Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13347 | −0.801485 | −0.400743 | − | 0.916191i | \(-0.631248\pi\) | ||||
−0.400743 | + | 0.916191i | \(0.631248\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.715244 | −0.357622 | ||||||||
\(5\) | −1.11166 | −0.497151 | −0.248576 | − | 0.968612i | \(-0.579962\pi\) | ||||
−0.248576 | + | 0.968612i | \(0.579962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.07765 | 1.08811 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.26004 | 0.398459 | ||||||||
\(11\) | −3.25471 | −0.981333 | −0.490667 | − | 0.871347i | \(-0.663247\pi\) | ||||
−0.490667 | + | 0.871347i | \(0.663247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.02587 | 1.67128 | 0.835638 | − | 0.549281i | \(-0.185098\pi\) | ||||
0.835638 | + | 0.549281i | \(0.185098\pi\) | |||||||
\(14\) | −1.13347 | −0.302933 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.05794 | −0.514485 | ||||||||
\(17\) | −2.98181 | −0.723196 | −0.361598 | − | 0.932334i | \(-0.617769\pi\) | ||||
−0.361598 | + | 0.932334i | \(0.617769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.12147 | −1.40436 | −0.702181 | − | 0.711998i | \(-0.747790\pi\) | ||||
−0.702181 | + | 0.711998i | \(0.747790\pi\) | |||||||
\(20\) | 0.795111 | 0.177792 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.68912 | 0.786524 | ||||||||
\(23\) | −5.74306 | −1.19751 | −0.598755 | − | 0.800932i | \(-0.704338\pi\) | ||||
−0.598755 | + | 0.800932i | \(0.704338\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.76420 | −0.752840 | ||||||||
\(26\) | −6.83015 | −1.33950 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.715244 | −0.135168 | ||||||||
\(29\) | −7.65283 | −1.42109 | −0.710547 | − | 0.703650i | \(-0.751552\pi\) | ||||
−0.710547 | + | 0.703650i | \(0.751552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.30587 | 1.31217 | 0.656087 | − | 0.754685i | \(-0.272211\pi\) | ||||
0.656087 | + | 0.754685i | \(0.272211\pi\) | |||||||
\(32\) | −3.82268 | −0.675762 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37980 | 0.579631 | ||||||||
\(35\) | −1.11166 | −0.187906 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.93067 | 0.974997 | 0.487498 | − | 0.873124i | \(-0.337910\pi\) | ||||
0.487498 | + | 0.873124i | \(0.337910\pi\) | |||||||
\(38\) | 6.93851 | 1.12558 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.42131 | −0.540957 | ||||||||
\(41\) | 4.23604 | 0.661558 | 0.330779 | − | 0.943708i | \(-0.392688\pi\) | ||||
0.330779 | + | 0.943708i | \(0.392688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6860 | −1.62961 | −0.814803 | − | 0.579737i | \(-0.803155\pi\) | ||||
−0.814803 | + | 0.579737i | \(0.803155\pi\) | |||||||
\(44\) | 2.32791 | 0.350946 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.50959 | 0.959787 | ||||||||
\(47\) | 10.9140 | 1.59196 | 0.795982 | − | 0.605320i | \(-0.206955\pi\) | ||||
0.795982 | + | 0.605320i | \(0.206955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.26661 | 0.603390 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.30996 | −0.597684 | ||||||||
\(53\) | 4.13316 | 0.567733 | 0.283866 | − | 0.958864i | \(-0.408383\pi\) | ||||
0.283866 | + | 0.958864i | \(0.408383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.61815 | 0.487871 | ||||||||
\(56\) | 3.07765 | 0.411268 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.67426 | 1.13899 | ||||||||
\(59\) | −7.82101 | −1.01821 | −0.509104 | − | 0.860705i | \(-0.670023\pi\) | ||||
−0.509104 | + | 0.860705i | \(0.670023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.32320 | −0.553529 | −0.276764 | − | 0.960938i | \(-0.589262\pi\) | ||||
−0.276764 | + | 0.960938i | \(0.589262\pi\) | |||||||
\(62\) | −8.28100 | −1.05169 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.44878 | 1.05610 | ||||||||
\(65\) | −6.69874 | −0.830877 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.91712 | −0.234214 | −0.117107 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117107 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(68\) | 2.13272 | 0.258631 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.26004 | 0.150604 | ||||||||
\(71\) | 1.98654 | 0.235759 | 0.117880 | − | 0.993028i | \(-0.462390\pi\) | ||||
0.117880 | + | 0.993028i | \(0.462390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.455884 | 0.0533572 | 0.0266786 | − | 0.999644i | \(-0.491507\pi\) | ||||
0.0266786 | + | 0.999644i | \(0.491507\pi\) | |||||||
\(74\) | −6.72225 | −0.781445 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.37834 | 0.502230 | ||||||||
\(77\) | −3.25471 | −0.370909 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00445 | 0.900571 | 0.450286 | − | 0.892885i | \(-0.351322\pi\) | ||||
0.450286 | + | 0.892885i | \(0.351322\pi\) | |||||||
\(80\) | 2.28774 | 0.255777 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.80143 | −0.530229 | ||||||||
\(83\) | 4.44407 | 0.487800 | 0.243900 | − | 0.969800i | \(-0.421573\pi\) | ||||
0.243900 | + | 0.969800i | \(0.421573\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.31478 | 0.359538 | ||||||||
\(86\) | 12.1123 | 1.30611 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.0169 | −1.06780 | ||||||||
\(89\) | 6.16675 | 0.653674 | 0.326837 | − | 0.945081i | \(-0.394017\pi\) | ||||
0.326837 | + | 0.945081i | \(0.394017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.02587 | 0.631683 | ||||||||
\(92\) | 4.10769 | 0.428256 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.3706 | −1.27594 | ||||||||
\(95\) | 6.80502 | 0.698181 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.77960 | 0.383760 | 0.191880 | − | 0.981418i | \(-0.438542\pi\) | ||||
0.191880 | + | 0.981418i | \(0.438542\pi\) | |||||||
\(98\) | −1.13347 | −0.114498 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.69232 | 0.269232 | ||||||||
\(101\) | −4.23530 | −0.421428 | −0.210714 | − | 0.977548i | \(-0.567579\pi\) | ||||
−0.210714 | + | 0.977548i | \(0.567579\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4322 | 1.81618 | 0.908091 | − | 0.418773i | \(-0.137540\pi\) | ||||
0.908091 | + | 0.418773i | \(0.137540\pi\) | |||||||
\(104\) | 18.5455 | 1.81854 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.68482 | −0.455029 | ||||||||
\(107\) | −5.51966 | −0.533606 | −0.266803 | − | 0.963751i | \(-0.585967\pi\) | ||||
−0.266803 | + | 0.963751i | \(0.585967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3691 | −1.28052 | −0.640262 | − | 0.768156i | \(-0.721174\pi\) | ||||
−0.640262 | + | 0.768156i | \(0.721174\pi\) | |||||||
\(110\) | −4.10107 | −0.391022 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.05794 | −0.194457 | ||||||||
\(113\) | −9.04421 | −0.850807 | −0.425404 | − | 0.905004i | \(-0.639868\pi\) | ||||
−0.425404 | + | 0.905004i | \(0.639868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.38435 | 0.595344 | ||||||||
\(116\) | 5.47363 | 0.508214 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.86489 | 0.816079 | ||||||||
\(119\) | −2.98181 | −0.273342 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.406833 | −0.0369848 | ||||||||
\(122\) | 4.90022 | 0.443645 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.22548 | −0.469262 | ||||||||
\(125\) | 9.74285 | 0.871427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −1.93108 | −0.170685 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.59283 | 0.665935 | ||||||||
\(131\) | −14.6257 | −1.27785 | −0.638927 | − | 0.769268i | \(-0.720621\pi\) | ||||
−0.638927 | + | 0.769268i | \(0.720621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.12147 | −0.530799 | ||||||||
\(134\) | 2.17301 | 0.187719 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.17698 | −0.786920 | ||||||||
\(137\) | 3.21791 | 0.274925 | 0.137462 | − | 0.990507i | \(-0.456105\pi\) | ||||
0.137462 | + | 0.990507i | \(0.456105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.2380 | 1.71657 | 0.858283 | − | 0.513177i | \(-0.171532\pi\) | ||||
0.858283 | + | 0.513177i | \(0.171532\pi\) | |||||||
\(140\) | 0.795111 | 0.0671991 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.25169 | −0.188957 | ||||||||
\(143\) | −19.6125 | −1.64008 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.50737 | 0.706499 | ||||||||
\(146\) | −0.516731 | −0.0427650 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.24188 | −0.348680 | ||||||||
\(149\) | −21.4254 | −1.75524 | −0.877619 | − | 0.479359i | \(-0.840869\pi\) | ||||
−0.877619 | + | 0.479359i | \(0.840869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1145 | −1.71827 | −0.859137 | − | 0.511746i | \(-0.828999\pi\) | ||||
−0.859137 | + | 0.511746i | \(0.828999\pi\) | |||||||
\(152\) | −18.8397 | −1.52811 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.68912 | 0.297278 | ||||||||
\(155\) | −8.12168 | −0.652349 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.49426 | −0.598107 | −0.299053 | − | 0.954236i | \(-0.596671\pi\) | ||||
−0.299053 | + | 0.954236i | \(0.596671\pi\) | |||||||
\(158\) | −9.07282 | −0.721794 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.24954 | 0.335956 | ||||||||
\(161\) | −5.74306 | −0.452616 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.72881 | 0.213737 | 0.106868 | − | 0.994273i | \(-0.465918\pi\) | ||||
0.106868 | + | 0.994273i | \(0.465918\pi\) | |||||||
\(164\) | −3.02980 | −0.236588 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.03722 | −0.390964 | ||||||||
\(167\) | −9.06194 | −0.701234 | −0.350617 | − | 0.936519i | \(-0.614028\pi\) | ||||
−0.350617 | + | 0.936519i | \(0.614028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.3111 | 1.79316 | ||||||||
\(170\) | −3.75720 | −0.288164 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.64313 | 0.582783 | ||||||||
\(173\) | 8.33046 | 0.633353 | 0.316677 | − | 0.948534i | \(-0.397433\pi\) | ||||
0.316677 | + | 0.948534i | \(0.397433\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.76420 | −0.284547 | ||||||||
\(176\) | 6.69801 | 0.504881 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.98984 | −0.523910 | ||||||||
\(179\) | −15.9945 | −1.19549 | −0.597743 | − | 0.801688i | \(-0.703936\pi\) | ||||
−0.597743 | + | 0.801688i | \(0.703936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.75440 | −0.502051 | −0.251025 | − | 0.967981i | \(-0.580768\pi\) | ||||
−0.251025 | + | 0.967981i | \(0.580768\pi\) | |||||||
\(182\) | −6.83015 | −0.506284 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.6751 | −1.30303 | ||||||||
\(185\) | −6.59292 | −0.484721 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.70495 | 0.709697 | ||||||||
\(188\) | −7.80613 | −0.569321 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.71330 | −0.559581 | ||||||||
\(191\) | −4.83394 | −0.349772 | −0.174886 | − | 0.984589i | \(-0.555956\pi\) | ||||
−0.174886 | + | 0.984589i | \(0.555956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.83823 | 0.420245 | 0.210122 | − | 0.977675i | \(-0.432614\pi\) | ||||
0.210122 | + | 0.977675i | \(0.432614\pi\) | |||||||
\(194\) | −4.28407 | −0.307578 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.715244 | −0.0510888 | ||||||||
\(197\) | −6.38000 | −0.454556 | −0.227278 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227278 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5731 | 0.891284 | 0.445642 | − | 0.895211i | \(-0.352975\pi\) | ||||
0.445642 | + | 0.895211i | \(0.352975\pi\) | |||||||
\(200\) | −11.5849 | −0.819176 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.80059 | 0.337769 | ||||||||
\(203\) | −7.65283 | −0.537123 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.70906 | −0.328895 | ||||||||
\(206\) | −20.8924 | −1.45564 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.4009 | −0.859846 | ||||||||
\(209\) | 19.9236 | 1.37815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1458 | 1.31805 | 0.659027 | − | 0.752120i | \(-0.270968\pi\) | ||||
0.659027 | + | 0.752120i | \(0.270968\pi\) | |||||||
\(212\) | −2.95621 | −0.203034 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.25638 | 0.427677 | ||||||||
\(215\) | 11.8793 | 0.810161 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.30587 | 0.495955 | ||||||||
\(218\) | 15.1535 | 1.02632 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.58786 | −0.174473 | ||||||||
\(221\) | −17.9680 | −1.20866 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9013 | 1.13180 | 0.565898 | − | 0.824475i | \(-0.308530\pi\) | ||||
0.565898 | + | 0.824475i | \(0.308530\pi\) | |||||||
\(224\) | −3.82268 | −0.255414 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.2513 | 0.681909 | ||||||||
\(227\) | 2.26636 | 0.150423 | 0.0752116 | − | 0.997168i | \(-0.476037\pi\) | ||||
0.0752116 | + | 0.997168i | \(0.476037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.42113 | −0.358238 | −0.179119 | − | 0.983827i | \(-0.557325\pi\) | ||||
−0.179119 | + | 0.983827i | \(0.557325\pi\) | |||||||
\(230\) | −7.23648 | −0.477159 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.5527 | −1.54631 | ||||||||
\(233\) | 28.1801 | 1.84614 | 0.923069 | − | 0.384635i | \(-0.125673\pi\) | ||||
0.923069 | + | 0.384635i | \(0.125673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1327 | −0.791447 | ||||||||
