Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.36147\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | −3.36147 | −1.94074 | −0.970372 | − | 0.241614i | \(-0.922323\pi\) | ||||
−0.970372 | + | 0.241614i | \(0.922323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.576535 | 0.217910 | 0.108955 | − | 0.994047i | \(-0.465250\pi\) | ||||
0.108955 | + | 0.994047i | \(0.465250\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.29947 | 2.76649 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.72294 | 1.03256 | 0.516279 | − | 0.856421i | \(-0.327317\pi\) | ||||
0.516279 | + | 0.856421i | \(0.327317\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.51454 | −1.58001 | −0.790004 | − | 0.613102i | \(-0.789921\pi\) | ||||
−0.790004 | + | 0.613102i | \(0.789921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.93800 | −0.422907 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.36147 | −0.909429 | −0.454715 | − | 0.890637i | \(-0.650259\pi\) | ||||
−0.454715 | + | 0.890637i | \(0.650259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −17.8140 | −3.42831 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.42347 | 0.450026 | 0.225013 | − | 0.974356i | \(-0.427758\pi\) | ||||
0.225013 | + | 0.974356i | \(0.427758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.15307 | −0.386703 | −0.193351 | − | 0.981130i | \(-0.561936\pi\) | ||||
−0.193351 | + | 0.981130i | \(0.561936\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.36147 | −0.585157 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.21507 | 0.528554 | 0.264277 | − | 0.964447i | \(-0.414867\pi\) | ||||
0.264277 | + | 0.964447i | \(0.414867\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.5145 | −2.00393 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.93800 | 0.927360 | 0.463680 | − | 0.886003i | \(-0.346529\pi\) | ||||
0.463680 | + | 0.886003i | \(0.346529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.93800 | 0.753038 | 0.376519 | − | 0.926409i | \(-0.377121\pi\) | ||||
0.376519 | + | 0.926409i | \(0.377121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.6609 | −1.84679 | −0.923394 | − | 0.383853i | \(-0.874597\pi\) | ||||
−0.923394 | + | 0.383853i | \(0.874597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66761 | −0.952515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.8984 | 3.06639 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.02241 | 1.10196 | 0.550981 | − | 0.834518i | \(-0.314254\pi\) | ||||
0.550981 | + | 0.834518i | \(0.314254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.36147 | 0.445237 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.660941 | 0.0860472 | 0.0430236 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430236 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4525 | −1.33831 | −0.669155 | − | 0.743122i | \(-0.733344\pi\) | ||||
−0.669155 | + | 0.743122i | \(0.733344\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.78493 | 0.602845 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.87601 | 0.717869 | 0.358934 | − | 0.933363i | \(-0.383140\pi\) | ||||
0.358934 | + | 0.933363i | \(0.383140\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.6609 | 1.76497 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.2308 | 1.80756 | 0.903782 | − | 0.427993i | \(-0.140779\pi\) | ||||
0.903782 | + | 0.427993i | \(0.140779\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5765 | −1.47197 | −0.735986 | − | 0.676997i | \(-0.763281\pi\) | ||||
−0.735986 | + | 0.676997i | \(0.763281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.576535 | 0.0657022 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0844 | −1.35960 | −0.679801 | − | 0.733397i | \(-0.737934\pi\) | ||||
−0.679801 | + | 0.733397i | \(0.737934\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 34.9828 | 3.88698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.45254 | 0.818023 | 0.409011 | − | 0.912529i | \(-0.365874\pi\) | ||||
0.409011 | + | 0.912529i | \(0.365874\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.14640 | −0.873386 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4525 | 1.21397 | 0.606983 | − | 0.794714i | \(-0.292379\pi\) | ||||
0.606983 | + | 0.794714i | \(0.292379\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.14640 | 0.225004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.23748 | 0.750491 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.6543 | −1.48792 | −0.743958 | − | 0.668226i | \(-0.767054\pi\) | ||||
−0.743958 | + | 0.668226i | \(0.767054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.29947 | 0.834128 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5145 | 1.74276 | 0.871381 | − | 0.490607i | \(-0.163225\pi\) | ||||
0.871381 | + | 0.490607i | \(0.163225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4392 | 1.32420 | 0.662102 | − | 0.749413i | \(-0.269664\pi\) | ||||
0.662102 | + | 0.749413i | \(0.269664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4459 | 1.39654 | 0.698268 | − | 0.715837i | \(-0.253955\pi\) | ||||
0.698268 | + | 0.715837i | \(0.253955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.99333 | −0.382492 | −0.191246 | − | 0.981542i | \(-0.561253\pi\) | ||||
−0.191246 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.8073 | −1.02579 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.21507 | −0.490592 | −0.245296 | − | 0.969448i | \(-0.578885\pi\) | ||||
