Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,30,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(133.195105958\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25675x^{2} + 164788569 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.3 | ||
Root | \(112.802i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.30.b.a.24.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17433.9i | 0.752419i | 0.926535 | + | 0.376209i | \(0.122773\pi\) | ||||
−0.926535 | + | 0.376209i | \(0.877227\pi\) | |||||||
\(3\) | 9.52434e6i | 1.14968i | 0.818266 | + | 0.574839i | \(0.194935\pi\) | ||||
−0.818266 | + | 0.574839i | \(0.805065\pi\) | |||||||
\(4\) | 2.32930e8 | 0.433866 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.66046e11 | −0.865040 | ||||||||
\(7\) | 2.98628e12i | 1.66421i | 0.554616 | + | 0.832106i | \(0.312865\pi\) | ||||
−0.554616 | + | 0.832106i | \(0.687135\pi\) | |||||||
\(8\) | 1.34206e13i | 1.07887i | ||||||||
\(9\) | −2.20826e13 | −0.321761 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.25811e15 | −0.998906 | −0.499453 | − | 0.866341i | \(-0.666466\pi\) | ||||
−0.499453 | + | 0.866341i | \(0.666466\pi\) | |||||||
\(12\) | 2.21850e15i | 0.498806i | ||||||||
\(13\) | 6.09036e15i | 0.429007i | 0.976723 | + | 0.214503i | \(0.0688133\pi\) | ||||
−0.976723 | + | 0.214503i | \(0.931187\pi\) | |||||||
\(14\) | −5.20625e16 | −1.25219 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.08921e17 | −0.377895 | ||||||||
\(17\) | − 8.28952e16i | − 0.119404i | −0.998216 | − | 0.0597021i | \(-0.980985\pi\) | ||||
0.998216 | − | 0.0597021i | \(-0.0190151\pi\) | |||||||
\(18\) | − 3.84986e17i | − 0.242099i | ||||||||
\(19\) | −3.72257e18 | −1.06885 | −0.534424 | − | 0.845217i | \(-0.679471\pi\) | ||||
−0.534424 | + | 0.845217i | \(0.679471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.84423e19 | −1.91331 | ||||||||
\(22\) | − 2.19338e19i | − 0.751596i | ||||||||
\(23\) | − 1.69513e19i | − 0.304894i | −0.988312 | − | 0.152447i | \(-0.951285\pi\) | ||||
0.988312 | − | 0.152447i | \(-0.0487154\pi\) | |||||||
\(24\) | −1.27823e20 | −1.24035 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.06179e20 | −0.322793 | ||||||||
\(27\) | 4.43337e20i | 0.779757i | ||||||||
\(28\) | 6.95594e20i | 0.722045i | ||||||||
\(29\) | 8.81402e20 | 0.550051 | 0.275026 | − | 0.961437i | \(-0.411314\pi\) | ||||
0.275026 | + | 0.961437i | \(0.411314\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.71093e21 | 0.880518 | 0.440259 | − | 0.897871i | \(-0.354887\pi\) | ||||
0.440259 | + | 0.897871i | \(0.354887\pi\) | |||||||
\(32\) | 5.30623e21i | 0.794532i | ||||||||
\(33\) | − 1.19827e22i | − 1.14842i | ||||||||
\(34\) | 1.44519e21 | 0.0898420 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.14369e21 | −0.139601 | ||||||||
\(37\) | − 1.97746e22i | − 0.360730i | −0.983600 | − | 0.180365i | \(-0.942272\pi\) | ||||
0.983600 | − | 0.180365i | \(-0.0577279\pi\) | |||||||
\(38\) | − 6.48990e22i | − 0.804221i | ||||||||
\(39\) | −5.80066e22 | −0.493220 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00635e23 | −0.414367 | −0.207183 | − | 0.978302i | \(-0.566430\pi\) | ||||
−0.207183 | + | 0.978302i | \(0.566430\pi\) | |||||||
\(42\) | − 4.95861e23i | − 1.43961i | ||||||||
\(43\) | − 1.61886e23i | − 0.334131i | −0.985946 | − | 0.167066i | \(-0.946571\pi\) | ||||
0.985946 | − | 0.167066i | \(-0.0534291\pi\) | |||||||
\(44\) | −2.93051e23 | −0.433391 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.95527e23 | 0.229408 | ||||||||
\(47\) | 2.61745e24i | 1.48751i | 0.668453 | + | 0.743755i | \(0.266957\pi\) | ||||
−0.668453 | + | 0.743755i | \(0.733043\pi\) | |||||||
\(48\) | − 1.03740e24i | − 0.434458i | ||||||||
\(49\) | −5.69796e24 | −1.76960 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.89521e23 | 0.137277 | ||||||||
\(52\) | 1.41863e24i | 0.186131i | ||||||||
\(53\) | − 1.44856e25i | − 1.44190i | −0.692986 | − | 0.720951i | \(-0.743705\pi\) | ||||
0.692986 | − | 0.720951i | \(-0.256295\pi\) | |||||||
\(54\) | −7.72909e24 | −0.586704 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.00778e25 | −1.79547 | ||||||||
\(57\) | − 3.54550e25i | − 1.22883i | ||||||||
\(58\) | 1.53663e25i | 0.413869i | ||||||||
\(59\) | −5.87125e24 | −0.123417 | −0.0617087 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617087 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.18692e25 | −0.802032 | −0.401016 | − | 0.916071i | \(-0.631343\pi\) | ||||
−0.401016 | + | 0.916071i | \(0.631343\pi\) | |||||||
\(62\) | 6.46960e25i | 0.662519i | ||||||||
\(63\) | − 6.59448e25i | − 0.535479i | ||||||||
\(64\) | −1.50985e26 | −0.975716 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.08905e26 | 0.864094 | ||||||||
\(67\) | − 1.29243e26i | − 0.429854i | −0.976630 | − | 0.214927i | \(-0.931049\pi\) | ||||
0.976630 | − | 0.214927i | \(-0.0689514\pi\) | |||||||
\(68\) | − 1.93088e25i | − 0.0518054i | ||||||||
\(69\) | 1.61450e26 | 0.350531 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.63672e26 | −0.521751 | −0.260876 | − | 0.965372i | \(-0.584011\pi\) | ||||
−0.260876 | + | 0.965372i | \(0.584011\pi\) | |||||||
\(72\) | − 2.96362e26i | − 0.347138i | ||||||||
\(73\) | 1.45255e27i | 1.39299i | 0.717561 | + | 0.696496i | \(0.245259\pi\) | ||||
−0.717561 | + | 0.696496i | \(0.754741\pi\) | |||||||
\(74\) | 3.44748e26 | 0.271420 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.67098e26 | −0.463736 | ||||||||
\(77\) | − 3.75707e27i | − 1.66239i | ||||||||
\(78\) | − 1.01128e27i | − 0.371108i | ||||||||
\(79\) | 3.93709e27 | 1.20111 | 0.600554 | − | 0.799584i | \(-0.294947\pi\) | ||||
0.600554 | + | 0.799584i | \(0.294947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.73802e27 | −1.21823 | ||||||||
\(82\) | − 1.75447e27i | − 0.311778i | ||||||||
\(83\) | 6.61171e27i | 0.985556i | 0.870155 | + | 0.492778i | \(0.164018\pi\) | ||||
−0.870155 | + | 0.492778i | \(0.835982\pi\) | |||||||
\(84\) | −6.62507e27 | −0.830120 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.82231e27 | 0.251407 | ||||||||
\(87\) | 8.39477e27i | 0.632382i | ||||||||
\(88\) | − 1.68846e28i | − 1.07769i | ||||||||
\(89\) | −6.47986e27 | −0.351084 | −0.175542 | − | 0.984472i | \(-0.556168\pi\) | ||||
−0.175542 | + | 0.984472i | \(0.556168\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.81875e28 | −0.713959 | ||||||||
\(92\) | − 3.94847e27i | − 0.132283i | ||||||||
\(93\) | 3.53442e28i | 1.01231i | ||||||||
\(94\) | −4.56324e28 | −1.11923 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.05383e28 | −0.913457 | ||||||||
\(97\) | − 9.52029e28i | − 1.48068i | −0.672235 | − | 0.740338i | \(-0.734666\pi\) | ||||
0.672235 | − | 0.740338i | \(-0.265334\pi\) | |||||||
\(98\) | − 9.93377e28i | − 1.33148i | ||||||||
\(99\) | 2.77823e28 | 0.321409 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.65862e28 | 0.403271 | 0.201635 | − | 0.979461i | \(-0.435374\pi\) | ||||
0.201635 | + | 0.979461i | \(0.435374\pi\) | |||||||
\(102\) | 1.37644e28i | 0.103289i | ||||||||
\(103\) | − 1.34288e29i | − 0.874775i | −0.899273 | − | 0.437388i | \(-0.855904\pi\) | ||||
0.899273 | − | 0.437388i | \(-0.144096\pi\) | |||||||
\(104\) | −8.17365e28 | −0.462842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.52540e29 | 1.08491 | ||||||||
\(107\) | 4.69036e29i | 1.75850i | 0.476364 | + | 0.879248i | \(0.341955\pi\) | ||||
−0.476364 | + | 0.879248i | \(0.658045\pi\) | |||||||
