Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.31808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 11x^{2} + 12x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.34975\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(5\) | −1.34975 | −0.603626 | −0.301813 | − | 0.953367i | \(-0.597592\pi\) | ||||
−0.301813 | + | 0.953367i | \(0.597592\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.34975 | −0.426828 | ||||||||
\(11\) | 5.25858 | 1.58552 | 0.792761 | − | 0.609532i | \(-0.208643\pi\) | ||||
0.792761 | + | 0.609532i | \(0.208643\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.34975 | 0.348504 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.25858 | 0.790323 | 0.395161 | − | 0.918612i | \(-0.370689\pi\) | ||||
0.395161 | + | 0.918612i | \(0.370689\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.34975 | −0.309654 | −0.154827 | − | 0.987942i | \(-0.549482\pi\) | ||||
−0.154827 | + | 0.987942i | \(0.549482\pi\) | |||||||
\(20\) | −1.34975 | −0.301813 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.25858 | 1.12113 | ||||||||
\(23\) | 0.650251 | 0.135587 | 0.0677933 | − | 0.997699i | \(-0.478404\pi\) | ||||
0.0677933 | + | 0.997699i | \(0.478404\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.17818 | −0.635635 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.155630 | 0.0288998 | 0.0144499 | − | 0.999896i | \(-0.495400\pi\) | ||||
0.0144499 | + | 0.999896i | \(0.495400\pi\) | |||||||
\(30\) | 1.34975 | 0.246429 | ||||||||
\(31\) | −1.90883 | −0.342837 | −0.171418 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171418 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.25858 | −0.915402 | ||||||||
\(34\) | 3.25858 | 0.558842 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.59239 | 1.24818 | 0.624091 | − | 0.781352i | \(-0.285470\pi\) | ||||
0.624091 | + | 0.781352i | \(0.285470\pi\) | |||||||
\(38\) | −1.34975 | −0.218958 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.34975 | −0.213414 | ||||||||
\(41\) | −3.32305 | −0.518973 | −0.259486 | − | 0.965747i | \(-0.583553\pi\) | ||||
−0.259486 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.16742 | −0.483027 | −0.241513 | − | 0.970398i | \(-0.577644\pi\) | ||||
−0.241513 | + | 0.970398i | \(0.577644\pi\) | |||||||
\(44\) | 5.25858 | 0.792761 | ||||||||
\(45\) | −1.34975 | −0.201209 | ||||||||
\(46\) | 0.650251 | 0.0958742 | ||||||||
\(47\) | 8.15147 | 1.18901 | 0.594507 | − | 0.804090i | \(-0.297347\pi\) | ||||
0.594507 | + | 0.804090i | \(0.297347\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.17818 | −0.449462 | ||||||||
\(51\) | −3.25858 | −0.456293 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 4.49462 | 0.617384 | 0.308692 | − | 0.951162i | \(-0.400109\pi\) | ||||
0.308692 | + | 0.951162i | \(0.400109\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.09777 | −0.957063 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.34975 | 0.178779 | ||||||||
\(58\) | 0.155630 | 0.0204353 | ||||||||
\(59\) | −1.90883 | −0.248509 | −0.124255 | − | 0.992250i | \(-0.539654\pi\) | ||||
−0.124255 | + | 0.992250i | \(0.539654\pi\) | |||||||
\(60\) | 1.34975 | 0.174252 | ||||||||
\(61\) | 2.26934 | 0.290560 | 0.145280 | − | 0.989391i | \(-0.453592\pi\) | ||||
0.145280 | + | 0.989391i | \(0.453592\pi\) | |||||||
\(62\) | −1.90883 | −0.242422 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.34975 | 0.167416 | ||||||||
\(66\) | −5.25858 | −0.647287 | ||||||||
\(67\) | 1.88629 | 0.230447 | 0.115223 | − | 0.993340i | \(-0.463242\pi\) | ||||
0.115223 | + | 0.993340i | \(0.463242\pi\) | |||||||
\(68\) | 3.25858 | 0.395161 | ||||||||
\(69\) | −0.650251 | −0.0782810 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.30783 | −0.629924 | −0.314962 | − | 0.949104i | \(-0.601992\pi\) | ||||
−0.314962 | + | 0.949104i | \(0.601992\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 5.34975 | 0.626141 | 0.313070 | − | 0.949730i | \(-0.398642\pi\) | ||||
0.313070 | + | 0.949730i | \(0.398642\pi\) | |||||||
\(74\) | 7.59239 | 0.882597 | ||||||||
\(75\) | 3.17818 | 0.366984 | ||||||||
\(76\) | −1.34975 | −0.154827 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 5.74802 | 0.646703 | 0.323351 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323351 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(80\) | −1.34975 | −0.150907 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.32305 | −0.366969 | ||||||||
\(83\) | −2.95736 | −0.324612 | −0.162306 | − | 0.986740i | \(-0.551893\pi\) | ||||
−0.162306 | + | 0.986740i | \(0.551893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.39827 | −0.477059 | ||||||||
\(86\) | −3.16742 | −0.341551 | ||||||||
\(87\) | −0.155630 | −0.0166853 | ||||||||
\(88\) | 5.25858 | 0.560567 | ||||||||
\(89\) | 10.7598 | 1.14054 | 0.570269 | − | 0.821458i | \(-0.306839\pi\) | ||||
0.570269 | + | 0.821458i | \(0.306839\pi\) | |||||||
\(90\) | −1.34975 | −0.142276 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.650251 | 0.0677933 | ||||||||
\(93\) | 1.90883 | 0.197937 | ||||||||
\(94\) | 8.15147 | 0.840760 | ||||||||
\(95\) | 1.82182 | 0.186915 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.3456 | −1.15197 | −0.575985 | − | 0.817460i | \(-0.695381\pi\) | ||||
−0.575985 | + | 0.817460i | \(0.695381\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.25858 | 0.528508 | ||||||||
\(100\) | −3.17818 | −0.317818 | ||||||||
\(101\) | 1.77991 | 0.177107 | 0.0885536 | − | 0.996071i | \(-0.471776\pi\) | ||||
0.0885536 | + | 0.996071i | \(0.471776\pi\) | |||||||
\(102\) | −3.25858 | −0.322648 | ||||||||
\(103\) | 17.9487 | 1.76854 | 0.884271 | − | 0.466974i | \(-0.154656\pi\) | ||||
0.884271 | + | 0.466974i | \(0.154656\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.49462 | 0.436556 | ||||||||
\(107\) | −11.4593 | −1.10781 | −0.553906 | − | 0.832579i | \(-0.686863\pi\) | ||||
−0.553906 | + | 0.832579i | \(0.686863\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.02182 | −0.0978726 | −0.0489363 | − | 0.998802i | \(-0.515583\pi\) | ||||
−0.0489363 | + | 0.998802i | \(0.515583\pi\) | |||||||
\(110\) | −7.09777 | −0.676746 | ||||||||
\(111\) | −7.59239 | −0.720638 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.9539 | 1.50082 | 0.750410 | − | 0.660973i | \(-0.229856\pi\) | ||||
0.750410 | + | 0.660973i | \(0.229856\pi\) | |||||||
\(114\) | 1.34975 | 0.126416 | ||||||||
\(115\) | −0.877675 | −0.0818436 | ||||||||
\(116\) | 0.155630 | 0.0144499 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −1.90883 | −0.175722 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.34975 | 0.123215 | ||||||||
\(121\) | 16.6527 | 1.51388 | ||||||||
\(122\) | 2.26934 | 0.205457 | ||||||||
\(123\) | 3.32305 | 0.299629 | ||||||||
\(124\) | −1.90883 | −0.171418 | ||||||||
\(125\) | 11.0385 | 0.987312 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.03776 | −0.180822 | −0.0904111 | − | 0.995905i | \(-0.528818\pi\) | ||||
−0.0904111 | + | 0.995905i | \(0.528818\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.16742 | 0.278876 | ||||||||
\(130\) | 1.34975 | 0.118381 | ||||||||
\(131\) | 15.5615 | 1.35962 | 0.679809 | − | 0.733389i | \(-0.262063\pi\) | ||||
0.679809 | + | 0.733389i | \(0.262063\pi\) | |||||||
\(132\) | −5.25858 | −0.457701 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.88629 | 0.162950 | ||||||||
\(135\) | 1.34975 | 0.116168 | ||||||||
\(136\) | 3.25858 | 0.279421 | ||||||||
\(137\) | 2.58060 | 0.220476 | 0.110238 | − | 0.993905i | \(-0.464839\pi\) | ||||
0.110238 | + | 0.993905i | \(0.464839\pi\) | |||||||
\(138\) | −0.650251 | −0.0553530 | ||||||||
\(139\) | 18.2059 | 1.54420 | 0.772102 | − | 0.635498i | \(-0.219205\pi\) | ||||
0.772102 | + | 0.635498i | \(0.219205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.15147 | −0.686478 | ||||||||
\(142\) | −5.30783 | −0.445423 | ||||||||
\(143\) | −5.25858 | −0.439745 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.210062 | −0.0174447 | ||||||||
\(146\) | 5.34975 | 0.442748 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.59239 | 0.624091 | ||||||||
\(149\) | 9.50641 | 0.778795 | 0.389398 | − | 0.921070i | \(-0.372683\pi\) | ||||
0.389398 | + | 0.921070i | \(0.372683\pi\) | |||||||
\(150\) | 3.17818 | 0.259497 | ||||||||
\(151\) | 13.1297 | 1.06848 | 0.534238 | − | 0.845334i | \(-0.320599\pi\) | ||||
0.534238 | + | 0.845334i | \(0.320599\pi\) | |||||||
\(152\) | −1.34975 | −0.109479 | ||||||||
\(153\) | 3.25858 | 0.263441 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.57645 | 0.206945 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 2.32275 | 0.185375 | 0.0926877 | − | 0.995695i | \(-0.470454\pi\) | ||||
0.0926877 | + | 0.995695i | \(0.470454\pi\) | |||||||
\(158\) | 5.74802 | 0.457288 | ||||||||
\(159\) | −4.49462 | −0.356447 | ||||||||
\(160\) | −1.34975 | −0.106707 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 21.5956 | 1.69150 | 0.845748 | − | 0.533583i | \(-0.179155\pi\) | ||||
0.845748 | + | 0.533583i | \(0.179155\pi\) | |||||||
\(164\) | −3.32305 | −0.259486 | ||||||||
\(165\) | 7.09777 | 0.552561 | ||||||||
\(166\) | −2.95736 | −0.229535 | ||||||||
\(167\) | −25.3321 | −1.96026 | −0.980128 | − | 0.198364i | \(-0.936437\pi\) | ||||
−0.980128 | + | 0.198364i | \(0.936437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −4.39827 | −0.337332 | ||||||||
\(171\) | −1.34975 | −0.103218 | ||||||||
\(172\) | −3.16742 | −0.241513 | ||||||||
\(173\) | 1.80142 | 0.136960 | 0.0684799 | − | 0.997652i | \(-0.478185\pi\) | ||||
0.0684799 | + | 0.997652i | \(0.478185\pi\) | |||||||
\(174\) | −0.155630 | −0.0117983 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.25858 | 0.396381 | ||||||||
\(177\) | 1.90883 | 0.143477 | ||||||||
\(178\) | 10.7598 | 0.806482 | ||||||||
\(179\) | −0.274526 | −0.0205190 | −0.0102595 | − | 0.999947i | \(-0.503266\pi\) | ||||
−0.0102595 | + | 0.999947i | \(0.503266\pi\) | |||||||
\(180\) | −1.34975 | −0.100604 | ||||||||
\(181\) | −12.7750 | −0.949560 | −0.474780 | − | 0.880105i | \(-0.657472\pi\) | ||||
−0.474780 | + | 0.880105i | \(0.657472\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.26934 | −0.167755 | ||||||||
\(184\) | 0.650251 | 0.0479371 | ||||||||
\(185\) | −10.2478 | −0.753435 | ||||||||
\(186\) | 1.90883 | 0.139962 | ||||||||
\(187\) | 17.1355 | 1.25307 | ||||||||
\(188\) | 8.15147 | 0.594507 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.82182 | 0.132169 | ||||||||
\(191\) | −19.1487 | −1.38555 | −0.692777 | − | 0.721152i | \(-0.743613\pi\) | ||||
−0.692777 | + | 0.721152i | \(0.743613\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 9.49016 | 0.683117 | 0.341558 | − | 0.939861i | \(-0.389045\pi\) | ||||
0.341558 | + | 0.939861i | \(0.389045\pi\) | |||||||
\(194\) | −11.3456 | −0.814566 | ||||||||
\(195\) | −1.34975 | −0.0966576 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.33826 | 0.0953473 | 0.0476737 | − | 0.998863i | \(-0.484819\pi\) | ||||
0.0476737 | + | 0.998863i | \(0.484819\pi\) | |||||||
\(198\) | 5.25858 | 0.373711 | ||||||||
\(199\) | 21.0988 | 1.49565 | 0.747827 | − | 0.663894i | \(-0.231097\pi\) | ||||
0.747827 | + | 0.663894i | \(0.231097\pi\) | |||||||
\(200\) | −3.17818 | −0.224731 | ||||||||
\(201\) | −1.88629 | −0.133048 | ||||||||
\(202\) | 1.77991 | 0.125234 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.25858 | −0.228146 | ||||||||
\(205\) | 4.48528 | 0.313266 | ||||||||
\(206\) | 17.9487 | 1.25055 | ||||||||
\(207\) | 0.650251 | 0.0451955 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −7.09777 | −0.490963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.16742 | 0.493425 | 0.246713 | − | 0.969089i | \(-0.420650\pi\) | ||||
0.246713 | + | 0.969089i | \(0.420650\pi\) | |||||||
\(212\) | 4.49462 | 0.308692 | ||||||||
\(213\) | 5.30783 | 0.363687 | ||||||||
\(214\) | −11.4593 | −0.783342 | ||||||||
\(215\) | 4.27522 | 0.291568 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.02182 | −0.0692064 | ||||||||
\(219\) | −5.34975 | −0.361503 | ||||||||
\(220\) | −7.09777 | −0.478532 | ||||||||
\(221\) | −3.25858 | −0.219196 | ||||||||
\(222\) | −7.59239 | −0.509568 | ||||||||
\(223\) | −12.6593 | −0.847730 | −0.423865 | − | 0.905725i | \(-0.639327\pi\) | ||||
−0.423865 | + | 0.905725i | \(0.639327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.17818 | −0.211878 | ||||||||
\(226\) | 15.9539 | 1.06124 | ||||||||
\(227\) | −9.77991 | −0.649115 | −0.324558 | − | 0.945866i | \(-0.605215\pi\) | ||||
−0.324558 | + | 0.945866i | \(0.605215\pi\) | |||||||
\(228\) | 1.34975 | 0.0893893 | ||||||||
\(229\) | 27.0721 | 1.78897 | 0.894487 | − | 0.447094i | \(-0.147541\pi\) | ||||
0.894487 | + | 0.447094i | \(0.147541\pi\) | |||||||
\(230\) | −0.877675 | −0.0578722 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.155630 | 0.0102176 | ||||||||
\(233\) | −22.5838 | −1.47951 | −0.739756 | − | 0.672875i | \(-0.765059\pi\) | ||||
−0.739756 | + | 0.672875i | \(0.765059\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −11.0024 | −0.717721 | ||||||||
\(236\) | −1.90883 | −0.124255 | ||||||||
\(237\) | −5.74802 | −0.373374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0617 | 0.844893 | 0.422447 | − | 0.906388i | \(-0.361171\pi\) | ||||
0.422447 | + | 0.906388i | \(0.361171\pi\) | |||||||
\(240\) | 1.34975 | 0.0871259 | ||||||||
\(241\) | −6.04509 | −0.389399 | −0.194699 | − | 0.980863i | \(-0.562373\pi\) | ||||
−0.194699 | + | 0.980863i | \(0.562373\pi\) | |||||||
\(242\) | 16.6527 | 1.07048 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.26934 | 0.145280 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.32305 | 0.211870 | ||||||||
\(247\) | 1.34975 | 0.0858825 | ||||||||
\(248\) | −1.90883 | −0.121211 | ||||||||
\(249\) | 2.95736 | 0.187415 | ||||||||
\(250\) | 11.0385 | 0.698135 | ||||||||
\(251\) | −10.7331 | −0.677468 | −0.338734 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338734 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.41940 | 0.214976 | ||||||||
\(254\) | −2.03776 | −0.127861 | ||||||||
\(255\) | 4.39827 | 0.275430 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.13969 | 0.0710918 | 0.0355459 | − | 0.999368i | \(-0.488683\pi\) | ||||
0.0355459 | + | 0.999368i | \(0.488683\pi\) | |||||||
\(258\) | 3.16742 | 0.197195 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.34975 | 0.0837079 | ||||||||
\(261\) | 0.155630 | 0.00963327 | ||||||||
\(262\) | 15.5615 | 0.961395 | ||||||||
\(263\) | 25.2922 | 1.55958 | 0.779792 | − | 0.626039i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626039i | \(0.215325\pi\) | |||||||
\(264\) | −5.25858 | −0.323643 | ||||||||
\(265\) | −6.06661 | −0.372669 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.7598 | −0.658490 | ||||||||
\(268\) | 1.88629 | 0.115223 | ||||||||
\(269\) | −4.66174 | −0.284231 | −0.142116 | − | 0.989850i | \(-0.545390\pi\) | ||||
−0.142116 | + | 0.989850i | \(0.545390\pi\) | |||||||
\(270\) | 1.34975 | 0.0821431 | ||||||||
\(271\) | 6.70538 | 0.407323 | 0.203661 | − | 0.979041i | \(-0.434716\pi\) | ||||
0.203661 | + | 0.979041i | \(0.434716\pi\) | |||||||
\(272\) | 3.25858 | 0.197581 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.58060 | 0.155900 | ||||||||
\(275\) | −16.7127 | −1.00781 | ||||||||
\(276\) | −0.650251 | −0.0391405 | ||||||||
\(277\) | −29.1068 | −1.74886 | −0.874430 | − | 0.485152i | \(-0.838764\pi\) | ||||
−0.874430 | + | 0.485152i | \(0.838764\pi\) | |||||||
\(278\) | 18.2059 | 1.09192 | ||||||||
\(279\) | −1.90883 | −0.114279 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.356353 | 0.0212582 | 0.0106291 | − | 0.999944i | \(-0.496617\pi\) | ||||
0.0106291 | + | 0.999944i | \(0.496617\pi\) | |||||||
\(282\) | −8.15147 | −0.485413 | ||||||||
\(283\) | 21.8392 | 1.29820 | 0.649102 | − | 0.760701i | \(-0.275145\pi\) | ||||
0.649102 | + | 0.760701i | \(0.275145\pi\) | |||||||
\(284\) | −5.30783 | −0.314962 | ||||||||
\(285\) | −1.82182 | −0.107916 | ||||||||
\(286\) | −5.25858 | −0.310947 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −6.38163 | −0.375390 | ||||||||
\(290\) | −0.210062 | −0.0123353 | ||||||||
\(291\) | 11.3456 | 0.665090 | ||||||||
\(292\) | 5.34975 | 0.313070 | ||||||||
\(293\) | −9.18478 | −0.536581 | −0.268290 | − | 0.963338i | \(-0.586459\pi\) | ||||
−0.268290 | + | 0.963338i | \(0.586459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.57645 | 0.150007 | ||||||||
\(296\) | 7.59239 | 0.441299 | ||||||||
\(297\) | −5.25858 | −0.305134 | ||||||||
\(298\) | 9.50641 | 0.550691 | ||||||||
\(299\) | −0.650251 | −0.0376050 | ||||||||
\(300\) | 3.17818 | 0.183492 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.1297 | 0.755527 | ||||||||
\(303\) | −1.77991 | −0.102253 | ||||||||
\(304\) | −1.34975 | −0.0774134 | ||||||||
\(305\) | −3.06304 | −0.175389 | ||||||||
\(306\) | 3.25858 | 0.186281 | ||||||||
\(307\) | −6.01321 | −0.343192 | −0.171596 | − | 0.985167i | \(-0.554892\pi\) | ||||
−0.171596 | + | 0.985167i | \(0.554892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.9487 | −1.02107 | ||||||||
\(310\) | 2.57645 | 0.146332 | ||||||||
\(311\) | −13.8926 | −0.787777 | −0.393888 | − | 0.919158i | \(-0.628870\pi\) | ||||
−0.393888 | + | 0.919158i | \(0.628870\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 12.9206 | 0.730317 | 0.365158 | − | 0.930945i | \(-0.381015\pi\) | ||||
0.365158 | + | 0.930945i | \(0.381015\pi\) | |||||||
\(314\) | 2.32275 | 0.131080 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.74802 | 0.323351 | ||||||||
\(317\) | −28.4696 | −1.59901 | −0.799507 | − | 0.600657i | \(-0.794906\pi\) | ||||
−0.799507 | + | 0.600657i | \(0.794906\pi\) | |||||||
\(318\) | −4.49462 | −0.252046 | ||||||||
\(319\) | 0.818395 | 0.0458213 | ||||||||
\(320\) | −1.34975 | −0.0754533 | ||||||||
\(321\) | 11.4593 | 0.639596 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.39827 | −0.244726 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.17818 | 0.176294 | ||||||||
\(326\) | 21.5956 | 1.19607 | ||||||||
\(327\) | 1.02182 | 0.0565068 | ||||||||
\(328\) | −3.32305 | −0.183485 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.09777 | 0.390719 | ||||||||
\(331\) | −18.7383 | −1.02995 | −0.514975 | − | 0.857205i | \(-0.672199\pi\) | ||||
−0.514975 | + | 0.857205i | \(0.672199\pi\) | |||||||
\(332\) | −2.95736 | −0.162306 | ||||||||
\(333\) | 7.59239 | 0.416060 | ||||||||
\(334\) | −25.3321 | −1.38611 | ||||||||
\(335\) | −2.54602 | −0.139104 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.30955 | 0.289230 | 0.144615 | − | 0.989488i | \(-0.453806\pi\) | ||||
0.144615 | + | 0.989488i | \(0.453806\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −15.9539 | −0.866498 | ||||||||
\(340\) | −4.39827 | −0.238530 | ||||||||
\(341\) | −10.0378 | −0.543575 | ||||||||
\(342\) | −1.34975 | −0.0729861 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.16742 | −0.170776 | ||||||||
\(345\) | 0.877675 | 0.0472525 | ||||||||
\(346\) | 1.80142 | 0.0968452 | ||||||||
\(347\) | 29.0628 | 1.56017 | 0.780085 | − | 0.625673i | \(-0.215176\pi\) | ||||
0.780085 | + | 0.625673i | \(0.215176\pi\) | |||||||
\(348\) | −0.155630 | −0.00834266 | ||||||||
\(349\) | 8.83576 | 0.472967 | 0.236484 | − | 0.971635i | \(-0.424005\pi\) | ||||
0.236484 | + | 0.971635i | \(0.424005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 5.25858 | 0.280283 | ||||||||
\(353\) | 25.7030 | 1.36803 | 0.684016 | − | 0.729467i | \(-0.260232\pi\) | ||||
0.684016 | + | 0.729467i | \(0.260232\pi\) | |||||||
\(354\) | 1.90883 | 0.101453 | ||||||||
\(355\) | 7.16424 | 0.380239 | ||||||||
\(356\) | 10.7598 | 0.570269 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.274526 | −0.0145091 | ||||||||
\(359\) | −23.4211 | −1.23612 | −0.618060 | − | 0.786131i | \(-0.712081\pi\) | ||||
−0.618060 | + | 0.786131i | \(0.712081\pi\) | |||||||
\(360\) | −1.34975 | −0.0711380 | ||||||||
\(361\) | −17.1782 | −0.904115 | ||||||||
\(362\) | −12.7750 | −0.671440 | ||||||||
\(363\) | −16.6527 | −0.874040 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.22082 | −0.377955 | ||||||||
\(366\) | −2.26934 | −0.118620 | ||||||||
\(367\) | 18.7442 | 0.978437 | 0.489219 | − | 0.872161i | \(-0.337282\pi\) | ||||
0.489219 | + | 0.872161i | \(0.337282\pi\) | |||||||
\(368\) | 0.650251 | 0.0338967 | ||||||||
\(369\) | −3.32305 | −0.172991 | ||||||||
\(370\) | −10.2478 | −0.532759 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.90883 | 0.0989684 | ||||||||
\(373\) | −19.9005 | −1.03041 | −0.515205 | − | 0.857067i | \(-0.672284\pi\) | ||||
−0.515205 | + | 0.857067i | \(0.672284\pi\) | |||||||
\(374\) | 17.1355 | 0.886057 | ||||||||
\(375\) | −11.0385 | −0.570025 | ||||||||
\(376\) | 8.15147 | 0.420380 | ||||||||
\(377\) | −0.155630 | −0.00801536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.6760 | −1.26752 | −0.633760 | − | 0.773530i | \(-0.718489\pi\) | ||||
−0.633760 | + | 0.773530i | \(0.718489\pi\) | |||||||
\(380\) | 1.82182 | 0.0934576 | ||||||||
\(381\) | 2.03776 | 0.104398 | ||||||||
\(382\) | −19.1487 | −0.979735 | ||||||||
\(383\) | −21.2115 | −1.08386 | −0.541928 | − | 0.840425i | \(-0.682305\pi\) | ||||
−0.541928 | + | 0.840425i | \(0.682305\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.49016 | 0.483037 | ||||||||
\(387\) | −3.16742 | −0.161009 | ||||||||
\(388\) | −11.3456 | −0.575985 | ||||||||
\(389\) | −33.2073 | −1.68368 | −0.841839 | − | 0.539729i | \(-0.818527\pi\) | ||||
−0.841839 | + | 0.539729i | \(0.818527\pi\) | |||||||
\(390\) | −1.34975 | −0.0683472 | ||||||||
\(391\) | 2.11890 | 0.107157 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5615 | −0.784975 | ||||||||
\(394\) | 1.33826 | 0.0674207 | ||||||||
\(395\) | −7.75839 | −0.390367 | ||||||||
\(396\) | 5.25858 | 0.264254 | ||||||||
\(397\) | 21.3907 | 1.07357 | 0.536784 | − | 0.843720i | \(-0.319639\pi\) | ||||
0.536784 | + | 0.843720i | \(0.319639\pi\) | |||||||
\(398\) | 21.0988 | 1.05759 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.17818 | −0.158909 | ||||||||
\(401\) | −21.4745 | −1.07239 | −0.536193 | − | 0.844095i | \(-0.680138\pi\) | ||||
−0.536193 | + | 0.844095i | \(0.680138\pi\) | |||||||
\(402\) | −1.88629 | −0.0940795 | ||||||||
\(403\) | 1.90883 | 0.0950858 | ||||||||
\(404\) | 1.77991 | 0.0885536 | ||||||||
\(405\) | −1.34975 | −0.0670696 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.9252 | 1.97902 | ||||||||
\(408\) | −3.25858 | −0.161324 | ||||||||
\(409\) | −4.18854 | −0.207110 | −0.103555 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103555 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(410\) | 4.48528 | 0.221512 | ||||||||
\(411\) | −2.58060 | −0.127292 | ||||||||
\(412\) | 17.9487 | 0.884271 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.650251 | 0.0319581 | ||||||||
\(415\) | 3.99169 | 0.195944 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −18.2059 | −0.891547 | ||||||||
\(418\) | −7.09777 | −0.347163 | ||||||||
\(419\) | 8.88501 | 0.434061 | 0.217030 | − | 0.976165i | \(-0.430363\pi\) | ||||
0.217030 | + | 0.976165i | \(0.430363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.59411 | 0.467588 | 0.233794 | − | 0.972286i | \(-0.424886\pi\) | ||||
0.233794 | + | 0.972286i | \(0.424886\pi\) | |||||||
\(422\) | 7.16742 | 0.348904 | ||||||||
\(423\) | 8.15147 | 0.396338 | ||||||||
\(424\) | 4.49462 | 0.218278 | ||||||||
\(425\) | −10.3564 | −0.502357 | ||||||||
\(426\) | 5.30783 | 0.257165 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.4593 | −0.553906 | ||||||||
\(429\) | 5.25858 | 0.253887 | ||||||||
\(430\) | 4.27522 | 0.206169 | ||||||||
\(431\) | 16.6897 | 0.803916 | 0.401958 | − | 0.915658i | \(-0.368330\pi\) | ||||
0.401958 | + | 0.915658i | \(0.368330\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −12.8613 | −0.618077 | −0.309038 | − | 0.951050i | \(-0.600007\pi\) | ||||
−0.309038 | + | 0.951050i | \(0.600007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.210062 | 0.0100717 | ||||||||
\(436\) | −1.02182 | −0.0489363 | ||||||||
\(437\) | −0.877675 | −0.0419849 | ||||||||
\(438\) | −5.34975 | −0.255621 | ||||||||
\(439\) | 2.23359 | 0.106603 | 0.0533017 | − | 0.998578i | \(-0.483025\pi\) | ||||
0.0533017 | + | 0.998578i | \(0.483025\pi\) | |||||||
\(440\) | −7.09777 | −0.338373 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.25858 | −0.154995 | ||||||||
\(443\) | 26.5093 | 1.25949 | 0.629747 | − | 0.776800i | \(-0.283159\pi\) | ||||
0.629747 | + | 0.776800i | \(0.283159\pi\) | |||||||
\(444\) | −7.59239 | −0.360319 | ||||||||
\(445\) | −14.5230 | −0.688458 | ||||||||
\(446\) | −12.6593 | −0.599435 | ||||||||
\(447\) | −9.50641 | −0.449638 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.1306 | −1.32757 | −0.663784 | − | 0.747925i | \(-0.731050\pi\) | ||||
−0.663784 | + | 0.747925i | \(0.731050\pi\) | |||||||
\(450\) | −3.17818 | −0.149821 | ||||||||
\(451\) | −17.4745 | −0.822843 | ||||||||
\(452\) | 15.9539 | 0.750410 | ||||||||
\(453\) | −13.1297 | −0.616885 | ||||||||
\(454\) | −9.77991 | −0.458994 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.34975 | 0.0632078 | ||||||||
\(457\) | −15.0715 | −0.705015 | −0.352507 | − | 0.935809i | \(-0.614671\pi\) | ||||
−0.352507 | + | 0.935809i | \(0.614671\pi\) | |||||||
\(458\) | 27.0721 | 1.26500 | ||||||||
\(459\) | −3.25858 | −0.152098 | ||||||||
\(460\) | −0.877675 | −0.0409218 | ||||||||
\(461\) | 10.4492 | 0.486670 | 0.243335 | − | 0.969942i | \(-0.421759\pi\) | ||||
0.243335 | + | 0.969942i | \(0.421759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0115 | 0.558221 | 0.279111 | − | 0.960259i | \(-0.409960\pi\) | ||||
0.279111 | + | 0.960259i | \(0.409960\pi\) | |||||||
\(464\) | 0.155630 | 0.00722495 | ||||||||
\(465\) | −2.57645 | −0.119480 | ||||||||
\(466\) | −22.5838 | −1.04617 | ||||||||
\(467\) | −21.6468 | −1.00170 | −0.500848 | − | 0.865535i | \(-0.666978\pi\) | ||||
−0.500848 | + | 0.865535i | \(0.666978\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11.0024 | −0.507505 | ||||||||
\(471\) | −2.32275 | −0.107027 | ||||||||
\(472\) | −1.90883 | −0.0878612 | ||||||||
\(473\) | −16.6561 | −0.765850 | ||||||||
\(474\) | −5.74802 | −0.264015 | ||||||||
\(475\) | 4.28974 | 0.196827 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.49462 | 0.205795 | ||||||||
\(478\) | 13.0617 | 0.597430 | ||||||||
\(479\) | −3.28211 | −0.149963 | −0.0749817 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749817 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(480\) | 1.34975 | 0.0616073 | ||||||||
\(481\) | −7.59239 | −0.346183 | ||||||||
\(482\) | −6.04509 | −0.275346 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.6527 | 0.756941 | ||||||||
\(485\) | 15.3137 | 0.695360 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 25.3907 | 1.15056 | 0.575281 | − | 0.817956i | \(-0.304893\pi\) | ||||
0.575281 | + | 0.817956i | \(0.304893\pi\) | |||||||
\(488\) | 2.26934 | 0.102728 | ||||||||
\(489\) | −21.5956 | −0.976585 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.6368 | −0.750806 | −0.375403 | − | 0.926862i | \(-0.622496\pi\) | ||||
−0.375403 | + | 0.926862i | \(0.622496\pi\) | |||||||
\(492\) | 3.32305 | 0.149815 | ||||||||
\(493\) | 0.507134 | 0.0228402 | ||||||||
\(494\) | 1.34975 | 0.0607281 | ||||||||
\(495\) | −7.09777 | −0.319021 | ||||||||
\(496\) | −1.90883 | −0.0857092 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.95736 | 0.132522 | ||||||||
\(499\) | −15.0495 | −0.673710 | −0.336855 | − | 0.941556i | \(-0.609363\pi\) | ||||
−0.336855 | + | 0.941556i | \(0.609363\pi\) | |||||||
\(500\) | 11.0385 | 0.493656 | ||||||||
\(501\) | 25.3321 | 1.13175 | ||||||||
\(502\) | −10.7331 | −0.479042 | ||||||||
\(503\) | −23.3529 | −1.04126 | −0.520628 | − | 0.853784i | \(-0.674302\pi\) | ||||
−0.520628 | + | 0.853784i | \(0.674302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.40243 | −0.106907 | ||||||||
\(506\) | 3.41940 | 0.152011 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −2.03776 | −0.0904111 | ||||||||
\(509\) | −6.67237 | −0.295748 | −0.147874 | − | 0.989006i | \(-0.547243\pi\) | ||||
−0.147874 | + | 0.989006i | \(0.547243\pi\) | |||||||
\(510\) | 4.39827 | 0.194759 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.34975 | 0.0595929 | ||||||||
\(514\) | 1.13969 | 0.0502695 | ||||||||
\(515\) | −24.2263 | −1.06754 | ||||||||
\(516\) | 3.16742 | 0.139438 | ||||||||
\(517\) | 42.8652 | 1.88521 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.80142 | −0.0790737 | ||||||||
\(520\) | 1.34975 | 0.0591904 | ||||||||
\(521\) | −13.4846 | −0.590769 | −0.295385 | − | 0.955378i | \(-0.595448\pi\) | ||||
−0.295385 | + | 0.955378i | \(0.595448\pi\) | |||||||
\(522\) | 0.155630 | 0.00681175 | ||||||||
\(523\) | −36.5162 | −1.59674 | −0.798371 | − | 0.602166i | \(-0.794304\pi\) | ||||
−0.798371 | + | 0.602166i | \(0.794304\pi\) | |||||||
\(524\) | 15.5615 | 0.679809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.2922 | 1.10279 | ||||||||
\(527\) | −6.22009 | −0.270952 | ||||||||
\(528\) | −5.25858 | −0.228850 | ||||||||
\(529\) | −22.5772 | −0.981616 | ||||||||
\(530\) | −6.06661 | −0.263517 | ||||||||
\(531\) | −1.90883 | −0.0828363 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.32305 | 0.143937 | ||||||||
\(534\) | −10.7598 | −0.465622 | ||||||||
\(535\) | 15.4672 | 0.668705 | ||||||||
\(536\) | 1.88629 | 0.0814752 | ||||||||
\(537\) | 0.274526 | 0.0118467 | ||||||||
\(538\) | −4.66174 | −0.200982 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.34975 | 0.0580840 | ||||||||
\(541\) | 31.7130 | 1.36345 | 0.681724 | − | 0.731609i | \(-0.261230\pi\) | ||||
0.681724 | + | 0.731609i | \(0.261230\pi\) | |||||||
\(542\) | 6.70538 | 0.288021 | ||||||||
\(543\) | 12.7750 | 0.548229 | ||||||||
\(544\) | 3.25858 | 0.139711 | ||||||||
\(545\) | 1.37920 | 0.0590785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1848 | 0.478227 | 0.239113 | − | 0.970992i | \(-0.423143\pi\) | ||||
0.239113 | + | 0.970992i | \(0.423143\pi\) | |||||||
\(548\) | 2.58060 | 0.110238 | ||||||||
\(549\) | 2.26934 | 0.0968532 | ||||||||
\(550\) | −16.7127 | −0.712632 | ||||||||
\(551\) | −0.210062 | −0.00894893 | ||||||||
\(552\) | −0.650251 | −0.0276765 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −29.1068 | −1.23663 | ||||||||
\(555\) | 10.2478 | 0.434996 | ||||||||
\(556\) | 18.2059 | 0.772102 | ||||||||
\(557\) | 44.9103 | 1.90291 | 0.951455 | − | 0.307787i | \(-0.0995884\pi\) | ||||
0.951455 | + | 0.307787i | \(0.0995884\pi\) | |||||||
\(558\) | −1.90883 | −0.0808074 | ||||||||
\(559\) | 3.16742 | 0.133967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.1355 | −0.723463 | ||||||||
\(562\) | 0.356353 | 0.0150318 | ||||||||
\(563\) | 18.9910 | 0.800374 | 0.400187 | − | 0.916434i | \(-0.368945\pi\) | ||||
0.400187 | + | 0.916434i | \(0.368945\pi\) | |||||||
\(564\) | −8.15147 | −0.343239 | ||||||||
\(565\) | −21.5338 | −0.905934 | ||||||||
\(566\) | 21.8392 | 0.917969 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.30783 | −0.222712 | ||||||||
\(569\) | 22.1657 | 0.929235 | 0.464617 | − | 0.885512i | \(-0.346192\pi\) | ||||
0.464617 | + | 0.885512i | \(0.346192\pi\) | |||||||
\(570\) | −1.82182 | −0.0763078 | ||||||||
\(571\) | −37.3269 | −1.56208 | −0.781041 | − | 0.624479i | \(-0.785311\pi\) | ||||
−0.781041 | + | 0.624479i | \(0.785311\pi\) | |||||||
\(572\) | −5.25858 | −0.219872 | ||||||||
\(573\) | 19.1487 | 0.799950 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.06661 | −0.0861836 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −27.2084 | −1.13270 | −0.566349 | − | 0.824165i | \(-0.691645\pi\) | ||||
−0.566349 | + | 0.824165i | \(0.691645\pi\) | |||||||
\(578\) | −6.38163 | −0.265441 | ||||||||
\(579\) | −9.49016 | −0.394398 | ||||||||
\(580\) | −0.210062 | −0.00872234 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.3456 | 0.470290 | ||||||||
\(583\) | 23.6353 | 0.978876 | ||||||||
\(584\) | 5.34975 | 0.221374 | ||||||||
\(585\) | 1.34975 | 0.0558053 | ||||||||
\(586\) | −9.18478 | −0.379420 | ||||||||
\(587\) | 30.5623 | 1.26144 | 0.630720 | − | 0.776011i | \(-0.282760\pi\) | ||||
0.630720 | + | 0.776011i | \(0.282760\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.57645 | 0.106161 | ||||||||
\(590\) | 2.57645 | 0.106071 | ||||||||
\(591\) | −1.33826 | −0.0550488 | ||||||||
\(592\) | 7.59239 | 0.312045 | ||||||||
\(593\) | −16.4167 | −0.674151 | −0.337076 | − | 0.941478i | \(-0.609438\pi\) | ||||
−0.337076 | + | 0.941478i | \(0.609438\pi\) | |||||||
\(594\) | −5.25858 | −0.215762 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.50641 | 0.389398 | ||||||||
\(597\) | −21.0988 | −0.863516 | ||||||||
\(598\) | −0.650251 | −0.0265907 | ||||||||
\(599\) | 2.96296 | 0.121063 | 0.0605317 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605317 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(600\) | 3.17818 | 0.129749 | ||||||||
\(601\) | −19.7966 | −0.807519 | −0.403760 | − | 0.914865i | \(-0.632297\pi\) | ||||
−0.403760 | + | 0.914865i | \(0.632297\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.88629 | 0.0768156 | ||||||||
\(604\) | 13.1297 | 0.534238 | ||||||||
\(605\) | −22.4770 | −0.913819 | ||||||||
\(606\) | −1.77991 | −0.0723037 | ||||||||
\(607\) | 29.0150 | 1.17768 | 0.588840 | − | 0.808249i | \(-0.299585\pi\) | ||||
0.588840 | + | 0.808249i | \(0.299585\pi\) | |||||||
\(608\) | −1.34975 | −0.0547396 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.06304 | −0.124019 | ||||||||
\(611\) | −8.15147 | −0.329773 | ||||||||
\(612\) | 3.25858 | 0.131720 | ||||||||
\(613\) | −21.2826 | −0.859595 | −0.429798 | − | 0.902925i | \(-0.641415\pi\) | ||||
−0.429798 | + | 0.902925i | \(0.641415\pi\) | |||||||
\(614\) | −6.01321 | −0.242673 | ||||||||
\(615\) | −4.48528 | −0.180864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.3601 | −1.86639 | −0.933194 | − | 0.359372i | \(-0.882991\pi\) | ||||
−0.933194 | + | 0.359372i | \(0.882991\pi\) | |||||||
\(618\) | −17.9487 | −0.722004 | ||||||||
\(619\) | 33.2340 | 1.33579 | 0.667894 | − | 0.744256i | \(-0.267196\pi\) | ||||
0.667894 | + | 0.744256i | \(0.267196\pi\) | |||||||
\(620\) | 2.57645 | 0.103473 | ||||||||
\(621\) | −0.650251 | −0.0260937 | ||||||||
\(622\) | −13.8926 | −0.557042 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0.991689 | 0.0396675 | ||||||||
\(626\) | 12.9206 | 0.516412 | ||||||||
\(627\) | 7.09777 | 0.283458 | ||||||||
\(628\) | 2.32275 | 0.0926877 | ||||||||
\(629\) | 24.7404 | 0.986466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4007 | −1.25004 | −0.625021 | − | 0.780608i | \(-0.714910\pi\) | ||||
−0.625021 | + | 0.780608i | \(0.714910\pi\) | |||||||
\(632\) | 5.74802 | 0.228644 | ||||||||
\(633\) | −7.16742 | −0.284879 | ||||||||
\(634\) | −28.4696 | −1.13067 | ||||||||
\(635\) | 2.75047 | 0.109149 | ||||||||
\(636\) | −4.49462 | −0.178223 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.818395 | 0.0324006 | ||||||||
\(639\) | −5.30783 | −0.209975 | ||||||||
\(640\) | −1.34975 | −0.0533535 | ||||||||
\(641\) | −39.3432 | −1.55396 | −0.776981 | − | 0.629524i | \(-0.783250\pi\) | ||||
−0.776981 | + | 0.629524i | \(0.783250\pi\) | |||||||
\(642\) | 11.4593 | 0.452263 | ||||||||
\(643\) | 25.9120 | 1.02187 | 0.510935 | − | 0.859619i | \(-0.329299\pi\) | ||||
0.510935 | + | 0.859619i | \(0.329299\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.27522 | −0.168337 | ||||||||
\(646\) | −4.39827 | −0.173048 | ||||||||
\(647\) | 1.30881 | 0.0514547 | 0.0257274 | − | 0.999669i | \(-0.491810\pi\) | ||||
0.0257274 | + | 0.999669i | \(0.491810\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −10.0378 | −0.394017 | ||||||||
\(650\) | 3.17818 | 0.124658 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.5956 | 0.845748 | ||||||||
\(653\) | 43.0639 | 1.68522 | 0.842610 | − | 0.538525i | \(-0.181018\pi\) | ||||
0.842610 | + | 0.538525i | \(0.181018\pi\) | |||||||
\(654\) | 1.02182 | 0.0399563 | ||||||||
\(655\) | −21.0042 | −0.820701 | ||||||||
\(656\) | −3.32305 | −0.129743 | ||||||||
\(657\) | 5.34975 | 0.208714 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6583 | 0.882641 | 0.441321 | − | 0.897350i | \(-0.354510\pi\) | ||||
0.441321 | + | 0.897350i | \(0.354510\pi\) | |||||||
\(660\) | 7.09777 | 0.276280 | ||||||||
\(661\) | −35.9411 | −1.39795 | −0.698974 | − | 0.715147i | \(-0.746360\pi\) | ||||
−0.698974 | + | 0.715147i | \(0.746360\pi\) | |||||||
\(662\) | −18.7383 | −0.728284 | ||||||||
\(663\) | 3.25858 | 0.126553 | ||||||||
\(664\) | −2.95736 | −0.114768 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.59239 | 0.294199 | ||||||||
\(667\) | 0.101199 | 0.00391843 | ||||||||
\(668\) | −25.3321 | −0.980128 | ||||||||
\(669\) | 12.6593 | 0.489437 | ||||||||
\(670\) | −2.54602 | −0.0983612 | ||||||||
\(671\) | 11.9335 | 0.460689 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.4296 | −1.21152 | −0.605760 | − | 0.795647i | \(-0.707131\pi\) | ||||
−0.605760 | + | 0.795647i | \(0.707131\pi\) | |||||||
\(674\) | 5.30955 | 0.204516 | ||||||||
\(675\) | 3.17818 | 0.122328 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 11.8524 | 0.455524 | 0.227762 | − | 0.973717i | \(-0.426859\pi\) | ||||
0.227762 | + | 0.973717i | \(0.426859\pi\) | |||||||
\(678\) | −15.9539 | −0.612707 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.39827 | −0.168666 | ||||||||
\(681\) | 9.77991 | 0.374767 | ||||||||
\(682\) | −10.0378 | −0.384366 | ||||||||
\(683\) | 25.0576 | 0.958801 | 0.479401 | − | 0.877596i | \(-0.340854\pi\) | ||||
0.479401 | + | 0.877596i | \(0.340854\pi\) | |||||||
\(684\) | −1.34975 | −0.0516090 | ||||||||
\(685\) | −3.48317 | −0.133085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.0721 | −1.03286 | ||||||||
\(688\) | −3.16742 | −0.120757 | ||||||||
\(689\) | −4.49462 | −0.171231 | ||||||||
\(690\) | 0.877675 | 0.0334125 | ||||||||
\(691\) | 36.9935 | 1.40730 | 0.703650 | − | 0.710547i | \(-0.251552\pi\) | ||||
0.703650 | + | 0.710547i | \(0.251552\pi\) | |||||||
\(692\) | 1.80142 | 0.0684799 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 29.0628 | 1.10321 | ||||||||
\(695\) | −24.5734 | −0.932123 | ||||||||
\(696\) | −0.155630 | −0.00589915 | ||||||||
\(697\) | −10.8284 | −0.410156 | ||||||||
\(698\) | 8.83576 | 0.334438 | ||||||||
\(699\) | 22.5838 | 0.854197 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9986 | −0.490950 | −0.245475 | − | 0.969403i | \(-0.578944\pi\) | ||||
−0.245475 | + | 0.969403i | \(0.578944\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −10.2478 | −0.386504 | ||||||||
\(704\) | 5.25858 | 0.198190 | ||||||||
\(705\) | 11.0024 | 0.414376 | ||||||||
\(706\) | 25.7030 | 0.967344 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.90883 | 0.0717384 | ||||||||
\(709\) | −37.1873 | −1.39660 | −0.698298 | − | 0.715807i | \(-0.746059\pi\) | ||||
−0.698298 | + | 0.715807i | \(0.746059\pi\) | |||||||
\(710\) | 7.16424 | 0.268869 | ||||||||
\(711\) | 5.74802 | 0.215568 | ||||||||
\(712\) | 10.7598 | 0.403241 | ||||||||
\(713\) | −1.24122 | −0.0464841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.09777 | 0.265442 | ||||||||
\(716\) | −0.274526 | −0.0102595 | ||||||||
\(717\) | −13.0617 | −0.487799 | ||||||||
\(718\) | −23.4211 | −0.874068 | ||||||||
\(719\) | −6.51268 | −0.242882 | −0.121441 | − | 0.992599i | \(-0.538752\pi\) | ||||
−0.121441 | + | 0.992599i | \(0.538752\pi\) | |||||||
\(720\) | −1.34975 | −0.0503022 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.1782 | −0.639306 | ||||||||
\(723\) | 6.04509 | 0.224819 | ||||||||
\(724\) | −12.7750 | −0.474780 | ||||||||
\(725\) | −0.494620 | −0.0183697 | ||||||||
\(726\) | −16.6527 | −0.618040 | ||||||||
\(727\) | −25.7968 | −0.956752 | −0.478376 | − | 0.878155i | \(-0.658774\pi\) | ||||
−0.478376 | + | 0.878155i | \(0.658774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.22082 | −0.267255 | ||||||||
\(731\) | −10.3213 | −0.381747 | ||||||||
\(732\) | −2.26934 | −0.0838773 | ||||||||
\(733\) | 46.2888 | 1.70971 | 0.854857 | − | 0.518863i | \(-0.173645\pi\) | ||||
0.854857 | + | 0.518863i | \(0.173645\pi\) | |||||||
\(734\) | 18.7442 | 0.691860 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.650251 | 0.0239686 | ||||||||
\(737\) | 9.91920 | 0.365378 | ||||||||
\(738\) | −3.32305 | −0.122323 | ||||||||
\(739\) | −1.87210 | −0.0688663 | −0.0344331 | − | 0.999407i | \(-0.510963\pi\) | ||||
−0.0344331 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(740\) | −10.2478 | −0.376718 | ||||||||
\(741\) | −1.34975 | −0.0495843 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.0211 | 0.404326 | 0.202163 | − | 0.979352i | \(-0.435203\pi\) | ||||
0.202163 | + | 0.979352i | \(0.435203\pi\) | |||||||
\(744\) | 1.90883 | 0.0699812 | ||||||||
\(745\) | −12.8313 | −0.470101 | ||||||||
\(746\) | −19.9005 | −0.728610 | ||||||||
\(747\) | −2.95736 | −0.108204 | ||||||||
\(748\) | 17.1355 | 0.626537 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.0385 | −0.403069 | ||||||||
\(751\) | 27.2892 | 0.995795 | 0.497898 | − | 0.867236i | \(-0.334106\pi\) | ||||
0.497898 | + | 0.867236i | \(0.334106\pi\) | |||||||
\(752\) | 8.15147 | 0.297254 | ||||||||
\(753\) | 10.7331 | 0.391136 | ||||||||
\(754\) | −0.155630 | −0.00566772 | ||||||||
\(755\) | −17.7217 | −0.644960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9754 | −0.507946 | −0.253973 | − | 0.967211i | \(-0.581737\pi\) | ||||
−0.253973 | + | 0.967211i | \(0.581737\pi\) | |||||||
\(758\) | −24.6760 | −0.896272 | ||||||||
\(759\) | −3.41940 | −0.124116 | ||||||||
\(760\) | 1.82182 | 0.0660845 | ||||||||
\(761\) | 6.01424 | 0.218016 | 0.109008 | − | 0.994041i | \(-0.465233\pi\) | ||||
0.109008 | + | 0.994041i | \(0.465233\pi\) | |||||||
\(762\) | 2.03776 | 0.0738203 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.1487 | −0.692777 | ||||||||
\(765\) | −4.39827 | −0.159020 | ||||||||
\(766\) | −21.2115 | −0.766402 | ||||||||
\(767\) | 1.90883 | 0.0689240 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 9.25125 | 0.333609 | 0.166804 | − | 0.985990i | \(-0.446655\pi\) | ||||
0.166804 | + | 0.985990i | \(0.446655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.13969 | −0.0410448 | ||||||||
\(772\) | 9.49016 | 0.341558 | ||||||||
\(773\) | −22.2218 | −0.799263 | −0.399632 | − | 0.916676i | \(-0.630862\pi\) | ||||
−0.399632 | + | 0.916676i | \(0.630862\pi\) | |||||||
\(774\) | −3.16742 | −0.113850 | ||||||||
\(775\) | 6.06661 | 0.217919 | ||||||||
\(776\) | −11.3456 | −0.407283 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.2073 | −1.19054 | ||||||||
\(779\) | 4.48528 | 0.160702 | ||||||||
\(780\) | −1.34975 | −0.0483288 | ||||||||
\(781\) | −27.9117 | −0.998758 | ||||||||
\(782\) | 2.11890 | 0.0757716 | ||||||||
\(783\) | −0.155630 | −0.00556177 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.13513 | −0.111897 | ||||||||
\(786\) | −15.5615 | −0.555061 | ||||||||
\(787\) | 29.5786 | 1.05436 | 0.527182 | − | 0.849752i | \(-0.323249\pi\) | ||||
0.527182 | + | 0.849752i | \(0.323249\pi\) | |||||||
\(788\) | 1.33826 | 0.0476737 | ||||||||
\(789\) | −25.2922 | −0.900426 | ||||||||
\(790\) | −7.75839 | −0.276031 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.25858 | 0.186856 | ||||||||
\(793\) | −2.26934 | −0.0805867 | ||||||||
\(794\) | 21.3907 | 0.759127 | ||||||||
\(795\) | 6.06661 | 0.215161 | ||||||||
\(796\) | 21.0988 | 0.747827 | ||||||||
\(797\) | −5.40203 | −0.191350 | −0.0956749 | − | 0.995413i | \(-0.530501\pi\) | ||||
−0.0956749 | + | 0.995413i | \(0.530501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.5623 | 0.939705 | ||||||||
\(800\) | −3.17818 | −0.112366 | ||||||||
\(801\) | 10.7598 | 0.380179 | ||||||||
\(802\) | −21.4745 | −0.758292 | ||||||||
\(803\) | 28.1321 | 0.992760 | ||||||||
\(804\) | −1.88629 | −0.0665242 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.90883 | 0.0672358 | ||||||||
\(807\) | 4.66174 | 0.164101 | ||||||||
\(808\) | 1.77991 | 0.0626169 | ||||||||
\(809\) | −44.1176 | −1.55109 | −0.775546 | − | 0.631291i | \(-0.782525\pi\) | ||||
−0.775546 | + | 0.631291i | \(0.782525\pi\) | |||||||
\(810\) | −1.34975 | −0.0474254 | ||||||||
\(811\) | −2.21006 | −0.0776058 | −0.0388029 | − | 0.999247i | \(-0.512354\pi\) | ||||
−0.0388029 | + | 0.999247i | \(0.512354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.70538 | −0.235168 | ||||||||
\(814\) | 39.9252 | 1.39938 | ||||||||
\(815\) | −29.1486 | −1.02103 | ||||||||
\(816\) | −3.25858 | −0.114073 | ||||||||
\(817\) | 4.27522 | 0.149571 | ||||||||
\(818\) | −4.18854 | −0.146449 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.48528 | 0.156633 | ||||||||
\(821\) | −27.5113 | −0.960151 | −0.480076 | − | 0.877227i | \(-0.659391\pi\) | ||||
−0.480076 | + | 0.877227i | \(0.659391\pi\) | |||||||
\(822\) | −2.58060 | −0.0900089 | ||||||||
\(823\) | 16.0711 | 0.560203 | 0.280102 | − | 0.959970i | \(-0.409632\pi\) | ||||
0.280102 | + | 0.959970i | \(0.409632\pi\) | |||||||
\(824\) | 17.9487 | 0.625274 | ||||||||
\(825\) | 16.7127 | 0.581862 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.9526 | −1.87612 | −0.938058 | − | 0.346478i | \(-0.887377\pi\) | ||||
−0.938058 | + | 0.346478i | \(0.887377\pi\) | |||||||
\(828\) | 0.650251 | 0.0225978 | ||||||||
\(829\) | 24.6125 | 0.854827 | 0.427414 | − | 0.904056i | \(-0.359425\pi\) | ||||
0.427414 | + | 0.904056i | \(0.359425\pi\) | |||||||
\(830\) | 3.99169 | 0.138554 | ||||||||
\(831\) | 29.1068 | 1.00970 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −18.2059 | −0.630419 | ||||||||
\(835\) | 34.1920 | 1.18326 | ||||||||
\(836\) | −7.09777 | −0.245481 | ||||||||
\(837\) | 1.90883 | 0.0659790 | ||||||||
\(838\) | 8.88501 | 0.306927 | ||||||||
\(839\) | −24.6672 | −0.851606 | −0.425803 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425803 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9758 | −0.999165 | ||||||||
\(842\) | 9.59411 | 0.330635 | ||||||||
\(843\) | −0.356353 | −0.0122735 | ||||||||
\(844\) | 7.16742 | 0.246713 | ||||||||
\(845\) | −1.34975 | −0.0464328 | ||||||||
\(846\) | 8.15147 | 0.280253 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.49462 | 0.154346 | ||||||||
\(849\) | −21.8392 | −0.749519 | ||||||||
\(850\) | −10.3564 | −0.355220 | ||||||||
\(851\) | 4.93696 | 0.169237 | ||||||||
\(852\) | 5.30783 | 0.181843 | ||||||||
\(853\) | 22.0347 | 0.754455 | 0.377227 | − | 0.926121i | \(-0.376878\pi\) | ||||
0.377227 | + | 0.926121i | \(0.376878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.82182 | 0.0623050 | ||||||||
\(856\) | −11.4593 | −0.391671 | ||||||||
\(857\) | −57.3284 | −1.95830 | −0.979150 | − | 0.203139i | \(-0.934886\pi\) | ||||
−0.979150 | + | 0.203139i | \(0.934886\pi\) | |||||||
\(858\) | 5.25858 | 0.179525 | ||||||||
\(859\) | −8.34804 | −0.284832 | −0.142416 | − | 0.989807i | \(-0.545487\pi\) | ||||
−0.142416 | + | 0.989807i | \(0.545487\pi\) | |||||||
\(860\) | 4.27522 | 0.145784 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.6897 | 0.568455 | ||||||||
\(863\) | −8.06661 | −0.274591 | −0.137295 | − | 0.990530i | \(-0.543841\pi\) | ||||
−0.137295 | + | 0.990530i | \(0.543841\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −2.43147 | −0.0826725 | ||||||||
\(866\) | −12.8613 | −0.437046 | ||||||||
\(867\) | 6.38163 | 0.216732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.2264 | 1.02536 | ||||||||
\(870\) | 0.210062 | 0.00712176 | ||||||||
\(871\) | −1.88629 | −0.0639144 | ||||||||
\(872\) | −1.02182 | −0.0346032 | ||||||||
\(873\) | −11.3456 | −0.383990 | ||||||||
\(874\) | −0.877675 | −0.0296878 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.34975 | −0.180751 | ||||||||
\(877\) | 26.4857 | 0.894359 | 0.447179 | − | 0.894444i | \(-0.352429\pi\) | ||||
0.447179 | + | 0.894444i | \(0.352429\pi\) | |||||||
\(878\) | 2.23359 | 0.0753800 | ||||||||
\(879\) | 9.18478 | 0.309795 | ||||||||
\(880\) | −7.09777 | −0.239266 | ||||||||
\(881\) | 9.38606 | 0.316224 | 0.158112 | − | 0.987421i | \(-0.449459\pi\) | ||||
0.158112 | + | 0.987421i | \(0.449459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.824271 | 0.0277389 | 0.0138695 | − | 0.999904i | \(-0.495585\pi\) | ||||
0.0138695 | + | 0.999904i | \(0.495585\pi\) | |||||||
\(884\) | −3.25858 | −0.109598 | ||||||||
\(885\) | −2.57645 | −0.0866063 | ||||||||
\(886\) | 26.5093 | 0.890597 | ||||||||
\(887\) | −19.4079 | −0.651654 | −0.325827 | − | 0.945429i | \(-0.605643\pi\) | ||||
−0.325827 | + | 0.945429i | \(0.605643\pi\) | |||||||
\(888\) | −7.59239 | −0.254784 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.5230 | −0.486814 | ||||||||
\(891\) | 5.25858 | 0.176169 | ||||||||
\(892\) | −12.6593 | −0.423865 | ||||||||
\(893\) | −11.0024 | −0.368183 | ||||||||
\(894\) | −9.50641 | −0.317942 | ||||||||
\(895\) | 0.370541 | 0.0123858 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.650251 | 0.0217112 | ||||||||
\(898\) | −28.1306 | −0.938732 | ||||||||
\(899\) | −0.297072 | −0.00990791 | ||||||||
\(900\) | −3.17818 | −0.105939 | ||||||||
\(901\) | 14.6461 | 0.487932 | ||||||||
\(902\) | −17.4745 | −0.581838 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.9539 | 0.530620 | ||||||||
\(905\) | 17.2431 | 0.573179 | ||||||||
\(906\) | −13.1297 | −0.436204 | ||||||||
\(907\) | −13.9377 | −0.462793 | −0.231397 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231397 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(908\) | −9.77991 | −0.324558 | ||||||||
\(909\) | 1.77991 | 0.0590357 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.9821 | 1.72224 | 0.861121 | − | 0.508400i | \(-0.169763\pi\) | ||||
0.861121 | + | 0.508400i | \(0.169763\pi\) | |||||||
\(912\) | 1.34975 | 0.0446947 | ||||||||
\(913\) | −15.5515 | −0.514680 | ||||||||
\(914\) | −15.0715 | −0.498521 | ||||||||
\(915\) | 3.06304 | 0.101261 | ||||||||
\(916\) | 27.0721 | 0.894487 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.25858 | −0.107549 | ||||||||
\(919\) | −22.0568 | −0.727588 | −0.363794 | − | 0.931479i | \(-0.618519\pi\) | ||||
−0.363794 | + | 0.931479i | \(0.618519\pi\) | |||||||
\(920\) | −0.877675 | −0.0289361 | ||||||||
\(921\) | 6.01321 | 0.198142 | ||||||||
\(922\) | 10.4492 | 0.344127 | ||||||||
\(923\) | 5.30783 | 0.174709 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.1300 | −0.793388 | ||||||||
\(926\) | 12.0115 | 0.394722 | ||||||||
\(927\) | 17.9487 | 0.589514 | ||||||||
\(928\) | 0.155630 | 0.00510881 | ||||||||
\(929\) | −44.7485 | −1.46815 | −0.734075 | − | 0.679069i | \(-0.762384\pi\) | ||||
−0.734075 | + | 0.679069i | \(0.762384\pi\) | |||||||
\(930\) | −2.57645 | −0.0844850 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.5838 | −0.739756 | ||||||||
\(933\) | 13.8926 | 0.454823 | ||||||||
\(934\) | −21.6468 | −0.708306 | ||||||||
\(935\) | −23.1287 | −0.756389 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 9.50440 | 0.310495 | 0.155248 | − | 0.987876i | \(-0.450382\pi\) | ||||
0.155248 | + | 0.987876i | \(0.450382\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.9206 | −0.421649 | ||||||||
\(940\) | −11.0024 | −0.358860 | ||||||||
\(941\) | −26.2392 | −0.855373 | −0.427686 | − | 0.903927i | \(-0.640671\pi\) | ||||
−0.427686 | + | 0.903927i | \(0.640671\pi\) | |||||||
\(942\) | −2.32275 | −0.0756792 | ||||||||
\(943\) | −2.16081 | −0.0703658 | ||||||||
\(944\) | −1.90883 | −0.0621273 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.6561 | −0.541537 | ||||||||
\(947\) | −22.1757 | −0.720615 | −0.360307 | − | 0.932834i | \(-0.617328\pi\) | ||||
−0.360307 | + | 0.932834i | \(0.617328\pi\) | |||||||
\(948\) | −5.74802 | −0.186687 | ||||||||
\(949\) | −5.34975 | −0.173660 | ||||||||
\(950\) | 4.28974 | 0.139178 | ||||||||
\(951\) | 28.4696 | 0.923191 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.2045 | 0.978418 | 0.489209 | − | 0.872167i | \(-0.337285\pi\) | ||||
0.489209 | + | 0.872167i | \(0.337285\pi\) | |||||||
\(954\) | 4.49462 | 0.145519 | ||||||||
\(955\) | 25.8460 | 0.836357 | ||||||||
\(956\) | 13.0617 | 0.422447 | ||||||||
\(957\) | −0.818395 | −0.0264549 | ||||||||
\(958\) | −3.28211 | −0.106040 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.34975 | 0.0435630 | ||||||||
\(961\) | −27.3564 | −0.882463 | ||||||||
\(962\) | −7.59239 | −0.244788 | ||||||||
\(963\) | −11.4593 | −0.369271 | ||||||||
\(964\) | −6.04509 | −0.194699 | ||||||||
\(965\) | −12.8093 | −0.412347 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.7193 | 1.95260 | 0.976301 | − | 0.216418i | \(-0.0694372\pi\) | ||||
0.976301 | + | 0.216418i | \(0.0694372\pi\) | |||||||
\(968\) | 16.6527 | 0.535238 | ||||||||
\(969\) | 4.39827 | 0.141293 | ||||||||
\(970\) | 15.3137 | 0.491694 | ||||||||
\(971\) | −35.5279 | −1.14015 | −0.570073 | − | 0.821594i | \(-0.693085\pi\) | ||||
−0.570073 | + | 0.821594i | \(0.693085\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 25.3907 | 0.813570 | ||||||||
\(975\) | −3.17818 | −0.101783 | ||||||||
\(976\) | 2.26934 | 0.0726399 | ||||||||
\(977\) | −6.06344 | −0.193987 | −0.0969933 | − | 0.995285i | \(-0.530923\pi\) | ||||
−0.0969933 | + | 0.995285i | \(0.530923\pi\) | |||||||
\(978\) | −21.5956 | −0.690550 | ||||||||
\(979\) | 56.5813 | 1.80835 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.02182 | −0.0326242 | ||||||||
\(982\) | −16.6368 | −0.530900 | ||||||||
\(983\) | −6.78021 | −0.216255 | −0.108128 | − | 0.994137i | \(-0.534485\pi\) | ||||
−0.108128 | + | 0.994137i | \(0.534485\pi\) | |||||||
\(984\) | 3.32305 | 0.105935 | ||||||||
\(985\) | −1.80632 | −0.0575541 | ||||||||
\(986\) | 0.507134 | 0.0161504 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.34975 | 0.0429412 | ||||||||
\(989\) | −2.05961 | −0.0654919 | ||||||||
\(990\) | −7.09777 | −0.225582 | ||||||||
\(991\) | −23.1225 | −0.734509 | −0.367255 | − | 0.930120i | \(-0.619702\pi\) | ||||
−0.367255 | + | 0.930120i | \(0.619702\pi\) | |||||||
\(992\) | −1.90883 | −0.0606055 | ||||||||
\(993\) | 18.7383 | 0.594642 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.4781 | −0.902816 | ||||||||
\(996\) | 2.95736 | 0.0937074 | ||||||||
\(997\) | −22.3460 | −0.707704 | −0.353852 | − | 0.935301i | \(-0.615128\pi\) | ||||
−0.353852 | + | 0.935301i | \(0.615128\pi\) | |||||||
\(998\) | −15.0495 | −0.476385 | ||||||||
\(999\) | −7.59239 | −0.240213 |
(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 | 3822.2.a.bz.1.2 | ✓ | 4 | |
7.6 | odd | 2 | 3822.2.a.ca.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3822.2.a.bz.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3822.2.a.ca.1.3 | yes | 4 | 7.6 | odd | 2 |