Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15529.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 6x^{2} - x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.491317\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-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 | ||||||||
\(3\) | 0.329452 | 0.190209 | 0.0951045 | − | 0.995467i | \(-0.469681\pi\) | ||||
0.0951045 | + | 0.995467i | \(0.469681\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.07069 | 1.53858 | 0.769289 | − | 0.638901i | \(-0.220611\pi\) | ||||
0.769289 | + | 0.638901i | \(0.220611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89146 | −0.963821 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.08806 | −0.931085 | −0.465542 | − | 0.885026i | \(-0.654141\pi\) | ||||
−0.465542 | + | 0.885026i | \(0.654141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.32062 | 1.75302 | 0.876512 | − | 0.481380i | \(-0.159864\pi\) | ||||
0.876512 | + | 0.481380i | \(0.159864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.982634 | −0.238324 | −0.119162 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119162 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.08806 | −1.62611 | −0.813056 | − | 0.582185i | \(-0.802198\pi\) | ||||
−0.813056 | + | 0.582185i | \(0.802198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.34110 | 0.292651 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.94095 | −0.373536 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.63270 | −1.41736 | −0.708679 | − | 0.705531i | \(-0.750708\pi\) | ||||
−0.708679 | + | 0.705531i | \(0.750708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92047 | −1.06335 | −0.531674 | − | 0.846949i | \(-0.678437\pi\) | ||||
−0.531674 | + | 0.846949i | \(0.678437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.01737 | −0.177101 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.4825 | −1.88771 | −0.943854 | − | 0.330362i | \(-0.892829\pi\) | ||||
−0.943854 | + | 0.330362i | \(0.892829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.08234 | 0.333441 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74124 | −0.896631 | −0.448316 | − | 0.893875i | \(-0.647976\pi\) | ||||
−0.448316 | + | 0.893875i | \(0.647976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.74696 | −0.266409 | −0.133205 | − | 0.991089i | \(-0.542527\pi\) | ||||
−0.133205 | + | 0.991089i | \(0.542527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.24992 | −0.328185 | −0.164093 | − | 0.986445i | \(-0.552470\pi\) | ||||
−0.164093 | + | 0.986445i | \(0.552470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.57054 | 1.36722 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.323730 | −0.0453313 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.31781 | −0.181015 | −0.0905073 | − | 0.995896i | \(-0.528849\pi\) | ||||
−0.0905073 | + | 0.995896i | \(0.528849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.33517 | −0.309301 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.92901 | 1.03227 | 0.516134 | − | 0.856508i | \(-0.327371\pi\) | ||||
0.516134 | + | 0.856508i | \(0.327371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.51722 | 1.21855 | 0.609277 | − | 0.792957i | \(-0.291460\pi\) | ||||
0.609277 | + | 0.792957i | \(0.291460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.7703 | −1.48291 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.34110 | 0.408180 | 0.204090 | − | 0.978952i | \(-0.434576\pi\) | ||||
0.204090 | + | 0.978952i | \(0.434576\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.329452 | −0.0396613 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.92619 | −0.465954 | −0.232977 | − | 0.972482i | \(-0.574847\pi\) | ||||
−0.232977 | + | 0.972482i | \(0.574847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.66744 | 0.195159 | 0.0975793 | − | 0.995228i | \(-0.468890\pi\) | ||||
0.0975793 | + | 0.995228i | \(0.468890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.5705 | −1.43255 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9231 | −1.79149 | −0.895743 | − | 0.444572i | \(-0.853356\pi\) | ||||
−0.895743 | + | 0.444572i | \(0.853356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.03493 | 0.892771 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.9116 | 1.30747 | 0.653736 | − | 0.756723i | \(-0.273201\pi\) | ||||
0.653736 | + | 0.756723i | \(0.273201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.51461 | −0.269594 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.4998 | −1.11298 | −0.556491 | − | 0.830854i | \(-0.687853\pi\) | ||||
−0.556491 | + | 0.830854i | \(0.687853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.7293 | 2.69716 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.95051 | −0.202258 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.84125 | −0.288485 | −0.144242 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144242 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.92901 | 0.897399 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.74696 | 0.472340 | 0.236170 | − | 0.971712i | \(-0.424108\pi\) | ||||
0.236170 | + | 0.971712i | \(0.424108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.05333 | −0.497919 | −0.248960 | − | 0.968514i | \(-0.580089\pi\) | ||||
−0.248960 | + | 0.968514i | \(0.580089\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1067 | 0.968042 | 0.484021 | − | 0.875056i | \(-0.339176\pi\) | ||||
