Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −178.085 | −1.96758 | −0.983792 | − | 0.179313i | \(-0.942613\pi\) | ||||
−0.983792 | + | 0.179313i | \(0.942613\pi\) | |||||||
\(3\) | −2212.53 | −1.75227 | −0.876136 | − | 0.482064i | \(-0.839887\pi\) | ||||
−0.876136 | + | 0.482064i | \(0.839887\pi\) | |||||||
\(4\) | 23522.4 | 2.87139 | ||||||||
\(5\) | 69269.3 | 1.98260 | 0.991302 | − | 0.131609i | \(-0.0420143\pi\) | ||||
0.991302 | + | 0.131609i | \(0.0420143\pi\) | |||||||
\(6\) | 394020. | 3.44774 | ||||||||
\(7\) | −342836. | −1.10141 | −0.550705 | − | 0.834700i | \(-0.685641\pi\) | ||||
−0.550705 | + | 0.834700i | \(0.685641\pi\) | |||||||
\(8\) | −2.73012e6 | −3.68211 | ||||||||
\(9\) | 3.30098e6 | 2.07046 | ||||||||
\(10\) | −1.23359e7 | −3.90094 | ||||||||
\(11\) | −2.18757e6 | −0.372315 | −0.186157 | − | 0.982520i | \(-0.559603\pi\) | ||||
−0.186157 | + | 0.982520i | \(0.559603\pi\) | |||||||
\(12\) | −5.20441e7 | −5.03145 | ||||||||
\(13\) | −2.49702e7 | −1.43480 | −0.717398 | − | 0.696664i | \(-0.754667\pi\) | ||||
−0.717398 | + | 0.696664i | \(0.754667\pi\) | |||||||
\(14\) | 6.10541e7 | 2.16712 | ||||||||
\(15\) | −1.53261e8 | −3.47406 | ||||||||
\(16\) | 2.93499e8 | 4.37348 | ||||||||
\(17\) | 8.28915e7 | 0.832898 | 0.416449 | − | 0.909159i | \(-0.363274\pi\) | ||||
0.416449 | + | 0.909159i | \(0.363274\pi\) | |||||||
\(18\) | −5.87855e8 | −4.07380 | ||||||||
\(19\) | −1.48465e6 | −0.00723980 | −0.00361990 | − | 0.999993i | \(-0.501152\pi\) | ||||
−0.00361990 | + | 0.999993i | \(0.501152\pi\) | |||||||
\(20\) | 1.62938e9 | 5.69282 | ||||||||
\(21\) | 7.58535e8 | 1.92997 | ||||||||
\(22\) | 3.89575e8 | 0.732561 | ||||||||
\(23\) | −7.83219e8 | −1.10320 | −0.551598 | − | 0.834110i | \(-0.685982\pi\) | ||||
−0.551598 | + | 0.834110i | \(0.685982\pi\) | |||||||
\(24\) | 6.04048e9 | 6.45206 | ||||||||
\(25\) | 3.57753e9 | 2.93072 | ||||||||
\(26\) | 4.44683e9 | 2.82308 | ||||||||
\(27\) | −3.77602e9 | −1.87573 | ||||||||
\(28\) | −8.06432e9 | −3.16257 | ||||||||
\(29\) | 7.67316e8 | 0.239545 | 0.119773 | − | 0.992801i | \(-0.461783\pi\) | ||||
0.119773 | + | 0.992801i | \(0.461783\pi\) | |||||||
\(30\) | 2.72935e10 | 6.83550 | ||||||||
\(31\) | −6.82093e9 | −1.38036 | −0.690180 | − | 0.723637i | \(-0.742469\pi\) | ||||
−0.690180 | + | 0.723637i | \(0.742469\pi\) | |||||||
\(32\) | −2.99028e10 | −4.92307 | ||||||||
\(33\) | 4.84008e9 | 0.652397 | ||||||||
\(34\) | −1.47618e10 | −1.63880 | ||||||||
\(35\) | −2.37480e10 | −2.18366 | ||||||||
\(36\) | 7.76469e10 | 5.94508 | ||||||||
\(37\) | 1.40105e10 | 0.897724 | 0.448862 | − | 0.893601i | \(-0.351829\pi\) | ||||
0.448862 | + | 0.893601i | \(0.351829\pi\) | |||||||
\(38\) | 2.64395e8 | 0.0142449 | ||||||||
\(39\) | 5.52473e10 | 2.51415 | ||||||||
\(40\) | −1.89114e11 | −7.30017 | ||||||||
\(41\) | 4.28687e10 | 1.40944 | 0.704718 | − | 0.709488i | \(-0.251074\pi\) | ||||
0.704718 | + | 0.709488i | \(0.251074\pi\) | |||||||
\(42\) | −1.35084e11 | −3.79738 | ||||||||
\(43\) | 4.73352e9 | 0.114193 | 0.0570964 | − | 0.998369i | \(-0.481816\pi\) | ||||
0.0570964 | + | 0.998369i | \(0.481816\pi\) | |||||||
\(44\) | −5.14570e10 | −1.06906 | ||||||||
\(45\) | 2.28656e11 | 4.10489 | ||||||||
\(46\) | 1.39480e11 | 2.17063 | ||||||||
\(47\) | −1.20240e10 | −0.162709 | −0.0813546 | − | 0.996685i | \(-0.525925\pi\) | ||||
−0.0813546 | + | 0.996685i | \(0.525925\pi\) | |||||||
\(48\) | −6.49376e11 | −7.66352 | ||||||||
\(49\) | 2.06474e10 | 0.213104 | ||||||||
\(50\) | −6.37107e11 | −5.76643 | ||||||||
\(51\) | −1.83400e11 | −1.45946 | ||||||||
\(52\) | −5.87359e11 | −4.11985 | ||||||||
\(53\) | −3.29928e10 | −0.204469 | −0.102234 | − | 0.994760i | \(-0.532599\pi\) | ||||
−0.102234 | + | 0.994760i | \(0.532599\pi\) | |||||||
\(54\) | 6.72455e11 | 3.69066 | ||||||||
\(55\) | −1.51532e11 | −0.738153 | ||||||||
\(56\) | 9.35984e11 | 4.05552 | ||||||||
\(57\) | 3.28484e9 | 0.0126861 | ||||||||
\(58\) | −1.36648e11 | −0.471325 | ||||||||
\(59\) | −4.61096e11 | −1.42316 | −0.711580 | − | 0.702605i | \(-0.752020\pi\) | ||||
−0.711580 | + | 0.702605i | \(0.752020\pi\) | |||||||
\(60\) | −3.60506e12 | −9.97537 | ||||||||
\(61\) | 5.00977e11 | 1.24501 | 0.622506 | − | 0.782615i | \(-0.286115\pi\) | ||||
0.622506 | + | 0.782615i | \(0.286115\pi\) | |||||||
\(62\) | 1.21471e12 | 2.71598 | ||||||||
\(63\) | −1.13169e12 | −2.28042 | ||||||||
\(64\) | 2.92090e12 | 5.31309 | ||||||||
\(65\) | −1.72967e12 | −2.84463 | ||||||||
\(66\) | −8.61947e11 | −1.28365 | ||||||||
\(67\) | 7.79136e11 | 1.05227 | 0.526135 | − | 0.850401i | \(-0.323641\pi\) | ||||
0.526135 | + | 0.850401i | \(0.323641\pi\) | |||||||
\(68\) | 1.94981e12 | 2.39157 | ||||||||
\(69\) | 1.73290e12 | 1.93310 | ||||||||
\(70\) | 4.22917e12 | 4.29653 | ||||||||
\(71\) | −9.28434e11 | −0.860145 | −0.430073 | − | 0.902794i | \(-0.641512\pi\) | ||||
−0.430073 | + | 0.902794i | \(0.641512\pi\) | |||||||
\(72\) | −9.01206e12 | −7.62365 | ||||||||
\(73\) | 2.57941e11 | 0.199491 | 0.0997453 | − | 0.995013i | \(-0.468197\pi\) | ||||
0.0997453 | + | 0.995013i | \(0.468197\pi\) | |||||||
\(74\) | −2.49507e12 | −1.76635 | ||||||||
\(75\) | −7.91541e12 | −5.13541 | ||||||||
\(76\) | −3.49226e10 | −0.0207883 | ||||||||
\(77\) | 7.49979e11 | 0.410071 | ||||||||
\(78\) | −9.83874e12 | −4.94680 | ||||||||
\(79\) | 1.44273e12 | 0.667741 | 0.333871 | − | 0.942619i | \(-0.391645\pi\) | ||||
0.333871 | + | 0.942619i | \(0.391645\pi\) | |||||||
\(80\) | 2.03305e13 | 8.67087 | ||||||||
\(81\) | 3.09175e12 | 1.21633 | ||||||||
\(82\) | −7.63429e12 | −2.77318 | ||||||||
\(83\) | −8.27855e11 | −0.277937 | −0.138969 | − | 0.990297i | \(-0.544379\pi\) | ||||
−0.138969 | + | 0.990297i | \(0.544379\pi\) | |||||||
\(84\) | 1.78426e13 | 5.54169 | ||||||||
\(85\) | 5.74184e12 | 1.65131 | ||||||||
\(86\) | −8.42970e11 | −0.224684 | ||||||||
\(87\) | −1.69771e12 | −0.419748 | ||||||||
\(88\) | 5.97234e12 | 1.37091 | ||||||||
\(89\) | −1.42047e12 | −0.302969 | −0.151485 | − | 0.988460i | \(-0.548405\pi\) | ||||
−0.151485 | + | 0.988460i | \(0.548405\pi\) | |||||||
\(90\) | −4.07203e13 | −8.07672 | ||||||||
\(91\) | 8.56068e12 | 1.58030 | ||||||||
\(92\) | −1.84232e13 | −3.16770 | ||||||||
\(93\) | 1.50915e13 | 2.41877 | ||||||||
\(94\) | 2.14130e12 | 0.320144 | ||||||||
\(95\) | −1.02841e11 | −0.0143537 | ||||||||
\(96\) | 6.61608e13 | 8.62656 | ||||||||
\(97\) | −9.65413e12 | −1.17678 | −0.588392 | − | 0.808576i | \(-0.700239\pi\) | ||||
−0.588392 | + | 0.808576i | \(0.700239\pi\) | |||||||
\(98\) | −3.67700e12 | −0.419300 | ||||||||
\(99\) | −7.22113e12 | −0.770861 | ||||||||
\(100\) | 8.41522e13 | 8.41522 | ||||||||
\(101\) | −3.33558e10 | −0.00312667 | −0.00156334 | − | 0.999999i | \(-0.500498\pi\) | ||||
−0.00156334 | + | 0.999999i | \(0.500498\pi\) | |||||||
\(102\) | 3.26609e13 | 2.87162 | ||||||||
\(103\) | 5.85816e12 | 0.483414 | 0.241707 | − | 0.970349i | \(-0.422293\pi\) | ||||
0.241707 | + | 0.970349i | \(0.422293\pi\) | |||||||
\(104\) | 6.81716e13 | 5.28308 | ||||||||
\(105\) | 5.25432e13 | 3.82636 | ||||||||
\(106\) | 5.87554e12 | 0.402309 | ||||||||
\(107\) | 9.37894e12 | 0.604170 | 0.302085 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302085 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(108\) | −8.88211e13 | −5.38595 | ||||||||
\(109\) | 5.90348e12 | 0.337160 | 0.168580 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168580 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(110\) | 2.69856e13 | 1.45238 | ||||||||
