Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −2.25613 | −1.30258 | −0.651289 | − | 0.758830i | \(-0.725771\pi\) | ||||
−0.651289 | + | 0.758830i | \(0.725771\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.34171 | 1.04724 | 0.523622 | − | 0.851951i | \(-0.324580\pi\) | ||||
0.523622 | + | 0.851951i | \(0.324580\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23682 | 0.845440 | 0.422720 | − | 0.906260i | \(-0.361075\pi\) | ||||
0.422720 | + | 0.906260i | \(0.361075\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09012 | 0.696708 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.83651 | 1.45826 | 0.729132 | − | 0.684374i | \(-0.239924\pi\) | ||||
0.729132 | + | 0.684374i | \(0.239924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.834816 | 0.231536 | 0.115768 | − | 0.993276i | \(-0.463067\pi\) | ||||
0.115768 | + | 0.993276i | \(0.463067\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.28320 | −1.36412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.54113 | −1.34392 | −0.671961 | − | 0.740587i | \(-0.734548\pi\) | ||||
−0.671961 | + | 0.740587i | \(0.734548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83270 | −0.420450 | −0.210225 | − | 0.977653i | \(-0.567420\pi\) | ||||
−0.210225 | + | 0.977653i | \(0.567420\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.04657 | −1.10125 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.33684 | −1.52984 | −0.764919 | − | 0.644127i | \(-0.777221\pi\) | ||||
−0.764919 | + | 0.644127i | \(0.777221\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.483606 | 0.0967212 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.05280 | 0.395061 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.35529 | −0.623062 | −0.311531 | − | 0.950236i | \(-0.600842\pi\) | ||||
−0.311531 | + | 0.950236i | \(0.600842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.777446 | 0.139633 | 0.0698167 | − | 0.997560i | \(-0.477759\pi\) | ||||
0.0698167 | + | 0.997560i | \(0.477759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.9118 | −1.89950 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.23799 | 0.885383 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.78842 | −1.28041 | −0.640204 | − | 0.768205i | \(-0.721150\pi\) | ||||
−0.640204 | + | 0.768205i | \(0.721150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.88345 | −0.301594 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.17412 | −1.43276 | −0.716379 | − | 0.697712i | \(-0.754202\pi\) | ||||
−0.716379 | + | 0.697712i | \(0.754202\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5622 | −1.76321 | −0.881606 | − | 0.471987i | \(-0.843537\pi\) | ||||
−0.881606 | + | 0.471987i | \(0.843537\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.89447 | 0.729624 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.92508 | −0.280801 | −0.140401 | − | 0.990095i | \(-0.544839\pi\) | ||||
−0.140401 | + | 0.990095i | \(0.544839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.99662 | −0.285231 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.5015 | 1.75056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.04619 | −0.281066 | −0.140533 | − | 0.990076i | \(-0.544882\pi\) | ||||
−0.140533 | + | 0.990076i | \(0.544882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3257 | 1.52716 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.13481 | 0.547669 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.668827 | 0.0870739 | 0.0435369 | − | 0.999052i | \(-0.486137\pi\) | ||||
0.0435369 | + | 0.999052i | \(0.486137\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.64673 | −1.10710 | −0.553550 | − | 0.832816i | \(-0.686727\pi\) | ||||
−0.553550 | + | 0.832816i | \(0.686727\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.67524 | 0.589025 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.95490 | 0.242475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6650 | 1.30294 | 0.651470 | − | 0.758675i | \(-0.274153\pi\) | ||||
0.651470 | + | 0.758675i | \(0.274153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.5529 | 1.99273 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.57854 | −0.424694 | −0.212347 | − | 0.977194i | \(-0.568111\pi\) | ||||
−0.212347 | + | 0.977194i | \(0.568111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.69843 | 0.666951 | 0.333476 | − | 0.942759i | \(-0.391779\pi\) | ||||
0.333476 | + | 0.942759i | \(0.391779\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.09108 | −0.125987 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8184 | 1.23287 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.38518 | −0.943407 | −0.471703 | − | 0.881757i | \(-0.656361\pi\) | ||||
−0.471703 | + | 0.881757i | \(0.656361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9018 | −1.21131 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7104 | 1.50491 | 0.752454 | − | 0.658644i | \(-0.228870\pi\) | ||||
0.752454 | + | 0.658644i | \(0.228870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.9757 | −1.40741 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.56997 | 0.811586 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.41401 | −0.891883 | −0.445942 | − | 0.895062i | \(-0.647131\pi\) | ||||
−0.445942 | + | 0.895062i | \(0.647131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.86734 | 0.195750 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.75402 | −0.181883 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.29165 | −0.440314 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.23181 | −0.328140 | −0.164070 | − | 0.986449i | \(-0.552462\pi\) | ||||
−0.164070 | + | 0.986449i | \(0.552462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1089 | 1.01598 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.70274 | −0.965459 | −0.482730 | − | 0.875769i | \(-0.660355\pi\) | ||||
−0.482730 | + | 0.875769i | \(0.660355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2046 | 1.20256 | 0.601279 | − | 0.799039i | \(-0.294658\pi\) | ||||
0.601279 | + | 0.799039i | \(0.294658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8176 | −1.15328 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.88079 | −0.858539 | −0.429269 | − | 0.903177i | \(-0.641229\pi\) | ||||
−0.429269 | + | 0.903177i | \(0.641229\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.62270 | 0.634340 | 0.317170 | − | 0.948369i | \(-0.397267\pi\) | ||||
