Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 125326x + 2416960 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-362.802\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −999.805 | −0.690399 | −0.345200 | − | 0.938529i | \(-0.612189\pi\) | ||||
−0.345200 | + | 0.938529i | \(0.612189\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −1.09754e6 | −0.523349 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.90375e7 | 0.398602 | ||||||||
\(7\) | −9.82313e7 | −0.131438 | −0.0657189 | − | 0.997838i | \(-0.520934\pi\) | ||||
−0.0657189 | + | 0.997838i | \(0.520934\pi\) | |||||||
\(8\) | 3.19407e9 | 1.05172 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.60815e10 | −1.11691 | −0.558453 | − | 0.829536i | \(-0.688605\pi\) | ||||
−0.558453 | + | 0.829536i | \(0.688605\pi\) | |||||||
\(12\) | 6.48088e10 | 0.302156 | ||||||||
\(13\) | −6.22052e11 | −1.25147 | −0.625736 | − | 0.780035i | \(-0.715201\pi\) | ||||
−0.625736 | + | 0.780035i | \(0.715201\pi\) | |||||||
\(14\) | 9.82121e10 | 0.0907446 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.91733e11 | −0.202757 | ||||||||
\(17\) | 1.42559e13 | 1.71507 | 0.857536 | − | 0.514425i | \(-0.171994\pi\) | ||||
0.857536 | + | 0.514425i | \(0.171994\pi\) | |||||||
\(18\) | −3.48610e12 | −0.230133 | ||||||||
\(19\) | −8.28760e12 | −0.310110 | −0.155055 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155055 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.80046e12 | 0.0758857 | ||||||||
\(22\) | 9.60627e13 | 0.771111 | ||||||||
\(23\) | 1.17504e14 | 0.591440 | 0.295720 | − | 0.955275i | \(-0.404440\pi\) | ||||
0.295720 | + | 0.955275i | \(0.404440\pi\) | |||||||
\(24\) | −1.88607e14 | −0.607210 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.21930e14 | 0.864015 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 1.07813e14 | 0.0687879 | ||||||||
\(29\) | −1.98798e15 | −0.877471 | −0.438735 | − | 0.898616i | \(-0.644573\pi\) | ||||
−0.438735 | + | 0.898616i | \(0.644573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.31766e15 | −1.16526 | −0.582629 | − | 0.812738i | \(-0.697976\pi\) | ||||
−0.582629 | + | 0.812738i | \(0.697976\pi\) | |||||||
\(32\) | −5.80689e15 | −0.911736 | ||||||||
\(33\) | 5.67352e15 | 0.644846 | ||||||||
\(34\) | −1.42532e16 | −1.18408 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.82689e15 | −0.174450 | ||||||||
\(37\) | −1.99479e16 | −0.681992 | −0.340996 | − | 0.940065i | \(-0.610764\pi\) | ||||
−0.340996 | + | 0.940065i | \(0.610764\pi\) | |||||||
\(38\) | 8.28598e15 | 0.214100 | ||||||||
\(39\) | 3.67315e16 | 0.722538 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.99615e16 | −0.348604 | −0.174302 | − | 0.984692i | \(-0.555767\pi\) | ||||
−0.174302 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(42\) | −5.79933e15 | −0.0523914 | ||||||||
\(43\) | 3.44307e16 | 0.242956 | 0.121478 | − | 0.992594i | \(-0.461237\pi\) | ||||
0.121478 | + | 0.992594i | \(0.461237\pi\) | |||||||
\(44\) | 1.05454e17 | 0.584532 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17481e17 | −0.408330 | ||||||||
\(47\) | 5.23092e17 | 1.45061 | 0.725305 | − | 0.688428i | \(-0.241699\pi\) | ||||
0.725305 | + | 0.688428i | \(0.241699\pi\) | |||||||
\(48\) | 5.26560e16 | 0.117062 | ||||||||
\(49\) | −5.48896e17 | −0.982724 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.41799e17 | −0.990197 | ||||||||
\(52\) | 6.82728e17 | 0.654957 | ||||||||
\(53\) | 1.54033e18 | 1.20981 | 0.604904 | − | 0.796298i | \(-0.293211\pi\) | ||||
0.604904 | + | 0.796298i | \(0.293211\pi\) | |||||||
\(54\) | 2.05851e17 | 0.132867 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.13758e17 | −0.138236 | ||||||||
\(57\) | 4.89374e17 | 0.179042 | ||||||||
\(58\) | 1.98759e18 | 0.605805 | ||||||||
\(59\) | −6.81914e17 | −0.173693 | −0.0868467 | − | 0.996222i | \(-0.527679\pi\) | ||||
−0.0868467 | + | 0.996222i | \(0.527679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.28598e18 | −0.589796 | −0.294898 | − | 0.955529i | \(-0.595286\pi\) | ||||
−0.294898 | + | 0.955529i | \(0.595286\pi\) | |||||||
\(62\) | 5.31662e18 | 0.804494 | ||||||||
\(63\) | −3.42511e17 | −0.0438126 | ||||||||
\(64\) | 7.67586e18 | 0.832218 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.67241e18 | −0.445201 | ||||||||
\(67\) | −1.07261e19 | −0.718882 | −0.359441 | − | 0.933168i | \(-0.617033\pi\) | ||||
−0.359441 | + | 0.933168i | \(0.617033\pi\) | |||||||
\(68\) | −1.56465e19 | −0.897581 | ||||||||
\(69\) | −6.93850e18 | −0.341468 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.71838e19 | 1.35563 | 0.677815 | − | 0.735232i | \(-0.262927\pi\) | ||||
0.677815 | + | 0.735232i | \(0.262927\pi\) | |||||||
\(72\) | 1.11370e19 | 0.350573 | ||||||||
\(73\) | 6.79746e19 | 1.85121 | 0.925607 | − | 0.378487i | \(-0.123555\pi\) | ||||
0.925607 | + | 0.378487i | \(0.123555\pi\) | |||||||
\(74\) | 1.99440e19 | 0.470847 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.09599e18 | 0.162296 | ||||||||
\(77\) | 9.43821e18 | 0.146804 | ||||||||
\(78\) | −3.67244e19 | −0.498839 | ||||||||
\(79\) | 1.28759e20 | 1.53001 | 0.765004 | − | 0.644026i | \(-0.222737\pi\) | ||||
0.765004 | + | 0.644026i | \(0.222737\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 2.99556e19 | 0.240676 | ||||||||
\(83\) | −1.24075e20 | −0.877738 | −0.438869 | − | 0.898551i | \(-0.644621\pi\) | ||||
−0.438869 | + | 0.898551i | \(0.644621\pi\) | |||||||
\(84\) | −6.36625e18 | −0.0397147 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.44240e19 | −0.167736 | ||||||||
\(87\) | 1.17388e20 | 0.506608 | ||||||||
\(88\) | −3.06891e20 | −1.17467 | ||||||||
\(89\) | 4.94950e20 | 1.68254 | 0.841271 | − | 0.540613i | \(-0.181808\pi\) | ||||
0.841271 | + | 0.540613i | \(0.181808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.11049e19 | 0.164491 | ||||||||
\(92\) | −1.28966e20 | −0.309530 | ||||||||
\(93\) | 3.14002e20 | 0.672763 | ||||||||
\(94\) | −5.22990e20 | −1.00150 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.42891e20 | 0.526391 | ||||||||
\(97\) | −4.69497e20 | −0.646443 | −0.323221 | − | 0.946323i | \(-0.604766\pi\) | ||||
−0.323221 | + | 0.946323i | \(0.604766\pi\) | |||||||
\(98\) | 5.48789e20 | 0.678472 | ||||||||
\(99\) | −3.35015e20 | −0.372302 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.69917e20 | 0.513378 | 0.256689 | − | 0.966494i | \(-0.417368\pi\) | ||||
0.256689 | + | 0.966494i | \(0.417368\pi\) | |||||||
\(102\) | 8.41635e20 | 0.683631 | ||||||||
\(103\) | −6.53842e19 | −0.0479382 | −0.0239691 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239691 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(104\) | −1.98688e21 | −1.31620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.54003e21 | −0.835250 | ||||||||
\(107\) | 1.83068e21 | 0.899669 | 0.449834 | − | 0.893112i | \(-0.351483\pi\) | ||||
0.449834 | + | 0.893112i | \(0.351483\pi\) | |||||||
\(108\) | 2.25974e20 | 0.100719 | ||||||||
\(109\) | 2.30722e21 | 0.933491 | 0.466745 | − | 0.884392i | \(-0.345426\pi\) | ||||
0.466745 | + | 0.884392i | \(0.345426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.17790e21 | 0.393748 | ||||||||
\(112\) | 8.75961e19 | 0.0266499 | ||||||||
\(113\) | 4.46490e21 | 1.23734 | 0.618668 | − | 0.785652i | \(-0.287673\pi\) | ||||
