Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
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: | \( x^{8} - 2x^{7} - 15x^{6} + 14x^{5} + 84x^{4} + 9x^{3} - 158x^{2} - 142x - 35 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.48295\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(5\) | 0.137387 | 0.0614413 | 0.0307207 | − | 0.999528i | \(-0.490220\pi\) | ||||
0.0307207 | + | 0.999528i | \(0.490220\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.345564 | 0.130611 | 0.0653055 | − | 0.997865i | \(-0.479198\pi\) | ||||
0.0653055 | + | 0.997865i | \(0.479198\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.137387 | −0.0434456 | ||||||||
\(11\) | 0.938926 | 0.283097 | 0.141548 | − | 0.989931i | \(-0.454792\pi\) | ||||
0.141548 | + | 0.989931i | \(0.454792\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.67869 | −1.02029 | −0.510143 | − | 0.860090i | \(-0.670407\pi\) | ||||
−0.510143 | + | 0.860090i | \(0.670407\pi\) | |||||||
\(14\) | −0.345564 | −0.0923560 | ||||||||
\(15\) | 0.137387 | 0.0354732 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.36538 | 1.00149 | 0.500743 | − | 0.865596i | \(-0.333060\pi\) | ||||
0.500743 | + | 0.865596i | \(0.333060\pi\) | |||||||
\(20\) | 0.137387 | 0.0307207 | ||||||||
\(21\) | 0.345564 | 0.0754083 | ||||||||
\(22\) | −0.938926 | −0.200180 | ||||||||
\(23\) | 7.24752 | 1.51121 | 0.755607 | − | 0.655026i | \(-0.227342\pi\) | ||||
0.755607 | + | 0.655026i | \(0.227342\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.98112 | −0.996225 | ||||||||
\(26\) | 3.67869 | 0.721451 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.345564 | 0.0653055 | ||||||||
\(29\) | −6.57606 | −1.22114 | −0.610572 | − | 0.791961i | \(-0.709060\pi\) | ||||
−0.610572 | + | 0.791961i | \(0.709060\pi\) | |||||||
\(30\) | −0.137387 | −0.0250833 | ||||||||
\(31\) | −7.20991 | −1.29494 | −0.647469 | − | 0.762092i | \(-0.724173\pi\) | ||||
−0.647469 | + | 0.762092i | \(0.724173\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.938926 | 0.163446 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0.0474760 | 0.00802492 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.0184 | −1.81141 | −0.905705 | − | 0.423909i | \(-0.860657\pi\) | ||||
−0.905705 | + | 0.423909i | \(0.860657\pi\) | |||||||
\(38\) | −4.36538 | −0.708158 | ||||||||
\(39\) | −3.67869 | −0.589062 | ||||||||
\(40\) | −0.137387 | −0.0217228 | ||||||||
\(41\) | −9.50459 | −1.48437 | −0.742184 | − | 0.670196i | \(-0.766210\pi\) | ||||
−0.742184 | + | 0.670196i | \(0.766210\pi\) | |||||||
\(42\) | −0.345564 | −0.0533217 | ||||||||
\(43\) | −4.77259 | −0.727813 | −0.363906 | − | 0.931435i | \(-0.618557\pi\) | ||||
−0.363906 | + | 0.931435i | \(0.618557\pi\) | |||||||
\(44\) | 0.938926 | 0.141548 | ||||||||
\(45\) | 0.137387 | 0.0204804 | ||||||||
\(46\) | −7.24752 | −1.06859 | ||||||||
\(47\) | −7.68081 | −1.12036 | −0.560180 | − | 0.828371i | \(-0.689268\pi\) | ||||
−0.560180 | + | 0.828371i | \(0.689268\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.88059 | −0.982941 | ||||||||
\(50\) | 4.98112 | 0.704437 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.67869 | −0.510143 | ||||||||
\(53\) | 6.35112 | 0.872394 | 0.436197 | − | 0.899851i | \(-0.356325\pi\) | ||||
0.436197 | + | 0.899851i | \(0.356325\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.128996 | 0.0173938 | ||||||||
\(56\) | −0.345564 | −0.0461780 | ||||||||
\(57\) | 4.36538 | 0.578209 | ||||||||
\(58\) | 6.57606 | 0.863479 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.137387 | 0.0177366 | ||||||||
\(61\) | 6.03607 | 0.772840 | 0.386420 | − | 0.922323i | \(-0.373712\pi\) | ||||
0.386420 | + | 0.922323i | \(0.373712\pi\) | |||||||
\(62\) | 7.20991 | 0.915660 | ||||||||
\(63\) | 0.345564 | 0.0435370 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.505404 | −0.0626877 | ||||||||
\(66\) | −0.938926 | −0.115574 | ||||||||
\(67\) | 15.2289 | 1.86051 | 0.930253 | − | 0.366918i | \(-0.119587\pi\) | ||||
0.930253 | + | 0.366918i | \(0.119587\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 7.24752 | 0.872499 | ||||||||
\(70\) | −0.0474760 | −0.00567447 | ||||||||
\(71\) | −9.14564 | −1.08539 | −0.542694 | − | 0.839931i | \(-0.682596\pi\) | ||||
−0.542694 | + | 0.839931i | \(0.682596\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 0.323795 | 0.0378974 | 0.0189487 | − | 0.999820i | \(-0.493968\pi\) | ||||
0.0189487 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(74\) | 11.0184 | 1.28086 | ||||||||
\(75\) | −4.98112 | −0.575171 | ||||||||
\(76\) | 4.36538 | 0.500743 | ||||||||
\(77\) | 0.324459 | 0.0369756 | ||||||||
\(78\) | 3.67869 | 0.416530 | ||||||||
\(79\) | 17.2714 | 1.94318 | 0.971590 | − | 0.236672i | \(-0.0760566\pi\) | ||||
0.971590 | + | 0.236672i | \(0.0760566\pi\) | |||||||
\(80\) | 0.137387 | 0.0153603 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.50459 | 1.04961 | ||||||||
\(83\) | 2.00956 | 0.220578 | 0.110289 | − | 0.993900i | \(-0.464822\pi\) | ||||
0.110289 | + | 0.993900i | \(0.464822\pi\) | |||||||
\(84\) | 0.345564 | 0.0377042 | ||||||||
\(85\) | 0.137387 | 0.0149017 | ||||||||
\(86\) | 4.77259 | 0.514642 | ||||||||
\(87\) | −6.57606 | −0.705027 | ||||||||
\(88\) | −0.938926 | −0.100090 | ||||||||
\(89\) | −10.7224 | −1.13657 | −0.568286 | − | 0.822831i | \(-0.692393\pi\) | ||||
−0.568286 | + | 0.822831i | \(0.692393\pi\) | |||||||
\(90\) | −0.137387 | −0.0144819 | ||||||||
\(91\) | −1.27122 | −0.133261 | ||||||||
\(92\) | 7.24752 | 0.755607 | ||||||||
\(93\) | −7.20991 | −0.747633 | ||||||||
\(94\) | 7.68081 | 0.792215 | ||||||||
\(95\) | 0.599746 | 0.0615327 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 7.02115 | 0.712889 | 0.356445 | − | 0.934316i | \(-0.383989\pi\) | ||||
0.356445 | + | 0.934316i | \(0.383989\pi\) | |||||||
\(98\) | 6.88059 | 0.695044 | ||||||||
\(99\) | 0.938926 | 0.0943656 | ||||||||
\(100\) | −4.98112 | −0.498112 | ||||||||
\(101\) | −19.8859 | −1.97872 | −0.989362 | − | 0.145478i | \(-0.953528\pi\) | ||||
−0.989362 | + | 0.145478i | \(0.953528\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 9.89319 | 0.974805 | 0.487402 | − | 0.873178i | \(-0.337945\pi\) | ||||
0.487402 | + | 0.873178i | \(0.337945\pi\) | |||||||
\(104\) | 3.67869 | 0.360725 | ||||||||
\(105\) | 0.0474760 | 0.00463319 | ||||||||
\(106\) | −6.35112 | −0.616876 | ||||||||
\(107\) | −11.7654 | −1.13740 | −0.568701 | − | 0.822544i | \(-0.692554\pi\) | ||||
−0.568701 | + | 0.822544i | \(0.692554\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 14.6202 | 1.40037 | 0.700183 | − | 0.713964i | \(-0.253102\pi\) | ||||
0.700183 | + | 0.713964i | \(0.253102\pi\) | |||||||
\(110\) | −0.128996 | −0.0122993 | ||||||||
\(111\) | −11.0184 | −1.04582 | ||||||||
\(112\) | 0.345564 | 0.0326528 | ||||||||
\(113\) | −20.0104 | −1.88242 | −0.941209 | − | 0.337824i | \(-0.890309\pi\) | ||||
−0.941209 | + | 0.337824i | \(0.890309\pi\) | |||||||
\(114\) | −4.36538 | −0.408855 | ||||||||
\(115\) | 0.995715 | 0.0928509 | ||||||||
\(116\) | −6.57606 | −0.610572 | ||||||||
\(117\) | −3.67869 | −0.340095 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 0.345564 | 0.0316778 | ||||||||
