Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.315468\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | −0.684532 | −0.306132 | −0.153066 | − | 0.988216i | \(-0.548915\pi\) | ||||
−0.153066 | + | 0.988216i | \(0.548915\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.46314 | −0.553014 | −0.276507 | − | 0.961012i | \(-0.589177\pi\) | ||||
−0.276507 | + | 0.961012i | \(0.589177\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.684532 | −0.216468 | ||||||||
\(11\) | −0.852331 | −0.256987 | −0.128494 | − | 0.991710i | \(-0.541014\pi\) | ||||
−0.128494 | + | 0.991710i | \(0.541014\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.46314 | −0.391040 | ||||||||
\(15\) | −0.684532 | −0.176745 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.18602 | 1.01526 | 0.507630 | − | 0.861575i | \(-0.330522\pi\) | ||||
0.507630 | + | 0.861575i | \(0.330522\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.25777 | −1.66505 | −0.832523 | − | 0.553991i | \(-0.813104\pi\) | ||||
−0.832523 | + | 0.553991i | \(0.813104\pi\) | |||||||
\(20\) | −0.684532 | −0.153066 | ||||||||
\(21\) | −1.46314 | −0.319283 | ||||||||
\(22\) | −0.852331 | −0.181718 | ||||||||
\(23\) | 8.93399 | 1.86287 | 0.931433 | − | 0.363913i | \(-0.118560\pi\) | ||||
0.931433 | + | 0.363913i | \(0.118560\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.53142 | −0.906283 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.46314 | −0.276507 | ||||||||
\(29\) | −9.35782 | −1.73770 | −0.868852 | − | 0.495072i | \(-0.835142\pi\) | ||||
−0.868852 | + | 0.495072i | \(0.835142\pi\) | |||||||
\(30\) | −0.684532 | −0.124978 | ||||||||
\(31\) | −7.80209 | −1.40130 | −0.700649 | − | 0.713506i | \(-0.747106\pi\) | ||||
−0.700649 | + | 0.713506i | \(0.747106\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.852331 | −0.148372 | ||||||||
\(34\) | 4.18602 | 0.717897 | ||||||||
\(35\) | 1.00156 | 0.169295 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.54810 | −0.912102 | −0.456051 | − | 0.889954i | \(-0.650736\pi\) | ||||
−0.456051 | + | 0.889954i | \(0.650736\pi\) | |||||||
\(38\) | −7.25777 | −1.17737 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.684532 | −0.108234 | ||||||||
\(41\) | 7.52426 | 1.17509 | 0.587546 | − | 0.809191i | \(-0.300094\pi\) | ||||
0.587546 | + | 0.809191i | \(0.300094\pi\) | |||||||
\(42\) | −1.46314 | −0.225767 | ||||||||
\(43\) | 10.1742 | 1.55155 | 0.775776 | − | 0.631008i | \(-0.217358\pi\) | ||||
0.775776 | + | 0.631008i | \(0.217358\pi\) | |||||||
\(44\) | −0.852331 | −0.128494 | ||||||||
\(45\) | −0.684532 | −0.102044 | ||||||||
\(46\) | 8.93399 | 1.31724 | ||||||||
\(47\) | −6.03336 | −0.880056 | −0.440028 | − | 0.897984i | \(-0.645031\pi\) | ||||
−0.440028 | + | 0.897984i | \(0.645031\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.85923 | −0.694175 | ||||||||
\(50\) | −4.53142 | −0.640839 | ||||||||
\(51\) | 4.18602 | 0.586160 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 4.03835 | 0.554710 | 0.277355 | − | 0.960767i | \(-0.410542\pi\) | ||||
0.277355 | + | 0.960767i | \(0.410542\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.583447 | 0.0786720 | ||||||||
\(56\) | −1.46314 | −0.195520 | ||||||||
\(57\) | −7.25777 | −0.961315 | ||||||||
\(58\) | −9.35782 | −1.22874 | ||||||||
\(59\) | −11.8277 | −1.53984 | −0.769918 | − | 0.638143i | \(-0.779703\pi\) | ||||
−0.769918 | + | 0.638143i | \(0.779703\pi\) | |||||||
\(60\) | −0.684532 | −0.0883727 | ||||||||
\(61\) | −5.34907 | −0.684878 | −0.342439 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342439 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(62\) | −7.80209 | −0.990867 | ||||||||
\(63\) | −1.46314 | −0.184338 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.684532 | 0.0849057 | ||||||||
\(66\) | −0.852331 | −0.104915 | ||||||||
\(67\) | −8.90152 | −1.08749 | −0.543747 | − | 0.839249i | \(-0.682995\pi\) | ||||
−0.543747 | + | 0.839249i | \(0.682995\pi\) | |||||||
\(68\) | 4.18602 | 0.507630 | ||||||||
\(69\) | 8.93399 | 1.07553 | ||||||||
\(70\) | 1.00156 | 0.119710 | ||||||||
\(71\) | 7.58775 | 0.900500 | 0.450250 | − | 0.892902i | \(-0.351335\pi\) | ||||
0.450250 | + | 0.892902i | \(0.351335\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −3.57276 | −0.418160 | −0.209080 | − | 0.977899i | \(-0.567047\pi\) | ||||
−0.209080 | + | 0.977899i | \(0.567047\pi\) | |||||||
\(74\) | −5.54810 | −0.644953 | ||||||||
\(75\) | −4.53142 | −0.523243 | ||||||||
\(76\) | −7.25777 | −0.832523 | ||||||||
\(77\) | 1.24708 | 0.142118 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 7.23728 | 0.814258 | 0.407129 | − | 0.913371i | \(-0.366530\pi\) | ||||
0.407129 | + | 0.913371i | \(0.366530\pi\) | |||||||
\(80\) | −0.684532 | −0.0765330 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.52426 | 0.830915 | ||||||||
\(83\) | −9.34849 | −1.02613 | −0.513065 | − | 0.858350i | \(-0.671490\pi\) | ||||
−0.513065 | + | 0.858350i | \(0.671490\pi\) | |||||||
\(84\) | −1.46314 | −0.159641 | ||||||||
\(85\) | −2.86546 | −0.310803 | ||||||||
\(86\) | 10.1742 | 1.09711 | ||||||||
\(87\) | −9.35782 | −1.00326 | ||||||||
\(88\) | −0.852331 | −0.0908588 | ||||||||
\(89\) | 1.49352 | 0.158313 | 0.0791564 | − | 0.996862i | \(-0.474777\pi\) | ||||
0.0791564 | + | 0.996862i | \(0.474777\pi\) | |||||||
\(90\) | −0.684532 | −0.0721560 | ||||||||
\(91\) | 1.46314 | 0.153378 | ||||||||
\(92\) | 8.93399 | 0.931433 | ||||||||
\(93\) | −7.80209 | −0.809039 | ||||||||
\(94\) | −6.03336 | −0.622293 | ||||||||
\(95\) | 4.96817 | 0.509724 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −13.1229 | −1.33242 | −0.666212 | − | 0.745762i | \(-0.732085\pi\) | ||||
−0.666212 | + | 0.745762i | \(0.732085\pi\) | |||||||
\(98\) | −4.85923 | −0.490856 | ||||||||
\(99\) | −0.852331 | −0.0856625 | ||||||||
\(100\) | −4.53142 | −0.453142 | ||||||||
\(101\) | 14.3892 | 1.43178 | 0.715892 | − | 0.698212i | \(-0.246021\pi\) | ||||
0.715892 | + | 0.698212i | \(0.246021\pi\) | |||||||
\(102\) | 4.18602 | 0.414478 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 1.00156 | 0.0977426 | ||||||||
\(106\) | 4.03835 | 0.392239 | ||||||||
\(107\) | −8.77589 | −0.848397 | −0.424199 | − | 0.905569i | \(-0.639444\pi\) | ||||
−0.424199 | + | 0.905569i | \(0.639444\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 2.87277 | 0.275161 | 0.137581 | − | 0.990491i | \(-0.456067\pi\) | ||||
0.137581 | + | 0.990491i | \(0.456067\pi\) | |||||||
\(110\) | 0.583447 | 0.0556295 | ||||||||
\(111\) | −5.54810 | −0.526602 | ||||||||
\(112\) | −1.46314 | −0.138254 | ||||||||
\(113\) | 4.54248 | 0.427321 | 0.213660 | − | 0.976908i | \(-0.431461\pi\) | ||||
0.213660 | + | 0.976908i | \(0.431461\pi\) | |||||||
\(114\) | −7.25777 | −0.679752 | ||||||||
\(115\) | −6.11560 | −0.570283 | ||||||||
\(116\) | −9.35782 | −0.868852 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −11.8277 | −1.08883 | ||||||||
\(119\) | −6.12472 | −0.561453 | ||||||||
\(120\) | −0.684532 | −0.0624889 | ||||||||
\(121\) | −10.2735 | −0.933957 | ||||||||
