Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 35 x^{13} + 32 x^{12} + 477 x^{11} - 392 x^{10} - 3236 x^{9} + 2330 x^{8} + \cdots + 2560 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.04397\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | −2.04397 | −1.18008 | −0.590042 | − | 0.807372i | \(-0.700889\pi\) | ||||
−0.590042 | + | 0.807372i | \(0.700889\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.25466 | 1.90274 | 0.951372 | − | 0.308045i | \(-0.0996746\pi\) | ||||
0.951372 | + | 0.308045i | \(0.0996746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.17780 | 0.392600 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.69639 | −2.24540 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.35304 | −0.570697 | −0.285348 | − | 0.958424i | \(-0.592109\pi\) | ||||
−0.285348 | + | 0.958424i | \(0.592109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.32087 | 1.22069 | 0.610346 | − | 0.792135i | \(-0.291031\pi\) | ||||
0.610346 | + | 0.792135i | \(0.291031\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.04397 | 0.446030 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.35219 | 0.698981 | 0.349490 | − | 0.936940i | \(-0.386355\pi\) | ||||
0.349490 | + | 0.936940i | \(0.386355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.1022 | 2.62043 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.72452 | 0.716784 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.720205 | −0.133739 | −0.0668693 | − | 0.997762i | \(-0.521301\pi\) | ||||
−0.0668693 | + | 0.997762i | \(0.521301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.19263 | −1.65104 | −0.825522 | − | 0.564369i | \(-0.809119\pi\) | ||||
−0.825522 | + | 0.564369i | \(0.809119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04397 | 0.355809 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.25466 | −0.719170 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.52534 | 1.23716 | 0.618579 | − | 0.785723i | \(-0.287709\pi\) | ||||
0.618579 | + | 0.785723i | \(0.287709\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.04397 | −0.327297 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.34603 | 0.210215 | 0.105108 | − | 0.994461i | \(-0.466481\pi\) | ||||
0.105108 | + | 0.994461i | \(0.466481\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.57303 | −0.849879 | −0.424940 | − | 0.905222i | \(-0.639705\pi\) | ||||
−0.424940 | + | 0.905222i | \(0.639705\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.01114 | 0.747016 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.81408 | −0.848070 | −0.424035 | − | 0.905646i | \(-0.639387\pi\) | ||||
−0.424035 | + | 0.905646i | \(0.639387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.80954 | 0.673470 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.10736 | 0.426829 | 0.213415 | − | 0.976962i | \(-0.431541\pi\) | ||||
0.213415 | + | 0.976962i | \(0.431541\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.25466 | −0.573699 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8757 | −1.44052 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.11450 | 0.275285 | 0.137642 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137642 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.70962 | 1.24319 | 0.621595 | − | 0.783339i | \(-0.286485\pi\) | ||||
0.621595 | + | 0.783339i | \(0.286485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.17780 | −0.148389 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.25466 | 0.527726 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.48070 | −0.669575 | −0.334787 | − | 0.942294i | \(-0.608664\pi\) | ||||
−0.334787 | + | 0.942294i | \(0.608664\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.85177 | −0.824857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.12854 | −0.846003 | −0.423001 | − | 0.906129i | \(-0.639023\pi\) | ||||
−0.423001 | + | 0.906129i | \(0.639023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.258610 | −0.0302681 | −0.0151340 | − | 0.999885i | \(-0.504817\pi\) | ||||
−0.0151340 | + | 0.999885i | \(0.504817\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −26.7804 | −3.09233 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.57983 | 0.740288 | 0.370144 | − | 0.928974i | \(-0.379308\pi\) | ||||
0.370144 | + | 0.928974i | \(0.379308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1462 | −1.23847 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7748 | 1.51198 | 0.755991 | − | 0.654582i | \(-0.227155\pi\) | ||||
0.755991 | + | 0.654582i | \(0.227155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.0114 | −1.08589 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.47207 | 0.157823 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.05729 | −0.324072 | −0.162036 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162036 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.7894 | 1.94837 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.6385 | 2.32266 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.67478 | −0.677722 | −0.338861 | − | 0.940837i | \(-0.610042\pi\) | ||||
−0.338861 | + | 0.940837i | \(0.610042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17780 | −0.118373 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35677 | 0.135003 | 0.0675017 | − | 0.997719i | \(-0.478497\pi\) | ||||
0.0675017 | + | 0.997719i | \(0.478497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.37969 | 0.924208 | 0.462104 | − | 0.886826i | \(-0.347095\pi\) | ||||
0.462104 | + | 0.886826i | \(0.347095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.69639 | 0.848681 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.08506 | 0.588265 | 0.294132 | − | 0.955765i | \(-0.404969\pi\) | ||||
0.294132 | + | 0.955765i | \(0.404969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.74046 | 0.549837 | 0.274918 | − | 0.961468i | \(-0.411349\pi\) | ||||
0.274918 | + | 0.961468i | \(0.411349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.3815 | −1.45995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.7217 | 1.57305 | 0.786523 | − | 0.617561i | \(-0.211879\pi\) | ||||