0.317170 | + | 0.948369i | \(0.397267\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.5717 | 1.66783 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3908 | 1.44784 | 0.723922 | − | 0.689882i | \(-0.242338\pi\) | ||||
0.723922 | + | 0.689882i | \(0.242338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.1808 | −1.60211 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.74487 | 0.161313 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.3945 | −1.13620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3918 | 1.12653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.6980 | 1.86628 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5761 | −0.945954 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6489 | 1.65482 | 0.827410 | − | 0.561598i | \(-0.189813\pi\) | ||||
0.827410 | + | 0.561598i | \(0.189813\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.0857 | 2.29672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6208 | −1.53954 | −0.769769 | − | 0.638323i | \(-0.779629\pi\) | ||||
−0.769769 | + | 0.638323i | \(0.779629\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.09943 | −0.355466 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.80706 | 0.413726 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4354 | 1.74591 | 0.872957 | − | 0.487797i | \(-0.162199\pi\) | ||||
0.872957 | + | 0.487797i | \(0.162199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.68318 | 0.312404 | 0.156202 | − | 0.987725i | \(-0.450075\pi\) | ||||
0.156202 | + | 0.987725i | \(0.450075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.34322 | 0.365765 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.03760 | 0.337641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.85711 | −0.652498 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.50463 | 0.371535 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.97233 | −0.489272 | −0.244636 | − | 0.969615i | \(-0.578669\pi\) | ||||
−0.244636 | + | 0.969615i | \(0.578669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4868 | −1.82995 | −0.914974 | − | 0.403513i | \(-0.867789\pi\) | ||||
−0.914974 | + | 0.403513i | \(0.867789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.5816 | −0.936321 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.82055 | 0.146230 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.15379 | 0.570934 | 0.285467 | − | 0.958388i | \(-0.407851\pi\) | ||||
0.285467 | + | 0.958388i | \(0.407851\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.61648 | 0.366111 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.4112 | −1.29339 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2023 | 1.50404 | 0.752020 | − | 0.659141i | \(-0.229080\pi\) | ||||
0.752020 | + | 0.659141i | \(0.229080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.5523 | −1.98924 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.7445 | −1.06358 | −0.531790 | − | 0.846876i | \(-0.678481\pi\) | ||||
−0.531790 | + | 0.846876i | \(0.678481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3031 | −0.946391 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.83057 | −0.292931 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.6597 | −0.962498 | −0.481249 | − | 0.876584i | \(-0.659817\pi\) | ||||
−0.481249 | + | 0.876584i | \(0.659817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.08174 | 0.0817720 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.50896 | −0.113420 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.2307 | 1.96057 | 0.980287 | − | 0.197581i | \(-0.0633086\pi\) | ||||
0.980287 | + | 0.197581i | \(0.0633086\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1620 | −1.27564 | −0.637822 | − | 0.770184i | \(-0.720164\pi\) | ||||
−0.637822 | + | 0.770184i | \(0.720164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.5082 | 1.44208 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.2382 | −1.34090 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.7997 | −1.95979 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.59175 | 0.334001 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3138 | 1.25278 | 0.626390 | − | 0.779510i | \(-0.284532\pi\) | ||||
0.626390 | + | 0.779510i | \(0.284532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.5094 | −1.47630 | −0.738151 | − | 0.674636i | \(-0.764301\pi\) | ||||
−0.738151 | + | 0.674636i | \(0.764301\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.41050 | −0.315843 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.84527 | 0.345211 | 0.172606 | − | 0.984991i | \(-0.444781\pi\) | ||||
0.172606 | + | 0.984991i | \(0.444781\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.7280 | 1.82381 | 0.911905 | − | 0.410402i | \(-0.134612\pi\) | ||||
0.911905 | + | 0.410402i | \(0.134612\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.0617 | −1.69718 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.50519 | −0.526761 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.4831 | −1.50045 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.3349 | −1.06585 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.86388 | −0.613127 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.8319 | −1.77834 | −0.889171 | − | 0.457574i | \(-0.848718\pi\) | ||||
−0.889171 | + | 0.457574i | \(0.848718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.07365 | 0.553197 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.0752 | −1.84651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.73901 | 0.118052 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.8564 | −0.868756 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.62582 | −0.311166 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2658 | 0.821376 | 0.410688 | − | 0.911776i | \(-0.365288\pi\) | ||||
0.410688 | + | 0.911776i | \(0.365288\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.01080 | 0.0673865 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1894 | −1.00816 | −0.504078 | − | 0.863658i | \(-0.668167\pi\) | ||||
−0.504078 | + | 0.863658i | \(0.668167\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.63534 | 0.174148 | 0.0870741 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870741 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.4078 | −1.60591 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.32971 | −0.611209 | −0.305605 | − | 0.952158i | \(-0.598859\pi\) | ||||
