Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.823534 | −0.475468 | −0.237734 | − | 0.971330i | \(-0.576405\pi\) | ||||
−0.237734 | + | 0.971330i | \(0.576405\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.63980 | 1.62777 | 0.813883 | − | 0.581029i | \(-0.197350\pi\) | ||||
0.813883 | + | 0.581029i | \(0.197350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.42292 | 1.29374 | 0.646870 | − | 0.762600i | \(-0.276078\pi\) | ||||
0.646870 | + | 0.762600i | \(0.276078\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.32179 | −0.773931 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67000 | −0.503524 | −0.251762 | − | 0.967789i | \(-0.581010\pi\) | ||||
−0.251762 | + | 0.967789i | \(0.581010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.71525 | 0.475725 | 0.237863 | − | 0.971299i | \(-0.423553\pi\) | ||||
0.237863 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.99750 | −0.773950 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.21569 | −1.88481 | −0.942405 | − | 0.334475i | \(-0.891441\pi\) | ||||
−0.942405 | + | 0.334475i | \(0.891441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.81889 | −0.615132 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.40727 | 0.293436 | 0.146718 | − | 0.989178i | \(-0.453129\pi\) | ||||
0.146718 | + | 0.989178i | \(0.453129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.24811 | 1.64962 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.38268 | 0.843447 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.95781 | −1.84912 | −0.924559 | − | 0.381039i | \(-0.875566\pi\) | ||||
−0.924559 | + | 0.381039i | \(0.875566\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.20012 | −1.11357 | −0.556787 | − | 0.830655i | \(-0.687966\pi\) | ||||
−0.556787 | + | 0.830655i | \(0.687966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.37530 | 0.239409 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.4587 | 2.10591 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.91074 | −0.314124 | −0.157062 | − | 0.987589i | \(-0.550202\pi\) | ||||
−0.157062 | + | 0.987589i | \(0.550202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.41257 | −0.226192 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14541 | 0.647405 | 0.323702 | − | 0.946159i | \(-0.395072\pi\) | ||||
0.323702 | + | 0.946159i | \(0.395072\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.78851 | −1.18774 | −0.593868 | − | 0.804563i | \(-0.702400\pi\) | ||||
−0.593868 | + | 0.804563i | \(0.702400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.45085 | −1.25978 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.59899 | 0.524967 | 0.262483 | − | 0.964936i | \(-0.415458\pi\) | ||||
0.262483 | + | 0.964936i | \(0.415458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.71635 | 0.673765 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.823534 | 0.115318 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.21150 | −1.26530 | −0.632649 | − | 0.774439i | \(-0.718032\pi\) | ||||
−0.632649 | + | 0.774439i | \(0.718032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.07845 | −0.819619 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.76590 | 0.896166 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.69562 | −1.24140 | −0.620698 | − | 0.784050i | \(-0.713151\pi\) | ||||
−0.620698 | + | 0.784050i | \(0.713151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.94730 | −1.00127 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.24317 | 0.774370 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.29905 | −0.891721 | −0.445861 | − | 0.895102i | \(-0.647102\pi\) | ||||
−0.445861 | + | 0.895102i | \(0.647102\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.15893 | −0.139519 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5788 | −1.61151 | −0.805756 | − | 0.592248i | \(-0.798241\pi\) | ||||
−0.805756 | + | 0.592248i | \(0.798241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.25258 | 0.497727 | 0.248863 | − | 0.968539i | \(-0.419943\pi\) | ||||
0.248863 | + | 0.968539i | \(0.419943\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.79260 | −0.784342 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.71627 | −0.651429 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.8841 | 1.78710 | 0.893552 | − | 0.448960i | \(-0.148205\pi\) | ||||
0.893552 | + | 0.448960i | \(0.148205\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.35609 | 0.372899 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.87799 | −0.864722 | −0.432361 | − | 0.901701i | \(-0.642319\pi\) | ||||
−0.432361 | + | 0.901701i | \(0.642319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.63980 | −0.394791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.20059 | 0.879196 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.32519 | 0.670469 | 0.335235 | − | 0.942135i | \(-0.391184\pi\) | ||||
0.335235 | + | 0.942135i | \(0.391184\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.87116 | 0.615465 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.10601 | 0.529469 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −29.9034 | −3.06803 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2886 | 1.24772 | 0.623861 | − | 0.781535i | \(-0.285563\pi\) | ||||
0.623861 | + | 0.781535i | \(0.285563\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.87739 | 0.389692 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.139659 | −0.0138966 | −0.00694828 | − | 0.999976i | \(-0.502212\pi\) | ||||
−0.00694828 | + | 0.999976i | \(0.502212\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.4212 | −1.71656 | −0.858282 | − | 0.513178i | \(-0.828468\pi\) | ||||
−0.858282 | + | 0.513178i | \(0.828468\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.2602 | −1.00129 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.8435 | −1.14496 | −0.572479 | − | 0.819919i | \(-0.694018\pi\) | ||||
−0.572479 | + | 0.819919i | \(0.694018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.88639 | 0.563814 | 0.281907 | − | 0.959442i | \(-0.409033\pi\) | ||||
0.281907 | + | 0.959442i | \(0.409033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.57356 | 0.149356 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.374802 | −0.0352584 | −0.0176292 | − | 0.999845i | \(-0.505612\pi\) | ||||