\(236\) | 5.59393 | 0.364134 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.37980 | 0.219080 | ||||||||
\(239\) | 11.6171 | 0.751449 | 0.375725 | − | 0.926731i | \(-0.377394\pi\) | ||||
0.375725 | + | 0.926731i | \(0.377394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.9005 | −1.15308 | −0.576538 | − | 0.817071i | \(-0.695597\pi\) | ||||
−0.576538 | + | 0.817071i | \(0.695597\pi\) | |||||||
\(242\) | 0.461134 | 0.0296428 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.09214 | 0.197954 | ||||||||
\(245\) | −1.11166 | −0.0710216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.8872 | −2.34708 | ||||||||
\(248\) | 22.4849 | 1.42779 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0432 | −0.698436 | ||||||||
\(251\) | 8.13941 | 0.513755 | 0.256877 | − | 0.966444i | \(-0.417306\pi\) | ||||
0.256877 | + | 0.966444i | \(0.417306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.6920 | 1.17516 | ||||||||
\(254\) | 1.13347 | 0.0711203 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.7087 | −0.919296 | ||||||||
\(257\) | 16.1852 | 1.00961 | 0.504804 | − | 0.863234i | \(-0.331565\pi\) | ||||
0.504804 | + | 0.863234i | \(0.331565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.93067 | 0.368514 | ||||||||
\(260\) | 4.79123 | 0.297140 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.5778 | 1.02418 | ||||||||
\(263\) | 7.37626 | 0.454840 | 0.227420 | − | 0.973797i | \(-0.426971\pi\) | ||||
0.227420 | + | 0.973797i | \(0.426971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.59468 | −0.282249 | ||||||||
\(266\) | 6.93851 | 0.425427 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.37121 | 0.0837601 | ||||||||
\(269\) | −28.8536 | −1.75923 | −0.879617 | − | 0.475683i | \(-0.842201\pi\) | ||||
−0.879617 | + | 0.475683i | \(0.842201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.8082 | 1.87146 | 0.935732 | − | 0.352712i | \(-0.114740\pi\) | ||||
0.935732 | + | 0.352712i | \(0.114740\pi\) | |||||||
\(272\) | 6.13639 | 0.372074 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.64741 | −0.220348 | ||||||||
\(275\) | 12.2514 | 0.738787 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.75477 | −0.345770 | −0.172885 | − | 0.984942i | \(-0.555309\pi\) | ||||
−0.172885 | + | 0.984942i | \(0.555309\pi\) | |||||||
\(278\) | −22.9392 | −1.37580 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.42131 | −0.204463 | ||||||||
\(281\) | 11.4370 | 0.682273 | 0.341136 | − | 0.940014i | \(-0.389188\pi\) | ||||
0.341136 | + | 0.940014i | \(0.389188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.9866 | 1.30697 | 0.653484 | − | 0.756940i | \(-0.273307\pi\) | ||||
0.653484 | + | 0.756940i | \(0.273307\pi\) | |||||||
\(284\) | −1.42086 | −0.0843125 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22.2302 | 1.31450 | ||||||||
\(287\) | 4.23604 | 0.250046 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.10878 | −0.476987 | ||||||||
\(290\) | −9.64286 | −0.566248 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.326068 | −0.0190817 | ||||||||
\(293\) | 24.5513 | 1.43430 | 0.717152 | − | 0.696917i | \(-0.245445\pi\) | ||||
0.717152 | + | 0.696917i | \(0.245445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.69434 | 0.506204 | ||||||||
\(296\) | 18.2525 | 1.06091 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2851 | 1.40680 | ||||||||
\(299\) | −34.6069 | −2.00137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6860 | −0.615933 | ||||||||
\(302\) | 23.9327 | 1.37717 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.5976 | 0.722523 | ||||||||
\(305\) | 4.80595 | 0.275188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0864 | 1.14639 | 0.573197 | − | 0.819418i | \(-0.305703\pi\) | ||||
0.573197 | + | 0.819418i | \(0.305703\pi\) | |||||||
\(308\) | 2.32791 | 0.132645 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.20569 | 0.522848 | ||||||||
\(311\) | 6.92673 | 0.392779 | 0.196389 | − | 0.980526i | \(-0.437078\pi\) | ||||
0.196389 | + | 0.980526i | \(0.437078\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.04097 | −0.341456 | −0.170728 | − | 0.985318i | \(-0.554612\pi\) | ||||
−0.170728 | + | 0.985318i | \(0.554612\pi\) | |||||||
\(314\) | 8.49452 | 0.479374 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.72513 | −0.322064 | ||||||||
\(317\) | −25.3538 | −1.42401 | −0.712007 | − | 0.702173i | \(-0.752213\pi\) | ||||
−0.712007 | + | 0.702173i | \(0.752213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9078 | 1.39457 | ||||||||
\(320\) | −9.39221 | −0.525040 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.50959 | 0.362765 | ||||||||
\(323\) | 18.2531 | 1.01563 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.6826 | −1.25820 | ||||||||
\(326\) | −3.09303 | −0.171307 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.0371 | 0.719851 | ||||||||
\(329\) | 10.9140 | 0.601706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.2950 | −1.50027 | −0.750135 | − | 0.661285i | \(-0.770011\pi\) | ||||
−0.750135 | + | 0.661285i | \(0.770011\pi\) | |||||||
\(332\) | −3.17859 | −0.174448 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.2715 | 0.562029 | ||||||||
\(335\) | 2.13120 | 0.116440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5755 | 0.902924 | 0.451462 | − | 0.892290i | \(-0.350903\pi\) | ||||
0.451462 | + | 0.892290i | \(0.350903\pi\) | |||||||
\(338\) | −26.4225 | −1.43719 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.37087 | −0.128579 | ||||||||
\(341\) | −23.7785 | −1.28768 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −32.8879 | −1.77320 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.44234 | −0.507623 | ||||||||
\(347\) | 33.5428 | 1.80067 | 0.900336 | − | 0.435195i | \(-0.143320\pi\) | ||||
0.900336 | + | 0.435195i | \(0.143320\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.49714 | 0.0801399 | 0.0400699 | − | 0.999197i | \(-0.487242\pi\) | ||||
0.0400699 | + | 0.999197i | \(0.487242\pi\) | |||||||
\(350\) | 4.26661 | 0.228060 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.4417 | 0.663147 | ||||||||
\(353\) | −6.55775 | −0.349034 | −0.174517 | − | 0.984654i | \(-0.555836\pi\) | ||||
−0.174517 | + | 0.984654i | \(0.555836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.20837 | −0.117208 | ||||||||
\(356\) | −4.41073 | −0.233768 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.1293 | 0.958164 | ||||||||
\(359\) | −25.8101 | −1.36220 | −0.681102 | − | 0.732188i | \(-0.738499\pi\) | ||||
−0.681102 | + | 0.732188i | \(0.738499\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4724 | 0.972233 | ||||||||
\(362\) | 7.65592 | 0.402386 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.30996 | −0.225903 | ||||||||
\(365\) | −0.506790 | −0.0265266 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6181 | 1.49385 | 0.746927 | − | 0.664906i | \(-0.231528\pi\) | ||||
0.746927 | + | 0.664906i | \(0.231528\pi\) | |||||||
\(368\) | 11.8189 | 0.616101 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.47288 | 0.388497 | ||||||||
\(371\) | 4.13316 | 0.214583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7901 | 1.33536 | 0.667680 | − | 0.744448i | \(-0.267287\pi\) | ||||
0.667680 | + | 0.744448i | \(0.267287\pi\) | |||||||
\(374\) | −11.0003 | −0.568811 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 33.5893 | 1.73224 | ||||||||
\(377\) | −46.1149 | −2.37504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0276 | 1.08011 | 0.540056 | − | 0.841629i | \(-0.318403\pi\) | ||||
0.540056 | + | 0.841629i | \(0.318403\pi\) | |||||||
\(380\) | −4.86725 | −0.249685 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.47913 | 0.280337 | ||||||||
\(383\) | 35.9979 | 1.83941 | 0.919704 | − | 0.392612i | \(-0.128429\pi\) | ||||
0.919704 | + | 0.392612i | \(0.128429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.61815 | 0.184398 | ||||||||
\(386\) | −6.61746 | −0.336820 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.70333 | −0.137241 | ||||||||
\(389\) | −4.67570 | −0.237067 | −0.118534 | − | 0.992950i | \(-0.537819\pi\) | ||||
−0.118534 | + | 0.992950i | \(0.537819\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1247 | 0.866035 | ||||||||
\(392\) | 3.07765 | 0.155445 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.23155 | 0.364320 | ||||||||
\(395\) | −8.89827 | −0.447720 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.8933 | −0.898041 | −0.449021 | − | 0.893521i | \(-0.648227\pi\) | ||||
−0.449021 | + | 0.893521i | \(0.648227\pi\) | |||||||
\(398\) | −14.2512 | −0.714351 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.74650 | 0.387325 | ||||||||
\(401\) | −25.2484 | −1.26084 | −0.630422 | − | 0.776253i | \(-0.717118\pi\) | ||||
−0.630422 | + | 0.776253i | \(0.717118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.0242 | 2.19300 | ||||||||
\(404\) | 3.02927 | 0.150712 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.67426 | 0.430496 | ||||||||
\(407\) | −19.3026 | −0.956797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1682 | 0.750017 | 0.375009 | − | 0.927021i | \(-0.377640\pi\) | ||||
0.375009 | + | 0.927021i | \(0.377640\pi\) | |||||||
\(410\) | 5.33758 | 0.263604 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.1835 | −0.649506 | ||||||||
\(413\) | −7.82101 | −0.384847 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.94031 | −0.242510 | ||||||||
\(416\) | −23.0350 | −1.12938 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.5829 | −1.10456 | ||||||||
\(419\) | −2.22005 | −0.108457 | −0.0542283 | − | 0.998529i | \(-0.517270\pi\) | ||||
−0.0542283 | + | 0.998529i | \(0.517270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.48135 | −0.169671 | −0.0848353 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848353 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(422\) | −21.7012 | −1.05640 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.7204 | 0.617758 | ||||||||
\(425\) | 11.2242 | 0.544451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.32320 | −0.209214 | ||||||||
\(428\) | 3.94790 | 0.190829 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.4648 | −0.649332 | ||||||||
\(431\) | 19.6652 | 0.947240 | 0.473620 | − | 0.880729i | \(-0.342947\pi\) | ||||
0.473620 | + | 0.880729i | \(0.342947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.8927 | −1.14821 | −0.574106 | − | 0.818781i | \(-0.694650\pi\) | ||||
−0.574106 | + | 0.818781i | \(0.694650\pi\) | |||||||
\(434\) | −8.28100 | −0.397500 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.56214 | 0.457944 | ||||||||
\(437\) | 35.1560 | 1.68174 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.49404 | −0.166761 | −0.0833806 | − | 0.996518i | \(-0.526572\pi\) | ||||
−0.0833806 | + | 0.996518i | \(0.526572\pi\) | |||||||
\(440\) | 11.1354 | 0.530859 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.3662 | 0.968723 | ||||||||
\(443\) | 18.6063 | 0.884011 | 0.442006 | − | 0.897012i | \(-0.354267\pi\) | ||||
0.442006 | + | 0.897012i | \(0.354267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.85536 | −0.324975 | ||||||||
\(446\) | −19.1571 | −0.907117 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.44878 | 0.399167 | ||||||||
\(449\) | −20.4734 | −0.966201 | −0.483101 | − | 0.875565i | \(-0.660490\pi\) | ||||
−0.483101 | + | 0.875565i | \(0.660490\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7871 | −0.649209 | ||||||||
\(452\) | 6.46881 | 0.304267 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.56885 | −0.120562 | ||||||||
\(455\) | −6.69874 | −0.314042 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.8314 | 1.44223 | 0.721115 | − | 0.692815i | \(-0.243630\pi\) | ||||
0.721115 | + | 0.692815i | \(0.243630\pi\) | |||||||
\(458\) | 6.14469 | 0.287123 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.56637 | −0.212908 | ||||||||
\(461\) | 33.3908 | 1.55517 | 0.777583 | − | 0.628781i | \(-0.216446\pi\) | ||||
0.777583 | + | 0.628781i | \(0.216446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.46991 | 0.207734 | 0.103867 | − | 0.994591i | \(-0.466878\pi\) | ||||
0.103867 | + | 0.994591i | \(0.466878\pi\) | |||||||
\(464\) | 15.7491 | 0.731131 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −31.9413 | −1.47965 | ||||||||
\(467\) | 35.4354 | 1.63976 | 0.819878 | − | 0.572538i | \(-0.194041\pi\) | ||||
0.819878 | + | 0.572538i | \(0.194041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91712 | −0.0885246 | ||||||||
\(470\) | 13.7520 | 0.634333 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −24.0703 | −1.10793 | ||||||||
\(473\) | 34.7800 | 1.59919 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.0425 | 1.05726 | ||||||||
\(476\) | 2.13272 | 0.0977532 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.1677 | −0.602275 | ||||||||
\(479\) | −16.7718 | −0.766324 | −0.383162 | − | 0.923681i | \(-0.625165\pi\) | ||||
−0.383162 | + | 0.923681i | \(0.625165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7375 | 1.62949 | ||||||||
\(482\) | 20.2897 | 0.924173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.290985 | 0.0132266 | ||||||||
\(485\) | −4.20165 | −0.190787 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8363 | 1.21607 | 0.608034 | − | 0.793911i | \(-0.291958\pi\) | ||||
0.608034 | + | 0.793911i | \(0.291958\pi\) | |||||||
\(488\) | −13.3053 | −0.602302 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.26004 | 0.0569228 | ||||||||
\(491\) | 40.7790 | 1.84033 | 0.920165 | − | 0.391530i | \(-0.128054\pi\) | ||||
0.920165 | + | 0.391530i | \(0.128054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8193 | 1.02773 | ||||||||
\(494\) | 41.8106 | 1.88115 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.0350 | −0.675094 | ||||||||
\(497\) | 1.98654 | 0.0891085 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.03766 | 0.180751 | 0.0903753 | − | 0.995908i | \(-0.471193\pi\) | ||||
0.0903753 | + | 0.995908i | \(0.471193\pi\) | |||||||
\(500\) | −6.96851 | −0.311641 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.22578 | −0.411767 | ||||||||
\(503\) | −40.3253 | −1.79802 | −0.899008 | − | 0.437932i | \(-0.855711\pi\) | ||||
−0.899008 | + | 0.437932i | \(0.855711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.70824 | 0.209514 | ||||||||
\(506\) | −21.1869 | −0.941871 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.715244 | 0.0317338 | ||||||||
\(509\) | 17.0735 | 0.756771 | 0.378386 | − | 0.925648i | \(-0.376479\pi\) | ||||
0.378386 | + | 0.925648i | \(0.376479\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.455884 | 0.0201671 | ||||||||
\(512\) | 20.5341 | 0.907487 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.3455 | −0.809185 | ||||||||
\(515\) | −20.4905 | −0.902918 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.5218 | −1.56225 | ||||||||
\(518\) | −6.72225 | −0.295359 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −20.6164 | −0.904088 | ||||||||
\(521\) | −10.5698 | −0.463073 | −0.231536 | − | 0.972826i | \(-0.574375\pi\) | ||||
−0.231536 | + | 0.972826i | \(0.574375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8649 | −0.518815 | −0.259407 | − | 0.965768i | \(-0.583527\pi\) | ||||
−0.259407 | + | 0.965768i | \(0.583527\pi\) | |||||||
\(524\) | 10.4609 | 0.456988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.36078 | −0.364547 | ||||||||
\(527\) | −21.7848 | −0.948959 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.98272 | 0.434031 | ||||||||
\(530\) | 5.20794 | 0.226219 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.37834 | 0.189825 | ||||||||
\(533\) | 25.5258 | 1.10565 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.13601 | 0.265283 | ||||||||
\(536\) | −5.90024 | −0.254852 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 32.7047 | 1.41000 | ||||||||
\(539\) | −3.25471 | −0.140190 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.62403 | −0.370776 | −0.185388 | − | 0.982665i | \(-0.559354\pi\) | ||||
−0.185388 | + | 0.982665i | \(0.559354\pi\) | |||||||
\(542\) | −34.9202 | −1.49995 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11.3985 | 0.488708 | ||||||||
\(545\) | 14.8619 | 0.636615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.5125 | 1.43289 | 0.716445 | − | 0.697644i | \(-0.245768\pi\) | ||||
0.716445 | + | 0.697644i | \(0.245768\pi\) | |||||||
\(548\) | −2.30159 | −0.0983190 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.8866 | −0.592127 | ||||||||
\(551\) | 46.8466 | 1.99573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00445 | 0.340384 | ||||||||
\(554\) | 6.52286 | 0.277130 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.4751 | −0.613881 | ||||||||
\(557\) | −15.0410 | −0.637306 | −0.318653 | − | 0.947871i | \(-0.603230\pi\) | ||||
−0.318653 | + | 0.947871i | \(0.603230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −64.3927 | −2.72352 | ||||||||
\(560\) | 2.28774 | 0.0966746 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.9635 | −0.546831 | ||||||||
\(563\) | −15.7124 | −0.662197 | −0.331099 | − | 0.943596i | \(-0.607419\pi\) | ||||
−0.331099 | + | 0.943596i | \(0.607419\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0541 | 0.422980 | ||||||||
\(566\) | −24.9212 | −1.04751 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.11388 | 0.256533 | ||||||||
\(569\) | 34.6546 | 1.45280 | 0.726399 | − | 0.687273i | \(-0.241193\pi\) | ||||
0.726399 | + | 0.687273i | \(0.241193\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.56214 | 0.400163 | 0.200082 | − | 0.979779i | \(-0.435879\pi\) | ||||
0.200082 | + | 0.979779i | \(0.435879\pi\) | |||||||
\(572\) | 14.0277 | 0.586528 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.80143 | −0.200408 | ||||||||
\(575\) | 21.6180 | 0.901534 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.8185 | 0.783424 | 0.391712 | − | 0.920088i | \(-0.371883\pi\) | ||||
0.391712 | + | 0.920088i | \(0.371883\pi\) | |||||||
\(578\) | 9.19107 | 0.382298 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.08484 | −0.252659 | ||||||||
\(581\) | 4.44407 | 0.184371 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4523 | −0.557135 | ||||||||
\(584\) | 1.40305 | 0.0580586 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.8282 | −1.14957 | ||||||||
\(587\) | 29.9799 | 1.23740 | 0.618701 | − | 0.785627i | \(-0.287659\pi\) | ||||
0.618701 | + | 0.785627i | \(0.287659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.7227 | −1.84277 | ||||||||
\(590\) | −9.85478 | −0.405715 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.2050 | −0.501621 | ||||||||
\(593\) | −20.0227 | −0.822232 | −0.411116 | − | 0.911583i | \(-0.634861\pi\) | ||||
−0.411116 | + | 0.911583i | \(0.634861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.31478 | 0.135893 | ||||||||
\(596\) | 15.3244 | 0.627711 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 39.2259 | 1.60407 | ||||||||
\(599\) | −42.4949 | −1.73630 | −0.868148 | − | 0.496305i | \(-0.834690\pi\) | ||||
−0.868148 | + | 0.496305i | \(0.834690\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.1112 | 0.820352 | 0.410176 | − | 0.912006i | \(-0.365467\pi\) | ||||
0.410176 | + | 0.912006i | \(0.365467\pi\) | |||||||
\(602\) | 12.1123 | 0.493661 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.1020 | 0.614492 | ||||||||
\(605\) | 0.452262 | 0.0183871 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.3581 | −0.745133 | −0.372567 | − | 0.928005i | \(-0.621522\pi\) | ||||
−0.372567 | + | 0.928005i | \(0.621522\pi\) | |||||||
\(608\) | 23.4005 | 0.949014 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.44740 | −0.220559 | ||||||||
\(611\) | 65.7661 | 2.66061 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0981 | −0.771364 | −0.385682 | − | 0.922632i | \(-0.626034\pi\) | ||||
−0.385682 | + | 0.922632i | \(0.626034\pi\) | |||||||
\(614\) | −22.7674 | −0.918817 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0169 | −0.403591 | ||||||||
\(617\) | −18.3387 | −0.738290 | −0.369145 | − | 0.929372i | \(-0.620349\pi\) | ||||
−0.369145 | + | 0.929372i | \(0.620349\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7695 | −0.553445 | −0.276722 | − | 0.960950i | \(-0.589248\pi\) | ||||
−0.276722 | + | 0.960950i | \(0.589248\pi\) | |||||||
\(620\) | 5.80898 | 0.233294 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.85124 | −0.314806 | ||||||||
\(623\) | 6.16675 | 0.247066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.99023 | 0.319609 | ||||||||
\(626\) | 6.84726 | 0.273672 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.36022 | 0.213896 | ||||||||
\(629\) | −17.6842 | −0.705114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3936 | −1.20995 | −0.604976 | − | 0.796244i | \(-0.706817\pi\) | ||||
−0.604976 | + | 0.796244i | \(0.706817\pi\) | |||||||
\(632\) | 24.6349 | 0.979924 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.7378 | 1.14133 | ||||||||
\(635\) | 1.11166 | 0.0441151 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.02587 | 0.238754 | ||||||||
\(638\) | −28.2322 | −1.11772 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.14671 | 0.0848563 | ||||||||
\(641\) | 15.3445 | 0.606071 | 0.303036 | − | 0.952979i | \(-0.402000\pi\) | ||||
0.303036 | + | 0.952979i | \(0.402000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.64052 | 0.261876 | 0.130938 | − | 0.991391i | \(-0.458201\pi\) | ||||
0.130938 | + | 0.991391i | \(0.458201\pi\) | |||||||
\(644\) | 4.10769 | 0.161865 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.6894 | −0.814012 | ||||||||
\(647\) | 31.1079 | 1.22298 | 0.611488 | − | 0.791253i | \(-0.290571\pi\) | ||||
0.611488 | + | 0.791253i | \(0.290571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.4552 | 0.999202 | ||||||||
\(650\) | 25.7101 | 1.00843 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.95176 | −0.0764369 | ||||||||
\(653\) | 13.8619 | 0.542460 | 0.271230 | − | 0.962515i | \(-0.412570\pi\) | ||||
0.271230 | + | 0.962515i | \(0.412570\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.2589 | 0.635287 | ||||||||
\(656\) | −8.71752 | −0.340362 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.3706 | −0.482258 | ||||||||
\(659\) | −32.7089 | −1.27416 | −0.637079 | − | 0.770798i | \(-0.719858\pi\) | ||||
−0.637079 | + | 0.770798i | \(0.719858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.66172 | 0.375797 | 0.187899 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187899 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(662\) | 30.9381 | 1.20244 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6773 | 0.530781 | ||||||||
\(665\) | 6.80502 | 0.263887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.9506 | 1.70177 | ||||||||
\(668\) | 6.48150 | 0.250777 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.41565 | −0.0933248 | ||||||||
\(671\) | 14.0708 | 0.543196 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.2693 | 0.395852 | 0.197926 | − | 0.980217i | \(-0.436579\pi\) | ||||
0.197926 | + | 0.980217i | \(0.436579\pi\) | |||||||
\(674\) | −18.7878 | −0.723680 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.6731 | −0.641273 | ||||||||
\(677\) | 47.3679 | 1.82049 | 0.910247 | − | 0.414065i | \(-0.135891\pi\) | ||||
0.910247 | + | 0.414065i | \(0.135891\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.77960 | 0.145048 | ||||||||
\(680\) | 10.2017 | 0.391218 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.9523 | 1.03206 | ||||||||
\(683\) | −44.8136 | −1.71475 | −0.857373 | − | 0.514696i | \(-0.827905\pi\) | ||||
−0.857373 | + | 0.514696i | \(0.827905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.57724 | −0.136679 | ||||||||
\(686\) | −1.13347 | −0.0432761 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21.9912 | 0.838408 | ||||||||
\(689\) | 24.9059 | 0.948838 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.80863 | −0.182929 | −0.0914645 | − | 0.995808i | \(-0.529155\pi\) | ||||
−0.0914645 | + | 0.995808i | \(0.529155\pi\) | |||||||
\(692\) | −5.95831 | −0.226501 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.0198 | −1.44321 | ||||||||
\(695\) | −22.4979 | −0.853393 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.6311 | −0.478437 | ||||||||
\(698\) | −1.69696 | −0.0642309 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.69232 | 0.101760 | ||||||||
\(701\) | 0.948236 | 0.0358144 | 0.0179072 | − | 0.999840i | \(-0.494300\pi\) | ||||
0.0179072 | + | 0.999840i | \(0.494300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.3045 | −1.36925 | ||||||||
\(704\) | −27.4984 | −1.03638 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.43302 | 0.279745 | ||||||||
\(707\) | −4.23530 | −0.159285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.4973 | −1.37068 | −0.685342 | − | 0.728221i | \(-0.740347\pi\) | ||||
−0.685342 | + | 0.728221i | \(0.740347\pi\) | |||||||
\(710\) | 2.50312 | 0.0939404 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 18.9791 | 0.711272 | ||||||||
\(713\) | −41.9581 | −1.57134 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.8025 | 0.815367 | ||||||||
\(716\) | 11.4400 | 0.427532 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.2550 | 1.09179 | ||||||||
\(719\) | 37.5806 | 1.40152 | 0.700760 | − | 0.713397i | \(-0.252844\pi\) | ||||
0.700760 | + | 0.713397i | \(0.252844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4322 | 0.686452 | ||||||||
\(722\) | −20.9380 | −0.779230 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.83104 | 0.179544 | ||||||||
\(725\) | 28.8068 | 1.06986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.1600 | −1.67489 | −0.837446 | − | 0.546521i | \(-0.815952\pi\) | ||||
−0.837446 | + | 0.546521i | \(0.815952\pi\) | |||||||
\(728\) | 18.5455 | 0.687342 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.574431 | 0.0212607 | ||||||||
\(731\) | 31.8638 | 1.17853 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.7090 | −0.875712 | −0.437856 | − | 0.899045i | \(-0.644262\pi\) | ||||
−0.437856 | + | 0.899045i | \(0.644262\pi\) | |||||||
\(734\) | −32.4378 | −1.19730 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.9539 | 0.809231 | ||||||||
\(737\) | 6.23969 | 0.229842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.95413 | −0.255812 | −0.127906 | − | 0.991786i | \(-0.540826\pi\) | ||||
−0.127906 | + | 0.991786i | \(0.540826\pi\) | |||||||
\(740\) | 4.71554 | 0.173347 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.68482 | −0.171985 | ||||||||
\(743\) | 31.6115 | 1.15971 | 0.579856 | − | 0.814719i | \(-0.303109\pi\) | ||||
0.579856 | + | 0.814719i | \(0.303109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.8179 | 0.872619 | ||||||||
\(746\) | −29.2323 | −1.07027 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.94141 | −0.253803 | ||||||||
\(749\) | −5.51966 | −0.201684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.32654 | 0.303840 | 0.151920 | − | 0.988393i | \(-0.451454\pi\) | ||||
0.151920 | + | 0.988393i | \(0.451454\pi\) | |||||||
\(752\) | −22.4603 | −0.819041 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 52.2699 | 1.90356 | ||||||||
\(755\) | 23.4722 | 0.854242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.4829 | −1.47138 | −0.735688 | − | 0.677320i | \(-0.763141\pi\) | ||||
−0.735688 | + | 0.677320i | \(0.763141\pi\) | |||||||
\(758\) | −23.8341 | −0.865694 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.9435 | 0.759700 | ||||||||
\(761\) | 0.945201 | 0.0342635 | 0.0171318 | − | 0.999853i | \(-0.494547\pi\) | ||||
0.0171318 | + | 0.999853i | \(0.494547\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.3691 | −0.483993 | ||||||||
\(764\) | 3.45745 | 0.125086 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −40.8026 | −1.47426 | ||||||||
\(767\) | −47.1284 | −1.70171 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.2859 | 0.515161 | 0.257581 | − | 0.966257i | \(-0.417075\pi\) | ||||
0.257581 | + | 0.966257i | \(0.417075\pi\) | |||||||
\(770\) | −4.10107 | −0.147792 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.17575 | −0.150289 | ||||||||
\(773\) | −47.1453 | −1.69570 | −0.847850 | − | 0.530237i | \(-0.822103\pi\) | ||||
−0.847850 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.5008 | −0.987857 | ||||||||
\(776\) | 11.6323 | 0.417575 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.29977 | 0.190006 | ||||||||
\(779\) | −25.9308 | −0.929068 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.46562 | −0.231358 | ||||||||
\(782\) | −19.4104 | −0.694114 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.05794 | −0.0734978 | ||||||||
\(785\) | 8.33110 | 0.297350 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.9185 | 1.77940 | 0.889702 | − | 0.456542i | \(-0.150912\pi\) | ||||
0.889702 | + | 0.456542i | \(0.150912\pi\) | |||||||
\(788\) | 4.56326 | 0.162559 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.0859 | 0.358841 | ||||||||
\(791\) | −9.04421 | −0.321575 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.0510 | −0.925099 | ||||||||
\(794\) | 20.2816 | 0.719767 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.99283 | −0.318742 | ||||||||
\(797\) | 28.1911 | 0.998580 | 0.499290 | − | 0.866435i | \(-0.333594\pi\) | ||||
0.499290 | + | 0.866435i | \(0.333594\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.5434 | −1.15130 | ||||||||
\(800\) | 14.3894 | 0.508741 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.6183 | 1.01055 | ||||||||
\(803\) | −1.48377 | −0.0523612 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.38435 | 0.225019 | ||||||||
\(806\) | −49.9002 | −1.75766 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.0348 | −0.458562 | ||||||||
\(809\) | 32.9492 | 1.15843 | 0.579216 | − | 0.815174i | \(-0.303359\pi\) | ||||
0.579216 | + | 0.815174i | \(0.303359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.6791 | −1.60401 | −0.802004 | − | 0.597318i | \(-0.796233\pi\) | ||||
−0.802004 | + | 0.597318i | \(0.796233\pi\) | |||||||
\(812\) | 5.47363 | 0.192087 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.8790 | 0.766858 | ||||||||
\(815\) | −3.03352 | −0.106260 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 65.4143 | 2.28856 | ||||||||
\(818\) | −17.1927 | −0.601127 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.36812 | 0.117620 | ||||||||
\(821\) | −12.0427 | −0.420294 | −0.210147 | − | 0.977670i | \(-0.567394\pi\) | ||||
−0.210147 | + | 0.977670i | \(0.567394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.4766 | 1.89894 | 0.949468 | − | 0.313865i | \(-0.101624\pi\) | ||||
0.949468 | + | 0.313865i | \(0.101624\pi\) | |||||||
\(824\) | 56.7280 | 1.97621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.86489 | 0.308449 | ||||||||
\(827\) | 5.46702 | 0.190107 | 0.0950534 | − | 0.995472i | \(-0.469698\pi\) | ||||
0.0950534 | + | 0.995472i | \(0.469698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.91752 | −0.240255 | −0.120128 | − | 0.992758i | \(-0.538330\pi\) | ||||
−0.120128 | + | 0.992758i | \(0.538330\pi\) | |||||||
\(830\) | 5.59970 | 0.194368 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 50.9112 | 1.76503 | ||||||||
\(833\) | −2.98181 | −0.103314 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0738 | 0.348620 | ||||||||
\(836\) | −14.2503 | −0.492856 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.51637 | 0.0869264 | ||||||||
\(839\) | 20.4883 | 0.707335 | 0.353668 | − | 0.935371i | \(-0.384934\pi\) | ||||
0.353668 | + | 0.935371i | \(0.384934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.5657 | 1.01951 | ||||||||
\(842\) | 3.94601 | 0.135988 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.6939 | −0.471364 | ||||||||
\(845\) | −25.9141 | −0.891473 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.406833 | −0.0139790 | ||||||||
\(848\) | −8.50579 | −0.292090 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.7223 | −0.436370 | ||||||||
\(851\) | −34.0602 | −1.16757 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.0273175 | 0.000935333 0 | 0.000467666 | − | 1.00000i | \(-0.499851\pi\) | ||||
0.000467666 | 1.00000i | \(0.499851\pi\) | ||||||||
\(854\) | 4.90022 | 0.167682 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.9876 | −0.580624 | ||||||||
\(857\) | 46.5967 | 1.59171 | 0.795856 | − | 0.605486i | \(-0.207021\pi\) | ||||
0.795856 | + | 0.605486i | \(0.207021\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.7542 | −0.503408 | −0.251704 | − | 0.967804i | \(-0.580991\pi\) | ||||
−0.251704 | + | 0.967804i | \(0.580991\pi\) | |||||||
\(860\) | −8.49659 | −0.289731 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.2900 | −0.759199 | ||||||||
\(863\) | 52.6741 | 1.79305 | 0.896523 | − | 0.442997i | \(-0.146085\pi\) | ||||
0.896523 | + | 0.442997i | \(0.146085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.26068 | −0.314873 | ||||||||
\(866\) | 27.0817 | 0.920275 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.22548 | −0.177364 | ||||||||
\(869\) | −26.0522 | −0.883761 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.5523 | −0.391436 | ||||||||
\(872\) | −41.1453 | −1.39336 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −39.8483 | −1.34789 | ||||||||
\(875\) | 9.74285 | 0.329368 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.3389 | −1.26085 | −0.630423 | − | 0.776252i | \(-0.717118\pi\) | ||||
−0.630423 | + | 0.776252i | \(0.717118\pi\) | |||||||
\(878\) | 3.96039 | 0.133657 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.44593 | −0.251002 | ||||||||
\(881\) | 19.6295 | 0.661334 | 0.330667 | − | 0.943748i | \(-0.392726\pi\) | ||||
0.330667 | + | 0.943748i | \(0.392726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.8052 | 1.84434 | 0.922172 | − | 0.386781i | \(-0.126413\pi\) | ||||
0.922172 | + | 0.386781i | \(0.126413\pi\) | |||||||
\(884\) | 12.8515 | 0.432243 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.0897 | −0.708522 | ||||||||
\(887\) | −11.0653 | −0.371536 | −0.185768 | − | 0.982594i | \(-0.559477\pi\) | ||||
−0.185768 | + | 0.982594i | \(0.559477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 7.77035 | 0.260463 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.0886 | −0.404755 | ||||||||
\(893\) | −66.8095 | −2.23569 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.7805 | 0.594337 | ||||||||
\(896\) | −1.93108 | −0.0645128 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.2061 | 0.774396 | ||||||||
\(899\) | −55.9106 | −1.86472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.3243 | −0.410582 | ||||||||
\(902\) | 15.6273 | 0.520332 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.8349 | −0.925775 | ||||||||
\(905\) | 7.50863 | 0.249595 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1569 | 1.59902 | 0.799511 | − | 0.600651i | \(-0.205092\pi\) | ||||
0.799511 | + | 0.600651i | \(0.205092\pi\) | |||||||
\(908\) | −1.62100 | −0.0537946 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.59283 | 0.251700 | ||||||||
\(911\) | 19.6703 | 0.651705 | 0.325852 | − | 0.945421i | \(-0.394349\pi\) | ||||
0.325852 | + | 0.945421i | \(0.394349\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.4642 | −0.478694 | ||||||||
\(914\) | −34.9464 | −1.15593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.87743 | 0.128114 | ||||||||
\(917\) | −14.6257 | −0.482983 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.5830 | −1.66858 | −0.834290 | − | 0.551327i | \(-0.814122\pi\) | ||||
−0.834290 | + | 0.551327i | \(0.814122\pi\) | |||||||
\(920\) | 19.6488 | 0.647802 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.8475 | −1.24644 | ||||||||
\(923\) | 11.9706 | 0.394018 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.3243 | −0.734017 | ||||||||
\(926\) | −5.06651 | −0.166496 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.2543 | 0.960321 | ||||||||
\(929\) | −27.0185 | −0.886449 | −0.443225 | − | 0.896411i | \(-0.646166\pi\) | ||||
−0.443225 | + | 0.896411i | \(0.646166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.12147 | −0.200623 | ||||||||
\(932\) | −20.1556 | −0.660219 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40.1650 | −1.31424 | ||||||||
\(935\) | −10.7887 | −0.352827 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.2124 | −0.758317 | −0.379159 | − | 0.925332i | \(-0.623787\pi\) | ||||
−0.379159 | + | 0.925332i | \(0.623787\pi\) | |||||||
\(938\) | 2.17301 | 0.0709511 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.67780 | 0.283039 | ||||||||
\(941\) | 14.3851 | 0.468941 | 0.234471 | − | 0.972123i | \(-0.424664\pi\) | ||||
0.234471 | + | 0.972123i | \(0.424664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.3278 | −0.792223 | ||||||||
\(944\) | 16.0952 | 0.523853 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.4222 | −1.28172 | ||||||||
\(947\) | −4.40420 | −0.143117 | −0.0715586 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715586 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.74710 | 0.0891745 | ||||||||
\(950\) | −26.1180 | −0.847379 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.17698 | −0.297428 | ||||||||
\(953\) | 4.33111 | 0.140298 | 0.0701492 | − | 0.997537i | \(-0.477652\pi\) | ||||
0.0701492 | + | 0.997537i | \(0.477652\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.37372 | 0.173890 | ||||||||
\(956\) | −8.30907 | −0.268735 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.0104 | 0.614197 | ||||||||
\(959\) | 3.21791 | 0.103912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3758 | 0.721799 | ||||||||
\(962\) | −40.5074 | −1.30601 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.8032 | 0.412365 | ||||||||
\(965\) | −6.49015 | −0.208925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9148 | −0.511784 | −0.255892 | − | 0.966705i | \(-0.582369\pi\) | ||||
−0.255892 | + | 0.966705i | \(0.582369\pi\) | |||||||
\(968\) | −1.25209 | −0.0402437 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.76244 | 0.152913 | ||||||||
\(971\) | −25.9388 | −0.832415 | −0.416208 | − | 0.909270i | \(-0.636641\pi\) | ||||
−0.416208 | + | 0.909270i | \(0.636641\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.2380 | 0.648801 | ||||||||
\(974\) | −30.4182 | −0.974660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.89688 | 0.284782 | ||||||||
\(977\) | 15.3064 | 0.489694 | 0.244847 | − | 0.969562i | \(-0.421262\pi\) | ||||
0.244847 | + | 0.969562i | \(0.421262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0710 | −0.641473 | ||||||||
\(980\) | 0.795111 | 0.0253989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −46.2218 | −1.47500 | ||||||||
\(983\) | 58.9802 | 1.88118 | 0.940588 | − | 0.339551i | \(-0.110275\pi\) | ||||
0.940588 | + | 0.339551i | \(0.110275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.09242 | 0.225983 | ||||||||
\(986\) | −25.8650 | −0.823710 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.3833 | 0.839365 | ||||||||
\(989\) | 61.3706 | 1.95147 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5746 | 0.875936 | 0.437968 | − | 0.898991i | \(-0.355698\pi\) | ||||
0.437968 | + | 0.898991i | \(0.355698\pi\) | |||||||
\(992\) | −27.9280 | −0.886716 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.25169 | −0.0714191 | ||||||||
\(995\) | −13.9771 | −0.443103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.1943 | −1.27297 | −0.636483 | − | 0.771291i | \(-0.719611\pi\) | ||||
−0.636483 | + | 0.771291i | \(0.719611\pi\) | |||||||
\(998\) | −4.57658 | −0.144869 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.ba.1.14 | ✓ | 40 | |
3.2 | odd | 2 | inner | 8001.2.a.ba.1.27 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.ba.1.14 | ✓ | 40 | 1.1 | even | 1 | trivial | |
8001.2.a.ba.1.27 | yes | 40 | 3.2 | odd | 2 | inner |