0.484021 | + | 0.875056i | \(0.339176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.78292 | −0.359059 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.335173 | −0.0315304 | −0.0157652 | − | 0.999876i | \(-0.505018\pi\) | ||||
−0.0157652 | + | 0.999876i | \(0.505018\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.2758 | −1.68960 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.46389 | −0.133081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.89146 | −0.170547 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.92047 | −0.525357 | −0.262679 | − | 0.964883i | \(-0.584606\pi\) | ||||
−0.262679 | + | 0.964883i | \(0.584606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.575540 | −0.0506735 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.02309 | 0.613610 | 0.306805 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306805 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.8533 | −2.50190 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.1414 | −1.03731 | −0.518654 | − | 0.854984i | \(-0.673567\pi\) | ||||
−0.518654 | + | 0.854984i | \(0.673567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2499 | −1.20866 | −0.604331 | − | 0.796733i | \(-0.706560\pi\) | ||||
−0.604331 | + | 0.796733i | \(0.706560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.741241 | −0.0624238 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.5184 | −1.63221 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.15303 | 0.260058 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.7826 | −1.53873 | −0.769366 | − | 0.638808i | \(-0.779428\pi\) | ||||
−0.769366 | + | 0.638808i | \(0.779428\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3566 | 1.00556 | 0.502782 | − | 0.864413i | \(-0.332310\pi\) | ||||
0.502782 | + | 0.864413i | \(0.332310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.84125 | 0.229701 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9997 | 1.03749 | 0.518744 | − | 0.854929i | \(-0.326400\pi\) | ||||
0.518744 | + | 0.854929i | \(0.326400\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.434154 | −0.0344306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.07069 | −0.320816 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.5384 | 0.982085 | 0.491042 | − | 0.871136i | \(-0.336616\pi\) | ||||
0.491042 | + | 0.871136i | \(0.336616\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.2121 | 0.867617 | 0.433808 | − | 0.901005i | \(-0.357169\pi\) | ||||
0.433808 | + | 0.901005i | \(0.357169\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9502 | 2.07309 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.4949 | 1.56728 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2133 | −1.30870 | −0.654352 | − | 0.756190i | \(-0.727058\pi\) | ||||
−0.654352 | + | 0.756190i | \(0.727058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.61222 | 0.196347 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.1859 | −1.88248 | −0.941240 | − | 0.337737i | \(-0.890339\pi\) | ||||
−0.941240 | + | 0.337737i | \(0.890339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3411 | 1.14029 | 0.570147 | − | 0.821542i | \(-0.306886\pi\) | ||||
0.570147 | + | 0.821542i | \(0.306886\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.13546 | 0.231780 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.03443 | 0.221900 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.90102 | −0.574715 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.2232 | −1.24623 | −0.623114 | − | 0.782131i | \(-0.714133\pi\) | ||||
−0.623114 | + | 0.782131i | \(0.714133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.30064 | 0.669475 | 0.334737 | − | 0.942311i | \(-0.391352\pi\) | ||||
0.334737 | + | 0.942311i | \(0.391352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.8938 | 1.63111 | 0.815557 | − | 0.578677i | \(-0.196431\pi\) | ||||
0.815557 | + | 0.578677i | \(0.196431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.35969 | −0.450827 | −0.225413 | − | 0.974263i | \(-0.572373\pi\) | ||||
−0.225413 | + | 0.974263i | \(0.572373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.10073 | 0.0776395 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −31.0704 | −2.18071 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.89146 | 0.200970 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8883 | 1.51405 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3656 | −0.713598 | −0.356799 | − | 0.934181i | \(-0.616132\pi\) | ||||
−0.356799 | + | 0.934181i | \(0.616132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.29349 | −0.0886286 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.1004 | −1.63604 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.549339 | 0.0371209 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.21085 | −0.417787 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.75289 | 0.385242 | 0.192621 | − | 0.981273i | \(-0.438301\pi\) | ||||
0.192621 | + | 0.981273i | \(0.438301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.49393 | −0.630134 | −0.315067 | − | 0.949069i | \(-0.602027\pi\) | ||||
−0.315067 | + | 0.949069i | \(0.602027\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.83532 | 0.121282 | 0.0606408 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606408 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.14139 | −0.272483 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.5687 | 1.34750 | 0.673749 | − | 0.738960i | \(-0.264683\pi\) | ||||