−0.0176292 | + | 0.999845i | \(0.505612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.12218 | 0.477645 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.98246 | −0.368178 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.42292 | −0.313778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.21110 | −0.746464 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41389 | −0.307820 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8225 | 1.05743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.86284 | −0.786450 | −0.393225 | − | 0.919442i | \(-0.628641\pi\) | ||||
−0.393225 | + | 0.919442i | \(0.628641\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.41410 | 0.564730 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.3583 | −1.86609 | −0.933043 | − | 0.359764i | \(-0.882857\pi\) | ||||
−0.933043 | + | 0.359764i | \(0.882857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.1216 | −2.43845 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.9520 | 1.37293 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7961 | −1.00781 | −0.503903 | − | 0.863760i | \(-0.668103\pi\) | ||||
−0.503903 | + | 0.863760i | \(0.668103\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.38315 | −0.626230 | −0.313115 | − | 0.949715i | \(-0.601373\pi\) | ||||
−0.313115 | + | 0.949715i | \(0.601373\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.96389 | −0.249605 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.86447 | −0.239539 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.2444 | −3.00993 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.88408 | −0.320353 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.2514 | 1.41329 | 0.706645 | − | 0.707568i | \(-0.250208\pi\) | ||||
0.706645 | + | 0.707568i | \(0.250208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7179 | −0.872209 | −0.436104 | − | 0.899896i | \(-0.643642\pi\) | ||||
−0.436104 | + | 0.899896i | \(0.643642\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.32179 | 0.187706 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.5672 | −1.81264 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8328 | 0.864551 | 0.432276 | − | 0.901741i | \(-0.357711\pi\) | ||||
0.432276 | + | 0.901741i | \(0.357711\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.58599 | 0.601608 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.81697 | 0.379630 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6522 | 1.06932 | 0.534661 | − | 0.845067i | \(-0.320439\pi\) | ||||
0.534661 | + | 0.845067i | \(0.320439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00581 | 0.389702 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.6055 | 1.43974 | 0.719869 | − | 0.694110i | \(-0.244202\pi\) | ||||
0.719869 | + | 0.694110i | \(0.244202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0579 | −0.773685 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.0751 | 1.45871 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.08486 | 0.690709 | 0.345354 | − | 0.938472i | \(-0.387759\pi\) | ||||
0.345354 | + | 0.938472i | \(0.387759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.2326 | 2.13418 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.823534 | 0.0619006 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.47002 | −0.633079 | −0.316539 | − | 0.948579i | \(-0.602521\pi\) | ||||
−0.316539 | + | 0.948579i | \(0.602521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8643 | −0.807537 | −0.403769 | − | 0.914861i | \(-0.632300\pi\) | ||||
−0.403769 | + | 0.914861i | \(0.632300\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.98467 | 0.590244 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.95470 | −0.511320 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.67000 | 0.122122 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.0015 | 1.09120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.82479 | 0.710897 | 0.355448 | − | 0.934696i | \(-0.384328\pi\) | ||||
0.355448 | + | 0.934696i | \(0.384328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.28013 | 0.236109 | 0.118054 | − | 0.993007i | \(-0.462334\pi\) | ||||
0.118054 | + | 0.993007i | \(0.462334\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.14146 | −0.368188 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3655 | 0.809761 | 0.404880 | − | 0.914370i | \(-0.367313\pi\) | ||||
0.404880 | + | 0.914370i | \(0.367313\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.8798 | 1.26746 | 0.633731 | − | 0.773554i | \(-0.281523\pi\) | ||||
0.633731 | + | 0.773554i | \(0.281523\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.01102 | 0.423985 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −34.0847 | −2.39228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0885 | 1.05382 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.26739 | −0.227099 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.7202 | 0.949046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.3055 | 0.847146 | 0.423573 | − | 0.905862i | \(-0.360776\pi\) | ||||
0.423573 | + | 0.905862i | \(0.360776\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.1826 | 0.766221 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.3486 | −1.93336 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.2225 | −1.44068 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.50214 | −0.236653 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.71525 | −0.115380 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.01903 | 0.470029 | 0.235015 | − | 0.971992i | \(-0.424486\pi\) | ||||
0.235015 | + | 0.971992i | \(0.424486\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.1504 | −1.27669 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.0704 | −0.801140 | −0.400570 | − | 0.916266i | \(-0.631188\pi\) | ||||
−0.400570 | + | 0.916266i | \(0.631188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8254 | 0.979689 | 0.489845 | − | 0.871810i | \(-0.337053\pi\) | ||||
0.489845 | + | 0.871810i | \(0.337053\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.70754 | 0.309733 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.32389 | −0.479804 | −0.239902 | − | 0.970797i | \(-0.577115\pi\) | ||||