\(120\) | −0.137387 | −0.0125417 | ||||||||
\(121\) | −10.1184 | −0.919856 | ||||||||
\(122\) | −6.03607 | −0.546480 | ||||||||
\(123\) | −9.50459 | −0.857000 | ||||||||
\(124\) | −7.20991 | −0.647469 | ||||||||
\(125\) | −1.37128 | −0.122651 | ||||||||
\(126\) | −0.345564 | −0.0307853 | ||||||||
\(127\) | −5.45205 | −0.483791 | −0.241895 | − | 0.970302i | \(-0.577769\pi\) | ||||
−0.241895 | + | 0.970302i | \(0.577769\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.77259 | −0.420203 | ||||||||
\(130\) | 0.505404 | 0.0443269 | ||||||||
\(131\) | 8.40908 | 0.734705 | 0.367352 | − | 0.930082i | \(-0.380264\pi\) | ||||
0.367352 | + | 0.930082i | \(0.380264\pi\) | |||||||
\(132\) | 0.938926 | 0.0817230 | ||||||||
\(133\) | 1.50852 | 0.130805 | ||||||||
\(134\) | −15.2289 | −1.31558 | ||||||||
\(135\) | 0.137387 | 0.0118244 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 7.63312 | 0.652141 | 0.326071 | − | 0.945345i | \(-0.394275\pi\) | ||||
0.326071 | + | 0.945345i | \(0.394275\pi\) | |||||||
\(138\) | −7.24752 | −0.616950 | ||||||||
\(139\) | −9.04306 | −0.767023 | −0.383511 | − | 0.923536i | \(-0.625285\pi\) | ||||
−0.383511 | + | 0.923536i | \(0.625285\pi\) | |||||||
\(140\) | 0.0474760 | 0.00401246 | ||||||||
\(141\) | −7.68081 | −0.646841 | ||||||||
\(142\) | 9.14564 | 0.767485 | ||||||||
\(143\) | −3.45402 | −0.288839 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.903464 | −0.0750286 | ||||||||
\(146\) | −0.323795 | −0.0267975 | ||||||||
\(147\) | −6.88059 | −0.567501 | ||||||||
\(148\) | −11.0184 | −0.905705 | ||||||||
\(149\) | −17.0907 | −1.40012 | −0.700062 | − | 0.714082i | \(-0.746844\pi\) | ||||
−0.700062 | + | 0.714082i | \(0.746844\pi\) | |||||||
\(150\) | 4.98112 | 0.406707 | ||||||||
\(151\) | 20.4170 | 1.66151 | 0.830755 | − | 0.556638i | \(-0.187909\pi\) | ||||
0.830755 | + | 0.556638i | \(0.187909\pi\) | |||||||
\(152\) | −4.36538 | −0.354079 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.324459 | −0.0261457 | ||||||||
\(155\) | −0.990548 | −0.0795627 | ||||||||
\(156\) | −3.67869 | −0.294531 | ||||||||
\(157\) | 2.07881 | 0.165907 | 0.0829534 | − | 0.996553i | \(-0.473565\pi\) | ||||
0.0829534 | + | 0.996553i | \(0.473565\pi\) | |||||||
\(158\) | −17.2714 | −1.37404 | ||||||||
\(159\) | 6.35112 | 0.503677 | ||||||||
\(160\) | −0.137387 | −0.0108614 | ||||||||
\(161\) | 2.50449 | 0.197381 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −12.9124 | −1.01137 | −0.505687 | − | 0.862717i | \(-0.668761\pi\) | ||||
−0.505687 | + | 0.862717i | \(0.668761\pi\) | |||||||
\(164\) | −9.50459 | −0.742184 | ||||||||
\(165\) | 0.128996 | 0.0100423 | ||||||||
\(166\) | −2.00956 | −0.155972 | ||||||||
\(167\) | 25.3307 | 1.96015 | 0.980073 | − | 0.198636i | \(-0.0636511\pi\) | ||||
0.980073 | + | 0.198636i | \(0.0636511\pi\) | |||||||
\(168\) | −0.345564 | −0.0266609 | ||||||||
\(169\) | 0.532763 | 0.0409818 | ||||||||
\(170\) | −0.137387 | −0.0105371 | ||||||||
\(171\) | 4.36538 | 0.333829 | ||||||||
\(172\) | −4.77259 | −0.363906 | ||||||||
\(173\) | −12.0318 | −0.914757 | −0.457379 | − | 0.889272i | \(-0.651212\pi\) | ||||
−0.457379 | + | 0.889272i | \(0.651212\pi\) | |||||||
\(174\) | 6.57606 | 0.498530 | ||||||||
\(175\) | −1.72130 | −0.130118 | ||||||||
\(176\) | 0.938926 | 0.0707742 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 10.7224 | 0.803677 | ||||||||
\(179\) | 8.82870 | 0.659888 | 0.329944 | − | 0.944001i | \(-0.392970\pi\) | ||||
0.329944 | + | 0.944001i | \(0.392970\pi\) | |||||||
\(180\) | 0.137387 | 0.0102402 | ||||||||
\(181\) | −12.7103 | −0.944748 | −0.472374 | − | 0.881398i | \(-0.656603\pi\) | ||||
−0.472374 | + | 0.881398i | \(0.656603\pi\) | |||||||
\(182\) | 1.27122 | 0.0942294 | ||||||||
\(183\) | 6.03607 | 0.446199 | ||||||||
\(184\) | −7.24752 | −0.534295 | ||||||||
\(185\) | −1.51378 | −0.111295 | ||||||||
\(186\) | 7.20991 | 0.528656 | ||||||||
\(187\) | 0.938926 | 0.0686611 | ||||||||
\(188\) | −7.68081 | −0.560180 | ||||||||
\(189\) | 0.345564 | 0.0251361 | ||||||||
\(190\) | −0.599746 | −0.0435102 | ||||||||
\(191\) | 6.50379 | 0.470598 | 0.235299 | − | 0.971923i | \(-0.424393\pi\) | ||||
0.235299 | + | 0.971923i | \(0.424393\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.87275 | 0.278767 | 0.139383 | − | 0.990239i | \(-0.455488\pi\) | ||||
0.139383 | + | 0.990239i | \(0.455488\pi\) | |||||||
\(194\) | −7.02115 | −0.504089 | ||||||||
\(195\) | −0.505404 | −0.0361927 | ||||||||
\(196\) | −6.88059 | −0.491470 | ||||||||
\(197\) | −20.1943 | −1.43878 | −0.719392 | − | 0.694605i | \(-0.755579\pi\) | ||||
−0.719392 | + | 0.694605i | \(0.755579\pi\) | |||||||
\(198\) | −0.938926 | −0.0667266 | ||||||||
\(199\) | −7.66649 | −0.543463 | −0.271731 | − | 0.962373i | \(-0.587596\pi\) | ||||
−0.271731 | + | 0.962373i | \(0.587596\pi\) | |||||||
\(200\) | 4.98112 | 0.352219 | ||||||||
\(201\) | 15.2289 | 1.07416 | ||||||||
\(202\) | 19.8859 | 1.39917 | ||||||||
\(203\) | −2.27245 | −0.159495 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −1.30581 | −0.0912015 | ||||||||
\(206\) | −9.89319 | −0.689291 | ||||||||
\(207\) | 7.24752 | 0.503738 | ||||||||
\(208\) | −3.67869 | −0.255071 | ||||||||
\(209\) | 4.09877 | 0.283518 | ||||||||
\(210\) | −0.0474760 | −0.00327616 | ||||||||
\(211\) | 5.70201 | 0.392543 | 0.196271 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196271 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(212\) | 6.35112 | 0.436197 | ||||||||
\(213\) | −9.14564 | −0.626649 | ||||||||
\(214\) | 11.7654 | 0.804265 | ||||||||
\(215\) | −0.655691 | −0.0447178 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −2.49149 | −0.169133 | ||||||||
\(218\) | −14.6202 | −0.990208 | ||||||||
\(219\) | 0.323795 | 0.0218801 | ||||||||
\(220\) | 0.128996 | 0.00869692 | ||||||||
\(221\) | −3.67869 | −0.247455 | ||||||||
\(222\) | 11.0184 | 0.739505 | ||||||||
\(223\) | −7.17632 | −0.480562 | −0.240281 | − | 0.970703i | \(-0.577240\pi\) | ||||
−0.240281 | + | 0.970703i | \(0.577240\pi\) | |||||||
\(224\) | −0.345564 | −0.0230890 | ||||||||
\(225\) | −4.98112 | −0.332075 | ||||||||
\(226\) | 20.0104 | 1.33107 | ||||||||
\(227\) | 21.5971 | 1.43345 | 0.716725 | − | 0.697356i | \(-0.245640\pi\) | ||||
0.716725 | + | 0.697356i | \(0.245640\pi\) | |||||||
\(228\) | 4.36538 | 0.289104 | ||||||||
\(229\) | −13.8214 | −0.913346 | −0.456673 | − | 0.889635i | \(-0.650959\pi\) | ||||
−0.456673 | + | 0.889635i | \(0.650959\pi\) | |||||||
\(230\) | −0.995715 | −0.0656555 | ||||||||
\(231\) | 0.324459 | 0.0213479 | ||||||||
\(232\) | 6.57606 | 0.431739 | ||||||||
\(233\) | 15.1962 | 0.995538 | 0.497769 | − | 0.867310i | \(-0.334153\pi\) | ||||
0.497769 | + | 0.867310i | \(0.334153\pi\) | |||||||
\(234\) | 3.67869 | 0.240484 | ||||||||
\(235\) | −1.05524 | −0.0688364 | ||||||||
\(236\) | −1.00000 | −0.0650945 | ||||||||
\(237\) | 17.2714 | 1.12190 | ||||||||
\(238\) | −0.345564 | −0.0223996 | ||||||||
\(239\) | −10.9114 | −0.705803 | −0.352901 | − | 0.935661i | \(-0.614805\pi\) | ||||
−0.352901 | + | 0.935661i | \(0.614805\pi\) | |||||||
