0.656944 | −0.328472 | − | 0.944514i | \(-0.606534\pi\) | ||||
−0.328472 | + | 0.944514i | \(0.606534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.47974 | −0.227115 | ||||||||
\(815\) | 1.64575 | 0.0576482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000 | 0.349856 | ||||||||
\(818\) | 16.8745 | 0.590003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.12549 | −0.283754 | ||||||||
\(821\) | 0.583005 | 0.0203470 | 0.0101735 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101735 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.1033 | 0.805329 | 0.402665 | − | 0.915348i | \(-0.368084\pi\) | ||||
0.402665 | + | 0.915348i | \(0.368084\pi\) | |||||||
\(824\) | 11.9373 | 0.415854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.7490 | −0.686741 | −0.343370 | − | 0.939200i | \(-0.611569\pi\) | ||||
−0.343370 | + | 0.939200i | \(0.611569\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.7085 | −0.649773 | −0.324886 | − | 0.945753i | \(-0.605326\pi\) | ||||
−0.324886 | + | 0.945753i | \(0.605326\pi\) | |||||||
\(830\) | 4.45751 | 0.154723 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.645751 | 0.0223874 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.7085 | 0.716647 | ||||||||
\(836\) | 3.29150 | 0.113839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.0627 | 0.451245 | ||||||||
\(839\) | 38.7085 | 1.33637 | 0.668183 | − | 0.743997i | \(-0.267072\pi\) | ||||
0.668183 | + | 0.743997i | \(0.267072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.4575 | 1.01578 | ||||||||
\(842\) | 25.2915 | 0.871603 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.8745 | −0.580845 | ||||||||
\(845\) | 20.7085 | 0.712394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.77124 | 0.129353 | ||||||||
\(851\) | −36.5830 | −1.25405 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.1255 | 0.552126 | 0.276063 | − | 0.961139i | \(-0.410970\pi\) | ||||
0.276063 | + | 0.961139i | \(0.410970\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | −20.8118 | −0.710916 | −0.355458 | − | 0.934692i | \(-0.615675\pi\) | ||||
−0.355458 | + | 0.934692i | \(0.615675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.00000 | −0.238837 | −0.119418 | − | 0.992844i | \(-0.538103\pi\) | ||||
−0.119418 | + | 0.992844i | \(0.538103\pi\) | |||||||
\(860\) | −8.22876 | −0.280598 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.81176 | −0.300130 | ||||||||
\(863\) | 13.1660 | 0.448176 | 0.224088 | − | 0.974569i | \(-0.428060\pi\) | ||||
0.224088 | + | 0.974569i | \(0.428060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8340 | 0.368367 | ||||||||
\(866\) | 19.0000 | 0.645646 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.0627 | −0.850195 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.35425 | 0.181422 | ||||||||
\(872\) | 8.64575 | 0.292782 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.5830 | 0.628580 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.3542 | 0.721082 | 0.360541 | − | 0.932743i | \(-0.382592\pi\) | ||||
0.360541 | + | 0.932743i | \(0.382592\pi\) | |||||||
\(878\) | 17.1660 | 0.579325 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.70850 | −0.0913034 | ||||||||
\(881\) | −27.8745 | −0.939116 | −0.469558 | − | 0.882902i | \(-0.655587\pi\) | ||||
−0.469558 | + | 0.882902i | \(0.655587\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8745 | 0.399609 | 0.199805 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199805 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(884\) | 1.06275 | 0.0357440 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.70850 | −0.292568 | ||||||||
\(887\) | 15.8745 | 0.533014 | 0.266507 | − | 0.963833i | \(-0.414130\pi\) | ||||
0.266507 | + | 0.963833i | \(0.414130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.8745 | 0.598483 | ||||||||
\(893\) | 21.8745 | 0.732002 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.74902 | 0.0584631 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.64575 | 0.255142 | ||||||||
\(899\) | −4.93725 | −0.164667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.87451 | −0.328968 | ||||||||
\(902\) | −8.12549 | −0.270549 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.64575 | 0.254294 | ||||||||
\(905\) | 21.8745 | 0.727133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.7085 | 0.853637 | 0.426818 | − | 0.904337i | \(-0.359634\pi\) | ||||
0.426818 | + | 0.904337i | \(0.359634\pi\) | |||||||
\(908\) | −6.00000 | −0.199117 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.0627 | −0.432788 | −0.216394 | − | 0.976306i | \(-0.569430\pi\) | ||||
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.45751 | 0.147522 | ||||||||
\(914\) | −2.29150 | −0.0757962 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.6458 | −0.483909 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.2288 | 1.82183 | 0.910914 | − | 0.412596i | \(-0.135378\pi\) | ||||
0.910914 | + | 0.412596i | \(0.135378\pi\) | |||||||
\(920\) | −15.2915 | −0.504146 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.22876 | −0.0734002 | ||||||||