0.786523 | + | 0.617561i | \(0.211879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.2625 | 1.32998 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.17780 | 0.108888 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35304 | 0.215703 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.75125 | −0.248072 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 34.4720 | 3.08327 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0817 | −1.07208 | −0.536040 | − | 0.844193i | \(-0.680080\pi\) | ||||
−0.536040 | + | 0.844193i | \(0.680080\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.3911 | 1.00293 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.32641 | 0.814852 | 0.407426 | − | 0.913238i | \(-0.366426\pi\) | ||||
0.407426 | + | 0.913238i | \(0.366426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.32087 | −0.461378 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.8466 | 1.36386 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.6463 | −1.67849 | −0.839247 | − | 0.543751i | \(-0.817004\pi\) | ||||
−0.839247 | + | 0.543751i | \(0.817004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6510 | −1.49713 | −0.748567 | − | 0.663059i | \(-0.769258\pi\) | ||||
−0.748567 | + | 0.663059i | \(0.769258\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8838 | 1.00079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.06423 | −0.254470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.04397 | −0.168584 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.60263 | 0.131293 | 0.0656463 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656463 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.21254 | −0.749706 | −0.374853 | − | 0.927084i | \(-0.622307\pi\) | ||||
−0.374853 | + | 0.927084i | \(0.622307\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.77141 | −0.224055 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −39.1115 | −3.14152 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7064 | 1.01408 | 0.507041 | − | 0.861922i | \(-0.330739\pi\) | ||||
0.507041 | + | 0.861922i | \(0.330739\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.35135 | −0.503695 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.35219 | −0.264190 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5036 | −1.05769 | −0.528843 | − | 0.848720i | \(-0.677374\pi\) | ||||
−0.528843 | + | 0.848720i | \(0.677374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.69639 | 0.677013 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1604 | 1.17315 | 0.586574 | − | 0.809895i | \(-0.300476\pi\) | ||||
0.586574 | + | 0.809895i | \(0.300476\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.26691 | 0.479243 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.12675 | −0.389780 | −0.194890 | − | 0.980825i | \(-0.562435\pi\) | ||||
−0.194890 | + | 0.980825i | \(0.562435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.1022 | −0.990431 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.32197 | −0.324859 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.3917 | 1.67364 | 0.836818 | − | 0.547481i | \(-0.184413\pi\) | ||||
0.836818 | + | 0.547481i | \(0.184413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4564 | 1.74350 | 0.871751 | − | 0.489948i | \(-0.162984\pi\) | ||||
0.871751 | + | 0.489948i | \(0.162984\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.8461 | −1.46707 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 32.0178 | 2.35399 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.35304 | 0.172071 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.72452 | −0.270919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.4771 | 1.55403 | 0.777014 | − | 0.629484i | \(-0.216733\pi\) | ||||
0.777014 | + | 0.629484i | \(0.216733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.48006 | −0.106537 | −0.0532686 | − | 0.998580i | \(-0.516964\pi\) | ||||
−0.0532686 | + | 0.998580i | \(0.516964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.69639 | −0.622762 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.37638 | −0.454298 | −0.227149 | − | 0.973860i | \(-0.572941\pi\) | ||||
−0.227149 | + | 0.973860i | \(0.572941\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.50808 | −0.248681 | −0.124341 | − | 0.992240i | \(-0.539682\pi\) | ||||
−0.124341 | + | 0.992240i | \(0.539682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2024 | 0.790155 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.720205 | 0.0505485 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.72692 | 0.399986 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.94821 | 0.274420 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.32087 | −0.368052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1802 | 1.38926 | 0.694632 | − | 0.719365i | \(-0.255567\pi\) | ||||
0.694632 | + | 0.719365i | \(0.255567\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.5705 | 0.998355 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.7114 | −1.61710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.19263 | 0.624036 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.528591 | 0.0357189 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.35304 | −0.158283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.38320 | −0.226556 | −0.113278 | − | 0.993563i | \(-0.536135\pi\) | ||||
−0.113278 | + | 0.993563i | \(0.536135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.4317 | 1.02878 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.82607 | 0.121200 | 0.0606001 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0606001 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 29.9751 | 1.98081 | 0.990407 | − | 0.138183i | \(-0.0441261\pi\) | ||||
0.990407 | + | 0.138183i | \(0.0441261\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.04397 | −0.134483 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.1806 | 1.58412 | 0.792062 | − | 0.610441i | \(-0.209008\pi\) | ||||
0.792062 | + | 0.610441i | \(0.209008\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.7369 | −1.61366 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.4489 | −0.873603 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8296 | −1.15330 | −0.576650 | − | 0.816991i | \(-0.695640\pi\) | ||||
−0.576650 | + | 0.816991i | \(0.695640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3192 | −0.922382 | −0.461191 | − | 0.887301i | \(-0.652578\pi\) | ||||
