Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.6148961.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 12x^{3} + 32x^{2} - 16x - 29 \) |
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 | 1.2 | ||
Root | \(-2.29987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(5\) | −3.86789 | −1.72977 | −0.864886 | − | 0.501968i | \(-0.832609\pi\) | ||||
−0.864886 | + | 0.501968i | \(0.832609\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.86789 | 1.22313 | ||||||||
\(11\) | 2.24284 | 0.676242 | 0.338121 | − | 0.941103i | \(-0.390209\pi\) | ||||
0.338121 | + | 0.941103i | \(0.390209\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.86789 | −0.998685 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.139361 | 0.0337999 | 0.0169000 | − | 0.999857i | \(-0.494620\pi\) | ||||
0.0169000 | + | 0.999857i | \(0.494620\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.18995 | −0.731825 | −0.365913 | − | 0.930649i | \(-0.619243\pi\) | ||||
−0.365913 | + | 0.930649i | \(0.619243\pi\) | |||||||
\(20\) | −3.86789 | −0.864886 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.24284 | −0.478175 | ||||||||
\(23\) | 1.05473 | 0.219927 | 0.109963 | − | 0.993936i | \(-0.464927\pi\) | ||||
0.109963 | + | 0.993936i | \(0.464927\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 9.96056 | 1.99211 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.34879 | −1.17894 | −0.589470 | − | 0.807790i | \(-0.700663\pi\) | ||||
−0.589470 | + | 0.807790i | \(0.700663\pi\) | |||||||
\(30\) | 3.86789 | 0.706177 | ||||||||
\(31\) | 3.91164 | 0.702552 | 0.351276 | − | 0.936272i | \(-0.385748\pi\) | ||||
0.351276 | + | 0.936272i | \(0.385748\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.24284 | 0.390428 | ||||||||
\(34\) | −0.139361 | −0.0239001 | ||||||||
\(35\) | −3.86789 | −0.653792 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.02354 | −0.497067 | −0.248533 | − | 0.968623i | \(-0.579949\pi\) | ||||
−0.248533 | + | 0.968623i | \(0.579949\pi\) | |||||||
\(38\) | 3.18995 | 0.517479 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.86789 | 0.611567 | ||||||||
\(41\) | −11.8139 | −1.84502 | −0.922509 | − | 0.385976i | \(-0.873865\pi\) | ||||
−0.922509 | + | 0.385976i | \(0.873865\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 8.07597 | 1.23157 | 0.615787 | − | 0.787913i | \(-0.288838\pi\) | ||||
0.615787 | + | 0.787913i | \(0.288838\pi\) | |||||||
\(44\) | 2.24284 | 0.338121 | ||||||||
\(45\) | −3.86789 | −0.576591 | ||||||||
\(46\) | −1.05473 | −0.155512 | ||||||||
\(47\) | −6.28681 | −0.917025 | −0.458512 | − | 0.888688i | \(-0.651618\pi\) | ||||
−0.458512 | + | 0.888688i | \(0.651618\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.96056 | −1.40864 | ||||||||
\(51\) | 0.139361 | 0.0195144 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.90676 | 1.22344 | 0.611719 | − | 0.791075i | \(-0.290478\pi\) | ||||
0.611719 | + | 0.791075i | \(0.290478\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −8.67506 | −1.16974 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −3.18995 | −0.422519 | ||||||||
\(58\) | 6.34879 | 0.833636 | ||||||||
\(59\) | 0.140899 | 0.0183435 | 0.00917176 | − | 0.999958i | \(-0.497080\pi\) | ||||
0.00917176 | + | 0.999958i | \(0.497080\pi\) | |||||||
\(60\) | −3.86789 | −0.499342 | ||||||||
\(61\) | −7.35955 | −0.942294 | −0.471147 | − | 0.882055i | \(-0.656160\pi\) | ||||
−0.471147 | + | 0.882055i | \(0.656160\pi\) | |||||||
\(62\) | −3.91164 | −0.496779 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.24284 | −0.276075 | ||||||||
\(67\) | 12.0213 | 1.46863 | 0.734316 | − | 0.678808i | \(-0.237503\pi\) | ||||
0.734316 | + | 0.678808i | \(0.237503\pi\) | |||||||
\(68\) | 0.139361 | 0.0169000 | ||||||||
\(69\) | 1.05473 | 0.126975 | ||||||||
\(70\) | 3.86789 | 0.462301 | ||||||||
\(71\) | 11.5292 | 1.36826 | 0.684131 | − | 0.729359i | \(-0.260182\pi\) | ||||
0.684131 | + | 0.729359i | \(0.260182\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 2.39940 | 0.280829 | 0.140414 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140414 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(74\) | 3.02354 | 0.351479 | ||||||||
\(75\) | 9.96056 | 1.15015 | ||||||||
\(76\) | −3.18995 | −0.365913 | ||||||||
\(77\) | 2.24284 | 0.255595 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.06021 | 0.794336 | 0.397168 | − | 0.917746i | \(-0.369993\pi\) | ||||
0.397168 | + | 0.917746i | \(0.369993\pi\) | |||||||
\(80\) | −3.86789 | −0.432443 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.8139 | 1.30462 | ||||||||
\(83\) | −16.0286 | −1.75937 | −0.879685 | − | 0.475556i | \(-0.842247\pi\) | ||||
−0.879685 | + | 0.475556i | \(0.842247\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | −0.539031 | −0.0584661 | ||||||||
\(86\) | −8.07597 | −0.870854 | ||||||||
\(87\) | −6.34879 | −0.680661 | ||||||||
\(88\) | −2.24284 | −0.239088 | ||||||||
\(89\) | −3.37495 | −0.357744 | −0.178872 | − | 0.983872i | \(-0.557245\pi\) | ||||
−0.178872 | + | 0.983872i | \(0.557245\pi\) | |||||||
\(90\) | 3.86789 | 0.407711 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.05473 | 0.109963 | ||||||||
\(93\) | 3.91164 | 0.405619 | ||||||||
\(94\) | 6.28681 | 0.648434 | ||||||||
\(95\) | 12.3384 | 1.26589 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.74831 | −0.786722 | −0.393361 | − | 0.919384i | \(-0.628688\pi\) | ||||
−0.393361 | + | 0.919384i | \(0.628688\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 2.24284 | 0.225414 | ||||||||
\(100\) | 9.96056 | 0.996056 | ||||||||
\(101\) | 11.0146 | 1.09599 | 0.547995 | − | 0.836482i | \(-0.315391\pi\) | ||||
0.547995 | + | 0.836482i | \(0.315391\pi\) | |||||||
\(102\) | −0.139361 | −0.0137988 | ||||||||
\(103\) | −7.70449 | −0.759146 | −0.379573 | − | 0.925162i | \(-0.623929\pi\) | ||||
−0.379573 | + | 0.925162i | \(0.623929\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.86789 | −0.377467 | ||||||||
\(106\) | −8.90676 | −0.865101 | ||||||||
\(107\) | −10.9871 | −1.06217 | −0.531083 | − | 0.847320i | \(-0.678215\pi\) | ||||
−0.531083 | + | 0.847320i | \(0.678215\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −14.7856 | −1.41620 | −0.708101 | − | 0.706111i | \(-0.750448\pi\) | ||||
−0.708101 | + | 0.706111i | \(0.750448\pi\) | |||||||
\(110\) | 8.67506 | 0.827134 | ||||||||
\(111\) | −3.02354 | −0.286981 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −0.462379 | −0.0434969 | −0.0217485 | − | 0.999763i | \(-0.506923\pi\) | ||||
−0.0217485 | + | 0.999763i | \(0.506923\pi\) | |||||||
\(114\) | 3.18995 | 0.298766 | ||||||||
\(115\) | −4.07958 | −0.380423 | ||||||||
\(116\) | −6.34879 | −0.589470 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.140899 | −0.0129708 | ||||||||
\(119\) | 0.139361 | 0.0127752 | ||||||||
\(120\) | 3.86789 | 0.353088 | ||||||||
\(121\) | −5.96967 | −0.542697 | ||||||||
\(122\) | 7.35955 | 0.666302 | ||||||||