0.618668 | + | 0.785652i | \(0.287673\pi\) | |||||||
\(114\) | −4.89279e20 | −0.123611 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.18189e21 | 0.459223 | ||||||||
\(117\) | −2.16896e21 | −0.417157 | ||||||||
\(118\) | 6.81781e20 | 0.119918 | ||||||||
\(119\) | −1.40038e21 | −0.225425 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83140e21 | 0.247479 | ||||||||
\(122\) | 3.28534e21 | 0.407195 | ||||||||
\(123\) | 1.76919e21 | 0.201267 | ||||||||
\(124\) | 5.83635e21 | 0.609837 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.42445e20 | 0.0302482 | ||||||||
\(127\) | −2.21160e22 | −1.79791 | −0.898955 | − | 0.438040i | \(-0.855673\pi\) | ||||
−0.898955 | + | 0.438040i | \(0.855673\pi\) | |||||||
\(128\) | 4.50358e21 | 0.337173 | ||||||||
\(129\) | −2.03310e21 | −0.140271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.93939e21 | 0.466057 | 0.233028 | − | 0.972470i | \(-0.425137\pi\) | ||||
0.233028 | + | 0.972470i | \(0.425137\pi\) | |||||||
\(132\) | −6.22693e21 | −0.337480 | ||||||||
\(133\) | 8.14102e20 | 0.0407602 | ||||||||
\(134\) | 1.07240e22 | 0.496315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.55345e22 | 1.80377 | ||||||||
\(137\) | −1.87691e22 | −0.688457 | −0.344229 | − | 0.938886i | \(-0.611860\pi\) | ||||
−0.344229 | + | 0.938886i | \(0.611860\pi\) | |||||||
\(138\) | 6.93715e21 | 0.235749 | ||||||||
\(139\) | 6.17628e21 | 0.194568 | 0.0972841 | − | 0.995257i | \(-0.468984\pi\) | ||||
0.0972841 | + | 0.995257i | \(0.468984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.08880e22 | −0.837510 | ||||||||
\(142\) | −3.71766e22 | −0.935926 | ||||||||
\(143\) | 5.97676e22 | 1.39778 | ||||||||
\(144\) | −3.10928e21 | −0.0675856 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.79613e22 | −1.27808 | ||||||||
\(147\) | 3.24118e22 | 0.567376 | ||||||||
\(148\) | 2.18937e22 | 0.356920 | ||||||||
\(149\) | −1.87086e22 | −0.284175 | −0.142088 | − | 0.989854i | \(-0.545381\pi\) | ||||
−0.142088 | + | 0.989854i | \(0.545381\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.39155e22 | 1.24016 | 0.620082 | − | 0.784537i | \(-0.287099\pi\) | ||||
0.620082 | + | 0.784537i | \(0.287099\pi\) | |||||||
\(152\) | −2.64712e22 | −0.326149 | ||||||||
\(153\) | 4.97074e22 | 0.571690 | ||||||||
\(154\) | −9.43637e21 | −0.101353 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.03144e22 | −0.378140 | ||||||||
\(157\) | 5.10719e22 | 0.447956 | 0.223978 | − | 0.974594i | \(-0.428096\pi\) | ||||
0.223978 | + | 0.974594i | \(0.428096\pi\) | |||||||
\(158\) | −1.28734e23 | −1.05632 | ||||||||
\(159\) | −9.09548e22 | −0.698483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.15426e22 | −0.0777377 | ||||||||
\(162\) | −1.21553e22 | −0.0767110 | ||||||||
\(163\) | 1.61660e22 | 0.0956386 | 0.0478193 | − | 0.998856i | \(-0.484773\pi\) | ||||
0.0478193 | + | 0.998856i | \(0.484773\pi\) | |||||||
\(164\) | 3.28840e22 | 0.182442 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.24051e23 | 0.605989 | ||||||||
\(167\) | 2.32624e23 | 1.06692 | 0.533459 | − | 0.845826i | \(-0.320892\pi\) | ||||
0.533459 | + | 0.845826i | \(0.320892\pi\) | |||||||
\(168\) | 1.85271e22 | 0.0798104 | ||||||||
\(169\) | 1.39884e23 | 0.566183 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.88971e22 | −0.103370 | ||||||||
\(172\) | −3.77892e22 | −0.127151 | ||||||||
\(173\) | 1.84508e23 | 0.584158 | 0.292079 | − | 0.956394i | \(-0.405653\pi\) | ||||
0.292079 | + | 0.956394i | \(0.405653\pi\) | |||||||
\(174\) | −1.17365e23 | −0.349762 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.56791e22 | 0.226460 | ||||||||
\(177\) | 4.02663e22 | 0.100282 | ||||||||
\(178\) | −4.94853e23 | −1.16163 | ||||||||
\(179\) | 4.64644e22 | 0.102840 | 0.0514202 | − | 0.998677i | \(-0.483625\pi\) | ||||
0.0514202 | + | 0.998677i | \(0.483625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.44640e23 | −1.86055 | −0.930275 | − | 0.366863i | \(-0.880432\pi\) | ||||
−0.930275 | + | 0.366863i | \(0.880432\pi\) | |||||||
\(182\) | −6.10930e22 | −0.113564 | ||||||||
\(183\) | 1.94034e23 | 0.340519 | ||||||||
\(184\) | 3.75317e23 | 0.622029 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.13941e23 | −0.464475 | ||||||||
\(187\) | −1.36973e24 | −1.91557 | ||||||||
\(188\) | −5.74116e23 | −0.759175 | ||||||||
\(189\) | 2.02250e22 | 0.0252952 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.05978e23 | −0.902554 | −0.451277 | − | 0.892384i | \(-0.649031\pi\) | ||||
−0.451277 | + | 0.892384i | \(0.649031\pi\) | |||||||
\(192\) | −4.53252e23 | −0.480481 | ||||||||
\(193\) | −1.40323e24 | −1.40857 | −0.704283 | − | 0.709919i | \(-0.748731\pi\) | ||||
−0.704283 | + | 0.709919i | \(0.748731\pi\) | |||||||
\(194\) | 4.69406e23 | 0.446303 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.02437e23 | 0.514308 | ||||||||
\(197\) | 1.78218e24 | 1.44230 | 0.721152 | − | 0.692777i | \(-0.243613\pi\) | ||||
0.721152 | + | 0.692777i | \(0.243613\pi\) | |||||||
\(198\) | 3.34950e23 | 0.257037 | ||||||||
\(199\) | 1.01185e24 | 0.736478 | 0.368239 | − | 0.929731i | \(-0.379961\pi\) | ||||
0.368239 | + | 0.929731i | \(0.379961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.33367e23 | 0.415047 | ||||||||
\(202\) | −5.69806e23 | −0.354436 | ||||||||
\(203\) | 1.95282e23 | 0.115333 | ||||||||
\(204\) | 9.23910e23 | 0.518219 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.53714e22 | 0.0330965 | ||||||||
\(207\) | 4.09712e23 | 0.197147 | ||||||||
\(208\) | 5.54704e23 | 0.253744 | ||||||||
\(209\) | 7.96285e23 | 0.346364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.73938e24 | −1.86533 | −0.932664 | − | 0.360745i | \(-0.882522\pi\) | ||||
−0.932664 | + | 0.360745i | \(0.882522\pi\) | |||||||
\(212\) | −1.69057e24 | −0.633152 | ||||||||
\(213\) | −2.19567e24 | −0.782674 | ||||||||
\(214\) | −1.83032e24 | −0.621130 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.57631e23 | −0.202403 | ||||||||
\(217\) | 5.22360e23 | 0.153159 | ||||||||
\(218\) | −2.30677e24 | −0.644481 | ||||||||
\(219\) | −4.01383e24 | −1.06880 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.86793e24 | −2.14636 | ||||||||
\(222\) | −1.17767e24 | −0.271843 | ||||||||
\(223\) | 7.74634e24 | 1.70567 | 0.852836 | − | 0.522179i | \(-0.174881\pi\) | ||||
0.852836 | + | 0.522179i | \(0.174881\pi\) | |||||||
\(224\) | 5.70419e23 | 0.119837 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.46402e24 | −0.854256 | ||||||||
\(227\) | −6.99617e24 | −1.27817 | −0.639085 | − | 0.769136i | \(-0.720687\pi\) | ||||
−0.639085 | + | 0.769136i | \(0.720687\pi\) | |||||||
\(228\) | −5.37109e23 | −0.0937015 | ||||||||
\(229\) | −4.76320e24 | −0.793645 | −0.396822 | − | 0.917895i | \(-0.629887\pi\) | ||||
−0.396822 | + | 0.917895i | \(0.629887\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.57317e23 | −0.0847572 | ||||||||
\(232\) | −6.34974e24 | −0.922852 | ||||||||
\(233\) | −2.30237e24 | −0.319843 | −0.159922 | − | 0.987130i | \(-0.551124\pi\) | ||||
−0.159922 | + | 0.987130i | \(0.551124\pi\) | |||||||
\(234\) | 2.16854e24 | 0.288005 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.48429e23 | 0.0909023 | ||||||||
\(237\) | −7.60310e24 | −0.883350 | ||||||||
