Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.22231\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22231 | −0.864306 | −0.432153 | − | 0.901800i | \(-0.642246\pi\) | ||||
−0.432153 | + | 0.901800i | \(0.642246\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.505952 | −0.252976 | ||||||||
\(5\) | −0.403117 | −0.180280 | −0.0901398 | − | 0.995929i | \(-0.528731\pi\) | ||||
−0.0901398 | + | 0.995929i | \(0.528731\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.45690 | −1.68455 | −0.842276 | − | 0.539047i | \(-0.818785\pi\) | ||||
−0.842276 | + | 0.539047i | \(0.818785\pi\) | |||||||
\(8\) | 3.06306 | 1.08295 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.492736 | 0.155817 | ||||||||
\(11\) | 2.17391 | 0.655460 | 0.327730 | − | 0.944772i | \(-0.393716\pi\) | ||||
0.327730 | + | 0.944772i | \(0.393716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.85396 | 1.62360 | 0.811798 | − | 0.583939i | \(-0.198489\pi\) | ||||
0.811798 | + | 0.583939i | \(0.198489\pi\) | |||||||
\(14\) | 5.44773 | 1.45597 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.73211 | −0.683027 | ||||||||
\(17\) | −7.98275 | −1.93610 | −0.968051 | − | 0.250753i | \(-0.919322\pi\) | ||||
−0.968051 | + | 0.250753i | \(0.919322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00460 | 0.459888 | 0.229944 | − | 0.973204i | \(-0.426146\pi\) | ||||
0.229944 | + | 0.973204i | \(0.426146\pi\) | |||||||
\(20\) | 0.203958 | 0.0456064 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.65720 | −0.566517 | ||||||||
\(23\) | −0.679568 | −0.141700 | −0.0708499 | − | 0.997487i | \(-0.522571\pi\) | ||||
−0.0708499 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.83750 | −0.967499 | ||||||||
\(26\) | −7.15536 | −1.40328 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.25498 | 0.426151 | ||||||||
\(29\) | 5.44529 | 1.01116 | 0.505582 | − | 0.862778i | \(-0.331278\pi\) | ||||
0.505582 | + | 0.862778i | \(0.331278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.595692 | −0.106989 | −0.0534947 | − | 0.998568i | \(-0.517036\pi\) | ||||
−0.0534947 | + | 0.998568i | \(0.517036\pi\) | |||||||
\(32\) | −2.78662 | −0.492610 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.75742 | 1.67338 | ||||||||
\(35\) | 1.79666 | 0.303690 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.86330 | 0.963921 | 0.481960 | − | 0.876193i | \(-0.339925\pi\) | ||||
0.481960 | + | 0.876193i | \(0.339925\pi\) | |||||||
\(38\) | −2.45025 | −0.397483 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.23477 | −0.195235 | ||||||||
\(41\) | −0.396926 | −0.0619894 | −0.0309947 | − | 0.999520i | \(-0.509867\pi\) | ||||
−0.0309947 | + | 0.999520i | \(0.509867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.0393 | 1.83598 | 0.917988 | − | 0.396609i | \(-0.129813\pi\) | ||||
0.917988 | + | 0.396609i | \(0.129813\pi\) | |||||||
\(44\) | −1.09990 | −0.165815 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.830645 | 0.122472 | ||||||||
\(47\) | 6.38497 | 0.931344 | 0.465672 | − | 0.884957i | \(-0.345813\pi\) | ||||
0.465672 | + | 0.884957i | \(0.345813\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.8640 | 1.83771 | ||||||||
\(50\) | 5.91293 | 0.836215 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.96182 | −0.410730 | ||||||||
\(53\) | −9.69118 | −1.33119 | −0.665593 | − | 0.746315i | \(-0.731821\pi\) | ||||
−0.665593 | + | 0.746315i | \(0.731821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.876342 | −0.118166 | ||||||||
\(56\) | −13.6518 | −1.82429 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.65585 | −0.873955 | ||||||||
\(59\) | −2.87181 | −0.373878 | −0.186939 | − | 0.982372i | \(-0.559857\pi\) | ||||
−0.186939 | + | 0.982372i | \(0.559857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.31211 | −0.296036 | −0.148018 | − | 0.988985i | \(-0.547289\pi\) | ||||
−0.148018 | + | 0.988985i | \(0.547289\pi\) | |||||||
\(62\) | 0.728121 | 0.0924715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.87034 | 1.10879 | ||||||||
\(65\) | −2.35983 | −0.292701 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4712 | 1.40143 | 0.700715 | − | 0.713442i | \(-0.252865\pi\) | ||||
0.700715 | + | 0.713442i | \(0.252865\pi\) | |||||||
\(68\) | 4.03889 | 0.489787 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.19608 | −0.262481 | ||||||||
\(71\) | −11.4938 | −1.36406 | −0.682030 | − | 0.731324i | \(-0.738903\pi\) | ||||
−0.682030 | + | 0.731324i | \(0.738903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.74678 | 0.906692 | 0.453346 | − | 0.891335i | \(-0.350230\pi\) | ||||
0.453346 | + | 0.891335i | \(0.350230\pi\) | |||||||
\(74\) | −7.16679 | −0.833122 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.01423 | −0.116340 | ||||||||
\(77\) | −9.68892 | −1.10416 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2836 | −1.60703 | −0.803514 | − | 0.595285i | \(-0.797039\pi\) | ||||
−0.803514 | + | 0.595285i | \(0.797039\pi\) | |||||||
\(80\) | 1.10136 | 0.123136 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.485167 | 0.0535778 | ||||||||
\(83\) | −6.99235 | −0.767510 | −0.383755 | − | 0.923435i | \(-0.625369\pi\) | ||||
−0.383755 | + | 0.923435i | \(0.625369\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.21799 | 0.349040 | ||||||||
\(86\) | −14.7158 | −1.58684 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.65882 | 0.709833 | ||||||||
\(89\) | −16.1528 | −1.71219 | −0.856096 | − | 0.516818i | \(-0.827117\pi\) | ||||
−0.856096 | + | 0.516818i | \(0.827117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.0905 | −2.73503 | ||||||||
\(92\) | 0.343829 | 0.0358466 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.80444 | −0.804966 | ||||||||
\(95\) | −0.808091 | −0.0829084 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.60226 | −0.873427 | −0.436714 | − | 0.899601i | \(-0.643858\pi\) | ||||
−0.436714 | + | 0.899601i | \(0.643858\pi\) | |||||||
\(98\) | −15.7238 | −1.58835 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.44754 | 0.244754 | ||||||||
\(101\) | −11.0688 | −1.10139 | −0.550693 | − | 0.834708i | \(-0.685636\pi\) | ||||
−0.550693 | + | 0.834708i | \(0.685636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.71739 | −0.563351 | −0.281675 | − | 0.959510i | \(-0.590890\pi\) | ||||
−0.281675 | + | 0.959510i | \(0.590890\pi\) | |||||||
\(104\) | 17.9310 | 1.75828 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.8456 | 1.15055 | ||||||||
\(107\) | −13.9647 | −1.35002 | −0.675011 | − | 0.737808i | \(-0.735861\pi\) | ||||
−0.675011 | + | 0.737808i | \(0.735861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.04998 | −0.675265 | −0.337633 | − | 0.941278i | \(-0.609626\pi\) | ||||