−0.461191 | + | 0.887301i | \(0.652578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.6089 | 0.744710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.25466 | 0.271821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.32087 | 0.338559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.1553 | −1.78427 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.83024 | −0.557360 | −0.278680 | − | 0.960384i | \(-0.589897\pi\) | ||||
−0.278680 | + | 0.960384i | \(0.589897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.35219 | −0.210751 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.4630 | 1.28144 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9347 | −0.931602 | −0.465801 | − | 0.884890i | \(-0.654234\pi\) | ||||
−0.465801 | + | 0.884890i | \(0.654234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.52534 | −0.467602 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.848256 | −0.0525057 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.67658 | −0.473358 | −0.236679 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236679 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.2208 | 0.812147 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.24900 | 0.382433 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0167 | 0.610729 | 0.305365 | − | 0.952236i | \(-0.401222\pi\) | ||||
0.305365 | + | 0.952236i | \(0.401222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.1625 | −1.22478 | −0.612392 | − | 0.790555i | \(-0.709792\pi\) | ||||
−0.612392 | + | 0.790555i | \(0.709792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.04397 | 0.123706 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.1022 | −0.790091 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.55993 | −0.514316 | −0.257158 | − | 0.966369i | \(-0.582786\pi\) | ||||
−0.257158 | + | 0.966369i | \(0.582786\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.8271 | −0.648199 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8748 | −1.00666 | −0.503332 | − | 0.864093i | \(-0.667893\pi\) | ||||
−0.503332 | + | 0.864093i | \(0.667893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.35859 | 0.318535 | 0.159268 | − | 0.987235i | \(-0.449087\pi\) | ||||
0.159268 | + | 0.987235i | \(0.449087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −46.2724 | −2.74094 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.34603 | −0.0794539 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4632 | −0.674305 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.6430 | 0.799769 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.4402 | −1.54466 | −0.772328 | − | 0.635224i | \(-0.780908\pi\) | ||||
−0.772328 | + | 0.635224i | \(0.780908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.99649 | 0.523796 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.72452 | −0.216118 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.35219 | 0.193862 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.57303 | 0.321224 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.77319 | −0.159315 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.3112 | 2.36547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.53916 | −0.259063 | −0.129532 | − | 0.991575i | \(-0.541347\pi\) | ||||
−0.129532 | + | 0.991575i | \(0.541347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.1718 | −1.09064 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.2870 | −1.20707 | −0.603537 | − | 0.797335i | \(-0.706242\pi\) | ||||
−0.603537 | + | 0.797335i | \(0.706242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.4052 | 1.04032 | 0.520162 | − | 0.854068i | \(-0.325872\pi\) | ||||
0.520162 | + | 0.854068i | \(0.325872\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.01114 | −0.282346 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.3848 | −1.59425 | −0.797125 | − | 0.603814i | \(-0.793647\pi\) | ||||
−0.797125 | + | 0.603814i | \(0.793647\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.720205 | 0.0403237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4377 | −0.694202 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.5202 | −0.696644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.1022 | 0.726778 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.7333 | −0.648854 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.81408 | 0.320540 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3055 | 0.841268 | 0.420634 | − | 0.907230i | \(-0.361808\pi\) | ||||
0.420634 | + | 0.907230i | \(0.361808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.86333 | 0.485708 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.3186 | −1.27403 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.4956 | 1.06200 | 0.530998 | − | 0.847373i | \(-0.321817\pi\) | ||||
0.530998 | + | 0.847373i | \(0.321817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.1786 | −1.85633 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.19263 | 0.497809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.1520 | −1.56949 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.10894 | 0.327945 | 0.163972 | − | 0.986465i | \(-0.447569\pi\) | ||||
0.163972 | + | 0.986465i | \(0.447569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.1983 | 0.652958 | 0.326479 | − | 0.945204i | \(-0.394138\pi\) | ||||
0.326479 | + | 0.945204i | \(0.394138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.72452 | 0.198800 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.6076 | 0.671034 | 0.335517 | − | 0.942034i | \(-0.391089\pi\) | ||||
0.335517 | + | 0.942034i | \(0.391089\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.3296 | −1.60973 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.80954 | −0.254548 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.2036 | 0.907974 | 0.453987 | − | 0.891008i | \(-0.350001\pi\) | ||||
0.453987 | + | 0.891008i | \(0.350001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.31165 | 0.490087 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.04397 | −0.107280 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.10030 | −0.0575924 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3213 | 1.37396 | 0.686980 | − | 0.726676i | \(-0.258936\pi\) | ||||