−0.239902 | + | 0.970797i | \(0.577115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0996 | 0.854523 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.0811 | −0.849710 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.14583 | −0.526910 | −0.263455 | − | 0.964672i | \(-0.584862\pi\) | ||||
−0.263455 | + | 0.964672i | \(0.584862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.717882 | 0.0462428 | 0.0231214 | − | 0.999733i | \(-0.492640\pi\) | ||||
0.0231214 | + | 0.999733i | \(0.492640\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9119 | −1.02075 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.1666 | 1.09673 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0920 | −0.896652 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.48779 | 0.411147 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 31.0093 | 1.95729 | 0.978645 | − | 0.205557i | \(-0.0659007\pi\) | ||||
0.978645 | + | 0.205557i | \(0.0659007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.35014 | −0.147752 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.99750 | 0.187710 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3229 | 1.39247 | 0.696233 | − | 0.717816i | \(-0.254858\pi\) | ||||
0.696233 | + | 0.717816i | \(0.254858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.54030 | −0.406394 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.1199 | 1.43109 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6184 | 1.39471 | 0.697355 | − | 0.716726i | \(-0.254360\pi\) | ||||
0.697355 | + | 0.716726i | \(0.254360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −33.5280 | −2.05961 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.20901 | −0.318786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.03588 | 0.489956 | 0.244978 | − | 0.969529i | \(-0.421219\pi\) | ||||
0.244978 | + | 0.969529i | \(0.421219\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90056 | 0.176196 | 0.0880982 | − | 0.996112i | \(-0.471921\pi\) | ||||
0.0880982 | + | 0.996112i | \(0.471921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.83510 | −0.292634 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.7743 | −0.830624 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.72804 | 0.464333 | 0.232167 | − | 0.972676i | \(-0.425419\pi\) | ||||
0.232167 | + | 0.972676i | \(0.425419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.3954 | 0.861830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.90146 | 0.352051 | 0.176026 | − | 0.984386i | \(-0.443676\pi\) | ||||
0.176026 | + | 0.984386i | \(0.443676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2948 | 1.80084 | 0.900419 | − | 0.435024i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435024i | \(0.143260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.6265 | 1.45875 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1894 | 0.837573 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.1201 | −0.593252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1311 | 1.17607 | 0.588036 | − | 0.808835i | \(-0.299901\pi\) | ||||
0.588036 | + | 0.808835i | \(0.299901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.63980 | −0.211917 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.31906 | −0.424695 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.41382 | 0.139595 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.6594 | −1.53662 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.115014 | 0.00660736 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.2901 | −2.02070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4030 | −0.593729 | −0.296864 | − | 0.954920i | \(-0.595941\pi\) | ||||
−0.296864 | + | 0.954920i | \(0.595941\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3470 | 0.816171 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0866 | −0.571959 | −0.285979 | − | 0.958236i | \(-0.592319\pi\) | ||||
−0.285979 | + | 0.958236i | \(0.592319\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.7156 | −0.775254 | −0.387627 | − | 0.921816i | \(-0.626705\pi\) | ||||
−0.387627 | + | 0.921816i | \(0.626705\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.9265 | −1.62983 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.6090 | −1.83150 | −0.915751 | − | 0.401745i | \(-0.868404\pi\) | ||||
−0.915751 | + | 0.401745i | \(0.868404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.6295 | 0.931074 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.75356 | 0.544390 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.21569 | 0.457133 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1476 | 0.784767 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.84764 | −0.268075 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.3190 | 0.679171 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.91630 | −0.160294 | −0.0801472 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801472 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43634 | 0.243110 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.5671 | −1.45151 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.45047 | −0.405853 | −0.202926 | − | 0.979194i | \(-0.565045\pi\) | ||||
−0.202926 | + | 0.979194i | \(0.565045\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.308662 | 0.0167642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3542 | 0.560711 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.81673 | −0.422064 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.21829 | −0.227105 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.08658 | 0.0583307 | 0.0291653 | − | 0.999575i | \(-0.490715\pi\) | ||||
0.0291653 | + | 0.999575i | \(0.490715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.8659 | 1.59869 | 0.799344 | − | 0.600874i | \(-0.205181\pi\) | ||||
0.799344 | + | 0.600874i | \(0.205181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.51740 | 0.401249 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.3790 | 1.61691 | 0.808454 | − | 0.588559i | \(-0.200305\pi\) | ||||
0.808454 | + | 0.588559i | \(0.200305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −49.4242 | −2.62316 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.81889 | 0.149191 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.7554 | 1.51765 | 0.758826 | − | 0.651293i | \(-0.225773\pi\) | ||||
