Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(2.18919\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18919 | 1.54799 | 0.773997 | − | 0.633189i | \(-0.218255\pi\) | ||||
0.773997 | + | 0.633189i | \(0.218255\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.79257 | 1.39629 | ||||||||
\(5\) | −0.868150 | −0.388249 | −0.194124 | − | 0.980977i | \(-0.562186\pi\) | ||||
−0.194124 | + | 0.980977i | \(0.562186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.73509 | 0.613447 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.90055 | −0.601006 | ||||||||
\(11\) | −0.280542 | −0.0845866 | −0.0422933 | − | 0.999105i | \(-0.513466\pi\) | ||||
−0.0422933 | + | 0.999105i | \(0.513466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.69064 | 1.02360 | 0.511800 | − | 0.859104i | \(-0.328979\pi\) | ||||
0.511800 | + | 0.859104i | \(0.328979\pi\) | |||||||
\(14\) | −2.18919 | −0.585087 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.78669 | −0.446673 | ||||||||
\(17\) | 1.92048 | 0.465784 | 0.232892 | − | 0.972503i | \(-0.425181\pi\) | ||||
0.232892 | + | 0.972503i | \(0.425181\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.42421 | 0.326736 | 0.163368 | − | 0.986565i | \(-0.447764\pi\) | ||||
0.163368 | + | 0.986565i | \(0.447764\pi\) | |||||||
\(20\) | −2.42437 | −0.542106 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.614161 | −0.130939 | ||||||||
\(23\) | 6.52129 | 1.35978 | 0.679891 | − | 0.733313i | \(-0.262027\pi\) | ||||
0.679891 | + | 0.733313i | \(0.262027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.24632 | −0.849263 | ||||||||
\(26\) | 8.07954 | 1.58453 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.79257 | −0.527746 | ||||||||
\(29\) | 3.07387 | 0.570803 | 0.285402 | − | 0.958408i | \(-0.407873\pi\) | ||||
0.285402 | + | 0.958408i | \(0.407873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0163952 | −0.00294467 | −0.00147234 | − | 0.999999i | \(-0.500469\pi\) | ||||
−0.00147234 | + | 0.999999i | \(0.500469\pi\) | |||||||
\(32\) | −7.38160 | −1.30489 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.20429 | 0.721031 | ||||||||
\(35\) | 0.868150 | 0.146744 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.359357 | 0.0590779 | 0.0295389 | − | 0.999564i | \(-0.490596\pi\) | ||||
0.0295389 | + | 0.999564i | \(0.490596\pi\) | |||||||
\(38\) | 3.11787 | 0.505786 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50632 | −0.238170 | ||||||||
\(41\) | −8.75364 | −1.36709 | −0.683544 | − | 0.729909i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729909i | \(0.739562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.09079 | 0.623840 | 0.311920 | − | 0.950108i | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950108i | \(0.399028\pi\) | |||||||
\(44\) | −0.783433 | −0.118107 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2764 | 2.10493 | ||||||||
\(47\) | −4.32210 | −0.630443 | −0.315222 | − | 0.949018i | \(-0.602079\pi\) | ||||
−0.315222 | + | 0.949018i | \(0.602079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.29601 | −1.31465 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.3064 | 1.42924 | ||||||||
\(53\) | 14.1066 | 1.93769 | 0.968846 | − | 0.247662i | \(-0.0796623\pi\) | ||||
0.968846 | + | 0.247662i | \(0.0796623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.243552 | 0.0328406 | ||||||||
\(56\) | −1.73509 | −0.231861 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.72929 | 0.883600 | ||||||||
\(59\) | 13.7905 | 1.79537 | 0.897685 | − | 0.440638i | \(-0.145248\pi\) | ||||
0.897685 | + | 0.440638i | \(0.145248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.486241 | 0.0622568 | 0.0311284 | − | 0.999515i | \(-0.490090\pi\) | ||||
0.0311284 | + | 0.999515i | \(0.490090\pi\) | |||||||
\(62\) | −0.0358923 | −0.00455833 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.5864 | −1.57329 | ||||||||
\(65\) | −3.20403 | −0.397411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.701192 | 0.0856643 | 0.0428321 | − | 0.999082i | \(-0.486362\pi\) | ||||
0.0428321 | + | 0.999082i | \(0.486362\pi\) | |||||||
\(68\) | 5.36306 | 0.650367 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.90055 | 0.227159 | ||||||||
\(71\) | 9.14768 | 1.08563 | 0.542815 | − | 0.839852i | \(-0.317358\pi\) | ||||
0.542815 | + | 0.839852i | \(0.317358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.554740 | −0.0649273 | −0.0324637 | − | 0.999473i | \(-0.510335\pi\) | ||||
−0.0324637 | + | 0.999473i | \(0.510335\pi\) | |||||||
\(74\) | 0.786702 | 0.0914522 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.97721 | 0.456217 | ||||||||
\(77\) | 0.280542 | 0.0319707 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4508 | −1.62584 | −0.812921 | − | 0.582374i | \(-0.802124\pi\) | ||||
−0.812921 | + | 0.582374i | \(0.802124\pi\) | |||||||
\(80\) | 1.55112 | 0.173420 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −19.1634 | −2.11624 | ||||||||
\(83\) | 11.1517 | 1.22405 | 0.612027 | − | 0.790837i | \(-0.290354\pi\) | ||||
0.612027 | + | 0.790837i | \(0.290354\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66726 | −0.180840 | ||||||||
\(86\) | 8.95554 | 0.965700 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.486765 | −0.0518894 | ||||||||
\(89\) | 16.6821 | 1.76830 | 0.884149 | − | 0.467205i | \(-0.154739\pi\) | ||||
0.884149 | + | 0.467205i | \(0.154739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.69064 | −0.386885 | ||||||||
\(92\) | 18.2111 | 1.89864 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.46192 | −0.975922 | ||||||||
\(95\) | −1.23643 | −0.126855 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.95594 | 0.807803 | 0.403902 | − | 0.914802i | \(-0.367654\pi\) | ||||
0.403902 | + | 0.914802i | \(0.367654\pi\) | |||||||
\(98\) | 2.18919 | 0.221142 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11.8581 | −1.18581 | ||||||||
\(101\) | −5.03438 | −0.500939 | −0.250470 | − | 0.968124i | \(-0.580585\pi\) | ||||
−0.250470 | + | 0.968124i | \(0.580585\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.57322 | 0.253547 | 0.126774 | − | 0.991932i | \(-0.459538\pi\) | ||||
0.126774 | + | 0.991932i | \(0.459538\pi\) | |||||||
\(104\) | 6.40360 | 0.627925 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 30.8821 | 2.99954 | ||||||||
\(107\) | 6.71132 | 0.648808 | 0.324404 | − | 0.945919i | \(-0.394836\pi\) | ||||
0.324404 | + | 0.945919i | \(0.394836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.76219 | 0.168787 | 0.0843935 | − | 0.996433i | \(-0.473105\pi\) | ||||
0.0843935 | + | 0.996433i | \(0.473105\pi\) | |||||||