\(111\) | −3.09987e13 | −1.57306 | ||||||||
\(112\) | −1.00622e14 | −4.81699 | ||||||||
\(113\) | −8.98954e12 | −0.406188 | −0.203094 | − | 0.979159i | \(-0.565100\pi\) | ||||
−0.203094 | + | 0.979159i | \(0.565100\pi\) | |||||||
\(114\) | −5.84983e11 | −0.0249610 | ||||||||
\(115\) | −5.42530e13 | −2.18720 | ||||||||
\(116\) | 1.80491e13 | 0.687827 | ||||||||
\(117\) | −8.24260e13 | −2.97068 | ||||||||
\(118\) | 8.21145e13 | 2.80019 | ||||||||
\(119\) | −2.84182e13 | −0.917362 | ||||||||
\(120\) | 4.18420e14 | 12.7919 | ||||||||
\(121\) | −2.97372e13 | −0.861382 | ||||||||
\(122\) | −8.92166e13 | −2.44967 | ||||||||
\(123\) | −9.48484e13 | −2.46971 | ||||||||
\(124\) | −1.60445e14 | −3.96355 | ||||||||
\(125\) | 1.63256e14 | 3.82784 | ||||||||
\(126\) | 2.01538e14 | 4.48692 | ||||||||
\(127\) | −2.88674e13 | −0.610497 | −0.305249 | − | 0.952273i | \(-0.598740\pi\) | ||||
−0.305249 | + | 0.952273i | \(0.598740\pi\) | |||||||
\(128\) | −2.75206e14 | −5.53087 | ||||||||
\(129\) | −1.04731e13 | −0.200097 | ||||||||
\(130\) | 3.08029e14 | 5.59705 | ||||||||
\(131\) | 4.43197e13 | 0.766185 | 0.383092 | − | 0.923710i | \(-0.374859\pi\) | ||||
0.383092 | + | 0.923710i | \(0.374859\pi\) | |||||||
\(132\) | 1.13850e14 | 1.87328 | ||||||||
\(133\) | 5.08992e11 | 0.00797399 | ||||||||
\(134\) | −1.38753e14 | −2.07043 | ||||||||
\(135\) | −2.61563e14 | −3.71883 | ||||||||
\(136\) | −2.26304e14 | −3.06682 | ||||||||
\(137\) | −5.69473e13 | −0.735850 | −0.367925 | − | 0.929855i | \(-0.619932\pi\) | ||||
−0.367925 | + | 0.929855i | \(0.619932\pi\) | |||||||
\(138\) | −3.08604e14 | −3.80353 | ||||||||
\(139\) | 1.42557e14 | 1.67645 | 0.838226 | − | 0.545322i | \(-0.183593\pi\) | ||||
0.838226 | + | 0.545322i | \(0.183593\pi\) | |||||||
\(140\) | −5.58610e14 | −6.27013 | ||||||||
\(141\) | 2.66034e13 | 0.285111 | ||||||||
\(142\) | 1.65341e14 | 1.69241 | ||||||||
\(143\) | 5.46241e13 | 0.534196 | ||||||||
\(144\) | 9.68834e14 | 9.05509 | ||||||||
\(145\) | 5.31515e13 | 0.474923 | ||||||||
\(146\) | −4.59356e13 | −0.392515 | ||||||||
\(147\) | −4.56831e13 | −0.373416 | ||||||||
\(148\) | 3.29561e14 | 2.57771 | ||||||||
\(149\) | −8.06929e13 | −0.604122 | −0.302061 | − | 0.953289i | \(-0.597675\pi\) | ||||
−0.302061 | + | 0.953289i | \(0.597675\pi\) | |||||||
\(150\) | 1.40962e15 | 10.1044 | ||||||||
\(151\) | −1.48573e14 | −1.01998 | −0.509988 | − | 0.860181i | \(-0.670350\pi\) | ||||
−0.509988 | + | 0.860181i | \(0.670350\pi\) | |||||||
\(152\) | 4.05328e12 | 0.0266578 | ||||||||
\(153\) | 2.73623e14 | 1.72448 | ||||||||
\(154\) | −1.33560e14 | −0.806850 | ||||||||
\(155\) | −4.72481e14 | −2.73671 | ||||||||
\(156\) | 1.29955e15 | 7.21910 | ||||||||
\(157\) | −2.48016e13 | −0.132170 | −0.0660848 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660848 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(158\) | −2.56929e14 | −1.31384 | ||||||||
\(159\) | 7.29977e13 | 0.358285 | ||||||||
\(160\) | −2.07134e15 | −9.76050 | ||||||||
\(161\) | 2.68516e14 | 1.21507 | ||||||||
\(162\) | −5.50596e14 | −2.39323 | ||||||||
\(163\) | −2.62399e14 | −1.09583 | −0.547915 | − | 0.836534i | \(-0.684578\pi\) | ||||
−0.547915 | + | 0.836534i | \(0.684578\pi\) | |||||||
\(164\) | 1.00838e15 | 4.04704 | ||||||||
\(165\) | 3.35269e14 | 1.29344 | ||||||||
\(166\) | 1.47429e14 | 0.546865 | ||||||||
\(167\) | 4.02884e14 | 1.43722 | 0.718610 | − | 0.695413i | \(-0.244779\pi\) | ||||
0.718610 | + | 0.695413i | \(0.244779\pi\) | |||||||
\(168\) | −2.07089e15 | −7.10636 | ||||||||
\(169\) | 3.20635e14 | 1.05864 | ||||||||
\(170\) | −1.02254e15 | −3.24909 | ||||||||
\(171\) | −4.90080e12 | −0.0149897 | ||||||||
\(172\) | 1.11344e14 | 0.327892 | ||||||||
\(173\) | 3.80550e13 | 0.107923 | 0.0539613 | − | 0.998543i | \(-0.482815\pi\) | ||||
0.0539613 | + | 0.998543i | \(0.482815\pi\) | |||||||
\(174\) | 3.02338e14 | 0.825890 | ||||||||
\(175\) | −1.22651e15 | −3.22792 | ||||||||
\(176\) | −6.42051e14 | −1.62831 | ||||||||
\(177\) | 1.02019e15 | 2.49376 | ||||||||
\(178\) | 2.52966e14 | 0.596117 | ||||||||
\(179\) | −1.63728e14 | −0.372031 | −0.186015 | − | 0.982547i | \(-0.559557\pi\) | ||||
−0.186015 | + | 0.982547i | \(0.559557\pi\) | |||||||
\(180\) | 5.37855e15 | 11.7867 | ||||||||
\(181\) | 2.83963e14 | 0.600277 | 0.300138 | − | 0.953896i | \(-0.402967\pi\) | ||||
0.300138 | + | 0.953896i | \(0.402967\pi\) | |||||||
\(182\) | −1.52453e15 | −3.10937 | ||||||||
\(183\) | −1.10843e15 | −2.18160 | ||||||||
\(184\) | 2.13828e15 | 4.06209 | ||||||||
\(185\) | 9.70499e14 | 1.77983 | ||||||||
\(186\) | −2.68758e15 | −4.75913 | ||||||||
\(187\) | −1.81331e14 | −0.310100 | ||||||||
\(188\) | −2.82833e14 | −0.467201 | ||||||||
\(189\) | 1.29456e15 | 2.06595 | ||||||||
\(190\) | 1.83145e13 | 0.0282420 | ||||||||
\(191\) | 8.97492e14 | 1.33756 | 0.668781 | − | 0.743460i | \(-0.266816\pi\) | ||||
0.668781 | + | 0.743460i | \(0.266816\pi\) | |||||||
\(192\) | −6.46258e15 | −9.30997 | ||||||||
\(193\) | −9.10942e14 | −1.26873 | −0.634364 | − | 0.773035i | \(-0.718738\pi\) | ||||
−0.634364 | + | 0.773035i | \(0.718738\pi\) | |||||||
\(194\) | 1.71926e15 | 2.31542 | ||||||||
\(195\) | 3.82695e15 | 4.98457 | ||||||||
\(196\) | 4.85677e14 | 0.611904 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | 1.28598e15 | 1.51673 | ||||||||
\(199\) | 1.57907e15 | 1.80243 | 0.901213 | − | 0.433376i | \(-0.142678\pi\) | ||||
0.901213 | + | 0.433376i | \(0.142678\pi\) | |||||||
\(200\) | −9.76710e15 | −10.7912 | ||||||||
\(201\) | −1.72386e15 | −1.84386 | ||||||||
\(202\) | 5.94018e12 | 0.00615199 | ||||||||
\(203\) | −2.63064e14 | −0.263837 | ||||||||
\(204\) | −4.31401e15 | −4.19069 | ||||||||
\(205\) | 2.96949e15 | 2.79435 | ||||||||
\(206\) | −1.04325e15 | −0.951158 | ||||||||
\(207\) | −2.58539e15 | −2.28412 | ||||||||
\(208\) | −7.32873e15 | −6.27505 | ||||||||
\(209\) | 3.24779e12 | 0.00269549 | ||||||||
\(210\) | −9.35718e15 | −7.52869 | ||||||||
\(211\) | 1.03026e15 | 0.803732 | 0.401866 | − | 0.915698i | \(-0.368362\pi\) | ||||
0.401866 | + | 0.915698i | \(0.368362\pi\) | |||||||
\(212\) | −7.76071e14 | −0.587109 | ||||||||
\(213\) | 2.05419e15 | 1.50721 | ||||||||
\(214\) | −1.67025e15 | −1.18875 | ||||||||
\(215\) | 3.27887e14 | 0.226399 | ||||||||
\(216\) | 1.03090e16 | 6.90665 | ||||||||
\(217\) | 2.33846e15 | 1.52034 | ||||||||
\(218\) | −1.05132e15 | −0.663390 | ||||||||
\(219\) | −5.70704e14 | −0.349562 | ||||||||
\(220\) | −3.56439e15 | −2.11952 | ||||||||
\(221\) | −2.06982e15 | −1.19504 | ||||||||
\(222\) | 5.52042e15 | 3.09512 | ||||||||
\(223\) | −2.01761e15 | −1.09864 | −0.549321 | − | 0.835611i | \(-0.685114\pi\) | ||||
−0.549321 | + | 0.835611i | \(0.685114\pi\) | |||||||
\(224\) | 1.02517e16 | 5.42232 | ||||||||
\(225\) | 1.18094e16 | 6.06792 | ||||||||
\(226\) | 1.60091e15 | 0.799210 | ||||||||
\(227\) | 2.58569e15 | 1.25432 | 0.627160 | − | 0.778890i | \(-0.284217\pi\) | ||||
0.627160 | + | 0.778890i | \(0.284217\pi\) | |||||||
\(228\) | 7.72674e13 | 0.0364267 | ||||||||
\(229\) | 1.89717e15 | 0.869314 | 0.434657 | − | 0.900596i | \(-0.356870\pi\) | ||||
0.434657 | + | 0.900596i | \(0.356870\pi\) | |||||||
\(230\) | 9.66168e15 | 4.30350 | ||||||||
\(231\) | −1.65935e15 | −0.718556 | ||||||||
\(232\) | −2.09487e15 | −0.882032 | ||||||||
\(233\) | 3.75124e15 | 1.53590 | 0.767948 | − | 0.640512i | \(-0.221278\pi\) | ||||
0.767948 | + | 0.640512i | \(0.221278\pi\) | |||||||
\(234\) | 1.46789e16 | 5.84506 | ||||||||
\(235\) | −8.32893e14 | −0.322588 | ||||||||
\(236\) | −1.08461e16 | −4.08644 | ||||||||
\(237\) | −3.19208e15 | −1.17006 | ||||||||
\(238\) | 5.06086e15 | 1.80499 | ||||||||
\(239\) | 3.82096e14 | 0.132613 | 0.0663065 | − | 0.997799i | \(-0.478878\pi\) | ||||
0.0663065 | + | 0.997799i | \(0.478878\pi\) | |||||||
\(240\) | −4.49819e16 | −15.1937 | ||||||||
\(241\) | 5.91654e14 | 0.194517 | 0.0972583 | − | 0.995259i | \(-0.468993\pi\) | ||||
0.0972583 | + | 0.995259i | \(0.468993\pi\) | |||||||
\(242\) | 5.29577e15 | 1.69484 | ||||||||
\(243\) | −8.20399e14 | −0.255614 | ||||||||
\(244\) | 1.17842e16 | 3.57491 | ||||||||
\(245\) | 1.43023e15 | 0.422501 | ||||||||
\(246\) | 1.68911e16 | 4.85937 | ||||||||
\(247\) | 3.70721e13 | 0.0103876 | ||||||||
\(248\) | 1.86220e16 | 5.08264 | ||||||||
\(249\) | 1.83165e15 | 0.487021 | ||||||||
\(250\) | −2.90735e16 | −7.53161 | ||||||||
\(251\) | −2.87355e15 | −0.725337 | −0.362669 | − | 0.931918i | \(-0.618134\pi\) | ||||
−0.362669 | + | 0.931918i | \(0.618134\pi\) | |||||||
\(252\) | −2.66201e16 | −6.54797 | ||||||||
\(253\) | 1.71335e15 | 0.410736 | ||||||||
\(254\) | 5.14086e15 | 1.20120 | ||||||||
\(255\) | −1.27040e16 | −2.89354 | ||||||||
\(256\) | 2.50822e16 | 5.56936 | ||||||||
\(257\) | 6.27074e14 | 0.135754 | 0.0678771 | − | 0.997694i | \(-0.478377\pi\) | ||||
0.0678771 | + | 0.997694i | \(0.478377\pi\) | |||||||
\(258\) | 1.86510e15 | 0.393707 | ||||||||
\(259\) | −4.80331e15 | −0.988762 | ||||||||
\(260\) | −4.06859e16 | −8.16804 | ||||||||
\(261\) | 2.53289e15 | 0.495968 | ||||||||
\(262\) | −7.89269e15 | −1.50753 | ||||||||
\(263\) | −1.88438e14 | −0.0351121 | −0.0175560 | − | 0.999846i | \(-0.505589\pi\) | ||||
−0.0175560 | + | 0.999846i | \(0.505589\pi\) | |||||||
\(264\) | −1.32140e16 | −2.40220 | ||||||||
\(265\) | −2.28539e15 | −0.405380 | ||||||||
\(266\) | −9.06441e13 | −0.0156895 | ||||||||
\(267\) | 3.14285e15 | 0.530884 | ||||||||
\(268\) | 1.83272e16 | 3.02148 | ||||||||
\(269\) | −2.98520e15 | −0.480379 | −0.240190 | − | 0.970726i | \(-0.577210\pi\) | ||||
−0.240190 | + | 0.970726i | \(0.577210\pi\) | |||||||
\(270\) | 4.65805e16 | 7.31711 | ||||||||
\(271\) | 3.45220e15 | 0.529414 | 0.264707 | − | 0.964329i | \(-0.414725\pi\) | ||||
0.264707 | + | 0.964329i | \(0.414725\pi\) | |||||||
\(272\) | 2.43286e16 | 3.64266 | ||||||||
\(273\) | −1.89408e16 | −2.76911 | ||||||||
\(274\) | 1.01415e16 | 1.44785 | ||||||||
\(275\) | −7.82612e15 | −1.09115 | ||||||||
\(276\) | 4.07619e16 | 5.55067 | ||||||||
\(277\) | −6.24722e15 | −0.830937 | −0.415469 | − | 0.909607i | \(-0.636382\pi\) | ||||
−0.415469 | + | 0.909607i | \(0.636382\pi\) | |||||||
\(278\) | −2.53873e16 | −3.29856 | ||||||||
\(279\) | −2.25157e16 | −2.85798 | ||||||||
\(280\) | 6.48349e16 | 8.04048 | ||||||||
\(281\) | −7.50392e15 | −0.909279 | −0.454639 | − | 0.890676i | \(-0.650232\pi\) | ||||
−0.454639 | + | 0.890676i | \(0.650232\pi\) | |||||||
\(282\) | −4.73768e15 | −0.560979 | ||||||||
\(283\) | 3.25678e15 | 0.376857 | 0.188428 | − | 0.982087i | \(-0.439661\pi\) | ||||
0.188428 | + | 0.982087i | \(0.439661\pi\) | |||||||
\(284\) | −2.18390e16 | −2.46981 | ||||||||
\(285\) | 2.27539e14 | 0.0251515 | ||||||||
\(286\) | −9.72776e15 | −1.05108 | ||||||||
\(287\) | −1.46969e16 | −1.55237 | ||||||||
\(288\) | −9.87083e16 | −10.1930 | ||||||||
\(289\) | −3.03358e15 | −0.306281 | ||||||||
\(290\) | −9.46550e15 | −0.934451 | ||||||||
\(291\) | 2.13601e16 | 2.06205 | ||||||||
\(292\) | 6.06740e15 | 0.572815 | ||||||||
\(293\) | −1.52824e16 | −1.41108 | −0.705542 | − | 0.708668i | \(-0.749296\pi\) | ||||
−0.705542 | + | 0.708668i | \(0.749296\pi\) | |||||||
\(294\) | 8.13549e15 | 0.734727 | ||||||||
\(295\) | −3.19398e16 | −2.82156 | ||||||||
\(296\) | −3.82504e16 | −3.30552 | ||||||||
\(297\) | 8.26033e15 | 0.698362 | ||||||||
\(298\) | 1.43702e16 | 1.18866 | ||||||||
\(299\) | 1.95571e16 | 1.58286 | ||||||||
\(300\) | −1.86189e17 | −14.7458 | ||||||||
\(301\) | −1.62282e15 | −0.125773 | ||||||||
\(302\) | 2.64587e16 | 2.00689 | ||||||||
\(303\) | 7.38007e13 | 0.00547878 | ||||||||
\(304\) | −4.35745e14 | −0.0316631 | ||||||||
\(305\) | 3.47023e16 | 2.46836 | ||||||||
\(306\) | −4.87282e16 | −3.39306 | ||||||||
\(307\) | 2.65054e16 | 1.80690 | 0.903451 | − | 0.428692i | \(-0.141026\pi\) | ||||
0.903451 | + | 0.428692i | \(0.141026\pi\) | |||||||
\(308\) | 1.76413e16 | 1.17747 | ||||||||
\(309\) | −1.29614e16 | −0.847073 | ||||||||
\(310\) | 8.41420e16 | 5.38470 | ||||||||
\(311\) | 5.88672e14 | 0.0368919 | 0.0184460 | − | 0.999830i | \(-0.494128\pi\) | ||||
0.0184460 | + | 0.999830i | \(0.494128\pi\) | |||||||
\(312\) | −1.50832e17 | −9.25739 | ||||||||
\(313\) | −1.23821e16 | −0.744315 | −0.372158 | − | 0.928170i | \(-0.621382\pi\) | ||||
−0.372158 | + | 0.928170i | \(0.621382\pi\) | |||||||
\(314\) | 4.41680e15 | 0.260055 | ||||||||
\(315\) | −7.83916e16 | −4.52117 | ||||||||
\(316\) | 3.39364e16 | 1.91734 | ||||||||
\(317\) | 6.78117e15 | 0.375335 | 0.187668 | − | 0.982233i | \(-0.439907\pi\) | ||||
0.187668 | + | 0.982233i | \(0.439907\pi\) | |||||||
\(318\) | −1.29998e16 | −0.704955 | ||||||||
\(319\) | −1.67856e15 | −0.0891862 | ||||||||
\(320\) | 2.02329e17 | 10.5337 | ||||||||
\(321\) | −2.07512e16 | −1.05867 | ||||||||
\(322\) | −4.78187e16 | −2.39075 | ||||||||
\(323\) | −1.23065e14 | −0.00603002 | ||||||||
\(324\) | 7.27254e16 | 3.49256 | ||||||||
\(325\) | −8.93317e16 | −4.20498 | ||||||||
\(326\) | 4.67295e16 | 2.15614 | ||||||||
\(327\) | −1.30616e16 | −0.590795 | ||||||||
\(328\) | −1.17037e17 | −5.18970 | ||||||||
\(329\) | 4.12225e15 | 0.179210 | ||||||||
\(330\) | −5.97065e16 | −2.54496 | ||||||||
\(331\) | 4.20545e16 | 1.75764 | 0.878821 | − | 0.477151i | \(-0.158330\pi\) | ||||
0.878821 | + | 0.477151i | \(0.158330\pi\) | |||||||
\(332\) | −1.94731e16 | −0.798065 | ||||||||
\(333\) | 4.62484e16 | 1.85870 | ||||||||
\(334\) | −7.17478e16 | −2.82785 | ||||||||
\(335\) | 5.39702e16 | 2.08623 | ||||||||
\(336\) | 2.22630e17 | 8.44068 | ||||||||
\(337\) | 1.15299e16 | 0.428779 | 0.214389 | − | 0.976748i | \(-0.431224\pi\) | ||||
0.214389 | + | 0.976748i | \(0.431224\pi\) | |||||||
\(338\) | −5.71004e16 | −2.08296 | ||||||||
\(339\) | 1.98896e16 | 0.711752 | ||||||||
\(340\) | 1.35062e17 | 4.74154 | ||||||||
\(341\) | 1.49213e16 | 0.513929 | ||||||||
\(342\) | 8.72762e14 | 0.0294935 | ||||||||
\(343\) | 2.61384e16 | 0.866695 | ||||||||
\(344\) | −1.29231e16 | −0.420471 | ||||||||
\(345\) | 1.20037e17 | 3.83257 | ||||||||
\(346\) | −6.77705e15 | −0.212347 | ||||||||
\(347\) | 3.34090e16 | 1.02736 | 0.513679 | − | 0.857982i | \(-0.328282\pi\) | ||||
0.513679 | + | 0.857982i | \(0.328282\pi\) | |||||||
\(348\) | −3.99343e16 | −1.20526 | ||||||||
\(349\) | −9.97927e15 | −0.295620 | −0.147810 | − | 0.989016i | \(-0.547222\pi\) | ||||
−0.147810 | + | 0.989016i | \(0.547222\pi\) | |||||||
\(350\) | 2.18423e17 | 6.35120 | ||||||||
\(351\) | 9.42880e16 | 2.69129 | ||||||||
\(352\) | 6.54145e16 | 1.83293 | ||||||||
\(353\) | −5.09999e16 | −1.40292 | −0.701461 | − | 0.712708i | \(-0.747469\pi\) | ||||
−0.701461 | + | 0.712708i | \(0.747469\pi\) | |||||||
\(354\) | −1.81681e17 | −4.90669 | ||||||||
\(355\) | −6.43120e16 | −1.70533 | ||||||||
\(356\) | −3.34130e16 | −0.869942 | ||||||||
\(357\) | 6.28761e16 | 1.60747 | ||||||||
\(358\) | 2.91576e16 | 0.732002 | ||||||||
\(359\) | 2.84374e16 | 0.701093 | 0.350547 | − | 0.936545i | \(-0.385996\pi\) | ||||
0.350547 | + | 0.936545i | \(0.385996\pi\) | |||||||
\(360\) | −6.24259e17 | −15.1147 | ||||||||
\(361\) | −4.20508e16 | −0.999948 | ||||||||