−0.305605 | + | 0.952158i | \(0.598859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.50797 | −0.294067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.9181 | 1.22886 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0306 | −1.55441 | −0.777204 | − | 0.629249i | \(-0.783363\pi\) | ||||
−0.777204 | + | 0.629249i | \(0.783363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.53600 | 0.227773 | 0.113887 | − | 0.993494i | \(-0.463670\pi\) | ||||
0.113887 | + | 0.993494i | \(0.463670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.4374 | 1.18276 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.67550 | −0.298706 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.52997 | −0.0973495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.9324 | −1.96026 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.9214 | −0.878709 | −0.439354 | − | 0.898314i | \(-0.644793\pi\) | ||||
−0.439354 | + | 0.898314i | \(0.644793\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.4847 | −2.23091 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 29.2749 | 1.83327 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.9636 | 1.37005 | 0.685025 | − | 0.728519i | \(-0.259791\pi\) | ||||
0.685025 | + | 0.728519i | \(0.259791\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.4213 | −1.08251 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.01297 | −0.434092 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8106 | 0.913260 | 0.456630 | − | 0.889657i | \(-0.349056\pi\) | ||||
0.456630 | + | 0.889657i | \(0.349056\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.79160 | −0.294345 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.9831 | 1.16175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.15656 | −0.131488 | −0.0657438 | − | 0.997837i | \(-0.520942\pi\) | ||||
−0.0657438 | + | 0.997837i | \(0.520942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6666 | 0.647948 | 0.323974 | − | 0.946066i | \(-0.394981\pi\) | ||||
0.323974 | + | 0.946066i | \(0.394981\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.21296 | −0.254980 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.33897 | 0.141045 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.51598 | 0.571760 | 0.285880 | − | 0.958265i | \(-0.407714\pi\) | ||||
0.285880 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.62496 | 0.0972838 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2666 | −1.03004 | −0.515020 | − | 0.857178i | \(-0.672216\pi\) | ||||
−0.515020 | + | 0.857178i | \(0.672216\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.4806 | −1.15800 | −0.579001 | − | 0.815327i | \(-0.696557\pi\) | ||||
−0.579001 | + | 0.815327i | \(0.696557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.68253 | 0.573544 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.5209 | −1.21131 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7041 | 0.806124 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.29138 | 0.427428 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.4790 | 1.02113 | 0.510566 | − | 0.859838i | \(-0.329436\pi\) | ||||
0.510566 | + | 0.859838i | \(0.329436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.56620 | 0.0911876 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.92838 | 0.576103 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.12491 | −0.354213 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.8625 | −1.49069 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.8907 | 1.25759 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.2481 | −1.15941 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.1714 | −0.580513 | −0.290256 | − | 0.956949i | \(-0.593741\pi\) | ||||
−0.290256 | + | 0.956949i | \(0.593741\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.5353 | −1.56643 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.7723 | 1.17789 | 0.588946 | − | 0.808172i | \(-0.299543\pi\) | ||||
0.588946 | + | 0.808172i | \(0.299543\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.40277 | −0.531476 | −0.265738 | − | 0.964045i | \(-0.585616\pi\) | ||||
−0.265738 | + | 0.964045i | \(0.585616\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.9481 | 0.616853 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.6489 | 1.27209 | 0.636046 | − | 0.771651i | \(-0.280569\pi\) | ||||
0.636046 | + | 0.771651i | \(0.280569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2279 | −0.908588 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.0362 | 1.11831 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.1552 | 0.565052 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.403722 | 0.0223945 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.9417 | −0.826277 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.30606 | −0.237401 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8139 | 0.979143 | 0.489571 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489571 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.2788 | −0.892071 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.9744 | 1.36450 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.74895 | 0.258692 | 0.129346 | − | 0.991600i | \(-0.458712\pi\) | ||||
0.129346 | + | 0.991600i | \(0.458712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.7236 | −1.88593 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.76013 | 0.203622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1239 | −1.08659 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 38.7620 | 2.08688 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.3445 | 0.770050 | 0.385025 | − | 0.922906i | \(-0.374193\pi\) | ||||
0.385025 | + | 0.922906i | \(0.374193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.44132 | 0.0771523 | 0.0385762 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385762 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.71371 | 0.0914710 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.80296 | −0.255636 | −0.127818 | − | 0.991798i | \(-0.540797\pi\) | ||||
−0.127818 | + | 0.991798i | \(0.540797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.37990 | −0.444759 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.9637 | 1.48000 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2320 | 1.70114 | 0.850570 | − | 0.525861i | \(-0.176257\pi\) | ||||