\(123\) | −11.8139 | −1.06522 | ||||||||
\(124\) | 3.91164 | 0.351276 | ||||||||
\(125\) | −19.1869 | −1.71613 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 17.2718 | 1.53262 | 0.766311 | − | 0.642470i | \(-0.222090\pi\) | ||||
0.766311 | + | 0.642470i | \(0.222090\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.07597 | 0.711050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.76749 | 0.241797 | 0.120898 | − | 0.992665i | \(-0.461422\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461422\pi\) | |||||||
\(132\) | 2.24284 | 0.195214 | ||||||||
\(133\) | −3.18995 | −0.276604 | ||||||||
\(134\) | −12.0213 | −1.03848 | ||||||||
\(135\) | −3.86789 | −0.332895 | ||||||||
\(136\) | −0.139361 | −0.0119501 | ||||||||
\(137\) | 10.1598 | 0.868010 | 0.434005 | − | 0.900910i | \(-0.357100\pi\) | ||||
0.434005 | + | 0.900910i | \(0.357100\pi\) | |||||||
\(138\) | −1.05473 | −0.0897846 | ||||||||
\(139\) | −16.7430 | −1.42012 | −0.710062 | − | 0.704139i | \(-0.751333\pi\) | ||||
−0.710062 | + | 0.704139i | \(0.751333\pi\) | |||||||
\(140\) | −3.86789 | −0.326896 | ||||||||
\(141\) | −6.28681 | −0.529445 | ||||||||
\(142\) | −11.5292 | −0.967507 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 24.5564 | 2.03930 | ||||||||
\(146\) | −2.39940 | −0.198576 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −3.02354 | −0.248533 | ||||||||
\(149\) | 1.87669 | 0.153744 | 0.0768722 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768722 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(150\) | −9.96056 | −0.813276 | ||||||||
\(151\) | 3.92238 | 0.319198 | 0.159599 | − | 0.987182i | \(-0.448980\pi\) | ||||
0.159599 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(152\) | 3.18995 | 0.258739 | ||||||||
\(153\) | 0.139361 | 0.0112666 | ||||||||
\(154\) | −2.24284 | −0.180733 | ||||||||
\(155\) | −15.1298 | −1.21525 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3473 | 0.825807 | 0.412903 | − | 0.910775i | \(-0.364515\pi\) | ||||
0.412903 | + | 0.910775i | \(0.364515\pi\) | |||||||
\(158\) | −7.06021 | −0.561680 | ||||||||
\(159\) | 8.90676 | 0.706352 | ||||||||
\(160\) | 3.86789 | 0.305783 | ||||||||
\(161\) | 1.05473 | 0.0831244 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.02161 | −0.314997 | −0.157498 | − | 0.987519i | \(-0.550343\pi\) | ||||
−0.157498 | + | 0.987519i | \(0.550343\pi\) | |||||||
\(164\) | −11.8139 | −0.922509 | ||||||||
\(165\) | −8.67506 | −0.675352 | ||||||||
\(166\) | 16.0286 | 1.24406 | ||||||||
\(167\) | 24.0977 | 1.86474 | 0.932369 | − | 0.361509i | \(-0.117738\pi\) | ||||
0.932369 | + | 0.361509i | \(0.117738\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.539031 | 0.0413418 | ||||||||
\(171\) | −3.18995 | −0.243942 | ||||||||
\(172\) | 8.07597 | 0.615787 | ||||||||
\(173\) | −22.1817 | −1.68644 | −0.843221 | − | 0.537567i | \(-0.819343\pi\) | ||||
−0.843221 | + | 0.537567i | \(0.819343\pi\) | |||||||
\(174\) | 6.34879 | 0.481300 | ||||||||
\(175\) | 9.96056 | 0.752948 | ||||||||
\(176\) | 2.24284 | 0.169060 | ||||||||
\(177\) | 0.140899 | 0.0105906 | ||||||||
\(178\) | 3.37495 | 0.252963 | ||||||||
\(179\) | −24.6368 | −1.84144 | −0.920721 | − | 0.390221i | \(-0.872398\pi\) | ||||
−0.920721 | + | 0.390221i | \(0.872398\pi\) | |||||||
\(180\) | −3.86789 | −0.288295 | ||||||||
\(181\) | 5.10254 | 0.379269 | 0.189635 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189635 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.35955 | −0.544034 | ||||||||
\(184\) | −1.05473 | −0.0777558 | ||||||||
\(185\) | 11.6947 | 0.859812 | ||||||||
\(186\) | −3.91164 | −0.286816 | ||||||||
\(187\) | 0.312563 | 0.0228569 | ||||||||
\(188\) | −6.28681 | −0.458512 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −12.3384 | −0.895120 | ||||||||
\(191\) | 8.61491 | 0.623353 | 0.311676 | − | 0.950188i | \(-0.399110\pi\) | ||||
0.311676 | + | 0.950188i | \(0.399110\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −4.77251 | −0.343533 | −0.171766 | − | 0.985138i | \(-0.554947\pi\) | ||||
−0.171766 | + | 0.985138i | \(0.554947\pi\) | |||||||
\(194\) | 7.74831 | 0.556296 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 20.7284 | 1.47684 | 0.738419 | − | 0.674342i | \(-0.235573\pi\) | ||||
0.738419 | + | 0.674342i | \(0.235573\pi\) | |||||||
\(198\) | −2.24284 | −0.159392 | ||||||||
\(199\) | 23.0544 | 1.63428 | 0.817141 | − | 0.576438i | \(-0.195558\pi\) | ||||
0.817141 | + | 0.576438i | \(0.195558\pi\) | |||||||
\(200\) | −9.96056 | −0.704318 | ||||||||
\(201\) | 12.0213 | 0.847915 | ||||||||
\(202\) | −11.0146 | −0.774982 | ||||||||
\(203\) | −6.34879 | −0.445597 | ||||||||
\(204\) | 0.139361 | 0.00975719 | ||||||||
\(205\) | 45.6948 | 3.19146 | ||||||||
\(206\) | 7.70449 | 0.536797 | ||||||||
\(207\) | 1.05473 | 0.0733088 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.15455 | −0.494891 | ||||||||
\(210\) | 3.86789 | 0.266910 | ||||||||
\(211\) | −24.8756 | −1.71250 | −0.856252 | − | 0.516558i | \(-0.827213\pi\) | ||||
−0.856252 | + | 0.516558i | \(0.827213\pi\) | |||||||
\(212\) | 8.90676 | 0.611719 | ||||||||
\(213\) | 11.5292 | 0.789966 | ||||||||
\(214\) | 10.9871 | 0.751065 | ||||||||
\(215\) | −31.2370 | −2.13034 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.91164 | 0.265540 | ||||||||
\(218\) | 14.7856 | 1.00141 | ||||||||
\(219\) | 2.39940 | 0.162137 | ||||||||
\(220\) | −8.67506 | −0.584872 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.02354 | 0.202927 | ||||||||
\(223\) | 1.66144 | 0.111258 | 0.0556292 | − | 0.998451i | \(-0.482284\pi\) | ||||
0.0556292 | + | 0.998451i | \(0.482284\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 9.96056 | 0.664037 | ||||||||
\(226\) | 0.462379 | 0.0307570 | ||||||||
\(227\) | 0.338882 | 0.0224924 | 0.0112462 | − | 0.999937i | \(-0.496420\pi\) | ||||
0.0112462 | + | 0.999937i | \(0.496420\pi\) | |||||||
\(228\) | −3.18995 | −0.211260 | ||||||||
\(229\) | −10.8351 | −0.716005 | −0.358003 | − | 0.933721i | \(-0.616542\pi\) | ||||
−0.358003 | + | 0.933721i | \(0.616542\pi\) | |||||||
\(230\) | 4.07958 | 0.269000 | ||||||||
\(231\) | 2.24284 | 0.147568 | ||||||||
\(232\) | 6.34879 | 0.416818 | ||||||||
\(233\) | −23.1718 | −1.51803 | −0.759016 | − | 0.651072i | \(-0.774320\pi\) | ||||
−0.759016 | + | 0.651072i | \(0.774320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.3167 | 1.58624 | ||||||||
\(236\) | 0.140899 | 0.00917176 | ||||||||
\(237\) | 7.06021 | 0.458610 | ||||||||
\(238\) | −0.139361 | −0.00903340 | ||||||||
\(239\) | −22.0531 | −1.42649 | −0.713247 | − | 0.700913i | \(-0.752776\pi\) | ||||
−0.713247 | + | 0.700913i | \(0.752776\pi\) | |||||||
\(240\) | −3.86789 | −0.249671 | ||||||||
\(241\) | −16.3750 | −1.05481 | −0.527404 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527404 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(242\) | 5.96967 | 0.383745 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.35955 | −0.471147 | ||||||||