\(110\) | 0.533184 | 0.0508371 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.78669 | 0.168827 | ||||||||
\(113\) | 8.28904 | 0.779768 | 0.389884 | − | 0.920864i | \(-0.372515\pi\) | ||||
0.389884 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.66145 | −0.527933 | ||||||||
\(116\) | 8.58399 | 0.797004 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 30.1901 | 2.77922 | ||||||||
\(119\) | −1.92048 | −0.176050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9213 | −0.992845 | ||||||||
\(122\) | 1.06448 | 0.0963732 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0457848 | −0.00411160 | ||||||||
\(125\) | 8.02719 | 0.717974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −12.7908 | −1.13056 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.01425 | −0.615190 | ||||||||
\(131\) | 15.0169 | 1.31203 | 0.656015 | − | 0.754748i | \(-0.272241\pi\) | ||||
0.656015 | + | 0.754748i | \(0.272241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.42421 | −0.123495 | ||||||||
\(134\) | 1.53505 | 0.132608 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.33220 | 0.285734 | ||||||||
\(137\) | −16.5669 | −1.41540 | −0.707702 | − | 0.706511i | \(-0.750268\pi\) | ||||
−0.707702 | + | 0.706511i | \(0.750268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5682 | −1.23566 | −0.617830 | − | 0.786312i | \(-0.711988\pi\) | ||||
−0.617830 | + | 0.786312i | \(0.711988\pi\) | |||||||
\(140\) | 2.42437 | 0.204897 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.0261 | 1.68055 | ||||||||
\(143\) | −1.03538 | −0.0865828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.66858 | −0.221613 | ||||||||
\(146\) | −1.21443 | −0.100507 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00353 | 0.0824896 | ||||||||
\(149\) | 11.3687 | 0.931364 | 0.465682 | − | 0.884952i | \(-0.345809\pi\) | ||||
0.465682 | + | 0.884952i | \(0.345809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.59570 | −0.780887 | −0.390443 | − | 0.920627i | \(-0.627678\pi\) | ||||
−0.390443 | + | 0.920627i | \(0.627678\pi\) | |||||||
\(152\) | 2.47113 | 0.200435 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.614161 | 0.0494905 | ||||||||
\(155\) | 0.0142335 | 0.00114326 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8227 | 0.863743 | 0.431871 | − | 0.901935i | \(-0.357853\pi\) | ||||
0.431871 | + | 0.901935i | \(0.357853\pi\) | |||||||
\(158\) | −31.6356 | −2.51679 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.40833 | 0.506623 | ||||||||
\(161\) | −6.52129 | −0.513949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.3493 | 1.90718 | 0.953590 | − | 0.301107i | \(-0.0973561\pi\) | ||||
0.953590 | + | 0.301107i | \(0.0973561\pi\) | |||||||
\(164\) | −24.4451 | −1.90885 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.4131 | 1.89483 | ||||||||
\(167\) | −14.3860 | −1.11322 | −0.556611 | − | 0.830773i | \(-0.687899\pi\) | ||||
−0.556611 | + | 0.830773i | \(0.687899\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.620853 | 0.0477579 | ||||||||
\(170\) | −3.64996 | −0.279939 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4238 | 0.871058 | ||||||||
\(173\) | 20.4335 | 1.55353 | 0.776765 | − | 0.629790i | \(-0.216859\pi\) | ||||
0.776765 | + | 0.629790i | \(0.216859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.24632 | 0.320991 | ||||||||
\(176\) | 0.501242 | 0.0377825 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 36.5203 | 2.73731 | ||||||||
\(179\) | 1.77187 | 0.132436 | 0.0662178 | − | 0.997805i | \(-0.478907\pi\) | ||||
0.0662178 | + | 0.997805i | \(0.478907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7325 | 1.02073 | 0.510365 | − | 0.859958i | \(-0.329510\pi\) | ||||
0.510365 | + | 0.859958i | \(0.329510\pi\) | |||||||
\(182\) | −8.07954 | −0.598895 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 11.3150 | 0.834154 | ||||||||
\(185\) | −0.311976 | −0.0229369 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.538774 | −0.0393991 | ||||||||
\(188\) | −12.0698 | −0.880279 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.70678 | −0.196371 | ||||||||
\(191\) | −7.22638 | −0.522883 | −0.261441 | − | 0.965219i | \(-0.584198\pi\) | ||||
−0.261441 | + | 0.965219i | \(0.584198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0486 | 0.939255 | 0.469628 | − | 0.882865i | \(-0.344388\pi\) | ||||
0.469628 | + | 0.882865i | \(0.344388\pi\) | |||||||
\(194\) | 17.4171 | 1.25047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.79257 | 0.199469 | ||||||||
\(197\) | 3.12406 | 0.222580 | 0.111290 | − | 0.993788i | \(-0.464502\pi\) | ||||
0.111290 | + | 0.993788i | \(0.464502\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9671 | −0.777438 | −0.388719 | − | 0.921356i | \(-0.627082\pi\) | ||||
−0.388719 | + | 0.921356i | \(0.627082\pi\) | |||||||
\(200\) | −7.36774 | −0.520978 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.0212 | −0.775451 | ||||||||
\(203\) | −3.07387 | −0.215743 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.59947 | 0.530770 | ||||||||
\(206\) | 5.63328 | 0.392489 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.59404 | −0.457215 | ||||||||
\(209\) | −0.399551 | −0.0276375 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8674 | −0.954668 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(212\) | 39.3937 | 2.70557 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.6924 | 1.00435 | ||||||||
\(215\) | −3.55142 | −0.242205 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.0163952 | 0.00111298 | ||||||||
\(218\) | 3.85777 | 0.261281 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.680137 | 0.0458548 | ||||||||
\(221\) | 7.08779 | 0.476777 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.77971 | 0.654898 | 0.327449 | − | 0.944869i | \(-0.393811\pi\) | ||||
0.327449 | + | 0.944869i | \(0.393811\pi\) | |||||||
\(224\) | 7.38160 | 0.493204 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.1463 | 1.20708 | ||||||||
\(227\) | 12.3932 | 0.822563 | 0.411282 | − | 0.911508i | \(-0.365081\pi\) | ||||
0.411282 | + | 0.911508i | \(0.365081\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.5147 | 1.61998 | 0.809988 | − | 0.586447i | \(-0.199474\pi\) | ||||
0.809988 | + | 0.586447i | \(0.199474\pi\) | |||||||
\(230\) | −12.3940 | −0.817238 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.33344 | 0.350157 | ||||||||
\(233\) | 7.75695 | 0.508175 | 0.254087 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254087 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.75223 | 0.244769 | ||||||||
\(236\) | 38.5109 | 2.50685 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.20429 | −0.272524 | ||||||||
\(239\) | −12.1161 | −0.783723 | −0.391862 | − | 0.920024i | \(-0.628169\pi\) | ||||
−0.391862 | + | 0.920024i | \(0.628169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.36131 | 0.216521 | 0.108261 | − | 0.994123i | \(-0.465472\pi\) | ||||
0.108261 | + | 0.994123i | \(0.465472\pi\) | |||||||
\(242\) | −23.9088 | −1.53692 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.35786 | 0.0869283 | ||||||||
\(245\) | −0.868150 | −0.0554641 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.25626 | 0.334448 | ||||||||
\(248\) | −0.0284472 | −0.00180640 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.5731 | 1.11142 | ||||||||
\(251\) | 23.2358 | 1.46663 | 0.733314 | − | 0.679890i | \(-0.237973\pi\) | ||||
0.733314 | + | 0.679890i | \(0.237973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.82949 | −0.115019 | ||||||||
\(254\) | −2.18919 | −0.137362 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.82880 | −0.176800 | ||||||||
\(257\) | −19.4430 | −1.21282 | −0.606411 | − | 0.795151i | \(-0.707392\pi\) | ||||
−0.606411 | + | 0.795151i | \(0.707392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.359357 | −0.0223293 | ||||||||
\(260\) | −8.94749 | −0.554900 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 32.8749 | 2.03102 | ||||||||
\(263\) | 4.25647 | 0.262465 | 0.131233 | − | 0.991352i | \(-0.458106\pi\) | ||||
0.131233 | + | 0.991352i | \(0.458106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2467 | −0.752306 | ||||||||
\(266\) | −3.11787 | −0.191169 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.95813 | 0.119612 | ||||||||
\(269\) | −4.00443 | −0.244154 | −0.122077 | − | 0.992521i | \(-0.538956\pi\) | ||||
−0.122077 | + | 0.992521i | \(0.538956\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.684262 | 0.0415659 | 0.0207830 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207830 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(272\) | −3.43130 | −0.208053 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.2681 | −2.19104 | ||||||||
\(275\) | 1.19127 | 0.0718362 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.19540 | 0.312162 | 0.156081 | − | 0.987744i | \(-0.450114\pi\) | ||||
0.156081 | + | 0.987744i | \(0.450114\pi\) | |||||||
\(278\) | −31.8926 | −1.91279 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.50632 | 0.0900197 | ||||||||
\(281\) | −23.1569 | −1.38143 | −0.690713 | − | 0.723129i | \(-0.742703\pi\) | ||||
−0.690713 | + | 0.723129i | \(0.742703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.107190 | −0.00637180 | −0.00318590 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318590 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(284\) | 25.5455 | 1.51585 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.26665 | −0.134030 | ||||||||
\(287\) | 8.75364 | 0.516711 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3118 | −0.783045 | ||||||||
\(290\) | −5.84204 | −0.343056 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.54915 | −0.0906571 | ||||||||
\(293\) | −10.5671 | −0.617337 | −0.308668 | − | 0.951170i | \(-0.599883\pi\) | ||||
−0.308668 | + | 0.951170i | \(0.599883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9722 | −0.697050 | ||||||||
\(296\) | 0.623516 | 0.0362411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.8884 | 1.44175 | ||||||||
\(299\) | 24.0677 | 1.39187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.09079 | −0.235789 | ||||||||
\(302\) | −21.0068 | −1.20881 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.54463 | −0.145944 | ||||||||
\(305\) | −0.422130 | −0.0241711 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.41074 | −0.194661 | −0.0973307 | − | 0.995252i | \(-0.531030\pi\) | ||||
−0.0973307 | + | 0.995252i | \(0.531030\pi\) | |||||||
\(308\) | 0.783433 | 0.0446402 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0311599 | 0.00176977 | ||||||||
\(311\) | −29.7332 | −1.68602 | −0.843008 | − | 0.537901i | \(-0.819218\pi\) | ||||
−0.843008 | + | 0.537901i | \(0.819218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5328 | 1.21710 | 0.608552 | − | 0.793514i | \(-0.291751\pi\) | ||||
0.608552 | + | 0.793514i | \(0.291751\pi\) | |||||||
\(314\) | 23.6929 | 1.33707 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −40.3549 | −2.27014 | ||||||||
\(317\) | −28.3682 | −1.59332 | −0.796660 | − | 0.604428i | \(-0.793402\pi\) | ||||
−0.796660 | + | 0.604428i | \(0.793402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.862349 | −0.0482823 | ||||||||
\(320\) | 10.9268 | 0.610829 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.2764 | −0.795590 | ||||||||
\(323\) | 2.73516 | 0.152189 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.6716 | −0.869306 | ||||||||
\(326\) | 53.3052 | 2.95230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −15.1883 | −0.838636 | ||||||||
\(329\) | 4.32210 | 0.238285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.53693 | −0.414267 | −0.207134 | − | 0.978313i | \(-0.566414\pi\) | ||||
−0.207134 | + | 0.978313i | \(0.566414\pi\) | |||||||
\(332\) | 31.1418 | 1.70913 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −31.4938 | −1.72326 | ||||||||
\(335\) | −0.608740 | −0.0332590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.9671 | 0.651888 | 0.325944 | − | 0.945389i | \(-0.394318\pi\) | ||||
0.325944 | + | 0.945389i | \(0.394318\pi\) | |||||||
\(338\) | 1.35917 | 0.0739289 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.65594 | −0.252504 | ||||||||
\(341\) | 0.00459955 | 0.000249080 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.09789 | 0.382693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 44.7329 | 2.40486 | ||||||||
\(347\) | −4.07527 | −0.218772 | −0.109386 | − | 0.993999i | \(-0.534888\pi\) | ||||
−0.109386 | + | 0.993999i | \(0.534888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.38630 | −0.127736 | −0.0638679 | − | 0.997958i | \(-0.520344\pi\) | ||||
−0.0638679 | + | 0.997958i | \(0.520344\pi\) | |||||||
\(350\) | 9.29601 | 0.496893 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.07085 | 0.110376 | ||||||||
\(353\) | −19.0735 | −1.01518 | −0.507591 | − | 0.861598i | \(-0.669464\pi\) | ||||
−0.507591 | + | 0.861598i | \(0.669464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.94156 | −0.421494 | ||||||||
\(356\) | 46.5859 | 2.46905 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.87896 | 0.205010 | ||||||||
\(359\) | −1.49830 | −0.0790775 | −0.0395387 | − | 0.999218i | \(-0.512589\pi\) | ||||
−0.0395387 | + | 0.999218i | \(0.512589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9716 | −0.893243 | ||||||||
\(362\) | 30.0631 | 1.58008 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.3064 | −0.540201 | ||||||||
\(365\) | 0.481597 | 0.0252079 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1206 | 0.528291 | 0.264146 | − | 0.964483i | \(-0.414910\pi\) | ||||
0.264146 | + | 0.964483i | \(0.414910\pi\) | |||||||
\(368\) | −11.6515 | −0.607378 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.682975 | −0.0355062 | ||||||||
\(371\) | −14.1066 | −0.732379 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.6071 | −1.32588 | −0.662942 | − | 0.748671i | \(-0.730693\pi\) | ||||
−0.662942 | + | 0.748671i | \(0.730693\pi\) | |||||||
\(374\) | −1.17948 | −0.0609895 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.49923 | −0.386743 | ||||||||
\(377\) | 11.3446 | 0.584274 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9735 | −0.717771 | −0.358886 | − | 0.933382i | \(-0.616843\pi\) | ||||
−0.358886 | + | 0.933382i | \(0.616843\pi\) | |||||||
\(380\) | −3.45281 | −0.177126 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.8199 | −0.809419 | ||||||||
\(383\) | 25.7039 | 1.31341 | 0.656705 | − | 0.754147i | \(-0.271950\pi\) | ||||
0.656705 | + | 0.754147i | \(0.271950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.243552 | −0.0124126 | ||||||||
\(386\) | 28.5658 | 1.45396 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.2175 | 1.12792 | ||||||||
\(389\) | −4.06415 | −0.206061 | −0.103030 | − | 0.994678i | \(-0.532854\pi\) | ||||
−0.103030 | + | 0.994678i | \(0.532854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.5240 | 0.633365 | ||||||||
\(392\) | 1.73509 | 0.0876353 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.83918 | 0.344553 | ||||||||
\(395\) | 12.5455 | 0.631231 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.03102 | 0.0517453 | 0.0258726 | − | 0.999665i | \(-0.491764\pi\) | ||||
0.0258726 | + | 0.999665i | \(0.491764\pi\) | |||||||
\(398\) | −24.0091 | −1.20347 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.58686 | 0.379343 | ||||||||
\(401\) | 3.59965 | 0.179758 | 0.0898789 | − | 0.995953i | \(-0.471352\pi\) | ||||
0.0898789 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0605090 | −0.00301417 | ||||||||
\(404\) | −14.0588 | −0.699454 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.72929 | −0.333969 | ||||||||
\(407\) | −0.100815 | −0.00499720 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.8694 | −1.08137 | −0.540685 | − | 0.841225i | \(-0.681835\pi\) | ||||
−0.540685 | + | 0.841225i | \(0.681835\pi\) | |||||||
\(410\) | 16.6367 | 0.821629 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.18590 | 0.354024 | ||||||||
\(413\) | −13.7905 | −0.678586 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.68131 | −0.475237 | ||||||||
\(416\) | −27.2428 | −1.33569 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.874694 | −0.0427827 | ||||||||
\(419\) | 14.5188 | 0.709288 | 0.354644 | − | 0.935001i | \(-0.384602\pi\) | ||||
0.354644 | + | 0.935001i | \(0.384602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.74372 | 0.0849836 | 0.0424918 | − | 0.999097i | \(-0.486470\pi\) | ||||
0.0424918 | + | 0.999097i | \(0.486470\pi\) | |||||||
\(422\) | −30.3583 | −1.47782 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.4762 | 1.18867 | ||||||||
\(425\) | −8.15495 | −0.395573 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.486241 | −0.0235309 | ||||||||
\(428\) | 18.7418 | 0.905920 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.77475 | −0.374932 | ||||||||
\(431\) | −24.6850 | −1.18904 | −0.594518 | − | 0.804082i | \(-0.702657\pi\) | ||||
−0.594518 | + | 0.804082i | \(0.702657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.9930 | −0.816633 | −0.408316 | − | 0.912840i | \(-0.633884\pi\) | ||||
−0.408316 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(434\) | 0.0358923 | 0.00172289 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.92103 | 0.235675 | ||||||||
\(437\) | 9.28769 | 0.444290 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.88431 | 0.471752 | 0.235876 | − | 0.971783i | \(-0.424204\pi\) | ||||
0.235876 | + | 0.971783i | \(0.424204\pi\) | |||||||
\(440\) | 0.422585 | 0.0201460 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.5166 | 0.738047 | ||||||||
\(443\) | −39.8440 | −1.89305 | −0.946523 | − | 0.322636i | \(-0.895431\pi\) | ||||
−0.946523 | + | 0.322636i | \(0.895431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4826 | −0.686539 | ||||||||
\(446\) | 21.4097 | 1.01378 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.5864 | 0.594650 | ||||||||
\(449\) | −24.0250 | −1.13381 | −0.566904 | − | 0.823784i | \(-0.691859\pi\) | ||||
−0.566904 | + | 0.823784i | \(0.691859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.45576 | 0.115637 | ||||||||
\(452\) | 23.1477 | 1.08878 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.1310 | 1.27332 | ||||||||
\(455\) | 3.20403 | 0.150207 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.81846 | 0.178620 | 0.0893101 | − | 0.996004i | \(-0.471534\pi\) | ||||
0.0893101 | + | 0.996004i | \(0.471534\pi\) | |||||||
\(458\) | 53.6674 | 2.50771 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.8100 | −0.737145 | ||||||||
\(461\) | 27.3775 | 1.27510 | 0.637549 | − | 0.770409i | \(-0.279948\pi\) | ||||
0.637549 | + | 0.770409i | \(0.279948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.11153 | −0.284027 | −0.142013 | − | 0.989865i | \(-0.545358\pi\) | ||||
−0.142013 | + | 0.989865i | \(0.545358\pi\) | |||||||
\(464\) | −5.49206 | −0.254962 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.9815 | 0.786652 | ||||||||
\(467\) | −23.4738 | −1.08624 | −0.543118 | − | 0.839656i | \(-0.682756\pi\) | ||||
−0.543118 | + | 0.839656i | \(0.682756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.701192 | −0.0323781 | ||||||||
\(470\) | 8.21437 | 0.378900 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.9278 | 1.10136 | ||||||||
\(473\) | −1.14764 | −0.0527685 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.04765 | −0.277485 | ||||||||
\(476\) | −5.36306 | −0.245816 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.5244 | −1.21320 | ||||||||
\(479\) | 30.4428 | 1.39097 | 0.695484 | − | 0.718541i | \(-0.255190\pi\) | ||||
0.695484 | + | 0.718541i | \(0.255190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.32626 | 0.0604722 | ||||||||
\(482\) | 7.35857 | 0.335173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.4985 | −1.38629 | ||||||||
\(485\) | −6.90695 | −0.313628 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −43.9485 | −1.99150 | −0.995749 | − | 0.0921094i | \(-0.970639\pi\) | ||||
−0.995749 | + | 0.0921094i | \(0.970639\pi\) | |||||||