0.673749 | + | 0.738960i | \(0.264683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.24589 | −0.340757 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4014 | −0.802178 | −0.401089 | − | 0.916039i | \(-0.631368\pi\) | ||||
−0.401089 | + | 0.916039i | \(0.631368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7829 | 1.01667 | 0.508334 | − | 0.861160i | \(-0.330262\pi\) | ||||
0.508334 | + | 0.861160i | \(0.330262\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.46998 | 0.543349 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −44.8009 | −2.85061 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.92431 | 0.248693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.71662 | −0.613308 | −0.306654 | − | 0.951821i | \(-0.599209\pi\) | ||||
−0.306654 | + | 0.951821i | \(0.599209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.08806 | 0.194145 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.3115 | 1.20462 | 0.602309 | − | 0.798263i | \(-0.294248\pi\) | ||||
0.602309 | + | 0.798263i | \(0.294248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −46.7417 | −2.90439 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.0697 | 1.36608 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.74819 | 0.107798 | 0.0538990 | − | 0.998546i | \(-0.482835\pi\) | ||||
0.0538990 | + | 0.998546i | \(0.482835\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.45919 | −0.211699 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.7079 | 0.713843 | 0.356921 | − | 0.934134i | \(-0.383826\pi\) | ||||
0.356921 | + | 0.934134i | \(0.383826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1051 | 0.613843 | 0.306921 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306921 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.47656 | 0.513025 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.29319 | 0.318037 | 0.159018 | − | 0.987276i | \(-0.449167\pi\) | ||||
0.159018 | + | 0.987276i | \(0.449167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.1188 | 1.02488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8062 | −0.823610 | −0.411805 | − | 0.911272i | \(-0.635101\pi\) | ||||
−0.411805 | + | 0.911272i | \(0.635101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.79437 | 0.463327 | 0.231663 | − | 0.972796i | \(-0.425583\pi\) | ||||
0.231663 | + | 0.972796i | \(0.425583\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.3708 | −1.37954 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0344 | −0.943202 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.936054 | −0.0548724 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0171 | −1.40309 | −0.701546 | − | 0.712624i | \(-0.747506\pi\) | ||||
−0.701546 | + | 0.712624i | \(0.747506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.99377 | 0.347794 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.32062 | −0.365531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.11135 | −0.409891 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.56389 | 0.0898434 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.66483 | −0.0947087 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.8507 | −1.52256 | −0.761282 | − | 0.648421i | \(-0.775430\pi\) | ||||
−0.761282 | + | 0.648421i | \(0.775430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.5110 | 1.78111 | 0.890553 | − | 0.454879i | \(-0.150318\pi\) | ||||
0.890553 | + | 0.454879i | \(0.150318\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.1110 | −1.24188 | −0.620940 | − | 0.783858i | \(-0.713249\pi\) | ||||
−0.620940 | + | 0.783858i | \(0.713249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.5702 | 1.31968 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.96497 | 0.387541 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.32965 | 0.184130 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.15875 | −0.504938 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8953 | 1.31340 | 0.656702 | − | 0.754150i | \(-0.271951\pi\) | ||||
0.656702 | + | 0.754150i | \(0.271951\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.2012 | 1.81941 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.1647 | −1.09844 | −0.549220 | − | 0.835678i | \(-0.685075\pi\) | ||||
−0.549220 | + | 0.835678i | \(0.685075\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.110423 | −0.00599737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.2828 | 0.990068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4639 | 0.564997 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.2465 | −1.73108 | −0.865542 | − | 0.500837i | \(-0.833026\pi\) | ||||
−0.865542 | + | 0.500837i | \(0.833026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.3203 | 1.89065 | 0.945327 | − | 0.326125i | \(-0.105743\pi\) | ||||
0.945327 | + | 0.326125i | \(0.105743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.2680 | −0.654818 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.7409 | −1.63618 | −0.818088 | − | 0.575094i | \(-0.804966\pi\) | ||||
−0.818088 | + | 0.575094i | \(0.804966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.31781 | −0.0697457 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.4053 | −1.81584 | −0.907920 | − | 0.419143i | \(-0.862331\pi\) | ||||