\(245\) | −3.86789 | −0.247110 | ||||||||
\(246\) | 11.8139 | 0.753225 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.91164 | −0.248390 | ||||||||
\(249\) | −16.0286 | −1.01577 | ||||||||
\(250\) | 19.1869 | 1.21349 | ||||||||
\(251\) | 14.6666 | 0.925747 | 0.462874 | − | 0.886424i | \(-0.346818\pi\) | ||||
0.462874 | + | 0.886424i | \(0.346818\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 2.36559 | 0.148724 | ||||||||
\(254\) | −17.2718 | −1.08373 | ||||||||
\(255\) | −0.539031 | −0.0337554 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.7051 | −1.04204 | −0.521018 | − | 0.853546i | \(-0.674448\pi\) | ||||
−0.521018 | + | 0.853546i | \(0.674448\pi\) | |||||||
\(258\) | −8.07597 | −0.502788 | ||||||||
\(259\) | −3.02354 | −0.187873 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.34879 | −0.392980 | ||||||||
\(262\) | −2.76749 | −0.170976 | ||||||||
\(263\) | −17.9218 | −1.10511 | −0.552554 | − | 0.833477i | \(-0.686347\pi\) | ||||
−0.552554 | + | 0.833477i | \(0.686347\pi\) | |||||||
\(264\) | −2.24284 | −0.138037 | ||||||||
\(265\) | −34.4504 | −2.11627 | ||||||||
\(266\) | 3.18995 | 0.195588 | ||||||||
\(267\) | −3.37495 | −0.206544 | ||||||||
\(268\) | 12.0213 | 0.734316 | ||||||||
\(269\) | −8.91367 | −0.543476 | −0.271738 | − | 0.962371i | \(-0.587598\pi\) | ||||
−0.271738 | + | 0.962371i | \(0.587598\pi\) | |||||||
\(270\) | 3.86789 | 0.235392 | ||||||||
\(271\) | 18.0947 | 1.09917 | 0.549586 | − | 0.835437i | \(-0.314785\pi\) | ||||
0.549586 | + | 0.835437i | \(0.314785\pi\) | |||||||
\(272\) | 0.139361 | 0.00844998 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1598 | −0.613776 | ||||||||
\(275\) | 22.3399 | 1.34715 | ||||||||
\(276\) | 1.05473 | 0.0634873 | ||||||||
\(277\) | −17.8010 | −1.06956 | −0.534778 | − | 0.844992i | \(-0.679605\pi\) | ||||
−0.534778 | + | 0.844992i | \(0.679605\pi\) | |||||||
\(278\) | 16.7430 | 1.00418 | ||||||||
\(279\) | 3.91164 | 0.234184 | ||||||||
\(280\) | 3.86789 | 0.231151 | ||||||||
\(281\) | −26.6085 | −1.58733 | −0.793664 | − | 0.608356i | \(-0.791829\pi\) | ||||
−0.793664 | + | 0.608356i | \(0.791829\pi\) | |||||||
\(282\) | 6.28681 | 0.374374 | ||||||||
\(283\) | −2.43370 | −0.144668 | −0.0723342 | − | 0.997380i | \(-0.523045\pi\) | ||||
−0.0723342 | + | 0.997380i | \(0.523045\pi\) | |||||||
\(284\) | 11.5292 | 0.684131 | ||||||||
\(285\) | 12.3384 | 0.730862 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.8139 | −0.697351 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.9806 | −0.998858 | ||||||||
\(290\) | −24.5564 | −1.44200 | ||||||||
\(291\) | −7.74831 | −0.454214 | ||||||||
\(292\) | 2.39940 | 0.140414 | ||||||||
\(293\) | −30.1152 | −1.75935 | −0.879674 | − | 0.475578i | \(-0.842239\pi\) | ||||
−0.879674 | + | 0.475578i | \(0.842239\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −0.544983 | −0.0317301 | ||||||||
\(296\) | 3.02354 | 0.175740 | ||||||||
\(297\) | 2.24284 | 0.130143 | ||||||||
\(298\) | −1.87669 | −0.108714 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9.96056 | 0.575073 | ||||||||
\(301\) | 8.07597 | 0.465491 | ||||||||
\(302\) | −3.92238 | −0.225707 | ||||||||
\(303\) | 11.0146 | 0.632770 | ||||||||
\(304\) | −3.18995 | −0.182956 | ||||||||
\(305\) | 28.4659 | 1.62995 | ||||||||
\(306\) | −0.139361 | −0.00796671 | ||||||||
\(307\) | 0.551365 | 0.0314681 | 0.0157340 | − | 0.999876i | \(-0.494991\pi\) | ||||
0.0157340 | + | 0.999876i | \(0.494991\pi\) | |||||||
\(308\) | 2.24284 | 0.127798 | ||||||||
\(309\) | −7.70449 | −0.438293 | ||||||||
\(310\) | 15.1298 | 0.859315 | ||||||||
\(311\) | −26.9438 | −1.52784 | −0.763922 | − | 0.645309i | \(-0.776729\pi\) | ||||
−0.763922 | + | 0.645309i | \(0.776729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.9518 | −1.41036 | −0.705179 | − | 0.709029i | \(-0.749133\pi\) | ||||
−0.705179 | + | 0.709029i | \(0.749133\pi\) | |||||||
\(314\) | −10.3473 | −0.583933 | ||||||||
\(315\) | −3.86789 | −0.217931 | ||||||||
\(316\) | 7.06021 | 0.397168 | ||||||||
\(317\) | −1.75675 | −0.0986688 | −0.0493344 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493344 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(318\) | −8.90676 | −0.499466 | ||||||||
\(319\) | −14.2393 | −0.797248 | ||||||||
\(320\) | −3.86789 | −0.216222 | ||||||||
\(321\) | −10.9871 | −0.613242 | ||||||||
\(322\) | −1.05473 | −0.0587778 | ||||||||
\(323\) | −0.444554 | −0.0247356 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.02161 | 0.222736 | ||||||||
\(327\) | −14.7856 | −0.817645 | ||||||||
\(328\) | 11.8139 | 0.652312 | ||||||||
\(329\) | −6.28681 | −0.346603 | ||||||||
\(330\) | 8.67506 | 0.477546 | ||||||||
\(331\) | 25.3386 | 1.39274 | 0.696368 | − | 0.717685i | \(-0.254798\pi\) | ||||
0.696368 | + | 0.717685i | \(0.254798\pi\) | |||||||
\(332\) | −16.0286 | −0.879685 | ||||||||
\(333\) | −3.02354 | −0.165689 | ||||||||
\(334\) | −24.0977 | −1.31857 | ||||||||
\(335\) | −46.4969 | −2.54040 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | −20.6628 | −1.12558 | −0.562788 | − | 0.826601i | \(-0.690271\pi\) | ||||
−0.562788 | + | 0.826601i | \(0.690271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.462379 | −0.0251130 | ||||||||
\(340\) | −0.539031 | −0.0292331 | ||||||||
\(341\) | 8.77319 | 0.475095 | ||||||||
\(342\) | 3.18995 | 0.172493 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.07597 | −0.435427 | ||||||||
\(345\) | −4.07958 | −0.219637 | ||||||||
\(346\) | 22.1817 | 1.19249 | ||||||||
\(347\) | −25.7221 | −1.38083 | −0.690417 | − | 0.723412i | \(-0.742573\pi\) | ||||
−0.690417 | + | 0.723412i | \(0.742573\pi\) | |||||||
\(348\) | −6.34879 | −0.340331 | ||||||||
\(349\) | 19.3295 | 1.03468 | 0.517342 | − | 0.855779i | \(-0.326922\pi\) | ||||
0.517342 | + | 0.855779i | \(0.326922\pi\) | |||||||
\(350\) | −9.96056 | −0.532414 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.24284 | −0.119544 | ||||||||
\(353\) | −14.9866 | −0.797654 | −0.398827 | − | 0.917026i | \(-0.630583\pi\) | ||||
−0.398827 | + | 0.917026i | \(0.630583\pi\) | |||||||
\(354\) | −0.140899 | −0.00748871 | ||||||||
\(355\) | −44.5936 | −2.36678 | ||||||||
\(356\) | −3.37495 | −0.178872 | ||||||||
\(357\) | 0.139361 | 0.00737574 | ||||||||
\(358\) | 24.6368 | 1.30210 | ||||||||
\(359\) | 0.508545 | 0.0268400 | 0.0134200 | − | 0.999910i | \(-0.495728\pi\) | ||||
0.0134200 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(360\) | 3.86789 | 0.203856 | ||||||||
\(361\) | −8.82421 | −0.464432 | ||||||||
\(362\) | −5.10254 | −0.268184 | ||||||||
\(363\) | −5.96967 | −0.313326 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.28062 | −0.485770 | ||||||||
\(366\) | 7.35955 | 0.384690 | ||||||||
\(367\) | 32.4060 | 1.69158 | 0.845790 | − | 0.533515i | \(-0.179129\pi\) | ||||
0.845790 | + | 0.533515i | \(0.179129\pi\) | |||||||