\(122\) | −5.34907 | −0.484282 | ||||||||
\(123\) | 7.52426 | 0.678440 | ||||||||
\(124\) | −7.80209 | −0.700649 | ||||||||
\(125\) | 6.52456 | 0.583574 | ||||||||
\(126\) | −1.46314 | −0.130347 | ||||||||
\(127\) | −18.0691 | −1.60337 | −0.801687 | − | 0.597743i | \(-0.796064\pi\) | ||||
−0.801687 | + | 0.597743i | \(0.796064\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.1742 | 0.895789 | ||||||||
\(130\) | 0.684532 | 0.0600374 | ||||||||
\(131\) | 18.7682 | 1.63978 | 0.819891 | − | 0.572520i | \(-0.194034\pi\) | ||||
0.819891 | + | 0.572520i | \(0.194034\pi\) | |||||||
\(132\) | −0.852331 | −0.0741859 | ||||||||
\(133\) | 10.6191 | 0.920794 | ||||||||
\(134\) | −8.90152 | −0.768974 | ||||||||
\(135\) | −0.684532 | −0.0589151 | ||||||||
\(136\) | 4.18602 | 0.358948 | ||||||||
\(137\) | −12.6165 | −1.07790 | −0.538950 | − | 0.842337i | \(-0.681179\pi\) | ||||
−0.538950 | + | 0.842337i | \(0.681179\pi\) | |||||||
\(138\) | 8.93399 | 0.760512 | ||||||||
\(139\) | −1.54440 | −0.130994 | −0.0654972 | − | 0.997853i | \(-0.520863\pi\) | ||||
−0.0654972 | + | 0.997853i | \(0.520863\pi\) | |||||||
\(140\) | 1.00156 | 0.0846476 | ||||||||
\(141\) | −6.03336 | −0.508100 | ||||||||
\(142\) | 7.58775 | 0.636750 | ||||||||
\(143\) | 0.852331 | 0.0712755 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 6.40572 | 0.531966 | ||||||||
\(146\) | −3.57276 | −0.295684 | ||||||||
\(147\) | −4.85923 | −0.400782 | ||||||||
\(148\) | −5.54810 | −0.456051 | ||||||||
\(149\) | −14.4252 | −1.18176 | −0.590880 | − | 0.806759i | \(-0.701219\pi\) | ||||
−0.590880 | + | 0.806759i | \(0.701219\pi\) | |||||||
\(150\) | −4.53142 | −0.369989 | ||||||||
\(151\) | −13.4386 | −1.09362 | −0.546808 | − | 0.837258i | \(-0.684157\pi\) | ||||
−0.546808 | + | 0.837258i | \(0.684157\pi\) | |||||||
\(152\) | −7.25777 | −0.588683 | ||||||||
\(153\) | 4.18602 | 0.338420 | ||||||||
\(154\) | 1.24708 | 0.100492 | ||||||||
\(155\) | 5.34078 | 0.428982 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −1.79833 | −0.143523 | −0.0717614 | − | 0.997422i | \(-0.522862\pi\) | ||||
−0.0717614 | + | 0.997422i | \(0.522862\pi\) | |||||||
\(158\) | 7.23728 | 0.575767 | ||||||||
\(159\) | 4.03835 | 0.320262 | ||||||||
\(160\) | −0.684532 | −0.0541170 | ||||||||
\(161\) | −13.0717 | −1.03019 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 13.8168 | 1.08222 | 0.541108 | − | 0.840953i | \(-0.318005\pi\) | ||||
0.541108 | + | 0.840953i | \(0.318005\pi\) | |||||||
\(164\) | 7.52426 | 0.587546 | ||||||||
\(165\) | 0.583447 | 0.0454213 | ||||||||
\(166\) | −9.34849 | −0.725584 | ||||||||
\(167\) | −1.72810 | −0.133724 | −0.0668622 | − | 0.997762i | \(-0.521299\pi\) | ||||
−0.0668622 | + | 0.997762i | \(0.521299\pi\) | |||||||
\(168\) | −1.46314 | −0.112884 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.86546 | −0.219771 | ||||||||
\(171\) | −7.25777 | −0.555015 | ||||||||
\(172\) | 10.1742 | 0.775776 | ||||||||
\(173\) | 15.9660 | 1.21387 | 0.606935 | − | 0.794751i | \(-0.292399\pi\) | ||||
0.606935 | + | 0.794751i | \(0.292399\pi\) | |||||||
\(174\) | −9.35782 | −0.709414 | ||||||||
\(175\) | 6.63009 | 0.501187 | ||||||||
\(176\) | −0.852331 | −0.0642468 | ||||||||
\(177\) | −11.8277 | −0.889025 | ||||||||
\(178\) | 1.49352 | 0.111944 | ||||||||
\(179\) | 2.82006 | 0.210781 | 0.105391 | − | 0.994431i | \(-0.466391\pi\) | ||||
0.105391 | + | 0.994431i | \(0.466391\pi\) | |||||||
\(180\) | −0.684532 | −0.0510220 | ||||||||
\(181\) | 1.24487 | 0.0925302 | 0.0462651 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462651 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(182\) | 1.46314 | 0.108455 | ||||||||
\(183\) | −5.34907 | −0.395414 | ||||||||
\(184\) | 8.93399 | 0.658622 | ||||||||
\(185\) | 3.79785 | 0.279223 | ||||||||
\(186\) | −7.80209 | −0.572077 | ||||||||
\(187\) | −3.56787 | −0.260909 | ||||||||
\(188\) | −6.03336 | −0.440028 | ||||||||
\(189\) | −1.46314 | −0.106428 | ||||||||
\(190\) | 4.96817 | 0.360429 | ||||||||
\(191\) | −20.9678 | −1.51718 | −0.758590 | − | 0.651569i | \(-0.774111\pi\) | ||||
−0.758590 | + | 0.651569i | \(0.774111\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 16.7859 | 1.20828 | 0.604140 | − | 0.796879i | \(-0.293517\pi\) | ||||
0.604140 | + | 0.796879i | \(0.293517\pi\) | |||||||
\(194\) | −13.1229 | −0.942166 | ||||||||
\(195\) | 0.684532 | 0.0490203 | ||||||||
\(196\) | −4.85923 | −0.347088 | ||||||||
\(197\) | −17.9766 | −1.28078 | −0.640390 | − | 0.768050i | \(-0.721227\pi\) | ||||
−0.640390 | + | 0.768050i | \(0.721227\pi\) | |||||||
\(198\) | −0.852331 | −0.0605725 | ||||||||
\(199\) | 25.9055 | 1.83639 | 0.918197 | − | 0.396124i | \(-0.129645\pi\) | ||||
0.918197 | + | 0.396124i | \(0.129645\pi\) | |||||||
\(200\) | −4.53142 | −0.320420 | ||||||||
\(201\) | −8.90152 | −0.627865 | ||||||||
\(202\) | 14.3892 | 1.01242 | ||||||||
\(203\) | 13.6918 | 0.960974 | ||||||||
\(204\) | 4.18602 | 0.293080 | ||||||||
\(205\) | −5.15059 | −0.359733 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 8.93399 | 0.620955 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 6.18602 | 0.427896 | ||||||||
\(210\) | 1.00156 | 0.0691145 | ||||||||
\(211\) | −24.6481 | −1.69684 | −0.848421 | − | 0.529322i | \(-0.822446\pi\) | ||||
−0.848421 | + | 0.529322i | \(0.822446\pi\) | |||||||
\(212\) | 4.03835 | 0.277355 | ||||||||
\(213\) | 7.58775 | 0.519904 | ||||||||
\(214\) | −8.77589 | −0.599908 | ||||||||
\(215\) | −6.96457 | −0.474980 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 11.4155 | 0.774937 | ||||||||
\(218\) | 2.87277 | 0.194568 | ||||||||
\(219\) | −3.57276 | −0.241425 | ||||||||
\(220\) | 0.583447 | 0.0393360 | ||||||||
\(221\) | −4.18602 | −0.281582 | ||||||||
\(222\) | −5.54810 | −0.372364 | ||||||||
\(223\) | 6.56161 | 0.439398 | 0.219699 | − | 0.975568i | \(-0.429493\pi\) | ||||
0.219699 | + | 0.975568i | \(0.429493\pi\) | |||||||
\(224\) | −1.46314 | −0.0977600 | ||||||||
\(225\) | −4.53142 | −0.302094 | ||||||||
\(226\) | 4.54248 | 0.302161 | ||||||||
\(227\) | −5.97922 | −0.396855 | −0.198427 | − | 0.980116i | \(-0.563583\pi\) | ||||
−0.198427 | + | 0.980116i | \(0.563583\pi\) | |||||||
\(228\) | −7.25777 | −0.480657 | ||||||||
\(229\) | 0.430082 | 0.0284206 | 0.0142103 | − | 0.999899i | \(-0.495477\pi\) | ||||
0.0142103 | + | 0.999899i | \(0.495477\pi\) | |||||||
\(230\) | −6.11560 | −0.403251 | ||||||||
\(231\) | 1.24708 | 0.0820516 | ||||||||
\(232\) | −9.35782 | −0.614371 | ||||||||
\(233\) | 6.90703 | 0.452495 | 0.226247 | − | 0.974070i | \(-0.427354\pi\) | ||||
0.226247 | + | 0.974070i | \(0.427354\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 4.13003 | 0.269413 | ||||||||
\(236\) | −11.8277 | −0.769918 | ||||||||
\(237\) | 7.23728 | 0.470112 | ||||||||
\(238\) | −6.12472 | −0.397007 | ||||||||
\(239\) | 9.90323 | 0.640587 | 0.320293 | − | 0.947318i | \(-0.396218\pi\) | ||||
0.320293 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(240\) | −0.684532 | −0.0441863 | ||||||||
\(241\) | −5.75164 | −0.370496 | −0.185248 | − | 0.982692i | \(-0.559309\pi\) | ||||