−0.907920 | + | 0.419143i | \(0.862331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.2406 | 1.64424 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.482281 | −0.0253132 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2524 | −0.535173 | −0.267586 | − | 0.963534i | \(-0.586226\pi\) | ||||
−0.267586 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.6006 | 0.864192 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.36439 | −0.278505 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6993 | 1.17532 | 0.587662 | − | 0.809107i | \(-0.300049\pi\) | ||||
0.587662 | + | 0.809107i | \(0.300049\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.2434 | −2.48466 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.03503 | −0.0531661 | −0.0265831 | − | 0.999647i | \(-0.508463\pi\) | ||||
−0.0265831 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.95051 | −0.0999276 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.8707 | −1.32193 | −0.660965 | − | 0.750417i | \(-0.729853\pi\) | ||||
−0.660965 | + | 0.750417i | \(0.729853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.05128 | 0.256771 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.21678 | −0.467309 | −0.233655 | − | 0.972320i | \(-0.575068\pi\) | ||||
−0.233655 | + | 0.972320i | \(0.575068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.982634 | 0.0496939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.31377 | 0.116714 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.84825 | −0.444081 | −0.222040 | − | 0.975037i | \(-0.571272\pi\) | ||||
−0.222040 | + | 0.975037i | \(0.571272\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.50577 | −0.475884 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7281 | 0.585672 | 0.292836 | − | 0.956163i | \(-0.405401\pi\) | ||||
0.292836 | + | 0.956163i | \(0.405401\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −37.4210 | −1.86408 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.4586 | 1.75762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8709 | −1.13089 | −0.565446 | − | 0.824785i | \(-0.691296\pi\) | ||||
−0.565446 | + | 0.824785i | \(0.691296\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.2765 | 1.58823 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.69466 | −0.229899 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.41771 | 0.118113 | 0.0590565 | − | 0.998255i | \(-0.481191\pi\) | ||||
0.0590565 | + | 0.998255i | \(0.481191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.6583 | −0.811876 | −0.405938 | − | 0.913901i | \(-0.633055\pi\) | ||||
−0.405938 | + | 0.913901i | \(0.633055\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.50557 | 0.316312 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.7417 | 1.87484 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.43038 | −0.310462 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.51722 | 0.362092 | 0.181046 | − | 0.983475i | \(-0.442052\pi\) | ||||
0.181046 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.6003 | 1.37444 | 0.687221 | − | 0.726449i | \(-0.258830\pi\) | ||||
0.687221 | + | 0.726449i | \(0.258830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.08806 | 0.339068 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.52886 | −0.407060 | −0.203530 | − | 0.979069i | \(-0.565241\pi\) | ||||
−0.203530 | + | 0.979069i | \(0.565241\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.6729 | −1.31776 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.9224 | −1.70673 | −0.853363 | − | 0.521317i | \(-0.825441\pi\) | ||||
−0.853363 | + | 0.521317i | \(0.825441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.18797 | −0.292681 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.11165 | 0.241234 | 0.120617 | − | 0.992699i | \(-0.461513\pi\) | ||||
0.120617 | + | 0.992699i | \(0.461513\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7293 | 0.834840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.07090 | 0.191267 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7944 | −0.551717 | −0.275859 | − | 0.961198i | \(-0.588962\pi\) | ||||
−0.275859 | + | 0.961198i | \(0.588962\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.90724 | 0.0890226 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.7079 | 0.731589 | 0.365795 | − | 0.930696i | \(-0.380797\pi\) | ||||
0.365795 | + | 0.930696i | \(0.380797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.7752 | −1.66261 | −0.831307 | − | 0.555814i | \(-0.812407\pi\) | ||||
−0.831307 | + | 0.555814i | \(0.812407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.2118 | 0.981564 | 0.490782 | − | 0.871282i | \(-0.336711\pi\) | ||||
0.490782 | + | 0.871282i | \(0.336711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6006 | 0.628016 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.28277 | 0.197340 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.39472 | 0.248050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.81039 | 0.174466 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6077 | 1.12436 | 0.562178 | − | 0.827016i | \(-0.309964\pi\) | ||||
0.562178 | + | 0.827016i | \(0.309964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −72.5764 | −3.30920 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.34110 | −0.0610220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3507 | −0.695605 | −0.347802 | − | 0.937568i | \(-0.613072\pi\) | ||||
−0.347802 | + | 0.937568i | \(0.613072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.13080 | 0.186801 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.1430 | −0.593134 | −0.296567 | − | 0.955012i | \(-0.595842\pi\) | ||||
−0.296567 | + | 0.955012i | \(0.595842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.50015 | 0.337790 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.9823 | −0.716906 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.6841 | −0.925949 | −0.462975 | − | 0.886371i | \(-0.653218\pi\) | ||||
−0.462975 | + | 0.886371i | \(0.653218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.69384 | 0.165029 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.7956 | −1.59605 | −0.798023 | − | 0.602627i | \(-0.794121\pi\) | ||||
−0.798023 | + | 0.602627i | \(0.794121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.87879 | 0.394321 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.9242 | 1.50366 | 0.751832 | − | 0.659355i | \(-0.229170\pi\) | ||||
0.751832 | + | 0.659355i | \(0.229170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.78762 | 0.300267 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.7576 | 0.607412 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.94790 | 0.305568 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.67095 | −0.248927 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.3346 | 0.540387 | 0.270194 | − | 0.962806i | \(-0.412912\pi\) | ||||
0.270194 | + | 0.962806i | \(0.412912\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.25274 | 0.229686 | 0.114843 | − | 0.993384i | \(-0.463363\pi\) | ||||
0.114843 | + | 0.993384i | \(0.463363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.81766 | 0.253421 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.9264 | −0.994922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.2882 | −1.57182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.29753 | −0.358065 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.5544 | −1.27300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.4715 | −1.22408 | −0.612042 | − | 0.790825i | \(-0.709652\pi\) | ||||
−0.612042 | + | 0.790825i | \(0.709652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.05415 | 0.216894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.6025 | 1.09468 | 0.547341 | − | 0.836910i | \(-0.315640\pi\) | ||||
0.547341 | + | 0.836910i | \(0.315640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.5187 | −1.17447 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1011 | 2.30478 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −64.8180 | −2.75634 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.7938 | 0.669203 | 0.334602 | − | 0.942360i | \(-0.391398\pi\) | ||||
0.334602 | + | 0.942360i | \(0.391398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0419 | −0.467022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.999698 | 0.0422073 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.8996 | 1.76586 | 0.882929 | − | 0.469507i | \(-0.155568\pi\) | ||||
0.882929 | + | 0.469507i | \(0.155568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.7078 | 1.37360 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.5485 | 1.02913 | 0.514563 | − | 0.857453i | \(-0.327954\pi\) | ||||
0.514563 | + | 0.857453i | \(0.327954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3231 | −1.60377 | −0.801886 | − | 0.597476i | \(-0.796170\pi\) | ||||
−0.801886 | + | 0.597476i | \(0.796170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.67422 | −0.237044 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.9288 | 0.996169 | 0.498085 | − | 0.867128i | \(-0.334037\pi\) | ||||
0.498085 | + | 0.867128i | \(0.334037\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.06411 | 0.127340 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.4886 | 2.01165 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.06947 | 0.168540 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.8130 | −1.43689 | −0.718443 | − | 0.695585i | \(-0.755145\pi\) | ||||
−0.718443 | + | 0.695585i | \(0.755145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.9647 | 1.72912 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.54239 | 0.310252 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5702 | −0.639393 | −0.319697 | − | 0.947520i | \(-0.603581\pi\) | ||||
−0.319697 | + | 0.947520i | \(0.603581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.09521 | −0.0857513 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2121 | 1.27529 | 0.637645 | − | 0.770330i | \(-0.279908\pi\) | ||||
0.637645 | + | 0.770330i | \(0.279908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.2553 | 1.27493 | 0.637466 | − | 0.770478i | \(-0.279983\pi\) | ||||
0.637466 | + | 0.770478i | \(0.279983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.66065 | −0.393412 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.6469 | 1.24392 | 0.621959 | − | 0.783050i | \(-0.286337\pi\) | ||||
0.621959 | + | 0.783050i | \(0.286337\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.2362 | −0.414791 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.2209 | −0.575317 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.459494 | 0.0185588 | 0.00927940 | − | 0.999957i | \(-0.497046\pi\) | ||||
0.00927940 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.6010 | −0.950140 | −0.475070 | − | 0.879948i | \(-0.657577\pi\) | ||||
−0.475070 | + | 0.879948i | \(0.657577\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8893 | 1.00038 | 0.500192 | − | 0.865914i | \(-0.333263\pi\) | ||||
0.500192 | + | 0.865914i | \(0.333263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.94095 | 0.0778877 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.7417 | −1.71241 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.21115 | 0.287986 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.2831 | 0.449886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8918 | −0.831690 | −0.415845 | − | 0.909435i | \(-0.636514\pi\) | ||||
−0.415845 | + | 0.909435i | \(0.636514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.41497 | −0.135733 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 60.4917 | 2.39677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3524 | 0.449096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.0056 | −0.632184 | −0.316092 | − | 0.948729i | \(-0.602371\pi\) | ||||
−0.316092 | + | 0.948729i | \(0.602371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0242 | 0.592497 | 0.296249 | − | 0.955111i | \(-0.404264\pi\) | ||||
0.296249 | + | 0.955111i | \(0.404264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.3791 | 1.78404 | 0.892018 | − | 0.452001i | \(-0.149290\pi\) | ||||
0.892018 | + | 0.452001i | \(0.149290\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4852 | −0.961130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.93993 | −0.311190 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.2506 | 0.557671 | 0.278835 | − | 0.960339i | \(-0.410052\pi\) | ||||
0.278835 | + | 0.960339i | \(0.410052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.82133 | −0.188098 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3535 | −0.403314 | −0.201657 | − | 0.979456i | \(-0.564633\pi\) | ||||
−0.201657 | + | 0.979456i | \(0.564633\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4651 | 1.02937 | 0.514687 | − | 0.857378i | \(-0.327908\pi\) | ||||
0.514687 | + | 0.857378i | \(0.327908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.04618 | −0.0794669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.63270 | 0.295539 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.89530 | 0.0732765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.3897 | −1.13458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0587 | 0.464831 | 0.232415 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232415 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.54878 | −0.213257 | −0.106629 | − | 0.994299i | \(-0.534006\pi\) | ||||
−0.106629 | + | 0.994299i | \(0.534006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5658 | −0.443856 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.12779 | −0.119857 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.397032 | 0.0151920 | 0.00759601 | − | 0.999971i | \(-0.497582\pi\) | ||||
0.00759601 | + | 0.999971i | \(0.497582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.604651 | 0.0230689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.32935 | −0.317323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.4949 | 0.817703 | 0.408851 | − | 0.912601i | \(-0.365929\pi\) | ||||
0.408851 | + | 0.912601i | \(0.365929\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 36.3472 | 1.38072 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.64154 | 0.213688 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.77638 | 0.256306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.6027 | 1.68462 | 0.842311 | − | 0.538992i | \(-0.181195\pi\) | ||||
0.842311 | + | 0.538992i | \(0.181195\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.3885 | 3.06963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.3234 | 0.726732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7476 | 1.11719 | 0.558597 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558597 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.0410 | 1.72667 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.92047 | 0.221723 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.08565 | −0.152582 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.1758 | 1.31184 | 0.655918 | − | 0.754832i | \(-0.272282\pi\) | ||||
0.655918 | + | 0.754832i | \(0.272282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.5705 | −0.766087 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.19971 | 0.193379 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.6030 | 1.02374 | 0.511870 | − | 0.859063i | \(-0.328953\pi\) | ||||
0.511870 | + | 0.859063i | \(0.328953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.3144 | −0.789421 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.71662 | 0.0634916 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.0939 | −1.88720 | −0.943598 | − | 0.331093i | \(-0.892583\pi\) | ||||
−0.943598 | + | 0.331093i | \(0.892583\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.3175 | −0.380050 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5558 | 0.498658 | 0.249329 | − | 0.968419i | \(-0.419790\pi\) | ||||
0.249329 | + | 0.968419i | \(0.419790\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.7597 | −0.542212 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.8006 | 1.97375 | 0.986877 | − | 0.161477i | \(-0.0516257\pi\) | ||||
0.986877 | + | 0.161477i | \(0.0516257\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −34.4420 | −1.26017 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.6539 | −1.62944 | −0.814722 | − | 0.579852i | \(-0.803111\pi\) | ||||
−0.814722 | + | 0.579852i | \(0.803111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.20116 | −0.116657 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1581 | −0.914388 | −0.457194 | − | 0.889367i | \(-0.651146\pi\) | ||||
−0.457194 | + | 0.889367i | \(0.651146\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.01737 | 0.0369281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.9387 | −0.831526 | −0.415763 | − | 0.909473i | \(-0.636485\pi\) | ||||
−0.415763 | + | 0.909473i | \(0.636485\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.1411 | 1.48941 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.1162 | 1.80959 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.7337 | −1.28859 | −0.644295 | − | 0.764777i | \(-0.722849\pi\) | ||||
−0.644295 | + | 0.764777i | \(0.722849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.36220 | 0.229129 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.9587 | 0.394158 | 0.197079 | − | 0.980388i | \(-0.436854\pi\) | ||||
0.197079 | + | 0.980388i | \(0.436854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3991 | −0.552440 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.6943 | 1.45802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.1243 | 0.433842 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.8147 | 0.529435 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.56216 | −0.126977 | −0.0634887 | − | 0.997983i | \(-0.520223\pi\) | ||||
−0.0634887 | + | 0.997983i | \(0.520223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.575944 | 0.0205042 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.36439 | −0.0485120 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.1547 | 2.13616 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.7128 | 1.58381 | 0.791903 | − | 0.610646i | \(-0.209090\pi\) | ||||
0.791903 | + | 0.610646i | \(0.209090\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.21085 | 0.0782143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 30.3599 | 1.07271 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.14914 | −0.181709 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.85718 | 0.135779 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.68159 | 0.340387 | 0.170193 | − | 0.985411i | \(-0.445561\pi\) | ||||
0.170193 | + | 0.985411i | \(0.445561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.5981 | −1.25002 | −0.625009 | − | 0.780618i | \(-0.714905\pi\) | ||||
−0.625009 | + | 0.780618i | \(0.714905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.32915 | 0.116758 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3826 | 0.433212 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −74.3953 | −2.59958 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.17888 | 0.285445 | 0.142722 | − | 0.989763i | \(-0.454414\pi\) | ||||
0.142722 | + | 0.989763i | \(0.454414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.50587 | 0.0524914 | 0.0262457 | − | 0.999656i | \(-0.491645\pi\) | ||||
0.0262457 | + | 0.999656i | \(0.491645\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3652 | 0.882035 | 0.441017 | − | 0.897499i | \(-0.354618\pi\) | ||||
0.441017 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.2130 | 1.32719 | 0.663596 | − | 0.748091i | \(-0.269029\pi\) | ||||
0.663596 | + | 0.748091i | \(0.269029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.74385 | 0.0604935 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.40434 | −0.325841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.4914 | 0.397199 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.1575 | −0.454248 | −0.227124 | − | 0.973866i | \(-0.572932\pi\) | ||||
−0.227124 | + | 0.973866i | \(0.572932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.2582 | 1.00890 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.54848 | −0.156658 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.95904 | −0.204755 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.56787 | 0.0881290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4825 | 0.393614 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2756 | −0.454549 | −0.227274 | − | 0.973831i | \(-0.572981\pi\) | ||||
−0.227274 | + | 0.973831i | \(0.572981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.18894 | −0.0747729 | −0.0373864 | − | 0.999301i | \(-0.511903\pi\) | ||||
−0.0373864 | + | 0.999301i | \(0.511903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4092 | 0.730472 | 0.365236 | − | 0.930915i | \(-0.380988\pi\) | ||||
0.365236 | + | 0.930915i | \(0.380988\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.69956 | −0.262400 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2923 | −0.486514 | −0.243257 | − | 0.969962i | \(-0.578216\pi\) | ||||
−0.243257 | + | 0.969962i | \(0.578216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.28257 | −0.179405 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.1714 | 1.66803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1178 | 0.715549 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.21536 | 0.278048 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.7835 | −0.769346 | −0.384673 | − | 0.923053i | \(-0.625686\pi\) | ||||
−0.384673 | + | 0.923053i | \(0.625686\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.91246 | −0.266881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.1007 | −1.45210 | −0.726050 | − | 0.687642i | \(-0.758646\pi\) | ||||