\(108\) | 1.03266e29i | 0.338310i | ||||||||
\(109\) | 5.33865e29 | 1.53020 | 0.765098 | − | 0.643913i | \(-0.222690\pi\) | ||||
0.765098 | + | 0.643913i | \(0.222690\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.88340e29 | 0.414723 | ||||||||
\(112\) | − 3.25268e29i | − 0.628897i | ||||||||
\(113\) | 7.95436e29i | 1.35197i | 0.736914 | + | 0.675987i | \(0.236282\pi\) | ||||
−0.736914 | + | 0.675987i | \(0.763718\pi\) | |||||||
\(114\) | 6.18120e29 | 0.924596 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.05305e29 | 0.238648 | ||||||||
\(117\) | − 1.34491e29i | − 0.138038i | ||||||||
\(118\) | − 1.02359e29i | − 0.0928615i | ||||||||
\(119\) | 2.47548e29 | 0.198714 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.46951e27 | −0.00218716 | ||||||||
\(122\) | − 1.07862e30i | − 0.603464i | ||||||||
\(123\) | − 9.58486e29i | − 0.476389i | ||||||||
\(124\) | 8.64387e29 | 0.382027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.14968e30 | 0.402905 | ||||||||
\(127\) | − 1.93923e29i | − 0.0606003i | −0.999541 | − | 0.0303002i | \(-0.990354\pi\) | ||||
0.999541 | − | 0.0303002i | \(-0.00964632\pi\) | |||||||
\(128\) | 2.16508e29i | 0.0603851i | ||||||||
\(129\) | 1.54186e30 | 0.384143 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.32229e30 | −0.462894 | −0.231447 | − | 0.972847i | \(-0.574346\pi\) | ||||
−0.231447 | + | 0.972847i | \(0.574346\pi\) | |||||||
\(132\) | − 2.79112e30i | − 0.498260i | ||||||||
\(133\) | − 1.11166e31i | − 1.77879i | ||||||||
\(134\) | 2.25320e30 | 0.323430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.11251e30 | 0.128821 | ||||||||
\(137\) | − 1.26990e31i | − 1.32228i | −0.750263 | − | 0.661139i | \(-0.770073\pi\) | ||||
0.750263 | − | 0.661139i | \(-0.229927\pi\) | |||||||
\(138\) | 2.81470e30i | 0.263746i | ||||||||
\(139\) | −1.14547e31 | −0.966648 | −0.483324 | − | 0.875442i | \(-0.660571\pi\) | ||||
−0.483324 | + | 0.875442i | \(0.660571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.49295e31 | −1.71016 | ||||||||
\(142\) | − 6.34022e30i | − 0.392575i | ||||||||
\(143\) | − 7.66234e30i | − 0.428538i | ||||||||
\(144\) | 2.40525e30 | 0.121592 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.53236e31 | −1.04811 | ||||||||
\(147\) | − 5.42693e31i | − 2.03448i | ||||||||
\(148\) | − 4.60609e30i | − 0.156508i | ||||||||
\(149\) | 5.74280e31 | 1.76979 | 0.884897 | − | 0.465787i | \(-0.154229\pi\) | ||||
0.884897 | + | 0.465787i | \(0.154229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.07974e31 | 1.29026 | 0.645128 | − | 0.764075i | \(-0.276804\pi\) | ||||
0.645128 | + | 0.764075i | \(0.276804\pi\) | |||||||
\(152\) | − 4.99593e31i | − 1.15315i | ||||||||
\(153\) | 1.83054e30i | 0.0384197i | ||||||||
\(154\) | 6.55003e31 | 1.25082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.35115e31 | −0.213991 | ||||||||
\(157\) | 9.31373e30i | 0.134455i | 0.997738 | + | 0.0672277i | \(0.0214154\pi\) | ||||
−0.997738 | + | 0.0672277i | \(0.978585\pi\) | |||||||
\(158\) | 6.86388e31i | 0.903736i | ||||||||
\(159\) | 1.37965e32 | 1.65772 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.06213e31 | 0.507409 | ||||||||
\(162\) | − 1.00036e32i | − 0.916620i | ||||||||
\(163\) | − 4.45351e31i | − 0.373235i | −0.982433 | − | 0.186617i | \(-0.940248\pi\) | ||||
0.982433 | − | 0.186617i | \(-0.0597525\pi\) | |||||||
\(164\) | −2.34410e31 | −0.179780 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.15268e32 | −0.741551 | ||||||||
\(167\) | − 1.74608e32i | − 1.02962i | −0.857305 | − | 0.514808i | \(-0.827863\pi\) | ||||
0.857305 | − | 0.514808i | \(-0.172137\pi\) | |||||||
\(168\) | − 3.81714e32i | − 2.06421i | ||||||||
\(169\) | 1.64446e32 | 0.815953 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.22040e31 | 0.343914 | ||||||||
\(172\) | − 3.77081e31i | − 0.144968i | ||||||||
\(173\) | 4.75360e31i | 0.168017i | 0.996465 | + | 0.0840086i | \(0.0267723\pi\) | ||||
−0.996465 | + | 0.0840086i | \(0.973228\pi\) | |||||||
\(174\) | −1.46354e32 | −0.475816 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.37034e32 | 0.377481 | ||||||||
\(177\) | − 5.59197e31i | − 0.141890i | ||||||||
\(178\) | − 1.12969e32i | − 0.264162i | ||||||||
\(179\) | 6.60198e32 | 1.42333 | 0.711664 | − | 0.702520i | \(-0.247942\pi\) | ||||
0.711664 | + | 0.702520i | \(0.247942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.34310e32 | 0.980515 | 0.490257 | − | 0.871578i | \(-0.336903\pi\) | ||||
0.490257 | + | 0.871578i | \(0.336903\pi\) | |||||||
\(182\) | − 3.17079e32i | − 0.537196i | ||||||||
\(183\) | − 5.89263e32i | − 0.922079i | ||||||||
\(184\) | 2.27497e32 | 0.328941 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.16187e32 | −0.761683 | ||||||||
\(187\) | 1.04291e32i | 0.119274i | ||||||||
\(188\) | 6.09683e32i | 0.645379i | ||||||||
\(189\) | −1.32393e33 | −1.29768 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.58754e32 | −0.806721 | −0.403360 | − | 0.915041i | \(-0.632158\pi\) | ||||
−0.403360 | + | 0.915041i | \(0.632158\pi\) | |||||||
\(192\) | − 1.43803e33i | − 1.12176i | ||||||||
\(193\) | 7.81683e31i | 0.0565522i | 0.999600 | + | 0.0282761i | \(0.00900177\pi\) | ||||
−0.999600 | + | 0.0282761i | \(0.990998\pi\) | |||||||
\(194\) | 1.65976e33 | 1.11409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.32722e33 | −0.767770 | ||||||||
\(197\) | 5.60393e32i | 0.301115i | 0.988601 | + | 0.150557i | \(0.0481068\pi\) | ||||
−0.988601 | + | 0.150557i | \(0.951893\pi\) | |||||||
\(198\) | 4.84354e32i | 0.241834i | ||||||||
\(199\) | −8.91542e32 | −0.413783 | −0.206891 | − | 0.978364i | \(-0.566335\pi\) | ||||
−0.206891 | + | 0.978364i | \(0.566335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.23095e33 | 0.494194 | ||||||||
\(202\) | 8.12179e32i | 0.303429i | ||||||||
\(203\) | 2.63211e33i | 0.915402i | ||||||||
\(204\) | 1.83903e32 | 0.0595596 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.34116e33 | 0.658198 | ||||||||
\(207\) | 3.74329e32i | 0.0981032i | ||||||||
\(208\) | − 6.63367e32i | − 0.162120i | ||||||||
\(209\) | 4.68340e33 | 1.06768 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07645e33 | 0.213746 | 0.106873 | − | 0.994273i | \(-0.465916\pi\) | ||||
0.106873 | + | 0.994273i | \(0.465916\pi\) | |||||||
\(212\) | − 3.37412e33i | − 0.625592i | ||||||||
\(213\) | − 3.46373e33i | − 0.599846i | ||||||||
\(214\) | −8.17713e33 | −1.32313 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.94986e33 | −0.841254 | ||||||||
\(217\) | 1.10819e34i | 1.46537i | ||||||||
\(218\) | 9.30735e33i | 1.15135i | ||||||||
\(219\) | −1.38345e34 | −1.60149 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.04861e32 | 0.0512253 | ||||||||
\(222\) | 3.28350e33i | 0.312046i | ||||||||
\(223\) | − 3.94073e33i | − 0.350878i | −0.984490 | − | 0.175439i | \(-0.943866\pi\) | ||||
0.984490 | − | 0.175439i | \(-0.0561344\pi\) | |||||||
\(224\) | −1.58459e34 | −1.32227 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.38676e34 | −1.01725 | ||||||||
\(227\) | 2.60531e34i | 1.79260i | 0.443445 | + | 0.896302i | \(0.353756\pi\) | ||||
−0.443445 | + | 0.896302i | \(0.646244\pi\) | |||||||
\(228\) | − 8.25853e33i | − 0.533148i | ||||||||
\(229\) | −1.02479e34 | −0.620898 | −0.310449 | − | 0.950590i | \(-0.600479\pi\) | ||||
−0.310449 | + | 0.950590i | \(0.600479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.57836e34 | 1.91122 | ||||||||
\(232\) | 1.18290e34i | 0.593432i | ||||||||
