Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-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 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82843 | −1.56655 | −0.783274 | − | 0.621676i | \(-0.786452\pi\) | ||||
−0.783274 | + | 0.621676i | \(0.786452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65685 | 0.679061 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17157 | −0.210421 | −0.105210 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105210 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685 | 0.252668 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.17157 | −0.170891 | −0.0854457 | − | 0.996343i | \(-0.527231\pi\) | ||||
−0.0854457 | + | 0.996343i | \(0.527231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.65685 | −1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843 | 0.904447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.48528 | 1.10469 | 0.552345 | − | 0.833616i | \(-0.313733\pi\) | ||||
0.552345 | + | 0.833616i | \(0.313733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.82843 | −0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.82843 | −0.345547 | −0.172774 | − | 0.984962i | \(-0.555273\pi\) | ||||
−0.172774 | + | 0.984962i | \(0.555273\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.8284 | 1.28510 | 0.642549 | − | 0.766245i | \(-0.277877\pi\) | ||||
0.642549 | + | 0.766245i | \(0.277877\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.34315 | 0.508327 | 0.254163 | − | 0.967161i | \(-0.418200\pi\) | ||||
0.254163 | + | 0.967161i | \(0.418200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.00000 | 0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6569 | 1.53652 | 0.768258 | − | 0.640140i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640140i | \(0.221124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.82843 | −0.749517 | −0.374759 | − | 0.927122i | \(-0.622274\pi\) | ||||
−0.374759 | + | 0.927122i | \(0.622274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65685 | −0.392056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.31371 | −0.563252 | −0.281626 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281626 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.17157 | 0.121486 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.82843 | 0.700582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65685 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.65685 | 0.363871 | 0.181935 | − | 0.983311i | \(-0.441764\pi\) | ||||
0.181935 | + | 0.983311i | \(0.441764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.65685 | 0.163255 | 0.0816274 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816274 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.82843 | −0.276026 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.31371 | 0.707043 | 0.353521 | − | 0.935426i | \(-0.384984\pi\) | ||||
0.353521 | + | 0.935426i | \(0.384984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6569 | −1.49965 | −0.749827 | − | 0.661634i | \(-0.769863\pi\) | ||||
−0.749827 | + | 0.661634i | \(0.769863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6569 | −1.09658 | −0.548292 | − | 0.836287i | \(-0.684722\pi\) | ||||
−0.548292 | + | 0.836287i | \(0.684722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.6569 | −1.98528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.65685 | −0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3137 | 1.67471 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.17157 | 0.0986642 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.82843 | −0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.65685 | −0.303685 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3137 | 1.09070 | 0.545351 | − | 0.838208i | \(-0.316396\pi\) | ||||
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.17157 | 0.0953412 | 0.0476706 | − | 0.998863i | \(-0.484820\pi\) | ||||
0.0476706 | + | 0.998863i | \(0.484820\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.65685 | 0.619020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.17157 | 0.0941030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3137 | −0.891645 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.14214 | 0.481089 | 0.240545 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240545 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82843 | −0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4853 | −0.966140 | −0.483070 | − | 0.875582i | \(-0.660478\pi\) | ||||
−0.483070 | + | 0.875582i | \(0.660478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.82843 | −0.522183 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.6274 | −1.87239 | −0.936194 | − | 0.351484i | \(-0.885677\pi\) | ||||
−0.936194 | + | 0.351484i | \(0.885677\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82843 | −0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.48528 | −0.637793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.34315 | −0.175135 | −0.0875675 | − | 0.996159i | \(-0.527909\pi\) | ||||
−0.0875675 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3137 | 1.28692 | 0.643459 | − | 0.765481i | \(-0.277499\pi\) | ||||
0.643459 | + | 0.765481i | \(0.277499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.6569 | −1.58371 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | 0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.65685 | 0.409316 | 0.204658 | − | 0.978834i | \(-0.434392\pi\) | ||||
0.204658 | + | 0.978834i | \(0.434392\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34315 | 0.312626 | 0.156313 | − | 0.987708i | \(-0.450039\pi\) | ||||
0.156313 | + | 0.987708i | \(0.450039\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0000 | −1.56744 | −0.783718 | − | 0.621117i | \(-0.786679\pi\) | ||||
