Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1338,2,Mod(1,1338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1338, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1338.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1338 = 2 \cdot 3 \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1338.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: | \(10.6839837904\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10273.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.641043\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1338.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.64104 | 0.733897 | 0.366948 | − | 0.930241i | \(-0.380403\pi\) | ||||
0.366948 | + | 0.930241i | \(0.380403\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −3.78585 | −1.43092 | −0.715458 | − | 0.698655i | \(-0.753782\pi\) | ||||
−0.715458 | + | 0.698655i | \(0.753782\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.64104 | −0.518943 | ||||||||
\(11\) | −0.948021 | −0.285839 | −0.142919 | − | 0.989734i | \(-0.545649\pi\) | ||||
−0.142919 | + | 0.989734i | \(0.545649\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.09283 | 0.580446 | 0.290223 | − | 0.956959i | \(-0.406271\pi\) | ||||
0.290223 | + | 0.956959i | \(0.406271\pi\) | |||||||
\(14\) | 3.78585 | 1.01181 | ||||||||
\(15\) | −1.64104 | −0.423716 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.0270879 | −0.00656977 | −0.00328489 | − | 0.999995i | \(-0.501046\pi\) | ||||
−0.00328489 | + | 0.999995i | \(0.501046\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.38464 | 1.23532 | 0.617660 | − | 0.786445i | \(-0.288081\pi\) | ||||
0.617660 | + | 0.786445i | \(0.288081\pi\) | |||||||
\(20\) | 1.64104 | 0.366948 | ||||||||
\(21\) | 3.78585 | 0.826140 | ||||||||
\(22\) | 0.948021 | 0.202119 | ||||||||
\(23\) | −3.61615 | −0.754020 | −0.377010 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377010 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.30698 | −0.461396 | ||||||||
\(26\) | −2.09283 | −0.410437 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.78585 | −0.715458 | ||||||||
\(29\) | 3.17189 | 0.589006 | 0.294503 | − | 0.955651i | \(-0.404846\pi\) | ||||
0.294503 | + | 0.955651i | \(0.404846\pi\) | |||||||
\(30\) | 1.64104 | 0.299612 | ||||||||
\(31\) | −7.38464 | −1.32632 | −0.663160 | − | 0.748478i | \(-0.730785\pi\) | ||||
−0.663160 | + | 0.748478i | \(0.730785\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.948021 | 0.165029 | ||||||||
\(34\) | 0.0270879 | 0.00464553 | ||||||||
\(35\) | −6.21274 | −1.05015 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.49624 | −0.410379 | −0.205189 | − | 0.978722i | \(-0.565781\pi\) | ||||
−0.205189 | + | 0.978722i | \(0.565781\pi\) | |||||||
\(38\) | −5.38464 | −0.873503 | ||||||||
\(39\) | −2.09283 | −0.335121 | ||||||||
\(40\) | −1.64104 | −0.259472 | ||||||||
\(41\) | −4.22247 | −0.659438 | −0.329719 | − | 0.944079i | \(-0.606954\pi\) | ||||
−0.329719 | + | 0.944079i | \(0.606954\pi\) | |||||||
\(42\) | −3.78585 | −0.584169 | ||||||||
\(43\) | −6.30698 | −0.961805 | −0.480903 | − | 0.876774i | \(-0.659691\pi\) | ||||
−0.480903 | + | 0.876774i | \(0.659691\pi\) | |||||||
\(44\) | −0.948021 | −0.142919 | ||||||||
\(45\) | 1.64104 | 0.244632 | ||||||||
\(46\) | 3.61615 | 0.533172 | ||||||||
\(47\) | 2.59879 | 0.379072 | 0.189536 | − | 0.981874i | \(-0.439302\pi\) | ||||
0.189536 | + | 0.981874i | \(0.439302\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 7.33266 | 1.04752 | ||||||||
\(50\) | 2.30698 | 0.326256 | ||||||||
\(51\) | 0.0270879 | 0.00379306 | ||||||||
\(52\) | 2.09283 | 0.290223 | ||||||||
\(53\) | 5.09502 | 0.699855 | 0.349928 | − | 0.936777i | \(-0.386206\pi\) | ||||
0.349928 | + | 0.936777i | \(0.386206\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.55574 | −0.209776 | ||||||||
\(56\) | 3.78585 | 0.505905 | ||||||||
\(57\) | −5.38464 | −0.713213 | ||||||||
\(58\) | −3.17189 | −0.416490 | ||||||||
\(59\) | 9.78444 | 1.27383 | 0.636913 | − | 0.770936i | \(-0.280211\pi\) | ||||
0.636913 | + | 0.770936i | \(0.280211\pi\) | |||||||
\(60\) | −1.64104 | −0.211858 | ||||||||
\(61\) | −2.50376 | −0.320574 | −0.160287 | − | 0.987070i | \(-0.551242\pi\) | ||||
−0.160287 | + | 0.987070i | \(0.551242\pi\) | |||||||
\(62\) | 7.38464 | 0.937850 | ||||||||
\(63\) | −3.78585 | −0.476972 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.43442 | 0.425987 | ||||||||
\(66\) | −0.948021 | −0.116693 | ||||||||
\(67\) | −4.35896 | −0.532531 | −0.266266 | − | 0.963900i | \(-0.585790\pi\) | ||||
−0.266266 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(68\) | −0.0270879 | −0.00328489 | ||||||||
\(69\) | 3.61615 | 0.435334 | ||||||||
\(70\) | 6.21274 | 0.742565 | ||||||||
\(71\) | −8.97370 | −1.06498 | −0.532491 | − | 0.846436i | \(-0.678744\pi\) | ||||
−0.532491 | + | 0.846436i | \(0.678744\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.0083 | −1.28843 | −0.644213 | − | 0.764846i | \(-0.722815\pi\) | ||||
−0.644213 | + | 0.764846i | \(0.722815\pi\) | |||||||
\(74\) | 2.49624 | 0.290182 | ||||||||
\(75\) | 2.30698 | 0.266387 | ||||||||
\(76\) | 5.38464 | 0.617660 | ||||||||
\(77\) | 3.58906 | 0.409012 | ||||||||
\(78\) | 2.09283 | 0.236966 | ||||||||
\(79\) | −12.7361 | −1.43292 | −0.716460 | − | 0.697628i | \(-0.754239\pi\) | ||||
−0.716460 | + | 0.697628i | \(0.754239\pi\) | |||||||
\(80\) | 1.64104 | 0.183474 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.22247 | 0.466293 | ||||||||
\(83\) | −8.87868 | −0.974561 | −0.487281 | − | 0.873245i | \(-0.662011\pi\) | ||||
−0.487281 | + | 0.873245i | \(0.662011\pi\) | |||||||
\(84\) | 3.78585 | 0.413070 | ||||||||
\(85\) | −0.0444524 | −0.00482154 | ||||||||
\(86\) | 6.30698 | 0.680099 | ||||||||
\(87\) | −3.17189 | −0.340063 | ||||||||
\(88\) | 0.948021 | 0.101059 | ||||||||
\(89\) | −0.793377 | −0.0840977 | −0.0420489 | − | 0.999116i | \(-0.513389\pi\) | ||||
−0.0420489 | + | 0.999116i | \(0.513389\pi\) | |||||||
\(90\) | −1.64104 | −0.172981 | ||||||||
\(91\) | −7.92313 | −0.830570 | ||||||||
\(92\) | −3.61615 | −0.377010 | ||||||||
\(93\) | 7.38464 | 0.765751 | ||||||||
\(94\) | −2.59879 | −0.268044 | ||||||||
\(95\) | 8.83642 | 0.906598 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.13728 | −0.826216 | −0.413108 | − | 0.910682i | \(-0.635557\pi\) | ||||
−0.413108 | + | 0.910682i | \(0.635557\pi\) | |||||||
\(98\) | −7.33266 | −0.740710 | ||||||||
\(99\) | −0.948021 | −0.0952797 | ||||||||
\(100\) | −2.30698 | −0.230698 | ||||||||
\(101\) | 14.2655 | 1.41947 | 0.709736 | − | 0.704468i | \(-0.248814\pi\) | ||||
0.709736 | + | 0.704468i | \(0.248814\pi\) | |||||||
\(102\) | −0.0270879 | −0.00268210 | ||||||||
\(103\) | −2.92987 | −0.288688 | −0.144344 | − | 0.989528i | \(-0.546107\pi\) | ||||
−0.144344 | + | 0.989528i | \(0.546107\pi\) | |||||||
\(104\) | −2.09283 | −0.205219 | ||||||||
\(105\) | 6.21274 | 0.606302 | ||||||||
\(106\) | −5.09502 | −0.494872 | ||||||||
\(107\) | −6.15233 | −0.594769 | −0.297384 | − | 0.954758i | \(-0.596114\pi\) | ||||
−0.297384 | + | 0.954758i | \(0.596114\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −1.92093 | −0.183992 | −0.0919960 | − | 0.995759i | \(-0.529325\pi\) | ||||