−0.245296 | + | 0.969448i | \(0.578885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 30.8984 | 2.85656 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.75586 | −0.344299 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.9604 | −1.79977 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3615 | −1.18564 | −0.592819 | − | 0.805335i | \(-0.701985\pi\) | ||||
−0.592819 | + | 0.805335i | \(0.701985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.5989 | −1.46146 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.6543 | −1.28035 | −0.640175 | − | 0.768229i | \(-0.721138\pi\) | ||||
−0.640175 | + | 0.768229i | \(0.721138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.576535 | −0.0499919 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.29947 | 0.196457 | 0.0982286 | − | 0.995164i | \(-0.468682\pi\) | ||||
0.0982286 | + | 0.995164i | \(0.468682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.43013 | −0.121302 | −0.0606511 | − | 0.998159i | \(-0.519318\pi\) | ||||
−0.0606511 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 42.5594 | 3.58414 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.72294 | 0.311328 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.4130 | 1.84859 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.87601 | −0.809074 | −0.404537 | − | 0.914522i | \(-0.632567\pi\) | ||||
−0.404537 | + | 0.914522i | \(0.632567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.21507 | 0.587154 | 0.293577 | − | 0.955935i | \(-0.405154\pi\) | ||||
0.293577 | + | 0.955935i | \(0.405154\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −54.0672 | −4.37108 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.1979 | −1.85139 | −0.925697 | − | 0.378267i | \(-0.876520\pi\) | ||||
−0.925697 | + | 0.378267i | \(0.876520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −26.9671 | −2.13863 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.51454 | −0.198173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.88267 | −0.539093 | −0.269546 | − | 0.962987i | \(-0.586874\pi\) | ||||
−0.269546 | + | 0.962987i | \(0.586874\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.6900 | 1.36889 | 0.684447 | − | 0.729062i | \(-0.260044\pi\) | ||||
0.684447 | + | 0.729062i | \(0.260044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.860264 | 0.0661741 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.29947 | −0.634677 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.44588 | −0.338014 | −0.169007 | − | 0.985615i | \(-0.554056\pi\) | ||||
−0.169007 | + | 0.985615i | \(0.554056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.22173 | −0.166996 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.70053 | −0.351334 | −0.175667 | − | 0.984450i | \(-0.556208\pi\) | ||||
−0.175667 | + | 0.984450i | \(0.556208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.8984 | −1.33038 | −0.665189 | − | 0.746675i | \(-0.731649\pi\) | ||||
−0.665189 | + | 0.746675i | \(0.731649\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.1359 | 2.59732 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.51454 | −0.476390 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.2704 | −0.747061 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.99333 | −0.578377 | −0.289189 | − | 0.957272i | \(-0.593385\pi\) | ||||
−0.289189 | + | 0.957272i | \(0.593385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7520 | 0.845928 | 0.422964 | − | 0.906146i | \(-0.360990\pi\) | ||||
0.422964 | + | 0.906146i | \(0.360990\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.2666 | −1.65767 | −0.828837 | − | 0.559491i | \(-0.810997\pi\) | ||||
−0.828837 | + | 0.559491i | \(0.810997\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.86934 | −0.557843 | −0.278921 | − | 0.960314i | \(-0.589977\pi\) | ||||
−0.278921 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.7520 | −1.39320 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.39721 | 0.0980651 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −36.1979 | −2.51593 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.23081 | −0.153575 | −0.0767876 | − | 0.997047i | \(-0.524466\pi\) | ||||
−0.0767876 | + | 0.997047i | \(0.524466\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −51.1979 | −3.50802 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24132 | −0.0842662 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.2756 | 2.85672 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.2532 | −1.63145 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.66094 | −0.312120 | −0.156060 | − | 0.987748i | \(-0.549879\pi\) | ||||
−0.156060 | + | 0.987748i | \(0.549879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.15974 | −0.0769744 | −0.0384872 | − | 0.999259i | \(-0.512254\pi\) | ||||
−0.0384872 | + | 0.999259i | \(0.512254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0844 | 0.666396 | 0.333198 | − | 0.942857i | \(-0.391872\pi\) | ||||
0.333198 | + | 0.942857i | \(0.391872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.93800 | −0.127511 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.29947 | −0.609229 | −0.304614 | − | 0.952476i | \(-0.598528\pi\) | ||||
−0.304614 | + | 0.952476i | \(0.598528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 40.6214 | 2.63864 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.13066 | 0.331875 | 0.165937 | − | 0.986136i | \(-0.446935\pi\) | ||||