\(923\) | −6.68627 | −0.220081 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.02223 | −0.296649 | ||||||||
\(926\) | −29.2915 | −0.962579 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.64575 | 0.250984 | ||||||||
\(929\) | 1.06275 | 0.0348676 | 0.0174338 | − | 0.999848i | \(-0.494450\pi\) | ||||
0.0174338 | + | 0.999848i | \(0.494450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.70850 | 0.285256 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.2288 | −0.858231 | ||||||||
\(935\) | −4.45751 | −0.145776 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.7490 | 0.612504 | 0.306252 | − | 0.951951i | \(-0.400925\pi\) | ||||
0.306252 | + | 0.951951i | \(0.400925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0000 | −0.587095 | ||||||||
\(941\) | −15.3948 | −0.501855 | −0.250928 | − | 0.968006i | \(-0.580736\pi\) | ||||
−0.250928 | + | 0.968006i | \(0.580736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.8745 | −1.49388 | ||||||||
\(944\) | −13.6458 | −0.444131 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.22876 | −0.267540 | ||||||||
\(947\) | −47.5203 | −1.54420 | −0.772100 | − | 0.635500i | \(-0.780794\pi\) | ||||
−0.772100 | + | 0.635500i | \(0.780794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.83399 | −0.221841 | ||||||||
\(950\) | 4.58301 | 0.148692 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3320 | 1.04734 | 0.523668 | − | 0.851922i | \(-0.324563\pi\) | ||||
0.523668 | + | 0.851922i | \(0.324563\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.1255 | 1.42787 | ||||||||
\(956\) | −4.93725 | −0.159682 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.64575 | −0.0531718 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5830 | −0.986549 | ||||||||
\(962\) | −2.54249 | −0.0819731 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.00000 | 0.161039 | ||||||||
\(965\) | 11.5203 | 0.370850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.9373 | 1.67019 | 0.835095 | − | 0.550106i | \(-0.185413\pi\) | ||||
0.835095 | + | 0.550106i | \(0.185413\pi\) | |||||||
\(968\) | 8.29150 | 0.266499 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.4797 | −0.400700 | ||||||||
\(971\) | −21.8745 | −0.701986 | −0.350993 | − | 0.936378i | \(-0.614156\pi\) | ||||
−0.350993 | + | 0.936378i | \(0.614156\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.87451 | 0.252316 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.6458 | 0.404781 | ||||||||
\(977\) | 20.1255 | 0.643872 | 0.321936 | − | 0.946762i | \(-0.395666\pi\) | ||||
0.321936 | + | 0.946762i | \(0.395666\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | 0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.7490 | −1.20462 | ||||||||
\(983\) | 26.8118 | 0.855162 | 0.427581 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427581 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1660 | 0.801856 | ||||||||
\(986\) | 12.5830 | 0.400725 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.29150 | 0.0410882 | ||||||||
\(989\) | −46.4575 | −1.47726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.9373 | −1.33218 | −0.666090 | − | 0.745871i | \(-0.732034\pi\) | ||||
−0.666090 | + | 0.745871i | \(0.732034\pi\) | |||||||
\(992\) | −0.645751 | −0.0205026 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.1033 | −1.14455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.6863 | −1.76360 | −0.881801 | − | 0.471622i | \(-0.843669\pi\) | ||||
−0.881801 | + | 0.471622i | \(0.843669\pi\) | |||||||
\(998\) | −36.1660 | −1.14482 | ||||||||
\(999\) | 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 | 2646.2.a.bi.1.1 | 2 | ||
3.2 | odd | 2 | 2646.2.a.bl.1.2 | 2 | |||
7.2 | even | 3 | 378.2.g.h.109.2 | yes | 4 | ||
7.4 | even | 3 | 378.2.g.h.163.2 | yes | 4 | ||
7.6 | odd | 2 | 2646.2.a.bf.1.2 | 2 | |||
21.2 | odd | 6 | 378.2.g.g.109.1 | ✓ | 4 | ||
21.11 | odd | 6 | 378.2.g.g.163.1 | yes | 4 | ||
21.20 | even | 2 | 2646.2.a.bo.1.1 | 2 | |||
63.2 | odd | 6 | 1134.2.h.q.109.2 | 4 | |||
63.4 | even | 3 | 1134.2.h.t.541.1 | 4 | |||
63.11 | odd | 6 | 1134.2.e.t.919.1 | 4 | |||
63.16 | even | 3 | 1134.2.h.t.109.1 | 4 | |||
63.23 | odd | 6 | 1134.2.e.t.865.1 | 4 | |||
63.25 | even | 3 | 1134.2.e.q.919.2 | 4 | |||
63.32 | odd | 6 | 1134.2.h.q.541.2 | 4 | |||
63.58 | even | 3 | 1134.2.e.q.865.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.g.109.1 | ✓ | 4 | 21.2 | odd | 6 | ||
378.2.g.g.163.1 | yes | 4 | 21.11 | odd | 6 | ||
378.2.g.h.109.2 | yes | 4 | 7.2 | even | 3 | ||
378.2.g.h.163.2 | yes | 4 | 7.4 | even | 3 | ||
1134.2.e.q.865.2 | 4 | 63.58 | even | 3 | |||
1134.2.e.q.919.2 | 4 | 63.25 | even | 3 | |||
1134.2.e.t.865.1 | 4 | 63.23 | odd | 6 | |||
1134.2.e.t.919.1 | 4 | 63.11 | odd | 6 | |||
1134.2.h.q.109.2 | 4 | 63.2 | odd | 6 | |||
1134.2.h.q.541.2 | 4 | 63.32 | odd | 6 | |||
1134.2.h.t.109.1 | 4 | 63.16 | even | 3 | |||
1134.2.h.t.541.1 | 4 | 63.4 | even | 3 | |||
2646.2.a.bf.1.2 | 2 | 7.6 | odd | 2 | |||
2646.2.a.bi.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2646.2.a.bl.1.2 | 2 | 3.2 | odd | 2 | |||
2646.2.a.bo.1.1 | 2 | 21.20 | even | 2 |