Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.151572.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} + 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.16566\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | 1.16566 | 0.672995 | 0.336498 | − | 0.941684i | \(-0.390758\pi\) | ||||
0.336498 | + | 0.941684i | \(0.390758\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.55010 | −0.693226 | −0.346613 | − | 0.938008i | \(-0.612668\pi\) | ||||
−0.346613 | + | 0.938008i | \(0.612668\pi\) | |||||||
\(6\) | 1.16566 | 0.475880 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.64123 | −0.547077 | ||||||||
\(10\) | −1.55010 | −0.490185 | ||||||||
\(11\) | 0.834338 | 0.251562 | 0.125781 | − | 0.992058i | \(-0.459856\pi\) | ||||
0.125781 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(12\) | 1.16566 | 0.336498 | ||||||||
\(13\) | −5.35699 | −1.48576 | −0.742881 | − | 0.669423i | \(-0.766541\pi\) | ||||
−0.742881 | + | 0.669423i | \(0.766541\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.80689 | −0.466538 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.47557 | 0.842949 | 0.421475 | − | 0.906840i | \(-0.361513\pi\) | ||||
0.421475 | + | 0.906840i | \(0.361513\pi\) | |||||||
\(18\) | −1.64123 | −0.386842 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.55010 | −0.346613 | ||||||||
\(21\) | 1.16566 | 0.254368 | ||||||||
\(22\) | 0.834338 | 0.177881 | ||||||||
\(23\) | 8.74143 | 1.82271 | 0.911357 | − | 0.411616i | \(-0.135036\pi\) | ||||
0.911357 | + | 0.411616i | \(0.135036\pi\) | |||||||
\(24\) | 1.16566 | 0.237940 | ||||||||
\(25\) | −2.59719 | −0.519438 | ||||||||
\(26\) | −5.35699 | −1.05059 | ||||||||
\(27\) | −5.41011 | −1.04118 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.23842 | 1.71553 | 0.857766 | − | 0.514041i | \(-0.171852\pi\) | ||||
0.857766 | + | 0.514041i | \(0.171852\pi\) | |||||||
\(30\) | −1.80689 | −0.329892 | ||||||||
\(31\) | −6.90710 | −1.24055 | −0.620275 | − | 0.784384i | \(-0.712979\pi\) | ||||
−0.620275 | + | 0.784384i | \(0.712979\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.972556 | 0.169300 | ||||||||
\(34\) | 3.47557 | 0.596055 | ||||||||
\(35\) | −1.55010 | −0.262015 | ||||||||
\(36\) | −1.64123 | −0.273539 | ||||||||
\(37\) | 1.10020 | 0.180872 | 0.0904360 | − | 0.995902i | \(-0.471174\pi\) | ||||
0.0904360 | + | 0.995902i | \(0.471174\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.24445 | −0.999912 | ||||||||
\(40\) | −1.55010 | −0.245092 | ||||||||
\(41\) | 5.16566 | 0.806741 | 0.403370 | − | 0.915037i | \(-0.367839\pi\) | ||||
0.403370 | + | 0.915037i | \(0.367839\pi\) | |||||||
\(42\) | 1.16566 | 0.179866 | ||||||||
\(43\) | 12.9071 | 1.96831 | 0.984157 | − | 0.177300i | \(-0.0567364\pi\) | ||||
0.984157 | + | 0.177300i | \(0.0567364\pi\) | |||||||
\(44\) | 0.834338 | 0.125781 | ||||||||
\(45\) | 2.54407 | 0.379248 | ||||||||
\(46\) | 8.74143 | 1.28885 | ||||||||
\(47\) | 9.23842 | 1.34756 | 0.673781 | − | 0.738931i | \(-0.264669\pi\) | ||||
0.673781 | + | 0.738931i | \(0.264669\pi\) | |||||||
\(48\) | 1.16566 | 0.168249 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.59719 | −0.367298 | ||||||||
\(51\) | 4.05134 | 0.567301 | ||||||||
\(52\) | −5.35699 | −0.742881 | ||||||||
\(53\) | 10.9071 | 1.49820 | 0.749102 | − | 0.662454i | \(-0.230485\pi\) | ||||
0.749102 | + | 0.662454i | \(0.230485\pi\) | |||||||
\(54\) | −5.41011 | −0.736222 | ||||||||
\(55\) | −1.29331 | −0.174390 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.23842 | 1.21306 | ||||||||
\(59\) | 7.09113 | 0.923187 | 0.461593 | − | 0.887092i | \(-0.347278\pi\) | ||||
0.461593 | + | 0.887092i | \(0.347278\pi\) | |||||||
\(60\) | −1.80689 | −0.233269 | ||||||||
\(61\) | −9.16389 | −1.17332 | −0.586658 | − | 0.809835i | \(-0.699557\pi\) | ||||
−0.586658 | + | 0.809835i | \(0.699557\pi\) | |||||||
\(62\) | −6.90710 | −0.877202 | ||||||||
\(63\) | −1.64123 | −0.206776 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.30388 | 1.02997 | ||||||||
\(66\) | 0.972556 | 0.119713 | ||||||||
\(67\) | −0.309907 | −0.0378612 | −0.0189306 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189306 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(68\) | 3.47557 | 0.421475 | ||||||||
\(69\) | 10.1896 | 1.22668 | ||||||||
\(70\) | −1.55010 | −0.185272 | ||||||||
\(71\) | −0.734136 | −0.0871260 | −0.0435630 | − | 0.999051i | \(-0.513871\pi\) | ||||
−0.0435630 | + | 0.999051i | \(0.513871\pi\) | |||||||
\(72\) | −1.64123 | −0.193421 | ||||||||
\(73\) | 6.79029 | 0.794744 | 0.397372 | − | 0.917658i | \(-0.369922\pi\) | ||||
0.397372 | + | 0.917658i | \(0.369922\pi\) | |||||||
\(74\) | 1.10020 | 0.127896 | ||||||||
\(75\) | −3.02744 | −0.349579 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.834338 | 0.0950816 | ||||||||
\(78\) | −6.24445 | −0.707044 | ||||||||
\(79\) | 7.61379 | 0.856618 | 0.428309 | − | 0.903632i | \(-0.359109\pi\) | ||||
0.428309 | + | 0.903632i | \(0.359109\pi\) | |||||||
\(80\) | −1.55010 | −0.173307 | ||||||||
\(81\) | −1.38266 | −0.153629 | ||||||||
\(82\) | 5.16566 | 0.570452 | ||||||||
\(83\) | −6.34039 | −0.695949 | −0.347974 | − | 0.937504i | \(-0.613130\pi\) | ||||
−0.347974 | + | 0.937504i | \(0.613130\pi\) | |||||||
\(84\) | 1.16566 | 0.127184 | ||||||||
\(85\) | −5.38748 | −0.584354 | ||||||||
\(86\) | 12.9071 | 1.39181 | ||||||||
\(87\) | 10.7689 | 1.15454 | ||||||||
\(88\) | 0.834338 | 0.0889407 | ||||||||
\(89\) | −10.3313 | −1.09512 | −0.547559 | − | 0.836767i | \(-0.684443\pi\) | ||||
−0.547559 | + | 0.836767i | \(0.684443\pi\) | |||||||
\(90\) | 2.54407 | 0.268169 | ||||||||
\(91\) | −5.35699 | −0.561566 | ||||||||
\(92\) | 8.74143 | 0.911357 | ||||||||
\(93\) | −8.05134 | −0.834885 | ||||||||
\(94\) | 9.23842 | 0.952870 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.16566 | 0.118970 | ||||||||
\(97\) | 1.49699 | 0.151996 | 0.0759980 | − | 0.997108i | \(-0.475786\pi\) | ||||
0.0759980 | + | 0.997108i | \(0.475786\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.36934 | −0.137624 | ||||||||
\(100\) | −2.59719 | −0.259719 | ||||||||
\(101\) | 1.80689 | 0.179793 | 0.0898963 | − | 0.995951i | \(-0.471346\pi\) | ||||
0.0898963 | + | 0.995951i | \(0.471346\pi\) | |||||||
\(102\) | 4.05134 | 0.401142 | ||||||||
\(103\) | 11.8069 | 1.16337 | 0.581684 | − | 0.813415i | \(-0.302394\pi\) | ||||
0.581684 | + | 0.813415i | \(0.302394\pi\) | |||||||
\(104\) | −5.35699 | −0.525297 | ||||||||
\(105\) | −1.80689 | −0.176335 | ||||||||
\(106\) | 10.9071 | 1.05939 | ||||||||
\(107\) | 10.5317 | 1.01814 | 0.509070 | − | 0.860725i | \(-0.329989\pi\) | ||||
0.509070 | + | 0.860725i | \(0.329989\pi\) | |||||||
\(108\) | −5.41011 | −0.520588 | ||||||||
\(109\) | −13.9011 | −1.33148 | −0.665740 | − | 0.746183i | \(-0.731884\pi\) | ||||
−0.665740 | + | 0.746183i | \(0.731884\pi\) | |||||||
\(110\) | −1.29331 | −0.123312 | ||||||||
\(111\) | 1.28246 | 0.121726 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.19311 | −0.112238 | −0.0561190 | − | 0.998424i | \(-0.517873\pi\) | ||||
−0.0561190 | + | 0.998424i | \(0.517873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.5501 | −1.26355 | ||||||||
\(116\) | 9.23842 | 0.857766 | ||||||||
\(117\) | 8.79207 | 0.812827 | ||||||||
\(118\) | 7.09113 | 0.652792 | ||||||||
\(119\) | 3.47557 | 0.318605 | ||||||||
\(120\) | −1.80689 | −0.164946 | ||||||||
\(121\) | −10.3039 | −0.936716 | ||||||||
\(122\) | −9.16389 | −0.829659 | ||||||||
\(123\) | 6.02142 | 0.542933 | ||||||||
\(124\) | −6.90710 | −0.620275 | ||||||||
\(125\) | 11.7764 | 1.05331 | ||||||||
\(126\) | −1.64123 | −0.146213 | ||||||||
\(127\) | −9.79029 | −0.868748 | −0.434374 | − | 0.900733i | \(-0.643030\pi\) | ||||
−0.434374 | + | 0.900733i | \(0.643030\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 15.0453 | 1.32467 | ||||||||
\(130\) | 8.30388 | 0.728298 | ||||||||
\(131\) | −14.6609 | −1.28093 | −0.640463 | − | 0.767989i | \(-0.721258\pi\) | ||||
−0.640463 | + | 0.767989i | \(0.721258\pi\) | |||||||
\(132\) | 0.972556 | 0.0846501 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.309907 | −0.0267719 | ||||||||
\(135\) | 8.38621 | 0.721770 | ||||||||
\(136\) | 3.47557 | 0.298028 | ||||||||
\(137\) | 15.7140 | 1.34254 | 0.671268 | − | 0.741214i | \(-0.265750\pi\) | ||||
0.671268 | + | 0.741214i | \(0.265750\pi\) | |||||||
\(138\) | 10.1896 | 0.867393 | ||||||||
\(139\) | 14.3172 | 1.21437 | 0.607185 | − | 0.794561i | \(-0.292299\pi\) | ||||
0.607185 | + | 0.794561i | \(0.292299\pi\) | |||||||
\(140\) | −1.55010 | −0.131007 | ||||||||
\(141\) | 10.7689 | 0.906903 | ||||||||
\(142\) | −0.734136 | −0.0616074 | ||||||||
\(143\) | −4.46954 | −0.373762 | ||||||||
\(144\) | −1.64123 | −0.136769 | ||||||||
\(145\) | −14.3205 | −1.18925 | ||||||||
\(146\) | 6.79029 | 0.561969 | ||||||||
\(147\) | 1.16566 | 0.0961422 | ||||||||
\(148\) | 1.10020 | 0.0904360 | ||||||||
\(149\) | 2.89980 | 0.237561 | 0.118780 | − | 0.992921i | \(-0.462102\pi\) | ||||
0.118780 | + | 0.992921i | \(0.462102\pi\) | |||||||
\(150\) | −3.02744 | −0.247190 | ||||||||
\(151\) | −10.3039 | −0.838518 | −0.419259 | − | 0.907867i | \(-0.637710\pi\) | ||||
−0.419259 | + | 0.907867i | \(0.637710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.70421 | −0.461158 | ||||||||
\(154\) | 0.834338 | 0.0672329 | ||||||||
\(155\) | 10.7067 | 0.859982 | ||||||||
\(156\) | −6.24445 | −0.499956 | ||||||||
\(157\) | 14.4572 | 1.15381 | 0.576905 | − | 0.816811i | \(-0.304260\pi\) | ||||
0.576905 | + | 0.816811i | \(0.304260\pi\) | |||||||
\(158\) | 7.61379 | 0.605720 | ||||||||
\(159\) | 12.7140 | 1.00828 | ||||||||
\(160\) | −1.55010 | −0.122546 | ||||||||
\(161\) | 8.74143 | 0.688921 | ||||||||
\(162\) | −1.38266 | −0.108632 | ||||||||
\(163\) | −8.21098 | −0.643133 | −0.321567 | − | 0.946887i | \(-0.604209\pi\) | ||||
−0.321567 | + | 0.946887i | \(0.604209\pi\) | |||||||
\(164\) | 5.16566 | 0.403370 | ||||||||
\(165\) | −1.50756 | −0.117363 | ||||||||
\(166\) | −6.34039 | −0.492110 | ||||||||
\(167\) | −11.7629 | −0.910237 | −0.455118 | − | 0.890431i | \(-0.650403\pi\) | ||||
−0.455118 | + | 0.890431i | \(0.650403\pi\) | |||||||
\(168\) | 1.16566 | 0.0899328 | ||||||||
\(169\) | 15.6974 | 1.20749 | ||||||||
\(170\) | −5.38748 | −0.413201 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.9071 | 0.984157 | ||||||||
\(173\) | 13.7505 | 1.04543 | 0.522716 | − | 0.852507i | \(-0.324919\pi\) | ||||
0.522716 | + | 0.852507i | \(0.324919\pi\) | |||||||
\(174\) | 10.7689 | 0.816386 | ||||||||
\(175\) | −2.59719 | −0.196329 | ||||||||
\(176\) | 0.834338 | 0.0628906 | ||||||||
\(177\) | 8.26586 | 0.621300 | ||||||||
\(178\) | −10.3313 | −0.774366 | ||||||||
\(179\) | −10.4481 | −0.780930 | −0.390465 | − | 0.920618i | \(-0.627686\pi\) | ||||
−0.390465 | + | 0.920618i | \(0.627686\pi\) | |||||||
\(180\) | 2.54407 | 0.189624 | ||||||||
\(181\) | 3.16389 | 0.235170 | 0.117585 | − | 0.993063i | \(-0.462485\pi\) | ||||
0.117585 | + | 0.993063i | \(0.462485\pi\) | |||||||
\(182\) | −5.35699 | −0.397087 | ||||||||
\(183\) | −10.6820 | −0.789636 | ||||||||
\(184\) | 8.74143 | 0.644427 | ||||||||
\(185\) | −1.70542 | −0.125385 | ||||||||
\(186\) | −8.05134 | −0.590353 | ||||||||
\(187\) | 2.89980 | 0.212054 | ||||||||
\(188\) | 9.23842 | 0.673781 | ||||||||
\(189\) | −5.41011 | −0.393527 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8283 | −0.783509 | −0.391755 | − | 0.920070i | \(-0.628132\pi\) | ||||
−0.391755 | + | 0.920070i | \(0.628132\pi\) | |||||||
\(192\) | 1.16566 | 0.0841244 | ||||||||
\(193\) | −7.50301 | −0.540079 | −0.270039 | − | 0.962849i | \(-0.587037\pi\) | ||||
−0.270039 | + | 0.962849i | \(0.587037\pi\) | |||||||
\(194\) | 1.49699 | 0.107477 | ||||||||
\(195\) | 9.67952 | 0.693165 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.3875 | 0.811325 | 0.405662 | − | 0.914023i | \(-0.367041\pi\) | ||||
0.405662 | + | 0.914023i | \(0.367041\pi\) | |||||||
\(198\) | −1.36934 | −0.0973149 | ||||||||
\(199\) | −2.90710 | −0.206079 | −0.103039 | − | 0.994677i | \(-0.532857\pi\) | ||||
−0.103039 | + | 0.994677i | \(0.532857\pi\) | |||||||
\(200\) | −2.59719 | −0.183649 | ||||||||
\(201\) | −0.361247 | −0.0254804 | ||||||||
\(202\) | 1.80689 | 0.127133 | ||||||||
\(203\) | 9.23842 | 0.648410 | ||||||||
\(204\) | 4.05134 | 0.283651 | ||||||||
\(205\) | −8.00730 | −0.559254 | ||||||||
\(206\) | 11.8069 | 0.822625 | ||||||||
\(207\) | −14.3467 | −0.997166 | ||||||||
\(208\) | −5.35699 | −0.371441 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.80689 | −0.124688 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 10.9071 | 0.749102 | ||||||||
\(213\) | −0.855755 | −0.0586354 | ||||||||
\(214\) | 10.5317 | 0.719934 | ||||||||
\(215\) | −20.0073 | −1.36449 | ||||||||
\(216\) | −5.41011 | −0.368111 | ||||||||
\(217\) | −6.90710 | −0.468884 | ||||||||
\(218\) | −13.9011 | −0.941499 | ||||||||
\(219\) | 7.91519 | 0.534859 | ||||||||
\(220\) | −1.29331 | −0.0871948 | ||||||||
\(221\) | −18.6186 | −1.25242 | ||||||||
\(222\) | 1.28246 | 0.0860733 | ||||||||
\(223\) | −11.8142 | −0.791137 | −0.395568 | − | 0.918437i | \(-0.629452\pi\) | ||||
−0.395568 | + | 0.918437i | \(0.629452\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 4.26259 | 0.284172 | ||||||||
\(226\) | −1.19311 | −0.0793642 | ||||||||
\(227\) | −17.1057 | −1.13535 | −0.567673 | − | 0.823254i | \(-0.692156\pi\) | ||||
−0.567673 | + | 0.823254i | \(0.692156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7837 | −1.57167 | −0.785836 | − | 0.618435i | \(-0.787767\pi\) | ||||
−0.785836 | + | 0.618435i | \(0.787767\pi\) | |||||||
\(230\) | −13.5501 | −0.893467 | ||||||||
\(231\) | 0.972556 | 0.0639895 | ||||||||
\(232\) | 9.23842 | 0.606532 | ||||||||
\(233\) | 9.71399 | 0.636385 | 0.318192 | − | 0.948026i | \(-0.396924\pi\) | ||||
0.318192 | + | 0.948026i | \(0.396924\pi\) | |||||||
\(234\) | 8.79207 | 0.574755 | ||||||||
\(235\) | −14.3205 | −0.934165 | ||||||||
\(236\) | 7.09113 | 0.461593 | ||||||||
\(237\) | 8.87510 | 0.576500 | ||||||||
\(238\) | 3.47557 | 0.225288 | ||||||||
\(239\) | −7.82349 | −0.506060 | −0.253030 | − | 0.967458i | \(-0.581427\pi\) | ||||
−0.253030 | + | 0.967458i | \(0.581427\pi\) | |||||||
\(240\) | −1.80689 | −0.116634 | ||||||||
\(241\) | 13.4970 | 0.869417 | 0.434709 | − | 0.900571i | \(-0.356851\pi\) | ||||
0.434709 | + | 0.900571i | \(0.356851\pi\) | |||||||
\(242\) | −10.3039 | −0.662359 | ||||||||
\(243\) | 14.6186 | 0.937784 | ||||||||
\(244\) | −9.16389 | −0.586658 | ||||||||
\(245\) | −1.55010 | −0.0990323 | ||||||||
\(246\) | 6.02142 | 0.383912 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.90710 | −0.438601 | ||||||||
\(249\) | −7.39076 | −0.468370 | ||||||||
\(250\) | 11.7764 | 0.744805 | ||||||||
\(251\) | −9.57881 | −0.604609 | −0.302305 | − | 0.953211i | \(-0.597756\pi\) | ||||
−0.302305 | + | 0.953211i | \(0.597756\pi\) | |||||||
\(252\) | −1.64123 | −0.103388 | ||||||||
\(253\) | 7.29331 | 0.458526 | ||||||||
\(254\) | −9.79029 | −0.614298 | ||||||||
\(255\) | −6.27998 | −0.393268 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.98588 | 0.498145 | 0.249073 | − | 0.968485i | \(-0.419874\pi\) | ||||
0.249073 | + | 0.968485i | \(0.419874\pi\) | |||||||
\(258\) | 15.0453 | 0.936680 | ||||||||
\(259\) | 1.10020 | 0.0683632 | ||||||||
\(260\) | 8.30388 | 0.514985 | ||||||||
\(261\) | −15.1624 | −0.938528 | ||||||||
\(262\) | −14.6609 | −0.905752 | ||||||||
\(263\) | −16.5483 | −1.02041 | −0.510207 | − | 0.860052i | \(-0.670431\pi\) | ||||
−0.510207 | + | 0.860052i | \(0.670431\pi\) | |||||||
\(264\) | 0.972556 | 0.0598567 | ||||||||
\(265\) | −16.9071 | −1.03859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0428 | −0.737010 | ||||||||
\(268\) | −0.309907 | −0.0189306 | ||||||||
\(269\) | −0.575771 | −0.0351054 | −0.0175527 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175527 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(270\) | 8.38621 | 0.510369 | ||||||||
\(271\) | −3.62108 | −0.219965 | −0.109983 | − | 0.993934i | \(-0.535080\pi\) | ||||
−0.109983 | + | 0.993934i | \(0.535080\pi\) | |||||||
\(272\) | 3.47557 | 0.210737 | ||||||||
\(273\) | −6.24445 | −0.377931 | ||||||||
\(274\) | 15.7140 | 0.949317 | ||||||||
\(275\) | −2.16693 | −0.130671 | ||||||||
\(276\) | 10.1896 | 0.613339 | ||||||||
\(277\) | 30.3278 | 1.82222 | 0.911110 | − | 0.412164i | \(-0.135227\pi\) | ||||
0.911110 | + | 0.412164i | \(0.135227\pi\) | |||||||
\(278\) | 14.3172 | 0.858689 | ||||||||
\(279\) | 11.3361 | 0.678677 | ||||||||
\(280\) | −1.55010 | −0.0926362 | ||||||||
\(281\) | −3.35877 | −0.200367 | −0.100184 | − | 0.994969i | \(-0.531943\pi\) | ||||
−0.100184 | + | 0.994969i | \(0.531943\pi\) | |||||||
\(282\) | 10.7689 | 0.641277 | ||||||||
\(283\) | 3.33437 | 0.198208 | 0.0991038 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991038 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(284\) | −0.734136 | −0.0435630 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.46954 | −0.264290 | ||||||||
\(287\) | 5.16566 | 0.304919 | ||||||||
\(288\) | −1.64123 | −0.0967105 | ||||||||
\(289\) | −4.92042 | −0.289436 | ||||||||
\(290\) | −14.3205 | −0.840928 | ||||||||
\(291\) | 1.74498 | 0.102293 | ||||||||
\(292\) | 6.79029 | 0.397372 | ||||||||
\(293\) | 22.8839 | 1.33689 | 0.668446 | − | 0.743761i | \(-0.266960\pi\) | ||||
0.668446 | + | 0.743761i | \(0.266960\pi\) | |||||||
\(294\) | 1.16566 | 0.0679828 | ||||||||
\(295\) | −10.9920 | −0.639977 | ||||||||
\(296\) | 1.10020 | 0.0639479 | ||||||||
\(297\) | −4.51386 | −0.261921 | ||||||||
\(298\) | 2.89980 | 0.167981 | ||||||||
\(299\) | −46.8278 | −2.70812 | ||||||||
\(300\) | −3.02744 | −0.174790 | ||||||||
\(301\) | 12.9071 | 0.743953 | ||||||||
\(302\) | −10.3039 | −0.592922 | ||||||||
\(303\) | 2.10623 | 0.121000 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.2049 | 0.813373 | ||||||||
\(306\) | −5.70421 | −0.326088 | ||||||||
\(307\) | −18.2867 | −1.04368 | −0.521839 | − | 0.853044i | \(-0.674754\pi\) | ||||
−0.521839 | + | 0.853044i | \(0.674754\pi\) | |||||||
\(308\) | 0.834338 | 0.0475408 | ||||||||
\(309\) | 13.7629 | 0.782941 | ||||||||
\(310\) | 10.7067 | 0.608099 | ||||||||
\(311\) | 7.23112 | 0.410039 | 0.205020 | − | 0.978758i | \(-0.434274\pi\) | ||||
0.205020 | + | 0.978758i | \(0.434274\pi\) | |||||||
\(312\) | −6.24445 | −0.353522 | ||||||||
\(313\) | 6.51031 | 0.367984 | 0.183992 | − | 0.982928i | \(-0.441098\pi\) | ||||
0.183992 | + | 0.982928i | \(0.441098\pi\) | |||||||
\(314\) | 14.4572 | 0.815867 | ||||||||
\(315\) | 2.54407 | 0.143342 | ||||||||
\(316\) | 7.61379 | 0.428309 | ||||||||
\(317\) | −29.4461 | −1.65386 | −0.826929 | − | 0.562306i | \(-0.809914\pi\) | ||||
−0.826929 | + | 0.562306i | \(0.809914\pi\) | |||||||
\(318\) | 12.7140 | 0.712965 | ||||||||
\(319\) | 7.70796 | 0.431563 | ||||||||
\(320\) | −1.55010 | −0.0866533 | ||||||||
\(321\) | 12.2764 | 0.685204 | ||||||||
\(322\) | 8.74143 | 0.487141 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.38266 | −0.0768147 | ||||||||
\(325\) | 13.9131 | 0.771761 | ||||||||
\(326\) | −8.21098 | −0.454764 | ||||||||
\(327\) | −16.2040 | −0.896081 | ||||||||
\(328\) | 5.16566 | 0.285226 | ||||||||
\(329\) | 9.23842 | 0.509331 | ||||||||
\(330\) | −1.50756 | −0.0829884 | ||||||||
\(331\) | −20.7976 | −1.14314 | −0.571569 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571569 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(332\) | −6.34039 | −0.347974 | ||||||||
\(333\) | −1.80569 | −0.0989509 | ||||||||
\(334\) | −11.7629 | −0.643635 | ||||||||
\(335\) | 0.480387 | 0.0262464 | ||||||||
\(336\) | 1.16566 | 0.0635921 | ||||||||
\(337\) | 28.2017 | 1.53624 | 0.768121 | − | 0.640304i | \(-0.221192\pi\) | ||||
0.768121 | + | 0.640304i | \(0.221192\pi\) | |||||||
\(338\) | 15.6974 | 0.853825 | ||||||||
\(339\) | −1.39076 | −0.0755357 | ||||||||
\(340\) | −5.38748 | −0.292177 | ||||||||
\(341\) | −5.76285 | −0.312076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 12.9071 | 0.695904 | ||||||||
\(345\) | −15.7948 | −0.850366 | ||||||||
\(346\) | 13.7505 | 0.739232 | ||||||||
\(347\) | 28.3064 | 1.51956 | 0.759782 | − | 0.650177i | \(-0.225305\pi\) | ||||
0.759782 | + | 0.650177i | \(0.225305\pi\) | |||||||
\(348\) | 10.7689 | 0.577272 | ||||||||
\(349\) | 19.6211 | 1.05029 | 0.525146 | − | 0.851012i | \(-0.324011\pi\) | ||||
0.525146 | + | 0.851012i | \(0.324011\pi\) | |||||||
\(350\) | −2.59719 | −0.138826 | ||||||||
\(351\) | 28.9819 | 1.54694 | ||||||||
\(352\) | 0.834338 | 0.0444704 | ||||||||
\(353\) | 1.82831 | 0.0973112 | 0.0486556 | − | 0.998816i | \(-0.484506\pi\) | ||||
0.0486556 | + | 0.998816i | \(0.484506\pi\) | |||||||
\(354\) | 8.26586 | 0.439326 | ||||||||
\(355\) | 1.13799 | 0.0603980 | ||||||||
\(356\) | −10.3313 | −0.547559 | ||||||||
\(357\) | 4.05134 | 0.214420 | ||||||||
\(358\) | −10.4481 | −0.552201 | ||||||||
\(359\) | 15.3006 | 0.807535 | 0.403767 | − | 0.914862i | \(-0.367700\pi\) | ||||
0.403767 | + | 0.914862i | \(0.367700\pi\) | |||||||
\(360\) | 2.54407 | 0.134084 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 3.16389 | 0.166290 | ||||||||
\(363\) | −12.0108 | −0.630406 | ||||||||
\(364\) | −5.35699 | −0.280783 | ||||||||
\(365\) | −10.5256 | −0.550937 | ||||||||
\(366\) | −10.6820 | −0.558357 | ||||||||
\(367\) | 19.9011 | 1.03883 | 0.519414 | − | 0.854523i | \(-0.326150\pi\) | ||||
0.519414 | + | 0.854523i | \(0.326150\pi\) | |||||||
\(368\) | 8.74143 | 0.455679 | ||||||||
\(369\) | −8.47805 | −0.441350 | ||||||||
\(370\) | −1.70542 | −0.0886607 | ||||||||
\(371\) | 10.9071 | 0.566268 | ||||||||
\(372\) | −8.05134 | −0.417443 | ||||||||
\(373\) | −36.9071 | −1.91098 | −0.955488 | − | 0.295028i | \(-0.904671\pi\) | ||||
−0.955488 | + | 0.295028i | \(0.904671\pi\) | |||||||
\(374\) | 2.89980 | 0.149945 | ||||||||
\(375\) | 13.7273 | 0.708875 | ||||||||
\(376\) | 9.23842 | 0.476435 | ||||||||
\(377\) | −49.4902 | −2.54887 | ||||||||
\(378\) | −5.41011 | −0.278266 | ||||||||
\(379\) | 3.10750 | 0.159621 | 0.0798107 | − | 0.996810i | \(-0.474568\pi\) | ||||
0.0798107 | + | 0.996810i | \(0.474568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.4122 | −0.584664 | ||||||||
\(382\) | −10.8283 | −0.554025 | ||||||||
\(383\) | 17.7200 | 0.905450 | 0.452725 | − | 0.891650i | \(-0.350452\pi\) | ||||
0.452725 | + | 0.891650i | \(0.350452\pi\) | |||||||
\(384\) | 1.16566 | 0.0594850 | ||||||||
\(385\) | −1.29331 | −0.0659131 | ||||||||
\(386\) | −7.50301 | −0.381893 | ||||||||
\(387\) | −21.1835 | −1.07682 | ||||||||
\(388\) | 1.49699 | 0.0759980 | ||||||||
\(389\) | 25.8069 | 1.30846 | 0.654231 | − | 0.756295i | \(-0.272993\pi\) | ||||
0.654231 | + | 0.756295i | \(0.272993\pi\) | |||||||
\(390\) | 9.67952 | 0.490142 | ||||||||
\(391\) | 30.3815 | 1.53646 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −17.0896 | −0.862058 | ||||||||
\(394\) | 11.3875 | 0.573693 | ||||||||
\(395\) | −11.8021 | −0.593830 | ||||||||
\(396\) | −1.36934 | −0.0688120 | ||||||||
\(397\) | 2.81292 | 0.141176 | 0.0705882 | − | 0.997506i | \(-0.477512\pi\) | ||||
0.0705882 | + | 0.997506i | \(0.477512\pi\) | |||||||
\(398\) | −2.90710 | −0.145720 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.59719 | −0.129859 | ||||||||
\(401\) | 13.7067 | 0.684480 | 0.342240 | − | 0.939613i | \(-0.388814\pi\) | ||||
0.342240 | + | 0.939613i | \(0.388814\pi\) | |||||||
\(402\) | −0.361247 | −0.0180174 | ||||||||
\(403\) | 37.0013 | 1.84316 | ||||||||
\(404\) | 1.80689 | 0.0898963 | ||||||||
\(405\) | 2.14327 | 0.106500 | ||||||||
\(406\) | 9.23842 | 0.458495 | ||||||||
\(407\) | 0.917939 | 0.0455006 | ||||||||
\(408\) | 4.05134 | 0.200571 | ||||||||
\(409\) | −27.9237 | −1.38074 | −0.690369 | − | 0.723458i | \(-0.742552\pi\) | ||||
−0.690369 | + | 0.723458i | \(0.742552\pi\) | |||||||
\(410\) | −8.00730 | −0.395452 | ||||||||
\(411\) | 18.3172 | 0.903521 | ||||||||
\(412\) | 11.8069 | 0.581684 | ||||||||
\(413\) | 7.09113 | 0.348932 | ||||||||
\(414\) | −14.3467 | −0.705103 | ||||||||
\(415\) | 9.82825 | 0.482450 | ||||||||
\(416\) | −5.35699 | −0.262648 | ||||||||
\(417\) | 16.6890 | 0.817265 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.5209 | −1.58875 | −0.794375 | − | 0.607428i | \(-0.792201\pi\) | ||||
−0.794375 | + | 0.607428i | \(0.792201\pi\) | |||||||
\(420\) | −1.80689 | −0.0881674 | ||||||||
\(421\) | 21.1075 | 1.02872 | 0.514358 | − | 0.857575i | \(-0.328030\pi\) | ||||
0.514358 | + | 0.857575i | \(0.328030\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | −15.1624 | −0.737220 | ||||||||
\(424\) | 10.9071 | 0.529695 | ||||||||
\(425\) | −9.02671 | −0.437860 | ||||||||
\(426\) | −0.855755 | −0.0414615 | ||||||||
\(427\) | −9.16389 | −0.443472 | ||||||||
\(428\) | 10.5317 | 0.509070 | ||||||||
\(429\) | −5.20998 | −0.251540 | ||||||||
\(430\) | −20.0073 | −0.964838 | ||||||||
\(431\) | 2.89980 | 0.139678 | 0.0698392 | − | 0.997558i | \(-0.477751\pi\) | ||||
0.0698392 | + | 0.997558i | \(0.477751\pi\) | |||||||
\(432\) | −5.41011 | −0.260294 | ||||||||
\(433\) | −23.9952 | −1.15314 | −0.576569 | − | 0.817049i | \(-0.695609\pi\) | ||||
−0.576569 | + | 0.817049i | \(0.695609\pi\) | |||||||
\(434\) | −6.90710 | −0.331551 | ||||||||
\(435\) | −16.6928 | −0.800361 | ||||||||
\(436\) | −13.9011 | −0.665740 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 7.91519 | 0.378202 | ||||||||
\(439\) | −38.5355 | −1.83920 | −0.919599 | − | 0.392858i | \(-0.871486\pi\) | ||||
−0.919599 | + | 0.392858i | \(0.871486\pi\) | |||||||
\(440\) | −1.29331 | −0.0616560 | ||||||||
\(441\) | −1.64123 | −0.0781539 | ||||||||
\(442\) | −18.6186 | −0.885597 | ||||||||
\(443\) | −26.6805 | −1.26763 | −0.633815 | − | 0.773485i | \(-0.718512\pi\) | ||||
−0.633815 | + | 0.773485i | \(0.718512\pi\) | |||||||
\(444\) | 1.28246 | 0.0608630 | ||||||||
\(445\) | 16.0146 | 0.759165 | ||||||||
\(446\) | −11.8142 | −0.559418 | ||||||||
\(447\) | 3.38019 | 0.159877 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −28.6284 | −1.35106 | −0.675528 | − | 0.737334i | \(-0.736084\pi\) | ||||
−0.675528 | + | 0.737334i | \(0.736084\pi\) | |||||||
\(450\) | 4.26259 | 0.200940 | ||||||||
\(451\) | 4.30991 | 0.202946 | ||||||||
\(452\) | −1.19311 | −0.0561190 | ||||||||
\(453\) | −12.0108 | −0.564319 | ||||||||
\(454\) | −17.1057 | −0.802811 | ||||||||
\(455\) | 8.30388 | 0.389292 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.28728 | 0.340885 | 0.170442 | − | 0.985368i | \(-0.445480\pi\) | ||||
0.170442 | + | 0.985368i | \(0.445480\pi\) | |||||||
\(458\) | −23.7837 | −1.11134 | ||||||||
\(459\) | −18.8032 | −0.877659 | ||||||||
\(460\) | −13.5501 | −0.631777 | ||||||||
\(461\) | 14.2019 | 0.661449 | 0.330724 | − | 0.943727i | \(-0.392707\pi\) | ||||
0.330724 | + | 0.943727i | \(0.392707\pi\) | |||||||
\(462\) | 0.972556 | 0.0452474 | ||||||||
\(463\) | 29.8308 | 1.38635 | 0.693177 | − | 0.720767i | \(-0.256210\pi\) | ||||
0.693177 | + | 0.720767i | \(0.256210\pi\) | |||||||
\(464\) | 9.23842 | 0.428883 | ||||||||
\(465\) | 12.4804 | 0.578764 | ||||||||
\(466\) | 9.71399 | 0.449992 | ||||||||
\(467\) | 5.87965 | 0.272078 | 0.136039 | − | 0.990703i | \(-0.456563\pi\) | ||||
0.136039 | + | 0.990703i | \(0.456563\pi\) | |||||||
\(468\) | 8.79207 | 0.406413 | ||||||||
\(469\) | −0.309907 | −0.0143102 | ||||||||
\(470\) | −14.3205 | −0.660554 | ||||||||
\(471\) | 16.8522 | 0.776509 | ||||||||
\(472\) | 7.09113 | 0.326396 | ||||||||
\(473\) | 10.7689 | 0.495153 | ||||||||
\(474\) | 8.87510 | 0.407647 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.47557 | 0.159302 | ||||||||
\(477\) | −17.9011 | −0.819634 | ||||||||
\(478\) | −7.82349 | −0.357838 | ||||||||
\(479\) | 16.8739 | 0.770988 | 0.385494 | − | 0.922710i | \(-0.374031\pi\) | ||||
0.385494 | + | 0.922710i | \(0.374031\pi\) | |||||||
\(480\) | −1.80689 | −0.0824730 | ||||||||
\(481\) | −5.89377 | −0.268733 | ||||||||
\(482\) | 13.4970 | 0.614771 | ||||||||
\(483\) | 10.1896 | 0.463641 | ||||||||
\(484\) | −10.3039 | −0.468358 | ||||||||
\(485\) | −2.32048 | −0.105368 | ||||||||
\(486\) | 14.6186 | 0.663113 | ||||||||
\(487\) | −17.1002 | −0.774884 | −0.387442 | − | 0.921894i | \(-0.626641\pi\) | ||||
−0.387442 | + | 0.921894i | \(0.626641\pi\) | |||||||
\(488\) | −9.16389 | −0.414830 | ||||||||
\(489\) | −9.57122 | −0.432826 | ||||||||
\(490\) | −1.55010 | −0.0700264 | ||||||||
\(491\) | −5.04886 | −0.227852 | −0.113926 | − | 0.993489i | \(-0.536343\pi\) | ||||
−0.113926 | + | 0.993489i | \(0.536343\pi\) | |||||||
\(492\) | 6.02142 | 0.271466 | ||||||||
\(493\) | 32.1088 | 1.44611 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.12262 | 0.0954045 | ||||||||
\(496\) | −6.90710 | −0.310138 | ||||||||
\(497\) | −0.734136 | −0.0329305 | ||||||||
\(498\) | −7.39076 | −0.331188 | ||||||||
\(499\) | −11.1108 | −0.497387 | −0.248693 | − | 0.968582i | \(-0.580001\pi\) | ||||
−0.248693 | + | 0.968582i | \(0.580001\pi\) | |||||||
\(500\) | 11.7764 | 0.526657 | ||||||||
\(501\) | −13.7115 | −0.612585 | ||||||||
\(502\) | −9.57881 | −0.427523 | ||||||||
\(503\) | −18.8190 | −0.839098 | −0.419549 | − | 0.907733i | \(-0.637812\pi\) | ||||
−0.419549 | + | 0.907733i | \(0.637812\pi\) | |||||||
\(504\) | −1.64123 | −0.0731063 | ||||||||
\(505\) | −2.80087 | −0.124637 | ||||||||
\(506\) | 7.29331 | 0.324227 | ||||||||
\(507\) | 18.2979 | 0.812636 | ||||||||
\(508\) | −9.79029 | −0.434374 | ||||||||
\(509\) | −32.6359 | −1.44656 | −0.723281 | − | 0.690554i | \(-0.757367\pi\) | ||||
−0.723281 | + | 0.690554i | \(0.757367\pi\) | |||||||
\(510\) | −6.27998 | −0.278082 | ||||||||
\(511\) | 6.79029 | 0.300385 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.98588 | 0.352242 | ||||||||
\(515\) | −18.3019 | −0.806477 | ||||||||
\(516\) | 15.0453 | 0.662333 | ||||||||
\(517\) | 7.70796 | 0.338996 | ||||||||
\(518\) | 1.10020 | 0.0483401 | ||||||||
\(519\) | 16.0284 | 0.703571 | ||||||||
\(520\) | 8.30388 | 0.364149 | ||||||||
\(521\) | 1.17296 | 0.0513882 | 0.0256941 | − | 0.999670i | \(-0.491820\pi\) | ||||
0.0256941 | + | 0.999670i | \(0.491820\pi\) | |||||||
\(522\) | −15.1624 | −0.663640 | ||||||||
\(523\) | 24.5209 | 1.07222 | 0.536112 | − | 0.844147i | \(-0.319893\pi\) | ||||
0.536112 | + | 0.844147i | \(0.319893\pi\) | |||||||
\(524\) | −14.6609 | −0.640463 | ||||||||
\(525\) | −3.02744 | −0.132128 | ||||||||
\(526\) | −16.5483 | −0.721541 | ||||||||
\(527\) | −24.0061 | −1.04572 | ||||||||
\(528\) | 0.972556 | 0.0423251 | ||||||||
\(529\) | 53.4126 | 2.32229 | ||||||||
\(530\) | −16.9071 | −0.734397 | ||||||||
\(531\) | −11.6382 | −0.505054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.6724 | −1.19863 | ||||||||
\(534\) | −12.0428 | −0.521144 | ||||||||
\(535\) | −16.3252 | −0.705802 | ||||||||
\(536\) | −0.309907 | −0.0133859 | ||||||||
\(537\) | −12.1790 | −0.525562 | ||||||||
\(538\) | −0.575771 | −0.0248232 | ||||||||
\(539\) | 0.834338 | 0.0359375 | ||||||||
\(540\) | 8.38621 | 0.360885 | ||||||||
\(541\) | 37.0418 | 1.59255 | 0.796275 | − | 0.604935i | \(-0.206801\pi\) | ||||
0.796275 | + | 0.604935i | \(0.206801\pi\) | |||||||
\(542\) | −3.62108 | −0.155539 | ||||||||
\(543\) | 3.68803 | 0.158268 | ||||||||
\(544\) | 3.47557 | 0.149014 | ||||||||
\(545\) | 21.5481 | 0.923017 | ||||||||
\(546\) | −6.24445 | −0.267238 | ||||||||
\(547\) | −0.506290 | −0.0216474 | −0.0108237 | − | 0.999941i | \(-0.503445\pi\) | ||||
−0.0108237 | + | 0.999941i | \(0.503445\pi\) | |||||||
\(548\) | 15.7140 | 0.671268 | ||||||||
\(549\) | 15.0401 | 0.641894 | ||||||||
\(550\) | −2.16693 | −0.0923983 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 10.1896 | 0.433696 | ||||||||
\(553\) | 7.61379 | 0.323771 | ||||||||
\(554\) | 30.3278 | 1.28850 | ||||||||
\(555\) | −1.98795 | −0.0843836 | ||||||||
\(556\) | 14.3172 | 0.607185 | ||||||||
\(557\) | 0.513586 | 0.0217613 | 0.0108807 | − | 0.999941i | \(-0.496537\pi\) | ||||
0.0108807 | + | 0.999941i | \(0.496537\pi\) | |||||||
\(558\) | 11.3361 | 0.479897 | ||||||||
\(559\) | −69.1432 | −2.92445 | ||||||||
\(560\) | −1.55010 | −0.0655037 | ||||||||
\(561\) | 3.38019 | 0.142712 | ||||||||
\(562\) | −3.35877 | −0.141681 | ||||||||
\(563\) | 29.3235 | 1.23584 | 0.617920 | − | 0.786241i | \(-0.287976\pi\) | ||||
0.617920 | + | 0.786241i | \(0.287976\pi\) | |||||||
\(564\) | 10.7689 | 0.453452 | ||||||||
\(565\) | 1.84943 | 0.0778063 | ||||||||
\(566\) | 3.33437 | 0.140154 | ||||||||
\(567\) | −1.38266 | −0.0580664 | ||||||||
\(568\) | −0.734136 | −0.0308037 | ||||||||
\(569\) | 1.21452 | 0.0509155 | 0.0254577 | − | 0.999676i | \(-0.491896\pi\) | ||||
0.0254577 | + | 0.999676i | \(0.491896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2097 | 0.887599 | 0.443799 | − | 0.896126i | \(-0.353630\pi\) | ||||
0.443799 | + | 0.896126i | \(0.353630\pi\) | |||||||
\(572\) | −4.46954 | −0.186881 | ||||||||
\(573\) | −12.6222 | −0.527298 | ||||||||
\(574\) | 5.16566 | 0.215611 | ||||||||
\(575\) | −22.7031 | −0.946787 | ||||||||
\(576\) | −1.64123 | −0.0683846 | ||||||||
\(577\) | 7.78427 | 0.324063 | 0.162032 | − | 0.986786i | \(-0.448195\pi\) | ||||
0.162032 | + | 0.986786i | \(0.448195\pi\) | |||||||
\(578\) | −4.92042 | −0.204662 | ||||||||
\(579\) | −8.74598 | −0.363470 | ||||||||
\(580\) | −14.3205 | −0.594626 | ||||||||
\(581\) | −6.34039 | −0.263044 | ||||||||
\(582\) | 1.74498 | 0.0723318 | ||||||||
\(583\) | 9.10020 | 0.376892 | ||||||||
\(584\) | 6.79029 | 0.280984 | ||||||||
\(585\) | −13.6286 | −0.563473 | ||||||||
\(586\) | 22.8839 | 0.945325 | ||||||||
\(587\) | 10.7128 | 0.442164 | 0.221082 | − | 0.975255i | \(-0.429041\pi\) | ||||
0.221082 | + | 0.975255i | \(0.429041\pi\) | |||||||
\(588\) | 1.16566 | 0.0480711 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −10.9920 | −0.452532 | ||||||||
\(591\) | 13.2740 | 0.546018 | ||||||||
\(592\) | 1.10020 | 0.0452180 | ||||||||
\(593\) | −31.9859 | −1.31350 | −0.656751 | − | 0.754107i | \(-0.728070\pi\) | ||||
−0.656751 | + | 0.754107i | \(0.728070\pi\) | |||||||
\(594\) | −4.51386 | −0.185206 | ||||||||
\(595\) | −5.38748 | −0.220865 | ||||||||
\(596\) | 2.89980 | 0.118780 | ||||||||
\(597\) | −3.38869 | −0.138690 | ||||||||
\(598\) | −46.8278 | −1.91493 | ||||||||
\(599\) | 10.7916 | 0.440931 | 0.220466 | − | 0.975395i | \(-0.429242\pi\) | ||||
0.220466 | + | 0.975395i | \(0.429242\pi\) | |||||||
\(600\) | −3.02744 | −0.123595 | ||||||||
\(601\) | −15.3908 | −0.627802 | −0.313901 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313901 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(602\) | 12.9071 | 0.526054 | ||||||||
\(603\) | 0.508629 | 0.0207130 | ||||||||
\(604\) | −10.3039 | −0.419259 | ||||||||
\(605\) | 15.9721 | 0.649356 | ||||||||
\(606\) | 2.10623 | 0.0855597 | ||||||||
\(607\) | −17.8142 | −0.723056 | −0.361528 | − | 0.932361i | \(-0.617745\pi\) | ||||
−0.361528 | + | 0.932361i | \(0.617745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7689 | 0.436377 | ||||||||
\(610\) | 14.2049 | 0.575142 | ||||||||
\(611\) | −49.4902 | −2.00216 | ||||||||
\(612\) | −5.70421 | −0.230579 | ||||||||
\(613\) | −45.5415 | −1.83940 | −0.919702 | − | 0.392617i | \(-0.871570\pi\) | ||||
−0.919702 | + | 0.392617i | \(0.871570\pi\) | |||||||
\(614\) | −18.2867 | −0.737992 | ||||||||
\(615\) | −9.33380 | −0.376375 | ||||||||
\(616\) | 0.834338 | 0.0336164 | ||||||||
\(617\) | −27.5390 | −1.10868 | −0.554340 | − | 0.832291i | \(-0.687029\pi\) | ||||
−0.554340 | + | 0.832291i | \(0.687029\pi\) | |||||||
\(618\) | 13.7629 | 0.553623 | ||||||||
\(619\) | −13.6370 | −0.548116 | −0.274058 | − | 0.961713i | \(-0.588366\pi\) | ||||
−0.274058 | + | 0.961713i | \(0.588366\pi\) | |||||||
\(620\) | 10.7067 | 0.429991 | ||||||||
\(621\) | −47.2921 | −1.89777 | ||||||||
\(622\) | 7.23112 | 0.289942 | ||||||||
\(623\) | −10.3313 | −0.413916 | ||||||||
\(624\) | −6.24445 | −0.249978 | ||||||||
\(625\) | −5.26867 | −0.210747 | ||||||||
\(626\) | 6.51031 | 0.260204 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.4572 | 0.576905 | ||||||||
\(629\) | 3.82383 | 0.152466 | ||||||||
\(630\) | 2.54407 | 0.101358 | ||||||||
\(631\) | 27.6284 | 1.09987 | 0.549934 | − | 0.835208i | \(-0.314653\pi\) | ||||
0.549934 | + | 0.835208i | \(0.314653\pi\) | |||||||
\(632\) | 7.61379 | 0.302860 | ||||||||
\(633\) | 4.66265 | 0.185324 | ||||||||
\(634\) | −29.4461 | −1.16945 | ||||||||
\(635\) | 15.1759 | 0.602239 | ||||||||
\(636\) | 12.7140 | 0.504142 | ||||||||
\(637\) | −5.35699 | −0.212252 | ||||||||
\(638\) | 7.70796 | 0.305161 | ||||||||
\(639\) | 1.20489 | 0.0476646 | ||||||||
\(640\) | −1.55010 | −0.0612731 | ||||||||
\(641\) | −14.2631 | −0.563359 | −0.281680 | − | 0.959509i | \(-0.590892\pi\) | ||||
−0.281680 | + | 0.959509i | \(0.590892\pi\) | |||||||
\(642\) | 12.2764 | 0.484512 | ||||||||
\(643\) | −1.75378 | −0.0691623 | −0.0345812 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345812 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(644\) | 8.74143 | 0.344461 | ||||||||
\(645\) | −23.3217 | −0.918293 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.58180 | −0.219443 | −0.109722 | − | 0.993962i | \(-0.534996\pi\) | ||||
−0.109722 | + | 0.993962i | \(0.534996\pi\) | |||||||
\(648\) | −1.38266 | −0.0543162 | ||||||||
\(649\) | 5.91640 | 0.232239 | ||||||||
\(650\) | 13.9131 | 0.545718 | ||||||||
\(651\) | −8.05134 | −0.315557 | ||||||||
\(652\) | −8.21098 | −0.321567 | ||||||||
\(653\) | 25.0098 | 0.978708 | 0.489354 | − | 0.872085i | \(-0.337233\pi\) | ||||
0.489354 | + | 0.872085i | \(0.337233\pi\) | |||||||
\(654\) | −16.2040 | −0.633625 | ||||||||
\(655\) | 22.7258 | 0.887972 | ||||||||
\(656\) | 5.16566 | 0.201685 | ||||||||
\(657\) | −11.1444 | −0.434786 | ||||||||
\(658\) | 9.23842 | 0.360151 | ||||||||
\(659\) | −27.2971 | −1.06334 | −0.531671 | − | 0.846951i | \(-0.678436\pi\) | ||||
−0.531671 | + | 0.846951i | \(0.678436\pi\) | |||||||
\(660\) | −1.50756 | −0.0586817 | ||||||||
\(661\) | 33.5647 | 1.30552 | 0.652758 | − | 0.757567i | \(-0.273612\pi\) | ||||
0.652758 | + | 0.757567i | \(0.273612\pi\) | |||||||
\(662\) | −20.7976 | −0.808321 | ||||||||
\(663\) | −21.7030 | −0.842875 | ||||||||
\(664\) | −6.34039 | −0.246055 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.80569 | −0.0699689 | ||||||||
\(667\) | 80.7570 | 3.12692 | ||||||||
\(668\) | −11.7629 | −0.455118 | ||||||||
\(669\) | −13.7714 | −0.532431 | ||||||||
\(670\) | 0.480387 | 0.0185590 | ||||||||
\(671\) | −7.64578 | −0.295162 | ||||||||
\(672\) | 1.16566 | 0.0449664 | ||||||||
\(673\) | −4.50428 | −0.173627 | −0.0868137 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868137 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(674\) | 28.2017 | 1.08629 | ||||||||
\(675\) | 14.0511 | 0.540826 | ||||||||
\(676\) | 15.6974 | 0.603746 | ||||||||
\(677\) | −17.3839 | −0.668119 | −0.334059 | − | 0.942552i | \(-0.608419\pi\) | ||||
−0.334059 | + | 0.942552i | \(0.608419\pi\) | |||||||
\(678\) | −1.39076 | −0.0534118 | ||||||||
\(679\) | 1.49699 | 0.0574491 | ||||||||
\(680\) | −5.38748 | −0.206601 | ||||||||
\(681\) | −19.9395 | −0.764083 | ||||||||
\(682\) | −5.76285 | −0.220671 | ||||||||
\(683\) | −17.4268 | −0.666817 | −0.333408 | − | 0.942783i | \(-0.608199\pi\) | ||||
−0.333408 | + | 0.942783i | \(0.608199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.3583 | −0.930681 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −27.7238 | −1.05773 | ||||||||
\(688\) | 12.9071 | 0.492078 | ||||||||
\(689\) | −58.4292 | −2.22598 | ||||||||
\(690\) | −15.7948 | −0.601299 | ||||||||
\(691\) | 28.0830 | 1.06833 | 0.534165 | − | 0.845381i | \(-0.320626\pi\) | ||||
0.534165 | + | 0.845381i | \(0.320626\pi\) | |||||||
\(692\) | 13.7505 | 0.522716 | ||||||||
\(693\) | −1.36934 | −0.0520170 | ||||||||
\(694\) | 28.3064 | 1.07449 | ||||||||
\(695\) | −22.1931 | −0.841833 | ||||||||
\(696\) | 10.7689 | 0.408193 | ||||||||
\(697\) | 17.9536 | 0.680042 | ||||||||
\(698\) | 19.6211 | 0.742669 | ||||||||
\(699\) | 11.3232 | 0.428284 | ||||||||
\(700\) | −2.59719 | −0.0981645 | ||||||||
\(701\) | 30.7201 | 1.16028 | 0.580141 | − | 0.814516i | \(-0.302998\pi\) | ||||
0.580141 | + | 0.814516i | \(0.302998\pi\) | |||||||
\(702\) | 28.9819 | 1.09385 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.834338 | 0.0314453 | ||||||||
\(705\) | −16.6928 | −0.628689 | ||||||||
\(706\) | 1.82831 | 0.0688094 | ||||||||
\(707\) | 1.80689 | 0.0679552 | ||||||||
\(708\) | 8.26586 | 0.310650 | ||||||||
\(709\) | −24.7213 | −0.928427 | −0.464214 | − | 0.885723i | \(-0.653663\pi\) | ||||
−0.464214 | + | 0.885723i | \(0.653663\pi\) | |||||||
\(710\) | 1.13799 | 0.0427078 | ||||||||
\(711\) | −12.4960 | −0.468636 | ||||||||
\(712\) | −10.3313 | −0.387183 | ||||||||
\(713\) | −60.3779 | −2.26117 | ||||||||
\(714\) | 4.05134 | 0.151618 | ||||||||
\(715\) | 6.92824 | 0.259102 | ||||||||
\(716\) | −10.4481 | −0.390465 | ||||||||
\(717\) | −9.11955 | −0.340576 | ||||||||
\(718\) | 15.3006 | 0.571013 | ||||||||
\(719\) | −23.2396 | −0.866692 | −0.433346 | − | 0.901228i | \(-0.642667\pi\) | ||||
−0.433346 | + | 0.901228i | \(0.642667\pi\) | |||||||
\(720\) | 2.54407 | 0.0948120 | ||||||||
\(721\) | 11.8069 | 0.439712 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.7329 | 0.585114 | ||||||||
\(724\) | 3.16389 | 0.117585 | ||||||||
\(725\) | −23.9939 | −0.891112 | ||||||||
\(726\) | −12.0108 | −0.445764 | ||||||||
\(727\) | 5.33380 | 0.197820 | 0.0989099 | − | 0.995096i | \(-0.468464\pi\) | ||||
0.0989099 | + | 0.995096i | \(0.468464\pi\) | |||||||
\(728\) | −5.35699 | −0.198543 | ||||||||
\(729\) | 21.1883 | 0.784754 | ||||||||
\(730\) | −10.5256 | −0.389571 | ||||||||
\(731\) | 44.8595 | 1.65919 | ||||||||
\(732\) | −10.6820 | −0.394818 | ||||||||
\(733\) | −26.8646 | −0.992265 | −0.496132 | − | 0.868247i | \(-0.665247\pi\) | ||||
−0.496132 | + | 0.868247i | \(0.665247\pi\) | |||||||
\(734\) | 19.9011 | 0.734562 | ||||||||
\(735\) | −1.80689 | −0.0666483 | ||||||||
\(736\) | 8.74143 | 0.322213 | ||||||||
\(737\) | −0.258567 | −0.00952444 | ||||||||
\(738\) | −8.47805 | −0.312081 | ||||||||
\(739\) | 3.98943 | 0.146753 | 0.0733767 | − | 0.997304i | \(-0.476622\pi\) | ||||
0.0733767 | + | 0.997304i | \(0.476622\pi\) | |||||||
\(740\) | −1.70542 | −0.0626926 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.9071 | 0.400412 | ||||||||
\(743\) | 14.6986 | 0.539239 | 0.269620 | − | 0.962967i | \(-0.413102\pi\) | ||||
0.269620 | + | 0.962967i | \(0.413102\pi\) | |||||||
\(744\) | −8.05134 | −0.295176 | ||||||||
\(745\) | −4.49498 | −0.164683 | ||||||||
\(746\) | −36.9071 | −1.35126 | ||||||||
\(747\) | 10.4061 | 0.380738 | ||||||||
\(748\) | 2.89980 | 0.106027 | ||||||||
\(749\) | 10.5317 | 0.384821 | ||||||||
\(750\) | 13.7273 | 0.501251 | ||||||||
\(751\) | −7.56854 | −0.276180 | −0.138090 | − | 0.990420i | \(-0.544096\pi\) | ||||
−0.138090 | + | 0.990420i | \(0.544096\pi\) | |||||||
\(752\) | 9.23842 | 0.336890 | ||||||||
\(753\) | −11.1657 | −0.406899 | ||||||||
\(754\) | −49.4902 | −1.80233 | ||||||||
\(755\) | 15.9721 | 0.581282 | ||||||||
\(756\) | −5.41011 | −0.196764 | ||||||||
\(757\) | 17.6934 | 0.643076 | 0.321538 | − | 0.946897i | \(-0.395800\pi\) | ||||
0.321538 | + | 0.946897i | \(0.395800\pi\) | |||||||
\(758\) | 3.10750 | 0.112869 | ||||||||
\(759\) | 8.50153 | 0.308586 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.277917 | 0.0100745 | 0.00503724 | − | 0.999987i | \(-0.498397\pi\) | ||||
0.00503724 | + | 0.999987i | \(0.498397\pi\) | |||||||
\(762\) | −11.4122 | −0.413420 | ||||||||
\(763\) | −13.9011 | −0.503252 | ||||||||
\(764\) | −10.8283 | −0.391755 | ||||||||
\(765\) | 8.84211 | 0.319687 | ||||||||
\(766\) | 17.7200 | 0.640250 | ||||||||
\(767\) | −37.9871 | −1.37164 | ||||||||
\(768\) | 1.16566 | 0.0420622 | ||||||||
\(769\) | −46.1347 | −1.66366 | −0.831829 | − | 0.555031i | \(-0.812706\pi\) | ||||
−0.831829 | + | 0.555031i | \(0.812706\pi\) | |||||||
\(770\) | −1.29331 | −0.0466076 | ||||||||
\(771\) | 9.30884 | 0.335250 | ||||||||
\(772\) | −7.50301 | −0.270039 | ||||||||
\(773\) | 30.0451 | 1.08065 | 0.540323 | − | 0.841458i | \(-0.318302\pi\) | ||||
0.540323 | + | 0.841458i | \(0.318302\pi\) | |||||||
\(774\) | −21.1835 | −0.761426 | ||||||||
\(775\) | 17.9390 | 0.644389 | ||||||||
\(776\) | 1.49699 | 0.0537387 | ||||||||
\(777\) | 1.28246 | 0.0460081 | ||||||||
\(778\) | 25.8069 | 0.925222 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9.67952 | 0.346582 | ||||||||
\(781\) | −0.612518 | −0.0219176 | ||||||||
\(782\) | 30.3815 | 1.08644 | ||||||||
\(783\) | −49.9809 | −1.78617 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −22.4101 | −0.799851 | ||||||||
\(786\) | −17.0896 | −0.609567 | ||||||||
\(787\) | 9.54682 | 0.340308 | 0.170154 | − | 0.985418i | \(-0.445574\pi\) | ||||
0.170154 | + | 0.985418i | \(0.445574\pi\) | |||||||
\(788\) | 11.3875 | 0.405662 | ||||||||
\(789\) | −19.2898 | −0.686734 | ||||||||
\(790\) | −11.8021 | −0.419901 | ||||||||
\(791\) | −1.19311 | −0.0424220 | ||||||||
\(792\) | −1.36934 | −0.0486574 | ||||||||
\(793\) | 49.0909 | 1.74327 | ||||||||
\(794\) | 2.81292 | 0.0998268 | ||||||||
\(795\) | −19.7080 | −0.698969 | ||||||||
\(796\) | −2.90710 | −0.103039 | ||||||||
\(797\) | 32.1652 | 1.13935 | 0.569674 | − | 0.821871i | \(-0.307069\pi\) | ||||
0.569674 | + | 0.821871i | \(0.307069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.1088 | 1.13593 | ||||||||
\(800\) | −2.59719 | −0.0918245 | ||||||||
\(801\) | 16.9561 | 0.599114 | ||||||||
\(802\) | 13.7067 | 0.484000 | ||||||||
\(803\) | 5.66540 | 0.199928 | ||||||||
\(804\) | −0.361247 | −0.0127402 | ||||||||
\(805\) | −13.5501 | −0.477578 | ||||||||
\(806\) | 37.0013 | 1.30331 | ||||||||
\(807\) | −0.671154 | −0.0236257 | ||||||||
\(808\) | 1.80689 | 0.0635663 | ||||||||
\(809\) | −32.6175 | −1.14677 | −0.573386 | − | 0.819286i | \(-0.694370\pi\) | ||||
−0.573386 | + | 0.819286i | \(0.694370\pi\) | |||||||
\(810\) | 2.14327 | 0.0753068 | ||||||||
\(811\) | −10.8009 | −0.379270 | −0.189635 | − | 0.981855i | \(-0.560730\pi\) | ||||
−0.189635 | + | 0.981855i | \(0.560730\pi\) | |||||||
\(812\) | 9.23842 | 0.324205 | ||||||||
\(813\) | −4.22096 | −0.148036 | ||||||||
\(814\) | 0.917939 | 0.0321738 | ||||||||
\(815\) | 12.7278 | 0.445837 | ||||||||
\(816\) | 4.05134 | 0.141825 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −27.9237 | −0.976329 | ||||||||
\(819\) | 8.79207 | 0.307220 | ||||||||
\(820\) | −8.00730 | −0.279627 | ||||||||
\(821\) | 17.9597 | 0.626798 | 0.313399 | − | 0.949622i | \(-0.398532\pi\) | ||||
0.313399 | + | 0.949622i | \(0.398532\pi\) | |||||||
\(822\) | 18.3172 | 0.638886 | ||||||||
\(823\) | 36.4784 | 1.27156 | 0.635778 | − | 0.771872i | \(-0.280679\pi\) | ||||
0.635778 | + | 0.771872i | \(0.280679\pi\) | |||||||
\(824\) | 11.8069 | 0.411313 | ||||||||
\(825\) | −2.52591 | −0.0879409 | ||||||||
\(826\) | 7.09113 | 0.246732 | ||||||||
\(827\) | 24.6365 | 0.856694 | 0.428347 | − | 0.903614i | \(-0.359096\pi\) | ||||
0.428347 | + | 0.903614i | \(0.359096\pi\) | |||||||
\(828\) | −14.3467 | −0.498583 | ||||||||
\(829\) | 5.95091 | 0.206684 | 0.103342 | − | 0.994646i | \(-0.467046\pi\) | ||||
0.103342 | + | 0.994646i | \(0.467046\pi\) | |||||||
\(830\) | 9.82825 | 0.341144 | ||||||||
\(831\) | 35.3519 | 1.22635 | ||||||||
\(832\) | −5.35699 | −0.185720 | ||||||||
\(833\) | 3.47557 | 0.120421 | ||||||||
\(834\) | 16.6890 | 0.577894 | ||||||||
\(835\) | 18.2336 | 0.631000 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.3681 | 1.29163 | ||||||||
\(838\) | −32.5209 | −1.12342 | ||||||||
\(839\) | 1.94866 | 0.0672752 | 0.0336376 | − | 0.999434i | \(-0.489291\pi\) | ||||
0.0336376 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(840\) | −1.80689 | −0.0623438 | ||||||||
\(841\) | 56.3484 | 1.94305 | ||||||||
\(842\) | 21.1075 | 0.727412 | ||||||||
\(843\) | −3.91519 | −0.134846 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | −24.3325 | −0.837065 | ||||||||
\(846\) | −15.1624 | −0.521294 | ||||||||
\(847\) | −10.3039 | −0.354046 | ||||||||
\(848\) | 10.9071 | 0.374551 | ||||||||
\(849\) | 3.88675 | 0.133393 | ||||||||
\(850\) | −9.02671 | −0.309613 | ||||||||
\(851\) | 9.61734 | 0.329678 | ||||||||
\(852\) | −0.855755 | −0.0293177 | ||||||||
\(853\) | −9.65428 | −0.330556 | −0.165278 | − | 0.986247i | \(-0.552852\pi\) | ||||
−0.165278 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(854\) | −9.16389 | −0.313582 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.5317 | 0.359967 | ||||||||
\(857\) | −4.07276 | −0.139123 | −0.0695614 | − | 0.997578i | \(-0.522160\pi\) | ||||
−0.0695614 | + | 0.997578i | \(0.522160\pi\) | |||||||
\(858\) | −5.20998 | −0.177866 | ||||||||
\(859\) | 1.60321 | 0.0547010 | 0.0273505 | − | 0.999626i | \(-0.491293\pi\) | ||||
0.0273505 | + | 0.999626i | \(0.491293\pi\) | |||||||
\(860\) | −20.0073 | −0.682243 | ||||||||
\(861\) | 6.02142 | 0.205209 | ||||||||
\(862\) | 2.89980 | 0.0987675 | ||||||||
\(863\) | −16.0574 | −0.546601 | −0.273301 | − | 0.961929i | \(-0.588115\pi\) | ||||
−0.273301 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(864\) | −5.41011 | −0.184056 | ||||||||
\(865\) | −21.3147 | −0.724720 | ||||||||
\(866\) | −23.9952 | −0.815392 | ||||||||
\(867\) | −5.73555 | −0.194789 | ||||||||
\(868\) | −6.90710 | −0.234442 | ||||||||
\(869\) | 6.35247 | 0.215493 | ||||||||
\(870\) | −16.6928 | −0.565940 | ||||||||
\(871\) | 1.66017 | 0.0562527 | ||||||||
\(872\) | −13.9011 | −0.470750 | ||||||||
\(873\) | −2.45690 | −0.0831535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.7764 | 0.398115 | ||||||||
\(876\) | 7.91519 | 0.267429 | ||||||||
\(877\) | 0.567266 | 0.0191552 | 0.00957760 | − | 0.999954i | \(-0.496951\pi\) | ||||
0.00957760 | + | 0.999954i | \(0.496951\pi\) | |||||||
\(878\) | −38.5355 | −1.30051 | ||||||||
\(879\) | 26.6749 | 0.899722 | ||||||||
\(880\) | −1.29331 | −0.0435974 | ||||||||
\(881\) | −5.63641 | −0.189896 | −0.0949478 | − | 0.995482i | \(-0.530268\pi\) | ||||
−0.0949478 | + | 0.995482i | \(0.530268\pi\) | |||||||
\(882\) | −1.64123 | −0.0552631 | ||||||||
\(883\) | 0.276708 | 0.00931196 | 0.00465598 | − | 0.999989i | \(-0.498518\pi\) | ||||
0.00465598 | + | 0.999989i | \(0.498518\pi\) | |||||||
\(884\) | −18.6186 | −0.626211 | ||||||||
\(885\) | −12.8129 | −0.430702 | ||||||||
\(886\) | −26.6805 | −0.896350 | ||||||||
\(887\) | −5.35850 | −0.179921 | −0.0899604 | − | 0.995945i | \(-0.528674\pi\) | ||||
−0.0899604 | + | 0.995945i | \(0.528674\pi\) | |||||||
\(888\) | 1.28246 | 0.0430366 | ||||||||
\(889\) | −9.79029 | −0.328356 | ||||||||
\(890\) | 16.0146 | 0.536810 | ||||||||
\(891\) | −1.15361 | −0.0386474 | ||||||||
\(892\) | −11.8142 | −0.395568 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.38019 | 0.113050 | ||||||||
\(895\) | 16.1956 | 0.541361 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −54.5854 | −1.82255 | ||||||||
\(898\) | −28.6284 | −0.955341 | ||||||||
\(899\) | −63.8106 | −2.12820 | ||||||||
\(900\) | 4.26259 | 0.142086 | ||||||||
\(901\) | 37.9084 | 1.26291 | ||||||||
\(902\) | 4.30991 | 0.143504 | ||||||||
\(903\) | 15.0453 | 0.500677 | ||||||||
\(904\) | −1.19311 | −0.0396821 | ||||||||
\(905\) | −4.90435 | −0.163026 | ||||||||
\(906\) | −12.0108 | −0.399034 | ||||||||
\(907\) | 35.6437 | 1.18353 | 0.591765 | − | 0.806111i | \(-0.298431\pi\) | ||||
0.591765 | + | 0.806111i | \(0.298431\pi\) | |||||||
\(908\) | −17.1057 | −0.567673 | ||||||||
\(909\) | −2.96553 | −0.0983605 | ||||||||
\(910\) | 8.30388 | 0.275271 | ||||||||
\(911\) | −1.71071 | −0.0566784 | −0.0283392 | − | 0.999598i | \(-0.509022\pi\) | ||||
−0.0283392 | + | 0.999598i | \(0.509022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.29003 | −0.175074 | ||||||||
\(914\) | 7.28728 | 0.241042 | ||||||||
\(915\) | 16.5582 | 0.547396 | ||||||||
\(916\) | −23.7837 | −0.785836 | ||||||||
\(917\) | −14.6609 | −0.484145 | ||||||||
\(918\) | −18.8032 | −0.620598 | ||||||||
\(919\) | 7.46981 | 0.246406 | 0.123203 | − | 0.992381i | \(-0.460683\pi\) | ||||
0.123203 | + | 0.992381i | \(0.460683\pi\) | |||||||
\(920\) | −13.5501 | −0.446734 | ||||||||
\(921\) | −21.3161 | −0.702390 | ||||||||
\(922\) | 14.2019 | 0.467715 | ||||||||
\(923\) | 3.93277 | 0.129449 | ||||||||
\(924\) | 0.972556 | 0.0319947 | ||||||||
\(925\) | −2.85743 | −0.0939517 | ||||||||
\(926\) | 29.8308 | 0.980301 | ||||||||
\(927\) | −19.3778 | −0.636452 | ||||||||
\(928\) | 9.23842 | 0.303266 | ||||||||
\(929\) | −25.3305 | −0.831068 | −0.415534 | − | 0.909578i | \(-0.636405\pi\) | ||||
−0.415534 | + | 0.909578i | \(0.636405\pi\) | |||||||
\(930\) | 12.4804 | 0.409248 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.71399 | 0.318192 | ||||||||
\(933\) | 8.42905 | 0.275955 | ||||||||
\(934\) | 5.87965 | 0.192388 | ||||||||
\(935\) | −4.49498 | −0.147002 | ||||||||
\(936\) | 8.79207 | 0.287378 | ||||||||
\(937\) | −22.9297 | −0.749081 | −0.374541 | − | 0.927210i | \(-0.622200\pi\) | ||||
−0.374541 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(938\) | −0.309907 | −0.0101188 | ||||||||
\(939\) | 7.58882 | 0.247652 | ||||||||
\(940\) | −14.3205 | −0.467083 | ||||||||
\(941\) | −14.1626 | −0.461688 | −0.230844 | − | 0.972991i | \(-0.574149\pi\) | ||||
−0.230844 | + | 0.972991i | \(0.574149\pi\) | |||||||
\(942\) | 16.8522 | 0.549075 | ||||||||
\(943\) | 45.1553 | 1.47046 | ||||||||
\(944\) | 7.09113 | 0.230797 | ||||||||
\(945\) | 8.38621 | 0.272804 | ||||||||
\(946\) | 10.7689 | 0.350126 | ||||||||
\(947\) | 36.7165 | 1.19313 | 0.596563 | − | 0.802566i | \(-0.296532\pi\) | ||||
0.596563 | + | 0.802566i | \(0.296532\pi\) | |||||||
\(948\) | 8.87510 | 0.288250 | ||||||||
\(949\) | −36.3756 | −1.18080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.3242 | −1.11304 | ||||||||
\(952\) | 3.47557 | 0.112644 | ||||||||
\(953\) | −22.6679 | −0.734285 | −0.367142 | − | 0.930165i | \(-0.619664\pi\) | ||||
−0.367142 | + | 0.930165i | \(0.619664\pi\) | |||||||
\(954\) | −17.9011 | −0.579568 | ||||||||
\(955\) | 16.7850 | 0.543149 | ||||||||
\(956\) | −7.82349 | −0.253030 | ||||||||
\(957\) | 8.98488 | 0.290440 | ||||||||
\(958\) | 16.8739 | 0.545171 | ||||||||
\(959\) | 15.7140 | 0.507431 | ||||||||
\(960\) | −1.80689 | −0.0583172 | ||||||||
\(961\) | 16.7080 | 0.538967 | ||||||||
\(962\) | −5.89377 | −0.190023 | ||||||||
\(963\) | −17.2850 | −0.557001 | ||||||||
\(964\) | 13.4970 | 0.434709 | ||||||||
\(965\) | 11.6304 | 0.374397 | ||||||||
\(966\) | 10.1896 | 0.327844 | ||||||||
\(967\) | −18.7379 | −0.602570 | −0.301285 | − | 0.953534i | \(-0.597416\pi\) | ||||
−0.301285 | + | 0.953534i | \(0.597416\pi\) | |||||||
\(968\) | −10.3039 | −0.331179 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.32048 | −0.0745061 | ||||||||
\(971\) | 41.0496 | 1.31735 | 0.658673 | − | 0.752430i | \(-0.271118\pi\) | ||||
0.658673 | + | 0.752430i | \(0.271118\pi\) | |||||||
\(972\) | 14.6186 | 0.468892 | ||||||||
\(973\) | 14.3172 | 0.458988 | ||||||||
\(974\) | −17.1002 | −0.547926 | ||||||||
\(975\) | 16.2180 | 0.519392 | ||||||||
\(976\) | −9.16389 | −0.293329 | ||||||||
\(977\) | −58.8681 | −1.88336 | −0.941678 | − | 0.336515i | \(-0.890752\pi\) | ||||
−0.941678 | + | 0.336515i | \(0.890752\pi\) | |||||||
\(978\) | −9.57122 | −0.306054 | ||||||||
\(979\) | −8.61981 | −0.275490 | ||||||||
\(980\) | −1.55010 | −0.0495161 | ||||||||
\(981\) | 22.8149 | 0.728423 | ||||||||
\(982\) | −5.04886 | −0.161116 | ||||||||
\(983\) | 4.33132 | 0.138148 | 0.0690739 | − | 0.997612i | \(-0.477996\pi\) | ||||
0.0690739 | + | 0.997612i | \(0.477996\pi\) | |||||||
\(984\) | 6.02142 | 0.191956 | ||||||||
\(985\) | −17.6517 | −0.562431 | ||||||||
\(986\) | 32.1088 | 1.02255 | ||||||||
\(987\) | 10.7689 | 0.342777 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 112.827 | 3.58767 | ||||||||
\(990\) | 2.12262 | 0.0674612 | ||||||||
\(991\) | −43.5388 | −1.38305 | −0.691527 | − | 0.722351i | \(-0.743062\pi\) | ||||
−0.691527 | + | 0.722351i | \(0.743062\pi\) | |||||||
\(992\) | −6.90710 | −0.219300 | ||||||||
\(993\) | −24.2430 | −0.769327 | ||||||||
\(994\) | −0.734136 | −0.0232854 | ||||||||
\(995\) | 4.50629 | 0.142859 | ||||||||
\(996\) | −7.39076 | −0.234185 | ||||||||
\(997\) | −34.3389 | −1.08752 | −0.543762 | − | 0.839239i | \(-0.683001\pi\) | ||||
−0.543762 | + | 0.839239i | \(0.683001\pi\) | |||||||
\(998\) | −11.1108 | −0.351705 | ||||||||
\(999\) | −5.95221 | −0.188320 |
(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 | 5054.2.a.x.1.3 | 4 | ||
19.8 | odd | 6 | 266.2.f.d.197.3 | ✓ | 8 | ||
19.12 | odd | 6 | 266.2.f.d.239.3 | yes | 8 | ||
19.18 | odd | 2 | 5054.2.a.w.1.2 | 4 | |||
57.8 | even | 6 | 2394.2.o.v.1261.2 | 8 | |||
57.50 | even | 6 | 2394.2.o.v.505.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.f.d.197.3 | ✓ | 8 | 19.8 | odd | 6 | ||
266.2.f.d.239.3 | yes | 8 | 19.12 | odd | 6 | ||
2394.2.o.v.505.2 | 8 | 57.50 | even | 6 | |||
2394.2.o.v.1261.2 | 8 | 57.8 | even | 6 | |||
5054.2.a.w.1.2 | 4 | 19.18 | odd | 2 | |||
5054.2.a.x.1.3 | 4 | 1.1 | even | 1 | trivial |