\(233\) | 1.94574e34i | 0.917113i | 0.888665 | + | 0.458557i | \(0.151633\pi\) | ||||
−0.888665 | + | 0.458557i | \(0.848367\pi\) | |||||||
\(234\) | 2.34470e33 | 0.103862 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.36759e33 | −0.0535465 | ||||||||
\(237\) | 3.74981e34i | 1.38089i | ||||||||
\(238\) | 4.31573e33i | 0.149516i | ||||||||
\(239\) | 4.56285e34 | 1.48753 | 0.743766 | − | 0.668440i | \(-0.233037\pi\) | ||||
0.743766 | + | 0.668440i | \(0.233037\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.90791e34 | 0.840107 | 0.420053 | − | 0.907499i | \(-0.362011\pi\) | ||||
0.420053 | + | 0.907499i | \(0.362011\pi\) | |||||||
\(242\) | − 6.04870e31i | − 0.00164566i | ||||||||
\(243\) | − 2.42245e34i | − 0.620817i | ||||||||
\(244\) | −1.44112e34 | −0.347974 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.67101e34 | 0.358444 | ||||||||
\(247\) | − 2.26718e34i | − 0.458543i | ||||||||
\(248\) | 4.98030e34i | 0.949963i | ||||||||
\(249\) | −6.29721e34 | −1.13307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.72418e34 | −0.276256 | −0.138128 | − | 0.990414i | \(-0.544109\pi\) | ||||
−0.138128 | + | 0.990414i | \(0.544109\pi\) | |||||||
\(252\) | − 1.53605e34i | − 0.232326i | ||||||||
\(253\) | 2.13266e34i | 0.304561i | ||||||||
\(254\) | 3.38083e33 | 0.0455968 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.48339e34 | −1.02115 | ||||||||
\(257\) | − 4.22826e33i | − 0.0480985i | −0.999711 | − | 0.0240493i | \(-0.992344\pi\) | ||||
0.999711 | − | 0.0240493i | \(-0.00765586\pi\) | |||||||
\(258\) | 2.68806e34i | 0.289037i | ||||||||
\(259\) | 5.90524e34 | 0.600331 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.94636e34 | −0.176985 | ||||||||
\(262\) | − 4.04865e34i | − 0.348290i | ||||||||
\(263\) | − 3.28330e34i | − 0.267271i | −0.991031 | − | 0.133635i | \(-0.957335\pi\) | ||||
0.991031 | − | 0.133635i | \(-0.0426651\pi\) | |||||||
\(264\) | 1.60815e35 | 1.23899 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.93806e35 | 1.33840 | ||||||||
\(267\) | − 6.17164e34i | − 0.403633i | ||||||||
\(268\) | − 3.01045e34i | − 0.186499i | ||||||||
\(269\) | −2.79966e35 | −1.64322 | −0.821612 | − | 0.570048i | \(-0.806925\pi\) | ||||
−0.821612 | + | 0.570048i | \(0.806925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.70768e35 | −1.95455 | −0.977277 | − | 0.211965i | \(-0.932014\pi\) | ||||
−0.977277 | + | 0.211965i | \(0.932014\pi\) | |||||||
\(272\) | 9.02901e33i | 0.0451223i | ||||||||
\(273\) | − 1.73224e35i | − 0.820823i | ||||||||
\(274\) | 2.21394e35 | 0.994907 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.76065e34 | 0.152083 | ||||||||
\(277\) | − 3.33125e35i | − 1.27835i | −0.769060 | − | 0.639176i | \(-0.779275\pi\) | ||||
0.769060 | − | 0.639176i | \(-0.220725\pi\) | |||||||
\(278\) | − 1.99700e35i | − 0.727324i | ||||||||
\(279\) | −8.19470e34 | −0.283317 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.19345e35 | −1.61888 | −0.809440 | − | 0.587203i | \(-0.800229\pi\) | ||||
−0.809440 | + | 0.587203i | \(0.800229\pi\) | |||||||
\(282\) | − 4.34618e35i | − 1.28676i | ||||||||
\(283\) | − 1.04587e34i | − 0.0294154i | −0.999892 | − | 0.0147077i | \(-0.995318\pi\) | ||||
0.999892 | − | 0.0147077i | \(-0.00468177\pi\) | |||||||
\(284\) | −8.47100e34 | −0.226370 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.33585e35 | 0.322440 | ||||||||
\(287\) | − 3.00526e35i | − 0.689595i | ||||||||
\(288\) | − 1.17175e35i | − 0.255650i | ||||||||
\(289\) | 4.75097e35 | 0.985743 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.06744e35 | 1.70230 | ||||||||
\(292\) | 3.38341e35i | 0.604371i | ||||||||
\(293\) | − 3.74269e35i | − 0.636214i | −0.948055 | − | 0.318107i | \(-0.896953\pi\) | ||||
0.948055 | − | 0.318107i | \(-0.103047\pi\) | |||||||
\(294\) | 9.46125e35 | 1.53078 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.65387e35 | 0.389180 | ||||||||
\(297\) | − 5.57766e35i | − 0.778904i | ||||||||
\(298\) | 1.00119e36i | 1.33163i | ||||||||
\(299\) | 1.03240e35 | 0.130802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83437e35 | 0.556065 | ||||||||
\(302\) | 8.85597e35i | 0.970813i | ||||||||
\(303\) | 4.43702e35i | 0.463632i | ||||||||
\(304\) | 4.05465e35 | 0.403912 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.19135e34 | −0.0289077 | ||||||||
\(307\) | 5.37563e35i | 0.464433i | 0.972664 | + | 0.232217i | \(0.0745978\pi\) | ||||
−0.972664 | + | 0.232217i | \(0.925402\pi\) | |||||||
\(308\) | − 8.75133e35i | − 0.721255i | ||||||||
\(309\) | 1.27900e36 | 1.00571 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.11459e35 | −0.294646 | −0.147323 | − | 0.989088i | \(-0.547066\pi\) | ||||
−0.147323 | + | 0.989088i | \(0.547066\pi\) | |||||||
\(312\) | − 7.78486e35i | − 0.532119i | ||||||||
\(313\) | − 1.66582e36i | − 1.08702i | −0.839404 | − | 0.543508i | \(-0.817096\pi\) | ||||
0.839404 | − | 0.543508i | \(-0.182904\pi\) | |||||||
\(314\) | −1.62375e35 | −0.101167 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.17065e35 | 0.521120 | ||||||||
\(317\) | − 2.49069e36i | − 1.35195i | −0.736925 | − | 0.675975i | \(-0.763723\pi\) | ||||
0.736925 | − | 0.675975i | \(-0.236277\pi\) | |||||||
\(318\) | 2.40528e36i | 1.24730i | ||||||||
\(319\) | −1.10890e36 | −0.549449 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.46726e36 | −2.02171 | ||||||||
\(322\) | 8.82527e35i | 0.381784i | ||||||||
\(323\) | 3.08583e35i | 0.127625i | ||||||||
\(324\) | −1.33656e36 | −0.528549 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.76421e35 | 0.280829 | ||||||||
\(327\) | 5.08471e36i | 1.75923i | ||||||||
\(328\) | − 1.35059e36i | − 0.447047i | ||||||||
\(329\) | −7.81644e36 | −2.47553 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.70323e36 | 0.494046 | 0.247023 | − | 0.969010i | \(-0.420548\pi\) | ||||
0.247023 | + | 0.969010i | \(0.420548\pi\) | |||||||
\(332\) | 1.54006e36i | 0.427599i | ||||||||
\(333\) | 4.36674e35i | 0.116069i | ||||||||
\(334\) | 3.04410e36 | 0.774703 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.09796e36 | 0.723030 | ||||||||
\(337\) | − 1.36026e36i | − 0.304080i | −0.988374 | − | 0.152040i | \(-0.951416\pi\) | ||||
0.988374 | − | 0.152040i | \(-0.0485843\pi\) | |||||||
\(338\) | 2.86693e36i | 0.613939i | ||||||||
\(339\) | −7.57600e36 | −1.55433 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.66876e36 | −0.879555 | ||||||||
\(342\) | 1.43314e36i | 0.258767i | ||||||||
\(343\) | − 7.40016e36i | − 1.28078i | ||||||||
\(344\) | 2.17261e36 | 0.360483 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.28738e35 | −0.126419 | ||||||||
\(347\) | 6.83587e36i | 1.00004i | 0.866015 | + | 0.500019i | \(0.166674\pi\) | ||||
−0.866015 | + | 0.500019i | \(0.833326\pi\) | |||||||
\(348\) | 1.95539e36i | 0.274369i | ||||||||
\(349\) | −4.60521e36 | −0.619842 | −0.309921 | − | 0.950762i | \(-0.600303\pi\) | ||||
−0.309921 | + | 0.950762i | \(0.600303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.70008e36 | −0.334521 | ||||||||
\(352\) | − 6.67582e36i | − 0.793663i | ||||||||
\(353\) | 1.14489e37i | 1.30627i | 0.757243 | + | 0.653134i | \(0.226546\pi\) | ||||
−0.757243 | + | 0.653134i | \(0.773454\pi\) | |||||||
\(354\) | 9.74899e35 | 0.106761 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.50935e36 | −0.152323 | ||||||||
\(357\) | 2.35773e36i | 0.228457i | ||||||||
\(358\) | 1.15098e37i | 1.07094i | ||||||||
