Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,96,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 96, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 96);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 96 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(57.1535908815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 12\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{104}\cdot 3^{38}\cdot 5^{12}\cdot 7^{7}\cdot 11\cdot 13\cdot 19^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.62871e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.90162e14 | 1.96029 | 0.980145 | − | 0.198283i | \(-0.0635364\pi\) | ||||
0.980145 | + | 0.198283i | \(0.0635364\pi\) | |||||||
\(3\) | 2.16924e22 | 0.471028 | 0.235514 | − | 0.971871i | \(-0.424323\pi\) | ||||
0.235514 | + | 0.971871i | \(0.424323\pi\) | |||||||
\(4\) | 1.12612e29 | 2.84274 | ||||||||
\(5\) | 1.39914e33 | 0.880614 | 0.440307 | − | 0.897847i | \(-0.354870\pi\) | ||||
0.440307 | + | 0.897847i | \(0.354870\pi\) | |||||||
\(6\) | 8.46353e36 | 0.923352 | ||||||||
\(7\) | 1.75361e40 | 1.26409 | 0.632044 | − | 0.774932i | \(-0.282216\pi\) | ||||
0.632044 | + | 0.774932i | \(0.282216\pi\) | |||||||
\(8\) | 2.84812e43 | 3.61230 | ||||||||
\(9\) | −1.65034e45 | −0.778132 | ||||||||
\(10\) | 5.45891e47 | 1.72626 | ||||||||
\(11\) | −5.41264e48 | −0.185036 | −0.0925181 | − | 0.995711i | \(-0.529492\pi\) | ||||
−0.0925181 | + | 0.995711i | \(0.529492\pi\) | |||||||
\(12\) | 2.44283e51 | 1.33901 | ||||||||
\(13\) | 1.04831e52 | 0.128286 | 0.0641430 | − | 0.997941i | \(-0.479569\pi\) | ||||
0.0641430 | + | 0.997941i | \(0.479569\pi\) | |||||||
\(14\) | 6.84194e54 | 2.47798 | ||||||||
\(15\) | 3.03506e55 | 0.414794 | ||||||||
\(16\) | 6.65124e57 | 4.23841 | ||||||||
\(17\) | −2.56029e58 | −0.916148 | −0.458074 | − | 0.888914i | \(-0.651461\pi\) | ||||
−0.458074 | + | 0.888914i | \(0.651461\pi\) | |||||||
\(18\) | −6.43899e59 | −1.52536 | ||||||||
\(19\) | −4.34204e60 | −0.788674 | −0.394337 | − | 0.918966i | \(-0.629026\pi\) | ||||
−0.394337 | + | 0.918966i | \(0.629026\pi\) | |||||||
\(20\) | 1.57560e62 | 2.50335 | ||||||||
\(21\) | 3.80400e62 | 0.595421 | ||||||||
\(22\) | −2.11181e63 | −0.362725 | ||||||||
\(23\) | −7.48379e64 | −1.55614 | −0.778071 | − | 0.628177i | \(-0.783802\pi\) | ||||
−0.778071 | + | 0.628177i | \(0.783802\pi\) | |||||||
\(24\) | 6.17824e65 | 1.70149 | ||||||||
\(25\) | −5.66766e65 | −0.224519 | ||||||||
\(26\) | 4.09009e66 | 0.251478 | ||||||||
\(27\) | −8.18069e67 | −0.837551 | ||||||||
\(28\) | 1.97479e69 | 3.59347 | ||||||||
\(29\) | 2.03053e69 | 0.697759 | 0.348880 | − | 0.937168i | \(-0.386562\pi\) | ||||
0.348880 | + | 0.937168i | \(0.386562\pi\) | |||||||
\(30\) | 1.18417e70 | 0.813117 | ||||||||
\(31\) | 3.72805e70 | 0.539264 | 0.269632 | − | 0.962963i | \(-0.413098\pi\) | ||||
0.269632 | + | 0.962963i | \(0.413098\pi\) | |||||||
\(32\) | 1.46681e72 | 4.69622 | ||||||||
\(33\) | −1.17413e71 | −0.0871573 | ||||||||
\(34\) | −9.98929e72 | −1.79592 | ||||||||
\(35\) | 2.45355e73 | 1.11317 | ||||||||
\(36\) | −1.85848e74 | −2.21202 | ||||||||
\(37\) | −1.43964e74 | −0.466305 | −0.233153 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233153 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(38\) | −1.69410e75 | −1.54603 | ||||||||
\(39\) | 2.27402e74 | 0.0604263 | ||||||||
\(40\) | 3.98491e76 | 3.18104 | ||||||||
\(41\) | −4.16311e76 | −1.02845 | −0.514227 | − | 0.857654i | \(-0.671921\pi\) | ||||
−0.514227 | + | 0.857654i | \(0.671921\pi\) | |||||||
\(42\) | 1.48418e77 | 1.16720 | ||||||||
\(43\) | 4.94148e76 | 0.127088 | 0.0635441 | − | 0.997979i | \(-0.479760\pi\) | ||||
0.0635441 | + | 0.997979i | \(0.479760\pi\) | |||||||
\(44\) | −6.09530e77 | −0.526009 | ||||||||
\(45\) | −2.30905e78 | −0.685234 | ||||||||
\(46\) | −2.91989e79 | −3.05049 | ||||||||
\(47\) | 4.71948e79 | 1.77519 | 0.887596 | − | 0.460622i | \(-0.152374\pi\) | ||||
0.887596 | + | 0.460622i | \(0.152374\pi\) | |||||||
\(48\) | 1.44281e80 | 1.99641 | ||||||||
\(49\) | 1.15068e80 | 0.597919 | ||||||||
\(50\) | −2.21131e80 | −0.440122 | ||||||||
\(51\) | −5.55388e80 | −0.431532 | ||||||||
\(52\) | 1.18052e81 | 0.364683 | ||||||||
\(53\) | 9.21253e80 | 0.115153 | 0.0575765 | − | 0.998341i | \(-0.481663\pi\) | ||||
0.0575765 | + | 0.998341i | \(0.481663\pi\) | |||||||
\(54\) | −3.19180e82 | −1.64184 | ||||||||
\(55\) | −7.57304e81 | −0.162945 | ||||||||
\(56\) | 4.99450e83 | 4.56626 | ||||||||
\(57\) | −9.41891e82 | −0.371488 | ||||||||
\(58\) | 7.92238e83 | 1.36781 | ||||||||
\(59\) | −1.44917e84 | −1.11083 | −0.555417 | − | 0.831572i | \(-0.687442\pi\) | ||||
−0.555417 | + | 0.831572i | \(0.687442\pi\) | |||||||
\(60\) | 3.41785e84 | 1.17915 | ||||||||
\(61\) | 2.68780e84 | 0.422892 | 0.211446 | − | 0.977390i | \(-0.432183\pi\) | ||||
0.211446 | + | 0.977390i | \(0.432183\pi\) | |||||||
\(62\) | 1.45454e85 | 1.05711 | ||||||||
\(63\) | −2.89406e85 | −0.983628 | ||||||||
\(64\) | 3.08809e86 | 4.96754 | ||||||||
\(65\) | 1.46673e85 | 0.112970 | ||||||||
\(66\) | −4.58101e85 | −0.170854 | ||||||||
\(67\) | 3.24337e86 | 0.592165 | 0.296083 | − | 0.955162i | \(-0.404320\pi\) | ||||
0.296083 | + | 0.955162i | \(0.404320\pi\) | |||||||
\(68\) | −2.88321e87 | −2.60437 | ||||||||
\(69\) | −1.62341e87 | −0.732987 | ||||||||
\(70\) | 9.57282e87 | 2.18214 | ||||||||
\(71\) | 2.78222e87 | 0.323311 | 0.161656 | − | 0.986847i | \(-0.448317\pi\) | ||||
0.161656 | + | 0.986847i | \(0.448317\pi\) | |||||||
\(72\) | −4.70035e88 | −2.81084 | ||||||||
\(73\) | 2.94316e88 | 0.914067 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(74\) | −5.61691e88 | −0.914094 | ||||||||
\(75\) | −1.22945e88 | −0.105755 | ||||||||
\(76\) | −4.88967e89 | −2.24199 | ||||||||
\(77\) | −9.49169e88 | −0.233902 | ||||||||
\(78\) | 8.87238e88 | 0.118453 | ||||||||
\(79\) | 9.20074e89 | 0.670712 | 0.335356 | − | 0.942092i | \(-0.391143\pi\) | ||||
0.335356 | + | 0.942092i | \(0.391143\pi\) | |||||||
\(80\) | 9.30600e90 | 3.73241 | ||||||||
\(81\) | 1.72561e90 | 0.383622 | ||||||||
\(82\) | −1.62429e91 | −2.01607 | ||||||||
\(83\) | −2.26821e90 | −0.158298 | −0.0791488 | − | 0.996863i | \(-0.525220\pi\) | ||||
−0.0791488 | + | 0.996863i | \(0.525220\pi\) | |||||||
\(84\) | 4.28378e91 | 1.69263 | ||||||||
\(85\) | −3.58220e91 | −0.806773 | ||||||||
\(86\) | 1.92798e91 | 0.249130 | ||||||||
\(87\) | 4.40471e91 | 0.328664 | ||||||||
\(88\) | −1.54158e92 | −0.668406 | ||||||||
\(89\) | 3.95651e92 | 1.00297 | 0.501484 | − | 0.865167i | \(-0.332788\pi\) | ||||
0.501484 | + | 0.865167i | \(0.332788\pi\) | |||||||
\(90\) | −9.00904e92 | −1.34326 | ||||||||
\(91\) | 1.83833e92 | 0.162165 | ||||||||
\(92\) | −8.42767e93 | −4.42370 | ||||||||
\(93\) | 8.08702e92 | 0.254009 | ||||||||
\(94\) | 1.84136e94 | 3.47989 | ||||||||
\(95\) | −6.07512e93 | −0.694518 | ||||||||
\(96\) | 3.18185e94 | 2.21205 | ||||||||
\(97\) | −3.21613e94 | −1.36671 | −0.683354 | − | 0.730087i | \(-0.739479\pi\) | ||||
−0.683354 | + | 0.730087i | \(0.739479\pi\) | |||||||
\(98\) | 4.48953e94 | 1.17209 | ||||||||
\(99\) | 8.93268e93 | 0.143983 | ||||||||
\(100\) | −6.38248e94 | −0.638248 | ||||||||
\(101\) | 1.10577e95 | 0.689289 | 0.344645 | − | 0.938733i | \(-0.387999\pi\) | ||||
0.344645 | + | 0.938733i | \(0.387999\pi\) | |||||||
\(102\) | −2.16691e95 | −0.845927 | ||||||||
\(103\) | −2.78781e95 | −0.684691 | −0.342345 | − | 0.939574i | \(-0.611221\pi\) | ||||
−0.342345 | + | 0.939574i | \(0.611221\pi\) | |||||||
\(104\) | 2.98570e95 | 0.463407 | ||||||||
\(105\) | 5.32233e95 | 0.524336 | ||||||||
\(106\) | 3.59438e95 | 0.225733 | ||||||||
\(107\) | −2.08016e96 | −0.836311 | −0.418155 | − | 0.908376i | \(-0.637323\pi\) | ||||