−0.783718 | + | 0.621117i | \(0.786679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.82843 | 0.199502 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3431 | −0.725947 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3137 | 1.33596 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.65685 | −0.389434 | −0.194717 | − | 0.980859i | \(-0.562379\pi\) | ||||
−0.194717 | + | 0.980859i | \(0.562379\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8284 | −0.741952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65685 | −0.112997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.31371 | 0.224949 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.34315 | −0.293483 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.65685 | 0.515056 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.8284 | 0.725125 | 0.362563 | − | 0.931959i | \(-0.381902\pi\) | ||||
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.8284 | −1.51518 | −0.757588 | − | 0.652733i | \(-0.773622\pi\) | ||||
−0.757588 | + | 0.652733i | \(0.773622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.6569 | 1.29896 | 0.649481 | − | 0.760378i | \(-0.274986\pi\) | ||||
0.649481 | + | 0.760378i | \(0.274986\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.9706 | −1.50485 | −0.752426 | − | 0.658677i | \(-0.771116\pi\) | ||||
−0.752426 | + | 0.658677i | \(0.771116\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.17157 | 0.0764250 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.6569 | −0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.4853 | −1.58382 | −0.791911 | − | 0.610637i | \(-0.790913\pi\) | ||||
−0.791911 | + | 0.610637i | \(0.790913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.31371 | −0.0846234 | −0.0423117 | − | 0.999104i | \(-0.513472\pi\) | ||||
−0.0423117 | + | 0.999104i | \(0.513472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.82843 | −0.434482 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.82843 | 0.432734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9706 | 1.57613 | 0.788064 | − | 0.615593i | \(-0.211084\pi\) | ||||
0.788064 | + | 0.615593i | \(0.211084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3137 | −0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.65685 | 0.479491 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9706 | 1.18335 | 0.591676 | − | 0.806176i | \(-0.298467\pi\) | ||||
0.591676 | + | 0.806176i | \(0.298467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.65685 | 0.351500 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65685 | 0.226354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.65685 | −0.595467 | −0.297734 | − | 0.954649i | \(-0.596231\pi\) | ||||
−0.297734 | + | 0.954649i | \(0.596231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.31371 | 0.325194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.65685 | −0.466847 | −0.233423 | − | 0.972375i | \(-0.574993\pi\) | ||||
−0.233423 | + | 0.972375i | \(0.574993\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.48528 | 0.272461 | 0.136231 | − | 0.990677i | \(-0.456501\pi\) | ||||
0.136231 | + | 0.990677i | \(0.456501\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843 | 0.171184 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.82843 | −0.170561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3137 | −1.76129 | −0.880645 | − | 0.473777i | \(-0.842890\pi\) | ||||
−0.880645 | + | 0.473777i | \(0.842890\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.17157 | −0.0701402 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.6274 | −1.46915 | −0.734574 | − | 0.678528i | \(-0.762618\pi\) | ||||
−0.734574 | + | 0.678528i | \(0.762618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6569 | −1.04959 | −0.524796 | − | 0.851228i | \(-0.675858\pi\) | ||||
−0.524796 | + | 0.851228i | \(0.675858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.82843 | −0.404481 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.65685 | 0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.65685 | −0.448853 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.31371 | −0.544113 | −0.272056 | − | 0.962281i | \(-0.587704\pi\) | ||||
−0.272056 | + | 0.962281i | \(0.587704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.48528 | −0.494032 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.82843 | 0.164122 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.68629 | −0.270113 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.65685 | −0.210081 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.1716 | −1.20833 | −0.604163 | − | 0.796861i | \(-0.706492\pi\) | ||||
−0.604163 | + | 0.796861i | \(0.706492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.65685 | −0.0942551 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.68629 | 0.265735 | 0.132868 | − | 0.991134i | \(-0.457581\pi\) | ||||
0.132868 | + | 0.991134i | \(0.457581\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.82843 | 0.159364 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.68629 | −0.150877 | −0.0754386 | − | 0.997150i | \(-0.524036\pi\) | ||||
−0.0754386 | + | 0.997150i | \(0.524036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3431 | −0.579105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.31371 | −0.408211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −52.2843 | −2.90917 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.6569 | 0.865826 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31371 | 0.182691 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1421 | −0.997182 | −0.498591 | − | 0.866837i | \(-0.666149\pi\) | ||||
