Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,24,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(10.0561211204\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{530401}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 132600 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-363.643\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1563.86 | 0.539949 | 0.269974 | − | 0.962867i | \(-0.412985\pi\) | ||||
0.269974 | + | 0.962867i | \(0.412985\pi\) | |||||||
\(3\) | −177147. | −0.577350 | ||||||||
\(4\) | −5.94295e6 | −0.708455 | ||||||||
\(5\) | 1.13630e8 | 1.04073 | 0.520365 | − | 0.853944i | \(-0.325796\pi\) | ||||
0.520365 | + | 0.853944i | \(0.325796\pi\) | |||||||
\(6\) | −2.77033e8 | −0.311740 | ||||||||
\(7\) | 7.85264e9 | 1.50103 | 0.750513 | − | 0.660856i | \(-0.229807\pi\) | ||||
0.750513 | + | 0.660856i | \(0.229807\pi\) | |||||||
\(8\) | −2.24125e10 | −0.922478 | ||||||||
\(9\) | 3.13811e10 | 0.333333 | ||||||||
\(10\) | 1.77701e11 | 0.561941 | ||||||||
\(11\) | 1.03137e12 | 1.08993 | 0.544966 | − | 0.838458i | \(-0.316543\pi\) | ||||
0.544966 | + | 0.838458i | \(0.316543\pi\) | |||||||
\(12\) | 1.05278e12 | 0.409027 | ||||||||
\(13\) | 8.08921e12 | 1.25187 | 0.625933 | − | 0.779877i | \(-0.284718\pi\) | ||||
0.625933 | + | 0.779877i | \(0.284718\pi\) | |||||||
\(14\) | 1.22804e13 | 0.810477 | ||||||||
\(15\) | −2.01292e13 | −0.600865 | ||||||||
\(16\) | 1.48030e13 | 0.210364 | ||||||||
\(17\) | −1.38649e14 | −0.981193 | −0.490597 | − | 0.871387i | \(-0.663221\pi\) | ||||
−0.490597 | + | 0.871387i | \(0.663221\pi\) | |||||||
\(18\) | 4.90756e13 | 0.179983 | ||||||||
\(19\) | −1.41905e14 | −0.279467 | −0.139734 | − | 0.990189i | \(-0.544625\pi\) | ||||
−0.139734 | + | 0.990189i | \(0.544625\pi\) | |||||||
\(20\) | −6.75297e14 | −0.737310 | ||||||||
\(21\) | −1.39107e15 | −0.866618 | ||||||||
\(22\) | 1.61292e15 | 0.588508 | ||||||||
\(23\) | 4.80770e15 | 1.05212 | 0.526062 | − | 0.850446i | \(-0.323668\pi\) | ||||
0.526062 | + | 0.850446i | \(0.323668\pi\) | |||||||
\(24\) | 3.97031e15 | 0.532593 | ||||||||
\(25\) | 9.90836e14 | 0.0831174 | ||||||||
\(26\) | 1.26504e16 | 0.675944 | ||||||||
\(27\) | −5.55906e15 | −0.192450 | ||||||||
\(28\) | −4.66679e16 | −1.06341 | ||||||||
\(29\) | −1.45614e16 | −0.221629 | −0.110814 | − | 0.993841i | \(-0.535346\pi\) | ||||
−0.110814 | + | 0.993841i | \(0.535346\pi\) | |||||||
\(30\) | −3.14792e16 | −0.324437 | ||||||||
\(31\) | −8.10883e16 | −0.573190 | −0.286595 | − | 0.958052i | \(-0.592523\pi\) | ||||
−0.286595 | + | 0.958052i | \(0.592523\pi\) | |||||||
\(32\) | 2.11160e17 | 1.03606 | ||||||||
\(33\) | −1.82704e17 | −0.629273 | ||||||||
\(34\) | −2.16828e17 | −0.529794 | ||||||||
\(35\) | 8.92295e17 | 1.56216 | ||||||||
\(36\) | −1.86496e17 | −0.236152 | ||||||||
\(37\) | 1.19418e18 | 1.10344 | 0.551720 | − | 0.834029i | \(-0.313972\pi\) | ||||
0.551720 | + | 0.834029i | \(0.313972\pi\) | |||||||
\(38\) | −2.21919e17 | −0.150898 | ||||||||
\(39\) | −1.43298e18 | −0.722765 | ||||||||
\(40\) | −2.54674e18 | −0.960050 | ||||||||
\(41\) | 6.63767e18 | 1.88365 | 0.941827 | − | 0.336098i | \(-0.109107\pi\) | ||||
0.941827 | + | 0.336098i | \(0.109107\pi\) | |||||||
\(42\) | −2.17544e18 | −0.467929 | ||||||||
\(43\) | −1.06144e19 | −1.74184 | −0.870920 | − | 0.491425i | \(-0.836476\pi\) | ||||
−0.870920 | + | 0.491425i | \(0.836476\pi\) | |||||||
\(44\) | −6.12940e18 | −0.772168 | ||||||||
\(45\) | 3.56583e18 | 0.346910 | ||||||||
\(46\) | 7.51856e18 | 0.568094 | ||||||||
\(47\) | 1.16951e19 | 0.690049 | 0.345024 | − | 0.938594i | \(-0.387871\pi\) | ||||
0.345024 | + | 0.938594i | \(0.387871\pi\) | |||||||
\(48\) | −2.62232e18 | −0.121454 | ||||||||
\(49\) | 3.42952e19 | 1.25308 | ||||||||
\(50\) | 1.54953e18 | 0.0448791 | ||||||||
\(51\) | 2.45613e19 | 0.566492 | ||||||||
\(52\) | −4.80738e19 | −0.886891 | ||||||||
\(53\) | −7.56809e19 | −1.12154 | −0.560769 | − | 0.827972i | \(-0.689494\pi\) | ||||
−0.560769 | + | 0.827972i | \(0.689494\pi\) | |||||||
\(54\) | −8.69359e18 | −0.103913 | ||||||||
\(55\) | 1.17195e20 | 1.13432 | ||||||||
\(56\) | −1.75998e20 | −1.38466 | ||||||||
\(57\) | 2.51380e19 | 0.161350 | ||||||||
\(58\) | −2.27720e19 | −0.119668 | ||||||||
\(59\) | −4.19627e19 | −0.181161 | −0.0905806 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905806 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(60\) | 1.19627e20 | 0.425686 | ||||||||
\(61\) | 7.45869e19 | 0.219467 | 0.109734 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109734 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(62\) | −1.26811e20 | −0.309493 | ||||||||
\(63\) | 2.46424e20 | 0.500342 | ||||||||
\(64\) | 2.06047e20 | 0.349058 | ||||||||
\(65\) | 9.19177e20 | 1.30285 | ||||||||
\(66\) | −2.85724e20 | −0.339775 | ||||||||
\(67\) | −1.29554e21 | −1.29595 | −0.647976 | − | 0.761661i | \(-0.724384\pi\) | ||||
−0.647976 | + | 0.761661i | \(0.724384\pi\) | |||||||
\(68\) | 8.23985e20 | 0.695131 | ||||||||
\(69\) | −8.51670e20 | −0.607444 | ||||||||
\(70\) | 1.39542e21 | 0.843487 | ||||||||
\(71\) | −2.37787e21 | −1.22101 | −0.610503 | − | 0.792014i | \(-0.709033\pi\) | ||||
−0.610503 | + | 0.792014i | \(0.709033\pi\) | |||||||
\(72\) | −7.03329e20 | −0.307493 | ||||||||
\(73\) | −3.03208e21 | −1.13117 | −0.565585 | − | 0.824690i | \(-0.691349\pi\) | ||||
−0.565585 | + | 0.824690i | \(0.691349\pi\) | |||||||
\(74\) | 1.86752e21 | 0.595801 | ||||||||
\(75\) | −1.75524e20 | −0.0479878 | ||||||||
\(76\) | 8.43334e20 | 0.197990 | ||||||||
\(77\) | 8.09899e21 | 1.63602 | ||||||||
\(78\) | −2.24098e21 | −0.390256 | ||||||||
\(79\) | 3.75756e20 | 0.0565190 | 0.0282595 | − | 0.999601i | \(-0.491004\pi\) | ||||
0.0282595 | + | 0.999601i | \(0.491004\pi\) | |||||||
\(80\) | 1.68207e21 | 0.218932 | ||||||||
\(81\) | 9.84771e20 | 0.111111 | ||||||||
\(82\) | 1.03804e22 | 1.01708 | ||||||||
\(83\) | −9.99994e21 | −0.852314 | −0.426157 | − | 0.904649i | \(-0.640133\pi\) | ||||
−0.426157 | + | 0.904649i | \(0.640133\pi\) | |||||||
\(84\) | 8.26707e21 | 0.613960 | ||||||||
\(85\) | −1.57547e22 | −1.02116 | ||||||||
\(86\) | −1.65994e22 | −0.940505 | ||||||||
\(87\) | 2.57951e21 | 0.127957 | ||||||||
\(88\) | −2.31157e22 | −1.00544 | ||||||||
\(89\) | −5.36043e21 | −0.204746 | −0.102373 | − | 0.994746i | \(-0.532643\pi\) | ||||
−0.102373 | + | 0.994746i | \(0.532643\pi\) | |||||||
\(90\) | 5.57645e21 | 0.187314 | ||||||||
\(91\) | 6.35217e22 | 1.87908 | ||||||||
\(92\) | −2.85719e22 | −0.745383 | ||||||||
\(93\) | 1.43645e22 | 0.330931 | ||||||||
\(94\) | 1.82895e22 | 0.372591 | ||||||||
\(95\) | −1.61246e22 | −0.290850 | ||||||||
\(96\) | −3.74063e22 | −0.598172 | ||||||||
\(97\) | 1.11058e22 | 0.157643 | 0.0788214 | − | 0.996889i | \(-0.474884\pi\) | ||||
0.0788214 | + | 0.996889i | \(0.474884\pi\) | |||||||
\(98\) | 5.36328e22 | 0.676598 | ||||||||
\(99\) | 3.23655e22 | 0.363311 | ||||||||
\(100\) | −5.88849e21 | −0.0588849 | ||||||||
\(101\) | 8.99589e22 | 0.802321 | 0.401160 | − | 0.916008i | \(-0.368607\pi\) | ||||
0.401160 | + | 0.916008i | \(0.368607\pi\) | |||||||
\(102\) | 3.84104e22 | 0.305877 | ||||||||
\(103\) | −8.83460e22 | −0.628867 | −0.314434 | − | 0.949279i | \(-0.601815\pi\) | ||||
−0.314434 | + | 0.949279i | \(0.601815\pi\) | |||||||
\(104\) | −1.81300e23 | −1.15482 | ||||||||
\(105\) | −1.58067e23 | −0.901914 | ||||||||
\(106\) | −1.18354e23 | −0.605573 | ||||||||
\(107\) | 2.32082e23 | 1.06593 | 0.532963 | − | 0.846138i | \(-0.321078\pi\) | ||||
0.532963 | + | 0.846138i | \(0.321078\pi\) | |||||||
\(108\) | 3.30372e22 | 0.136342 | ||||||||
