Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,74,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(67.4967947474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2 x^{3} + \cdots + 21\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{14}\cdot 5^{5}\cdot 7^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.89813e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.87195e10 | 0.707107 | ||||||||
\(3\) | 4.40707e17 | 1.69521 | 0.847606 | − | 0.530626i | \(-0.178043\pi\) | ||||
0.847606 | + | 0.530626i | \(0.178043\pi\) | |||||||
\(4\) | 4.72237e21 | 0.500000 | ||||||||
\(5\) | −6.01656e25 | −1.84903 | −0.924513 | − | 0.381151i | \(-0.875528\pi\) | ||||
−0.924513 | + | 0.381151i | \(0.875528\pi\) | |||||||
\(6\) | 3.02852e28 | 1.19870 | ||||||||
\(7\) | 1.36725e30 | 0.194880 | 0.0974402 | − | 0.995241i | \(-0.468935\pi\) | ||||
0.0974402 | + | 0.995241i | \(0.468935\pi\) | |||||||
\(8\) | 3.24519e32 | 0.353553 | ||||||||
\(9\) | 1.26637e35 | 1.87374 | ||||||||
\(10\) | −4.13455e36 | −1.30746 | ||||||||
\(11\) | 1.17371e38 | 1.14479 | 0.572396 | − | 0.819978i | \(-0.306014\pi\) | ||||
0.572396 | + | 0.819978i | \(0.306014\pi\) | |||||||
\(12\) | 2.08118e39 | 0.847606 | ||||||||
\(13\) | −4.64177e40 | −1.01801 | −0.509004 | − | 0.860764i | \(-0.669986\pi\) | ||||
−0.509004 | + | 0.860764i | \(0.669986\pi\) | |||||||
\(14\) | 9.39565e40 | 0.137801 | ||||||||
\(15\) | −2.65154e43 | −3.13449 | ||||||||
\(16\) | 2.23007e43 | 0.250000 | ||||||||
\(17\) | 7.41645e44 | 0.909517 | 0.454758 | − | 0.890615i | \(-0.349726\pi\) | ||||
0.454758 | + | 0.890615i | \(0.349726\pi\) | |||||||
\(18\) | 8.70246e45 | 1.32494 | ||||||||
\(19\) | 3.86997e46 | 0.818844 | 0.409422 | − | 0.912345i | \(-0.365730\pi\) | ||||
0.409422 | + | 0.912345i | \(0.365730\pi\) | |||||||
\(20\) | −2.84124e47 | −0.924513 | ||||||||
\(21\) | 6.02555e47 | 0.330364 | ||||||||
\(22\) | 8.06565e48 | 0.809490 | ||||||||
\(23\) | 5.58055e49 | 1.10563 | 0.552816 | − | 0.833303i | \(-0.313553\pi\) | ||||
0.552816 | + | 0.833303i | \(0.313553\pi\) | |||||||
\(24\) | 1.43018e50 | 0.599348 | ||||||||
\(25\) | 2.56110e51 | 2.41889 | ||||||||
\(26\) | −3.18980e51 | −0.719840 | ||||||||
\(27\) | 2.60247e52 | 1.48118 | ||||||||
\(28\) | 6.45664e51 | 0.0974402 | ||||||||
\(29\) | −1.18607e53 | −0.497261 | −0.248631 | − | 0.968598i | \(-0.579981\pi\) | ||||
−0.248631 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(30\) | −1.82212e54 | −2.21642 | ||||||||
\(31\) | 2.47658e52 | 0.00910227 | 0.00455114 | − | 0.999990i | \(-0.498551\pi\) | ||||
0.00455114 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(32\) | 1.53250e54 | 0.176777 | ||||||||
\(33\) | 5.17260e55 | 1.94066 | ||||||||
\(34\) | 5.09655e55 | 0.643125 | ||||||||
\(35\) | −8.22612e55 | −0.360339 | ||||||||
\(36\) | 5.98028e56 | 0.936872 | ||||||||
\(37\) | 2.03375e57 | 1.17202 | 0.586010 | − | 0.810303i | \(-0.300698\pi\) | ||||
0.586010 | + | 0.810303i | \(0.300698\pi\) | |||||||
\(38\) | 2.65942e57 | 0.579010 | ||||||||
\(39\) | −2.04566e58 | −1.72574 | ||||||||
\(40\) | −1.95248e58 | −0.653729 | ||||||||