−0.498591 | + | 0.866837i | \(0.666149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.82843 | 0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6569 | 0.633113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.31371 | 0.179447 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.6274 | 0.570510 | 0.285255 | − | 0.958452i | \(-0.407922\pi\) | ||||
0.285255 | + | 0.958452i | \(0.407922\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.97056 | −0.159011 | −0.0795053 | − | 0.996834i | \(-0.525334\pi\) | ||||
−0.0795053 | + | 0.996834i | \(0.525334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3137 | 0.921516 | 0.460758 | − | 0.887526i | \(-0.347578\pi\) | ||||
0.460758 | + | 0.887526i | \(0.347578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.8284 | −0.574713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.6569 | 1.14620 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.4853 | 0.870060 | 0.435030 | − | 0.900416i | \(-0.356738\pi\) | ||||
0.435030 | + | 0.900416i | \(0.356738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.6274 | 1.45407 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00000 | 0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.34315 | −0.227331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.68629 | −0.453421 | −0.226710 | − | 0.973962i | \(-0.572797\pi\) | ||||
−0.226710 | + | 0.973962i | \(0.572797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65685 | 0.293689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.6274 | 1.48227 | 0.741136 | − | 0.671355i | \(-0.234287\pi\) | ||||
0.741136 | + | 0.671355i | \(0.234287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.65685 | 0.188338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.1421 | −0.931899 | −0.465949 | − | 0.884811i | \(-0.654287\pi\) | ||||
−0.465949 | + | 0.884811i | \(0.654287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.65685 | 0.494736 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.8284 | −0.757697 | −0.378849 | − | 0.925459i | \(-0.623680\pi\) | ||||
−0.378849 | + | 0.925459i | \(0.623680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | −0.407718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65685 | 0.0842226 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.6569 | −1.19945 | −0.599725 | − | 0.800206i | \(-0.704723\pi\) | ||||
−0.599725 | + | 0.800206i | \(0.704723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6274 | 1.54890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | 0.807093 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.6569 | −0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.6274 | −0.834506 | −0.417253 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417253 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.3137 | −0.966895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.68629 | −0.333897 | −0.166949 | − | 0.985966i | \(-0.553391\pi\) | ||||
−0.166949 | + | 0.985966i | \(0.553391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17157 | −0.0583602 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685 | 0.280400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.6274 | −1.01996 | −0.509980 | − | 0.860186i | \(-0.670347\pi\) | ||||
−0.509980 | + | 0.860186i | \(0.670347\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | −1.18096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.82843 | 0.335194 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.9706 | 0.831052 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6274 | 0.714596 | 0.357298 | − | 0.933990i | \(-0.383698\pi\) | ||||
0.357298 | + | 0.933990i | \(0.383698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.9706 | −0.924569 | −0.462284 | − | 0.886732i | \(-0.652970\pi\) | ||||
−0.462284 | + | 0.886732i | \(0.652970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.17157 | −0.0569638 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.65685 | 0.371412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.9706 | −0.821263 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.82843 | 0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.1421 | 1.45190 | 0.725948 | − | 0.687750i | \(-0.241401\pi\) | ||||
0.725948 | + | 0.687750i | \(0.241401\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.31371 | −0.447588 | −0.223794 | − | 0.974636i | \(-0.571844\pi\) | ||||
−0.223794 | + | 0.974636i | \(0.571844\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.65685 | 0.175333 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.3137 | −1.30659 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6274 | −0.698129 | −0.349064 | − | 0.937099i | \(-0.613501\pi\) | ||||
−0.349064 | + | 0.937099i | \(0.613501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.6274 | −0.885015 | −0.442508 | − | 0.896765i | \(-0.645911\pi\) | ||||
−0.442508 | + | 0.896765i | \(0.645911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.31371 | 0.251894 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.3137 | −0.629717 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6274 | 1.72855 | 0.864277 | − | 0.503016i | \(-0.167776\pi\) | ||||
0.864277 | + | 0.503016i | \(0.167776\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.65685 | 0.266371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.17157 | −0.0550453 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.82843 | 0.132599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.2843 | 1.04241 | 0.521207 | − | 0.853430i | \(-0.325482\pi\) | ||||
0.521207 | + | 0.853430i | \(0.325482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.65685 | −0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.31371 | −0.433783 | −0.216891 | − | 0.976196i | \(-0.569592\pi\) | ||||