−0.418155 | + | 0.908376i | \(0.637323\pi\) | |||||||
\(108\) | −9.21247e96 | −2.38094 | ||||||||
\(109\) | 4.86869e95 | 0.0812182 | 0.0406091 | − | 0.999175i | \(-0.487070\pi\) | ||||
0.0406091 | + | 0.999175i | \(0.487070\pi\) | |||||||
\(110\) | −2.95471e96 | −0.319420 | ||||||||
\(111\) | −3.12291e96 | −0.219643 | ||||||||
\(112\) | 1.16637e98 | 5.35773 | ||||||||
\(113\) | −1.92348e97 | −0.579246 | −0.289623 | − | 0.957141i | \(-0.593530\pi\) | ||||
−0.289623 | + | 0.957141i | \(0.593530\pi\) | |||||||
\(114\) | −3.67490e97 | −0.728224 | ||||||||
\(115\) | −1.04709e98 | −1.37036 | ||||||||
\(116\) | 2.28663e98 | 1.98354 | ||||||||
\(117\) | −1.73006e97 | −0.0998234 | ||||||||
\(118\) | −5.65412e98 | −2.17756 | ||||||||
\(119\) | −4.48977e98 | −1.15809 | ||||||||
\(120\) | 8.64421e98 | 1.49836 | ||||||||
\(121\) | −8.26371e98 | −0.965762 | ||||||||
\(122\) | 1.04868e99 | 0.828991 | ||||||||
\(123\) | −9.03076e98 | −0.484431 | ||||||||
\(124\) | 4.19825e99 | 1.53298 | ||||||||
\(125\) | −4.32491e99 | −1.07833 | ||||||||
\(126\) | −1.12915e100 | −1.92820 | ||||||||
\(127\) | −1.37038e100 | −1.60755 | −0.803777 | − | 0.594930i | \(-0.797180\pi\) | ||||
−0.803777 | + | 0.594930i | \(0.797180\pi\) | |||||||
\(128\) | 6.23795e100 | 5.04160 | ||||||||
\(129\) | 1.07192e99 | 0.0598621 | ||||||||
\(130\) | 5.72261e99 | 0.221455 | ||||||||
\(131\) | −3.14879e98 | −0.00846754 | −0.00423377 | − | 0.999991i | \(-0.501348\pi\) | ||||
−0.00423377 | + | 0.999991i | \(0.501348\pi\) | |||||||
\(132\) | −1.32222e100 | −0.247765 | ||||||||
\(133\) | −7.61427e100 | −0.996954 | ||||||||
\(134\) | 1.26544e101 | 1.16082 | ||||||||
\(135\) | −1.14459e101 | −0.737559 | ||||||||
\(136\) | −7.29201e101 | −3.30940 | ||||||||
\(137\) | 5.08244e101 | 1.62872 | 0.814358 | − | 0.580363i | \(-0.197089\pi\) | ||||
0.814358 | + | 0.580363i | \(0.197089\pi\) | |||||||
\(138\) | −6.33393e101 | −1.43687 | ||||||||
\(139\) | −3.57121e101 | −0.574927 | −0.287464 | − | 0.957792i | \(-0.592812\pi\) | ||||
−0.287464 | + | 0.957792i | \(0.592812\pi\) | |||||||
\(140\) | 2.76300e102 | 3.16446 | ||||||||
\(141\) | 1.02377e102 | 0.836166 | ||||||||
\(142\) | 1.08552e102 | 0.633783 | ||||||||
\(143\) | −5.67411e100 | −0.0237375 | ||||||||
\(144\) | −1.09768e103 | −3.29805 | ||||||||
\(145\) | 2.84100e102 | 0.614456 | ||||||||
\(146\) | 1.14831e103 | 1.79184 | ||||||||
\(147\) | 2.49610e102 | 0.281637 | ||||||||
\(148\) | −1.62121e103 | −1.32558 | ||||||||
\(149\) | 3.30116e103 | 1.96029 | 0.980143 | − | 0.198293i | \(-0.0635398\pi\) | ||||
0.980143 | + | 0.198293i | \(0.0635398\pi\) | |||||||
\(150\) | −4.79684e102 | −0.207310 | ||||||||
\(151\) | −1.44275e103 | −0.454763 | −0.227381 | − | 0.973806i | \(-0.573016\pi\) | ||||
−0.227381 | + | 0.973806i | \(0.573016\pi\) | |||||||
\(152\) | −1.23666e104 | −2.84893 | ||||||||
\(153\) | 4.22534e103 | 0.712884 | ||||||||
\(154\) | −3.70330e103 | −0.458516 | ||||||||
\(155\) | 5.21606e103 | 0.474883 | ||||||||
\(156\) | 2.56083e103 | 0.171776 | ||||||||
\(157\) | −2.05317e104 | −1.01670 | −0.508349 | − | 0.861151i | \(-0.669744\pi\) | ||||
−0.508349 | + | 0.861151i | \(0.669744\pi\) | |||||||
\(158\) | 3.58978e104 | 1.31479 | ||||||||
\(159\) | 1.99841e103 | 0.0542403 | ||||||||
\(160\) | 2.05226e105 | 4.13556 | ||||||||
\(161\) | −1.31237e105 | −1.96710 | ||||||||
\(162\) | 6.73266e104 | 0.752010 | ||||||||
\(163\) | −6.60439e104 | −0.550708 | −0.275354 | − | 0.961343i | \(-0.588795\pi\) | ||||
−0.275354 | + | 0.961343i | \(0.588795\pi\) | |||||||
\(164\) | −4.68818e105 | −2.92362 | ||||||||
\(165\) | −1.64277e104 | −0.0767520 | ||||||||
\(166\) | −8.84970e104 | −0.310309 | ||||||||
\(167\) | 1.63767e105 | 0.431712 | 0.215856 | − | 0.976425i | \(-0.430746\pi\) | ||||
0.215856 | + | 0.976425i | \(0.430746\pi\) | |||||||
\(168\) | 1.08342e106 | 2.15084 | ||||||||
\(169\) | −6.56768e105 | −0.983543 | ||||||||
\(170\) | −1.39764e106 | −1.58151 | ||||||||
\(171\) | 7.16583e105 | 0.613693 | ||||||||
\(172\) | 5.56472e105 | 0.361278 | ||||||||
\(173\) | 7.86049e105 | 0.387489 | 0.193745 | − | 0.981052i | \(-0.437937\pi\) | ||||
0.193745 | + | 0.981052i | \(0.437937\pi\) | |||||||
\(174\) | 1.71855e106 | 0.644277 | ||||||||
\(175\) | −9.93889e105 | −0.283812 | ||||||||
\(176\) | −3.60008e106 | −0.784260 | ||||||||
\(177\) | −3.14360e106 | −0.523235 | ||||||||
\(178\) | 1.54368e107 | 1.96611 | ||||||||
\(179\) | 1.21900e107 | 1.18983 | 0.594916 | − | 0.803788i | \(-0.297185\pi\) | ||||
0.594916 | + | 0.803788i | \(0.297185\pi\) | |||||||
\(180\) | −2.60028e107 | −1.94794 | ||||||||
\(181\) | 3.05359e107 | 1.75824 | 0.879120 | − | 0.476600i | \(-0.158131\pi\) | ||||
0.879120 | + | 0.476600i | \(0.158131\pi\) | |||||||
\(182\) | 7.17245e106 | 0.317890 | ||||||||
\(183\) | 5.83047e106 | 0.199194 | ||||||||
\(184\) | −2.13147e108 | −5.62125 | ||||||||
\(185\) | −2.01425e107 | −0.410635 | ||||||||
\(186\) | 3.15525e107 | 0.497931 | ||||||||
\(187\) | 1.38579e107 | 0.169521 | ||||||||
\(188\) | 5.31471e108 | 5.04640 | ||||||||
\(189\) | −1.43458e108 | −1.05874 | ||||||||
\(190\) | −2.37028e108 | −1.36146 | ||||||||
\(191\) | −3.48114e107 | −0.155825 | −0.0779124 | − | 0.996960i | \(-0.524825\pi\) | ||||
−0.0779124 | + | 0.996960i | \(0.524825\pi\) | |||||||
\(192\) | 6.69880e108 | 2.33985 | ||||||||
\(193\) | 2.23194e108 | 0.609130 | 0.304565 | − | 0.952492i | \(-0.401489\pi\) | ||||
0.304565 | + | 0.952492i | \(0.401489\pi\) | |||||||
\(194\) | −1.25481e109 | −2.67914 | ||||||||
\(195\) | 3.18167e107 | 0.0532123 | ||||||||
\(196\) | 1.29581e109 | 1.69973 | ||||||||
\(197\) | −1.91029e109 | −1.96767 | −0.983837 | − | 0.179065i | \(-0.942693\pi\) | ||||
−0.983837 | + | 0.179065i | \(0.942693\pi\) | |||||||
\(198\) | 3.48519e108 | 0.282248 | ||||||||
\(199\) | −5.55220e108 | −0.353952 | −0.176976 | − | 0.984215i | \(-0.556631\pi\) | ||||
−0.176976 | + | 0.984215i | \(0.556631\pi\) | |||||||
\(200\) | −1.61422e109 | −0.811029 | ||||||||
\(201\) | 7.03563e108 | 0.278927 | ||||||||
\(202\) | 4.31431e109 | 1.35121 | ||||||||
\(203\) | 3.56078e109 | 0.882029 | ||||||||
\(204\) | −6.25435e109 | −1.22673 | ||||||||
\(205\) | −5.82477e109 | −0.905670 | ||||||||
\(206\) | −1.08770e110 | −1.34219 | ||||||||
\(207\) | 1.23508e110 | 1.21088 | ||||||||
\(208\) | 6.97253e109 | 0.543729 | ||||||||
\(209\) | 2.35019e109 | 0.145933 | ||||||||
\(210\) | 2.07657e110 | 1.02785 | ||||||||
\(211\) | 3.40905e110 | 1.34653 | 0.673266 | − | 0.739401i | \(-0.264891\pi\) | ||||
0.673266 | + | 0.739401i | \(0.264891\pi\) | |||||||
\(212\) | 1.03744e110 | 0.327349 | ||||||||
\(213\) | 6.03530e109 | 0.152289 | ||||||||
\(214\) | −8.11600e110 | −1.63941 | ||||||||
\(215\) | 6.91381e109 | 0.111916 | ||||||||
\(216\) | −2.32996e111 | −3.02548 | ||||||||
\(217\) | 6.53757e110 | 0.681677 | ||||||||
\(218\) | 1.89958e110 | 0.159211 | ||||||||
\(219\) | 6.38441e110 | 0.430552 | ||||||||
\(220\) | −8.52818e110 | −0.463211 | ||||||||
\(221\) | −2.68397e110 | −0.117529 | ||||||||
\(222\) | −1.21844e111 | −0.430564 | ||||||||
\(223\) | −3.82469e111 | −1.09173 | −0.545864 | − | 0.837874i | \(-0.683799\pi\) | ||||
−0.545864 | + | 0.837874i | \(0.683799\pi\) | |||||||
\(224\) | 2.57221e112 | 5.93644 | ||||||||
\(225\) | 9.35354e110 | 0.174705 | ||||||||
\(226\) | −7.50471e111 | −1.13549 | ||||||||
\(227\) | −1.17158e112 | −1.43729 | −0.718645 | − | 0.695377i | \(-0.755237\pi\) | ||||
−0.718645 | + | 0.695377i | \(0.755237\pi\) | |||||||
\(228\) | −1.06069e112 | −1.05604 | ||||||||
\(229\) | 1.67490e112 | 1.35458 | 0.677288 | − | 0.735718i | \(-0.263155\pi\) | ||||
0.677288 | + | 0.735718i | \(0.263155\pi\) | |||||||
\(230\) | −4.08533e112 | −2.68630 | ||||||||
\(231\) | −2.05897e111 | −0.110175 | ||||||||