\(238\) | 1.40011e24 | 0.155633 | ||||||||
\(239\) | 4.40816e24 | 0.468899 | 0.234450 | − | 0.972128i | \(-0.424671\pi\) | ||||
0.234450 | + | 0.972128i | \(0.424671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.88573e24 | −0.281240 | −0.140620 | − | 0.990064i | \(-0.544910\pi\) | ||||
−0.140620 | + | 0.990064i | \(0.544910\pi\) | |||||||
\(242\) | −1.83105e24 | −0.170859 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 3.60650e24 | 0.308669 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.76885e24 | −0.138954 | ||||||||
\(247\) | 5.15531e24 | 0.388094 | ||||||||
\(248\) | −1.69850e25 | −1.22552 | ||||||||
\(249\) | 7.32651e24 | 0.506762 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.06385e24 | 0.385633 | 0.192817 | − | 0.981235i | \(-0.438238\pi\) | ||||
0.192817 | + | 0.981235i | \(0.438238\pi\) | |||||||
\(252\) | 3.75921e23 | 0.0229293 | ||||||||
\(253\) | −1.12900e25 | −0.660583 | ||||||||
\(254\) | 2.21117e25 | 1.24128 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.06001e25 | −1.06500 | ||||||||
\(257\) | −3.42813e25 | −1.70122 | −0.850608 | − | 0.525800i | \(-0.823766\pi\) | ||||
−0.850608 | + | 0.525800i | \(0.823766\pi\) | |||||||
\(258\) | 2.03270e24 | 0.0968426 | ||||||||
\(259\) | 1.95951e24 | 0.0896396 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.93165e24 | −0.292490 | ||||||||
\(262\) | −7.93784e24 | −0.321765 | ||||||||
\(263\) | 3.93877e25 | 1.53400 | 0.767000 | − | 0.641647i | \(-0.221748\pi\) | ||||
0.767000 | + | 0.641647i | \(0.221748\pi\) | |||||||
\(264\) | 1.81216e25 | 0.678197 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.13943e23 | −0.0281408 | ||||||||
\(267\) | −2.92263e25 | −0.971416 | ||||||||
\(268\) | 1.17724e25 | 0.376226 | ||||||||
\(269\) | 1.18456e25 | 0.364049 | 0.182024 | − | 0.983294i | \(-0.441735\pi\) | ||||
0.182024 | + | 0.983294i | \(0.441735\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.63162e25 | −0.463918 | −0.231959 | − | 0.972726i | \(-0.574514\pi\) | ||||
−0.231959 | + | 0.972726i | \(0.574514\pi\) | |||||||
\(272\) | −1.27125e25 | −0.347742 | ||||||||
\(273\) | −3.60819e24 | −0.0949688 | ||||||||
\(274\) | 1.87654e25 | 0.475310 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.61530e24 | 0.178707 | ||||||||
\(277\) | −2.06084e24 | −0.0465594 | −0.0232797 | − | 0.999729i | \(-0.507411\pi\) | ||||
−0.0232797 | + | 0.999729i | \(0.507411\pi\) | |||||||
\(278\) | −6.17508e24 | −0.134330 | ||||||||
\(279\) | −1.85415e25 | −0.388420 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.23966e25 | −1.60138 | −0.800688 | − | 0.599082i | \(-0.795532\pi\) | ||||
−0.800688 | + | 0.599082i | \(0.795532\pi\) | |||||||
\(282\) | 3.08820e25 | 0.578216 | ||||||||
\(283\) | 6.15303e25 | 1.11002 | 0.555011 | − | 0.831843i | \(-0.312714\pi\) | ||||
0.555011 | + | 0.831843i | \(0.312714\pi\) | |||||||
\(284\) | −4.08108e25 | −0.709468 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.97560e25 | −0.965024 | ||||||||
\(287\) | 2.94315e24 | 0.0458198 | ||||||||
\(288\) | −2.02474e25 | −0.303912 | ||||||||
\(289\) | 1.34140e26 | 1.94147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.77234e25 | 0.373224 | ||||||||
\(292\) | −7.46050e25 | −0.968831 | ||||||||
\(293\) | −2.98062e24 | −0.0373419 | −0.0186709 | − | 0.999826i | \(-0.505943\pi\) | ||||
−0.0186709 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(294\) | −3.24055e25 | −0.391716 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.37150e25 | −0.717264 | ||||||||
\(297\) | 1.97823e25 | 0.214949 | ||||||||
\(298\) | 1.87050e25 | 0.196194 | ||||||||
\(299\) | −7.30936e25 | −0.740171 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.38217e24 | −0.0319336 | ||||||||
\(302\) | −9.38972e25 | −0.856208 | ||||||||
\(303\) | −3.36530e25 | −0.296399 | ||||||||
\(304\) | 7.39033e24 | 0.0628769 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.96977e25 | −0.394695 | ||||||||
\(307\) | −1.83958e26 | −1.41177 | −0.705886 | − | 0.708325i | \(-0.749451\pi\) | ||||
−0.705886 | + | 0.708325i | \(0.749451\pi\) | |||||||
\(308\) | −1.03588e25 | −0.0768296 | ||||||||
\(309\) | 3.86087e24 | 0.0276771 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.01647e26 | −0.680944 | −0.340472 | − | 0.940255i | \(-0.610587\pi\) | ||||
−0.340472 | + | 0.940255i | \(0.610587\pi\) | |||||||
\(312\) | 1.17323e26 | 0.759907 | ||||||||
\(313\) | −2.15822e26 | −1.35170 | −0.675850 | − | 0.737040i | \(-0.736223\pi\) | ||||
−0.675850 | + | 0.737040i | \(0.736223\pi\) | |||||||
\(314\) | −5.10619e25 | −0.309269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.41319e26 | −0.800728 | ||||||||
\(317\) | −1.10445e26 | −0.605376 | −0.302688 | − | 0.953090i | \(-0.597884\pi\) | ||||
−0.302688 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(318\) | 9.09370e25 | 0.482232 | ||||||||
\(319\) | 1.91008e26 | 0.980052 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.08100e26 | −0.519424 | ||||||||
\(322\) | 1.15403e25 | 0.0536700 | ||||||||
\(323\) | −1.18147e26 | −0.531861 | ||||||||
\(324\) | −1.33436e25 | −0.0581499 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.61629e25 | −0.0660288 | ||||||||
\(327\) | −1.36239e26 | −0.538951 | ||||||||
\(328\) | −9.56990e25 | −0.366634 | ||||||||
\(329\) | −5.13840e25 | −0.190665 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.13586e26 | 0.743668 | 0.371834 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371834 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(332\) | 1.36178e26 | 0.459363 | ||||||||
\(333\) | −6.95540e25 | −0.227331 | ||||||||
\(334\) | −2.32578e26 | −0.736599 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.17246e24 | −0.0153863 | ||||||||
\(337\) | −1.22428e26 | −0.352994 | −0.176497 | − | 0.984301i | \(-0.556477\pi\) | ||||
−0.176497 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(338\) | −1.39856e26 | −0.390892 | ||||||||
\(339\) | −2.63648e26 | −0.714376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.10928e26 | 1.30148 | ||||||||
\(342\) | 2.88914e25 | 0.0713666 | ||||||||
\(343\) | 1.08786e26 | 0.260605 | ||||||||
\(344\) | 1.09974e26 | 0.255521 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.84472e26 | −0.403302 | ||||||||
\(347\) | −3.11301e26 | −0.660270 | −0.330135 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330135 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(348\) | −1.28838e26 | −0.265133 | ||||||||
\(349\) | 7.85942e26 | 1.56936 | 0.784681 | − | 0.619899i | \(-0.212827\pi\) | ||||
0.784681 | + | 0.619899i | \(0.212827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.28075e26 | 0.240846 | ||||||||
\(352\) | 5.57935e26 | 1.01832 | ||||||||
\(353\) | 1.02640e26 | 0.181837 | 0.0909185 | − | 0.995858i | \(-0.471020\pi\) | ||||
0.0909185 | + | 0.995858i | \(0.471020\pi\) | |||||||
\(354\) | −4.02585e25 | −0.0692346 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.43228e26 | −0.880557 | ||||||||
\(357\) | 8.26910e25 | 0.130149 | ||||||||
\(358\) | −4.64553e25 | −0.0710009 | ||||||||
\(359\) | −9.30102e26 | −1.38051 | −0.690254 | − | 0.723568i | \(-0.742501\pi\) | ||||
−0.690254 | + | 0.723568i | \(0.742501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.45525e26 | −0.903832 | ||||||||