−0.216891 | + | 0.976196i | \(0.569592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.1421 | −1.02903 | −0.514516 | − | 0.857481i | \(-0.672028\pi\) | ||||
−0.514516 | + | 0.857481i | \(0.672028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.17157 | −0.0543304 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9706 | −1.34060 | −0.670299 | − | 0.742091i | \(-0.733834\pi\) | ||||
−0.670299 | + | 0.742091i | \(0.733834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | 0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0000 | −0.645086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.68629 | −0.215476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.82843 | −0.313310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.4853 | 1.11876 | 0.559381 | − | 0.828911i | \(-0.311039\pi\) | ||||
0.559381 | + | 0.828911i | \(0.311039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3137 | 0.514792 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.65685 | −0.347680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.4558 | 1.15351 | 0.576757 | − | 0.816916i | \(-0.304318\pi\) | ||||
0.576757 | + | 0.816916i | \(0.304318\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.14214 | −0.277757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.6569 | 0.616325 | 0.308163 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308163 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0000 | 1.26106 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.6274 | −1.37383 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.8284 | −1.38007 | −0.690035 | − | 0.723776i | \(-0.742405\pi\) | ||||
−0.690035 | + | 0.723776i | \(0.742405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4853 | 0.557801 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.65685 | 0.0738755 | 0.0369377 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369377 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.65685 | −0.162728 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.3137 | 1.29931 | 0.649654 | − | 0.760230i | \(-0.274914\pi\) | ||||
0.649654 | + | 0.760230i | \(0.274914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.2843 | −0.543424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.82843 | 0.301482 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.65685 | −0.0730097 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.31371 | 0.145737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.6274 | 1.08102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.627417 | 0.0274876 | 0.0137438 | − | 0.999906i | \(-0.495625\pi\) | ||||
0.0137438 | + | 0.999906i | \(0.495625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.31371 | −0.319806 | −0.159903 | − | 0.987133i | \(-0.551118\pi\) | ||||
−0.159903 | + | 0.987133i | \(0.551118\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82843 | 0.123443 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.97056 | −0.390764 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.48528 | 0.368230 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.31371 | −0.316199 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.34315 | 0.101114 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.9706 | 0.987582 | 0.493791 | − | 0.869581i | \(-0.335611\pi\) | ||||
0.493791 | + | 0.869581i | \(0.335611\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3137 | −0.743002 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.6569 | 0.670666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.9706 | −1.06378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −38.6274 | −1.64260 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.00000 | −0.0848953 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.9411 | −1.69236 | −0.846180 | − | 0.532897i | \(-0.821103\pi\) | ||||
−0.846180 | + | 0.532897i | \(0.821103\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.65685 | 0.0700775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.6569 | 0.914353 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.02944 | 0.127676 | 0.0638378 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638378 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6569 | 0.490408 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.82843 | −0.118783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.3137 | −1.06121 | −0.530603 | − | 0.847621i | \(-0.678034\pi\) | ||||
−0.530603 | + | 0.847621i | \(0.678034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6274 | 1.28172 | 0.640859 | − | 0.767659i | \(-0.278578\pi\) | ||||
0.640859 | + | 0.767659i | \(0.278578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.65685 | −0.236318 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.9706 | −1.62237 | −0.811183 | − | 0.584793i | \(-0.801176\pi\) | ||||
−0.811183 | + | 0.584793i | \(0.801176\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.34315 | −0.180495 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.3137 | 0.801268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.65685 | 0.234283 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.1421 | −1.07900 | −0.539501 | − | 0.841985i | \(-0.681387\pi\) | ||||
−0.539501 | + | 0.841985i | \(0.681387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.0000 | 0.904959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.68629 | −0.274573 | −0.137287 | − | 0.990531i | \(-0.543838\pi\) | ||||
−0.137287 | + | 0.990531i | \(0.543838\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.6569 | 0.887844 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.6569 | −1.53862 | −0.769309 | − | 0.638877i | \(-0.779399\pi\) | ||||