−0.0919960 | + | 0.995759i | \(0.529325\pi\) | |||||||
\(110\) | 1.55574 | 0.148334 | ||||||||
\(111\) | 2.49624 | 0.236932 | ||||||||
\(112\) | −3.78585 | −0.357729 | ||||||||
\(113\) | −12.3153 | −1.15853 | −0.579263 | − | 0.815141i | \(-0.696659\pi\) | ||||
−0.579263 | + | 0.815141i | \(0.696659\pi\) | |||||||
\(114\) | 5.38464 | 0.504317 | ||||||||
\(115\) | −5.93426 | −0.553373 | ||||||||
\(116\) | 3.17189 | 0.294503 | ||||||||
\(117\) | 2.09283 | 0.193482 | ||||||||
\(118\) | −9.78444 | −0.900731 | ||||||||
\(119\) | 0.102551 | 0.00940080 | ||||||||
\(120\) | 1.64104 | 0.149806 | ||||||||
\(121\) | −10.1013 | −0.918296 | ||||||||
\(122\) | 2.50376 | 0.226680 | ||||||||
\(123\) | 4.22247 | 0.380727 | ||||||||
\(124\) | −7.38464 | −0.663160 | ||||||||
\(125\) | −11.9911 | −1.07251 | ||||||||
\(126\) | 3.78585 | 0.337270 | ||||||||
\(127\) | −15.4851 | −1.37408 | −0.687040 | − | 0.726619i | \(-0.741090\pi\) | ||||
−0.687040 | + | 0.726619i | \(0.741090\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 6.30698 | 0.555298 | ||||||||
\(130\) | −3.43442 | −0.301219 | ||||||||
\(131\) | 3.90357 | 0.341056 | 0.170528 | − | 0.985353i | \(-0.445453\pi\) | ||||
0.170528 | + | 0.985353i | \(0.445453\pi\) | |||||||
\(132\) | 0.948021 | 0.0825146 | ||||||||
\(133\) | −20.3854 | −1.76764 | ||||||||
\(134\) | 4.35896 | 0.376557 | ||||||||
\(135\) | −1.64104 | −0.141239 | ||||||||
\(136\) | 0.0270879 | 0.00232277 | ||||||||
\(137\) | 4.38464 | 0.374605 | 0.187302 | − | 0.982302i | \(-0.440026\pi\) | ||||
0.187302 | + | 0.982302i | \(0.440026\pi\) | |||||||
\(138\) | −3.61615 | −0.307827 | ||||||||
\(139\) | −14.5565 | −1.23467 | −0.617334 | − | 0.786701i | \(-0.711787\pi\) | ||||
−0.617334 | + | 0.786701i | \(0.711787\pi\) | |||||||
\(140\) | −6.21274 | −0.525073 | ||||||||
\(141\) | −2.59879 | −0.218857 | ||||||||
\(142\) | 8.97370 | 0.753056 | ||||||||
\(143\) | −1.98404 | −0.165914 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.20522 | 0.432270 | ||||||||
\(146\) | 11.0083 | 0.911055 | ||||||||
\(147\) | −7.33266 | −0.604787 | ||||||||
\(148\) | −2.49624 | −0.205189 | ||||||||
\(149\) | 16.4783 | 1.34995 | 0.674976 | − | 0.737840i | \(-0.264154\pi\) | ||||
0.674976 | + | 0.737840i | \(0.264154\pi\) | |||||||
\(150\) | −2.30698 | −0.188364 | ||||||||
\(151\) | −4.31450 | −0.351109 | −0.175555 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175555 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(152\) | −5.38464 | −0.436752 | ||||||||
\(153\) | −0.0270879 | −0.00218992 | ||||||||
\(154\) | −3.58906 | −0.289215 | ||||||||
\(155\) | −12.1185 | −0.973382 | ||||||||
\(156\) | −2.09283 | −0.167560 | ||||||||
\(157\) | 7.51219 | 0.599538 | 0.299769 | − | 0.954012i | \(-0.403090\pi\) | ||||
0.299769 | + | 0.954012i | \(0.403090\pi\) | |||||||
\(158\) | 12.7361 | 1.01323 | ||||||||
\(159\) | −5.09502 | −0.404062 | ||||||||
\(160\) | −1.64104 | −0.129736 | ||||||||
\(161\) | 13.6902 | 1.07894 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.94179 | −0.465397 | −0.232698 | − | 0.972549i | \(-0.574755\pi\) | ||||
−0.232698 | + | 0.972549i | \(0.574755\pi\) | |||||||
\(164\) | −4.22247 | −0.329719 | ||||||||
\(165\) | 1.55574 | 0.121114 | ||||||||
\(166\) | 8.87868 | 0.689119 | ||||||||
\(167\) | 3.87868 | 0.300141 | 0.150071 | − | 0.988675i | \(-0.452050\pi\) | ||||
0.150071 | + | 0.988675i | \(0.452050\pi\) | |||||||
\(168\) | −3.78585 | −0.292085 | ||||||||
\(169\) | −8.62007 | −0.663083 | ||||||||
\(170\) | 0.0444524 | 0.00340934 | ||||||||
\(171\) | 5.38464 | 0.411773 | ||||||||
\(172\) | −6.30698 | −0.480903 | ||||||||
\(173\) | −7.89244 | −0.600051 | −0.300025 | − | 0.953931i | \(-0.596995\pi\) | ||||
−0.300025 | + | 0.953931i | \(0.596995\pi\) | |||||||
\(174\) | 3.17189 | 0.240461 | ||||||||
\(175\) | 8.73387 | 0.660219 | ||||||||
\(176\) | −0.948021 | −0.0714597 | ||||||||
\(177\) | −9.78444 | −0.735444 | ||||||||
\(178\) | 0.793377 | 0.0594661 | ||||||||
\(179\) | −4.44994 | −0.332604 | −0.166302 | − | 0.986075i | \(-0.553183\pi\) | ||||
−0.166302 | + | 0.986075i | \(0.553183\pi\) | |||||||
\(180\) | 1.64104 | 0.122316 | ||||||||
\(181\) | 8.23972 | 0.612453 | 0.306227 | − | 0.951959i | \(-0.400933\pi\) | ||||
0.306227 | + | 0.951959i | \(0.400933\pi\) | |||||||
\(182\) | 7.92313 | 0.587301 | ||||||||
\(183\) | 2.50376 | 0.185084 | ||||||||
\(184\) | 3.61615 | 0.266586 | ||||||||
\(185\) | −4.09643 | −0.301176 | ||||||||
\(186\) | −7.38464 | −0.541468 | ||||||||
\(187\) | 0.0256799 | 0.00187790 | ||||||||
\(188\) | 2.59879 | 0.189536 | ||||||||
\(189\) | 3.78585 | 0.275380 | ||||||||
\(190\) | −8.83642 | −0.641061 | ||||||||
\(191\) | −5.91408 | −0.427928 | −0.213964 | − | 0.976842i | \(-0.568637\pi\) | ||||
−0.213964 | + | 0.976842i | \(0.568637\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 16.7133 | 1.20305 | 0.601523 | − | 0.798855i | \(-0.294561\pi\) | ||||
0.601523 | + | 0.798855i | \(0.294561\pi\) | |||||||
\(194\) | 8.13728 | 0.584223 | ||||||||
\(195\) | −3.43442 | −0.245944 | ||||||||
\(196\) | 7.33266 | 0.523761 | ||||||||
\(197\) | −6.95010 | −0.495174 | −0.247587 | − | 0.968866i | \(-0.579638\pi\) | ||||
−0.247587 | + | 0.968866i | \(0.579638\pi\) | |||||||
\(198\) | 0.948021 | 0.0673729 | ||||||||
\(199\) | −18.5053 | −1.31181 | −0.655904 | − | 0.754844i | \(-0.727713\pi\) | ||||
−0.655904 | + | 0.754844i | \(0.727713\pi\) | |||||||
\(200\) | 2.30698 | 0.163128 | ||||||||
\(201\) | 4.35896 | 0.307457 | ||||||||
\(202\) | −14.2655 | −1.00372 | ||||||||
\(203\) | −12.0083 | −0.842819 | ||||||||
\(204\) | 0.0270879 | 0.00189653 | ||||||||
\(205\) | −6.92925 | −0.483960 | ||||||||
\(206\) | 2.92987 | 0.204134 | ||||||||
\(207\) | −3.61615 | −0.251340 | ||||||||
\(208\) | 2.09283 | 0.145111 | ||||||||
\(209\) | −5.10475 | −0.353103 | ||||||||
\(210\) | −6.21274 | −0.428720 | ||||||||
\(211\) | 20.8892 | 1.43807 | 0.719036 | − | 0.694973i | \(-0.244584\pi\) | ||||
0.719036 | + | 0.694973i | \(0.244584\pi\) | |||||||
\(212\) | 5.09502 | 0.349928 | ||||||||
\(213\) | 8.97370 | 0.614868 | ||||||||
\(214\) | 6.15233 | 0.420565 | ||||||||
\(215\) | −10.3500 | −0.705866 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 27.9571 | 1.89785 | ||||||||
\(218\) | 1.92093 | 0.130102 | ||||||||
\(219\) | 11.0083 | 0.743873 | ||||||||
\(220\) | −1.55574 | −0.104888 | ||||||||
\(221\) | −0.0566902 | −0.00381340 | ||||||||
\(222\) | −2.49624 | −0.167536 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 3.78585 | 0.252953 | ||||||||
\(225\) | −2.30698 | −0.153799 | ||||||||
\(226\) | 12.3153 | 0.819201 | ||||||||
\(227\) | 5.44959 | 0.361702 | 0.180851 | − | 0.983511i | \(-0.442115\pi\) | ||||
0.180851 | + | 0.983511i | \(0.442115\pi\) | |||||||
\(228\) | −5.38464 | −0.356606 | ||||||||
\(229\) | 20.9369 | 1.38355 | 0.691774 | − | 0.722114i | \(-0.256829\pi\) | ||||
0.691774 | + | 0.722114i | \(0.256829\pi\) | |||||||
\(230\) | 5.93426 | 0.391294 | ||||||||
\(231\) | −3.58906 | −0.236143 | ||||||||
\(232\) | −3.17189 | −0.208245 | ||||||||
\(233\) | −27.0478 | −1.77196 | −0.885979 | − | 0.463726i | \(-0.846512\pi\) | ||||
−0.885979 | + | 0.463726i | \(0.846512\pi\) | |||||||
\(234\) | −2.09283 | −0.136812 | ||||||||