0.850570 | + | 0.525861i | \(0.176257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6412 | −0.823222 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.9576 | −1.46739 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.3441 | 0.698461 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.3212 | −0.747559 | −0.373780 | − | 0.927518i | \(-0.621938\pi\) | ||||
−0.373780 | + | 0.927518i | \(0.621938\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −19.1751 | −0.998214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.57698 | −0.237625 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.84129 | 0.354228 | 0.177114 | − | 0.984190i | \(-0.443324\pi\) | ||||
0.177114 | + | 0.984190i | \(0.443324\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.8610 | 1.23218 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.80105 | −0.144261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0591 | −0.876266 | −0.438133 | − | 0.898910i | \(-0.644360\pi\) | ||||
−0.438133 | + | 0.898910i | \(0.644360\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42.0743 | −2.15553 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.0812 | −0.872810 | −0.436405 | − | 0.899750i | \(-0.643748\pi\) | ||||
−0.436405 | + | 0.899750i | \(0.643748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.3336 | 1.29112 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.1663 | −1.22844 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0141 | −0.609137 | −0.304568 | − | 0.952491i | \(-0.598512\pi\) | ||||
−0.304568 | + | 0.952491i | \(0.598512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.6544 | 2.05598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39.7549 | 2.00537 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.6357 | −0.987978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.1001 | −1.61106 | −0.805530 | − | 0.592555i | \(-0.798119\pi\) | ||||
−0.805530 | + | 0.592555i | \(0.798119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.24885 | 0.463022 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.36837 | −0.268084 | −0.134042 | − | 0.990976i | \(-0.542796\pi\) | ||||
−0.134042 | + | 0.990976i | \(0.542796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.649024 | 0.0323302 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.5287 | −1.26853 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.6688 | −1.86717 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4937 | 1.45837 | 0.729184 | − | 0.684318i | \(-0.239900\pi\) | ||||
0.729184 | + | 0.684318i | \(0.239900\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −46.1049 | −2.27419 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.49605 | 0.0736158 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.1057 | 1.57601 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.30974 | −0.406930 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.6861 | −1.40141 | −0.700705 | − | 0.713451i | \(-0.747131\pi\) | ||||
−0.700705 | + | 0.713451i | \(0.747131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8197 | 1.35585 | 0.677924 | − | 0.735132i | \(-0.262880\pi\) | ||||
0.677924 | + | 0.735132i | \(0.262880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.02365 | −0.195636 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.67972 | −0.129986 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.3412 | −0.935987 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.10934 | −0.439803 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4518 | −1.03330 | −0.516649 | − | 0.856197i | \(-0.672821\pi\) | ||||
−0.516649 | + | 0.856197i | \(0.672821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.3986 | 1.50892 | 0.754459 | − | 0.656347i | \(-0.227899\pi\) | ||||
0.754459 | + | 0.656347i | \(0.227899\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.7267 | 0.849929 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4462 | 0.643221 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.7221 | 1.08447 | 0.542234 | − | 0.840228i | \(-0.317579\pi\) | ||||
0.542234 | + | 0.840228i | \(0.317579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.17318 | −0.198723 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8897 | −0.612410 | −0.306205 | − | 0.951966i | \(-0.599059\pi\) | ||||
−0.306205 | + | 0.951966i | \(0.599059\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.7032 | −0.934020 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.4744 | 0.637315 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.8866 | 1.41043 | 0.705217 | − | 0.708991i | \(-0.250850\pi\) | ||||
0.705217 | + | 0.708991i | \(0.250850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3707 | −2.08934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 50.7331 | 2.38365 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.37276 | 0.204998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.07693 | 0.424601 | 0.212301 | − | 0.977204i | \(-0.431904\pi\) | ||||
0.212301 | + | 0.977204i | \(0.431904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.3748 | −0.530931 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.239249 | 0.0111429 | 0.00557147 | − | 0.999984i | \(-0.498227\pi\) | ||||
0.00557147 | + | 0.999984i | \(0.498227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.2908 | −0.524726 | −0.262363 | − | 0.964969i | \(-0.584502\pi\) | ||||
−0.262363 | + | 0.964969i | \(0.584502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.10741 | −0.190476 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9345 | 0.644809 | 0.322405 | − | 0.946602i | \(-0.395509\pi\) | ||||
0.322405 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.8558 | 1.10156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.1399 | −0.743686 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −55.9205 | −2.57123 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.886305 | −0.0406665 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.27680 | −0.195821 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.9989 | 1.82760 | 0.913798 | − | 0.406169i | \(-0.133136\pi\) | ||||
0.913798 | + | 0.406169i | \(0.133136\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.50190 | −0.296461 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.0259 | 1.68474 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.56795 | −0.343643 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.91070 | −0.222525 | −0.111263 | − | 0.993791i | \(-0.535489\pi\) | ||||
−0.111263 | + | 0.993791i | \(0.535489\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −43.3229 | −1.95913 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.23885 | 0.326685 | 0.163342 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163342 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.5921 | 0.837346 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.6721 | 1.06398 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.00456 | −0.359054 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8028 | −0.483600 | −0.241800 | − | 0.970326i | \(-0.577738\pi\) | ||||
−0.241800 | + | 0.970326i | \(0.577738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.0094 | 1.38540 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.7210 | −1.01107 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.7574 | 1.23275 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.6925 | 0.518261 | 0.259131 | − | 0.965842i | \(-0.416564\pi\) | ||||
0.259131 | + | 0.965842i | \(0.416564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7464 | 0.563867 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.76216 | −0.166104 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.5797 | 1.25937 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.31065 | −0.409482 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.5619 | 1.25373 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.55894 | 0.112109 | 0.0560546 | − | 0.998428i | \(-0.482148\pi\) | ||||
0.0560546 | + | 0.998428i | \(0.482148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.24097 | 0.272898 | 0.136449 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136449 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.44055 | −0.106514 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.30793 | −0.187656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.8293 | 1.34040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.39793 | 0.0606651 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.65870 | −0.331735 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.7962 | −0.899100 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −59.1798 | −2.55380 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.65666 | −0.415942 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.9363 | −1.24407 | −0.622034 | − | 0.782990i | \(-0.713693\pi\) | ||||
−0.622034 | + | 0.782990i | \(0.713693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.7198 | 1.66162 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.5084 | 0.664309 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.36518 | −0.357669 | −0.178835 | − | 0.983879i | \(-0.557233\pi\) | ||||
−0.178835 | + | 0.983879i | \(0.557233\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0727 | −0.771326 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.14924 | 0.261966 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.7562 | −0.797594 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 41.1478 | 1.74663 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.53757 | −0.404120 | −0.202060 | − | 0.979373i | \(-0.564764\pi\) | ||||
−0.202060 | + | 0.979373i | \(0.564764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.65227 | −0.408247 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 60.4637 | 2.55278 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.53621 | −0.106888 | −0.0534442 | − | 0.998571i | \(-0.517020\pi\) | ||||
−0.0534442 | + | 0.998571i | \(0.517020\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.0408 | 1.51625 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.3853 | −1.02409 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.1709 | −1.30675 | −0.653375 | − | 0.757034i | \(-0.726648\pi\) | ||||
−0.653375 | + | 0.757034i | \(0.726648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.4824 | −1.69413 | −0.847067 | − | 0.531486i | \(-0.821634\pi\) | ||||
−0.847067 | + | 0.531486i | \(0.821634\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −39.0621 | −1.63184 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.54814 | −0.147968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8137 | 1.49094 | 0.745472 | − | 0.666537i | \(-0.232224\pi\) | ||||
0.745472 | + | 0.666537i | \(0.232224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.2720 | 1.92300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.6677 | 1.27231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.89644 | −0.409869 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.08598 | 0.168934 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.1701 | −1.28653 | −0.643264 | − | 0.765644i | \(-0.722420\pi\) | ||||
−0.643264 | + | 0.765644i | \(0.722420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.42483 | −0.0587089 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.9316 | −0.449665 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.6221 | 0.928977 | 0.464488 | − | 0.885579i | \(-0.346238\pi\) | ||||
0.464488 | + | 0.885579i | \(0.346238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −29.0244 | −1.18988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −58.0457 | −2.37565 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.2164 | −1.11203 | −0.556016 | − | 0.831172i | \(-0.687671\pi\) | ||||
−0.556016 | + | 0.831172i | \(0.687671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.31940 | 0.216983 | 0.108492 | − | 0.994097i | \(-0.465398\pi\) | ||||
0.108492 | + | 0.994097i | \(0.465398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.2912 | 0.907769 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.0181 | 1.17975 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.9274 | 1.49884 | 0.749419 | − | 0.662096i | \(-0.230333\pi\) | ||||
0.749419 | + | 0.662096i | \(0.230333\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.9327 | 0.686147 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.60708 | −0.0650157 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −45.7494 | −1.84780 | −0.923900 | − | 0.382634i | \(-0.875017\pi\) | ||||
−0.923900 | + | 0.382634i | \(0.875017\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.4687 | 1.95445 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8664 | −0.840052 | −0.420026 | − | 0.907512i | \(-0.637979\pi\) | ||||
−0.420026 | + | 0.907512i | \(0.637979\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.81322 | 0.0728795 | 0.0364398 | − | 0.999336i | \(-0.488398\pi\) | ||||
0.0364398 | + | 0.999336i | \(0.488398\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.0611 | −0.604379 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.8207 | −0.754034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1842 | −1.08737 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.9981 | 0.798646 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.1566 | 1.72077 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7480 | 0.666729 | 0.333364 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333364 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58.2802 | 2.31643 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43.6703 | 1.73300 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.66681 | −0.0660413 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.47959 | −0.295888 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.6738 | 0.737571 | 0.368786 | − | 0.929514i | \(-0.379774\pi\) | ||||
0.368786 | + | 0.929514i | \(0.379774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.70773 | 0.225091 | 0.112545 | − | 0.993647i | \(-0.464100\pi\) | ||||
0.112545 | + | 0.993647i | \(0.464100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 61.0852 | 2.40523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.1702 | −0.832286 | −0.416143 | − | 0.909299i | \(-0.636618\pi\) | ||||
−0.416143 | + | 0.909299i | \(0.636618\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.23479 | 0.126977 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.92343 | −0.153772 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.92038 | −0.349082 | −0.174541 | − | 0.984650i | \(-0.555844\pi\) | ||||
−0.174541 | + | 0.984650i | \(0.555844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.2628 | −1.61227 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9104 | 0.464670 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.1114 | 0.705522 | 0.352761 | − | 0.935714i | \(-0.385243\pi\) | ||||
0.352761 | + | 0.935714i | \(0.385243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7241 | 1.19503 | 0.597515 | − | 0.801858i | \(-0.296155\pi\) | ||||
0.597515 | + | 0.801858i | \(0.296155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4365 | 0.405318 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.59968 | −0.372259 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.6172 | 0.953183 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.6732 | −1.06991 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.8200 | −1.61444 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.89455 | 0.111577 | 0.0557883 | − | 0.998443i | \(-0.482233\pi\) | ||||
0.0557883 | + | 0.998443i | \(0.482233\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.992745 | 0.0382108 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8588 | 1.07070 | 0.535351 | − | 0.844630i | \(-0.320179\pi\) | ||||
0.535351 | + | 0.844630i | \(0.320179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.22899 | −0.277423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.2692 | 1.31320 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.1880 | −1.07859 | −0.539293 | − | 0.842118i | \(-0.681308\pi\) | ||||
−0.539293 | + | 0.842118i | \(0.681308\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 47.8538 | 1.82840 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.94567 | −0.226841 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.70820 | −0.0650771 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.40269 | 0.167486 | 0.0837432 | − | 0.996487i | \(-0.473312\pi\) | ||||
0.0837432 | + | 0.996487i | \(0.473312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.6119 | 0.858954 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.62495 | 0.327163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.8350 | 1.92551 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0490 | 0.796148 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.3240 | −0.956475 | −0.478238 | − | 0.878230i | \(-0.658724\pi\) | ||||
−0.478238 | + | 0.878230i | \(0.658724\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2738 | 0.538348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1706 | 0.383046 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.7033 | −0.816238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7502 | 0.629066 | 0.314533 | − | 0.949247i | \(-0.398152\pi\) | ||||
0.314533 | + | 0.949247i | \(0.398152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.5261 | −0.657279 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.70400 | −0.213616 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.45488 | 0.353592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 54.2161 | 2.02474 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.99858 | −0.298297 | −0.149148 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149148 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.2996 | 1.01669 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.97767 | −0.296693 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.62264 | −0.0602633 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.6208 | 1.28401 | 0.642007 | − | 0.766699i | \(-0.278102\pi\) | ||||
0.642007 | + | 0.766699i | \(0.278102\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.89189 | −0.329329 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 64.0674 | 2.36962 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.95052 | −0.0720441 | −0.0360221 | − | 0.999351i | \(-0.511469\pi\) | ||||
−0.0360221 | + | 0.999351i | \(0.511469\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.5485 | 0.389088 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.5815 | 1.90003 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.1600 | −1.36695 | −0.683476 | − | 0.729973i | \(-0.739533\pi\) | ||||
−0.683476 | + | 0.729973i | \(0.739533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.45181 | 0.126805 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.7445 | −1.01785 | −0.508924 | − | 0.860811i | \(-0.669957\pi\) | ||||
−0.508924 | + | 0.860811i | \(0.669957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.9855 | −0.512388 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.6564 | 1.04848 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.8648 | −0.725843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.0130 | 1.71553 | 0.857764 | − | 0.514043i | \(-0.171853\pi\) | ||||
0.857764 | + | 0.514043i | \(0.171853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.4084 | 1.14459 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −52.6575 | −1.91640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0594 | −1.12887 | −0.564436 | − | 0.825477i | \(-0.690906\pi\) | ||||
−0.564436 | + | 0.825477i | \(0.690906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80.0582 | 2.90593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.98902 | 0.362102 | 0.181051 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181051 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8138 | 0.536296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.1209 | −0.980557 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.558348 | 0.0201608 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.7684 | 1.25378 | 0.626890 | − | 0.779108i | \(-0.284328\pi\) | ||||
0.626890 | + | 0.779108i | \(0.284328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.5527 | −1.78460 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.4865 | −1.45620 | −0.728100 | − | 0.685471i | \(-0.759596\pi\) | ||||
−0.728100 | + | 0.685471i | \(0.759596\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.375978 | 0.0135055 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.3048 | 1.41005 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.8134 | 0.602403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.3076 | −0.619316 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.88773 | −0.246147 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.7521 | 0.597908 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.3012 | −0.688013 | −0.344007 | − | 0.938967i | \(-0.611784\pi\) | ||||
−0.344007 | + | 0.938967i | \(0.611784\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.4146 | −1.18959 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.4265 | 1.22407 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.21843 | −0.256334 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.8105 | 0.383408 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.1738 | 0.537482 | 0.268741 | − | 0.963212i | \(-0.413392\pi\) | ||||
0.268741 | + | 0.963212i | \(0.413392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.6671 | 0.377375 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.5863 | −0.621383 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.5605 | 0.972590 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.4303 | −1.35449 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.86547 | 0.171273 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.0124 | −0.668440 | −0.334220 | − | 0.942495i | \(-0.608473\pi\) | ||||
−0.334220 | + | 0.942495i | \(0.608473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9235 | 0.488921 | 0.244460 | − | 0.969659i | \(-0.421389\pi\) | ||||
0.244460 | + | 0.969659i | \(0.421389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.0652 | −0.844003 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.9662 | 1.57510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.1900 | 0.741343 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.90297 | 0.136381 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.6868 | −1.00117 | −0.500587 | − | 0.865686i | \(-0.666883\pi\) | ||||
−0.500587 | + | 0.865686i | \(0.666883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.4739 | 0.434814 | 0.217407 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217407 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.27701 | −0.183722 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.9770 | −1.66832 | −0.834162 | − | 0.551519i | \(-0.814048\pi\) | ||||
−0.834162 | + | 0.551519i | \(0.814048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2740 | 0.877802 | 0.438901 | − | 0.898535i | \(-0.355368\pi\) | ||||
0.438901 | + | 0.898535i | \(0.355368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.4693 | −0.744761 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.0635 | 0.383328 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.1856 | −1.11383 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.59594 | 0.0551637 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.16546 | −0.212855 | −0.106428 | − | 0.994320i | \(-0.533941\pi\) | ||||
−0.106428 | + | 0.994320i | \(0.533941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.7420 | −0.611794 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.9557 | 1.34171 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.8103 | −0.991103 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.7184 | 0.952415 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 43.9508 | 1.50839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.1424 | 1.95882 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.8675 | 1.70743 | 0.853715 | − | 0.520741i | \(-0.174344\pi\) | ||||
0.853715 | + | 0.520741i | \(0.174344\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.97009 | −0.306771 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.3701 | −0.729990 | −0.364995 | − | 0.931009i | \(-0.618929\pi\) | ||||
−0.364995 | + | 0.931009i | \(0.618929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.6587 | 0.500149 | 0.250075 | − | 0.968227i | \(-0.419545\pi\) | ||||
0.250075 | + | 0.968227i | \(0.419545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 46.2978 | 1.57783 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.8017 | 1.62719 | 0.813594 | − | 0.581434i | \(-0.197508\pi\) | ||||
0.813594 | + | 0.581434i | \(0.197508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.6453 | −1.00797 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.9183 | −1.05004 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.5550 | −1.37574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.90333 | 0.301678 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.75488 | −0.228618 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.6568 | −0.799747 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.2557 | 1.62948 | 0.814740 | − | 0.579826i | \(-0.196880\pi\) | ||||