−0.185248 | + | 0.982692i | \(0.559309\pi\) | |||||||
\(242\) | −10.2735 | −0.660408 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.34907 | −0.342439 | ||||||||
\(245\) | 3.32630 | 0.212509 | ||||||||
\(246\) | 7.52426 | 0.479729 | ||||||||
\(247\) | 7.25777 | 0.461801 | ||||||||
\(248\) | −7.80209 | −0.495433 | ||||||||
\(249\) | −9.34849 | −0.592437 | ||||||||
\(250\) | 6.52456 | 0.412649 | ||||||||
\(251\) | −11.5382 | −0.728282 | −0.364141 | − | 0.931344i | \(-0.618637\pi\) | ||||
−0.364141 | + | 0.931344i | \(0.618637\pi\) | |||||||
\(252\) | −1.46314 | −0.0921690 | ||||||||
\(253\) | −7.61471 | −0.478733 | ||||||||
\(254\) | −18.0691 | −1.13376 | ||||||||
\(255\) | −2.86546 | −0.179442 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.3502 | −1.39416 | −0.697082 | − | 0.716991i | \(-0.745519\pi\) | ||||
−0.697082 | + | 0.716991i | \(0.745519\pi\) | |||||||
\(258\) | 10.1742 | 0.633419 | ||||||||
\(259\) | 8.11763 | 0.504405 | ||||||||
\(260\) | 0.684532 | 0.0424529 | ||||||||
\(261\) | −9.35782 | −0.579234 | ||||||||
\(262\) | 18.7682 | 1.15950 | ||||||||
\(263\) | −31.2570 | −1.92739 | −0.963696 | − | 0.267003i | \(-0.913967\pi\) | ||||
−0.963696 | + | 0.267003i | \(0.913967\pi\) | |||||||
\(264\) | −0.852331 | −0.0524573 | ||||||||
\(265\) | −2.76438 | −0.169815 | ||||||||
\(266\) | 10.6191 | 0.651099 | ||||||||
\(267\) | 1.49352 | 0.0914019 | ||||||||
\(268\) | −8.90152 | −0.543747 | ||||||||
\(269\) | −25.3631 | −1.54642 | −0.773209 | − | 0.634151i | \(-0.781350\pi\) | ||||
−0.773209 | + | 0.634151i | \(0.781350\pi\) | |||||||
\(270\) | −0.684532 | −0.0416593 | ||||||||
\(271\) | 12.2195 | 0.742280 | 0.371140 | − | 0.928577i | \(-0.378967\pi\) | ||||
0.371140 | + | 0.928577i | \(0.378967\pi\) | |||||||
\(272\) | 4.18602 | 0.253815 | ||||||||
\(273\) | 1.46314 | 0.0885531 | ||||||||
\(274\) | −12.6165 | −0.762191 | ||||||||
\(275\) | 3.86227 | 0.232903 | ||||||||
\(276\) | 8.93399 | 0.537763 | ||||||||
\(277\) | −25.3017 | −1.52023 | −0.760115 | − | 0.649789i | \(-0.774857\pi\) | ||||
−0.760115 | + | 0.649789i | \(0.774857\pi\) | |||||||
\(278\) | −1.54440 | −0.0926271 | ||||||||
\(279\) | −7.80209 | −0.467099 | ||||||||
\(280\) | 1.00156 | 0.0598549 | ||||||||
\(281\) | −19.7540 | −1.17842 | −0.589212 | − | 0.807978i | \(-0.700562\pi\) | ||||
−0.589212 | + | 0.807978i | \(0.700562\pi\) | |||||||
\(282\) | −6.03336 | −0.359281 | ||||||||
\(283\) | 3.83554 | 0.227999 | 0.114000 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.114000 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(284\) | 7.58775 | 0.450250 | ||||||||
\(285\) | 4.96817 | 0.294289 | ||||||||
\(286\) | 0.852331 | 0.0503994 | ||||||||
\(287\) | −11.0090 | −0.649842 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.522771 | 0.0307512 | ||||||||
\(290\) | 6.40572 | 0.376157 | ||||||||
\(291\) | −13.1229 | −0.769276 | ||||||||
\(292\) | −3.57276 | −0.209080 | ||||||||
\(293\) | −14.5198 | −0.848257 | −0.424128 | − | 0.905602i | \(-0.639419\pi\) | ||||
−0.424128 | + | 0.905602i | \(0.639419\pi\) | |||||||
\(294\) | −4.85923 | −0.283396 | ||||||||
\(295\) | 8.09644 | 0.471393 | ||||||||
\(296\) | −5.54810 | −0.322477 | ||||||||
\(297\) | −0.852331 | −0.0494572 | ||||||||
\(298\) | −14.4252 | −0.835631 | ||||||||
\(299\) | −8.93399 | −0.516666 | ||||||||
\(300\) | −4.53142 | −0.261621 | ||||||||
\(301\) | −14.8863 | −0.858030 | ||||||||
\(302\) | −13.4386 | −0.773304 | ||||||||
\(303\) | 14.3892 | 0.826640 | ||||||||
\(304\) | −7.25777 | −0.416261 | ||||||||
\(305\) | 3.66161 | 0.209663 | ||||||||
\(306\) | 4.18602 | 0.239299 | ||||||||
\(307\) | 7.02841 | 0.401132 | 0.200566 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200566 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(308\) | 1.24708 | 0.0710588 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 5.34078 | 0.303336 | ||||||||
\(311\) | 32.0849 | 1.81937 | 0.909683 | − | 0.415304i | \(-0.136325\pi\) | ||||
0.909683 | + | 0.415304i | \(0.136325\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 28.9318 | 1.63532 | 0.817661 | − | 0.575699i | \(-0.195270\pi\) | ||||
0.817661 | + | 0.575699i | \(0.195270\pi\) | |||||||
\(314\) | −1.79833 | −0.101486 | ||||||||
\(315\) | 1.00156 | 0.0564317 | ||||||||
\(316\) | 7.23728 | 0.407129 | ||||||||
\(317\) | 9.30284 | 0.522500 | 0.261250 | − | 0.965271i | \(-0.415865\pi\) | ||||
0.261250 | + | 0.965271i | \(0.415865\pi\) | |||||||
\(318\) | 4.03835 | 0.226460 | ||||||||
\(319\) | 7.97596 | 0.446568 | ||||||||
\(320\) | −0.684532 | −0.0382665 | ||||||||
\(321\) | −8.77589 | −0.489822 | ||||||||
\(322\) | −13.0717 | −0.728455 | ||||||||
\(323\) | −30.3812 | −1.69045 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.53142 | 0.251358 | ||||||||
\(326\) | 13.8168 | 0.765242 | ||||||||
\(327\) | 2.87277 | 0.158864 | ||||||||
\(328\) | 7.52426 | 0.415458 | ||||||||
\(329\) | 8.82763 | 0.486683 | ||||||||
\(330\) | 0.583447 | 0.0321177 | ||||||||
\(331\) | −31.1194 | −1.71048 | −0.855240 | − | 0.518233i | \(-0.826590\pi\) | ||||
−0.855240 | + | 0.518233i | \(0.826590\pi\) | |||||||
\(332\) | −9.34849 | −0.513065 | ||||||||
\(333\) | −5.54810 | −0.304034 | ||||||||
\(334\) | −1.72810 | −0.0945574 | ||||||||
\(335\) | 6.09337 | 0.332917 | ||||||||
\(336\) | −1.46314 | −0.0798207 | ||||||||
\(337\) | −20.6049 | −1.12242 | −0.561211 | − | 0.827673i | \(-0.689665\pi\) | ||||
−0.561211 | + | 0.827673i | \(0.689665\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 4.54248 | 0.246714 | ||||||||
\(340\) | −2.86546 | −0.155402 | ||||||||
\(341\) | 6.64996 | 0.360116 | ||||||||
\(342\) | −7.25777 | −0.392455 | ||||||||
\(343\) | 17.3517 | 0.936903 | ||||||||
\(344\) | 10.1742 | 0.548557 | ||||||||
\(345\) | −6.11560 | −0.329253 | ||||||||
\(346\) | 15.9660 | 0.858336 | ||||||||
\(347\) | 10.1696 | 0.545934 | 0.272967 | − | 0.962023i | \(-0.411995\pi\) | ||||
0.272967 | + | 0.962023i | \(0.411995\pi\) | |||||||
\(348\) | −9.35782 | −0.501632 | ||||||||
\(349\) | 28.8819 | 1.54601 | 0.773007 | − | 0.634397i | \(-0.218752\pi\) | ||||
0.773007 | + | 0.634397i | \(0.218752\pi\) | |||||||
\(350\) | 6.63009 | 0.354393 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −0.852331 | −0.0454294 | ||||||||
\(353\) | −6.13386 | −0.326473 | −0.163236 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163236 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(354\) | −11.8277 | −0.628635 | ||||||||
\(355\) | −5.19406 | −0.275672 | ||||||||
\(356\) | 1.49352 | 0.0791564 | ||||||||
\(357\) | −6.12472 | −0.324155 | ||||||||
\(358\) | 2.82006 | 0.149045 | ||||||||
\(359\) | 0.812147 | 0.0428635 | 0.0214317 | − | 0.999770i | \(-0.493178\pi\) | ||||
0.0214317 | + | 0.999770i | \(0.493178\pi\) | |||||||
\(360\) | −0.684532 | −0.0360780 | ||||||||
\(361\) | 33.6752 | 1.77238 | ||||||||
\(362\) | 1.24487 | 0.0654288 | ||||||||
\(363\) | −10.2735 | −0.539221 | ||||||||
\(364\) | 1.46314 | 0.0766892 | ||||||||
\(365\) | 2.44567 | 0.128012 | ||||||||
\(366\) | −5.34907 | −0.279600 | ||||||||