\(232\) | 5.78320e112 | 2.52051 | ||||||||
\(233\) | 6.96313e111 | 0.247399 | 0.123700 | − | 0.992320i | \(-0.460524\pi\) | ||||
0.123700 | + | 0.992320i | \(0.460524\pi\) | |||||||
\(234\) | −6.75003e111 | −0.195683 | ||||||||
\(235\) | 6.60320e112 | 1.56326 | ||||||||
\(236\) | −1.63195e113 | −3.15781 | ||||||||
\(237\) | 1.99586e112 | 0.315924 | ||||||||
\(238\) | −1.75174e113 | −2.27020 | ||||||||
\(239\) | 5.54701e112 | 0.589059 | 0.294530 | − | 0.955642i | \(-0.404837\pi\) | ||||
0.294530 | + | 0.955642i | \(0.404837\pi\) | |||||||
\(240\) | 2.01869e113 | 1.75807 | ||||||||
\(241\) | 1.57841e113 | 1.12827 | 0.564133 | − | 0.825684i | \(-0.309211\pi\) | ||||
0.564133 | + | 0.825684i | \(0.309211\pi\) | |||||||
\(242\) | −3.22419e113 | −1.89317 | ||||||||
\(243\) | 2.10936e113 | 1.01825 | ||||||||
\(244\) | 3.02679e113 | 1.20217 | ||||||||
\(245\) | 1.60997e113 | 0.526536 | ||||||||
\(246\) | −3.52346e113 | −0.949625 | ||||||||
\(247\) | −4.55179e112 | −0.101176 | ||||||||
\(248\) | 1.06179e114 | 1.94798 | ||||||||
\(249\) | −4.92029e112 | −0.0745627 | ||||||||
\(250\) | −1.68741e114 | −2.11384 | ||||||||
\(251\) | 1.09858e114 | 1.13849 | 0.569244 | − | 0.822168i | \(-0.307236\pi\) | ||||
0.569244 | + | 0.822168i | \(0.307236\pi\) | |||||||
\(252\) | −3.25906e114 | −2.79619 | ||||||||
\(253\) | 4.05070e113 | 0.287943 | ||||||||
\(254\) | −5.34672e114 | −3.15127 | ||||||||
\(255\) | −7.77064e113 | −0.380013 | ||||||||
\(256\) | 1.21049e115 | 4.91545 | ||||||||
\(257\) | 2.55612e114 | 0.862498 | 0.431249 | − | 0.902233i | \(-0.358073\pi\) | ||||
0.431249 | + | 0.902233i | \(0.358073\pi\) | |||||||
\(258\) | 4.18224e113 | 0.117347 | ||||||||
\(259\) | −2.52457e114 | −0.589451 | ||||||||
\(260\) | 1.65172e114 | 0.321145 | ||||||||
\(261\) | −3.35107e114 | −0.542949 | ||||||||
\(262\) | −1.22854e113 | −0.0165988 | ||||||||
\(263\) | 4.76486e114 | 0.537220 | 0.268610 | − | 0.963249i | \(-0.413436\pi\) | ||||
0.268610 | + | 0.963249i | \(0.413436\pi\) | |||||||
\(264\) | −3.34406e114 | −0.314838 | ||||||||
\(265\) | 1.28896e114 | 0.101405 | ||||||||
\(266\) | −2.97080e115 | −1.95432 | ||||||||
\(267\) | 8.58260e114 | 0.472426 | ||||||||
\(268\) | 3.65243e115 | 1.68337 | ||||||||
\(269\) | 7.95205e114 | 0.307076 | 0.153538 | − | 0.988143i | \(-0.450933\pi\) | ||||
0.153538 | + | 0.988143i | \(0.450933\pi\) | |||||||
\(270\) | −4.46576e115 | −1.44583 | ||||||||
\(271\) | 6.86155e115 | 1.86372 | 0.931861 | − | 0.362816i | \(-0.118185\pi\) | ||||
0.931861 | + | 0.362816i | \(0.118185\pi\) | |||||||
\(272\) | −1.70291e116 | −3.88301 | ||||||||
\(273\) | 3.98776e114 | 0.0763842 | ||||||||
\(274\) | 1.98297e116 | 3.19275 | ||||||||
\(275\) | 3.06770e114 | 0.0415442 | ||||||||
\(276\) | −1.82816e116 | −2.08369 | ||||||||
\(277\) | −4.72757e115 | −0.453783 | −0.226892 | − | 0.973920i | \(-0.572856\pi\) | ||||
−0.226892 | + | 0.973920i | \(0.572856\pi\) | |||||||
\(278\) | −1.39335e116 | −1.12702 | ||||||||
\(279\) | −6.15254e115 | −0.419619 | ||||||||
\(280\) | 6.98800e116 | 4.02111 | ||||||||
\(281\) | 4.14167e115 | 0.201199 | 0.100599 | − | 0.994927i | \(-0.467924\pi\) | ||||
0.100599 | + | 0.994927i | \(0.467924\pi\) | |||||||
\(282\) | 3.99434e116 | 1.63913 | ||||||||
\(283\) | −3.67313e116 | −1.27403 | −0.637016 | − | 0.770851i | \(-0.719831\pi\) | ||||
−0.637016 | + | 0.770851i | \(0.719831\pi\) | |||||||
\(284\) | 3.13313e116 | 0.919088 | ||||||||
\(285\) | −1.31784e116 | −0.327138 | ||||||||
\(286\) | −2.21382e115 | −0.0465325 | ||||||||
\(287\) | −7.30049e116 | −1.30006 | ||||||||
\(288\) | −2.42072e117 | −3.65428 | ||||||||
\(289\) | −1.25484e116 | −0.160673 | ||||||||
\(290\) | 1.10845e117 | 1.20451 | ||||||||
\(291\) | −6.97653e116 | −0.643758 | ||||||||
\(292\) | 3.31436e117 | 2.59845 | ||||||||
\(293\) | 1.78692e115 | 0.0119095 | 0.00595475 | − | 0.999982i | \(-0.498105\pi\) | ||||
0.00595475 | + | 0.999982i | \(0.498105\pi\) | |||||||
\(294\) | 9.73885e116 | 0.552090 | ||||||||
\(295\) | −2.02759e117 | −0.978217 | ||||||||
\(296\) | −4.10025e117 | −1.68443 | ||||||||
\(297\) | 4.42791e116 | 0.154977 | ||||||||
\(298\) | 1.28799e118 | 3.84273 | ||||||||
\(299\) | −7.84530e116 | −0.199631 | ||||||||
\(300\) | −1.38451e117 | −0.300633 | ||||||||
\(301\) | 8.66545e116 | 0.160651 | ||||||||
\(302\) | −5.62905e117 | −0.891466 | ||||||||
\(303\) | 2.39869e117 | 0.324675 | ||||||||
\(304\) | −2.88799e118 | −3.34273 | ||||||||
\(305\) | 3.76060e117 | 0.372405 | ||||||||
\(306\) | 1.64857e118 | 1.39746 | ||||||||
\(307\) | 1.98631e118 | 1.44203 | 0.721016 | − | 0.692918i | \(-0.243675\pi\) | ||||
0.721016 | + | 0.692918i | \(0.243675\pi\) | |||||||
\(308\) | −1.06888e118 | −0.664922 | ||||||||
\(309\) | −6.04741e117 | −0.322509 | ||||||||
\(310\) | 2.03511e118 | 0.930909 | ||||||||
\(311\) | −1.19899e118 | −0.470648 | −0.235324 | − | 0.971917i | \(-0.575615\pi\) | ||||
−0.235324 | + | 0.971917i | \(0.575615\pi\) | |||||||
\(312\) | 6.47669e117 | 0.218278 | ||||||||
\(313\) | −4.85938e118 | −1.40678 | −0.703388 | − | 0.710806i | \(-0.748330\pi\) | ||||
−0.703388 | + | 0.710806i | \(0.748330\pi\) | |||||||
\(314\) | −8.01070e118 | −1.99302 | ||||||||
\(315\) | −4.04919e118 | −0.866196 | ||||||||
\(316\) | 1.03612e119 | 1.90666 | ||||||||
\(317\) | 8.42986e118 | 1.33507 | 0.667537 | − | 0.744577i | \(-0.267349\pi\) | ||||
0.667537 | + | 0.744577i | \(0.267349\pi\) | |||||||
\(318\) | 7.79705e117 | 0.106327 | ||||||||
\(319\) | −1.09906e118 | −0.129111 | ||||||||
\(320\) | 4.32067e119 | 4.37449 | ||||||||
\(321\) | −4.51236e118 | −0.393926 | ||||||||
\(322\) | −5.12036e119 | −3.85609 | ||||||||
\(323\) | 1.11169e119 | 0.722543 | ||||||||
\(324\) | 1.94325e119 | 1.09054 | ||||||||
\(325\) | −5.94144e117 | −0.0288026 | ||||||||
\(326\) | −2.57678e119 | −1.07955 | ||||||||
\(327\) | 1.05613e118 | 0.0382561 | ||||||||
\(328\) | −1.18570e120 | −3.71508 | ||||||||
\(329\) | 8.27614e119 | 2.24400 | ||||||||
\(330\) | −6.40947e118 | −0.150456 | ||||||||
\(331\) | −3.58104e119 | −0.728081 | −0.364040 | − | 0.931383i | \(-0.618603\pi\) | ||||
−0.364040 | + | 0.931383i | \(0.618603\pi\) | |||||||
\(332\) | −2.55429e119 | −0.449998 | ||||||||
\(333\) | 2.37588e119 | 0.362847 | ||||||||
\(334\) | 6.38956e119 | 0.846280 | ||||||||
\(335\) | 4.53792e119 | 0.521469 | ||||||||
\(336\) | 2.53013e120 | 2.52364 | ||||||||
\(337\) | 1.94649e120 | 1.68590 | 0.842951 | − | 0.537990i | \(-0.180816\pi\) | ||||
0.842951 | + | 0.537990i | \(0.180816\pi\) | |||||||
\(338\) | −2.56246e120 | −1.92803 | ||||||||
\(339\) | −4.17249e119 | −0.272841 | ||||||||
\(340\) | −4.03400e120 | −2.29344 | ||||||||
\(341\) | −2.01786e119 | −0.0997833 | ||||||||
\(342\) | 2.79583e120 | 1.20302 | ||||||||
\(343\) | −1.35694e120 | −0.508266 | ||||||||
\(344\) | 1.40739e120 | 0.459080 | ||||||||
\(345\) | −2.27137e120 | −0.645479 | ||||||||
\(346\) | 3.06686e120 | 0.759591 | ||||||||
\(347\) | −2.05011e120 | −0.442718 | −0.221359 | − | 0.975192i | \(-0.571049\pi\) | ||||
−0.221359 | + | 0.975192i | \(0.571049\pi\) | |||||||
\(348\) | 4.96025e120 | 0.934306 | ||||||||
\(349\) | −3.62930e119 | −0.0596507 | −0.0298254 | − | 0.999555i | \(-0.509495\pi\) | ||||
−0.0298254 | + | 0.999555i | \(0.509495\pi\) | |||||||
\(350\) | −3.87778e120 | −0.556353 | ||||||||
\(351\) | −8.57587e119 | −0.107446 | ||||||||
\(352\) | −7.93929e120 | −0.868971 | ||||||||
\(353\) | −1.01830e121 | −0.974045 | −0.487023 | − | 0.873389i | \(-0.661917\pi\) | ||||
−0.487023 | + | 0.873389i | \(0.661917\pi\) | |||||||
\(354\) | −1.22651e121 | −1.02569 | ||||||||
\(355\) | 3.89272e120 | 0.284712 | ||||||||
\(356\) | 4.45552e121 | 2.85117 | ||||||||
\(357\) | −9.73936e120 | −0.545494 | ||||||||
\(358\) | 4.75609e121 | 2.33242 | ||||||||