\(41\) | 1.41862e59 | 1.92866 | 0.964332 | − | 0.264696i | \(-0.0852717\pi\) | ||||
0.964332 | + | 0.264696i | \(0.0852717\pi\) | |||||||
\(42\) | 4.14073e58 | 0.233602 | ||||||||
\(43\) | 2.36476e59 | 0.565182 | 0.282591 | − | 0.959241i | \(-0.408806\pi\) | ||||
0.282591 | + | 0.959241i | \(0.408806\pi\) | |||||||
\(44\) | 5.54267e59 | 0.572396 | ||||||||
\(45\) | −7.61921e60 | −3.46460 | ||||||||
\(46\) | 3.83492e60 | 0.781800 | ||||||||
\(47\) | −7.61861e60 | −0.708441 | −0.354221 | − | 0.935162i | \(-0.615254\pi\) | ||||
−0.354221 | + | 0.935162i | \(0.615254\pi\) | |||||||
\(48\) | 9.82809e60 | 0.423803 | ||||||||
\(49\) | −4.73524e61 | −0.962022 | ||||||||
\(50\) | 1.75998e62 | 1.71042 | ||||||||
\(51\) | 3.26848e62 | 1.54182 | ||||||||
\(52\) | −2.19201e62 | −0.509004 | ||||||||
\(53\) | −6.20840e62 | −0.719300 | −0.359650 | − | 0.933087i | \(-0.617104\pi\) | ||||
−0.359650 | + | 0.933087i | \(0.617104\pi\) | |||||||
\(54\) | 1.78841e63 | 1.04735 | ||||||||
\(55\) | −7.06167e63 | −2.11675 | ||||||||
\(56\) | 4.43697e62 | 0.0689007 | ||||||||
\(57\) | 1.70552e64 | 1.38812 | ||||||||
\(58\) | −8.15063e63 | −0.351617 | ||||||||
\(59\) | 4.74332e64 | 1.09644 | 0.548219 | − | 0.836335i | \(-0.315306\pi\) | ||||
0.548219 | + | 0.836335i | \(0.315306\pi\) | |||||||
\(60\) | −1.25215e65 | −1.56725 | ||||||||
\(61\) | 6.52682e64 | 0.446851 | 0.223425 | − | 0.974721i | \(-0.428276\pi\) | ||||
0.223425 | + | 0.974721i | \(0.428276\pi\) | |||||||
\(62\) | 1.70189e63 | 0.00643628 | ||||||||
\(63\) | 1.73145e65 | 0.365156 | ||||||||
\(64\) | 1.05312e65 | 0.125000 | ||||||||
\(65\) | 2.79275e66 | 1.88232 | ||||||||
\(66\) | 3.55459e66 | 1.37226 | ||||||||
\(67\) | −7.25393e66 | −1.61750 | −0.808748 | − | 0.588156i | \(-0.799854\pi\) | ||||
−0.808748 | + | 0.588156i | \(0.799854\pi\) | |||||||
\(68\) | 3.50232e66 | 0.454758 | ||||||||
\(69\) | 2.45939e67 | 1.87428 | ||||||||
\(70\) | −5.65294e66 | −0.254798 | ||||||||
\(71\) | −2.81253e67 | −0.755385 | −0.377692 | − | 0.925931i | \(-0.623282\pi\) | ||||
−0.377692 | + | 0.925931i | \(0.623282\pi\) | |||||||
\(72\) | 4.10962e67 | 0.662469 | ||||||||
\(73\) | 5.22665e67 | 0.509260 | 0.254630 | − | 0.967039i | \(-0.418046\pi\) | ||||
0.254630 | + | 0.967039i | \(0.418046\pi\) | |||||||
\(74\) | 1.39758e68 | 0.828744 | ||||||||
\(75\) | 1.12870e69 | 4.10054 | ||||||||
\(76\) | 1.82754e68 | 0.409422 | ||||||||
\(77\) | 1.60475e68 | 0.223098 | ||||||||
\(78\) | −1.40577e69 | −1.22028 | ||||||||
\(79\) | 6.42026e68 | 0.350077 | 0.175039 | − | 0.984562i | \(-0.443995\pi\) | ||||
0.175039 | + | 0.984562i | \(0.443995\pi\) | |||||||
\(80\) | −1.34174e69 | −0.462256 | ||||||||
\(81\) | 2.91046e69 | 0.637175 | ||||||||
\(82\) | 9.74871e69 | 1.36377 | ||||||||
\(83\) | 1.58123e69 | 0.142117 | 0.0710584 | − | 0.997472i | \(-0.477362\pi\) | ||||
0.0710584 | + | 0.997472i | \(0.477362\pi\) | |||||||
\(84\) | 2.84549e69 | 0.165182 | ||||||||
\(85\) | −4.46215e70 | −1.68172 | ||||||||
\(86\) | 1.62505e70 | 0.399644 | ||||||||
\(87\) | −5.22711e70 | −0.842963 | ||||||||
\(88\) | 3.80889e70 | 0.404745 | ||||||||
\(89\) | 4.25333e69 | 0.0299222 | 0.0149611 | − | 0.999888i | \(-0.495238\pi\) | ||||