0.814740 | + | 0.579826i | \(0.196880\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −39.4349 | −1.33010 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.1880 | −1.42135 | −0.710674 | − | 0.703521i | \(-0.751610\pi\) | ||||
−0.710674 | + | 0.703521i | \(0.751610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6532 | 0.459468 | 0.229734 | − | 0.973253i | \(-0.426214\pi\) | ||||
0.229734 | + | 0.973253i | \(0.426214\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.53355 | −0.118779 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.4101 | 0.618151 | 0.309075 | − | 0.951038i | \(-0.399980\pi\) | ||||
0.309075 | + | 0.951038i | \(0.399980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.7143 | 1.39905 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −52.7265 | −1.76640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.52809 | 0.118063 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 61.4246 | 2.05320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.8186 | 0.461390 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.60856 | −0.0870002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3382 | 0.377731 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 58.3492 | 1.94174 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.1885 | −1.33591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.5302 | 1.87705 | 0.938527 | − | 0.345206i | \(-0.112191\pi\) | ||||
0.938527 | + | 0.345206i | \(0.112191\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.2799 | −0.672643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5516 | −0.515247 | −0.257623 | − | 0.966245i | \(-0.582939\pi\) | ||||
−0.257623 | + | 0.966245i | \(0.582939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.3104 | 2.19455 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 45.6824 | 1.51022 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.4147 | −1.30159 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.04563 | −0.0344921 | −0.0172461 | − | 0.999851i | \(-0.505490\pi\) | ||||
−0.0172461 | + | 0.999851i | \(0.505490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.9480 | 0.756163 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.98742 | −0.0983322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.76653 | −0.123843 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.5092 | 0.837833 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.796090 | 0.0261189 | 0.0130594 | − | 0.999915i | \(-0.495843\pi\) | ||||
0.0130594 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.65920 | 0.119925 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.8651 | −1.53430 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −62.7572 | −2.05238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3836 | −0.665904 | −0.332952 | − | 0.942944i | \(-0.608045\pi\) | ||||
−0.332952 | + | 0.942944i | \(0.608045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2139 | 0.692288 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.8415 | −0.418621 | −0.209310 | − | 0.977849i | \(-0.567122\pi\) | ||||
−0.209310 | + | 0.977849i | \(0.567122\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.3091 | 2.19189 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.7525 | 0.349780 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.0108 | 1.36517 | 0.682585 | − | 0.730807i | \(-0.260856\pi\) | ||||
0.682585 | + | 0.730807i | \(0.260856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.75714 | 0.154423 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.0990 | −1.65700 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.5148 | −0.502575 | −0.251287 | − | 0.967913i | \(-0.580854\pi\) | ||||
−0.251287 | + | 0.967913i | \(0.580854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.5438 | 1.31197 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 36.6122 | 1.18351 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.7104 | 1.47607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3956 | −0.980503 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.5620 | −0.598151 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.0272 | −1.54605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.9778 | −0.964022 | −0.482011 | − | 0.876165i | \(-0.660094\pi\) | ||||
−0.482011 | + | 0.876165i | \(0.660094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.9115 | −0.736024 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.14021 | 0.100774 | 0.0503870 | − | 0.998730i | \(-0.483955\pi\) | ||||
0.0503870 | + | 0.998730i | \(0.483955\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.23864 | 0.264119 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.910850 | −0.0291705 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.3894 | 0.460357 | 0.230178 | − | 0.973148i | \(-0.426069\pi\) | ||||
0.230178 | + | 0.973148i | \(0.426069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.6945 | −1.30060 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8423 | 0.441950 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −59.6676 | −1.90310 | −0.951550 | − | 0.307495i | \(-0.900509\pi\) | ||||
−0.951550 | + | 0.307495i | \(0.900509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.3462 | 0.361521 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.71503 | 0.309233 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 84.8297 | 2.69743 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.6315 | −1.35424 | −0.677118 | − | 0.735875i | \(-0.736771\pi\) | ||||
−0.677118 | + | 0.735875i | \(0.736771\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.1906 | −1.27541 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60.2475 | 1.90997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.5552 | 1.22105 | 0.610527 | − | 0.791995i | \(-0.290958\pi\) | ||||
0.610527 | + | 0.791995i | \(0.290958\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.9880 | −0.505839 |
(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 | 4024.2.a.d.1.4 | ✓ | 28 | |
4.3 | odd | 2 | 8048.2.a.v.1.25 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.4 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8048.2.a.v.1.25 | 28 | 4.3 | odd | 2 |