\(359\) | −2.37747e121 | −1.02124 | −0.510621 | − | 0.859806i | \(-0.670584\pi\) | ||||
−0.510621 | + | 0.859806i | \(0.670584\pi\) | |||||||
\(360\) | −6.57645e121 | −2.47527 | ||||||||
\(361\) | −1.14571e121 | −0.377993 | ||||||||
\(362\) | 1.19139e122 | 3.44666 | ||||||||
\(363\) | −1.79259e121 | −0.454901 | ||||||||
\(364\) | 2.07018e121 | 0.460992 | ||||||||
\(365\) | 4.11789e121 | 0.804940 | ||||||||
\(366\) | 2.27483e121 | 0.390478 | ||||||||
\(367\) | 6.39719e121 | 0.964608 | 0.482304 | − | 0.876004i | \(-0.339800\pi\) | ||||
0.482304 | + | 0.876004i | \(0.339800\pi\) | |||||||
\(368\) | −4.97764e122 | −6.59557 | ||||||||
\(369\) | 6.87053e121 | 0.800273 | ||||||||
\(370\) | −7.85884e121 | −0.804964 | ||||||||
\(371\) | 1.61552e121 | 0.145563 | ||||||||
\(372\) | 9.10699e121 | 0.722079 | ||||||||
\(373\) | −1.37493e122 | −0.959649 | −0.479825 | − | 0.877364i | \(-0.659300\pi\) | ||||
−0.479825 | + | 0.877364i | \(0.659300\pi\) | |||||||
\(374\) | 5.40684e121 | 0.332309 | ||||||||
\(375\) | −9.38174e121 | −0.507923 | ||||||||
\(376\) | 1.34416e123 | 6.41252 | ||||||||
\(377\) | 2.12862e121 | 0.0895127 | ||||||||
\(378\) | −5.59718e122 | −2.07543 | ||||||||
\(379\) | 2.70086e122 | 0.883363 | 0.441681 | − | 0.897172i | \(-0.354382\pi\) | ||||
0.441681 | + | 0.897172i | \(0.354382\pi\) | |||||||
\(380\) | −6.84133e122 | −1.97433 | ||||||||
\(381\) | −2.97269e122 | −0.757204 | ||||||||
\(382\) | −1.35821e122 | −0.305462 | ||||||||
\(383\) | −3.51647e122 | −0.698497 | −0.349249 | − | 0.937030i | \(-0.613563\pi\) | ||||
−0.349249 | + | 0.937030i | \(0.613563\pi\) | |||||||
\(384\) | 1.35316e123 | 2.37474 | ||||||||
\(385\) | −1.32802e122 | −0.205977 | ||||||||
\(386\) | 8.70817e122 | 1.19407 | ||||||||
\(387\) | −8.15510e121 | −0.0988914 | ||||||||
\(388\) | −3.62176e123 | −3.88519 | ||||||||
\(389\) | 2.25584e122 | 0.214142 | 0.107071 | − | 0.994251i | \(-0.465853\pi\) | ||||
0.107071 | + | 0.994251i | \(0.465853\pi\) | |||||||
\(390\) | 1.24137e122 | 0.104311 | ||||||||
\(391\) | 1.91607e123 | 1.42566 | ||||||||
\(392\) | 3.27728e123 | 2.15986 | ||||||||
\(393\) | −6.83047e120 | −0.00398845 | ||||||||
\(394\) | −7.45322e123 | −3.85721 | ||||||||
\(395\) | 1.28731e123 | 0.590638 | ||||||||
\(396\) | 1.00593e123 | 0.409305 | ||||||||
\(397\) | 3.71554e123 | 1.34113 | 0.670567 | − | 0.741849i | \(-0.266051\pi\) | ||||
0.670567 | + | 0.741849i | \(0.266051\pi\) | |||||||
\(398\) | −2.16626e123 | −0.693848 | ||||||||
\(399\) | −1.65171e123 | −0.469594 | ||||||||
\(400\) | −3.76969e123 | −0.951604 | ||||||||
\(401\) | 2.99501e123 | 0.671492 | 0.335746 | − | 0.941953i | \(-0.391012\pi\) | ||||
0.335746 | + | 0.941953i | \(0.391012\pi\) | |||||||
\(402\) | 2.74503e123 | 0.546777 | ||||||||
\(403\) | 3.90814e122 | 0.0691800 | ||||||||
\(404\) | 1.24524e124 | 1.95947 | ||||||||
\(405\) | 2.41436e123 | 0.337823 | ||||||||
\(406\) | 1.38928e124 | 1.72903 | ||||||||
\(407\) | 7.79223e122 | 0.0862834 | ||||||||
\(408\) | −1.58181e124 | −1.55882 | ||||||||
\(409\) | −1.54307e124 | −1.35372 | −0.676858 | − | 0.736114i | \(-0.736659\pi\) | ||||
−0.676858 | + | 0.736114i | \(0.736659\pi\) | |||||||
\(410\) | −2.27260e124 | −1.77538 | ||||||||
\(411\) | 1.10250e124 | 0.767171 | ||||||||
\(412\) | −3.13941e124 | −1.94639 | ||||||||
\(413\) | −2.54129e124 | −1.40419 | ||||||||
\(414\) | 4.81880e124 | 2.37368 | ||||||||
\(415\) | −3.17354e123 | −0.139399 | ||||||||
\(416\) | 1.53766e124 | 0.602459 | ||||||||
\(417\) | −7.74681e123 | −0.270807 | ||||||||
\(418\) | 9.16955e123 | 0.286072 | ||||||||
\(419\) | −1.58097e124 | −0.440308 | −0.220154 | − | 0.975465i | \(-0.570656\pi\) | ||||
−0.220154 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(420\) | 5.99360e124 | 1.49055 | ||||||||
\(421\) | −3.10214e124 | −0.689068 | −0.344534 | − | 0.938774i | \(-0.611963\pi\) | ||||
−0.344534 | + | 0.938774i | \(0.611963\pi\) | |||||||
\(422\) | 1.33008e125 | 2.63959 | ||||||||
\(423\) | −7.78872e124 | −1.38133 | ||||||||
\(424\) | 2.62384e124 | 0.415966 | ||||||||
\(425\) | 1.45109e124 | 0.205693 | ||||||||
\(426\) | 2.35474e124 | 0.298530 | ||||||||
\(427\) | 4.71336e124 | 0.534573 | ||||||||
\(428\) | −2.34252e125 | −2.37741 | ||||||||
\(429\) | −1.23085e123 | −0.0111811 | ||||||||
\(430\) | 2.69751e124 | 0.219387 | ||||||||
\(431\) | −2.08983e124 | −0.152209 | −0.0761045 | − | 0.997100i | \(-0.524248\pi\) | ||||
−0.0761045 | + | 0.997100i | \(0.524248\pi\) | |||||||
\(432\) | −5.44117e125 | −3.54989 | ||||||||
\(433\) | 2.84740e125 | 1.66446 | 0.832232 | − | 0.554428i | \(-0.187063\pi\) | ||||
0.832232 | + | 0.554428i | \(0.187063\pi\) | |||||||
\(434\) | 2.55071e125 | 1.33628 | ||||||||
\(435\) | 6.16280e124 | 0.289426 | ||||||||
\(436\) | 5.48275e124 | 0.230882 | ||||||||
\(437\) | 3.24949e125 | 1.22729 | ||||||||
\(438\) | 2.49095e125 | 0.844006 | ||||||||
\(439\) | −5.91270e125 | −1.79772 | −0.898859 | − | 0.438238i | \(-0.855603\pi\) | ||||
−0.898859 | + | 0.438238i | \(0.855603\pi\) | |||||||
\(440\) | −2.15689e125 | −0.588607 | ||||||||
\(441\) | −1.89902e125 | −0.465260 | ||||||||
\(442\) | −1.04718e125 | −0.230391 | ||||||||
\(443\) | −4.39519e124 | −0.0868561 | −0.0434281 | − | 0.999057i | \(-0.513828\pi\) | ||||
−0.0434281 | + | 0.999057i | \(0.513828\pi\) | |||||||
\(444\) | −3.51678e125 | −0.624387 | ||||||||
\(445\) | 5.53570e125 | 0.883227 | ||||||||
\(446\) | −1.49225e126 | −2.14010 | ||||||||
\(447\) | 7.16100e125 | 0.923350 | ||||||||
\(448\) | 5.41532e126 | 6.27941 | ||||||||
\(449\) | −1.31183e126 | −1.36829 | −0.684144 | − | 0.729347i | \(-0.739824\pi\) | ||||
−0.684144 | + | 0.729347i | \(0.739824\pi\) | |||||||
\(450\) | 3.64940e125 | 0.342473 | ||||||||
\(451\) | 2.25334e125 | 0.190301 | ||||||||
\(452\) | −2.16608e126 | −1.64664 | ||||||||
\(453\) | −3.12965e125 | −0.214206 | ||||||||
\(454\) | −4.57107e126 | −2.81750 | ||||||||
\(455\) | 2.57207e125 | 0.142805 | ||||||||
\(456\) | −2.68261e126 | −1.34193 | ||||||||
\(457\) | 2.56681e126 | 1.15711 | 0.578554 | − | 0.815644i | \(-0.303617\pi\) | ||||
0.578554 | + | 0.815644i | \(0.303617\pi\) | |||||||
\(458\) | 6.53483e126 | 2.65536 | ||||||||
\(459\) | 2.09450e126 | 0.767321 | ||||||||
\(460\) | −1.17915e127 | −3.89557 | ||||||||
\(461\) | −4.70807e126 | −1.40297 | −0.701486 | − | 0.712683i | \(-0.747480\pi\) | ||||
−0.701486 | + | 0.712683i | \(0.747480\pi\) | |||||||
\(462\) | −8.03332e125 | −0.215974 | ||||||||
\(463\) | 1.07726e126 | 0.261350 | 0.130675 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130675 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(464\) | 1.35056e127 | 2.95739 | ||||||||
\(465\) | 1.13149e126 | 0.223684 | ||||||||
\(466\) | 2.71675e126 | 0.484974 | ||||||||
\(467\) | 3.14969e126 | 0.507828 | 0.253914 | − | 0.967227i | \(-0.418282\pi\) | ||||
0.253914 | + | 0.967227i | \(0.418282\pi\) | |||||||
\(468\) | −1.94826e126 | −0.283772 | ||||||||
\(469\) | 5.68762e126 | 0.748549 | ||||||||
\(470\) | 2.57632e127 | 3.06444 | ||||||||
\(471\) | −4.45382e126 | −0.478894 | ||||||||
\(472\) | −4.12741e127 | −4.01267 | ||||||||
\(473\) | −2.67464e125 | −0.0235159 | ||||||||
\(474\) | 7.78708e126 | 0.619303 | ||||||||
\(475\) | 2.46092e126 | 0.177072 | ||||||||
\(476\) | −5.05603e127 | −3.29215 | ||||||||
\(477\) | −1.52038e126 | −0.0896042 | ||||||||
\(478\) | 2.16423e127 | 1.15473 | ||||||||
\(479\) | −5.24878e126 | −0.253584 | −0.126792 | − | 0.991929i | \(-0.540468\pi\) | ||||
−0.126792 | + | 0.991929i | \(0.540468\pi\) | |||||||
\(480\) | 4.45184e127 | 1.94796 | ||||||||
\(481\) | −1.50918e126 | −0.0598204 | ||||||||
\(482\) | 6.15837e127 | 2.21173 | ||||||||
\(483\) | −2.84683e127 | −0.926560 | ||||||||
\(484\) | −9.30596e127 | −2.74541 | ||||||||