\(235\) | 4.26472 | 0.278200 | ||||||||
\(236\) | 9.78444 | 0.636913 | ||||||||
\(237\) | 12.7361 | 0.827296 | ||||||||
\(238\) | −0.102551 | −0.00664737 | ||||||||
\(239\) | 30.6714 | 1.98397 | 0.991985 | − | 0.126355i | \(-0.0403279\pi\) | ||||
0.991985 | + | 0.126355i | \(0.0403279\pi\) | |||||||
\(240\) | −1.64104 | −0.105929 | ||||||||
\(241\) | −9.66531 | −0.622598 | −0.311299 | − | 0.950312i | \(-0.600764\pi\) | ||||
−0.311299 | + | 0.950312i | \(0.600764\pi\) | |||||||
\(242\) | 10.1013 | 0.649333 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.50376 | −0.160287 | ||||||||
\(245\) | 12.0332 | 0.768773 | ||||||||
\(246\) | −4.22247 | −0.269215 | ||||||||
\(247\) | 11.2691 | 0.717037 | ||||||||
\(248\) | 7.38464 | 0.468925 | ||||||||
\(249\) | 8.87868 | 0.562663 | ||||||||
\(250\) | 11.9911 | 0.758382 | ||||||||
\(251\) | 14.8004 | 0.934193 | 0.467096 | − | 0.884206i | \(-0.345300\pi\) | ||||
0.467096 | + | 0.884206i | \(0.345300\pi\) | |||||||
\(252\) | −3.78585 | −0.238486 | ||||||||
\(253\) | 3.42819 | 0.215528 | ||||||||
\(254\) | 15.4851 | 0.971622 | ||||||||
\(255\) | 0.0444524 | 0.00278372 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.5800 | 0.847098 | 0.423549 | − | 0.905873i | \(-0.360784\pi\) | ||||
0.423549 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(258\) | −6.30698 | −0.392655 | ||||||||
\(259\) | 9.45038 | 0.587218 | ||||||||
\(260\) | 3.43442 | 0.212994 | ||||||||
\(261\) | 3.17189 | 0.196335 | ||||||||
\(262\) | −3.90357 | −0.241163 | ||||||||
\(263\) | 7.89420 | 0.486777 | 0.243389 | − | 0.969929i | \(-0.421741\pi\) | ||||
0.243389 | + | 0.969929i | \(0.421741\pi\) | |||||||
\(264\) | −0.948021 | −0.0583466 | ||||||||
\(265\) | 8.36115 | 0.513622 | ||||||||
\(266\) | 20.3854 | 1.24991 | ||||||||
\(267\) | 0.793377 | 0.0485539 | ||||||||
\(268\) | −4.35896 | −0.266266 | ||||||||
\(269\) | −14.8946 | −0.908142 | −0.454071 | − | 0.890966i | \(-0.650029\pi\) | ||||
−0.454071 | + | 0.890966i | \(0.650029\pi\) | |||||||
\(270\) | 1.64104 | 0.0998707 | ||||||||
\(271\) | 3.27769 | 0.199106 | 0.0995528 | − | 0.995032i | \(-0.468259\pi\) | ||||
0.0995528 | + | 0.995032i | \(0.468259\pi\) | |||||||
\(272\) | −0.0270879 | −0.00164244 | ||||||||
\(273\) | 7.92313 | 0.479530 | ||||||||
\(274\) | −4.38464 | −0.264886 | ||||||||
\(275\) | 2.18706 | 0.131885 | ||||||||
\(276\) | 3.61615 | 0.217667 | ||||||||
\(277\) | −8.26018 | −0.496306 | −0.248153 | − | 0.968721i | \(-0.579824\pi\) | ||||
−0.248153 | + | 0.968721i | \(0.579824\pi\) | |||||||
\(278\) | 14.5565 | 0.873043 | ||||||||
\(279\) | −7.38464 | −0.442107 | ||||||||
\(280\) | 6.21274 | 0.371282 | ||||||||
\(281\) | −14.6209 | −0.872208 | −0.436104 | − | 0.899896i | \(-0.643642\pi\) | ||||
−0.436104 | + | 0.899896i | \(0.643642\pi\) | |||||||
\(282\) | 2.59879 | 0.154756 | ||||||||
\(283\) | 24.5961 | 1.46209 | 0.731043 | − | 0.682332i | \(-0.239034\pi\) | ||||
0.731043 | + | 0.682332i | \(0.239034\pi\) | |||||||
\(284\) | −8.97370 | −0.532491 | ||||||||
\(285\) | −8.83642 | −0.523424 | ||||||||
\(286\) | 1.98404 | 0.117319 | ||||||||
\(287\) | 15.9856 | 0.943601 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9993 | −0.999957 | ||||||||
\(290\) | −5.20522 | −0.305661 | ||||||||
\(291\) | 8.13728 | 0.477016 | ||||||||
\(292\) | −11.0083 | −0.644213 | ||||||||
\(293\) | −2.60282 | −0.152059 | −0.0760293 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760293 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(294\) | 7.33266 | 0.427649 | ||||||||
\(295\) | 16.0567 | 0.934857 | ||||||||
\(296\) | 2.49624 | 0.145091 | ||||||||
\(297\) | 0.948021 | 0.0550097 | ||||||||
\(298\) | −16.4783 | −0.954560 | ||||||||
\(299\) | −7.56798 | −0.437668 | ||||||||
\(300\) | 2.30698 | 0.133193 | ||||||||
\(301\) | 23.8773 | 1.37626 | ||||||||
\(302\) | 4.31450 | 0.248272 | ||||||||
\(303\) | −14.2655 | −0.819532 | ||||||||
\(304\) | 5.38464 | 0.308830 | ||||||||
\(305\) | −4.10878 | −0.235268 | ||||||||
\(306\) | 0.0270879 | 0.00154851 | ||||||||
\(307\) | −7.52944 | −0.429728 | −0.214864 | − | 0.976644i | \(-0.568931\pi\) | ||||
−0.214864 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(308\) | 3.58906 | 0.204506 | ||||||||
\(309\) | 2.92987 | 0.166674 | ||||||||
\(310\) | 12.1185 | 0.688285 | ||||||||
\(311\) | 17.8696 | 1.01329 | 0.506647 | − | 0.862154i | \(-0.330885\pi\) | ||||
0.506647 | + | 0.862154i | \(0.330885\pi\) | |||||||
\(312\) | 2.09283 | 0.118483 | ||||||||
\(313\) | 6.41094 | 0.362368 | 0.181184 | − | 0.983449i | \(-0.442007\pi\) | ||||
0.181184 | + | 0.983449i | \(0.442007\pi\) | |||||||
\(314\) | −7.51219 | −0.423938 | ||||||||
\(315\) | −6.21274 | −0.350048 | ||||||||
\(316\) | −12.7361 | −0.716460 | ||||||||
\(317\) | 1.66593 | 0.0935682 | 0.0467841 | − | 0.998905i | \(-0.485103\pi\) | ||||
0.0467841 | + | 0.998905i | \(0.485103\pi\) | |||||||
\(318\) | 5.09502 | 0.285715 | ||||||||
\(319\) | −3.00702 | −0.168361 | ||||||||
\(320\) | 1.64104 | 0.0917371 | ||||||||
\(321\) | 6.15233 | 0.343390 | ||||||||
\(322\) | −13.6902 | −0.762925 | ||||||||
\(323\) | −0.145858 | −0.00811578 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.82811 | −0.267815 | ||||||||
\(326\) | 5.94179 | 0.329085 | ||||||||
\(327\) | 1.92093 | 0.106228 | ||||||||
\(328\) | 4.22247 | 0.233147 | ||||||||
\(329\) | −9.83862 | −0.542421 | ||||||||
\(330\) | −1.55574 | −0.0856408 | ||||||||
\(331\) | 19.0695 | 1.04816 | 0.524078 | − | 0.851671i | \(-0.324410\pi\) | ||||
0.524078 | + | 0.851671i | \(0.324410\pi\) | |||||||
\(332\) | −8.87868 | −0.487281 | ||||||||
\(333\) | −2.49624 | −0.136793 | ||||||||
\(334\) | −3.87868 | −0.212232 | ||||||||
\(335\) | −7.15324 | −0.390823 | ||||||||
\(336\) | 3.78585 | 0.206535 | ||||||||
\(337\) | 26.7929 | 1.45950 | 0.729750 | − | 0.683714i | \(-0.239636\pi\) | ||||
0.729750 | + | 0.683714i | \(0.239636\pi\) | |||||||
\(338\) | 8.62007 | 0.468870 | ||||||||
\(339\) | 12.3153 | 0.668875 | ||||||||
\(340\) | −0.0444524 | −0.00241077 | ||||||||
\(341\) | 7.00079 | 0.379114 | ||||||||
\(342\) | −5.38464 | −0.291168 | ||||||||
\(343\) | −1.25939 | −0.0680007 | ||||||||
\(344\) | 6.30698 | 0.340049 | ||||||||
\(345\) | 5.93426 | 0.319490 | ||||||||
\(346\) | 7.89244 | 0.424300 | ||||||||
\(347\) | −5.95645 | −0.319759 | −0.159880 | − | 0.987137i | \(-0.551111\pi\) | ||||
−0.159880 | + | 0.987137i | \(0.551111\pi\) | |||||||
\(348\) | −3.17189 | −0.170031 | ||||||||
\(349\) | 20.4552 | 1.09494 | 0.547471 | − | 0.836825i | \(-0.315591\pi\) | ||||
0.547471 | + | 0.836825i | \(0.315591\pi\) | |||||||
\(350\) | −8.73387 | −0.466845 | ||||||||
\(351\) | −2.09283 | −0.111707 | ||||||||
\(352\) | 0.948021 | 0.0505297 | ||||||||
\(353\) | −18.0301 | −0.959644 | −0.479822 | − | 0.877366i | \(-0.659299\pi\) | ||||
−0.479822 | + | 0.877366i | \(0.659299\pi\) | |||||||
\(354\) | 9.78444 | 0.520037 | ||||||||
\(355\) | −14.7262 | −0.781587 | ||||||||
\(356\) | −0.793377 | −0.0420489 | ||||||||
\(357\) | −0.102551 | −0.00542755 | ||||||||
\(358\) | 4.44994 | 0.235187 | ||||||||
\(359\) | 2.62901 | 0.138754 | 0.0693769 | − | 0.997591i | \(-0.477899\pi\) | ||||
0.0693769 | + | 0.997591i | \(0.477899\pi\) | |||||||
\(360\) | −1.64104 | −0.0864906 | ||||||||