\(368\) | 1.05473 | 0.0549816 | ||||||||
\(369\) | −11.8139 | −0.615006 | ||||||||
\(370\) | −11.6947 | −0.607979 | ||||||||
\(371\) | 8.90676 | 0.462416 | ||||||||
\(372\) | 3.91164 | 0.202809 | ||||||||
\(373\) | −16.9364 | −0.876933 | −0.438467 | − | 0.898747i | \(-0.644478\pi\) | ||||
−0.438467 | + | 0.898747i | \(0.644478\pi\) | |||||||
\(374\) | −0.312563 | −0.0161623 | ||||||||
\(375\) | −19.1869 | −0.990807 | ||||||||
\(376\) | 6.28681 | 0.324217 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 17.3124 | 0.889277 | 0.444639 | − | 0.895710i | \(-0.353332\pi\) | ||||
0.444639 | + | 0.895710i | \(0.353332\pi\) | |||||||
\(380\) | 12.3384 | 0.632945 | ||||||||
\(381\) | 17.2718 | 0.884860 | ||||||||
\(382\) | −8.61491 | −0.440777 | ||||||||
\(383\) | 26.1955 | 1.33853 | 0.669264 | − | 0.743024i | \(-0.266609\pi\) | ||||
0.669264 | + | 0.743024i | \(0.266609\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −8.67506 | −0.442122 | ||||||||
\(386\) | 4.77251 | 0.242914 | ||||||||
\(387\) | 8.07597 | 0.410525 | ||||||||
\(388\) | −7.74831 | −0.393361 | ||||||||
\(389\) | −12.3683 | −0.627096 | −0.313548 | − | 0.949572i | \(-0.601518\pi\) | ||||
−0.313548 | + | 0.949572i | \(0.601518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.146988 | 0.00743350 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 2.76749 | 0.139602 | ||||||||
\(394\) | −20.7284 | −1.04428 | ||||||||
\(395\) | −27.3081 | −1.37402 | ||||||||
\(396\) | 2.24284 | 0.112707 | ||||||||
\(397\) | 31.5113 | 1.58151 | 0.790753 | − | 0.612135i | \(-0.209689\pi\) | ||||
0.790753 | + | 0.612135i | \(0.209689\pi\) | |||||||
\(398\) | −23.0544 | −1.15561 | ||||||||
\(399\) | −3.18995 | −0.159697 | ||||||||
\(400\) | 9.96056 | 0.498028 | ||||||||
\(401\) | −11.2879 | −0.563691 | −0.281846 | − | 0.959460i | \(-0.590947\pi\) | ||||
−0.281846 | + | 0.959460i | \(0.590947\pi\) | |||||||
\(402\) | −12.0213 | −0.599566 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.0146 | 0.547995 | ||||||||
\(405\) | −3.86789 | −0.192197 | ||||||||
\(406\) | 6.34879 | 0.315085 | ||||||||
\(407\) | −6.78131 | −0.336137 | ||||||||
\(408\) | −0.139361 | −0.00689938 | ||||||||
\(409\) | −28.1324 | −1.39106 | −0.695528 | − | 0.718499i | \(-0.744829\pi\) | ||||
−0.695528 | + | 0.718499i | \(0.744829\pi\) | |||||||
\(410\) | −45.6948 | −2.25670 | ||||||||
\(411\) | 10.1598 | 0.501146 | ||||||||
\(412\) | −7.70449 | −0.379573 | ||||||||
\(413\) | 0.140899 | 0.00693320 | ||||||||
\(414\) | −1.05473 | −0.0518372 | ||||||||
\(415\) | 61.9970 | 3.04331 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.7430 | −0.819910 | ||||||||
\(418\) | 7.15455 | 0.349941 | ||||||||
\(419\) | 26.8087 | 1.30969 | 0.654844 | − | 0.755764i | \(-0.272734\pi\) | ||||
0.654844 | + | 0.755764i | \(0.272734\pi\) | |||||||
\(420\) | −3.86789 | −0.188734 | ||||||||
\(421\) | −18.7350 | −0.913090 | −0.456545 | − | 0.889700i | \(-0.650913\pi\) | ||||
−0.456545 | + | 0.889700i | \(0.650913\pi\) | |||||||
\(422\) | 24.8756 | 1.21092 | ||||||||
\(423\) | −6.28681 | −0.305675 | ||||||||
\(424\) | −8.90676 | −0.432550 | ||||||||
\(425\) | 1.38811 | 0.0673332 | ||||||||
\(426\) | −11.5292 | −0.558591 | ||||||||
\(427\) | −7.35955 | −0.356154 | ||||||||
\(428\) | −10.9871 | −0.531083 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.2370 | 1.50638 | ||||||||
\(431\) | −6.57093 | −0.316510 | −0.158255 | − | 0.987398i | \(-0.550587\pi\) | ||||
−0.158255 | + | 0.987398i | \(0.550587\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 5.84123 | 0.280711 | 0.140356 | − | 0.990101i | \(-0.455175\pi\) | ||||
0.140356 | + | 0.990101i | \(0.455175\pi\) | |||||||
\(434\) | −3.91164 | −0.187765 | ||||||||
\(435\) | 24.5564 | 1.17739 | ||||||||
\(436\) | −14.7856 | −0.708101 | ||||||||
\(437\) | −3.36454 | −0.160948 | ||||||||
\(438\) | −2.39940 | −0.114648 | ||||||||
\(439\) | −3.21503 | −0.153445 | −0.0767225 | − | 0.997052i | \(-0.524446\pi\) | ||||
−0.0767225 | + | 0.997052i | \(0.524446\pi\) | |||||||
\(440\) | 8.67506 | 0.413567 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9746 | −1.23409 | −0.617046 | − | 0.786927i | \(-0.711671\pi\) | ||||
−0.617046 | + | 0.786927i | \(0.711671\pi\) | |||||||
\(444\) | −3.02354 | −0.143491 | ||||||||
\(445\) | 13.0539 | 0.618816 | ||||||||
\(446\) | −1.66144 | −0.0786716 | ||||||||
\(447\) | 1.87669 | 0.0887644 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 10.3628 | 0.489052 | 0.244526 | − | 0.969643i | \(-0.421368\pi\) | ||||
0.244526 | + | 0.969643i | \(0.421368\pi\) | |||||||
\(450\) | −9.96056 | −0.469545 | ||||||||
\(451\) | −26.4966 | −1.24768 | ||||||||
\(452\) | −0.462379 | −0.0217485 | ||||||||
\(453\) | 3.92238 | 0.184289 | ||||||||
\(454\) | −0.338882 | −0.0159045 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.18995 | 0.149383 | ||||||||
\(457\) | −11.5925 | −0.542275 | −0.271137 | − | 0.962541i | \(-0.587400\pi\) | ||||
−0.271137 | + | 0.962541i | \(0.587400\pi\) | |||||||
\(458\) | 10.8351 | 0.506292 | ||||||||
\(459\) | 0.139361 | 0.00650479 | ||||||||
\(460\) | −4.07958 | −0.190211 | ||||||||
\(461\) | −26.0552 | −1.21351 | −0.606756 | − | 0.794888i | \(-0.707530\pi\) | ||||
−0.606756 | + | 0.794888i | \(0.707530\pi\) | |||||||
\(462\) | −2.24284 | −0.104346 | ||||||||
\(463\) | 4.21320 | 0.195804 | 0.0979021 | − | 0.995196i | \(-0.468787\pi\) | ||||
0.0979021 | + | 0.995196i | \(0.468787\pi\) | |||||||
\(464\) | −6.34879 | −0.294735 | ||||||||
\(465\) | −15.1298 | −0.701628 | ||||||||
\(466\) | 23.1718 | 1.07341 | ||||||||
\(467\) | −27.1787 | −1.25768 | −0.628841 | − | 0.777534i | \(-0.716470\pi\) | ||||
−0.628841 | + | 0.777534i | \(0.716470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0213 | 0.555090 | ||||||||
\(470\) | −24.3167 | −1.12164 | ||||||||
\(471\) | 10.3473 | 0.476780 | ||||||||
\(472\) | −0.140899 | −0.00648542 | ||||||||
\(473\) | 18.1131 | 0.832842 | ||||||||
\(474\) | −7.06021 | −0.324286 | ||||||||
\(475\) | −31.7737 | −1.45788 | ||||||||
\(476\) | 0.139361 | 0.00638758 | ||||||||
\(477\) | 8.90676 | 0.407813 | ||||||||
\(478\) | 22.0531 | 1.00868 | ||||||||
\(479\) | −5.50802 | −0.251668 | −0.125834 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125834 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(480\) | 3.86789 | 0.176544 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 16.3750 | 0.745862 | ||||||||
\(483\) | 1.05473 | 0.0479919 | ||||||||
\(484\) | −5.96967 | −0.271349 | ||||||||
\(485\) | 29.9696 | 1.36085 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −4.98323 | −0.225812 | −0.112906 | − | 0.993606i | \(-0.536016\pi\) | ||||
−0.112906 | + | 0.993606i | \(0.536016\pi\) | |||||||
\(488\) | 7.35955 | 0.333151 | ||||||||
\(489\) | −4.02161 | −0.181863 | ||||||||
\(490\) | 3.86789 | 0.174733 | ||||||||
\(491\) | −5.28048 | −0.238305 | −0.119152 | − | 0.992876i | \(-0.538018\pi\) | ||||
−0.119152 | + | 0.992876i | \(0.538018\pi\) | |||||||
\(492\) | −11.8139 | −0.532611 | ||||||||
\(493\) | −0.884770 | −0.0398481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.67506 | −0.389915 | ||||||||
\(496\) | 3.91164 | 0.175638 | ||||||||
\(497\) | 11.5292 | 0.517154 | ||||||||
\(498\) | 16.0286 | 0.718260 | ||||||||
\(499\) | 8.54700 | 0.382616 | 0.191308 | − | 0.981530i | \(-0.438727\pi\) | ||||
0.191308 | + | 0.981530i | \(0.438727\pi\) | |||||||
\(500\) | −19.1869 | −0.858064 | ||||||||
\(501\) | 24.0977 | 1.07661 | ||||||||
\(502\) | −14.6666 | −0.654602 | ||||||||
\(503\) | −0.223190 | −0.00995153 | −0.00497577 | − | 0.999988i | \(-0.501584\pi\) | ||||
−0.00497577 | + | 0.999988i | \(0.501584\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −42.6031 | −1.89581 | ||||||||
\(506\) | −2.36559 | −0.105163 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.2718 | 0.766311 | ||||||||
\(509\) | 6.01539 | 0.266628 | 0.133314 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133314 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(510\) | 0.539031 | 0.0238687 | ||||||||
\(511\) | 2.39940 | 0.106143 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.18995 | −0.140840 | ||||||||
\(514\) | 16.7051 | 0.736831 | ||||||||
\(515\) | 29.8001 | 1.31315 | ||||||||
\(516\) | 8.07597 | 0.355525 | ||||||||
\(517\) | −14.1003 | −0.620130 | ||||||||
\(518\) | 3.02354 | 0.132847 | ||||||||
\(519\) | −22.1817 | −0.973668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.2178 | −0.973381 | −0.486691 | − | 0.873574i | \(-0.661796\pi\) | ||||
−0.486691 | + | 0.873574i | \(0.661796\pi\) | |||||||
\(522\) | 6.34879 | 0.277879 | ||||||||
\(523\) | −15.2139 | −0.665255 | −0.332628 | − | 0.943058i | \(-0.607935\pi\) | ||||
−0.332628 | + | 0.943058i | \(0.607935\pi\) | |||||||
\(524\) | 2.76749 | 0.120898 | ||||||||
\(525\) | 9.96056 | 0.434715 | ||||||||
\(526\) | 17.9218 | 0.781429 | ||||||||
\(527\) | 0.545129 | 0.0237462 | ||||||||
\(528\) | 2.24284 | 0.0976071 | ||||||||
\(529\) | −21.8875 | −0.951632 | ||||||||
\(530\) | 34.4504 | 1.49643 | ||||||||
\(531\) | 0.140899 | 0.00611451 | ||||||||
\(532\) | −3.18995 | −0.138302 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.37495 | 0.146048 | ||||||||
\(535\) | 42.4970 | 1.83731 | ||||||||
\(536\) | −12.0213 | −0.519240 | ||||||||
\(537\) | −24.6368 | −1.06316 | ||||||||
\(538\) | 8.91367 | 0.384296 | ||||||||
\(539\) | 2.24284 | 0.0966060 | ||||||||
\(540\) | −3.86789 | −0.166447 | ||||||||
\(541\) | −30.4739 | −1.31017 | −0.655087 | − | 0.755554i | \(-0.727368\pi\) | ||||
−0.655087 | + | 0.755554i | \(0.727368\pi\) | |||||||
\(542\) | −18.0947 | −0.777232 | ||||||||
\(543\) | 5.10254 | 0.218971 | ||||||||
\(544\) | −0.139361 | −0.00597504 | ||||||||
\(545\) | 57.1890 | 2.44971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7680 | −0.460408 | −0.230204 | − | 0.973142i | \(-0.573939\pi\) | ||||
−0.230204 | + | 0.973142i | \(0.573939\pi\) | |||||||
\(548\) | 10.1598 | 0.434005 | ||||||||
\(549\) | −7.35955 | −0.314098 | ||||||||
\(550\) | −22.3399 | −0.952579 | ||||||||
\(551\) | 20.2523 | 0.862778 | ||||||||
\(552\) | −1.05473 | −0.0448923 | ||||||||
\(553\) | 7.06021 | 0.300231 | ||||||||
\(554\) | 17.8010 | 0.756291 | ||||||||
\(555\) | 11.6947 | 0.496413 | ||||||||
\(556\) | −16.7430 | −0.710062 | ||||||||
\(557\) | −12.1663 | −0.515502 | −0.257751 | − | 0.966211i | \(-0.582981\pi\) | ||||
−0.257751 | + | 0.966211i | \(0.582981\pi\) | |||||||
\(558\) | −3.91164 | −0.165593 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.86789 | −0.163448 | ||||||||
\(561\) | 0.312563 | 0.0131964 | ||||||||
\(562\) | 26.6085 | 1.12241 | ||||||||
\(563\) | 15.3757 | 0.648008 | 0.324004 | − | 0.946056i | \(-0.394971\pi\) | ||||
0.324004 | + | 0.946056i | \(0.394971\pi\) | |||||||
\(564\) | −6.28681 | −0.264722 | ||||||||
\(565\) | 1.78843 | 0.0752398 | ||||||||
\(566\) | 2.43370 | 0.102296 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −11.5292 | −0.483754 | ||||||||
\(569\) | 37.1485 | 1.55735 | 0.778674 | − | 0.627429i | \(-0.215893\pi\) | ||||
0.778674 | + | 0.627429i | \(0.215893\pi\) | |||||||
\(570\) | −12.3384 | −0.516798 | ||||||||
\(571\) | 8.86859 | 0.371139 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.61491 | 0.359893 | ||||||||
\(574\) | 11.8139 | 0.493102 | ||||||||
\(575\) | 10.5057 | 0.438118 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −16.8429 | −0.701177 | −0.350589 | − | 0.936530i | \(-0.614018\pi\) | ||||
−0.350589 | + | 0.936530i | \(0.614018\pi\) | |||||||
\(578\) | 16.9806 | 0.706299 | ||||||||
\(579\) | −4.77251 | −0.198339 | ||||||||
\(580\) | 24.5564 | 1.01965 | ||||||||
\(581\) | −16.0286 | −0.664980 | ||||||||
\(582\) | 7.74831 | 0.321178 | ||||||||
\(583\) | 19.9764 | 0.827340 | ||||||||
\(584\) | −2.39940 | −0.0992880 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.1152 | 1.24405 | ||||||||
\(587\) | 16.3655 | 0.675475 | 0.337737 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337737 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −12.4780 | −0.514145 | ||||||||
\(590\) | 0.544983 | 0.0224366 | ||||||||
\(591\) | 20.7284 | 0.852653 | ||||||||
\(592\) | −3.02354 | −0.124267 | ||||||||
\(593\) | 28.3867 | 1.16570 | 0.582852 | − | 0.812579i | \(-0.301937\pi\) | ||||
0.582852 | + | 0.812579i | \(0.301937\pi\) | |||||||
\(594\) | −2.24284 | −0.0920248 | ||||||||
\(595\) | −0.539031 | −0.0220981 | ||||||||
\(596\) | 1.87669 | 0.0768722 | ||||||||
\(597\) | 23.0544 | 0.943553 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.92546 | 0.364685 | 0.182342 | − | 0.983235i | \(-0.441632\pi\) | ||||
0.182342 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(600\) | −9.96056 | −0.406638 | ||||||||
\(601\) | −29.0218 | −1.18382 | −0.591912 | − | 0.806003i | \(-0.701627\pi\) | ||||
−0.591912 | + | 0.806003i | \(0.701627\pi\) | |||||||
\(602\) | −8.07597 | −0.329152 | ||||||||
\(603\) | 12.0213 | 0.489544 | ||||||||
\(604\) | 3.92238 | 0.159599 | ||||||||
\(605\) | 23.0900 | 0.938742 | ||||||||
\(606\) | −11.0146 | −0.447436 | ||||||||
\(607\) | 15.3453 | 0.622845 | 0.311423 | − | 0.950272i | \(-0.399195\pi\) | ||||
0.311423 | + | 0.950272i | \(0.399195\pi\) | |||||||
\(608\) | 3.18995 | 0.129370 | ||||||||
\(609\) | −6.34879 | −0.257266 | ||||||||
\(610\) | −28.4659 | −1.15255 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.139361 | 0.00563332 | ||||||||
\(613\) | −48.0959 | −1.94257 | −0.971287 | − | 0.237910i | \(-0.923538\pi\) | ||||
−0.971287 | + | 0.237910i | \(0.923538\pi\) | |||||||
\(614\) | −0.551365 | −0.0222513 | ||||||||
\(615\) | 45.6948 | 1.84259 | ||||||||
\(616\) | −2.24284 | −0.0903666 | ||||||||
\(617\) | −22.9255 | −0.922946 | −0.461473 | − | 0.887154i | \(-0.652679\pi\) | ||||
−0.461473 | + | 0.887154i | \(0.652679\pi\) | |||||||
\(618\) | 7.70449 | 0.309920 | ||||||||
\(619\) | 8.54959 | 0.343637 | 0.171818 | − | 0.985129i | \(-0.445036\pi\) | ||||
0.171818 | + | 0.985129i | \(0.445036\pi\) | |||||||
\(620\) | −15.1298 | −0.607627 | ||||||||
\(621\) | 1.05473 | 0.0423249 | ||||||||
\(622\) | 26.9438 | 1.08035 | ||||||||
\(623\) | −3.37495 | −0.135215 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4100 | 0.976399 | ||||||||
\(626\) | 24.9518 | 0.997274 | ||||||||
\(627\) | −7.15455 | −0.285725 | ||||||||
\(628\) | 10.3473 | 0.412903 | ||||||||
\(629\) | −0.421362 | −0.0168008 | ||||||||
\(630\) | 3.86789 | 0.154100 | ||||||||
\(631\) | 39.5572 | 1.57475 | 0.787373 | − | 0.616477i | \(-0.211441\pi\) | ||||
0.787373 | + | 0.616477i | \(0.211441\pi\) | |||||||
\(632\) | −7.06021 | −0.280840 | ||||||||
\(633\) | −24.8756 | −0.988715 | ||||||||
\(634\) | 1.75675 | 0.0697694 | ||||||||
\(635\) | −66.8053 | −2.65109 | ||||||||
\(636\) | 8.90676 | 0.353176 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 14.2393 | 0.563740 | ||||||||
\(639\) | 11.5292 | 0.456087 | ||||||||
\(640\) | 3.86789 | 0.152892 | ||||||||
\(641\) | 48.2978 | 1.90765 | 0.953824 | − | 0.300366i | \(-0.0971087\pi\) | ||||
0.953824 | + | 0.300366i | \(0.0971087\pi\) | |||||||
\(642\) | 10.9871 | 0.433628 | ||||||||
\(643\) | 22.8990 | 0.903048 | 0.451524 | − | 0.892259i | \(-0.350881\pi\) | ||||
0.451524 | + | 0.892259i | \(0.350881\pi\) | |||||||
\(644\) | 1.05473 | 0.0415622 | ||||||||
\(645\) | −31.2370 | −1.22995 | ||||||||
\(646\) | 0.444554 | 0.0174907 | ||||||||
\(647\) | 14.7982 | 0.581776 | 0.290888 | − | 0.956757i | \(-0.406049\pi\) | ||||
0.290888 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0.316015 | 0.0124047 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.91164 | 0.153309 | ||||||||
\(652\) | −4.02161 | −0.157498 | ||||||||
\(653\) | 38.8845 | 1.52167 | 0.760835 | − | 0.648946i | \(-0.224790\pi\) | ||||
0.760835 | + | 0.648946i | \(0.224790\pi\) | |||||||
\(654\) | 14.7856 | 0.578162 | ||||||||
\(655\) | −10.7044 | −0.418254 | ||||||||
\(656\) | −11.8139 | −0.461254 | ||||||||
\(657\) | 2.39940 | 0.0936096 | ||||||||
\(658\) | 6.28681 | 0.245085 | ||||||||
\(659\) | 27.3178 | 1.06415 | 0.532075 | − | 0.846698i | \(-0.321413\pi\) | ||||
0.532075 | + | 0.846698i | \(0.321413\pi\) | |||||||
\(660\) | −8.67506 | −0.337676 | ||||||||
\(661\) | −40.6662 | −1.58173 | −0.790866 | − | 0.611989i | \(-0.790370\pi\) | ||||
−0.790866 | + | 0.611989i | \(0.790370\pi\) | |||||||
\(662\) | −25.3386 | −0.984814 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.0286 | 0.622032 | ||||||||
\(665\) | 12.3384 | 0.478462 | ||||||||
\(666\) | 3.02354 | 0.117160 | ||||||||
\(667\) | −6.69626 | −0.259280 | ||||||||
\(668\) | 24.0977 | 0.932369 | ||||||||
\(669\) | 1.66144 | 0.0642351 | ||||||||
\(670\) | 46.4969 | 1.79633 | ||||||||
\(671\) | −16.5063 | −0.637218 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 27.8723 | 1.07440 | 0.537199 | − | 0.843456i | \(-0.319483\pi\) | ||||
0.537199 | + | 0.843456i | \(0.319483\pi\) | |||||||
\(674\) | 20.6628 | 0.795902 | ||||||||
\(675\) | 9.96056 | 0.383382 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −46.5331 | −1.78841 | −0.894206 | − | 0.447656i | \(-0.852259\pi\) | ||||
−0.894206 | + | 0.447656i | \(0.852259\pi\) | |||||||
\(678\) | 0.462379 | 0.0177575 | ||||||||
\(679\) | −7.74831 | −0.297353 | ||||||||
\(680\) | 0.539031 | 0.0206709 | ||||||||
\(681\) | 0.338882 | 0.0129860 | ||||||||
\(682\) | −8.77319 | −0.335943 | ||||||||
\(683\) | −15.9747 | −0.611253 | −0.305627 | − | 0.952151i | \(-0.598866\pi\) | ||||
−0.305627 | + | 0.952151i | \(0.598866\pi\) | |||||||
\(684\) | −3.18995 | −0.121971 | ||||||||
\(685\) | −39.2970 | −1.50146 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −10.8351 | −0.413386 | ||||||||
\(688\) | 8.07597 | 0.307894 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.07958 | 0.155307 | ||||||||
\(691\) | 23.4458 | 0.891919 | 0.445959 | − | 0.895053i | \(-0.352863\pi\) | ||||
0.445959 | + | 0.895053i | \(0.352863\pi\) | |||||||
\(692\) | −22.1817 | −0.843221 | ||||||||
\(693\) | 2.24284 | 0.0851985 | ||||||||
\(694\) | 25.7221 | 0.976397 | ||||||||
\(695\) | 64.7602 | 2.45649 | ||||||||
\(696\) | 6.34879 | 0.240650 | ||||||||
\(697\) | −1.64639 | −0.0623614 | ||||||||
\(698\) | −19.3295 | −0.731632 | ||||||||
\(699\) | −23.1718 | −0.876436 | ||||||||
\(700\) | 9.96056 | 0.376474 | ||||||||
\(701\) | −2.74217 | −0.103570 | −0.0517851 | − | 0.998658i | \(-0.516491\pi\) | ||||
−0.0517851 | + | 0.998658i | \(0.516491\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.64494 | 0.363766 | ||||||||
\(704\) | 2.24284 | 0.0845302 | ||||||||
\(705\) | 24.3167 | 0.915819 | ||||||||
\(706\) | 14.9866 | 0.564027 | ||||||||
\(707\) | 11.0146 | 0.414245 | ||||||||
\(708\) | 0.140899 | 0.00529532 | ||||||||
\(709\) | 40.4098 | 1.51762 | 0.758811 | − | 0.651310i | \(-0.225780\pi\) | ||||
0.758811 | + | 0.651310i | \(0.225780\pi\) | |||||||
\(710\) | 44.5936 | 1.67357 | ||||||||
\(711\) | 7.06021 | 0.264779 | ||||||||
\(712\) | 3.37495 | 0.126482 | ||||||||
\(713\) | 4.12573 | 0.154510 | ||||||||
\(714\) | −0.139361 | −0.00521544 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.6368 | −0.920721 | ||||||||
\(717\) | −22.0531 | −0.823587 | ||||||||
\(718\) | −0.508545 | −0.0189787 | ||||||||
\(719\) | 14.5158 | 0.541348 | 0.270674 | − | 0.962671i | \(-0.412753\pi\) | ||||
0.270674 | + | 0.962671i | \(0.412753\pi\) | |||||||
\(720\) | −3.86789 | −0.144148 | ||||||||
\(721\) | −7.70449 | −0.286930 | ||||||||
\(722\) | 8.82421 | 0.328403 | ||||||||
\(723\) | −16.3750 | −0.608994 | ||||||||
\(724\) | 5.10254 | 0.189635 | ||||||||
\(725\) | −63.2375 | −2.34858 | ||||||||
\(726\) | 5.96967 | 0.221555 | ||||||||
\(727\) | −30.0166 | −1.11325 | −0.556627 | − | 0.830762i | \(-0.687905\pi\) | ||||
−0.556627 | + | 0.830762i | \(0.687905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.28062 | 0.343491 | ||||||||
\(731\) | 1.12547 | 0.0416271 | ||||||||
\(732\) | −7.35955 | −0.272017 | ||||||||
\(733\) | −31.5831 | −1.16655 | −0.583275 | − | 0.812275i | \(-0.698229\pi\) | ||||
−0.583275 | + | 0.812275i | \(0.698229\pi\) | |||||||
\(734\) | −32.4060 | −1.19613 | ||||||||
\(735\) | −3.86789 | −0.142669 | ||||||||
\(736\) | −1.05473 | −0.0388779 | ||||||||
\(737\) | 26.9618 | 0.993150 | ||||||||
\(738\) | 11.8139 | 0.434875 | ||||||||
\(739\) | −32.2913 | −1.18786 | −0.593928 | − | 0.804518i | \(-0.702424\pi\) | ||||
−0.593928 | + | 0.804518i | \(0.702424\pi\) | |||||||
\(740\) | 11.6947 | 0.429906 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.90676 | −0.326977 | ||||||||
\(743\) | −37.6673 | −1.38188 | −0.690939 | − | 0.722913i | \(-0.742803\pi\) | ||||
−0.690939 | + | 0.722913i | \(0.742803\pi\) | |||||||
\(744\) | −3.91164 | −0.143408 | ||||||||
\(745\) | −7.25883 | −0.265943 | ||||||||
\(746\) | 16.9364 | 0.620086 | ||||||||
\(747\) | −16.0286 | −0.586457 | ||||||||
\(748\) | 0.312563 | 0.0114285 | ||||||||