\(362\) | 9.44455e26 | 1.28452 | ||||||||
\(363\) | −1.08143e26 | −0.142882 | ||||||||
\(364\) | −6.70653e25 | −0.0860861 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.93996e26 | −0.235094 | ||||||||
\(367\) | 1.27277e27 | 1.49884 | 0.749422 | − | 0.662093i | \(-0.230332\pi\) | ||||
0.749422 | + | 0.662093i | \(0.230332\pi\) | |||||||
\(368\) | −1.04782e26 | −0.119918 | ||||||||
\(369\) | −1.04469e26 | −0.116201 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.51308e26 | −0.159015 | ||||||||
\(372\) | −3.44631e26 | −0.352090 | ||||||||
\(373\) | 1.92075e27 | 1.90778 | 0.953889 | − | 0.300159i | \(-0.0970397\pi\) | ||||
0.953889 | + | 0.300159i | \(0.0970397\pi\) | |||||||
\(374\) | 1.36946e27 | 1.32251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.67079e27 | 1.52563 | ||||||||
\(377\) | 1.23662e27 | 1.09813 | ||||||||
\(378\) | −2.02210e25 | −0.0174638 | ||||||||
\(379\) | 4.90168e26 | 0.411750 | 0.205875 | − | 0.978578i | \(-0.433996\pi\) | ||||
0.205875 | + | 0.978578i | \(0.433996\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.30593e27 | 1.03802 | ||||||||
\(382\) | 8.05821e26 | 0.623122 | ||||||||
\(383\) | −2.45414e26 | −0.184634 | −0.0923170 | − | 0.995730i | \(-0.529427\pi\) | ||||
−0.0923170 | + | 0.995730i | \(0.529427\pi\) | |||||||
\(384\) | −2.65932e26 | −0.194667 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.40296e27 | 0.972473 | ||||||||
\(387\) | 1.20052e26 | 0.0809852 | ||||||||
\(388\) | 5.15293e26 | 0.338315 | ||||||||
\(389\) | −1.02936e27 | −0.657802 | −0.328901 | − | 0.944364i | \(-0.606678\pi\) | ||||
−0.328901 | + | 0.944364i | \(0.606678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.67513e27 | 1.01436 | ||||||||
\(392\) | −1.75321e27 | −1.03355 | ||||||||
\(393\) | −4.68813e26 | −0.269078 | ||||||||
\(394\) | −1.78184e27 | −0.995766 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.67694e26 | 0.194844 | ||||||||
\(397\) | −1.36083e27 | −0.702270 | −0.351135 | − | 0.936325i | \(-0.614204\pi\) | ||||
−0.351135 | + | 0.936325i | \(0.614204\pi\) | |||||||
\(398\) | −1.01165e27 | −0.508464 | ||||||||
\(399\) | −4.80719e25 | −0.0235329 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.27496e27 | 1.52121 | 0.760606 | − | 0.649214i | \(-0.224902\pi\) | ||||
0.760606 | + | 0.649214i | \(0.224902\pi\) | |||||||
\(402\) | −6.33243e26 | −0.286548 | ||||||||
\(403\) | 3.30786e27 | 1.45829 | ||||||||
\(404\) | −6.25508e26 | −0.268676 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.95244e26 | −0.0796257 | ||||||||
\(407\) | 1.91662e27 | 0.761721 | ||||||||
\(408\) | −2.68877e27 | −1.04141 | ||||||||
\(409\) | −6.11720e26 | −0.230918 | −0.115459 | − | 0.993312i | \(-0.536834\pi\) | ||||
−0.115459 | + | 0.993312i | \(0.536834\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10830e27 | 0.397481 | ||||||||
\(412\) | 7.17619e25 | 0.0250884 | ||||||||
\(413\) | 6.69853e25 | 0.0228299 | ||||||||
\(414\) | −4.09632e26 | −0.136110 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.61219e27 | 1.14101 | ||||||||
\(417\) | −3.64703e26 | −0.112334 | ||||||||
\(418\) | −7.96129e26 | −0.239129 | ||||||||
\(419\) | −1.85944e27 | −0.544673 | −0.272336 | − | 0.962202i | \(-0.587796\pi\) | ||||
−0.272336 | + | 0.962202i | \(0.587796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.61982e27 | −0.729976 | −0.364988 | − | 0.931012i | \(-0.618927\pi\) | ||||
−0.364988 | + | 0.931012i | \(0.618927\pi\) | |||||||
\(422\) | 4.73845e27 | 1.28782 | ||||||||
\(423\) | 1.82391e27 | 0.483536 | ||||||||
\(424\) | 4.91991e27 | 1.27238 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.19524e27 | 0.540357 | ||||||||
\(427\) | 3.22786e26 | 0.0775215 | ||||||||
\(428\) | −2.00925e27 | −0.470841 | ||||||||
\(429\) | −3.52922e27 | −0.807007 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.46324e27 | 1.84300 | 0.921500 | − | 0.388378i | \(-0.126965\pi\) | ||||
0.921500 | + | 0.388378i | \(0.126965\pi\) | |||||||
\(432\) | 1.83600e26 | 0.0390205 | ||||||||
\(433\) | 7.14150e27 | 1.48138 | 0.740690 | − | 0.671847i | \(-0.234499\pi\) | ||||
0.740690 | + | 0.671847i | \(0.234499\pi\) | |||||||
\(434\) | −5.22258e26 | −0.105741 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.53227e27 | −0.488542 | ||||||||
\(437\) | −9.73827e26 | −0.183412 | ||||||||
\(438\) | 4.01305e27 | 0.737898 | ||||||||
\(439\) | −2.98385e27 | −0.535672 | −0.267836 | − | 0.963464i | \(-0.586309\pi\) | ||||
−0.267836 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.91388e27 | −0.327575 | ||||||||
\(442\) | 8.86620e27 | 1.48185 | ||||||||
\(443\) | −1.36610e27 | −0.222969 | −0.111484 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111484 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(444\) | −1.29280e27 | −0.206068 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.74483e27 | −1.17759 | ||||||||
\(447\) | 1.10473e27 | 0.164069 | ||||||||
\(448\) | −7.54010e26 | −0.109385 | ||||||||
\(449\) | −5.56569e27 | −0.788737 | −0.394369 | − | 0.918952i | \(-0.629037\pi\) | ||||
−0.394369 | + | 0.918952i | \(0.629037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.87874e27 | 0.389358 | ||||||||
\(452\) | −4.90041e27 | −0.647559 | ||||||||
\(453\) | −5.54562e27 | −0.716009 | ||||||||
\(454\) | 6.99480e27 | 0.882448 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.56310e27 | 0.188302 | ||||||||
\(457\) | −3.92206e27 | −0.461736 | −0.230868 | − | 0.972985i | \(-0.574157\pi\) | ||||
−0.230868 | + | 0.972985i | \(0.574157\pi\) | |||||||
\(458\) | 4.76227e27 | 0.547932 | ||||||||
\(459\) | −2.93517e27 | −0.330066 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.51086e28 | −1.62317 | −0.811585 | − | 0.584235i | \(-0.801395\pi\) | ||||
−0.811585 | + | 0.584235i | \(0.801395\pi\) | |||||||
\(462\) | 5.57208e26 | 0.0585163 | ||||||||
\(463\) | −6.41081e27 | −0.658131 | −0.329066 | − | 0.944307i | \(-0.606734\pi\) | ||||
−0.329066 | + | 0.944307i | \(0.606734\pi\) | |||||||
\(464\) | 1.77275e27 | 0.177913 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.30192e27 | 0.220820 | ||||||||
\(467\) | 2.82682e27 | 0.265137 | 0.132569 | − | 0.991174i | \(-0.457678\pi\) | ||||
0.132569 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(468\) | 2.38053e27 | 0.218319 | ||||||||
\(469\) | 1.05364e27 | 0.0944883 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.01574e27 | −0.258628 | ||||||||
\(472\) | −2.17808e27 | −0.182677 | ||||||||
\(473\) | −3.30815e27 | −0.271359 | ||||||||
\(474\) | 7.60161e27 | 0.609864 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.53698e27 | 0.117976 | ||||||||
\(477\) | 5.37079e27 | 0.403269 | ||||||||
\(478\) | −4.40730e27 | −0.323728 | ||||||||
\(479\) | 8.65614e27 | 0.622016 | 0.311008 | − | 0.950407i | \(-0.399333\pi\) | ||||
0.311008 | + | 0.950407i | \(0.399333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.24086e28 | 0.853494 | ||||||||
\(482\) | 2.88517e27 | 0.194168 | ||||||||
\(483\) | 6.81578e26 | 0.0448819 | ||||||||
\(484\) | −2.01004e27 | −0.129518 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.17758e26 | 0.0442891 | ||||||||
\(487\) | 3.37782e27 | 0.203978 | 0.101989 | − | 0.994786i | \(-0.467479\pi\) | ||||
0.101989 | + | 0.994786i | \(0.467479\pi\) | |||||||