0.0149611 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(90\) | −5.23588e71 | −2.44984 | ||||||||
\(91\) | −6.34644e70 | −0.198390 | ||||||||
\(92\) | 2.63534e71 | 0.552816 | ||||||||
\(93\) | 1.09144e70 | 0.0154303 | ||||||||
\(94\) | −5.23547e71 | −0.500944 | ||||||||
\(95\) | −2.32839e72 | −1.51406 | ||||||||
\(96\) | 6.75381e71 | 0.299674 | ||||||||
\(97\) | −2.34394e72 | −0.712490 | −0.356245 | − | 0.934393i | \(-0.615943\pi\) | ||||
−0.356245 | + | 0.934393i | \(0.615943\pi\) | |||||||
\(98\) | −3.25403e72 | −0.680252 | ||||||||
\(99\) | 1.48635e73 | 2.14505 | ||||||||
\(100\) | 1.20945e73 | 1.20945 | ||||||||
\(101\) | 5.56733e72 | 0.387183 | 0.193592 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193592 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(102\) | 2.24608e73 | 1.09023 | ||||||||
\(103\) | 7.78162e72 | 0.264552 | 0.132276 | − | 0.991213i | \(-0.457771\pi\) | ||||
0.132276 | + | 0.991213i | \(0.457771\pi\) | |||||||
\(104\) | −1.50634e73 | −0.359920 | ||||||||
\(105\) | −3.62531e73 | −0.610851 | ||||||||
\(106\) | −4.26638e73 | −0.508622 | ||||||||
\(107\) | 1.02093e74 | 0.863947 | 0.431974 | − | 0.901886i | \(-0.357817\pi\) | ||||
0.431974 | + | 0.901886i | \(0.357817\pi\) | |||||||
\(108\) | 1.22898e74 | 0.740591 | ||||||||
\(109\) | 4.14598e73 | 0.178468 | 0.0892340 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892340 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(110\) | −4.85274e74 | −1.49677 | ||||||||
\(111\) | 8.96289e74 | 1.98682 | ||||||||
\(112\) | 3.04906e73 | 0.0487201 | ||||||||
\(113\) | −1.34444e75 | −1.55303 | −0.776515 | − | 0.630099i | \(-0.783014\pi\) | ||||
−0.776515 | + | 0.630099i | \(0.783014\pi\) | |||||||
\(114\) | 1.17203e75 | 0.981546 | ||||||||
\(115\) | −3.35757e75 | −2.04434 | ||||||||
\(116\) | −5.60107e74 | −0.248631 | ||||||||
\(117\) | −5.87822e75 | −1.90749 | ||||||||
\(118\) | 3.25959e75 | 0.775299 | ||||||||
\(119\) | 1.01401e75 | 0.177247 | ||||||||
\(120\) | −8.60473e75 | −1.10821 | ||||||||
\(121\) | 3.26433e75 | 0.310547 | ||||||||
\(122\) | 4.48520e75 | 0.315971 | ||||||||
\(123\) | 6.25197e76 | 3.26949 | ||||||||
\(124\) | 1.16953e74 | 0.00455114 | ||||||||
\(125\) | −9.03875e76 | −2.62357 | ||||||||
\(126\) | 1.18984e76 | 0.258205 | ||||||||
\(127\) | 6.87081e76 | 1.11731 | 0.558653 | − | 0.829401i | \(-0.311318\pi\) | ||||
0.558653 | + | 0.829401i | \(0.311318\pi\) | |||||||
\(128\) | 7.23701e75 | 0.0883883 | ||||||||
\(129\) | 1.04217e77 | 0.958103 | ||||||||
\(130\) | 1.91916e77 | 1.33100 | ||||||||
\(131\) | −1.63020e77 | −0.854747 | −0.427373 | − | 0.904075i | \(-0.640561\pi\) | ||||
−0.427373 | + | 0.904075i | \(0.640561\pi\) | |||||||
\(132\) | 2.44269e77 | 0.970332 | ||||||||
\(133\) | 5.29121e76 | 0.159577 | ||||||||
\(134\) | −4.98486e77 | −1.14374 | ||||||||
\(135\) | −1.56579e78 | −2.73874 | ||||||||
\(136\) | 2.40678e77 | 0.321563 | ||||||||
\(137\) | −3.23319e77 | −0.330621 | −0.165311 | − | 0.986242i | \(-0.552863\pi\) | ||||
−0.165311 | + | 0.986242i | \(0.552863\pi\) | |||||||
\(138\) | 1.69008e78 | 1.32532 | ||||||||