\(240\) | 0.137387 | 0.00886829 | ||||||||
\(241\) | 21.4567 | 1.38215 | 0.691075 | − | 0.722783i | \(-0.257137\pi\) | ||||
0.691075 | + | 0.722783i | \(0.257137\pi\) | |||||||
\(242\) | 10.1184 | 0.650437 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.03607 | 0.386420 | ||||||||
\(245\) | −0.945303 | −0.0603932 | ||||||||
\(246\) | 9.50459 | 0.605991 | ||||||||
\(247\) | −16.0589 | −1.02180 | ||||||||
\(248\) | 7.20991 | 0.457830 | ||||||||
\(249\) | 2.00956 | 0.127351 | ||||||||
\(250\) | 1.37128 | 0.0867271 | ||||||||
\(251\) | −23.0178 | −1.45287 | −0.726436 | − | 0.687234i | \(-0.758825\pi\) | ||||
−0.726436 | + | 0.687234i | \(0.758825\pi\) | |||||||
\(252\) | 0.345564 | 0.0217685 | ||||||||
\(253\) | 6.80489 | 0.427820 | ||||||||
\(254\) | 5.45205 | 0.342092 | ||||||||
\(255\) | 0.137387 | 0.00860350 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.8570 | −0.926751 | −0.463376 | − | 0.886162i | \(-0.653362\pi\) | ||||
−0.463376 | + | 0.886162i | \(0.653362\pi\) | |||||||
\(258\) | 4.77259 | 0.297128 | ||||||||
\(259\) | −3.80756 | −0.236590 | ||||||||
\(260\) | −0.505404 | −0.0313438 | ||||||||
\(261\) | −6.57606 | −0.407048 | ||||||||
\(262\) | −8.40908 | −0.519515 | ||||||||
\(263\) | −24.4118 | −1.50529 | −0.752647 | − | 0.658424i | \(-0.771223\pi\) | ||||
−0.752647 | + | 0.658424i | \(0.771223\pi\) | |||||||
\(264\) | −0.938926 | −0.0577869 | ||||||||
\(265\) | 0.872561 | 0.0536010 | ||||||||
\(266\) | −1.50852 | −0.0924933 | ||||||||
\(267\) | −10.7224 | −0.656200 | ||||||||
\(268\) | 15.2289 | 0.930253 | ||||||||
\(269\) | 23.2264 | 1.41614 | 0.708070 | − | 0.706143i | \(-0.249566\pi\) | ||||
0.708070 | + | 0.706143i | \(0.249566\pi\) | |||||||
\(270\) | −0.137387 | −0.00836110 | ||||||||
\(271\) | −13.4958 | −0.819813 | −0.409907 | − | 0.912127i | \(-0.634439\pi\) | ||||
−0.409907 | + | 0.912127i | \(0.634439\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −1.27122 | −0.0769380 | ||||||||
\(274\) | −7.63312 | −0.461134 | ||||||||
\(275\) | −4.67691 | −0.282028 | ||||||||
\(276\) | 7.24752 | 0.436250 | ||||||||
\(277\) | −11.0605 | −0.664563 | −0.332282 | − | 0.943180i | \(-0.607818\pi\) | ||||
−0.332282 | + | 0.943180i | \(0.607818\pi\) | |||||||
\(278\) | 9.04306 | 0.542367 | ||||||||
\(279\) | −7.20991 | −0.431646 | ||||||||
\(280\) | −0.0474760 | −0.00283724 | ||||||||
\(281\) | 13.5455 | 0.808055 | 0.404027 | − | 0.914747i | \(-0.367610\pi\) | ||||
0.404027 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(282\) | 7.68081 | 0.457385 | ||||||||
\(283\) | 7.82780 | 0.465315 | 0.232657 | − | 0.972559i | \(-0.425258\pi\) | ||||
0.232657 | + | 0.972559i | \(0.425258\pi\) | |||||||
\(284\) | −9.14564 | −0.542694 | ||||||||
\(285\) | 0.599746 | 0.0355259 | ||||||||
\(286\) | 3.45402 | 0.204240 | ||||||||
\(287\) | −3.28445 | −0.193875 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.903464 | 0.0530533 | ||||||||
\(291\) | 7.02115 | 0.411587 | ||||||||
\(292\) | 0.323795 | 0.0189487 | ||||||||
\(293\) | −17.4268 | −1.01808 | −0.509042 | − | 0.860742i | \(-0.670000\pi\) | ||||
−0.509042 | + | 0.860742i | \(0.670000\pi\) | |||||||
\(294\) | 6.88059 | 0.401284 | ||||||||
\(295\) | −0.137387 | −0.00799898 | ||||||||
\(296\) | 11.0184 | 0.640430 | ||||||||
\(297\) | 0.938926 | 0.0544820 | ||||||||
\(298\) | 17.0907 | 0.990038 | ||||||||
\(299\) | −26.6614 | −1.54187 | ||||||||
\(300\) | −4.98112 | −0.287585 | ||||||||
\(301\) | −1.64924 | −0.0950604 | ||||||||
\(302\) | −20.4170 | −1.17487 | ||||||||
\(303\) | −19.8859 | −1.14242 | ||||||||
\(304\) | 4.36538 | 0.250372 | ||||||||
\(305\) | 0.829277 | 0.0474843 | ||||||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −4.27751 | −0.244131 | −0.122065 | − | 0.992522i | \(-0.538952\pi\) | ||||
−0.122065 | + | 0.992522i | \(0.538952\pi\) | |||||||
\(308\) | 0.324459 | 0.0184878 | ||||||||
\(309\) | 9.89319 | 0.562804 | ||||||||
\(310\) | 0.990548 | 0.0562593 | ||||||||
\(311\) | 3.63996 | 0.206403 | 0.103201 | − | 0.994660i | \(-0.467091\pi\) | ||||
0.103201 | + | 0.994660i | \(0.467091\pi\) | |||||||
\(312\) | 3.67869 | 0.208265 | ||||||||
\(313\) | 19.4906 | 1.10168 | 0.550838 | − | 0.834612i | \(-0.314308\pi\) | ||||
0.550838 | + | 0.834612i | \(0.314308\pi\) | |||||||
\(314\) | −2.07881 | −0.117314 | ||||||||
\(315\) | 0.0474760 | 0.00267497 | ||||||||
\(316\) | 17.2714 | 0.971590 | ||||||||
\(317\) | −22.5891 | −1.26873 | −0.634365 | − | 0.773033i | \(-0.718738\pi\) | ||||
−0.634365 | + | 0.773033i | \(0.718738\pi\) | |||||||
\(318\) | −6.35112 | −0.356153 | ||||||||
\(319\) | −6.17443 | −0.345702 | ||||||||
\(320\) | 0.137387 | 0.00768016 | ||||||||
\(321\) | −11.7654 | −0.656679 | ||||||||
\(322\) | −2.50449 | −0.139570 | ||||||||
\(323\) | 4.36538 | 0.242896 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 18.3240 | 1.01643 | ||||||||
\(326\) | 12.9124 | 0.715149 | ||||||||
\(327\) | 14.6202 | 0.808501 | ||||||||
\(328\) | 9.50459 | 0.524803 | ||||||||
\(329\) | −2.65421 | −0.146332 | ||||||||
\(330\) | −0.128996 | −0.00710100 | ||||||||
\(331\) | 8.85067 | 0.486477 | 0.243238 | − | 0.969967i | \(-0.421790\pi\) | ||||
0.243238 | + | 0.969967i | \(0.421790\pi\) | |||||||
\(332\) | 2.00956 | 0.110289 | ||||||||
\(333\) | −11.0184 | −0.603803 | ||||||||
\(334\) | −25.3307 | −1.38603 | ||||||||
\(335\) | 2.09225 | 0.114312 | ||||||||
\(336\) | 0.345564 | 0.0188521 | ||||||||
\(337\) | −26.4703 | −1.44193 | −0.720966 | − | 0.692971i | \(-0.756301\pi\) | ||||
−0.720966 | + | 0.692971i | \(0.756301\pi\) | |||||||
\(338\) | −0.532763 | −0.0289785 | ||||||||
\(339\) | −20.0104 | −1.08681 | ||||||||
\(340\) | 0.137387 | 0.00745085 | ||||||||
\(341\) | −6.76957 | −0.366593 | ||||||||
\(342\) | −4.36538 | −0.236053 | ||||||||
\(343\) | −4.79664 | −0.258994 | ||||||||
\(344\) | 4.77259 | 0.257321 | ||||||||
\(345\) | 0.995715 | 0.0536075 | ||||||||
\(346\) | 12.0318 | 0.646831 | ||||||||
\(347\) | −18.2675 | −0.980649 | −0.490324 | − | 0.871540i | \(-0.663122\pi\) | ||||
−0.490324 | + | 0.871540i | \(0.663122\pi\) | |||||||
\(348\) | −6.57606 | −0.352514 | ||||||||
\(349\) | 8.69797 | 0.465591 | 0.232796 | − | 0.972526i | \(-0.425213\pi\) | ||||
0.232796 | + | 0.972526i | \(0.425213\pi\) | |||||||
\(350\) | 1.72130 | 0.0920073 | ||||||||
\(351\) | −3.67869 | −0.196354 | ||||||||
\(352\) | −0.938926 | −0.0500449 | ||||||||
\(353\) | 13.7344 | 0.731006 | 0.365503 | − | 0.930810i | \(-0.380897\pi\) | ||||
0.365503 | + | 0.930810i | \(0.380897\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | −1.25649 | −0.0666876 | ||||||||
\(356\) | −10.7224 | −0.568286 | ||||||||
\(357\) | 0.345564 | 0.0182892 | ||||||||
\(358\) | −8.82870 | −0.466611 | ||||||||
\(359\) | 0.257712 | 0.0136015 | 0.00680075 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680075 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(360\) | −0.137387 | −0.00724093 | ||||||||
\(361\) | 0.0565421 | 0.00297590 | ||||||||
\(362\) | 12.7103 | 0.668038 | ||||||||
\(363\) | −10.1184 | −0.531079 | ||||||||
\(364\) | −1.27122 | −0.0666303 | ||||||||
\(365\) | 0.0444853 | 0.00232847 | ||||||||
\(366\) | −6.03607 | −0.315510 | ||||||||