\(361\) | 9.99431 | 0.526016 | ||||||||
\(362\) | −8.23972 | −0.433070 | ||||||||
\(363\) | 10.1013 | 0.530178 | ||||||||
\(364\) | −7.92313 | −0.415285 | ||||||||
\(365\) | −18.0651 | −0.945572 | ||||||||
\(366\) | −2.50376 | −0.130874 | ||||||||
\(367\) | −12.3616 | −0.645270 | −0.322635 | − | 0.946524i | \(-0.604569\pi\) | ||||
−0.322635 | + | 0.946524i | \(0.604569\pi\) | |||||||
\(368\) | −3.61615 | −0.188505 | ||||||||
\(369\) | −4.22247 | −0.219813 | ||||||||
\(370\) | 4.09643 | 0.212963 | ||||||||
\(371\) | −19.2890 | −1.00143 | ||||||||
\(372\) | 7.38464 | 0.382876 | ||||||||
\(373\) | −7.62796 | −0.394961 | −0.197480 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197480 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(374\) | −0.0256799 | −0.00132787 | ||||||||
\(375\) | 11.9911 | 0.619216 | ||||||||
\(376\) | −2.59879 | −0.134022 | ||||||||
\(377\) | 6.63823 | 0.341886 | ||||||||
\(378\) | −3.78585 | −0.194723 | ||||||||
\(379\) | −13.1004 | −0.672920 | −0.336460 | − | 0.941698i | \(-0.609230\pi\) | ||||
−0.336460 | + | 0.941698i | \(0.609230\pi\) | |||||||
\(380\) | 8.83642 | 0.453299 | ||||||||
\(381\) | 15.4851 | 0.793326 | ||||||||
\(382\) | 5.91408 | 0.302591 | ||||||||
\(383\) | 9.78260 | 0.499868 | 0.249934 | − | 0.968263i | \(-0.419591\pi\) | ||||
0.249934 | + | 0.968263i | \(0.419591\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 5.88981 | 0.300172 | ||||||||
\(386\) | −16.7133 | −0.850682 | ||||||||
\(387\) | −6.30698 | −0.320602 | ||||||||
\(388\) | −8.13728 | −0.413108 | ||||||||
\(389\) | 11.6978 | 0.593104 | 0.296552 | − | 0.955017i | \(-0.404163\pi\) | ||||
0.296552 | + | 0.955017i | \(0.404163\pi\) | |||||||
\(390\) | 3.43442 | 0.173909 | ||||||||
\(391\) | 0.0979539 | 0.00495374 | ||||||||
\(392\) | −7.33266 | −0.370355 | ||||||||
\(393\) | −3.90357 | −0.196909 | ||||||||
\(394\) | 6.95010 | 0.350141 | ||||||||
\(395\) | −20.9004 | −1.05161 | ||||||||
\(396\) | −0.948021 | −0.0476398 | ||||||||
\(397\) | 12.8336 | 0.644100 | 0.322050 | − | 0.946723i | \(-0.395628\pi\) | ||||
0.322050 | + | 0.946723i | \(0.395628\pi\) | |||||||
\(398\) | 18.5053 | 0.927589 | ||||||||
\(399\) | 20.3854 | 1.02055 | ||||||||
\(400\) | −2.30698 | −0.115349 | ||||||||
\(401\) | −4.45606 | −0.222525 | −0.111263 | − | 0.993791i | \(-0.535489\pi\) | ||||
−0.111263 | + | 0.993791i | \(0.535489\pi\) | |||||||
\(402\) | −4.35896 | −0.217405 | ||||||||
\(403\) | −15.4548 | −0.769857 | ||||||||
\(404\) | 14.2655 | 0.709736 | ||||||||
\(405\) | 1.64104 | 0.0815441 | ||||||||
\(406\) | 12.0083 | 0.595963 | ||||||||
\(407\) | 2.36648 | 0.117302 | ||||||||
\(408\) | −0.0270879 | −0.00134105 | ||||||||
\(409\) | 5.99236 | 0.296303 | 0.148152 | − | 0.988965i | \(-0.452668\pi\) | ||||
0.148152 | + | 0.988965i | \(0.452668\pi\) | |||||||
\(410\) | 6.92925 | 0.342211 | ||||||||
\(411\) | −4.38464 | −0.216278 | ||||||||
\(412\) | −2.92987 | −0.144344 | ||||||||
\(413\) | −37.0424 | −1.82274 | ||||||||
\(414\) | 3.61615 | 0.177724 | ||||||||
\(415\) | −14.5703 | −0.715227 | ||||||||
\(416\) | −2.09283 | −0.102609 | ||||||||
\(417\) | 14.5565 | 0.712836 | ||||||||
\(418\) | 5.10475 | 0.249681 | ||||||||
\(419\) | −12.6376 | −0.617385 | −0.308692 | − | 0.951162i | \(-0.599891\pi\) | ||||
−0.308692 | + | 0.951162i | \(0.599891\pi\) | |||||||
\(420\) | 6.21274 | 0.303151 | ||||||||
\(421\) | −16.3801 | −0.798317 | −0.399158 | − | 0.916882i | \(-0.630698\pi\) | ||||
−0.399158 | + | 0.916882i | \(0.630698\pi\) | |||||||
\(422\) | −20.8892 | −1.01687 | ||||||||
\(423\) | 2.59879 | 0.126357 | ||||||||
\(424\) | −5.09502 | −0.247436 | ||||||||
\(425\) | 0.0624911 | 0.00303126 | ||||||||
\(426\) | −8.97370 | −0.434777 | ||||||||
\(427\) | 9.47887 | 0.458715 | ||||||||
\(428\) | −6.15233 | −0.297384 | ||||||||
\(429\) | 1.98404 | 0.0957905 | ||||||||
\(430\) | 10.3500 | 0.499122 | ||||||||
\(431\) | 28.8933 | 1.39174 | 0.695872 | − | 0.718166i | \(-0.255018\pi\) | ||||
0.695872 | + | 0.718166i | \(0.255018\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 24.1503 | 1.16059 | 0.580295 | − | 0.814406i | \(-0.302937\pi\) | ||||
0.580295 | + | 0.814406i | \(0.302937\pi\) | |||||||
\(434\) | −27.9571 | −1.34198 | ||||||||
\(435\) | −5.20522 | −0.249571 | ||||||||
\(436\) | −1.92093 | −0.0919960 | ||||||||
\(437\) | −19.4717 | −0.931456 | ||||||||
\(438\) | −11.0083 | −0.525998 | ||||||||
\(439\) | 20.0038 | 0.954728 | 0.477364 | − | 0.878706i | \(-0.341592\pi\) | ||||
0.477364 | + | 0.878706i | \(0.341592\pi\) | |||||||
\(440\) | 1.55574 | 0.0741671 | ||||||||
\(441\) | 7.33266 | 0.349174 | ||||||||
\(442\) | 0.0566902 | 0.00269648 | ||||||||
\(443\) | 41.2816 | 1.96135 | 0.980675 | − | 0.195645i | \(-0.0626799\pi\) | ||||
0.980675 | + | 0.195645i | \(0.0626799\pi\) | |||||||
\(444\) | 2.49624 | 0.118466 | ||||||||
\(445\) | −1.30197 | −0.0617191 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | −16.4783 | −0.779395 | ||||||||
\(448\) | −3.78585 | −0.178865 | ||||||||
\(449\) | −15.7414 | −0.742882 | −0.371441 | − | 0.928456i | \(-0.621136\pi\) | ||||
−0.371441 | + | 0.928456i | \(0.621136\pi\) | |||||||
\(450\) | 2.30698 | 0.108752 | ||||||||
\(451\) | 4.00298 | 0.188493 | ||||||||
\(452\) | −12.3153 | −0.579263 | ||||||||
\(453\) | 4.31450 | 0.202713 | ||||||||
\(454\) | −5.44959 | −0.255762 | ||||||||
\(455\) | −13.0022 | −0.609552 | ||||||||
\(456\) | 5.38464 | 0.252159 | ||||||||
\(457\) | −41.5156 | −1.94202 | −0.971009 | − | 0.239042i | \(-0.923167\pi\) | ||||
−0.971009 | + | 0.239042i | \(0.923167\pi\) | |||||||
\(458\) | −20.9369 | −0.978317 | ||||||||
\(459\) | 0.0270879 | 0.00126435 | ||||||||
\(460\) | −5.93426 | −0.276686 | ||||||||
\(461\) | −12.7813 | −0.595285 | −0.297642 | − | 0.954677i | \(-0.596200\pi\) | ||||
−0.297642 | + | 0.954677i | \(0.596200\pi\) | |||||||
\(462\) | 3.58906 | 0.166978 | ||||||||
\(463\) | −0.386833 | −0.0179777 | −0.00898883 | − | 0.999960i | \(-0.502861\pi\) | ||||
−0.00898883 | + | 0.999960i | \(0.502861\pi\) | |||||||
\(464\) | 3.17189 | 0.147252 | ||||||||
\(465\) | 12.1185 | 0.561982 | ||||||||
\(466\) | 27.0478 | 1.25296 | ||||||||
\(467\) | −22.6179 | −1.04663 | −0.523315 | − | 0.852139i | \(-0.675305\pi\) | ||||
−0.523315 | + | 0.852139i | \(0.675305\pi\) | |||||||
\(468\) | 2.09283 | 0.0967410 | ||||||||
\(469\) | 16.5024 | 0.762008 | ||||||||
\(470\) | −4.26472 | −0.196717 | ||||||||
\(471\) | −7.51219 | −0.346144 | ||||||||
\(472\) | −9.78444 | −0.450365 | ||||||||
\(473\) | 5.97915 | 0.274921 | ||||||||
\(474\) | −12.7361 | −0.584987 | ||||||||
\(475\) | −12.4222 | −0.569971 | ||||||||
\(476\) | 0.102551 | 0.00470040 | ||||||||
\(477\) | 5.09502 | 0.233285 | ||||||||
\(478\) | −30.6714 | −1.40288 | ||||||||
\(479\) | 5.46476 | 0.249691 | 0.124846 | − | 0.992176i | \(-0.460156\pi\) | ||||
0.124846 | + | 0.992176i | \(0.460156\pi\) | |||||||
\(480\) | 1.64104 | 0.0749030 | ||||||||
\(481\) | −5.22419 | −0.238203 | ||||||||
\(482\) | 9.66531 | 0.440243 | ||||||||
\(483\) | −13.6902 | −0.622926 | ||||||||
\(484\) | −10.1013 | −0.459148 | ||||||||
\(485\) | −13.3536 | −0.606357 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 0.0270879 | 0.00122747 | 0.000613734 | − | 1.00000i | \(-0.499805\pi\) | ||||