\(485\) | −4.49981e127 | −1.20354 | ||||||||
\(486\) | 8.22994e127 | 1.99606 | ||||||||
\(487\) | −4.92430e127 | −1.08322 | −0.541612 | − | 0.840628i | \(-0.682186\pi\) | ||||
−0.541612 | + | 0.840628i | \(0.682186\pi\) | |||||||
\(488\) | 7.65516e127 | 1.52761 | ||||||||
\(489\) | −1.43265e127 | −0.259399 | ||||||||
\(490\) | 6.28148e127 | 1.03216 | ||||||||
\(491\) | 3.83490e127 | 0.571983 | 0.285991 | − | 0.958232i | \(-0.407677\pi\) | ||||
0.285991 | + | 0.958232i | \(0.407677\pi\) | |||||||
\(492\) | −1.01698e128 | −1.37711 | ||||||||
\(493\) | −5.19876e127 | −0.639251 | ||||||||
\(494\) | −1.77594e127 | −0.198334 | ||||||||
\(495\) | 1.24981e127 | 0.126793 | ||||||||
\(496\) | 2.47961e128 | 2.28562 | ||||||||
\(497\) | 4.87895e127 | 0.408694 | ||||||||
\(498\) | −1.91971e127 | −0.146164 | ||||||||
\(499\) | 6.32043e127 | 0.437492 | 0.218746 | − | 0.975782i | \(-0.429803\pi\) | ||||
0.218746 | + | 0.975782i | \(0.429803\pi\) | |||||||
\(500\) | −4.87038e128 | −3.06540 | ||||||||
\(501\) | 3.55249e127 | 0.203348 | ||||||||
\(502\) | 4.28623e128 | 2.23177 | ||||||||
\(503\) | 2.36417e128 | 1.11995 | 0.559976 | − | 0.828509i | \(-0.310810\pi\) | ||||
0.559976 | + | 0.828509i | \(0.310810\pi\) | |||||||
\(504\) | −8.24261e128 | −3.55316 | ||||||||
\(505\) | 1.54713e128 | 0.606998 | ||||||||
\(506\) | 1.58043e128 | 0.564451 | ||||||||
\(507\) | −1.42468e128 | −0.463277 | ||||||||
\(508\) | −1.54322e129 | −4.56985 | ||||||||
\(509\) | 1.67765e128 | 0.452488 | 0.226244 | − | 0.974071i | \(-0.427355\pi\) | ||||
0.226244 | + | 0.974071i | \(0.427355\pi\) | |||||||
\(510\) | −3.03181e128 | −0.744935 | ||||||||
\(511\) | 5.16117e128 | 1.15546 | ||||||||
\(512\) | 2.25177e129 | 4.59411 | ||||||||
\(513\) | 3.55209e128 | 0.660555 | ||||||||
\(514\) | 9.97301e128 | 1.69075 | ||||||||
\(515\) | −3.90053e128 | −0.602948 | ||||||||
\(516\) | 1.20712e128 | 0.170172 | ||||||||
\(517\) | −2.55448e128 | −0.328475 | ||||||||
\(518\) | −9.84990e128 | −1.15550 | ||||||||
\(519\) | 1.70512e128 | 0.182518 | ||||||||
\(520\) | 4.17741e128 | 0.408083 | ||||||||
\(521\) | −8.31621e128 | −0.741539 | −0.370769 | − | 0.928725i | \(-0.620906\pi\) | ||||
−0.370769 | + | 0.928725i | \(0.620906\pi\) | |||||||
\(522\) | −1.30746e129 | −1.06434 | ||||||||
\(523\) | −1.77551e129 | −1.31975 | −0.659876 | − | 0.751375i | \(-0.729391\pi\) | ||||
−0.659876 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(524\) | −3.54593e127 | −0.0240710 | ||||||||
\(525\) | −2.15598e128 | −0.133683 | ||||||||
\(526\) | 1.85907e129 | 1.05311 | ||||||||
\(527\) | −9.54490e128 | −0.494046 | ||||||||
\(528\) | −7.80941e128 | −0.369409 | ||||||||
\(529\) | 3.28787e129 | 1.42158 | ||||||||
\(530\) | 5.02903e128 | 0.198784 | ||||||||
\(531\) | 2.39162e129 | 0.864376 | ||||||||
\(532\) | −8.57461e129 | −2.83408 | ||||||||
\(533\) | −4.36421e128 | −0.131936 | ||||||||
\(534\) | 3.34860e129 | 0.926092 | ||||||||
\(535\) | −2.91043e129 | −0.736467 | ||||||||
\(536\) | 9.23749e129 | 2.13908 | ||||||||
\(537\) | 2.64431e129 | 0.560445 | ||||||||
\(538\) | 3.10259e129 | 0.601958 | ||||||||
\(539\) | −6.22824e128 | −0.110637 | ||||||||
\(540\) | −1.28895e130 | −2.09669 | ||||||||
\(541\) | −8.69602e129 | −1.29554 | −0.647769 | − | 0.761836i | \(-0.724298\pi\) | ||||
−0.647769 | + | 0.761836i | \(0.724298\pi\) | |||||||
\(542\) | 2.67712e130 | 3.65343 | ||||||||
\(543\) | 6.62395e129 | 0.828181 | ||||||||
\(544\) | −3.75545e130 | −4.30243 | ||||||||
\(545\) | 6.81197e128 | 0.0715219 | ||||||||
\(546\) | 1.55587e129 | 0.149735 | ||||||||
\(547\) | −1.69219e129 | −0.149297 | −0.0746486 | − | 0.997210i | \(-0.523784\pi\) | ||||
−0.0746486 | + | 0.997210i | \(0.523784\pi\) | |||||||
\(548\) | 5.72345e130 | 4.63001 | ||||||||
\(549\) | −4.43577e129 | −0.329066 | ||||||||
\(550\) | 1.19690e129 | 0.0814386 | ||||||||
\(551\) | −8.81666e129 | −0.550305 | ||||||||
\(552\) | −4.62366e130 | −2.64777 | ||||||||
\(553\) | 1.61346e130 | 0.847839 | ||||||||
\(554\) | −1.84452e130 | −0.889547 | ||||||||
\(555\) | −4.36938e129 | −0.193421 | ||||||||
\(556\) | −4.02163e130 | −1.63437 | ||||||||
\(557\) | −3.92915e130 | −1.46615 | −0.733073 | − | 0.680150i | \(-0.761915\pi\) | ||||
−0.733073 | + | 0.680150i | \(0.761915\pi\) | |||||||
\(558\) | −2.40049e130 | −0.822574 | ||||||||
\(559\) | 5.18018e128 | 0.0163036 | ||||||||
\(560\) | 1.63191e131 | 4.71809 | ||||||||
\(561\) | 3.00611e129 | 0.0798490 | ||||||||
\(562\) | 1.61592e130 | 0.394408 | ||||||||
\(563\) | −1.16339e130 | −0.260961 | −0.130480 | − | 0.991451i | \(-0.541652\pi\) | ||||
−0.130480 | + | 0.991451i | \(0.541652\pi\) | |||||||
\(564\) | 1.15289e131 | 2.37700 | ||||||||
\(565\) | −2.69122e130 | −0.510092 | ||||||||
\(566\) | −1.43311e131 | −2.49747 | ||||||||
\(567\) | 3.02605e130 | 0.484932 | ||||||||
\(568\) | 7.92410e130 | 1.16790 | ||||||||
\(569\) | 1.94656e130 | 0.263897 | 0.131949 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131949 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(570\) | −5.14170e130 | −0.641284 | ||||||||
\(571\) | 1.14236e131 | 1.31095 | 0.655477 | − | 0.755215i | \(-0.272468\pi\) | ||||
0.655477 | + | 0.755215i | \(0.272468\pi\) | |||||||
\(572\) | −6.38975e129 | −0.0674796 | ||||||||
\(573\) | −7.55142e129 | −0.0733979 | ||||||||
\(574\) | −2.84837e131 | −2.54849 | ||||||||
\(575\) | 4.24155e130 | 0.349383 | ||||||||
\(576\) | −5.09639e131 | −3.86540 | ||||||||
\(577\) | 2.21067e131 | 1.54409 | 0.772046 | − | 0.635566i | \(-0.219233\pi\) | ||||
0.772046 | + | 0.635566i | \(0.219233\pi\) | |||||||
\(578\) | −4.89592e130 | −0.314965 | ||||||||
\(579\) | 4.84160e130 | 0.286917 | ||||||||
\(580\) | 3.19932e131 | 1.74674 | ||||||||
\(581\) | −3.97757e130 | −0.200102 | ||||||||
\(582\) | −2.72198e131 | −1.26195 | ||||||||
\(583\) | −4.98641e129 | −0.0213075 | ||||||||
\(584\) | 8.38246e131 | 3.30188 | ||||||||
\(585\) | −2.42059e130 | −0.0879059 | ||||||||
\(586\) | 6.97190e129 | 0.0233461 | ||||||||
\(587\) | 2.31134e131 | 0.713762 | 0.356881 | − | 0.934150i | \(-0.383840\pi\) | ||||
0.356881 | + | 0.934150i | \(0.383840\pi\) | |||||||
\(588\) | 2.81092e131 | 0.800619 | ||||||||
\(589\) | −1.61873e131 | −0.425304 | ||||||||
\(590\) | −7.91090e131 | −1.91759 | ||||||||
\(591\) | −4.14387e131 | −0.926831 | ||||||||
\(592\) | −9.57535e131 | −1.97640 | ||||||||
\(593\) | 3.62448e131 | 0.690475 | 0.345237 | − | 0.938515i | \(-0.387798\pi\) | ||||
0.345237 | + | 0.938515i | \(0.387798\pi\) | |||||||
\(594\) | 1.72760e131 | 0.303800 | ||||||||
\(595\) | −6.28181e131 | −1.01983 | ||||||||
\(596\) | 3.71752e132 | 5.57257 | ||||||||
\(597\) | −1.20440e131 | −0.166721 | ||||||||
\(598\) | −3.06094e131 | −0.391335 | ||||||||
\(599\) | −1.56783e132 | −1.85151 | −0.925755 | − | 0.378123i | \(-0.876570\pi\) | ||||
−0.925755 | + | 0.378123i | \(0.876570\pi\) | |||||||
\(600\) | −3.50161e131 | −0.382018 | ||||||||
\(601\) | 5.86108e131 | 0.590800 | 0.295400 | − | 0.955374i | \(-0.404547\pi\) | ||||
0.295400 | + | 0.955374i | \(0.404547\pi\) | |||||||
\(602\) | 3.38093e131 | 0.314922 | ||||||||
\(603\) | −5.35265e131 | −0.460783 | ||||||||
\(604\) | −1.62471e132 | −1.29277 | ||||||||
\(605\) | −1.15621e132 | −0.850463 | ||||||||
\(606\) | 9.35876e131 | 0.636457 | ||||||||
\(607\) | 2.12158e132 | 1.33412 | 0.667062 | − | 0.745002i | \(-0.267552\pi\) | ||||
0.667062 | + | 0.745002i | \(0.267552\pi\) | |||||||
\(608\) | −6.36893e132 | −3.70379 | ||||||||
\(609\) | 7.72416e131 | 0.415461 | ||||||||
\(610\) | 1.46724e132 | 0.730021 | ||||||||
\(611\) | 4.94746e131 | 0.227732 | ||||||||
\(612\) | 4.75826e132 | 2.02654 | ||||||||
\(613\) | −3.13561e132 | −1.23580 | −0.617902 | − | 0.786255i | \(-0.712017\pi\) | ||||