0.758826 | + | 0.651293i | \(0.225773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.4976 | 2.55251 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.76212 | 0.354919 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.4785 | 0.810183 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1650 | −0.530609 | −0.265305 | − | 0.964165i | \(-0.585473\pi\) | ||||
−0.265305 | + | 0.964165i | \(0.585473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.62478 | −0.501046 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.5302 | −1.63697 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3167 | −0.637733 | −0.318866 | − | 0.947800i | \(-0.603302\pi\) | ||||
−0.318866 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.73620 | −0.502775 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.0801 | −0.879672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.7104 | −1.11519 | −0.557593 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557593 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.29885 | 0.373932 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.1847 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.8060 | −1.06037 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.0833 | 0.919225 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.3852 | 0.982870 | 0.491435 | − | 0.870914i | \(-0.336472\pi\) | ||||
0.491435 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.40727 | −0.0711687 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.5893 | 0.887264 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 57.8150 | 2.90899 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.35493 | −0.419322 | −0.209661 | − | 0.977774i | \(-0.567236\pi\) | ||||
−0.209661 | + | 0.977774i | \(0.567236\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.1591 | 1.15941 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7173 | −0.734946 | −0.367473 | − | 0.930034i | \(-0.619777\pi\) | ||||
−0.367473 | + | 0.930034i | \(0.619777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.6348 | −0.529756 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.2155 | 0.606992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.19093 | 0.158169 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.5965 | −0.771195 | −0.385597 | − | 0.922667i | \(-0.626005\pi\) | ||||
−0.385597 | + | 0.922667i | \(0.626005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.71446 | 0.479179 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.42292 | −0.168431 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.6743 | −1.40757 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.08027 | 0.297752 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.7769 | −1.16158 | −0.580789 | − | 0.814054i | \(-0.697256\pi\) | ||||
−0.580789 | + | 0.814054i | \(0.697256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.13183 | 0.250110 | 0.125055 | − | 0.992150i | \(-0.460089\pi\) | ||||
0.125055 | + | 0.992150i | \(0.460089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.35611 | −0.406288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.24811 | −0.400092 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.1873 | −1.60604 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.35899 | 0.113893 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5724 | −0.750094 | −0.375047 | − | 0.927006i | \(-0.622374\pi\) | ||||
−0.375047 | + | 0.927006i | \(0.622374\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.35744 | 0.161348 | 0.0806742 | − | 0.996741i | \(-0.474293\pi\) | ||||
0.0806742 | + | 0.996741i | \(0.474293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.8485 | 1.43113 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.5617 | −0.553071 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2109 | 0.630521 | 0.315261 | − | 0.949005i | \(-0.397908\pi\) | ||||
0.315261 | + | 0.949005i | \(0.397908\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.9504 | −0.521447 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8529 | −0.753195 | −0.376598 | − | 0.926377i | \(-0.622906\pi\) | ||||
−0.376598 | + | 0.926377i | \(0.622906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.0224 | 1.09137 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.2071 | −0.671974 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.2691 | 1.61726 | 0.808630 | − | 0.588317i | \(-0.200209\pi\) | ||||
0.808630 | + | 0.588317i | \(0.200209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.92283 | −0.325983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.82654 | 0.414707 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 21.3698 | 1.00183 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.3054 | −0.903068 | −0.451534 | − | 0.892254i | \(-0.649123\pi\) | ||||
−0.451534 | + | 0.892254i | \(0.649123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.38268 | −0.204566 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.8151 | −0.783157 | −0.391579 | − | 0.920145i | \(-0.628071\pi\) | ||||
−0.391579 | + | 0.920145i | \(0.628071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.5431 | −1.09414 | −0.547070 | − | 0.837087i | \(-0.684257\pi\) | ||||
−0.547070 | + | 0.837087i | \(0.684257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.5848 | 0.861851 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.8183 | −0.963356 | −0.481678 | − | 0.876348i | \(-0.659972\pi\) | ||||
−0.481678 | + | 0.876348i | \(0.659972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.9841 | −1.15366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.92118 | −0.411066 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.0068 | 0.598053 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −67.7640 | −3.10922 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.3872 | 0.979252 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0694 | −1.32821 | −0.664107 | − | 0.747637i | \(-0.731188\pi\) | ||||
−0.664107 | + | 0.747637i | \(0.731188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.27740 | −0.149437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.96694 | −0.180502 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.7282 | 2.03100 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2714 | −0.556068 | −0.278034 | − | 0.960571i | \(-0.589683\pi\) | ||||
−0.278034 | + | 0.960571i | \(0.589683\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.2430 | −0.508428 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8158 | 0.894277 | 0.447138 | − | 0.894465i | \(-0.352443\pi\) | ||||
0.447138 | + | 0.894465i | \(0.352443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.95781 | 0.448477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.1129 | 0.634328 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.4792 | −2.08488 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.43165 | −0.287920 | −0.143960 | − | 0.989584i | \(-0.545984\pi\) | ||||
−0.143960 | + | 0.989584i | \(0.545984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.3223 | −0.684549 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.2693 | 0.457886 | 0.228943 | − | 0.973440i | \(-0.426473\pi\) | ||||
0.228943 | + | 0.973440i | \(0.426473\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.508329 | −0.0226203 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.28303 | 0.367862 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.6208 | 0.692380 | 0.346190 | − | 0.938164i | \(-0.387475\pi\) | ||||
0.346190 | + | 0.938164i | \(0.387475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5562 | 0.643929 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.0067 | −1.58974 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −63.4097 | −2.79416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.01031 | −0.264333 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.48169 | −0.328410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.55808 | 0.243504 | 0.121752 | − | 0.992561i | \(-0.461149\pi\) | ||||
0.121752 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.22156 | 0.184596 | 0.0922980 | − | 0.995731i | \(-0.470579\pi\) | ||||
0.0922980 | + | 0.995731i | \(0.470579\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.2505 | −1.01474 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.20012 | 0.270082 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0196 | −0.913895 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.32179 | 0.100757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.11043 | 0.307987 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.1081 | −1.86372 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.97535 | 0.301009 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.87630 | −0.339256 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.0422 | −1.67856 | −0.839278 | − | 0.543703i | \(-0.817022\pi\) | ||||
−0.839278 | + | 0.543703i | \(0.817022\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.94712 | 0.383958 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.4253 | 0.917757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8232 | −1.18964 | −0.594818 | − | 0.803861i | \(-0.702776\pi\) | ||||
−0.594818 | + | 0.803861i | \(0.702776\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.5112 | 0.960755 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 81.8103 | 3.48523 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.3700 | 2.31205 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.72743 | 0.243116 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.7360 | −1.51418 | −0.757092 | − | 0.653308i | \(-0.773381\pi\) | ||||
−0.757092 | + | 0.653308i | \(0.773381\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.3593 | −0.565036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.37530 | −0.0580652 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.5933 | −1.54222 | −0.771112 | − | 0.636700i | \(-0.780299\pi\) | ||||
−0.771112 | + | 0.636700i | \(0.780299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.36420 | −0.0573924 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.4876 | 0.482435 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.6467 | 1.62016 | 0.810078 | − | 0.586323i | \(-0.199425\pi\) | ||||
0.810078 | + | 0.586323i | \(0.199425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.8657 | 0.998747 | 0.499374 | − | 0.866387i | \(-0.333564\pi\) | ||||
0.499374 | + | 0.866387i | \(0.333564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.09105 | −0.338008 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.6073 | 0.484059 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.29767 | 0.345437 | 0.172718 | − | 0.984971i | \(-0.444745\pi\) | ||||
0.172718 | + | 0.984971i | \(0.444745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.70130 | −0.112262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.9657 | −1.11873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.3832 | 0.637107 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.4953 | −0.599308 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.22441 | −0.0505367 | −0.0252684 | − | 0.999681i | \(-0.508044\pi\) | ||||
−0.0252684 | + | 0.999681i | \(0.508044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.9383 | 2.09888 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.35990 | −0.385015 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.8137 | 1.18324 | 0.591618 | − | 0.806219i | \(-0.298490\pi\) | ||||
0.591618 | + | 0.806219i | \(0.298490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4587 | −0.510758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.7246 | −0.602637 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.4720 | 1.44935 | 0.724673 | − | 0.689093i | \(-0.241991\pi\) | ||||
0.724673 | + | 0.689093i | \(0.241991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8542 | −1.05461 | −0.527307 | − | 0.849675i | \(-0.676798\pi\) | ||||
−0.527307 | + | 0.849675i | \(0.676798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.9469 | 0.690130 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.8867 | −1.21507 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6106 | −0.917737 | −0.458869 | − | 0.888504i | \(-0.651745\pi\) | ||||
−0.458869 | + | 0.888504i | \(0.651745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.0699 | 1.13745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.17318 | 0.249740 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9462 | 0.846009 | 0.423005 | − | 0.906128i | \(-0.360975\pi\) | ||||
0.423005 | + | 0.906128i | \(0.360975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.4259 | −0.501059 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.7620 | −1.19817 | −0.599086 | − | 0.800685i | \(-0.704469\pi\) | ||||