\(488\) | −1.04957e28 | −0.620299 | ||||||||
\(489\) | −9.54588e26 | −0.0552170 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.94209e28 | −1.63042 | −0.815212 | − | 0.579163i | \(-0.803379\pi\) | ||||
−0.815212 | + | 0.579163i | \(0.803379\pi\) | |||||||
\(492\) | −1.94177e27 | −0.105333 | ||||||||
\(493\) | −2.83405e28 | −1.50492 | ||||||||
\(494\) | −5.15431e27 | −0.267940 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.74193e27 | 0.236264 | ||||||||
\(497\) | −3.65262e27 | −0.178181 | ||||||||
\(498\) | −7.32508e27 | −0.349868 | ||||||||
\(499\) | 3.12544e28 | 1.46169 | 0.730846 | − | 0.682543i | \(-0.239126\pi\) | ||||
0.730846 | + | 0.682543i | \(0.239126\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.37362e28 | −0.615985 | ||||||||
\(502\) | −6.06267e27 | −0.266241 | ||||||||
\(503\) | −1.52567e28 | −0.656140 | −0.328070 | − | 0.944653i | \(-0.606398\pi\) | ||||
−0.328070 | + | 0.944653i | \(0.606398\pi\) | |||||||
\(504\) | −1.09401e27 | −0.0460786 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.12878e28 | 0.456066 | ||||||||
\(507\) | −8.25999e27 | −0.326886 | ||||||||
\(508\) | 2.42733e28 | 0.940935 | ||||||||
\(509\) | −2.89297e28 | −1.09852 | −0.549259 | − | 0.835652i | \(-0.685090\pi\) | ||||
−0.549259 | + | 0.835652i | \(0.685090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.67723e27 | −0.243320 | ||||||||
\(512\) | 1.11514e28 | 0.398104 | ||||||||
\(513\) | 1.70634e27 | 0.0596807 | ||||||||
\(514\) | 3.42746e28 | 1.17452 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.23141e27 | 0.0734104 | ||||||||
\(517\) | −5.02594e28 | −1.62019 | ||||||||
\(518\) | −1.95913e27 | −0.0618871 | ||||||||
\(519\) | −1.08950e28 | −0.337264 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.88105e28 | −0.559247 | −0.279623 | − | 0.960110i | \(-0.590210\pi\) | ||||
−0.279623 | + | 0.960110i | \(0.590210\pi\) | |||||||
\(522\) | 6.93030e27 | 0.201935 | ||||||||
\(523\) | 2.81334e28 | 0.803443 | 0.401722 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401722 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(524\) | −8.71382e27 | −0.243910 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.93800e28 | −1.05907 | ||||||||
\(527\) | −7.58082e28 | −1.99850 | ||||||||
\(528\) | −5.05926e27 | −0.130747 | ||||||||
\(529\) | −2.56644e28 | −0.650198 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.37769e27 | −0.0578978 | ||||||||
\(532\) | −8.93511e26 | −0.0213318 | ||||||||
\(533\) | 1.86376e28 | 0.436268 | ||||||||
\(534\) | 2.92206e28 | 0.670665 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.42600e28 | −0.756061 | ||||||||
\(537\) | −2.74368e27 | −0.0593749 | ||||||||
\(538\) | −1.18433e28 | −0.251339 | ||||||||
\(539\) | 5.27388e28 | 1.09761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.42394e28 | −1.68634 | −0.843168 | − | 0.537650i | \(-0.819312\pi\) | ||||
−0.843168 | + | 0.537650i | \(0.819312\pi\) | |||||||
\(542\) | 1.63130e28 | 0.320289 | ||||||||
\(543\) | 5.57800e28 | 1.07419 | ||||||||
\(544\) | −8.27827e28 | −1.56369 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.60748e27 | 0.0655664 | ||||||||
\(547\) | −5.96331e28 | −1.06321 | −0.531607 | − | 0.846991i | \(-0.678412\pi\) | ||||
−0.531607 | + | 0.846991i | \(0.678412\pi\) | |||||||
\(548\) | 2.05999e28 | 0.360304 | ||||||||
\(549\) | −1.14575e28 | −0.196599 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.64756e28 | 0.272112 | ||||||||
\(552\) | −2.21621e28 | −0.359129 | ||||||||
\(553\) | −1.26482e28 | −0.201101 | ||||||||
\(554\) | 2.06044e27 | 0.0321445 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.77873e27 | −0.101827 | ||||||||
\(557\) | −2.67043e28 | −0.393642 | −0.196821 | − | 0.980439i | \(-0.563062\pi\) | ||||
−0.196821 | + | 0.980439i | \(0.563062\pi\) | |||||||
\(558\) | 1.85379e28 | 0.268165 | ||||||||
\(559\) | −2.14177e28 | −0.304052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.08813e28 | 1.10596 | ||||||||
\(562\) | 8.23805e28 | 1.10559 | ||||||||
\(563\) | 2.15210e28 | 0.283482 | 0.141741 | − | 0.989904i | \(-0.454730\pi\) | ||||
0.141741 | + | 0.989904i | \(0.454730\pi\) | |||||||
\(564\) | 3.39009e28 | 0.438310 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.15183e28 | −0.766358 | ||||||||
\(567\) | −1.19426e27 | −0.0146042 | ||||||||
\(568\) | 1.18768e29 | 1.42574 | ||||||||
\(569\) | 6.95667e28 | 0.819827 | 0.409914 | − | 0.912124i | \(-0.365559\pi\) | ||||
0.409914 | + | 0.912124i | \(0.365559\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.52815e28 | 0.627915 | 0.313957 | − | 0.949437i | \(-0.398345\pi\) | ||||
0.313957 | + | 0.949437i | \(0.398345\pi\) | |||||||
\(572\) | −6.55975e28 | −0.731525 | ||||||||
\(573\) | 4.75922e28 | 0.521090 | ||||||||
\(574\) | −2.94258e27 | −0.0316339 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.67641e28 | 0.277406 | ||||||||
\(577\) | −4.36967e28 | −0.444736 | −0.222368 | − | 0.974963i | \(-0.571379\pi\) | ||||
−0.222368 | + | 0.974963i | \(0.571379\pi\) | |||||||
\(578\) | −1.34114e29 | −1.34039 | ||||||||
\(579\) | 8.28594e28 | 0.813236 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.21881e28 | 0.115368 | ||||||||
\(582\) | −2.77179e28 | −0.257673 | ||||||||
\(583\) | −1.47997e29 | −1.35124 | ||||||||
\(584\) | 2.17116e29 | 1.94696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.98003e27 | 0.0257808 | ||||||||
\(587\) | 8.04739e28 | 0.683841 | 0.341921 | − | 0.939729i | \(-0.388923\pi\) | ||||
0.341921 | + | 0.939729i | \(0.388923\pi\) | |||||||
\(588\) | −3.55733e28 | −0.296936 | ||||||||
\(589\) | 4.40706e28 | 0.361359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.05236e29 | −0.832715 | ||||||||
\(592\) | 1.77882e28 | 0.138278 | ||||||||
\(593\) | −1.36633e29 | −1.04348 | −0.521738 | − | 0.853106i | \(-0.674716\pi\) | ||||
−0.521738 | + | 0.853106i | \(0.674716\pi\) | |||||||
\(594\) | −1.97785e28 | −0.148400 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.05335e28 | 0.148723 | ||||||||
\(597\) | −5.97489e28 | −0.425206 | ||||||||
\(598\) | 7.30794e28 | 0.511013 | ||||||||
\(599\) | −2.62483e29 | −1.80351 | −0.901757 | − | 0.432243i | \(-0.857722\pi\) | ||||
−0.901757 | + | 0.432243i | \(0.857722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.24428e29 | 1.48900 | 0.744501 | − | 0.667621i | \(-0.232687\pi\) | ||||
0.744501 | + | 0.667621i | \(0.232687\pi\) | |||||||
\(602\) | 3.38151e27 | 0.0220469 | ||||||||
\(603\) | −3.73997e28 | −0.239627 | ||||||||
\(604\) | −1.03076e29 | −0.649039 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.36465e28 | 0.204634 | ||||||||
\(607\) | −1.15112e29 | −0.688081 | −0.344041 | − | 0.938955i | \(-0.611796\pi\) | ||||
−0.344041 | + | 0.938955i | \(0.611796\pi\) | |||||||
\(608\) | 4.81252e28 | 0.282738 | ||||||||
\(609\) | −1.15312e28 | −0.0665875 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.25390e29 | −1.81540 | ||||||||
\(612\) | −5.45560e28 | −0.299194 | ||||||||
\(613\) | 1.38014e29 | 0.744028 | 0.372014 | − | 0.928227i | \(-0.378667\pi\) | ||||
0.372014 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(614\) | 1.83922e29 | 0.974686 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.01463e28 | 0.154396 | ||||||||