0.000613734 | 1.00000i | \(0.499805\pi\) | ||||||||
\(488\) | 2.50376 | 0.113340 | ||||||||
\(489\) | 5.94179 | 0.268697 | ||||||||
\(490\) | −12.0332 | −0.543605 | ||||||||
\(491\) | −20.0131 | −0.903180 | −0.451590 | − | 0.892225i | \(-0.649143\pi\) | ||||
−0.451590 | + | 0.892225i | \(0.649143\pi\) | |||||||
\(492\) | 4.22247 | 0.190363 | ||||||||
\(493\) | −0.0859199 | −0.00386964 | ||||||||
\(494\) | −11.2691 | −0.507021 | ||||||||
\(495\) | −1.55574 | −0.0699254 | ||||||||
\(496\) | −7.38464 | −0.331580 | ||||||||
\(497\) | 33.9731 | 1.52390 | ||||||||
\(498\) | −8.87868 | −0.397863 | ||||||||
\(499\) | −36.4407 | −1.63131 | −0.815655 | − | 0.578539i | \(-0.803623\pi\) | ||||
−0.815655 | + | 0.578539i | \(0.803623\pi\) | |||||||
\(500\) | −11.9911 | −0.536257 | ||||||||
\(501\) | −3.87868 | −0.173287 | ||||||||
\(502\) | −14.8004 | −0.660574 | ||||||||
\(503\) | −5.49325 | −0.244932 | −0.122466 | − | 0.992473i | \(-0.539080\pi\) | ||||
−0.122466 | + | 0.992473i | \(0.539080\pi\) | |||||||
\(504\) | 3.78585 | 0.168635 | ||||||||
\(505\) | 23.4103 | 1.04175 | ||||||||
\(506\) | −3.42819 | −0.152401 | ||||||||
\(507\) | 8.62007 | 0.382831 | ||||||||
\(508\) | −15.4851 | −0.687040 | ||||||||
\(509\) | 11.1585 | 0.494590 | 0.247295 | − | 0.968940i | \(-0.420458\pi\) | ||||
0.247295 | + | 0.968940i | \(0.420458\pi\) | |||||||
\(510\) | −0.0444524 | −0.00196838 | ||||||||
\(511\) | 41.6758 | 1.84363 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.38464 | −0.237738 | ||||||||
\(514\) | −13.5800 | −0.598989 | ||||||||
\(515\) | −4.80804 | −0.211868 | ||||||||
\(516\) | 6.30698 | 0.277649 | ||||||||
\(517\) | −2.46370 | −0.108354 | ||||||||
\(518\) | −9.45038 | −0.415226 | ||||||||
\(519\) | 7.89244 | 0.346440 | ||||||||
\(520\) | −3.43442 | −0.150609 | ||||||||
\(521\) | 24.6217 | 1.07869 | 0.539347 | − | 0.842084i | \(-0.318671\pi\) | ||||
0.539347 | + | 0.842084i | \(0.318671\pi\) | |||||||
\(522\) | −3.17189 | −0.138830 | ||||||||
\(523\) | 7.45222 | 0.325863 | 0.162931 | − | 0.986637i | \(-0.447905\pi\) | ||||
0.162931 | + | 0.986637i | \(0.447905\pi\) | |||||||
\(524\) | 3.90357 | 0.170528 | ||||||||
\(525\) | −8.73387 | −0.381177 | ||||||||
\(526\) | −7.89420 | −0.344204 | ||||||||
\(527\) | 0.200034 | 0.00871362 | ||||||||
\(528\) | 0.948021 | 0.0412573 | ||||||||
\(529\) | −9.92345 | −0.431454 | ||||||||
\(530\) | −8.36115 | −0.363185 | ||||||||
\(531\) | 9.78444 | 0.424609 | ||||||||
\(532\) | −20.3854 | −0.883820 | ||||||||
\(533\) | −8.83689 | −0.382768 | ||||||||
\(534\) | −0.793377 | −0.0343328 | ||||||||
\(535\) | −10.0962 | −0.436499 | ||||||||
\(536\) | 4.35896 | 0.188278 | ||||||||
\(537\) | 4.44994 | 0.192029 | ||||||||
\(538\) | 14.8946 | 0.642153 | ||||||||
\(539\) | −6.95151 | −0.299423 | ||||||||
\(540\) | −1.64104 | −0.0706193 | ||||||||
\(541\) | 21.7032 | 0.933093 | 0.466546 | − | 0.884497i | \(-0.345498\pi\) | ||||
0.466546 | + | 0.884497i | \(0.345498\pi\) | |||||||
\(542\) | −3.27769 | −0.140789 | ||||||||
\(543\) | −8.23972 | −0.353600 | ||||||||
\(544\) | 0.0270879 | 0.00116138 | ||||||||
\(545\) | −3.15233 | −0.135031 | ||||||||
\(546\) | −7.92313 | −0.339079 | ||||||||
\(547\) | 11.0550 | 0.472676 | 0.236338 | − | 0.971671i | \(-0.424053\pi\) | ||||
0.236338 | + | 0.971671i | \(0.424053\pi\) | |||||||
\(548\) | 4.38464 | 0.187302 | ||||||||
\(549\) | −2.50376 | −0.106858 | ||||||||
\(550\) | −2.18706 | −0.0932567 | ||||||||
\(551\) | 17.0795 | 0.727611 | ||||||||
\(552\) | −3.61615 | −0.153914 | ||||||||
\(553\) | 48.2168 | 2.05039 | ||||||||
\(554\) | 8.26018 | 0.350941 | ||||||||
\(555\) | 4.09643 | 0.173884 | ||||||||
\(556\) | −14.5565 | −0.617334 | ||||||||
\(557\) | 39.8283 | 1.68758 | 0.843789 | − | 0.536675i | \(-0.180320\pi\) | ||||
0.843789 | + | 0.536675i | \(0.180320\pi\) | |||||||
\(558\) | 7.38464 | 0.312617 | ||||||||
\(559\) | −13.1994 | −0.558276 | ||||||||
\(560\) | −6.21274 | −0.262536 | ||||||||
\(561\) | −0.0256799 | −0.00108420 | ||||||||
\(562\) | 14.6209 | 0.616744 | ||||||||
\(563\) | −4.41392 | −0.186025 | −0.0930123 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930123 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(564\) | −2.59879 | −0.109429 | ||||||||
\(565\) | −20.2099 | −0.850238 | ||||||||
\(566\) | −24.5961 | −1.03385 | ||||||||
\(567\) | −3.78585 | −0.158991 | ||||||||
\(568\) | 8.97370 | 0.376528 | ||||||||
\(569\) | −4.68863 | −0.196558 | −0.0982788 | − | 0.995159i | \(-0.531334\pi\) | ||||
−0.0982788 | + | 0.995159i | \(0.531334\pi\) | |||||||
\(570\) | 8.83642 | 0.370117 | ||||||||
\(571\) | 35.2974 | 1.47715 | 0.738576 | − | 0.674171i | \(-0.235499\pi\) | ||||
0.738576 | + | 0.674171i | \(0.235499\pi\) | |||||||
\(572\) | −1.98404 | −0.0829570 | ||||||||
\(573\) | 5.91408 | 0.247064 | ||||||||
\(574\) | −15.9856 | −0.667227 | ||||||||
\(575\) | 8.34238 | 0.347901 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.19146 | 0.216123 | 0.108062 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108062 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(578\) | 16.9993 | 0.707076 | ||||||||
\(579\) | −16.7133 | −0.694579 | ||||||||
\(580\) | 5.20522 | 0.216135 | ||||||||
\(581\) | 33.6133 | 1.39452 | ||||||||
\(582\) | −8.13728 | −0.337301 | ||||||||
\(583\) | −4.83019 | −0.200046 | ||||||||
\(584\) | 11.0083 | 0.455527 | ||||||||
\(585\) | 3.43442 | 0.141996 | ||||||||
\(586\) | 2.60282 | 0.107522 | ||||||||
\(587\) | −15.1913 | −0.627014 | −0.313507 | − | 0.949586i | \(-0.601504\pi\) | ||||
−0.313507 | + | 0.949586i | \(0.601504\pi\) | |||||||
\(588\) | −7.33266 | −0.302394 | ||||||||
\(589\) | −39.7636 | −1.63843 | ||||||||
\(590\) | −16.0567 | −0.661043 | ||||||||
\(591\) | 6.95010 | 0.285889 | ||||||||
\(592\) | −2.49624 | −0.102595 | ||||||||
\(593\) | 44.8330 | 1.84107 | 0.920535 | − | 0.390660i | \(-0.127753\pi\) | ||||
0.920535 | + | 0.390660i | \(0.127753\pi\) | |||||||
\(594\) | −0.948021 | −0.0388978 | ||||||||
\(595\) | 0.168290 | 0.00689922 | ||||||||
\(596\) | 16.4783 | 0.674976 | ||||||||
\(597\) | 18.5053 | 0.757373 | ||||||||
\(598\) | 7.56798 | 0.309478 | ||||||||
\(599\) | 10.9904 | 0.449055 | 0.224528 | − | 0.974468i | \(-0.427916\pi\) | ||||
0.224528 | + | 0.974468i | \(0.427916\pi\) | |||||||
\(600\) | −2.30698 | −0.0941820 | ||||||||
\(601\) | 3.17471 | 0.129499 | 0.0647496 | − | 0.997902i | \(-0.479375\pi\) | ||||
0.0647496 | + | 0.997902i | \(0.479375\pi\) | |||||||
\(602\) | −23.8773 | −0.973165 | ||||||||
\(603\) | −4.35896 | −0.177510 | ||||||||
\(604\) | −4.31450 | −0.175555 | ||||||||
\(605\) | −16.5766 | −0.673935 | ||||||||
\(606\) | 14.2655 | 0.579497 | ||||||||
\(607\) | −20.1193 | −0.816617 | −0.408309 | − | 0.912844i | \(-0.633881\pi\) | ||||
−0.408309 | + | 0.912844i | \(0.633881\pi\) | |||||||
\(608\) | −5.38464 | −0.218376 | ||||||||
\(609\) | 12.0083 | 0.486601 | ||||||||
\(610\) | 4.10878 | 0.166360 | ||||||||
\(611\) | 5.43881 | 0.220031 | ||||||||
\(612\) | −0.0270879 | −0.00109496 | ||||||||
\(613\) | −28.4725 | −1.14999 | −0.574996 | − | 0.818156i | \(-0.694996\pi\) | ||||
−0.574996 | + | 0.818156i | \(0.694996\pi\) | |||||||
\(614\) | 7.52944 | 0.303864 | ||||||||
\(615\) | 6.92925 | 0.279414 | ||||||||
\(616\) | −3.58906 | −0.144608 | ||||||||
\(617\) | 24.7637 | 0.996950 | 0.498475 | − | 0.866904i | \(-0.333894\pi\) | ||||
0.498475 | + | 0.866904i | \(0.333894\pi\) | |||||||
\(618\) | −2.92987 | −0.117857 | ||||||||
\(619\) | 20.6260 | 0.829031 | 0.414515 | − | 0.910042i | \(-0.363951\pi\) | ||||
0.414515 | + | 0.910042i | \(0.363951\pi\) | |||||||
\(620\) | −12.1185 | −0.486691 | ||||||||
\(621\) | 3.61615 | 0.145111 | ||||||||
\(622\) | −17.8696 | −0.716507 | ||||||||
\(623\) | 3.00360 | 0.120337 | ||||||||
\(624\) | −2.09283 | −0.0837801 | ||||||||
\(625\) | −8.14297 | −0.325719 | ||||||||
\(626\) | −6.41094 | −0.256233 | ||||||||
\(627\) | 5.10475 | 0.203864 | ||||||||
\(628\) | 7.51219 | 0.299769 | ||||||||
\(629\) | 0.0676177 | 0.00269610 | ||||||||
\(630\) | 6.21274 | 0.247522 | ||||||||
\(631\) | −3.65060 | −0.145328 | −0.0726640 | − | 0.997356i | \(-0.523150\pi\) | ||||
−0.0726640 | + | 0.997356i | \(0.523150\pi\) | |||||||
\(632\) | 12.7361 | 0.506614 | ||||||||
\(633\) | −20.8892 | −0.830271 | ||||||||
\(634\) | −1.66593 | −0.0661627 | ||||||||
\(635\) | −25.4117 | −1.00843 | ||||||||
\(636\) | −5.09502 | −0.202031 | ||||||||
\(637\) | 15.3460 | 0.608030 | ||||||||
\(638\) | 3.00702 | 0.119049 | ||||||||
\(639\) | −8.97370 | −0.354994 | ||||||||
\(640\) | −1.64104 | −0.0648679 | ||||||||
\(641\) | −34.4091 | −1.35908 | −0.679538 | − | 0.733640i | \(-0.737820\pi\) | ||||
−0.679538 | + | 0.733640i | \(0.737820\pi\) | |||||||
\(642\) | −6.15233 | −0.242813 | ||||||||
\(643\) | 28.6486 | 1.12979 | 0.564896 | − | 0.825162i | \(-0.308916\pi\) | ||||
0.564896 | + | 0.825162i | \(0.308916\pi\) | |||||||
\(644\) | 13.6902 | 0.539470 | ||||||||
\(645\) | 10.3500 | 0.407532 | ||||||||
\(646\) | 0.145858 | 0.00573872 | ||||||||
\(647\) | 6.35045 | 0.249662 | 0.124831 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124831 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −9.27585 | −0.364109 | ||||||||
\(650\) | 4.82811 | 0.189374 | ||||||||
\(651\) | −27.9571 | −1.09573 | ||||||||
\(652\) | −5.94179 | −0.232698 | ||||||||
\(653\) | −12.1639 | −0.476010 | −0.238005 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238005 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(654\) | −1.92093 | −0.0751144 | ||||||||
\(655\) | 6.40592 | 0.250300 | ||||||||
\(656\) | −4.22247 | −0.164860 | ||||||||
\(657\) | −11.0083 | −0.429475 | ||||||||
\(658\) | 9.83862 | 0.383549 | ||||||||
\(659\) | 21.9037 | 0.853248 | 0.426624 | − | 0.904429i | \(-0.359703\pi\) | ||||
0.426624 | + | 0.904429i | \(0.359703\pi\) | |||||||
\(660\) | 1.55574 | 0.0605572 | ||||||||
\(661\) | −21.5772 | −0.839256 | −0.419628 | − | 0.907696i | \(-0.637839\pi\) | ||||
−0.419628 | + | 0.907696i | \(0.637839\pi\) | |||||||
\(662\) | −19.0695 | −0.741158 | ||||||||
\(663\) | 0.0566902 | 0.00220167 | ||||||||
\(664\) | 8.87868 | 0.344559 | ||||||||
\(665\) | −33.4534 | −1.29727 | ||||||||
\(666\) | 2.49624 | 0.0967272 | ||||||||
\(667\) | −11.4701 | −0.444122 | ||||||||
\(668\) | 3.87868 | 0.150071 | ||||||||
\(669\) | 1.00000 | 0.0386622 | ||||||||
\(670\) | 7.15324 | 0.276354 | ||||||||
\(671\) | 2.37362 | 0.0916326 | ||||||||
\(672\) | −3.78585 | −0.146042 | ||||||||
\(673\) | 18.7512 | 0.722807 | 0.361403 | − | 0.932410i | \(-0.382298\pi\) | ||||
0.361403 | + | 0.932410i | \(0.382298\pi\) | |||||||
\(674\) | −26.7929 | −1.03202 | ||||||||
\(675\) | 2.30698 | 0.0887956 | ||||||||
\(676\) | −8.62007 | −0.331541 | ||||||||
\(677\) | −11.2434 | −0.432120 | −0.216060 | − | 0.976380i | \(-0.569321\pi\) | ||||
−0.216060 | + | 0.976380i | \(0.569321\pi\) | |||||||
\(678\) | −12.3153 | −0.472966 | ||||||||
\(679\) | 30.8065 | 1.18225 | ||||||||
\(680\) | 0.0444524 | 0.00170467 | ||||||||
\(681\) | −5.44959 | −0.208829 | ||||||||
\(682\) | −7.00079 | −0.268074 | ||||||||
\(683\) | −19.5387 | −0.747626 | −0.373813 | − | 0.927504i | \(-0.621950\pi\) | ||||
−0.373813 | + | 0.927504i | \(0.621950\pi\) | |||||||
\(684\) | 5.38464 | 0.205887 | ||||||||
\(685\) | 7.19538 | 0.274921 | ||||||||
\(686\) | 1.25939 | 0.0480838 | ||||||||
\(687\) | −20.9369 | −0.798792 | ||||||||
\(688\) | −6.30698 | −0.240451 | ||||||||
\(689\) | 10.6630 | 0.406228 | ||||||||
\(690\) | −5.93426 | −0.225913 | ||||||||
\(691\) | −42.2422 | −1.60697 | −0.803484 | − | 0.595326i | \(-0.797023\pi\) | ||||
−0.803484 | + | 0.595326i | \(0.797023\pi\) | |||||||
\(692\) | −7.89244 | −0.300025 | ||||||||
\(693\) | 3.58906 | 0.136337 | ||||||||
\(694\) | 5.95645 | 0.226104 | ||||||||
\(695\) | −23.8879 | −0.906119 | ||||||||
\(696\) | 3.17189 | 0.120230 | ||||||||
\(697\) | 0.114378 | 0.00433236 | ||||||||
\(698\) | −20.4552 | −0.774241 | ||||||||
\(699\) | 27.0478 | 1.02304 | ||||||||
\(700\) | 8.73387 | 0.330109 | ||||||||
\(701\) | −20.5501 | −0.776165 | −0.388082 | − | 0.921625i | \(-0.626862\pi\) | ||||
−0.388082 | + | 0.921625i | \(0.626862\pi\) | |||||||
\(702\) | 2.09283 | 0.0789887 | ||||||||
\(703\) | −13.4413 | −0.506949 | ||||||||
\(704\) | −0.948021 | −0.0357299 | ||||||||
\(705\) | −4.26472 | −0.160619 | ||||||||
\(706\) | 18.0301 | 0.678571 | ||||||||
\(707\) | −54.0071 | −2.03115 | ||||||||
\(708\) | −9.78444 | −0.367722 | ||||||||
\(709\) | −18.0271 | −0.677021 | −0.338511 | − | 0.940963i | \(-0.609923\pi\) | ||||
−0.338511 | + | 0.940963i | \(0.609923\pi\) | |||||||
\(710\) | 14.7262 | 0.552666 | ||||||||
\(711\) | −12.7361 | −0.477640 | ||||||||
\(712\) | 0.793377 | 0.0297330 | ||||||||
\(713\) | 26.7040 | 1.00007 | ||||||||
\(714\) | 0.102551 | 0.00383786 | ||||||||
\(715\) | −3.25590 | −0.121764 | ||||||||
\(716\) | −4.44994 | −0.166302 | ||||||||
\(717\) | −30.6714 | −1.14545 | ||||||||
\(718\) | −2.62901 | −0.0981137 | ||||||||
\(719\) | −27.9105 | −1.04089 | −0.520443 | − | 0.853897i | \(-0.674233\pi\) | ||||
−0.520443 | + | 0.853897i | \(0.674233\pi\) | |||||||
\(720\) | 1.64104 | 0.0611581 | ||||||||
\(721\) | 11.0920 | 0.413089 | ||||||||
\(722\) | −9.99431 | −0.371950 | ||||||||
\(723\) | 9.66531 | 0.359457 | ||||||||
\(724\) | 8.23972 | 0.306227 | ||||||||
\(725\) | −7.31749 | −0.271765 | ||||||||
\(726\) | −10.1013 | −0.374893 | ||||||||
\(727\) | −46.4208 | −1.72165 | −0.860827 | − | 0.508898i | \(-0.830053\pi\) | ||||
−0.860827 | + | 0.508898i | \(0.830053\pi\) | |||||||
\(728\) | 7.92313 | 0.293651 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.0651 | 0.668620 | ||||||||
\(731\) | 0.170843 | 0.00631884 | ||||||||
\(732\) | 2.50376 | 0.0925418 | ||||||||
\(733\) | 30.1465 | 1.11349 | 0.556743 | − | 0.830685i | \(-0.312051\pi\) | ||||
0.556743 | + | 0.830685i | \(0.312051\pi\) | |||||||
\(734\) | 12.3616 | 0.456274 | ||||||||
\(735\) | −12.0332 | −0.443852 | ||||||||
\(736\) | 3.61615 | 0.133293 | ||||||||
\(737\) | 4.13238 | 0.152218 | ||||||||
\(738\) | 4.22247 | 0.155431 | ||||||||
\(739\) | 22.4392 | 0.825441 | 0.412720 | − | 0.910858i | \(-0.364579\pi\) | ||||
0.412720 | + | 0.910858i | \(0.364579\pi\) | |||||||
\(740\) | −4.09643 | −0.150588 | ||||||||
\(741\) | −11.2691 | −0.413981 | ||||||||
\(742\) | 19.2890 | 0.708121 | ||||||||
\(743\) | −45.5002 | −1.66924 | −0.834620 | − | 0.550825i | \(-0.814313\pi\) | ||||
−0.834620 | + | 0.550825i | \(0.814313\pi\) | |||||||
\(744\) | −7.38464 | −0.270734 | ||||||||
\(745\) | 27.0415 | 0.990725 | ||||||||
\(746\) | 7.62796 | 0.279279 | ||||||||
\(747\) | −8.87868 | −0.324854 | ||||||||
\(748\) | 0.0256799 | 0.000938949 0 | ||||||||
\(749\) | 23.2918 | 0.851064 | ||||||||
\(750\) | −11.9911 | −0.437852 | ||||||||
\(751\) | −14.7463 | −0.538101 | −0.269051 | − | 0.963126i | \(-0.586710\pi\) | ||||
−0.269051 | + | 0.963126i | \(0.586710\pi\) | |||||||
\(752\) | 2.59879 | 0.0947680 | ||||||||
\(753\) | −14.8004 | −0.539356 | ||||||||
\(754\) | −6.63823 | −0.241750 | ||||||||
\(755\) | −7.08029 | −0.257678 | ||||||||
\(756\) | 3.78585 | 0.137690 | ||||||||
\(757\) | −21.6569 | −0.787133 | −0.393566 | − | 0.919296i | \(-0.628759\pi\) | ||||
−0.393566 | + | 0.919296i | \(0.628759\pi\) | |||||||
\(758\) | 13.1004 | 0.475826 | ||||||||
\(759\) | −3.42819 | −0.124435 | ||||||||
\(760\) | −8.83642 | −0.320531 | ||||||||
\(761\) | −9.81348 | −0.355739 | −0.177869 | − | 0.984054i | \(-0.556920\pi\) | ||||
−0.177869 | + | 0.984054i | \(0.556920\pi\) | |||||||
\(762\) | −15.4851 | −0.560966 | ||||||||
\(763\) | 7.27236 | 0.263277 | ||||||||
\(764\) | −5.91408 | −0.213964 | ||||||||
\(765\) | −0.0444524 | −0.00160718 | ||||||||
\(766\) | −9.78260 | −0.353460 | ||||||||
\(767\) | 20.4771 | 0.739387 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −6.83685 | −0.246543 | −0.123272 | − | 0.992373i | \(-0.539339\pi\) | ||||
−0.123272 | + | 0.992373i | \(0.539339\pi\) | |||||||
\(770\) | −5.88981 | −0.212254 | ||||||||
\(771\) | −13.5800 | −0.489072 | ||||||||
\(772\) | 16.7133 | 0.601523 | ||||||||
\(773\) | −49.2899 | −1.77283 | −0.886417 | − | 0.462887i | \(-0.846813\pi\) | ||||
−0.886417 | + | 0.462887i | \(0.846813\pi\) | |||||||
\(774\) | 6.30698 | 0.226700 | ||||||||
\(775\) | 17.0362 | 0.611958 | ||||||||
\(776\) | 8.13728 | 0.292111 | ||||||||
\(777\) | −9.45038 | −0.339030 | ||||||||
\(778\) | −11.6978 | −0.419388 | ||||||||
\(779\) | −22.7364 | −0.814618 | ||||||||
\(780\) | −3.43442 | −0.122972 | ||||||||
\(781\) | 8.50725 | 0.304413 | ||||||||
\(782\) | −0.0979539 | −0.00350282 | ||||||||
\(783\) | −3.17189 | −0.113354 | ||||||||
\(784\) | 7.33266 | 0.261881 | ||||||||
\(785\) | 12.3278 | 0.439999 | ||||||||
\(786\) | 3.90357 | 0.139236 | ||||||||
\(787\) | −46.6575 | −1.66316 | −0.831580 | − | 0.555405i | \(-0.812563\pi\) | ||||
−0.831580 | + | 0.555405i | \(0.812563\pi\) | |||||||
\(788\) | −6.95010 | −0.247587 | ||||||||
\(789\) | −7.89420 | −0.281041 | ||||||||
\(790\) | 20.9004 | 0.743604 | ||||||||
\(791\) | 46.6238 | 1.65775 | ||||||||
\(792\) | 0.948021 | 0.0336864 | ||||||||
\(793\) | −5.23994 | −0.186076 | ||||||||
\(794\) | −12.8336 | −0.455448 | ||||||||
\(795\) | −8.36115 | −0.296540 | ||||||||
\(796\) | −18.5053 | −0.655904 | ||||||||
\(797\) | −22.8186 | −0.808277 | −0.404139 | − | 0.914698i | \(-0.632429\pi\) | ||||
−0.404139 | + | 0.914698i | \(0.632429\pi\) | |||||||
\(798\) | −20.3854 | −0.721636 | ||||||||
\(799\) | −0.0703956 | −0.00249042 | ||||||||
\(800\) | 2.30698 | 0.0815640 | ||||||||
\(801\) | −0.793377 | −0.0280326 | ||||||||
\(802\) | 4.45606 | 0.157349 | ||||||||
\(803\) | 10.4361 | 0.368282 | ||||||||
\(804\) | 4.35896 | 0.153729 | ||||||||
\(805\) | 22.4662 | 0.791830 | ||||||||
\(806\) | 15.4548 | 0.544371 | ||||||||
\(807\) | 14.8946 | 0.524316 | ||||||||
\(808\) | −14.2655 | −0.501859 | ||||||||
\(809\) | 21.3057 | 0.749070 | 0.374535 | − | 0.927213i | \(-0.377802\pi\) | ||||
0.374535 | + | 0.927213i | \(0.377802\pi\) | |||||||
\(810\) | −1.64104 | −0.0576604 | ||||||||
\(811\) | −4.37178 | −0.153514 | −0.0767570 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767570 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(812\) | −12.0083 | −0.421409 | ||||||||
\(813\) | −3.27769 | −0.114954 | ||||||||
\(814\) | −2.36648 | −0.0829452 | ||||||||
\(815\) | −9.75073 | −0.341553 | ||||||||
\(816\) | 0.0270879 | 0.000948265 0 | ||||||||
\(817\) | −33.9608 | −1.18814 | ||||||||
\(818\) | −5.99236 | −0.209518 | ||||||||
\(819\) | −7.92313 | −0.276857 | ||||||||
\(820\) | −6.92925 | −0.241980 | ||||||||
\(821\) | 48.6264 | 1.69707 | 0.848536 | − | 0.529138i | \(-0.177485\pi\) | ||||
0.848536 | + | 0.529138i | \(0.177485\pi\) | |||||||
\(822\) | 4.38464 | 0.152932 | ||||||||
\(823\) | 23.9936 | 0.836364 | 0.418182 | − | 0.908363i | \(-0.362667\pi\) | ||||
0.418182 | + | 0.908363i | \(0.362667\pi\) | |||||||
\(824\) | 2.92987 | 0.102067 | ||||||||
\(825\) | −2.18706 | −0.0761437 | ||||||||
\(826\) | 37.0424 | 1.28887 | ||||||||
\(827\) | 43.1952 | 1.50204 | 0.751022 | − | 0.660277i | \(-0.229561\pi\) | ||||
0.751022 | + | 0.660277i | \(0.229561\pi\) | |||||||
\(828\) | −3.61615 | −0.125670 | ||||||||
\(829\) | −27.2828 | −0.947569 | −0.473785 | − | 0.880641i | \(-0.657113\pi\) | ||||
−0.473785 | + | 0.880641i | \(0.657113\pi\) | |||||||
\(830\) | 14.5703 | 0.505742 | ||||||||
\(831\) | 8.26018 | 0.286542 | ||||||||
\(832\) | 2.09283 | 0.0725557 | ||||||||
\(833\) | −0.198626 | −0.00688199 | ||||||||
\(834\) | −14.5565 | −0.504051 | ||||||||
\(835\) | 6.36508 | 0.220273 | ||||||||
\(836\) | −5.10475 | −0.176551 | ||||||||
\(837\) | 7.38464 | 0.255250 | ||||||||
\(838\) | 12.6376 | 0.436557 | ||||||||
\(839\) | −1.65139 | −0.0570122 | −0.0285061 | − | 0.999594i | \(-0.509075\pi\) | ||||
−0.0285061 | + | 0.999594i | \(0.509075\pi\) | |||||||
\(840\) | −6.21274 | −0.214360 | ||||||||
\(841\) | −18.9391 | −0.653072 | ||||||||
\(842\) | 16.3801 | 0.564495 | ||||||||
\(843\) | 14.6209 | 0.503569 | ||||||||
\(844\) | 20.8892 | 0.719036 | ||||||||
\(845\) | −14.1459 | −0.486634 | ||||||||
\(846\) | −2.59879 | −0.0893481 | ||||||||
\(847\) | 38.2418 | 1.31401 | ||||||||
\(848\) | 5.09502 | 0.174964 | ||||||||
\(849\) | −24.5961 | −0.844135 | ||||||||
\(850\) | −0.0624911 | −0.00214343 | ||||||||
\(851\) | 9.02677 | 0.309434 | ||||||||
\(852\) | 8.97370 | 0.307434 | ||||||||
\(853\) | 6.90638 | 0.236470 | 0.118235 | − | 0.992986i | \(-0.462276\pi\) | ||||
0.118235 | + | 0.992986i | \(0.462276\pi\) | |||||||
\(854\) | −9.47887 | −0.324360 | ||||||||
\(855\) | 8.83642 | 0.302199 | ||||||||
\(856\) | 6.15233 | 0.210282 | ||||||||
\(857\) | −25.8488 | −0.882977 | −0.441489 | − | 0.897267i | \(-0.645549\pi\) | ||||
−0.441489 | + | 0.897267i | \(0.645549\pi\) | |||||||
\(858\) | −1.98404 | −0.0677341 | ||||||||
\(859\) | −33.9690 | −1.15901 | −0.579504 | − | 0.814969i | \(-0.696754\pi\) | ||||
−0.579504 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(860\) | −10.3500 | −0.352933 | ||||||||
\(861\) | −15.9856 | −0.544788 | ||||||||
\(862\) | −28.8933 | −0.984111 | ||||||||
\(863\) | −8.63729 | −0.294017 | −0.147008 | − | 0.989135i | \(-0.546964\pi\) | ||||
−0.147008 | + | 0.989135i | \(0.546964\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −12.9518 | −0.440375 | ||||||||
\(866\) | −24.1503 | −0.820661 | ||||||||
\(867\) | 16.9993 | 0.577325 | ||||||||
\(868\) | 27.9571 | 0.948927 | ||||||||
\(869\) | 12.0741 | 0.409584 | ||||||||
\(870\) | 5.20522 | 0.176473 | ||||||||
\(871\) | −9.12254 | −0.309106 | ||||||||
\(872\) | 1.92093 | 0.0650510 | ||||||||
\(873\) | −8.13728 | −0.275405 | ||||||||
\(874\) | 19.4717 | 0.658639 | ||||||||