\(359\) | 1.33540e37 | 1.19328 | 0.596638 | − | 0.802510i | \(-0.296503\pi\) | ||||
0.596638 | + | 0.802510i | \(0.296503\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.72772e36 | 0.142436 | ||||||||
\(362\) | 9.31511e36i | 0.737758i | ||||||||
\(363\) | − 3.30447e34i | − 0.00251453i | ||||||||
\(364\) | −4.23642e36 | −0.309762 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.02732e37 | 0.693790 | ||||||||
\(367\) | 1.51022e37i | 0.980353i | 0.871623 | + | 0.490177i | \(0.163068\pi\) | ||||
−0.871623 | + | 0.490177i | \(0.836932\pi\) | |||||||
\(368\) | 1.84635e36i | 0.115218i | ||||||||
\(369\) | 2.22229e36 | 0.133327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.32580e37 | 2.39963 | ||||||||
\(372\) | 8.23271e36i | 0.439208i | ||||||||
\(373\) | − 1.09297e36i | − 0.0560828i | −0.999607 | − | 0.0280414i | \(-0.991073\pi\) | ||||
0.999607 | − | 0.0280414i | \(-0.00892702\pi\) | |||||||
\(374\) | −1.81820e36 | −0.0897437 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.51279e37 | −1.60483 | ||||||||
\(377\) | 5.36806e36i | 0.235976i | ||||||||
\(378\) | − 2.30812e37i | − 0.976400i | ||||||||
\(379\) | −1.45750e37 | −0.593392 | −0.296696 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296696 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.84699e36 | 0.0696709 | ||||||||
\(382\) | − 1.67148e37i | − 0.606992i | ||||||||
\(383\) | − 5.82118e36i | − 0.203530i | −0.994808 | − | 0.101765i | \(-0.967551\pi\) | ||||
0.994808 | − | 0.101765i | \(-0.0324490\pi\) | |||||||
\(384\) | −2.06210e36 | −0.0694235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.36278e36 | −0.0425510 | ||||||||
\(387\) | 3.57486e36i | 0.107510i | ||||||||
\(388\) | − 2.21756e37i | − 0.642414i | ||||||||
\(389\) | 6.42121e36 | 0.179204 | 0.0896020 | − | 0.995978i | \(-0.471440\pi\) | ||||
0.0896020 | + | 0.995978i | \(0.471440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.40518e36 | −0.0364057 | ||||||||
\(392\) | − 7.64702e37i | − 1.90917i | ||||||||
\(393\) | − 2.21182e37i | − 0.532180i | ||||||||
\(394\) | −9.76983e36 | −0.226564 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.47133e36 | 0.139448 | ||||||||
\(397\) | − 6.76912e37i | − 1.40627i | −0.711054 | − | 0.703137i | \(-0.751782\pi\) | ||||
0.711054 | − | 0.703137i | \(-0.248218\pi\) | |||||||
\(398\) | − 1.55431e37i | − 0.311338i | ||||||||
\(399\) | 1.05879e38 | 2.04504 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.28993e37 | −1.48922 | −0.744608 | − | 0.667502i | \(-0.767364\pi\) | ||||
−0.744608 | + | 0.667502i | \(0.767364\pi\) | |||||||
\(402\) | 2.14603e37i | 0.371841i | ||||||||
\(403\) | 2.26009e37i | 0.377748i | ||||||||
\(404\) | 1.08513e37 | 0.174965 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.58880e37 | −0.688766 | ||||||||
\(407\) | 2.48786e37i | 0.360335i | ||||||||
\(408\) | 1.05959e37i | 0.148103i | ||||||||
\(409\) | −2.19435e37 | −0.296018 | −0.148009 | − | 0.988986i | \(-0.547286\pi\) | ||||
−0.148009 | + | 0.988986i | \(0.547286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.20950e38 | 1.52019 | ||||||||
\(412\) | − 3.12796e37i | − 0.379535i | ||||||||
\(413\) | − 1.75332e37i | − 0.205393i | ||||||||
\(414\) | −6.52601e36 | −0.0738147 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.23169e37 | −0.340860 | ||||||||
\(417\) | − 1.09098e38i | − 1.11133i | ||||||||
\(418\) | 8.16500e37i | 0.803341i | ||||||||
\(419\) | 1.94941e37 | 0.185268 | 0.0926338 | − | 0.995700i | \(-0.470471\pi\) | ||||
0.0926338 | + | 0.995700i | \(0.470471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.14435e37 | −0.278895 | −0.139447 | − | 0.990229i | \(-0.544533\pi\) | ||||
−0.139447 | + | 0.990229i | \(0.544533\pi\) | |||||||
\(422\) | 1.87667e37i | 0.160827i | ||||||||
\(423\) | − 5.78001e37i | − 0.478623i | ||||||||
\(424\) | 1.94406e38 | 1.55562 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.03863e37 | 0.451336 | ||||||||
\(427\) | − 1.84759e38i | − 1.33475i | ||||||||
\(428\) | 1.09253e38i | 0.762951i | ||||||||
\(429\) | 7.29787e37 | 0.492680 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.71956e38 | −1.71624 | −0.858120 | − | 0.513449i | \(-0.828367\pi\) | ||||
−0.858120 | + | 0.513449i | \(0.828367\pi\) | |||||||
\(432\) | − 4.82886e37i | − 0.294666i | ||||||||
\(433\) | 1.20292e38i | 0.709842i | 0.934896 | + | 0.354921i | \(0.115492\pi\) | ||||
−0.934896 | + | 0.354921i | \(0.884508\pi\) | |||||||
\(434\) | −1.93200e38 | −1.10257 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.24353e38 | 0.663900 | ||||||||
\(437\) | 6.31025e37i | 0.325886i | ||||||||
\(438\) | − 2.41190e38i | − 1.20499i | ||||||||
\(439\) | 6.48441e37 | 0.313426 | 0.156713 | − | 0.987644i | \(-0.449910\pi\) | ||||
0.156713 | + | 0.987644i | \(0.449910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.25826e38 | 0.569390 | ||||||||
\(442\) | 8.80171e36i | 0.0385429i | ||||||||
\(443\) | − 1.25901e38i | − 0.533550i | −0.963759 | − | 0.266775i | \(-0.914042\pi\) | ||||
0.963759 | − | 0.266775i | \(-0.0859580\pi\) | |||||||
\(444\) | 4.38699e37 | 0.179934 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.87022e37 | 0.264007 | ||||||||
\(447\) | 5.46963e38i | 2.03469i | ||||||||
\(448\) | − 4.50883e38i | − 1.62380i | ||||||||
\(449\) | −4.32701e38 | −1.50874 | −0.754372 | − | 0.656447i | \(-0.772059\pi\) | ||||
−0.754372 | + | 0.656447i | \(0.772059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.26610e38 | 0.413914 | ||||||||
\(452\) | 1.85281e38i | 0.586575i | ||||||||
\(453\) | 4.83812e38i | 1.48338i | ||||||||
\(454\) | −4.54207e38 | −1.34879 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.75829e38 | 1.32575 | ||||||||
\(457\) | 5.34446e38i | 1.44251i | 0.692670 | + | 0.721255i | \(0.256434\pi\) | ||||
−0.692670 | + | 0.721255i | \(0.743566\pi\) | |||||||
\(458\) | − 1.78661e38i | − 0.467176i | ||||||||
\(459\) | 3.67505e37 | 0.0931063 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.70831e38 | −0.644220 | −0.322110 | − | 0.946702i | \(-0.604392\pi\) | ||||
−0.322110 | + | 0.946702i | \(0.604392\pi\) | |||||||
\(462\) | 6.23847e38i | 1.43804i | ||||||||
\(463\) | 5.36275e38i | 1.19802i | 0.800742 | + | 0.599009i | \(0.204439\pi\) | ||||
−0.800742 | + | 0.599009i | \(0.795561\pi\) | |||||||
\(464\) | −9.60030e37 | −0.207862 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.39218e38 | −0.690054 | ||||||||
\(467\) | − 9.88390e38i | − 1.94910i | −0.224177 | − | 0.974549i | \(-0.571969\pi\) | ||||
0.224177 | − | 0.974549i | \(-0.428031\pi\) | |||||||
\(468\) | − 3.13270e37i | − 0.0598899i | ||||||||
\(469\) | 3.85954e38 | 0.715368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.87071e37 | −0.154581 | ||||||||
\(472\) | − 7.87958e37i | − 0.133151i | ||||||||
\(473\) | 2.03670e38i | 0.333765i | ||||||||
\(474\) | −6.53739e38 | −1.03901 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.76614e37 | 0.0862152 | ||||||||
\(477\) | 3.19879e38i | 0.463948i | ||||||||
\(478\) | 7.95483e38i | 1.11925i | ||||||||
\(479\) | 1.66145e38 | 0.226789 | 0.113395 | − | 0.993550i | \(-0.463828\pi\) | ||||
0.113395 | + | 0.993550i | \(0.463828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.20434e38 | 0.154756 | ||||||||
\(482\) | 5.06963e38i | 0.632112i | ||||||||
\(483\) | 4.82135e38i | 0.583358i | ||||||||
\(484\) | −8.08152e35 | −0.000948932 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.22328e38 | 0.467115 | ||||||||
\(487\) | 5.21209e38i | 0.559554i | 0.960065 | + | 0.279777i | \(0.0902605\pi\) | ||||
−0.960065 | + | 0.279777i | \(0.909740\pi\) | |||||||
\(488\) | − 8.30323e38i | − 0.865286i | ||||||||
\(489\) | 4.24167e38 | 0.429100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.08070e38 | −0.579791 | −0.289896 | − | 0.957058i | \(-0.593621\pi\) | ||||
−0.289896 | + | 0.957058i | \(0.593621\pi\) | |||||||
\(492\) | − 2.23260e38i | − 0.206689i | ||||||||
\(493\) | − 7.30640e37i | − 0.0656785i | ||||||||
\(494\) | 3.95258e38 | 0.345017 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.04197e38 | −0.332743 | ||||||||
\(497\) | − 1.08602e39i | − 0.868305i | ||||||||
\(498\) | − 1.09785e39i | − 0.852545i | ||||||||
\(499\) | −1.92541e39 | −1.45233 | −0.726165 | − | 0.687521i | \(-0.758699\pi\) | ||||
−0.726165 | + | 0.687521i | \(0.758699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.66303e39 | 1.18373 | ||||||||
\(502\) | − 3.00591e38i | − 0.207861i | ||||||||
\(503\) | 1.47205e39i | 0.988981i | 0.869183 | + | 0.494490i | \(0.164645\pi\) | ||||
−0.869183 | + | 0.494490i | \(0.835355\pi\) | |||||||
\(504\) | 8.85021e38 | 0.577711 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.71806e38 | −0.229157 | ||||||||
\(507\) | 1.56624e39i | 0.938084i | ||||||||
\(508\) | − 4.51704e37i | − 0.0262924i | ||||||||
\(509\) | −9.86933e37 | −0.0558316 | −0.0279158 | − | 0.999610i | \(-0.508887\pi\) | ||||
−0.0279158 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.33771e39 | −2.31823 | ||||||||
\(512\) | − 1.36275e39i | − 0.707948i | ||||||||
\(513\) | − 1.65035e39i | − 0.833441i | ||||||||
\(514\) | 7.37152e37 | 0.0361903 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.59145e38 | 0.166667 | ||||||||
\(517\) | − 3.29304e39i | − 1.48588i | ||||||||
\(518\) | 1.02951e39i | 0.451701i | ||||||||
\(519\) | −4.52749e38 | −0.193166 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.36208e39 | 0.549613 | 0.274806 | − | 0.961500i | \(-0.411386\pi\) | ||||
0.274806 | + | 0.961500i | \(0.411386\pi\) | |||||||
\(522\) | − 3.39327e38i | − 0.133167i | ||||||||
\(523\) | − 3.92619e39i | − 1.49864i | −0.662208 | − | 0.749320i | \(-0.730381\pi\) | ||||
0.662208 | − | 0.749320i | \(-0.269619\pi\) | |||||||
\(524\) | −5.40930e38 | −0.200834 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.72407e38 | 0.201100 | ||||||||
\(527\) | − 3.07618e38i | − 0.105138i | ||||||||
\(528\) | 1.30516e39i | 0.433982i | ||||||||
\(529\) | 2.80371e39 | 0.907039 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.29652e38 | 0.0397109 | ||||||||
\(532\) | − 2.58940e39i | − 0.771756i | ||||||||
\(533\) | − 6.12906e38i | − 0.177766i | ||||||||
\(534\) | 1.07596e39 | 0.303701 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.73452e39 | 0.463756 | ||||||||
\(537\) | 6.28794e39i | 1.63637i | ||||||||
\(538\) | − 4.88089e39i | − 1.23639i | ||||||||
\(539\) | 7.16866e39 | 1.76767 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.64331e39 | 0.851405 | 0.425702 | − | 0.904863i | \(-0.360027\pi\) | ||||
0.425702 | + | 0.904863i | \(0.360027\pi\) | |||||||
\(542\) | − 6.46394e39i | − 1.47064i | ||||||||
\(543\) | 5.08895e39i | 1.12728i | ||||||||
\(544\) | 4.39861e38 | 0.0948706 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.01997e39 | 0.617603 | ||||||||
\(547\) | 9.64716e38i | 0.192125i | 0.995375 | + | 0.0960624i | \(0.0306248\pi\) | ||||
−0.995375 | + | 0.0960624i | \(0.969375\pi\) | |||||||
\(548\) | − 2.95799e39i | − 0.573691i | ||||||||
\(549\) | 1.36623e39 | 0.258063 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.28108e39 | −0.587921 | ||||||||
\(552\) | 2.16676e39i | 0.378176i | ||||||||
\(553\) | 1.17572e40i | 1.99890i | ||||||||
\(554\) | 5.80767e39 | 0.961857 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.66814e39 | −0.419395 | ||||||||
\(557\) | 4.34857e39i | 0.665956i | 0.942935 | + | 0.332978i | \(0.108054\pi\) | ||||
−0.942935 | + | 0.332978i | \(0.891946\pi\) | |||||||
\(558\) | − 1.42866e39i | − 0.213173i | ||||||||
\(559\) | 9.85944e38 | 0.143345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.93305e38 | −0.137126 | ||||||||
\(562\) | − 9.05422e39i | − 1.21808i | ||||||||
\(563\) | − 5.22292e39i | − 0.684765i | −0.939561 | − | 0.342382i | \(-0.888766\pi\) | ||||
0.939561 | − | 0.342382i | \(-0.111234\pi\) | |||||||
\(564\) | −5.80682e39 | −0.741979 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.82336e38 | 0.0221327 | ||||||||
\(567\) | − 1.71353e40i | − 2.02740i | ||||||||
\(568\) | − 4.88070e39i | − 0.562900i | ||||||||
\(569\) | −8.52031e39 | −0.957916 | −0.478958 | − | 0.877838i | \(-0.658985\pi\) | ||||
−0.478958 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.06636e38 | 0.0861894 | 0.0430947 | − | 0.999071i | \(-0.486278\pi\) | ||||
0.0430947 | + | 0.999071i | \(0.486278\pi\) | |||||||
\(572\) | − 1.78479e39i | − 0.185928i | ||||||||
\(573\) | − 9.13149e39i | − 0.927470i | ||||||||
\(574\) | 5.23933e39 | 0.518864 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.33413e39 | 0.313948 | ||||||||
\(577\) | 1.60079e40i | 1.46989i | 0.678125 | + | 0.734947i | \(0.262793\pi\) | ||||
−0.678125 | + | 0.734947i | \(0.737207\pi\) | |||||||
\(578\) | 8.28280e39i | 0.741691i | ||||||||
\(579\) | −7.44501e38 | −0.0650169 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.97444e40 | −1.64017 | ||||||||
\(582\) | 1.58081e40i | 1.28084i | ||||||||
\(583\) | 1.82244e40i | 1.44032i | ||||||||
\(584\) | −1.94941e40 | −1.50285 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.52496e39 | 0.478699 | ||||||||
\(587\) | 7.25470e39i | 0.519239i | 0.965711 | + | 0.259619i | \(0.0835971\pi\) | ||||
−0.965711 | + | 0.259619i | \(0.916403\pi\) | |||||||
\(588\) | − 1.26409e40i | − 0.882689i | ||||||||
\(589\) | −1.38142e40 | −0.941140 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.33737e39 | −0.346185 | ||||||||
\(592\) | 2.15386e39i | 0.136318i | ||||||||
\(593\) | 4.67095e39i | 0.288478i | 0.989543 | + | 0.144239i | \(0.0460734\pi\) | ||||
−0.989543 | + | 0.144239i | \(0.953927\pi\) | |||||||
\(594\) | 9.72404e39 | 0.586062 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.33767e40 | 0.767853 | ||||||||
\(597\) | − 8.49135e39i | − 0.475717i | ||||||||
\(598\) | 1.79987e39i | 0.0984178i | ||||||||
\(599\) | −3.02320e40 | −1.61353 | −0.806766 | − | 0.590871i | \(-0.798784\pi\) | ||||
−0.806766 | + | 0.590871i | \(0.798784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.75696e40 | −0.893476 | −0.446738 | − | 0.894665i | \(-0.647414\pi\) | ||||
−0.446738 | + | 0.894665i | \(0.647414\pi\) | |||||||
\(602\) | 8.42819e39i | 0.418394i | ||||||||
\(603\) | 2.85401e39i | 0.138310i | ||||||||
\(604\) | 1.18322e40 | 0.559798 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.73546e39 | −0.348846 | ||||||||
\(607\) | 2.78325e40i | 1.22551i | 0.790273 | + | 0.612755i | \(0.209939\pi\) | ||||
−0.790273 | + | 0.612755i | \(0.790061\pi\) | |||||||
\(608\) | − 1.97528e40i | − 0.849234i | ||||||||
\(609\) | −2.50691e40 | −1.05242 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.59412e40 | −0.638152 | ||||||||
\(612\) | 4.26387e38i | 0.0166690i | ||||||||
\(613\) | 2.63728e40i | 1.00688i | 0.864030 | + | 0.503441i | \(0.167933\pi\) | ||||
−0.864030 | + | 0.503441i | \(0.832067\pi\) | |||||||
\(614\) | −9.37183e39 | −0.349448 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.04222e40 | 1.79350 | ||||||||
\(617\) | − 9.21532e38i | − 0.0320166i | −0.999872 | − | 0.0160083i | \(-0.994904\pi\) | ||||
0.999872 | − | 0.0160083i | \(-0.00509582\pi\) | |||||||
\(618\) | 2.22980e40i | 0.756716i | ||||||||
\(619\) | 4.42763e40 | 1.46777 | 0.733883 | − | 0.679276i | \(-0.237706\pi\) | ||||
0.733883 | + | 0.679276i | \(0.237706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.51514e39 | 0.237744 | ||||||||
\(622\) | − 7.17333e39i | − 0.221697i | ||||||||
\(623\) | − 1.93507e40i | − 0.584278i | ||||||||
\(624\) | 6.31813e39 | 0.186385 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.90418e40 | 0.817891 | ||||||||
\(627\) | 4.46063e40i | 1.22749i | ||||||||
\(628\) | 2.16945e39i | 0.0583356i | ||||||||
\(629\) | −1.63922e39 | −0.0430727 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.23643e40 | 1.06310 | 0.531551 | − | 0.847026i | \(-0.321609\pi\) | ||||
0.531551 | + | 0.847026i | \(0.321609\pi\) | |||||||
\(632\) | 5.28382e40i | 1.29584i | ||||||||
\(633\) | 1.02525e40i | 0.245739i | ||||||||
\(634\) | 4.34225e40 | 1.01723 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.21363e40 | 0.719229 | ||||||||
\(637\) | − 3.47026e40i | − 0.759172i | ||||||||
\(638\) | − 1.93325e40i | − 0.413416i | ||||||||
\(639\) | 8.03081e39 | 0.167879 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.13775e40 | −0.826652 | −0.413326 | − | 0.910583i | \(-0.635633\pi\) | ||||
−0.413326 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(642\) | − 7.78818e40i | − 1.52117i | ||||||||
\(643\) | 9.84722e40i | 1.88042i | 0.340598 | + | 0.940209i | \(0.389370\pi\) | ||||
−0.340598 | + | 0.940209i | \(0.610630\pi\) | |||||||
\(644\) | 1.17912e40 | 0.220147 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.37981e39 | −0.0960275 | ||||||||
\(647\) | 6.78001e39i | 0.118336i | 0.998248 | + | 0.0591682i | \(0.0188448\pi\) | ||||
−0.998248 | + | 0.0591682i | \(0.981155\pi\) | |||||||
\(648\) | − 7.70079e40i | − 1.31431i | ||||||||
\(649\) | 7.38667e39 | 0.123282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05548e41 | −1.68470 | ||||||||
\(652\) | − 1.03736e40i | − 0.161934i | ||||||||
\(653\) | 3.23913e40i | 0.494524i | 0.968949 | + | 0.247262i | \(0.0795308\pi\) | ||||
−0.968949 | + | 0.247262i | \(0.920469\pi\) | |||||||
\(654\) | −8.86464e40 | −1.32368 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.09613e40 | 0.156587 | ||||||||
\(657\) | − 3.20760e40i | − 0.448211i | ||||||||
\(658\) | − 1.36271e41i | − 1.86264i | ||||||||
\(659\) | 1.40926e40 | 0.188431 | 0.0942156 | − | 0.995552i | \(-0.469966\pi\) | ||||
0.0942156 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.56737e40 | −1.22425 | −0.612127 | − | 0.790759i | \(-0.709686\pi\) | ||||
−0.612127 | + | 0.790759i | \(0.709686\pi\) | |||||||
\(662\) | 2.96940e40i | 0.371730i | ||||||||
\(663\) | 4.80847e39i | 0.0588926i | ||||||||
\(664\) | −8.87333e40 | −1.06328 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.61293e39 | −0.0873324 | ||||||||
\(667\) | − 1.49409e40i | − 0.167708i | ||||||||
\(668\) | − 4.06714e40i | − 0.446715i | ||||||||
\(669\) | 3.75328e40 | 0.403397 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.78382e40 | 0.801154 | ||||||||
\(672\) | − 1.50922e41i | − 1.52019i | ||||||||
\(673\) | − 1.43434e40i | − 0.141394i | −0.997498 | − | 0.0706972i | \(-0.977478\pi\) | ||||
0.997498 | − | 0.0706972i | \(-0.0225224\pi\) | |||||||
\(674\) | 2.37146e40 | 0.228796 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.83043e40 | 0.354014 | ||||||||
\(677\) | − 8.89678e40i | − 0.804817i | −0.915460 | − | 0.402408i | \(-0.868173\pi\) | ||||
0.915460 | − | 0.402408i | \(-0.131827\pi\) | |||||||
\(678\) | − 1.32079e41i | − 1.16951i | ||||||||
\(679\) | 2.84302e41 | 2.46416 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.48138e41 | −2.06092 | ||||||||
\(682\) | − 8.13947e40i | − 0.661794i | ||||||||
\(683\) | 1.49228e41i | 1.18782i | 0.804531 | + | 0.593910i | \(0.202417\pi\) | ||||
−0.804531 | + | 0.593910i | \(0.797583\pi\) | |||||||
\(684\) | 1.91478e40 | 0.149212 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.29014e41 | 0.963687 | ||||||||
\(687\) | − 9.76045e40i | − 0.713834i | ||||||||
\(688\) | 1.76328e40i | 0.126266i | ||||||||
\(689\) | 8.82224e40 | 0.618586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.54015e41 | 1.70776 | 0.853880 | − | 0.520469i | \(-0.174243\pi\) | ||||
0.853880 | + | 0.520469i | \(0.174243\pi\) | |||||||
\(692\) | 1.10725e40i | 0.0728969i | ||||||||
\(693\) | 8.29658e40i | 0.534893i | ||||||||
\(694\) | −1.19176e41 | −0.752447 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.12663e41 | −0.682257 | ||||||||
\(697\) | 8.34219e39i | 0.0494772i | ||||||||
\(698\) | − 8.02868e40i | − 0.466381i | ||||||||
\(699\) | −1.85318e41 | −1.05439 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.56415e40 | −0.0853824 | −0.0426912 | − | 0.999088i | \(-0.513593\pi\) | ||||
−0.0426912 | + | 0.999088i | \(0.513593\pi\) | |||||||
\(702\) | − 4.70729e40i | − 0.251700i | ||||||||
\(703\) | 7.36123e40i | 0.385565i | ||||||||
\(704\) | 1.89955e41 | 0.974649 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.99600e41 | −0.982860 | ||||||||
\(707\) | 1.39119e41i | 0.671129i | ||||||||
\(708\) | − 1.30254e40i | − 0.0615613i | ||||||||
\(709\) | 7.96882e40 | 0.368998 | 0.184499 | − | 0.982833i | \(-0.440934\pi\) | ||||
0.184499 | + | 0.982833i | \(0.440934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.69411e40 | −0.386470 | ||||||||
\(712\) | − 8.69638e40i | − 0.378773i | ||||||||
\(713\) | − 6.29051e40i | − 0.268465i | ||||||||
\(714\) | −4.11045e40 | −0.171896 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.53780e41 | 0.617533 | ||||||||
\(717\) | 4.34581e41i | 1.71018i | ||||||||
\(718\) | 2.32812e41i | 0.897844i | ||||||||
\(719\) | −6.70217e39 | −0.0253306 | −0.0126653 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126653 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.01021e41 | 1.45581 | ||||||||
\(722\) | 3.01209e40i | 0.107171i | ||||||||
\(723\) | 2.76960e41i | 0.965853i | ||||||||
\(724\) | 1.24457e41 | 0.425412 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.76099e38 | 0.00189198 | ||||||||
\(727\) | 3.08325e41i | 0.992565i | 0.868161 | + | 0.496283i | \(0.165302\pi\) | ||||
−0.868161 | + | 0.496283i | \(0.834698\pi\) | |||||||
\(728\) | − 2.44088e41i | − 0.770267i | ||||||||
\(729\) | −1.63080e41 | −0.504490 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.34196e40 | −0.0398967 | ||||||||
\(732\) | − 1.37257e41i | − 0.400058i | ||||||||
\(733\) | − 2.79480e41i | − 0.798626i | −0.916815 | − | 0.399313i | \(-0.869249\pi\) | ||||
0.916815 | − | 0.399313i | \(-0.130751\pi\) | |||||||
\(734\) | −2.63290e41 | −0.737636 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.99476e40 | 0.242249 | ||||||||
\(737\) | 1.62601e41i | 0.429384i | ||||||||
\(738\) | 3.87432e40i | 0.100318i | ||||||||
\(739\) | 4.36349e41 | 1.10787 | 0.553936 | − | 0.832560i | \(-0.313125\pi\) | ||||
0.553936 | + | 0.832560i | \(0.313125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.15934e41 | 0.527177 | ||||||||
\(742\) | 7.54155e41i | 1.80553i | ||||||||
\(743\) | − 1.06242e41i | − 0.249437i | −0.992192 | − | 0.124718i | \(-0.960197\pi\) | ||||
0.992192 | − | 0.124718i | \(-0.0398027\pi\) | |||||||
\(744\) | −4.74341e41 | −1.09215 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.90547e40 | 0.0421977 | ||||||||