\(362\) | −5.05697e16 | −1.18109 | ||||||||
\(363\) | 6.57946e16 | 1.50937 | ||||||||
\(364\) | 2.01368e17 | 4.53765 | ||||||||
\(365\) | 1.78674e16 | 0.395511 | ||||||||
\(366\) | 1.97395e17 | 4.29248 | ||||||||
\(367\) | 2.03905e16 | 0.435612 | 0.217806 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217806 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(368\) | −2.29874e17 | −4.82480 | ||||||||
\(369\) | 1.41509e17 | 2.91817 | ||||||||
\(370\) | −1.72832e17 | −3.50197 | ||||||||
\(371\) | 1.13111e16 | 0.225204 | ||||||||
\(372\) | 3.54989e17 | 6.94522 | ||||||||
\(373\) | −6.12728e15 | −0.117804 | −0.0589020 | − | 0.998264i | \(-0.518760\pi\) | ||||
−0.0589020 | + | 0.998264i | \(0.518760\pi\) | |||||||
\(374\) | 3.22925e16 | 0.610149 | ||||||||
\(375\) | −3.61209e17 | −6.70742 | ||||||||
\(376\) | 3.28269e16 | 0.599114 | ||||||||
\(377\) | −1.91600e16 | −0.343698 | ||||||||
\(378\) | −2.30542e17 | −4.06492 | ||||||||
\(379\) | −8.67573e16 | −1.50367 | −0.751833 | − | 0.659354i | \(-0.770830\pi\) | ||||
−0.751833 | + | 0.659354i | \(0.770830\pi\) | |||||||
\(380\) | −2.41907e15 | −0.0412149 | ||||||||
\(381\) | 6.38701e16 | 1.06976 | ||||||||
\(382\) | −1.59830e17 | −2.63176 | ||||||||
\(383\) | −1.29511e14 | −0.00209660 | −0.00104830 | − | 0.999999i | \(-0.500334\pi\) | ||||
−0.00104830 | + | 0.999999i | \(0.500334\pi\) | |||||||
\(384\) | 6.08902e17 | 9.69158 | ||||||||
\(385\) | 5.19505e16 | 0.813009 | ||||||||
\(386\) | 1.62226e17 | 2.49633 | ||||||||
\(387\) | 1.56252e16 | 0.236431 | ||||||||
\(388\) | −2.27088e17 | −3.37900 | ||||||||
\(389\) | 6.67342e16 | 0.976509 | 0.488255 | − | 0.872701i | \(-0.337634\pi\) | ||||
0.488255 | + | 0.872701i | \(0.337634\pi\) | |||||||
\(390\) | −6.81523e17 | −9.80755 | ||||||||
\(391\) | −6.49222e16 | −0.918849 | ||||||||
\(392\) | −5.63700e16 | −0.784672 | ||||||||
\(393\) | −9.80588e16 | −1.34256 | ||||||||
\(394\) | 1.04094e16 | 0.140185 | ||||||||
\(395\) | 9.99367e16 | 1.32387 | ||||||||
\(396\) | −1.69858e17 | −2.21344 | ||||||||
\(397\) | −8.21917e16 | −1.05363 | −0.526817 | − | 0.849979i | \(-0.676615\pi\) | ||||
−0.526817 | + | 0.849979i | \(0.676615\pi\) | |||||||
\(398\) | −2.81210e17 | −3.54643 | ||||||||
\(399\) | −1.12616e15 | −0.0139726 | ||||||||
\(400\) | 1.05000e18 | 12.8174 | ||||||||
\(401\) | 1.44947e17 | 1.74089 | 0.870445 | − | 0.492266i | \(-0.163831\pi\) | ||||
0.870445 | + | 0.492266i | \(0.163831\pi\) | |||||||
\(402\) | 3.06995e17 | 3.62796 | ||||||||
\(403\) | 1.70320e17 | 1.98054 | ||||||||
\(404\) | −7.84608e14 | −0.00897788 | ||||||||
\(405\) | 2.14163e17 | 2.41150 | ||||||||
\(406\) | 4.68478e16 | 0.519122 | ||||||||
\(407\) | −3.06490e16 | −0.334236 | ||||||||
\(408\) | 5.00704e17 | 5.37391 | ||||||||
\(409\) | −1.29062e17 | −1.36332 | −0.681658 | − | 0.731671i | \(-0.738741\pi\) | ||||
−0.681658 | + | 0.731671i | \(0.738741\pi\) | |||||||
\(410\) | −5.28822e17 | −5.49812 | ||||||||
\(411\) | 1.25998e17 | 1.28941 | ||||||||
\(412\) | 1.37798e17 | 1.38807 | ||||||||
\(413\) | 1.58080e17 | 1.56748 | ||||||||
\(414\) | 4.60420e17 | 4.49419 | ||||||||
\(415\) | −5.73449e16 | −0.551039 | ||||||||
\(416\) | 7.46678e17 | 7.06361 | ||||||||
\(417\) | −3.15411e17 | −2.93760 | ||||||||
\(418\) | −5.78384e14 | −0.00530360 | ||||||||
\(419\) | −1.16966e17 | −1.05601 | −0.528007 | − | 0.849240i | \(-0.677061\pi\) | ||||
−0.528007 | + | 0.849240i | \(0.677061\pi\) | |||||||
\(420\) | 1.23594e18 | 10.9870 | ||||||||
\(421\) | −6.65288e16 | −0.582339 | −0.291169 | − | 0.956671i | \(-0.594044\pi\) | ||||
−0.291169 | + | 0.956671i | \(0.594044\pi\) | |||||||
\(422\) | −1.83474e17 | −1.58141 | ||||||||
\(423\) | −3.96909e16 | −0.336882 | ||||||||
\(424\) | 9.00745e16 | 0.752876 | ||||||||
\(425\) | 2.96547e17 | 2.44099 | ||||||||
\(426\) | −3.65821e17 | −2.96556 | ||||||||
\(427\) | −1.71753e17 | −1.37127 | ||||||||
\(428\) | 2.20615e17 | 1.73481 | ||||||||
\(429\) | −1.20858e17 | −0.936056 | ||||||||
\(430\) | −5.83920e16 | −0.445459 | ||||||||
\(431\) | −1.36907e16 | −0.102878 | −0.0514391 | − | 0.998676i | \(-0.516381\pi\) | ||||
−0.0514391 | + | 0.998676i | \(0.516381\pi\) | |||||||
\(432\) | −1.10826e18 | −8.20346 | ||||||||
\(433\) | −1.53714e17 | −1.12084 | −0.560419 | − | 0.828209i | \(-0.689360\pi\) | ||||
−0.560419 | + | 0.828209i | \(0.689360\pi\) | |||||||
\(434\) | −4.16446e17 | −2.99140 | ||||||||
\(435\) | −1.17599e17 | −0.832194 | ||||||||
\(436\) | 1.38864e17 | 0.968116 | ||||||||
\(437\) | 1.16281e15 | 0.00798691 | ||||||||
\(438\) | 1.01634e17 | 0.687792 | ||||||||
\(439\) | −2.35077e16 | −0.156744 | −0.0783720 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783720 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(440\) | 4.13700e17 | 2.71796 | ||||||||
\(441\) | 6.81566e16 | 0.441222 | ||||||||
\(442\) | 3.68604e17 | 2.35134 | ||||||||
\(443\) | 1.30104e17 | 0.817837 | 0.408918 | − | 0.912571i | \(-0.365906\pi\) | ||||
0.408918 | + | 0.912571i | \(0.365906\pi\) | |||||||
\(444\) | −7.29164e17 | −4.51685 | ||||||||
\(445\) | −9.83953e16 | −0.600668 | ||||||||
\(446\) | 3.59308e17 | 2.16167 | ||||||||
\(447\) | 1.78536e17 | 1.05859 | ||||||||
\(448\) | −1.00139e18 | −5.85189 | ||||||||
\(449\) | 3.14233e17 | 1.80988 | 0.904942 | − | 0.425536i | \(-0.139914\pi\) | ||||
0.904942 | + | 0.425536i | \(0.139914\pi\) | |||||||
\(450\) | −2.10307e18 | −11.9391 | ||||||||
\(451\) | −9.37785e16 | −0.524754 | ||||||||
\(452\) | −2.11456e17 | −1.16632 | ||||||||
\(453\) | 3.28723e17 | 1.78728 | ||||||||
\(454\) | −4.60474e17 | −2.46798 | ||||||||
\(455\) | 5.92992e17 | 3.13310 | ||||||||
\(456\) | −8.96802e15 | −0.0467116 | ||||||||
\(457\) | 2.87374e17 | 1.47568 | 0.737839 | − | 0.674977i | \(-0.235846\pi\) | ||||
0.737839 | + | 0.674977i | \(0.235846\pi\) | |||||||
\(458\) | −3.37859e17 | −1.71045 | ||||||||
\(459\) | −3.13000e17 | −1.56229 | ||||||||
\(460\) | −1.27616e18 | −6.28029 | ||||||||
\(461\) | −2.17081e17 | −1.05333 | −0.526667 | − | 0.850072i | \(-0.676558\pi\) | ||||
−0.526667 | + | 0.850072i | \(0.676558\pi\) | |||||||
\(462\) | 2.95506e17 | 1.41382 | ||||||||
\(463\) | −3.60580e16 | −0.170108 | −0.0850540 | − | 0.996376i | \(-0.527106\pi\) | ||||
−0.0850540 | + | 0.996376i | \(0.527106\pi\) | |||||||
\(464\) | 2.25207e17 | 1.04765 | ||||||||
\(465\) | 1.04538e18 | 4.79546 | ||||||||
\(466\) | −6.68042e17 | −3.02200 | ||||||||
\(467\) | 1.64369e17 | 0.733262 | 0.366631 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366631 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(468\) | −1.93886e18 | −8.52998 | ||||||||
\(469\) | −2.67116e17 | −1.15898 | ||||||||
\(470\) | 1.48326e17 | 0.634719 | ||||||||
\(471\) | 5.48743e16 | 0.231597 | ||||||||
\(472\) | 1.25885e18 | 5.24023 | ||||||||
\(473\) | −1.03549e16 | −0.0425157 | ||||||||
\(474\) | 5.68463e17 | 2.30220 | ||||||||
\(475\) | −5.31140e15 | −0.0212178 | ||||||||
\(476\) | −6.68464e17 | −2.63410 | ||||||||
\(477\) | −1.08909e17 | −0.423343 | ||||||||
\(478\) | −6.80457e16 | −0.260927 | ||||||||
\(479\) | 2.36207e17 | 0.893534 | 0.446767 | − | 0.894650i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894650i | \(0.352575\pi\) | |||||||
\(480\) | 4.58291e18 | 17.1031 | ||||||||
\(481\) | −3.49845e17 | −1.28805 | ||||||||
\(482\) | −1.05365e17 | −0.382728 | ||||||||
\(483\) | −5.94099e17 | −2.12913 | ||||||||
\(484\) | −6.99491e17 | −2.47336 | ||||||||
\(485\) | −6.68735e17 | −2.33310 | ||||||||
\(486\) | 1.46101e17 | 0.502942 | ||||||||
\(487\) | 1.77167e16 | 0.0601791 | 0.0300895 | − | 0.999547i | \(-0.490421\pi\) | ||||
0.0300895 | + | 0.999547i | \(0.490421\pi\) | |||||||
\(488\) | −1.36773e18 | −4.58427 | ||||||||
\(489\) | 5.80567e17 | 1.92019 | ||||||||
\(490\) | −2.54704e17 | −0.831305 | ||||||||
\(491\) | −4.33637e17 | −1.39668 | −0.698339 | − | 0.715767i | \(-0.746077\pi\) | ||||
−0.698339 | + | 0.715767i | \(0.746077\pi\) | |||||||
\(492\) | −2.23106e18 | −7.09151 | ||||||||
\(493\) | 6.36040e16 | 0.199517 | ||||||||
\(494\) | −6.60200e15 | −0.0204385 | ||||||||
\(495\) | −5.00203e17 | −1.52831 | ||||||||
\(496\) | −2.00194e18 | −6.03698 | ||||||||
\(497\) | 3.18300e17 | 0.947372 | ||||||||
\(498\) | −3.26191e17 | −0.958255 | ||||||||
\(499\) | 3.40601e17 | 0.987625 | 0.493813 | − | 0.869568i | \(-0.335603\pi\) | ||||
0.493813 | + | 0.869568i | \(0.335603\pi\) | |||||||
\(500\) | 3.84018e18 | 10.9912 | ||||||||
\(501\) | −8.91394e17 | −2.51840 | ||||||||
\(502\) | 5.11738e17 | 1.42716 | ||||||||
\(503\) | 6.25663e17 | 1.72246 | 0.861228 | − | 0.508218i | \(-0.169696\pi\) | ||||
0.861228 | + | 0.508218i | \(0.169696\pi\) | |||||||
\(504\) | 3.08966e18 | 8.39677 | ||||||||
\(505\) | −2.31053e15 | −0.00619895 | ||||||||
\(506\) | −3.05123e17 | −0.808158 | ||||||||
\(507\) | −7.09416e17 | −1.85502 | ||||||||
\(508\) | −6.79031e17 | −1.75297 | ||||||||
\(509\) | −6.84799e17 | −1.74541 | −0.872706 | − | 0.488247i | \(-0.837637\pi\) | ||||
−0.872706 | + | 0.488247i | \(0.837637\pi\) | |||||||
\(510\) | 2.26240e18 | 5.69328 | ||||||||
\(511\) | −8.84316e16 | −0.219721 | ||||||||
\(512\) | −2.21228e18 | −5.42732 | ||||||||
\(513\) | 5.60609e15 | 0.0135799 | ||||||||
\(514\) | −1.11673e17 | −0.267108 | ||||||||
\(515\) | 4.05791e17 | 0.958419 | ||||||||
\(516\) | −2.46351e17 | −0.574556 | ||||||||
\(517\) | 2.63034e16 | 0.0605791 | ||||||||
\(518\) | 8.55399e17 | 1.94547 | ||||||||
\(519\) | −8.41980e16 | −0.189110 | ||||||||
\(520\) | 4.72220e18 | 10.4742 | ||||||||
\(521\) | −8.01589e17 | −1.75593 | −0.877963 | − | 0.478728i | \(-0.841098\pi\) | ||||
−0.877963 | + | 0.478728i | \(0.841098\pi\) | |||||||
\(522\) | −4.51071e17 | −0.975858 | ||||||||
\(523\) | −1.93207e17 | −0.412821 | −0.206411 | − | 0.978465i | \(-0.566178\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566178\pi\) | |||||||
\(524\) | 1.04251e18 | 2.20001 | ||||||||
\(525\) | 2.71369e18 | 5.65619 | ||||||||
\(526\) | 3.35581e16 | 0.0690859 | ||||||||
\(527\) | −5.65397e17 | −1.14970 | ||||||||
\(528\) | 1.42056e18 | 2.85324 | ||||||||
\(529\) | 1.09396e17 | 0.217039 | ||||||||
\(530\) | 4.06995e17 | 0.797620 | ||||||||
\(531\) | −1.52207e18 | −2.94659 | ||||||||
\(532\) | 1.19727e16 | 0.0228964 | ||||||||
\(533\) | −1.07044e18 | −2.02225 | ||||||||
\(534\) | −5.59695e17 | −1.04456 | ||||||||
\(535\) | 6.49672e17 | 1.19783 | ||||||||
\(536\) | −2.12714e18 | −3.87458 | ||||||||
\(537\) | 3.62254e17 | 0.651899 | ||||||||
\(538\) | 5.31621e17 | 0.945187 | ||||||||
\(539\) | −4.51678e16 | −0.0793417 | ||||||||
\(540\) | −6.15258e18 | −10.6782 | ||||||||
\(541\) | 4.64430e17 | 0.796412 | 0.398206 | − | 0.917296i | \(-0.369633\pi\) | ||||
0.398206 | + | 0.917296i | \(0.369633\pi\) | |||||||
\(542\) | −6.14786e17 | −1.04167 | ||||||||
\(543\) | −6.28278e17 | −1.05185 | ||||||||
\(544\) | −2.47868e18 | −4.10042 | ||||||||
\(545\) | 4.08930e17 | 0.668454 | ||||||||
\(546\) | 3.37307e18 | 5.44846 | ||||||||
\(547\) | 1.15138e18 | 1.83781 | 0.918903 | − | 0.394483i | \(-0.129076\pi\) | ||||
0.918903 | + | 0.394483i | \(0.129076\pi\) | |||||||
\(548\) | −1.33954e18 | −2.11291 | ||||||||
\(549\) | 1.65371e18 | 2.57774 | ||||||||
\(550\) | 1.39372e18 | 2.14693 | ||||||||
\(551\) | −1.13920e15 | −0.00173426 | ||||||||
\(552\) | −4.73102e18 | −7.11788 | ||||||||
\(553\) | −4.94619e17 | −0.735457 | ||||||||
\(554\) | 1.11254e18 | 1.63494 | ||||||||
\(555\) | −2.14726e18 | −3.11875 | ||||||||
\(556\) | 3.35328e18 | 4.81375 | ||||||||
\(557\) | −6.20451e17 | −0.880336 | −0.440168 | − | 0.897915i | \(-0.645081\pi\) | ||||
−0.440168 | + | 0.897915i | \(0.645081\pi\) | |||||||
\(558\) | 4.00972e18 | 5.62331 | ||||||||
\(559\) | −1.18197e17 | −0.163843 | ||||||||
\(560\) | −6.97002e18 | −9.55019 | ||||||||
\(561\) | 4.01201e17 | 0.543380 | ||||||||
\(562\) | 1.33634e18 | 1.78908 | ||||||||
\(563\) | 1.00927e17 | 0.133569 | 0.0667844 | − | 0.997767i | \(-0.478726\pi\) | ||||
0.0667844 | + | 0.997767i | \(0.478726\pi\) | |||||||
\(564\) | 6.25777e17 | 0.818663 | ||||||||
\(565\) | −6.22699e17 | −0.805311 | ||||||||
\(566\) | −5.79985e17 | −0.741498 | ||||||||
\(567\) | −1.05996e18 | −1.33968 | ||||||||
\(568\) | 2.53474e18 | 3.16715 | ||||||||
\(569\) | −3.73997e17 | −0.461996 | −0.230998 | − | 0.972954i | \(-0.574199\pi\) | ||||
−0.230998 | + | 0.972954i | \(0.574199\pi\) | |||||||
\(570\) | −4.05213e16 | −0.0494877 | ||||||||
\(571\) | −9.79136e17 | −1.18225 | −0.591123 | − | 0.806581i | \(-0.701315\pi\) | ||||
−0.591123 | + | 0.806581i | \(0.701315\pi\) | |||||||
\(572\) | 1.28489e18 | 1.53388 | ||||||||
\(573\) | −1.98573e18 | −2.34377 | ||||||||
\(574\) | 2.61731e18 | 3.05441 | ||||||||
\(575\) | −2.80199e18 | −3.23315 | ||||||||
\(576\) | 9.64182e18 | 11.0005 | ||||||||
\(577\) | 1.45364e17 | 0.163989 | 0.0819944 | − | 0.996633i | \(-0.473871\pi\) | ||||
0.0819944 | + | 0.996633i | \(0.473871\pi\) | |||||||
\(578\) | 5.40236e17 | 0.602633 | ||||||||
\(579\) | 2.01549e18 | 2.22316 | ||||||||
\(580\) | 1.25025e18 | 1.36369 | ||||||||
\(581\) | 2.83818e17 | 0.306123 | ||||||||
\(582\) | −3.80392e18 | −4.05725 | ||||||||
\(583\) | 7.21743e16 | 0.0761267 | ||||||||
\(584\) | −7.04211e17 | −0.734547 | ||||||||
\(585\) | −5.70959e18 | −5.88968 | ||||||||
\(586\) | 2.72158e18 | 2.77643 | ||||||||
\(587\) | −4.65718e17 | −0.469868 | −0.234934 | − | 0.972011i | \(-0.575487\pi\) | ||||
−0.234934 | + | 0.972011i | \(0.575487\pi\) | |||||||
\(588\) | −1.07458e18 | −1.07222 | ||||||||
\(589\) | 1.01267e16 | 0.00999354 | ||||||||
\(590\) | 5.68802e18 | 5.55166 | ||||||||
\(591\) | 1.29326e17 | 0.124844 | ||||||||
\(592\) | 4.11207e18 | 3.92618 | ||||||||
\(593\) | 1.31998e18 | 1.24656 | 0.623278 | − | 0.782000i | \(-0.285800\pi\) | ||||
0.623278 | + | 0.782000i | \(0.285800\pi\) | |||||||
\(594\) | −1.47104e18 | −1.37409 | ||||||||
\(595\) | −1.96851e18 | −1.81877 | ||||||||
\(596\) | −1.89809e18 | −1.73467 | ||||||||
\(597\) | −3.49375e18 | −3.15834 | ||||||||
\(598\) | −3.48284e18 | −3.11441 | ||||||||
\(599\) | 7.50536e16 | 0.0663891 | 0.0331946 | − | 0.999449i | \(-0.489432\pi\) | ||||
0.0331946 | + | 0.999449i | \(0.489432\pi\) | |||||||
\(600\) | 2.16100e19 | 18.9092 | ||||||||
\(601\) | −8.02156e17 | −0.694344 | −0.347172 | − | 0.937801i | \(-0.612858\pi\) | ||||
−0.347172 | + | 0.937801i | \(0.612858\pi\) | |||||||
\(602\) | 2.89000e17 | 0.247469 | ||||||||
\(603\) | 2.57191e18 | 2.17868 | ||||||||
\(604\) | −3.49480e18 | −2.92875 | ||||||||
\(605\) | −2.05988e18 | −1.70778 | ||||||||
\(606\) | −1.31428e16 | −0.0107800 | ||||||||
\(607\) | −3.24862e17 | −0.263617 | −0.131808 | − | 0.991275i | \(-0.542078\pi\) | ||||
−0.131808 | + | 0.991275i | \(0.542078\pi\) | |||||||
\(608\) | 4.43952e16 | 0.0356421 | ||||||||
\(609\) | 5.82036e17 | 0.462315 | ||||||||
\(610\) | −6.17997e18 | −4.85671 | ||||||||
\(611\) | 3.00241e17 | 0.233454 | ||||||||
\(612\) | 6.43627e18 | 4.95165 | ||||||||
\(613\) | −2.25554e18 | −1.71695 | −0.858476 | − | 0.512854i | \(-0.828588\pi\) | ||||
−0.858476 | + | 0.512854i | \(0.828588\pi\) | |||||||
\(614\) | −4.72022e18 | −3.55523 | ||||||||
\(615\) | −6.57008e18 | −4.89646 | ||||||||
\(616\) | −2.04753e18 | −1.50993 | ||||||||
\(617\) | 1.09822e18 | 0.801373 | 0.400687 | − | 0.916215i | \(-0.368772\pi\) | ||||
0.400687 | + | 0.916215i | \(0.368772\pi\) | |||||||
\(618\) | 2.30823e18 | 1.66669 | ||||||||
\(619\) | 1.18029e18 | 0.843333 | 0.421666 | − | 0.906751i | \(-0.361445\pi\) | ||||
0.421666 | + | 0.906751i | \(0.361445\pi\) | |||||||
\(620\) | −1.11139e19 | −7.85815 | ||||||||
\(621\) | 2.95745e18 | 2.06930 | ||||||||
\(622\) | −1.04834e17 | −0.0725879 | ||||||||
\(623\) | 4.86990e17 | 0.333693 | ||||||||
\(624\) | 1.62150e19 | 10.9956 | ||||||||
\(625\) | 6.94153e18 | 4.65838 | ||||||||
\(626\) | 2.20508e18 | 1.46450 | ||||||||
\(627\) | −7.18584e15 | −0.00472322 | ||||||||
\(628\) | −5.83392e17 | −0.379510 | ||||||||
\(629\) | 1.16135e18 | 0.747713 | ||||||||
\(630\) | 1.39604e19 | 8.89578 | ||||||||
\(631\) | −1.91174e18 | −1.20569 | −0.602847 | − | 0.797857i | \(-0.705967\pi\) | ||||
−0.602847 | + | 0.797857i | \(0.705967\pi\) | |||||||
\(632\) | −3.93882e18 | −2.45870 | ||||||||
\(633\) | −2.27949e18 | −1.40836 | ||||||||
\(634\) | −1.20763e18 | −0.738504 | ||||||||
\(635\) | −1.99963e18 | −1.21037 | ||||||||
\(636\) | 1.71708e18 | 1.02877 | ||||||||
\(637\) | −5.15570e17 | −0.305761 | ||||||||
\(638\) | 2.98927e17 | 0.175481 | ||||||||
\(639\) | −3.06474e18 | −1.78089 | ||||||||
\(640\) | −1.90633e19 | −10.9655 | ||||||||
\(641\) | 2.33767e18 | 1.33109 | 0.665544 | − | 0.746358i | \(-0.268200\pi\) | ||||
0.665544 | + | 0.746358i | \(0.268200\pi\) | |||||||
\(642\) | 3.69548e18 | 2.08302 | ||||||||
\(643\) | −1.43444e18 | −0.800405 | −0.400202 | − | 0.916427i | \(-0.631060\pi\) | ||||
−0.400202 | + | 0.916427i | \(0.631060\pi\) | |||||||
\(644\) | 6.31613e18 | 3.48894 | ||||||||
\(645\) | −7.25461e17 | −0.396713 | ||||||||
\(646\) | 2.19161e16 | 0.0118646 | ||||||||
\(647\) | −1.59309e17 | −0.0853814 | −0.0426907 | − | 0.999088i | \(-0.513593\pi\) | ||||
−0.0426907 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(648\) | −8.44086e18 | −4.47867 | ||||||||
\(649\) | 1.00868e18 | 0.529863 | ||||||||
\(650\) | 1.59087e19 | 8.27365 | ||||||||
\(651\) | −5.17392e18 | −2.66405 | ||||||||
\(652\) | −6.17226e18 | −3.14655 | ||||||||
\(653\) | 1.39803e18 | 0.705635 | 0.352818 | − | 0.935692i | \(-0.385224\pi\) | ||||
0.352818 | + | 0.935692i | \(0.385224\pi\) | |||||||
\(654\) | 2.32609e18 | 1.16244 | ||||||||
\(655\) | 3.07000e18 | 1.51904 | ||||||||
\(656\) | 1.25819e19 | 6.16414 | ||||||||
\(657\) | 8.51458e17 | 0.413037 | ||||||||
\(658\) | −7.34113e17 | −0.352610 | ||||||||
\(659\) | 1.98080e17 | 0.0942074 | 0.0471037 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471037 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(660\) | 7.88633e18 | 3.71398 | ||||||||
\(661\) | 4.09992e18 | 1.91190 | 0.955951 | − | 0.293528i | \(-0.0948293\pi\) | ||||
0.955951 | + | 0.293528i | \(0.0948293\pi\) | |||||||
\(662\) | −7.48929e18 | −3.45831 | ||||||||
\(663\) | 4.57953e18 | 2.09403 | ||||||||
\(664\) | 2.26014e18 | 1.02340 | ||||||||
\(665\) | 3.52576e16 | 0.0158093 | ||||||||
\(666\) | −8.23616e18 | −3.65714 | ||||||||
\(667\) | −6.00977e17 | −0.264265 | ||||||||
\(668\) | 9.47681e18 | 4.12682 | ||||||||
\(669\) | 4.46404e18 | 1.92512 | ||||||||
\(670\) | −9.61131e18 | −4.10484 | ||||||||
\(671\) | −1.09592e18 | −0.463536 | ||||||||
\(672\) | −2.26823e19 | −9.50138 | ||||||||
\(673\) | −1.34946e18 | −0.559839 | −0.279920 | − | 0.960023i | \(-0.590308\pi\) | ||||
−0.279920 | + | 0.960023i | \(0.590308\pi\) | |||||||
\(674\) | −2.05332e18 | −0.843658 | ||||||||
\(675\) | −1.35089e19 | −5.49723 | ||||||||
\(676\) | 7.54211e18 | 3.03976 | ||||||||
\(677\) | 1.82857e18 | 0.729936 | 0.364968 | − | 0.931020i | \(-0.381080\pi\) | ||||
0.364968 | + | 0.931020i | \(0.381080\pi\) | |||||||
\(678\) | −3.54206e18 | −1.40043 | ||||||||
\(679\) | 3.30978e18 | 1.29612 | ||||||||
\(680\) | −1.56759e19 | −6.08030 | ||||||||
\(681\) | −5.72092e18 | −2.19791 | ||||||||
\(682\) | −2.65726e18 | −1.01120 | ||||||||
\(683\) | 1.26830e18 | 0.478065 | 0.239032 | − | 0.971012i | \(-0.423170\pi\) | ||||
0.239032 | + | 0.971012i | \(0.423170\pi\) | |||||||
\(684\) | −1.15279e17 | −0.0430412 | ||||||||
\(685\) | −3.94470e18 | −1.45890 | ||||||||
\(686\) | −4.65486e18 | −1.70530 | ||||||||
\(687\) | −4.19756e18 | −1.52327 | ||||||||
\(688\) | 1.38928e18 | 0.499420 | ||||||||
\(689\) | 8.23838e17 | 0.293371 | ||||||||
\(690\) | −2.13768e19 | −7.54090 | ||||||||
\(691\) | −2.66885e18 | −0.932645 | −0.466323 | − | 0.884615i | \(-0.654421\pi\) | ||||
−0.466323 | + | 0.884615i | \(0.654421\pi\) | |||||||
\(692\) | 8.95146e17 | 0.309888 | ||||||||
\(693\) | 2.47566e18 | 0.849035 | ||||||||
\(694\) | −5.94965e18 | −2.02141 | ||||||||
\(695\) | 9.87480e18 | 3.32374 | ||||||||
\(696\) | 4.63496e18 | 1.54556 | ||||||||
\(697\) | 3.55345e18 | 1.17392 | ||||||||
\(698\) | 1.77716e18 | 0.581657 | ||||||||
\(699\) | −8.29975e18 | −2.69131 | ||||||||
\(700\) | −2.88504e19 | −9.26861 | ||||||||
\(701\) | −3.51309e18 | −1.11821 | −0.559104 | − | 0.829097i | \(-0.688855\pi\) | ||||
−0.559104 | + | 0.829097i | \(0.688855\pi\) | |||||||
\(702\) | −1.67913e19 | −5.29534 | ||||||||
\(703\) | −2.08008e16 | −0.00649934 | ||||||||
\(704\) | −6.38969e18 | −1.97814 | ||||||||
\(705\) | 1.84280e18 | 0.565262 | ||||||||
\(706\) | 9.08234e18 | 2.76037 | ||||||||
\(707\) | 1.14356e16 | 0.00344375 | ||||||||
\(708\) | 2.39973e19 | 7.16056 | ||||||||
\(709\) | −3.85661e18 | −1.14026 | −0.570131 | − | 0.821554i | \(-0.693108\pi\) | ||||
−0.570131 | + | 0.821554i | \(0.693108\pi\) | |||||||
\(710\) | 1.14530e19 | 3.35537 | ||||||||
\(711\) | 4.76241e18 | 1.38253 | ||||||||
\(712\) | 3.87807e18 | 1.11557 | ||||||||
\(713\) | 5.34228e18 | 1.52281 | ||||||||
\(714\) | −1.11973e19 | −3.16283 | ||||||||
\(715\) | 3.78378e18 | 1.05910 | ||||||||
\(716\) | −3.85128e18 | −1.06824 | ||||||||
\(717\) | −8.45400e17 | −0.232374 | ||||||||
\(718\) | −5.06428e18 | −1.37946 | ||||||||
\(719\) | 2.57885e18 | 0.696127 | 0.348063 | − | 0.937471i | \(-0.386839\pi\) | ||||
0.348063 | + | 0.937471i | \(0.386839\pi\) | |||||||
\(720\) | 6.71104e19 | 17.9527 | ||||||||
\(721\) | −2.00839e18 | −0.532437 | ||||||||
\(722\) | 7.48863e18 | 1.96748 | ||||||||
\(723\) | −1.30905e18 | −0.340846 | ||||||||
\(724\) | 6.67950e18 | 1.72363 | ||||||||
\(725\) | 2.74510e18 | 0.702039 | ||||||||
\(726\) | −1.17171e19 | −2.96982 | ||||||||
\(727\) | −6.19582e18 | −1.55641 | −0.778206 | − | 0.628009i | \(-0.783870\pi\) | ||||
−0.778206 | + | 0.628009i | \(0.783870\pi\) | |||||||
\(728\) | −2.33717e19 | −5.81884 | ||||||||
\(729\) | −3.11409e18 | −0.768427 | ||||||||
\(730\) | −3.18193e18 | −0.778201 | ||||||||
\(731\) | 3.92368e17 | 0.0951110 | ||||||||
\(732\) | −2.60729e19 | −6.26422 | ||||||||
\(733\) | −8.44589e17 | −0.201127 | −0.100563 | − | 0.994931i | \(-0.532065\pi\) | ||||
−0.100563 | + | 0.994931i | \(0.532065\pi\) | |||||||
\(734\) | −3.63126e18 | −0.857102 | ||||||||
\(735\) | −3.16444e18 | −0.740336 | ||||||||
\(736\) | 2.34204e19 | 5.43111 | ||||||||
\(737\) | −1.70442e18 | −0.391776 | ||||||||
\(738\) | −2.52006e19 | −5.74175 | ||||||||
\(739\) | −4.17152e18 | −0.942117 | −0.471059 | − | 0.882102i | \(-0.656128\pi\) | ||||
−0.471059 | + | 0.882102i | \(0.656128\pi\) | |||||||
\(740\) | 2.28285e19 | 5.11058 | ||||||||
\(741\) | −8.20232e16 | −0.0182020 | ||||||||
\(742\) | −2.01435e18 | −0.443107 | ||||||||