\(749\) | −10.9871 | −0.401461 | ||||||||
\(750\) | 19.1869 | 0.700606 | ||||||||
\(751\) | 5.32524 | 0.194321 | 0.0971603 | − | 0.995269i | \(-0.469024\pi\) | ||||
0.0971603 | + | 0.995269i | \(0.469024\pi\) | |||||||
\(752\) | −6.28681 | −0.229256 | ||||||||
\(753\) | 14.6666 | 0.534480 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.1713 | −0.552141 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | −22.6684 | −0.823898 | −0.411949 | − | 0.911207i | \(-0.635152\pi\) | ||||
−0.411949 | + | 0.911207i | \(0.635152\pi\) | |||||||
\(758\) | −17.3124 | −0.628814 | ||||||||
\(759\) | 2.36559 | 0.0858656 | ||||||||
\(760\) | −12.3384 | −0.447560 | ||||||||
\(761\) | −10.3154 | −0.373934 | −0.186967 | − | 0.982366i | \(-0.559866\pi\) | ||||
−0.186967 | + | 0.982366i | \(0.559866\pi\) | |||||||
\(762\) | −17.2718 | −0.625690 | ||||||||
\(763\) | −14.7856 | −0.535274 | ||||||||
\(764\) | 8.61491 | 0.311676 | ||||||||
\(765\) | −0.539031 | −0.0194887 | ||||||||
\(766\) | −26.1955 | −0.946483 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −36.4505 | −1.31444 | −0.657220 | − | 0.753699i | \(-0.728268\pi\) | ||||
−0.657220 | + | 0.753699i | \(0.728268\pi\) | |||||||
\(770\) | 8.67506 | 0.312627 | ||||||||
\(771\) | −16.7051 | −0.601620 | ||||||||
\(772\) | −4.77251 | −0.171766 | ||||||||
\(773\) | −32.1023 | −1.15464 | −0.577320 | − | 0.816518i | \(-0.695902\pi\) | ||||
−0.577320 | + | 0.816518i | \(0.695902\pi\) | |||||||
\(774\) | −8.07597 | −0.290285 | ||||||||
\(775\) | 38.9622 | 1.39956 | ||||||||
\(776\) | 7.74831 | 0.278148 | ||||||||
\(777\) | −3.02354 | −0.108469 | ||||||||
\(778\) | 12.3683 | 0.443424 | ||||||||
\(779\) | 37.6857 | 1.35023 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8581 | 0.925276 | ||||||||
\(782\) | −0.146988 | −0.00525628 | ||||||||
\(783\) | −6.34879 | −0.226887 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −40.0223 | −1.42846 | ||||||||
\(786\) | −2.76749 | −0.0987132 | ||||||||
\(787\) | 2.80320 | 0.0999234 | 0.0499617 | − | 0.998751i | \(-0.484090\pi\) | ||||
0.0499617 | + | 0.998751i | \(0.484090\pi\) | |||||||
\(788\) | 20.7284 | 0.738419 | ||||||||
\(789\) | −17.9218 | −0.638034 | ||||||||
\(790\) | 27.3081 | 0.971579 | ||||||||
\(791\) | −0.462379 | −0.0164403 | ||||||||
\(792\) | −2.24284 | −0.0796959 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −31.5113 | −1.11829 | ||||||||
\(795\) | −34.4504 | −1.22183 | ||||||||
\(796\) | 23.0544 | 0.817141 | ||||||||
\(797\) | −32.5356 | −1.15247 | −0.576236 | − | 0.817283i | \(-0.695479\pi\) | ||||
−0.576236 | + | 0.817283i | \(0.695479\pi\) | |||||||
\(798\) | 3.18995 | 0.112923 | ||||||||
\(799\) | −0.876133 | −0.0309954 | ||||||||
\(800\) | −9.96056 | −0.352159 | ||||||||
\(801\) | −3.37495 | −0.119248 | ||||||||
\(802\) | 11.2879 | 0.398590 | ||||||||
\(803\) | 5.38148 | 0.189908 | ||||||||
\(804\) | 12.0213 | 0.423957 | ||||||||
\(805\) | −4.07958 | −0.143786 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.91367 | −0.313776 | ||||||||
\(808\) | −11.0146 | −0.387491 | ||||||||
\(809\) | 33.0597 | 1.16232 | 0.581159 | − | 0.813790i | \(-0.302600\pi\) | ||||
0.581159 | + | 0.813790i | \(0.302600\pi\) | |||||||
\(810\) | 3.86789 | 0.135904 | ||||||||
\(811\) | 19.8406 | 0.696697 | 0.348348 | − | 0.937365i | \(-0.386743\pi\) | ||||
0.348348 | + | 0.937365i | \(0.386743\pi\) | |||||||
\(812\) | −6.34879 | −0.222799 | ||||||||
\(813\) | 18.0947 | 0.634607 | ||||||||
\(814\) | 6.78131 | 0.237685 | ||||||||
\(815\) | 15.5551 | 0.544872 | ||||||||
\(816\) | 0.139361 | 0.00487860 | ||||||||
\(817\) | −25.7620 | −0.901297 | ||||||||
\(818\) | 28.1324 | 0.983625 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 45.6948 | 1.59573 | ||||||||
\(821\) | 43.0221 | 1.50148 | 0.750741 | − | 0.660597i | \(-0.229697\pi\) | ||||
0.750741 | + | 0.660597i | \(0.229697\pi\) | |||||||
\(822\) | −10.1598 | −0.354364 | ||||||||
\(823\) | −20.0391 | −0.698521 | −0.349260 | − | 0.937026i | \(-0.613567\pi\) | ||||
−0.349260 | + | 0.937026i | \(0.613567\pi\) | |||||||
\(824\) | 7.70449 | 0.268399 | ||||||||
\(825\) | 22.3399 | 0.777777 | ||||||||
\(826\) | −0.140899 | −0.00490251 | ||||||||
\(827\) | −31.4823 | −1.09475 | −0.547373 | − | 0.836889i | \(-0.684372\pi\) | ||||
−0.547373 | + | 0.836889i | \(0.684372\pi\) | |||||||
\(828\) | 1.05473 | 0.0366544 | ||||||||
\(829\) | 8.84242 | 0.307110 | 0.153555 | − | 0.988140i | \(-0.450928\pi\) | ||||
0.153555 | + | 0.988140i | \(0.450928\pi\) | |||||||
\(830\) | −61.9970 | −2.15195 | ||||||||
\(831\) | −17.8010 | −0.617509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.139361 | 0.00482856 | ||||||||
\(834\) | 16.7430 | 0.579764 | ||||||||
\(835\) | −93.2073 | −3.22557 | ||||||||
\(836\) | −7.15455 | −0.247445 | ||||||||
\(837\) | 3.91164 | 0.135206 | ||||||||
\(838\) | −26.8087 | −0.926090 | ||||||||
\(839\) | 22.7336 | 0.784850 | 0.392425 | − | 0.919784i | \(-0.371636\pi\) | ||||
0.392425 | + | 0.919784i | \(0.371636\pi\) | |||||||
\(840\) | 3.86789 | 0.133455 | ||||||||
\(841\) | 11.3071 | 0.389899 | ||||||||
\(842\) | 18.7350 | 0.645652 | ||||||||
\(843\) | −26.6085 | −0.916444 | ||||||||
\(844\) | −24.8756 | −0.856252 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.28681 | 0.216145 | ||||||||
\(847\) | −5.96967 | −0.205120 | ||||||||
\(848\) | 8.90676 | 0.305859 | ||||||||
\(849\) | −2.43370 | −0.0835244 | ||||||||
\(850\) | −1.38811 | −0.0476118 | ||||||||
\(851\) | −3.18902 | −0.109318 | ||||||||
\(852\) | 11.5292 | 0.394983 | ||||||||
\(853\) | 19.1797 | 0.656702 | 0.328351 | − | 0.944556i | \(-0.393507\pi\) | ||||
0.328351 | + | 0.944556i | \(0.393507\pi\) | |||||||
\(854\) | 7.35955 | 0.251839 | ||||||||
\(855\) | 12.3384 | 0.421964 | ||||||||
\(856\) | 10.9871 | 0.375532 | ||||||||
\(857\) | 35.2664 | 1.20468 | 0.602338 | − | 0.798241i | \(-0.294236\pi\) | ||||
0.602338 | + | 0.798241i | \(0.294236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.08052 | 0.139226 | 0.0696128 | − | 0.997574i | \(-0.477824\pi\) | ||||
0.0696128 | + | 0.997574i | \(0.477824\pi\) | |||||||
\(860\) | −31.2370 | −1.06517 | ||||||||
\(861\) | −11.8139 | −0.402616 | ||||||||
\(862\) | 6.57093 | 0.223807 | ||||||||
\(863\) | −13.0268 | −0.443437 | −0.221718 | − | 0.975111i | \(-0.571167\pi\) | ||||
−0.221718 | + | 0.975111i | \(0.571167\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 85.7963 | 2.91716 | ||||||||
\(866\) | −5.84123 | −0.198493 | ||||||||
\(867\) | −16.9806 | −0.576691 | ||||||||
\(868\) | 3.91164 | 0.132770 | ||||||||
\(869\) | 15.8349 | 0.537163 | ||||||||
\(870\) | −24.5564 | −0.832540 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.7856 | 0.500703 | ||||||||
\(873\) | −7.74831 | −0.262241 | ||||||||
\(874\) | 3.36454 | 0.113807 | ||||||||
\(875\) | −19.1869 | −0.648636 | ||||||||
\(876\) | 2.39940 | 0.0810683 | ||||||||
\(877\) | −2.57514 | −0.0869563 | −0.0434781 | − | 0.999054i | \(-0.513844\pi\) | ||||