−0.617902 | + | 0.786255i | \(0.712017\pi\) | |||||||
\(614\) | 7.74984e132 | 2.82680 | ||||||||
\(615\) | −1.26353e132 | −0.426596 | ||||||||
\(616\) | −2.70334e132 | −0.844924 | ||||||||
\(617\) | −1.81663e132 | −0.525679 | −0.262840 | − | 0.964840i | \(-0.584659\pi\) | ||||
−0.262840 | + | 0.964840i | \(0.584659\pi\) | |||||||
\(618\) | −2.35947e132 | −0.632211 | ||||||||
\(619\) | 3.22452e132 | 0.800127 | 0.400063 | − | 0.916487i | \(-0.368988\pi\) | ||||
0.400063 | + | 0.916487i | \(0.368988\pi\) | |||||||
\(620\) | 5.87393e132 | 1.34997 | ||||||||
\(621\) | 6.12225e132 | 1.30335 | ||||||||
\(622\) | −4.67799e132 | −0.922606 | ||||||||
\(623\) | 6.93819e132 | 1.26784 | ||||||||
\(624\) | 1.51251e132 | 0.256112 | ||||||||
\(625\) | −4.62043e132 | −0.725072 | ||||||||
\(626\) | −1.89595e133 | −2.75769 | ||||||||
\(627\) | 5.09812e131 | 0.0687387 | ||||||||
\(628\) | −2.31213e133 | −2.89021 | ||||||||
\(629\) | 3.68589e132 | 0.427205 | ||||||||
\(630\) | −1.57984e133 | −1.69800 | ||||||||
\(631\) | −3.95456e132 | −0.394188 | −0.197094 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197094 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(632\) | 2.62048e133 | 2.42281 | ||||||||
\(633\) | 7.39503e132 | 0.634255 | ||||||||
\(634\) | 3.28901e133 | 2.61713 | ||||||||
\(635\) | −1.91736e133 | −1.41563 | ||||||||
\(636\) | 2.25046e132 | 0.154191 | ||||||||
\(637\) | 1.20627e132 | 0.0767046 | ||||||||
\(638\) | −4.28810e132 | −0.253094 | ||||||||
\(639\) | −4.59161e132 | −0.251579 | ||||||||
\(640\) | 8.72776e133 | 4.43970 | ||||||||
\(641\) | −6.24712e132 | −0.295069 | −0.147534 | − | 0.989057i | \(-0.547134\pi\) | ||||
−0.147534 | + | 0.989057i | \(0.547134\pi\) | |||||||
\(642\) | −1.76055e133 | −0.772209 | ||||||||
\(643\) | −5.89855e131 | −0.0240283 | −0.0120142 | − | 0.999928i | \(-0.503824\pi\) | ||||
−0.0120142 | + | 0.999928i | \(0.503824\pi\) | |||||||
\(644\) | −1.47789e134 | −5.59195 | ||||||||
\(645\) | 1.49977e132 | 0.0527154 | ||||||||
\(646\) | 4.33739e133 | 1.41639 | ||||||||
\(647\) | 3.09467e133 | 0.938989 | 0.469494 | − | 0.882935i | \(-0.344436\pi\) | ||||
0.469494 | + | 0.882935i | \(0.344436\pi\) | |||||||
\(648\) | 4.91473e133 | 1.38576 | ||||||||
\(649\) | 7.84385e132 | 0.205545 | ||||||||
\(650\) | −2.31813e132 | −0.0564615 | ||||||||
\(651\) | 1.41815e133 | 0.321089 | ||||||||
\(652\) | −7.43736e133 | −1.56552 | ||||||||
\(653\) | 4.75857e133 | 0.931322 | 0.465661 | − | 0.884963i | \(-0.345817\pi\) | ||||
0.465661 | + | 0.884963i | \(0.345817\pi\) | |||||||
\(654\) | 4.12063e132 | 0.0749930 | ||||||||
\(655\) | −4.40560e131 | −0.00745664 | ||||||||
\(656\) | −2.76898e134 | −4.35901 | ||||||||
\(657\) | −4.85721e133 | −0.711265 | ||||||||
\(658\) | 3.22904e134 | 4.39889 | ||||||||
\(659\) | 1.16586e134 | 1.47770 | 0.738852 | − | 0.673867i | \(-0.235368\pi\) | ||||
0.738852 | + | 0.673867i | \(0.235368\pi\) | |||||||
\(660\) | −1.84996e133 | −0.218186 | ||||||||
\(661\) | −4.41100e133 | −0.484136 | −0.242068 | − | 0.970259i | \(-0.577826\pi\) | ||||
−0.242068 | + | 0.970259i | \(0.577826\pi\) | |||||||
\(662\) | −1.39719e134 | −1.42725 | ||||||||
\(663\) | −5.82216e132 | −0.0553595 | ||||||||
\(664\) | −6.46013e133 | −0.571818 | ||||||||
\(665\) | −1.06534e134 | −0.877932 | ||||||||
\(666\) | 9.26979e133 | 0.711286 | ||||||||
\(667\) | −1.51961e134 | −1.08581 | ||||||||
\(668\) | 1.84422e134 | 1.22724 | ||||||||
\(669\) | −8.29664e133 | −0.514235 | ||||||||
\(670\) | 1.77052e134 | 1.02223 | ||||||||
\(671\) | −1.45481e133 | −0.0782503 | ||||||||
\(672\) | 5.57973e134 | 2.79623 | ||||||||
\(673\) | −1.51508e134 | −0.707488 | −0.353744 | − | 0.935342i | \(-0.615092\pi\) | ||||
−0.353744 | + | 0.935342i | \(0.615092\pi\) | |||||||
\(674\) | 7.59448e134 | 3.30486 | ||||||||
\(675\) | 4.63654e133 | 0.188046 | ||||||||
\(676\) | −7.39602e134 | −2.79595 | ||||||||
\(677\) | 3.47460e134 | 1.22446 | 0.612229 | − | 0.790681i | \(-0.290273\pi\) | ||||
0.612229 | + | 0.790681i | \(0.290273\pi\) | |||||||
\(678\) | −1.62795e134 | −0.534848 | ||||||||
\(679\) | −5.63985e134 | −1.72764 | ||||||||
\(680\) | −1.02025e135 | −2.91430 | ||||||||
\(681\) | −2.54144e134 | −0.677004 | ||||||||
\(682\) | −7.87293e133 | −0.195604 | ||||||||
\(683\) | −5.39257e134 | −1.24972 | −0.624860 | − | 0.780737i | \(-0.714844\pi\) | ||||
−0.624860 | + | 0.780737i | \(0.714844\pi\) | |||||||
\(684\) | 8.06961e134 | 1.74457 | ||||||||
\(685\) | 7.11104e134 | 1.43427 | ||||||||
\(686\) | −5.29428e134 | −0.996349 | ||||||||
\(687\) | 3.63325e134 | 0.638044 | ||||||||
\(688\) | 3.28669e134 | 0.538652 | ||||||||
\(689\) | 9.65755e132 | 0.0147725 | ||||||||
\(690\) | −8.86204e134 | −1.26532 | ||||||||
\(691\) | 1.29214e135 | 1.72228 | 0.861139 | − | 0.508370i | \(-0.169752\pi\) | ||||
0.861139 | + | 0.508370i | \(0.169752\pi\) | |||||||
\(692\) | 8.85188e134 | 1.10153 | ||||||||
\(693\) | 1.56645e134 | 0.182007 | ||||||||
\(694\) | −7.99875e134 | −0.867855 | ||||||||
\(695\) | −4.99662e134 | −0.506289 | ||||||||
\(696\) | 1.25451e135 | 1.18723 | ||||||||
\(697\) | 1.06588e135 | 0.942215 | ||||||||
\(698\) | −1.41602e134 | −0.116933 | ||||||||
\(699\) | 1.51047e134 | 0.116532 | ||||||||
\(700\) | −1.11924e135 | −0.806802 | ||||||||
\(701\) | −3.40450e134 | −0.229323 | −0.114661 | − | 0.993405i | \(-0.536578\pi\) | ||||
−0.114661 | + | 0.993405i | \(0.536578\pi\) | |||||||
\(702\) | −3.34598e134 | −0.210625 | ||||||||
\(703\) | 6.25095e134 | 0.367763 | ||||||||
\(704\) | −1.67147e135 | −0.919175 | ||||||||
\(705\) | 1.43239e135 | 0.736340 | ||||||||
\(706\) | −3.97304e135 | −1.90941 | ||||||||
\(707\) | 1.93910e135 | 0.871322 | ||||||||
\(708\) | −3.54008e135 | −1.48742 | ||||||||
\(709\) | −1.83195e135 | −0.719808 | −0.359904 | − | 0.932989i | \(-0.617190\pi\) | ||||
−0.359904 | + | 0.932989i | \(0.617190\pi\) | |||||||
\(710\) | 1.51879e135 | 0.558118 | ||||||||
\(711\) | −1.51843e135 | −0.521902 | ||||||||
\(712\) | 1.12686e136 | 3.62302 | ||||||||
\(713\) | −2.78999e135 | −0.839171 | ||||||||
\(714\) | −3.79993e135 | −1.06933 | ||||||||
\(715\) | −7.93886e133 | −0.0209036 | ||||||||
\(716\) | 1.37275e136 | 3.38238 | ||||||||
\(717\) | 1.20328e135 | 0.277464 | ||||||||
\(718\) | −9.27598e135 | −2.00193 | ||||||||
\(719\) | −2.23041e135 | −0.450571 | −0.225285 | − | 0.974293i | \(-0.572331\pi\) | ||||
−0.225285 | + | 0.974293i | \(0.572331\pi\) | |||||||
\(720\) | −1.53580e136 | −2.90430 | ||||||||
\(721\) | −4.88874e135 | −0.865509 | ||||||||
\(722\) | −4.47013e135 | −0.740975 | ||||||||
\(723\) | 3.42395e135 | 0.531445 | ||||||||
\(724\) | 3.43872e136 | 4.99821 | ||||||||
\(725\) | −1.15084e135 | −0.156660 | ||||||||
\(726\) | −6.99402e135 | −0.891738 | ||||||||
\(727\) | −3.98658e135 | −0.476119 | −0.238060 | − | 0.971251i | \(-0.576511\pi\) | ||||
−0.238060 | + | 0.971251i | \(0.576511\pi\) | |||||||
\(728\) | 5.23577e135 | 0.585787 | ||||||||
\(729\) | 9.15875e134 | 0.0960016 | ||||||||
\(730\) | 1.60664e136 | 1.57792 | ||||||||
\(731\) | −1.26516e135 | −0.116432 | ||||||||
\(732\) | 6.56583e135 | 0.566256 | ||||||||
\(733\) | −5.71056e135 | −0.461572 | −0.230786 | − | 0.973004i | \(-0.574130\pi\) | ||||
−0.230786 | + | 0.973004i | \(0.574130\pi\) | |||||||
\(734\) | 2.49594e136 | 1.89091 | ||||||||
\(735\) | 3.49240e135 | 0.248013 | ||||||||
\(736\) | −1.09773e137 | −7.30798 | ||||||||
\(737\) | −1.75552e135 | −0.109572 | ||||||||
\(738\) | 2.68062e136 | 1.56877 | ||||||||
\(739\) | 5.69069e135 | 0.312287 | 0.156143 | − | 0.987734i | \(-0.450094\pi\) | ||||
0.156143 | + | 0.987734i | \(0.450094\pi\) | |||||||
\(740\) | −2.26829e136 | −1.16733 | ||||||||
\(741\) | −9.87390e134 | −0.0476567 | ||||||||
\(742\) | 6.30316e135 | 0.285346 | ||||||||
