Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.138768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 11x^{2} + 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 966) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.47903\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.47903 | 0.661442 | 0.330721 | − | 0.943729i | \(-0.392708\pi\) | ||||
0.330721 | + | 0.943729i | \(0.392708\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.47903 | −0.467710 | ||||||||
\(11\) | 5.70448 | 1.71996 | 0.859982 | − | 0.510324i | \(-0.170474\pi\) | ||||
0.859982 | + | 0.510324i | \(0.170474\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 6.35023 | 1.76124 | 0.880618 | − | 0.473826i | \(-0.157128\pi\) | ||||
0.880618 | + | 0.473826i | \(0.157128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.47903 | −0.381884 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.12478 | −1.00041 | −0.500203 | − | 0.865908i | \(-0.666741\pi\) | ||||
−0.500203 | + | 0.865908i | \(0.666741\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 3.39217 | 0.778217 | 0.389109 | − | 0.921192i | \(-0.372783\pi\) | ||||
0.389109 | + | 0.921192i | \(0.372783\pi\) | |||||||
\(20\) | 1.47903 | 0.330721 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.70448 | −1.21620 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.81247 | −0.562495 | ||||||||
\(26\) | −6.35023 | −1.24538 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39217 | 0.444215 | 0.222108 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222108 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(30\) | 1.47903 | 0.270032 | ||||||||
\(31\) | −7.81247 | −1.40316 | −0.701581 | − | 0.712590i | \(-0.747522\pi\) | ||||
−0.701581 | + | 0.712590i | \(0.747522\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.70448 | −0.993022 | ||||||||
\(34\) | 4.12478 | 0.707394 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.35023 | 1.37277 | 0.686385 | − | 0.727239i | \(-0.259197\pi\) | ||||
0.686385 | + | 0.727239i | \(0.259197\pi\) | |||||||
\(38\) | −3.39217 | −0.550283 | ||||||||
\(39\) | −6.35023 | −1.01685 | ||||||||
\(40\) | −1.47903 | −0.233855 | ||||||||
\(41\) | 7.39217 | 1.15446 | 0.577232 | − | 0.816580i | \(-0.304133\pi\) | ||||
0.577232 | + | 0.816580i | \(0.304133\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 5.70448 | 0.859982 | ||||||||
\(45\) | 1.47903 | 0.220481 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 10.2214 | 1.49095 | 0.745474 | − | 0.666534i | \(-0.232223\pi\) | ||||
0.745474 | + | 0.666534i | \(0.232223\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.81247 | 0.397744 | ||||||||
\(51\) | 4.12478 | 0.577585 | ||||||||
\(52\) | 6.35023 | 0.880618 | ||||||||
\(53\) | 0.520971 | 0.0715609 | 0.0357804 | − | 0.999360i | \(-0.488608\pi\) | ||||
0.0357804 | + | 0.999360i | \(0.488608\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 8.43709 | 1.13766 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.39217 | −0.449304 | ||||||||
\(58\) | −2.39217 | −0.314107 | ||||||||
\(59\) | 7.37836 | 0.960581 | 0.480290 | − | 0.877110i | \(-0.340531\pi\) | ||||
0.480290 | + | 0.877110i | \(0.340531\pi\) | |||||||
\(60\) | −1.47903 | −0.190942 | ||||||||
\(61\) | −5.04194 | −0.645555 | −0.322777 | − | 0.946475i | \(-0.604616\pi\) | ||||
−0.322777 | + | 0.946475i | \(0.604616\pi\) | |||||||
\(62\) | 7.81247 | 0.992185 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.39217 | 1.16496 | ||||||||
\(66\) | 5.70448 | 0.702173 | ||||||||
\(67\) | 15.4090 | 1.88250 | 0.941252 | − | 0.337706i | \(-0.109651\pi\) | ||||
0.941252 | + | 0.337706i | \(0.109651\pi\) | |||||||
\(68\) | −4.12478 | −0.500203 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.87120 | 1.17150 | 0.585748 | − | 0.810493i | \(-0.300801\pi\) | ||||
0.585748 | + | 0.810493i | \(0.300801\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.92993 | 1.04517 | 0.522584 | − | 0.852588i | \(-0.324968\pi\) | ||||
0.522584 | + | 0.852588i | \(0.324968\pi\) | |||||||
\(74\) | −8.35023 | −0.970694 | ||||||||
\(75\) | 2.81247 | 0.324757 | ||||||||
\(76\) | 3.39217 | 0.389109 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.35023 | 0.719022 | ||||||||
\(79\) | −13.4301 | −1.51100 | −0.755502 | − | 0.655147i | \(-0.772607\pi\) | ||||
−0.755502 | + | 0.655147i | \(0.772607\pi\) | |||||||
\(80\) | 1.47903 | 0.165360 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.39217 | −0.816329 | ||||||||
\(83\) | −9.22143 | −1.01218 | −0.506092 | − | 0.862480i | \(-0.668910\pi\) | ||||
−0.506092 | + | 0.862480i | \(0.668910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.10067 | −0.661710 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | −2.39217 | −0.256468 | ||||||||
\(88\) | −5.70448 | −0.608099 | ||||||||
\(89\) | −6.43411 | −0.682015 | −0.341007 | − | 0.940061i | \(-0.610768\pi\) | ||||
−0.341007 | + | 0.940061i | \(0.610768\pi\) | |||||||
\(90\) | −1.47903 | −0.155903 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 7.81247 | 0.810116 | ||||||||
\(94\) | −10.2214 | −1.05426 | ||||||||
\(95\) | 5.01712 | 0.514746 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −10.3640 | −1.05231 | −0.526154 | − | 0.850389i | \(-0.676367\pi\) | ||||
−0.526154 | + | 0.850389i | \(0.676367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.70448 | 0.573322 | ||||||||
\(100\) | −2.81247 | −0.281247 | ||||||||
\(101\) | 2.81247 | 0.279852 | 0.139926 | − | 0.990162i | \(-0.455314\pi\) | ||||
0.139926 | + | 0.990162i | \(0.455314\pi\) | |||||||
\(102\) | −4.12478 | −0.408414 | ||||||||
\(103\) | −12.5589 | −1.23746 | −0.618732 | − | 0.785602i | \(-0.712353\pi\) | ||||
−0.618732 | + | 0.785602i | \(0.712353\pi\) | |||||||
\(104\) | −6.35023 | −0.622691 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.520971 | −0.0506012 | ||||||||
\(107\) | −5.22143 | −0.504775 | −0.252387 | − | 0.967626i | \(-0.581216\pi\) | ||||
−0.252387 | + | 0.967626i | \(0.581216\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −8.47501 | −0.811759 | −0.405879 | − | 0.913927i | \(-0.633035\pi\) | ||||
−0.405879 | + | 0.913927i | \(0.633035\pi\) | |||||||
\(110\) | −8.43709 | −0.804445 | ||||||||
\(111\) | −8.35023 | −0.792569 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.725281 | 0.0682287 | 0.0341144 | − | 0.999418i | \(-0.489139\pi\) | ||||
0.0341144 | + | 0.999418i | \(0.489139\pi\) | |||||||
\(114\) | 3.39217 | 0.317706 | ||||||||
\(115\) | 1.47903 | 0.137920 | ||||||||
\(116\) | 2.39217 | 0.222108 | ||||||||
\(117\) | 6.35023 | 0.587079 | ||||||||
\(118\) | −7.37836 | −0.679233 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.47903 | 0.135016 | ||||||||
\(121\) | 21.5411 | 1.95828 | ||||||||
\(122\) | 5.04194 | 0.456476 | ||||||||
\(123\) | −7.39217 | −0.666530 | ||||||||
\(124\) | −7.81247 | −0.701581 | ||||||||