\(367\) | 1.98331 | 0.103528 | 0.0517639 | − | 0.998659i | \(-0.483516\pi\) | ||||
0.0517639 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(368\) | 7.24752 | 0.377803 | ||||||||
\(369\) | −9.50459 | −0.494789 | ||||||||
\(370\) | 1.51378 | 0.0786977 | ||||||||
\(371\) | 2.19472 | 0.113944 | ||||||||
\(372\) | −7.20991 | −0.373816 | ||||||||
\(373\) | −27.8035 | −1.43961 | −0.719806 | − | 0.694176i | \(-0.755769\pi\) | ||||
−0.719806 | + | 0.694176i | \(0.755769\pi\) | |||||||
\(374\) | −0.938926 | −0.0485507 | ||||||||
\(375\) | −1.37128 | −0.0708124 | ||||||||
\(376\) | 7.68081 | 0.396107 | ||||||||
\(377\) | 24.1913 | 1.24591 | ||||||||
\(378\) | −0.345564 | −0.0177739 | ||||||||
\(379\) | 27.9432 | 1.43535 | 0.717673 | − | 0.696380i | \(-0.245207\pi\) | ||||
0.717673 | + | 0.696380i | \(0.245207\pi\) | |||||||
\(380\) | 0.599746 | 0.0307663 | ||||||||
\(381\) | −5.45205 | −0.279317 | ||||||||
\(382\) | −6.50379 | −0.332763 | ||||||||
\(383\) | −0.143967 | −0.00735639 | −0.00367820 | − | 0.999993i | \(-0.501171\pi\) | ||||
−0.00367820 | + | 0.999993i | \(0.501171\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0.0445765 | 0.00227183 | ||||||||
\(386\) | −3.87275 | −0.197118 | ||||||||
\(387\) | −4.77259 | −0.242604 | ||||||||
\(388\) | 7.02115 | 0.356445 | ||||||||
\(389\) | −0.462499 | −0.0234497 | −0.0117248 | − | 0.999931i | \(-0.503732\pi\) | ||||
−0.0117248 | + | 0.999931i | \(0.503732\pi\) | |||||||
\(390\) | 0.505404 | 0.0255921 | ||||||||
\(391\) | 7.24752 | 0.366523 | ||||||||
\(392\) | 6.88059 | 0.347522 | ||||||||
\(393\) | 8.40908 | 0.424182 | ||||||||
\(394\) | 20.1943 | 1.01737 | ||||||||
\(395\) | 2.37286 | 0.119391 | ||||||||
\(396\) | 0.938926 | 0.0471828 | ||||||||
\(397\) | −19.3807 | −0.972688 | −0.486344 | − | 0.873767i | \(-0.661670\pi\) | ||||
−0.486344 | + | 0.873767i | \(0.661670\pi\) | |||||||
\(398\) | 7.66649 | 0.384286 | ||||||||
\(399\) | 1.50852 | 0.0755205 | ||||||||
\(400\) | −4.98112 | −0.249056 | ||||||||
\(401\) | −31.4582 | −1.57095 | −0.785474 | − | 0.618894i | \(-0.787581\pi\) | ||||
−0.785474 | + | 0.618894i | \(0.787581\pi\) | |||||||
\(402\) | −15.2289 | −0.759549 | ||||||||
\(403\) | 26.5230 | 1.32121 | ||||||||
\(404\) | −19.8859 | −0.989362 | ||||||||
\(405\) | 0.137387 | 0.00682681 | ||||||||
\(406\) | 2.27245 | 0.112780 | ||||||||
\(407\) | −10.3454 | −0.512804 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 34.8856 | 1.72498 | 0.862490 | − | 0.506074i | \(-0.168904\pi\) | ||||
0.862490 | + | 0.506074i | \(0.168904\pi\) | |||||||
\(410\) | 1.30581 | 0.0644892 | ||||||||
\(411\) | 7.63312 | 0.376514 | ||||||||
\(412\) | 9.89319 | 0.487402 | ||||||||
\(413\) | −0.345564 | −0.0170041 | ||||||||
\(414\) | −7.24752 | −0.356196 | ||||||||
\(415\) | 0.276088 | 0.0135526 | ||||||||
\(416\) | 3.67869 | 0.180363 | ||||||||
\(417\) | −9.04306 | −0.442841 | ||||||||
\(418\) | −4.09877 | −0.200477 | ||||||||
\(419\) | 22.8910 | 1.11830 | 0.559149 | − | 0.829067i | \(-0.311128\pi\) | ||||
0.559149 | + | 0.829067i | \(0.311128\pi\) | |||||||
\(420\) | 0.0474760 | 0.00231659 | ||||||||
\(421\) | 22.4390 | 1.09361 | 0.546805 | − | 0.837260i | \(-0.315844\pi\) | ||||
0.546805 | + | 0.837260i | \(0.315844\pi\) | |||||||
\(422\) | −5.70201 | −0.277570 | ||||||||
\(423\) | −7.68081 | −0.373454 | ||||||||
\(424\) | −6.35112 | −0.308438 | ||||||||
\(425\) | −4.98112 | −0.241620 | ||||||||
\(426\) | 9.14564 | 0.443107 | ||||||||
\(427\) | 2.08585 | 0.100941 | ||||||||
\(428\) | −11.7654 | −0.568701 | ||||||||
\(429\) | −3.45402 | −0.166762 | ||||||||
\(430\) | 0.655691 | 0.0316202 | ||||||||
\(431\) | −38.5035 | −1.85465 | −0.927325 | − | 0.374257i | \(-0.877898\pi\) | ||||
−0.927325 | + | 0.374257i | \(0.877898\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −9.54628 | −0.458765 | −0.229383 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229383 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(434\) | 2.49149 | 0.119595 | ||||||||
\(435\) | −0.903464 | −0.0433178 | ||||||||
\(436\) | 14.6202 | 0.700183 | ||||||||
\(437\) | 31.6382 | 1.51346 | ||||||||
\(438\) | −0.323795 | −0.0154715 | ||||||||
\(439\) | −24.8236 | −1.18477 | −0.592383 | − | 0.805657i | \(-0.701813\pi\) | ||||
−0.592383 | + | 0.805657i | \(0.701813\pi\) | |||||||
\(440\) | −0.128996 | −0.00614965 | ||||||||
\(441\) | −6.88059 | −0.327647 | ||||||||
\(442\) | 3.67869 | 0.174977 | ||||||||
\(443\) | −15.3324 | −0.728462 | −0.364231 | − | 0.931309i | \(-0.618668\pi\) | ||||
−0.364231 | + | 0.931309i | \(0.618668\pi\) | |||||||
\(444\) | −11.0184 | −0.522909 | ||||||||
\(445\) | −1.47312 | −0.0698324 | ||||||||
\(446\) | 7.17632 | 0.339809 | ||||||||
\(447\) | −17.0907 | −0.808362 | ||||||||
\(448\) | 0.345564 | 0.0163264 | ||||||||
\(449\) | 11.6472 | 0.549667 | 0.274834 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274834 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(450\) | 4.98112 | 0.234812 | ||||||||
\(451\) | −8.92411 | −0.420220 | ||||||||
\(452\) | −20.0104 | −0.941209 | ||||||||
\(453\) | 20.4170 | 0.959274 | ||||||||
\(454\) | −21.5971 | −1.01360 | ||||||||
\(455\) | −0.174650 | −0.00818770 | ||||||||
\(456\) | −4.36538 | −0.204428 | ||||||||
\(457\) | −17.1014 | −0.799968 | −0.399984 | − | 0.916522i | \(-0.630984\pi\) | ||||
−0.399984 | + | 0.916522i | \(0.630984\pi\) | |||||||
\(458\) | 13.8214 | 0.645833 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.995715 | 0.0464255 | ||||||||
\(461\) | 13.1734 | 0.613548 | 0.306774 | − | 0.951782i | \(-0.400750\pi\) | ||||
0.306774 | + | 0.951782i | \(0.400750\pi\) | |||||||
\(462\) | −0.324459 | −0.0150952 | ||||||||
\(463\) | 40.4441 | 1.87959 | 0.939797 | − | 0.341732i | \(-0.111014\pi\) | ||||
0.939797 | + | 0.341732i | \(0.111014\pi\) | |||||||
\(464\) | −6.57606 | −0.305286 | ||||||||
\(465\) | −0.990548 | −0.0459355 | ||||||||
\(466\) | −15.1962 | −0.703952 | ||||||||
\(467\) | 6.48173 | 0.299939 | 0.149969 | − | 0.988691i | \(-0.452082\pi\) | ||||
0.149969 | + | 0.988691i | \(0.452082\pi\) | |||||||
\(468\) | −3.67869 | −0.170048 | ||||||||
\(469\) | 5.26257 | 0.243003 | ||||||||
\(470\) | 1.05524 | 0.0486747 | ||||||||
\(471\) | 2.07881 | 0.0957864 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | −4.48111 | −0.206042 | ||||||||
\(474\) | −17.2714 | −0.793300 | ||||||||
\(475\) | −21.7445 | −0.997706 | ||||||||
\(476\) | 0.345564 | 0.0158389 | ||||||||
\(477\) | 6.35112 | 0.290798 | ||||||||
\(478\) | 10.9114 | 0.499078 | ||||||||
\(479\) | −23.9511 | −1.09436 | −0.547178 | − | 0.837017i | \(-0.684298\pi\) | ||||
−0.547178 | + | 0.837017i | \(0.684298\pi\) | |||||||
\(480\) | −0.137387 | −0.00627083 | ||||||||
\(481\) | 40.5332 | 1.84815 | ||||||||
\(482\) | −21.4567 | −0.977328 | ||||||||
\(483\) | 2.50449 | 0.113958 | ||||||||
\(484\) | −10.1184 | −0.459928 | ||||||||
\(485\) | 0.964614 | 0.0438009 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −41.4050 | −1.87624 | −0.938120 | − | 0.346311i | \(-0.887434\pi\) | ||||
−0.938120 | + | 0.346311i | \(0.887434\pi\) | |||||||
\(488\) | −6.03607 | −0.273240 | ||||||||
\(489\) | −12.9124 | −0.583917 | ||||||||