−0.337633 | + | 0.941278i | \(0.609626\pi\) | |||||||
\(110\) | 1.07116 | 0.102132 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.1767 | 1.15059 | ||||||||
\(113\) | 17.5817 | 1.65394 | 0.826972 | − | 0.562243i | \(-0.190062\pi\) | ||||
0.826972 | + | 0.562243i | \(0.190062\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.273946 | 0.0255456 | ||||||||
\(116\) | −2.75505 | −0.255800 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.51025 | 0.323144 | ||||||||
\(119\) | 35.5784 | 3.26146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.27410 | −0.570373 | ||||||||
\(122\) | 2.82612 | 0.255865 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.301391 | 0.0270657 | ||||||||
\(125\) | 3.96567 | 0.354700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0188127 | 0.00166936 | 0.000834680 | − | 1.00000i | \(-0.499734\pi\) | ||||
0.000834680 | 1.00000i | \(0.499734\pi\) | ||||||||
\(128\) | −5.26909 | −0.465726 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.88445 | 0.252983 | ||||||||
\(131\) | −5.31238 | −0.464145 | −0.232072 | − | 0.972699i | \(-0.574551\pi\) | ||||
−0.232072 | + | 0.972699i | \(0.574551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.93433 | −0.774704 | ||||||||
\(134\) | −14.0214 | −1.21126 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.4516 | −2.09671 | ||||||||
\(137\) | −5.05773 | −0.432111 | −0.216055 | − | 0.976381i | \(-0.569319\pi\) | ||||
−0.216055 | + | 0.976381i | \(0.569319\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.89513 | −0.839294 | −0.419647 | − | 0.907687i | \(-0.637846\pi\) | ||||
−0.419647 | + | 0.907687i | \(0.637846\pi\) | |||||||
\(140\) | −0.909021 | −0.0768263 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.0490 | 1.17897 | ||||||||
\(143\) | 12.7260 | 1.06420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.19509 | −0.182292 | ||||||||
\(146\) | −9.46899 | −0.783659 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.96655 | −0.243849 | ||||||||
\(149\) | −4.84892 | −0.397239 | −0.198620 | − | 0.980077i | \(-0.563646\pi\) | ||||
−0.198620 | + | 0.980077i | \(0.563646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.196098 | 0.0159583 | 0.00797913 | − | 0.999968i | \(-0.497460\pi\) | ||||
0.00797913 | + | 0.999968i | \(0.497460\pi\) | |||||||
\(152\) | 6.14021 | 0.498037 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.8429 | 0.954328 | ||||||||
\(155\) | 0.240134 | 0.0192880 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.28786 | −0.422018 | −0.211009 | − | 0.977484i | \(-0.567675\pi\) | ||||
−0.211009 | + | 0.977484i | \(0.567675\pi\) | |||||||
\(158\) | 17.4590 | 1.38896 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.12334 | 0.0888075 | ||||||||
\(161\) | 3.02877 | 0.238701 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1799 | −1.03233 | −0.516165 | − | 0.856489i | \(-0.672641\pi\) | ||||
−0.516165 | + | 0.856489i | \(0.672641\pi\) | |||||||
\(164\) | 0.200825 | 0.0156818 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.54684 | 0.663364 | ||||||||
\(167\) | 24.2342 | 1.87530 | 0.937651 | − | 0.347579i | \(-0.112996\pi\) | ||||
0.937651 | + | 0.347579i | \(0.112996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.2688 | 1.63606 | ||||||||
\(170\) | −3.93339 | −0.301677 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.09130 | −0.464458 | ||||||||
\(173\) | −23.9278 | −1.81920 | −0.909599 | − | 0.415488i | \(-0.863611\pi\) | ||||
−0.909599 | + | 0.415488i | \(0.863611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.5603 | 1.62980 | ||||||||
\(176\) | −5.93937 | −0.447697 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.7437 | 1.47986 | ||||||||
\(179\) | −8.14397 | −0.608709 | −0.304354 | − | 0.952559i | \(-0.598441\pi\) | ||||
−0.304354 | + | 0.952559i | \(0.598441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0482 | −1.63883 | −0.819414 | − | 0.573203i | \(-0.805701\pi\) | ||||
−0.819414 | + | 0.573203i | \(0.805701\pi\) | |||||||
\(182\) | 31.8908 | 2.36390 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.08156 | −0.153454 | ||||||||
\(185\) | −2.36360 | −0.173775 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3538 | −1.26904 | ||||||||
\(188\) | −3.23049 | −0.235608 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.987739 | 0.0716582 | ||||||||
\(191\) | 23.0122 | 1.66511 | 0.832553 | − | 0.553945i | \(-0.186878\pi\) | ||||
0.832553 | + | 0.553945i | \(0.186878\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.80810 | 0.562039 | 0.281020 | − | 0.959702i | \(-0.409327\pi\) | ||||
0.281020 | + | 0.959702i | \(0.409327\pi\) | |||||||
\(194\) | 10.5147 | 0.754908 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50856 | −0.464897 | ||||||||
\(197\) | −6.78508 | −0.483417 | −0.241708 | − | 0.970349i | \(-0.577708\pi\) | ||||
−0.241708 | + | 0.970349i | \(0.577708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.79051 | −0.694031 | −0.347015 | − | 0.937859i | \(-0.612805\pi\) | ||||
−0.347015 | + | 0.937859i | \(0.612805\pi\) | |||||||
\(200\) | −14.8175 | −1.04776 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.5295 | 0.951934 | ||||||||
\(203\) | −24.2691 | −1.70336 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.160008 | 0.0111754 | ||||||||
\(206\) | 6.98843 | 0.486907 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.9936 | −1.10896 | ||||||||
\(209\) | 4.35783 | 0.301438 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.8919 | −0.818673 | −0.409337 | − | 0.912383i | \(-0.634240\pi\) | ||||
−0.409337 | + | 0.912383i | \(0.634240\pi\) | |||||||
\(212\) | 4.90327 | 0.336758 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.0693 | 1.16683 | ||||||||
\(215\) | −4.85325 | −0.330989 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.65494 | 0.180229 | ||||||||
\(218\) | 8.61727 | 0.583635 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.443387 | 0.0298931 | ||||||||
\(221\) | −46.7307 | −3.14345 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0443 | 1.40923 | 0.704614 | − | 0.709591i | \(-0.251120\pi\) | ||||
0.704614 | + | 0.709591i | \(0.251120\pi\) | |||||||
\(224\) | 12.4197 | 0.829827 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.4903 | −1.42951 | ||||||||
\(227\) | 16.5049 | 1.09547 | 0.547734 | − | 0.836653i | \(-0.315491\pi\) | ||||
0.547734 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.18227 | −0.342454 | −0.171227 | − | 0.985232i | \(-0.554773\pi\) | ||||
−0.171227 | + | 0.985232i | \(0.554773\pi\) | |||||||
\(230\) | −0.334848 | −0.0220792 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.6792 | 1.09505 | ||||||||