−0.726050 | + | 0.687642i | \(0.758646\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.35101 | −0.314687 | −0.157343 | − | 0.987544i | \(-0.550293\pi\) | ||||
−0.157343 | + | 0.987544i | \(0.550293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.9902 | −0.771936 | −0.385968 | − | 0.922512i | \(-0.626132\pi\) | ||||
−0.385968 | + | 0.922512i | \(0.626132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.1004 | −0.808302 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −24.8124 | −0.831245 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.9476 | 0.533666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.08234 | −0.0695272 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.1892 | 1.50714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29492 | 0.0431401 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.34285 | −0.0779650 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.3070 | 0.973123 | 0.486561 | − | 0.873646i | \(-0.338251\pi\) | ||||
0.486561 | + | 0.873646i | \(0.338251\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7257 | −0.455251 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.8533 | −1.75111 | −0.875554 | − | 0.483120i | \(-0.839504\pi\) | ||||
−0.875554 | + | 0.483120i | \(0.839504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.7838 | −1.21737 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.5888 | 0.944086 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.3696 | −0.902840 | −0.451420 | − | 0.892312i | \(-0.649082\pi\) | ||||
−0.451420 | + | 0.892312i | \(0.649082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.8160 | −0.816828 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6115 | 0.479905 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.64485 | 0.152393 | 0.0761963 | − | 0.997093i | \(-0.475722\pi\) | ||||
0.0761963 | + | 0.997093i | \(0.475722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −67.8366 | −2.22325 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.84601 | −0.289605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.6704 | −0.642606 | −0.321303 | − | 0.946977i | \(-0.604121\pi\) | ||||
−0.321303 | + | 0.946977i | \(0.604121\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.3813 | 0.338783 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.31259 | −0.238384 | −0.119192 | − | 0.992871i | \(-0.538030\pi\) | ||||
−0.119192 | + | 0.992871i | \(0.538030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.74124 | 0.186961 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.3846 | −1.18234 | −0.591170 | − | 0.806547i | \(-0.701334\pi\) | ||||
−0.591170 | + | 0.806547i | \(0.701334\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5392 | 0.342118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.28452 | −0.236217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.2456 | 0.720605 | 0.360303 | − | 0.932835i | \(-0.382673\pi\) | ||||
0.360303 | + | 0.932835i | \(0.382673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.76526 | 0.251015 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.4239 | −1.59598 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.05200 | 0.130710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.4661 | −1.59072 | −0.795361 | − | 0.606136i | \(-0.792719\pi\) | ||||
−0.795361 | + | 0.606136i | \(0.792719\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.29462 | 0.0737138 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.9113 | 0.927809 | 0.463904 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463904 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −58.0071 | −1.85962 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.1228 | 1.76354 | 0.881768 | − | 0.471684i | \(-0.156354\pi\) | ||||
0.881768 | + | 0.471684i | \(0.156354\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.4242 | 1.03628 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.2230 | −0.933019 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.6824 | −0.851037 | −0.425518 | − | 0.904950i | \(-0.639908\pi\) | ||||
−0.425518 | + | 0.904950i | \(0.639908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.01737 | −0.0960438 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.74696 | 0.0555502 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.7063 | −0.816588 | −0.408294 | − | 0.912851i | \(-0.633876\pi\) | ||||
−0.408294 | + | 0.912851i | \(0.633876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.87235 | 0.249821 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.95372 | 0.0618750 | 0.0309375 | − | 0.999521i | \(-0.490151\pi\) | ||||
0.0309375 | + | 0.999521i | \(0.490151\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.2869 | 0.705128 |
(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 | 4600.2.a.bb.1.2 | yes | 4 | |
4.3 | odd | 2 | 9200.2.a.cn.1.3 | 4 | |||
5.2 | odd | 4 | 4600.2.e.t.4049.4 | 8 | |||
5.3 | odd | 4 | 4600.2.e.t.4049.5 | 8 | |||
5.4 | even | 2 | 4600.2.a.ba.1.3 | ✓ | 4 | ||
20.19 | odd | 2 | 9200.2.a.cp.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.ba.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
4600.2.a.bb.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
4600.2.e.t.4049.4 | 8 | 5.2 | odd | 4 | |||
4600.2.e.t.4049.5 | 8 | 5.3 | odd | 4 | |||
9200.2.a.cn.1.3 | 4 | 4.3 | odd | 2 | |||
9200.2.a.cp.1.2 | 4 | 20.19 | odd | 2 |