\(617\) | 3.29841e29 | 1.66077 | 0.830387 | − | 0.557188i | \(-0.188120\pi\) | ||||
0.830387 | + | 0.557188i | \(0.188120\pi\) | |||||||
\(618\) | −3.86012e27 | −0.0191083 | ||||||||
\(619\) | −3.27323e29 | −1.59304 | −0.796518 | − | 0.604615i | \(-0.793327\pi\) | ||||
−0.796518 | + | 0.604615i | \(0.793327\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.41931e28 | −0.113823 | ||||||||
\(622\) | 1.01627e29 | 0.470123 | ||||||||
\(623\) | −4.86196e28 | −0.221150 | ||||||||
\(624\) | −3.27547e28 | −0.146499 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.15780e29 | 0.933212 | ||||||||
\(627\) | −4.70198e28 | −0.199973 | ||||||||
\(628\) | −5.60536e28 | −0.234437 | ||||||||
\(629\) | −2.84376e29 | −1.16966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.40426e29 | 0.558649 | 0.279325 | − | 0.960197i | \(-0.409889\pi\) | ||||
0.279325 | + | 0.960197i | \(0.409889\pi\) | |||||||
\(632\) | 4.11266e29 | 1.60914 | ||||||||
\(633\) | 2.79855e29 | 1.07695 | ||||||||
\(634\) | 1.10424e29 | 0.417951 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.98268e28 | 0.365550 | ||||||||
\(637\) | 3.41442e29 | 1.22985 | ||||||||
\(638\) | −1.90971e29 | −0.676627 | ||||||||
\(639\) | 1.29652e29 | 0.451877 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.83660e29 | −1.29401 | −0.647004 | − | 0.762487i | \(-0.723978\pi\) | ||||
−0.647004 | + | 0.762487i | \(0.723978\pi\) | |||||||
\(642\) | 1.08079e29 | 0.358610 | ||||||||
\(643\) | −5.53770e29 | −1.80765 | −0.903824 | − | 0.427903i | \(-0.859252\pi\) | ||||
−0.903824 | + | 0.427903i | \(0.859252\pi\) | |||||||
\(644\) | 1.26685e28 | 0.0406839 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.18124e29 | 0.367196 | ||||||||
\(647\) | 6.57835e28 | 0.201197 | 0.100599 | − | 0.994927i | \(-0.467924\pi\) | ||||
0.100599 | + | 0.994927i | \(0.467924\pi\) | |||||||
\(648\) | 3.88324e28 | 0.116858 | ||||||||
\(649\) | 6.55193e28 | 0.193999 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.08449e28 | −0.0884265 | ||||||||
\(652\) | −1.77429e28 | −0.0500524 | ||||||||
\(653\) | −1.12463e29 | −0.312193 | −0.156096 | − | 0.987742i | \(-0.549891\pi\) | ||||
−0.156096 | + | 0.987742i | \(0.549891\pi\) | |||||||
\(654\) | 1.36212e29 | 0.372091 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.67176e28 | 0.0706818 | ||||||||
\(657\) | 2.37013e29 | 0.617071 | ||||||||
\(658\) | 5.13740e28 | 0.131635 | ||||||||
\(659\) | 2.28737e29 | 0.576820 | 0.288410 | − | 0.957507i | \(-0.406873\pi\) | ||||
0.288410 | + | 0.957507i | \(0.406873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.05209e29 | 1.23412 | 0.617058 | − | 0.786918i | \(-0.288325\pi\) | ||||
0.617058 | + | 0.786918i | \(0.288325\pi\) | |||||||
\(662\) | −2.13544e29 | −0.513427 | ||||||||
\(663\) | 5.23642e29 | 1.23920 | ||||||||
\(664\) | −3.96305e29 | −0.923133 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.95405e28 | 0.156949 | ||||||||
\(667\) | −2.33596e29 | −0.518971 | ||||||||
\(668\) | −2.55314e29 | −0.558370 | ||||||||
\(669\) | −4.57414e29 | −0.984770 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.15722e29 | 0.658747 | ||||||||
\(672\) | −3.36827e28 | −0.0691877 | ||||||||
\(673\) | 3.47080e29 | 0.701894 | 0.350947 | − | 0.936395i | \(-0.385860\pi\) | ||||
0.350947 | + | 0.936395i | \(0.385860\pi\) | |||||||
\(674\) | 1.22404e29 | 0.243707 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.53528e29 | −0.296311 | ||||||||
\(677\) | 4.53881e29 | 0.862504 | 0.431252 | − | 0.902232i | \(-0.358072\pi\) | ||||
0.431252 | + | 0.902232i | \(0.358072\pi\) | |||||||
\(678\) | 2.63596e29 | 0.493205 | ||||||||
\(679\) | 4.61194e28 | 0.0849671 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.13117e29 | 0.737952 | ||||||||
\(682\) | −5.10829e29 | −0.898544 | ||||||||
\(683\) | 3.49762e29 | 0.605836 | 0.302918 | − | 0.953017i | \(-0.402039\pi\) | ||||
0.302918 | + | 0.953017i | \(0.402039\pi\) | |||||||
\(684\) | 3.17158e28 | 0.0540986 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.08764e29 | −0.179921 | ||||||||
\(687\) | 2.81262e29 | 0.458211 | ||||||||
\(688\) | −3.07030e28 | −0.0492609 | ||||||||
\(689\) | −9.58163e29 | −1.51404 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.19978e30 | 1.83900 | 0.919502 | − | 0.393085i | \(-0.128592\pi\) | ||||
0.919502 | + | 0.393085i | \(0.128592\pi\) | |||||||
\(692\) | −2.02505e29 | −0.305719 | ||||||||
\(693\) | 3.29090e28 | 0.0489346 | ||||||||
\(694\) | 3.11240e29 | 0.455850 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.74946e29 | 0.532809 | ||||||||
\(697\) | −4.27129e29 | −0.597881 | ||||||||
\(698\) | −7.85788e29 | −1.08349 | ||||||||
\(699\) | 1.35952e29 | 0.184662 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.17850e29 | −0.550784 | −0.275392 | − | 0.961332i | \(-0.588808\pi\) | ||||
−0.275392 | + | 0.961332i | \(0.588808\pi\) | |||||||
\(702\) | −1.28050e29 | −0.166280 | ||||||||
\(703\) | 1.65320e29 | 0.211493 | ||||||||
\(704\) | −7.37508e29 | −0.929509 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.02620e29 | −0.125540 | ||||||||
\(707\) | −5.59837e28 | −0.0674773 | ||||||||
\(708\) | −4.41940e28 | −0.0524825 | ||||||||
\(709\) | 9.29367e29 | 1.08743 | 0.543716 | − | 0.839270i | \(-0.317017\pi\) | ||||
0.543716 | + | 0.839270i | \(0.317017\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.48955e29 | 0.510002 | ||||||||
\(712\) | 1.58090e30 | 1.76956 | ||||||||
\(713\) | −6.24847e29 | −0.689181 | ||||||||
\(714\) | −8.26749e28 | −0.0898550 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.09967e28 | −0.0538214 | ||||||||
\(717\) | −2.60298e29 | −0.270719 | ||||||||
\(718\) | 9.29920e29 | 0.953101 | ||||||||
\(719\) | 9.87158e29 | 0.997088 | 0.498544 | − | 0.866864i | \(-0.333868\pi\) | ||||
0.498544 | + | 0.866864i | \(0.333868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.42278e27 | 0.00630090 | ||||||||
\(722\) | 6.45399e29 | 0.624005 | ||||||||
\(723\) | 1.70400e29 | 0.162374 | ||||||||
\(724\) | 1.03678e30 | 0.973717 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.08121e29 | 0.0986455 | ||||||||
\(727\) | −1.00668e30 | −0.905271 | −0.452636 | − | 0.891696i | \(-0.649516\pi\) | ||||
−0.452636 | + | 0.891696i | \(0.649516\pi\) | |||||||
\(728\) | 1.95174e29 | 0.172998 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.90842e29 | 0.416686 | ||||||||
\(732\) | −2.12960e29 | −0.178210 | ||||||||
\(733\) | 1.72342e30 | 1.42167 | 0.710837 | − | 0.703356i | \(-0.248316\pi\) | ||||
0.710837 | + | 0.703356i | \(0.248316\pi\) | |||||||
\(734\) | −1.27252e30 | −1.03480 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.82334e29 | −0.539237 | ||||||||
\(737\) | 1.03058e30 | 0.802923 | ||||||||
\(738\) | 1.04449e29 | 0.0802253 | ||||||||
\(739\) | −1.92102e30 | −1.45467 | −0.727337 | − | 0.686280i | \(-0.759242\pi\) | ||||
−0.727337 | + | 0.686280i | \(0.759242\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.04416e29 | −0.224066 | ||||||||
\(742\) | 1.51279e29 | 0.109784 | ||||||||
\(743\) | −1.99512e30 | −1.42753 | −0.713766 | − | 0.700384i | \(-0.753012\pi\) | ||||
−0.713766 | + | 0.700384i | \(0.753012\pi\) | |||||||
\(744\) | 1.00295e30 | 0.707557 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.92037e30 | −1.31713 | ||||||||