\(743\) | 3.56985e18 | 0.778436 | 0.389218 | − | 0.921146i | \(-0.372745\pi\) | ||||
0.389218 | + | 0.921146i | \(0.372745\pi\) | |||||||
\(744\) | −4.12017e19 | −8.90617 | ||||||||
\(745\) | −5.58954e18 | −1.19773 | ||||||||
\(746\) | 1.09118e18 | 0.231789 | ||||||||
\(747\) | −2.73273e18 | −0.575456 | ||||||||
\(748\) | −4.26535e18 | −0.890418 | ||||||||
\(749\) | −3.21544e18 | −0.665439 | ||||||||
\(750\) | 6.43261e19 | 13.1974 | ||||||||
\(751\) | −2.79175e18 | −0.567828 | −0.283914 | − | 0.958850i | \(-0.591633\pi\) | ||||
−0.283914 | + | 0.958850i | \(0.591633\pi\) | |||||||
\(752\) | −3.52903e18 | −0.711605 | ||||||||
\(753\) | 6.35783e18 | 1.27099 | ||||||||
\(754\) | 3.41212e18 | 0.676255 | ||||||||
\(755\) | −1.02916e19 | −2.02221 | ||||||||
\(756\) | 3.04511e19 | 5.93213 | ||||||||
\(757\) | 6.80907e18 | 1.31512 | 0.657559 | − | 0.753403i | \(-0.271589\pi\) | ||||
0.657559 | + | 0.753403i | \(0.271589\pi\) | |||||||
\(758\) | 1.54502e19 | 2.95859 | ||||||||
\(759\) | −3.79084e18 | −0.719721 | ||||||||
\(760\) | 2.80768e17 | 0.0528518 | ||||||||
\(761\) | −1.38388e18 | −0.258284 | −0.129142 | − | 0.991626i | \(-0.541222\pi\) | ||||
−0.129142 | + | 0.991626i | \(0.541222\pi\) | |||||||
\(762\) | −1.13743e19 | −2.10484 | ||||||||
\(763\) | −2.02392e18 | −0.371351 | ||||||||
\(764\) | 2.11112e19 | 3.84066 | ||||||||
\(765\) | 1.89537e19 | 3.41896 | ||||||||
\(766\) | 2.30640e16 | 0.00412523 | ||||||||
\(767\) | 1.15137e19 | 2.04194 | ||||||||
\(768\) | −5.54951e19 | −9.75904 | ||||||||
\(769\) | −1.00650e19 | −1.75506 | −0.877532 | − | 0.479517i | \(-0.840812\pi\) | ||||
−0.877532 | + | 0.479517i | \(0.840812\pi\) | |||||||
\(770\) | −9.25163e18 | −1.59966 | ||||||||
\(771\) | −1.38742e18 | −0.237878 | ||||||||
\(772\) | −2.14276e19 | −3.64301 | ||||||||
\(773\) | 1.17031e18 | 0.197303 | 0.0986516 | − | 0.995122i | \(-0.468547\pi\) | ||||
0.0986516 | + | 0.995122i | \(0.468547\pi\) | |||||||
\(774\) | −2.78262e18 | −0.465198 | ||||||||
\(775\) | −2.44021e19 | −4.04545 | ||||||||
\(776\) | 2.63569e19 | 4.33305 | ||||||||
\(777\) | 1.06275e19 | 1.73258 | ||||||||
\(778\) | −1.18844e19 | −1.92136 | ||||||||
\(779\) | −6.36452e16 | −0.0102040 | ||||||||
\(780\) | 9.00190e19 | 14.3126 | ||||||||
\(781\) | 2.03102e18 | 0.320245 | ||||||||
\(782\) | 1.15617e19 | 1.80791 | ||||||||
\(783\) | −2.89740e18 | −0.449322 | ||||||||
\(784\) | 6.06000e18 | 0.932005 | ||||||||
\(785\) | −1.71799e18 | −0.262040 | ||||||||
\(786\) | 1.74628e19 | 2.64161 | ||||||||
\(787\) | −9.73964e17 | −0.146119 | −0.0730596 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730596 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(788\) | −1.37493e18 | −0.204578 | ||||||||
\(789\) | 4.16925e17 | 0.0615259 | ||||||||
\(790\) | −1.77973e19 | −2.60482 | ||||||||
\(791\) | 3.08194e18 | 0.447380 | ||||||||
\(792\) | 1.97146e19 | 2.83840 | ||||||||
\(793\) | −1.25095e19 | −1.78634 | ||||||||
\(794\) | 1.46371e19 | 2.07311 | ||||||||
\(795\) | 5.05650e18 | 0.710336 | ||||||||
\(796\) | 3.71436e19 | 5.17546 | ||||||||
\(797\) | 1.30069e18 | 0.179760 | 0.0898802 | − | 0.995953i | \(-0.471352\pi\) | ||||
0.0898802 | + | 0.995953i | \(0.471352\pi\) | |||||||
\(798\) | 2.00553e17 | 0.0274923 | ||||||||
\(799\) | −9.96686e17 | −0.135520 | ||||||||
\(800\) | −1.06978e20 | −14.4281 | ||||||||
\(801\) | −4.68895e18 | −0.627284 | ||||||||
\(802\) | −2.58130e19 | −3.42535 | ||||||||
\(803\) | −5.64266e17 | −0.0742733 | ||||||||
\(804\) | −4.05494e19 | −5.29445 | ||||||||
\(805\) | 1.85999e19 | 2.40900 | ||||||||
\(806\) | −3.03315e19 | −3.89687 | ||||||||
\(807\) | 6.60486e18 | 0.841755 | ||||||||
\(808\) | 9.10653e16 | 0.0115128 | ||||||||
\(809\) | −7.49277e18 | −0.939674 | −0.469837 | − | 0.882753i | \(-0.655687\pi\) | ||||
−0.469837 | + | 0.882753i | \(0.655687\pi\) | |||||||
\(810\) | −3.81394e19 | −4.74484 | ||||||||
\(811\) | −1.49228e19 | −1.84168 | −0.920840 | − | 0.389940i | \(-0.872496\pi\) | ||||
−0.920840 | + | 0.389940i | \(0.872496\pi\) | |||||||
\(812\) | −6.18789e18 | −0.757579 | ||||||||
\(813\) | −7.63810e18 | −0.927677 | ||||||||
\(814\) | 5.45815e18 | 0.657637 | ||||||||
\(815\) | −1.81762e19 | −2.17260 | ||||||||
\(816\) | −5.38278e19 | −6.38293 | ||||||||
\(817\) | −7.02763e15 | −0.000826734 0 | ||||||||
\(818\) | 2.29840e19 | 2.68244 | ||||||||
\(819\) | 2.82586e19 | 3.27194 | ||||||||
\(820\) | 6.98495e19 | 8.02367 | ||||||||
\(821\) | 1.17393e18 | 0.133787 | 0.0668933 | − | 0.997760i | \(-0.478691\pi\) | ||||
0.0668933 | + | 0.997760i | \(0.478691\pi\) | |||||||
\(822\) | −2.24383e19 | −2.53702 | ||||||||
\(823\) | −2.20418e18 | −0.247257 | −0.123628 | − | 0.992329i | \(-0.539453\pi\) | ||||
−0.123628 | + | 0.992329i | \(0.539453\pi\) | |||||||
\(824\) | −1.59935e19 | −1.77999 | ||||||||
\(825\) | 1.73155e19 | 1.91199 | ||||||||
\(826\) | −2.81518e19 | −3.08415 | ||||||||
\(827\) | −5.49950e18 | −0.597774 | −0.298887 | − | 0.954288i | \(-0.596615\pi\) | ||||
−0.298887 | + | 0.954288i | \(0.596615\pi\) | |||||||
\(828\) | −6.08145e19 | −6.55858 | ||||||||
\(829\) | −6.12336e18 | −0.655217 | −0.327608 | − | 0.944814i | \(-0.606243\pi\) | ||||
−0.327608 | + | 0.944814i | \(0.606243\pi\) | |||||||
\(830\) | 1.02123e19 | 1.08422 | ||||||||
\(831\) | 1.38222e19 | 1.45603 | ||||||||
\(832\) | −7.29354e19 | −7.62319 | ||||||||
\(833\) | 1.71150e18 | 0.177494 | ||||||||
\(834\) | 5.61701e19 | 5.77998 | ||||||||
\(835\) | 2.79075e19 | 2.84944 | ||||||||
\(836\) | 7.63958e16 | 0.00773978 | ||||||||
\(837\) | 2.57560e19 | 2.58918 | ||||||||
\(838\) | 2.08300e19 | 2.07780 | ||||||||
\(839\) | −9.02974e18 | −0.893763 | −0.446882 | − | 0.894593i | \(-0.647465\pi\) | ||||
−0.446882 | + | 0.894593i | \(0.647465\pi\) | |||||||
\(840\) | −1.43449e20 | −14.0891 | ||||||||
\(841\) | −9.67185e18 | −0.942618 | ||||||||
\(842\) | 1.18478e19 | 1.14580 | ||||||||
\(843\) | 1.66027e19 | 1.59330 | ||||||||
\(844\) | 2.42342e19 | 2.30783 | ||||||||
\(845\) | 2.22102e19 | 2.09886 | ||||||||
\(846\) | 7.06836e18 | 0.662844 | ||||||||
\(847\) | 1.01950e19 | 0.948734 | ||||||||
\(848\) | −9.68337e18 | −0.894239 | ||||||||
\(849\) | −7.20573e18 | −0.660356 | ||||||||
\(850\) | −5.28107e19 | −4.80285 | ||||||||
\(851\) | −1.09733e19 | −0.990365 | ||||||||
\(852\) | 4.83195e19 | 4.32778 | ||||||||
\(853\) | −6.55050e18 | −0.582245 | −0.291122 | − | 0.956686i | \(-0.594029\pi\) | ||||
−0.291122 | + | 0.956686i | \(0.594029\pi\) | |||||||
\(854\) | 3.05867e19 | 2.69809 | ||||||||
\(855\) | −3.39475e17 | −0.0297186 | ||||||||
\(856\) | −2.56056e19 | −2.22462 | ||||||||
\(857\) | 6.50889e18 | 0.561218 | 0.280609 | − | 0.959822i | \(-0.409464\pi\) | ||||
0.280609 | + | 0.959822i | \(0.409464\pi\) | |||||||
\(858\) | 2.15230e19 | 1.84177 | ||||||||
\(859\) | 9.41857e18 | 0.799888 | 0.399944 | − | 0.916540i | \(-0.369030\pi\) | ||||
0.399944 | + | 0.916540i | \(0.369030\pi\) | |||||||
\(860\) | 7.71270e18 | 0.650080 | ||||||||
\(861\) | 3.25174e19 | 2.72017 | ||||||||
\(862\) | 2.43811e18 | 0.202422 | ||||||||
\(863\) | −2.27295e19 | −1.87292 | −0.936462 | − | 0.350770i | \(-0.885920\pi\) | ||||
−0.936462 | + | 0.350770i | \(0.885920\pi\) | |||||||
\(864\) | 1.12914e20 | 9.23436 | ||||||||
\(865\) | 2.63605e18 | 0.213968 | ||||||||
\(866\) | 2.73743e19 | 2.20534 | ||||||||
\(867\) | 6.71189e18 | 0.536687 | ||||||||
\(868\) | 5.50062e19 | 4.36549 | ||||||||
\(869\) | −3.15607e18 | −0.248610 | ||||||||
\(870\) | 2.09427e19 | 1.63741 | ||||||||
\(871\) | −1.94552e19 | −1.50979 | ||||||||
\(872\) | −1.61172e19 | −1.24146 | ||||||||
\(873\) | −3.18680e19 | −2.43648 | ||||||||
\(874\) | −2.07079e17 | −0.0157149 | ||||||||
\(875\) | −5.59700e19 | −4.21603 | ||||||||
\(876\) | −1.34243e19 | −1.00373 | ||||||||
\(877\) | 1.76604e19 | 1.31070 | 0.655349 | − | 0.755326i | \(-0.272521\pi\) | ||||
0.655349 | + | 0.755326i | \(0.272521\pi\) | |||||||
\(878\) | 4.18638e18 | 0.308407 | ||||||||
\(879\) | 3.38129e19 | 2.47260 | ||||||||
\(880\) | −4.44745e19 | −3.22830 | ||||||||
\(881\) | 5.96749e18 | 0.429980 | 0.214990 | − | 0.976616i | \(-0.431028\pi\) | ||||
0.214990 | + | 0.976616i | \(0.431028\pi\) | |||||||
\(882\) | −1.21377e19 | −0.868142 | ||||||||
\(883\) | −2.08226e19 | −1.47840 | −0.739199 | − | 0.673487i | \(-0.764796\pi\) | ||||
−0.739199 | + | 0.673487i | \(0.764796\pi\) | |||||||
\(884\) | −4.86871e19 | −3.43142 | ||||||||
\(885\) | 7.06679e19 | 4.94414 | ||||||||
\(886\) | −2.31696e19 | −1.60916 | ||||||||
\(887\) | 2.04703e19 | 1.41130 | 0.705652 | − | 0.708559i | \(-0.250654\pi\) | ||||
0.705652 | + | 0.708559i | \(0.250654\pi\) | |||||||
\(888\) | 8.46302e19 | 5.79217 | ||||||||
\(889\) | 9.89678e18 | 0.672408 | ||||||||
\(890\) | 1.75228e19 | 1.18186 | ||||||||
\(891\) | −6.76344e18 | −0.452858 | ||||||||
\(892\) | −4.74591e19 | −3.15463 | ||||||||
\(893\) | 1.78514e16 | 0.00117798 | ||||||||
\(894\) | −3.17946e19 | −2.08286 | ||||||||
\(895\) | −1.13413e19 | −0.737589 | ||||||||
\(896\) | 9.43505e19 | 6.09175 | ||||||||
\(897\) | −4.32708e19 | −2.77360 | ||||||||
\(898\) | −5.59603e19 | −3.56110 | ||||||||
\(899\) | −5.23381e18 | −0.330659 | ||||||||
\(900\) | 2.77784e20 | 17.4233 | ||||||||
\(901\) | −2.73483e18 | −0.170302 | ||||||||
\(902\) | 1.67006e19 | 1.03250 | ||||||||
\(903\) | 3.59054e18 | 0.220389 | ||||||||
\(904\) | 2.45425e19 | 1.49563 | ||||||||
\(905\) | 1.96699e19 | 1.19011 | ||||||||
\(906\) | −5.85407e19 | −3.51662 | ||||||||
\(907\) | 4.29432e18 | 0.256122 | 0.128061 | − | 0.991766i | \(-0.459125\pi\) | ||||
0.128061 | + | 0.991766i | \(0.459125\pi\) | |||||||
\(908\) | 6.08217e19 | 3.60164 | ||||||||
\(909\) | −1.10107e17 | −0.00647363 | ||||||||
\(910\) | −1.05603e20 | −6.16465 | ||||||||
\(911\) | 7.01680e18 | 0.406696 | 0.203348 | − | 0.979107i | \(-0.434818\pi\) | ||||
0.203348 | + | 0.979107i | \(0.434818\pi\) | |||||||
\(912\) | 9.64099e17 | 0.0554824 | ||||||||
\(913\) | 1.81099e18 | 0.103480 | ||||||||
\(914\) | −5.11771e19 | −2.90352 | ||||||||
\(915\) | −7.67800e19 | −4.32525 | ||||||||
\(916\) | 4.46261e19 | 2.49614 | ||||||||
\(917\) | −1.51944e19 | −0.843884 | ||||||||
\(918\) | 5.57408e19 | 3.07394 | ||||||||
\(919\) | −1.05945e19 | −0.580138 | −0.290069 | − | 0.957006i | \(-0.593678\pi\) | ||||
−0.290069 | + | 0.957006i | \(0.593678\pi\) | |||||||
\(920\) | 1.48117e20 | 8.05351 | ||||||||
\(921\) | −5.86440e19 | −3.16618 | ||||||||
\(922\) | 3.86590e19 | 2.07252 | ||||||||
\(923\) | 2.31832e19 | 1.23413 | ||||||||
\(924\) | −3.90320e19 | −2.06325 | ||||||||
\(925\) | 5.01231e19 | 2.63097 | ||||||||
\(926\) | 6.42140e18 | 0.334702 | ||||||||
\(927\) | 1.93376e19 | 1.00089 | ||||||||
\(928\) | −2.29449e19 | −1.17930 | ||||||||
\(929\) | 3.37128e19 | 1.72065 | 0.860325 | − | 0.509745i | \(-0.170260\pi\) | ||||
0.860325 | + | 0.509745i | \(0.170260\pi\) | |||||||
\(930\) | −1.86167e20 | −9.43546 | ||||||||
\(931\) | −3.06543e16 | −0.00154283 | ||||||||
\(932\) | 8.82383e19 | 4.41015 | ||||||||
\(933\) | −1.30246e18 | −0.0646446 | ||||||||
\(934\) | −2.92716e19 | −1.44275 | ||||||||
\(935\) | −1.25607e19 | −0.614806 | ||||||||
\(936\) | 2.25033e20 | 10.9384 | ||||||||
\(937\) | −2.27391e19 | −1.09765 | −0.548827 | − | 0.835936i | \(-0.684926\pi\) | ||||
−0.548827 | + | 0.835936i | \(0.684926\pi\) | |||||||
\(938\) | 4.75694e19 | 2.28039 | ||||||||
\(939\) | 2.73958e19 | 1.30424 | ||||||||
\(940\) | −1.95916e19 | −0.926275 | ||||||||
\(941\) | −3.61551e19 | −1.69761 | −0.848803 | − | 0.528710i | \(-0.822676\pi\) | ||||
−0.848803 | + | 0.528710i | \(0.822676\pi\) | |||||||
\(942\) | −9.77230e18 | −0.455686 | ||||||||
\(943\) | −3.35756e19 | −1.55488 | ||||||||
\(944\) | −1.35331e20 | −6.22416 | ||||||||
\(945\) | 8.96730e19 | 4.09595 | ||||||||
\(946\) | 1.84406e18 | 0.0836532 | ||||||||
\(947\) | −9.62334e18 | −0.433562 | −0.216781 | − | 0.976220i | \(-0.569556\pi\) | ||||
−0.216781 | + | 0.976220i | \(0.569556\pi\) | |||||||
\(948\) | −7.50854e19 | −3.35971 | ||||||||
\(949\) | −6.44085e18 | −0.286228 | ||||||||
\(950\) | 9.45883e17 | 0.0417478 | ||||||||
\(951\) | −1.50036e19 | −0.657689 | ||||||||
\(952\) | 7.75851e19 | 3.37783 | ||||||||
\(953\) | 3.47215e18 | 0.150139 | 0.0750696 | − | 0.997178i | \(-0.476082\pi\) | ||||
0.0750696 | + | 0.997178i | \(0.476082\pi\) | |||||||
\(954\) | 1.93950e19 | 0.832963 | ||||||||
\(955\) | 6.21687e19 | 2.65185 | ||||||||
\(956\) | 8.98782e18 | 0.380783 | ||||||||
\(957\) | 3.71387e18 | 0.156278 | ||||||||
\(958\) | −4.20650e19 | −1.75810 | ||||||||
\(959\) | 1.95236e19 | 0.810472 | ||||||||
\(960\) | −4.47659e20 | −18.4580 | ||||||||
\(961\) | 2.21076e19 | 0.905396 | ||||||||
\(962\) | 6.23023e19 | 2.53435 | ||||||||
\(963\) | 3.09596e19 | 1.25091 | ||||||||
\(964\) | 1.39171e19 | 0.558533 | ||||||||
\(965\) | −6.31004e19 | −2.51538 | ||||||||
\(966\) | 1.05800e20 | 4.18925 | ||||||||
\(967\) | −3.43617e19 | −1.35146 | −0.675728 | − | 0.737151i | \(-0.736171\pi\) | ||||
−0.675728 | + | 0.737151i | \(0.736171\pi\) | |||||||
\(968\) | 8.11862e19 | 3.17170 | ||||||||
\(969\) | 2.72286e17 | 0.0105662 | ||||||||
\(970\) | 1.19092e20 | 4.59056 | ||||||||
\(971\) | −1.02390e19 | −0.392043 | −0.196022 | − | 0.980600i | \(-0.562802\pi\) | ||||
−0.196022 | + | 0.980600i | \(0.562802\pi\) | |||||||
\(972\) | −1.92978e19 | −0.733966 | ||||||||
\(973\) | −4.88735e19 | −1.84646 | ||||||||
\(974\) | −3.15509e18 | −0.118407 | ||||||||
\(975\) | 1.97649e20 | 7.36827 | ||||||||
\(976\) | 1.47036e20 | 5.44503 | ||||||||
\(977\) | −3.73637e19 | −1.37447 | −0.687234 | − | 0.726436i | \(-0.741175\pi\) | ||||
−0.687234 | + | 0.726436i | \(0.741175\pi\) | |||||||
\(978\) | −1.03390e20 | −3.77814 | ||||||||
\(979\) | 3.10739e18 | 0.112800 | ||||||||
\(980\) | 3.36425e19 | 1.21316 | ||||||||
\(981\) | 1.94872e19 | 0.698074 | ||||||||
\(982\) | 7.72244e19 | 2.74808 | ||||||||
\(983\) | −1.02116e19 | −0.360990 | −0.180495 | − | 0.983576i | \(-0.557770\pi\) | ||||
−0.180495 | + | 0.983576i | \(0.557770\pi\) | |||||||
\(984\) | 2.58948e20 | 9.09377 | ||||||||
\(985\) | −4.04891e18 | −0.141255 | ||||||||
\(986\) | −1.13269e19 | −0.392566 | ||||||||
\(987\) | −9.12061e18 | −0.314024 | ||||||||
\(988\) | 8.72024e17 | 0.0298269 | ||||||||
\(989\) | −3.70738e18 | −0.125977 | ||||||||
\(990\) | 8.90788e19 | 3.00708 | ||||||||
\(991\) | 4.03029e19 | 1.35163 | 0.675815 | − | 0.737071i | \(-0.263792\pi\) | ||||
0.675815 | + | 0.737071i | \(0.263792\pi\) | |||||||
\(992\) | 2.03965e20 | 6.79562 | ||||||||
\(993\) | −9.30470e19 | −3.07987 | ||||||||
\(994\) | −5.66847e19 | −1.86403 | ||||||||
\(995\) | 1.09381e20 | 3.57350 | ||||||||
\(996\) | 4.30849e19 | 1.39843 | ||||||||
\(997\) | 1.98736e19 | 0.640851 | 0.320426 | − | 0.947274i | \(-0.396174\pi\) | ||||
0.320426 | + | 0.947274i | \(0.396174\pi\) | |||||||
\(998\) | −6.06560e19 | −1.94324 | ||||||||
\(999\) | −5.29040e19 | −1.68389 |
(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 | 197.14.a.a.1.1 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.1 | ✓ | 104 | 1.1 | even | 1 | trivial |