\(488\) | 0.843672 | 0.0381912 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.90055 | −0.0858580 | ||||||||
\(491\) | 4.76508 | 0.215045 | 0.107522 | − | 0.994203i | \(-0.465708\pi\) | ||||
0.107522 | + | 0.994203i | \(0.465708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.90329 | 0.265871 | ||||||||
\(494\) | 11.5070 | 0.517723 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0292932 | 0.00131531 | ||||||||
\(497\) | −9.14768 | −0.410330 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.87038 | −0.441859 | −0.220929 | − | 0.975290i | \(-0.570909\pi\) | ||||
−0.220929 | + | 0.975290i | \(0.570909\pi\) | |||||||
\(500\) | 22.4165 | 1.00250 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 50.8676 | 2.27033 | ||||||||
\(503\) | 29.9723 | 1.33640 | 0.668200 | − | 0.743982i | \(-0.267065\pi\) | ||||
0.668200 | + | 0.743982i | \(0.267065\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.37059 | 0.194489 | ||||||||
\(506\) | −4.00512 | −0.178049 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.79257 | −0.123900 | ||||||||
\(509\) | −33.7727 | −1.49695 | −0.748474 | − | 0.663165i | \(-0.769213\pi\) | ||||
−0.748474 | + | 0.663165i | \(0.769213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.554740 | 0.0245402 | ||||||||
\(512\) | 19.3888 | 0.856871 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −42.5646 | −1.87744 | ||||||||
\(515\) | −2.23394 | −0.0984393 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.21253 | 0.0533270 | ||||||||
\(518\) | −0.786702 | −0.0345657 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.55928 | −0.243791 | ||||||||
\(521\) | −23.4277 | −1.02639 | −0.513194 | − | 0.858273i | \(-0.671538\pi\) | ||||
−0.513194 | + | 0.858273i | \(0.671538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.337038 | 0.0147376 | 0.00736882 | − | 0.999973i | \(-0.497654\pi\) | ||||
0.00736882 | + | 0.999973i | \(0.497654\pi\) | |||||||
\(524\) | 41.9357 | 1.83197 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.31825 | 0.406295 | ||||||||
\(527\) | −0.0314867 | −0.00137158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.5272 | 0.849007 | ||||||||
\(530\) | −26.8103 | −1.16457 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.97721 | −0.172434 | ||||||||
\(533\) | −32.3066 | −1.39935 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.82643 | −0.251899 | ||||||||
\(536\) | 1.21663 | 0.0525505 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.76646 | −0.377949 | ||||||||
\(539\) | −0.280542 | −0.0120838 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.85948 | 0.251919 | 0.125959 | − | 0.992035i | \(-0.459799\pi\) | ||||
0.125959 | + | 0.992035i | \(0.459799\pi\) | |||||||
\(542\) | 1.49798 | 0.0643438 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.1762 | −0.607799 | ||||||||
\(545\) | −1.52984 | −0.0655313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.8131 | 1.36023 | 0.680114 | − | 0.733106i | \(-0.261930\pi\) | ||||
0.680114 | + | 0.733106i | \(0.261930\pi\) | |||||||
\(548\) | −46.2642 | −1.97631 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.60792 | 0.111202 | ||||||||
\(551\) | 4.37784 | 0.186502 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.4508 | 0.614510 | ||||||||
\(554\) | 11.3737 | 0.483224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.6827 | −1.72533 | ||||||||
\(557\) | 7.19289 | 0.304773 | 0.152386 | − | 0.988321i | \(-0.451304\pi\) | ||||
0.152386 | + | 0.988321i | \(0.451304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0977 | 0.638563 | ||||||||
\(560\) | −1.55112 | −0.0655467 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −50.6950 | −2.13844 | ||||||||
\(563\) | −28.3208 | −1.19358 | −0.596789 | − | 0.802398i | \(-0.703557\pi\) | ||||
−0.596789 | + | 0.802398i | \(0.703557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.19613 | −0.302744 | ||||||||
\(566\) | −0.234660 | −0.00986351 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.8721 | 0.665977 | ||||||||
\(569\) | −26.6346 | −1.11658 | −0.558290 | − | 0.829646i | \(-0.688542\pi\) | ||||
−0.558290 | + | 0.829646i | \(0.688542\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4515 | 0.646625 | 0.323313 | − | 0.946292i | \(-0.395203\pi\) | ||||
0.323313 | + | 0.946292i | \(0.395203\pi\) | |||||||
\(572\) | −2.89137 | −0.120894 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.1634 | 0.799865 | ||||||||
\(575\) | −27.6914 | −1.15481 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.0575 | −1.00153 | −0.500763 | − | 0.865585i | \(-0.666947\pi\) | ||||
−0.500763 | + | 0.865585i | \(0.666947\pi\) | |||||||
\(578\) | −29.1420 | −1.21215 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.45219 | −0.309436 | ||||||||
\(581\) | −11.1517 | −0.462649 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.95750 | −0.163903 | ||||||||
\(584\) | −0.962523 | −0.0398295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.1334 | −0.955634 | ||||||||
\(587\) | 38.3645 | 1.58347 | 0.791736 | − | 0.610863i | \(-0.209177\pi\) | ||||
0.791736 | + | 0.610863i | \(0.209177\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0233503 | −0.000962131 0 | ||||||||
\(590\) | −26.2095 | −1.07903 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.642060 | −0.0263885 | ||||||||
\(593\) | 39.1039 | 1.60580 | 0.802902 | − | 0.596111i | \(-0.203288\pi\) | ||||
0.802902 | + | 0.596111i | \(0.203288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.66726 | 0.0683511 | ||||||||
\(596\) | 31.7480 | 1.30045 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 52.6890 | 2.15461 | ||||||||
\(599\) | 34.6581 | 1.41609 | 0.708045 | − | 0.706167i | \(-0.249577\pi\) | ||||
0.708045 | + | 0.706167i | \(0.249577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.9773 | 1.30438 | 0.652190 | − | 0.758056i | \(-0.273850\pi\) | ||||
0.652190 | + | 0.758056i | \(0.273850\pi\) | |||||||
\(602\) | −8.95554 | −0.365000 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −26.7967 | −1.09034 | ||||||||
\(605\) | 9.48132 | 0.385471 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.7650 | −1.00518 | −0.502591 | − | 0.864525i | \(-0.667620\pi\) | ||||
−0.502591 | + | 0.864525i | \(0.667620\pi\) | |||||||
\(608\) | −10.5129 | −0.426356 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.924125 | −0.0374167 | ||||||||
\(611\) | −15.9513 | −0.645322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3938 | 1.14681 | 0.573407 | − | 0.819271i | \(-0.305621\pi\) | ||||
0.573407 | + | 0.819271i | \(0.305621\pi\) | |||||||
\(614\) | −7.46678 | −0.301335 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.486765 | 0.0196123 | ||||||||
\(617\) | −5.98355 | −0.240889 | −0.120444 | − | 0.992720i | \(-0.538432\pi\) | ||||
−0.120444 | + | 0.992720i | \(0.538432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.70457 | 0.189093 | 0.0945464 | − | 0.995520i | \(-0.469860\pi\) | ||||
0.0945464 | + | 0.995520i | \(0.469860\pi\) | |||||||
\(620\) | 0.0397481 | 0.00159632 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −65.0918 | −2.60994 | ||||||||
\(623\) | −16.6821 | −0.668354 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.2628 | 0.570511 | ||||||||
\(626\) | 47.1394 | 1.88407 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.2231 | 1.20603 | ||||||||
\(629\) | 0.690136 | 0.0275175 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1503 | −0.841978 | −0.420989 | − | 0.907066i | \(-0.638317\pi\) | ||||
−0.420989 | + | 0.907066i | \(0.638317\pi\) | |||||||
\(632\) | −25.0734 | −0.997367 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −62.1036 | −2.46645 | ||||||||
\(635\) | 0.868150 | 0.0344515 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.69064 | 0.146229 | ||||||||
\(638\) | −1.88785 | −0.0747406 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1043 | 0.438937 | ||||||||
\(641\) | −8.70143 | −0.343686 | −0.171843 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171843 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9855 | −0.512100 | −0.256050 | − | 0.966664i | \(-0.582421\pi\) | ||||
−0.256050 | + | 0.966664i | \(0.582421\pi\) | |||||||
\(644\) | −18.2111 | −0.717620 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.98780 | 0.235587 | ||||||||
\(647\) | 29.0762 | 1.14310 | 0.571552 | − | 0.820566i | \(-0.306342\pi\) | ||||
0.571552 | + | 0.820566i | \(0.306342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.86881 | −0.151864 | ||||||||
\(650\) | −34.3083 | −1.34568 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 67.9970 | 2.66297 | ||||||||
\(653\) | −0.0994735 | −0.00389270 | −0.00194635 | − | 0.999998i | \(-0.500620\pi\) | ||||
−0.00194635 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.0369 | −0.509394 | ||||||||
\(656\) | 15.6401 | 0.610642 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.46192 | 0.368864 | ||||||||
\(659\) | −31.4715 | −1.22596 | −0.612978 | − | 0.790100i | \(-0.710029\pi\) | ||||
−0.612978 | + | 0.790100i | \(0.710029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.6056 | −1.61827 | −0.809135 | − | 0.587623i | \(-0.800064\pi\) | ||||
−0.809135 | + | 0.587623i | \(0.800064\pi\) | |||||||
\(662\) | −16.4998 | −0.641283 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.3491 | 0.750892 | ||||||||
\(665\) | 1.23643 | 0.0479467 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0456 | 0.776168 | ||||||||
\(668\) | −40.1739 | −1.55438 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.33265 | −0.0514848 | ||||||||
\(671\) | −0.136411 | −0.00526609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.99578 | 0.115479 | 0.0577394 | − | 0.998332i | \(-0.481611\pi\) | ||||
0.0577394 | + | 0.998332i | \(0.481611\pi\) | |||||||
\(674\) | 26.1982 | 1.00912 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.73377 | 0.0666837 | ||||||||
\(677\) | −48.2569 | −1.85466 | −0.927332 | − | 0.374239i | \(-0.877904\pi\) | ||||
−0.927332 | + | 0.374239i | \(0.877904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.95594 | −0.305321 | ||||||||
\(680\) | −2.89285 | −0.110936 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.0100693 | 0.000385574 0 | ||||||||
\(683\) | −12.9192 | −0.494338 | −0.247169 | − | 0.968972i | \(-0.579500\pi\) | ||||
−0.247169 | + | 0.968972i | \(0.579500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.3825 | 0.549529 | ||||||||
\(686\) | −2.18919 | −0.0835838 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.30899 | −0.278652 | ||||||||
\(689\) | 52.0625 | 1.98342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8880 | 0.794616 | 0.397308 | − | 0.917685i | \(-0.369945\pi\) | ||||
0.397308 | + | 0.917685i | \(0.369945\pi\) | |||||||
\(692\) | 57.0620 | 2.16917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.92155 | −0.338657 | ||||||||
\(695\) | 12.6474 | 0.479743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.8111 | −0.636768 | ||||||||
\(698\) | −5.22407 | −0.197734 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.8581 | 0.448195 | ||||||||
\(701\) | −46.8697 | −1.77024 | −0.885122 | − | 0.465358i | \(-0.845926\pi\) | ||||
−0.885122 | + | 0.465358i | \(0.845926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.511800 | 0.0193029 | ||||||||
\(704\) | 3.53100 | 0.133080 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.7557 | −1.57150 | ||||||||
\(707\) | 5.03438 | 0.189337 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.3937 | −1.25413 | −0.627064 | − | 0.778968i | \(-0.715744\pi\) | ||||
−0.627064 | + | 0.778968i | \(0.715744\pi\) | |||||||
\(710\) | −17.3856 | −0.652471 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.9449 | 1.08476 | ||||||||
\(713\) | −0.106918 | −0.00400411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.898865 | 0.0336157 | ||||||||
\(716\) | 4.94807 | 0.184918 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.28008 | −0.122411 | ||||||||
\(719\) | 14.6697 | 0.547088 | 0.273544 | − | 0.961860i | \(-0.411804\pi\) | ||||
0.273544 | + | 0.961860i | \(0.411804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.57322 | −0.0958318 | ||||||||
\(722\) | −37.1542 | −1.38274 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 38.3490 | 1.42523 | ||||||||
\(725\) | −13.0526 | −0.484762 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.9187 | −1.48050 | −0.740250 | − | 0.672331i | \(-0.765293\pi\) | ||||
−0.740250 | + | 0.672331i | \(0.765293\pi\) | |||||||
\(728\) | −6.40360 | −0.237333 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.05431 | 0.0390217 | ||||||||
\(731\) | 7.85627 | 0.290575 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.3086 | 1.63657 | 0.818287 | − | 0.574810i | \(-0.194924\pi\) | ||||
0.818287 | + | 0.574810i | \(0.194924\pi\) | |||||||
\(734\) | 22.1560 | 0.817792 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.1375 | −1.77437 | ||||||||
\(737\) | −0.196714 | −0.00724605 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.90080 | −0.364207 | −0.182103 | − | 0.983279i | \(-0.558291\pi\) | ||||
−0.182103 | + | 0.983279i | \(0.558291\pi\) | |||||||
\(740\) | −0.871214 | −0.0320265 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.8821 | −1.13372 | ||||||||
\(743\) | −43.7246 | −1.60410 | −0.802049 | − | 0.597258i | \(-0.796257\pi\) | ||||
−0.802049 | + | 0.597258i | \(0.796257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.86977 | −0.361601 | ||||||||
\(746\) | −56.0589 | −2.05246 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.50456 | −0.0550123 | ||||||||
\(749\) | −6.71132 | −0.245226 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.71759 | −0.0626756 | −0.0313378 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313378 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(752\) | 7.72227 | 0.281602 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.8354 | 0.904453 | ||||||||
\(755\) | 8.33050 | 0.303178 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.7461 | 1.22652 | 0.613261 | − | 0.789880i | \(-0.289857\pi\) | ||||
0.613261 | + | 0.789880i | \(0.289857\pi\) | |||||||
\(758\) | −30.5907 | −1.11111 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.14532 | −0.0778188 | ||||||||
\(761\) | 5.95307 | 0.215799 | 0.107899 | − | 0.994162i | \(-0.465588\pi\) | ||||
0.107899 | + | 0.994162i | \(0.465588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.76219 | −0.0637955 | ||||||||
\(764\) | −20.1802 | −0.730093 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 56.2709 | 2.03315 | ||||||||
\(767\) | 50.8958 | 1.83774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4719 | 0.702173 | 0.351087 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351087 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(770\) | −0.533184 | −0.0192146 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.4390 | 1.31147 | ||||||||
\(773\) | 34.4291 | 1.23833 | 0.619165 | − | 0.785261i | \(-0.287471\pi\) | ||||
0.619165 | + | 0.785261i | \(0.287471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0696193 | 0.00250080 | ||||||||
\(776\) | 13.8043 | 0.495544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.89721 | −0.318981 | ||||||||
\(779\) | −12.4670 | −0.446678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56631 | −0.0918297 | ||||||||
\(782\) | 27.4174 | 0.980444 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.78669 | −0.0638104 | ||||||||
\(785\) | −9.39570 | −0.335347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.7540 | −0.953676 | −0.476838 | − | 0.878991i | \(-0.658217\pi\) | ||||
−0.476838 | + | 0.878991i | \(0.658217\pi\) | |||||||
\(788\) | 8.72416 | 0.310785 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.4644 | 0.977141 | ||||||||
\(791\) | −8.28904 | −0.294724 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.79454 | 0.0637261 | ||||||||
\(794\) | 2.25710 | 0.0801014 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.6264 | −1.08552 | ||||||||
\(797\) | −4.82222 | −0.170812 | −0.0854058 | − | 0.996346i | \(-0.527219\pi\) | ||||
−0.0854058 | + | 0.996346i | \(0.527219\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.30049 | −0.293650 | ||||||||
\(800\) | 31.3446 | 1.10820 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.88033 | 0.278264 | ||||||||
\(803\) | 0.155628 | 0.00549198 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.66145 | 0.199540 | ||||||||
\(806\) | −0.132466 | −0.00466591 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.73509 | −0.307300 | ||||||||
\(809\) | −7.80400 | −0.274374 | −0.137187 | − | 0.990545i | \(-0.543806\pi\) | ||||
−0.137187 | + | 0.990545i | \(0.543806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.2261 | 0.920924 | 0.460462 | − | 0.887679i | \(-0.347684\pi\) | ||||
0.460462 | + | 0.887679i | \(0.347684\pi\) | |||||||
\(812\) | −8.58399 | −0.301239 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.220703 | −0.00773563 | ||||||||
\(815\) | −21.1388 | −0.740460 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.82615 | 0.203831 | ||||||||
\(818\) | −47.8762 | −1.67395 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.2221 | 0.741106 | ||||||||
\(821\) | −2.81989 | −0.0984148 | −0.0492074 | − | 0.998789i | \(-0.515670\pi\) | ||||
−0.0492074 | + | 0.998789i | \(0.515670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.8534 | 1.28463 | 0.642314 | − | 0.766441i | \(-0.277974\pi\) | ||||
0.642314 | + | 0.766441i | \(0.277974\pi\) | |||||||
\(824\) | 4.46477 | 0.155538 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.1901 | −1.05045 | ||||||||
\(827\) | 17.0927 | 0.594371 | 0.297186 | − | 0.954820i | \(-0.403952\pi\) | ||||
0.297186 | + | 0.954820i | \(0.403952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.5735 | −1.20079 | −0.600394 | − | 0.799704i | \(-0.704990\pi\) | ||||
−0.600394 | + | 0.799704i | \(0.704990\pi\) | |||||||
\(830\) | −21.1943 | −0.735664 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −46.4518 | −1.61043 | ||||||||
\(833\) | 1.92048 | 0.0665406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4892 | 0.432207 | ||||||||
\(836\) | −1.11577 | −0.0385898 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.7844 | 1.09797 | ||||||||
\(839\) | 17.1104 | 0.590718 | 0.295359 | − | 0.955386i | \(-0.404561\pi\) | ||||
0.295359 | + | 0.955386i | \(0.404561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.5513 | −0.674184 | ||||||||
\(842\) | 3.81733 | 0.131554 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −38.7256 | −1.33299 | ||||||||
\(845\) | −0.538993 | −0.0185419 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9213 | 0.375260 | ||||||||
\(848\) | −25.2042 | −0.865515 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.8528 | −0.612345 | ||||||||
\(851\) | 2.34347 | 0.0803331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.5681 | −1.56022 | −0.780111 | − | 0.625642i | \(-0.784837\pi\) | ||||
−0.780111 | + | 0.625642i | \(0.784837\pi\) | |||||||
\(854\) | −1.06448 | −0.0364256 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.6447 | 0.398009 | ||||||||
\(857\) | 30.0586 | 1.02678 | 0.513391 | − | 0.858155i | \(-0.328389\pi\) | ||||
0.513391 | + | 0.858155i | \(0.328389\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.8645 | 0.848365 | 0.424183 | − | 0.905577i | \(-0.360561\pi\) | ||||
0.424183 | + | 0.905577i | \(0.360561\pi\) | |||||||
\(860\) | −9.91759 | −0.338187 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54.0403 | −1.84062 | ||||||||
\(863\) | 14.4612 | 0.492264 | 0.246132 | − | 0.969236i | \(-0.420840\pi\) | ||||
0.246132 | + | 0.969236i | \(0.420840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7393 | −0.603156 | ||||||||
\(866\) | −37.2010 | −1.26414 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0457848 | 0.00155404 | ||||||||
\(869\) | 4.05405 | 0.137524 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58785 | 0.0876860 | ||||||||
\(872\) | 3.05755 | 0.103542 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.3325 | 0.687759 | ||||||||
\(875\) | −8.02719 | −0.271369 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.6606 | −1.10287 | −0.551435 | − | 0.834218i | \(-0.685920\pi\) | ||||
−0.551435 | + | 0.834218i | \(0.685920\pi\) | |||||||
\(878\) | 21.6387 | 0.730269 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.435153 | −0.0146690 | ||||||||
\(881\) | −11.2108 | −0.377700 | −0.188850 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188850 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.6874 | 0.931754 | 0.465877 | − | 0.884849i | \(-0.345739\pi\) | ||||
0.465877 | + | 0.884849i | \(0.345739\pi\) | |||||||
\(884\) | 19.7932 | 0.665716 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −87.2263 | −2.93042 | ||||||||
\(887\) | −9.88366 | −0.331861 | −0.165930 | − | 0.986137i | \(-0.553063\pi\) | ||||
−0.165930 | + | 0.986137i | \(0.553063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −31.7051 | −1.06276 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.3105 | 0.914424 | ||||||||
\(893\) | −6.15558 | −0.205989 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.53825 | −0.0514179 | ||||||||
\(896\) | 12.7908 | 0.427310 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.5953 | −1.75513 | ||||||||
\(899\) | −0.0503968 | −0.00168083 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.0914 | 0.902546 | ||||||||
\(902\) | 5.37614 | 0.179006 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.3822 | 0.478346 | ||||||||
\(905\) | −11.9219 | −0.396297 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.03008 | −0.0674076 | −0.0337038 | − | 0.999432i | \(-0.510730\pi\) | ||||
−0.0337038 | + | 0.999432i | \(0.510730\pi\) | |||||||
\(908\) | 34.6088 | 1.14853 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.01425 | 0.232520 | ||||||||
\(911\) | 29.2269 | 0.968330 | 0.484165 | − | 0.874977i | \(-0.339123\pi\) | ||||
0.484165 | + | 0.874977i | \(0.339123\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.12851 | −0.103538 | ||||||||
\(914\) | 8.35936 | 0.276503 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 68.4590 | 2.26195 | ||||||||
\(917\) | −15.0169 | −0.495901 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.5165 | 0.511842 | 0.255921 | − | 0.966698i | \(-0.417621\pi\) | ||||
0.255921 | + | 0.966698i | \(0.417621\pi\) | |||||||
\(920\) | −9.82313 | −0.323859 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 59.9347 | 1.97385 | ||||||||
\(923\) | 33.7608 | 1.11125 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.52594 | −0.0501727 | ||||||||
\(926\) | −13.3793 | −0.439672 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −22.6901 | −0.744838 | ||||||||
\(929\) | −53.4586 | −1.75392 | −0.876960 | − | 0.480562i | \(-0.840433\pi\) | ||||
−0.876960 | + | 0.480562i | \(0.840433\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.42421 | 0.0466766 | ||||||||
\(932\) | 21.6618 | 0.709557 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −51.3886 | −1.68149 | ||||||||
\(935\) | 0.467737 | 0.0152966 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9970 | −0.849285 | −0.424642 | − | 0.905361i | \(-0.639600\pi\) | ||||
−0.424642 | + | 0.905361i | \(0.639600\pi\) | |||||||
\(938\) | −1.53505 | −0.0501210 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.4784 | 0.341767 | ||||||||
\(941\) | 45.2741 | 1.47589 | 0.737947 | − | 0.674858i | \(-0.235795\pi\) | ||||
0.737947 | + | 0.674858i | \(0.235795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57.0850 | −1.85894 | ||||||||
\(944\) | −24.6394 | −0.801943 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.51240 | −0.0816853 | ||||||||
\(947\) | 24.4990 | 0.796111 | 0.398056 | − | 0.917361i | \(-0.369685\pi\) | ||||
0.398056 | + | 0.917361i | \(0.369685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.04735 | −0.0664597 | ||||||||
\(950\) | −13.2395 | −0.429545 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.33220 | −0.107997 | ||||||||
\(953\) | −11.2283 | −0.363720 | −0.181860 | − | 0.983324i | \(-0.558212\pi\) | ||||
−0.181860 | + | 0.983324i | \(0.558212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.27358 | 0.203008 | ||||||||
\(956\) | −33.8350 | −1.09430 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.6453 | 2.15321 | ||||||||
\(959\) | 16.5669 | 0.534973 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9997 | −0.999991 | ||||||||
\(962\) | 2.90344 | 0.0936105 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.38670 | 0.302325 | ||||||||
\(965\) | −11.3281 | −0.364665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.25392 | 0.136797 | 0.0683984 | − | 0.997658i | \(-0.478211\pi\) | ||||
0.0683984 | + | 0.997658i | \(0.478211\pi\) | |||||||
\(968\) | −18.9494 | −0.609058 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.1206 | −0.485495 | ||||||||
\(971\) | 33.0193 | 1.05964 | 0.529821 | − | 0.848110i | \(-0.322259\pi\) | ||||
0.529821 | + | 0.848110i | \(0.322259\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.5682 | 0.467035 | ||||||||
\(974\) | −96.2118 | −3.08283 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.868763 | −0.0278084 | ||||||||
\(977\) | −28.1942 | −0.902013 | −0.451006 | − | 0.892521i | \(-0.648935\pi\) | ||||
−0.451006 | + | 0.892521i | \(0.648935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.68002 | −0.149574 | ||||||||
\(980\) | −2.42437 | −0.0774437 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.4317 | 0.332888 | ||||||||
\(983\) | 40.8708 | 1.30358 | 0.651788 | − | 0.758401i | \(-0.274019\pi\) | ||||
0.651788 | + | 0.758401i | \(0.274019\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.71215 | −0.0864164 | ||||||||
\(986\) | 12.9234 | 0.411566 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.6785 | 0.466984 | ||||||||
\(989\) | 26.6772 | 0.848286 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.56939 | −0.0816194 | −0.0408097 | − | 0.999167i | \(-0.512994\pi\) | ||||
−0.0408097 | + | 0.999167i | \(0.512994\pi\) | |||||||
\(992\) | 0.121023 | 0.00384248 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.0261 | −0.635188 | ||||||||
\(995\) | 9.52110 | 0.301839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.9676 | −1.17077 | −0.585387 | − | 0.810754i | \(-0.699057\pi\) | ||||
−0.585387 | + | 0.810754i | \(0.699057\pi\) | |||||||
\(998\) | −21.6082 | −0.683995 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.t.1.14 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.3 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.3 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.3 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.14 | 16 | 1.1 | even | 1 | trivial |