\(125\) | −11.5549 | −1.03350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0138109 | 0.00122552 | 0.000612760 | − | 1.00000i | \(-0.499805\pi\) | ||||
0.000612760 | 1.00000i | \(0.499805\pi\) | ||||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | −9.39217 | −0.823748 | ||||||||
\(131\) | −14.4961 | −1.26653 | −0.633267 | − | 0.773933i | \(-0.718287\pi\) | ||||
−0.633267 | + | 0.773933i | \(0.718287\pi\) | |||||||
\(132\) | −5.70448 | −0.496511 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −15.4090 | −1.33113 | ||||||||
\(135\) | −1.47903 | −0.127295 | ||||||||
\(136\) | 4.12478 | 0.353697 | ||||||||
\(137\) | 8.02411 | 0.685546 | 0.342773 | − | 0.939418i | \(-0.388634\pi\) | ||||
0.342773 | + | 0.939418i | \(0.388634\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 14.2214 | 1.20625 | 0.603123 | − | 0.797648i | \(-0.293923\pi\) | ||||
0.603123 | + | 0.797648i | \(0.293923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.2214 | −0.860800 | ||||||||
\(142\) | −9.87120 | −0.828373 | ||||||||
\(143\) | 36.2247 | 3.02926 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.53809 | 0.293822 | ||||||||
\(146\) | −8.92993 | −0.739046 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.35023 | 0.686385 | ||||||||
\(149\) | −23.2835 | −1.90746 | −0.953728 | − | 0.300671i | \(-0.902789\pi\) | ||||
−0.953728 | + | 0.300671i | \(0.902789\pi\) | |||||||
\(150\) | −2.81247 | −0.229638 | ||||||||
\(151\) | −6.01381 | −0.489397 | −0.244698 | − | 0.969599i | \(-0.578689\pi\) | ||||
−0.244698 | + | 0.969599i | \(0.578689\pi\) | |||||||
\(152\) | −3.39217 | −0.275141 | ||||||||
\(153\) | −4.12478 | −0.333469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5549 | −0.928110 | ||||||||
\(156\) | −6.35023 | −0.508425 | ||||||||
\(157\) | −17.8672 | −1.42596 | −0.712978 | − | 0.701186i | \(-0.752654\pi\) | ||||
−0.712978 | + | 0.701186i | \(0.752654\pi\) | |||||||
\(158\) | 13.4301 | 1.06844 | ||||||||
\(159\) | −0.520971 | −0.0413157 | ||||||||
\(160\) | −1.47903 | −0.116927 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 13.8712 | 1.08648 | 0.543238 | − | 0.839579i | \(-0.317198\pi\) | ||||
0.543238 | + | 0.839579i | \(0.317198\pi\) | |||||||
\(164\) | 7.39217 | 0.577232 | ||||||||
\(165\) | −8.43709 | −0.656826 | ||||||||
\(166\) | 9.22143 | 0.715722 | ||||||||
\(167\) | 5.07551 | 0.392755 | 0.196377 | − | 0.980528i | \(-0.437082\pi\) | ||||
0.196377 | + | 0.980528i | \(0.437082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.3254 | 2.10195 | ||||||||
\(170\) | 6.10067 | 0.467900 | ||||||||
\(171\) | 3.39217 | 0.259406 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 2.92993 | 0.222758 | 0.111379 | − | 0.993778i | \(-0.464473\pi\) | ||||
0.111379 | + | 0.993778i | \(0.464473\pi\) | |||||||
\(174\) | 2.39217 | 0.181350 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.70448 | 0.429991 | ||||||||
\(177\) | −7.37836 | −0.554592 | ||||||||
\(178\) | 6.43411 | 0.482257 | ||||||||
\(179\) | −7.94374 | −0.593743 | −0.296871 | − | 0.954917i | \(-0.595943\pi\) | ||||
−0.296871 | + | 0.954917i | \(0.595943\pi\) | |||||||
\(180\) | 1.47903 | 0.110240 | ||||||||
\(181\) | −7.39950 | −0.550000 | −0.275000 | − | 0.961444i | \(-0.588678\pi\) | ||||
−0.275000 | + | 0.961444i | \(0.588678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.04194 | 0.372711 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 12.3502 | 0.908007 | ||||||||
\(186\) | −7.81247 | −0.572838 | ||||||||
\(187\) | −23.5297 | −1.72066 | ||||||||
\(188\) | 10.2214 | 0.745474 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.01712 | −0.363980 | ||||||||
\(191\) | 20.1765 | 1.45992 | 0.729961 | − | 0.683489i | \(-0.239538\pi\) | ||||
0.729961 | + | 0.683489i | \(0.239538\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.8880 | 0.927697 | 0.463849 | − | 0.885914i | \(-0.346468\pi\) | ||||
0.463849 | + | 0.885914i | \(0.346468\pi\) | |||||||
\(194\) | 10.3640 | 0.744095 | ||||||||
\(195\) | −9.39217 | −0.672587 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.80410 | −0.698513 | −0.349257 | − | 0.937027i | \(-0.613566\pi\) | ||||
−0.349257 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(198\) | −5.70448 | −0.405400 | ||||||||
\(199\) | 3.31561 | 0.235038 | 0.117519 | − | 0.993071i | \(-0.462506\pi\) | ||||
0.117519 | + | 0.993071i | \(0.462506\pi\) | |||||||
\(200\) | 2.81247 | 0.198872 | ||||||||
\(201\) | −15.4090 | −1.08686 | ||||||||
\(202\) | −2.81247 | −0.197885 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.12478 | 0.288792 | ||||||||
\(205\) | 10.9332 | 0.763610 | ||||||||
\(206\) | 12.5589 | 0.875020 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 6.35023 | 0.440309 | ||||||||
\(209\) | 19.3506 | 1.33851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.9638 | −1.23668 | −0.618340 | − | 0.785910i | \(-0.712195\pi\) | ||||
−0.618340 | + | 0.785910i | \(0.712195\pi\) | |||||||
\(212\) | 0.520971 | 0.0357804 | ||||||||
\(213\) | −9.87120 | −0.676363 | ||||||||
\(214\) | 5.22143 | 0.356930 | ||||||||
\(215\) | 2.95806 | 0.201738 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.47501 | 0.574000 | ||||||||
\(219\) | −8.92993 | −0.603428 | ||||||||
\(220\) | 8.43709 | 0.568828 | ||||||||
\(221\) | −26.1933 | −1.76195 | ||||||||
\(222\) | 8.35023 | 0.560431 | ||||||||
\(223\) | −1.22947 | −0.0823313 | −0.0411657 | − | 0.999152i | \(-0.513107\pi\) | ||||
−0.0411657 | + | 0.999152i | \(0.513107\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.81247 | −0.187498 | ||||||||
\(226\) | −0.725281 | −0.0482450 | ||||||||
\(227\) | 16.4130 | 1.08937 | 0.544684 | − | 0.838642i | \(-0.316650\pi\) | ||||
0.544684 | + | 0.838642i | \(0.316650\pi\) | |||||||
\(228\) | −3.39217 | −0.224652 | ||||||||
\(229\) | −25.4163 | −1.67956 | −0.839778 | − | 0.542931i | \(-0.817315\pi\) | ||||
−0.839778 | + | 0.542931i | \(0.817315\pi\) | |||||||
\(230\) | −1.47903 | −0.0975243 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.39217 | −0.157054 | ||||||||
\(233\) | 0.551566 | 0.0361343 | 0.0180671 | − | 0.999837i | \(-0.494249\pi\) | ||||
0.0180671 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(234\) | −6.35023 | −0.415127 | ||||||||
\(235\) | 15.1178 | 0.986176 | ||||||||
\(236\) | 7.37836 | 0.480290 | ||||||||
\(237\) | 13.4301 | 0.872378 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2634 | −0.728567 | −0.364283 | − | 0.931288i | \(-0.618686\pi\) | ||||
−0.364283 | + | 0.931288i | \(0.618686\pi\) | |||||||
\(240\) | −1.47903 | −0.0954709 | ||||||||
\(241\) | −28.3284 | −1.82479 | −0.912396 | − | 0.409309i | \(-0.865770\pi\) | ||||
−0.912396 | + | 0.409309i | \(0.865770\pi\) | |||||||
\(242\) | −21.5411 | −1.38471 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.04194 | −0.322777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.39217 | 0.471308 | ||||||||
\(247\) | 21.5411 | 1.37063 | ||||||||
\(248\) | 7.81247 | 0.496093 | ||||||||
\(249\) | 9.22143 | 0.584384 | ||||||||
\(250\) | 11.5549 | 0.730794 | ||||||||
\(251\) | −7.83659 | −0.494641 | −0.247320 | − | 0.968934i | \(-0.579550\pi\) | ||||
−0.247320 | + | 0.968934i | \(0.579550\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.70448 | 0.358637 | ||||||||
\(254\) | −0.0138109 | −0.000866573 0 | ||||||||
\(255\) | 6.10067 | 0.382039 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.72562 | 0.232398 | 0.116199 | − | 0.993226i | \(-0.462929\pi\) | ||||
0.116199 | + | 0.993226i | \(0.462929\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.39217 | 0.582478 | ||||||||
\(261\) | 2.39217 | 0.148072 | ||||||||
\(262\) | 14.4961 | 0.895575 | ||||||||
\(263\) | 28.8661 | 1.77996 | 0.889981 | − | 0.455998i | \(-0.150717\pi\) | ||||
0.889981 | + | 0.455998i | \(0.150717\pi\) | |||||||
\(264\) | 5.70448 | 0.351086 | ||||||||
\(265\) | 0.770531 | 0.0473334 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.43411 | 0.393761 | ||||||||
\(268\) | 15.4090 | 0.941252 | ||||||||
\(269\) | −0.482002 | −0.0293882 | −0.0146941 | − | 0.999892i | \(-0.504677\pi\) | ||||
−0.0146941 | + | 0.999892i | \(0.504677\pi\) | |||||||
\(270\) | 1.47903 | 0.0900108 | ||||||||
\(271\) | −4.89602 | −0.297412 | −0.148706 | − | 0.988881i | \(-0.547511\pi\) | ||||
−0.148706 | + | 0.988881i | \(0.547511\pi\) | |||||||
\(272\) | −4.12478 | −0.250102 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.02411 | −0.484754 | ||||||||
\(275\) | −16.0437 | −0.967471 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 15.5264 | 0.932891 | 0.466446 | − | 0.884550i | \(-0.345534\pi\) | ||||
0.466446 | + | 0.884550i | \(0.345534\pi\) | |||||||
\(278\) | −14.2214 | −0.852945 | ||||||||
\(279\) | −7.81247 | −0.467721 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.2003 | 0.787463 | 0.393732 | − | 0.919225i | \(-0.371184\pi\) | ||||
0.393732 | + | 0.919225i | \(0.371184\pi\) | |||||||
\(282\) | 10.2214 | 0.608677 | ||||||||
\(283\) | −2.75672 | −0.163870 | −0.0819350 | − | 0.996638i | \(-0.526110\pi\) | ||||
−0.0819350 | + | 0.996638i | \(0.526110\pi\) | |||||||
\(284\) | 9.87120 | 0.585748 | ||||||||
\(285\) | −5.01712 | −0.297188 | ||||||||
\(286\) | −36.2247 | −2.14201 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0.0138109 | 0.000812406 0 | ||||||||
\(290\) | −3.53809 | −0.207764 | ||||||||
\(291\) | 10.3640 | 0.607551 | ||||||||
\(292\) | 8.92993 | 0.522584 | ||||||||
\(293\) | 0.0976957 | 0.00570745 | 0.00285372 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285372 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9128 | 0.635368 | ||||||||
\(296\) | −8.35023 | −0.485347 | ||||||||
\(297\) | −5.70448 | −0.331007 | ||||||||
\(298\) | 23.2835 | 1.34877 | ||||||||
\(299\) | 6.35023 | 0.367243 | ||||||||
\(300\) | 2.81247 | 0.162378 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.01381 | 0.346056 | ||||||||
\(303\) | −2.81247 | −0.161572 | ||||||||
\(304\) | 3.39217 | 0.194554 | ||||||||
\(305\) | −7.45718 | −0.426997 | ||||||||
\(306\) | 4.12478 | 0.235798 | ||||||||
\(307\) | −24.9467 | −1.42378 | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5589 | 0.714450 | ||||||||
\(310\) | 11.5549 | 0.656273 | ||||||||
\(311\) | 26.4878 | 1.50198 | 0.750992 | − | 0.660311i | \(-0.229576\pi\) | ||||
0.750992 | + | 0.660311i | \(0.229576\pi\) | |||||||
\(312\) | 6.35023 | 0.359511 | ||||||||
\(313\) | −19.2382 | −1.08741 | −0.543704 | − | 0.839277i | \(-0.682979\pi\) | ||||
−0.543704 | + | 0.839277i | \(0.682979\pi\) | |||||||
\(314\) | 17.8672 | 1.00830 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.4301 | −0.755502 | ||||||||
\(317\) | 25.3784 | 1.42539 | 0.712695 | − | 0.701474i | \(-0.247474\pi\) | ||||
0.712695 | + | 0.701474i | \(0.247474\pi\) | |||||||
\(318\) | 0.520971 | 0.0292146 | ||||||||
\(319\) | 13.6461 | 0.764034 | ||||||||
\(320\) | 1.47903 | 0.0826802 | ||||||||
\(321\) | 5.22143 | 0.291432 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.9920 | −0.778533 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −17.8599 | −0.990686 | ||||||||
\(326\) | −13.8712 | −0.768255 | ||||||||
\(327\) | 8.47501 | 0.468669 | ||||||||
\(328\) | −7.39217 | −0.408164 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 8.43709 | 0.464446 | ||||||||
\(331\) | 2.84273 | 0.156251 | 0.0781254 | − | 0.996944i | \(-0.475107\pi\) | ||||
0.0781254 | + | 0.996944i | \(0.475107\pi\) | |||||||
\(332\) | −9.22143 | −0.506092 | ||||||||
\(333\) | 8.35023 | 0.457590 | ||||||||
\(334\) | −5.07551 | −0.277720 | ||||||||
\(335\) | 22.7903 | 1.24517 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.7793 | 1.45876 | 0.729380 | − | 0.684109i | \(-0.239809\pi\) | ||||
0.729380 | + | 0.684109i | \(0.239809\pi\) | |||||||
\(338\) | −27.3254 | −1.48631 | ||||||||
\(339\) | −0.725281 | −0.0393919 | ||||||||
\(340\) | −6.10067 | −0.330855 | ||||||||
\(341\) | −44.5661 | −2.41339 | ||||||||
\(342\) | −3.39217 | −0.183428 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | −1.47903 | −0.0796282 | ||||||||
\(346\) | −2.92993 | −0.157514 | ||||||||
\(347\) | −5.62495 | −0.301963 | −0.150982 | − | 0.988537i | \(-0.548243\pi\) | ||||
−0.150982 | + | 0.988537i | \(0.548243\pi\) | |||||||
\(348\) | −2.39217 | −0.128234 | ||||||||
\(349\) | 20.8011 | 1.11346 | 0.556729 | − | 0.830694i | \(-0.312056\pi\) | ||||
0.556729 | + | 0.830694i | \(0.312056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.35023 | −0.338950 | ||||||||
\(352\) | −5.70448 | −0.304050 | ||||||||
\(353\) | −34.7092 | −1.84738 | −0.923692 | − | 0.383135i | \(-0.874844\pi\) | ||||
−0.923692 | + | 0.383135i | \(0.874844\pi\) | |||||||
\(354\) | 7.37836 | 0.392155 | ||||||||
\(355\) | 14.5998 | 0.774876 | ||||||||
\(356\) | −6.43411 | −0.341007 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.94374 | 0.419840 | ||||||||
\(359\) | −5.78401 | −0.305268 | −0.152634 | − | 0.988283i | \(-0.548776\pi\) | ||||
−0.152634 | + | 0.988283i | \(0.548776\pi\) | |||||||
\(360\) | −1.47903 | −0.0779517 | ||||||||
\(361\) | −7.49317 | −0.394378 | ||||||||
\(362\) | 7.39950 | 0.388909 | ||||||||
\(363\) | −21.5411 | −1.13061 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.2076 | 0.691318 | ||||||||
\(366\) | −5.04194 | −0.263547 | ||||||||
\(367\) | 0.669863 | 0.0349666 | 0.0174833 | − | 0.999847i | \(-0.494435\pi\) | ||||
0.0174833 | + | 0.999847i | \(0.494435\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 7.39217 | 0.384821 | ||||||||
\(370\) | −12.3502 | −0.642058 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.81247 | 0.405058 | ||||||||
\(373\) | −9.80008 | −0.507429 | −0.253714 | − | 0.967279i | \(-0.581652\pi\) | ||||
−0.253714 | + | 0.967279i | \(0.581652\pi\) | |||||||
\(374\) | 23.5297 | 1.21669 | ||||||||
\(375\) | 11.5549 | 0.596691 | ||||||||
\(376\) | −10.2214 | −0.527130 | ||||||||
\(377\) | 15.1908 | 0.782368 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.742065 | −0.0381173 | −0.0190587 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190587 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(380\) | 5.01712 | 0.257373 | ||||||||
\(381\) | −0.0138109 | −0.000707554 0 | ||||||||
\(382\) | −20.1765 | −1.03232 | ||||||||
\(383\) | 30.4114 | 1.55395 | 0.776975 | − | 0.629531i | \(-0.216753\pi\) | ||||
0.776975 | + | 0.629531i | \(0.216753\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.8880 | −0.655981 | ||||||||
\(387\) | 2.00000 | 0.101666 | ||||||||
\(388\) | −10.3640 | −0.526154 | ||||||||
\(389\) | −0.674930 | −0.0342203 | −0.0171102 | − | 0.999854i | \(-0.505447\pi\) | ||||
−0.0171102 | + | 0.999854i | \(0.505447\pi\) | |||||||
\(390\) | 9.39217 | 0.475591 | ||||||||
\(391\) | −4.12478 | −0.208599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.4961 | 0.731234 | ||||||||
\(394\) | 9.80410 | 0.493923 | ||||||||
\(395\) | −19.8635 | −0.999441 | ||||||||
\(396\) | 5.70448 | 0.286661 | ||||||||
\(397\) | 8.42607 | 0.422893 | 0.211446 | − | 0.977390i | \(-0.432183\pi\) | ||||
0.211446 | + | 0.977390i | \(0.432183\pi\) | |||||||
\(398\) | −3.31561 | −0.166197 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.81247 | −0.140624 | ||||||||
\(401\) | 35.1192 | 1.75377 | 0.876885 | − | 0.480701i | \(-0.159618\pi\) | ||||
0.876885 | + | 0.480701i | \(0.159618\pi\) | |||||||
\(402\) | 15.4090 | 0.768529 | ||||||||
\(403\) | −49.6110 | −2.47130 | ||||||||
\(404\) | 2.81247 | 0.139926 | ||||||||
\(405\) | 1.47903 | 0.0734935 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.6337 | 2.36111 | ||||||||
\(408\) | −4.12478 | −0.204207 | ||||||||
\(409\) | 19.7281 | 0.975491 | 0.487745 | − | 0.872986i | \(-0.337819\pi\) | ||||
0.487745 | + | 0.872986i | \(0.337819\pi\) | |||||||
\(410\) | −10.9332 | −0.539954 | ||||||||
\(411\) | −8.02411 | −0.395800 | ||||||||
\(412\) | −12.5589 | −0.618732 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | −13.6388 | −0.669500 | ||||||||
\(416\) | −6.35023 | −0.311346 | ||||||||
\(417\) | −14.2214 | −0.696426 | ||||||||
\(418\) | −19.3506 | −0.946467 | ||||||||
\(419\) | 7.26739 | 0.355035 | 0.177518 | − | 0.984118i | \(-0.443193\pi\) | ||||
0.177518 | + | 0.984118i | \(0.443193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.82277 | 0.186311 | 0.0931553 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931553 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(422\) | 17.9638 | 0.874465 | ||||||||
\(423\) | 10.2214 | 0.496983 | ||||||||
\(424\) | −0.520971 | −0.0253006 | ||||||||
\(425\) | 11.6008 | 0.562723 | ||||||||
\(426\) | 9.87120 | 0.478261 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.22143 | −0.252387 | ||||||||
\(429\) | −36.2247 | −1.74895 | ||||||||
\(430\) | −2.95806 | −0.142650 | ||||||||
\(431\) | −1.97238 | −0.0950061 | −0.0475031 | − | 0.998871i | \(-0.515126\pi\) | ||||
−0.0475031 | + | 0.998871i | \(0.515126\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −31.3929 | −1.50865 | −0.754323 | − | 0.656504i | \(-0.772035\pi\) | ||||
−0.754323 | + | 0.656504i | \(0.772035\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.53809 | −0.169638 | ||||||||
\(436\) | −8.47501 | −0.405879 | ||||||||
\(437\) | 3.39217 | 0.162270 | ||||||||
\(438\) | 8.92993 | 0.426688 | ||||||||
\(439\) | −35.7205 | −1.70485 | −0.852424 | − | 0.522851i | \(-0.824869\pi\) | ||||
−0.852424 | + | 0.522851i | \(0.824869\pi\) | |||||||
\(440\) | −8.43709 | −0.402222 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 26.1933 | 1.24589 | ||||||||
\(443\) | −0.114479 | −0.00543908 | −0.00271954 | − | 0.999996i | \(-0.500866\pi\) | ||||
−0.00271954 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(444\) | −8.35023 | −0.396284 | ||||||||
\(445\) | −9.51624 | −0.451113 | ||||||||
\(446\) | 1.22947 | 0.0582170 | ||||||||
\(447\) | 23.2835 | 1.10127 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.26006 | −0.437009 | −0.218505 | − | 0.975836i | \(-0.570118\pi\) | ||||
−0.218505 | + | 0.975836i | \(0.570118\pi\) | |||||||
\(450\) | 2.81247 | 0.132581 | ||||||||
\(451\) | 42.1685 | 1.98564 | ||||||||
\(452\) | 0.725281 | 0.0341144 | ||||||||
\(453\) | 6.01381 | 0.282553 | ||||||||
\(454\) | −16.4130 | −0.770299 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.39217 | 0.158853 | ||||||||
\(457\) | 5.83730 | 0.273057 | 0.136529 | − | 0.990636i | \(-0.456405\pi\) | ||||
0.136529 | + | 0.990636i | \(0.456405\pi\) | |||||||
\(458\) | 25.4163 | 1.18762 | ||||||||
\(459\) | 4.12478 | 0.192528 | ||||||||
\(460\) | 1.47903 | 0.0689601 | ||||||||
\(461\) | 23.1660 | 1.07895 | 0.539474 | − | 0.842002i | \(-0.318623\pi\) | ||||
0.539474 | + | 0.842002i | \(0.318623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.140148 | 0.00651322 | 0.00325661 | − | 0.999995i | \(-0.498963\pi\) | ||||
0.00325661 | + | 0.999995i | \(0.498963\pi\) | |||||||
\(464\) | 2.39217 | 0.111054 | ||||||||
\(465\) | 11.5549 | 0.535844 | ||||||||
\(466\) | −0.551566 | −0.0255508 | ||||||||
\(467\) | 15.5170 | 0.718039 | 0.359019 | − | 0.933330i | \(-0.383111\pi\) | ||||
0.359019 | + | 0.933330i | \(0.383111\pi\) | |||||||
\(468\) | 6.35023 | 0.293539 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.1178 | −0.697332 | ||||||||
\(471\) | 17.8672 | 0.823276 | ||||||||
\(472\) | −7.37836 | −0.339617 | ||||||||
\(473\) | 11.4090 | 0.524584 | ||||||||
\(474\) | −13.4301 | −0.616865 | ||||||||
\(475\) | −9.54039 | −0.437743 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.520971 | 0.0238536 | ||||||||
\(478\) | 11.2634 | 0.515175 | ||||||||
\(479\) | 15.3922 | 0.703286 | 0.351643 | − | 0.936134i | \(-0.385623\pi\) | ||||
0.351643 | + | 0.936134i | \(0.385623\pi\) | |||||||
\(480\) | 1.47903 | 0.0675081 | ||||||||
\(481\) | 53.0259 | 2.41777 | ||||||||
\(482\) | 28.3284 | 1.29032 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5411 | 0.979139 | ||||||||
\(485\) | −15.3287 | −0.696041 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −0.554539 | −0.0251285 | −0.0125643 | − | 0.999921i | \(-0.503999\pi\) | ||||
−0.0125643 | + | 0.999921i | \(0.503999\pi\) | |||||||
\(488\) | 5.04194 | 0.228238 | ||||||||
\(489\) | −13.8712 | −0.627277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.1966 | 1.94944 | 0.974718 | − | 0.223440i | \(-0.0717286\pi\) | ||||
0.974718 | + | 0.223440i | \(0.0717286\pi\) | |||||||
\(492\) | −7.39217 | −0.333265 | ||||||||
\(493\) | −9.86718 | −0.444395 | ||||||||
\(494\) | −21.5411 | −0.969178 | ||||||||
\(495\) | 8.43709 | 0.379219 | ||||||||
\(496\) | −7.81247 | −0.350790 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.22143 | −0.413222 | ||||||||
\(499\) | −20.8943 | −0.935356 | −0.467678 | − | 0.883899i | \(-0.654909\pi\) | ||||
−0.467678 | + | 0.883899i | \(0.654909\pi\) | |||||||
\(500\) | −11.5549 | −0.516750 | ||||||||
\(501\) | −5.07551 | −0.226757 | ||||||||
\(502\) | 7.83659 | 0.349764 | ||||||||
\(503\) | −10.1657 | −0.453265 | −0.226633 | − | 0.973980i | \(-0.572772\pi\) | ||||
−0.226633 | + | 0.973980i | \(0.572772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.15973 | 0.185106 | ||||||||
\(506\) | −5.70448 | −0.253595 | ||||||||
\(507\) | −27.3254 | −1.21356 | ||||||||
\(508\) | 0.0138109 | 0.000612760 0 | ||||||||
\(509\) | −13.7319 | −0.608656 | −0.304328 | − | 0.952567i | \(-0.598432\pi\) | ||||
−0.304328 | + | 0.952567i | \(0.598432\pi\) | |||||||
\(510\) | −6.10067 | −0.270142 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.39217 | −0.149768 | ||||||||
\(514\) | −3.72562 | −0.164330 | ||||||||
\(515\) | −18.5750 | −0.818511 | ||||||||
\(516\) | −2.00000 | −0.0880451 | ||||||||
\(517\) | 58.3079 | 2.56438 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.92993 | −0.128609 | ||||||||
\(520\) | −9.39217 | −0.411874 | ||||||||
\(521\) | −3.62495 | −0.158812 | −0.0794059 | − | 0.996842i | \(-0.525302\pi\) | ||||
−0.0794059 | + | 0.996842i | \(0.525302\pi\) | |||||||
\(522\) | −2.39217 | −0.104702 | ||||||||
\(523\) | −28.9420 | −1.26554 | −0.632772 | − | 0.774338i | \(-0.718083\pi\) | ||||
−0.632772 | + | 0.774338i | \(0.718083\pi\) | |||||||
\(524\) | −14.4961 | −0.633267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.8661 | −1.25862 | ||||||||
\(527\) | 32.2247 | 1.40373 | ||||||||
\(528\) | −5.70448 | −0.248256 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.770531 | −0.0334697 | ||||||||
\(531\) | 7.37836 | 0.320194 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.9420 | 2.03328 | ||||||||
\(534\) | −6.43411 | −0.278431 | ||||||||
\(535\) | −7.72264 | −0.333879 | ||||||||
\(536\) | −15.4090 | −0.665565 | ||||||||
\(537\) | 7.94374 | 0.342798 | ||||||||
\(538\) | 0.482002 | 0.0207806 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.47903 | −0.0636473 | ||||||||
\(541\) | −33.0171 | −1.41952 | −0.709758 | − | 0.704445i | \(-0.751196\pi\) | ||||
−0.709758 | + | 0.704445i | \(0.751196\pi\) | |||||||
\(542\) | 4.89602 | 0.210302 | ||||||||
\(543\) | 7.39950 | 0.317543 | ||||||||
\(544\) | 4.12478 | 0.176848 | ||||||||
\(545\) | −12.5348 | −0.536931 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.6891 | 1.56871 | 0.784357 | − | 0.620310i | \(-0.212993\pi\) | ||||
0.784357 | + | 0.620310i | \(0.212993\pi\) | |||||||
\(548\) | 8.02411 | 0.342773 | ||||||||
\(549\) | −5.04194 | −0.215185 | ||||||||
\(550\) | 16.0437 | 0.684105 | ||||||||
\(551\) | 8.11465 | 0.345696 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −15.5264 | −0.659654 | ||||||||
\(555\) | −12.3502 | −0.524238 | ||||||||
\(556\) | 14.2214 | 0.603123 | ||||||||
\(557\) | 30.9362 | 1.31081 | 0.655405 | − | 0.755278i | \(-0.272498\pi\) | ||||
0.655405 | + | 0.755278i | \(0.272498\pi\) | |||||||
\(558\) | 7.81247 | 0.330728 | ||||||||
\(559\) | 12.7005 | 0.537172 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.5297 | 0.993425 | ||||||||
\(562\) | −13.2003 | −0.556821 | ||||||||
\(563\) | 0.553123 | 0.0233113 | 0.0116557 | − | 0.999932i | \(-0.496290\pi\) | ||||
0.0116557 | + | 0.999932i | \(0.496290\pi\) | |||||||
\(564\) | −10.2214 | −0.430400 | ||||||||
\(565\) | 1.07271 | 0.0451293 | ||||||||
\(566\) | 2.75672 | 0.115874 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.87120 | −0.414186 | ||||||||
\(569\) | 2.38167 | 0.0998447 | 0.0499224 | − | 0.998753i | \(-0.484103\pi\) | ||||
0.0499224 | + | 0.998753i | \(0.484103\pi\) | |||||||
\(570\) | 5.01712 | 0.210144 | ||||||||
\(571\) | 26.5662 | 1.11176 | 0.555881 | − | 0.831262i | \(-0.312381\pi\) | ||||
0.555881 | + | 0.831262i | \(0.312381\pi\) | |||||||
\(572\) | 36.2247 | 1.51463 | ||||||||
\(573\) | −20.1765 | −0.842886 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.81247 | −0.117288 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.72315 | −0.238258 | −0.119129 | − | 0.992879i | \(-0.538010\pi\) | ||||
−0.119129 | + | 0.992879i | \(0.538010\pi\) | |||||||
\(578\) | −0.0138109 | −0.000574458 0 | ||||||||
\(579\) | −12.8880 | −0.535606 | ||||||||
\(580\) | 3.53809 | 0.146911 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.3640 | −0.429603 | ||||||||
\(583\) | 2.97187 | 0.123082 | ||||||||
\(584\) | −8.92993 | −0.369523 | ||||||||
\(585\) | 9.39217 | 0.388318 | ||||||||
\(586\) | −0.0976957 | −0.00403577 | ||||||||
\(587\) | 19.2323 | 0.793801 | 0.396900 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396900 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.5012 | −1.09196 | ||||||||
\(590\) | −10.9128 | −0.449273 | ||||||||
\(591\) | 9.80410 | 0.403287 | ||||||||
\(592\) | 8.35023 | 0.343192 | ||||||||
\(593\) | −20.6858 | −0.849464 | −0.424732 | − | 0.905319i | \(-0.639632\pi\) | ||||
−0.424732 | + | 0.905319i | \(0.639632\pi\) | |||||||
\(594\) | 5.70448 | 0.234058 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −23.2835 | −0.953728 | ||||||||
\(597\) | −3.31561 | −0.135699 | ||||||||
\(598\) | −6.35023 | −0.259680 | ||||||||
\(599\) | −19.6195 | −0.801633 | −0.400816 | − | 0.916158i | \(-0.631273\pi\) | ||||
−0.400816 | + | 0.916158i | \(0.631273\pi\) | |||||||
\(600\) | −2.81247 | −0.114819 | ||||||||
\(601\) | −8.88798 | −0.362548 | −0.181274 | − | 0.983433i | \(-0.558022\pi\) | ||||
−0.181274 | + | 0.983433i | \(0.558022\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.4090 | 0.627501 | ||||||||
\(604\) | −6.01381 | −0.244698 | ||||||||
\(605\) | 31.8599 | 1.29529 | ||||||||
\(606\) | 2.81247 | 0.114249 | ||||||||
\(607\) | −11.7789 | −0.478091 | −0.239046 | − | 0.971008i | \(-0.576835\pi\) | ||||
−0.239046 | + | 0.971008i | \(0.576835\pi\) | |||||||
\(608\) | −3.39217 | −0.137571 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.45718 | 0.301932 | ||||||||
\(611\) | 64.9084 | 2.62591 | ||||||||
\(612\) | −4.12478 | −0.166734 | ||||||||
\(613\) | 24.7186 | 0.998376 | 0.499188 | − | 0.866494i | \(-0.333632\pi\) | ||||
0.499188 | + | 0.866494i | \(0.333632\pi\) | |||||||
\(614\) | 24.9467 | 1.00677 | ||||||||
\(615\) | −10.9332 | −0.440871 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.0580 | −0.767247 | −0.383623 | − | 0.923490i | \(-0.625324\pi\) | ||||
−0.383623 | + | 0.923490i | \(0.625324\pi\) | |||||||
\(618\) | −12.5589 | −0.505193 | ||||||||
\(619\) | −19.5096 | −0.784158 | −0.392079 | − | 0.919932i | \(-0.628244\pi\) | ||||
−0.392079 | + | 0.919932i | \(0.628244\pi\) | |||||||
\(620\) | −11.5549 | −0.464055 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −26.4878 | −1.06206 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.35023 | −0.254213 | ||||||||
\(625\) | −3.02762 | −0.121105 | ||||||||
\(626\) | 19.2382 | 0.768914 | ||||||||
\(627\) | −19.3506 | −0.772787 | ||||||||
\(628\) | −17.8672 | −0.712978 | ||||||||
\(629\) | −34.4429 | −1.37333 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.6443 | −1.85688 | −0.928441 | − | 0.371481i | \(-0.878850\pi\) | ||||
−0.928441 | + | 0.371481i | \(0.878850\pi\) | |||||||
\(632\) | 13.4301 | 0.534220 | ||||||||
\(633\) | 17.9638 | 0.713998 | ||||||||
\(634\) | −25.3784 | −1.00790 | ||||||||
\(635\) | 0.0204267 | 0.000810610 0 | ||||||||
\(636\) | −0.520971 | −0.0206579 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.6461 | −0.540254 | ||||||||
\(639\) | 9.87120 | 0.390499 | ||||||||
\(640\) | −1.47903 | −0.0584637 | ||||||||
\(641\) | −26.5341 | −1.04803 | −0.524016 | − | 0.851708i | \(-0.675567\pi\) | ||||
−0.524016 | + | 0.851708i | \(0.675567\pi\) | |||||||
\(642\) | −5.22143 | −0.206073 | ||||||||
\(643\) | 1.53826 | 0.0606632 | 0.0303316 | − | 0.999540i | \(-0.490344\pi\) | ||||
0.0303316 | + | 0.999540i | \(0.490344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.95806 | −0.116473 | ||||||||
\(646\) | 13.9920 | 0.550506 | ||||||||
\(647\) | 37.0620 | 1.45706 | 0.728529 | − | 0.685014i | \(-0.240204\pi\) | ||||
0.728529 | + | 0.685014i | \(0.240204\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 42.0897 | 1.65216 | ||||||||
\(650\) | 17.8599 | 0.700521 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.8712 | 0.543238 | ||||||||
\(653\) | 8.19083 | 0.320532 | 0.160266 | − | 0.987074i | \(-0.448765\pi\) | ||||
0.160266 | + | 0.987074i | \(0.448765\pi\) | |||||||
\(654\) | −8.47501 | −0.331399 | ||||||||
\(655\) | −21.4402 | −0.837739 | ||||||||
\(656\) | 7.39217 | 0.288616 | ||||||||
\(657\) | 8.92993 | 0.348390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2174 | 0.943376 | 0.471688 | − | 0.881765i | \(-0.343645\pi\) | ||||
0.471688 | + | 0.881765i | \(0.343645\pi\) | |||||||
\(660\) | −8.43709 | −0.328413 | ||||||||
\(661\) | −37.5928 | −1.46219 | −0.731095 | − | 0.682276i | \(-0.760990\pi\) | ||||
−0.731095 | + | 0.682276i | \(0.760990\pi\) | |||||||
\(662\) | −2.84273 | −0.110486 | ||||||||
\(663\) | 26.1933 | 1.01726 | ||||||||
\(664\) | 9.22143 | 0.357861 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.35023 | −0.323565 | ||||||||
\(667\) | 2.39217 | 0.0926252 | ||||||||
\(668\) | 5.07551 | 0.196377 | ||||||||
\(669\) | 1.22947 | 0.0475340 | ||||||||
\(670\) | −22.7903 | −0.880466 | ||||||||
\(671\) | −28.7616 | −1.11033 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.15939 | 0.160333 | 0.0801664 | − | 0.996781i | \(-0.474455\pi\) | ||||
0.0801664 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(674\) | −26.7793 | −1.03150 | ||||||||
\(675\) | 2.81247 | 0.108252 | ||||||||
\(676\) | 27.3254 | 1.05098 | ||||||||
\(677\) | 12.3452 | 0.474463 | 0.237232 | − | 0.971453i | \(-0.423760\pi\) | ||||
0.237232 | + | 0.971453i | \(0.423760\pi\) | |||||||
\(678\) | 0.725281 | 0.0278543 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.10067 | 0.233950 | ||||||||
\(681\) | −16.4130 | −0.628947 | ||||||||
\(682\) | 44.5661 | 1.70652 | ||||||||
\(683\) | 41.1463 | 1.57442 | 0.787209 | − | 0.616686i | \(-0.211525\pi\) | ||||
0.787209 | + | 0.616686i | \(0.211525\pi\) | |||||||
\(684\) | 3.39217 | 0.129703 | ||||||||
\(685\) | 11.8679 | 0.453449 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4163 | 0.969692 | ||||||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | 3.30829 | 0.126036 | ||||||||
\(690\) | 1.47903 | 0.0563057 | ||||||||
\(691\) | −6.16237 | −0.234428 | −0.117214 | − | 0.993107i | \(-0.537396\pi\) | ||||
−0.117214 | + | 0.993107i | \(0.537396\pi\) | |||||||
\(692\) | 2.92993 | 0.111379 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.62495 | 0.213520 | ||||||||
\(695\) | 21.0339 | 0.797861 | ||||||||
\(696\) | 2.39217 | 0.0906750 | ||||||||
\(697\) | −30.4911 | −1.15493 | ||||||||
\(698\) | −20.8011 | −0.787334 | ||||||||
\(699\) | −0.551566 | −0.0208621 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.6447 | −1.04413 | −0.522063 | − | 0.852907i | \(-0.674837\pi\) | ||||
−0.522063 | + | 0.852907i | \(0.674837\pi\) | |||||||
\(702\) | 6.35023 | 0.239674 | ||||||||
\(703\) | 28.3254 | 1.06831 | ||||||||
\(704\) | 5.70448 | 0.214996 | ||||||||
\(705\) | −15.1178 | −0.569369 | ||||||||
\(706\) | 34.7092 | 1.30630 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.37836 | −0.277296 | ||||||||
\(709\) | 25.2426 | 0.948005 | 0.474002 | − | 0.880524i | \(-0.342809\pi\) | ||||
0.474002 | + | 0.880524i | \(0.342809\pi\) | |||||||
\(710\) | −14.5998 | −0.547920 | ||||||||
\(711\) | −13.4301 | −0.503668 | ||||||||
\(712\) | 6.43411 | 0.241129 | ||||||||
\(713\) | −7.81247 | −0.292579 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.5774 | 2.00368 | ||||||||
\(716\) | −7.94374 | −0.296871 | ||||||||
\(717\) | 11.2634 | 0.420638 | ||||||||
\(718\) | 5.78401 | 0.215857 | ||||||||
\(719\) | 39.4075 | 1.46965 | 0.734826 | − | 0.678255i | \(-0.237264\pi\) | ||||
0.734826 | + | 0.678255i | \(0.237264\pi\) | |||||||
\(720\) | 1.47903 | 0.0551201 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.49317 | 0.278867 | ||||||||
\(723\) | 28.3284 | 1.05354 | ||||||||
\(724\) | −7.39950 | −0.275000 | ||||||||
\(725\) | −6.72792 | −0.249869 | ||||||||
\(726\) | 21.5411 | 0.799464 | ||||||||
\(727\) | 33.9963 | 1.26085 | 0.630427 | − | 0.776248i | \(-0.282880\pi\) | ||||
0.630427 | + | 0.776248i | \(0.282880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.2076 | −0.488836 | ||||||||
\(731\) | −8.24956 | −0.305121 | ||||||||
\(732\) | 5.04194 | 0.186356 | ||||||||
\(733\) | −2.49179 | −0.0920365 | −0.0460182 | − | 0.998941i | \(-0.514653\pi\) | ||||
−0.0460182 | + | 0.998941i | \(0.514653\pi\) | |||||||
\(734\) | −0.669863 | −0.0247251 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 87.9000 | 3.23784 | ||||||||
\(738\) | −7.39217 | −0.272110 | ||||||||
\(739\) | 47.2976 | 1.73987 | 0.869935 | − | 0.493166i | \(-0.164160\pi\) | ||||
0.869935 | + | 0.493166i | \(0.164160\pi\) | |||||||
\(740\) | 12.3502 | 0.454003 | ||||||||
\(741\) | −21.5411 | −0.791331 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.5435 | 1.63414 | 0.817072 | − | 0.576536i | \(-0.195596\pi\) | ||||
0.817072 | + | 0.576536i | \(0.195596\pi\) | |||||||
\(744\) | −7.81247 | −0.286419 | ||||||||
\(745\) | −34.4369 | −1.26167 | ||||||||
\(746\) | 9.80008 | 0.358806 | ||||||||
\(747\) | −9.22143 | −0.337394 | ||||||||
\(748\) | −23.5297 | −0.860332 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.5549 | −0.421924 | ||||||||
\(751\) | −13.5105 | −0.493004 | −0.246502 | − | 0.969142i | \(-0.579281\pi\) | ||||
−0.246502 | + | 0.969142i | \(0.579281\pi\) | |||||||
\(752\) | 10.2214 | 0.372737 | ||||||||
\(753\) | 7.83659 | 0.285581 | ||||||||
\(754\) | −15.1908 | −0.553218 | ||||||||
\(755\) | −8.89460 | −0.323708 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.9895 | −0.908259 | −0.454129 | − | 0.890936i | \(-0.650050\pi\) | ||||
−0.454129 | + | 0.890936i | \(0.650050\pi\) | |||||||
\(758\) | 0.742065 | 0.0269530 | ||||||||
\(759\) | −5.70448 | −0.207059 | ||||||||
\(760\) | −5.01712 | −0.181990 | ||||||||
\(761\) | −2.53860 | −0.0920242 | −0.0460121 | − | 0.998941i | \(-0.514651\pi\) | ||||
−0.0460121 | + | 0.998941i | \(0.514651\pi\) | |||||||
\(762\) | 0.0138109 | 0.000500316 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.1765 | 0.729961 | ||||||||
\(765\) | −6.10067 | −0.220570 | ||||||||
\(766\) | −30.4114 | −1.09881 | ||||||||
\(767\) | 46.8543 | 1.69181 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −7.59435 | −0.273859 | −0.136930 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136930 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.72562 | −0.134175 | ||||||||
\(772\) | 12.8880 | 0.463849 | ||||||||
\(773\) | −21.5687 | −0.775772 | −0.387886 | − | 0.921707i | \(-0.626795\pi\) | ||||
−0.387886 | + | 0.921707i | \(0.626795\pi\) | |||||||
\(774\) | −2.00000 | −0.0718885 | ||||||||
\(775\) | 21.9724 | 0.789271 | ||||||||
\(776\) | 10.3640 | 0.372047 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.674930 | 0.0241974 | ||||||||
\(779\) | 25.0755 | 0.898423 | ||||||||
\(780\) | −9.39217 | −0.336294 | ||||||||
\(781\) | 56.3100 | 2.01493 | ||||||||
\(782\) | 4.12478 | 0.147502 | ||||||||
\(783\) | −2.39217 | −0.0854892 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.4261 | −0.943187 | ||||||||
\(786\) | −14.4961 | −0.517060 | ||||||||
\(787\) | −45.2192 | −1.61189 | −0.805944 | − | 0.591991i | \(-0.798342\pi\) | ||||
−0.805944 | + | 0.591991i | \(0.798342\pi\) | |||||||
\(788\) | −9.80410 | −0.349257 | ||||||||
\(789\) | −28.8661 | −1.02766 | ||||||||
\(790\) | 19.8635 | 0.706711 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.70448 | −0.202700 | ||||||||
\(793\) | −32.0175 | −1.13697 | ||||||||
\(794\) | −8.42607 | −0.299030 | ||||||||
\(795\) | −0.770531 | −0.0273279 | ||||||||
\(796\) | 3.31561 | 0.117519 | ||||||||
\(797\) | 26.6028 | 0.942318 | 0.471159 | − | 0.882048i | \(-0.343836\pi\) | ||||
0.471159 | + | 0.882048i | \(0.343836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.1611 | −1.49155 | ||||||||
\(800\) | 2.81247 | 0.0994360 | ||||||||
\(801\) | −6.43411 | −0.227338 | ||||||||
\(802\) | −35.1192 | −1.24010 | ||||||||
\(803\) | 50.9406 | 1.79765 | ||||||||
\(804\) | −15.4090 | −0.543432 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 49.6110 | 1.74747 | ||||||||
\(807\) | 0.482002 | 0.0169673 | ||||||||
\(808\) | −2.81247 | −0.0989425 | ||||||||
\(809\) | −40.5582 | −1.42595 | −0.712975 | − | 0.701190i | \(-0.752653\pi\) | ||||
−0.712975 | + | 0.701190i | \(0.752653\pi\) | |||||||
\(810\) | −1.47903 | −0.0519678 | ||||||||
\(811\) | 17.7894 | 0.624672 | 0.312336 | − | 0.949972i | \(-0.398889\pi\) | ||||
0.312336 | + | 0.949972i | \(0.398889\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.89602 | 0.171711 | ||||||||
\(814\) | −47.6337 | −1.66956 | ||||||||
\(815\) | 20.5159 | 0.718641 | ||||||||
\(816\) | 4.12478 | 0.144396 | ||||||||
\(817\) | 6.78434 | 0.237354 | ||||||||
\(818\) | −19.7281 | −0.689776 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.9332 | 0.381805 | ||||||||
\(821\) | 3.44006 | 0.120059 | 0.0600294 | − | 0.998197i | \(-0.480881\pi\) | ||||
0.0600294 | + | 0.998197i | \(0.480881\pi\) | |||||||
\(822\) | 8.02411 | 0.279873 | ||||||||
\(823\) | 7.28489 | 0.253935 | 0.126968 | − | 0.991907i | \(-0.459476\pi\) | ||||
0.126968 | + | 0.991907i | \(0.459476\pi\) | |||||||
\(824\) | 12.5589 | 0.437510 | ||||||||
\(825\) | 16.0437 | 0.558570 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4665 | −0.885556 | −0.442778 | − | 0.896631i | \(-0.646007\pi\) | ||||
−0.442778 | + | 0.896631i | \(0.646007\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 0.00661582 | 0.000229777 0 | 0.000114889 | − | 1.00000i | \(-0.499963\pi\) | ||||
0.000114889 | 1.00000i | \(0.499963\pi\) | ||||||||
\(830\) | 13.6388 | 0.473408 | ||||||||
\(831\) | −15.5264 | −0.538605 | ||||||||
\(832\) | 6.35023 | 0.220155 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.2214 | 0.492448 | ||||||||
\(835\) | 7.50683 | 0.259784 | ||||||||
\(836\) | 19.3506 | 0.669253 | ||||||||
\(837\) | 7.81247 | 0.270039 | ||||||||
\(838\) | −7.26739 | −0.251048 | ||||||||
\(839\) | 14.8092 | 0.511269 | 0.255635 | − | 0.966773i | \(-0.417716\pi\) | ||||
0.255635 | + | 0.966773i | \(0.417716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.2775 | −0.802673 | ||||||||
\(842\) | −3.82277 | −0.131742 | ||||||||
\(843\) | −13.2003 | −0.454642 | ||||||||
\(844\) | −17.9638 | −0.618340 | ||||||||
\(845\) | 40.4151 | 1.39032 | ||||||||
\(846\) | −10.2214 | −0.351420 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.520971 | 0.0178902 | ||||||||
\(849\) | 2.75672 | 0.0946104 | ||||||||
\(850\) | −11.6008 | −0.397905 | ||||||||
\(851\) | 8.35023 | 0.286242 | ||||||||
\(852\) | −9.87120 | −0.338182 | ||||||||
\(853\) | −13.5264 | −0.463135 | −0.231568 | − | 0.972819i | \(-0.574385\pi\) | ||||
−0.231568 | + | 0.972819i | \(0.574385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.01712 | 0.171582 | ||||||||
\(856\) | 5.22143 | 0.178465 | ||||||||
\(857\) | 8.62741 | 0.294707 | 0.147353 | − | 0.989084i | \(-0.452925\pi\) | ||||
0.147353 | + | 0.989084i | \(0.452925\pi\) | |||||||
\(858\) | 36.2247 | 1.23669 | ||||||||
\(859\) | 24.3074 | 0.829359 | 0.414680 | − | 0.909967i | \(-0.363894\pi\) | ||||
0.414680 | + | 0.909967i | \(0.363894\pi\) | |||||||
\(860\) | 2.95806 | 0.100869 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.97238 | 0.0671795 | ||||||||
\(863\) | −14.7796 | −0.503104 | −0.251552 | − | 0.967844i | \(-0.580941\pi\) | ||||
−0.251552 | + | 0.967844i | \(0.580941\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 4.33345 | 0.147342 | ||||||||
\(866\) | 31.3929 | 1.06677 | ||||||||
\(867\) | −0.0138109 | −0.000469043 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −76.6117 | −2.59887 | ||||||||
\(870\) | 3.53809 | 0.119952 | ||||||||
\(871\) | 97.8504 | 3.31553 | ||||||||
\(872\) | 8.47501 | 0.287000 | ||||||||
\(873\) | −10.3640 | −0.350770 | ||||||||
\(874\) | −3.39217 | −0.114742 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.92993 | −0.301714 | ||||||||
\(877\) | −52.7092 | −1.77986 | −0.889932 | − | 0.456094i | \(-0.849248\pi\) | ||||
−0.889932 | + | 0.456094i | \(0.849248\pi\) | |||||||
\(878\) | 35.7205 | 1.20551 | ||||||||
\(879\) | −0.0976957 | −0.00329520 | ||||||||
\(880\) | 8.43709 | 0.284414 | ||||||||
\(881\) | 35.2594 | 1.18792 | 0.593959 | − | 0.804495i | \(-0.297564\pi\) | ||||
0.593959 | + | 0.804495i | \(0.297564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.05906 | 0.203904 | 0.101952 | − | 0.994789i | \(-0.467491\pi\) | ||||
0.101952 | + | 0.994789i | \(0.467491\pi\) | |||||||
\(884\) | −26.1933 | −0.880976 | ||||||||
\(885\) | −10.9128 | −0.366830 | ||||||||
\(886\) | 0.114479 | 0.00384601 | ||||||||
\(887\) | −4.91527 | −0.165039 | −0.0825193 | − | 0.996589i | \(-0.526297\pi\) | ||||
−0.0825193 | + | 0.996589i | \(0.526297\pi\) | |||||||
\(888\) | 8.35023 | 0.280215 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.51624 | 0.318985 | ||||||||
\(891\) | 5.70448 | 0.191107 | ||||||||
\(892\) | −1.22947 | −0.0411657 | ||||||||
\(893\) | 34.6728 | 1.16028 | ||||||||
\(894\) | −23.2835 | −0.778715 | ||||||||
\(895\) | −11.7490 | −0.392726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.35023 | −0.212028 | ||||||||
\(898\) | 9.26006 | 0.309012 | ||||||||
\(899\) | −18.6888 | −0.623306 | ||||||||
\(900\) | −2.81247 | −0.0937491 | ||||||||
\(901\) | −2.14889 | −0.0715900 | ||||||||
\(902\) | −42.1685 | −1.40406 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.725281 | −0.0241225 | ||||||||
\(905\) | −10.9441 | −0.363793 | ||||||||
\(906\) | −6.01381 | −0.199795 | ||||||||
\(907\) | 34.1538 | 1.13406 | 0.567029 | − | 0.823698i | \(-0.308093\pi\) | ||||
0.567029 | + | 0.823698i | \(0.308093\pi\) | |||||||
\(908\) | 16.4130 | 0.544684 | ||||||||
\(909\) | 2.81247 | 0.0932839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.3590 | −1.73473 | −0.867365 | − | 0.497672i | \(-0.834188\pi\) | ||||
−0.867365 | + | 0.497672i | \(0.834188\pi\) | |||||||
\(912\) | −3.39217 | −0.112326 | ||||||||
\(913\) | −52.6034 | −1.74092 | ||||||||
\(914\) | −5.83730 | −0.193081 | ||||||||
\(915\) | 7.45718 | 0.246527 | ||||||||
\(916\) | −25.4163 | −0.839778 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.12478 | −0.136138 | ||||||||
\(919\) | 36.4464 | 1.20225 | 0.601127 | − | 0.799153i | \(-0.294718\pi\) | ||||
0.601127 | + | 0.799153i | \(0.294718\pi\) | |||||||
\(920\) | −1.47903 | −0.0487621 | ||||||||
\(921\) | 24.9467 | 0.822022 | ||||||||
\(922\) | −23.1660 | −0.762932 | ||||||||
\(923\) | 62.6844 | 2.06328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.4848 | −0.772175 | ||||||||
\(926\) | −0.140148 | −0.00460554 | ||||||||
\(927\) | −12.5589 | −0.412488 | ||||||||
\(928\) | −2.39217 | −0.0785269 | ||||||||
\(929\) | −55.4453 | −1.81910 | −0.909551 | − | 0.415592i | \(-0.863574\pi\) | ||||
−0.909551 | + | 0.415592i | \(0.863574\pi\) | |||||||
\(930\) | −11.5549 | −0.378899 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.551566 | 0.0180671 | ||||||||
\(933\) | −26.4878 | −0.867171 | ||||||||
\(934\) | −15.5170 | −0.507730 | ||||||||
\(935\) | −34.8011 | −1.13812 | ||||||||
\(936\) | −6.35023 | −0.207564 | ||||||||
\(937\) | −0.308796 | −0.0100879 | −0.00504396 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504396 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2382 | 0.627815 | ||||||||
\(940\) | 15.1178 | 0.493088 | ||||||||
\(941\) | −15.5046 | −0.505434 | −0.252717 | − | 0.967540i | \(-0.581324\pi\) | ||||
−0.252717 | + | 0.967540i | \(0.581324\pi\) | |||||||
\(942\) | −17.8672 | −0.582144 | ||||||||
\(943\) | 7.39217 | 0.240722 | ||||||||
\(944\) | 7.37836 | 0.240145 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.4090 | −0.370937 | ||||||||
\(947\) | 58.6924 | 1.90725 | 0.953624 | − | 0.301002i | \(-0.0973209\pi\) | ||||
0.953624 | + | 0.301002i | \(0.0973209\pi\) | |||||||
\(948\) | 13.4301 | 0.436189 | ||||||||
\(949\) | 56.7071 | 1.84079 | ||||||||
\(950\) | 9.54039 | 0.309531 | ||||||||
\(951\) | −25.3784 | −0.822950 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.6120 | 0.926835 | 0.463417 | − | 0.886140i | \(-0.346623\pi\) | ||||
0.463417 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(954\) | −0.520971 | −0.0168671 | ||||||||
\(955\) | 29.8416 | 0.965653 | ||||||||
\(956\) | −11.2634 | −0.364283 | ||||||||
\(957\) | −13.6461 | −0.441115 | ||||||||
\(958\) | −15.3922 | −0.497298 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.47903 | −0.0477354 | ||||||||
\(961\) | 30.0347 | 0.968863 | ||||||||
\(962\) | −53.0259 | −1.70962 | ||||||||
\(963\) | −5.22143 | −0.168258 | ||||||||
\(964\) | −28.3284 | −0.912396 | ||||||||
\(965\) | 19.0617 | 0.613618 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.7059 | −0.505067 | −0.252534 | − | 0.967588i | \(-0.581264\pi\) | ||||
−0.252534 | + | 0.967588i | \(0.581264\pi\) | |||||||
\(968\) | −21.5411 | −0.692356 | ||||||||
\(969\) | 13.9920 | 0.449487 | ||||||||
\(970\) | 15.3287 | 0.492175 | ||||||||
\(971\) | 16.7660 | 0.538047 | 0.269023 | − | 0.963134i | \(-0.413299\pi\) | ||||
0.269023 | + | 0.963134i | \(0.413299\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.554539 | 0.0177686 | ||||||||
\(975\) | 17.8599 | 0.571973 | ||||||||
\(976\) | −5.04194 | −0.161389 | ||||||||
\(977\) | 17.3733 | 0.555821 | 0.277910 | − | 0.960607i | \(-0.410358\pi\) | ||||
0.277910 | + | 0.960607i | \(0.410358\pi\) | |||||||
\(978\) | 13.8712 | 0.443552 | ||||||||
\(979\) | −36.7033 | −1.17304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.47501 | −0.270586 | ||||||||
\(982\) | −43.1966 | −1.37846 | ||||||||
\(983\) | 24.0867 | 0.768246 | 0.384123 | − | 0.923282i | \(-0.374504\pi\) | ||||
0.384123 | + | 0.923282i | \(0.374504\pi\) | |||||||
\(984\) | 7.39217 | 0.235654 | ||||||||
\(985\) | −14.5005 | −0.462026 | ||||||||
\(986\) | 9.86718 | 0.314235 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 21.5411 | 0.685313 | ||||||||
\(989\) | 2.00000 | 0.0635963 | ||||||||
\(990\) | −8.43709 | −0.268148 | ||||||||
\(991\) | 56.6793 | 1.80048 | 0.900238 | − | 0.435398i | \(-0.143392\pi\) | ||||
0.900238 | + | 0.435398i | \(0.143392\pi\) | |||||||
\(992\) | 7.81247 | 0.248046 | ||||||||
\(993\) | −2.84273 | −0.0902114 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.90389 | 0.155464 | ||||||||
\(996\) | 9.22143 | 0.292192 | ||||||||
\(997\) | 41.4037 | 1.31127 | 0.655634 | − | 0.755079i | \(-0.272401\pi\) | ||||
0.655634 | + | 0.755079i | \(0.272401\pi\) | |||||||
\(998\) | 20.8943 | 0.661396 | ||||||||
\(999\) | −8.35023 | −0.264190 |
(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 | 6762.2.a.cg.1.3 | 4 | ||
7.2 | even | 3 | 966.2.i.n.277.2 | ✓ | 8 | ||
7.4 | even | 3 | 966.2.i.n.415.2 | yes | 8 | ||
7.6 | odd | 2 | 6762.2.a.ch.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.n.277.2 | ✓ | 8 | 7.2 | even | 3 | ||
966.2.i.n.415.2 | yes | 8 | 7.4 | even | 3 | ||
6762.2.a.cg.1.3 | 4 | 1.1 | even | 1 | trivial | ||
6762.2.a.ch.1.2 | 4 | 7.6 | odd | 2 |