\(747\) | − 1.46004e41i | − 0.317114i | ||||||||
\(748\) | 2.42925e40i | 0.0517487i | ||||||||
\(749\) | −1.40067e42 | −2.92651 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.53315e41 | −0.308181 | −0.154091 | − | 0.988057i | \(-0.549245\pi\) | ||||
−0.154091 | + | 0.988057i | \(0.549245\pi\) | |||||||
\(752\) | − 2.85095e41i | − 0.562122i | ||||||||
\(753\) | − 1.64216e41i | − 0.317606i | ||||||||
\(754\) | −9.35862e40 | −0.177553 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.08382e41 | −0.563019 | ||||||||
\(757\) | 1.29063e41i | 0.231160i | 0.993298 | + | 0.115580i | \(0.0368727\pi\) | ||||
−0.993298 | + | 0.115580i | \(0.963127\pi\) | |||||||
\(758\) | − 2.54100e41i | − 0.446479i | ||||||||
\(759\) | −2.03122e41 | −0.350147 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.01002e42 | −1.67592 | −0.837962 | − | 0.545728i | \(-0.816253\pi\) | ||||
−0.837962 | + | 0.545728i | \(0.816253\pi\) | |||||||
\(762\) | 3.22002e40i | 0.0524217i | ||||||||
\(763\) | 1.59427e42i | 2.54657i | ||||||||
\(764\) | −2.23322e41 | −0.350008 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.01486e41 | 0.153140 | ||||||||
\(767\) | − 3.57580e40i | − 0.0529469i | ||||||||
\(768\) | − 8.07987e41i | − 1.17400i | ||||||||
\(769\) | 8.10252e41 | 1.15528 | 0.577641 | − | 0.816291i | \(-0.303973\pi\) | ||||
0.577641 | + | 0.816291i | \(0.303973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.02714e40 | 0.0552979 | ||||||||
\(772\) | 1.82077e40i | 0.0245361i | ||||||||
\(773\) | 3.13830e41i | 0.415042i | 0.978231 | + | 0.207521i | \(0.0665395\pi\) | ||||
−0.978231 | + | 0.207521i | \(0.933461\pi\) | |||||||
\(774\) | −6.23238e40 | −0.0808929 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.27768e42 | 1.59745 | ||||||||
\(777\) | 5.62435e41i | 0.690188i | ||||||||
\(778\) | 1.11947e41i | 0.134836i | ||||||||
\(779\) | 3.74623e41 | 0.442895 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.57539e41 | 0.521180 | ||||||||
\(782\) | − 2.44978e40i | − 0.0273923i | ||||||||
\(783\) | 3.90758e41i | 0.428906i | ||||||||
\(784\) | 6.20626e41 | 0.668724 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.85607e41 | 0.400422 | ||||||||
\(787\) | − 8.07245e41i | − 0.822947i | −0.911422 | − | 0.411473i | \(-0.865014\pi\) | ||||
0.911422 | − | 0.411473i | \(-0.134986\pi\) | |||||||
\(788\) | 1.30532e41i | 0.130643i | ||||||||
\(789\) | 3.12712e41 | 0.307276 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.37540e42 | −2.24997 | ||||||||
\(792\) | 3.72856e41i | 0.346758i | ||||||||
\(793\) | − 3.76805e41i | − 0.344077i | ||||||||
\(794\) | 1.18012e42 | 1.05811 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.07667e41 | −0.179526 | ||||||||
\(797\) | − 2.35976e41i | − 0.200319i | −0.994971 | − | 0.100160i | \(-0.968065\pi\) | ||||
0.994971 | − | 0.100160i | \(-0.0319353\pi\) | |||||||
\(798\) | 1.84588e42i | 1.53872i | ||||||||
\(799\) | 2.16974e41 | 0.177615 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.43092e41 | 0.112965 | ||||||||
\(802\) | − 1.44526e42i | − 1.12051i | ||||||||
\(803\) | − 1.82746e42i | − 1.39147i | ||||||||
\(804\) | 2.86725e41 | 0.214414 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.94022e41 | −0.284225 | ||||||||
\(807\) | − 2.66649e42i | − 1.88918i | ||||||||
\(808\) | 6.25216e41i | 0.435076i | ||||||||
\(809\) | −2.25512e42 | −1.54140 | −0.770700 | − | 0.637198i | \(-0.780093\pi\) | ||||
−0.770700 | + | 0.637198i | \(0.780093\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.17269e41 | 0.538967 | 0.269484 | − | 0.963005i | \(-0.413147\pi\) | ||||
0.269484 | + | 0.963005i | \(0.413147\pi\) | |||||||
\(812\) | 6.13098e41i | 0.397162i | ||||||||
\(813\) | − 3.53132e42i | − 2.24711i | ||||||||
\(814\) | −4.33731e41 | −0.271123 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.59953e40 | −0.0518761 | ||||||||
\(817\) | 6.02632e41i | 0.357135i | ||||||||
\(818\) | − 3.82560e41i | − 0.222729i | ||||||||
\(819\) | 4.01627e41 | 0.229724 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.86919e39 | 0.00489675 | 0.00244838 | − | 0.999997i | \(-0.499221\pi\) | ||||
0.00244838 | + | 0.999997i | \(0.499221\pi\) | |||||||
\(822\) | 2.10863e42i | 1.14382i | ||||||||
\(823\) | 4.50695e41i | 0.240207i | 0.992761 | + | 0.120103i | \(0.0383226\pi\) | ||||
−0.992761 | + | 0.120103i | \(0.961677\pi\) | |||||||
\(824\) | 1.80223e42 | 0.943767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.05672e41 | 0.154541 | ||||||||
\(827\) | − 1.64298e42i | − 0.816211i | −0.912935 | − | 0.408106i | \(-0.866190\pi\) | ||||
0.912935 | − | 0.408106i | \(-0.133810\pi\) | |||||||
\(828\) | 8.71923e40i | 0.0425636i | ||||||||
\(829\) | −9.28693e41 | −0.445483 | −0.222742 | − | 0.974878i | \(-0.571501\pi\) | ||||
−0.222742 | + | 0.974878i | \(0.571501\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.17280e42 | 1.46970 | ||||||||
\(832\) | − 9.19552e41i | − 0.418589i | ||||||||
\(833\) | 4.72333e41i | 0.211298i | ||||||||
\(834\) | 1.90201e42 | 0.836189 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.09090e42 | 0.463229 | ||||||||
\(837\) | 1.64519e42i | 0.686590i | ||||||||
\(838\) | 3.39858e41i | 0.139399i | ||||||||
\(839\) | 1.59653e42 | 0.643620 | 0.321810 | − | 0.946804i | \(-0.395709\pi\) | ||||
0.321810 | + | 0.946804i | \(0.395709\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.79082e42 | −0.697444 | ||||||||
\(842\) | − 5.48183e41i | − 0.209846i | ||||||||
\(843\) | − 4.94642e42i | − 1.86119i | ||||||||
\(844\) | 2.50737e41 | 0.0927371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.00768e42 | 0.360125 | ||||||||
\(847\) | − 1.03609e40i | − 0.00363989i | ||||||||
\(848\) | 1.57778e42i | 0.544887i | ||||||||
\(849\) | 9.96121e40 | 0.0338182 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.35205e41 | −0.109985 | ||||||||
\(852\) | − 8.06806e41i | − 0.260253i | ||||||||
\(853\) | − 2.50802e42i | − 0.795373i | −0.917521 | − | 0.397686i | \(-0.869813\pi\) | ||||
0.917521 | − | 0.397686i | \(-0.130187\pi\) | |||||||
\(854\) | 3.22106e42 | 1.00429 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.29476e42 | −1.89719 | ||||||||
\(857\) | − 4.74569e42i | − 1.40630i | −0.711043 | − | 0.703149i | \(-0.751777\pi\) | ||||
0.711043 | − | 0.703149i | \(-0.248223\pi\) | |||||||
\(858\) | 1.27230e42i | 0.370702i | ||||||||
\(859\) | 1.19413e42 | 0.342098 | 0.171049 | − | 0.985263i | \(-0.445284\pi\) | ||||
0.171049 | + | 0.985263i | \(0.445284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.86231e42 | 0.792812 | ||||||||
\(862\) | − 4.74125e42i | − 1.29133i | ||||||||
\(863\) | 5.51388e42i | 1.47673i | 0.674402 | + | 0.738364i | \(0.264401\pi\) | ||||
−0.674402 | + | 0.738364i | \(0.735599\pi\) | |||||||
\(864\) | −2.35245e42 | −0.619542 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.09716e42 | −0.534099 | ||||||||
\(867\) | 4.52498e42i | 1.13329i | ||||||||
\(868\) | 2.58130e42i | 0.635774i | ||||||||
\(869\) | −4.95329e42 | −1.19979 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.87134e41 | 0.184410 | ||||||||
\(872\) | 7.16481e42i | 1.65088i | ||||||||
\(873\) | 2.10233e42i | 0.476424i | ||||||||
\(874\) | −1.10012e42 | −0.245203 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.22248e42 | −0.694833 | ||||||||
\(877\) | − 3.25016e42i | − 0.689304i | −0.938731 | − | 0.344652i | \(-0.887997\pi\) | ||||
0.938731 | − | 0.344652i | \(-0.112003\pi\) | |||||||
\(878\) | 1.13049e42i | 0.235828i | ||||||||
\(879\) | 3.56466e42 | 0.731441 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.07364e42 | 0.213162 | 0.106581 | − | 0.994304i | \(-0.466010\pi\) | ||||
0.106581 | + | 0.994304i | \(0.466010\pi\) | |||||||
\(882\) | 2.19363e42i | 0.428420i | ||||||||
\(883\) | 4.03526e42i | 0.775250i | 0.921817 | + | 0.387625i | \(0.126704\pi\) | ||||
−0.921817 | + | 0.387625i | \(0.873296\pi\) | |||||||
\(884\) | 1.17597e41 | 0.0222249 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.19495e42 | 0.401453 | ||||||||
\(887\) | 1.14783e42i | 0.206532i | 0.994654 | + | 0.103266i | \(0.0329292\pi\) | ||||
−0.994654 | + | 0.103266i | \(0.967071\pi\) | |||||||
\(888\) | 2.52764e42i | 0.447432i | ||||||||
\(889\) | 5.79108e41 | 0.100852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.21906e42 | 1.21690 | ||||||||
\(892\) | − 9.17913e41i | − 0.152234i | ||||||||
\(893\) | − 9.74365e42i | − 1.58992i | ||||||||
\(894\) | −9.53571e42 | −1.53094 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.46554e41 | −0.100494 | ||||||||
\(897\) | 9.83288e41i | 0.150380i | ||||||||
\(898\) | − 7.54366e42i | − 1.13521i | ||||||||
\(899\) | 3.27082e42 | 0.484330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.20078e42 | −0.172169 | ||||||||
\(902\) | 2.20731e42i | 0.311436i | ||||||||
\(903\) | 4.60442e42i | 0.639296i | ||||||||
\(904\) | −1.06753e43 | −1.45860 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.43472e42 | −1.11612 | ||||||||
\(907\) | 1.34894e43i | 1.75666i | 0.478058 | + | 0.878328i | \(0.341341\pi\) | ||||
−0.478058 | + | 0.878328i | \(0.658659\pi\) | |||||||
\(908\) | 6.06854e42i | 0.777749i | ||||||||
\(909\) | −1.02874e42 | −0.129757 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.01049e42 | 0.367807 | 0.183904 | − | 0.982944i | \(-0.441127\pi\) | ||||
0.183904 | + | 0.982944i | \(0.441127\pi\) | |||||||
\(912\) | 3.86179e42i | 0.464369i | ||||||||
\(913\) | − 8.31825e42i | − 0.984477i | ||||||||
\(914\) | −9.31747e42 | −1.08537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.38704e42 | −0.269386 | ||||||||
\(917\) | − 6.93499e42i | − 0.770355i | ||||||||
\(918\) | 6.40704e41i | 0.0700549i | ||||||||
\(919\) | −6.28761e42 | −0.676723 | −0.338361 | − | 0.941016i | \(-0.609873\pi\) | ||||
−0.338361 | + | 0.941016i | \(0.609873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.11993e42 | −0.533949 | ||||||||
\(922\) | − 4.72163e42i | − 0.484723i | ||||||||
\(923\) | − 2.21489e42i | − 0.223835i | ||||||||
\(924\) | 8.33506e42 | 0.829211 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.34937e42 | −0.901412 | ||||||||
\(927\) | 2.96542e42i | 0.281469i | ||||||||
\(928\) | 4.67692e42i | 0.437034i | ||||||||
\(929\) | −1.66684e43 | −1.53344 | −0.766720 | − | 0.641982i | \(-0.778112\pi\) | ||||
−0.766720 | + | 0.641982i | \(0.778112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.12111e43 | 1.89144 | ||||||||
\(932\) | 4.53220e42i | 0.397904i | ||||||||
\(933\) | − 3.91887e42i | − 0.338748i | ||||||||
\(934\) | 1.72315e43 | 1.46654 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.80495e42 | 0.148925 | ||||||||
\(937\) | 1.87621e43i | 1.52426i | 0.647425 | + | 0.762129i | \(0.275846\pi\) | ||||
−0.647425 | + | 0.762129i | \(0.724154\pi\) | |||||||
\(938\) | 6.72869e42i | 0.538257i | ||||||||
\(939\) | 1.58659e43 | 1.24972 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.14783e42 | 0.393165 | 0.196582 | − | 0.980487i | \(-0.437016\pi\) | ||||
0.196582 | + | 0.980487i | \(0.437016\pi\) | |||||||
\(942\) | − 1.54651e42i | − 0.116309i | ||||||||
\(943\) | 1.70590e42i | 0.126338i | ||||||||
\(944\) | 6.39501e41 | 0.0466388 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.55077e42 | −0.251131 | ||||||||
\(947\) | 2.96240e42i | 0.206333i | 0.994664 | + | 0.103167i | \(0.0328975\pi\) | ||||
−0.994664 | + | 0.103167i | \(0.967103\pi\) | |||||||
\(948\) | 8.73443e42i | 0.599120i | ||||||||
\(949\) | −8.84653e42 | −0.597603 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.37222e43 | 1.55431 | ||||||||
\(952\) | 3.32225e42i | 0.214386i | ||||||||
\(953\) | 1.30942e43i | 0.832208i | 0.909317 | + | 0.416104i | \(0.136605\pi\) | ||||
−0.909317 | + | 0.416104i | \(0.863395\pi\) | |||||||
\(954\) | −5.57674e42 | −0.349083 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.06282e43 | 0.645390 | ||||||||
\(957\) | − 1.05615e43i | − 0.631690i | ||||||||
\(958\) | 2.89656e42i | 0.170640i | ||||||||
\(959\) | 3.79229e43 | 2.20055 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.99088e42 | −0.224688 | ||||||||
\(962\) | 2.09964e42i | 0.116441i | ||||||||
\(963\) | − 1.03575e43i | − 0.565816i | ||||||||
\(964\) | 6.77340e42 | 0.364493 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.40549e42 | −0.438929 | ||||||||
\(967\) | − 2.64169e43i | − 1.35894i | −0.733706 | − | 0.679468i | \(-0.762211\pi\) | ||||
0.733706 | − | 0.679468i | \(-0.237789\pi\) | |||||||
\(968\) | − 4.65630e40i | − 0.00235965i | ||||||||
\(969\) | −2.93905e42 | −0.146728 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.41602e43 | −1.65517 | −0.827583 | − | 0.561343i | \(-0.810285\pi\) | ||||
−0.827583 | + | 0.561343i | \(0.810285\pi\) | |||||||
\(972\) | − 5.64261e42i | − 0.269351i | ||||||||
\(973\) | − 3.42069e43i | − 1.60871i | ||||||||
\(974\) | −9.08670e42 | −0.421019 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.73884e42 | 0.303084 | ||||||||
\(977\) | − 2.06179e43i | − 0.913636i | −0.889560 | − | 0.456818i | \(-0.848989\pi\) | ||||
0.889560 | − | 0.456818i | \(-0.151011\pi\) | |||||||
\(978\) | 7.39489e42i | 0.322863i | ||||||||
\(979\) | 8.15238e42 | 0.350700 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.17891e43 | −0.492358 | ||||||||
\(982\) | − 1.06010e43i | − 0.436246i | ||||||||
\(983\) | − 1.21841e43i | − 0.494047i | −0.969009 | − | 0.247023i | \(-0.920548\pi\) | ||||
0.969009 | − | 0.247023i | \(-0.0794525\pi\) | |||||||
\(984\) | 1.28635e43 | 0.513961 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.27379e42 | 0.0494177 | ||||||||
\(987\) | − 7.44464e43i | − 2.84607i | ||||||||
\(988\) | − 5.28094e42i | − 0.198946i | ||||||||
\(989\) | −2.74418e42 | −0.101875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.94686e43 | −0.701888 | −0.350944 | − | 0.936397i | \(-0.614139\pi\) | ||||
−0.350944 | + | 0.936397i | \(0.614139\pi\) | |||||||
\(992\) | 1.96911e43i | 0.699600i | ||||||||
\(993\) | 1.62221e43i | 0.567994i | ||||||||
\(994\) | 1.89337e43 | 0.653329 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.46681e43 | −0.491601 | ||||||||
\(997\) | − 2.12798e43i | − 0.702891i | −0.936208 | − | 0.351446i | \(-0.885690\pi\) | ||||
0.936208 | − | 0.351446i | \(-0.114310\pi\) | |||||||
\(998\) | − 3.35674e43i | − 1.09276i | ||||||||
\(999\) | 8.76679e42 | 0.281282 |
(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 | 25.30.b.a.24.3 | 4 | ||
5.2 | odd | 4 | 1.30.a.a.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 25.30.a.a.1.2 | 2 | |||
5.4 | even | 2 | inner | 25.30.b.a.24.2 | 4 | ||
15.2 | even | 4 | 9.30.a.a.1.2 | 2 | |||
20.7 | even | 4 | 16.30.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.30.a.a.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
9.30.a.a.1.2 | 2 | 15.2 | even | 4 | |||
16.30.a.c.1.1 | 2 | 20.7 | even | 4 | |||
25.30.a.a.1.2 | 2 | 5.3 | odd | 4 | |||
25.30.b.a.24.2 | 4 | 5.4 | even | 2 | inner | ||
25.30.b.a.24.3 | 4 | 1.1 | even | 1 | trivial |