−0.0434781 | + | 0.999054i | \(0.513844\pi\) | |||||||
\(878\) | 3.21503 | 0.108502 | ||||||||
\(879\) | −30.1152 | −1.01576 | ||||||||
\(880\) | −8.67506 | −0.292436 | ||||||||
\(881\) | 17.5766 | 0.592172 | 0.296086 | − | 0.955161i | \(-0.404319\pi\) | ||||
0.296086 | + | 0.955161i | \(0.404319\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | −1.49250 | −0.0502266 | −0.0251133 | − | 0.999685i | \(-0.507995\pi\) | ||||
−0.0251133 | + | 0.999685i | \(0.507995\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.544983 | −0.0183194 | ||||||||
\(886\) | 25.9746 | 0.872634 | ||||||||
\(887\) | 22.4040 | 0.752251 | 0.376126 | − | 0.926569i | \(-0.377256\pi\) | ||||
0.376126 | + | 0.926569i | \(0.377256\pi\) | |||||||
\(888\) | 3.02354 | 0.101463 | ||||||||
\(889\) | 17.2718 | 0.579277 | ||||||||
\(890\) | −13.0539 | −0.437569 | ||||||||
\(891\) | 2.24284 | 0.0751380 | ||||||||
\(892\) | 1.66144 | 0.0556292 | ||||||||
\(893\) | 20.0546 | 0.671102 | ||||||||
\(894\) | −1.87669 | −0.0627659 | ||||||||
\(895\) | 95.2925 | 3.18528 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.3628 | −0.345812 | ||||||||
\(899\) | −24.8342 | −0.828267 | ||||||||
\(900\) | 9.96056 | 0.332019 | ||||||||
\(901\) | 1.24125 | 0.0413521 | ||||||||
\(902\) | 26.4966 | 0.882242 | ||||||||
\(903\) | 8.07597 | 0.268751 | ||||||||
\(904\) | 0.462379 | 0.0153785 | ||||||||
\(905\) | −19.7361 | −0.656049 | ||||||||
\(906\) | −3.92238 | −0.130312 | ||||||||
\(907\) | 5.77228 | 0.191665 | 0.0958327 | − | 0.995397i | \(-0.469449\pi\) | ||||
0.0958327 | + | 0.995397i | \(0.469449\pi\) | |||||||
\(908\) | 0.338882 | 0.0112462 | ||||||||
\(909\) | 11.0146 | 0.365330 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.97933 | −0.198104 | −0.0990520 | − | 0.995082i | \(-0.531581\pi\) | ||||
−0.0990520 | + | 0.995082i | \(0.531581\pi\) | |||||||
\(912\) | −3.18995 | −0.105630 | ||||||||
\(913\) | −35.9497 | −1.18976 | ||||||||
\(914\) | 11.5925 | 0.383446 | ||||||||
\(915\) | 28.4659 | 0.941054 | ||||||||
\(916\) | −10.8351 | −0.358003 | ||||||||
\(917\) | 2.76749 | 0.0913907 | ||||||||
\(918\) | −0.139361 | −0.00459958 | ||||||||
\(919\) | −50.7209 | −1.67313 | −0.836565 | − | 0.547868i | \(-0.815440\pi\) | ||||
−0.836565 | + | 0.547868i | \(0.815440\pi\) | |||||||
\(920\) | 4.07958 | 0.134500 | ||||||||
\(921\) | 0.551365 | 0.0181681 | ||||||||
\(922\) | 26.0552 | 0.858083 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.24284 | 0.0737840 | ||||||||
\(925\) | −30.1161 | −0.990212 | ||||||||
\(926\) | −4.21320 | −0.138454 | ||||||||
\(927\) | −7.70449 | −0.253049 | ||||||||
\(928\) | 6.34879 | 0.208409 | ||||||||
\(929\) | −10.0913 | −0.331083 | −0.165542 | − | 0.986203i | \(-0.552937\pi\) | ||||
−0.165542 | + | 0.986203i | \(0.552937\pi\) | |||||||
\(930\) | 15.1298 | 0.496126 | ||||||||
\(931\) | −3.18995 | −0.104546 | ||||||||
\(932\) | −23.1718 | −0.759016 | ||||||||
\(933\) | −26.9438 | −0.882101 | ||||||||
\(934\) | 27.1787 | 0.889315 | ||||||||
\(935\) | −1.20896 | −0.0395372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.3366 | 1.48108 | 0.740542 | − | 0.672010i | \(-0.234569\pi\) | ||||
0.740542 | + | 0.672010i | \(0.234569\pi\) | |||||||
\(938\) | −12.0213 | −0.392508 | ||||||||
\(939\) | −24.9518 | −0.814271 | ||||||||
\(940\) | 24.3167 | 0.793122 | ||||||||
\(941\) | −40.1238 | −1.30800 | −0.653999 | − | 0.756495i | \(-0.726910\pi\) | ||||
−0.653999 | + | 0.756495i | \(0.726910\pi\) | |||||||
\(942\) | −10.3473 | −0.337134 | ||||||||
\(943\) | −12.4605 | −0.405768 | ||||||||
\(944\) | 0.140899 | 0.00458588 | ||||||||
\(945\) | −3.86789 | −0.125822 | ||||||||
\(946\) | −18.1131 | −0.588908 | ||||||||
\(947\) | 13.2272 | 0.429826 | 0.214913 | − | 0.976633i | \(-0.431053\pi\) | ||||
0.214913 | + | 0.976633i | \(0.431053\pi\) | |||||||
\(948\) | 7.06021 | 0.229305 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 31.7737 | 1.03088 | ||||||||
\(951\) | −1.75675 | −0.0569665 | ||||||||
\(952\) | −0.139361 | −0.00451670 | ||||||||
\(953\) | −5.57685 | −0.180652 | −0.0903260 | − | 0.995912i | \(-0.528791\pi\) | ||||
−0.0903260 | + | 0.995912i | \(0.528791\pi\) | |||||||
\(954\) | −8.90676 | −0.288367 | ||||||||
\(955\) | −33.3215 | −1.07826 | ||||||||
\(956\) | −22.0531 | −0.713247 | ||||||||
\(957\) | −14.2393 | −0.460292 | ||||||||
\(958\) | 5.50802 | 0.177956 | ||||||||
\(959\) | 10.1598 | 0.328077 | ||||||||
\(960\) | −3.86789 | −0.124836 | ||||||||
\(961\) | −15.6990 | −0.506421 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.9871 | −0.354055 | ||||||||
\(964\) | −16.3750 | −0.527404 | ||||||||
\(965\) | 18.4595 | 0.594234 | ||||||||
\(966\) | −1.05473 | −0.0339354 | ||||||||
\(967\) | −26.6772 | −0.857882 | −0.428941 | − | 0.903332i | \(-0.641113\pi\) | ||||
−0.428941 | + | 0.903332i | \(0.641113\pi\) | |||||||
\(968\) | 5.96967 | 0.191872 | ||||||||
\(969\) | −0.444554 | −0.0142811 | ||||||||
\(970\) | −29.9696 | −0.962266 | ||||||||
\(971\) | 11.6045 | 0.372406 | 0.186203 | − | 0.982511i | \(-0.440382\pi\) | ||||
0.186203 | + | 0.982511i | \(0.440382\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −16.7430 | −0.536757 | ||||||||
\(974\) | 4.98323 | 0.159673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.35955 | −0.235573 | ||||||||
\(977\) | −13.1162 | −0.419624 | −0.209812 | − | 0.977742i | \(-0.567285\pi\) | ||||
−0.209812 | + | 0.977742i | \(0.567285\pi\) | |||||||
\(978\) | 4.02161 | 0.128597 | ||||||||
\(979\) | −7.56948 | −0.241922 | ||||||||
\(980\) | −3.86789 | −0.123555 | ||||||||
\(981\) | −14.7856 | −0.472067 | ||||||||
\(982\) | 5.28048 | 0.168507 | ||||||||
\(983\) | 39.2505 | 1.25190 | 0.625948 | − | 0.779865i | \(-0.284712\pi\) | ||||
0.625948 | + | 0.779865i | \(0.284712\pi\) | |||||||
\(984\) | 11.8139 | 0.376613 | ||||||||
\(985\) | −80.1752 | −2.55459 | ||||||||
\(986\) | 0.884770 | 0.0281768 | ||||||||
\(987\) | −6.28681 | −0.200111 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.51797 | 0.270856 | ||||||||
\(990\) | 8.67506 | 0.275711 | ||||||||
\(991\) | 32.9814 | 1.04769 | 0.523844 | − | 0.851814i | \(-0.324498\pi\) | ||||
0.523844 | + | 0.851814i | \(0.324498\pi\) | |||||||
\(992\) | −3.91164 | −0.124195 | ||||||||
\(993\) | 25.3386 | 0.804097 | ||||||||
\(994\) | −11.5292 | −0.365683 | ||||||||
\(995\) | −89.1718 | −2.82693 | ||||||||
\(996\) | −16.0286 | −0.507887 | ||||||||
\(997\) | −50.2260 | −1.59067 | −0.795337 | − | 0.606167i | \(-0.792706\pi\) | ||||
−0.795337 | + | 0.606167i | \(0.792706\pi\) | |||||||
\(998\) | −8.54700 | −0.270551 | ||||||||
\(999\) | −3.02354 | −0.0956605 |
(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 | 7098.2.a.cq.1.2 | ✓ | 6 | |
13.12 | even | 2 | 7098.2.a.cu.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cq.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
7098.2.a.cu.1.5 | yes | 6 | 13.12 | even | 2 |