\(109\) | −2.76863e23 | −1.02768 | −0.513842 | − | 0.857885i | \(-0.671778\pi\) | ||||
−0.513842 | + | 0.857885i | \(0.671778\pi\) | |||||||
\(110\) | 1.83276e23 | 0.612477 | ||||||||
\(111\) | −2.11545e23 | −0.637071 | ||||||||
\(112\) | 1.16243e23 | 0.315762 | ||||||||
\(113\) | 3.71795e23 | 0.911803 | 0.455901 | − | 0.890030i | \(-0.349317\pi\) | ||||
0.455901 | + | 0.890030i | \(0.349317\pi\) | |||||||
\(114\) | 3.93123e22 | 0.0871210 | ||||||||
\(115\) | 5.46299e23 | 1.09498 | ||||||||
\(116\) | 8.65376e22 | 0.157014 | ||||||||
\(117\) | 2.53848e23 | 0.417289 | ||||||||
\(118\) | −6.56237e22 | −0.0978178 | ||||||||
\(119\) | −1.08876e24 | −1.47280 | ||||||||
\(120\) | 4.51147e23 | 0.554285 | ||||||||
\(121\) | 1.68298e23 | 0.187952 | ||||||||
\(122\) | 1.16643e23 | 0.118501 | ||||||||
\(123\) | −1.17584e24 | −1.08753 | ||||||||
\(124\) | 4.81904e23 | 0.406080 | ||||||||
\(125\) | −1.24199e24 | −0.954227 | ||||||||
\(126\) | 3.85373e23 | 0.270159 | ||||||||
\(127\) | −1.60553e24 | −1.02772 | −0.513861 | − | 0.857874i | \(-0.671785\pi\) | ||||
−0.513861 | + | 0.857874i | \(0.671785\pi\) | |||||||
\(128\) | −1.44911e24 | −0.847591 | ||||||||
\(129\) | 1.88031e24 | 1.00565 | ||||||||
\(130\) | 1.43746e24 | 0.703474 | ||||||||
\(131\) | 2.07814e24 | 0.931228 | 0.465614 | − | 0.884988i | \(-0.345834\pi\) | ||||
0.465614 | + | 0.884988i | \(0.345834\pi\) | |||||||
\(132\) | 1.08580e24 | 0.445811 | ||||||||
\(133\) | −1.11433e24 | −0.419487 | ||||||||
\(134\) | −2.02603e24 | −0.699748 | ||||||||
\(135\) | −6.31676e23 | −0.200288 | ||||||||
\(136\) | 3.10748e24 | 0.905130 | ||||||||
\(137\) | 4.86669e24 | 1.30301 | 0.651504 | − | 0.758645i | \(-0.274138\pi\) | ||||
0.651504 | + | 0.758645i | \(0.274138\pi\) | |||||||
\(138\) | −1.33189e24 | −0.327989 | ||||||||
\(139\) | 9.05962e23 | 0.205324 | 0.102662 | − | 0.994716i | \(-0.467264\pi\) | ||||
0.102662 | + | 0.994716i | \(0.467264\pi\) | |||||||
\(140\) | −5.30287e24 | −1.10672 | ||||||||
\(141\) | −2.07176e24 | −0.398400 | ||||||||
\(142\) | −3.71866e24 | −0.659281 | ||||||||
\(143\) | 8.34299e24 | 1.36445 | ||||||||
\(144\) | 4.64535e23 | 0.0701213 | ||||||||
\(145\) | −1.65461e24 | −0.230655 | ||||||||
\(146\) | −4.74175e24 | −0.610774 | ||||||||
\(147\) | −6.07529e24 | −0.723465 | ||||||||
\(148\) | −7.09694e24 | −0.781738 | ||||||||
\(149\) | 9.86509e24 | 1.00568 | 0.502839 | − | 0.864380i | \(-0.332289\pi\) | ||||
0.502839 | + | 0.864380i | \(0.332289\pi\) | |||||||
\(150\) | −2.74494e23 | −0.0259110 | ||||||||
\(151\) | −4.82721e24 | −0.422145 | −0.211072 | − | 0.977470i | \(-0.567696\pi\) | ||||
−0.211072 | + | 0.977470i | \(0.567696\pi\) | |||||||
\(152\) | 3.18045e24 | 0.257802 | ||||||||
\(153\) | −4.35096e24 | −0.327064 | ||||||||
\(154\) | 1.26657e25 | 0.883365 | ||||||||
\(155\) | −9.21406e24 | −0.596536 | ||||||||
\(156\) | 8.51613e24 | 0.512047 | ||||||||
\(157\) | 1.87063e24 | 0.104506 | 0.0522529 | − | 0.998634i | \(-0.483360\pi\) | ||||
0.0522529 | + | 0.998634i | \(0.483360\pi\) | |||||||
\(158\) | 5.87629e23 | 0.0305174 | ||||||||
\(159\) | 1.34067e25 | 0.647520 | ||||||||
\(160\) | 2.39941e25 | 1.07826 | ||||||||
\(161\) | 3.77531e25 | 1.57927 | ||||||||
\(162\) | 1.54004e24 | 0.0599943 | ||||||||
\(163\) | −3.92032e25 | −1.42286 | −0.711432 | − | 0.702755i | \(-0.751953\pi\) | ||||
−0.711432 | + | 0.702755i | \(0.751953\pi\) | |||||||
\(164\) | −3.94473e25 | −1.33448 | ||||||||
\(165\) | −2.07607e25 | −0.654902 | ||||||||
\(166\) | −1.56385e25 | −0.460206 | ||||||||
\(167\) | −4.64021e25 | −1.27438 | −0.637188 | − | 0.770708i | \(-0.719903\pi\) | ||||
−0.637188 | + | 0.770708i | \(0.719903\pi\) | |||||||
\(168\) | 3.11774e25 | 0.799436 | ||||||||
\(169\) | 2.36815e25 | 0.567168 | ||||||||
\(170\) | −2.46381e25 | −0.551372 | ||||||||
\(171\) | −4.45312e24 | −0.0931557 | ||||||||
\(172\) | 6.30809e25 | 1.23402 | ||||||||
\(173\) | −4.74788e25 | −0.868900 | −0.434450 | − | 0.900696i | \(-0.643057\pi\) | ||||
−0.434450 | + | 0.900696i | \(0.643057\pi\) | |||||||
\(174\) | 4.03398e24 | 0.0690904 | ||||||||
\(175\) | 7.78068e24 | 0.124761 | ||||||||
\(176\) | 1.52674e25 | 0.229282 | ||||||||
\(177\) | 7.43356e24 | 0.104593 | ||||||||
\(178\) | −8.38295e24 | −0.110552 | ||||||||
\(179\) | 5.97561e25 | 0.738878 | 0.369439 | − | 0.929255i | \(-0.379550\pi\) | ||||
0.369439 | + | 0.929255i | \(0.379550\pi\) | |||||||
\(180\) | −2.11915e25 | −0.245770 | ||||||||
\(181\) | 3.92753e25 | 0.427381 | 0.213691 | − | 0.976901i | \(-0.431452\pi\) | ||||
0.213691 | + | 0.976901i | \(0.431452\pi\) | |||||||
\(182\) | 9.93389e25 | 1.01461 | ||||||||
\(183\) | −1.32128e25 | −0.126709 | ||||||||
\(184\) | −1.07753e26 | −0.970562 | ||||||||
\(185\) | 1.35694e26 | 1.14838 | ||||||||
\(186\) | 2.24641e25 | 0.178686 | ||||||||
\(187\) | −1.42999e26 | −1.06943 | ||||||||
\(188\) | −6.95036e25 | −0.488869 | ||||||||
\(189\) | −4.36533e25 | −0.288873 | ||||||||
\(190\) | −2.52167e25 | −0.157044 | ||||||||
\(191\) | −9.94591e25 | −0.583124 | −0.291562 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291562 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(192\) | −3.65007e25 | −0.201529 | ||||||||
\(193\) | 2.11752e26 | 1.10133 | 0.550667 | − | 0.834725i | \(-0.314373\pi\) | ||||
0.550667 | + | 0.834725i | \(0.314373\pi\) | |||||||
\(194\) | 1.73679e25 | 0.0851190 | ||||||||
\(195\) | −1.62829e26 | −0.752203 | ||||||||
\(196\) | −2.03815e26 | −0.887750 | ||||||||
\(197\) | 2.43182e26 | 0.999009 | 0.499505 | − | 0.866311i | \(-0.333515\pi\) | ||||
0.499505 | + | 0.866311i | \(0.333515\pi\) | |||||||
\(198\) | 5.06151e25 | 0.196169 | ||||||||
\(199\) | −2.49955e26 | −0.914220 | −0.457110 | − | 0.889410i | \(-0.651115\pi\) | ||||
−0.457110 | + | 0.889410i | \(0.651115\pi\) | |||||||
\(200\) | −2.22072e25 | −0.0766740 | ||||||||
\(201\) | 2.29500e26 | 0.748218 | ||||||||
\(202\) | 1.40683e26 | 0.433212 | ||||||||
\(203\) | −1.14345e26 | −0.332670 | ||||||||
\(204\) | −1.45967e26 | −0.401334 | ||||||||
\(205\) | 7.54238e26 | 1.96037 | ||||||||
\(206\) | −1.38161e26 | −0.339556 | ||||||||
\(207\) | 1.50871e26 | 0.350708 | ||||||||
\(208\) | 1.19745e26 | 0.263347 | ||||||||
\(209\) | −1.46357e26 | −0.304600 | ||||||||
\(210\) | −2.47195e26 | −0.486988 | ||||||||
\(211\) | −2.68608e26 | −0.501038 | −0.250519 | − | 0.968112i | \(-0.580601\pi\) | ||||
−0.250519 | + | 0.968112i | \(0.580601\pi\) | |||||||
\(212\) | 4.49768e26 | 0.794560 | ||||||||
\(213\) | 4.21233e26 | 0.704948 | ||||||||
\(214\) | 3.62943e26 | 0.575546 | ||||||||
\(215\) | −1.20611e27 | −1.81278 | ||||||||
\(216\) | 1.24593e26 | 0.177531 | ||||||||
\(217\) | −6.36757e26 | −0.860373 | ||||||||
\(218\) | −4.32974e26 | −0.554897 | ||||||||
\(219\) | 5.37124e26 | 0.653081 | ||||||||
\(220\) | −6.96483e26 | −0.803618 | ||||||||
\(221\) | −1.12156e27 | −1.22832 | ||||||||
\(222\) | −3.30826e26 | −0.343986 | ||||||||
\(223\) | 4.28148e25 | 0.0422754 | 0.0211377 | − | 0.999777i | \(-0.493271\pi\) | ||||
0.0211377 | + | 0.999777i | \(0.493271\pi\) | |||||||
\(224\) | 1.65816e27 | 1.55516 | ||||||||
\(225\) | 3.10935e25 | 0.0277058 | ||||||||
\(226\) | 5.81434e26 | 0.492327 | ||||||||
\(227\) | 1.04141e27 | 0.838154 | 0.419077 | − | 0.907951i | \(-0.362354\pi\) | ||||
0.419077 | + | 0.907951i | \(0.362354\pi\) | |||||||
\(228\) | −1.49394e26 | −0.114310 | ||||||||
\(229\) | 3.17314e26 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(230\) | 8.54334e26 | 0.591232 | ||||||||
\(231\) | −1.43471e27 | −0.944554 | ||||||||
\(232\) | 3.26358e26 | 0.204448 | ||||||||
\(233\) | 1.07463e27 | 0.640715 | 0.320357 | − | 0.947297i | \(-0.396197\pi\) | ||||