\(367\) | 12.5112 | 0.653080 | 0.326540 | − | 0.945183i | \(-0.394117\pi\) | ||||
0.326540 | + | 0.945183i | \(0.394117\pi\) | |||||||
\(368\) | 8.93399 | 0.465716 | ||||||||
\(369\) | 7.52426 | 0.391697 | ||||||||
\(370\) | 3.79785 | 0.197441 | ||||||||
\(371\) | −5.90866 | −0.306763 | ||||||||
\(372\) | −7.80209 | −0.404520 | ||||||||
\(373\) | −30.5555 | −1.58210 | −0.791051 | − | 0.611751i | \(-0.790466\pi\) | ||||
−0.791051 | + | 0.611751i | \(0.790466\pi\) | |||||||
\(374\) | −3.56787 | −0.184490 | ||||||||
\(375\) | 6.52456 | 0.336927 | ||||||||
\(376\) | −6.03336 | −0.311147 | ||||||||
\(377\) | 9.35782 | 0.481952 | ||||||||
\(378\) | −1.46314 | −0.0752557 | ||||||||
\(379\) | 15.5193 | 0.797175 | 0.398587 | − | 0.917130i | \(-0.369501\pi\) | ||||
0.398587 | + | 0.917130i | \(0.369501\pi\) | |||||||
\(380\) | 4.96817 | 0.254862 | ||||||||
\(381\) | −18.0691 | −0.925709 | ||||||||
\(382\) | −20.9678 | −1.07281 | ||||||||
\(383\) | 10.4672 | 0.534850 | 0.267425 | − | 0.963579i | \(-0.413827\pi\) | ||||
0.267425 | + | 0.963579i | \(0.413827\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.853664 | −0.0435067 | ||||||||
\(386\) | 16.7859 | 0.854382 | ||||||||
\(387\) | 10.1742 | 0.517184 | ||||||||
\(388\) | −13.1229 | −0.666212 | ||||||||
\(389\) | −2.93656 | −0.148890 | −0.0744448 | − | 0.997225i | \(-0.523718\pi\) | ||||
−0.0744448 | + | 0.997225i | \(0.523718\pi\) | |||||||
\(390\) | 0.684532 | 0.0346626 | ||||||||
\(391\) | 37.3979 | 1.89129 | ||||||||
\(392\) | −4.85923 | −0.245428 | ||||||||
\(393\) | 18.7682 | 0.946728 | ||||||||
\(394\) | −17.9766 | −0.905648 | ||||||||
\(395\) | −4.95415 | −0.249270 | ||||||||
\(396\) | −0.852331 | −0.0428312 | ||||||||
\(397\) | 22.2722 | 1.11781 | 0.558906 | − | 0.829231i | \(-0.311221\pi\) | ||||
0.558906 | + | 0.829231i | \(0.311221\pi\) | |||||||
\(398\) | 25.9055 | 1.29853 | ||||||||
\(399\) | 10.6191 | 0.531620 | ||||||||
\(400\) | −4.53142 | −0.226571 | ||||||||
\(401\) | −18.6195 | −0.929812 | −0.464906 | − | 0.885360i | \(-0.653912\pi\) | ||||
−0.464906 | + | 0.885360i | \(0.653912\pi\) | |||||||
\(402\) | −8.90152 | −0.443967 | ||||||||
\(403\) | 7.80209 | 0.388650 | ||||||||
\(404\) | 14.3892 | 0.715892 | ||||||||
\(405\) | −0.684532 | −0.0340147 | ||||||||
\(406\) | 13.6918 | 0.679511 | ||||||||
\(407\) | 4.72881 | 0.234399 | ||||||||
\(408\) | 4.18602 | 0.207239 | ||||||||
\(409\) | 10.9971 | 0.543770 | 0.271885 | − | 0.962330i | \(-0.412353\pi\) | ||||
0.271885 | + | 0.962330i | \(0.412353\pi\) | |||||||
\(410\) | −5.15059 | −0.254370 | ||||||||
\(411\) | −12.6165 | −0.622326 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 17.3056 | 0.851551 | ||||||||
\(414\) | 8.93399 | 0.439082 | ||||||||
\(415\) | 6.39934 | 0.314131 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −1.54440 | −0.0756297 | ||||||||
\(418\) | 6.18602 | 0.302568 | ||||||||
\(419\) | 39.0531 | 1.90787 | 0.953934 | − | 0.300016i | \(-0.0969921\pi\) | ||||
0.953934 | + | 0.300016i | \(0.0969921\pi\) | |||||||
\(420\) | 1.00156 | 0.0488713 | ||||||||
\(421\) | 11.4572 | 0.558388 | 0.279194 | − | 0.960235i | \(-0.409933\pi\) | ||||
0.279194 | + | 0.960235i | \(0.409933\pi\) | |||||||
\(422\) | −24.6481 | −1.19985 | ||||||||
\(423\) | −6.03336 | −0.293352 | ||||||||
\(424\) | 4.03835 | 0.196120 | ||||||||
\(425\) | −18.9686 | −0.920112 | ||||||||
\(426\) | 7.58775 | 0.367628 | ||||||||
\(427\) | 7.82642 | 0.378747 | ||||||||
\(428\) | −8.77589 | −0.424199 | ||||||||
\(429\) | 0.852331 | 0.0411509 | ||||||||
\(430\) | −6.96457 | −0.335861 | ||||||||
\(431\) | 39.7986 | 1.91703 | 0.958516 | − | 0.285040i | \(-0.0920068\pi\) | ||||
0.958516 | + | 0.285040i | \(0.0920068\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −11.5754 | −0.556280 | −0.278140 | − | 0.960541i | \(-0.589718\pi\) | ||||
−0.278140 | + | 0.960541i | \(0.589718\pi\) | |||||||
\(434\) | 11.4155 | 0.547963 | ||||||||
\(435\) | 6.40572 | 0.307131 | ||||||||
\(436\) | 2.87277 | 0.137581 | ||||||||
\(437\) | −64.8408 | −3.10176 | ||||||||
\(438\) | −3.57276 | −0.170713 | ||||||||
\(439\) | −20.5325 | −0.979963 | −0.489982 | − | 0.871733i | \(-0.662997\pi\) | ||||
−0.489982 | + | 0.871733i | \(0.662997\pi\) | |||||||
\(440\) | 0.583447 | 0.0278148 | ||||||||
\(441\) | −4.85923 | −0.231392 | ||||||||
\(442\) | −4.18602 | −0.199109 | ||||||||
\(443\) | −36.0312 | −1.71189 | −0.855947 | − | 0.517064i | \(-0.827025\pi\) | ||||
−0.855947 | + | 0.517064i | \(0.827025\pi\) | |||||||
\(444\) | −5.54810 | −0.263301 | ||||||||
\(445\) | −1.02236 | −0.0484646 | ||||||||
\(446\) | 6.56161 | 0.310701 | ||||||||
\(447\) | −14.4252 | −0.682290 | ||||||||
\(448\) | −1.46314 | −0.0691268 | ||||||||
\(449\) | 9.61670 | 0.453840 | 0.226920 | − | 0.973913i | \(-0.427134\pi\) | ||||
0.226920 | + | 0.973913i | \(0.427134\pi\) | |||||||
\(450\) | −4.53142 | −0.213613 | ||||||||
\(451\) | −6.41316 | −0.301984 | ||||||||
\(452\) | 4.54248 | 0.213660 | ||||||||
\(453\) | −13.4386 | −0.631400 | ||||||||
\(454\) | −5.97922 | −0.280619 | ||||||||
\(455\) | −1.00156 | −0.0469540 | ||||||||
\(456\) | −7.25777 | −0.339876 | ||||||||
\(457\) | 29.8318 | 1.39547 | 0.697736 | − | 0.716355i | \(-0.254191\pi\) | ||||
0.697736 | + | 0.716355i | \(0.254191\pi\) | |||||||
\(458\) | 0.430082 | 0.0200964 | ||||||||
\(459\) | 4.18602 | 0.195387 | ||||||||
\(460\) | −6.11560 | −0.285141 | ||||||||
\(461\) | 36.5689 | 1.70318 | 0.851592 | − | 0.524205i | \(-0.175638\pi\) | ||||
0.851592 | + | 0.524205i | \(0.175638\pi\) | |||||||
\(462\) | 1.24708 | 0.0580193 | ||||||||
\(463\) | −18.0887 | −0.840654 | −0.420327 | − | 0.907373i | \(-0.638085\pi\) | ||||
−0.420327 | + | 0.907373i | \(0.638085\pi\) | |||||||
\(464\) | −9.35782 | −0.434426 | ||||||||
\(465\) | 5.34078 | 0.247673 | ||||||||
\(466\) | 6.90703 | 0.319962 | ||||||||
\(467\) | −5.84376 | −0.270417 | −0.135209 | − | 0.990817i | \(-0.543170\pi\) | ||||
−0.135209 | + | 0.990817i | \(0.543170\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 13.0241 | 0.601399 | ||||||||
\(470\) | 4.13003 | 0.190504 | ||||||||
\(471\) | −1.79833 | −0.0828629 | ||||||||
\(472\) | −11.8277 | −0.544414 | ||||||||
\(473\) | −8.67179 | −0.398729 | ||||||||
\(474\) | 7.23728 | 0.332419 | ||||||||
\(475\) | 32.8880 | 1.50900 | ||||||||
\(476\) | −6.12472 | −0.280726 | ||||||||
\(477\) | 4.03835 | 0.184903 | ||||||||
\(478\) | 9.90323 | 0.452963 | ||||||||
\(479\) | 17.0996 | 0.781299 | 0.390650 | − | 0.920539i | \(-0.372250\pi\) | ||||
0.390650 | + | 0.920539i | \(0.372250\pi\) | |||||||
\(480\) | −0.684532 | −0.0312445 | ||||||||
\(481\) | 5.54810 | 0.252971 | ||||||||
\(482\) | −5.75164 | −0.261980 | ||||||||
\(483\) | −13.0717 | −0.594781 | ||||||||
\(484\) | −10.2735 | −0.466979 | ||||||||
\(485\) | 8.98301 | 0.407898 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 3.52339 | 0.159660 | 0.0798300 | − | 0.996808i | \(-0.474562\pi\) | ||||
0.0798300 | + | 0.996808i | \(0.474562\pi\) | |||||||
\(488\) | −5.34907 | −0.242141 | ||||||||
\(489\) | 13.8168 | 0.624817 | ||||||||
\(490\) | 3.32630 | 0.150267 | ||||||||