−0.769309 | + | 0.638877i | \(0.779399\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82843 | −0.115182 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | 0.121967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6274 | 1.40548 | 0.702742 | − | 0.711445i | \(-0.251959\pi\) | ||||
0.702742 | + | 0.711445i | \(0.251959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.3431 | 0.419125 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.17157 | −0.0473968 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.6863 | 0.754732 | 0.377366 | − | 0.926064i | \(-0.376830\pi\) | ||||
0.377366 | + | 0.926064i | \(0.376830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.0000 | 1.20775 | 0.603877 | − | 0.797077i | \(-0.293622\pi\) | ||||
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7990 | −0.956562 | −0.478281 | − | 0.878207i | \(-0.658740\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0294 | 0.602142 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.3137 | −0.771315 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.3137 | −0.610598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.85786 | 0.233198 | 0.116599 | − | 0.993179i | \(-0.462801\pi\) | ||||
0.116599 | + | 0.993179i | \(0.462801\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.65685 | 0.224840 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.65685 | 0.383221 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.8284 | 0.428366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.6863 | −0.422083 | −0.211042 | − | 0.977477i | \(-0.567686\pi\) | ||||
−0.211042 | + | 0.977477i | \(0.567686\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.485281 | 0.0191376 | 0.00956881 | − | 0.999954i | \(-0.496954\pi\) | ||||
0.00956881 | + | 0.999954i | \(0.496954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.65685 | 0.0652386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.00000 | 0.157256 | 0.0786281 | − | 0.996904i | \(-0.474946\pi\) | ||||
0.0786281 | + | 0.996904i | \(0.474946\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31371 | −0.129874 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.31371 | 0.0514094 | 0.0257047 | − | 0.999670i | \(-0.491817\pi\) | ||||
0.0257047 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000 | 0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.34315 | 0.169442 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.9706 | −0.426705 | −0.213353 | − | 0.976975i | \(-0.568438\pi\) | ||||
−0.213353 | + | 0.976975i | \(0.568438\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.65685 | −0.297368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.3137 | −0.748953 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6274 | 0.566376 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.8284 | −0.418651 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.9706 | −0.655141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.31371 | 0.204828 | 0.102414 | − | 0.994742i | \(-0.467343\pi\) | ||||
0.102414 | + | 0.994742i | \(0.467343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.9411 | −1.38133 | −0.690665 | − | 0.723175i | \(-0.742682\pi\) | ||||
−0.690665 | + | 0.723175i | \(0.742682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.6569 | −0.831114 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.8284 | 0.874787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.17157 | −0.350940 | −0.175470 | − | 0.984485i | \(-0.556145\pi\) | ||||
−0.175470 | + | 0.984485i | \(0.556145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6569 | −0.749956 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.00000 | −0.0761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.7990 | 1.81836 | 0.909180 | − | 0.416404i | \(-0.136710\pi\) | ||||
0.909180 | + | 0.416404i | \(0.136710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.00000 | 0.303895 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9706 | 0.643730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.3137 | −0.580048 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.9706 | 0.868826 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.6569 | −0.591351 | −0.295676 | − | 0.955288i | \(-0.595545\pi\) | ||||
−0.295676 | + | 0.955288i | \(0.595545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.6569 | 0.515078 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17157 | −0.0441240 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.3431 | −0.388994 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3431 | −0.463557 | −0.231778 | − | 0.972769i | \(-0.574454\pi\) | ||||
−0.231778 | + | 0.972769i | \(0.574454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6569 | 0.512172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.68629 | −0.175503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82843 | 0.105777 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.4853 | 0.914420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.31371 | −0.123580 | −0.0617902 | − | 0.998089i | \(-0.519681\pi\) | ||||
−0.0617902 | + | 0.998089i | \(0.519681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.68629 | −0.174527 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.31371 | 0.0488573 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.65685 | 0.135812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.97056 | −0.184348 | −0.0921740 | − | 0.995743i | \(-0.529382\pi\) | ||||
−0.0921740 | + | 0.995743i | \(0.529382\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.6863 | 0.469219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.3137 | 1.52596 | 0.762978 | − | 0.646424i | \(-0.223736\pi\) | ||||