0.320357 | + | 0.947297i | \(0.396197\pi\) | |||||||
\(234\) | 3.96983e26 | 0.225315 | ||||||||
\(235\) | 1.32892e27 | 0.718154 | ||||||||
\(236\) | 2.49382e26 | 0.128345 | ||||||||
\(237\) | −6.65640e25 | −0.0326312 | ||||||||
\(238\) | −1.70267e27 | −0.795235 | ||||||||
\(239\) | −2.91187e27 | −1.29598 | −0.647988 | − | 0.761651i | \(-0.724389\pi\) | ||||
−0.647988 | + | 0.761651i | \(0.724389\pi\) | |||||||
\(240\) | −2.97974e26 | −0.126400 | ||||||||
\(241\) | −1.77639e27 | −0.718362 | −0.359181 | − | 0.933268i | \(-0.616944\pi\) | ||||
−0.359181 | + | 0.933268i | \(0.616944\pi\) | |||||||
\(242\) | 2.63194e26 | 0.101484 | ||||||||
\(243\) | −1.74449e26 | −0.0641500 | ||||||||
\(244\) | −4.43266e26 | −0.155483 | ||||||||
\(245\) | 3.89696e27 | 1.30411 | ||||||||
\(246\) | −1.83885e27 | −0.587210 | ||||||||
\(247\) | −1.14790e27 | −0.349855 | ||||||||
\(248\) | 1.81739e27 | 0.528756 | ||||||||
\(249\) | 1.77146e27 | 0.492084 | ||||||||
\(250\) | −1.94229e27 | −0.515234 | ||||||||
\(251\) | −4.39892e27 | −1.11455 | −0.557274 | − | 0.830329i | \(-0.688153\pi\) | ||||
−0.557274 | + | 0.830329i | \(0.688153\pi\) | |||||||
\(252\) | −1.46449e27 | −0.354470 | ||||||||
\(253\) | 4.95853e27 | 1.14674 | ||||||||
\(254\) | −2.51082e27 | −0.554917 | ||||||||
\(255\) | 2.79090e27 | 0.589565 | ||||||||
\(256\) | −3.99465e27 | −0.806714 | ||||||||
\(257\) | 3.06305e27 | 0.591457 | 0.295729 | − | 0.955272i | \(-0.404438\pi\) | ||||
0.295729 | + | 0.955272i | \(0.404438\pi\) | |||||||
\(258\) | 2.94054e27 | 0.543001 | ||||||||
\(259\) | 9.37744e27 | 1.65629 | ||||||||
\(260\) | −5.46263e27 | −0.923013 | ||||||||
\(261\) | −4.56952e26 | −0.0738762 | ||||||||
\(262\) | 3.24992e27 | 0.502815 | ||||||||
\(263\) | 4.37920e27 | 0.648491 | 0.324246 | − | 0.945973i | \(-0.394890\pi\) | ||||
0.324246 | + | 0.945973i | \(0.394890\pi\) | |||||||
\(264\) | 4.09487e27 | 0.580490 | ||||||||
\(265\) | −8.59962e27 | −1.16722 | ||||||||
\(266\) | −1.74265e27 | −0.226502 | ||||||||
\(267\) | 9.49584e26 | 0.118210 | ||||||||
\(268\) | 7.69930e27 | 0.918124 | ||||||||
\(269\) | −1.36648e28 | −1.56118 | −0.780588 | − | 0.625046i | \(-0.785080\pi\) | ||||
−0.780588 | + | 0.625046i | \(0.785080\pi\) | |||||||
\(270\) | −9.87852e26 | −0.108146 | ||||||||
\(271\) | −7.06980e27 | −0.741755 | −0.370878 | − | 0.928682i | \(-0.620943\pi\) | ||||
−0.370878 | + | 0.928682i | \(0.620943\pi\) | |||||||
\(272\) | −2.05243e27 | −0.206408 | ||||||||
\(273\) | −1.12527e28 | −1.08489 | ||||||||
\(274\) | 7.61081e27 | 0.703558 | ||||||||
\(275\) | 1.02192e27 | 0.0905923 | ||||||||
\(276\) | 5.06143e27 | 0.430347 | ||||||||
\(277\) | 1.02188e28 | 0.833460 | 0.416730 | − | 0.909030i | \(-0.363176\pi\) | ||||
0.416730 | + | 0.909030i | \(0.363176\pi\) | |||||||
\(278\) | 1.41680e27 | 0.110865 | ||||||||
\(279\) | −2.54464e27 | −0.191063 | ||||||||
\(280\) | −1.99986e28 | −1.44106 | ||||||||
\(281\) | −8.03841e26 | −0.0555965 | −0.0277983 | − | 0.999614i | \(-0.508850\pi\) | ||||
−0.0277983 | + | 0.999614i | \(0.508850\pi\) | |||||||
\(282\) | −3.23994e27 | −0.215116 | ||||||||
\(283\) | −2.15414e28 | −1.37318 | −0.686592 | − | 0.727043i | \(-0.740894\pi\) | ||||
−0.686592 | + | 0.727043i | \(0.740894\pi\) | |||||||
\(284\) | 1.41316e28 | 0.865028 | ||||||||
\(285\) | 2.85643e27 | 0.167922 | ||||||||
\(286\) | 1.30473e28 | 0.736733 | ||||||||
\(287\) | 5.21232e28 | 2.82741 | ||||||||
\(288\) | 6.62642e27 | 0.345355 | ||||||||
\(289\) | −7.43986e26 | −0.0372597 | ||||||||
\(290\) | −2.58758e27 | −0.124542 | ||||||||
\(291\) | −1.96735e27 | −0.0910151 | ||||||||
\(292\) | 1.80195e28 | 0.801383 | ||||||||
\(293\) | −2.33106e28 | −0.996725 | −0.498363 | − | 0.866969i | \(-0.666065\pi\) | ||||
−0.498363 | + | 0.866969i | \(0.666065\pi\) | |||||||
\(294\) | −9.50089e27 | −0.390634 | ||||||||
\(295\) | −4.76822e27 | −0.188540 | ||||||||
\(296\) | −2.67645e28 | −1.01790 | ||||||||
\(297\) | −5.73346e27 | −0.209758 | ||||||||
\(298\) | 1.54276e28 | 0.543015 | ||||||||
\(299\) | 3.88905e28 | 1.31712 | ||||||||
\(300\) | 1.04313e27 | 0.0339972 | ||||||||
\(301\) | −8.33511e28 | −2.61455 | ||||||||
\(302\) | −7.54907e27 | −0.227936 | ||||||||
\(303\) | −1.59359e28 | −0.463220 | ||||||||
\(304\) | −2.10062e27 | −0.0587898 | ||||||||
\(305\) | 8.47531e27 | 0.228406 | ||||||||
\(306\) | −6.80428e27 | −0.176598 | ||||||||
\(307\) | 6.97395e28 | 1.74336 | 0.871681 | − | 0.490074i | \(-0.163030\pi\) | ||||
0.871681 | + | 0.490074i | \(0.163030\pi\) | |||||||
\(308\) | −4.81319e28 | −1.15904 | ||||||||
\(309\) | 1.56502e28 | 0.363077 | ||||||||
\(310\) | −1.44095e28 | −0.322099 | ||||||||
\(311\) | −4.01460e28 | −0.864765 | −0.432382 | − | 0.901690i | \(-0.642327\pi\) | ||||
−0.432382 | + | 0.901690i | \(0.642327\pi\) | |||||||
\(312\) | 3.21167e28 | 0.666735 | ||||||||
\(313\) | 7.08075e28 | 1.41683 | 0.708417 | − | 0.705794i | \(-0.249409\pi\) | ||||
0.708417 | + | 0.705794i | \(0.249409\pi\) | |||||||
\(314\) | 2.92539e27 | 0.0564278 | ||||||||
\(315\) | 2.80012e28 | 0.520720 | ||||||||
\(316\) | −2.23310e27 | −0.0400412 | ||||||||
\(317\) | −3.21150e28 | −0.555298 | −0.277649 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277649 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(318\) | 2.09661e28 | 0.349628 | ||||||||
\(319\) | −1.50182e28 | −0.241560 | ||||||||
\(320\) | 2.34132e28 | 0.363275 | ||||||||
\(321\) | −4.11126e28 | −0.615413 | ||||||||
\(322\) | 5.90406e28 | 0.852723 | ||||||||
\(323\) | 1.96750e28 | 0.274211 | ||||||||
\(324\) | −5.85245e27 | −0.0787172 | ||||||||
\(325\) | 8.01509e27 | 0.104052 | ||||||||
\(326\) | −6.13082e28 | −0.768274 | ||||||||
\(327\) | 4.90454e28 | 0.593333 | ||||||||
\(328\) | −1.48767e29 | −1.73763 | ||||||||
\(329\) | 9.18377e28 | 1.03578 | ||||||||
\(330\) | −3.24668e28 | −0.353614 | ||||||||
\(331\) | 8.40986e28 | 0.884640 | 0.442320 | − | 0.896857i | \(-0.354155\pi\) | ||||
0.442320 | + | 0.896857i | \(0.354155\pi\) | |||||||
\(332\) | 5.94292e28 | 0.603826 | ||||||||
\(333\) | 3.74745e28 | 0.367813 | ||||||||
\(334\) | −7.25663e28 | −0.688098 | ||||||||
\(335\) | −1.47212e29 | −1.34874 | ||||||||
\(336\) | −2.05921e28 | −0.182305 | ||||||||
\(337\) | −1.63996e29 | −1.40311 | −0.701553 | − | 0.712618i | \(-0.747510\pi\) | ||||
−0.701553 | + | 0.712618i | \(0.747510\pi\) | |||||||
\(338\) | 3.70345e28 | 0.306242 | ||||||||
\(339\) | −6.58623e28 | −0.526430 | ||||||||
\(340\) | 9.36294e28 | 0.723444 | ||||||||
\(341\) | −8.36322e28 | −0.624738 | ||||||||
\(342\) | −6.96406e27 | −0.0502993 | ||||||||
\(343\) | 5.43907e28 | 0.379877 | ||||||||
\(344\) | 2.37896e29 | 1.60681 | ||||||||
\(345\) | −9.67752e28 | −0.632185 | ||||||||
\(346\) | −7.42502e28 | −0.469162 | ||||||||
\(347\) | 6.78465e28 | 0.414704 | 0.207352 | − | 0.978266i | \(-0.433515\pi\) | ||||
0.207352 | + | 0.978266i | \(0.433515\pi\) | |||||||
\(348\) | −1.53299e28 | −0.0906520 | ||||||||
\(349\) | 1.82821e29 | 1.04601 | 0.523003 | − | 0.852331i | \(-0.324812\pi\) | ||||
0.523003 | + | 0.852331i | \(0.324812\pi\) | |||||||
\(350\) | 1.21679e28 | 0.0673647 | ||||||||
\(351\) | −4.49684e28 | −0.240922 | ||||||||
\(352\) | 2.17784e29 | 1.12924 | ||||||||
\(353\) | 1.44105e29 | 0.723218 | 0.361609 | − | 0.932330i | \(-0.382228\pi\) | ||||
0.361609 | + | 0.932330i | \(0.382228\pi\) | |||||||
\(354\) | 1.16250e28 | 0.0564751 | ||||||||
\(355\) | −2.70198e29 | −1.27074 | ||||||||
\(356\) | 3.18568e28 | 0.145053 | ||||||||
\(357\) | 1.92871e29 | 0.850319 | ||||||||
\(358\) | 9.34501e28 | 0.398956 | ||||||||