\(491\) | 29.6720 | 1.33908 | 0.669540 | − | 0.742776i | \(-0.266491\pi\) | ||||
0.669540 | + | 0.742776i | \(0.266491\pi\) | |||||||
\(492\) | 7.52426 | 0.339220 | ||||||||
\(493\) | −39.1720 | −1.76422 | ||||||||
\(494\) | 7.25777 | 0.326542 | ||||||||
\(495\) | 0.583447 | 0.0262240 | ||||||||
\(496\) | −7.80209 | −0.350324 | ||||||||
\(497\) | −11.1019 | −0.497989 | ||||||||
\(498\) | −9.34849 | −0.418916 | ||||||||
\(499\) | −40.7675 | −1.82500 | −0.912501 | − | 0.409073i | \(-0.865852\pi\) | ||||
−0.912501 | + | 0.409073i | \(0.865852\pi\) | |||||||
\(500\) | 6.52456 | 0.291787 | ||||||||
\(501\) | −1.72810 | −0.0772058 | ||||||||
\(502\) | −11.5382 | −0.514973 | ||||||||
\(503\) | 17.0140 | 0.758616 | 0.379308 | − | 0.925270i | \(-0.376162\pi\) | ||||
0.379308 | + | 0.925270i | \(0.376162\pi\) | |||||||
\(504\) | −1.46314 | −0.0651733 | ||||||||
\(505\) | −9.84989 | −0.438314 | ||||||||
\(506\) | −7.61471 | −0.338515 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −18.0691 | −0.801687 | ||||||||
\(509\) | −40.3013 | −1.78632 | −0.893161 | − | 0.449736i | \(-0.851518\pi\) | ||||
−0.893161 | + | 0.449736i | \(0.851518\pi\) | |||||||
\(510\) | −2.86546 | −0.126885 | ||||||||
\(511\) | 5.22744 | 0.231248 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.25777 | −0.320438 | ||||||||
\(514\) | −22.3502 | −0.985823 | ||||||||
\(515\) | 0.684532 | 0.0301641 | ||||||||
\(516\) | 10.1742 | 0.447895 | ||||||||
\(517\) | 5.14242 | 0.226163 | ||||||||
\(518\) | 8.11763 | 0.356668 | ||||||||
\(519\) | 15.9660 | 0.700829 | ||||||||
\(520\) | 0.684532 | 0.0300187 | ||||||||
\(521\) | 11.5494 | 0.505988 | 0.252994 | − | 0.967468i | \(-0.418585\pi\) | ||||
0.252994 | + | 0.967468i | \(0.418585\pi\) | |||||||
\(522\) | −9.35782 | −0.409581 | ||||||||
\(523\) | −8.70958 | −0.380843 | −0.190422 | − | 0.981702i | \(-0.560986\pi\) | ||||
−0.190422 | + | 0.981702i | \(0.560986\pi\) | |||||||
\(524\) | 18.7682 | 0.819891 | ||||||||
\(525\) | 6.63009 | 0.289361 | ||||||||
\(526\) | −31.2570 | −1.36287 | ||||||||
\(527\) | −32.6597 | −1.42268 | ||||||||
\(528\) | −0.852331 | −0.0370929 | ||||||||
\(529\) | 56.8162 | 2.47027 | ||||||||
\(530\) | −2.76438 | −0.120077 | ||||||||
\(531\) | −11.8277 | −0.513279 | ||||||||
\(532\) | 10.6191 | 0.460397 | ||||||||
\(533\) | −7.52426 | −0.325912 | ||||||||
\(534\) | 1.49352 | 0.0646309 | ||||||||
\(535\) | 6.00738 | 0.259722 | ||||||||
\(536\) | −8.90152 | −0.384487 | ||||||||
\(537\) | 2.82006 | 0.121695 | ||||||||
\(538\) | −25.3631 | −1.09348 | ||||||||
\(539\) | 4.14167 | 0.178394 | ||||||||
\(540\) | −0.684532 | −0.0294576 | ||||||||
\(541\) | 4.66688 | 0.200645 | 0.100322 | − | 0.994955i | \(-0.468013\pi\) | ||||
0.100322 | + | 0.994955i | \(0.468013\pi\) | |||||||
\(542\) | 12.2195 | 0.524871 | ||||||||
\(543\) | 1.24487 | 0.0534224 | ||||||||
\(544\) | 4.18602 | 0.179474 | ||||||||
\(545\) | −1.96650 | −0.0842356 | ||||||||
\(546\) | 1.46314 | 0.0626165 | ||||||||
\(547\) | 4.57821 | 0.195750 | 0.0978750 | − | 0.995199i | \(-0.468795\pi\) | ||||
0.0978750 | + | 0.995199i | \(0.468795\pi\) | |||||||
\(548\) | −12.6165 | −0.538950 | ||||||||
\(549\) | −5.34907 | −0.228293 | ||||||||
\(550\) | 3.86227 | 0.164688 | ||||||||
\(551\) | 67.9169 | 2.89336 | ||||||||
\(552\) | 8.93399 | 0.380256 | ||||||||
\(553\) | −10.5891 | −0.450296 | ||||||||
\(554\) | −25.3017 | −1.07496 | ||||||||
\(555\) | 3.79785 | 0.161210 | ||||||||
\(556\) | −1.54440 | −0.0654972 | ||||||||
\(557\) | −3.88709 | −0.164701 | −0.0823506 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823506 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(558\) | −7.80209 | −0.330289 | ||||||||
\(559\) | −10.1742 | −0.430323 | ||||||||
\(560\) | 1.00156 | 0.0423238 | ||||||||
\(561\) | −3.56787 | −0.150636 | ||||||||
\(562\) | −19.7540 | −0.833272 | ||||||||
\(563\) | −5.37558 | −0.226554 | −0.113277 | − | 0.993563i | \(-0.536135\pi\) | ||||
−0.113277 | + | 0.993563i | \(0.536135\pi\) | |||||||
\(564\) | −6.03336 | −0.254050 | ||||||||
\(565\) | −3.10947 | −0.130816 | ||||||||
\(566\) | 3.83554 | 0.161220 | ||||||||
\(567\) | −1.46314 | −0.0614460 | ||||||||
\(568\) | 7.58775 | 0.318375 | ||||||||
\(569\) | −39.2744 | −1.64647 | −0.823235 | − | 0.567701i | \(-0.807833\pi\) | ||||
−0.823235 | + | 0.567701i | \(0.807833\pi\) | |||||||
\(570\) | 4.96817 | 0.208094 | ||||||||
\(571\) | −41.4880 | −1.73622 | −0.868109 | − | 0.496374i | \(-0.834664\pi\) | ||||
−0.868109 | + | 0.496374i | \(0.834664\pi\) | |||||||
\(572\) | 0.852331 | 0.0356377 | ||||||||
\(573\) | −20.9678 | −0.875944 | ||||||||
\(574\) | −11.0090 | −0.459508 | ||||||||
\(575\) | −40.4836 | −1.68828 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.07627 | −0.336220 | −0.168110 | − | 0.985768i | \(-0.553766\pi\) | ||||
−0.168110 | + | 0.985768i | \(0.553766\pi\) | |||||||
\(578\) | 0.522771 | 0.0217444 | ||||||||
\(579\) | 16.7859 | 0.697600 | ||||||||
\(580\) | 6.40572 | 0.265983 | ||||||||
\(581\) | 13.6781 | 0.567464 | ||||||||
\(582\) | −13.1229 | −0.543960 | ||||||||
\(583\) | −3.44201 | −0.142554 | ||||||||
\(584\) | −3.57276 | −0.147842 | ||||||||
\(585\) | 0.684532 | 0.0283019 | ||||||||
\(586\) | −14.5198 | −0.599808 | ||||||||
\(587\) | 19.5273 | 0.805978 | 0.402989 | − | 0.915205i | \(-0.367971\pi\) | ||||
0.402989 | + | 0.915205i | \(0.367971\pi\) | |||||||
\(588\) | −4.85923 | −0.200391 | ||||||||
\(589\) | 56.6258 | 2.33322 | ||||||||
\(590\) | 8.09644 | 0.333325 | ||||||||
\(591\) | −17.9766 | −0.739459 | ||||||||
\(592\) | −5.54810 | −0.228025 | ||||||||
\(593\) | −0.575372 | −0.0236277 | −0.0118138 | − | 0.999930i | \(-0.503761\pi\) | ||||
−0.0118138 | + | 0.999930i | \(0.503761\pi\) | |||||||
\(594\) | −0.852331 | −0.0349716 | ||||||||
\(595\) | 4.19257 | 0.171879 | ||||||||
\(596\) | −14.4252 | −0.590880 | ||||||||
\(597\) | 25.9055 | 1.06024 | ||||||||
\(598\) | −8.93399 | −0.365338 | ||||||||
\(599\) | 25.9104 | 1.05867 | 0.529335 | − | 0.848413i | \(-0.322441\pi\) | ||||
0.529335 | + | 0.848413i | \(0.322441\pi\) | |||||||
\(600\) | −4.53142 | −0.184994 | ||||||||
\(601\) | −22.9714 | −0.937021 | −0.468511 | − | 0.883458i | \(-0.655209\pi\) | ||||
−0.468511 | + | 0.883458i | \(0.655209\pi\) | |||||||
\(602\) | −14.8863 | −0.606719 | ||||||||
\(603\) | −8.90152 | −0.362498 | ||||||||
\(604\) | −13.4386 | −0.546808 | ||||||||
\(605\) | 7.03256 | 0.285914 | ||||||||
\(606\) | 14.3892 | 0.584523 | ||||||||
\(607\) | 36.9422 | 1.49944 | 0.749718 | − | 0.661758i | \(-0.230189\pi\) | ||||
0.749718 | + | 0.661758i | \(0.230189\pi\) | |||||||
\(608\) | −7.25777 | −0.294341 | ||||||||
\(609\) | 13.6918 | 0.554819 | ||||||||
\(610\) | 3.66161 | 0.148254 | ||||||||
\(611\) | 6.03336 | 0.244084 | ||||||||
\(612\) | 4.18602 | 0.169210 | ||||||||
\(613\) | −33.7561 | −1.36340 | −0.681698 | − | 0.731634i | \(-0.738758\pi\) | ||||
−0.681698 | + | 0.731634i | \(0.738758\pi\) | |||||||
\(614\) | 7.02841 | 0.283643 | ||||||||
\(615\) | −5.15059 | −0.207692 | ||||||||
\(616\) | 1.24708 | 0.0502462 | ||||||||