\(875\) | 45.3964 | 1.53468 | ||||||||
\(876\) | 11.0083 | 0.371937 | ||||||||
\(877\) | 30.1650 | 1.01860 | 0.509301 | − | 0.860589i | \(-0.329904\pi\) | ||||
0.509301 | + | 0.860589i | \(0.329904\pi\) | |||||||
\(878\) | −20.0038 | −0.675095 | ||||||||
\(879\) | 2.60282 | 0.0877911 | ||||||||
\(880\) | −1.55574 | −0.0524441 | ||||||||
\(881\) | 12.4248 | 0.418603 | 0.209301 | − | 0.977851i | \(-0.432881\pi\) | ||||
0.209301 | + | 0.977851i | \(0.432881\pi\) | |||||||
\(882\) | −7.33266 | −0.246903 | ||||||||
\(883\) | 11.3493 | 0.381934 | 0.190967 | − | 0.981596i | \(-0.438838\pi\) | ||||
0.190967 | + | 0.981596i | \(0.438838\pi\) | |||||||
\(884\) | −0.0566902 | −0.00190670 | ||||||||
\(885\) | −16.0567 | −0.539740 | ||||||||
\(886\) | −41.2816 | −1.38688 | ||||||||
\(887\) | −8.39412 | −0.281847 | −0.140923 | − | 0.990020i | \(-0.545007\pi\) | ||||
−0.140923 | + | 0.990020i | \(0.545007\pi\) | |||||||
\(888\) | −2.49624 | −0.0837682 | ||||||||
\(889\) | 58.6243 | 1.96620 | ||||||||
\(890\) | 1.30197 | 0.0436420 | ||||||||
\(891\) | −0.948021 | −0.0317599 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 13.9935 | 0.468275 | ||||||||
\(894\) | 16.4783 | 0.551115 | ||||||||
\(895\) | −7.30255 | −0.244097 | ||||||||
\(896\) | 3.78585 | 0.126476 | ||||||||
\(897\) | 7.56798 | 0.252688 | ||||||||
\(898\) | 15.7414 | 0.525297 | ||||||||
\(899\) | −23.4233 | −0.781210 | ||||||||
\(900\) | −2.30698 | −0.0768993 | ||||||||
\(901\) | −0.138013 | −0.00459789 | ||||||||
\(902\) | −4.00298 | −0.133285 | ||||||||
\(903\) | −23.8773 | −0.794586 | ||||||||
\(904\) | 12.3153 | 0.409601 | ||||||||
\(905\) | 13.5217 | 0.449477 | ||||||||
\(906\) | −4.31450 | −0.143340 | ||||||||
\(907\) | 12.7461 | 0.423229 | 0.211614 | − | 0.977353i | \(-0.432128\pi\) | ||||
0.211614 | + | 0.977353i | \(0.432128\pi\) | |||||||
\(908\) | 5.44959 | 0.180851 | ||||||||
\(909\) | 14.2655 | 0.473157 | ||||||||
\(910\) | 13.0022 | 0.431019 | ||||||||
\(911\) | 15.4866 | 0.513095 | 0.256547 | − | 0.966532i | \(-0.417415\pi\) | ||||
0.256547 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(912\) | −5.38464 | −0.178303 | ||||||||
\(913\) | 8.41717 | 0.278568 | ||||||||
\(914\) | 41.5156 | 1.37321 | ||||||||
\(915\) | 4.10878 | 0.135832 | ||||||||
\(916\) | 20.9369 | 0.691774 | ||||||||
\(917\) | −14.7783 | −0.488023 | ||||||||
\(918\) | −0.0270879 | −0.000894033 0 | ||||||||
\(919\) | −1.68380 | −0.0555436 | −0.0277718 | − | 0.999614i | \(-0.508841\pi\) | ||||
−0.0277718 | + | 0.999614i | \(0.508841\pi\) | |||||||
\(920\) | 5.93426 | 0.195647 | ||||||||
\(921\) | 7.52944 | 0.248104 | ||||||||
\(922\) | 12.7813 | 0.420930 | ||||||||
\(923\) | −18.7804 | −0.618165 | ||||||||
\(924\) | −3.58906 | −0.118072 | ||||||||
\(925\) | 5.75876 | 0.189347 | ||||||||
\(926\) | 0.386833 | 0.0127121 | ||||||||
\(927\) | −2.92987 | −0.0962295 | ||||||||
\(928\) | −3.17189 | −0.104123 | ||||||||
\(929\) | −54.6754 | −1.79384 | −0.896921 | − | 0.442190i | \(-0.854202\pi\) | ||||
−0.896921 | + | 0.442190i | \(0.854202\pi\) | |||||||
\(930\) | −12.1185 | −0.397382 | ||||||||
\(931\) | 39.4837 | 1.29403 | ||||||||
\(932\) | −27.0478 | −0.885979 | ||||||||
\(933\) | −17.8696 | −0.585025 | ||||||||
\(934\) | 22.6179 | 0.740080 | ||||||||
\(935\) | 0.0421418 | 0.00137818 | ||||||||
\(936\) | −2.09283 | −0.0684062 | ||||||||
\(937\) | −5.35265 | −0.174863 | −0.0874317 | − | 0.996171i | \(-0.527866\pi\) | ||||
−0.0874317 | + | 0.996171i | \(0.527866\pi\) | |||||||
\(938\) | −16.5024 | −0.538821 | ||||||||
\(939\) | −6.41094 | −0.209213 | ||||||||
\(940\) | 4.26472 | 0.139100 | ||||||||
\(941\) | 29.1362 | 0.949811 | 0.474906 | − | 0.880037i | \(-0.342482\pi\) | ||||
0.474906 | + | 0.880037i | \(0.342482\pi\) | |||||||
\(942\) | 7.51219 | 0.244760 | ||||||||
\(943\) | 15.2691 | 0.497230 | ||||||||
\(944\) | 9.78444 | 0.318456 | ||||||||
\(945\) | 6.21274 | 0.202101 | ||||||||
\(946\) | −5.97915 | −0.194399 | ||||||||
\(947\) | −22.3852 | −0.727421 | −0.363711 | − | 0.931512i | \(-0.618490\pi\) | ||||
−0.363711 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(948\) | 12.7361 | 0.413648 | ||||||||
\(949\) | −23.0385 | −0.747861 | ||||||||
\(950\) | 12.4222 | 0.403031 | ||||||||
\(951\) | −1.66593 | −0.0540216 | ||||||||
\(952\) | −0.102551 | −0.00332368 | ||||||||
\(953\) | −32.7939 | −1.06230 | −0.531149 | − | 0.847278i | \(-0.678240\pi\) | ||||
−0.531149 | + | 0.847278i | \(0.678240\pi\) | |||||||
\(954\) | −5.09502 | −0.164957 | ||||||||
\(955\) | −9.70526 | −0.314055 | ||||||||
\(956\) | 30.6714 | 0.991985 | ||||||||
\(957\) | 3.00702 | 0.0972032 | ||||||||
\(958\) | −5.46476 | −0.176558 | ||||||||
\(959\) | −16.5996 | −0.536028 | ||||||||
\(960\) | −1.64104 | −0.0529644 | ||||||||
\(961\) | 23.5329 | 0.759125 | ||||||||
\(962\) | 5.22419 | 0.168435 | ||||||||
\(963\) | −6.15233 | −0.198256 | ||||||||
\(964\) | −9.66531 | −0.311299 | ||||||||
\(965\) | 27.4272 | 0.882912 | ||||||||
\(966\) | 13.6902 | 0.440475 | ||||||||
\(967\) | −16.6658 | −0.535936 | −0.267968 | − | 0.963428i | \(-0.586352\pi\) | ||||
−0.267968 | + | 0.963428i | \(0.586352\pi\) | |||||||
\(968\) | 10.1013 | 0.324667 | ||||||||
\(969\) | 0.145858 | 0.00468565 | ||||||||
\(970\) | 13.3536 | 0.428759 | ||||||||
\(971\) | −54.9760 | −1.76426 | −0.882131 | − | 0.471004i | \(-0.843892\pi\) | ||||
−0.882131 | + | 0.471004i | \(0.843892\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 55.1088 | 1.76671 | ||||||||
\(974\) | −0.0270879 | −0.000867951 0 | ||||||||
\(975\) | 4.82811 | 0.154623 | ||||||||
\(976\) | −2.50376 | −0.0801435 | ||||||||
\(977\) | −24.4672 | −0.782776 | −0.391388 | − | 0.920226i | \(-0.628005\pi\) | ||||
−0.391388 | + | 0.920226i | \(0.628005\pi\) | |||||||
\(978\) | −5.94179 | −0.189997 | ||||||||
\(979\) | 0.752137 | 0.0240384 | ||||||||
\(980\) | 12.0332 | 0.384387 | ||||||||
\(981\) | −1.92093 | −0.0613307 | ||||||||
\(982\) | 20.0131 | 0.638645 | ||||||||
\(983\) | 3.46248 | 0.110436 | 0.0552180 | − | 0.998474i | \(-0.482415\pi\) | ||||
0.0552180 | + | 0.998474i | \(0.482415\pi\) | |||||||
\(984\) | −4.22247 | −0.134607 | ||||||||
\(985\) | −11.4054 | −0.363407 | ||||||||
\(986\) | 0.0859199 | 0.00273625 | ||||||||
\(987\) | 9.83862 | 0.313167 | ||||||||
\(988\) | 11.2691 | 0.358518 | ||||||||
\(989\) | 22.8070 | 0.725220 | ||||||||
\(990\) | 1.55574 | 0.0494448 | ||||||||
\(991\) | −1.65963 | −0.0527198 | −0.0263599 | − | 0.999653i | \(-0.508392\pi\) | ||||
−0.0263599 | + | 0.999653i | \(0.508392\pi\) | |||||||
\(992\) | 7.38464 | 0.234462 | ||||||||
\(993\) | −19.0695 | −0.605153 | ||||||||
\(994\) | −33.9731 | −1.07756 | ||||||||
\(995\) | −30.3681 | −0.962732 | ||||||||
\(996\) | 8.87868 | 0.281332 | ||||||||
\(997\) | 46.9184 | 1.48592 | 0.742960 | − | 0.669335i | \(-0.233421\pi\) | ||||
0.742960 | + | 0.669335i | \(0.233421\pi\) | |||||||
\(998\) | 36.4407 | 1.15351 | ||||||||
\(999\) | 2.49624 | 0.0789774 |
(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 | 1338.2.a.g.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 4014.2.a.q.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.g.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4014.2.a.q.1.2 | 4 | 3.2 | odd | 2 |