\(743\) | 1.72036e135 | 0.0730549 | 0.0365275 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365275 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(744\) | 2.30328e136 | 0.917555 | ||||||||
\(745\) | 4.61879e136 | 1.72625 | ||||||||
\(746\) | −5.36447e136 | −1.88119 | ||||||||
\(747\) | 3.74331e135 | 0.123176 | ||||||||
\(748\) | 1.56058e136 | 0.481902 | ||||||||
\(749\) | −3.64780e136 | −1.05717 | ||||||||
\(750\) | −3.66040e136 | −0.995677 | ||||||||
\(751\) | −2.76595e136 | −0.706231 | −0.353116 | − | 0.935580i | \(-0.614878\pi\) | ||||
−0.353116 | + | 0.935580i | \(0.614878\pi\) | |||||||
\(752\) | 3.13903e137 | 7.52400 | ||||||||
\(753\) | 2.38307e136 | 0.536260 | ||||||||
\(754\) | 8.30508e135 | 0.175471 | ||||||||
\(755\) | −2.01860e136 | −0.400470 | ||||||||
\(756\) | −1.61551e137 | −3.00971 | ||||||||
\(757\) | −8.70498e136 | −1.52305 | −0.761524 | − | 0.648137i | \(-0.775549\pi\) | ||||
−0.761524 | + | 0.648137i | \(0.775549\pi\) | |||||||
\(758\) | 1.05377e137 | 1.73165 | ||||||||
\(759\) | 8.78693e135 | 0.135629 | ||||||||
\(760\) | −1.73026e137 | −2.50880 | ||||||||
\(761\) | 5.14381e136 | 0.700670 | 0.350335 | − | 0.936624i | \(-0.386068\pi\) | ||||
0.350335 | + | 0.936624i | \(0.386068\pi\) | |||||||
\(762\) | −1.15983e137 | −1.48434 | ||||||||
\(763\) | 8.53781e135 | 0.102667 | ||||||||
\(764\) | −3.92020e136 | −0.442969 | ||||||||
\(765\) | 5.91184e136 | 0.627776 | ||||||||
\(766\) | −1.37199e137 | −1.36926 | ||||||||
\(767\) | −1.51918e136 | −0.142504 | ||||||||
\(768\) | 2.62584e137 | 2.31532 | ||||||||
\(769\) | 3.53433e136 | 0.292959 | 0.146479 | − | 0.989214i | \(-0.453206\pi\) | ||||
0.146479 | + | 0.989214i | \(0.453206\pi\) | |||||||
\(770\) | −5.18143e136 | −0.403775 | ||||||||
\(771\) | 5.54483e136 | 0.406261 | ||||||||
\(772\) | 2.51344e137 | 1.73159 | ||||||||
\(773\) | 1.53305e137 | 0.993184 | 0.496592 | − | 0.867984i | \(-0.334585\pi\) | ||||
0.496592 | + | 0.867984i | \(0.334585\pi\) | |||||||
\(774\) | −3.18181e136 | −0.193856 | ||||||||
\(775\) | −2.11293e136 | −0.121075 | ||||||||
\(776\) | −9.15990e137 | −4.93695 | ||||||||
\(777\) | −5.47638e136 | −0.277648 | ||||||||
\(778\) | 8.80143e136 | 0.419780 | ||||||||
\(779\) | 1.80764e137 | 0.811115 | ||||||||
\(780\) | 3.58296e136 | 0.151268 | ||||||||
\(781\) | −1.50592e136 | −0.0598242 | ||||||||
\(782\) | 7.47577e137 | 2.79470 | ||||||||
\(783\) | −1.66112e137 | −0.584409 | ||||||||
\(784\) | 7.65347e137 | 2.53423 | ||||||||
\(785\) | −2.87267e137 | −0.895319 | ||||||||
\(786\) | −2.66499e135 | −0.00781853 | ||||||||
\(787\) | 6.40179e137 | 1.76808 | 0.884040 | − | 0.467412i | \(-0.154813\pi\) | ||||
0.884040 | + | 0.467412i | \(0.154813\pi\) | |||||||
\(788\) | −2.15122e138 | −5.59358 | ||||||||
\(789\) | 1.03361e137 | 0.253046 | ||||||||
\(790\) | 5.02260e137 | 1.15782 | ||||||||
\(791\) | −3.37305e137 | −0.732217 | ||||||||
\(792\) | 2.54413e137 | 0.520108 | ||||||||
\(793\) | 2.81764e136 | 0.0542511 | ||||||||
\(794\) | 1.44966e138 | 2.62901 | ||||||||
\(795\) | 2.79606e136 | 0.0477648 | ||||||||
\(796\) | −6.25247e137 | −1.00619 | ||||||||
\(797\) | −8.24222e136 | −0.124961 | −0.0624804 | − | 0.998046i | \(-0.519901\pi\) | ||||
−0.0624804 | + | 0.998046i | \(0.519901\pi\) | |||||||
\(798\) | −6.44436e137 | −0.920540 | ||||||||
\(799\) | −1.20832e138 | −1.62634 | ||||||||
\(800\) | −8.31335e137 | −1.05439 | ||||||||
\(801\) | −6.52957e137 | −0.780441 | ||||||||
\(802\) | 1.16854e138 | 1.31632 | ||||||||
\(803\) | −1.59303e137 | −0.169135 | ||||||||
\(804\) | 7.92299e137 | 0.792915 | ||||||||
\(805\) | −1.83618e138 | −1.73226 | ||||||||
\(806\) | 1.52481e137 | 0.135613 | ||||||||
\(807\) | 1.72499e137 | 0.144641 | ||||||||
\(808\) | 3.14938e138 | 2.48992 | ||||||||
\(809\) | −1.90271e137 | −0.141846 | −0.0709231 | − | 0.997482i | \(-0.522594\pi\) | ||||
−0.0709231 | + | 0.997482i | \(0.522594\pi\) | |||||||
\(810\) | 9.41993e137 | 0.662231 | ||||||||
\(811\) | 1.34401e138 | 0.891071 | 0.445535 | − | 0.895264i | \(-0.353013\pi\) | ||||
0.445535 | + | 0.895264i | \(0.353013\pi\) | |||||||
\(812\) | 4.00987e138 | 2.50738 | ||||||||
\(813\) | 1.48843e138 | 0.877866 | ||||||||
\(814\) | 3.04023e137 | 0.169140 | ||||||||
\(815\) | −9.24046e137 | −0.484961 | ||||||||
\(816\) | −3.69401e138 | −1.82901 | ||||||||
\(817\) | −2.14561e137 | −0.100231 | ||||||||
\(818\) | −6.02046e138 | −2.65368 | ||||||||
\(819\) | −3.03386e137 | −0.126186 | ||||||||
\(820\) | −6.55941e138 | −2.57458 | ||||||||
\(821\) | 3.82835e138 | 1.41811 | 0.709057 | − | 0.705151i | \(-0.249121\pi\) | ||||
0.709057 | + | 0.705151i | \(0.249121\pi\) | |||||||
\(822\) | 4.30154e138 | 1.50388 | ||||||||
\(823\) | 1.99636e138 | 0.658790 | 0.329395 | − | 0.944192i | \(-0.393155\pi\) | ||||
0.329395 | + | 0.944192i | \(0.393155\pi\) | |||||||
\(824\) | −7.94000e138 | −2.47331 | ||||||||
\(825\) | 6.65456e136 | 0.0195685 | ||||||||
\(826\) | −9.91515e138 | −2.75263 | ||||||||
\(827\) | 4.51785e138 | 1.18419 | 0.592093 | − | 0.805869i | \(-0.298302\pi\) | ||||
0.592093 | + | 0.805869i | \(0.298302\pi\) | |||||||
\(828\) | 1.39085e139 | 3.44222 | ||||||||
\(829\) | 2.58042e138 | 0.603046 | 0.301523 | − | 0.953459i | \(-0.402505\pi\) | ||||
0.301523 | + | 0.953459i | \(0.402505\pi\) | |||||||
\(830\) | −1.23820e138 | −0.273263 | ||||||||
\(831\) | −1.02552e138 | −0.213745 | ||||||||
\(832\) | 3.23727e138 | 0.637266 | ||||||||
\(833\) | −2.94609e138 | −0.547782 | ||||||||
\(834\) | −3.02251e138 | −0.530860 | ||||||||
\(835\) | 2.29133e138 | 0.380171 | ||||||||
\(836\) | 2.64661e138 | 0.414850 | ||||||||
\(837\) | −3.04980e138 | −0.451661 | ||||||||
\(838\) | −6.16833e138 | −0.863131 | ||||||||
\(839\) | 2.88363e138 | 0.381282 | 0.190641 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190641 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(840\) | 1.51586e139 | 1.89406 | ||||||||
\(841\) | −4.34549e138 | −0.513132 | ||||||||
\(842\) | −1.21034e139 | −1.35077 | ||||||||
\(843\) | 8.98426e137 | 0.0947704 | ||||||||
\(844\) | 3.83901e139 | 3.82783 | ||||||||
\(845\) | −9.18909e138 | −0.866121 | ||||||||
\(846\) | −3.03886e139 | −2.70782 | ||||||||
\(847\) | −1.44914e139 | −1.22081 | ||||||||
\(848\) | 6.12747e138 | 0.488066 | ||||||||
\(849\) | −7.96787e138 | −0.600105 | ||||||||
\(850\) | 5.66159e138 | 0.403217 | ||||||||
\(851\) | 1.07739e139 | 0.725637 | ||||||||
\(852\) | 6.79649e138 | 0.432917 | ||||||||
\(853\) | 2.15831e139 | 1.30027 | 0.650136 | − | 0.759818i | \(-0.274712\pi\) | ||||
0.650136 | + | 0.759818i | \(0.274712\pi\) | |||||||
\(854\) | 1.83898e139 | 1.04792 | ||||||||
\(855\) | 1.00260e139 | 0.540427 | ||||||||
\(856\) | −5.92454e139 | −3.02100 | ||||||||
\(857\) | −2.64220e138 | −0.127461 | −0.0637303 | − | 0.997967i | \(-0.520300\pi\) | ||||
−0.0637303 | + | 0.997967i | \(0.520300\pi\) | |||||||
\(858\) | −4.80230e137 | −0.0219181 | ||||||||
\(859\) | −1.09312e139 | −0.472055 | −0.236028 | − | 0.971746i | \(-0.575846\pi\) | ||||
−0.236028 | + | 0.971746i | \(0.575846\pi\) | |||||||
\(860\) | 7.78581e138 | 0.318147 | ||||||||
\(861\) | −1.58365e139 | −0.612363 | ||||||||
\(862\) | −8.15372e138 | −0.298374 | ||||||||
\(863\) | −2.73262e138 | −0.0946384 | −0.0473192 | − | 0.998880i | \(-0.515068\pi\) | ||||
−0.0473192 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(864\) | −1.19995e140 | −3.93332 | ||||||||
\(865\) | 1.09979e139 | 0.341228 | ||||||||
\(866\) | 1.11095e140 | 3.26283 | ||||||||
\(867\) | −2.72205e138 | −0.0756814 | ||||||||
\(868\) | 7.36211e139 | 1.93783 | ||||||||
\(869\) | −4.98003e138 | −0.124106 | ||||||||
\(870\) | 2.40449e139 | 0.567360 | ||||||||
\(871\) | 3.40004e138 | 0.0759665 | ||||||||
\(872\) | 1.38666e139 | 0.293384 | ||||||||