\(747\) | −4.32623e29 | −0.292579 | ||||||||
\(748\) | 1.50334e30 | 1.00251 | ||||||||
\(749\) | −1.79830e29 | −0.118251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.59166e30 | 1.65714 | 0.828570 | − | 0.559885i | \(-0.189155\pi\) | ||||
0.828570 | + | 0.559885i | \(0.189155\pi\) | |||||||
\(752\) | −4.66458e29 | −0.294121 | ||||||||
\(753\) | −3.58065e29 | −0.222646 | ||||||||
\(754\) | −1.23638e30 | −0.758148 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.21978e28 | −0.0132382 | ||||||||
\(757\) | 7.37403e29 | 0.433709 | 0.216854 | − | 0.976204i | \(-0.430420\pi\) | ||||
0.216854 | + | 0.976204i | \(0.430420\pi\) | |||||||
\(758\) | −4.90072e29 | −0.284272 | ||||||||
\(759\) | 6.66662e29 | 0.381388 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.89068e30 | −1.60865 | −0.804325 | − | 0.594189i | \(-0.797473\pi\) | ||||
−0.804325 | + | 0.594189i | \(0.797473\pi\) | |||||||
\(762\) | −1.30567e30 | −0.716651 | ||||||||
\(763\) | −2.26641e29 | −0.122696 | ||||||||
\(764\) | 8.84596e29 | 0.472351 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.45366e29 | 0.127471 | ||||||||
\(767\) | 4.24186e29 | 0.217372 | ||||||||
\(768\) | 1.21642e30 | 0.614879 | ||||||||
\(769\) | 1.48232e30 | 0.739119 | 0.369559 | − | 0.929207i | \(-0.379509\pi\) | ||||
0.369559 | + | 0.929207i | \(0.379509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.02428e30 | 0.982198 | ||||||||
\(772\) | 1.54011e30 | 0.737172 | ||||||||
\(773\) | −2.57666e30 | −1.21667 | −0.608335 | − | 0.793680i | \(-0.708162\pi\) | ||||
−0.608335 | + | 0.793680i | \(0.708162\pi\) | |||||||
\(774\) | −1.20029e29 | −0.0559121 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.49961e30 | −0.679876 | ||||||||
\(777\) | −1.15707e29 | −0.0517534 | ||||||||
\(778\) | 1.02916e30 | 0.454146 | ||||||||
\(779\) | 2.48309e29 | 0.108106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.57268e30 | −1.51411 | ||||||||
\(782\) | −1.67480e30 | −0.700315 | ||||||||
\(783\) | 4.09307e29 | 0.168869 | ||||||||
\(784\) | 4.89469e29 | 0.199254 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.68722e29 | 0.185771 | ||||||||
\(787\) | −2.25891e30 | −0.883413 | −0.441707 | − | 0.897160i | \(-0.645627\pi\) | ||||
−0.441707 | + | 0.897160i | \(0.645627\pi\) | |||||||
\(788\) | −1.95602e30 | −0.754829 | ||||||||
\(789\) | −2.32581e30 | −0.885656 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.38593e29 | −0.162633 | ||||||||
\(792\) | −1.07006e30 | −0.391557 | ||||||||
\(793\) | 2.04405e30 | 0.738113 | ||||||||
\(794\) | 1.36057e30 | 0.484847 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.11055e30 | −0.385435 | ||||||||
\(797\) | −4.64460e30 | −1.59087 | −0.795437 | − | 0.606036i | \(-0.792759\pi\) | ||||
−0.795437 | + | 0.606036i | \(0.792759\pi\) | |||||||
\(798\) | 4.80625e28 | 0.0162471 | ||||||||
\(799\) | 7.45717e30 | 2.48790 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.72578e30 | 0.560847 | ||||||||
\(802\) | −3.27432e30 | −1.05024 | ||||||||
\(803\) | −6.53110e30 | −2.06763 | ||||||||
\(804\) | −6.95147e29 | −0.217214 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.30721e30 | −1.00680 | ||||||||
\(807\) | −6.99473e29 | −0.210184 | ||||||||
\(808\) | 1.82036e30 | 0.539929 | ||||||||
\(809\) | 2.89685e30 | 0.848139 | 0.424069 | − | 0.905630i | \(-0.360601\pi\) | ||||
0.424069 | + | 0.905630i | \(0.360601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.60886e30 | −1.60013 | −0.800066 | − | 0.599912i | \(-0.795202\pi\) | ||||
−0.800066 | + | 0.599912i | \(0.795202\pi\) | |||||||
\(812\) | −2.14330e29 | −0.0603594 | ||||||||
\(813\) | 9.63455e29 | 0.267843 | ||||||||
\(814\) | −1.91625e30 | −0.525891 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.50660e29 | 0.200769 | ||||||||
\(817\) | −2.85348e29 | −0.0753430 | ||||||||
\(818\) | 6.11600e29 | 0.159426 | ||||||||
\(819\) | 2.13060e29 | 0.0548303 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.41255e30 | −1.35768 | −0.678842 | − | 0.734284i | \(-0.737518\pi\) | ||||
−0.678842 | + | 0.734284i | \(0.737518\pi\) | |||||||
\(822\) | −1.10808e30 | −0.274421 | ||||||||
\(823\) | −2.61047e30 | −0.638293 | −0.319147 | − | 0.947705i | \(-0.603396\pi\) | ||||
−0.319147 | + | 0.947705i | \(0.603396\pi\) | |||||||
\(824\) | −2.08842e29 | −0.0504175 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.69722e28 | −0.0157617 | ||||||||
\(827\) | 7.22685e30 | 1.67935 | 0.839675 | − | 0.543090i | \(-0.182746\pi\) | ||||
0.839675 | + | 0.543090i | \(0.182746\pi\) | |||||||
\(828\) | −4.49676e29 | −0.103177 | ||||||||
\(829\) | −3.91702e30 | −0.887429 | −0.443715 | − | 0.896168i | \(-0.646340\pi\) | ||||
−0.443715 | + | 0.896168i | \(0.646340\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.21691e29 | 0.0268811 | ||||||||
\(832\) | −4.77478e30 | −1.04150 | ||||||||
\(833\) | −7.82503e30 | −1.68544 | ||||||||
\(834\) | 3.64632e29 | 0.0775553 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.73956e29 | −0.181269 | ||||||||
\(837\) | 1.09486e30 | 0.224254 | ||||||||
\(838\) | 1.85908e30 | 0.376041 | ||||||||
\(839\) | −8.21745e30 | −1.64148 | −0.820742 | − | 0.571299i | \(-0.806440\pi\) | ||||
−0.820742 | + | 0.571299i | \(0.806440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.18079e30 | −0.230045 | ||||||||
\(842\) | 2.61930e30 | 0.503975 | ||||||||
\(843\) | 4.86544e30 | 0.924554 | ||||||||
\(844\) | 5.20167e30 | 0.976218 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.82355e30 | −0.333833 | ||||||||
\(847\) | −1.79901e29 | −0.0325281 | ||||||||
\(848\) | −1.37356e30 | −0.245297 | ||||||||
\(849\) | −3.63330e30 | −0.640871 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.34396e30 | −0.403357 | ||||||||
\(852\) | 2.40984e30 | 0.409612 | ||||||||
\(853\) | 8.59334e30 | 1.44277 | 0.721385 | − | 0.692534i | \(-0.243506\pi\) | ||||
0.721385 | + | 0.692534i | \(0.243506\pi\) | |||||||
\(854\) | −3.22723e29 | −0.0535208 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.84732e30 | 0.946198 | ||||||||
\(857\) | 3.26828e30 | 0.522421 | 0.261211 | − | 0.965282i | \(-0.415878\pi\) | ||||
0.261211 | + | 0.965282i | \(0.415878\pi\) | |||||||
\(858\) | 3.52853e30 | 0.557157 | ||||||||
\(859\) | 9.63038e29 | 0.150216 | 0.0751078 | − | 0.997175i | \(-0.476070\pi\) | ||||
0.0751078 | + | 0.997175i | \(0.476070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.73790e29 | −0.0264541 | ||||||||
\(862\) | −8.46159e30 | −1.27241 | ||||||||
\(863\) | −3.97633e30 | −0.590702 | −0.295351 | − | 0.955389i | \(-0.595437\pi\) | ||||
−0.295351 | + | 0.955389i | \(0.595437\pi\) | |||||||
\(864\) | 1.19559e30 | 0.175464 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.14011e30 | −1.02274 | ||||||||
\(867\) | −7.92083e30 | −1.12091 | ||||||||
\(868\) | −5.73313e29 | −0.0801557 | ||||||||
\(869\) | −1.23714e31 | −1.70887 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.67220e30 | 0.899661 | ||||||||
\(872\) | 7.36941e30 | 0.981770 | ||||||||
\(873\) | −1.63704e30 | −0.215481 | ||||||||
\(874\) | 9.73637e29 | 0.126627 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.40535e30 | 0.559355 | ||||||||
\(877\) | 5.52079e29 | 0.0692636 | 0.0346318 | − | 0.999400i | \(-0.488974\pi\) | ||||
0.0346318 | + | 0.999400i | \(0.488974\pi\) | |||||||