\(359\) | −3.54388e28 | −0.146519 | −0.0732593 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732593 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(360\) | −7.99193e28 | −0.320017 | ||||||||
\(361\) | −2.37693e29 | −0.921898 | ||||||||
\(362\) | 6.14210e28 | 0.230764 | ||||||||
\(363\) | −2.98135e28 | −0.108514 | ||||||||
\(364\) | −3.77506e29 | −1.33125 | ||||||||
\(365\) | −3.44535e29 | −1.17724 | ||||||||
\(366\) | −2.06630e28 | −0.0684166 | ||||||||
\(367\) | 1.57063e29 | 0.503981 | 0.251990 | − | 0.967730i | \(-0.418915\pi\) | ||||
0.251990 | + | 0.967730i | \(0.418915\pi\) | |||||||
\(368\) | 7.11686e28 | 0.221329 | ||||||||
\(369\) | 2.08297e29 | 0.627885 | ||||||||
\(370\) | 2.12207e29 | 0.620068 | ||||||||
\(371\) | −5.94295e29 | −1.68346 | ||||||||
\(372\) | −8.53678e28 | −0.234450 | ||||||||
\(373\) | 4.68656e29 | 1.24796 | 0.623982 | − | 0.781438i | \(-0.285514\pi\) | ||||
0.623982 | + | 0.781438i | \(0.285514\pi\) | |||||||
\(374\) | −2.23630e29 | −0.577440 | ||||||||
\(375\) | 2.20014e29 | 0.550923 | ||||||||
\(376\) | −2.62118e29 | −0.636555 | ||||||||
\(377\) | −1.17790e29 | −0.277449 | ||||||||
\(378\) | −6.82676e28 | −0.155976 | ||||||||
\(379\) | 4.57537e28 | 0.101409 | 0.0507044 | − | 0.998714i | \(-0.483853\pi\) | ||||
0.0507044 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(380\) | 9.58280e28 | 0.206054 | ||||||||
\(381\) | 2.84415e29 | 0.593355 | ||||||||
\(382\) | −1.55540e29 | −0.314857 | ||||||||
\(383\) | 4.53749e29 | 0.891312 | 0.445656 | − | 0.895204i | \(-0.352970\pi\) | ||||
0.445656 | + | 0.895204i | \(0.352970\pi\) | |||||||
\(384\) | 2.56705e29 | 0.489357 | ||||||||
\(385\) | 9.20288e29 | 1.70265 | ||||||||
\(386\) | 3.31151e29 | 0.594664 | ||||||||
\(387\) | −3.33091e29 | −0.580613 | ||||||||
\(388\) | −6.60011e28 | −0.111683 | ||||||||
\(389\) | 3.59874e29 | 0.591195 | 0.295597 | − | 0.955313i | \(-0.404481\pi\) | ||||
0.295597 | + | 0.955313i | \(0.404481\pi\) | |||||||
\(390\) | −2.54642e29 | −0.406151 | ||||||||
\(391\) | −6.66583e29 | −1.03234 | ||||||||
\(392\) | −7.68642e29 | −1.15594 | ||||||||
\(393\) | −3.68137e29 | −0.537644 | ||||||||
\(394\) | 3.80302e29 | 0.539414 | ||||||||
\(395\) | 4.26971e28 | 0.0588210 | ||||||||
\(396\) | −1.92347e29 | −0.257389 | ||||||||
\(397\) | −9.62669e28 | −0.125137 | −0.0625686 | − | 0.998041i | \(-0.519929\pi\) | ||||
−0.0625686 | + | 0.998041i | \(0.519929\pi\) | |||||||
\(398\) | −3.90894e29 | −0.493632 | ||||||||
\(399\) | 1.97400e29 | 0.242191 | ||||||||
\(400\) | 1.46674e28 | 0.0174849 | ||||||||
\(401\) | 4.97920e29 | 0.576766 | 0.288383 | − | 0.957515i | \(-0.406882\pi\) | ||||
0.288383 | + | 0.957515i | \(0.406882\pi\) | |||||||
\(402\) | 3.58906e29 | 0.404000 | ||||||||
\(403\) | −6.55941e29 | −0.717557 | ||||||||
\(404\) | −5.34621e29 | −0.568408 | ||||||||
\(405\) | 1.11899e29 | 0.115637 | ||||||||
\(406\) | −1.78820e29 | −0.179625 | ||||||||
\(407\) | 1.23164e30 | 1.20267 | ||||||||
\(408\) | −5.50481e29 | −0.522577 | ||||||||
\(409\) | −1.48649e30 | −1.37197 | −0.685985 | − | 0.727616i | \(-0.740628\pi\) | ||||
−0.685985 | + | 0.727616i | \(0.740628\pi\) | |||||||
\(410\) | 1.17952e30 | 1.05850 | ||||||||
\(411\) | −8.62119e29 | −0.752292 | ||||||||
\(412\) | 5.25036e29 | 0.445524 | ||||||||
\(413\) | −3.29518e29 | −0.271928 | ||||||||
\(414\) | 2.35941e29 | 0.189365 | ||||||||
\(415\) | −1.13629e30 | −0.887028 | ||||||||
\(416\) | 1.70812e30 | 1.29701 | ||||||||
\(417\) | −1.60489e29 | −0.118544 | ||||||||
\(418\) | −2.28881e29 | −0.164469 | ||||||||
\(419\) | −5.07194e29 | −0.354579 | −0.177289 | − | 0.984159i | \(-0.556733\pi\) | ||||
−0.177289 | + | 0.984159i | \(0.556733\pi\) | |||||||
\(420\) | 9.39387e29 | 0.638966 | ||||||||
\(421\) | 2.56153e30 | 1.69533 | 0.847666 | − | 0.530531i | \(-0.178007\pi\) | ||||
0.847666 | + | 0.530531i | \(0.178007\pi\) | |||||||
\(422\) | −4.20065e29 | −0.270535 | ||||||||
\(423\) | 3.67006e29 | 0.230016 | ||||||||
\(424\) | 1.69620e30 | 1.03459 | ||||||||
\(425\) | −1.37379e29 | −0.0815542 | ||||||||
\(426\) | 6.58749e29 | 0.380636 | ||||||||
\(427\) | 5.85704e29 | 0.329426 | ||||||||
\(428\) | −1.37925e30 | −0.755161 | ||||||||
\(429\) | −1.47794e30 | −0.787765 | ||||||||
\(430\) | −1.88619e30 | −0.978811 | ||||||||
\(431\) | −1.21646e30 | −0.614625 | −0.307312 | − | 0.951609i | \(-0.599430\pi\) | ||||
−0.307312 | + | 0.951609i | \(0.599430\pi\) | |||||||
\(432\) | −8.22910e28 | −0.0404846 | ||||||||
\(433\) | 1.79430e30 | 0.859577 | 0.429789 | − | 0.902930i | \(-0.358588\pi\) | ||||
0.429789 | + | 0.902930i | \(0.358588\pi\) | |||||||
\(434\) | −9.95798e29 | −0.464558 | ||||||||
\(435\) | 2.93109e29 | 0.133169 | ||||||||
\(436\) | 1.64538e30 | 0.728068 | ||||||||
\(437\) | −6.82236e29 | −0.294034 | ||||||||
\(438\) | 8.39986e29 | 0.352630 | ||||||||
\(439\) | −3.97063e30 | −1.62374 | −0.811871 | − | 0.583837i | \(-0.801551\pi\) | ||||
−0.811871 | + | 0.583837i | \(0.801551\pi\) | |||||||
\(440\) | −2.62663e30 | −1.04639 | ||||||||
\(441\) | 1.07622e30 | 0.417693 | ||||||||
\(442\) | −1.75397e30 | −0.663231 | ||||||||
\(443\) | −1.28735e30 | −0.474301 | −0.237151 | − | 0.971473i | \(-0.576213\pi\) | ||||
−0.237151 | + | 0.971473i | \(0.576213\pi\) | |||||||
\(444\) | 1.25720e30 | 0.451337 | ||||||||
\(445\) | −6.09105e29 | −0.213085 | ||||||||
\(446\) | 6.69562e28 | 0.0228265 | ||||||||
\(447\) | −1.74757e30 | −0.580628 | ||||||||
\(448\) | 1.61802e30 | 0.523945 | ||||||||
\(449\) | 3.17012e30 | 1.00056 | 0.500279 | − | 0.865864i | \(-0.333231\pi\) | ||||
0.500279 | + | 0.865864i | \(0.333231\pi\) | |||||||
\(450\) | 4.86258e28 | 0.0149597 | ||||||||
\(451\) | 6.84590e30 | 2.05305 | ||||||||
\(452\) | −2.20956e30 | −0.645971 | ||||||||
\(453\) | 8.55126e29 | 0.243725 | ||||||||
\(454\) | 1.62862e30 | 0.452560 | ||||||||
\(455\) | 7.21796e30 | 1.95562 | ||||||||
\(456\) | −5.63407e29 | −0.148842 | ||||||||
\(457\) | −6.89795e30 | −1.77699 | −0.888493 | − | 0.458891i | \(-0.848247\pi\) | ||||
−0.888493 | + | 0.458891i | \(0.848247\pi\) | |||||||
\(458\) | 4.96234e29 | 0.124662 | ||||||||
\(459\) | 7.70759e29 | 0.188831 | ||||||||
\(460\) | −3.24663e30 | −0.775742 | ||||||||
\(461\) | −1.25314e30 | −0.292038 | −0.146019 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146019 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(462\) | −2.24369e30 | −0.510011 | ||||||||
\(463\) | 4.87399e30 | 1.08070 | 0.540348 | − | 0.841442i | \(-0.318293\pi\) | ||||
0.540348 | + | 0.841442i | \(0.318293\pi\) | |||||||
\(464\) | −2.15553e29 | −0.0466227 | ||||||||
\(465\) | 1.63224e30 | 0.344410 | ||||||||
\(466\) | 1.68057e30 | 0.345953 | ||||||||
\(467\) | 4.35835e30 | 0.875343 | 0.437671 | − | 0.899135i | \(-0.355803\pi\) | ||||
0.437671 | + | 0.899135i | \(0.355803\pi\) | |||||||
\(468\) | −1.50861e30 | −0.295630 | ||||||||
\(469\) | −1.01734e31 | −1.94526 | ||||||||
\(470\) | 2.07824e30 | 0.387766 | ||||||||
\(471\) | −3.31376e29 | −0.0603365 | ||||||||
\(472\) | 9.40490e29 | 0.167117 | ||||||||
\(473\) | −1.09474e31 | −1.89849 | ||||||||
\(474\) | −1.04097e29 | −0.0176192 | ||||||||
\(475\) | −1.40604e29 | −0.0232286 | ||||||||
\(476\) | 6.47046e30 | 1.04341 | ||||||||
\(477\) | −2.37495e30 | −0.373846 | ||||||||
\(478\) | −4.55376e30 | −0.699760 | ||||||||
\(479\) | 4.80333e30 | 0.720582 | 0.360291 | − | 0.932840i | \(-0.382677\pi\) | ||||
0.360291 | + | 0.932840i | \(0.382677\pi\) | |||||||
\(480\) | −4.25048e30 | −0.622535 | ||||||||
\(481\) | 9.65995e30 | 1.38136 | ||||||||
\(482\) | −2.77803e30 | −0.387879 | ||||||||
\(483\) | −6.68785e30 | −0.911790 | ||||||||
\(484\) | −1.00019e30 | −0.133156 | ||||||||
\(485\) | 1.26195e30 | 0.164063 | ||||||||
\(486\) | −2.72814e29 | −0.0346377 | ||||||||
\(487\) | −3.71714e30 | −0.460920 | −0.230460 | − | 0.973082i | \(-0.574023\pi\) | ||||
−0.230460 | + | 0.973082i | \(0.574023\pi\) | |||||||
\(488\) | −1.67168e30 | −0.202454 | ||||||||
\(489\) | 6.94472e30 | 0.821491 | ||||||||
\(490\) | 6.09429e30 | 0.704155 | ||||||||
\(491\) | 7.53933e30 | 0.850933 | 0.425466 | − | 0.904974i | \(-0.360110\pi\) | ||||
0.425466 | + | 0.904974i | \(0.360110\pi\) | |||||||
\(492\) | 6.98798e30 | 0.770465 | ||||||||
\(493\) | 2.01892e30 | 0.217460 | ||||||||
\(494\) | −1.79515e30 | −0.188904 | ||||||||
\(495\) | 3.67770e30 | 0.378108 | ||||||||
\(496\) | −1.20035e30 | −0.120579 | ||||||||
\(497\) | −1.86726e31 | −1.83276 | ||||||||
\(498\) | 2.77031e30 | 0.265700 | ||||||||
\(499\) | 3.09263e30 | 0.289849 | 0.144925 | − | 0.989443i | \(-0.453706\pi\) | ||||
0.144925 | + | 0.989443i | \(0.453706\pi\) | |||||||
\(500\) | 7.38106e30 | 0.676027 | ||||||||
\(501\) | 8.21999e30 | 0.735762 | ||||||||
\(502\) | −6.87930e30 | −0.601799 | ||||||||
\(503\) | −4.43628e30 | −0.379304 | −0.189652 | − | 0.981851i | \(-0.560736\pi\) | ||||
−0.189652 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(504\) | −5.52299e30 | −0.461555 | ||||||||
\(505\) | 1.02220e31 | 0.834999 | ||||||||
\(506\) | 7.75444e30 | 0.619183 | ||||||||
\(507\) | −4.19510e30 | −0.327455 | ||||||||
\(508\) | 9.54158e30 | 0.728094 | ||||||||
\(509\) | −2.05052e31 | −1.52971 | −0.764855 | − | 0.644203i | \(-0.777189\pi\) | ||||
−0.764855 | + | 0.644203i | \(0.777189\pi\) | |||||||
\(510\) | 4.36457e30 | 0.318335 | ||||||||
\(511\) | −2.38098e31 | −1.69791 | ||||||||
\(512\) | 5.90893e30 | 0.412007 | ||||||||
\(513\) | 7.88858e29 | 0.0537835 | ||||||||
\(514\) | 4.79018e30 | 0.319357 | ||||||||
\(515\) | −1.00388e31 | −0.654481 | ||||||||
\(516\) | −1.11746e31 | −0.712459 | ||||||||
\(517\) | 1.20620e31 | 0.752106 | ||||||||
\(518\) | 1.46650e31 | 0.894313 | ||||||||
\(519\) | 8.41073e30 | 0.501660 | ||||||||
\(520\) | −2.06011e31 | −1.20185 | ||||||||
\(521\) | −2.13126e31 | −1.21620 | −0.608098 | − | 0.793862i | \(-0.708067\pi\) | ||||
−0.608098 | + | 0.793862i | \(0.708067\pi\) | |||||||
\(522\) | −7.14608e29 | −0.0398894 | ||||||||
\(523\) | 5.37551e30 | 0.293528 | 0.146764 | − | 0.989172i | \(-0.453114\pi\) | ||||
0.146764 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(524\) | −1.23503e31 | −0.659733 | ||||||||
\(525\) | −1.37832e30 | −0.0720310 | ||||||||
\(526\) | 6.84846e30 | 0.350152 | ||||||||
\(527\) | 1.12428e31 | 0.562410 | ||||||||
\(528\) | −2.70458e30 | −0.132376 | ||||||||
\(529\) | 2.23351e30 | 0.106966 | ||||||||
\(530\) | −1.34486e31 | −0.630238 | ||||||||
\(531\) | −1.31683e30 | −0.0603870 | ||||||||
\(532\) | 6.62240e30 | 0.297188 | ||||||||
\(533\) | 5.36935e31 | 2.35808 | ||||||||
\(534\) | 1.48502e30 | 0.0638273 | ||||||||
\(535\) | 2.63714e31 | 1.10934 | ||||||||
\(536\) | 2.90362e31 | 1.19549 | ||||||||
\(537\) | −1.05856e31 | −0.426591 | ||||||||
\(538\) | −2.13698e31 | −0.842955 | ||||||||
\(539\) | 3.53711e31 | 1.36577 | ||||||||
\(540\) | 3.75402e30 | 0.141895 | ||||||||
\(541\) | −3.74692e30 | −0.138646 | −0.0693228 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693228 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(542\) | −1.10562e31 | −0.400510 | ||||||||
\(543\) | −6.95750e30 | −0.246749 | ||||||||
\(544\) | −2.92771e31 | −1.01658 | ||||||||
\(545\) | −3.14599e31 | −1.06954 | ||||||||
\(546\) | −1.75976e31 | −0.585785 | ||||||||
\(547\) | −3.43148e30 | −0.111848 | −0.0559239 | − | 0.998435i | \(-0.517810\pi\) | ||||
−0.0559239 | + | 0.998435i | \(0.517810\pi\) | |||||||
\(548\) | −2.89225e31 | −0.923123 | ||||||||
\(549\) | 2.34062e30 | 0.0731557 | ||||||||
\(550\) | 1.59814e30 | 0.0489152 | ||||||||
\(551\) | 2.06633e30 | 0.0619379 | ||||||||
\(552\) | 1.90881e31 | 0.560354 | ||||||||
\(553\) | 2.95068e30 | 0.0848364 | ||||||||
\(554\) | 1.59808e31 | 0.450026 | ||||||||
\(555\) | −2.40378e31 | −0.663019 | ||||||||
\(556\) | −5.38409e30 | −0.145463 | ||||||||
\(557\) | 3.40780e31 | 0.901860 | 0.450930 | − | 0.892559i | \(-0.351092\pi\) | ||||
0.450930 | + | 0.892559i | \(0.351092\pi\) | |||||||
\(558\) | −3.97945e30 | −0.103164 | ||||||||
\(559\) | −8.58622e31 | −2.18055 | ||||||||
\(560\) | 1.32087e31 | 0.328622 | ||||||||
\(561\) | 2.53318e31 | 0.617438 | ||||||||
\(562\) | −1.25709e30 | −0.0300193 | ||||||||
\(563\) | −2.39242e31 | −0.559747 | −0.279873 | − | 0.960037i | \(-0.590292\pi\) | ||||
−0.279873 | + | 0.960037i | \(0.590292\pi\) | |||||||
\(564\) | 1.23124e31 | 0.282248 | ||||||||
\(565\) | 4.22470e31 | 0.948940 | ||||||||
\(566\) | −3.36876e31 | −0.741450 | ||||||||
\(567\) | 7.73305e30 | 0.166781 | ||||||||
\(568\) | 5.32942e31 | 1.12635 | ||||||||
\(569\) | −1.92696e31 | −0.399101 | −0.199550 | − | 0.979888i | \(-0.563948\pi\) | ||||
−0.199550 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(570\) | 4.46706e30 | 0.0906694 | ||||||||
\(571\) | 1.76715e31 | 0.351526 | 0.175763 | − | 0.984433i | \(-0.443761\pi\) | ||||
0.175763 | + | 0.984433i | \(0.443761\pi\) | |||||||
\(572\) | −4.95820e31 | −0.966651 | ||||||||
\(573\) | 1.76189e31 | 0.336667 | ||||||||
\(574\) | 8.15133e31 | 1.52666 | ||||||||
\(575\) | 4.76364e30 | 0.0874498 | ||||||||
\(576\) | 6.46598e30 | 0.116353 | ||||||||
\(577\) | 5.86874e31 | 1.03520 | 0.517599 | − | 0.855624i | \(-0.326826\pi\) | ||||
0.517599 | + | 0.855624i | \(0.326826\pi\) | |||||||
\(578\) | −1.16349e30 | −0.0201183 | ||||||||
\(579\) | −3.75113e31 | −0.635856 | ||||||||
\(580\) | 9.83327e30 | 0.163409 | ||||||||
\(581\) | −7.85259e31 | −1.27934 | ||||||||
\(582\) | −3.07667e30 | −0.0491435 | ||||||||
\(583\) | −7.80552e31 | −1.22240 | ||||||||
\(584\) | 6.79566e31 | 1.04348 | ||||||||
\(585\) | 2.88447e31 | 0.434284 | ||||||||
\(586\) | −3.64545e31 | −0.538181 | ||||||||
\(587\) | 6.89187e31 | 0.997697 | 0.498849 | − | 0.866689i | \(-0.333756\pi\) | ||||
0.498849 | + | 0.866689i | \(0.333756\pi\) | |||||||
\(588\) | 3.61051e31 | 0.512542 | ||||||||
\(589\) | 1.15068e31 | 0.160188 | ||||||||
\(590\) | −7.45682e30 | −0.101802 | ||||||||
\(591\) | −4.30789e31 | −0.576778 | ||||||||
\(592\) | 1.76775e31 | 0.232124 | ||||||||
\(593\) | −7.35782e31 | −0.947589 | −0.473795 | − | 0.880635i | \(-0.657116\pi\) | ||||
−0.473795 | + | 0.880635i | \(0.657116\pi\) | |||||||
\(594\) | −8.96632e30 | −0.113258 | ||||||||
\(595\) | −1.23716e32 | −1.53278 | ||||||||
\(596\) | −5.86278e31 | −0.712478 | ||||||||
\(597\) | 4.42787e31 | 0.527825 | ||||||||
\(598\) | 6.08193e31 | 0.711177 | ||||||||
\(599\) | 1.35998e32 | 1.56000 | 0.779999 | − | 0.625780i | \(-0.215219\pi\) | ||||
0.779999 | + | 0.625780i | \(0.215219\pi\) | |||||||
\(600\) | 3.93393e30 | 0.0442677 | ||||||||
\(601\) | −7.89659e31 | −0.871732 | −0.435866 | − | 0.900011i | \(-0.643558\pi\) | ||||
−0.435866 | + | 0.900011i | \(0.643558\pi\) | |||||||
\(602\) | −1.30349e32 | −1.41172 | ||||||||
\(603\) | −4.06553e31 | −0.431984 | ||||||||
\(604\) | 2.86879e31 | 0.299070 | ||||||||
\(605\) | 1.91237e31 | 0.195607 | ||||||||
\(606\) | −2.49216e31 | −0.250115 | ||||||||
\(607\) | −4.65196e31 | −0.458106 | −0.229053 | − | 0.973414i | \(-0.573563\pi\) | ||||
−0.229053 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(608\) | −2.99646e31 | −0.289546 | ||||||||
\(609\) | 2.02559e31 | 0.192067 | ||||||||
\(610\) | 1.32542e31 | 0.123327 | ||||||||
\(611\) | 9.46044e31 | 0.863849 | ||||||||
\(612\) | 2.58575e31 | 0.231710 | ||||||||
\(613\) | 1.41819e32 | 1.24721 | 0.623606 | − | 0.781739i | \(-0.285667\pi\) | ||||
0.623606 | + | 0.781739i | \(0.285667\pi\) | |||||||
\(614\) | 1.09063e32 | 0.941326 | ||||||||
\(615\) | −1.33611e32 | −1.13182 | ||||||||
\(616\) | −1.81519e32 | −1.50919 | ||||||||
\(617\) | 2.38519e32 | 1.94645 | 0.973227 | − | 0.229848i | \(-0.0738228\pi\) | ||||
0.973227 | + | 0.229848i | \(0.0738228\pi\) | |||||||
\(618\) | 2.44748e31 | 0.196043 | ||||||||
\(619\) | 1.46333e32 | 1.15054 | 0.575268 | − | 0.817965i | \(-0.304898\pi\) | ||||
0.575268 | + | 0.817965i | \(0.304898\pi\) | |||||||
\(620\) | 5.47587e31 | 0.422619 | ||||||||
\(621\) | −2.67263e31 | −0.202481 | ||||||||
\(622\) | −6.27827e31 | −0.466929 | ||||||||
\(623\) | −4.20935e31 | −0.307328 | ||||||||
\(624\) | −2.12125e31 | −0.152044 | ||||||||
\(625\) | −1.52938e32 | −1.07621 | ||||||||
\(626\) | 1.10733e32 | 0.765018 | ||||||||
\(627\) | 2.59266e31 | 0.175861 | ||||||||
\(628\) | −1.11170e31 | −0.0740377 | ||||||||
\(629\) | −1.65572e32 | −1.08269 | ||||||||
\(630\) | 4.37899e31 | 0.281162 | ||||||||
\(631\) | 2.57610e32 | 1.62414 | 0.812072 | − | 0.583557i | \(-0.198339\pi\) | ||||
0.812072 | + | 0.583557i | \(0.198339\pi\) | |||||||
\(632\) | −8.42164e30 | −0.0521375 | ||||||||
\(633\) | 4.75831e31 | 0.289274 | ||||||||
\(634\) | −5.02233e31 | −0.299833 | ||||||||
\(635\) | −1.82436e32 | −1.06958 | ||||||||
\(636\) | −7.96751e31 | −0.458739 | ||||||||
\(637\) | 2.77421e32 | 1.56869 | ||||||||
\(638\) | −2.34864e31 | −0.130430 | ||||||||
\(639\) | −7.46202e31 | −0.407002 | ||||||||
\(640\) | −1.64662e32 | −0.882113 | ||||||||
\(641\) | −2.91189e32 | −1.53217 | −0.766086 | − | 0.642739i | \(-0.777798\pi\) | ||||
−0.766086 | + | 0.642739i | \(0.777798\pi\) | |||||||
\(642\) | −6.42943e31 | −0.332292 | ||||||||
\(643\) | −3.58958e32 | −1.82229 | −0.911144 | − | 0.412088i | \(-0.864800\pi\) | ||||
−0.911144 | + | 0.412088i | \(0.864800\pi\) | |||||||
\(644\) | −2.24365e32 | −1.11884 | ||||||||
\(645\) | 2.13659e32 | 1.04661 | ||||||||
\(646\) | 3.07689e31 | 0.148060 | ||||||||
\(647\) | 3.52744e32 | 1.66748 | 0.833740 | − | 0.552157i | \(-0.186195\pi\) | ||||
0.833740 | + | 0.552157i | \(0.186195\pi\) | |||||||
\(648\) | −2.20712e31 | −0.102498 | ||||||||
\(649\) | −4.32791e31 | −0.197453 | ||||||||
\(650\) | 1.25345e31 | 0.0561827 | ||||||||
\(651\) | 1.12800e32 | 0.496737 | ||||||||
\(652\) | 2.32983e32 | 1.00804 | ||||||||
\(653\) | −2.22542e32 | −0.946041 | −0.473021 | − | 0.881051i | \(-0.656836\pi\) | ||||
−0.473021 | + | 0.881051i | \(0.656836\pi\) | |||||||
\(654\) | 7.67000e31 | 0.320370 | ||||||||
\(655\) | 2.36139e32 | 0.969156 | ||||||||
\(656\) | 9.82577e31 | 0.396253 | ||||||||
\(657\) | −9.51499e31 | −0.377057 | ||||||||
\(658\) | 1.43621e32 | 0.559269 | ||||||||
\(659\) | 1.21818e31 | 0.0466152 | 0.0233076 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233076 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(660\) | 1.23380e32 | 0.463969 | ||||||||
\(661\) | −3.10145e32 | −1.14617 | −0.573084 | − | 0.819496i | \(-0.694253\pi\) | ||||
−0.573084 | + | 0.819496i | \(0.694253\pi\) | |||||||
\(662\) | 1.31518e32 | 0.477661 | ||||||||
\(663\) | 1.98681e32 | 0.709172 | ||||||||
\(664\) | 2.24124e32 | 0.786241 | ||||||||
\(665\) | −1.26621e32 | −0.436573 | ||||||||
\(666\) | 5.86049e31 | 0.198600 | ||||||||
\(667\) | −7.00068e31 | −0.233181 | ||||||||
\(668\) | 2.75765e32 | 0.902839 | ||||||||
\(669\) | −7.58451e30 | −0.0244077 | ||||||||
\(670\) | −2.30218e32 | −0.728248 | ||||||||
\(671\) | 7.69268e31 | 0.239204 | ||||||||
\(672\) | −2.93738e32 | −0.897872 | ||||||||
\(673\) | 1.82996e32 | 0.549880 | 0.274940 | − | 0.961461i | \(-0.411342\pi\) | ||||
0.274940 | + | 0.961461i | \(0.411342\pi\) | |||||||
\(674\) | −2.56467e32 | −0.757605 | ||||||||
\(675\) | −5.50812e30 | −0.0159959 | ||||||||
\(676\) | −1.40738e32 | −0.401813 | ||||||||
\(677\) | −5.90638e32 | −1.65788 | −0.828938 | − | 0.559341i | \(-0.811054\pi\) | ||||
−0.828938 | + | 0.559341i | \(0.811054\pi\) | |||||||
\(678\) | −1.02999e32 | −0.284245 | ||||||||
\(679\) | 8.72096e31 | 0.236626 | ||||||||
\(680\) | 3.53103e32 | 0.941995 | ||||||||
\(681\) | −1.84482e32 | −0.483908 | ||||||||
\(682\) | −1.30789e32 | −0.337327 | ||||||||
\(683\) | 3.47709e32 | 0.881815 | 0.440907 | − | 0.897553i | \(-0.354657\pi\) | ||||
0.440907 | + | 0.897553i | \(0.354657\pi\) | |||||||
\(684\) | 2.64647e31 | 0.0659967 | ||||||||
\(685\) | 5.53001e32 | 1.35608 | ||||||||
\(686\) | 8.50594e31 | 0.205114 | ||||||||
\(687\) | −5.62112e31 | −0.133297 | ||||||||
\(688\) | −1.57125e32 | −0.366420 | ||||||||
\(689\) | −6.12199e32 | −1.40402 | ||||||||
\(690\) | −1.51343e32 | −0.341348 | ||||||||
\(691\) | −4.28793e32 | −0.951151 | −0.475576 | − | 0.879675i | \(-0.657760\pi\) | ||||
−0.475576 | + | 0.879675i | \(0.657760\pi\) | |||||||
\(692\) | 2.82164e32 | 0.615577 | ||||||||
\(693\) | 2.54155e32 | 0.545339 | ||||||||
\(694\) | 1.06102e32 | 0.223919 | ||||||||
\(695\) | 1.02944e32 | 0.213687 | ||||||||
\(696\) | −5.78133e31 | −0.118038 | ||||||||
\(697\) | −9.20307e32 | −1.84823 | ||||||||
\(698\) | 2.85907e32 | 0.564790 | ||||||||
\(699\) | −1.90367e32 | −0.369917 | ||||||||
\(700\) | −4.62402e31 | −0.0883878 | ||||||||
\(701\) | 8.63465e32 | 1.62363 | 0.811816 | − | 0.583913i | \(-0.198479\pi\) | ||||
0.811816 | + | 0.583913i | \(0.198479\pi\) | |||||||
\(702\) | −7.03243e31 | −0.130085 | ||||||||
\(703\) | −1.69459e32 | −0.308375 | ||||||||
\(704\) | 2.12511e32 | 0.380449 | ||||||||
\(705\) | −2.35414e32 | −0.414626 | ||||||||
\(706\) | 2.25359e32 | 0.390501 | ||||||||
\(707\) | 7.06414e32 | 1.20430 | ||||||||
\(708\) | −4.41773e31 | −0.0740998 | ||||||||
\(709\) | 7.56772e32 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(710\) | −4.22551e32 | −0.686133 | ||||||||
\(711\) | 1.17916e31 | 0.0188397 | ||||||||
\(712\) | 1.20141e32 | 0.188873 | ||||||||
\(713\) | −3.89848e32 | −0.603068 | ||||||||
\(714\) | 3.01623e32 | 0.459129 | ||||||||
\(715\) | 9.48013e32 | 1.42002 | ||||||||
\(716\) | −3.55128e32 | −0.523462 | ||||||||
\(717\) | 5.15830e32 | 0.748232 | ||||||||
\(718\) | −5.54213e31 | −0.0791126 | ||||||||
\(719\) | −3.98801e32 | −0.560240 | −0.280120 | − | 0.959965i | \(-0.590374\pi\) | ||||
−0.280120 | + | 0.959965i | \(0.590374\pi\) | |||||||
\(720\) | 5.27851e31 | 0.0729773 | ||||||||
\(721\) | −6.93749e32 | −0.943946 | ||||||||
\(722\) | −3.71718e32 | −0.497778 | ||||||||
\(723\) | 3.14683e32 | 0.414746 | ||||||||
\(724\) | −2.33411e32 | −0.302781 | ||||||||
\(725\) | −1.44279e31 | −0.0184212 | ||||||||
\(726\) | −4.66241e31 | −0.0585921 | ||||||||
\(727\) | −7.76270e32 | −0.960211 | −0.480106 | − | 0.877211i | \(-0.659402\pi\) | ||||
−0.480106 | + | 0.877211i | \(0.659402\pi\) | |||||||
\(728\) | −1.42368e33 | −1.73341 | ||||||||
\(729\) | 3.09032e31 | 0.0370370 | ||||||||
\(730\) | −5.38804e32 | −0.635650 | ||||||||
\(731\) | 1.47168e33 | 1.70908 | ||||||||
\(732\) | 7.85233e31 | 0.0897679 | ||||||||
\(733\) | 8.56762e32 | 0.964195 | 0.482097 | − | 0.876118i | \(-0.339875\pi\) | ||||
0.482097 | + | 0.876118i | \(0.339875\pi\) | |||||||
\(734\) | 2.45624e32 | 0.272124 | ||||||||
\(735\) | −6.90335e32 | −0.752931 | ||||||||
\(736\) | 1.01519e33 | 1.09007 | ||||||||
\(737\) | −1.33618e33 | −1.41250 | ||||||||
\(738\) | 3.25747e32 | 0.339026 | ||||||||
\(739\) | −5.55833e32 | −0.569552 | −0.284776 | − | 0.958594i | \(-0.591919\pi\) | ||||
−0.284776 | + | 0.958594i | \(0.591919\pi\) | |||||||
\(740\) | −8.06424e32 | −0.813577 | ||||||||
\(741\) | 2.03347e32 | 0.201989 | ||||||||
\(742\) | −9.29394e32 | −0.908981 | ||||||||
\(743\) | −1.55682e33 | −1.49923 | −0.749613 | − | 0.661876i | \(-0.769760\pi\) | ||||
−0.749613 | + | 0.661876i | \(0.769760\pi\) | |||||||
\(744\) | −3.21946e32 | −0.305277 | ||||||||
\(745\) | 1.12097e33 | 1.04664 | ||||||||
\(746\) | 7.32911e32 | 0.673837 | ||||||||
\(747\) | −3.13809e32 | −0.284105 | ||||||||
\(748\) | 8.49835e32 | 0.757646 | ||||||||
\(749\) | 1.82245e33 | 1.59998 | ||||||||
\(750\) | 3.44071e32 | 0.297470 | ||||||||
\(751\) | 1.66899e33 | 1.42100 | 0.710501 | − | 0.703696i | \(-0.248468\pi\) | ||||
0.710501 | + | 0.703696i | \(0.248468\pi\) | |||||||
\(752\) | 1.73124e32 | 0.145161 | ||||||||
\(753\) | 7.79256e32 | 0.643484 | ||||||||
\(754\) | −1.84207e32 | −0.149808 | ||||||||
\(755\) | −5.48515e32 | −0.439338 | ||||||||
\(756\) | 2.59429e32 | 0.204653 | ||||||||
\(757\) | −7.88666e31 | −0.0612760 | −0.0306380 | − | 0.999531i | \(-0.509754\pi\) | ||||
−0.0306380 | + | 0.999531i | \(0.509754\pi\) | |||||||
\(758\) | 7.15524e31 | 0.0547556 | ||||||||
\(759\) | −8.78388e32 | −0.662073 | ||||||||
\(760\) | 3.61394e32 | 0.268303 | ||||||||
\(761\) | 7.62229e32 | 0.557394 | 0.278697 | − | 0.960379i | \(-0.410098\pi\) | ||||
0.278697 | + | 0.960379i | \(0.410098\pi\) | |||||||
\(762\) | 4.44784e32 | 0.320381 | ||||||||
\(763\) | −2.17410e33 | −1.54258 | ||||||||
\(764\) | 5.91081e32 | 0.413117 | ||||||||
\(765\) | −4.94399e32 | −0.340386 | ||||||||
\(766\) | 7.09600e32 | 0.481263 | ||||||||
\(767\) | −3.39445e32 | −0.226789 | ||||||||
\(768\) | 7.07641e32 | 0.465756 | ||||||||
\(769\) | −2.24557e33 | −1.45604 | −0.728020 | − | 0.685556i | \(-0.759559\pi\) | ||||
−0.728020 | + | 0.685556i | \(0.759559\pi\) | |||||||
\(770\) | 1.43920e33 | 0.919344 | ||||||||
\(771\) | −5.42610e32 | −0.341478 | ||||||||
\(772\) | −1.25843e33 | −0.780246 | ||||||||
\(773\) | 1.77063e33 | 1.08159 | 0.540795 | − | 0.841154i | \(-0.318123\pi\) | ||||
0.540795 | + | 0.841154i | \(0.318123\pi\) | |||||||
\(774\) | −5.20908e32 | −0.313502 | ||||||||
\(775\) | −8.03452e31 | −0.0476421 | ||||||||
\(776\) | −2.48909e32 | −0.145422 | ||||||||
\(777\) | −1.66118e33 | −0.956260 | ||||||||
\(778\) | 5.62793e32 | 0.319215 | ||||||||
\(779\) | −9.41917e32 | −0.526419 | ||||||||
\(780\) | 9.67688e32 | 0.532902 | ||||||||
\(781\) | −2.45247e33 | −1.33081 | ||||||||
\(782\) | −1.04244e33 | −0.557410 | ||||||||
\(783\) | 8.09476e31 | 0.0426524 | ||||||||
\(784\) | 5.07673e32 | 0.263602 | ||||||||
\(785\) | 2.12559e32 | 0.108762 | ||||||||
\(786\) | −5.75714e32 | −0.290301 | ||||||||
\(787\) | 1.41877e33 | 0.705024 | 0.352512 | − | 0.935807i | \(-0.385328\pi\) | ||||
0.352512 | + | 0.935807i | \(0.385328\pi\) | |||||||
\(788\) | −1.44522e33 | −0.707753 | ||||||||
\(789\) | −7.75763e32 | −0.374406 | ||||||||
\(790\) | 6.67723e31 | 0.0317603 | ||||||||
\(791\) | 2.91957e33 | 1.36864 | ||||||||
\(792\) | −7.25394e32 | −0.335146 | ||||||||
\(793\) | 6.03349e32 | 0.274743 | ||||||||
\(794\) | −1.50548e32 | −0.0675676 | ||||||||
\(795\) | 1.52340e33 | 0.673893 | ||||||||
\(796\) | 1.48547e33 | 0.647684 | ||||||||
\(797\) | 2.58083e33 | 1.10915 | 0.554573 | − | 0.832135i | \(-0.312882\pi\) | ||||
0.554573 | + | 0.832135i | \(0.312882\pi\) | |||||||
\(798\) | 3.08705e32 | 0.130771 | ||||||||
\(799\) | −1.62152e33 | −0.677071 | ||||||||
\(800\) | 2.09225e32 | 0.0861149 | ||||||||
\(801\) | −1.68216e32 | −0.0682485 | ||||||||
\(802\) | 7.78677e32 | 0.311424 | ||||||||
\(803\) | −3.12720e33 | −1.23290 | ||||||||
\(804\) | −1.36391e33 | −0.530079 | ||||||||
\(805\) | 4.28989e33 | 1.64359 | ||||||||
\(806\) | −1.02580e33 | −0.387444 | ||||||||
\(807\) | 2.42068e33 | 0.901345 | ||||||||
\(808\) | −2.01621e33 | −0.740124 | ||||||||
\(809\) | −1.24432e33 | −0.450323 | −0.225161 | − | 0.974321i | \(-0.572291\pi\) | ||||
−0.225161 | + | 0.974321i | \(0.572291\pi\) | |||||||
\(810\) | 1.74995e32 | 0.0624378 | ||||||||
\(811\) | 1.55059e32 | 0.0545453 | 0.0272727 | − | 0.999628i | \(-0.491318\pi\) | ||||
0.0272727 | + | 0.999628i | \(0.491318\pi\) | |||||||
\(812\) | 6.79549e32 | 0.235682 | ||||||||
\(813\) | 1.25239e33 | 0.428253 | ||||||||
\(814\) | 1.92611e33 | 0.649383 | ||||||||
\(815\) | −4.45465e33 | −1.48082 | ||||||||
\(816\) | 3.63582e32 | 0.119170 | ||||||||
\(817\) | 1.50624e33 | 0.486787 | ||||||||
\(818\) | −2.32466e33 | −0.740793 | ||||||||
\(819\) | 1.99338e33 | 0.626361 | ||||||||
\(820\) | −4.48240e33 | −1.38884 | ||||||||
\(821\) | 5.00186e33 | 1.52822 | 0.764108 | − | 0.645088i | \(-0.223179\pi\) | ||||
0.764108 | + | 0.645088i | \(0.223179\pi\) | |||||||
\(822\) | −1.34823e33 | −0.406199 | ||||||||
\(823\) | 2.77022e33 | 0.823030 | 0.411515 | − | 0.911403i | \(-0.365000\pi\) | ||||
0.411515 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(824\) | 1.98006e33 | 0.580116 | ||||||||
\(825\) | −1.81030e32 | −0.0523035 | ||||||||
\(826\) | −5.15319e32 | −0.146827 | ||||||||
\(827\) | −2.81604e33 | −0.791270 | −0.395635 | − | 0.918408i | \(-0.629475\pi\) | ||||
−0.395635 | + | 0.918408i | \(0.629475\pi\) | |||||||
\(828\) | −8.96618e32 | −0.248461 | ||||||||
\(829\) | −6.05152e32 | −0.165382 | −0.0826908 | − | 0.996575i | \(-0.526351\pi\) | ||||
−0.0826908 | + | 0.996575i | \(0.526351\pi\) | |||||||
\(830\) | −1.77700e33 | −0.478950 | ||||||||
\(831\) | −1.81024e33 | −0.481198 | ||||||||
\(832\) | 1.66676e33 | 0.436974 | ||||||||
\(833\) | −4.75500e33 | −1.22951 | ||||||||
\(834\) | −2.50981e32 | −0.0640077 | ||||||||
\(835\) | −5.27266e33 | −1.32628 | ||||||||
\(836\) | 8.69791e32 | 0.215796 | ||||||||
\(837\) | 4.50775e32 | 0.110310 | ||||||||
\(838\) | −7.93180e32 | −0.191454 | ||||||||
\(839\) | −2.21831e33 | −0.528152 | −0.264076 | − | 0.964502i | \(-0.585067\pi\) | ||||
−0.264076 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(840\) | 3.54269e33 | 0.831996 | ||||||||
\(841\) | −4.10469e33 | −0.950881 | ||||||||
\(842\) | 4.00587e33 | 0.915392 | ||||||||
\(843\) | 1.42398e32 | 0.0320987 | ||||||||
\(844\) | 1.59632e33 | 0.354963 | ||||||||
\(845\) | 2.69093e33 | 0.590268 | ||||||||
\(846\) | 5.73945e32 | 0.124197 | ||||||||
\(847\) | 1.32158e33 | 0.282121 | ||||||||
\(848\) | −1.12031e33 | −0.235931 | ||||||||
\(849\) | 3.81599e33 | 0.792809 | ||||||||
\(850\) | −2.14841e32 | −0.0440351 | ||||||||
\(851\) | 5.74124e33 | 1.16096 | ||||||||
\(852\) | −2.50337e33 | −0.499424 | ||||||||
\(853\) | 9.69232e33 | 1.90772 | 0.953858 | − | 0.300257i | \(-0.0970723\pi\) | ||||
0.953858 | + | 0.300257i | \(0.0970723\pi\) | |||||||
\(854\) | 9.15958e32 | 0.177873 | ||||||||
\(855\) | −5.06008e32 | −0.0969499 | ||||||||
\(856\) | −5.20154e33 | −0.983295 | ||||||||
\(857\) | −3.54610e33 | −0.661411 | −0.330705 | − | 0.943734i | \(-0.607287\pi\) | ||||
−0.330705 | + | 0.943734i | \(0.607287\pi\) | |||||||
\(858\) | −2.31128e33 | −0.425353 | ||||||||
\(859\) | 9.58348e33 | 1.74021 | 0.870105 | − | 0.492866i | \(-0.164051\pi\) | ||||
0.870105 | + | 0.492866i | \(0.164051\pi\) | |||||||
\(860\) | 7.16788e33 | 1.28428 | ||||||||
\(861\) | −9.23347e33 | −1.63241 | ||||||||
\(862\) | −1.90238e33 | −0.331866 | ||||||||
\(863\) | 3.43280e33 | 0.590915 | 0.295457 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295457 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(864\) | −1.17385e33 | −0.199391 | ||||||||
\(865\) | −5.39502e33 | −0.904290 | ||||||||
\(866\) | 2.80604e33 | 0.464128 | ||||||||
\(867\) | 1.31795e32 | 0.0215119 | ||||||||
\(868\) | 3.78422e33 | 0.609536 | ||||||||
\(869\) | 3.87544e32 | 0.0616018 | ||||||||
\(870\) | 4.58381e32 | 0.0719044 | ||||||||
\(871\) | −1.04799e34 | −1.62236 | ||||||||
\(872\) | 6.20519e33 | 0.948016 | ||||||||
\(873\) | 3.48511e32 | 0.0525476 | ||||||||
\(874\) | −1.06692e33 | −0.158764 | ||||||||
\(875\) | −9.75287e33 | −1.43232 | ||||||||
\(876\) | −3.19210e33 | −0.462679 | ||||||||
\(877\) | −8.57680e33 | −1.22696 | −0.613480 | − | 0.789711i | \(-0.710231\pi\) | ||||
−0.613480 | + | 0.789711i | \(0.710231\pi\) | |||||||
\(878\) | −6.20950e33 | −0.876738 | ||||||||
\(879\) | 4.12940e33 | 0.575460 | ||||||||
\(880\) | 1.73484e33 | 0.238621 | ||||||||
\(881\) | −8.23643e33 | −1.11819 | −0.559096 | − | 0.829103i | \(-0.688852\pi\) | ||||
−0.559096 | + | 0.829103i | \(0.688852\pi\) | |||||||
\(882\) | 1.68305e33 | 0.225533 | ||||||||
\(883\) | 1.05626e34 | 1.39709 | 0.698545 | − | 0.715566i | \(-0.253831\pi\) | ||||
0.698545 | + | 0.715566i | \(0.253831\pi\) | |||||||
\(884\) | 6.66539e33 | 0.870211 | ||||||||
\(885\) | 8.44675e32 | 0.108853 | ||||||||
\(886\) | −2.01324e33 | −0.256098 | ||||||||
\(887\) | 6.30164e33 | 0.791283 | 0.395642 | − | 0.918405i | \(-0.370522\pi\) | ||||
0.395642 | + | 0.918405i | \(0.370522\pi\) | |||||||
\(888\) | 4.74126e33 | 0.587685 | ||||||||
\(889\) | −1.26076e34 | −1.54264 | ||||||||
\(890\) | −9.52555e32 | −0.115055 | ||||||||
\(891\) | 1.01567e33 | 0.121104 | ||||||||
\(892\) | −2.54446e32 | −0.0299502 | ||||||||
\(893\) | −1.65960e33 | −0.192846 | ||||||||
\(894\) | −2.73295e33 | −0.313510 | ||||||||
\(895\) | 6.79008e33 | 0.768972 | ||||||||
\(896\) | −1.13793e34 | −1.27226 | ||||||||
\(897\) | −6.88934e33 | −0.760439 | ||||||||
\(898\) | 4.95762e33 | 0.540250 | ||||||||
\(899\) | 1.18076e33 | 0.127035 | ||||||||
\(900\) | −1.84787e32 | −0.0196283 | ||||||||
\(901\) | 1.04931e34 | 1.10045 | ||||||||
\(902\) | 1.07060e34 | 1.10854 | ||||||||
\(903\) | 1.47654e34 | 1.50951 | ||||||||
\(904\) | −8.33286e33 | −0.841118 | ||||||||
\(905\) | 4.46285e33 | 0.444788 | ||||||||
\(906\) | 1.33730e33 | 0.131599 | ||||||||
\(907\) | 1.10592e34 | 1.07458 | 0.537292 | − | 0.843396i | \(-0.319447\pi\) | ||||
0.537292 | + | 0.843396i | \(0.319447\pi\) | |||||||
\(908\) | −6.18904e33 | −0.593795 | ||||||||
\(909\) | 2.82300e33 | 0.267440 | ||||||||
\(910\) | 1.12879e34 | 1.05593 | ||||||||
\(911\) | −8.48544e33 | −0.783814 | −0.391907 | − | 0.920005i | \(-0.628185\pi\) | ||||
−0.391907 | + | 0.920005i | \(0.628185\pi\) | |||||||
\(912\) | 3.72119e32 | 0.0339423 | ||||||||
\(913\) | −1.03137e34 | −0.928964 | ||||||||
\(914\) | −1.07874e34 | −0.959481 | ||||||||
\(915\) | −1.50138e33 | −0.131870 | ||||||||
\(916\) | −1.88578e33 | −0.163566 | ||||||||
\(917\) | 1.63189e34 | 1.39780 | ||||||||
\(918\) | 1.20536e33 | 0.101959 | ||||||||
\(919\) | 2.82637e33 | 0.236102 | 0.118051 | − | 0.993008i | \(-0.462335\pi\) | ||||
0.118051 | + | 0.993008i | \(0.462335\pi\) | |||||||
\(920\) | −1.22439e34 | −1.01009 | ||||||||
\(921\) | −1.23541e34 | −1.00653 | ||||||||
\(922\) | −1.95973e33 | −0.157685 | ||||||||
\(923\) | −1.92351e34 | −1.52853 | ||||||||
\(924\) | 8.52643e33 | 0.669174 | ||||||||
\(925\) | 1.18323e33 | 0.0917150 | ||||||||
\(926\) | 7.62223e33 | 0.583520 | ||||||||
\(927\) | −2.77239e33 | −0.209622 | ||||||||
\(928\) | −3.07478e33 | −0.229621 | ||||||||
\(929\) | 2.09040e34 | 1.54187 | 0.770936 | − | 0.636913i | \(-0.219789\pi\) | ||||
0.770936 | + | 0.636913i | \(0.219789\pi\) | |||||||
\(930\) | 2.55260e33 | 0.185964 | ||||||||
\(931\) | −4.86665e33 | −0.350194 | ||||||||
\(932\) | −6.38646e33 | −0.453918 | ||||||||
\(933\) | 7.11175e33 | 0.499272 | ||||||||
\(934\) | 6.81585e33 | 0.472640 | ||||||||
\(935\) | −1.62489e34 | −1.11299 | ||||||||
\(936\) | −5.68938e33 | −0.384940 | ||||||||
\(937\) | −9.77881e33 | −0.653553 | −0.326776 | − | 0.945102i | \(-0.605962\pi\) | ||||
−0.326776 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(938\) | −1.59097e34 | −1.05034 | ||||||||
\(939\) | −1.25433e34 | −0.818010 | ||||||||
\(940\) | −7.89769e33 | −0.508780 | ||||||||
\(941\) | 2.28884e34 | 1.45658 | 0.728290 | − | 0.685270i | \(-0.240316\pi\) | ||||
0.728290 | + | 0.685270i | \(0.240316\pi\) | |||||||
\(942\) | −5.18225e32 | −0.0325786 | ||||||||
\(943\) | 3.19119e34 | 1.98184 | ||||||||
\(944\) | −6.21175e32 | −0.0381098 | ||||||||
\(945\) | −4.96032e33 | −0.300638 | ||||||||
\(946\) | −1.71202e34 | −1.02509 | ||||||||
\(947\) | 1.58194e34 | 0.935763 | 0.467882 | − | 0.883791i | \(-0.345017\pi\) | ||||
0.467882 | + | 0.883791i | \(0.345017\pi\) | |||||||
\(948\) | 3.95587e32 | 0.0231178 | ||||||||
\(949\) | −2.45271e34 | −1.41607 | ||||||||
\(950\) | −2.19886e32 | −0.0125422 | ||||||||
\(951\) | 5.68907e33 | 0.320601 | ||||||||
\(952\) | 2.44019e34 | 1.35862 | ||||||||
\(953\) | −1.70079e34 | −0.935582 | −0.467791 | − | 0.883839i | \(-0.654950\pi\) | ||||
−0.467791 | + | 0.883839i | \(0.654950\pi\) | |||||||
\(954\) | −3.71408e33 | −0.201858 | ||||||||
\(955\) | −1.13015e34 | −0.606874 | ||||||||
\(956\) | 1.73051e34 | 0.918140 | ||||||||
\(957\) | 2.66043e33 | 0.139465 | ||||||||
\(958\) | 7.51172e33 | 0.389078 | ||||||||
\(959\) | 3.82163e34 | 1.95585 | ||||||||
\(960\) | −4.14757e33 | −0.209737 | ||||||||
\(961\) | −1.34380e34 | −0.671453 | ||||||||
\(962\) | 1.51068e34 | 0.745863 | ||||||||
\(963\) | 7.28297e33 | 0.355309 | ||||||||
\(964\) | 1.05570e34 | 0.508927 | ||||||||
\(965\) | 2.40614e34 | 1.14619 | ||||||||
\(966\) | −1.04589e34 | −0.492320 | ||||||||
\(967\) | −3.44351e34 | −1.60176 | −0.800880 | − | 0.598825i | \(-0.795634\pi\) | ||||
−0.800880 | + | 0.598825i | \(0.795634\pi\) | |||||||
\(968\) | −3.77198e33 | −0.173382 | ||||||||
\(969\) | −3.48536e33 | −0.158316 | ||||||||
\(970\) | 1.97351e33 | 0.0885859 | ||||||||
\(971\) | 1.73462e33 | 0.0769456 | 0.0384728 | − | 0.999260i | \(-0.487751\pi\) | ||||
0.0384728 | + | 0.999260i | \(0.487751\pi\) | |||||||
\(972\) | 1.03674e33 | 0.0454474 | ||||||||
\(973\) | 7.11419e33 | 0.308197 | ||||||||
\(974\) | −5.81308e33 | −0.248873 | ||||||||
\(975\) | −1.41985e33 | −0.0600743 | ||||||||
\(976\) | 1.10411e33 | 0.0461680 | ||||||||
\(977\) | 1.44173e33 | 0.0595794 | 0.0297897 | − | 0.999556i | \(-0.490516\pi\) | ||||
0.0297897 | + | 0.999556i | \(0.490516\pi\) | |||||||
\(978\) | 1.08606e34 | 0.443563 | ||||||||
\(979\) | −5.52859e33 | −0.223159 | ||||||||
\(980\) | −2.31594e34 | −0.923907 | ||||||||
\(981\) | −8.68824e33 | −0.342561 | ||||||||
\(982\) | 1.17904e34 | 0.459460 | ||||||||
\(983\) | −4.62857e34 | −1.78271 | −0.891357 | − | 0.453303i | \(-0.850246\pi\) | ||||
−0.891357 | + | 0.453303i | \(0.850246\pi\) | |||||||
\(984\) | 2.63536e34 | 1.00322 | ||||||||
\(985\) | 2.76327e34 | 1.03970 | ||||||||
\(986\) | 3.15731e33 | 0.117418 | ||||||||
\(987\) | −1.62688e34 | −0.598008 | ||||||||
\(988\) | 6.82191e33 | 0.247857 | ||||||||
\(989\) | −5.10309e34 | −1.83263 | ||||||||
\(990\) | 5.75140e33 | 0.204159 | ||||||||
\(991\) | −1.68657e34 | −0.591776 | −0.295888 | − | 0.955223i | \(-0.595615\pi\) | ||||
−0.295888 | + | 0.955223i | \(0.595615\pi\) | |||||||
\(992\) | −1.71226e34 | −0.593862 | ||||||||
\(993\) | −1.48978e34 | −0.510747 | ||||||||
\(994\) | −2.92013e34 | −0.989597 | ||||||||
\(995\) | −2.84023e34 | −0.951455 | ||||||||
\(996\) | −1.05277e34 | −0.348619 | ||||||||
\(997\) | 2.01747e34 | 0.660410 | 0.330205 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330205 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(998\) | 4.83644e33 | 0.156504 | ||||||||
\(999\) | −6.63850e33 | −0.212357 |
(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 | 3.24.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.24.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 48.24.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.24.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.24.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
48.24.a.g.1.2 | 2 | 4.3 | odd | 2 |