\(617\) | 1.86602 | 0.0751230 | 0.0375615 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375615 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −10.9504 | −0.440135 | −0.220067 | − | 0.975485i | \(-0.570628\pi\) | ||||
−0.220067 | + | 0.975485i | \(0.570628\pi\) | |||||||
\(620\) | 5.34078 | 0.214491 | ||||||||
\(621\) | 8.93399 | 0.358509 | ||||||||
\(622\) | 32.0849 | 1.28649 | ||||||||
\(623\) | −2.18522 | −0.0875492 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 18.1908 | 0.727633 | ||||||||
\(626\) | 28.9318 | 1.15635 | ||||||||
\(627\) | 6.18602 | 0.247046 | ||||||||
\(628\) | −1.79833 | −0.0717614 | ||||||||
\(629\) | −23.2245 | −0.926020 | ||||||||
\(630\) | 1.00156 | 0.0399033 | ||||||||
\(631\) | 25.2078 | 1.00350 | 0.501752 | − | 0.865011i | \(-0.332689\pi\) | ||||
0.501752 | + | 0.865011i | \(0.332689\pi\) | |||||||
\(632\) | 7.23728 | 0.287884 | ||||||||
\(633\) | −24.6481 | −0.979672 | ||||||||
\(634\) | 9.30284 | 0.369463 | ||||||||
\(635\) | 12.3689 | 0.490844 | ||||||||
\(636\) | 4.03835 | 0.160131 | ||||||||
\(637\) | 4.85923 | 0.192530 | ||||||||
\(638\) | 7.97596 | 0.315771 | ||||||||
\(639\) | 7.58775 | 0.300167 | ||||||||
\(640\) | −0.684532 | −0.0270585 | ||||||||
\(641\) | −2.86519 | −0.113168 | −0.0565841 | − | 0.998398i | \(-0.518021\pi\) | ||||
−0.0565841 | + | 0.998398i | \(0.518021\pi\) | |||||||
\(642\) | −8.77589 | −0.346357 | ||||||||
\(643\) | −19.7103 | −0.777300 | −0.388650 | − | 0.921385i | \(-0.627059\pi\) | ||||
−0.388650 | + | 0.921385i | \(0.627059\pi\) | |||||||
\(644\) | −13.0717 | −0.515095 | ||||||||
\(645\) | −6.96457 | −0.274230 | ||||||||
\(646\) | −30.3812 | −1.19533 | ||||||||
\(647\) | 1.42474 | 0.0560124 | 0.0280062 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280062 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 10.0811 | 0.395718 | ||||||||
\(650\) | 4.53142 | 0.177737 | ||||||||
\(651\) | 11.4155 | 0.447410 | ||||||||
\(652\) | 13.8168 | 0.541108 | ||||||||
\(653\) | 0.388474 | 0.0152022 | 0.00760109 | − | 0.999971i | \(-0.497580\pi\) | ||||
0.00760109 | + | 0.999971i | \(0.497580\pi\) | |||||||
\(654\) | 2.87277 | 0.112334 | ||||||||
\(655\) | −12.8474 | −0.501989 | ||||||||
\(656\) | 7.52426 | 0.293773 | ||||||||
\(657\) | −3.57276 | −0.139387 | ||||||||
\(658\) | 8.82763 | 0.344137 | ||||||||
\(659\) | 10.4609 | 0.407501 | 0.203750 | − | 0.979023i | \(-0.434687\pi\) | ||||
0.203750 | + | 0.979023i | \(0.434687\pi\) | |||||||
\(660\) | 0.583447 | 0.0227107 | ||||||||
\(661\) | 23.1355 | 0.899866 | 0.449933 | − | 0.893062i | \(-0.351448\pi\) | ||||
0.449933 | + | 0.893062i | \(0.351448\pi\) | |||||||
\(662\) | −31.1194 | −1.20949 | ||||||||
\(663\) | −4.18602 | −0.162572 | ||||||||
\(664\) | −9.34849 | −0.362792 | ||||||||
\(665\) | −7.26912 | −0.281884 | ||||||||
\(666\) | −5.54810 | −0.214984 | ||||||||
\(667\) | −83.6027 | −3.23711 | ||||||||
\(668\) | −1.72810 | −0.0668622 | ||||||||
\(669\) | 6.56161 | 0.253686 | ||||||||
\(670\) | 6.09337 | 0.235408 | ||||||||
\(671\) | 4.55917 | 0.176005 | ||||||||
\(672\) | −1.46314 | −0.0564418 | ||||||||
\(673\) | 38.6514 | 1.48990 | 0.744952 | − | 0.667118i | \(-0.232472\pi\) | ||||
0.744952 | + | 0.667118i | \(0.232472\pi\) | |||||||
\(674\) | −20.6049 | −0.793673 | ||||||||
\(675\) | −4.53142 | −0.174414 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −0.167047 | −0.00642015 | −0.00321007 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321007 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(678\) | 4.54248 | 0.174453 | ||||||||
\(679\) | 19.2005 | 0.736849 | ||||||||
\(680\) | −2.86546 | −0.109886 | ||||||||
\(681\) | −5.97922 | −0.229124 | ||||||||
\(682\) | 6.64996 | 0.254640 | ||||||||
\(683\) | 39.5523 | 1.51343 | 0.756714 | − | 0.653746i | \(-0.226804\pi\) | ||||
0.756714 | + | 0.653746i | \(0.226804\pi\) | |||||||
\(684\) | −7.25777 | −0.277508 | ||||||||
\(685\) | 8.63640 | 0.329980 | ||||||||
\(686\) | 17.3517 | 0.662490 | ||||||||
\(687\) | 0.430082 | 0.0164087 | ||||||||
\(688\) | 10.1742 | 0.387888 | ||||||||
\(689\) | −4.03835 | −0.153849 | ||||||||
\(690\) | −6.11560 | −0.232817 | ||||||||
\(691\) | 24.2086 | 0.920938 | 0.460469 | − | 0.887676i | \(-0.347681\pi\) | ||||
0.460469 | + | 0.887676i | \(0.347681\pi\) | |||||||
\(692\) | 15.9660 | 0.606935 | ||||||||
\(693\) | 1.24708 | 0.0473725 | ||||||||
\(694\) | 10.1696 | 0.386034 | ||||||||
\(695\) | 1.05719 | 0.0401016 | ||||||||
\(696\) | −9.35782 | −0.354707 | ||||||||
\(697\) | 31.4967 | 1.19302 | ||||||||
\(698\) | 28.8819 | 1.09320 | ||||||||
\(699\) | 6.90703 | 0.261248 | ||||||||
\(700\) | 6.63009 | 0.250594 | ||||||||
\(701\) | 51.5781 | 1.94808 | 0.974038 | − | 0.226382i | \(-0.0726899\pi\) | ||||
0.974038 | + | 0.226382i | \(0.0726899\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 40.2668 | 1.51869 | ||||||||
\(704\) | −0.852331 | −0.0321234 | ||||||||
\(705\) | 4.13003 | 0.155546 | ||||||||
\(706\) | −6.13386 | −0.230851 | ||||||||
\(707\) | −21.0534 | −0.791796 | ||||||||
\(708\) | −11.8277 | −0.444512 | ||||||||
\(709\) | 24.1093 | 0.905443 | 0.452722 | − | 0.891652i | \(-0.350453\pi\) | ||||
0.452722 | + | 0.891652i | \(0.350453\pi\) | |||||||
\(710\) | −5.19406 | −0.194929 | ||||||||
\(711\) | 7.23728 | 0.271419 | ||||||||
\(712\) | 1.49352 | 0.0559720 | ||||||||
\(713\) | −69.7038 | −2.61043 | ||||||||
\(714\) | −6.12472 | −0.229212 | ||||||||
\(715\) | −0.583447 | −0.0218197 | ||||||||
\(716\) | 2.82006 | 0.105391 | ||||||||
\(717\) | 9.90323 | 0.369843 | ||||||||
\(718\) | 0.812147 | 0.0303090 | ||||||||
\(719\) | 4.60391 | 0.171697 | 0.0858484 | − | 0.996308i | \(-0.472640\pi\) | ||||
0.0858484 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(720\) | −0.684532 | −0.0255110 | ||||||||
\(721\) | 1.46314 | 0.0544901 | ||||||||
\(722\) | 33.6752 | 1.25326 | ||||||||
\(723\) | −5.75164 | −0.213906 | ||||||||
\(724\) | 1.24487 | 0.0462651 | ||||||||
\(725\) | 42.4042 | 1.57485 | ||||||||
\(726\) | −10.2735 | −0.381287 | ||||||||
\(727\) | −16.3844 | −0.607665 | −0.303832 | − | 0.952726i | \(-0.598266\pi\) | ||||
−0.303832 | + | 0.952726i | \(0.598266\pi\) | |||||||
\(728\) | 1.46314 | 0.0542275 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.44567 | 0.0905182 | ||||||||
\(731\) | 42.5895 | 1.57523 | ||||||||
\(732\) | −5.34907 | −0.197707 | ||||||||
\(733\) | 42.0161 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(734\) | 12.5112 | 0.461797 | ||||||||
\(735\) | 3.32630 | 0.122692 | ||||||||
\(736\) | 8.93399 | 0.329311 | ||||||||
\(737\) | 7.58704 | 0.279472 | ||||||||
\(738\) | 7.52426 | 0.276972 | ||||||||
\(739\) | −8.32382 | −0.306197 | −0.153098 | − | 0.988211i | \(-0.548925\pi\) | ||||
−0.153098 | + | 0.988211i | \(0.548925\pi\) | |||||||
\(740\) | 3.79785 | 0.139612 | ||||||||
\(741\) | 7.25777 | 0.266621 | ||||||||
\(742\) | −5.90866 | −0.216914 | ||||||||
\(743\) | 18.0533 | 0.662313 | 0.331156 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331156 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(744\) | −7.80209 | −0.286039 | ||||||||