\(490\) | 0.945303 | 0.0427044 | ||||||||
\(491\) | 25.2342 | 1.13880 | 0.569401 | − | 0.822060i | \(-0.307175\pi\) | ||||
0.569401 | + | 0.822060i | \(0.307175\pi\) | |||||||
\(492\) | −9.50459 | −0.428500 | ||||||||
\(493\) | −6.57606 | −0.296171 | ||||||||
\(494\) | 16.0589 | 0.722523 | ||||||||
\(495\) | 0.128996 | 0.00579795 | ||||||||
\(496\) | −7.20991 | −0.323735 | ||||||||
\(497\) | −3.16041 | −0.141764 | ||||||||
\(498\) | −2.00956 | −0.0900506 | ||||||||
\(499\) | 27.4823 | 1.23028 | 0.615139 | − | 0.788419i | \(-0.289100\pi\) | ||||
0.615139 | + | 0.788419i | \(0.289100\pi\) | |||||||
\(500\) | −1.37128 | −0.0613253 | ||||||||
\(501\) | 25.3307 | 1.13169 | ||||||||
\(502\) | 23.0178 | 1.02734 | ||||||||
\(503\) | −23.8912 | −1.06525 | −0.532627 | − | 0.846350i | \(-0.678795\pi\) | ||||
−0.532627 | + | 0.846350i | \(0.678795\pi\) | |||||||
\(504\) | −0.345564 | −0.0153927 | ||||||||
\(505\) | −2.73207 | −0.121575 | ||||||||
\(506\) | −6.80489 | −0.302514 | ||||||||
\(507\) | 0.532763 | 0.0236609 | ||||||||
\(508\) | −5.45205 | −0.241895 | ||||||||
\(509\) | −36.9407 | −1.63737 | −0.818684 | − | 0.574244i | \(-0.805296\pi\) | ||||
−0.818684 | + | 0.574244i | \(0.805296\pi\) | |||||||
\(510\) | −0.137387 | −0.00608360 | ||||||||
\(511\) | 0.111892 | 0.00494982 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.36538 | 0.192736 | ||||||||
\(514\) | 14.8570 | 0.655312 | ||||||||
\(515\) | 1.35919 | 0.0598933 | ||||||||
\(516\) | −4.77259 | −0.210102 | ||||||||
\(517\) | −7.21171 | −0.317171 | ||||||||
\(518\) | 3.80756 | 0.167294 | ||||||||
\(519\) | −12.0318 | −0.528135 | ||||||||
\(520\) | 0.505404 | 0.0221634 | ||||||||
\(521\) | 25.0379 | 1.09693 | 0.548466 | − | 0.836173i | \(-0.315212\pi\) | ||||
0.548466 | + | 0.836173i | \(0.315212\pi\) | |||||||
\(522\) | 6.57606 | 0.287826 | ||||||||
\(523\) | −21.0156 | −0.918946 | −0.459473 | − | 0.888192i | \(-0.651962\pi\) | ||||
−0.459473 | + | 0.888192i | \(0.651962\pi\) | |||||||
\(524\) | 8.40908 | 0.367352 | ||||||||
\(525\) | −1.72130 | −0.0751237 | ||||||||
\(526\) | 24.4118 | 1.06440 | ||||||||
\(527\) | −7.20991 | −0.314069 | ||||||||
\(528\) | 0.938926 | 0.0408615 | ||||||||
\(529\) | 29.5266 | 1.28377 | ||||||||
\(530\) | −0.872561 | −0.0379016 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 1.50852 | 0.0654026 | ||||||||
\(533\) | 34.9645 | 1.51448 | ||||||||
\(534\) | 10.7224 | 0.464003 | ||||||||
\(535\) | −1.61641 | −0.0698835 | ||||||||
\(536\) | −15.2289 | −0.657789 | ||||||||
\(537\) | 8.82870 | 0.380986 | ||||||||
\(538\) | −23.2264 | −1.00136 | ||||||||
\(539\) | −6.46036 | −0.278267 | ||||||||
\(540\) | 0.137387 | 0.00591219 | ||||||||
\(541\) | −40.7798 | −1.75326 | −0.876630 | − | 0.481165i | \(-0.840214\pi\) | ||||
−0.876630 | + | 0.481165i | \(0.840214\pi\) | |||||||
\(542\) | 13.4958 | 0.579695 | ||||||||
\(543\) | −12.7103 | −0.545451 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 2.00863 | 0.0860403 | ||||||||
\(546\) | 1.27122 | 0.0544034 | ||||||||
\(547\) | −12.6863 | −0.542427 | −0.271214 | − | 0.962519i | \(-0.587425\pi\) | ||||
−0.271214 | + | 0.962519i | \(0.587425\pi\) | |||||||
\(548\) | 7.63312 | 0.326071 | ||||||||
\(549\) | 6.03607 | 0.257613 | ||||||||
\(550\) | 4.67691 | 0.199424 | ||||||||
\(551\) | −28.7070 | −1.22296 | ||||||||
\(552\) | −7.24752 | −0.308475 | ||||||||
\(553\) | 5.96837 | 0.253801 | ||||||||
\(554\) | 11.0605 | 0.469917 | ||||||||
\(555\) | −1.51378 | −0.0642564 | ||||||||
\(556\) | −9.04306 | −0.383511 | ||||||||
\(557\) | 26.4094 | 1.11900 | 0.559500 | − | 0.828830i | \(-0.310993\pi\) | ||||
0.559500 | + | 0.828830i | \(0.310993\pi\) | |||||||
\(558\) | 7.20991 | 0.305220 | ||||||||
\(559\) | 17.5569 | 0.742577 | ||||||||
\(560\) | 0.0474760 | 0.00200623 | ||||||||
\(561\) | 0.938926 | 0.0396415 | ||||||||
\(562\) | −13.5455 | −0.571381 | ||||||||
\(563\) | −5.04256 | −0.212519 | −0.106259 | − | 0.994338i | \(-0.533887\pi\) | ||||
−0.106259 | + | 0.994338i | \(0.533887\pi\) | |||||||
\(564\) | −7.68081 | −0.323420 | ||||||||
\(565\) | −2.74917 | −0.115658 | ||||||||
\(566\) | −7.82780 | −0.329027 | ||||||||
\(567\) | 0.345564 | 0.0145123 | ||||||||
\(568\) | 9.14564 | 0.383742 | ||||||||
\(569\) | 35.8589 | 1.50328 | 0.751641 | − | 0.659572i | \(-0.229263\pi\) | ||||
0.751641 | + | 0.659572i | \(0.229263\pi\) | |||||||
\(570\) | −0.599746 | −0.0251206 | ||||||||
\(571\) | −3.06163 | −0.128125 | −0.0640626 | − | 0.997946i | \(-0.520406\pi\) | ||||
−0.0640626 | + | 0.997946i | \(0.520406\pi\) | |||||||
\(572\) | −3.45402 | −0.144420 | ||||||||
\(573\) | 6.50379 | 0.271700 | ||||||||
\(574\) | 3.28445 | 0.137090 | ||||||||
\(575\) | −36.1008 | −1.50551 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.4619 | 0.726946 | 0.363473 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363473 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 3.87275 | 0.160946 | ||||||||
\(580\) | −0.903464 | −0.0375143 | ||||||||
\(581\) | 0.694433 | 0.0288099 | ||||||||
\(582\) | −7.02115 | −0.291036 | ||||||||
\(583\) | 5.96323 | 0.246972 | ||||||||
\(584\) | −0.323795 | −0.0133988 | ||||||||
\(585\) | −0.505404 | −0.0208959 | ||||||||
\(586\) | 17.4268 | 0.719894 | ||||||||
\(587\) | −7.17144 | −0.295997 | −0.147999 | − | 0.988988i | \(-0.547283\pi\) | ||||
−0.147999 | + | 0.988988i | \(0.547283\pi\) | |||||||
\(588\) | −6.88059 | −0.283751 | ||||||||
\(589\) | −31.4740 | −1.29686 | ||||||||
\(590\) | 0.137387 | 0.00565613 | ||||||||
\(591\) | −20.1943 | −0.830682 | ||||||||
\(592\) | −11.0184 | −0.452852 | ||||||||
\(593\) | −16.8864 | −0.693442 | −0.346721 | − | 0.937968i | \(-0.612705\pi\) | ||||
−0.346721 | + | 0.937968i | \(0.612705\pi\) | |||||||
\(594\) | −0.938926 | −0.0385246 | ||||||||
\(595\) | 0.0474760 | 0.00194633 | ||||||||
\(596\) | −17.0907 | −0.700062 | ||||||||
\(597\) | −7.66649 | −0.313768 | ||||||||
\(598\) | 26.6614 | 1.09027 | ||||||||
\(599\) | 6.96003 | 0.284379 | 0.142190 | − | 0.989839i | \(-0.454586\pi\) | ||||
0.142190 | + | 0.989839i | \(0.454586\pi\) | |||||||
\(600\) | 4.98112 | 0.203354 | ||||||||
\(601\) | −38.7198 | −1.57942 | −0.789708 | − | 0.613483i | \(-0.789768\pi\) | ||||
−0.789708 | + | 0.613483i | \(0.789768\pi\) | |||||||
\(602\) | 1.64924 | 0.0672179 | ||||||||
\(603\) | 15.2289 | 0.620169 | ||||||||
\(604\) | 20.4170 | 0.830755 | ||||||||
\(605\) | −1.39014 | −0.0565172 | ||||||||
\(606\) | 19.8859 | 0.807810 | ||||||||
\(607\) | −9.80579 | −0.398005 | −0.199002 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199002 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(608\) | −4.36538 | −0.177040 | ||||||||
\(609\) | −2.27245 | −0.0920844 | ||||||||
\(610\) | −0.829277 | −0.0335765 | ||||||||
\(611\) | 28.2553 | 1.14309 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | 6.64177 | 0.268259 | 0.134129 | − | 0.990964i | \(-0.457176\pi\) | ||||
0.134129 | + | 0.990964i | \(0.457176\pi\) | |||||||
\(614\) | 4.27751 | 0.172626 | ||||||||
\(615\) | −1.30581 | −0.0526552 | ||||||||
\(616\) | −0.324459 | −0.0130728 | ||||||||
\(617\) | −43.4600 | −1.74963 | −0.874817 | − | 0.484453i | \(-0.839019\pi\) | ||||
−0.874817 | + | 0.484453i | \(0.839019\pi\) | |||||||
\(618\) | −9.89319 | −0.397962 | ||||||||
\(619\) | 38.3738 | 1.54237 | 0.771187 | − | 0.636608i | \(-0.219663\pi\) | ||||
0.771187 | + | 0.636608i | \(0.219663\pi\) | |||||||
\(620\) | −0.990548 | −0.0397814 | ||||||||
\(621\) | 7.24752 | 0.290833 | ||||||||
\(622\) | −3.63996 | −0.145949 | ||||||||
\(623\) | −3.70528 | −0.148449 | ||||||||
\(624\) | −3.67869 | −0.147265 | ||||||||
\(625\) | 24.7172 | 0.988689 | ||||||||
\(626\) | −19.4906 | −0.779003 | ||||||||
\(627\) | 4.09877 | 0.163689 | ||||||||
\(628\) | 2.07881 | 0.0829534 | ||||||||
\(629\) | −11.0184 | −0.439331 | ||||||||
\(630\) | −0.0474760 | −0.00189149 | ||||||||
\(631\) | 22.9340 | 0.912989 | 0.456494 | − | 0.889726i | \(-0.349105\pi\) | ||||
0.456494 | + | 0.889726i | \(0.349105\pi\) | |||||||
\(632\) | −17.2714 | −0.687018 | ||||||||
\(633\) | 5.70201 | 0.226635 | ||||||||
\(634\) | 22.5891 | 0.897128 | ||||||||
\(635\) | −0.749040 | −0.0297248 | ||||||||
\(636\) | 6.35112 | 0.251838 | ||||||||
\(637\) | 25.3115 | 1.00288 | ||||||||
\(638\) | 6.17443 | 0.244448 | ||||||||
\(639\) | −9.14564 | −0.361796 | ||||||||
\(640\) | −0.137387 | −0.00543070 | ||||||||
\(641\) | −4.50324 | −0.177867 | −0.0889335 | − | 0.996038i | \(-0.528346\pi\) | ||||
−0.0889335 | + | 0.996038i | \(0.528346\pi\) | |||||||
\(642\) | 11.7654 | 0.464342 | ||||||||
\(643\) | −3.56518 | −0.140597 | −0.0702984 | − | 0.997526i | \(-0.522395\pi\) | ||||
−0.0702984 | + | 0.997526i | \(0.522395\pi\) | |||||||
\(644\) | 2.50449 | 0.0986906 | ||||||||
\(645\) | −0.655691 | −0.0258178 | ||||||||
\(646\) | −4.36538 | −0.171754 | ||||||||
\(647\) | 23.2416 | 0.913720 | 0.456860 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456860 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.938926 | −0.0368561 | ||||||||
\(650\) | −18.3240 | −0.718727 | ||||||||
\(651\) | −2.49149 | −0.0976491 | ||||||||
\(652\) | −12.9124 | −0.505687 | ||||||||
\(653\) | 10.5574 | 0.413142 | 0.206571 | − | 0.978432i | \(-0.433770\pi\) | ||||
0.206571 | + | 0.978432i | \(0.433770\pi\) | |||||||
\(654\) | −14.6202 | −0.571697 | ||||||||
\(655\) | 1.15530 | 0.0451412 | ||||||||
\(656\) | −9.50459 | −0.371092 | ||||||||
\(657\) | 0.323795 | 0.0126325 | ||||||||
\(658\) | 2.65421 | 0.103472 | ||||||||
\(659\) | −4.61820 | −0.179900 | −0.0899499 | − | 0.995946i | \(-0.528671\pi\) | ||||
−0.0899499 | + | 0.995946i | \(0.528671\pi\) | |||||||
\(660\) | 0.128996 | 0.00502117 | ||||||||
\(661\) | 45.8352 | 1.78278 | 0.891392 | − | 0.453233i | \(-0.149729\pi\) | ||||
0.891392 | + | 0.453233i | \(0.149729\pi\) | |||||||
\(662\) | −8.85067 | −0.343991 | ||||||||
\(663\) | −3.67869 | −0.142868 | ||||||||
\(664\) | −2.00956 | −0.0779861 | ||||||||
\(665\) | 0.207251 | 0.00803685 | ||||||||
\(666\) | 11.0184 | 0.426953 | ||||||||
\(667\) | −47.6601 | −1.84541 | ||||||||
\(668\) | 25.3307 | 0.980073 | ||||||||
\(669\) | −7.17632 | −0.277453 | ||||||||
\(670\) | −2.09225 | −0.0808308 | ||||||||
\(671\) | 5.66742 | 0.218788 | ||||||||
\(672\) | −0.345564 | −0.0133304 | ||||||||
\(673\) | −38.9777 | −1.50248 | −0.751239 | − | 0.660030i | \(-0.770544\pi\) | ||||
−0.751239 | + | 0.660030i | \(0.770544\pi\) | |||||||
\(674\) | 26.4703 | 1.01960 | ||||||||
\(675\) | −4.98112 | −0.191724 | ||||||||
\(676\) | 0.532763 | 0.0204909 | ||||||||
\(677\) | 45.9523 | 1.76609 | 0.883045 | − | 0.469289i | \(-0.155490\pi\) | ||||
0.883045 | + | 0.469289i | \(0.155490\pi\) | |||||||
\(678\) | 20.0104 | 0.768494 | ||||||||
\(679\) | 2.42626 | 0.0931113 | ||||||||
\(680\) | −0.137387 | −0.00526855 | ||||||||
\(681\) | 21.5971 | 0.827603 | ||||||||
\(682\) | 6.76957 | 0.259220 | ||||||||
\(683\) | 15.6440 | 0.598602 | 0.299301 | − | 0.954159i | \(-0.403247\pi\) | ||||
0.299301 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(684\) | 4.36538 | 0.166914 | ||||||||
\(685\) | 1.04869 | 0.0400684 | ||||||||
\(686\) | 4.79664 | 0.183136 | ||||||||
\(687\) | −13.8214 | −0.527321 | ||||||||
\(688\) | −4.77259 | −0.181953 | ||||||||
\(689\) | −23.3638 | −0.890090 | ||||||||
\(690\) | −0.995715 | −0.0379062 | ||||||||
\(691\) | 23.8275 | 0.906440 | 0.453220 | − | 0.891399i | \(-0.350275\pi\) | ||||
0.453220 | + | 0.891399i | \(0.350275\pi\) | |||||||
\(692\) | −12.0318 | −0.457379 | ||||||||
\(693\) | 0.324459 | 0.0123252 | ||||||||
\(694\) | 18.2675 | 0.693423 | ||||||||
\(695\) | −1.24240 | −0.0471269 | ||||||||
\(696\) | 6.57606 | 0.249265 | ||||||||
\(697\) | −9.50459 | −0.360012 | ||||||||
\(698\) | −8.69797 | −0.329223 | ||||||||
\(699\) | 15.1962 | 0.574774 | ||||||||
\(700\) | −1.72130 | −0.0650590 | ||||||||
\(701\) | −37.9578 | −1.43365 | −0.716823 | − | 0.697256i | \(-0.754404\pi\) | ||||
−0.716823 | + | 0.697256i | \(0.754404\pi\) | |||||||
\(702\) | 3.67869 | 0.138843 | ||||||||
\(703\) | −48.0994 | −1.81410 | ||||||||
\(704\) | 0.938926 | 0.0353871 | ||||||||
\(705\) | −1.05524 | −0.0397427 | ||||||||
\(706\) | −13.7344 | −0.516899 | ||||||||
\(707\) | −6.87187 | −0.258443 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 0.102634 | 0.00385451 | 0.00192726 | − | 0.999998i | \(-0.499387\pi\) | ||||
0.00192726 | + | 0.999998i | \(0.499387\pi\) | |||||||
\(710\) | 1.25649 | 0.0471553 | ||||||||
\(711\) | 17.2714 | 0.647726 | ||||||||
\(712\) | 10.7224 | 0.401839 | ||||||||
\(713\) | −52.2540 | −1.95693 | ||||||||
\(714\) | −0.345564 | −0.0129324 | ||||||||
\(715\) | −0.474537 | −0.0177467 | ||||||||
\(716\) | 8.82870 | 0.329944 | ||||||||
\(717\) | −10.9114 | −0.407495 | ||||||||
\(718\) | −0.257712 | −0.00961771 | ||||||||
\(719\) | 43.0967 | 1.60723 | 0.803617 | − | 0.595147i | \(-0.202906\pi\) | ||||
0.803617 | + | 0.595147i | \(0.202906\pi\) | |||||||
\(720\) | 0.137387 | 0.00512011 | ||||||||
\(721\) | 3.41873 | 0.127320 | ||||||||
\(722\) | −0.0565421 | −0.00210428 | ||||||||
\(723\) | 21.4567 | 0.797985 | ||||||||
\(724\) | −12.7103 | −0.472374 | ||||||||
\(725\) | 32.7562 | 1.21653 | ||||||||
\(726\) | 10.1184 | 0.375530 | ||||||||
\(727\) | −13.0087 | −0.482464 | −0.241232 | − | 0.970467i | \(-0.577552\pi\) | ||||
−0.241232 | + | 0.970467i | \(0.577552\pi\) | |||||||
\(728\) | 1.27122 | 0.0471147 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.0444853 | −0.00164647 | ||||||||
\(731\) | −4.77259 | −0.176521 | ||||||||
\(732\) | 6.03607 | 0.223100 | ||||||||
\(733\) | −16.1827 | −0.597721 | −0.298860 | − | 0.954297i | \(-0.596607\pi\) | ||||
−0.298860 | + | 0.954297i | \(0.596607\pi\) | |||||||
\(734\) | −1.98331 | −0.0732052 | ||||||||
\(735\) | −0.945303 | −0.0348680 | ||||||||
\(736\) | −7.24752 | −0.267147 | ||||||||
\(737\) | 14.2988 | 0.526704 | ||||||||
\(738\) | 9.50459 | 0.349869 | ||||||||
\(739\) | 20.7042 | 0.761618 | 0.380809 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380809 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(740\) | −1.51378 | −0.0556477 | ||||||||
\(741\) | −16.0589 | −0.589938 | ||||||||
\(742\) | −2.19472 | −0.0805708 | ||||||||
\(743\) | −43.5121 | −1.59630 | −0.798151 | − | 0.602457i | \(-0.794189\pi\) | ||||
−0.798151 | + | 0.602457i | \(0.794189\pi\) | |||||||
\(744\) | 7.20991 | 0.264328 | ||||||||
\(745\) | −2.34804 | −0.0860255 | ||||||||
\(746\) | 27.8035 | 1.01796 | ||||||||
\(747\) | 2.00956 | 0.0735260 | ||||||||
\(748\) | 0.938926 | 0.0343305 | ||||||||
\(749\) | −4.06570 | −0.148557 | ||||||||
\(750\) | 1.37128 | 0.0500719 | ||||||||
\(751\) | −15.6680 | −0.571735 | −0.285867 | − | 0.958269i | \(-0.592282\pi\) | ||||
−0.285867 | + | 0.958269i | \(0.592282\pi\) | |||||||
\(752\) | −7.68081 | −0.280090 | ||||||||
\(753\) | −23.0178 | −0.838816 | ||||||||
\(754\) | −24.1913 | −0.880994 | ||||||||
\(755\) | 2.80503 | 0.102085 | ||||||||
\(756\) | 0.345564 | 0.0125681 | ||||||||
\(757\) | 24.3621 | 0.885454 | 0.442727 | − | 0.896656i | \(-0.354011\pi\) | ||||
0.442727 | + | 0.896656i | \(0.354011\pi\) | |||||||
\(758\) | −27.9432 | −1.01494 | ||||||||
\(759\) | 6.80489 | 0.247002 | ||||||||
\(760\) | −0.599746 | −0.0217551 | ||||||||
\(761\) | −12.2356 | −0.443540 | −0.221770 | − | 0.975099i | \(-0.571183\pi\) | ||||
−0.221770 | + | 0.975099i | \(0.571183\pi\) | |||||||
\(762\) | 5.45205 | 0.197507 | ||||||||
\(763\) | 5.05223 | 0.182903 | ||||||||
\(764\) | 6.50379 | 0.235299 | ||||||||
\(765\) | 0.137387 | 0.00496724 | ||||||||
\(766\) | 0.143967 | 0.00520176 | ||||||||
\(767\) | 3.67869 | 0.132830 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 12.9692 | 0.467682 | 0.233841 | − | 0.972275i | \(-0.424870\pi\) | ||||
0.233841 | + | 0.972275i | \(0.424870\pi\) | |||||||
\(770\) | −0.0445765 | −0.00160642 | ||||||||
\(771\) | −14.8570 | −0.535060 | ||||||||
\(772\) | 3.87275 | 0.139383 | ||||||||
\(773\) | −7.05682 | −0.253816 | −0.126908 | − | 0.991914i | \(-0.540505\pi\) | ||||
−0.126908 | + | 0.991914i | \(0.540505\pi\) | |||||||
\(774\) | 4.77259 | 0.171547 | ||||||||
\(775\) | 35.9135 | 1.29005 | ||||||||
\(776\) | −7.02115 | −0.252044 | ||||||||
\(777\) | −3.80756 | −0.136595 | ||||||||
\(778\) | 0.462499 | 0.0165814 | ||||||||
\(779\) | −41.4912 | −1.48658 | ||||||||
\(780\) | −0.505404 | −0.0180964 | ||||||||
\(781\) | −8.58707 | −0.307270 | ||||||||
\(782\) | −7.24752 | −0.259171 | ||||||||
\(783\) | −6.57606 | −0.235009 | ||||||||
\(784\) | −6.88059 | −0.245735 | ||||||||
\(785\) | 0.285601 | 0.0101935 | ||||||||
\(786\) | −8.40908 | −0.299942 | ||||||||
\(787\) | 40.4620 | 1.44231 | 0.721157 | − | 0.692772i | \(-0.243611\pi\) | ||||
0.721157 | + | 0.692772i | \(0.243611\pi\) | |||||||
\(788\) | −20.1943 | −0.719392 | ||||||||
\(789\) | −24.4118 | −0.869082 | ||||||||
\(790\) | −2.37286 | −0.0844225 | ||||||||
\(791\) | −6.91488 | −0.245865 | ||||||||
\(792\) | −0.938926 | −0.0333633 | ||||||||
\(793\) | −22.2048 | −0.788517 | ||||||||
\(794\) | 19.3807 | 0.687794 | ||||||||
\(795\) | 0.872561 | 0.0309466 | ||||||||
\(796\) | −7.66649 | −0.271731 | ||||||||
\(797\) | −6.97545 | −0.247083 | −0.123542 | − | 0.992339i | \(-0.539425\pi\) | ||||
−0.123542 | + | 0.992339i | \(0.539425\pi\) | |||||||
\(798\) | −1.50852 | −0.0534010 | ||||||||
\(799\) | −7.68081 | −0.271727 | ||||||||
\(800\) | 4.98112 | 0.176109 | ||||||||
\(801\) | −10.7224 | −0.378857 | ||||||||
\(802\) | 31.4582 | 1.11083 | ||||||||
\(803\) | 0.304020 | 0.0107286 | ||||||||
\(804\) | 15.2289 | 0.537082 | ||||||||
\(805\) | 0.344084 | 0.0121274 | ||||||||
\(806\) | −26.5230 | −0.934234 | ||||||||
\(807\) | 23.2264 | 0.817608 | ||||||||
\(808\) | 19.8859 | 0.699584 | ||||||||
\(809\) | −46.7124 | −1.64232 | −0.821160 | − | 0.570698i | \(-0.806673\pi\) | ||||
−0.821160 | + | 0.570698i | \(0.806673\pi\) | |||||||
\(810\) | −0.137387 | −0.00482729 | ||||||||
\(811\) | −5.27253 | −0.185144 | −0.0925718 | − | 0.995706i | \(-0.529509\pi\) | ||||
−0.0925718 | + | 0.995706i | \(0.529509\pi\) | |||||||
\(812\) | −2.27245 | −0.0797474 | ||||||||
\(813\) | −13.4958 | −0.473319 | ||||||||
\(814\) | 10.3454 | 0.362607 | ||||||||
\(815\) | −1.77399 | −0.0621401 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −20.8342 | −0.728895 | ||||||||
\(818\) | −34.8856 | −1.21974 | ||||||||
\(819\) | −1.27122 | −0.0444202 | ||||||||
\(820\) | −1.30581 | −0.0456008 | ||||||||
\(821\) | 13.6207 | 0.475366 | 0.237683 | − | 0.971343i | \(-0.423612\pi\) | ||||
0.237683 | + | 0.971343i | \(0.423612\pi\) | |||||||
\(822\) | −7.63312 | −0.266236 | ||||||||
\(823\) | −3.97482 | −0.138554 | −0.0692768 | − | 0.997597i | \(-0.522069\pi\) | ||||
−0.0692768 | + | 0.997597i | \(0.522069\pi\) | |||||||
\(824\) | −9.89319 | −0.344645 | ||||||||
\(825\) | −4.67691 | −0.162829 | ||||||||
\(826\) | 0.345564 | 0.0120237 | ||||||||
\(827\) | −42.0343 | −1.46167 | −0.730837 | − | 0.682552i | \(-0.760870\pi\) | ||||
−0.730837 | + | 0.682552i | \(0.760870\pi\) | |||||||
\(828\) | 7.24752 | 0.251869 | ||||||||
\(829\) | −11.4306 | −0.397001 | −0.198501 | − | 0.980101i | \(-0.563607\pi\) | ||||
−0.198501 | + | 0.980101i | \(0.563607\pi\) | |||||||
\(830\) | −0.276088 | −0.00958314 | ||||||||
\(831\) | −11.0605 | −0.383686 | ||||||||
\(832\) | −3.67869 | −0.127536 | ||||||||
\(833\) | −6.88059 | −0.238398 | ||||||||
\(834\) | 9.04306 | 0.313136 | ||||||||
\(835\) | 3.48010 | 0.120434 | ||||||||
\(836\) | 4.09877 | 0.141759 | ||||||||
\(837\) | −7.20991 | −0.249211 | ||||||||
\(838\) | −22.8910 | −0.790757 | ||||||||
\(839\) | 33.2839 | 1.14909 | 0.574543 | − | 0.818474i | \(-0.305180\pi\) | ||||
0.574543 | + | 0.818474i | \(0.305180\pi\) | |||||||
\(840\) | −0.0474760 | −0.00163808 | ||||||||
\(841\) | 14.2445 | 0.491190 | ||||||||
\(842\) | −22.4390 | −0.773299 | ||||||||
\(843\) | 13.5455 | 0.466531 | ||||||||
\(844\) | 5.70201 | 0.196271 | ||||||||
\(845\) | 0.0731947 | 0.00251798 | ||||||||
\(846\) | 7.68081 | 0.264072 | ||||||||
\(847\) | −3.49657 | −0.120143 | ||||||||
\(848\) | 6.35112 | 0.218098 | ||||||||
\(849\) | 7.82780 | 0.268650 | ||||||||
\(850\) | 4.98112 | 0.170851 | ||||||||
\(851\) | −79.8559 | −2.73743 | ||||||||
\(852\) | −9.14564 | −0.313324 | ||||||||
\(853\) | −18.7812 | −0.643056 | −0.321528 | − | 0.946900i | \(-0.604196\pi\) | ||||
−0.321528 | + | 0.946900i | \(0.604196\pi\) | |||||||
\(854\) | −2.08585 | −0.0713764 | ||||||||
\(855\) | 0.599746 | 0.0205109 | ||||||||
\(856\) | 11.7654 | 0.402132 | ||||||||
\(857\) | 14.9719 | 0.511431 | 0.255716 | − | 0.966752i | \(-0.417689\pi\) | ||||
0.255716 | + | 0.966752i | \(0.417689\pi\) | |||||||
\(858\) | 3.45402 | 0.117918 | ||||||||
\(859\) | −12.6595 | −0.431936 | −0.215968 | − | 0.976400i | \(-0.569291\pi\) | ||||
−0.215968 | + | 0.976400i | \(0.569291\pi\) | |||||||
\(860\) | −0.655691 | −0.0223589 | ||||||||
\(861\) | −3.28445 | −0.111934 | ||||||||
\(862\) | 38.5035 | 1.31144 | ||||||||
\(863\) | 37.5196 | 1.27718 | 0.638591 | − | 0.769546i | \(-0.279518\pi\) | ||||
0.638591 | + | 0.769546i | \(0.279518\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.65301 | −0.0562039 | ||||||||
\(866\) | 9.54628 | 0.324396 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −2.49149 | −0.0845666 | ||||||||
\(869\) | 16.2165 | 0.550108 | ||||||||
\(870\) | 0.903464 | 0.0306303 | ||||||||
\(871\) | −56.0224 | −1.89825 | ||||||||
\(872\) | −14.6202 | −0.495104 | ||||||||
\(873\) | 7.02115 | 0.237630 | ||||||||
\(874\) | −31.6382 | −1.07018 | ||||||||
\(875\) | −0.473864 | −0.0160195 | ||||||||
\(876\) | 0.323795 | 0.0109400 | ||||||||
\(877\) | 19.5094 | 0.658787 | 0.329393 | − | 0.944193i | \(-0.393156\pi\) | ||||
0.329393 | + | 0.944193i | \(0.393156\pi\) | |||||||
\(878\) | 24.8236 | 0.837756 | ||||||||
\(879\) | −17.4268 | −0.587791 | ||||||||
\(880\) | 0.128996 | 0.00434846 | ||||||||
\(881\) | 16.6025 | 0.559351 | 0.279676 | − | 0.960095i | \(-0.409773\pi\) | ||||
0.279676 | + | 0.960095i | \(0.409773\pi\) | |||||||
\(882\) | 6.88059 | 0.231681 | ||||||||
\(883\) | 27.0987 | 0.911944 | 0.455972 | − | 0.889994i | \(-0.349292\pi\) | ||||
0.455972 | + | 0.889994i | \(0.349292\pi\) | |||||||
\(884\) | −3.67869 | −0.123728 | ||||||||
\(885\) | −0.137387 | −0.00461821 | ||||||||
\(886\) | 15.3324 | 0.515101 | ||||||||
\(887\) | 4.87561 | 0.163707 | 0.0818536 | − | 0.996644i | \(-0.473916\pi\) | ||||
0.0818536 | + | 0.996644i | \(0.473916\pi\) | |||||||
\(888\) | 11.0184 | 0.369752 | ||||||||
\(889\) | −1.88403 | −0.0631885 | ||||||||
\(890\) | 1.47312 | 0.0493790 | ||||||||
\(891\) | 0.938926 | 0.0314552 | ||||||||
\(892\) | −7.17632 | −0.240281 | ||||||||
\(893\) | −33.5296 | −1.12203 | ||||||||
\(894\) | 17.0907 | 0.571599 | ||||||||
\(895\) | 1.21295 | 0.0405444 | ||||||||
\(896\) | −0.345564 | −0.0115445 | ||||||||
\(897\) | −26.6614 | −0.890198 | ||||||||
\(898\) | −11.6472 | −0.388673 | ||||||||
\(899\) | 47.4128 | 1.58130 | ||||||||
\(900\) | −4.98112 | −0.166037 | ||||||||
\(901\) | 6.35112 | 0.211587 | ||||||||
\(902\) | 8.92411 | 0.297140 | ||||||||
\(903\) | −1.64924 | −0.0548832 | ||||||||
\(904\) | 20.0104 | 0.665535 | ||||||||
\(905\) | −1.74623 | −0.0580466 | ||||||||
\(906\) | −20.4170 | −0.678309 | ||||||||
\(907\) | −1.36382 | −0.0452850 | −0.0226425 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226425 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(908\) | 21.5971 | 0.716725 | ||||||||
\(909\) | −19.8859 | −0.659574 | ||||||||
\(910\) | 0.174650 | 0.00578958 | ||||||||
\(911\) | 28.8789 | 0.956802 | 0.478401 | − | 0.878142i | \(-0.341217\pi\) | ||||
0.478401 | + | 0.878142i | \(0.341217\pi\) | |||||||
\(912\) | 4.36538 | 0.144552 | ||||||||
\(913\) | 1.88683 | 0.0624450 | ||||||||
\(914\) | 17.1014 | 0.565663 | ||||||||
\(915\) | 0.829277 | 0.0274151 | ||||||||
\(916\) | −13.8214 | −0.456673 | ||||||||
\(917\) | 2.90588 | 0.0959606 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 25.5971 | 0.844369 | 0.422184 | − | 0.906510i | \(-0.361263\pi\) | ||||
0.422184 | + | 0.906510i | \(0.361263\pi\) | |||||||
\(920\) | −0.995715 | −0.0328278 | ||||||||
\(921\) | −4.27751 | −0.140949 | ||||||||
\(922\) | −13.1734 | −0.433844 | ||||||||
\(923\) | 33.6440 | 1.10740 | ||||||||
\(924\) | 0.324459 | 0.0106739 | ||||||||
\(925\) | 54.8839 | 1.80457 | ||||||||
\(926\) | −40.4441 | −1.32907 | ||||||||
\(927\) | 9.89319 | 0.324935 | ||||||||
\(928\) | 6.57606 | 0.215870 | ||||||||
\(929\) | −20.6552 | −0.677675 | −0.338838 | − | 0.940845i | \(-0.610034\pi\) | ||||
−0.338838 | + | 0.940845i | \(0.610034\pi\) | |||||||
\(930\) | 0.990548 | 0.0324813 | ||||||||
\(931\) | −30.0364 | −0.984402 | ||||||||
\(932\) | 15.1962 | 0.497769 | ||||||||
\(933\) | 3.63996 | 0.119167 | ||||||||
\(934\) | −6.48173 | −0.212089 | ||||||||
\(935\) | 0.128996 | 0.00421863 | ||||||||
\(936\) | 3.67869 | 0.120242 | ||||||||
\(937\) | 12.7082 | 0.415158 | 0.207579 | − | 0.978218i | \(-0.433442\pi\) | ||||
0.207579 | + | 0.978218i | \(0.433442\pi\) | |||||||
\(938\) | −5.26257 | −0.171829 | ||||||||
\(939\) | 19.4906 | 0.636053 | ||||||||
\(940\) | −1.05524 | −0.0344182 | ||||||||
\(941\) | 25.1131 | 0.818665 | 0.409332 | − | 0.912385i | \(-0.365762\pi\) | ||||
0.409332 | + | 0.912385i | \(0.365762\pi\) | |||||||
\(942\) | −2.07881 | −0.0677312 | ||||||||
\(943\) | −68.8848 | −2.24320 | ||||||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | 0.0474760 | 0.00154440 | ||||||||
\(946\) | 4.48111 | 0.145693 | ||||||||
\(947\) | 23.7168 | 0.770691 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(948\) | 17.2714 | 0.560948 | ||||||||
\(949\) | −1.19114 | −0.0386661 | ||||||||
\(950\) | 21.7445 | 0.705485 | ||||||||
\(951\) | −22.5891 | −0.732502 | ||||||||
\(952\) | −0.345564 | −0.0111998 | ||||||||
\(953\) | −35.1775 | −1.13951 | −0.569755 | − | 0.821815i | \(-0.692962\pi\) | ||||
−0.569755 | + | 0.821815i | \(0.692962\pi\) | |||||||
\(954\) | −6.35112 | −0.205625 | ||||||||
\(955\) | 0.893536 | 0.0289142 | ||||||||
\(956\) | −10.9114 | −0.352901 | ||||||||
\(957\) | −6.17443 | −0.199591 | ||||||||
\(958\) | 23.9511 | 0.773826 | ||||||||
\(959\) | 2.63773 | 0.0851769 | ||||||||
\(960\) | 0.137387 | 0.00443414 | ||||||||
\(961\) | 20.9828 | 0.676865 | ||||||||
\(962\) | −40.5332 | −1.30684 | ||||||||
\(963\) | −11.7654 | −0.379134 | ||||||||
\(964\) | 21.4567 | 0.691075 | ||||||||
\(965\) | 0.532065 | 0.0171278 | ||||||||
\(966\) | −2.50449 | −0.0805805 | ||||||||
\(967\) | −42.3535 | −1.36200 | −0.680998 | − | 0.732285i | \(-0.738454\pi\) | ||||
−0.680998 | + | 0.732285i | \(0.738454\pi\) | |||||||
\(968\) | 10.1184 | 0.325218 | ||||||||
\(969\) | 4.36538 | 0.140236 | ||||||||
\(970\) | −0.964614 | −0.0309719 | ||||||||
\(971\) | −58.7810 | −1.88637 | −0.943186 | − | 0.332265i | \(-0.892187\pi\) | ||||
−0.943186 | + | 0.332265i | \(0.892187\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −3.12496 | −0.100182 | ||||||||
\(974\) | 41.4050 | 1.32670 | ||||||||
\(975\) | 18.3240 | 0.586838 | ||||||||
\(976\) | 6.03607 | 0.193210 | ||||||||
\(977\) | 0.535541 | 0.0171335 | 0.00856673 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856673 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(978\) | 12.9124 | 0.412891 | ||||||||
\(979\) | −10.0675 | −0.321760 | ||||||||
\(980\) | −0.945303 | −0.0301966 | ||||||||
\(981\) | 14.6202 | 0.466788 | ||||||||
\(982\) | −25.2342 | −0.805254 | ||||||||
\(983\) | −8.54989 | −0.272699 | −0.136350 | − | 0.990661i | \(-0.543537\pi\) | ||||
−0.136350 | + | 0.990661i | \(0.543537\pi\) | |||||||
\(984\) | 9.50459 | 0.302995 | ||||||||
\(985\) | −2.77443 | −0.0884007 | ||||||||
\(986\) | 6.57606 | 0.209424 | ||||||||
\(987\) | −2.65421 | −0.0844845 | ||||||||
\(988\) | −16.0589 | −0.510901 | ||||||||
\(989\) | −34.5895 | −1.09988 | ||||||||
\(990\) | −0.128996 | −0.00409977 | ||||||||
\(991\) | 8.14458 | 0.258721 | 0.129361 | − | 0.991598i | \(-0.458708\pi\) | ||||
0.129361 | + | 0.991598i | \(0.458708\pi\) | |||||||
\(992\) | 7.20991 | 0.228915 | ||||||||
\(993\) | 8.85067 | 0.280867 | ||||||||
\(994\) | 3.16041 | 0.100242 | ||||||||
\(995\) | −1.05328 | −0.0333911 | ||||||||
\(996\) | 2.00956 | 0.0636754 | ||||||||
\(997\) | −36.5882 | −1.15876 | −0.579380 | − | 0.815058i | \(-0.696705\pi\) | ||||
−0.579380 | + | 0.815058i | \(0.696705\pi\) | |||||||
\(998\) | −27.4823 | −0.869938 | ||||||||
\(999\) | −11.0184 | −0.348606 |
(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 | 6018.2.a.t.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.t.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |