Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99802 | −1.41281 | −0.706406 | − | 0.707807i | \(-0.749685\pi\) | ||||
−0.706406 | + | 0.707807i | \(0.749685\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.99208 | 0.996039 | ||||||||
\(5\) | −1.55092 | −0.693593 | −0.346797 | − | 0.937940i | \(-0.612731\pi\) | ||||
−0.346797 | + | 0.937940i | \(0.612731\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.0158280 | 0.00559603 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.09877 | 0.979917 | ||||||||
\(11\) | −5.13227 | −1.54744 | −0.773719 | − | 0.633529i | \(-0.781606\pi\) | ||||
−0.773719 | + | 0.633529i | \(0.781606\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23567 | 0.897414 | 0.448707 | − | 0.893679i | \(-0.351885\pi\) | ||||
0.448707 | + | 0.893679i | \(0.351885\pi\) | |||||||
\(14\) | 1.99802 | 0.533993 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.01578 | −1.00395 | ||||||||
\(17\) | 3.98079 | 0.965484 | 0.482742 | − | 0.875763i | \(-0.339641\pi\) | ||||
0.482742 | + | 0.875763i | \(0.339641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.86954 | 0.658317 | 0.329159 | − | 0.944275i | \(-0.393235\pi\) | ||||
0.329159 | + | 0.944275i | \(0.393235\pi\) | |||||||
\(20\) | −3.08956 | −0.690846 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.2544 | 2.18624 | ||||||||
\(23\) | −1.67857 | −0.350006 | −0.175003 | − | 0.984568i | \(-0.555993\pi\) | ||||
−0.175003 | + | 0.984568i | \(0.555993\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.59464 | −0.518928 | ||||||||
\(26\) | −6.46494 | −1.26788 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.99208 | −0.376467 | ||||||||
\(29\) | −7.42810 | −1.37936 | −0.689682 | − | 0.724112i | \(-0.742250\pi\) | ||||
−0.689682 | + | 0.724112i | \(0.742250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.815589 | 0.146484 | 0.0732420 | − | 0.997314i | \(-0.476665\pi\) | ||||
0.0732420 | + | 0.997314i | \(0.476665\pi\) | |||||||
\(32\) | 7.99195 | 1.41279 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.95370 | −1.36405 | ||||||||
\(35\) | 1.55092 | 0.262154 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.873940 | 0.143675 | 0.0718374 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718374 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(38\) | −5.73339 | −0.930079 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0245479 | −0.00388137 | ||||||||
\(41\) | −5.56058 | −0.868417 | −0.434208 | − | 0.900812i | \(-0.642972\pi\) | ||||
−0.434208 | + | 0.900812i | \(0.642972\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.95707 | 0.755946 | 0.377973 | − | 0.925817i | \(-0.376621\pi\) | ||||
0.377973 | + | 0.925817i | \(0.376621\pi\) | |||||||
\(44\) | −10.2239 | −1.54131 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.35381 | 0.494493 | ||||||||
\(47\) | −6.85565 | −1.00000 | −0.500000 | − | 0.866026i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866026i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.18414 | 0.733148 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.44571 | 0.893860 | ||||||||
\(53\) | 8.02140 | 1.10182 | 0.550912 | − | 0.834563i | \(-0.314280\pi\) | ||||
0.550912 | + | 0.834563i | \(0.314280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.95975 | 1.07329 | ||||||||
\(56\) | −0.0158280 | −0.00211510 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.8415 | 1.94878 | ||||||||
\(59\) | 9.91489 | 1.29081 | 0.645405 | − | 0.763841i | \(-0.276689\pi\) | ||||
0.645405 | + | 0.763841i | \(0.276689\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.38875 | −0.817996 | −0.408998 | − | 0.912535i | \(-0.634122\pi\) | ||||
−0.408998 | + | 0.912535i | \(0.634122\pi\) | |||||||
\(62\) | −1.62956 | −0.206955 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.93650 | −0.992063 | ||||||||
\(65\) | −5.01828 | −0.622441 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.256190 | −0.0312986 | −0.0156493 | − | 0.999878i | \(-0.504982\pi\) | ||||
−0.0156493 | + | 0.999878i | \(0.504982\pi\) | |||||||
\(68\) | 7.93005 | 0.961660 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.09877 | −0.370374 | ||||||||
\(71\) | −1.58801 | −0.188462 | −0.0942311 | − | 0.995550i | \(-0.530039\pi\) | ||||
−0.0942311 | + | 0.995550i | \(0.530039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.67421 | 1.13228 | 0.566141 | − | 0.824309i | \(-0.308436\pi\) | ||||
0.566141 | + | 0.824309i | \(0.308436\pi\) | |||||||
\(74\) | −1.74615 | −0.202986 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.71635 | 0.655710 | ||||||||
\(77\) | 5.13227 | 0.584876 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.34418 | 0.488758 | 0.244379 | − | 0.969680i | \(-0.421416\pi\) | ||||
0.244379 | + | 0.969680i | \(0.421416\pi\) | |||||||
\(80\) | 6.22816 | 0.696330 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1101 | 1.22691 | ||||||||
\(83\) | −2.94073 | −0.322787 | −0.161393 | − | 0.986890i | \(-0.551599\pi\) | ||||
−0.161393 | + | 0.986890i | \(0.551599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.17390 | −0.669654 | ||||||||
\(86\) | −9.90432 | −1.06801 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0812334 | −0.00865950 | ||||||||
\(89\) | −17.8737 | −1.89461 | −0.947305 | − | 0.320334i | \(-0.896205\pi\) | ||||
−0.947305 | + | 0.320334i | \(0.896205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23567 | −0.339191 | ||||||||
\(92\) | −3.34384 | −0.348619 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.6977 | 1.41281 | ||||||||
\(95\) | −4.45043 | −0.456605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.77305 | −0.383095 | −0.191547 | − | 0.981483i | \(-0.561351\pi\) | ||||
−0.191547 | + | 0.981483i | \(0.561351\pi\) | |||||||
\(98\) | −1.99802 | −0.201830 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.16873 | −0.516873 | ||||||||
\(101\) | −14.2674 | −1.41966 | −0.709830 | − | 0.704373i | \(-0.751228\pi\) | ||||
−0.709830 | + | 0.704373i | \(0.751228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.7257 | −1.05683 | −0.528417 | − | 0.848985i | \(-0.677214\pi\) | ||||
−0.528417 | + | 0.848985i | \(0.677214\pi\) | |||||||
\(104\) | 0.0512141 | 0.00502196 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.0269 | −1.55667 | ||||||||
\(107\) | 6.64559 | 0.642453 | 0.321227 | − | 0.947002i | \(-0.395905\pi\) | ||||
0.321227 | + | 0.947002i | \(0.395905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.55843 | 0.628184 | 0.314092 | − | 0.949393i | \(-0.398300\pi\) | ||||
0.314092 | + | 0.949393i | \(0.398300\pi\) | |||||||
\(110\) | −15.9037 | −1.51636 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.01578 | 0.379456 | ||||||||
\(113\) | −7.71152 | −0.725439 | −0.362719 | − | 0.931898i | \(-0.618152\pi\) | ||||
−0.362719 | + | 0.931898i | \(0.618152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.60333 | 0.242762 | ||||||||
\(116\) | −14.7974 | −1.37390 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.8101 | −1.82367 | ||||||||
\(119\) | −3.98079 | −0.364919 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.3402 | 1.39456 | ||||||||
\(122\) | 12.7648 | 1.15567 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.62472 | 0.145904 | ||||||||
\(125\) | 11.7787 | 1.05352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −0.126623 | −0.0111920 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.0266 | 0.879392 | ||||||||
\(131\) | −8.92539 | −0.779815 | −0.389908 | − | 0.920854i | \(-0.627493\pi\) | ||||
−0.389908 | + | 0.920854i | \(0.627493\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.86954 | −0.248821 | ||||||||
\(134\) | 0.511872 | 0.0442190 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0630079 | 0.00540288 | ||||||||
\(137\) | 3.87525 | 0.331085 | 0.165542 | − | 0.986203i | \(-0.447063\pi\) | ||||
0.165542 | + | 0.986203i | \(0.447063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.869547 | −0.0737540 | −0.0368770 | − | 0.999320i | \(-0.511741\pi\) | ||||
−0.0368770 | + | 0.999320i | \(0.511741\pi\) | |||||||
\(140\) | 3.08956 | 0.261115 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.17287 | 0.266262 | ||||||||
\(143\) | −16.6063 | −1.38869 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.5204 | 0.956718 | ||||||||
\(146\) | −19.3293 | −1.59970 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.74096 | 0.143106 | ||||||||
\(149\) | −6.13788 | −0.502835 | −0.251417 | − | 0.967879i | \(-0.580897\pi\) | ||||
−0.251417 | + | 0.967879i | \(0.580897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5483 | −1.26530 | −0.632651 | − | 0.774437i | \(-0.718033\pi\) | ||||
−0.632651 | + | 0.774437i | \(0.718033\pi\) | |||||||
\(152\) | 0.0454189 | 0.00368396 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.2544 | −0.826321 | ||||||||
\(155\) | −1.26491 | −0.101600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.57703 | 0.205669 | 0.102835 | − | 0.994698i | \(-0.467209\pi\) | ||||
0.102835 | + | 0.994698i | \(0.467209\pi\) | |||||||
\(158\) | −8.67975 | −0.690524 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.3949 | −0.979902 | ||||||||
\(161\) | 1.67857 | 0.132290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.26237 | 0.725485 | 0.362743 | − | 0.931889i | \(-0.381840\pi\) | ||||
0.362743 | + | 0.931889i | \(0.381840\pi\) | |||||||
\(164\) | −11.0771 | −0.864977 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.87563 | 0.456037 | ||||||||
\(167\) | −7.38632 | −0.571570 | −0.285785 | − | 0.958294i | \(-0.592254\pi\) | ||||
−0.285785 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.53042 | −0.194648 | ||||||||
\(170\) | 12.3356 | 0.946095 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.87487 | 0.752952 | ||||||||
\(173\) | 22.4222 | 1.70473 | 0.852363 | − | 0.522951i | \(-0.175169\pi\) | ||||
0.852363 | + | 0.522951i | \(0.175169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.59464 | 0.196136 | ||||||||
\(176\) | 20.6101 | 1.55354 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 35.7120 | 2.67673 | ||||||||
\(179\) | −1.05233 | −0.0786550 | −0.0393275 | − | 0.999226i | \(-0.512522\pi\) | ||||
−0.0393275 | + | 0.999226i | \(0.512522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.92545 | 0.737753 | 0.368876 | − | 0.929478i | \(-0.379743\pi\) | ||||
0.368876 | + | 0.929478i | \(0.379743\pi\) | |||||||
\(182\) | 6.46494 | 0.479213 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0265683 | −0.00195864 | ||||||||
\(185\) | −1.35541 | −0.0996520 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.4305 | −1.49403 | ||||||||
\(188\) | −13.6570 | −0.996039 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.89204 | 0.645097 | ||||||||
\(191\) | −4.83520 | −0.349863 | −0.174931 | − | 0.984581i | \(-0.555970\pi\) | ||||
−0.174931 | + | 0.984581i | \(0.555970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.41421 | −0.245760 | −0.122880 | − | 0.992422i | \(-0.539213\pi\) | ||||
−0.122880 | + | 0.992422i | \(0.539213\pi\) | |||||||
\(194\) | 7.53862 | 0.541241 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.99208 | 0.142291 | ||||||||
\(197\) | 17.9837 | 1.28129 | 0.640643 | − | 0.767839i | \(-0.278668\pi\) | ||||
0.640643 | + | 0.767839i | \(0.278668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.01040 | −0.284290 | −0.142145 | − | 0.989846i | \(-0.545400\pi\) | ||||
−0.142145 | + | 0.989846i | \(0.545400\pi\) | |||||||
\(200\) | −0.0410679 | −0.00290394 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.5065 | 2.00571 | ||||||||
\(203\) | 7.42810 | 0.521351 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.62403 | 0.602328 | ||||||||
\(206\) | 21.4301 | 1.49311 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.9938 | −0.900955 | ||||||||
\(209\) | −14.7272 | −1.01870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.28023 | −0.294663 | −0.147332 | − | 0.989087i | \(-0.547068\pi\) | ||||
−0.147332 | + | 0.989087i | \(0.547068\pi\) | |||||||
\(212\) | 15.9793 | 1.09746 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.2780 | −0.907666 | ||||||||
\(215\) | −7.68803 | −0.524319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.815589 | −0.0553658 | ||||||||
\(218\) | −13.1039 | −0.887506 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.8564 | 1.06904 | ||||||||
\(221\) | 12.8805 | 0.866440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.6251 | 1.04633 | 0.523166 | − | 0.852231i | \(-0.324751\pi\) | ||||
0.523166 | + | 0.852231i | \(0.324751\pi\) | |||||||
\(224\) | −7.99195 | −0.533985 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.4078 | 1.02491 | ||||||||
\(227\) | 15.1144 | 1.00318 | 0.501588 | − | 0.865107i | \(-0.332749\pi\) | ||||
0.501588 | + | 0.865107i | \(0.332749\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.96211 | 0.526151 | 0.263075 | − | 0.964775i | \(-0.415263\pi\) | ||||
0.263075 | + | 0.964775i | \(0.415263\pi\) | |||||||
\(230\) | −5.20150 | −0.342977 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.117572 | −0.00771896 | ||||||||
\(233\) | −28.0381 | −1.83684 | −0.918420 | − | 0.395608i | \(-0.870534\pi\) | ||||
−0.918420 | + | 0.395608i | \(0.870534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6326 | 0.693593 | ||||||||
\(236\) | 19.7512 | 1.28570 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.95370 | 0.515562 | ||||||||
\(239\) | −20.4983 | −1.32592 | −0.662961 | − | 0.748654i | \(-0.730700\pi\) | ||||
−0.662961 | + | 0.748654i | \(0.730700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.11170 | −0.522521 | −0.261260 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261260 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(242\) | −30.6500 | −1.97025 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.7269 | −0.814756 | ||||||||
\(245\) | −1.55092 | −0.0990848 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.28489 | 0.590783 | ||||||||
\(248\) | 0.0129091 | 0.000819729 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −23.5341 | −1.48842 | ||||||||
\(251\) | −6.67584 | −0.421376 | −0.210688 | − | 0.977553i | \(-0.567570\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567570\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.61487 | 0.541612 | ||||||||
\(254\) | −1.99802 | −0.125367 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1260 | 1.00787 | ||||||||
\(257\) | 2.60249 | 0.162339 | 0.0811695 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811695 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.873940 | −0.0543040 | ||||||||
\(260\) | −9.99680 | −0.619975 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.8331 | 1.10173 | ||||||||
\(263\) | 25.9889 | 1.60255 | 0.801273 | − | 0.598299i | \(-0.204157\pi\) | ||||
0.801273 | + | 0.598299i | \(0.204157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4406 | −0.764218 | ||||||||
\(266\) | 5.73339 | 0.351537 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.510350 | −0.0311746 | ||||||||
\(269\) | −29.2094 | −1.78093 | −0.890464 | − | 0.455053i | \(-0.849620\pi\) | ||||
−0.890464 | + | 0.455053i | \(0.849620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.63001 | −0.281253 | −0.140627 | − | 0.990063i | \(-0.544912\pi\) | ||||
−0.140627 | + | 0.990063i | \(0.544912\pi\) | |||||||
\(272\) | −15.9860 | −0.969293 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.74282 | −0.467761 | ||||||||
\(275\) | 13.3164 | 0.803009 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2022 | 1.15375 | 0.576873 | − | 0.816834i | \(-0.304273\pi\) | ||||
0.576873 | + | 0.816834i | \(0.304273\pi\) | |||||||
\(278\) | 1.73737 | 0.104201 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0245479 | 0.00146702 | ||||||||
\(281\) | 6.10537 | 0.364216 | 0.182108 | − | 0.983279i | \(-0.441708\pi\) | ||||
0.182108 | + | 0.983279i | \(0.441708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.84704 | −0.466458 | −0.233229 | − | 0.972422i | \(-0.574929\pi\) | ||||
−0.233229 | + | 0.972422i | \(0.574929\pi\) | |||||||
\(284\) | −3.16344 | −0.187716 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 33.1798 | 1.96196 | ||||||||
\(287\) | 5.56058 | 0.328231 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.15328 | −0.0678399 | ||||||||
\(290\) | −23.0180 | −1.35166 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.2718 | 1.12780 | ||||||||
\(293\) | −16.3463 | −0.954961 | −0.477480 | − | 0.878642i | \(-0.658450\pi\) | ||||
−0.477480 | + | 0.878642i | \(0.658450\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3772 | −0.895297 | ||||||||
\(296\) | 0.0138327 | 0.000804009 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.2636 | 0.710411 | ||||||||
\(299\) | −5.43130 | −0.314100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.95707 | −0.285721 | ||||||||
\(302\) | 31.0658 | 1.78764 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.5234 | −0.660914 | ||||||||
\(305\) | 9.90846 | 0.567357 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.200702 | 0.0114547 | 0.00572733 | − | 0.999984i | \(-0.498177\pi\) | ||||
0.00572733 | + | 0.999984i | \(0.498177\pi\) | |||||||
\(308\) | 10.2239 | 0.582560 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.52732 | 0.143542 | ||||||||
\(311\) | 6.82716 | 0.387133 | 0.193566 | − | 0.981087i | \(-0.437994\pi\) | ||||
0.193566 | + | 0.981087i | \(0.437994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.0662 | −1.07769 | −0.538843 | − | 0.842406i | \(-0.681138\pi\) | ||||
−0.538843 | + | 0.842406i | \(0.681138\pi\) | |||||||
\(314\) | −5.14895 | −0.290572 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.65394 | 0.486822 | ||||||||
\(317\) | 13.1116 | 0.736419 | 0.368209 | − | 0.929743i | \(-0.379971\pi\) | ||||
0.368209 | + | 0.929743i | \(0.379971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38.1230 | 2.13448 | ||||||||
\(320\) | 12.3089 | 0.688088 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.35381 | −0.186901 | ||||||||
\(323\) | 11.4230 | 0.635595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.39541 | −0.465694 | ||||||||
\(326\) | −18.5064 | −1.02497 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.0880127 | −0.00485969 | ||||||||
\(329\) | 6.85565 | 0.377964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.5040 | −1.23693 | −0.618467 | − | 0.785811i | \(-0.712246\pi\) | ||||
−0.618467 | + | 0.785811i | \(0.712246\pi\) | |||||||
\(332\) | −5.85816 | −0.321508 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7580 | 0.807522 | ||||||||
\(335\) | 0.397331 | 0.0217085 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.07864 | 0.113231 | 0.0566154 | − | 0.998396i | \(-0.481969\pi\) | ||||
0.0566154 | + | 0.998396i | \(0.481969\pi\) | |||||||
\(338\) | 5.05582 | 0.275000 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.2989 | −0.667001 | ||||||||
\(341\) | −4.18582 | −0.226675 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.0784603 | 0.00423030 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.7999 | −2.40846 | ||||||||
\(347\) | 28.1043 | 1.50872 | 0.754360 | − | 0.656461i | \(-0.227947\pi\) | ||||
0.754360 | + | 0.656461i | \(0.227947\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.51546 | 0.295236 | 0.147618 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147618 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(350\) | −5.18414 | −0.277104 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −41.0168 | −2.18620 | ||||||||
\(353\) | 6.64296 | 0.353569 | 0.176784 | − | 0.984250i | \(-0.443430\pi\) | ||||
0.176784 | + | 0.984250i | \(0.443430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.46288 | 0.130716 | ||||||||
\(356\) | −35.6058 | −1.88710 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.10258 | 0.111125 | ||||||||
\(359\) | 31.7116 | 1.67368 | 0.836838 | − | 0.547451i | \(-0.184402\pi\) | ||||
0.836838 | + | 0.547451i | \(0.184402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.7657 | −0.566618 | ||||||||
