Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, 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("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.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: | \(60.4387692899\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.21072\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.21072 | 0.856107 | 0.428054 | − | 0.903753i | \(-0.359199\pi\) | ||||
0.428054 | + | 0.903753i | \(0.359199\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.534161 | −0.267081 | ||||||||
\(5\) | −1.79844 | −0.804285 | −0.402142 | − | 0.915577i | \(-0.631734\pi\) | ||||
−0.402142 | + | 0.915577i | \(0.631734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.27693 | 1.61653 | 0.808264 | − | 0.588821i | \(-0.200408\pi\) | ||||
0.808264 | + | 0.588821i | \(0.200408\pi\) | |||||||
\(8\) | −3.06816 | −1.08476 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.17740 | −0.688554 | ||||||||
\(11\) | −1.05626 | −0.318474 | −0.159237 | − | 0.987240i | \(-0.550903\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.28193 | −1.46494 | −0.732471 | − | 0.680798i | \(-0.761633\pi\) | ||||
−0.732471 | + | 0.680798i | \(0.761633\pi\) | |||||||
\(14\) | 5.17816 | 1.38392 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.64635 | −0.661587 | ||||||||
\(17\) | −5.61769 | −1.36249 | −0.681245 | − | 0.732056i | \(-0.738561\pi\) | ||||
−0.681245 | + | 0.732056i | \(0.738561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.41175 | 1.47096 | 0.735478 | − | 0.677548i | \(-0.236958\pi\) | ||||
0.735478 | + | 0.677548i | \(0.236958\pi\) | |||||||
\(20\) | 0.960655 | 0.214809 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.27883 | −0.272648 | ||||||||
\(23\) | −2.04633 | −0.426689 | −0.213345 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213345 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76563 | −0.353126 | ||||||||
\(26\) | −6.39492 | −1.25415 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.28457 | −0.431743 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.82471 | 0.686937 | 0.343469 | − | 0.939164i | \(-0.388398\pi\) | ||||
0.343469 | + | 0.939164i | \(0.388398\pi\) | |||||||
\(32\) | 2.93233 | 0.518367 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.80144 | −1.16644 | ||||||||
\(35\) | −7.69178 | −1.30015 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.350297 | −0.0575884 | −0.0287942 | − | 0.999585i | \(-0.509167\pi\) | ||||
−0.0287942 | + | 0.999585i | \(0.509167\pi\) | |||||||
\(38\) | 7.76282 | 1.25930 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.51788 | 0.872453 | ||||||||
\(41\) | 3.62240 | 0.565725 | 0.282862 | − | 0.959161i | \(-0.408716\pi\) | ||||
0.282862 | + | 0.959161i | \(0.408716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74900 | 0.266721 | 0.133360 | − | 0.991068i | \(-0.457423\pi\) | ||||
0.133360 | + | 0.991068i | \(0.457423\pi\) | |||||||
\(44\) | 0.564212 | 0.0850582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.47753 | −0.365292 | ||||||||
\(47\) | −6.98005 | −1.01814 | −0.509072 | − | 0.860724i | \(-0.670011\pi\) | ||||
−0.509072 | + | 0.860724i | \(0.670011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.2921 | 1.61316 | ||||||||
\(50\) | −2.13768 | −0.302314 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.82140 | 0.391258 | ||||||||
\(53\) | 7.81869 | 1.07398 | 0.536990 | − | 0.843589i | \(-0.319561\pi\) | ||||
0.536990 | + | 0.843589i | \(0.319561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89961 | 0.256144 | ||||||||
\(56\) | −13.1223 | −1.75354 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.382668 | −0.0498191 | −0.0249096 | − | 0.999690i | \(-0.507930\pi\) | ||||
−0.0249096 | + | 0.999690i | \(0.507930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.46644 | −0.699906 | −0.349953 | − | 0.936767i | \(-0.613803\pi\) | ||||
−0.349953 | + | 0.936767i | \(0.613803\pi\) | |||||||
\(62\) | 4.63064 | 0.588092 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.84292 | 1.10537 | ||||||||
\(65\) | 9.49920 | 1.17823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.81166 | 0.954346 | 0.477173 | − | 0.878809i | \(-0.341662\pi\) | ||||
0.477173 | + | 0.878809i | \(0.341662\pi\) | |||||||
\(68\) | 3.00075 | 0.363895 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.31258 | −1.11307 | ||||||||
\(71\) | 15.6115 | 1.85274 | 0.926370 | − | 0.376615i | \(-0.122912\pi\) | ||||
0.926370 | + | 0.376615i | \(0.122912\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.54289 | −0.297623 | −0.148811 | − | 0.988866i | \(-0.547545\pi\) | ||||
−0.148811 | + | 0.988866i | \(0.547545\pi\) | |||||||
\(74\) | −0.424110 | −0.0493018 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.42491 | −0.392864 | ||||||||
\(77\) | −4.51754 | −0.514822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2680 | 1.15524 | 0.577619 | − | 0.816306i | \(-0.303982\pi\) | ||||
0.577619 | + | 0.816306i | \(0.303982\pi\) | |||||||
\(80\) | 4.75929 | 0.532104 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.38571 | 0.484321 | ||||||||
\(83\) | −1.52139 | −0.166994 | −0.0834971 | − | 0.996508i | \(-0.526609\pi\) | ||||
−0.0834971 | + | 0.996508i | \(0.526609\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.1030 | 1.09583 | ||||||||
\(86\) | 2.11755 | 0.228341 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.24076 | 0.345467 | ||||||||
\(89\) | 17.9444 | 1.90210 | 0.951049 | − | 0.309041i | \(-0.100008\pi\) | ||||
0.951049 | + | 0.309041i | \(0.100008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.5904 | −2.36812 | ||||||||
\(92\) | 1.09307 | 0.113960 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.45087 | −0.871641 | ||||||||
\(95\) | −11.5311 | −1.18307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.80968 | −0.691418 | −0.345709 | − | 0.938342i | \(-0.612362\pi\) | ||||
−0.345709 | + | 0.938342i | \(0.612362\pi\) | |||||||
\(98\) | 13.6716 | 1.38104 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.943132 | 0.0943132 | ||||||||
\(101\) | −4.72573 | −0.470228 | −0.235114 | − | 0.971968i | \(-0.575546\pi\) | ||||
−0.235114 | + | 0.971968i | \(0.575546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.49491 | 0.344364 | 0.172182 | − | 0.985065i | \(-0.444918\pi\) | ||||
0.172182 | + | 0.985065i | \(0.444918\pi\) | |||||||
\(104\) | 16.2058 | 1.58911 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.46624 | 0.919442 | ||||||||
\(107\) | 4.92192 | 0.475820 | 0.237910 | − | 0.971287i | \(-0.423538\pi\) | ||||
0.237910 | + | 0.971287i | \(0.423538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.8847 | −1.42569 | −0.712846 | − | 0.701321i | \(-0.752594\pi\) | ||||
−0.712846 | + | 0.701321i | \(0.752594\pi\) | |||||||
\(110\) | 2.29989 | 0.219286 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.3182 | −1.06947 | ||||||||
\(113\) | 6.34278 | 0.596678 | 0.298339 | − | 0.954460i | \(-0.403567\pi\) | ||||
0.298339 | + | 0.954460i | \(0.403567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.68019 | 0.343180 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.463303 | −0.0426505 | ||||||||
\(119\) | −24.0265 | −2.20250 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.88432 | −0.898574 | ||||||||
\(122\) | −6.61832 | −0.599195 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.04301 | −0.183468 | ||||||||
\(125\) | 12.1675 | 1.08830 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.46569 | −0.396266 | −0.198133 | − | 0.980175i | \(-0.563488\pi\) | ||||
−0.198133 | + | 0.980175i | \(0.563488\pi\) | |||||||
\(128\) | 4.84163 | 0.427944 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.5009 | 1.00869 | ||||||||
\(131\) | −0.00995943 | −0.000870160 0 | −0.000435080 | − | 1.00000i | \(-0.500138\pi\) | ||||
−0.000435080 | 1.00000i | \(0.500138\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 27.4226 | 2.37784 | ||||||||
\(134\) | 9.45772 | 0.817022 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.2359 | 1.47797 | ||||||||
\(137\) | −12.2134 | −1.04346 | −0.521732 | − | 0.853109i | \(-0.674714\pi\) | ||||
−0.521732 | + | 0.853109i | \(0.674714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.94561 | 0.419481 | 0.209741 | − | 0.977757i | \(-0.432738\pi\) | ||||
0.209741 | + | 0.977757i | \(0.432738\pi\) | |||||||
\(140\) | 4.10865 | 0.347245 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.9011 | 1.58614 | ||||||||
\(143\) | 5.57908 | 0.466546 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.07873 | −0.254797 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.187115 | 0.0153808 | ||||||||
\(149\) | −14.0140 | −1.14807 | −0.574035 | − | 0.818831i | \(-0.694623\pi\) | ||||
−0.574035 | + | 0.818831i | \(0.694623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.93392 | 0.238759 | 0.119379 | − | 0.992849i | \(-0.461910\pi\) | ||||
0.119379 | + | 0.992849i | \(0.461910\pi\) | |||||||
\(152\) | −19.6722 | −1.59563 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.46947 | −0.440742 | ||||||||
\(155\) | −6.87849 | −0.552493 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1919 | 1.29226 | 0.646128 | − | 0.763229i | \(-0.276387\pi\) | ||||
0.646128 | + | 0.763229i | \(0.276387\pi\) | |||||||
\(158\) | 12.4316 | 0.989008 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.27360 | −0.416915 | ||||||||
\(161\) | −8.75201 | −0.689755 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5734 | 1.06315 | 0.531575 | − | 0.847011i | \(-0.321600\pi\) | ||||
0.531575 | + | 0.847011i | \(0.321600\pi\) | |||||||
\(164\) | −1.93495 | −0.151094 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.84197 | −0.142965 | ||||||||
\(167\) | 16.3616 | 1.26610 | 0.633050 | − | 0.774111i | \(-0.281803\pi\) | ||||
0.633050 | + | 0.774111i | \(0.281803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8987 | 1.14606 | ||||||||
\(170\) | 12.2319 | 0.938147 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.934250 | −0.0712359 | ||||||||
\(173\) | 4.46374 | 0.339372 | 0.169686 | − | 0.985498i | \(-0.445725\pi\) | ||||
0.169686 | + | 0.985498i | \(0.445725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.55148 | −0.570838 | ||||||||
\(176\) | 2.79523 | 0.210698 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 21.7256 | 1.62840 | ||||||||
\(179\) | −3.40063 | −0.254175 | −0.127088 | − | 0.991891i | \(-0.540563\pi\) | ||||
−0.127088 | + | 0.991891i | \(0.540563\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.62134 | 0.492160 | 0.246080 | − | 0.969250i | \(-0.420857\pi\) | ||||
0.246080 | + | 0.969250i | \(0.420857\pi\) | |||||||
\(182\) | −27.3506 | −2.02736 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.27846 | 0.462854 | ||||||||
\(185\) | 0.629986 | 0.0463175 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.93373 | 0.433917 | ||||||||
\(188\) | 3.72847 | 0.271927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.9609 | −1.01283 | ||||||||
\(191\) | −17.6196 | −1.27491 | −0.637454 | − | 0.770489i | \(-0.720012\pi\) | ||||
−0.637454 | + | 0.770489i | \(0.720012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3986 | −0.964454 | −0.482227 | − | 0.876046i | \(-0.660172\pi\) | ||||
−0.482227 | + | 0.876046i | \(0.660172\pi\) | |||||||
\(194\) | −8.24460 | −0.591928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.03182 | −0.430844 | ||||||||
\(197\) | 8.20476 | 0.584565 | 0.292282 | − | 0.956332i | \(-0.405585\pi\) | ||||
0.292282 | + | 0.956332i | \(0.405585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.4954 | 1.73643 | 0.868216 | − | 0.496187i | \(-0.165267\pi\) | ||||
0.868216 | + | 0.496187i | \(0.165267\pi\) | |||||||
\(200\) | 5.41723 | 0.383056 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.72153 | −0.402565 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.51466 | −0.455004 | ||||||||
\(206\) | 4.23135 | 0.294812 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.9778 | 0.969187 | ||||||||
\(209\) | −6.77246 | −0.468461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.21143 | −0.152241 | −0.0761205 | − | 0.997099i | \(-0.524253\pi\) | ||||
−0.0761205 | + | 0.997099i | \(0.524253\pi\) | |||||||
\(212\) | −4.17644 | −0.286839 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.95905 | 0.407353 | ||||||||
\(215\) | −3.14547 | −0.214519 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.3580 | 1.11045 | ||||||||
\(218\) | −18.0211 | −1.22054 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.01470 | −0.0684110 | ||||||||
\(221\) | 29.6722 | 1.99597 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.70437 | 0.181098 | 0.0905491 | − | 0.995892i | \(-0.471138\pi\) | ||||
0.0905491 | + | 0.995892i | \(0.471138\pi\) | |||||||
\(224\) | 12.5414 | 0.837955 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.67932 | 0.510820 | ||||||||
\(227\) | −14.4225 | −0.957258 | −0.478629 | − | 0.878017i | \(-0.658866\pi\) | ||||
−0.478629 | + | 0.878017i | \(0.658866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7467 | 1.70139 | 0.850694 | − | 0.525662i | \(-0.176182\pi\) | ||||
0.850694 | + | 0.525662i | \(0.176182\pi\) | |||||||
\(230\) | 4.45567 | 0.293798 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.6039 | 1.48083 | 0.740417 | − | 0.672148i | \(-0.234628\pi\) | ||||
0.740417 | + | 0.672148i | \(0.234628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.5532 | 0.818878 | ||||||||
\(236\) | 0.204406 | 0.0133057 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −29.0893 | −1.88558 | ||||||||
\(239\) | −23.4233 | −1.51513 | −0.757565 | − | 0.652760i | \(-0.773611\pi\) | ||||
−0.757565 | + | 0.652760i | \(0.773611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3826 | 1.44179 | 0.720896 | − | 0.693043i | \(-0.243730\pi\) | ||||
0.720896 | + | 0.693043i | \(0.243730\pi\) | |||||||
\(242\) | −11.9671 | −0.769276 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.91996 | 0.186932 | ||||||||
\(245\) | −20.3082 | −1.29744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33.8664 | −2.15487 | ||||||||
\(248\) | −11.7348 | −0.745160 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.7315 | 0.931700 | ||||||||
\(251\) | 5.95981 | 0.376180 | 0.188090 | − | 0.982152i | \(-0.439770\pi\) | ||||
0.188090 | + | 0.982152i | \(0.439770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.16145 | 0.135889 | ||||||||
\(254\) | −5.40669 | −0.339246 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.8240 | −0.739000 | ||||||||
\(257\) | 15.0723 | 0.940185 | 0.470092 | − | 0.882617i | \(-0.344221\pi\) | ||||
0.470092 | + | 0.882617i | \(0.344221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.49819 | −0.0930932 | ||||||||
\(260\) | −5.07411 | −0.314683 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0120581 | −0.000744950 0 | ||||||||
\(263\) | 18.7252 | 1.15465 | 0.577324 | − | 0.816515i | \(-0.304097\pi\) | ||||
0.577324 | + | 0.816515i | \(0.304097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.0614 | −0.863786 | ||||||||
\(266\) | 33.2010 | 2.03569 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.17269 | −0.254887 | ||||||||
\(269\) | 23.1259 | 1.41001 | 0.705006 | − | 0.709202i | \(-0.250944\pi\) | ||||
0.705006 | + | 0.709202i | \(0.250944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3469 | 1.29673 | 0.648365 | − | 0.761330i | \(-0.275453\pi\) | ||||
0.648365 | + | 0.761330i | \(0.275453\pi\) | |||||||
\(272\) | 14.8664 | 0.901406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.7870 | −0.893317 | ||||||||
\(275\) | 1.86496 | 0.112461 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.32181 | −0.500009 | −0.250004 | − | 0.968245i | \(-0.580432\pi\) | ||||
−0.250004 | + | 0.968245i | \(0.580432\pi\) | |||||||
\(278\) | 5.98774 | 0.359121 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 23.5996 | 1.41034 | ||||||||
\(281\) | 28.9202 | 1.72524 | 0.862618 | − | 0.505856i | \(-0.168823\pi\) | ||||
0.862618 | + | 0.505856i | \(0.168823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.9799 | 1.78212 | 0.891060 | − | 0.453885i | \(-0.149962\pi\) | ||||
0.891060 | + | 0.453885i | \(0.149962\pi\) | |||||||
\(284\) | −8.33904 | −0.494831 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.75469 | 0.399413 | ||||||||
\(287\) | 15.4928 | 0.914509 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.5584 | 0.856378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.35831 | 0.0794893 | ||||||||
\(293\) | −8.75406 | −0.511418 | −0.255709 | − | 0.966754i | \(-0.582309\pi\) | ||||
−0.255709 | + | 0.966754i | \(0.582309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.688204 | 0.0400688 | ||||||||
\(296\) | 1.07476 | 0.0624694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.9670 | −0.982871 | ||||||||
\(299\) | 10.8086 | 0.625075 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.48036 | 0.431161 | ||||||||
\(302\) | 3.55215 | 0.204403 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.9677 | −0.973166 | ||||||||
\(305\) | 9.83105 | 0.562924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.9161 | −1.93570 | −0.967848 | − | 0.251536i | \(-0.919064\pi\) | ||||
−0.967848 | + | 0.251536i | \(0.919064\pi\) | |||||||
\(308\) | 2.41310 | 0.137499 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.32791 | −0.472993 | ||||||||
\(311\) | −8.12574 | −0.460769 | −0.230384 | − | 0.973100i | \(-0.573998\pi\) | ||||
−0.230384 | + | 0.973100i | \(0.573998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.52738 | 0.142856 | 0.0714280 | − | 0.997446i | \(-0.477244\pi\) | ||||
0.0714280 | + | 0.997446i | \(0.477244\pi\) | |||||||
\(314\) | 19.6039 | 1.10631 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.48476 | −0.308542 | ||||||||
\(317\) | −16.6383 | −0.934499 | −0.467250 | − | 0.884125i | \(-0.654755\pi\) | ||||
−0.467250 | + | 0.884125i | \(0.654755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −15.9034 | −0.889028 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.5962 | −0.590504 | ||||||||
\(323\) | −36.0192 | −2.00416 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.32593 | 0.517309 | ||||||||
\(326\) | 16.4336 | 0.910170 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.1141 | −0.613673 | ||||||||
\(329\) | −29.8532 | −1.64586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9286 | 0.710619 | 0.355309 | − | 0.934749i | \(-0.384375\pi\) | ||||
0.355309 | + | 0.934749i | \(0.384375\pi\) | |||||||
\(332\) | 0.812667 | 0.0446009 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.8093 | 1.08392 | ||||||||
\(335\) | −14.0488 | −0.767566 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.56273 | −0.303021 | −0.151511 | − | 0.988456i | \(-0.548414\pi\) | ||||
−0.151511 | + | 0.988456i | \(0.548414\pi\) | |||||||
\(338\) | 18.0382 | 0.981148 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.39666 | −0.292675 | ||||||||
\(341\) | −4.03988 | −0.218772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3571 | 0.991192 | ||||||||
\(344\) | −5.36621 | −0.289327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.40433 | 0.290539 | ||||||||
\(347\) | 8.78686 | 0.471703 | 0.235852 | − | 0.971789i | \(-0.424212\pi\) | ||||
0.235852 | + | 0.971789i | \(0.424212\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.1943 | 0.813332 | 0.406666 | − | 0.913577i | \(-0.366691\pi\) | ||||
0.406666 | + | 0.913577i | \(0.366691\pi\) | |||||||
\(350\) | −9.14271 | −0.488698 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.09729 | −0.165086 | ||||||||
\(353\) | 12.3667 | 0.658214 | 0.329107 | − | 0.944293i | \(-0.393252\pi\) | ||||
0.329107 | + | 0.944293i | \(0.393252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.0762 | −1.49013 | ||||||||
\(356\) | −9.58518 | −0.508014 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.11721 | −0.217601 | ||||||||
\(359\) | 16.0164 | 0.845312 | 0.422656 | − | 0.906290i | \(-0.361098\pi\) | ||||
0.422656 | + | 0.906290i | \(0.361098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.1105 | 1.16371 | ||||||||
\(362\) | 8.01657 | 0.421342 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0669 | 0.632479 | ||||||||
\(365\) | 4.57323 | 0.239374 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.2447 | −1.16116 | −0.580581 | − | 0.814203i | \(-0.697174\pi\) | ||||
−0.580581 | + | 0.814203i | \(0.697174\pi\) | |||||||
\(368\) | 5.41530 | 0.282292 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.762735 | 0.0396527 | ||||||||
\(371\) | 33.4400 | 1.73612 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.93029 | 0.358837 | 0.179418 | − | 0.983773i | \(-0.442578\pi\) | ||||
0.179418 | + | 0.983773i | \(0.442578\pi\) | |||||||
\(374\) | 7.18407 | 0.371480 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.4159 | 1.10444 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.78848 | −0.400067 | −0.200034 | − | 0.979789i | \(-0.564105\pi\) | ||||
−0.200034 | + | 0.979789i | \(0.564105\pi\) | |||||||
\(380\) | 6.15948 | 0.315975 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.3323 | −1.09146 | ||||||||
\(383\) | −25.4625 | −1.30107 | −0.650537 | − | 0.759475i | \(-0.725456\pi\) | ||||
−0.650537 | + | 0.759475i | \(0.725456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.12451 | 0.414063 | ||||||||
\(386\) | −16.2220 | −0.825676 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.63747 | 0.184664 | ||||||||
\(389\) | −10.9838 | −0.556902 | −0.278451 | − | 0.960450i | \(-0.589821\pi\) | ||||
−0.278451 | + | 0.960450i | \(0.589821\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.4956 | 0.581359 | ||||||||
\(392\) | −34.6460 | −1.74989 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.93365 | 0.500450 | ||||||||
\(395\) | −18.4663 | −0.929140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.10047 | 0.255985 | 0.127993 | − | 0.991775i | \(-0.459147\pi\) | ||||
0.127993 | + | 0.991775i | \(0.459147\pi\) | |||||||
\(398\) | 29.6570 | 1.48657 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.67247 | 0.233624 | ||||||||
\(401\) | 19.5421 | 0.975886 | 0.487943 | − | 0.872875i | \(-0.337747\pi\) | ||||
0.487943 | + | 0.872875i | \(0.337747\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.2018 | −1.00632 | ||||||||
\(404\) | 2.52430 | 0.125589 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.370004 | 0.0183404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.9244 | −0.886305 | −0.443152 | − | 0.896446i | \(-0.646140\pi\) | ||||
−0.443152 | + | 0.896446i | \(0.646140\pi\) | |||||||
\(410\) | −7.88742 | −0.389532 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.86685 | −0.0919730 | ||||||||
\(413\) | −1.63664 | −0.0805340 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.73612 | 0.134311 | ||||||||
\(416\) | −15.4883 | −0.759378 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.19954 | −0.401053 | ||||||||
\(419\) | −3.73821 | −0.182623 | −0.0913116 | − | 0.995822i | \(-0.529106\pi\) | ||||
−0.0913116 | + | 0.995822i | \(0.529106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.28779 | 0.403922 | 0.201961 | − | 0.979394i | \(-0.435269\pi\) | ||||
0.201961 | + | 0.979394i | \(0.435269\pi\) | |||||||
\(422\) | −2.67742 | −0.130335 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.9890 | −1.16501 | ||||||||
\(425\) | 9.91876 | 0.481131 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.3796 | −1.13142 | ||||||||
\(428\) | −2.62910 | −0.127082 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.80828 | −0.183651 | ||||||||
\(431\) | −19.1294 | −0.921432 | −0.460716 | − | 0.887548i | \(-0.652407\pi\) | ||||
−0.460716 | + | 0.887548i | \(0.652407\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1509 | −0.776163 | −0.388081 | − | 0.921625i | \(-0.626862\pi\) | ||||
−0.388081 | + | 0.921625i | \(0.626862\pi\) | |||||||
\(434\) | 19.8049 | 0.950667 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.95081 | 0.380775 | ||||||||
\(437\) | −13.1206 | −0.627641 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.96836 | 0.141672 | 0.0708360 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708360 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(440\) | −5.82830 | −0.277853 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.9247 | 1.70876 | ||||||||
\(443\) | −10.4916 | −0.498471 | −0.249235 | − | 0.968443i | \(-0.580179\pi\) | ||||
−0.249235 | + | 0.968443i | \(0.580179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.2718 | −1.52983 | ||||||||
\(446\) | 3.27423 | 0.155039 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37.8206 | 1.78685 | ||||||||
\(449\) | 4.40325 | 0.207802 | 0.103901 | − | 0.994588i | \(-0.466867\pi\) | ||||
0.103901 | + | 0.994588i | \(0.466867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.82619 | −0.180168 | ||||||||
\(452\) | −3.38807 | −0.159361 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.4616 | −0.819515 | ||||||||
\(455\) | 40.6274 | 1.90464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3485 | 0.530860 | 0.265430 | − | 0.964130i | \(-0.414486\pi\) | ||||
0.265430 | + | 0.964130i | \(0.414486\pi\) | |||||||
\(458\) | 31.1720 | 1.45657 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.96582 | −0.0916566 | ||||||||
\(461\) | −19.7092 | −0.917947 | −0.458973 | − | 0.888450i | \(-0.651783\pi\) | ||||
−0.458973 | + | 0.888450i | \(0.651783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.753315 | 0.0350095 | 0.0175048 | − | 0.999847i | \(-0.494428\pi\) | ||||
0.0175048 | + | 0.999847i | \(0.494428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.3670 | 1.26775 | ||||||||
\(467\) | −10.4450 | −0.483339 | −0.241670 | − | 0.970359i | \(-0.577695\pi\) | ||||
−0.241670 | + | 0.970359i | \(0.577695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.4099 | 1.54273 | ||||||||
\(470\) | 15.1983 | 0.701047 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.17408 | 0.0540416 | ||||||||
\(473\) | −1.84740 | −0.0849435 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.3208 | −0.519433 | ||||||||
\(476\) | 12.8340 | 0.588246 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.3591 | −1.29711 | ||||||||
\(479\) | 13.9781 | 0.638673 | 0.319337 | − | 0.947641i | \(-0.396540\pi\) | ||||
0.319337 | + | 0.947641i | \(0.396540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.85024 | 0.0843637 | ||||||||
\(482\) | 27.0991 | 1.23433 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.27982 | 0.239992 | ||||||||
\(485\) | 12.2468 | 0.556097 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.46028 | −0.0661718 | −0.0330859 | − | 0.999453i | \(-0.510533\pi\) | ||||
−0.0330859 | + | 0.999453i | \(0.510533\pi\) | |||||||
\(488\) | 16.7719 | 0.759228 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −24.5875 | −1.11075 | ||||||||
\(491\) | 12.1522 | 0.548421 | 0.274210 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274210 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −41.0027 | −1.84480 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1215 | −0.454469 | ||||||||
\(497\) | 66.7691 | 2.99501 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.9679 | −1.61014 | −0.805071 | − | 0.593178i | \(-0.797873\pi\) | ||||
−0.805071 | + | 0.593178i | \(0.797873\pi\) | |||||||
\(500\) | −6.49943 | −0.290664 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.21565 | 0.322050 | ||||||||
\(503\) | 14.3546 | 0.640041 | 0.320020 | − | 0.947411i | \(-0.396310\pi\) | ||||
0.320020 | + | 0.947411i | \(0.396310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.49892 | 0.378197 | ||||||||
\(506\) | 2.61691 | 0.116336 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.38540 | 0.105835 | ||||||||
\(509\) | 31.0049 | 1.37427 | 0.687135 | − | 0.726530i | \(-0.258868\pi\) | ||||
0.687135 | + | 0.726530i | \(0.258868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8758 | −0.481116 | ||||||||
\(512\) | −23.9988 | −1.06061 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.2483 | 0.804899 | ||||||||
\(515\) | −6.28537 | −0.276967 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.37273 | 0.324252 | ||||||||
\(518\) | −1.81389 | −0.0796978 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −29.1450 | −1.27809 | ||||||||
\(521\) | 14.9084 | 0.653150 | 0.326575 | − | 0.945171i | \(-0.394105\pi\) | ||||
0.326575 | + | 0.945171i | \(0.394105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9505 | −0.566284 | −0.283142 | − | 0.959078i | \(-0.591377\pi\) | ||||
−0.283142 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(524\) | 0.00531995 | 0.000232403 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.6710 | 0.988502 | ||||||||
\(527\) | −21.4860 | −0.935945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8125 | −0.817936 | ||||||||
\(530\) | −17.0244 | −0.739493 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.6481 | −0.635076 | ||||||||
\(533\) | −19.1333 | −0.828754 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.85175 | −0.382694 | ||||||||
\(536\) | −23.9674 | −1.03523 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.9990 | 1.20712 | ||||||||
\(539\) | −11.9274 | −0.513750 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8732 | 0.467475 | 0.233737 | − | 0.972300i | \(-0.424904\pi\) | ||||
0.233737 | + | 0.972300i | \(0.424904\pi\) | |||||||
\(542\) | 25.8450 | 1.11014 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.4729 | −0.706270 | ||||||||
\(545\) | 26.7691 | 1.14666 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1301 | −0.988970 | −0.494485 | − | 0.869186i | \(-0.664643\pi\) | ||||
−0.494485 | + | 0.869186i | \(0.664643\pi\) | |||||||
\(548\) | 6.52394 | 0.278689 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.25794 | 0.0962790 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.9154 | 1.86747 | ||||||||
\(554\) | −10.0754 | −0.428061 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.64175 | −0.112035 | ||||||||
\(557\) | 43.1297 | 1.82746 | 0.913731 | − | 0.406319i | \(-0.133188\pi\) | ||||
0.913731 | + | 0.406319i | \(0.133188\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.23811 | −0.390730 | ||||||||
\(560\) | 20.3551 | 0.860162 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 35.0142 | 1.47699 | ||||||||
\(563\) | −34.1036 | −1.43729 | −0.718647 | − | 0.695375i | \(-0.755238\pi\) | ||||
−0.718647 | + | 0.695375i | \(0.755238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4071 | −0.479899 | ||||||||
\(566\) | 36.2972 | 1.52569 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −47.8984 | −2.00977 | ||||||||
\(569\) | 19.0810 | 0.799917 | 0.399958 | − | 0.916533i | \(-0.369025\pi\) | ||||
0.399958 | + | 0.916533i | \(0.369025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.56641 | −0.274796 | −0.137398 | − | 0.990516i | \(-0.543874\pi\) | ||||
−0.137398 | + | 0.990516i | \(0.543874\pi\) | |||||||
\(572\) | −2.98013 | −0.124605 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.7574 | 0.782918 | ||||||||
\(575\) | 3.61306 | 0.150675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.5602 | −0.855934 | −0.427967 | − | 0.903794i | \(-0.640770\pi\) | ||||
−0.427967 | + | 0.903794i | \(0.640770\pi\) | |||||||
\(578\) | 17.6261 | 0.733151 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.50687 | −0.269951 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.25856 | −0.342035 | ||||||||
\(584\) | 7.80199 | 0.322849 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.5987 | −0.437828 | ||||||||
\(587\) | 9.69142 | 0.400008 | 0.200004 | − | 0.979795i | \(-0.435905\pi\) | ||||
0.200004 | + | 0.979795i | \(0.435905\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.5231 | 1.01046 | ||||||||
\(590\) | 0.833221 | 0.0343032 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.927007 | 0.0380997 | ||||||||
\(593\) | 13.1810 | 0.541279 | 0.270639 | − | 0.962681i | \(-0.412765\pi\) | ||||
0.270639 | + | 0.962681i | \(0.412765\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 43.2100 | 1.77144 | ||||||||
\(596\) | 7.48573 | 0.306627 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.0861 | 0.535131 | ||||||||
\(599\) | 14.4397 | 0.589991 | 0.294995 | − | 0.955499i | \(-0.404682\pi\) | ||||
0.294995 | + | 0.955499i | \(0.404682\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.88823 | 0.199395 | 0.0996976 | − | 0.995018i | \(-0.468212\pi\) | ||||
0.0996976 | + | 0.995018i | \(0.468212\pi\) | |||||||
\(602\) | 9.05661 | 0.369120 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.56718 | −0.0637678 | ||||||||
\(605\) | 17.7763 | 0.722710 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5548 | −0.509583 | −0.254792 | − | 0.966996i | \(-0.582007\pi\) | ||||
−0.254792 | + | 0.966996i | \(0.582007\pi\) | |||||||
\(608\) | 18.8014 | 0.762496 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.9026 | 0.481923 | ||||||||
\(611\) | 36.8681 | 1.49152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.49761 | 0.141267 | 0.0706336 | − | 0.997502i | \(-0.477498\pi\) | ||||
0.0706336 | + | 0.997502i | \(0.477498\pi\) | |||||||
\(614\) | −41.0629 | −1.65716 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.8605 | 0.558456 | ||||||||
\(617\) | 27.2896 | 1.09864 | 0.549318 | − | 0.835613i | \(-0.314887\pi\) | ||||
0.549318 | + | 0.835613i | \(0.314887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5410 | −1.02658 | −0.513289 | − | 0.858216i | \(-0.671573\pi\) | ||||
−0.513289 | + | 0.858216i | \(0.671573\pi\) | |||||||
\(620\) | 3.67422 | 0.147560 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.83798 | −0.394467 | ||||||||
\(623\) | 76.7467 | 3.07479 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0544 | −0.522176 | ||||||||
\(626\) | 3.05995 | 0.122300 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.64911 | −0.345137 | ||||||||
\(629\) | 1.96786 | 0.0784636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7956 | 0.827858 | 0.413929 | − | 0.910309i | \(-0.364156\pi\) | ||||
0.413929 | + | 0.910309i | \(0.364156\pi\) | |||||||
\(632\) | −31.5038 | −1.25315 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.1443 | −0.800031 | ||||||||
\(635\) | 8.03126 | 0.318711 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −59.6442 | −2.36319 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.70736 | −0.344188 | ||||||||
\(641\) | 14.1393 | 0.558468 | 0.279234 | − | 0.960223i | \(-0.409920\pi\) | ||||
0.279234 | + | 0.960223i | \(0.409920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.4943 | 1.39976 | 0.699878 | − | 0.714262i | \(-0.253238\pi\) | ||||
0.699878 | + | 0.714262i | \(0.253238\pi\) | |||||||
\(644\) | 4.67498 | 0.184220 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −43.6091 | −1.71578 | ||||||||
\(647\) | 20.0626 | 0.788743 | 0.394371 | − | 0.918951i | \(-0.370962\pi\) | ||||
0.394371 | + | 0.918951i | \(0.370962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.404196 | 0.0158661 | ||||||||
\(650\) | 11.2911 | 0.442872 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.25038 | −0.283947 | ||||||||
\(653\) | −13.3537 | −0.522569 | −0.261285 | − | 0.965262i | \(-0.584146\pi\) | ||||
−0.261285 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0179114 | 0.000699856 0 | ||||||||
\(656\) | −9.58615 | −0.374276 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.1438 | −1.40903 | ||||||||
\(659\) | −11.3791 | −0.443267 | −0.221633 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221633 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0298 | −1.44029 | −0.720145 | − | 0.693823i | \(-0.755925\pi\) | ||||
−0.720145 | + | 0.693823i | \(0.755925\pi\) | |||||||
\(662\) | 15.6529 | 0.608366 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.66786 | 0.181148 | ||||||||
\(665\) | −49.3178 | −1.91246 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −8.73974 | −0.338151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.0091 | −0.657119 | ||||||||
\(671\) | 5.77398 | 0.222902 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.2436 | 1.43563 | 0.717817 | − | 0.696232i | \(-0.245141\pi\) | ||||
0.717817 | + | 0.696232i | \(0.245141\pi\) | |||||||
\(674\) | −6.73490 | −0.259419 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.95833 | −0.306090 | ||||||||
\(677\) | −44.9350 | −1.72699 | −0.863496 | − | 0.504356i | \(-0.831730\pi\) | ||||
−0.863496 | + | 0.504356i | \(0.831730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1245 | −1.11770 | ||||||||
\(680\) | −30.9977 | −1.18871 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.89115 | −0.187292 | ||||||||
\(683\) | −22.6022 | −0.864848 | −0.432424 | − | 0.901670i | \(-0.642342\pi\) | ||||
−0.432424 | + | 0.901670i | \(0.642342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.9651 | 0.839242 | ||||||||
\(686\) | 22.2253 | 0.848567 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.62847 | −0.176459 | ||||||||
\(689\) | −41.2978 | −1.57332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8727 | −1.47879 | −0.739394 | − | 0.673273i | \(-0.764888\pi\) | ||||
−0.739394 | + | 0.673273i | \(0.764888\pi\) | |||||||
\(692\) | −2.38436 | −0.0906397 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.6384 | 0.403828 | ||||||||
\(695\) | −8.89436 | −0.337382 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.3495 | −0.770794 | ||||||||
\(698\) | 18.3960 | 0.696299 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.03371 | 0.152460 | ||||||||
\(701\) | 39.4427 | 1.48973 | 0.744865 | − | 0.667215i | \(-0.232514\pi\) | ||||
0.744865 | + | 0.667215i | \(0.232514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.24601 | −0.0847100 | ||||||||
\(704\) | −9.34041 | −0.352030 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.9726 | 0.563501 | ||||||||
\(707\) | −20.2116 | −0.760136 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.07382 | −0.152996 | −0.0764978 | − | 0.997070i | \(-0.524374\pi\) | ||||
−0.0764978 | + | 0.997070i | \(0.524374\pi\) | |||||||
\(710\) | −33.9924 | −1.27571 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −55.0561 | −2.06331 | ||||||||
\(713\) | −7.82661 | −0.293109 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0336 | −0.375236 | ||||||||
\(716\) | 1.81649 | 0.0678853 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.3913 | 0.723677 | ||||||||
\(719\) | 18.4303 | 0.687335 | 0.343667 | − | 0.939091i | \(-0.388331\pi\) | ||||
0.343667 | + | 0.939091i | \(0.388331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9475 | 0.556674 | ||||||||
\(722\) | 26.7696 | 0.996263 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.53686 | −0.131446 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6150 | 0.653306 | 0.326653 | − | 0.945144i | \(-0.394079\pi\) | ||||
0.326653 | + | 0.945144i | \(0.394079\pi\) | |||||||
\(728\) | 69.3109 | 2.56883 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.53689 | 0.204929 | ||||||||
\(731\) | −9.82535 | −0.363404 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.22724 | −0.303880 | −0.151940 | − | 0.988390i | \(-0.548552\pi\) | ||||
−0.151940 | + | 0.988390i | \(0.548552\pi\) | |||||||
\(734\) | −26.9320 | −0.994079 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00051 | −0.221182 | ||||||||
\(737\) | −8.25113 | −0.303934 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8226 | 1.31776 | 0.658878 | − | 0.752250i | \(-0.271031\pi\) | ||||
0.658878 | + | 0.752250i | \(0.271031\pi\) | |||||||
\(740\) | −0.336514 | −0.0123705 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.4864 | 1.48630 | ||||||||
\(743\) | −9.29461 | −0.340986 | −0.170493 | − | 0.985359i | \(-0.554536\pi\) | ||||
−0.170493 | + | 0.985359i | \(0.554536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.2032 | 0.923375 | ||||||||
\(746\) | 8.39063 | 0.307203 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.16957 | −0.115891 | ||||||||
\(749\) | 21.0507 | 0.769175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.8712 | −1.63737 | −0.818687 | − | 0.574240i | \(-0.805298\pi\) | ||||
−0.818687 | + | 0.574240i | \(0.805298\pi\) | |||||||
\(752\) | 18.4716 | 0.673592 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.27646 | −0.192030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.6178 | 0.785712 | 0.392856 | − | 0.919600i | \(-0.371487\pi\) | ||||
0.392856 | + | 0.919600i | \(0.371487\pi\) | |||||||
\(758\) | −9.42966 | −0.342501 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 35.3793 | 1.28334 | ||||||||
\(761\) | 39.3758 | 1.42737 | 0.713685 | − | 0.700466i | \(-0.247025\pi\) | ||||
0.713685 | + | 0.700466i | \(0.247025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.6606 | −2.30467 | ||||||||
\(764\) | 9.41169 | 0.340503 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.8279 | −1.11386 | ||||||||
\(767\) | 2.02122 | 0.0729822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.29550 | 0.154900 | 0.0774499 | − | 0.996996i | \(-0.475322\pi\) | ||||
0.0774499 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(770\) | 9.83649 | 0.354482 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.15703 | 0.257587 | ||||||||
\(773\) | −27.9002 | −1.00350 | −0.501751 | − | 0.865012i | \(-0.667310\pi\) | ||||
−0.501751 | + | 0.865012i | \(0.667310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.75302 | −0.242576 | ||||||||
\(776\) | 20.8932 | 0.750021 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.2983 | −0.476768 | ||||||||
\(779\) | 23.2260 | 0.832156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.4897 | −0.590049 | ||||||||
\(782\) | 13.9180 | 0.497706 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −29.8829 | −1.06725 | ||||||||
\(785\) | −29.1201 | −1.03934 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.90689 | −0.210558 | −0.105279 | − | 0.994443i | \(-0.533574\pi\) | ||||
−0.105279 | + | 0.994443i | \(0.533574\pi\) | |||||||
\(788\) | −4.38266 | −0.156126 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.3575 | −0.795444 | ||||||||
\(791\) | 27.1276 | 0.964547 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.8734 | 1.02532 | ||||||||
\(794\) | 6.17523 | 0.219151 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0845 | −0.463767 | ||||||||
\(797\) | 7.59899 | 0.269170 | 0.134585 | − | 0.990902i | \(-0.457030\pi\) | ||||
0.134585 | + | 0.990902i | \(0.457030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.2117 | 1.38721 | ||||||||
\(800\) | −5.17741 | −0.183049 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.6600 | 0.835463 | ||||||||
\(803\) | 2.68595 | 0.0947851 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.7399 | 0.554759 | ||||||||
\(806\) | −24.4587 | −0.861521 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.4993 | 0.510083 | ||||||||
\(809\) | 9.85027 | 0.346317 | 0.173159 | − | 0.984894i | \(-0.444603\pi\) | ||||
0.173159 | + | 0.984894i | \(0.444603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.3250 | 1.62669 | 0.813346 | − | 0.581780i | \(-0.197644\pi\) | ||||
0.813346 | + | 0.581780i | \(0.197644\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.447970 | 0.0157013 | ||||||||
\(815\) | −24.4109 | −0.855075 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.2142 | 0.392334 | ||||||||
\(818\) | −21.7014 | −0.758772 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.47988 | 0.121523 | ||||||||
\(821\) | −18.0554 | −0.630136 | −0.315068 | − | 0.949069i | \(-0.602027\pi\) | ||||
−0.315068 | + | 0.949069i | \(0.602027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.6347 | −1.17243 | −0.586216 | − | 0.810155i | \(-0.699383\pi\) | ||||
−0.586216 | + | 0.810155i | \(0.699383\pi\) | |||||||
\(824\) | −10.7229 | −0.373551 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.98151 | −0.0689457 | ||||||||
\(827\) | −41.1338 | −1.43036 | −0.715181 | − | 0.698939i | \(-0.753656\pi\) | ||||
−0.715181 | + | 0.698939i | \(0.753656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.95542 | 0.276303 | 0.138152 | − | 0.990411i | \(-0.455884\pi\) | ||||
0.138152 | + | 0.990411i | \(0.455884\pi\) | |||||||
\(830\) | 3.31267 | 0.114984 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −46.7077 | −1.61930 | ||||||||
\(833\) | −63.4357 | −2.19792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.4253 | −1.01830 | ||||||||
\(836\) | 3.61759 | 0.125117 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.52591 | −0.156345 | ||||||||
\(839\) | 11.3228 | 0.390908 | 0.195454 | − | 0.980713i | \(-0.437382\pi\) | ||||
0.195454 | + | 0.980713i | \(0.437382\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 10.0342 | 0.345801 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.18126 | 0.0406606 | ||||||||
\(845\) | −26.7944 | −0.921756 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −42.2745 | −1.45257 | ||||||||
\(848\) | −20.6910 | −0.710532 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0088 | 0.411899 | ||||||||
\(851\) | 0.716822 | 0.0245723 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5146 | 0.496971 | 0.248486 | − | 0.968636i | \(-0.420067\pi\) | ||||
0.248486 | + | 0.968636i | \(0.420067\pi\) | |||||||
\(854\) | −28.3061 | −0.968615 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.1012 | −0.516148 | ||||||||
\(857\) | 10.7169 | 0.366083 | 0.183042 | − | 0.983105i | \(-0.441406\pi\) | ||||
0.183042 | + | 0.983105i | \(0.441406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7139 | 0.536150 | 0.268075 | − | 0.963398i | \(-0.413612\pi\) | ||||
0.268075 | + | 0.963398i | \(0.413612\pi\) | |||||||
\(860\) | 1.68019 | 0.0572939 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.1603 | −0.788844 | ||||||||
\(863\) | 14.4146 | 0.490679 | 0.245340 | − | 0.969437i | \(-0.421101\pi\) | ||||
0.245340 | + | 0.969437i | \(0.421101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.02775 | −0.272952 | ||||||||
\(866\) | −19.5542 | −0.664478 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.73781 | −0.296581 | ||||||||
\(869\) | −10.8456 | −0.367913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.2606 | −1.39806 | ||||||||
\(872\) | 45.6684 | 1.54653 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.8853 | −0.537328 | ||||||||
\(875\) | 52.0398 | 1.75926 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.5829 | 0.458662 | 0.229331 | − | 0.973348i | \(-0.426346\pi\) | ||||
0.229331 | + | 0.973348i | \(0.426346\pi\) | |||||||
\(878\) | 3.59384 | 0.121286 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.02703 | −0.169461 | ||||||||
\(881\) | −21.3996 | −0.720972 | −0.360486 | − | 0.932765i | \(-0.617389\pi\) | ||||
−0.360486 | + | 0.932765i | \(0.617389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1221 | −0.374288 | −0.187144 | − | 0.982332i | \(-0.559923\pi\) | ||||
−0.187144 | + | 0.982332i | \(0.559923\pi\) | |||||||
\(884\) | −15.8498 | −0.533085 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.7024 | −0.426744 | ||||||||
\(887\) | 1.53319 | 0.0514795 | 0.0257397 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257397 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.0995 | −0.640575 | ||||||||
\(890\) | −39.0720 | −1.30970 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.44457 | −0.0483678 | ||||||||
\(893\) | −44.7543 | −1.49765 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.11582 | 0.204429 | ||||||||
\(896\) | 20.7073 | 0.691783 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.33110 | 0.177901 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.9230 | −1.46329 | ||||||||
\(902\) | −4.63244 | −0.154243 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.4606 | −0.647251 | ||||||||
\(905\) | −11.9080 | −0.395837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.68948 | 0.255325 | 0.127663 | − | 0.991818i | \(-0.459253\pi\) | ||||
0.127663 | + | 0.991818i | \(0.459253\pi\) | |||||||
\(908\) | 7.70396 | 0.255665 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 49.1884 | 1.63058 | ||||||||
\(911\) | 29.5727 | 0.979788 | 0.489894 | − | 0.871782i | \(-0.337036\pi\) | ||||
0.489894 | + | 0.871782i | \(0.337036\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.60698 | 0.0531832 | ||||||||
\(914\) | 13.7398 | 0.454473 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.7529 | −0.454408 | ||||||||
\(917\) | −0.0425958 | −0.00140664 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.2295 | −1.12913 | −0.564564 | − | 0.825389i | \(-0.690956\pi\) | ||||
−0.564564 | + | 0.825389i | \(0.690956\pi\) | |||||||
\(920\) | −11.2914 | −0.372266 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.8622 | −0.785861 | ||||||||
\(923\) | −82.4586 | −2.71416 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.618494 | 0.0203360 | ||||||||
\(926\) | 0.912053 | 0.0299719 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.1477 | −1.57967 | −0.789837 | − | 0.613317i | \(-0.789835\pi\) | ||||
−0.789837 | + | 0.613317i | \(0.789835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.4023 | 2.37289 | ||||||||
\(932\) | −12.0742 | −0.395502 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.6460 | −0.413790 | ||||||||
\(935\) | −10.6714 | −0.348993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7375 | −0.448784 | −0.224392 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224392 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(938\) | 40.4500 | 1.32074 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.70542 | −0.218707 | ||||||||
\(941\) | 37.2514 | 1.21436 | 0.607181 | − | 0.794563i | \(-0.292300\pi\) | ||||
0.607181 | + | 0.794563i | \(0.292300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.41263 | −0.241389 | ||||||||
\(944\) | 1.01267 | 0.0329597 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.23668 | −0.0727207 | ||||||||
\(947\) | −16.4787 | −0.535486 | −0.267743 | − | 0.963490i | \(-0.586278\pi\) | ||||
−0.267743 | + | 0.963490i | \(0.586278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4314 | 0.436001 | ||||||||
\(950\) | −13.7063 | −0.444690 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 73.7169 | 2.38918 | ||||||||
\(953\) | 27.7913 | 0.900247 | 0.450124 | − | 0.892966i | \(-0.351380\pi\) | ||||
0.450124 | + | 0.892966i | \(0.351380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.6877 | 1.02539 | ||||||||
\(956\) | 12.5118 | 0.404662 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.9235 | 0.546773 | ||||||||
\(959\) | −52.2360 | −1.68679 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.3716 | −0.528117 | ||||||||
\(962\) | 2.24012 | 0.0722244 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.9559 | −0.385075 | ||||||||
\(965\) | 24.0966 | 0.775696 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.9876 | −1.67181 | −0.835904 | − | 0.548876i | \(-0.815056\pi\) | ||||
−0.835904 | + | 0.548876i | \(0.815056\pi\) | |||||||
\(968\) | 30.3266 | 0.974735 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.8274 | 0.476079 | ||||||||
\(971\) | −26.6145 | −0.854099 | −0.427049 | − | 0.904228i | \(-0.640447\pi\) | ||||
−0.427049 | + | 0.904228i | \(0.640447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.1520 | 0.678103 | ||||||||
\(974\) | −1.76799 | −0.0566502 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.4661 | 0.463049 | ||||||||
\(977\) | −60.8959 | −1.94823 | −0.974116 | − | 0.226050i | \(-0.927419\pi\) | ||||
−0.974116 | + | 0.226050i | \(0.927419\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9539 | −0.605768 | ||||||||
\(980\) | 10.8478 | 0.346521 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.7129 | 0.469507 | ||||||||
\(983\) | −46.9308 | −1.49686 | −0.748430 | − | 0.663214i | \(-0.769192\pi\) | ||||
−0.748430 | + | 0.663214i | \(0.769192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.7557 | −0.470156 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.0901 | 0.575523 | ||||||||
\(989\) | −3.57904 | −0.113807 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.7905 | 1.61341 | 0.806707 | − | 0.590952i | \(-0.201248\pi\) | ||||
0.806707 | + | 0.590952i | \(0.201248\pi\) | |||||||
\(992\) | 11.2153 | 0.356086 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 80.8386 | 2.56405 | ||||||||
\(995\) | −44.0534 | −1.39659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.8087 | −1.45078 | −0.725389 | − | 0.688339i | \(-0.758340\pi\) | ||||
−0.725389 | + | 0.688339i | \(0.758340\pi\) | |||||||
\(998\) | −43.5469 | −1.37845 | ||||||||
\(999\) | 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 | 7569.2.a.bj.1.8 | 9 | ||
3.2 | odd | 2 | 2523.2.a.r.1.2 | 9 | |||
29.16 | even | 7 | 261.2.k.c.82.3 | 18 | |||
29.20 | even | 7 | 261.2.k.c.226.3 | 18 | |||
29.28 | even | 2 | 7569.2.a.bm.1.2 | 9 | |||
87.20 | odd | 14 | 87.2.g.a.52.1 | ✓ | 18 | ||
87.74 | odd | 14 | 87.2.g.a.82.1 | yes | 18 | ||
87.86 | odd | 2 | 2523.2.a.o.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.g.a.52.1 | ✓ | 18 | 87.20 | odd | 14 | ||
87.2.g.a.82.1 | yes | 18 | 87.74 | odd | 14 | ||
261.2.k.c.82.3 | 18 | 29.16 | even | 7 | |||
261.2.k.c.226.3 | 18 | 29.20 | even | 7 | |||
2523.2.a.o.1.8 | 9 | 87.86 | odd | 2 | |||
2523.2.a.r.1.2 | 9 | 3.2 | odd | 2 | |||
7569.2.a.bj.1.8 | 9 | 1.1 | even | 1 | trivial | ||
7569.2.a.bm.1.2 | 9 | 29.28 | even | 2 |