−0.599086 | + | 0.800685i | \(0.704469\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5098 | −1.02533 | −0.512663 | − | 0.858590i | \(-0.671341\pi\) | ||||
−0.512663 | + | 0.858590i | \(0.671341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.16761 | 0.247498 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.6506 | 0.867413 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.79080 | 0.0716321 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.2990 | −0.451241 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.91074 | 0.0761862 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.66481 | 0.0662751 | 0.0331376 | − | 0.999451i | \(-0.489450\pi\) | ||||
0.0331376 | + | 0.999451i | \(0.489450\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.1340 | −0.402790 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.2589 | −1.28016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.08974 | 0.320527 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.5272 | 1.24720 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.10967 | −0.0833271 | −0.0416636 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416636 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0991497 | 0.00391008 | 0.00195504 | − | 0.999998i | \(-0.499378\pi\) | ||||
0.00195504 | + | 0.999998i | \(0.499378\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.3460 | 0.919248 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.7453 | −0.736956 | −0.368478 | − | 0.929637i | \(-0.620121\pi\) | ||||
−0.368478 | + | 0.929637i | \(0.620121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.67000 | 0.0655532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.4775 | 0.684995 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.5985 | −1.19741 | −0.598707 | − | 0.800968i | \(-0.704318\pi\) | ||||
−0.598707 | + | 0.800968i | \(0.704318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −77.7400 | −3.03755 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.87361 | −0.385206 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.2995 | −1.33612 | −0.668059 | − | 0.744108i | \(-0.732875\pi\) | ||||
−0.668059 | + | 0.744108i | \(0.732875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6750 | 0.492999 | 0.246500 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246500 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.41257 | 0.0548596 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −102.357 | −3.96923 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0133 | −0.542598 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.78041 | −0.223484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.1917 | 0.625072 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.4390 | −0.440940 | −0.220470 | − | 0.975394i | \(-0.570759\pi\) | ||||
−0.220470 | + | 0.975394i | \(0.570759\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.1488 | 1.39137 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5089 | 1.09569 | 0.547844 | − | 0.836581i | \(-0.315449\pi\) | ||||
0.547844 | + | 0.836581i | \(0.315449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.0630 | 1.61423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.94038 | 0.380916 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.8553 | −1.02759 | −0.513795 | − | 0.857913i | \(-0.671761\pi\) | ||||
−0.513795 | + | 0.857913i | \(0.671761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.9353 | −1.64047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.2092 | −0.465811 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.8001 | −0.601934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.7700 | 1.55096 | 0.775482 | − | 0.631370i | \(-0.217507\pi\) | ||||
0.775482 | + | 0.631370i | \(0.217507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.2720 | 0.504161 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.8732 | −1.01936 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.14541 | −0.157019 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.03148 | 0.228131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4972 | 0.963016 | 0.481508 | − | 0.876442i | \(-0.340089\pi\) | ||||
0.481508 | + | 0.876442i | \(0.340089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.6980 | 0.592063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.7880 | −0.406298 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.478040 | −0.0179785 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0923 | 0.529246 | 0.264623 | − | 0.964352i | \(-0.414752\pi\) | ||||
0.264623 | + | 0.964352i | \(0.414752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.8796 | −1.38309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.72525 | −0.326763 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.4261 | −0.389913 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.70837 | 0.250529 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.8851 | 1.37558 | 0.687791 | − | 0.725909i | \(-0.258581\pi\) | ||||
0.687791 | + | 0.725909i | \(0.258581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.6314 | −2.22079 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.591200 | −0.0219870 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −82.1331 | −3.05035 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.3173 | −1.01314 | −0.506572 | − | 0.862198i | \(-0.669087\pi\) | ||||
−0.506572 | + | 0.862198i | \(0.669087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.03571 | 0.112434 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.78851 | 0.288068 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.50008 | −0.240086 | −0.120043 | − | 0.992769i | \(-0.538303\pi\) | ||||
−0.120043 | + | 0.992769i | \(0.538303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.1372 | −0.521460 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.1894 | 0.449003 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.5474 | 1.96977 | 0.984887 | − | 0.173201i | \(-0.0554109\pi\) | ||||
0.984887 | + | 0.173201i | \(0.0554109\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6052 | 0.426329 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.3363 | −0.819441 | −0.409720 | − | 0.912211i | \(-0.634374\pi\) | ||||