0.762978 | + | 0.646424i | \(0.223736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.00000 | 0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.7696 | 1.20545 | 0.602724 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602724 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.82843 | 0.250849 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7990 | 0.579609 | 0.289804 | − | 0.957086i | \(-0.406410\pi\) | ||||
0.289804 | + | 0.957086i | \(0.406410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.3137 | −0.487777 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.82843 | −0.249839 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.6863 | −0.755861 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.9706 | −0.909978 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.17157 | −0.0426379 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3137 | −0.483895 | −0.241947 | − | 0.970289i | \(-0.577786\pi\) | ||||
−0.241947 | + | 0.970289i | \(0.577786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3137 | 0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.6863 | 0.677378 | 0.338689 | − | 0.940898i | \(-0.390017\pi\) | ||||
0.338689 | + | 0.940898i | \(0.390017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.2843 | 1.60320 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.65685 | −0.276834 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.48528 | 0.306386 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9706 | −0.683208 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.3137 | 0.478861 | 0.239430 | − | 0.970914i | \(-0.423039\pi\) | ||||
0.239430 | + | 0.970914i | \(0.423039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.17157 | −0.0420841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.65685 | −0.202939 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.6569 | 0.489308 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.6274 | −1.09594 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.65685 | −0.130685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.7990 | −1.56127 | −0.780633 | − | 0.624990i | \(-0.785103\pi\) | ||||
−0.780633 | + | 0.624990i | \(0.785103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.65685 | 0.343793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.9706 | 1.17230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.00000 | −0.0709327 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.0000 | −1.20434 | −0.602171 | − | 0.798367i | \(-0.705697\pi\) | ||||
−0.602171 | + | 0.798367i | \(0.705697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.97056 | −0.317356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.31371 | −0.187751 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.2843 | −0.433503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.3137 | 0.398756 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.65685 | 0.269534 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.3137 | −1.17125 | −0.585624 | − | 0.810583i | \(-0.699150\pi\) | ||||
−0.585624 | + | 0.810583i | \(0.699150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.4264 | 1.63025 | 0.815126 | − | 0.579284i | \(-0.196668\pi\) | ||||
0.815126 | + | 0.579284i | \(0.196668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.48528 | −0.157306 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.14214 | −0.215150 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.3137 | −0.395817 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3137 | 0.464652 | 0.232326 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232326 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.6569 | 1.17320 | 0.586602 | − | 0.809875i | \(-0.300465\pi\) | ||||
0.586602 | + | 0.809875i | \(0.300465\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.82843 | 0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4853 | −0.434156 | −0.217078 | − | 0.976154i | \(-0.569653\pi\) | ||||
−0.217078 | + | 0.976154i | \(0.569653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.6274 | −1.13320 | −0.566599 | − | 0.823994i | \(-0.691741\pi\) | ||||
−0.566599 | + | 0.823994i | \(0.691741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.3137 | 1.01688 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4853 | 0.432071 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.17157 | 0.0404955 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.1421 | −1.59300 | −0.796502 | − | 0.604636i | \(-0.793318\pi\) | ||||
−0.796502 | + | 0.604636i | \(0.793318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.6274 | 0.848213 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.48528 | 0.291558 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.2548 | 1.48102 | 0.740509 | − | 0.672047i | \(-0.234585\pi\) | ||||
0.740509 | + | 0.672047i | \(0.234585\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.82843 | 0.233527 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.6569 | −0.398191 | −0.199095 | − | 0.979980i | \(-0.563800\pi\) | ||||
−0.199095 | + | 0.979980i | \(0.563800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.6569 | −1.01188 | −0.505939 | − | 0.862569i | \(-0.668854\pi\) | ||||
−0.505939 | + | 0.862569i | \(0.668854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.65685 | −0.192785 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.1127 | 1.19525 | 0.597625 | − | 0.801776i | \(-0.296111\pi\) | ||||
0.597625 | + | 0.801776i | \(0.296111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.6274 | 0.837357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.6274 | −1.41374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.6274 | −1.31035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82843 | −0.0958376 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.65685 | 0.259145 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0000 | 1.28317 | 0.641584 | − | 0.767052i | \(-0.278277\pi\) | ||||
0.641584 | + | 0.767052i | \(0.278277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.31371 | 0.314144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.9411 | −0.806597 | −0.403299 | − | 0.915068i | \(-0.632136\pi\) | ||||
−0.403299 | + | 0.915068i | \(0.632136\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2843 | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.48528 | 0.285230 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.97056 | −0.166895 | −0.0834476 | − | 0.996512i | \(-0.526593\pi\) | ||||
−0.0834476 | + | 0.996512i | \(0.526593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.3137 | 0.916072 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.82843 | −0.0947559 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.34315 | 0.0783227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.00000 | −0.133556 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.28427 | −0.142888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3137 | −0.510174 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.68629 | 0.155950 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.3137 | −0.575527 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.9706 | −1.22759 | −0.613794 | − | 0.789466i | \(-0.710357\pi\) | ||||
−0.613794 | + | 0.789466i | \(0.710357\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.65685 | 0.121290 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.5980 | −1.31194 | −0.655970 | − | 0.754787i | \(-0.727740\pi\) | ||||
−0.655970 | + | 0.754787i | \(0.727740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.3137 | 0.639190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.2548 | 1.49445 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.2843 | −1.19691 | −0.598454 | − | 0.801157i | \(-0.704218\pi\) | ||||
−0.598454 | + | 0.801157i | \(0.704218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.1716 | 0.697627 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.8284 | 0.356422 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.65685 | 0.0544182 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6274 | −0.545528 | −0.272764 | − | 0.962081i | \(-0.587938\pi\) | ||||
−0.272764 | + | 0.962081i | \(0.587938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82843 | −0.223793 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.68629 | −0.153422 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.6569 | 0.708255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.627417 | 0.0204968 | 0.0102484 | − | 0.999947i | \(-0.496738\pi\) | ||||
0.0102484 | + | 0.999947i | \(0.496738\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6274 | 1.06362 | 0.531812 | − | 0.846863i | \(-0.321511\pi\) | ||||
0.531812 | + | 0.846863i | \(0.321511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.00000 | −0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.82843 | −0.0920087 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.1716 | −1.33790 | −0.668948 | − | 0.743309i | \(-0.733255\pi\) | ||||
−0.668948 | + | 0.743309i | \(0.733255\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.34315 | 0.140984 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.68629 | 0.0871090 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.343146 | −0.0111156 | −0.00555779 | − | 0.999985i | \(-0.501769\pi\) | ||||
−0.00555779 | + | 0.999985i | \(0.501769\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.65685 | −0.183052 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3431 | 0.334346 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.9117 | 1.64402 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.31371 | 0.235681 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.34315 | −0.139811 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4853 | −0.787394 | −0.393697 | − | 0.919240i | \(-0.628804\pi\) | ||||
−0.393697 | + | 0.919240i | \(0.628804\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 52.2843 | 1.67961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.3137 | 1.13327 | 0.566635 | − | 0.823969i | \(-0.308245\pi\) | ||||
0.566635 | + | 0.823969i | \(0.308245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.0000 | 1.53881 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.00000 | −0.0639857 | −0.0319928 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319928 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0294 | 0.480343 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.6569 | −0.499885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.7696 | 1.55551 | 0.777754 | − | 0.628569i | \(-0.216359\pi\) | ||||
0.777754 | + | 0.628569i | \(0.216359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0000 | 0.700978 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.31371 | −0.105477 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.62742 | 0.210740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.97056 | −0.284959 | −0.142480 | − | 0.989798i | \(-0.545508\pi\) | ||||
−0.142480 | + | 0.989798i | \(0.545508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1421 | 0.575723 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.3137 | 0.801693 | 0.400847 | − | 0.916145i | \(-0.368716\pi\) | ||||
0.400847 | + | 0.916145i | \(0.368716\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 6240.2.a.bh.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 6240.2.a.br.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.bh.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6240.2.a.br.1.2 | yes | 2 | 4.3 | odd | 2 |