0.165937 | + | 0.986136i | \(0.446935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1135 | −1.48887 | −0.744435 | − | 0.667695i | \(-0.767281\pi\) | ||||
−0.744435 | + | 0.667695i | \(0.767281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −64.1516 | −4.11533 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.72294 | −0.236885 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.0515 | −1.58757 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.06866 | −0.0674534 | −0.0337267 | − | 0.999431i | \(-0.510738\pi\) | ||||
−0.0337267 | + | 0.999431i | \(0.510738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.36147 | −0.274203 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.5079 | −0.780220 | −0.390110 | − | 0.920768i | \(-0.627563\pi\) | ||||
−0.390110 | + | 0.920768i | \(0.627563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.85360 | 0.115177 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.1135 | 1.24499 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.64520 | −0.348098 | −0.174049 | − | 0.984737i | \(-0.555685\pi\) | ||||
−0.174049 | + | 0.984737i | \(0.555685\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −38.4974 | −2.35600 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3772 | 0.632710 | 0.316355 | − | 0.948641i | \(-0.397541\pi\) | ||||
0.316355 | + | 0.948641i | \(0.397541\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1201 | −1.10072 | −0.550360 | − | 0.834927i | \(-0.685510\pi\) | ||||
−0.550360 | + | 0.834927i | \(0.685510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.21507 | −0.436676 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9537 | 0.658147 | 0.329073 | − | 0.944304i | \(-0.393264\pi\) | ||||
0.329073 | + | 0.944304i | \(0.393264\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.8693 | −1.06981 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.77160 | −0.165340 | −0.0826699 | − | 0.996577i | \(-0.526345\pi\) | ||||
−0.0826699 | + | 0.996577i | \(0.526345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.80734 | 0.404655 | 0.202327 | − | 0.979318i | \(-0.435150\pi\) | ||||
0.202327 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.42347 | 0.202081 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.4392 | 1.49642 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 49.2599 | 2.88767 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.6123 | 1.08734 | 0.543670 | − | 0.839299i | \(-0.317034\pi\) | ||||
0.543670 | + | 0.839299i | \(0.317034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.8140 | −1.03367 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2375 | −0.939037 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.84693 | 0.164094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −58.8746 | −3.38226 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.8231 | 1.47380 | 0.736901 | − | 0.676001i | \(-0.236289\pi\) | ||||
0.736901 | + | 0.676001i | \(0.236289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −45.1755 | −2.56994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8760 | −1.07036 | −0.535180 | − | 0.844738i | \(-0.679756\pi\) | ||||
−0.535180 | + | 0.844738i | \(0.679756\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.6147 | 0.882594 | 0.441297 | − | 0.897361i | \(-0.354518\pi\) | ||||
0.441297 | + | 0.897361i | \(0.354518\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.1001 | −1.52210 | −0.761048 | − | 0.648696i | \(-0.775315\pi\) | ||||
−0.761048 | + | 0.648696i | \(0.775315\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.42347 | 0.135688 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −48.5594 | −2.71032 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.51454 | 0.362479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.4235 | 0.742319 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.29947 | −0.402433 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.93800 | 0.546242 | 0.273121 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273121 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.6834 | 1.46224 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.30614 | −0.234570 | −0.117285 | − | 0.993098i | \(-0.537419\pi\) | ||||
−0.117285 | + | 0.993098i | \(0.537419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.5303 | 0.952114 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.15307 | −0.116595 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.87985 | −0.425472 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5765 | 1.31934 | 0.659669 | − | 0.751556i | \(-0.270697\pi\) | ||||
0.659669 | + | 0.751556i | \(0.270697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.1240 | −0.702511 | −0.351256 | − | 0.936280i | \(-0.614245\pi\) | ||||
−0.351256 | + | 0.936280i | \(0.614245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −66.3204 | −3.53992 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4459 | 1.51402 | 0.757011 | − | 0.653403i | \(-0.226659\pi\) | ||||
0.757011 | + | 0.653403i | \(0.226659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.6252 | 0.668196 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.6280 | −1.88038 | −0.940188 | − | 0.340657i | \(-0.889350\pi\) | ||||
−0.940188 | + | 0.340657i | \(0.889350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.36147 | −0.176431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0844 | −0.683000 | −0.341500 | − | 0.939882i | \(-0.610935\pi\) | ||||
−0.341500 | + | 0.939882i | \(0.610935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 49.2823 | 2.56553 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.62520 | 0.240128 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1226 | −1.61147 | −0.805733 | − | 0.592280i | \(-0.798228\pi\) | ||||
−0.805733 | + | 0.592280i | \(0.798228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.02241 | 0.464678 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9537 | −0.562656 | −0.281328 | − | 0.959612i | \(-0.590775\pi\) | ||||
−0.281328 | + | 0.959612i | \(0.590775\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.9142 | 2.30102 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.8298 | 1.42203 | 0.711017 | − | 0.703175i | \(-0.248235\pi\) | ||||
0.711017 | + | 0.703175i | \(0.248235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 40.9828 | 2.08327 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.4459 | −1.08735 | −0.543675 | − | 0.839296i | \(-0.682967\pi\) | ||||
−0.543675 | + | 0.839296i | \(0.682967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.4130 | 1.43690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49.2599 | 2.48483 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2666 | 0.615641 | 0.307820 | − | 0.951445i | \(-0.400400\pi\) | ||||
0.307820 | + | 0.951445i | \(0.400400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.93800 | 0.0970215 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9380 | 0.845844 | 0.422922 | − | 0.906166i | \(-0.361005\pi\) | ||||
0.422922 | + | 0.906166i | \(0.361005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.01574 | −0.399293 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.21507 | 0.159365 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.6767 | −1.96189 | −0.980943 | − | 0.194296i | \(-0.937758\pi\) | ||||
−0.980943 | + | 0.194296i | \(0.937758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.72960 | −0.381273 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.381055 | 0.0187505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.80734 | 0.235417 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0276 | −1.95548 | −0.977739 | − | 0.209824i | \(-0.932711\pi\) | ||||
−0.977739 | + | 0.209824i | \(0.932711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.13307 | −0.298908 | −0.149454 | − | 0.988769i | \(-0.547752\pi\) | ||||
−0.149454 | + | 0.988769i | \(0.547752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −105.079 | −5.10912 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.02625 | −0.291631 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.5145 | −0.604208 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.67427 | 0.321488 | 0.160744 | − | 0.986996i | \(-0.448611\pi\) | ||||
0.160744 | + | 0.986996i | \(0.448611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.62802 | 0.318522 | 0.159261 | − | 0.987236i | \(-0.449089\pi\) | ||||
0.159261 | + | 0.987236i | \(0.449089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.36147 | 0.208637 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.4063 | −0.639847 | −0.319924 | − | 0.947443i | \(-0.603657\pi\) | ||||
−0.319924 | + | 0.947443i | \(0.603657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −55.3376 | −2.63513 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.9208 | −1.89670 | −0.948348 | − | 0.317232i | \(-0.897247\pi\) | ||||
−0.948348 | + | 0.317232i | \(0.897247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 33.1979 | 1.57021 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8207 | 1.02978 | 0.514891 | − | 0.857256i | \(-0.327832\pi\) | ||||
0.514891 | + | 0.857256i | \(0.327832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.93800 | 0.279610 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.2532 | −1.13952 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00667 | −0.327758 | −0.163879 | − | 0.986480i | \(-0.552401\pi\) | ||||
−0.163879 | + | 0.986480i | \(0.552401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 116.050 | 5.41675 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0911 | 0.609712 | 0.304856 | − | 0.952398i | \(-0.401392\pi\) | ||||
0.304856 | + | 0.952398i | \(0.401392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.7811 | 1.38404 | 0.692022 | − | 0.721876i | \(-0.256720\pi\) | ||||
0.692022 | + | 0.721876i | \(0.256720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.9671 | 0.970241 | 0.485120 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485120 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.38772 | 0.156430 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 77.9790 | 3.59308 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.93800 | 0.227050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66.5818 | 3.04857 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2466 | −0.879397 | −0.439699 | − | 0.898145i | \(-0.644915\pi\) | ||||
−0.439699 | + | 0.898145i | \(0.644915\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.9695 | 0.545762 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.45254 | 0.384604 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2771 | −0.646955 | −0.323478 | − | 0.946236i | \(-0.604852\pi\) | ||||
−0.323478 | + | 0.946236i | \(0.604852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.1359 | 1.04624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.18215 | 0.233867 | 0.116933 | − | 0.993140i | \(-0.462694\pi\) | ||||
0.116933 | + | 0.993140i | \(0.462694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7878 | −0.711045 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.78109 | 0.393886 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.315215 | 0.0141110 | 0.00705549 | − | 0.999975i | \(-0.497754\pi\) | ||||
0.00705549 | + | 0.999975i | \(0.497754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −59.4644 | −2.65668 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.6147 | 1.23128 | 0.615639 | − | 0.788028i | \(-0.288898\pi\) | ||||
0.615639 | + | 0.788028i | \(0.288898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.89175 | −0.128427 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.71627 | −0.430666 | −0.215333 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215333 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.25081 | −0.320757 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.8140 | 0.786508 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.6609 | −0.556828 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.9447 | 0.655998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.5527 | −0.725187 | −0.362593 | − | 0.931947i | \(-0.618109\pi\) | ||||
−0.362593 | + | 0.931947i | \(0.618109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.30998 | 0.144735 | 0.0723677 | − | 0.997378i | \(-0.476944\pi\) | ||||
0.0723677 | + | 0.997378i | \(0.476944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.0263 | 0.610993 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.97759 | −0.172939 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.48546 | 0.238049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.1068 | 0.957552 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.8007 | 0.681850 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.66761 | −0.287194 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.09774 | 0.133182 | 0.0665911 | − | 0.997780i | \(-0.478788\pi\) | ||||
0.0665911 | + | 0.997780i | \(0.478788\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.1650 | 2.58193 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.22414 | −0.0950975 | −0.0475487 | − | 0.998869i | \(-0.515141\pi\) | ||||
−0.0475487 | + | 0.998869i | \(0.515141\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −86.7506 | −3.70242 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.42347 | −0.103243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.96708 | −0.296270 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.7968 | −1.22016 | −0.610080 | − | 0.792339i | \(-0.708863\pi\) | ||||
−0.610080 | + | 0.792339i | \(0.708863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.3839 | 0.777555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.8984 | 0.924552 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.3128 | −1.06681 | −0.533404 | − | 0.845861i | \(-0.679087\pi\) | ||||
−0.533404 | + | 0.845861i | \(0.679087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.1688 | 0.847011 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4235 | −0.814274 | −0.407137 | − | 0.913367i | \(-0.633473\pi\) | ||||
−0.407137 | + | 0.913367i | \(0.633473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.4354 | −1.65032 | −0.825159 | − | 0.564900i | \(-0.808915\pi\) | ||||
−0.825159 | + | 0.564900i | \(0.808915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.8693 | 1.12248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.6543 | −1.65083 | −0.825415 | − | 0.564527i | \(-0.809059\pi\) | ||||
−0.825415 | + | 0.564527i | \(0.809059\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.5040 | −1.64173 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.29665 | 0.178255 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.02241 | 0.332254 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.49880 | −0.309508 | −0.154754 | − | 0.987953i | \(-0.549459\pi\) | ||||
−0.154754 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.15307 | 0.0887157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 78.2098 | 3.21712 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.0935 | −0.743010 | −0.371505 | − | 0.928431i | \(-0.621158\pi\) | ||||
−0.371505 | + | 0.928431i | \(0.621158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.4525 | 1.08263 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.8364 | 0.483623 | 0.241812 | − | 0.970323i | \(-0.422258\pi\) | ||||
0.241812 | + | 0.970323i | \(0.422258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.05149 | 0.124473 | 0.0622364 | − | 0.998061i | \(-0.480177\pi\) | ||||
0.0622364 | + | 0.998061i | \(0.480177\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 48.7678 | 1.98598 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.5040 | −1.84695 | −0.923476 | − | 0.383657i | \(-0.874665\pi\) | ||||
−0.923476 | + | 0.383657i | \(0.874665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69668 | −0.190319 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.1359 | −1.90691 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3615 | 0.943561 | 0.471780 | − | 0.881716i | \(-0.343612\pi\) | ||||
0.471780 | + | 0.881716i | \(0.343612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0329 | −0.484427 | −0.242214 | − | 0.970223i | \(-0.577873\pi\) | ||||
−0.242214 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.67668 | −0.308552 | −0.154276 | − | 0.988028i | \(-0.549304\pi\) | ||||
−0.154276 | + | 0.988028i | \(0.549304\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 77.6953 | 3.11780 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.60279 | 0.264535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.36147 | 0.134244 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.9447 | −0.835119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.28614 | −0.369675 | −0.184838 | − | 0.982769i | \(-0.559176\pi\) | ||||
−0.184838 | + | 0.982769i | \(0.559176\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.49880 | 0.298050 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.8231 | −0.983527 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 126.408 | 5.00061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2795 | 0.445512 | 0.222756 | − | 0.974874i | \(-0.428495\pi\) | ||||
0.222756 | + | 0.974874i | \(0.428495\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.76776 | 0.109150 | 0.0545748 | − | 0.998510i | \(-0.482620\pi\) | ||||
0.0545748 | + | 0.998510i | \(0.482620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.3996 | −0.566108 | −0.283054 | − | 0.959104i | \(-0.591347\pi\) | ||||
−0.283054 | + | 0.959104i | \(0.591347\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.660941 | 0.0259442 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.17266 | 0.163539 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.9471 | −0.624057 | −0.312029 | − | 0.950073i | \(-0.601009\pi\) | ||||
−0.312029 | + | 0.950073i | \(0.601009\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −104.379 | −4.07220 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.560792 | −0.0218453 | −0.0109227 | − | 0.999940i | \(-0.503477\pi\) | ||||
−0.0109227 | + | 0.999940i | \(0.503477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.6609 | −1.42595 | −0.712973 | − | 0.701192i | \(-0.752652\pi\) | ||||
−0.712973 | + | 0.701192i | \(0.752652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 81.5264 | 3.16622 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5699 | −0.409267 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.6676 | 0.605745 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.4525 | −0.403516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3681 | −0.785134 | −0.392567 | − | 0.919723i | \(-0.628413\pi\) | ||||
−0.392567 | + | 0.919723i | \(0.628413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.23081 | −0.354769 | −0.177384 | − | 0.984142i | \(-0.556764\pi\) | ||||
−0.177384 | + | 0.984142i | \(0.556764\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.44870 | −0.324231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.89842 | 0.149388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.7034 | −1.21310 | −0.606548 | − | 0.795047i | \(-0.707446\pi\) | ||||
−0.606548 | + | 0.795047i | \(0.707446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.8984 | −1.29331 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.8669 | 1.13784 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6080 | 0.860050 | 0.430025 | − | 0.902817i | \(-0.358505\pi\) | ||||
0.430025 | + | 0.902817i | \(0.358505\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.78493 | 0.181765 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −38.6834 | −1.46524 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.2599 | 1.18236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1092 | 1.36383 | 0.681913 | − | 0.731433i | \(-0.261148\pi\) | ||||
0.681913 | + | 0.731433i | \(0.261148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.21507 | −0.121259 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0977 | 0.379765 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0582 | 0.678188 | 0.339094 | − | 0.940752i | \(-0.389879\pi\) | ||||
0.339094 | + | 0.940752i | \(0.389879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −100.294 | −3.76133 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.39055 | 0.351679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.2466 | −0.644084 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6319 | −0.881320 | −0.440660 | − | 0.897674i | \(-0.645256\pi\) | ||||
−0.440660 | + | 0.897674i | \(0.645256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.74817 | 0.288557 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 77.6953 | 2.88952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.0382 | 1.48493 | 0.742466 | − | 0.669883i | \(-0.233656\pi\) | ||||
0.742466 | + | 0.669883i | \(0.233656\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 110.695 | 4.09982 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.1688 | −1.18981 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4883 | −0.572073 | −0.286036 | − | 0.958219i | \(-0.592338\pi\) | ||||
−0.286036 | + | 0.958219i | \(0.592338\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.87601 | 0.216445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.3867 | 1.70636 | 0.853181 | − | 0.521615i | \(-0.174670\pi\) | ||||
0.853181 | + | 0.521615i | \(0.174670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.5145 | 0.459733 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.7453 | −0.687700 | −0.343850 | − | 0.939025i | \(-0.611731\pi\) | ||||
−0.343850 | + | 0.939025i | \(0.611731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 61.8522 | 2.26305 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.32855 | 0.304319 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6504 | 0.680564 | 0.340282 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340282 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.59228 | 0.130910 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4921 | 1.03556 | 0.517782 | − | 0.855513i | \(-0.326758\pi\) | ||||
0.517782 | + | 0.855513i | \(0.326758\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6609 | 0.532158 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8918 | −0.539826 | −0.269913 | − | 0.962885i | \(-0.586995\pi\) | ||||
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.30230 | −0.0833487 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.46064 | 0.0888486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.2175 | 0.945426 | 0.472713 | − | 0.881216i | \(-0.343275\pi\) | ||||
0.472713 | + | 0.881216i | \(0.343275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42.0448 | 1.51421 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.7744 | 1.35865 | 0.679326 | − | 0.733837i | \(-0.262272\pi\) | ||||
0.679326 | + | 0.733837i | \(0.262272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.23081 | −0.223529 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.93800 | −0.212751 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2308 | 0.545001 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.1716 | −1.54283 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.2441 | −1.14938 | −0.574690 | − | 0.818371i | \(-0.694877\pi\) | ||||
−0.574690 | + | 0.818371i | \(0.694877\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.9762 | 0.675569 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.00667 | −0.106905 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.9142 | −1.38188 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.77827 | −0.204677 | −0.102338 | − | 0.994750i | \(-0.532632\pi\) | ||||
−0.102338 | + | 0.994750i | \(0.532632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.4802 | 2.91794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 95.0501 | 3.35843 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.5765 | −0.443816 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.8827 | −1.22793 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.9656 | −1.19417 | −0.597084 | − | 0.802179i | \(-0.703674\pi\) | ||||
−0.597084 | + | 0.802179i | \(0.703674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.412955 | 0.0145008 | 0.00725041 | − | 0.999974i | \(-0.497692\pi\) | ||||
0.00725041 | + | 0.999974i | \(0.497692\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 60.9103 | 2.13622 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.93800 | −0.172759 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.8140 | 0.622472 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.17025 | 0.215343 | 0.107672 | − | 0.994187i | \(-0.465661\pi\) | ||||
0.107672 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.3061 | 1.19584 | 0.597918 | − | 0.801557i | \(-0.295995\pi\) | ||||
0.597918 | + | 0.801557i | \(0.295995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.6108 | −1.06444 | −0.532222 | − | 0.846605i | \(-0.678643\pi\) | ||||
−0.532222 | + | 0.846605i | \(0.678643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.44064 | 0.119498 | 0.0597492 | − | 0.998213i | \(-0.480970\pi\) | ||||
0.0597492 | + | 0.998213i | \(0.480970\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.8207 | −1.27730 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.4364 | 1.50498 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.3548 | 1.32574 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7611 | 0.406038 | 0.203019 | − | 0.979175i | \(-0.434925\pi\) | ||||
0.203019 | + | 0.979175i | \(0.434925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1268 | −0.797476 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.31665 | 0.320882 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.576535 | 0.0198100 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.8827 | −0.785331 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0224 | −0.480682 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5279 | 0.634382 | 0.317191 | − | 0.948362i | \(-0.397260\pi\) | ||||
0.317191 | + | 0.948362i | \(0.397260\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.7348 | 1.56227 | 0.781136 | − | 0.624361i | \(-0.214640\pi\) | ||||
0.781136 | + | 0.624361i | \(0.214640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0606 | −0.445621 | −0.222810 | − | 0.974862i | \(-0.571523\pi\) | ||||
−0.222810 | + | 0.974862i | \(0.571523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.5079 | −0.392187 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7520 | 0.910649 | 0.455325 | − | 0.890326i | \(-0.349523\pi\) | ||||
0.455325 | + | 0.890326i | \(0.349523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −85.5131 | −2.90418 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0844 | −0.409935 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8760 | 0.741240 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −121.623 | −4.11631 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.3023 | −1.19207 | −0.596037 | − | 0.802957i | \(-0.703259\pi\) | ||||
−0.596037 | + | 0.802957i | \(0.703259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −62.5646 | −2.11025 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.7282 | 1.06895 | 0.534475 | − | 0.845185i | \(-0.320510\pi\) | ||||
0.534475 | + | 0.845185i | \(0.320510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.9380 | 1.00749 | 0.503747 | − | 0.863851i | \(-0.331954\pi\) | ||||
0.503747 | + | 0.863851i | \(0.331954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.66094 | 0.223653 | 0.111826 | − | 0.993728i | \(-0.464330\pi\) | ||||
0.111826 | + | 0.993728i | \(0.464330\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.70335 | −0.258362 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34.9828 | 1.17197 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.6609 | 0.423682 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 54.5818 | 1.82243 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.21789 | −0.174026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.2623 | −1.74111 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.56987 | −0.318465 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.0157 | −1.49472 | −0.747362 | − | 0.664418i | \(-0.768680\pi\) | ||||
−0.747362 | + | 0.664418i | \(0.768680\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 145.361 | 4.82133 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.0739 | 0.830735 | 0.415368 | − | 0.909654i | \(-0.363653\pi\) | ||||
0.415368 | + | 0.909654i | \(0.363653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.45254 | 0.246643 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.44870 | −0.279001 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.9184 | −0.756009 | −0.378004 | − | 0.925804i | \(-0.623390\pi\) | ||||
−0.378004 | + | 0.925804i | \(0.623390\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −86.8035 | −2.86027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.7034 | 1.86641 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 111.538 | 3.66340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.45921 | −0.146302 | −0.0731509 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731509 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66761 | 0.218522 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 63.4511 | 2.07730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.15548 | 0.135754 | 0.0678768 | − | 0.997694i | \(-0.478378\pi\) | ||||
0.0678768 | + | 0.997694i | \(0.478378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.4883 | −1.71289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.5079 | 1.09233 | 0.546163 | − | 0.837679i | \(-0.316088\pi\) | ||||
0.546163 | + | 0.837679i | \(0.316088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.8984 | −0.843368 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.0329 | 0.618487 | 0.309243 | − | 0.950983i | \(-0.399924\pi\) | ||||
0.309243 | + | 0.950983i | \(0.399924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.8217 | −1.51990 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 91.0963 | 2.95400 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.1979 | 1.14017 | 0.570086 | − | 0.821585i | \(-0.306910\pi\) | ||||
0.570086 | + | 0.821585i | \(0.306910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.14640 | −0.263336 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.32573 | 0.0428099 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.3643 | −0.850461 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 119.893 | 3.86350 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.4855 | −0.883873 | −0.441936 | − | 0.897046i | \(-0.645708\pi\) | ||||
−0.441936 | + | 0.897046i | \(0.645708\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.8984 | −0.703479 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.92749 | 0.286497 | 0.143248 | − | 0.989687i | \(-0.454245\pi\) | ||||
0.143248 | + | 0.989687i | \(0.454245\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.824521 | −0.0264329 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.7191 | −0.790834 | −0.395417 | − | 0.918502i | \(-0.629400\pi\) | ||||
−0.395417 | + | 0.918502i | \(0.629400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4525 | 0.366025 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.1426 | −1.05816 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.2017 | −0.389175 | −0.194587 | − | 0.980885i | \(-0.562337\pi\) | ||||
−0.194587 | + | 0.980885i | \(0.562337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.5369 | 0.781020 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.5369 | −0.684835 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.9737 | −0.825083 | −0.412542 | − | 0.910939i | \(-0.635359\pi\) | ||||
−0.412542 | + | 0.910939i | \(0.635359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.4063 | −1.06012 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62.2980 | 1.97300 | 0.986499 | − | 0.163765i | \(-0.0523640\pi\) | ||||
0.986499 | + | 0.163765i | \(0.0523640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −57.2732 | −1.81204 |
(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 | 4400.2.a.bx.1.1 | 3 | ||
4.3 | odd | 2 | 2200.2.a.w.1.3 | yes | 3 | ||
5.2 | odd | 4 | 4400.2.b.bc.4049.6 | 6 | |||
5.3 | odd | 4 | 4400.2.b.bc.4049.1 | 6 | |||
5.4 | even | 2 | 4400.2.a.ca.1.3 | 3 | |||
20.3 | even | 4 | 2200.2.b.l.1849.6 | 6 | |||
20.7 | even | 4 | 2200.2.b.l.1849.1 | 6 | |||
20.19 | odd | 2 | 2200.2.a.t.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.t.1.1 | ✓ | 3 | 20.19 | odd | 2 | ||
2200.2.a.w.1.3 | yes | 3 | 4.3 | odd | 2 | ||
2200.2.b.l.1849.1 | 6 | 20.7 | even | 4 | |||
2200.2.b.l.1849.6 | 6 | 20.3 | even | 4 | |||
4400.2.a.bx.1.1 | 3 | 1.1 | even | 1 | trivial | ||
4400.2.a.ca.1.3 | 3 | 5.4 | even | 2 | |||
4400.2.b.bc.4049.1 | 6 | 5.3 | odd | 4 | |||
4400.2.b.bc.4049.6 | 6 | 5.2 | odd | 4 |