−0.409720 | + | 0.912211i | \(0.634374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.7916 | 2.30051 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.2911 | 0.669235 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.5394 | −1.48128 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.5529 | 0.677004 | 0.338502 | − | 0.940966i | \(-0.390080\pi\) | ||||
0.338502 | + | 0.940966i | \(0.390080\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.5372 | −0.930628 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0109 | −1.41975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2770 | 0.955054 | 0.477527 | − | 0.878617i | \(-0.341533\pi\) | ||||
0.477527 | + | 0.878617i | \(0.341533\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.93542 | 0.0702513 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.6124 | −1.32720 | −0.663600 | − | 0.748088i | \(-0.730972\pi\) | ||||
−0.663600 | + | 0.748088i | \(0.730972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.1486 | 0.729429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.45085 | 0.305541 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.71525 | −0.0619342 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.6282 | 1.53721 | 0.768606 | − | 0.639723i | \(-0.220951\pi\) | ||||
0.768606 | + | 0.639723i | \(0.220951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.3837 | −0.662073 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.55031 | 0.163663 | 0.0818316 | − | 0.996646i | \(-0.473923\pi\) | ||||
0.0818316 | + | 0.996646i | \(0.473923\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −51.1393 | −1.83698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.38616 | 0.193227 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.0574 | −1.22023 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.6766 | 0.811434 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.6418 | −1.55963 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.4292 | 1.40729 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.8442 | 1.45594 | 0.727969 | − | 0.685610i | \(-0.240464\pi\) | ||||
0.727969 | + | 0.685610i | \(0.240464\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.6270 | −0.663139 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.28291 | −0.0456152 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.6304 | −0.590564 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.6114 | 0.979277 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.3181 | 1.39272 | 0.696359 | − | 0.717694i | \(-0.254802\pi\) | ||||
0.696359 | + | 0.717694i | \(0.254802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.59899 | −0.127323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6858 | −0.518897 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.10180 | −0.250617 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5328 | 0.617949 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.61782 | −0.232958 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.0635 | 0.810871 | 0.405435 | − | 0.914124i | \(-0.367120\pi\) | ||||
0.405435 | + | 0.914124i | \(0.367120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.6779 | −1.21770 | −0.608852 | − | 0.793284i | \(-0.708370\pi\) | ||||
−0.608852 | + | 0.793284i | \(0.708370\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.38871 | −0.0837757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.6912 | 1.74061 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 63.9880 | 2.23866 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.6316 | −0.476327 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.0009 | −0.558434 | −0.279217 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279217 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.6078 | −0.683485 | −0.341742 | − | 0.939794i | \(-0.611017\pi\) | ||||
−0.341742 | + | 0.939794i | \(0.611017\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.3436 | 0.394935 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.558266 | 0.0194128 | 0.00970641 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970641 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.5804 | −1.47888 | −0.739439 | − | 0.673224i | \(-0.764909\pi\) | ||||
−0.739439 | + | 0.673224i | \(0.764909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.36431 | −0.220775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.71635 | −0.163412 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.7203 | 2.34356 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.1731 | −0.939241 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.9527 | 0.447178 | 0.223589 | − | 0.974684i | \(-0.428223\pi\) | ||||
0.223589 | + | 0.974684i | \(0.428223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 70.1579 | 2.41924 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.86005 | −0.167389 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.6087 | −1.25938 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.1059 | −0.965731 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.9488 | −0.856240 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.68893 | −0.0921752 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.7420 | 1.39498 | 0.697490 | − | 0.716594i | \(-0.254300\pi\) | ||||
0.697490 | + | 0.716594i | \(0.254300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 69.4296 | 2.37444 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.3564 | −1.54934 | −0.774672 | − | 0.632363i | \(-0.782085\pi\) | ||||
−0.774672 | + | 0.632363i | \(0.782085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.30053 | −0.112613 | −0.0563064 | − | 0.998414i | \(-0.517932\pi\) | ||||
−0.0563064 | + | 0.998414i | \(0.517932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6855 | −0.398239 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.4319 | −1.10399 | −0.551997 | − | 0.833846i | \(-0.686134\pi\) | ||||
−0.551997 | + | 0.833846i | \(0.686134\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.0670 | 1.12431 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.823534 | −0.0279687 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.5265 | −0.899849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5197 | −0.424215 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.5317 | −0.965651 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.4673 | 1.36804 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1805 | −0.951587 | −0.475794 | − | 0.879557i | \(-0.657839\pi\) | ||||