\(745\) | 9.87452 | 0.361775 | ||||||||
\(746\) | −30.5555 | −1.11871 | ||||||||
\(747\) | −9.34849 | −0.342043 | ||||||||
\(748\) | −3.56787 | −0.130454 | ||||||||
\(749\) | 12.8403 | 0.469176 | ||||||||
\(750\) | 6.52456 | 0.238243 | ||||||||
\(751\) | 1.59769 | 0.0583006 | 0.0291503 | − | 0.999575i | \(-0.490720\pi\) | ||||
0.0291503 | + | 0.999575i | \(0.490720\pi\) | |||||||
\(752\) | −6.03336 | −0.220014 | ||||||||
\(753\) | −11.5382 | −0.420474 | ||||||||
\(754\) | 9.35782 | 0.340792 | ||||||||
\(755\) | 9.19914 | 0.334791 | ||||||||
\(756\) | −1.46314 | −0.0532138 | ||||||||
\(757\) | 3.29104 | 0.119615 | 0.0598075 | − | 0.998210i | \(-0.480951\pi\) | ||||
0.0598075 | + | 0.998210i | \(0.480951\pi\) | |||||||
\(758\) | 15.5193 | 0.563688 | ||||||||
\(759\) | −7.61471 | −0.276397 | ||||||||
\(760\) | 4.96817 | 0.180215 | ||||||||
\(761\) | −8.64206 | −0.313274 | −0.156637 | − | 0.987656i | \(-0.550065\pi\) | ||||
−0.156637 | + | 0.987656i | \(0.550065\pi\) | |||||||
\(762\) | −18.0691 | −0.654575 | ||||||||
\(763\) | −4.20325 | −0.152168 | ||||||||
\(764\) | −20.9678 | −0.758590 | ||||||||
\(765\) | −2.86546 | −0.103601 | ||||||||
\(766\) | 10.4672 | 0.378196 | ||||||||
\(767\) | 11.8277 | 0.427074 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 0.571955 | 0.0206252 | 0.0103126 | − | 0.999947i | \(-0.496717\pi\) | ||||
0.0103126 | + | 0.999947i | \(0.496717\pi\) | |||||||
\(770\) | −0.853664 | −0.0307639 | ||||||||
\(771\) | −22.3502 | −0.804921 | ||||||||
\(772\) | 16.7859 | 0.604140 | ||||||||
\(773\) | −19.1356 | −0.688260 | −0.344130 | − | 0.938922i | \(-0.611826\pi\) | ||||
−0.344130 | + | 0.938922i | \(0.611826\pi\) | |||||||
\(774\) | 10.1742 | 0.365705 | ||||||||
\(775\) | 35.3545 | 1.26997 | ||||||||
\(776\) | −13.1229 | −0.471083 | ||||||||
\(777\) | 8.11763 | 0.291218 | ||||||||
\(778\) | −2.93656 | −0.105281 | ||||||||
\(779\) | −54.6093 | −1.95658 | ||||||||
\(780\) | 0.684532 | 0.0245102 | ||||||||
\(781\) | −6.46727 | −0.231417 | ||||||||
\(782\) | 37.3979 | 1.33735 | ||||||||
\(783\) | −9.35782 | −0.334421 | ||||||||
\(784\) | −4.85923 | −0.173544 | ||||||||
\(785\) | 1.23102 | 0.0439369 | ||||||||
\(786\) | 18.7682 | 0.669438 | ||||||||
\(787\) | −42.5567 | −1.51698 | −0.758491 | − | 0.651684i | \(-0.774063\pi\) | ||||
−0.758491 | + | 0.651684i | \(0.774063\pi\) | |||||||
\(788\) | −17.9766 | −0.640390 | ||||||||
\(789\) | −31.2570 | −1.11278 | ||||||||
\(790\) | −4.95415 | −0.176261 | ||||||||
\(791\) | −6.64627 | −0.236314 | ||||||||
\(792\) | −0.852331 | −0.0302863 | ||||||||
\(793\) | 5.34907 | 0.189951 | ||||||||
\(794\) | 22.2722 | 0.790412 | ||||||||
\(795\) | −2.76438 | −0.0980425 | ||||||||
\(796\) | 25.9055 | 0.918197 | ||||||||
\(797\) | 0.0328812 | 0.00116471 | 0.000582356 | − | 1.00000i | \(-0.499815\pi\) | ||||
0.000582356 | 1.00000i | \(0.499815\pi\) | ||||||||
\(798\) | 10.6191 | 0.375912 | ||||||||
\(799\) | −25.2558 | −0.893485 | ||||||||
\(800\) | −4.53142 | −0.160210 | ||||||||
\(801\) | 1.49352 | 0.0527709 | ||||||||
\(802\) | −18.6195 | −0.657476 | ||||||||
\(803\) | 3.04517 | 0.107462 | ||||||||
\(804\) | −8.90152 | −0.313932 | ||||||||
\(805\) | 8.94796 | 0.315374 | ||||||||
\(806\) | 7.80209 | 0.274817 | ||||||||
\(807\) | −25.3631 | −0.892825 | ||||||||
\(808\) | 14.3892 | 0.506212 | ||||||||
\(809\) | 19.4008 | 0.682097 | 0.341049 | − | 0.940046i | \(-0.389218\pi\) | ||||
0.341049 | + | 0.940046i | \(0.389218\pi\) | |||||||
\(810\) | −0.684532 | −0.0240520 | ||||||||
\(811\) | 38.7459 | 1.36055 | 0.680275 | − | 0.732957i | \(-0.261860\pi\) | ||||
0.680275 | + | 0.732957i | \(0.261860\pi\) | |||||||
\(812\) | 13.6918 | 0.480487 | ||||||||
\(813\) | 12.2195 | 0.428555 | ||||||||
\(814\) | 4.72881 | 0.165745 | ||||||||
\(815\) | −9.45804 | −0.331301 | ||||||||
\(816\) | 4.18602 | 0.146540 | ||||||||
\(817\) | −73.8420 | −2.58341 | ||||||||
\(818\) | 10.9971 | 0.384504 | ||||||||
\(819\) | 1.46314 | 0.0511262 | ||||||||
\(820\) | −5.15059 | −0.179867 | ||||||||
\(821\) | −24.2407 | −0.846007 | −0.423004 | − | 0.906128i | \(-0.639024\pi\) | ||||
−0.423004 | + | 0.906128i | \(0.639024\pi\) | |||||||
\(822\) | −12.6165 | −0.440051 | ||||||||
\(823\) | 38.9787 | 1.35871 | 0.679356 | − | 0.733809i | \(-0.262259\pi\) | ||||
0.679356 | + | 0.733809i | \(0.262259\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 3.86227 | 0.134467 | ||||||||
\(826\) | 17.3056 | 0.602137 | ||||||||
\(827\) | 8.70842 | 0.302821 | 0.151411 | − | 0.988471i | \(-0.451618\pi\) | ||||
0.151411 | + | 0.988471i | \(0.451618\pi\) | |||||||
\(828\) | 8.93399 | 0.310478 | ||||||||
\(829\) | −6.34971 | −0.220535 | −0.110267 | − | 0.993902i | \(-0.535171\pi\) | ||||
−0.110267 | + | 0.993902i | \(0.535171\pi\) | |||||||
\(830\) | 6.39934 | 0.222124 | ||||||||
\(831\) | −25.3017 | −0.877705 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −20.3408 | −0.704768 | ||||||||
\(834\) | −1.54440 | −0.0534783 | ||||||||
\(835\) | 1.18294 | 0.0409373 | ||||||||
\(836\) | 6.18602 | 0.213948 | ||||||||
\(837\) | −7.80209 | −0.269680 | ||||||||
\(838\) | 39.0531 | 1.34907 | ||||||||
\(839\) | −15.7795 | −0.544769 | −0.272384 | − | 0.962189i | \(-0.587812\pi\) | ||||
−0.272384 | + | 0.962189i | \(0.587812\pi\) | |||||||
\(840\) | 1.00156 | 0.0345572 | ||||||||
\(841\) | 58.5688 | 2.01961 | ||||||||
\(842\) | 11.4572 | 0.394840 | ||||||||
\(843\) | −19.7540 | −0.680364 | ||||||||
\(844\) | −24.6481 | −0.848421 | ||||||||
\(845\) | −0.684532 | −0.0235486 | ||||||||
\(846\) | −6.03336 | −0.207431 | ||||||||
\(847\) | 15.0316 | 0.516492 | ||||||||
\(848\) | 4.03835 | 0.138678 | ||||||||
\(849\) | 3.83554 | 0.131635 | ||||||||
\(850\) | −18.9686 | −0.650618 | ||||||||
\(851\) | −49.5666 | −1.69912 | ||||||||
\(852\) | 7.58775 | 0.259952 | ||||||||
\(853\) | −20.0221 | −0.685544 | −0.342772 | − | 0.939419i | \(-0.611366\pi\) | ||||
−0.342772 | + | 0.939419i | \(0.611366\pi\) | |||||||
\(854\) | 7.82642 | 0.267815 | ||||||||
\(855\) | 4.96817 | 0.169908 | ||||||||
\(856\) | −8.77589 | −0.299954 | ||||||||
\(857\) | −9.39879 | −0.321057 | −0.160528 | − | 0.987031i | \(-0.551320\pi\) | ||||
−0.160528 | + | 0.987031i | \(0.551320\pi\) | |||||||
\(858\) | 0.852331 | 0.0290981 | ||||||||
\(859\) | 5.29957 | 0.180819 | 0.0904095 | − | 0.995905i | \(-0.471182\pi\) | ||||
0.0904095 | + | 0.995905i | \(0.471182\pi\) | |||||||
\(860\) | −6.96457 | −0.237490 | ||||||||
\(861\) | −11.0090 | −0.375187 | ||||||||
\(862\) | 39.7986 | 1.35555 | ||||||||
\(863\) | −2.97386 | −0.101231 | −0.0506157 | − | 0.998718i | \(-0.516118\pi\) | ||||
−0.0506157 | + | 0.998718i | \(0.516118\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −10.9292 | −0.371605 | ||||||||
\(866\) | −11.5754 | −0.393349 | ||||||||
\(867\) | 0.522771 | 0.0177542 | ||||||||
\(868\) | 11.4155 | 0.387469 | ||||||||
\(869\) | −6.16856 | −0.209254 | ||||||||
\(870\) | 6.40572 | 0.217174 | ||||||||
\(871\) | 8.90152 | 0.301616 | ||||||||
\(872\) | 2.87277 | 0.0972842 | ||||||||
\(873\) | −13.1229 | −0.444141 | ||||||||
\(874\) | −64.8408 | −2.19327 | ||||||||
\(875\) | −9.54632 | −0.322725 | ||||||||
\(876\) | −3.57276 | −0.120712 | ||||||||
\(877\) | −26.9787 | −0.911005 | −0.455503 | − | 0.890234i | \(-0.650540\pi\) | ||||
−0.455503 | + | 0.890234i | \(0.650540\pi\) | |||||||
\(878\) | −20.5325 | −0.692939 | ||||||||
\(879\) | −14.5198 | −0.489741 | ||||||||
\(880\) | 0.583447 | 0.0196680 | ||||||||
\(881\) | −34.1276 | −1.14979 | −0.574895 | − | 0.818228i | \(-0.694957\pi\) | ||||
−0.574895 | + | 0.818228i | \(0.694957\pi\) | |||||||
\(882\) | −4.85923 | −0.163619 | ||||||||
\(883\) | −46.6544 | −1.57004 | −0.785022 | − | 0.619468i | \(-0.787349\pi\) | ||||
−0.785022 | + | 0.619468i | \(0.787349\pi\) | |||||||
\(884\) | −4.18602 | −0.140791 | ||||||||
\(885\) | 8.09644 | 0.272159 | ||||||||
\(886\) | −36.0312 | −1.21049 | ||||||||
\(887\) | −24.5155 | −0.823150 | −0.411575 | − | 0.911376i | \(-0.635021\pi\) | ||||
−0.411575 | + | 0.911376i | \(0.635021\pi\) | |||||||
\(888\) | −5.54810 | −0.186182 | ||||||||
\(889\) | 26.4376 | 0.886689 | ||||||||
\(890\) | −1.02236 | −0.0342696 | ||||||||
\(891\) | −0.852331 | −0.0285542 | ||||||||
\(892\) | 6.56161 | 0.219699 | ||||||||
\(893\) | 43.7887 | 1.46533 | ||||||||
\(894\) | −14.4252 | −0.482452 | ||||||||
\(895\) | −1.93042 | −0.0645269 | ||||||||
\(896\) | −1.46314 | −0.0488800 | ||||||||
\(897\) | −8.93399 | −0.298297 | ||||||||
\(898\) | 9.61670 | 0.320913 | ||||||||
\(899\) | 73.0106 | 2.43504 | ||||||||
\(900\) | −4.53142 | −0.151047 | ||||||||
\(901\) | 16.9046 | 0.563175 | ||||||||
\(902\) | −6.41316 | −0.213535 | ||||||||
\(903\) | −14.8863 | −0.495384 | ||||||||
\(904\) | 4.54248 | 0.151081 | ||||||||
\(905\) | −0.852151 | −0.0283265 | ||||||||
\(906\) | −13.4386 | −0.446467 | ||||||||
\(907\) | 2.23575 | 0.0742369 | 0.0371184 | − | 0.999311i | \(-0.488182\pi\) | ||||
0.0371184 | + | 0.999311i | \(0.488182\pi\) | |||||||
\(908\) | −5.97922 | −0.198427 | ||||||||
\(909\) | 14.3892 | 0.477261 | ||||||||
\(910\) | −1.00156 | −0.0332015 | ||||||||
\(911\) | 18.3515 | 0.608013 | 0.304006 | − | 0.952670i | \(-0.401676\pi\) | ||||
0.304006 | + | 0.952670i | \(0.401676\pi\) | |||||||
\(912\) | −7.25777 | −0.240329 | ||||||||
\(913\) | 7.96801 | 0.263702 | ||||||||
\(914\) | 29.8318 | 0.986747 | ||||||||
\(915\) | 3.66161 | 0.121049 | ||||||||
\(916\) | 0.430082 | 0.0142103 | ||||||||
\(917\) | −27.4604 | −0.906822 | ||||||||
\(918\) | 4.18602 | 0.138159 | ||||||||
\(919\) | 21.8184 | 0.719722 | 0.359861 | − | 0.933006i | \(-0.382824\pi\) | ||||
0.359861 | + | 0.933006i | \(0.382824\pi\) | |||||||
\(920\) | −6.11560 | −0.201625 | ||||||||
\(921\) | 7.02841 | 0.231594 | ||||||||
\(922\) | 36.5689 | 1.20433 | ||||||||
\(923\) | −7.58775 | −0.249754 | ||||||||
\(924\) | 1.24708 | 0.0410258 | ||||||||
\(925\) | 25.1407 | 0.826622 | ||||||||
\(926\) | −18.0887 | −0.594432 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −9.35782 | −0.307185 | ||||||||
\(929\) | −7.80628 | −0.256116 | −0.128058 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128058 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(930\) | 5.34078 | 0.175131 | ||||||||
\(931\) | 35.2671 | 1.15583 | ||||||||
\(932\) | 6.90703 | 0.226247 | ||||||||
\(933\) | 32.0849 | 1.05041 | ||||||||
\(934\) | −5.84376 | −0.191214 | ||||||||
\(935\) | 2.44232 | 0.0798725 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 38.5723 | 1.26010 | 0.630052 | − | 0.776553i | \(-0.283034\pi\) | ||||
0.630052 | + | 0.776553i | \(0.283034\pi\) | |||||||
\(938\) | 13.0241 | 0.425253 | ||||||||
\(939\) | 28.9318 | 0.944154 | ||||||||
\(940\) | 4.13003 | 0.134707 | ||||||||
\(941\) | −51.8436 | −1.69005 | −0.845026 | − | 0.534725i | \(-0.820415\pi\) | ||||
−0.845026 | + | 0.534725i | \(0.820415\pi\) | |||||||
\(942\) | −1.79833 | −0.0585929 | ||||||||
\(943\) | 67.2216 | 2.18904 | ||||||||
\(944\) | −11.8277 | −0.384959 | ||||||||
\(945\) | 1.00156 | 0.0325809 | ||||||||
\(946\) | −8.67179 | −0.281944 | ||||||||
\(947\) | 2.87685 | 0.0934851 | 0.0467425 | − | 0.998907i | \(-0.485116\pi\) | ||||
0.0467425 | + | 0.998907i | \(0.485116\pi\) | |||||||
\(948\) | 7.23728 | 0.235056 | ||||||||
\(949\) | 3.57276 | 0.115977 | ||||||||
\(950\) | 32.8880 | 1.06703 | ||||||||
\(951\) | 9.30284 | 0.301665 | ||||||||
\(952\) | −6.12472 | −0.198503 | ||||||||
\(953\) | −21.8274 | −0.707057 | −0.353529 | − | 0.935424i | \(-0.615018\pi\) | ||||
−0.353529 | + | 0.935424i | \(0.615018\pi\) | |||||||
\(954\) | 4.03835 | 0.130746 | ||||||||
\(955\) | 14.3531 | 0.464457 | ||||||||
\(956\) | 9.90323 | 0.320293 | ||||||||
\(957\) | 7.97596 | 0.257826 | ||||||||
\(958\) | 17.0996 | 0.552462 | ||||||||
\(959\) | 18.4597 | 0.596094 | ||||||||
\(960\) | −0.684532 | −0.0220932 | ||||||||
\(961\) | 29.8727 | 0.963634 | ||||||||
\(962\) | 5.54810 | 0.178878 | ||||||||
\(963\) | −8.77589 | −0.282799 | ||||||||
\(964\) | −5.75164 | −0.185248 | ||||||||
\(965\) | −11.4905 | −0.369893 | ||||||||
\(966\) | −13.0717 | −0.420574 | ||||||||
\(967\) | 21.5613 | 0.693363 | 0.346682 | − | 0.937983i | \(-0.387308\pi\) | ||||
0.346682 | + | 0.937983i | \(0.387308\pi\) | |||||||
\(968\) | −10.2735 | −0.330204 | ||||||||
\(969\) | −30.3812 | −0.975983 | ||||||||
\(970\) | 8.98301 | 0.288427 | ||||||||
\(971\) | −8.58069 | −0.275367 | −0.137684 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137684 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.25967 | 0.0724418 | ||||||||
\(974\) | 3.52339 | 0.112897 | ||||||||
\(975\) | 4.53142 | 0.145121 | ||||||||
\(976\) | −5.34907 | −0.171219 | ||||||||
\(977\) | 27.0817 | 0.866419 | 0.433210 | − | 0.901293i | \(-0.357381\pi\) | ||||
0.433210 | + | 0.901293i | \(0.357381\pi\) | |||||||
\(978\) | 13.8168 | 0.441813 | ||||||||
\(979\) | −1.27297 | −0.0406844 | ||||||||
\(980\) | 3.32630 | 0.106255 | ||||||||
\(981\) | 2.87277 | 0.0917204 | ||||||||
\(982\) | 29.6720 | 0.946872 | ||||||||
\(983\) | 16.2844 | 0.519391 | 0.259695 | − | 0.965691i | \(-0.416378\pi\) | ||||
0.259695 | + | 0.965691i | \(0.416378\pi\) | |||||||
\(984\) | 7.52426 | 0.239865 | ||||||||
\(985\) | 12.3056 | 0.392088 | ||||||||
\(986\) | −39.1720 | −1.24749 | ||||||||
\(987\) | 8.82763 | 0.280987 | ||||||||
\(988\) | 7.25777 | 0.230900 | ||||||||
\(989\) | 90.8963 | 2.89033 | ||||||||
\(990\) | 0.583447 | 0.0185432 | ||||||||
\(991\) | 6.54497 | 0.207908 | 0.103954 | − | 0.994582i | \(-0.466851\pi\) | ||||
0.103954 | + | 0.994582i | \(0.466851\pi\) | |||||||
\(992\) | −7.80209 | −0.247717 | ||||||||
\(993\) | −31.1194 | −0.987546 | ||||||||
\(994\) | −11.1019 | −0.352132 | ||||||||
\(995\) | −17.7332 | −0.562179 | ||||||||
\(996\) | −9.34849 | −0.296218 | ||||||||
\(997\) | 29.6005 | 0.937457 | 0.468728 | − | 0.883342i | \(-0.344712\pi\) | ||||
0.468728 | + | 0.883342i | \(0.344712\pi\) | |||||||
\(998\) | −40.7675 | −1.29047 | ||||||||
\(999\) | −5.54810 | −0.175534 |
(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 | 8034.2.a.q.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.q.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |