Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.01040 | −0.583353 | −0.291676 | − | 0.956517i | \(-0.594213\pi\) | ||||
−0.291676 | + | 0.956517i | \(0.594213\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.91784 | −0.857682 | −0.428841 | − | 0.903380i | \(-0.641078\pi\) | ||||
−0.428841 | + | 0.903380i | \(0.641078\pi\) | |||||||
\(6\) | 1.01040 | 0.412493 | ||||||||
\(7\) | 4.92355 | 1.86093 | 0.930464 | − | 0.366383i | \(-0.119404\pi\) | ||||
0.930464 | + | 0.366383i | \(0.119404\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.97910 | −0.659699 | ||||||||
\(10\) | 1.91784 | 0.606473 | ||||||||
\(11\) | −0.589054 | −0.177607 | −0.0888033 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888033 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(12\) | −1.01040 | −0.291676 | ||||||||
\(13\) | 2.74206 | 0.760511 | 0.380255 | − | 0.924882i | \(-0.375836\pi\) | ||||
0.380255 | + | 0.924882i | \(0.375836\pi\) | |||||||
\(14\) | −4.92355 | −1.31588 | ||||||||
\(15\) | 1.93778 | 0.500332 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.63182 | −0.395774 | −0.197887 | − | 0.980225i | \(-0.563408\pi\) | ||||
−0.197887 | + | 0.980225i | \(0.563408\pi\) | |||||||
\(18\) | 1.97910 | 0.466478 | ||||||||
\(19\) | −1.23798 | −0.284013 | −0.142006 | − | 0.989866i | \(-0.545355\pi\) | ||||
−0.142006 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(20\) | −1.91784 | −0.428841 | ||||||||
\(21\) | −4.97474 | −1.08558 | ||||||||
\(22\) | 0.589054 | 0.125587 | ||||||||
\(23\) | 1.68163 | 0.350645 | 0.175322 | − | 0.984511i | \(-0.443903\pi\) | ||||
0.175322 | + | 0.984511i | \(0.443903\pi\) | |||||||
\(24\) | 1.01040 | 0.206246 | ||||||||
\(25\) | −1.32190 | −0.264381 | ||||||||
\(26\) | −2.74206 | −0.537762 | ||||||||
\(27\) | 5.03087 | 0.968190 | ||||||||
\(28\) | 4.92355 | 0.930464 | ||||||||
\(29\) | −7.46754 | −1.38669 | −0.693343 | − | 0.720607i | \(-0.743863\pi\) | ||||
−0.693343 | + | 0.720607i | \(0.743863\pi\) | |||||||
\(30\) | −1.93778 | −0.353788 | ||||||||
\(31\) | 1.54014 | 0.276618 | 0.138309 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138309 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.595179 | 0.103607 | ||||||||
\(34\) | 1.63182 | 0.279854 | ||||||||
\(35\) | −9.44257 | −1.59609 | ||||||||
\(36\) | −1.97910 | −0.329850 | ||||||||
\(37\) | 3.02720 | 0.497668 | 0.248834 | − | 0.968546i | \(-0.419953\pi\) | ||||
0.248834 | + | 0.968546i | \(0.419953\pi\) | |||||||
\(38\) | 1.23798 | 0.200827 | ||||||||
\(39\) | −2.77057 | −0.443646 | ||||||||
\(40\) | 1.91784 | 0.303237 | ||||||||
\(41\) | 5.29308 | 0.826639 | 0.413320 | − | 0.910586i | \(-0.364369\pi\) | ||||
0.413320 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(42\) | 4.97474 | 0.767620 | ||||||||
\(43\) | −9.29844 | −1.41800 | −0.708999 | − | 0.705209i | \(-0.750853\pi\) | ||||
−0.708999 | + | 0.705209i | \(0.750853\pi\) | |||||||
\(44\) | −0.589054 | −0.0888033 | ||||||||
\(45\) | 3.79559 | 0.565813 | ||||||||
\(46\) | −1.68163 | −0.247943 | ||||||||
\(47\) | −3.13361 | −0.457083 | −0.228542 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228542 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(48\) | −1.01040 | −0.145838 | ||||||||
\(49\) | 17.2414 | 2.46305 | ||||||||
\(50\) | 1.32190 | 0.186946 | ||||||||
\(51\) | 1.64878 | 0.230876 | ||||||||
\(52\) | 2.74206 | 0.380255 | ||||||||
\(53\) | −13.2036 | −1.81365 | −0.906826 | − | 0.421504i | \(-0.861502\pi\) | ||||
−0.906826 | + | 0.421504i | \(0.861502\pi\) | |||||||
\(54\) | −5.03087 | −0.684614 | ||||||||
\(55\) | 1.12971 | 0.152330 | ||||||||
\(56\) | −4.92355 | −0.657938 | ||||||||
\(57\) | 1.25085 | 0.165680 | ||||||||
\(58\) | 7.46754 | 0.980536 | ||||||||
\(59\) | −10.9069 | −1.41996 | −0.709980 | − | 0.704222i | \(-0.751296\pi\) | ||||
−0.709980 | + | 0.704222i | \(0.751296\pi\) | |||||||
\(60\) | 1.93778 | 0.250166 | ||||||||
\(61\) | 7.96946 | 1.02038 | 0.510192 | − | 0.860060i | \(-0.329574\pi\) | ||||
0.510192 | + | 0.860060i | \(0.329574\pi\) | |||||||
\(62\) | −1.54014 | −0.195598 | ||||||||
\(63\) | −9.74420 | −1.22765 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.25882 | −0.652277 | ||||||||
\(66\) | −0.595179 | −0.0732614 | ||||||||
\(67\) | 2.77260 | 0.338727 | 0.169363 | − | 0.985554i | \(-0.445829\pi\) | ||||
0.169363 | + | 0.985554i | \(0.445829\pi\) | |||||||
\(68\) | −1.63182 | −0.197887 | ||||||||
\(69\) | −1.69912 | −0.204550 | ||||||||
\(70\) | 9.44257 | 1.12860 | ||||||||
\(71\) | 2.80193 | 0.332528 | 0.166264 | − | 0.986081i | \(-0.446830\pi\) | ||||
0.166264 | + | 0.986081i | \(0.446830\pi\) | |||||||
\(72\) | 1.97910 | 0.233239 | ||||||||
\(73\) | 0.952283 | 0.111456 | 0.0557282 | − | 0.998446i | \(-0.482252\pi\) | ||||
0.0557282 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(74\) | −3.02720 | −0.351905 | ||||||||
\(75\) | 1.33565 | 0.154227 | ||||||||
\(76\) | −1.23798 | −0.142006 | ||||||||
\(77\) | −2.90024 | −0.330513 | ||||||||
\(78\) | 2.77057 | 0.313705 | ||||||||
\(79\) | −9.00919 | −1.01361 | −0.506807 | − | 0.862060i | \(-0.669174\pi\) | ||||
−0.506807 | + | 0.862060i | \(0.669174\pi\) | |||||||
\(80\) | −1.91784 | −0.214421 | ||||||||
\(81\) | 0.854123 | 0.0949026 | ||||||||
\(82\) | −5.29308 | −0.584522 | ||||||||
\(83\) | 3.06925 | 0.336894 | 0.168447 | − | 0.985711i | \(-0.446125\pi\) | ||||
0.168447 | + | 0.985711i | \(0.446125\pi\) | |||||||
\(84\) | −4.97474 | −0.542789 | ||||||||
\(85\) | 3.12956 | 0.339448 | ||||||||
\(86\) | 9.29844 | 1.00268 | ||||||||
\(87\) | 7.54518 | 0.808928 | ||||||||
\(88\) | 0.589054 | 0.0627934 | ||||||||
\(89\) | 13.9420 | 1.47784 | 0.738922 | − | 0.673791i | \(-0.235335\pi\) | ||||
0.738922 | + | 0.673791i | \(0.235335\pi\) | |||||||
\(90\) | −3.79559 | −0.400090 | ||||||||
\(91\) | 13.5007 | 1.41526 | ||||||||
\(92\) | 1.68163 | 0.175322 | ||||||||
\(93\) | −1.55615 | −0.161366 | ||||||||
\(94\) | 3.13361 | 0.323207 | ||||||||
\(95\) | 2.37425 | 0.243593 | ||||||||
\(96\) | 1.01040 | 0.103123 | ||||||||
\(97\) | −8.87552 | −0.901173 | −0.450586 | − | 0.892733i | \(-0.648785\pi\) | ||||
−0.450586 | + | 0.892733i | \(0.648785\pi\) | |||||||
\(98\) | −17.2414 | −1.74164 | ||||||||
\(99\) | 1.16580 | 0.117167 | ||||||||
\(100\) | −1.32190 | −0.132190 | ||||||||
\(101\) | 19.4019 | 1.93056 | 0.965282 | − | 0.261211i | \(-0.0841219\pi\) | ||||
0.965282 | + | 0.261211i | \(0.0841219\pi\) | |||||||
\(102\) | −1.64878 | −0.163254 | ||||||||
\(103\) | 1.25490 | 0.123649 | 0.0618245 | − | 0.998087i | \(-0.480308\pi\) | ||||
0.0618245 | + | 0.998087i | \(0.480308\pi\) | |||||||
\(104\) | −2.74206 | −0.268881 | ||||||||
\(105\) | 9.54074 | 0.931081 | ||||||||
\(106\) | 13.2036 | 1.28245 | ||||||||
\(107\) | −2.53644 | −0.245207 | −0.122603 | − | 0.992456i | \(-0.539124\pi\) | ||||
−0.122603 | + | 0.992456i | \(0.539124\pi\) | |||||||
\(108\) | 5.03087 | 0.484095 | ||||||||
\(109\) | 0.224723 | 0.0215246 | 0.0107623 | − | 0.999942i | \(-0.496574\pi\) | ||||
0.0107623 | + | 0.999942i | \(0.496574\pi\) | |||||||
\(110\) | −1.12971 | −0.107714 | ||||||||
\(111\) | −3.05867 | −0.290316 | ||||||||
\(112\) | 4.92355 | 0.465232 | ||||||||
\(113\) | −16.0607 | −1.51087 | −0.755434 | − | 0.655225i | \(-0.772574\pi\) | ||||
−0.755434 | + | 0.655225i | \(0.772574\pi\) | |||||||
\(114\) | −1.25085 | −0.117153 | ||||||||
\(115\) | −3.22510 | −0.300742 | ||||||||
\(116\) | −7.46754 | −0.693343 | ||||||||
\(117\) | −5.42681 | −0.501708 | ||||||||
\(118\) | 10.9069 | 1.00406 | ||||||||
\(119\) | −8.03434 | −0.736506 | ||||||||
\(120\) | −1.93778 | −0.176894 | ||||||||
\(121\) | −10.6530 | −0.968456 | ||||||||
\(122\) | −7.96946 | −0.721521 | ||||||||
\(123\) | −5.34811 | −0.482223 | ||||||||
\(124\) | 1.54014 | 0.138309 | ||||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 9.74420 | 0.868082 | ||||||||
\(127\) | −9.84140 | −0.873283 | −0.436641 | − | 0.899636i | \(-0.643832\pi\) | ||||
−0.436641 | + | 0.899636i | \(0.643832\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.39512 | 0.827194 | ||||||||
\(130\) | 5.25882 | 0.461229 | ||||||||
\(131\) | −14.5707 | −1.27305 | −0.636523 | − | 0.771258i | \(-0.719628\pi\) | ||||
−0.636523 | + | 0.771258i | \(0.719628\pi\) | |||||||
\(132\) | 0.595179 | 0.0518037 | ||||||||
\(133\) | −6.09527 | −0.528527 | ||||||||
\(134\) | −2.77260 | −0.239516 | ||||||||
\(135\) | −9.64838 | −0.830400 | ||||||||
\(136\) | 1.63182 | 0.139927 | ||||||||
\(137\) | 12.5220 | 1.06982 | 0.534912 | − | 0.844908i | \(-0.320345\pi\) | ||||
0.534912 | + | 0.844908i | \(0.320345\pi\) | |||||||
\(138\) | 1.69912 | 0.144639 | ||||||||
\(139\) | 11.1585 | 0.946455 | 0.473228 | − | 0.880940i | \(-0.343089\pi\) | ||||
0.473228 | + | 0.880940i | \(0.343089\pi\) | |||||||
\(140\) | −9.44257 | −0.798043 | ||||||||
\(141\) | 3.16619 | 0.266641 | ||||||||
\(142\) | −2.80193 | −0.235133 | ||||||||
\(143\) | −1.61522 | −0.135072 | ||||||||
\(144\) | −1.97910 | −0.164925 | ||||||||
\(145\) | 14.3215 | 1.18934 | ||||||||
\(146\) | −0.952283 | −0.0788115 | ||||||||
\(147\) | −17.4206 | −1.43683 | ||||||||
\(148\) | 3.02720 | 0.248834 | ||||||||
\(149\) | −6.36321 | −0.521294 | −0.260647 | − | 0.965434i | \(-0.583936\pi\) | ||||
−0.260647 | + | 0.965434i | \(0.583936\pi\) | |||||||
\(150\) | −1.33565 | −0.109055 | ||||||||
\(151\) | −12.0980 | −0.984522 | −0.492261 | − | 0.870448i | \(-0.663829\pi\) | ||||
−0.492261 | + | 0.870448i | \(0.663829\pi\) | |||||||
\(152\) | 1.23798 | 0.100414 | ||||||||
\(153\) | 3.22952 | 0.261092 | ||||||||
\(154\) | 2.90024 | 0.233708 | ||||||||
\(155\) | −2.95374 | −0.237250 | ||||||||
\(156\) | −2.77057 | −0.221823 | ||||||||
\(157\) | −6.06828 | −0.484302 | −0.242151 | − | 0.970239i | \(-0.577853\pi\) | ||||
−0.242151 | + | 0.970239i | \(0.577853\pi\) | |||||||
\(158\) | 9.00919 | 0.716733 | ||||||||
\(159\) | 13.3409 | 1.05800 | ||||||||
\(160\) | 1.91784 | 0.151618 | ||||||||
\(161\) | 8.27962 | 0.652525 | ||||||||
\(162\) | −0.854123 | −0.0671063 | ||||||||
\(163\) | 10.4152 | 0.815782 | 0.407891 | − | 0.913031i | \(-0.366264\pi\) | ||||
0.407891 | + | 0.913031i | \(0.366264\pi\) | |||||||
\(164\) | 5.29308 | 0.413320 | ||||||||
\(165\) | −1.14146 | −0.0888622 | ||||||||
\(166\) | −3.06925 | −0.238220 | ||||||||
\(167\) | 14.3386 | 1.10955 | 0.554776 | − | 0.832000i | \(-0.312804\pi\) | ||||
0.554776 | + | 0.832000i | \(0.312804\pi\) | |||||||
\(168\) | 4.97474 | 0.383810 | ||||||||
\(169\) | −5.48111 | −0.421624 | ||||||||
\(170\) | −3.12956 | −0.240026 | ||||||||
\(171\) | 2.45009 | 0.187363 | ||||||||
\(172\) | −9.29844 | −0.708999 | ||||||||
\(173\) | 7.72458 | 0.587289 | 0.293645 | − | 0.955915i | \(-0.405132\pi\) | ||||
0.293645 | + | 0.955915i | \(0.405132\pi\) | |||||||
\(174\) | −7.54518 | −0.571998 | ||||||||
\(175\) | −6.50847 | −0.491994 | ||||||||
\(176\) | −0.589054 | −0.0444016 | ||||||||
\(177\) | 11.0203 | 0.828338 | ||||||||
\(178\) | −13.9420 | −1.04499 | ||||||||
\(179\) | −26.4956 | −1.98038 | −0.990188 | − | 0.139739i | \(-0.955374\pi\) | ||||
−0.990188 | + | 0.139739i | \(0.955374\pi\) | |||||||
\(180\) | 3.79559 | 0.282906 | ||||||||
\(181\) | 11.5693 | 0.859943 | 0.429971 | − | 0.902843i | \(-0.358524\pi\) | ||||
0.429971 | + | 0.902843i | \(0.358524\pi\) | |||||||
\(182\) | −13.5007 | −1.00074 | ||||||||
\(183\) | −8.05232 | −0.595245 | ||||||||
\(184\) | −1.68163 | −0.123972 | ||||||||
\(185\) | −5.80567 | −0.426841 | ||||||||
\(186\) | 1.55615 | 0.114103 | ||||||||
\(187\) | 0.961228 | 0.0702920 | ||||||||
\(188\) | −3.13361 | −0.228542 | ||||||||
\(189\) | 24.7697 | 1.80173 | ||||||||
\(190\) | −2.37425 | −0.172246 | ||||||||
\(191\) | 21.4697 | 1.55349 | 0.776747 | − | 0.629813i | \(-0.216868\pi\) | ||||
0.776747 | + | 0.629813i | \(0.216868\pi\) | |||||||
\(192\) | −1.01040 | −0.0729191 | ||||||||
\(193\) | −4.65467 | −0.335050 | −0.167525 | − | 0.985868i | \(-0.553578\pi\) | ||||
−0.167525 | + | 0.985868i | \(0.553578\pi\) | |||||||
\(194\) | 8.87552 | 0.637225 | ||||||||
\(195\) | 5.31350 | 0.380507 | ||||||||
\(196\) | 17.2414 | 1.23153 | ||||||||
\(197\) | −19.6822 | −1.40230 | −0.701148 | − | 0.713016i | \(-0.747329\pi\) | ||||
−0.701148 | + | 0.713016i | \(0.747329\pi\) | |||||||
\(198\) | −1.16580 | −0.0828495 | ||||||||
\(199\) | 12.9398 | 0.917280 | 0.458640 | − | 0.888622i | \(-0.348337\pi\) | ||||
0.458640 | + | 0.888622i | \(0.348337\pi\) | |||||||
\(200\) | 1.32190 | 0.0934728 | ||||||||
\(201\) | −2.80143 | −0.197597 | ||||||||
\(202\) | −19.4019 | −1.36511 | ||||||||
\(203\) | −36.7668 | −2.58052 | ||||||||
\(204\) | 1.64878 | 0.115438 | ||||||||
\(205\) | −10.1513 | −0.708994 | ||||||||
\(206\) | −1.25490 | −0.0874330 | ||||||||
\(207\) | −3.32812 | −0.231320 | ||||||||
\(208\) | 2.74206 | 0.190128 | ||||||||
\(209\) | 0.729239 | 0.0504425 | ||||||||
\(210\) | −9.54074 | −0.658374 | ||||||||
\(211\) | −8.18019 | −0.563147 | −0.281574 | − | 0.959540i | \(-0.590856\pi\) | ||||
−0.281574 | + | 0.959540i | \(0.590856\pi\) | |||||||
\(212\) | −13.2036 | −0.906826 | ||||||||
\(213\) | −2.83106 | −0.193981 | ||||||||
\(214\) | 2.53644 | 0.173387 | ||||||||
\(215\) | 17.8329 | 1.21619 | ||||||||
\(216\) | −5.03087 | −0.342307 | ||||||||
\(217\) | 7.58297 | 0.514766 | ||||||||
\(218\) | −0.224723 | −0.0152202 | ||||||||
\(219\) | −0.962184 | −0.0650184 | ||||||||
\(220\) | 1.12971 | 0.0761650 | ||||||||
\(221\) | −4.47454 | −0.300990 | ||||||||
\(222\) | 3.05867 | 0.205285 | ||||||||
\(223\) | −2.90656 | −0.194638 | −0.0973190 | − | 0.995253i | \(-0.531027\pi\) | ||||
−0.0973190 | + | 0.995253i | \(0.531027\pi\) | |||||||
\(224\) | −4.92355 | −0.328969 | ||||||||
\(225\) | 2.61618 | 0.174412 | ||||||||
\(226\) | 16.0607 | 1.06834 | ||||||||
\(227\) | −15.2841 | −1.01444 | −0.507220 | − | 0.861817i | \(-0.669327\pi\) | ||||
−0.507220 | + | 0.861817i | \(0.669327\pi\) | |||||||
\(228\) | 1.25085 | 0.0828398 | ||||||||
\(229\) | −27.4284 | −1.81252 | −0.906259 | − | 0.422724i | \(-0.861074\pi\) | ||||
−0.906259 | + | 0.422724i | \(0.861074\pi\) | |||||||
\(230\) | 3.22510 | 0.212657 | ||||||||
\(231\) | 2.93039 | 0.192806 | ||||||||
\(232\) | 7.46754 | 0.490268 | ||||||||
\(233\) | 4.80887 | 0.315039 | 0.157520 | − | 0.987516i | \(-0.449650\pi\) | ||||
0.157520 | + | 0.987516i | \(0.449650\pi\) | |||||||
\(234\) | 5.42681 | 0.354761 | ||||||||
\(235\) | 6.00974 | 0.392032 | ||||||||