−0.475794 | + | 0.879557i | \(0.657839\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.5787 | −0.559184 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2321 | −1.38915 | −0.694573 | − | 0.719423i | \(-0.744407\pi\) | ||||
−0.694573 | + | 0.719423i | \(0.744407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8254 | −0.465263 | −0.232631 | − | 0.972565i | \(-0.574734\pi\) | ||||
−0.232631 | + | 0.972565i | \(0.574734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.99750 | 0.100760 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.1521 | −0.475181 | −0.237590 | − | 0.971365i | \(-0.576358\pi\) | ||||
−0.237590 | + | 0.971365i | \(0.576358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.3368 | −1.01746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.60467 | −0.187763 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.5682 | −0.989462 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.8291 | −1.03050 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.98787 | −0.0663729 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.7396 | 2.05913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.21150 | 0.306880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.9549 | 0.730614 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −39.5438 | −1.31448 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.85160 | 0.260708 | 0.130354 | − | 0.991468i | \(-0.458389\pi\) | ||||
0.130354 | + | 0.991468i | \(0.458389\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.324258 | 0.0107550 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2329 | 0.504688 | 0.252344 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252344 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1562 | 0.435408 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.0626 | 0.960779 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −73.1078 | −2.41423 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.1711 | −1.32512 | −0.662561 | − | 0.749008i | \(-0.730530\pi\) | ||||
−0.662561 | + | 0.749008i | \(0.730530\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.56720 | 0.282299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.2911 | −0.766637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.7600 | −0.518185 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.4484 | 1.32850 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.497465 | −0.0163213 | −0.00816065 | − | 0.999967i | \(-0.502598\pi\) | ||||
−0.00816065 | + | 0.999967i | \(0.502598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.7481 | −1.26992 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.30666 | 0.271948 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.07845 | 0.198787 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.7000 | −1.91765 | −0.958823 | − | 0.284004i | \(-0.908337\pi\) | ||||
−0.958823 | + | 0.284004i | \(0.908337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2953 | 0.368608 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7858 | −0.677598 | −0.338799 | − | 0.940859i | \(-0.610021\pi\) | ||||
−0.338799 | + | 0.940859i | \(0.610021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.83371 | 0.189972 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 54.6025 | 1.77622 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0761 | −0.392421 | −0.196210 | − | 0.980562i | \(-0.562864\pi\) | ||||
−0.196210 | + | 0.980562i | \(0.562864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.29425 | 0.236781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.8546 | 0.870820 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −60.9157 | −1.97325 | −0.986627 | − | 0.162995i | \(-0.947885\pi\) | ||||
−0.986627 | + | 0.162995i | \(0.947885\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.7602 | 1.15717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.6950 | −0.442696 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.3769 | −1.30384 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.44152 | 0.240049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.4982 | 0.886118 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.9390 | 0.384330 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.76303 | −0.217484 | −0.108742 | − | 0.994070i | \(-0.534682\pi\) | ||||
−0.108742 | + | 0.994070i | \(0.534682\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.76590 | −0.217352 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.29604 | 0.234141 | 0.117070 | − | 0.993124i | \(-0.462650\pi\) | ||||
0.117070 | + | 0.993124i | \(0.462650\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.2719 | −0.810180 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.6510 | −0.373131 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.0345 | 0.800924 | 0.400462 | − | 0.916313i | \(-0.368850\pi\) | ||||
0.400462 | + | 0.916313i | \(0.368850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.5631 | −0.337597 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6670 | −0.436353 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.9355 | 1.59270 | 0.796348 | − | 0.604838i | \(-0.206762\pi\) | ||||
0.796348 | + | 0.604838i | \(0.206762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.3682 | 1.31810 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.1452 | −0.322924 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.9605 | −0.348525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.6320 | 0.560098 | 0.280049 | − | 0.959986i | \(-0.409649\pi\) | ||||
0.280049 | + | 0.959986i | \(0.409649\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.40167 | 0.0762148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 65.0786 | 2.06313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.4382 | −0.330580 | −0.165290 | − | 0.986245i | \(-0.552856\pi\) | ||||
−0.165290 | + | 0.986245i | \(0.552856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.37415 | −0.264946 |
(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 | 8024.2.a.y.1.11 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.y.1.11 | ✓ | 23 | 1.1 | even | 1 | trivial |