\(873\) | 5.30769e139 | 1.06348 | ||||||||
\(874\) | 1.26783e140 | 2.40584 | ||||||||
\(875\) | −7.58422e139 | −1.36310 | ||||||||
\(876\) | 7.18963e139 | 1.22394 | ||||||||
\(877\) | −5.68771e139 | −0.917184 | −0.458592 | − | 0.888647i | \(-0.651646\pi\) | ||||
−0.458592 | + | 0.888647i | \(0.651646\pi\) | |||||||
\(878\) | −2.30691e140 | −3.52405 | ||||||||
\(879\) | 3.87626e137 | 0.00560972 | ||||||||
\(880\) | −5.03701e139 | −0.690630 | ||||||||
\(881\) | 6.46811e138 | 0.0840276 | 0.0420138 | − | 0.999117i | \(-0.486623\pi\) | ||||
0.0420138 | + | 0.999117i | \(0.486623\pi\) | |||||||
\(882\) | −7.40924e139 | −0.912044 | ||||||||
\(883\) | 1.39161e140 | 1.62324 | 0.811621 | − | 0.584184i | \(-0.198585\pi\) | ||||
0.811621 | + | 0.584184i | \(0.198585\pi\) | |||||||
\(884\) | −3.02248e139 | −0.334104 | ||||||||
\(885\) | −4.39833e139 | −0.460768 | ||||||||
\(886\) | −1.71484e139 | −0.170263 | ||||||||
\(887\) | 1.27807e140 | 1.20277 | 0.601387 | − | 0.798958i | \(-0.294615\pi\) | ||||
0.601387 | + | 0.798958i | \(0.294615\pi\) | |||||||
\(888\) | −8.89441e139 | −0.793416 | ||||||||
\(889\) | −2.40313e140 | −2.03209 | ||||||||
\(890\) | 2.15982e140 | 1.73138 | ||||||||
\(891\) | −9.34009e138 | −0.0709840 | ||||||||
\(892\) | −4.30707e140 | −3.10350 | ||||||||
\(893\) | −2.04921e140 | −1.40005 | ||||||||
\(894\) | 2.79395e140 | 1.81003 | ||||||||
\(895\) | 1.70555e140 | 1.04778 | ||||||||
\(896\) | 1.09390e141 | 6.37302 | ||||||||
\(897\) | −1.70183e139 | −0.0940319 | ||||||||
\(898\) | −5.11827e140 | −2.68224 | ||||||||
\(899\) | 7.56993e139 | 0.376276 | ||||||||
\(900\) | 1.05332e140 | 0.496642 | ||||||||
\(901\) | −2.35868e139 | −0.105497 | ||||||||
\(902\) | 8.79168e139 | 0.373045 | ||||||||
\(903\) | 1.87974e139 | 0.0756710 | ||||||||
\(904\) | −5.47831e140 | −2.09241 | ||||||||
\(905\) | 4.27240e140 | 1.54833 | ||||||||
\(906\) | −1.22107e140 | −0.419906 | ||||||||
\(907\) | 2.75948e140 | 0.900496 | 0.450248 | − | 0.892904i | \(-0.351336\pi\) | ||||
0.450248 | + | 0.892904i | \(0.351336\pi\) | |||||||
\(908\) | −1.31935e141 | −4.08584 | ||||||||
\(909\) | −1.82490e140 | −0.536358 | ||||||||
\(910\) | 1.00353e140 | 0.279938 | ||||||||
\(911\) | 3.02990e140 | 0.802243 | 0.401121 | − | 0.916025i | \(-0.368621\pi\) | ||||
0.401121 | + | 0.916025i | \(0.368621\pi\) | |||||||
\(912\) | −6.26474e140 | −1.57452 | ||||||||
\(913\) | 1.22770e139 | 0.0292908 | ||||||||
\(914\) | 1.00147e141 | 2.26827 | ||||||||
\(915\) | 8.15763e139 | 0.175413 | ||||||||
\(916\) | 1.88615e141 | 3.85070 | ||||||||
\(917\) | −5.52177e138 | −0.0107037 | ||||||||
\(918\) | 8.17193e140 | 1.50417 | ||||||||
\(919\) | −5.12257e140 | −0.895366 | −0.447683 | − | 0.894192i | \(-0.647751\pi\) | ||||
−0.447683 | + | 0.894192i | \(0.647751\pi\) | |||||||
\(920\) | −2.98222e141 | −4.95015 | ||||||||
\(921\) | 4.30878e140 | 0.679238 | ||||||||
\(922\) | −1.83691e141 | −2.75023 | ||||||||
\(923\) | 2.91662e139 | 0.0414763 | ||||||||
\(924\) | −2.31866e140 | −0.313197 | ||||||||
\(925\) | 8.15936e139 | 0.104694 | ||||||||
\(926\) | 4.20305e140 | 0.512321 | ||||||||
\(927\) | 4.60082e140 | 0.532780 | ||||||||
\(928\) | 2.97840e141 | 3.27683 | ||||||||
\(929\) | −1.51285e141 | −1.58142 | −0.790712 | − | 0.612188i | \(-0.790289\pi\) | ||||
−0.790712 | + | 0.612188i | \(0.790289\pi\) | |||||||
\(930\) | 4.41463e140 | 0.438485 | ||||||||
\(931\) | −4.99631e140 | −0.471563 | ||||||||
\(932\) | 7.84135e140 | 0.703291 | ||||||||
\(933\) | −2.60088e140 | −0.221688 | ||||||||
\(934\) | 1.22889e141 | 0.995490 | ||||||||
\(935\) | 1.93892e140 | 0.149282 | ||||||||
\(936\) | −4.92741e140 | −0.360592 | ||||||||
\(937\) | −1.80808e141 | −1.25773 | −0.628864 | − | 0.777515i | \(-0.716480\pi\) | ||||
−0.628864 | + | 0.777515i | \(0.716480\pi\) | |||||||
\(938\) | 2.21909e141 | 1.46737 | ||||||||
\(939\) | −1.05411e141 | −0.662632 | ||||||||
\(940\) | 7.43602e141 | 4.44393 | ||||||||
\(941\) | −2.33281e141 | −1.32548 | −0.662738 | − | 0.748851i | \(-0.730606\pi\) | ||||
−0.662738 | + | 0.748851i | \(0.730606\pi\) | |||||||
\(942\) | −1.73771e141 | −0.938771 | ||||||||
\(943\) | 3.11558e141 | 1.60042 | ||||||||
\(944\) | −9.63879e141 | −4.70818 | ||||||||
\(945\) | −2.00717e141 | −0.932340 | ||||||||
\(946\) | −1.04354e140 | −0.0460980 | ||||||||
\(947\) | 6.08703e140 | 0.255730 | 0.127865 | − | 0.991792i | \(-0.459188\pi\) | ||||
0.127865 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(948\) | 2.24758e141 | 0.898090 | ||||||||
\(949\) | 3.08533e140 | 0.117262 | ||||||||
\(950\) | 9.60157e140 | 0.347113 | ||||||||
\(951\) | 1.82863e141 | 0.628858 | ||||||||
\(952\) | −1.27874e142 | −4.18337 | ||||||||
\(953\) | 3.26685e140 | 0.101675 | 0.0508377 | − | 0.998707i | \(-0.483811\pi\) | ||||
0.0508377 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(954\) | −5.93193e140 | −0.175650 | ||||||||
\(955\) | −4.87060e140 | −0.137222 | ||||||||
\(956\) | 6.24662e141 | 1.67454 | ||||||||
\(957\) | −2.38411e140 | −0.0608148 | ||||||||
\(958\) | −2.04788e141 | −0.497098 | ||||||||
\(959\) | 8.91264e141 | 2.05884 | ||||||||
\(960\) | 9.37255e141 | 2.06051 | ||||||||
\(961\) | −3.38943e141 | −0.709194 | ||||||||
\(962\) | −5.88824e140 | −0.117265 | ||||||||
\(963\) | 3.43297e141 | 0.650760 | ||||||||
\(964\) | 1.77749e142 | 3.20736 | ||||||||
\(965\) | 3.12279e141 | 0.536408 | ||||||||
\(966\) | −1.11073e142 | −1.81633 | ||||||||
\(967\) | 3.77302e140 | 0.0587397 | 0.0293698 | − | 0.999569i | \(-0.490650\pi\) | ||||
0.0293698 | + | 0.999569i | \(0.490650\pi\) | |||||||
\(968\) | −2.35360e142 | −3.48862 | ||||||||
\(969\) | 2.41152e141 | 0.340338 | ||||||||
\(970\) | −1.75565e142 | −2.35929 | ||||||||
\(971\) | 5.65420e141 | 0.723532 | 0.361766 | − | 0.932269i | \(-0.382174\pi\) | ||||
0.361766 | + | 0.932269i | \(0.382174\pi\) | |||||||
\(972\) | 2.37540e142 | 2.89461 | ||||||||
\(973\) | −6.26254e141 | −0.726759 | ||||||||
\(974\) | −1.92127e142 | −2.12343 | ||||||||
\(975\) | −1.28884e140 | −0.0135669 | ||||||||
\(976\) | 1.78772e142 | 1.79239 | ||||||||
\(977\) | −1.49169e142 | −1.42458 | −0.712288 | − | 0.701887i | \(-0.752341\pi\) | ||||
−0.712288 | + | 0.701887i | \(0.752341\pi\) | |||||||
\(978\) | −5.58965e141 | −0.508498 | ||||||||
\(979\) | −2.14152e141 | −0.185585 | ||||||||
\(980\) | 1.81302e142 | 1.49680 | ||||||||
\(981\) | −8.03498e140 | −0.0631985 | ||||||||
\(982\) | 1.49623e142 | 1.12125 | ||||||||
\(983\) | 2.48585e142 | 1.77494 | 0.887469 | − | 0.460868i | \(-0.152462\pi\) | ||||
0.887469 | + | 0.460868i | \(0.152462\pi\) | |||||||
\(984\) | −2.57207e142 | −1.74991 | ||||||||
\(985\) | −2.67276e142 | −1.73276 | ||||||||
\(986\) | −2.02836e142 | −1.25312 | ||||||||
\(987\) | 1.79529e142 | 1.05699 | ||||||||
\(988\) | −5.12588e141 | −0.287616 | ||||||||
\(989\) | −3.69810e141 | −0.197767 | ||||||||
\(990\) | 4.87627e141 | 0.248551 | ||||||||
\(991\) | −6.94710e141 | −0.337524 | −0.168762 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168762 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(992\) | 5.46832e142 | 2.53250 | ||||||||
\(993\) | −7.76812e141 | −0.342947 | ||||||||
\(994\) | 1.90358e142 | 0.801158 | ||||||||
\(995\) | −7.76830e141 | −0.311695 | ||||||||
\(996\) | −5.54085e141 | −0.211962 | ||||||||
\(997\) | −2.05676e142 | −0.750175 | −0.375088 | − | 0.926989i | \(-0.622387\pi\) | ||||
−0.375088 | + | 0.926989i | \(0.622387\pi\) | |||||||
\(998\) | 2.46599e142 | 0.857612 | ||||||||
\(999\) | 1.17772e142 | 0.390555 |
(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 | 1.96.a.a.1.8 | ✓ | 8 | |
3.2 | odd | 2 | 9.96.a.c.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.96.a.a.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9.96.a.c.1.1 | 8 | 3.2 | odd | 2 |