\(362\) | −19.8312 | −1.04231 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.44571 | −0.337847 | ||||||||
\(365\) | −15.0040 | −0.785343 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.4792 | 1.95640 | 0.978198 | − | 0.207673i | \(-0.0665889\pi\) | ||||
0.978198 | + | 0.207673i | \(0.0665889\pi\) | |||||||
\(368\) | 6.74076 | 0.351387 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.70814 | 0.140790 | ||||||||
\(371\) | −8.02140 | −0.416451 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.523333 | 0.0270972 | 0.0135486 | − | 0.999908i | \(-0.495687\pi\) | ||||
0.0135486 | + | 0.999908i | \(0.495687\pi\) | |||||||
\(374\) | 40.8205 | 2.11078 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.108511 | −0.00559603 | ||||||||
\(377\) | −24.0349 | −1.23786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0604 | 1.39000 | 0.695000 | − | 0.719009i | \(-0.255404\pi\) | ||||
0.695000 | + | 0.719009i | \(0.255404\pi\) | |||||||
\(380\) | −8.86561 | −0.454796 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.66082 | 0.494291 | ||||||||
\(383\) | −3.70250 | −0.189189 | −0.0945945 | − | 0.995516i | \(-0.530155\pi\) | ||||
−0.0945945 | + | 0.995516i | \(0.530155\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.95975 | −0.405666 | ||||||||
\(386\) | 6.82165 | 0.347213 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.51621 | −0.381578 | ||||||||
\(389\) | 11.6605 | 0.591209 | 0.295604 | − | 0.955310i | \(-0.404479\pi\) | ||||
0.295604 | + | 0.955310i | \(0.404479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.68204 | −0.337925 | ||||||||
\(392\) | 0.0158280 | 0.000799433 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −35.9318 | −1.81022 | ||||||||
\(395\) | −6.73748 | −0.338999 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9316 | −1.15090 | −0.575451 | − | 0.817836i | \(-0.695174\pi\) | ||||
−0.575451 | + | 0.817836i | \(0.695174\pi\) | |||||||
\(398\) | 8.01286 | 0.401648 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.4195 | 0.520975 | ||||||||
\(401\) | −18.0860 | −0.903173 | −0.451586 | − | 0.892227i | \(-0.649142\pi\) | ||||
−0.451586 | + | 0.892227i | \(0.649142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.63898 | 0.131457 | ||||||||
\(404\) | −28.4218 | −1.41404 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.8415 | −0.736571 | ||||||||
\(407\) | −4.48530 | −0.222328 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.52170 | −0.174137 | −0.0870684 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870684 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(410\) | −17.2310 | −0.850977 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.3664 | −1.05265 | ||||||||
\(413\) | −9.91489 | −0.487880 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.56084 | 0.223883 | ||||||||
\(416\) | 25.8593 | 1.26786 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.4253 | 1.43924 | ||||||||
\(419\) | −0.101725 | −0.00496960 | −0.00248480 | − | 0.999997i | \(-0.500791\pi\) | ||||
−0.00248480 | + | 0.999997i | \(0.500791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6284 | −0.615472 | −0.307736 | − | 0.951472i | \(-0.599571\pi\) | ||||
−0.307736 | + | 0.951472i | \(0.599571\pi\) | |||||||
\(422\) | 8.55198 | 0.416304 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.126962 | 0.00616584 | ||||||||
\(425\) | −10.3287 | −0.501017 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.38875 | 0.309173 | ||||||||
\(428\) | 13.2385 | 0.639909 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.3608 | 0.740765 | ||||||||
\(431\) | 15.8922 | 0.765500 | 0.382750 | − | 0.923852i | \(-0.374977\pi\) | ||||
0.382750 | + | 0.923852i | \(0.374977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.32317 | −0.399986 | −0.199993 | − | 0.979797i | \(-0.564092\pi\) | ||||
−0.199993 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(434\) | 1.62956 | 0.0782215 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.0649 | 0.625696 | ||||||||
\(437\) | −4.81672 | −0.230415 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3660 | 0.781105 | 0.390552 | − | 0.920581i | \(-0.372284\pi\) | ||||
0.390552 | + | 0.920581i | \(0.372284\pi\) | |||||||
\(440\) | 0.125987 | 0.00600618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.7356 | −1.22412 | ||||||||
\(443\) | 25.5970 | 1.21615 | 0.608074 | − | 0.793880i | \(-0.291942\pi\) | ||||
0.608074 | + | 0.793880i | \(0.291942\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.7207 | 1.31409 | ||||||||
\(446\) | −31.2192 | −1.47827 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.93650 | 0.374964 | ||||||||
\(449\) | 18.6338 | 0.879386 | 0.439693 | − | 0.898148i | \(-0.355087\pi\) | ||||
0.439693 | + | 0.898148i | \(0.355087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.5384 | 1.34382 | ||||||||
\(452\) | −15.3620 | −0.722566 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.1988 | −1.41730 | ||||||||
\(455\) | 5.01828 | 0.235260 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.2257 | 0.665451 | 0.332726 | − | 0.943024i | \(-0.392032\pi\) | ||||
0.332726 | + | 0.943024i | \(0.392032\pi\) | |||||||
\(458\) | −15.9084 | −0.743353 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.18604 | 0.241800 | ||||||||
\(461\) | 1.81891 | 0.0847151 | 0.0423575 | − | 0.999103i | \(-0.486513\pi\) | ||||
0.0423575 | + | 0.999103i | \(0.486513\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.9051 | 1.38981 | 0.694904 | − | 0.719103i | \(-0.255447\pi\) | ||||
0.694904 | + | 0.719103i | \(0.255447\pi\) | |||||||
\(464\) | 29.8296 | 1.38481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 56.0207 | 2.59511 | ||||||||
\(467\) | −9.18692 | −0.425120 | −0.212560 | − | 0.977148i | \(-0.568180\pi\) | ||||
−0.212560 | + | 0.977148i | \(0.568180\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.256190 | 0.0118298 | ||||||||
\(470\) | −21.2441 | −0.979917 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.156933 | 0.00722341 | ||||||||
\(473\) | −25.4410 | −1.16978 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.44542 | −0.341619 | ||||||||
\(476\) | −7.93005 | −0.363473 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 40.9559 | 1.87328 | ||||||||
\(479\) | 16.0675 | 0.734142 | 0.367071 | − | 0.930193i | \(-0.380361\pi\) | ||||
0.367071 | + | 0.930193i | \(0.380361\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.82779 | 0.128936 | ||||||||
\(482\) | 16.2073 | 0.738224 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.5588 | 1.38904 | ||||||||
\(485\) | 5.85170 | 0.265712 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.6113 | 1.25119 | 0.625594 | − | 0.780149i | \(-0.284857\pi\) | ||||
0.625594 | + | 0.780149i | \(0.284857\pi\) | |||||||
\(488\) | −0.101121 | −0.00457753 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.09877 | 0.139988 | ||||||||
\(491\) | −17.9258 | −0.808982 | −0.404491 | − | 0.914542i | \(-0.632551\pi\) | ||||
−0.404491 | + | 0.914542i | \(0.632551\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.5697 | −1.33175 | ||||||||
\(494\) | −18.5514 | −0.834666 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.27523 | −0.147062 | ||||||||
\(497\) | 1.58801 | 0.0712320 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.73826 | −0.167347 | −0.0836737 | − | 0.996493i | \(-0.526665\pi\) | ||||
−0.0836737 | + | 0.996493i | \(0.526665\pi\) | |||||||
\(500\) | 23.4641 | 1.04935 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.3385 | 0.595325 | ||||||||
\(503\) | 10.8739 | 0.484843 | 0.242422 | − | 0.970171i | \(-0.422058\pi\) | ||||
0.242422 | + | 0.970171i | \(0.422058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1276 | 0.984667 | ||||||||
\(506\) | −17.2127 | −0.765196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.99208 | 0.0883842 | ||||||||
\(509\) | 2.99993 | 0.132970 | 0.0664849 | − | 0.997787i | \(-0.478822\pi\) | ||||
0.0664849 | + | 0.997787i | \(0.478822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.67421 | −0.427962 | ||||||||
\(512\) | −31.9668 | −1.41275 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.19983 | −0.229355 | ||||||||
\(515\) | 16.6347 | 0.733013 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.1850 | 1.54744 | ||||||||
\(518\) | 1.74615 | 0.0767214 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0794291 | −0.00348320 | ||||||||
\(521\) | 11.3414 | 0.496877 | 0.248439 | − | 0.968648i | \(-0.420083\pi\) | ||||
0.248439 | + | 0.968648i | \(0.420083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8401 | −0.954999 | −0.477500 | − | 0.878632i | \(-0.658457\pi\) | ||||
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(524\) | −17.7801 | −0.776727 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −51.9263 | −2.26410 | ||||||||
\(527\) | 3.24669 | 0.141428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1824 | −0.877496 | ||||||||
\(530\) | 24.8565 | 1.07970 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.71635 | −0.247835 | ||||||||
\(533\) | −17.9922 | −0.779330 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.3068 | −0.445601 | ||||||||
\(536\) | −0.00405497 | −0.000175148 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 58.3609 | 2.51612 | ||||||||
\(539\) | −5.13227 | −0.221062 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.1107 | −1.07959 | −0.539796 | − | 0.841796i | \(-0.681499\pi\) | ||||
−0.539796 | + | 0.841796i | \(0.681499\pi\) | |||||||
\(542\) | 9.25085 | 0.397358 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 31.8143 | 1.36403 | ||||||||
\(545\) | −10.1716 | −0.435704 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.0426 | −1.41280 | −0.706399 | − | 0.707813i | \(-0.749682\pi\) | ||||
−0.706399 | + | 0.707813i | \(0.749682\pi\) | |||||||
\(548\) | 7.71980 | 0.329774 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.6064 | −1.13450 | ||||||||
\(551\) | −21.3152 | −0.908059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.34418 | −0.184733 | ||||||||
\(554\) | −38.3663 | −1.63003 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.73221 | −0.0734619 | ||||||||
\(557\) | −24.9659 | −1.05784 | −0.528919 | − | 0.848672i | \(-0.677402\pi\) | ||||
−0.528919 | + | 0.848672i | \(0.677402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0395 | 0.678397 | ||||||||
\(560\) | −6.22816 | −0.263188 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.1986 | −0.514568 | ||||||||
\(563\) | −17.1234 | −0.721667 | −0.360834 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360834 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9600 | 0.503160 | ||||||||
\(566\) | 15.6785 | 0.659018 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.0251350 | −0.00105464 | ||||||||
\(569\) | 32.4727 | 1.36132 | 0.680662 | − | 0.732597i | \(-0.261692\pi\) | ||||
0.680662 | + | 0.732597i | \(0.261692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.4947 | −0.941375 | −0.470688 | − | 0.882300i | \(-0.655994\pi\) | ||||
−0.470688 | + | 0.882300i | \(0.655994\pi\) | |||||||
\(572\) | −33.0811 | −1.38319 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.1101 | −0.463728 | ||||||||
\(575\) | 4.35528 | 0.181628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.42913 | 0.101126 | 0.0505630 | − | 0.998721i | \(-0.483898\pi\) | ||||
0.0505630 | + | 0.998721i | \(0.483898\pi\) | |||||||
\(578\) | 2.30427 | 0.0958451 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.9496 | 0.952928 | ||||||||
\(581\) | 2.94073 | 0.122002 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.1680 | −1.70500 | ||||||||
\(584\) | 0.153123 | 0.00633628 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.6602 | 1.34918 | ||||||||
\(587\) | −11.9885 | −0.494818 | −0.247409 | − | 0.968911i | \(-0.579579\pi\) | ||||
−0.247409 | + | 0.968911i | \(0.579579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34036 | 0.0964330 | ||||||||
\(590\) | 30.7240 | 1.26489 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.50955 | −0.144242 | ||||||||
\(593\) | 10.8653 | 0.446185 | 0.223092 | − | 0.974797i | \(-0.428385\pi\) | ||||
0.223092 | + | 0.974797i | \(0.428385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.17390 | 0.253105 | ||||||||
\(596\) | −12.2271 | −0.500843 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.8518 | 0.443765 | ||||||||
\(599\) | 40.4780 | 1.65389 | 0.826943 | − | 0.562285i | \(-0.190078\pi\) | ||||
0.826943 | + | 0.562285i | \(0.190078\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.6000 | 1.00345 | 0.501727 | − | 0.865026i | \(-0.332698\pi\) | ||||
0.501727 | + | 0.865026i | \(0.332698\pi\) | |||||||
\(602\) | 9.90432 | 0.403670 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −30.9734 | −1.26029 | ||||||||
\(605\) | −23.7914 | −0.967259 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7065 | −0.921629 | −0.460815 | − | 0.887496i | \(-0.652443\pi\) | ||||
−0.460815 | + | 0.887496i | \(0.652443\pi\) | |||||||
\(608\) | 22.9332 | 0.930064 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.7973 | −0.801569 | ||||||||
\(611\) | −22.1826 | −0.897414 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.3737 | −1.34795 | −0.673975 | − | 0.738754i | \(-0.735414\pi\) | ||||
−0.673975 | + | 0.738754i | \(0.735414\pi\) | |||||||
\(614\) | −0.401006 | −0.0161833 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0812334 | 0.00327299 | ||||||||
\(617\) | 36.6644 | 1.47605 | 0.738026 | − | 0.674772i | \(-0.235758\pi\) | ||||
0.738026 | + | 0.674772i | \(0.235758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 49.0015 | 1.96954 | 0.984768 | − | 0.173875i | \(-0.0556288\pi\) | ||||
0.984768 | + | 0.173875i | \(0.0556288\pi\) | |||||||
\(620\) | −2.51981 | −0.101198 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.6408 | −0.546946 | ||||||||
\(623\) | 17.8737 | 0.716095 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.29464 | −0.211785 | ||||||||
\(626\) | 38.0947 | 1.52257 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.13364 | 0.204854 | ||||||||
\(629\) | 3.47898 | 0.138716 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2194 | 1.28263 | 0.641316 | − | 0.767277i | \(-0.278389\pi\) | ||||
0.641316 | + | 0.767277i | \(0.278389\pi\) | |||||||
\(632\) | 0.0687595 | 0.00273511 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.1972 | −1.04042 | ||||||||
\(635\) | −1.55092 | −0.0615465 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23567 | 0.128202 | ||||||||
\(638\) | −76.1705 | −3.01562 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.196382 | 0.00776268 | ||||||||
\(641\) | 44.1868 | 1.74527 | 0.872637 | − | 0.488369i | \(-0.162408\pi\) | ||||
0.872637 | + | 0.488369i | \(0.162408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.9872 | 1.77412 | 0.887062 | − | 0.461651i | \(-0.152743\pi\) | ||||
0.887062 | + | 0.461651i | \(0.152743\pi\) | |||||||
\(644\) | 3.34384 | 0.131766 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8234 | −0.897977 | ||||||||
\(647\) | 12.3832 | 0.486836 | 0.243418 | − | 0.969922i | \(-0.421731\pi\) | ||||
0.243418 | + | 0.969922i | \(0.421731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.8859 | −1.99745 | ||||||||
\(650\) | 16.7742 | 0.657938 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.4514 | 0.722612 | ||||||||
\(653\) | 13.5523 | 0.530342 | 0.265171 | − | 0.964201i | \(-0.414572\pi\) | ||||
0.265171 | + | 0.964201i | \(0.414572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.8426 | 0.540875 | ||||||||
\(656\) | 22.3301 | 0.871843 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.6977 | −0.533993 | ||||||||
\(659\) | −12.9849 | −0.505819 | −0.252910 | − | 0.967490i | \(-0.581387\pi\) | ||||
−0.252910 | + | 0.967490i | \(0.581387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.31636 | 0.0900961 | 0.0450481 | − | 0.998985i | \(-0.485656\pi\) | ||||
0.0450481 | + | 0.998985i | \(0.485656\pi\) | |||||||
\(662\) | 44.9635 | 1.74756 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.0465458 | −0.00180633 | ||||||||
\(665\) | 4.45043 | 0.172580 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.4686 | 0.482785 | ||||||||
\(668\) | −14.7141 | −0.569306 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.793874 | −0.0306700 | ||||||||
\(671\) | 32.7888 | 1.26580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.50998 | 0.212394 | 0.106197 | − | 0.994345i | \(-0.466133\pi\) | ||||
0.106197 | + | 0.994345i | \(0.466133\pi\) | |||||||
\(674\) | −4.15316 | −0.159974 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.04079 | −0.193877 | ||||||||
\(677\) | 37.0593 | 1.42430 | 0.712152 | − | 0.702026i | \(-0.247721\pi\) | ||||
0.712152 | + | 0.702026i | \(0.247721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.77305 | 0.144796 | ||||||||
\(680\) | −0.0977203 | −0.00374740 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.36335 | 0.320249 | ||||||||
\(683\) | 31.3466 | 1.19945 | 0.599723 | − | 0.800208i | \(-0.295278\pi\) | ||||
0.599723 | + | 0.800208i | \(0.295278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.01021 | −0.229638 | ||||||||
\(686\) | 1.99802 | 0.0762847 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19.9065 | −0.758929 | ||||||||
\(689\) | 25.9546 | 0.988793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.3304 | 1.03970 | 0.519849 | − | 0.854258i | \(-0.325988\pi\) | ||||
0.519849 | + | 0.854258i | \(0.325988\pi\) | |||||||
\(692\) | 44.6667 | 1.69797 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56.1530 | −2.13154 | ||||||||
\(695\) | 1.34860 | 0.0511553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.1355 | −0.838443 | ||||||||
\(698\) | −11.0200 | −0.417112 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.16873 | 0.195360 | ||||||||
\(701\) | 27.0821 | 1.02288 | 0.511438 | − | 0.859320i | \(-0.329113\pi\) | ||||
0.511438 | + | 0.859320i | \(0.329113\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.50781 | 0.0945837 | ||||||||
\(704\) | 40.7323 | 1.53515 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.2727 | −0.499526 | ||||||||
\(707\) | 14.2674 | 0.536581 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.36902 | −0.239193 | −0.119597 | − | 0.992823i | \(-0.538160\pi\) | ||||
−0.119597 | + | 0.992823i | \(0.538160\pi\) | |||||||
\(710\) | −4.92088 | −0.184677 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.282904 | −0.0106023 | ||||||||
\(713\) | −1.36902 | −0.0512703 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.7551 | 0.963188 | ||||||||
\(716\) | −2.09633 | −0.0783434 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −63.3604 | −2.36459 | ||||||||
\(719\) | 11.6862 | 0.435822 | 0.217911 | − | 0.975969i | \(-0.430076\pi\) | ||||
0.217911 | + | 0.975969i | \(0.430076\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7257 | 0.399446 | ||||||||
\(722\) | 21.5102 | 0.800525 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.7723 | 0.734831 | ||||||||
\(725\) | 19.2733 | 0.715791 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.8229 | 0.586840 | 0.293420 | − | 0.955984i | \(-0.405207\pi\) | ||||
0.293420 | + | 0.955984i | \(0.405207\pi\) | |||||||
\(728\) | −0.0512141 | −0.00189812 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 29.9782 | 1.10954 | ||||||||
\(731\) | 19.7331 | 0.729854 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.0289 | −1.66318 | −0.831589 | − | 0.555391i | \(-0.812569\pi\) | ||||
−0.831589 | + | 0.555391i | \(0.812569\pi\) | |||||||
\(734\) | −74.8841 | −2.76402 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.4150 | −0.494485 | ||||||||
\(737\) | 1.31484 | 0.0484326 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.6395 | 0.538522 | 0.269261 | − | 0.963067i | \(-0.413221\pi\) | ||||
0.269261 | + | 0.963067i | \(0.413221\pi\) | |||||||
\(740\) | −2.70009 | −0.0992572 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.0269 | 0.588367 | ||||||||
\(743\) | 13.0736 | 0.479622 | 0.239811 | − | 0.970820i | \(-0.422914\pi\) | ||||
0.239811 | + | 0.970820i | \(0.422914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.51938 | 0.348763 | ||||||||
\(746\) | −1.04563 | −0.0382832 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.6992 | −1.48811 | ||||||||
\(749\) | −6.64559 | −0.242825 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5692 | −0.385676 | −0.192838 | − | 0.981231i | \(-0.561769\pi\) | ||||
−0.192838 | + | 0.981231i | \(0.561769\pi\) | |||||||
\(752\) | 27.5308 | 1.00394 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 48.0222 | 1.74887 | ||||||||
\(755\) | 24.1142 | 0.877606 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.3384 | −1.50247 | −0.751234 | − | 0.660036i | \(-0.770541\pi\) | ||||
−0.751234 | + | 0.660036i | \(0.770541\pi\) | |||||||
\(758\) | −54.0672 | −1.96381 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0704412 | −0.00255517 | ||||||||
\(761\) | −20.7335 | −0.751588 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.55843 | −0.237431 | ||||||||
\(764\) | −9.63210 | −0.348477 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.39766 | 0.267288 | ||||||||
\(767\) | 32.0814 | 1.15839 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0797 | 0.724092 | 0.362046 | − | 0.932160i | \(-0.382078\pi\) | ||||
0.362046 | + | 0.932160i | \(0.382078\pi\) | |||||||
\(770\) | 15.9037 | 0.573130 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.80136 | −0.244786 | ||||||||
\(773\) | 21.8177 | 0.784727 | 0.392363 | − | 0.919810i | \(-0.371658\pi\) | ||||
0.392363 | + | 0.919810i | \(0.371658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.11616 | −0.0760147 | ||||||||
\(776\) | −0.0597197 | −0.00214381 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.2978 | −0.835267 | ||||||||
\(779\) | −15.9563 | −0.571694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.15009 | 0.291633 | ||||||||
\(782\) | 13.3508 | 0.477425 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.01578 | −0.143421 | ||||||||
\(785\) | −3.99677 | −0.142651 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.1914 | −1.32573 | −0.662865 | − | 0.748739i | \(-0.730660\pi\) | ||||
−0.662865 | + | 0.748739i | \(0.730660\pi\) | |||||||
\(788\) | 35.8249 | 1.27621 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.4616 | 0.478943 | ||||||||
\(791\) | 7.71152 | 0.274190 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.6719 | −0.734081 | ||||||||
\(794\) | 45.8177 | 1.62601 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.98903 | −0.283164 | ||||||||
\(797\) | 45.6760 | 1.61793 | 0.808963 | − | 0.587860i | \(-0.200029\pi\) | ||||
0.808963 | + | 0.587860i | \(0.200029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2909 | −0.965484 | ||||||||
\(800\) | −20.7362 | −0.733137 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 36.1362 | 1.27601 | ||||||||
\(803\) | −49.6507 | −1.75213 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.60333 | −0.0917553 | ||||||||
\(806\) | −5.27273 | −0.185724 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.225824 | −0.00794446 | ||||||||
\(809\) | 15.7808 | 0.554822 | 0.277411 | − | 0.960751i | \(-0.410524\pi\) | ||||
0.277411 | + | 0.960751i | \(0.410524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0351 | 1.30048 | 0.650239 | − | 0.759730i | \(-0.274669\pi\) | ||||
0.650239 | + | 0.759730i | \(0.274669\pi\) | |||||||
\(812\) | 14.7974 | 0.519286 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.96170 | 0.314108 | ||||||||
\(815\) | −14.3652 | −0.503192 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.2245 | 0.497652 | ||||||||
\(818\) | 7.03642 | 0.246023 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.1797 | 0.599942 | ||||||||
\(821\) | 42.9138 | 1.49770 | 0.748851 | − | 0.662738i | \(-0.230606\pi\) | ||||
0.748851 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.42351 | 0.119336 | 0.0596681 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596681 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(824\) | −0.169766 | −0.00591407 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.8101 | 0.689283 | ||||||||
\(827\) | 43.0420 | 1.49672 | 0.748359 | − | 0.663294i | \(-0.230842\pi\) | ||||
0.748359 | + | 0.663294i | \(0.230842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.7436 | 1.41508 | 0.707542 | − | 0.706671i | \(-0.249804\pi\) | ||||
0.707542 | + | 0.706671i | \(0.249804\pi\) | |||||||
\(830\) | −9.11265 | −0.316305 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −25.6799 | −0.890291 | ||||||||
\(833\) | 3.98079 | 0.137926 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.4556 | 0.396437 | ||||||||
\(836\) | −29.3378 | −1.01467 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.203249 | 0.00702111 | ||||||||
\(839\) | 40.7380 | 1.40643 | 0.703215 | − | 0.710977i | \(-0.251747\pi\) | ||||
0.703215 | + | 0.710977i | \(0.251747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.1767 | 0.902645 | ||||||||
\(842\) | 25.2319 | 0.869547 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.52656 | −0.293496 | ||||||||
\(845\) | 3.92448 | 0.135006 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.3402 | −0.527095 | ||||||||
\(848\) | −32.2122 | −1.10617 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.6370 | 0.707843 | ||||||||
\(851\) | −1.46697 | −0.0502870 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.0623 | −1.20051 | −0.600255 | − | 0.799809i | \(-0.704934\pi\) | ||||
−0.600255 | + | 0.799809i | \(0.704934\pi\) | |||||||
\(854\) | −12.7648 | −0.436804 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.105186 | 0.00359519 | ||||||||
\(857\) | 10.4998 | 0.358666 | 0.179333 | − | 0.983788i | \(-0.442606\pi\) | ||||
0.179333 | + | 0.983788i | \(0.442606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9157 | −0.850112 | −0.425056 | − | 0.905167i | \(-0.639746\pi\) | ||||
−0.425056 | + | 0.905167i | \(0.639746\pi\) | |||||||
\(860\) | −15.3152 | −0.522243 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.7529 | −1.08151 | ||||||||
\(863\) | −1.65282 | −0.0562628 | −0.0281314 | − | 0.999604i | \(-0.508956\pi\) | ||||
−0.0281314 | + | 0.999604i | \(0.508956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.7750 | −1.18239 | ||||||||
\(866\) | 16.6299 | 0.565105 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.62472 | −0.0551465 | ||||||||
\(869\) | −22.2955 | −0.756323 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.828947 | −0.0280878 | ||||||||
\(872\) | 0.103807 | 0.00351534 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.62389 | 0.325533 | ||||||||
\(875\) | −11.7787 | −0.398193 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1172 | 0.881915 | 0.440957 | − | 0.897528i | \(-0.354639\pi\) | ||||
0.440957 | + | 0.897528i | \(0.354639\pi\) | |||||||
\(878\) | −32.6995 | −1.10355 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.9646 | −1.07753 | ||||||||
\(881\) | 44.7117 | 1.50637 | 0.753187 | − | 0.657806i | \(-0.228515\pi\) | ||||
0.753187 | + | 0.657806i | \(0.228515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.3655 | −1.45936 | −0.729682 | − | 0.683787i | \(-0.760332\pi\) | ||||
−0.729682 | + | 0.683787i | \(0.760332\pi\) | |||||||
\(884\) | 25.6591 | 0.863008 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51.1432 | −1.71819 | ||||||||
\(887\) | −26.6987 | −0.896455 | −0.448227 | − | 0.893920i | \(-0.647945\pi\) | ||||
−0.448227 | + | 0.893920i | \(0.647945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −55.3865 | −1.85656 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 31.1263 | 1.04219 | ||||||||
\(893\) | −19.6726 | −0.658317 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.63208 | 0.0545546 | ||||||||
\(896\) | 0.126623 | 0.00423017 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.2308 | −1.24241 | ||||||||
\(899\) | −6.05828 | −0.202055 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.9316 | 1.06379 | ||||||||
\(902\) | −57.0202 | −1.89857 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.122058 | −0.00405958 | ||||||||
\(905\) | −15.3936 | −0.511701 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7281 | 0.688266 | 0.344133 | − | 0.938921i | \(-0.388173\pi\) | ||||
0.344133 | + | 0.938921i | \(0.388173\pi\) | |||||||
\(908\) | 30.1090 | 0.999202 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0266 | −0.332379 | ||||||||
\(911\) | −40.0495 | −1.32690 | −0.663450 | − | 0.748220i | \(-0.730909\pi\) | ||||
−0.663450 | + | 0.748220i | \(0.730909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0926 | 0.499493 | ||||||||
\(914\) | −28.4233 | −0.940158 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.8611 | 0.524067 | ||||||||
\(917\) | 8.92539 | 0.294743 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.4606 | −0.542984 | −0.271492 | − | 0.962441i | \(-0.587517\pi\) | ||||
−0.271492 | + | 0.962441i | \(0.587517\pi\) | |||||||
\(920\) | 0.0412054 | 0.00135850 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.63422 | −0.119687 | ||||||||
\(923\) | −5.13828 | −0.169129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.26756 | −0.0745569 | ||||||||
\(926\) | −59.7510 | −1.96354 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −59.3650 | −1.94875 | ||||||||
\(929\) | 12.0241 | 0.394498 | 0.197249 | − | 0.980353i | \(-0.436799\pi\) | ||||
0.197249 | + | 0.980353i | \(0.436799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.86954 | 0.0940453 | ||||||||
\(932\) | −55.8542 | −1.82956 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.3556 | 0.600615 | ||||||||
\(935\) | 31.6861 | 1.03625 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.4952 | 1.25758 | 0.628791 | − | 0.777574i | \(-0.283550\pi\) | ||||
0.628791 | + | 0.777574i | \(0.283550\pi\) | |||||||
\(938\) | −0.511872 | −0.0167132 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.1809 | 0.690846 | ||||||||
\(941\) | −3.32398 | −0.108359 | −0.0541794 | − | 0.998531i | \(-0.517254\pi\) | ||||
−0.0541794 | + | 0.998531i | \(0.517254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.33382 | 0.303951 | ||||||||
\(944\) | −39.8160 | −1.29590 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50.8316 | 1.65268 | ||||||||
\(947\) | −15.6069 | −0.507157 | −0.253578 | − | 0.967315i | \(-0.581608\pi\) | ||||
−0.253578 | + | 0.967315i | \(0.581608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.3026 | 1.01613 | ||||||||
\(950\) | 14.8761 | 0.482644 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.0630079 | −0.00204210 | ||||||||
\(953\) | −13.0607 | −0.423078 | −0.211539 | − | 0.977370i | \(-0.567847\pi\) | ||||
−0.211539 | + | 0.977370i | \(0.567847\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.49902 | 0.242663 | ||||||||
\(956\) | −40.8341 | −1.32067 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.1031 | −1.03720 | ||||||||
\(959\) | −3.87525 | −0.125138 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3348 | −0.978542 | ||||||||
\(962\) | −5.64997 | −0.182162 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.1591 | −0.520451 | ||||||||
\(965\) | 5.29517 | 0.170457 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.0766 | −0.516988 | −0.258494 | − | 0.966013i | \(-0.583226\pi\) | ||||
−0.258494 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(968\) | 0.242804 | 0.00780401 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.6918 | −0.375401 | ||||||||
\(971\) | −16.3263 | −0.523937 | −0.261968 | − | 0.965076i | \(-0.584372\pi\) | ||||
−0.261968 | + | 0.965076i | \(0.584372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.869547 | 0.0278764 | ||||||||
\(974\) | −55.1679 | −1.76769 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.6558 | 0.821223 | ||||||||
\(977\) | 10.7672 | 0.344474 | 0.172237 | − | 0.985056i | \(-0.444901\pi\) | ||||
0.172237 | + | 0.985056i | \(0.444901\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 91.7327 | 2.93179 | ||||||||
\(980\) | −3.08956 | −0.0986923 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.8161 | 1.14294 | ||||||||
\(983\) | 15.5930 | 0.497338 | 0.248669 | − | 0.968588i | \(-0.420007\pi\) | ||||
0.248669 | + | 0.968588i | \(0.420007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.8913 | −0.888692 | ||||||||
\(986\) | 59.0809 | 1.88152 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.4962 | 0.588443 | ||||||||
\(989\) | −8.32078 | −0.264586 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.87536 | 0.218403 | 0.109202 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109202 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(992\) | 6.51814 | 0.206951 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.17287 | −0.100637 | ||||||||
\(995\) | 6.21982 | 0.197182 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.2889 | 1.40264 | 0.701322 | − | 0.712845i | \(-0.252594\pi\) | ||||
0.701322 | + | 0.712845i | \(0.252594\pi\) | |||||||
\(998\) | 7.46911 | 0.236431 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.y.1.6 | ✓ | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.23 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.6 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8001.2.a.y.1.23 | yes | 28 | 3.2 | odd | 2 | inner |