\(233\) | −11.8271 | −0.774817 | −0.387409 | − | 0.921908i | \(-0.626630\pi\) | ||||
−0.387409 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.57389 | −0.167902 | ||||||||
\(236\) | 1.45300 | 0.0945820 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −43.4879 | −2.81890 | ||||||||
\(239\) | −1.00000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1921 | −0.978607 | −0.489304 | − | 0.872113i | \(-0.662749\pi\) | ||||
−0.489304 | + | 0.872113i | \(0.662749\pi\) | |||||||
\(242\) | 7.66891 | 0.492976 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.16982 | 0.0748899 | ||||||||
\(245\) | −5.18570 | −0.331302 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.7349 | 0.746671 | ||||||||
\(248\) | −1.82464 | −0.115865 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.84728 | −0.306569 | ||||||||
\(251\) | 7.88110 | 0.497451 | 0.248725 | − | 0.968574i | \(-0.419988\pi\) | ||||
0.248725 | + | 0.968574i | \(0.419988\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47732 | −0.0928785 | ||||||||
\(254\) | −0.0229950 | −0.00144284 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.3002 | −0.706263 | ||||||||
\(257\) | −28.3840 | −1.77055 | −0.885273 | − | 0.465072i | \(-0.846028\pi\) | ||||
−0.885273 | + | 0.465072i | \(0.846028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.1322 | −1.62377 | ||||||||
\(260\) | 1.19396 | 0.0740463 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.49339 | 0.401163 | ||||||||
\(263\) | −16.8514 | −1.03910 | −0.519552 | − | 0.854439i | \(-0.673901\pi\) | ||||
−0.519552 | + | 0.854439i | \(0.673901\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.90668 | 0.239986 | ||||||||
\(266\) | 10.9205 | 0.669581 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.80387 | −0.354528 | ||||||||
\(269\) | 7.79527 | 0.475286 | 0.237643 | − | 0.971353i | \(-0.423625\pi\) | ||||
0.237643 | + | 0.971353i | \(0.423625\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.75917 | 0.106862 | 0.0534309 | − | 0.998572i | \(-0.482984\pi\) | ||||
0.0534309 | + | 0.998572i | \(0.482984\pi\) | |||||||
\(272\) | 21.8098 | 1.32241 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.18212 | 0.373476 | ||||||||
\(275\) | −10.5163 | −0.634157 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0737 | 1.68679 | 0.843394 | − | 0.537296i | \(-0.180554\pi\) | ||||
0.843394 | + | 0.537296i | \(0.180554\pi\) | |||||||
\(278\) | 12.0949 | 0.725407 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.50326 | 0.328883 | ||||||||
\(281\) | −16.8365 | −1.00438 | −0.502190 | − | 0.864758i | \(-0.667472\pi\) | ||||
−0.502190 | + | 0.864758i | \(0.667472\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.3487 | 0.852941 | 0.426470 | − | 0.904502i | \(-0.359757\pi\) | ||||
0.426470 | + | 0.904502i | \(0.359757\pi\) | |||||||
\(284\) | 5.81530 | 0.345075 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.5551 | −0.919795 | ||||||||
\(287\) | 1.76906 | 0.104424 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 46.7244 | 2.74849 | ||||||||
\(290\) | 2.68309 | 0.157556 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.91950 | −0.229371 | ||||||||
\(293\) | −13.4805 | −0.787538 | −0.393769 | − | 0.919209i | \(-0.628829\pi\) | ||||
−0.393769 | + | 0.919209i | \(0.628829\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.15768 | 0.0674025 | ||||||||
\(296\) | 17.9596 | 1.04388 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.92690 | 0.343336 | ||||||||
\(299\) | −3.97816 | −0.230063 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.6580 | −3.09280 | ||||||||
\(302\) | −0.239693 | −0.0137928 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.47680 | −0.314116 | ||||||||
\(305\) | 0.932052 | 0.0533692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.9529 | −0.853408 | −0.426704 | − | 0.904391i | \(-0.640325\pi\) | ||||
−0.426704 | + | 0.904391i | \(0.640325\pi\) | |||||||
\(308\) | 4.90213 | 0.279325 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.293518 | −0.0166707 | ||||||||
\(311\) | 11.1362 | 0.631478 | 0.315739 | − | 0.948846i | \(-0.397748\pi\) | ||||
0.315739 | + | 0.948846i | \(0.397748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.43716 | 0.363850 | 0.181925 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181925 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(314\) | 6.46342 | 0.364752 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.22681 | 0.406540 | ||||||||
\(317\) | −16.0732 | −0.902763 | −0.451382 | − | 0.892331i | \(-0.649069\pi\) | ||||
−0.451382 | + | 0.892331i | \(0.649069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.8376 | 0.662778 | ||||||||
\(320\) | −3.57579 | −0.199893 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.70211 | −0.206310 | ||||||||
\(323\) | −16.0023 | −0.890390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.3185 | −1.57083 | ||||||||
\(326\) | 16.1100 | 0.892248 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.21581 | −0.0671317 | ||||||||
\(329\) | −28.4572 | −1.56890 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3812 | 0.625567 | 0.312784 | − | 0.949824i | \(-0.398739\pi\) | ||||
0.312784 | + | 0.949824i | \(0.398739\pi\) | |||||||
\(332\) | 3.53779 | 0.194162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −29.6218 | −1.62083 | ||||||||
\(335\) | −4.62424 | −0.252649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.74602 | 0.367479 | 0.183740 | − | 0.982975i | \(-0.441180\pi\) | ||||
0.183740 | + | 0.982975i | \(0.441180\pi\) | |||||||
\(338\) | −25.9971 | −1.41406 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.62815 | −0.0882986 | ||||||||
\(341\) | −1.29498 | −0.0701272 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26.1353 | −1.41117 | ||||||||
\(344\) | 36.8770 | 1.98828 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.2473 | 1.57234 | ||||||||
\(347\) | 6.94503 | 0.372829 | 0.186414 | − | 0.982471i | \(-0.440313\pi\) | ||||
0.186414 | + | 0.982471i | \(0.440313\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7152 | 0.841217 | 0.420609 | − | 0.907242i | \(-0.361817\pi\) | ||||
0.420609 | + | 0.907242i | \(0.361817\pi\) | |||||||
\(350\) | −26.3534 | −1.40865 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.05787 | −0.322886 | ||||||||
\(353\) | 11.7091 | 0.623215 | 0.311607 | − | 0.950211i | \(-0.399133\pi\) | ||||
0.311607 | + | 0.950211i | \(0.399133\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.63334 | 0.245912 | ||||||||
\(356\) | 8.17253 | 0.433143 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.95448 | 0.526110 | ||||||||
\(359\) | −20.0346 | −1.05738 | −0.528692 | − | 0.848814i | \(-0.677317\pi\) | ||||
−0.528692 | + | 0.848814i | \(0.677317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9816 | −0.788503 | ||||||||
\(362\) | 26.9497 | 1.41645 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.2005 | 0.691897 | ||||||||
\(365\) | −3.12286 | −0.163458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.9033 | −1.09114 | −0.545572 | − | 0.838064i | \(-0.683688\pi\) | ||||
−0.545572 | + | 0.838064i | \(0.683688\pi\) | |||||||
\(368\) | 1.85666 | 0.0967848 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.88906 | 0.150195 | ||||||||
\(371\) | 43.1927 | 2.24245 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.89285 | 0.149786 | 0.0748930 | − | 0.997192i | \(-0.476138\pi\) | ||||
0.0748930 | + | 0.997192i | \(0.476138\pi\) | |||||||
\(374\) | 21.2118 | 1.09684 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.5575 | 1.00860 | ||||||||
\(377\) | 31.8765 | 1.64172 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5553 | 1.20995 | 0.604977 | − | 0.796243i | \(-0.293182\pi\) | ||||
0.604977 | + | 0.796243i | \(0.293182\pi\) | |||||||
\(380\) | 0.408855 | 0.0209738 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −28.1281 | −1.43916 | ||||||||
\(383\) | −8.52161 | −0.435434 | −0.217717 | − | 0.976012i | \(-0.569861\pi\) | ||||
−0.217717 | + | 0.976012i | \(0.569861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.90577 | 0.199057 | ||||||||
\(386\) | −9.54394 | −0.485774 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.35233 | 0.220956 | ||||||||
\(389\) | 20.0809 | 1.01814 | 0.509072 | − | 0.860724i | \(-0.329989\pi\) | ||||
0.509072 | + | 0.860724i | \(0.329989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.42483 | 0.274345 | ||||||||
\(392\) | 39.4032 | 1.99016 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.29349 | 0.417820 | ||||||||
\(395\) | 5.75796 | 0.289714 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3899 | 1.27428 | 0.637141 | − | 0.770748i | \(-0.280117\pi\) | ||||
0.637141 | + | 0.770748i | \(0.280117\pi\) | |||||||
\(398\) | 11.9671 | 0.599855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2166 | 0.660828 | ||||||||
\(401\) | 1.99676 | 0.0997136 | 0.0498568 | − | 0.998756i | \(-0.484124\pi\) | ||||
0.0498568 | + | 0.998756i | \(0.484124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.48715 | −0.173707 | ||||||||
\(404\) | 5.60027 | 0.278624 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29.6645 | 1.47222 | ||||||||
\(407\) | 12.7463 | 0.631811 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.0181 | −1.13817 | −0.569085 | − | 0.822279i | \(-0.692702\pi\) | ||||
−0.569085 | + | 0.822279i | \(0.692702\pi\) | |||||||
\(410\) | −0.195579 | −0.00965898 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.89272 | 0.142514 | ||||||||
\(413\) | 12.7994 | 0.629816 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.81874 | 0.138366 | ||||||||
\(416\) | −16.3128 | −0.799799 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.32664 | −0.260534 | ||||||||
\(419\) | 3.68635 | 0.180090 | 0.0900450 | − | 0.995938i | \(-0.471299\pi\) | ||||
0.0900450 | + | 0.995938i | \(0.471299\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3486 | 0.942992 | 0.471496 | − | 0.881868i | \(-0.343714\pi\) | ||||
0.471496 | + | 0.881868i | \(0.343714\pi\) | |||||||
\(422\) | 14.5356 | 0.707584 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.6846 | −1.44161 | ||||||||
\(425\) | 38.6165 | 1.87318 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3049 | 0.498687 | ||||||||
\(428\) | 7.06549 | 0.341523 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.93219 | 0.286076 | ||||||||
\(431\) | 10.1280 | 0.487848 | 0.243924 | − | 0.969794i | \(-0.421565\pi\) | ||||
0.243924 | + | 0.969794i | \(0.421565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.6573 | −1.66552 | −0.832761 | − | 0.553632i | \(-0.813241\pi\) | ||||
−0.832761 | + | 0.553632i | \(0.813241\pi\) | |||||||
\(434\) | −3.24517 | −0.155773 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.56695 | 0.170826 | ||||||||
\(437\) | −1.36227 | −0.0651660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.02301 | 0.144280 | 0.0721402 | − | 0.997395i | \(-0.477017\pi\) | ||||
0.0721402 | + | 0.997395i | \(0.477017\pi\) | |||||||
\(440\) | −2.68429 | −0.127968 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 57.1195 | 2.71690 | ||||||||
\(443\) | 23.1069 | 1.09784 | 0.548922 | − | 0.835874i | \(-0.315038\pi\) | ||||
0.548922 | + | 0.835874i | \(0.315038\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.51147 | 0.308673 | ||||||||
\(446\) | −25.7227 | −1.21800 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −39.5343 | −1.86782 | ||||||||
\(449\) | −13.0483 | −0.615787 | −0.307894 | − | 0.951421i | \(-0.599624\pi\) | ||||
−0.307894 | + | 0.951421i | \(0.599624\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.862882 | −0.0406315 | ||||||||
\(452\) | −8.89548 | −0.418408 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.1741 | −0.946819 | ||||||||
\(455\) | 10.5175 | 0.493070 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9529 | −1.07369 | −0.536846 | − | 0.843680i | \(-0.680384\pi\) | ||||
−0.536846 | + | 0.843680i | \(0.680384\pi\) | |||||||
\(458\) | 6.33436 | 0.295985 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.138603 | −0.00646242 | ||||||||
\(461\) | −29.2496 | −1.36229 | −0.681145 | − | 0.732148i | \(-0.738518\pi\) | ||||
−0.681145 | + | 0.732148i | \(0.738518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.209955 | −0.00975742 | −0.00487871 | − | 0.999988i | \(-0.501553\pi\) | ||||
−0.00487871 | + | 0.999988i | \(0.501553\pi\) | |||||||
\(464\) | −14.8771 | −0.690653 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.4564 | 0.669679 | ||||||||
\(467\) | −25.6201 | −1.18556 | −0.592778 | − | 0.805366i | \(-0.701969\pi\) | ||||
−0.592778 | + | 0.805366i | \(0.701969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −51.1260 | −2.36078 | ||||||||
\(470\) | 3.14610 | 0.145119 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.79651 | −0.404892 | ||||||||
\(473\) | 26.1724 | 1.20341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.69726 | −0.444941 | ||||||||
\(476\) | −18.0009 | −0.825072 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.22231 | 0.0559073 | ||||||||
\(479\) | 31.5384 | 1.44103 | 0.720513 | − | 0.693441i | \(-0.243906\pi\) | ||||
0.720513 | + | 0.693441i | \(0.243906\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.3235 | 1.56502 | ||||||||
\(482\) | 18.5695 | 0.845816 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.17439 | 0.144291 | ||||||||
\(485\) | 3.46772 | 0.157461 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.2957 | −0.602486 | −0.301243 | − | 0.953547i | \(-0.597402\pi\) | ||||
−0.301243 | + | 0.953547i | \(0.597402\pi\) | |||||||
\(488\) | −7.08213 | −0.320593 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.33855 | 0.286346 | ||||||||
\(491\) | −13.8843 | −0.626588 | −0.313294 | − | 0.949656i | \(-0.601432\pi\) | ||||
−0.313294 | + | 0.949656i | \(0.601432\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.4684 | −1.95772 | ||||||||
\(494\) | −14.3437 | −0.645352 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.62749 | 0.0730767 | ||||||||
\(497\) | 51.2267 | 2.29783 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.25368 | 0.324719 | 0.162360 | − | 0.986732i | \(-0.448090\pi\) | ||||
0.162360 | + | 0.986732i | \(0.448090\pi\) | |||||||
\(500\) | −2.00644 | −0.0897305 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.63317 | −0.429949 | ||||||||
\(503\) | −6.18887 | −0.275948 | −0.137974 | − | 0.990436i | \(-0.544059\pi\) | ||||
−0.137974 | + | 0.990436i | \(0.544059\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.46202 | 0.198557 | ||||||||
\(506\) | 1.80575 | 0.0802754 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.00951833 | −0.000422308 0 | ||||||||
\(509\) | −9.55970 | −0.423726 | −0.211863 | − | 0.977299i | \(-0.567953\pi\) | ||||
−0.211863 | + | 0.977299i | \(0.567953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.5267 | −1.52737 | ||||||||
\(512\) | 24.3506 | 1.07615 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.6941 | 1.53029 | ||||||||
\(515\) | 2.30478 | 0.101561 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8804 | 0.610458 | ||||||||
\(518\) | 31.9417 | 1.40344 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.22830 | −0.316982 | ||||||||
\(521\) | −38.5824 | −1.69033 | −0.845163 | − | 0.534509i | \(-0.820497\pi\) | ||||
−0.845163 | + | 0.534509i | \(0.820497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.4407 | 1.06872 | 0.534359 | − | 0.845258i | \(-0.320553\pi\) | ||||
0.534359 | + | 0.845258i | \(0.320553\pi\) | |||||||
\(524\) | 2.68781 | 0.117417 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5977 | 0.898104 | ||||||||
\(527\) | 4.75526 | 0.207142 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5382 | −0.979921 | ||||||||
\(530\) | −4.77519 | −0.207421 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.52034 | 0.195982 | ||||||||
\(533\) | −2.32359 | −0.100646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.62943 | 0.243381 | ||||||||
\(536\) | 35.1369 | 1.51768 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.52825 | −0.410792 | ||||||||
\(539\) | 27.9652 | 1.20455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.78761 | 0.334815 | 0.167408 | − | 0.985888i | \(-0.446460\pi\) | ||||
0.167408 | + | 0.985888i | \(0.446460\pi\) | |||||||
\(542\) | −2.15025 | −0.0923612 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.2449 | 0.953743 | ||||||||
\(545\) | 2.84197 | 0.121737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.826426 | 0.0353354 | 0.0176677 | − | 0.999844i | \(-0.494376\pi\) | ||||
0.0176677 | + | 0.999844i | \(0.494376\pi\) | |||||||
\(548\) | 2.55897 | 0.109314 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.8542 | 0.548105 | ||||||||
\(551\) | 10.9156 | 0.465022 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 63.6606 | 2.70712 | ||||||||
\(554\) | −34.3149 | −1.45790 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.00646 | 0.212321 | ||||||||
\(557\) | −27.4842 | −1.16454 | −0.582272 | − | 0.812994i | \(-0.697836\pi\) | ||||
−0.582272 | + | 0.812994i | \(0.697836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 70.4775 | 2.98088 | ||||||||
\(560\) | −4.90866 | −0.207429 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.5794 | 0.868090 | ||||||||
\(563\) | −9.93084 | −0.418535 | −0.209267 | − | 0.977858i | \(-0.567108\pi\) | ||||
−0.209267 | + | 0.977858i | \(0.567108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.08748 | −0.298172 | ||||||||
\(566\) | −17.5386 | −0.737201 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.2061 | −1.47722 | ||||||||
\(569\) | −35.7909 | −1.50043 | −0.750216 | − | 0.661193i | \(-0.770050\pi\) | ||||
−0.750216 | + | 0.661193i | \(0.770050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.5947 | 1.11295 | 0.556476 | − | 0.830864i | \(-0.312153\pi\) | ||||
0.556476 | + | 0.830864i | \(0.312153\pi\) | |||||||
\(572\) | −6.43874 | −0.269217 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.16234 | −0.0902545 | ||||||||
\(575\) | 3.28741 | 0.137094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.2595 | −0.760154 | −0.380077 | − | 0.924955i | \(-0.624102\pi\) | ||||
−0.380077 | + | 0.924955i | \(0.624102\pi\) | |||||||
\(578\) | −57.1118 | −2.37554 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.11061 | 0.0461156 | ||||||||
\(581\) | 31.1643 | 1.29291 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.0678 | −0.872538 | ||||||||
\(584\) | 23.7288 | 0.981906 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.4774 | 0.680673 | ||||||||
\(587\) | −33.6391 | −1.38843 | −0.694217 | − | 0.719766i | \(-0.744249\pi\) | ||||
−0.694217 | + | 0.719766i | \(0.744249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.19413 | −0.0492031 | ||||||||
\(590\) | −1.41504 | −0.0582564 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.0192 | −0.658384 | ||||||||
\(593\) | 42.7234 | 1.75444 | 0.877221 | − | 0.480088i | \(-0.159395\pi\) | ||||
0.877221 | + | 0.480088i | \(0.159395\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.3423 | −0.587975 | ||||||||
\(596\) | 2.45332 | 0.100492 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.86256 | 0.198845 | ||||||||
\(599\) | −39.6329 | −1.61936 | −0.809679 | − | 0.586873i | \(-0.800359\pi\) | ||||
−0.809679 | + | 0.586873i | \(0.800359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.109685 | −0.00447414 | −0.00223707 | − | 0.999997i | \(-0.500712\pi\) | ||||
−0.00223707 | + | 0.999997i | \(0.500712\pi\) | |||||||
\(602\) | 65.5869 | 2.67312 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.0992163 | −0.00403705 | ||||||||
\(605\) | 2.52920 | 0.102827 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6085 | 0.998827 | 0.499414 | − | 0.866364i | \(-0.333549\pi\) | ||||
0.499414 | + | 0.866364i | \(0.333549\pi\) | |||||||
\(608\) | −5.58607 | −0.226545 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.13926 | −0.0461273 | ||||||||
\(611\) | 37.3774 | 1.51213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.4684 | −0.745931 | −0.372965 | − | 0.927845i | \(-0.621659\pi\) | ||||
−0.372965 | + | 0.927845i | \(0.621659\pi\) | |||||||
\(614\) | 18.2771 | 0.737605 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.6777 | −1.19575 | ||||||||
\(617\) | 6.85488 | 0.275967 | 0.137983 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137983 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9096 | 0.961007 | 0.480503 | − | 0.876993i | \(-0.340454\pi\) | ||||
0.480503 | + | 0.876993i | \(0.340454\pi\) | |||||||
\(620\) | −0.121496 | −0.00487940 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.6120 | −0.545790 | ||||||||
\(623\) | 71.9914 | 2.88427 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.5889 | 0.903554 | ||||||||
\(626\) | −7.86823 | −0.314478 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.67540 | 0.106760 | ||||||||
\(629\) | −46.8053 | −1.86625 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1531 | 1.20037 | 0.600187 | − | 0.799859i | \(-0.295093\pi\) | ||||
0.600187 | + | 0.799859i | \(0.295093\pi\) | |||||||
\(632\) | −43.7514 | −1.74034 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.6465 | 0.780263 | ||||||||
\(635\) | −0.00758374 | −0.000300951 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 75.3053 | 2.98370 | ||||||||
\(638\) | −14.4692 | −0.572842 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12406 | 0.0839609 | ||||||||
\(641\) | 3.69224 | 0.145835 | 0.0729174 | − | 0.997338i | \(-0.476769\pi\) | ||||
0.0729174 | + | 0.997338i | \(0.476769\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.0966 | 1.62069 | 0.810346 | − | 0.585952i | \(-0.199279\pi\) | ||||
0.810346 | + | 0.585952i | \(0.199279\pi\) | |||||||
\(644\) | −1.53241 | −0.0603855 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.5598 | 0.769569 | ||||||||
\(647\) | −6.20476 | −0.243934 | −0.121967 | − | 0.992534i | \(-0.538920\pi\) | ||||
−0.121967 | + | 0.992534i | \(0.538920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.24306 | −0.245062 | ||||||||
\(650\) | 34.6140 | 1.35767 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.66839 | 0.261154 | ||||||||
\(653\) | 1.87880 | 0.0735231 | 0.0367615 | − | 0.999324i | \(-0.488296\pi\) | ||||
0.0367615 | + | 0.999324i | \(0.488296\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.14151 | 0.0836758 | ||||||||
\(656\) | 1.08444 | 0.0423404 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34.7836 | 1.35601 | ||||||||
\(659\) | −36.3588 | −1.41634 | −0.708170 | − | 0.706042i | \(-0.750479\pi\) | ||||
−0.708170 | + | 0.706042i | \(0.750479\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.1205 | −1.87167 | −0.935836 | − | 0.352436i | \(-0.885353\pi\) | ||||
−0.935836 | + | 0.352436i | \(0.885353\pi\) | |||||||
\(662\) | −13.9114 | −0.540681 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.4180 | −0.831179 | ||||||||
\(665\) | 3.60158 | 0.139663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.70045 | −0.143282 | ||||||||
\(668\) | −12.2614 | −0.474406 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.65226 | 0.218366 | ||||||||
\(671\) | −5.02633 | −0.194039 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7655 | 0.684811 | 0.342405 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342405 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(674\) | −8.24575 | −0.317614 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.7610 | −0.413884 | ||||||||
\(677\) | 18.9540 | 0.728463 | 0.364232 | − | 0.931308i | \(-0.381332\pi\) | ||||
0.364232 | + | 0.931308i | \(0.381332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.3395 | 1.47133 | ||||||||
\(680\) | 9.85688 | 0.377994 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.58287 | 0.0606113 | ||||||||
\(683\) | 19.7409 | 0.755363 | 0.377681 | − | 0.925936i | \(-0.376721\pi\) | ||||
0.377681 | + | 0.925936i | \(0.376721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.03886 | 0.0779007 | ||||||||
\(686\) | 31.9455 | 1.21968 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.8927 | −1.25402 | ||||||||
\(689\) | −56.7317 | −2.16131 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4678 | −0.512338 | −0.256169 | − | 0.966632i | \(-0.582460\pi\) | ||||
−0.256169 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(692\) | 12.1063 | 0.460213 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.48900 | −0.322238 | ||||||||
\(695\) | 3.98890 | 0.151308 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.16856 | 0.120018 | ||||||||
\(698\) | −19.2089 | −0.727069 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.9085 | −0.412301 | ||||||||
\(701\) | 36.8430 | 1.39154 | 0.695770 | − | 0.718265i | \(-0.255063\pi\) | ||||
0.695770 | + | 0.718265i | \(0.255063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.7536 | 0.443295 | ||||||||
\(704\) | 19.2834 | 0.726769 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.3122 | −0.538648 | ||||||||
\(707\) | 49.3325 | 1.85534 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.68748 | −0.100931 | −0.0504653 | − | 0.998726i | \(-0.516070\pi\) | ||||
−0.0504653 | + | 0.998726i | \(0.516070\pi\) | |||||||
\(710\) | −5.66339 | −0.212543 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −49.4769 | −1.85422 | ||||||||
\(713\) | 0.404813 | 0.0151604 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.13007 | −0.191854 | ||||||||
\(716\) | 4.12046 | 0.153989 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 24.4885 | 0.913903 | ||||||||
\(719\) | −18.2224 | −0.679582 | −0.339791 | − | 0.940501i | \(-0.610356\pi\) | ||||
−0.339791 | + | 0.940501i | \(0.610356\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.4818 | 0.948993 | ||||||||
\(722\) | 18.3122 | 0.681508 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.1553 | 0.414584 | ||||||||
\(725\) | −26.3416 | −0.978301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.91643 | −0.293604 | −0.146802 | − | 0.989166i | \(-0.546898\pi\) | ||||
−0.146802 | + | 0.989166i | \(0.546898\pi\) | |||||||
\(728\) | −79.9167 | −2.96191 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.81711 | 0.141278 | ||||||||
\(731\) | −96.1068 | −3.55464 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.87435 | 0.0692307 | 0.0346154 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346154 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(734\) | 25.5504 | 0.943082 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.89370 | 0.0698027 | ||||||||
\(737\) | 24.9374 | 0.918580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.7482 | −1.02074 | −0.510368 | − | 0.859956i | \(-0.670491\pi\) | ||||
−0.510368 | + | 0.859956i | \(0.670491\pi\) | |||||||
\(740\) | 1.19587 | 0.0439610 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −52.7949 | −1.93816 | ||||||||
\(743\) | 44.2764 | 1.62434 | 0.812171 | − | 0.583420i | \(-0.198286\pi\) | ||||
0.812171 | + | 0.583420i | \(0.198286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.95469 | 0.0716141 | ||||||||
\(746\) | −3.53597 | −0.129461 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.78020 | 0.321036 | ||||||||
\(749\) | 62.2395 | 2.27418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.6448 | −1.41017 | −0.705084 | − | 0.709124i | \(-0.749091\pi\) | ||||
−0.705084 | + | 0.709124i | \(0.749091\pi\) | |||||||
\(752\) | −17.4444 | −0.636134 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.9630 | −1.41895 | ||||||||
\(755\) | −0.0790506 | −0.00287695 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.7185 | −0.898408 | −0.449204 | − | 0.893429i | \(-0.648292\pi\) | ||||
−0.449204 | + | 0.893429i | \(0.648292\pi\) | |||||||
\(758\) | −28.7919 | −1.04577 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.47523 | −0.0897859 | ||||||||
\(761\) | 48.9136 | 1.77312 | 0.886559 | − | 0.462616i | \(-0.153089\pi\) | ||||
0.886559 | + | 0.462616i | \(0.153089\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.4211 | 1.13752 | ||||||||
\(764\) | −11.6431 | −0.421232 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.4161 | 0.376348 | ||||||||
\(767\) | −16.8114 | −0.607026 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.2367 | −1.59522 | −0.797609 | − | 0.603175i | \(-0.793902\pi\) | ||||
−0.797609 | + | 0.603175i | \(0.793902\pi\) | |||||||
\(770\) | −4.77408 | −0.172046 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.95052 | −0.142182 | ||||||||
\(773\) | −1.82530 | −0.0656513 | −0.0328257 | − | 0.999461i | \(-0.510451\pi\) | ||||
−0.0328257 | + | 0.999461i | \(0.510451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.88166 | 0.103512 | ||||||||
\(776\) | −26.3492 | −0.945882 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.5452 | −0.879988 | ||||||||
\(779\) | −0.795679 | −0.0285082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9865 | −0.894087 | ||||||||
\(782\) | −6.63084 | −0.237118 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −35.1458 | −1.25521 | ||||||||
\(785\) | 2.13163 | 0.0760811 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.69705 | −0.167432 | −0.0837159 | − | 0.996490i | \(-0.526679\pi\) | ||||
−0.0837159 | + | 0.996490i | \(0.526679\pi\) | |||||||
\(788\) | 3.43292 | 0.122293 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.03803 | −0.250402 | ||||||||
\(791\) | −78.3598 | −2.78615 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.5350 | −0.480642 | ||||||||
\(794\) | −31.0344 | −1.10137 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.95353 | 0.175573 | ||||||||
\(797\) | 27.0924 | 0.959663 | 0.479831 | − | 0.877361i | \(-0.340698\pi\) | ||||
0.479831 | + | 0.877361i | \(0.340698\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.9697 | −1.80318 | ||||||||
\(800\) | 13.4803 | 0.476600 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.44067 | −0.0861830 | ||||||||
\(803\) | 16.8408 | 0.594300 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.22095 | −0.0430329 | ||||||||
\(806\) | 4.26239 | 0.150136 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.9043 | −1.19275 | ||||||||
\(809\) | 25.4431 | 0.894533 | 0.447266 | − | 0.894401i | \(-0.352398\pi\) | ||||
0.447266 | + | 0.894401i | \(0.352398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.52467 | −0.0535386 | −0.0267693 | − | 0.999642i | \(-0.508522\pi\) | ||||
−0.0267693 | + | 0.999642i | \(0.508522\pi\) | |||||||
\(812\) | 12.2790 | 0.430909 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.5800 | −0.546078 | ||||||||
\(815\) | 5.31305 | 0.186108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.1340 | 0.844343 | ||||||||
\(818\) | 28.1353 | 0.983727 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0809562 | −0.00282711 | ||||||||
\(821\) | −25.4471 | −0.888111 | −0.444056 | − | 0.895999i | \(-0.646461\pi\) | ||||
−0.444056 | + | 0.895999i | \(0.646461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.2594 | 1.71708 | 0.858538 | − | 0.512750i | \(-0.171373\pi\) | ||||
0.858538 | + | 0.512750i | \(0.171373\pi\) | |||||||
\(824\) | −17.5127 | −0.610083 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.6448 | −0.544354 | ||||||||
\(827\) | −23.6493 | −0.822367 | −0.411183 | − | 0.911553i | \(-0.634884\pi\) | ||||
−0.411183 | + | 0.911553i | \(0.634884\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.2134 | 0.806234 | 0.403117 | − | 0.915149i | \(-0.367927\pi\) | ||||
0.403117 | + | 0.915149i | \(0.367927\pi\) | |||||||
\(830\) | −3.44538 | −0.119591 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 51.9266 | 1.80023 | ||||||||
\(833\) | −102.690 | −3.55800 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.76924 | −0.338079 | ||||||||
\(836\) | −2.20485 | −0.0762565 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.50587 | −0.155653 | ||||||||
\(839\) | −22.9974 | −0.793957 | −0.396978 | − | 0.917828i | \(-0.629941\pi\) | ||||
−0.396978 | + | 0.917828i | \(0.629941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.651179 | 0.0224545 | ||||||||
\(842\) | −23.6500 | −0.815033 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.01674 | 0.207105 | ||||||||
\(845\) | −8.57382 | −0.294948 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.9631 | 0.960822 | ||||||||
\(848\) | 26.4774 | 0.909236 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.2015 | −1.61900 | ||||||||
\(851\) | −3.98452 | −0.136587 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.94006 | 0.203384 | 0.101692 | − | 0.994816i | \(-0.467574\pi\) | ||||
0.101692 | + | 0.994816i | \(0.467574\pi\) | |||||||
\(854\) | −12.5958 | −0.431018 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.7748 | −1.46201 | ||||||||
\(857\) | 45.2128 | 1.54444 | 0.772219 | − | 0.635356i | \(-0.219147\pi\) | ||||
0.772219 | + | 0.635356i | \(0.219147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9258 | 1.29401 | 0.647006 | − | 0.762485i | \(-0.276021\pi\) | ||||
0.647006 | + | 0.762485i | \(0.276021\pi\) | |||||||
\(860\) | 2.45551 | 0.0837322 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.3796 | −0.421650 | ||||||||
\(863\) | 0.597129 | 0.0203265 | 0.0101633 | − | 0.999948i | \(-0.496765\pi\) | ||||
0.0101633 | + | 0.999948i | \(0.496765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.64571 | 0.327964 | ||||||||
\(866\) | 42.3620 | 1.43952 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.34327 | −0.0455936 | ||||||||
\(869\) | −31.0513 | −1.05334 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.1518 | 2.27535 | ||||||||
\(872\) | −21.5945 | −0.731281 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.66511 | 0.0563233 | ||||||||
\(875\) | −17.6746 | −0.597510 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.9382 | 0.369357 | 0.184679 | − | 0.982799i | \(-0.440876\pi\) | ||||
0.184679 | + | 0.982799i | \(0.440876\pi\) | |||||||
\(878\) | −3.69506 | −0.124702 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.39426 | 0.0807106 | ||||||||
\(881\) | 22.2215 | 0.748663 | 0.374331 | − | 0.927295i | \(-0.377872\pi\) | ||||
0.374331 | + | 0.927295i | \(0.377872\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.4126 | −1.89843 | −0.949217 | − | 0.314623i | \(-0.898122\pi\) | ||||
−0.949217 | + | 0.314623i | \(0.898122\pi\) | |||||||
\(884\) | 23.6435 | 0.795216 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.2439 | −0.948873 | ||||||||
\(887\) | 12.6609 | 0.425112 | 0.212556 | − | 0.977149i | \(-0.431821\pi\) | ||||
0.212556 | + | 0.977149i | \(0.431821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0838465 | −0.00281212 | ||||||||
\(890\) | −7.95905 | −0.266788 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.6474 | −0.356501 | ||||||||
\(893\) | 12.7993 | 0.428314 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.28298 | 0.109738 | ||||||||
\(896\) | 23.4838 | 0.784539 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.9491 | 0.532228 | ||||||||
\(899\) | −3.24371 | −0.108184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 77.3623 | 2.57731 | ||||||||
\(902\) | 1.05471 | 0.0351181 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.8536 | 1.79115 | ||||||||
\(905\) | 8.88800 | 0.295447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.0352 | −1.32935 | −0.664673 | − | 0.747134i | \(-0.731429\pi\) | ||||
−0.664673 | + | 0.747134i | \(0.731429\pi\) | |||||||
\(908\) | −8.35068 | −0.277127 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.8557 | −0.426163 | ||||||||
\(911\) | 17.5878 | 0.582708 | 0.291354 | − | 0.956615i | \(-0.405894\pi\) | ||||
0.291354 | + | 0.956615i | \(0.405894\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.2008 | −0.503072 | ||||||||
\(914\) | 28.0556 | 0.927998 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.62198 | 0.0866327 | ||||||||
\(917\) | 23.6768 | 0.781876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7906 | −0.520883 | −0.260442 | − | 0.965490i | \(-0.583868\pi\) | ||||
−0.260442 | + | 0.965490i | \(0.583868\pi\) | |||||||
\(920\) | 0.839112 | 0.0276647 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35.7522 | 1.17744 | ||||||||
\(923\) | −67.2841 | −2.21468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.3637 | −0.932593 | ||||||||
\(926\) | 0.256630 | 0.00843339 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.1740 | −0.498110 | ||||||||
\(929\) | −40.0331 | −1.31344 | −0.656722 | − | 0.754133i | \(-0.728057\pi\) | ||||
−0.656722 | + | 0.754133i | \(0.728057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.7872 | 0.845142 | ||||||||
\(932\) | 5.98393 | 0.196010 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.3158 | 1.02468 | ||||||||
\(935\) | 6.99563 | 0.228781 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.9832 | −1.30620 | −0.653098 | − | 0.757274i | \(-0.726531\pi\) | ||||
−0.653098 | + | 0.757274i | \(0.726531\pi\) | |||||||
\(938\) | 62.4920 | 2.04044 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.30227 | 0.0424753 | ||||||||
\(941\) | −13.1615 | −0.429052 | −0.214526 | − | 0.976718i | \(-0.568821\pi\) | ||||
−0.214526 | + | 0.976718i | \(0.568821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.269738 | 0.00878389 | ||||||||
\(944\) | 7.84609 | 0.255369 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.9908 | −1.04011 | ||||||||
\(947\) | 18.6968 | 0.607565 | 0.303783 | − | 0.952741i | \(-0.401750\pi\) | ||||
0.303783 | + | 0.952741i | \(0.401750\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.3493 | 1.47210 | ||||||||
\(950\) | 11.8531 | 0.384565 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 108.979 | 3.53202 | ||||||||
\(953\) | −4.57308 | −0.148137 | −0.0740684 | − | 0.997253i | \(-0.523598\pi\) | ||||
−0.0740684 | + | 0.997253i | \(0.523598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.27663 | −0.300185 | ||||||||
\(956\) | 0.505952 | 0.0163637 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.5498 | −1.24549 | ||||||||
\(959\) | 22.5418 | 0.727913 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6452 | −0.988553 | ||||||||
\(962\) | −41.9541 | −1.35265 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.68646 | 0.247564 | ||||||||
\(965\) | −3.14758 | −0.101324 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.1643 | −0.970020 | −0.485010 | − | 0.874509i | \(-0.661184\pi\) | ||||
−0.485010 | + | 0.874509i | \(0.661184\pi\) | |||||||
\(968\) | −19.2179 | −0.617688 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.23864 | −0.136095 | ||||||||
\(971\) | 29.5541 | 0.948437 | 0.474219 | − | 0.880407i | \(-0.342731\pi\) | ||||
0.474219 | + | 0.880407i | \(0.342731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 44.1017 | 1.41383 | ||||||||
\(974\) | 16.2515 | 0.520732 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.31694 | 0.202200 | ||||||||
\(977\) | 25.0126 | 0.800223 | 0.400112 | − | 0.916466i | \(-0.368971\pi\) | ||||
0.400112 | + | 0.916466i | \(0.368971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.1147 | −1.12227 | ||||||||
\(980\) | 2.62372 | 0.0838115 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.9709 | 0.541563 | ||||||||
\(983\) | 6.59634 | 0.210391 | 0.105195 | − | 0.994452i | \(-0.466453\pi\) | ||||
0.105195 | + | 0.994452i | \(0.466453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.73518 | 0.0871502 | ||||||||
\(986\) | 53.1320 | 1.69207 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.93727 | −0.188890 | ||||||||
\(989\) | −8.18153 | −0.260157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.17310 | −0.164329 | −0.0821645 | − | 0.996619i | \(-0.526183\pi\) | ||||
−0.0821645 | + | 0.996619i | \(0.526183\pi\) | |||||||
\(992\) | 1.65997 | 0.0527040 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −62.6150 | −1.98603 | ||||||||
\(995\) | 3.94673 | 0.125120 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.1810 | −1.01918 | −0.509591 | − | 0.860417i | \(-0.670203\pi\) | ||||
−0.509591 | + | 0.860417i | \(0.670203\pi\) | |||||||
\(998\) | −8.86627 | −0.280657 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.2.a.j.1.7 | ✓ | 20 | |
3.2 | odd | 2 | 2151.2.a.k.1.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2151.2.a.k.1.14 | yes | 20 | 3.2 | odd | 2 |