0.686980 | + | 0.726676i | \(0.258936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.58536 | 0.0825304 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.10736 | −0.161326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3855 | −0.537740 | −0.268870 | − | 0.963177i | \(-0.586650\pi\) | ||||
−0.268870 | + | 0.963177i | \(0.586650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −70.4596 | −3.63852 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.720205 | −0.0370924 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.17551 | 0.317215 | 0.158607 | − | 0.987342i | \(-0.449300\pi\) | ||||
0.158607 | + | 0.987342i | \(0.449300\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.6946 | 1.26515 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.0723 | 1.58772 | 0.793859 | − | 0.608102i | \(-0.208069\pi\) | ||||
0.793859 | + | 0.608102i | \(0.208069\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.25466 | 0.216838 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.56391 | −0.333662 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5890 | 1.19601 | 0.598005 | − | 0.801492i | \(-0.295960\pi\) | ||||
0.598005 | + | 0.801492i | \(0.295960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.88785 | −0.398906 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.0629 | −0.961595 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.9950 | 1.40858 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.7356 | 1.14107 | 0.570533 | − | 0.821275i | \(-0.306737\pi\) | ||||
0.570533 | + | 0.821275i | \(0.306737\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.8757 | 0.544465 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.5650 | −1.27665 | −0.638326 | − | 0.769766i | \(-0.720373\pi\) | ||||
−0.638326 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.19263 | −0.457917 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −47.4233 | −2.35648 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.52534 | −0.373017 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.1816 | −1.19571 | −0.597853 | − | 0.801606i | \(-0.703979\pi\) | ||||
−0.597853 | + | 0.801606i | \(0.703979\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.1563 | 1.98076 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.11450 | −0.104048 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 58.6072 | 2.87691 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.0780 | 1.76674 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.41809 | 0.0692780 | 0.0346390 | − | 0.999400i | \(-0.488972\pi\) | ||||
0.0346390 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.43848 | 0.362529 | 0.181265 | − | 0.983434i | \(-0.441981\pi\) | ||||
0.181265 | + | 0.983434i | \(0.441981\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.84781 | −0.332952 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.8300 | −1.49547 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.70962 | −0.469881 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.04397 | 0.0986836 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.3898 | 1.22299 | 0.611493 | − | 0.791250i | \(-0.290569\pi\) | ||||
0.611493 | + | 0.791250i | \(0.290569\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.6332 | 1.03962 | 0.519812 | − | 0.854281i | \(-0.326002\pi\) | ||||
0.519812 | + | 0.854281i | \(0.326002\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.26318 | 0.300297 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.8366 | 0.853240 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.0140 | 0.955218 | 0.477609 | − | 0.878573i | \(-0.341504\pi\) | ||||
0.477609 | + | 0.878573i | \(0.341504\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.17780 | 0.0560857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3744 | 0.872995 | 0.436497 | − | 0.899705i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899705i | \(0.356219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.0078 | −0.616627 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.27572 | −0.154936 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.2373 | 0.719093 | 0.359547 | − | 0.933127i | \(-0.382931\pi\) | ||||
0.359547 | + | 0.933127i | \(0.382931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.34603 | −0.0633822 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.8301 | 0.884716 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.25466 | −0.199462 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9361 | 0.979350 | 0.489675 | − | 0.871905i | \(-0.337115\pi\) | ||||
0.489675 | + | 0.871905i | \(0.337115\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.76395 | −0.409066 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.3491 | −1.04090 | −0.520451 | − | 0.853891i | \(-0.674236\pi\) | ||||
−0.520451 | + | 0.853891i | \(0.674236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.56648 | −0.305170 | −0.152585 | − | 0.988290i | \(-0.548760\pi\) | ||||
−0.152585 | + | 0.988290i | \(0.548760\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 79.9427 | 3.70725 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.0743 | 1.29912 | 0.649561 | − | 0.760309i | \(-0.274953\pi\) | ||||
0.649561 | + | 0.760309i | \(0.274953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.48070 | 0.253075 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.9715 | −1.19670 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.57303 | 0.256248 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 69.7149 | 3.19874 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.65985 | 0.167573 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.0758 | −1.73973 | −0.869864 | − | 0.493291i | \(-0.835794\pi\) | ||||
−0.869864 | + | 0.493291i | \(0.835794\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.52534 | 0.343126 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.85177 | 0.311766 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.3990 | −1.28953 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.1870 | 1.23196 | 0.615979 | − | 0.787762i | \(-0.288761\pi\) | ||||
0.615979 | + | 0.787762i | \(0.288761\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.6010 | 1.24816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0141 | 0.632449 | 0.316225 | − | 0.948684i | \(-0.397585\pi\) | ||||
0.316225 | + | 0.948684i | \(0.397585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.69467 | 0.0763242 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.01114 | −0.225234 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.12854 | 0.319759 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3518 | 0.821541 | 0.410771 | − | 0.911739i | \(-0.365260\pi\) | ||||
0.410771 | + | 0.911739i | \(0.365260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.9874 | −1.38441 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.21422 | −0.366254 | −0.183127 | − | 0.983089i | \(-0.558622\pi\) | ||||
−0.183127 | + | 0.983089i | \(0.558622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.77259 | 0.256877 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.04397 | −0.0907757 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5294 | −0.776977 | −0.388489 | − | 0.921453i | \(-0.627003\pi\) | ||||
−0.388489 | + | 0.921453i | \(0.627003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.258610 | 0.0114402 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.8177 | 0.874972 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.9074 | 1.75853 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.81408 | 0.255703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.4789 | 0.459973 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.53159 | 0.198532 | 0.0992662 | − | 0.995061i | \(-0.468350\pi\) | ||||
0.0992662 | + | 0.995061i | \(0.468350\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.3441 | −1.76413 | −0.882063 | − | 0.471132i | \(-0.843845\pi\) | ||||
−0.882063 | + | 0.471132i | \(0.843845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.7804 | 1.16879 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.6306 | 0.942245 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7628 | −0.511426 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.49046 | 0.108077 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.34603 | 0.0583032 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.8899 | 1.11932 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −45.7679 | −1.97503 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7233 | −1.10593 | −0.552965 | − | 0.833204i | \(-0.686504\pi\) | ||||
−0.552965 | + | 0.833204i | \(0.686504\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −47.9442 | −2.05748 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.4238 | 1.04620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.6637 | 1.52487 | 0.762434 | − | 0.647066i | \(-0.224004\pi\) | ||||
0.762434 | + | 0.647066i | \(0.224004\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.4360 | 0.488076 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.83212 | −0.163254 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.57983 | −0.279803 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −65.4433 | −2.77791 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.6296 | 0.789363 | 0.394682 | − | 0.918818i | \(-0.370855\pi\) | ||||
0.394682 | + | 0.918818i | \(0.370855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.57303 | −0.235714 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.80954 | −0.203059 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.3809 | 1.61756 | 0.808780 | − | 0.588111i | \(-0.200128\pi\) | ||||
0.808780 | + | 0.588111i | \(0.200128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 71.1452 | 2.99310 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.1462 | 0.468096 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.02816 | 0.168869 | 0.0844347 | − | 0.996429i | \(-0.473092\pi\) | ||||
0.0844347 | + | 0.996429i | \(0.473092\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.0099 | 1.29772 | 0.648862 | − | 0.760906i | \(-0.275245\pi\) | ||||
0.648862 | + | 0.760906i | \(0.275245\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −43.8984 | −1.83388 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 43.9210 | 1.83163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.72564 | 0.238362 | 0.119181 | − | 0.992873i | \(-0.461973\pi\) | ||||
0.119181 | + | 0.992873i | \(0.461973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.02520 | 0.125723 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.7748 | −0.571476 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.10736 | −0.128694 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.01114 | 0.207185 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.7308 | 1.26840 | 0.634198 | − | 0.773171i | \(-0.281330\pi\) | ||||
0.634198 | + | 0.773171i | \(0.281330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.9128 | −2.01542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0331 | 0.536111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.9751 | 1.76478 | 0.882388 | − | 0.470523i | \(-0.155935\pi\) | ||||
0.882388 | + | 0.470523i | \(0.155935\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0114 | 0.410428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.17040 | 0.293465 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6264 | −1.70081 | −0.850403 | − | 0.526131i | \(-0.823642\pi\) | ||||
−0.850403 | + | 0.526131i | \(0.823642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.74626 | −0.193604 | −0.0968021 | − | 0.995304i | \(-0.530861\pi\) | ||||
−0.0968021 | + | 0.995304i | \(0.530861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.45517 | −0.262875 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.25466 | 0.172977 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.16607 | 0.250273 | 0.125137 | − | 0.992140i | \(-0.460063\pi\) | ||||
0.125137 | + | 0.992140i | \(0.460063\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.47207 | −0.0596515 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.81408 | −0.235212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9582 | 0.482986 | 0.241493 | − | 0.970403i | \(-0.422363\pi\) | ||||
0.241493 | + | 0.970403i | \(0.422363\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.7056 | −0.472017 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.16087 | 0.248027 | 0.124014 | − | 0.992281i | \(-0.460423\pi\) | ||||
0.124014 | + | 0.992281i | \(0.460423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5729 | 0.987667 | 0.493834 | − | 0.869556i | \(-0.335595\pi\) | ||||
0.493834 | + | 0.869556i | \(0.335595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.4853 | 0.501018 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.05729 | 0.122488 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 81.1560 | 3.24624 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.8757 | 0.434333 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.7074 | −0.706042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7080 | 0.784562 | 0.392281 | − | 0.919845i | \(-0.371686\pi\) | ||||
0.392281 | + | 0.919845i | \(0.371686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −41.2477 | −1.63945 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.4037 | −2.03989 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.39599 | −0.332140 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2023 | 1.66689 | 0.833445 | − | 0.552602i | \(-0.186365\pi\) | ||||
0.833445 | + | 0.552602i | \(0.186365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.39415 | 0.133852 | 0.0669262 | − | 0.997758i | \(-0.478681\pi\) | ||||
0.0669262 | + | 0.997758i | \(0.478681\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.4653 | 1.90832 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9597 | 0.470184 | 0.235092 | − | 0.971973i | \(-0.424461\pi\) | ||||
0.235092 | + | 0.971973i | \(0.424461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.11450 | −0.0830014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.7894 | −0.736416 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.5304 | 1.11648 | 0.558241 | − | 0.829679i | \(-0.311477\pi\) | ||||
0.558241 | + | 0.829679i | \(0.311477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.6808 | 1.55046 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.304591 | −0.0118832 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.49617 | −0.214100 | −0.107050 | − | 0.994254i | \(-0.534141\pi\) | ||||
−0.107050 | + | 0.994254i | \(0.534141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.6877 | 1.38809 | 0.694045 | − | 0.719931i | \(-0.255827\pi\) | ||||
0.694045 | + | 0.719931i | \(0.255827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.80954 | 0.186787 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.6385 | −0.877884 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.41427 | −0.0934808 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.91514 | 0.267355 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.70962 | −0.374836 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7375 | 0.799372 | 0.399686 | − | 0.916652i | \(-0.369119\pi\) | ||||
0.399686 | + | 0.916652i | \(0.369119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 48.7993 | 1.87828 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.2675 | 0.586779 | 0.293390 | − | 0.955993i | \(-0.405217\pi\) | ||||
0.293390 | + | 0.955993i | \(0.405217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.67478 | 0.256155 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.73242 | −0.143027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.5772 | −0.749100 | −0.374550 | − | 0.927207i | \(-0.622203\pi\) | ||||
−0.374550 | + | 0.927207i | \(0.622203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −83.5882 | −3.19374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −61.2682 | −2.33753 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.10736 | 0.118381 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.5110 | −1.00853 | −0.504264 | − | 0.863550i | \(-0.668236\pi\) | ||||
−0.504264 | + | 0.863550i | \(0.668236\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.17780 | 0.0447409 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −75.0989 | −2.84866 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.16727 | −0.119969 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.4243 | −1.86940 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1777 | 1.06426 | 0.532128 | − | 0.846664i | \(-0.321392\pi\) | ||||
0.532128 | + | 0.846664i | \(0.321392\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.0413 | 1.51019 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.5615 | 1.90426 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.35677 | −0.0510265 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.1055 | −0.567298 | −0.283649 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283649 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.74971 | 0.290637 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.8155 | −1.15405 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.25466 | −0.159115 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36.4431 | 1.36099 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.54607 | −0.281421 | −0.140710 | − | 0.990051i | \(-0.544939\pi\) | ||||
−0.140710 | + | 0.990051i | \(0.544939\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.37969 | −0.349318 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.2680 | 1.08849 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.43624 | −0.350453 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.4012 | 0.608289 | 0.304144 | − | 0.952626i | \(-0.401630\pi\) | ||||
0.304144 | + | 0.952626i | \(0.401630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.71041 | 0.359645 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.1136 | 0.485023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.5200 | −1.34890 | −0.674449 | − | 0.738321i | \(-0.735619\pi\) | ||||
−0.674449 | + | 0.738321i | \(0.735619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.69639 | −0.320771 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.48070 | 0.201884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6235 | −0.464362 | −0.232181 | − | 0.972673i | \(-0.574586\pi\) | ||||
−0.232181 | + | 0.972673i | \(0.574586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.8757 | −0.399528 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.30740 | −0.341455 | −0.170728 | − | 0.985318i | \(-0.554612\pi\) | ||||
−0.170728 | + | 0.985318i | \(0.554612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.81866 | 0.249816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.2240 | 0.593604 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.08506 | −0.222343 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6242 | −0.752587 | −0.376294 | − | 0.926500i | \(-0.622802\pi\) | ||||
−0.376294 | + | 0.926500i | \(0.622802\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.0487 | 0.657732 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.1963 | −1.42650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.1060 | −1.42133 | −0.710665 | − | 0.703531i | \(-0.751606\pi\) | ||||
−0.710665 | + | 0.703531i | \(0.751606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.85177 | 0.248704 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.7553 | −1.87613 | −0.938064 | − | 0.346463i | \(-0.887383\pi\) | ||||
−0.938064 | + | 0.346463i | \(0.887383\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.74046 | −0.207819 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.7914 | −0.426320 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.11450 | 0.0763502 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5671 | −0.597426 | −0.298713 | − | 0.954343i | \(-0.596557\pi\) | ||||
−0.298713 | + | 0.954343i | \(0.596557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.5261 | 1.09937 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2905 | −0.585928 | −0.292964 | − | 0.956123i | \(-0.594642\pi\) | ||||
−0.292964 | + | 0.956123i | \(0.594642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −120.443 | −4.32645 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.3815 | 0.551809 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.16207 | 0.256608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.12854 | 0.255079 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.68242 | −0.0958617 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54.0615 | 1.92954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.1269 | 0.966969 | 0.483484 | − | 0.875353i | \(-0.339371\pi\) | ||||
0.483484 | + | 0.875353i | \(0.339371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.6907 | 0.558603 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.7217 | −0.594555 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.70962 | 0.344799 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.0229 | −0.958402 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.5297 | −0.443826 | −0.221913 | − | 0.975067i | \(-0.571230\pi\) | ||||
−0.221913 | + | 0.975067i | \(0.571230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6808 | 0.483991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.60087 | −0.127231 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.258610 | 0.00912616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.2625 | −0.502686 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.4738 | −0.720712 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.51409 | −0.229023 | −0.114512 | − | 0.993422i | \(-0.536530\pi\) | ||||
−0.114512 | + | 0.993422i | \(0.536530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.1838 | −0.392717 | −0.196358 | − | 0.980532i | \(-0.562912\pi\) | ||||
−0.196358 | + | 0.980532i | \(0.562912\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.2114 | 1.44535 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −57.4534 | −2.01251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.6534 | −1.03744 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.17780 | −0.0411556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.88261 | 0.100604 | 0.0503019 | − | 0.998734i | \(-0.483982\pi\) | ||||
0.0503019 | + | 0.998734i | \(0.483982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.4628 | 1.41045 | 0.705223 | − | 0.708986i | \(-0.250847\pi\) | ||||
0.705223 | + | 0.708986i | \(0.250847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.7804 | 0.932374 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.5984 | 1.41174 | 0.705872 | − | 0.708339i | \(-0.250555\pi\) | ||||
0.705872 | + | 0.708339i | \(0.250555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.7496 | −0.373349 | −0.186674 | − | 0.982422i | \(-0.559771\pi\) | ||||
−0.186674 | + | 0.982422i | \(0.559771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4962 | 0.606937 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.35304 | −0.0815281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.5025 | 2.23220 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.2381 | −1.18344 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45.8016 | 1.58125 | 0.790624 | − | 0.612303i | \(-0.209757\pi\) | ||||
0.790624 | + | 0.612303i | \(0.209757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4813 | −0.982114 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.4915 | 1.18795 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.25466 | 0.146365 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.9528 | −0.375899 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.2264 | 0.864749 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.5317 | −0.566035 | −0.283018 | − | 0.959115i | \(-0.591336\pi\) | ||||
−0.283018 | + | 0.959115i | \(0.591336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 26.6636 | 0.911876 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.7692 | −0.880259 | −0.440129 | − | 0.897934i | \(-0.645067\pi\) | ||||
−0.440129 | + | 0.897934i | \(0.645067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.6228 | −0.942479 | −0.471239 | − | 0.882005i | \(-0.656193\pi\) | ||||
−0.471239 | + | 0.882005i | \(0.656193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.75125 | 0.0937623 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.7060 | 1.79413 | 0.897066 | − | 0.441896i | \(-0.145694\pi\) | ||||
0.897066 | + | 0.441896i | \(0.145694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.8126 | −0.741651 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.4304 | 0.795738 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.57983 | −0.223205 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.48070 | −0.185707 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.86155 | −0.266073 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.4720 | −1.16537 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.9075 | −0.368320 | −0.184160 | − | 0.982896i | \(-0.558956\pi\) | ||||
−0.184160 | + | 0.982896i | \(0.558956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.0430 | 1.82282 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.7056 | −1.30402 | −0.652012 | − | 0.758209i | \(-0.726075\pi\) | ||||
−0.652012 | + | 0.758209i | \(0.726075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.1567 | −1.14946 | −0.574732 | − | 0.818342i | \(-0.694894\pi\) | ||||
−0.574732 | + | 0.818342i | \(0.694894\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.3885 | −0.618123 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −56.9048 | −1.91068 | −0.955338 | − | 0.295515i | \(-0.904509\pi\) | ||||
−0.955338 | + | 0.295515i | \(0.904509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.0817 | 0.405208 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.1462 | 0.373411 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.9359 | −1.03523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 95.2693 | 3.18450 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.85177 | −0.228774 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.62057 | 0.220809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.31176 | −0.243590 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.3911 | −0.379072 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 99.7992 | 3.31744 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.3467 | 1.97058 | 0.985288 | − | 0.170902i | \(-0.0546682\pi\) | ||||
0.985288 | + | 0.170902i | \(0.0546682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.59800 | 0.0530023 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.6951 | −1.01697 | −0.508487 | − | 0.861069i | \(-0.669795\pi\) | ||||
−0.508487 | + | 0.861069i | \(0.669795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7748 | −0.455880 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −84.4386 | −2.79146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.32641 | −0.307985 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.25510 | 0.206337 | 0.103168 | − | 0.994664i | \(-0.467102\pi\) | ||||
0.103168 | + | 0.994664i | \(0.467102\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.27788 | 0.305717 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.12854 | −0.234639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 98.5982 | 3.24189 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0474 | 0.362844 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.1670 | −1.02255 | −0.511277 | − | 0.859416i | \(-0.670827\pi\) | ||||
−0.511277 | + | 0.859416i | \(0.670827\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.32087 | 0.174384 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43.5098 | 1.42445 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0114 | 0.327408 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.8319 | −1.03990 | −0.519951 | − | 0.854196i | \(-0.674050\pi\) | ||||
−0.519951 | + | 0.854196i | \(0.674050\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −37.6196 | −1.22767 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.1604 | −1.70038 | −0.850190 | − | 0.526476i | \(-0.823513\pi\) | ||||
−0.850190 | + | 0.526476i | \(0.823513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.51217 | 0.146936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.8466 | −0.515489 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.2096 | −0.819203 | −0.409602 | − | 0.912264i | \(-0.634332\pi\) | ||||
−0.409602 | + | 0.912264i | \(0.634332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.258610 | −0.00839485 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 58.0176 | 1.88135 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.6030 | 0.861757 | 0.430878 | − | 0.902410i | \(-0.358204\pi\) | ||||
0.430878 | + | 0.902410i | \(0.358204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 91.3778 | 2.95692 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.47207 | −0.0475854 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.6463 | 0.634411 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.5044 | 1.72595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.16697 | 0.230952 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.29717 | −0.202713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.5404 | 0.885641 | 0.442821 | − | 0.896610i | \(-0.353978\pi\) | ||||
0.442821 | + | 0.896610i | \(0.353978\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.5909 | 0.822099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.11187 | −0.0356817 | −0.0178408 | − | 0.999841i | \(-0.505679\pi\) | ||||
−0.0178408 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.6510 | 0.565864 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.7804 | −0.857659 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.41320 | 0.141191 | 0.0705953 | − | 0.997505i | \(-0.477510\pi\) | ||||
0.0705953 | + | 0.997505i | \(0.477510\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.05729 | 0.0977115 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.76111 | 0.215866 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.520610 | −0.0166049 | −0.00830245 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830245 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.1294 | −0.864414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.8838 | −0.378265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.6819 | −0.594049 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3800 | 0.456795 | 0.228397 | − | 0.973568i | \(-0.426651\pi\) | ||||
0.228397 | + | 0.973568i | \(0.426651\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.2840 | −0.992768 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9257 | −0.473176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.8253 | −0.532863 | −0.266432 | − | 0.963854i | \(-0.585845\pi\) | ||||
−0.266432 | + | 0.963854i | \(0.585845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.0283 | 0.886775 |
(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 | 8008.2.a.z.1.4 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.z.1.4 | ✓ | 15 | 1.1 | even | 1 | trivial |