\(236\) | −10.9069 | −0.709980 | ||||||||
\(237\) | 9.10286 | 0.591294 | ||||||||
\(238\) | 8.03434 | 0.520789 | ||||||||
\(239\) | −13.9477 | −0.902200 | −0.451100 | − | 0.892473i | \(-0.648968\pi\) | ||||
−0.451100 | + | 0.892473i | \(0.648968\pi\) | |||||||
\(240\) | 1.93778 | 0.125083 | ||||||||
\(241\) | 2.26986 | 0.146214 | 0.0731072 | − | 0.997324i | \(-0.476708\pi\) | ||||
0.0731072 | + | 0.997324i | \(0.476708\pi\) | |||||||
\(242\) | 10.6530 | 0.684802 | ||||||||
\(243\) | −15.9556 | −1.02355 | ||||||||
\(244\) | 7.96946 | 0.510192 | ||||||||
\(245\) | −33.0661 | −2.11252 | ||||||||
\(246\) | 5.34811 | 0.340983 | ||||||||
\(247\) | −3.39462 | −0.215995 | ||||||||
\(248\) | −1.54014 | −0.0977991 | ||||||||
\(249\) | −3.10117 | −0.196528 | ||||||||
\(250\) | −12.1244 | −0.766813 | ||||||||
\(251\) | −23.3456 | −1.47356 | −0.736782 | − | 0.676130i | \(-0.763656\pi\) | ||||
−0.736782 | + | 0.676130i | \(0.763656\pi\) | |||||||
\(252\) | −9.74420 | −0.613827 | ||||||||
\(253\) | −0.990574 | −0.0622768 | ||||||||
\(254\) | 9.84140 | 0.617504 | ||||||||
\(255\) | −3.16209 | −0.198018 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.6872 | −1.41519 | −0.707594 | − | 0.706619i | \(-0.750219\pi\) | ||||
−0.707594 | + | 0.706619i | \(0.750219\pi\) | |||||||
\(258\) | −9.39512 | −0.584914 | ||||||||
\(259\) | 14.9046 | 0.926125 | ||||||||
\(260\) | −5.25882 | −0.326138 | ||||||||
\(261\) | 14.7790 | 0.914796 | ||||||||
\(262\) | 14.5707 | 0.900179 | ||||||||
\(263\) | −2.12047 | −0.130754 | −0.0653769 | − | 0.997861i | \(-0.520825\pi\) | ||||
−0.0653769 | + | 0.997861i | \(0.520825\pi\) | |||||||
\(264\) | −0.595179 | −0.0366307 | ||||||||
\(265\) | 25.3223 | 1.55554 | ||||||||
\(266\) | 6.09527 | 0.373725 | ||||||||
\(267\) | −14.0869 | −0.862105 | ||||||||
\(268\) | 2.77260 | 0.169363 | ||||||||
\(269\) | −28.4298 | −1.73339 | −0.866697 | − | 0.498835i | \(-0.833761\pi\) | ||||
−0.866697 | + | 0.498835i | \(0.833761\pi\) | |||||||
\(270\) | 9.64838 | 0.587181 | ||||||||
\(271\) | −16.4021 | −0.996359 | −0.498180 | − | 0.867074i | \(-0.665998\pi\) | ||||
−0.498180 | + | 0.867074i | \(0.665998\pi\) | |||||||
\(272\) | −1.63182 | −0.0989434 | ||||||||
\(273\) | −13.6410 | −0.825594 | ||||||||
\(274\) | −12.5220 | −0.756480 | ||||||||
\(275\) | 0.778673 | 0.0469558 | ||||||||
\(276\) | −1.69912 | −0.102275 | ||||||||
\(277\) | 3.09097 | 0.185719 | 0.0928593 | − | 0.995679i | \(-0.470399\pi\) | ||||
0.0928593 | + | 0.995679i | \(0.470399\pi\) | |||||||
\(278\) | −11.1585 | −0.669245 | ||||||||
\(279\) | −3.04809 | −0.182484 | ||||||||
\(280\) | 9.44257 | 0.564301 | ||||||||
\(281\) | 9.46291 | 0.564510 | 0.282255 | − | 0.959339i | \(-0.408918\pi\) | ||||
0.282255 | + | 0.959339i | \(0.408918\pi\) | |||||||
\(282\) | −3.16619 | −0.188544 | ||||||||
\(283\) | −7.00252 | −0.416256 | −0.208128 | − | 0.978102i | \(-0.566737\pi\) | ||||
−0.208128 | + | 0.978102i | \(0.566737\pi\) | |||||||
\(284\) | 2.80193 | 0.166264 | ||||||||
\(285\) | −2.39893 | −0.142100 | ||||||||
\(286\) | 1.61522 | 0.0955101 | ||||||||
\(287\) | 26.0607 | 1.53832 | ||||||||
\(288\) | 1.97910 | 0.116619 | ||||||||
\(289\) | −14.3372 | −0.843363 | ||||||||
\(290\) | −14.3215 | −0.840988 | ||||||||
\(291\) | 8.96780 | 0.525702 | ||||||||
\(292\) | 0.952283 | 0.0557282 | ||||||||
\(293\) | −11.8399 | −0.691696 | −0.345848 | − | 0.938291i | \(-0.612409\pi\) | ||||
−0.345848 | + | 0.938291i | \(0.612409\pi\) | |||||||
\(294\) | 17.4206 | 1.01599 | ||||||||
\(295\) | 20.9177 | 1.21787 | ||||||||
\(296\) | −3.02720 | −0.175952 | ||||||||
\(297\) | −2.96345 | −0.171957 | ||||||||
\(298\) | 6.36321 | 0.368611 | ||||||||
\(299\) | 4.61114 | 0.266669 | ||||||||
\(300\) | 1.33565 | 0.0771137 | ||||||||
\(301\) | −45.7814 | −2.63879 | ||||||||
\(302\) | 12.0980 | 0.696162 | ||||||||
\(303\) | −19.6036 | −1.12620 | ||||||||
\(304\) | −1.23798 | −0.0710032 | ||||||||
\(305\) | −15.2841 | −0.875166 | ||||||||
\(306\) | −3.22952 | −0.184620 | ||||||||
\(307\) | −5.64301 | −0.322063 | −0.161032 | − | 0.986949i | \(-0.551482\pi\) | ||||
−0.161032 | + | 0.986949i | \(0.551482\pi\) | |||||||
\(308\) | −2.90024 | −0.165257 | ||||||||
\(309\) | −1.26795 | −0.0721310 | ||||||||
\(310\) | 2.95374 | 0.167761 | ||||||||
\(311\) | 9.93607 | 0.563423 | 0.281711 | − | 0.959499i | \(-0.409098\pi\) | ||||
0.281711 | + | 0.959499i | \(0.409098\pi\) | |||||||
\(312\) | 2.77057 | 0.156853 | ||||||||
\(313\) | −25.7823 | −1.45730 | −0.728651 | − | 0.684885i | \(-0.759852\pi\) | ||||
−0.728651 | + | 0.684885i | \(0.759852\pi\) | |||||||
\(314\) | 6.06828 | 0.342453 | ||||||||
\(315\) | 18.6878 | 1.05294 | ||||||||
\(316\) | −9.00919 | −0.506807 | ||||||||
\(317\) | 5.29714 | 0.297517 | 0.148758 | − | 0.988874i | \(-0.452472\pi\) | ||||
0.148758 | + | 0.988874i | \(0.452472\pi\) | |||||||
\(318\) | −13.3409 | −0.748119 | ||||||||
\(319\) | 4.39879 | 0.246285 | ||||||||
\(320\) | −1.91784 | −0.107210 | ||||||||
\(321\) | 2.56281 | 0.143042 | ||||||||
\(322\) | −8.27962 | −0.461405 | ||||||||
\(323\) | 2.02016 | 0.112405 | ||||||||
\(324\) | 0.854123 | 0.0474513 | ||||||||
\(325\) | −3.62474 | −0.201064 | ||||||||
\(326\) | −10.4152 | −0.576845 | ||||||||
\(327\) | −0.227060 | −0.0125564 | ||||||||
\(328\) | −5.29308 | −0.292261 | ||||||||
\(329\) | −15.4285 | −0.850599 | ||||||||
\(330\) | 1.14146 | 0.0628350 | ||||||||
\(331\) | −12.5579 | −0.690246 | −0.345123 | − | 0.938557i | \(-0.612163\pi\) | ||||
−0.345123 | + | 0.938557i | \(0.612163\pi\) | |||||||
\(332\) | 3.06925 | 0.168447 | ||||||||
\(333\) | −5.99112 | −0.328311 | ||||||||
\(334\) | −14.3386 | −0.784571 | ||||||||
\(335\) | −5.31739 | −0.290520 | ||||||||
\(336\) | −4.97474 | −0.271395 | ||||||||
\(337\) | 24.9458 | 1.35888 | 0.679441 | − | 0.733730i | \(-0.262222\pi\) | ||||
0.679441 | + | 0.733730i | \(0.262222\pi\) | |||||||
\(338\) | 5.48111 | 0.298133 | ||||||||
\(339\) | 16.2277 | 0.881369 | ||||||||
\(340\) | 3.12956 | 0.169724 | ||||||||
\(341\) | −0.907227 | −0.0491291 | ||||||||
\(342\) | −2.45009 | −0.132486 | ||||||||
\(343\) | 50.4240 | 2.72264 | ||||||||
\(344\) | 9.29844 | 0.501338 | ||||||||
\(345\) | 3.25863 | 0.175439 | ||||||||
\(346\) | −7.72458 | −0.415276 | ||||||||
\(347\) | −28.8371 | −1.54806 | −0.774028 | − | 0.633151i | \(-0.781761\pi\) | ||||
−0.774028 | + | 0.633151i | \(0.781761\pi\) | |||||||
\(348\) | 7.54518 | 0.404464 | ||||||||
\(349\) | 32.0778 | 1.71709 | 0.858543 | − | 0.512741i | \(-0.171370\pi\) | ||||
0.858543 | + | 0.512741i | \(0.171370\pi\) | |||||||
\(350\) | 6.50847 | 0.347892 | ||||||||
\(351\) | 13.7949 | 0.736319 | ||||||||
\(352\) | 0.589054 | 0.0313967 | ||||||||
\(353\) | −21.1127 | −1.12372 | −0.561859 | − | 0.827233i | \(-0.689914\pi\) | ||||
−0.561859 | + | 0.827233i | \(0.689914\pi\) | |||||||
\(354\) | −11.0203 | −0.585723 | ||||||||
\(355\) | −5.37365 | −0.285204 | ||||||||
\(356\) | 13.9420 | 0.738922 | ||||||||
\(357\) | 8.11787 | 0.429643 | ||||||||
\(358\) | 26.4956 | 1.40034 | ||||||||
\(359\) | 12.9014 | 0.680910 | 0.340455 | − | 0.940261i | \(-0.389419\pi\) | ||||
0.340455 | + | 0.940261i | \(0.389419\pi\) | |||||||
\(360\) | −3.79559 | −0.200045 | ||||||||
\(361\) | −17.4674 | −0.919337 | ||||||||
\(362\) | −11.5693 | −0.608071 | ||||||||
\(363\) | 10.7638 | 0.564952 | ||||||||
\(364\) | 13.5007 | 0.707628 | ||||||||
\(365\) | −1.82632 | −0.0955941 | ||||||||
\(366\) | 8.05232 | 0.420901 | ||||||||
\(367\) | −6.91139 | −0.360772 | −0.180386 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180386 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(368\) | 1.68163 | 0.0876612 | ||||||||
\(369\) | −10.4755 | −0.545334 | ||||||||
\(370\) | 5.80567 | 0.301822 | ||||||||
\(371\) | −65.0086 | −3.37508 | ||||||||
\(372\) | −1.55615 | −0.0806828 | ||||||||
\(373\) | −13.5218 | −0.700132 | −0.350066 | − | 0.936725i | \(-0.613841\pi\) | ||||
−0.350066 | + | 0.936725i | \(0.613841\pi\) | |||||||
\(374\) | −0.961228 | −0.0497039 | ||||||||
\(375\) | −12.2504 | −0.632610 | ||||||||
\(376\) | 3.13361 | 0.161603 | ||||||||
\(377\) | −20.4764 | −1.05459 | ||||||||
\(378\) | −24.7697 | −1.27402 | ||||||||
\(379\) | 16.9666 | 0.871517 | 0.435759 | − | 0.900064i | \(-0.356480\pi\) | ||||
0.435759 | + | 0.900064i | \(0.356480\pi\) | |||||||
\(380\) | 2.37425 | 0.121796 | ||||||||
\(381\) | 9.94372 | 0.509432 | ||||||||
\(382\) | −21.4697 | −1.09849 | ||||||||
\(383\) | 20.5382 | 1.04945 | 0.524727 | − | 0.851271i | \(-0.324168\pi\) | ||||
0.524727 | + | 0.851271i | \(0.324168\pi\) | |||||||
\(384\) | 1.01040 | 0.0515616 | ||||||||
\(385\) | 5.56219 | 0.283475 | ||||||||
\(386\) | 4.65467 | 0.236916 | ||||||||
\(387\) | 18.4025 | 0.935453 | ||||||||
\(388\) | −8.87552 | −0.450586 | ||||||||
\(389\) | −10.0617 | −0.510146 | −0.255073 | − | 0.966922i | \(-0.582100\pi\) | ||||
−0.255073 | + | 0.966922i | \(0.582100\pi\) | |||||||
\(390\) | −5.31350 | −0.269059 | ||||||||
\(391\) | −2.74412 | −0.138776 | ||||||||
\(392\) | −17.2414 | −0.870821 | ||||||||
\(393\) | 14.7222 | 0.742635 | ||||||||
\(394\) | 19.6822 | 0.991573 | ||||||||
\(395\) | 17.2782 | 0.869358 | ||||||||
\(396\) | 1.16580 | 0.0585835 | ||||||||
\(397\) | −22.9490 | −1.15178 | −0.575889 | − | 0.817528i | \(-0.695344\pi\) | ||||
−0.575889 | + | 0.817528i | \(0.695344\pi\) | |||||||
\(398\) | −12.9398 | −0.648615 | ||||||||
\(399\) | 6.15864 | 0.308318 | ||||||||
\(400\) | −1.32190 | −0.0660952 | ||||||||
\(401\) | −2.94535 | −0.147084 | −0.0735418 | − | 0.997292i | \(-0.523430\pi\) | ||||
−0.0735418 | + | 0.997292i | \(0.523430\pi\) | |||||||
\(402\) | 2.80143 | 0.139722 | ||||||||
\(403\) | 4.22316 | 0.210371 | ||||||||
\(404\) | 19.4019 | 0.965282 | ||||||||
\(405\) | −1.63807 | −0.0813963 | ||||||||
\(406\) | 36.7668 | 1.82471 | ||||||||
\(407\) | −1.78318 | −0.0883891 | ||||||||
\(408\) | −1.64878 | −0.0816269 | ||||||||
\(409\) | −11.2664 | −0.557088 | −0.278544 | − | 0.960423i | \(-0.589852\pi\) | ||||
−0.278544 | + | 0.960423i | \(0.589852\pi\) | |||||||
\(410\) | 10.1513 | 0.501335 | ||||||||
\(411\) | −12.6522 | −0.624085 | ||||||||
\(412\) | 1.25490 | 0.0618245 | ||||||||
\(413\) | −53.7008 | −2.64244 | ||||||||
\(414\) | 3.32812 | 0.163568 | ||||||||
\(415\) | −5.88633 | −0.288948 | ||||||||
\(416\) | −2.74206 | −0.134441 | ||||||||
\(417\) | −11.2746 | −0.552118 | ||||||||
\(418\) | −0.729239 | −0.0356682 | ||||||||
\(419\) | −37.6652 | −1.84007 | −0.920033 | − | 0.391841i | \(-0.871838\pi\) | ||||
−0.920033 | + | 0.391841i | \(0.871838\pi\) | |||||||
\(420\) | 9.54074 | 0.465541 | ||||||||
\(421\) | −7.13465 | −0.347722 | −0.173861 | − | 0.984770i | \(-0.555624\pi\) | ||||
−0.173861 | + | 0.984770i | \(0.555624\pi\) | |||||||
\(422\) | 8.18019 | 0.398205 | ||||||||
\(423\) | 6.20171 | 0.301538 | ||||||||
\(424\) | 13.2036 | 0.641223 | ||||||||
\(425\) | 2.15711 | 0.104635 | ||||||||
\(426\) | 2.83106 | 0.137166 | ||||||||
\(427\) | 39.2381 | 1.89886 | ||||||||
\(428\) | −2.53644 | −0.122603 | ||||||||
\(429\) | 1.63202 | 0.0787945 | ||||||||
\(430\) | −17.8329 | −0.859978 | ||||||||
\(431\) | 34.1950 | 1.64711 | 0.823557 | − | 0.567233i | \(-0.191986\pi\) | ||||
0.823557 | + | 0.567233i | \(0.191986\pi\) | |||||||
\(432\) | 5.03087 | 0.242048 | ||||||||
\(433\) | −9.54238 | −0.458577 | −0.229289 | − | 0.973358i | \(-0.573640\pi\) | ||||
−0.229289 | + | 0.973358i | \(0.573640\pi\) | |||||||
\(434\) | −7.58297 | −0.363994 | ||||||||
\(435\) | −14.4704 | −0.693803 | ||||||||
\(436\) | 0.224723 | 0.0107623 | ||||||||
\(437\) | −2.08183 | −0.0995876 | ||||||||
\(438\) | 0.962184 | 0.0459749 | ||||||||
\(439\) | −13.2757 | −0.633614 | −0.316807 | − | 0.948490i | \(-0.602611\pi\) | ||||
−0.316807 | + | 0.948490i | \(0.602611\pi\) | |||||||
\(440\) | −1.12971 | −0.0538568 | ||||||||
\(441\) | −34.1224 | −1.62488 | ||||||||
\(442\) | 4.47454 | 0.212832 | ||||||||
\(443\) | −1.32775 | −0.0630835 | −0.0315418 | − | 0.999502i | \(-0.510042\pi\) | ||||
−0.0315418 | + | 0.999502i | \(0.510042\pi\) | |||||||
\(444\) | −3.05867 | −0.145158 | ||||||||
\(445\) | −26.7384 | −1.26752 | ||||||||
\(446\) | 2.90656 | 0.137630 | ||||||||
\(447\) | 6.42936 | 0.304098 | ||||||||
\(448\) | 4.92355 | 0.232616 | ||||||||
\(449\) | −1.61845 | −0.0763793 | −0.0381896 | − | 0.999271i | \(-0.512159\pi\) | ||||
−0.0381896 | + | 0.999271i | \(0.512159\pi\) | |||||||
\(450\) | −2.61618 | −0.123328 | ||||||||
\(451\) | −3.11791 | −0.146817 | ||||||||
\(452\) | −16.0607 | −0.755434 | ||||||||
\(453\) | 12.2238 | 0.574324 | ||||||||
\(454\) | 15.2841 | 0.717318 | ||||||||
\(455\) | −25.8921 | −1.21384 | ||||||||
\(456\) | −1.25085 | −0.0585766 | ||||||||
\(457\) | −3.08609 | −0.144361 | −0.0721807 | − | 0.997392i | \(-0.522996\pi\) | ||||
−0.0721807 | + | 0.997392i | \(0.522996\pi\) | |||||||
\(458\) | 27.4284 | 1.28164 | ||||||||
\(459\) | −8.20945 | −0.383184 | ||||||||
\(460\) | −3.22510 | −0.150371 | ||||||||
\(461\) | 5.52833 | 0.257480 | 0.128740 | − | 0.991678i | \(-0.458907\pi\) | ||||
0.128740 | + | 0.991678i | \(0.458907\pi\) | |||||||
\(462\) | −2.93039 | −0.136334 | ||||||||
\(463\) | −1.80724 | −0.0839896 | −0.0419948 | − | 0.999118i | \(-0.513371\pi\) | ||||
−0.0419948 | + | 0.999118i | \(0.513371\pi\) | |||||||
\(464\) | −7.46754 | −0.346672 | ||||||||
\(465\) | 2.98445 | 0.138401 | ||||||||
\(466\) | −4.80887 | −0.222766 | ||||||||
\(467\) | −25.9918 | −1.20276 | −0.601378 | − | 0.798965i | \(-0.705381\pi\) | ||||
−0.601378 | + | 0.798965i | \(0.705381\pi\) | |||||||
\(468\) | −5.42681 | −0.250854 | ||||||||
\(469\) | 13.6510 | 0.630347 | ||||||||
\(470\) | −6.00974 | −0.277209 | ||||||||
\(471\) | 6.13137 | 0.282519 | ||||||||
\(472\) | 10.9069 | 0.502032 | ||||||||
\(473\) | 5.47729 | 0.251846 | ||||||||
\(474\) | −9.10286 | −0.418108 | ||||||||
\(475\) | 1.63649 | 0.0750875 | ||||||||
\(476\) | −8.03434 | −0.368253 | ||||||||
\(477\) | 26.1312 | 1.19647 | ||||||||
\(478\) | 13.9477 | 0.637952 | ||||||||
\(479\) | −13.5652 | −0.619812 | −0.309906 | − | 0.950767i | \(-0.600298\pi\) | ||||
−0.309906 | + | 0.950767i | \(0.600298\pi\) | |||||||
\(480\) | −1.93778 | −0.0884470 | ||||||||
\(481\) | 8.30076 | 0.378482 | ||||||||
\(482\) | −2.26986 | −0.103389 | ||||||||
\(483\) | −8.36570 | −0.380652 | ||||||||
\(484\) | −10.6530 | −0.484228 | ||||||||
\(485\) | 17.0218 | 0.772920 | ||||||||
\(486\) | 15.9556 | 0.723761 | ||||||||
\(487\) | 17.3330 | 0.785432 | 0.392716 | − | 0.919660i | \(-0.371536\pi\) | ||||
0.392716 | + | 0.919660i | \(0.371536\pi\) | |||||||
\(488\) | −7.96946 | −0.360761 | ||||||||
\(489\) | −10.5235 | −0.475889 | ||||||||
\(490\) | 33.0661 | 1.49378 | ||||||||
\(491\) | −6.48844 | −0.292819 | −0.146410 | − | 0.989224i | \(-0.546772\pi\) | ||||
−0.146410 | + | 0.989224i | \(0.546772\pi\) | |||||||
\(492\) | −5.34811 | −0.241111 | ||||||||
\(493\) | 12.1856 | 0.548814 | ||||||||
\(494\) | 3.39462 | 0.152731 | ||||||||
\(495\) | −2.23581 | −0.100492 | ||||||||
\(496\) | 1.54014 | 0.0691544 | ||||||||
\(497\) | 13.7955 | 0.618811 | ||||||||
\(498\) | 3.10117 | 0.138967 | ||||||||
\(499\) | 24.4381 | 1.09400 | 0.547001 | − | 0.837132i | \(-0.315769\pi\) | ||||
0.547001 | + | 0.837132i | \(0.315769\pi\) | |||||||
\(500\) | 12.1244 | 0.542219 | ||||||||
\(501\) | −14.4876 | −0.647260 | ||||||||
\(502\) | 23.3456 | 1.04197 | ||||||||
\(503\) | 1.99699 | 0.0890413 | 0.0445206 | − | 0.999008i | \(-0.485824\pi\) | ||||
0.0445206 | + | 0.999008i | \(0.485824\pi\) | |||||||
\(504\) | 9.74420 | 0.434041 | ||||||||
\(505\) | −37.2097 | −1.65581 | ||||||||
\(506\) | 0.990574 | 0.0440364 | ||||||||
\(507\) | 5.53809 | 0.245955 | ||||||||
\(508\) | −9.84140 | −0.436641 | ||||||||
\(509\) | 25.4817 | 1.12946 | 0.564728 | − | 0.825277i | \(-0.308981\pi\) | ||||
0.564728 | + | 0.825277i | \(0.308981\pi\) | |||||||
\(510\) | 3.16209 | 0.140020 | ||||||||
\(511\) | 4.68862 | 0.207412 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.22812 | −0.274978 | ||||||||
\(514\) | 22.6872 | 1.00069 | ||||||||
\(515\) | −2.40669 | −0.106052 | ||||||||
\(516\) | 9.39512 | 0.413597 | ||||||||
\(517\) | 1.84586 | 0.0811810 | ||||||||
\(518\) | −14.9046 | −0.654869 | ||||||||
\(519\) | −7.80490 | −0.342597 | ||||||||
\(520\) | 5.25882 | 0.230615 | ||||||||
\(521\) | 43.5402 | 1.90753 | 0.953765 | − | 0.300554i | \(-0.0971717\pi\) | ||||
0.953765 | + | 0.300554i | \(0.0971717\pi\) | |||||||
\(522\) | −14.7790 | −0.646859 | ||||||||
\(523\) | −8.51651 | −0.372401 | −0.186201 | − | 0.982512i | \(-0.559617\pi\) | ||||
−0.186201 | + | 0.982512i | \(0.559617\pi\) | |||||||
\(524\) | −14.5707 | −0.636523 | ||||||||
\(525\) | 6.57613 | 0.287006 | ||||||||
\(526\) | 2.12047 | 0.0924569 | ||||||||
\(527\) | −2.51323 | −0.109478 | ||||||||
\(528\) | 0.595179 | 0.0259018 | ||||||||
\(529\) | −20.1721 | −0.877048 | ||||||||
\(530\) | −25.3223 | −1.09993 | ||||||||
\(531\) | 21.5859 | 0.936747 | ||||||||
\(532\) | −6.09527 | −0.264264 | ||||||||
\(533\) | 14.5139 | 0.628668 | ||||||||
\(534\) | 14.0869 | 0.609600 | ||||||||
\(535\) | 4.86448 | 0.210310 | ||||||||
\(536\) | −2.77260 | −0.119758 | ||||||||
\(537\) | 26.7711 | 1.15526 | ||||||||
\(538\) | 28.4298 | 1.22569 | ||||||||
\(539\) | −10.1561 | −0.437455 | ||||||||
\(540\) | −9.64838 | −0.415200 | ||||||||
\(541\) | 8.66645 | 0.372600 | 0.186300 | − | 0.982493i | \(-0.440350\pi\) | ||||
0.186300 | + | 0.982493i | \(0.440350\pi\) | |||||||
\(542\) | 16.4021 | 0.704532 | ||||||||
\(543\) | −11.6896 | −0.501650 | ||||||||
\(544\) | 1.63182 | 0.0699636 | ||||||||
\(545\) | −0.430983 | −0.0184613 | ||||||||
\(546\) | 13.6410 | 0.583783 | ||||||||
\(547\) | −5.21352 | −0.222914 | −0.111457 | − | 0.993769i | \(-0.535552\pi\) | ||||
−0.111457 | + | 0.993769i | \(0.535552\pi\) | |||||||
\(548\) | 12.5220 | 0.534912 | ||||||||
\(549\) | −15.7723 | −0.673147 | ||||||||
\(550\) | −0.778673 | −0.0332027 | ||||||||
\(551\) | 9.24468 | 0.393837 | ||||||||
\(552\) | 1.69912 | 0.0723193 | ||||||||
\(553\) | −44.3572 | −1.88626 | ||||||||
\(554\) | −3.09097 | −0.131323 | ||||||||
\(555\) | 5.86603 | 0.248999 | ||||||||
\(556\) | 11.1585 | 0.473228 | ||||||||
\(557\) | 36.7210 | 1.55592 | 0.777959 | − | 0.628315i | \(-0.216255\pi\) | ||||
0.777959 | + | 0.628315i | \(0.216255\pi\) | |||||||
\(558\) | 3.04809 | 0.129036 | ||||||||
\(559\) | −25.4969 | −1.07840 | ||||||||
\(560\) | −9.44257 | −0.399021 | ||||||||
\(561\) | −0.971222 | −0.0410050 | ||||||||
\(562\) | −9.46291 | −0.399169 | ||||||||
\(563\) | 13.4193 | 0.565556 | 0.282778 | − | 0.959185i | \(-0.408744\pi\) | ||||
0.282778 | + | 0.959185i | \(0.408744\pi\) | |||||||
\(564\) | 3.16619 | 0.133320 | ||||||||
\(565\) | 30.8019 | 1.29584 | ||||||||
\(566\) | 7.00252 | 0.294338 | ||||||||
\(567\) | 4.20532 | 0.176607 | ||||||||
\(568\) | −2.80193 | −0.117566 | ||||||||
\(569\) | 29.1981 | 1.22405 | 0.612024 | − | 0.790839i | \(-0.290355\pi\) | ||||
0.612024 | + | 0.790839i | \(0.290355\pi\) | |||||||
\(570\) | 2.39893 | 0.100480 | ||||||||
\(571\) | −14.7944 | −0.619128 | −0.309564 | − | 0.950879i | \(-0.600183\pi\) | ||||
−0.309564 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(572\) | −1.61522 | −0.0675358 | ||||||||
\(573\) | −21.6929 | −0.906235 | ||||||||
\(574\) | −26.0607 | −1.08775 | ||||||||
\(575\) | −2.22296 | −0.0927038 | ||||||||
\(576\) | −1.97910 | −0.0824624 | ||||||||
\(577\) | −1.18517 | −0.0493393 | −0.0246697 | − | 0.999696i | \(-0.507853\pi\) | ||||
−0.0246697 | + | 0.999696i | \(0.507853\pi\) | |||||||
\(578\) | 14.3372 | 0.596348 | ||||||||
\(579\) | 4.70306 | 0.195453 | ||||||||
\(580\) | 14.3215 | 0.594668 | ||||||||
\(581\) | 15.1116 | 0.626936 | ||||||||
\(582\) | −8.96780 | −0.371727 | ||||||||
\(583\) | 7.77763 | 0.322117 | ||||||||
\(584\) | −0.952283 | −0.0394058 | ||||||||
\(585\) | 10.4077 | 0.430306 | ||||||||
\(586\) | 11.8399 | 0.489103 | ||||||||
\(587\) | 32.0501 | 1.32285 | 0.661425 | − | 0.750012i | \(-0.269952\pi\) | ||||
0.661425 | + | 0.750012i | \(0.269952\pi\) | |||||||
\(588\) | −17.4206 | −0.718415 | ||||||||
\(589\) | −1.90667 | −0.0785629 | ||||||||
\(590\) | −20.9177 | −0.861167 | ||||||||
\(591\) | 19.8868 | 0.818033 | ||||||||
\(592\) | 3.02720 | 0.124417 | ||||||||
\(593\) | 17.8899 | 0.734650 | 0.367325 | − | 0.930093i | \(-0.380274\pi\) | ||||
0.367325 | + | 0.930093i | \(0.380274\pi\) | |||||||
\(594\) | 2.96345 | 0.121592 | ||||||||
\(595\) | 15.4085 | 0.631689 | ||||||||
\(596\) | −6.36321 | −0.260647 | ||||||||
\(597\) | −13.0744 | −0.535098 | ||||||||
\(598\) | −4.61114 | −0.188564 | ||||||||
\(599\) | −45.7826 | −1.87063 | −0.935313 | − | 0.353822i | \(-0.884882\pi\) | ||||
−0.935313 | + | 0.353822i | \(0.884882\pi\) | |||||||
\(600\) | −1.33565 | −0.0545276 | ||||||||
\(601\) | −34.2047 | −1.39524 | −0.697620 | − | 0.716468i | \(-0.745758\pi\) | ||||
−0.697620 | + | 0.716468i | \(0.745758\pi\) | |||||||
\(602\) | 45.7814 | 1.86591 | ||||||||
\(603\) | −5.48725 | −0.223458 | ||||||||
\(604\) | −12.0980 | −0.492261 | ||||||||
\(605\) | 20.4307 | 0.830628 | ||||||||
\(606\) | 19.6036 | 0.796344 | ||||||||
\(607\) | −18.1883 | −0.738239 | −0.369119 | − | 0.929382i | \(-0.620341\pi\) | ||||
−0.369119 | + | 0.929382i | \(0.620341\pi\) | |||||||
\(608\) | 1.23798 | 0.0502068 | ||||||||
\(609\) | 37.1491 | 1.50536 | ||||||||
\(610\) | 15.2841 | 0.618836 | ||||||||
\(611\) | −8.59253 | −0.347617 | ||||||||
\(612\) | 3.22952 | 0.130546 | ||||||||
\(613\) | −29.6645 | −1.19814 | −0.599069 | − | 0.800698i | \(-0.704462\pi\) | ||||
−0.599069 | + | 0.800698i | \(0.704462\pi\) | |||||||
\(614\) | 5.64301 | 0.227733 | ||||||||
\(615\) | 10.2568 | 0.413594 | ||||||||
\(616\) | 2.90024 | 0.116854 | ||||||||
\(617\) | 17.1785 | 0.691580 | 0.345790 | − | 0.938312i | \(-0.387611\pi\) | ||||
0.345790 | + | 0.938312i | \(0.387611\pi\) | |||||||
\(618\) | 1.26795 | 0.0510043 | ||||||||
\(619\) | −35.8224 | −1.43983 | −0.719913 | − | 0.694065i | \(-0.755818\pi\) | ||||
−0.719913 | + | 0.694065i | \(0.755818\pi\) | |||||||
\(620\) | −2.95374 | −0.118625 | ||||||||
\(621\) | 8.46007 | 0.339491 | ||||||||
\(622\) | −9.93607 | −0.398400 | ||||||||
\(623\) | 68.6439 | 2.75016 | ||||||||
\(624\) | −2.77057 | −0.110912 | ||||||||
\(625\) | −16.6430 | −0.665722 | ||||||||
\(626\) | 25.7823 | 1.03047 | ||||||||
\(627\) | −0.736821 | −0.0294258 | ||||||||
\(628\) | −6.06828 | −0.242151 | ||||||||
\(629\) | −4.93983 | −0.196964 | ||||||||
\(630\) | −18.6878 | −0.744539 | ||||||||
\(631\) | 14.7580 | 0.587508 | 0.293754 | − | 0.955881i | \(-0.405095\pi\) | ||||
0.293754 | + | 0.955881i | \(0.405095\pi\) | |||||||
\(632\) | 9.00919 | 0.358366 | ||||||||
\(633\) | 8.26524 | 0.328514 | ||||||||
\(634\) | −5.29714 | −0.210376 | ||||||||
\(635\) | 18.8742 | 0.748999 | ||||||||
\(636\) | 13.3409 | 0.529000 | ||||||||
\(637\) | 47.2769 | 1.87318 | ||||||||
\(638\) | −4.39879 | −0.174150 | ||||||||
\(639\) | −5.54530 | −0.219369 | ||||||||
\(640\) | 1.91784 | 0.0758091 | ||||||||
\(641\) | −38.0087 | −1.50125 | −0.750627 | − | 0.660726i | \(-0.770249\pi\) | ||||
−0.750627 | + | 0.660726i | \(0.770249\pi\) | |||||||
\(642\) | −2.56281 | −0.101146 | ||||||||
\(643\) | 24.2289 | 0.955495 | 0.477748 | − | 0.878497i | \(-0.341453\pi\) | ||||
0.477748 | + | 0.878497i | \(0.341453\pi\) | |||||||
\(644\) | 8.27962 | 0.326263 | ||||||||
\(645\) | −18.0183 | −0.709470 | ||||||||
\(646\) | −2.02016 | −0.0794821 | ||||||||
\(647\) | −31.5069 | −1.23866 | −0.619331 | − | 0.785130i | \(-0.712596\pi\) | ||||
−0.619331 | + | 0.785130i | \(0.712596\pi\) | |||||||
\(648\) | −0.854123 | −0.0335531 | ||||||||
\(649\) | 6.42477 | 0.252194 | ||||||||
\(650\) | 3.62474 | 0.142174 | ||||||||
\(651\) | −7.66181 | −0.300290 | ||||||||
\(652\) | 10.4152 | 0.407891 | ||||||||
\(653\) | 14.0442 | 0.549594 | 0.274797 | − | 0.961502i | \(-0.411389\pi\) | ||||
0.274797 | + | 0.961502i | \(0.411389\pi\) | |||||||
\(654\) | 0.227060 | 0.00887874 | ||||||||
\(655\) | 27.9442 | 1.09187 | ||||||||
\(656\) | 5.29308 | 0.206660 | ||||||||
\(657\) | −1.88466 | −0.0735277 | ||||||||
\(658\) | 15.4285 | 0.601465 | ||||||||
\(659\) | −47.7699 | −1.86085 | −0.930425 | − | 0.366483i | \(-0.880562\pi\) | ||||
−0.930425 | + | 0.366483i | \(0.880562\pi\) | |||||||
\(660\) | −1.14146 | −0.0444311 | ||||||||
\(661\) | −14.1247 | −0.549389 | −0.274695 | − | 0.961532i | \(-0.588577\pi\) | ||||
−0.274695 | + | 0.961532i | \(0.588577\pi\) | |||||||
\(662\) | 12.5579 | 0.488078 | ||||||||
\(663\) | 4.52106 | 0.175583 | ||||||||
\(664\) | −3.06925 | −0.119110 | ||||||||
\(665\) | 11.6897 | 0.453308 | ||||||||
\(666\) | 5.99112 | 0.232151 | ||||||||
\(667\) | −12.5577 | −0.486235 | ||||||||
\(668\) | 14.3386 | 0.554776 | ||||||||
\(669\) | 2.93678 | 0.113543 | ||||||||
\(670\) | 5.31739 | 0.205429 | ||||||||
\(671\) | −4.69445 | −0.181227 | ||||||||
\(672\) | 4.97474 | 0.191905 | ||||||||
\(673\) | −45.2810 | −1.74546 | −0.872728 | − | 0.488207i | \(-0.837651\pi\) | ||||
−0.872728 | + | 0.488207i | \(0.837651\pi\) | |||||||
\(674\) | −24.9458 | −0.960875 | ||||||||
\(675\) | −6.65032 | −0.255971 | ||||||||
\(676\) | −5.48111 | −0.210812 | ||||||||
\(677\) | −4.74458 | −0.182349 | −0.0911746 | − | 0.995835i | \(-0.529062\pi\) | ||||
−0.0911746 | + | 0.995835i | \(0.529062\pi\) | |||||||
\(678\) | −16.2277 | −0.623222 | ||||||||
\(679\) | −43.6991 | −1.67702 | ||||||||
\(680\) | −3.12956 | −0.120013 | ||||||||
\(681\) | 15.4430 | 0.591777 | ||||||||
\(682\) | 0.907227 | 0.0347395 | ||||||||
\(683\) | 41.8833 | 1.60262 | 0.801311 | − | 0.598248i | \(-0.204136\pi\) | ||||
0.801311 | + | 0.598248i | \(0.204136\pi\) | |||||||
\(684\) | 2.45009 | 0.0936815 | ||||||||
\(685\) | −24.0151 | −0.917569 | ||||||||
\(686\) | −50.4240 | −1.92520 | ||||||||
\(687\) | 27.7135 | 1.05734 | ||||||||
\(688\) | −9.29844 | −0.354500 | ||||||||
\(689\) | −36.2050 | −1.37930 | ||||||||
\(690\) | −3.25863 | −0.124054 | ||||||||
\(691\) | 18.4628 | 0.702357 | 0.351178 | − | 0.936309i | \(-0.385781\pi\) | ||||
0.351178 | + | 0.936309i | \(0.385781\pi\) | |||||||
\(692\) | 7.72458 | 0.293645 | ||||||||
\(693\) | 5.73986 | 0.218039 | ||||||||
\(694\) | 28.8371 | 1.09464 | ||||||||
\(695\) | −21.4003 | −0.811758 | ||||||||
\(696\) | −7.54518 | −0.285999 | ||||||||
\(697\) | −8.63733 | −0.327162 | ||||||||
\(698\) | −32.0778 | −1.21416 | ||||||||
\(699\) | −4.85886 | −0.183779 | ||||||||
\(700\) | −6.50847 | −0.245997 | ||||||||
\(701\) | 16.6555 | 0.629068 | 0.314534 | − | 0.949246i | \(-0.398152\pi\) | ||||
0.314534 | + | 0.949246i | \(0.398152\pi\) | |||||||
\(702\) | −13.7949 | −0.520656 | ||||||||
\(703\) | −3.74762 | −0.141344 | ||||||||
\(704\) | −0.589054 | −0.0222008 | ||||||||
\(705\) | −6.07222 | −0.228693 | ||||||||
\(706\) | 21.1127 | 0.794588 | ||||||||
\(707\) | 95.5264 | 3.59264 | ||||||||
\(708\) | 11.0203 | 0.414169 | ||||||||
\(709\) | 27.0443 | 1.01567 | 0.507835 | − | 0.861455i | \(-0.330446\pi\) | ||||
0.507835 | + | 0.861455i | \(0.330446\pi\) | |||||||
\(710\) | 5.37365 | 0.201669 | ||||||||
\(711\) | 17.8301 | 0.668680 | ||||||||
\(712\) | −13.9420 | −0.522497 | ||||||||
\(713\) | 2.58995 | 0.0969946 | ||||||||
\(714\) | −8.11787 | −0.303804 | ||||||||
\(715\) | 3.09773 | 0.115849 | ||||||||
\(716\) | −26.4956 | −0.990188 | ||||||||
\(717\) | 14.0927 | 0.526301 | ||||||||
\(718\) | −12.9014 | −0.481476 | ||||||||
\(719\) | −16.6817 | −0.622124 | −0.311062 | − | 0.950390i | \(-0.600685\pi\) | ||||
−0.311062 | + | 0.950390i | \(0.600685\pi\) | |||||||
\(720\) | 3.79559 | 0.141453 | ||||||||
\(721\) | 6.17857 | 0.230102 | ||||||||
\(722\) | 17.4674 | 0.650069 | ||||||||
\(723\) | −2.29346 | −0.0852946 | ||||||||
\(724\) | 11.5693 | 0.429971 | ||||||||
\(725\) | 9.87137 | 0.366613 | ||||||||
\(726\) | −10.7638 | −0.399481 | ||||||||
\(727\) | 25.8999 | 0.960574 | 0.480287 | − | 0.877112i | \(-0.340533\pi\) | ||||
0.480287 | + | 0.877112i | \(0.340533\pi\) | |||||||
\(728\) | −13.5007 | −0.500368 | ||||||||
\(729\) | 13.5591 | 0.502190 | ||||||||
\(730\) | 1.82632 | 0.0675952 | ||||||||
\(731\) | 15.1733 | 0.561207 | ||||||||
\(732\) | −8.05232 | −0.297622 | ||||||||
\(733\) | 16.0897 | 0.594287 | 0.297143 | − | 0.954833i | \(-0.403966\pi\) | ||||
0.297143 | + | 0.954833i | \(0.403966\pi\) | |||||||
\(734\) | 6.91139 | 0.255104 | ||||||||
\(735\) | 33.4099 | 1.23234 | ||||||||
\(736\) | −1.68163 | −0.0619859 | ||||||||
\(737\) | −1.63321 | −0.0601601 | ||||||||
\(738\) | 10.4755 | 0.385609 | ||||||||
\(739\) | −52.3111 | −1.92429 | −0.962147 | − | 0.272531i | \(-0.912139\pi\) | ||||
−0.962147 | + | 0.272531i | \(0.912139\pi\) | |||||||
\(740\) | −5.80567 | −0.213421 | ||||||||
\(741\) | 3.42992 | 0.126001 | ||||||||
\(742\) | 65.0086 | 2.38654 | ||||||||
\(743\) | 33.3998 | 1.22532 | 0.612659 | − | 0.790347i | \(-0.290100\pi\) | ||||
0.612659 | + | 0.790347i | \(0.290100\pi\) | |||||||
\(744\) | 1.55615 | 0.0570514 | ||||||||
\(745\) | 12.2036 | 0.447105 | ||||||||
\(746\) | 13.5218 | 0.495068 | ||||||||
\(747\) | −6.07436 | −0.222249 | ||||||||
\(748\) | 0.961228 | 0.0351460 | ||||||||
\(749\) | −12.4883 | −0.456313 | ||||||||
\(750\) | 12.2504 | 0.447323 | ||||||||
\(751\) | 19.9295 | 0.727237 | 0.363619 | − | 0.931548i | \(-0.381541\pi\) | ||||
0.363619 | + | 0.931548i | \(0.381541\pi\) | |||||||
\(752\) | −3.13361 | −0.114271 | ||||||||
\(753\) | 23.5884 | 0.859608 | ||||||||
\(754\) | 20.4764 | 0.745708 | ||||||||
\(755\) | 23.2020 | 0.844407 | ||||||||
\(756\) | 24.7697 | 0.900867 | ||||||||
\(757\) | 2.43071 | 0.0883457 | 0.0441729 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441729 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(758\) | −16.9666 | −0.616256 | ||||||||
\(759\) | 1.00087 | 0.0363294 | ||||||||
\(760\) | −2.37425 | −0.0861230 | ||||||||
\(761\) | −46.5808 | −1.68855 | −0.844276 | − | 0.535908i | \(-0.819969\pi\) | ||||
−0.844276 | + | 0.535908i | \(0.819969\pi\) | |||||||
\(762\) | −9.94372 | −0.360223 | ||||||||
\(763\) | 1.10644 | 0.0400557 | ||||||||
\(764\) | 21.4697 | 0.776747 | ||||||||
\(765\) | −6.19370 | −0.223934 | ||||||||
\(766\) | −20.5382 | −0.742076 | ||||||||
\(767\) | −29.9074 | −1.07989 | ||||||||
\(768\) | −1.01040 | −0.0364596 | ||||||||
\(769\) | 45.7293 | 1.64904 | 0.824520 | − | 0.565833i | \(-0.191445\pi\) | ||||
0.824520 | + | 0.565833i | \(0.191445\pi\) | |||||||
\(770\) | −5.56219 | −0.200447 | ||||||||
\(771\) | 22.9231 | 0.825554 | ||||||||
\(772\) | −4.65467 | −0.167525 | ||||||||
\(773\) | −41.4701 | −1.49158 | −0.745788 | − | 0.666183i | \(-0.767927\pi\) | ||||
−0.745788 | + | 0.666183i | \(0.767927\pi\) | |||||||
\(774\) | −18.4025 | −0.661465 | ||||||||
\(775\) | −2.03592 | −0.0731324 | ||||||||
\(776\) | 8.87552 | 0.318613 | ||||||||
\(777\) | −15.0595 | −0.540258 | ||||||||
\(778\) | 10.0617 | 0.360728 | ||||||||
\(779\) | −6.55273 | −0.234776 | ||||||||
\(780\) | 5.31350 | 0.190254 | ||||||||
\(781\) | −1.65049 | −0.0590592 | ||||||||
\(782\) | 2.74412 | 0.0981295 | ||||||||
\(783\) | −37.5682 | −1.34258 | ||||||||
\(784\) | 17.2414 | 0.615764 | ||||||||
\(785\) | 11.6380 | 0.415377 | ||||||||
\(786\) | −14.7222 | −0.525122 | ||||||||
\(787\) | −52.9062 | −1.88590 | −0.942950 | − | 0.332933i | \(-0.891962\pi\) | ||||
−0.942950 | + | 0.332933i | \(0.891962\pi\) | |||||||
\(788\) | −19.6822 | −0.701148 | ||||||||
\(789\) | 2.14252 | 0.0762756 | ||||||||
\(790\) | −17.2782 | −0.614729 | ||||||||
\(791\) | −79.0759 | −2.81162 | ||||||||
\(792\) | −1.16580 | −0.0414248 | ||||||||
\(793\) | 21.8527 | 0.776014 | ||||||||
\(794\) | 22.9490 | 0.814430 | ||||||||
\(795\) | −25.5856 | −0.907428 | ||||||||
\(796\) | 12.9398 | 0.458640 | ||||||||
\(797\) | −7.15087 | −0.253297 | −0.126648 | − | 0.991948i | \(-0.540422\pi\) | ||||
−0.126648 | + | 0.991948i | \(0.540422\pi\) | |||||||
\(798\) | −6.15864 | −0.218014 | ||||||||
\(799\) | 5.11347 | 0.180902 | ||||||||
\(800\) | 1.32190 | 0.0467364 | ||||||||
\(801\) | −27.5925 | −0.974933 | ||||||||
\(802\) | 2.94535 | 0.104004 | ||||||||
\(803\) | −0.560946 | −0.0197954 | ||||||||
\(804\) | −2.80143 | −0.0987987 | ||||||||
\(805\) | −15.8789 | −0.559659 | ||||||||
\(806\) | −4.22316 | −0.148754 | ||||||||
\(807\) | 28.7254 | 1.01118 | ||||||||
\(808\) | −19.4019 | −0.682557 | ||||||||
\(809\) | −15.3286 | −0.538924 | −0.269462 | − | 0.963011i | \(-0.586846\pi\) | ||||
−0.269462 | + | 0.963011i | \(0.586846\pi\) | |||||||
\(810\) | 1.63807 | 0.0575559 | ||||||||
\(811\) | −10.5619 | −0.370878 | −0.185439 | − | 0.982656i | \(-0.559371\pi\) | ||||
−0.185439 | + | 0.982656i | \(0.559371\pi\) | |||||||
\(812\) | −36.7668 | −1.29026 | ||||||||
\(813\) | 16.5727 | 0.581229 | ||||||||
\(814\) | 1.78318 | 0.0625006 | ||||||||
\(815\) | −19.9747 | −0.699682 | ||||||||
\(816\) | 1.64878 | 0.0577189 | ||||||||
\(817\) | 11.5113 | 0.402730 | ||||||||
\(818\) | 11.2664 | 0.393921 | ||||||||
\(819\) | −26.7192 | −0.933643 | ||||||||
\(820\) | −10.1513 | −0.354497 | ||||||||
\(821\) | −11.8945 | −0.415122 | −0.207561 | − | 0.978222i | \(-0.566553\pi\) | ||||
−0.207561 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(822\) | 12.6522 | 0.441295 | ||||||||
\(823\) | 46.2657 | 1.61272 | 0.806360 | − | 0.591424i | \(-0.201434\pi\) | ||||
0.806360 | + | 0.591424i | \(0.201434\pi\) | |||||||
\(824\) | −1.25490 | −0.0437165 | ||||||||
\(825\) | −0.786769 | −0.0273918 | ||||||||
\(826\) | 53.7008 | 1.86849 | ||||||||
\(827\) | 50.4903 | 1.75572 | 0.877859 | − | 0.478919i | \(-0.158971\pi\) | ||||
0.877859 | + | 0.478919i | \(0.158971\pi\) | |||||||
\(828\) | −3.32812 | −0.115660 | ||||||||
\(829\) | −54.9080 | −1.90703 | −0.953516 | − | 0.301342i | \(-0.902565\pi\) | ||||
−0.953516 | + | 0.301342i | \(0.902565\pi\) | |||||||
\(830\) | 5.88633 | 0.204317 | ||||||||
\(831\) | −3.12311 | −0.108339 | ||||||||
\(832\) | 2.74206 | 0.0950638 | ||||||||
\(833\) | −28.1348 | −0.974812 | ||||||||
\(834\) | 11.2746 | 0.390406 | ||||||||
\(835\) | −27.4990 | −0.951643 | ||||||||
\(836\) | 0.729239 | 0.0252213 | ||||||||
\(837\) | 7.74825 | 0.267819 | ||||||||
\(838\) | 37.6652 | 1.30112 | ||||||||
\(839\) | −1.23023 | −0.0424722 | −0.0212361 | − | 0.999774i | \(-0.506760\pi\) | ||||
−0.0212361 | + | 0.999774i | \(0.506760\pi\) | |||||||
\(840\) | −9.54074 | −0.329187 | ||||||||
\(841\) | 26.7641 | 0.922900 | ||||||||
\(842\) | 7.13465 | 0.245876 | ||||||||
\(843\) | −9.56129 | −0.329308 | ||||||||
\(844\) | −8.18019 | −0.281574 | ||||||||
\(845\) | 10.5119 | 0.361619 | ||||||||
\(846\) | −6.20171 | −0.213219 | ||||||||
\(847\) | −52.4507 | −1.80223 | ||||||||
\(848\) | −13.2036 | −0.453413 | ||||||||
\(849\) | 7.07532 | 0.242824 | ||||||||
\(850\) | −2.15711 | −0.0739881 | ||||||||
\(851\) | 5.09064 | 0.174505 | ||||||||
\(852\) | −2.83106 | −0.0969907 | ||||||||
\(853\) | 39.3405 | 1.34699 | 0.673497 | − | 0.739190i | \(-0.264791\pi\) | ||||
0.673497 | + | 0.739190i | \(0.264791\pi\) | |||||||
\(854\) | −39.2381 | −1.34270 | ||||||||
\(855\) | −4.69887 | −0.160698 | ||||||||
\(856\) | 2.53644 | 0.0866937 | ||||||||
\(857\) | 11.0738 | 0.378273 | 0.189137 | − | 0.981951i | \(-0.439431\pi\) | ||||
0.189137 | + | 0.981951i | \(0.439431\pi\) | |||||||
\(858\) | −1.63202 | −0.0557161 | ||||||||
\(859\) | −8.72568 | −0.297716 | −0.148858 | − | 0.988859i | \(-0.547560\pi\) | ||||
−0.148858 | + | 0.988859i | \(0.547560\pi\) | |||||||
\(860\) | 17.8329 | 0.608096 | ||||||||
\(861\) | −26.3317 | −0.897382 | ||||||||
\(862\) | −34.1950 | −1.16469 | ||||||||
\(863\) | 16.7026 | 0.568562 | 0.284281 | − | 0.958741i | \(-0.408245\pi\) | ||||
0.284281 | + | 0.958741i | \(0.408245\pi\) | |||||||
\(864\) | −5.03087 | −0.171154 | ||||||||
\(865\) | −14.8145 | −0.503708 | ||||||||
\(866\) | 9.54238 | 0.324263 | ||||||||
\(867\) | 14.4862 | 0.491978 | ||||||||
\(868\) | 7.58297 | 0.257383 | ||||||||
\(869\) | 5.30690 | 0.180024 | ||||||||
\(870\) | 14.4704 | 0.490593 | ||||||||
\(871\) | 7.60263 | 0.257605 | ||||||||
\(872\) | −0.224723 | −0.00761009 | ||||||||
\(873\) | 17.5655 | 0.594503 | ||||||||
\(874\) | 2.08183 | 0.0704191 | ||||||||
\(875\) | 59.6950 | 2.01806 | ||||||||
\(876\) | −0.962184 | −0.0325092 | ||||||||
\(877\) | 4.38034 | 0.147914 | 0.0739568 | − | 0.997261i | \(-0.476437\pi\) | ||||
0.0739568 | + | 0.997261i | \(0.476437\pi\) | |||||||
\(878\) | 13.2757 | 0.448032 | ||||||||
\(879\) | 11.9630 | 0.403503 | ||||||||
\(880\) | 1.12971 | 0.0380825 | ||||||||
\(881\) | 33.3166 | 1.12246 | 0.561232 | − | 0.827659i | \(-0.310328\pi\) | ||||
0.561232 | + | 0.827659i | \(0.310328\pi\) | |||||||
\(882\) | 34.1224 | 1.14896 | ||||||||
\(883\) | 37.6755 | 1.26788 | 0.633941 | − | 0.773381i | \(-0.281436\pi\) | ||||
0.633941 | + | 0.773381i | \(0.281436\pi\) | |||||||
\(884\) | −4.47454 | −0.150495 | ||||||||
\(885\) | −21.1352 | −0.710451 | ||||||||
\(886\) | 1.32775 | 0.0446068 | ||||||||
\(887\) | 23.2146 | 0.779470 | 0.389735 | − | 0.920927i | \(-0.372567\pi\) | ||||
0.389735 | + | 0.920927i | \(0.372567\pi\) | |||||||
\(888\) | 3.05867 | 0.102642 | ||||||||
\(889\) | −48.4546 | −1.62512 | ||||||||
\(890\) | 26.7384 | 0.896272 | ||||||||
\(891\) | −0.503125 | −0.0168553 | ||||||||
\(892\) | −2.90656 | −0.0973190 | ||||||||
\(893\) | 3.87935 | 0.129817 | ||||||||
\(894\) | −6.42936 | −0.215030 | ||||||||
\(895\) | 50.8143 | 1.69853 | ||||||||
\(896\) | −4.92355 | −0.164484 | ||||||||
\(897\) | −4.65908 | −0.155562 | ||||||||
\(898\) | 1.61845 | 0.0540083 | ||||||||
\(899\) | −11.5011 | −0.383582 | ||||||||
\(900\) | 2.61618 | 0.0872059 | ||||||||
\(901\) | 21.5458 | 0.717796 | ||||||||
\(902\) | 3.11791 | 0.103815 | ||||||||
\(903\) | 46.2574 | 1.53935 | ||||||||
\(904\) | 16.0607 | 0.534172 | ||||||||
\(905\) | −22.1881 | −0.737558 | ||||||||
\(906\) | −12.2238 | −0.406108 | ||||||||
\(907\) | 31.3556 | 1.04115 | 0.520573 | − | 0.853817i | \(-0.325718\pi\) | ||||
0.520573 | + | 0.853817i | \(0.325718\pi\) | |||||||
\(908\) | −15.2841 | −0.507220 | ||||||||
\(909\) | −38.3983 | −1.27359 | ||||||||
\(910\) | 25.8921 | 0.858315 | ||||||||
\(911\) | 53.3962 | 1.76910 | 0.884548 | − | 0.466450i | \(-0.154467\pi\) | ||||
0.884548 | + | 0.466450i | \(0.154467\pi\) | |||||||
\(912\) | 1.25085 | 0.0414199 | ||||||||
\(913\) | −1.80796 | −0.0598347 | ||||||||
\(914\) | 3.08609 | 0.102079 | ||||||||
\(915\) | 15.4430 | 0.510531 | ||||||||
\(916\) | −27.4284 | −0.906259 | ||||||||
\(917\) | −71.7395 | −2.36905 | ||||||||
\(918\) | 8.20945 | 0.270952 | ||||||||
\(919\) | 22.0206 | 0.726392 | 0.363196 | − | 0.931713i | \(-0.381686\pi\) | ||||
0.363196 | + | 0.931713i | \(0.381686\pi\) | |||||||
\(920\) | 3.22510 | 0.106328 | ||||||||
\(921\) | 5.70168 | 0.187877 | ||||||||
\(922\) | −5.52833 | −0.182066 | ||||||||
\(923\) | 7.68307 | 0.252891 | ||||||||
\(924\) | 2.93039 | 0.0964029 | ||||||||
\(925\) | −4.00167 | −0.131574 | ||||||||
\(926\) | 1.80724 | 0.0593896 | ||||||||
\(927\) | −2.48357 | −0.0815712 | ||||||||
\(928\) | 7.46754 | 0.245134 | ||||||||
\(929\) | 41.3847 | 1.35779 | 0.678894 | − | 0.734236i | \(-0.262459\pi\) | ||||
0.678894 | + | 0.734236i | \(0.262459\pi\) | |||||||
\(930\) | −2.98445 | −0.0978639 | ||||||||
\(931\) | −21.3445 | −0.699539 | ||||||||
\(932\) | 4.80887 | 0.157520 | ||||||||
\(933\) | −10.0394 | −0.328674 | ||||||||
\(934\) | 25.9918 | 0.850477 | ||||||||
\(935\) | −1.84348 | −0.0602882 | ||||||||
\(936\) | 5.42681 | 0.177381 | ||||||||
\(937\) | 26.5907 | 0.868679 | 0.434339 | − | 0.900749i | \(-0.356982\pi\) | ||||
0.434339 | + | 0.900749i | \(0.356982\pi\) | |||||||
\(938\) | −13.6510 | −0.445722 | ||||||||
\(939\) | 26.0504 | 0.850121 | ||||||||
\(940\) | 6.00974 | 0.196016 | ||||||||
\(941\) | 12.5119 | 0.407878 | 0.203939 | − | 0.978984i | \(-0.434626\pi\) | ||||
0.203939 | + | 0.978984i | \(0.434626\pi\) | |||||||
\(942\) | −6.13137 | −0.199771 | ||||||||
\(943\) | 8.90102 | 0.289857 | ||||||||
\(944\) | −10.9069 | −0.354990 | ||||||||
\(945\) | −47.5043 | −1.54531 | ||||||||
\(946\) | −5.47729 | −0.178082 | ||||||||
\(947\) | 10.4645 | 0.340050 | 0.170025 | − | 0.985440i | \(-0.445615\pi\) | ||||
0.170025 | + | 0.985440i | \(0.445615\pi\) | |||||||
\(948\) | 9.10286 | 0.295647 | ||||||||
\(949\) | 2.61122 | 0.0847637 | ||||||||
\(950\) | −1.63649 | −0.0530949 | ||||||||
\(951\) | −5.35221 | −0.173557 | ||||||||
\(952\) | 8.03434 | 0.260394 | ||||||||
\(953\) | −34.9366 | −1.13171 | −0.565854 | − | 0.824505i | \(-0.691454\pi\) | ||||
−0.565854 | + | 0.824505i | \(0.691454\pi\) | |||||||
\(954\) | −26.1312 | −0.846029 | ||||||||
\(955\) | −41.1754 | −1.33240 | ||||||||
\(956\) | −13.9477 | −0.451100 | ||||||||
\(957\) | −4.44452 | −0.143671 | ||||||||
\(958\) | 13.5652 | 0.438273 | ||||||||
\(959\) | 61.6526 | 1.99087 | ||||||||
\(960\) | 1.93778 | 0.0625414 | ||||||||
\(961\) | −28.6280 | −0.923483 | ||||||||
\(962\) | −8.30076 | −0.267627 | ||||||||
\(963\) | 5.01986 | 0.161763 | ||||||||
\(964\) | 2.26986 | 0.0731072 | ||||||||
\(965\) | 8.92689 | 0.287367 | ||||||||
\(966\) | 8.36570 | 0.269162 | ||||||||
\(967\) | 25.3003 | 0.813602 | 0.406801 | − | 0.913517i | \(-0.366644\pi\) | ||||
0.406801 | + | 0.913517i | \(0.366644\pi\) | |||||||
\(968\) | 10.6530 | 0.342401 | ||||||||
\(969\) | −2.04116 | −0.0655716 | ||||||||
\(970\) | −17.0218 | −0.546537 | ||||||||
\(971\) | −21.9834 | −0.705482 | −0.352741 | − | 0.935721i | \(-0.614750\pi\) | ||||
−0.352741 | + | 0.935721i | \(0.614750\pi\) | |||||||
\(972\) | −15.9556 | −0.511776 | ||||||||
\(973\) | 54.9397 | 1.76129 | ||||||||
\(974\) | −17.3330 | −0.555384 | ||||||||
\(975\) | 3.66243 | 0.117292 | ||||||||
\(976\) | 7.96946 | 0.255096 | ||||||||
\(977\) | −10.7079 | −0.342577 | −0.171289 | − | 0.985221i | \(-0.554793\pi\) | ||||
−0.171289 | + | 0.985221i | \(0.554793\pi\) | |||||||
\(978\) | 10.5235 | 0.336504 | ||||||||
\(979\) | −8.21257 | −0.262475 | ||||||||
\(980\) | −33.0661 | −1.05626 | ||||||||
\(981\) | −0.444750 | −0.0141998 | ||||||||
\(982\) | 6.48844 | 0.207054 | ||||||||
\(983\) | −16.5144 | −0.526728 | −0.263364 | − | 0.964697i | \(-0.584832\pi\) | ||||
−0.263364 | + | 0.964697i | \(0.584832\pi\) | |||||||
\(984\) | 5.34811 | 0.170491 | ||||||||
\(985\) | 37.7471 | 1.20272 | ||||||||
\(986\) | −12.1856 | −0.388070 | ||||||||
\(987\) | 15.5889 | 0.496200 | ||||||||
\(988\) | −3.39462 | −0.107997 | ||||||||
\(989\) | −15.6366 | −0.497214 | ||||||||
\(990\) | 2.23581 | 0.0710586 | ||||||||
\(991\) | 24.0186 | 0.762977 | 0.381488 | − | 0.924374i | \(-0.375412\pi\) | ||||
0.381488 | + | 0.924374i | \(0.375412\pi\) | |||||||
\(992\) | −1.54014 | −0.0488995 | ||||||||
\(993\) | 12.6885 | 0.402657 | ||||||||
\(994\) | −13.7955 | −0.437566 | ||||||||
\(995\) | −24.8165 | −0.786735 | ||||||||
\(996\) | −3.10117 | −0.0982642 | ||||||||
\(997\) | −2.89432 | −0.0916641 | −0.0458320 | − | 0.998949i | \(-0.514594\pi\) | ||||
−0.0458320 | + | 0.998949i | \(0.514594\pi\) | |||||||
\(998\) | −24.4381 | −0.773576 | ||||||||
\(999\) | 15.2294 | 0.481838 |
(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 | 4006.2.a.g.1.13 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.13 | ✓ | 40 | 1.1 | even | 1 | trivial |