\(878\) | 2.98326e30 | 0.369828 | ||||||||
\(879\) | 1.76002e29 | 0.0215593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.98610e30 | −0.476761 | −0.238380 | − | 0.971172i | \(-0.576617\pi\) | ||||
−0.238380 | + | 0.971172i | \(0.576617\pi\) | |||||||
\(882\) | 1.91351e30 | 0.226157 | ||||||||
\(883\) | −1.11066e31 | −1.29717 | −0.648583 | − | 0.761144i | \(-0.724638\pi\) | ||||
−0.648583 | + | 0.761144i | \(0.724638\pi\) | |||||||
\(884\) | 9.73293e30 | 1.12330 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.36583e30 | 0.153937 | ||||||||
\(887\) | 2.93164e30 | 0.326522 | 0.163261 | − | 0.986583i | \(-0.447799\pi\) | ||||
0.163261 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(888\) | 3.76231e30 | 0.414112 | ||||||||
\(889\) | 2.17249e30 | 0.236314 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.16813e30 | −0.124101 | ||||||||
\(892\) | −8.50194e30 | −0.892662 | ||||||||
\(893\) | −4.33517e30 | −0.449848 | ||||||||
\(894\) | −1.10451e30 | −0.113273 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.42392e29 | −0.0443173 | ||||||||
\(897\) | 4.31611e30 | 0.427338 | ||||||||
\(898\) | 5.56460e30 | 0.544544 | ||||||||
\(899\) | 1.05714e31 | 1.02248 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.19588e31 | 2.07491 | ||||||||
\(902\) | −2.87818e30 | −0.268812 | ||||||||
\(903\) | 1.99714e29 | 0.0184369 | ||||||||
\(904\) | 1.42612e31 | 1.30133 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.54453e30 | 0.494332 | ||||||||
\(907\) | 1.45433e31 | 1.28170 | 0.640852 | − | 0.767665i | \(-0.278581\pi\) | ||||
0.640852 | + | 0.767665i | \(0.278581\pi\) | |||||||
\(908\) | 7.67859e30 | 0.668929 | ||||||||
\(909\) | 1.98718e30 | 0.171126 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.40205e30 | 0.538736 | 0.269368 | − | 0.963037i | \(-0.413185\pi\) | ||||
0.269368 | + | 0.963037i | \(0.413185\pi\) | |||||||
\(912\) | −4.36391e29 | −0.0363020 | ||||||||
\(913\) | 1.19213e31 | 0.980350 | ||||||||
\(914\) | 3.92129e30 | 0.318782 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.22781e30 | 0.415353 | ||||||||
\(917\) | −7.79897e29 | −0.0612575 | ||||||||
\(918\) | 2.93460e30 | 0.227877 | ||||||||
\(919\) | −5.93034e30 | −0.455268 | −0.227634 | − | 0.973747i | \(-0.573099\pi\) | ||||
−0.227634 | + | 0.973747i | \(0.573099\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.08625e31 | 0.815087 | ||||||||
\(922\) | 1.51056e31 | 1.12063 | ||||||||
\(923\) | −2.31303e31 | −1.69653 | ||||||||
\(924\) | 6.11679e29 | 0.0443576 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.40956e30 | 0.454373 | ||||||||
\(927\) | −2.27981e29 | −0.0159794 | ||||||||
\(928\) | 1.15440e31 | 0.800021 | ||||||||
\(929\) | −1.75288e31 | −1.20112 | −0.600561 | − | 0.799579i | \(-0.705056\pi\) | ||||
−0.600561 | + | 0.799579i | \(0.705056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.54903e30 | 0.304753 | ||||||||
\(932\) | 2.52695e30 | 0.167390 | ||||||||
\(933\) | 6.00217e30 | 0.393143 | ||||||||
\(934\) | −2.82627e30 | −0.183051 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.92781e30 | −0.438732 | ||||||||
\(937\) | 1.86505e31 | 1.16795 | 0.583977 | − | 0.811770i | \(-0.301496\pi\) | ||||
0.583977 | + | 0.811770i | \(0.301496\pi\) | |||||||
\(938\) | −1.05344e30 | −0.0652346 | ||||||||
\(939\) | 1.27441e31 | 0.780404 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.81711e30 | −0.468118 | −0.234059 | − | 0.972222i | \(-0.575201\pi\) | ||||
−0.234059 | + | 0.972222i | \(0.575201\pi\) | |||||||
\(942\) | 3.01515e30 | 0.178556 | ||||||||
\(943\) | −3.52060e30 | −0.206179 | ||||||||
\(944\) | 6.08085e29 | 0.0352175 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.30751e30 | 0.187346 | ||||||||
\(947\) | −1.46277e31 | −0.819411 | −0.409705 | − | 0.912218i | \(-0.634368\pi\) | ||||
−0.409705 | + | 0.912218i | \(0.634368\pi\) | |||||||
\(948\) | 8.34472e30 | 0.462301 | ||||||||
\(949\) | −4.22837e31 | −2.31674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.52169e30 | 0.349514 | ||||||||
\(952\) | −4.47291e30 | −0.237084 | ||||||||
\(953\) | 1.47934e31 | 0.775521 | 0.387760 | − | 0.921760i | \(-0.373249\pi\) | ||||
0.387760 | + | 0.921760i | \(0.373249\pi\) | |||||||
\(954\) | −5.36974e30 | −0.278417 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4.83815e30 | −0.245398 | ||||||||
\(957\) | −1.12788e31 | −0.565833 | ||||||||
\(958\) | −8.65445e30 | −0.429439 | ||||||||
\(959\) | 1.84371e30 | 0.0904894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.45196e30 | 0.357828 | ||||||||
\(962\) | −1.24062e31 | −0.589251 | ||||||||
\(963\) | 6.38318e30 | 0.299890 | ||||||||
\(964\) | 3.16722e30 | 0.147187 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.81445e29 | −0.0309864 | ||||||||
\(967\) | −1.70219e31 | −0.765649 | −0.382824 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382824 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(968\) | 5.84963e30 | 0.260278 | ||||||||
\(969\) | 6.97649e30 | 0.307070 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.36139e31 | 1.01711 | 0.508553 | − | 0.861031i | \(-0.330181\pi\) | ||||
0.508553 | + | 0.861031i | \(0.330181\pi\) | |||||||
\(972\) | 7.87924e29 | 0.0335729 | ||||||||
\(973\) | −6.06704e29 | −0.0255736 | ||||||||
\(974\) | −3.37716e30 | −0.140826 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.93022e30 | 0.119585 | ||||||||
\(977\) | 4.50176e31 | 1.81756 | 0.908781 | − | 0.417273i | \(-0.137014\pi\) | ||||
0.908781 | + | 0.417273i | \(0.137014\pi\) | |||||||
\(978\) | 9.54401e29 | 0.0381218 | ||||||||
\(979\) | −4.75555e31 | −1.87924 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.04477e30 | 0.311164 | ||||||||
\(982\) | 2.94152e31 | 1.12564 | ||||||||
\(983\) | 1.95413e31 | 0.739845 | 0.369922 | − | 0.929063i | \(-0.379384\pi\) | ||||
0.369922 | + | 0.929063i | \(0.379384\pi\) | |||||||
\(984\) | 5.65093e30 | 0.211676 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.83350e31 | 1.03900 | ||||||||
\(987\) | 3.03417e30 | 0.110080 | ||||||||
\(988\) | −5.65818e30 | −0.203109 | ||||||||
\(989\) | 4.04575e30 | 0.143694 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.06722e31 | −1.06653 | −0.533263 | − | 0.845950i | \(-0.679034\pi\) | ||||
−0.533263 | + | 0.845950i | \(0.679034\pi\) | |||||||
\(992\) | 3.08791e31 | 1.06241 | ||||||||
\(993\) | −1.26120e31 | −0.429357 | ||||||||
\(994\) | 3.65190e30 | 0.123016 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.04116e30 | −0.265213 | ||||||||
\(997\) | 8.72776e30 | 0.284842 | 0.142421 | − | 0.989806i | \(-0.454511\pi\) | ||||
0.142421 | + | 0.989806i | \(0.454511\pi\) | |||||||
\(998\) | −3.12483e31 | −1.00915 | ||||||||
\(999\) | 4.10710e30 | 0.131249 |
(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 | 75.22.a.g.1.1 | 3 | ||
5.2 | odd | 4 | 75.22.b.g.49.2 | 6 | |||
5.3 | odd | 4 | 75.22.b.g.49.5 | 6 | |||
5.4 | even | 2 | 15.22.a.b.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 45.22.a.e.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.a.b.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
45.22.a.e.1.1 | 3 | 15.14 | odd | 2 | |||
75.22.a.g.1.1 | 3 | 1.1 | even | 1 | trivial | ||
75.22.b.g.49.2 | 6 | 5.2 | odd | 4 | |||
75.22.b.g.49.5 | 6 | 5.3 | odd | 4 |