\(139\) | 1.33914e78 | 0.806838 | 0.403419 | − | 0.915015i | \(-0.367822\pi\) | ||||
0.403419 | + | 0.915015i | \(0.367822\pi\) | |||||||
\(140\) | −3.88467e77 | −0.180169 | ||||||||
\(141\) | −3.35757e78 | −1.20096 | ||||||||
\(142\) | −1.93276e78 | −0.534138 | ||||||||
\(143\) | −5.44807e78 | −1.16541 | ||||||||
\(144\) | 2.82411e78 | 0.468436 | ||||||||
\(145\) | 7.13608e78 | 0.919448 | ||||||||
\(146\) | 3.59173e78 | 0.360101 | ||||||||
\(147\) | −2.08685e79 | −1.63083 | ||||||||
\(148\) | 9.60413e78 | 0.586010 | ||||||||
\(149\) | −1.70860e79 | −0.815347 | −0.407674 | − | 0.913128i | \(-0.633660\pi\) | ||||
−0.407674 | + | 0.913128i | \(0.633660\pi\) | |||||||
\(150\) | 7.75634e79 | 2.89952 | ||||||||
\(151\) | 5.81417e78 | 0.170541 | 0.0852705 | − | 0.996358i | \(-0.472825\pi\) | ||||
0.0852705 | + | 0.996358i | \(0.472825\pi\) | |||||||
\(152\) | 1.25588e79 | 0.289505 | ||||||||
\(153\) | 9.39200e79 | 1.70420 | ||||||||
\(154\) | 1.10277e79 | 0.157754 | ||||||||
\(155\) | −1.49005e78 | −0.0168303 | ||||||||
\(156\) | −9.66036e79 | −0.862870 | ||||||||
\(157\) | −2.65451e80 | −1.87779 | −0.938895 | − | 0.344204i | \(-0.888149\pi\) | ||||
−0.938895 | + | 0.344204i | \(0.888149\pi\) | |||||||
\(158\) | 4.41197e79 | 0.247542 | ||||||||
\(159\) | −2.73608e80 | −1.21937 | ||||||||
\(160\) | −9.22035e79 | −0.326865 | ||||||||
\(161\) | 7.62998e79 | 0.215466 | ||||||||
\(162\) | 2.00005e80 | 0.450551 | ||||||||
\(163\) | 5.19219e80 | 0.934335 | 0.467168 | − | 0.884169i | \(-0.345274\pi\) | ||||
0.467168 | + | 0.884169i | \(0.345274\pi\) | |||||||
\(164\) | 6.69926e80 | 0.964332 | ||||||||
\(165\) | −3.11213e81 | −3.58834 | ||||||||
\(166\) | 1.08661e80 | 0.100492 | ||||||||
\(167\) | 1.52156e81 | 1.13015 | 0.565076 | − | 0.825039i | \(-0.308847\pi\) | ||||
0.565076 | + | 0.825039i | \(0.308847\pi\) | |||||||
\(168\) | 1.95540e80 | 0.116801 | ||||||||
\(169\) | 7.55530e79 | 0.0363402 | ||||||||
\(170\) | −3.06637e81 | −1.18916 | ||||||||
\(171\) | 4.90083e81 | 1.53431 | ||||||||
\(172\) | 1.11673e81 | 0.282591 | ||||||||
\(173\) | 1.82325e81 | 0.373391 | 0.186695 | − | 0.982418i | \(-0.440222\pi\) | ||||
0.186695 | + | 0.982418i | \(0.440222\pi\) | |||||||
\(174\) | −3.59204e81 | −0.596065 | ||||||||
\(175\) | 3.50166e81 | 0.471395 | ||||||||
\(176\) | 2.61745e81 | 0.286198 | ||||||||
\(177\) | 2.09042e82 | 1.85870 | ||||||||
\(178\) | 2.92287e80 | 0.0211582 | ||||||||
\(179\) | −9.69849e80 | −0.0572227 | −0.0286114 | − | 0.999591i | \(-0.509109\pi\) | ||||
−0.0286114 | + | 0.999591i | \(0.509109\pi\) | |||||||
\(180\) | −3.59807e82 | −1.73230 | ||||||||
\(181\) | −4.27027e81 | −0.167953 | −0.0839765 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839765 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(182\) | −4.36124e81 | −0.140283 | ||||||||
\(183\) | 2.87641e82 | 0.757507 | ||||||||
\(184\) | 1.81099e82 | 0.390900 | ||||||||
\(185\) | −1.22362e83 | −2.16710 | ||||||||
\(186\) | 7.50035e80 | 0.0109109 | ||||||||
\(187\) | 8.70474e82 | 1.04121 | ||||||||
\(188\) | −3.59779e82 | −0.354221 | ||||||||
\(189\) | 3.55822e82 | 0.288654 | ||||||||
\(190\) | −1.60006e83 | −1.07061 | ||||||||
\(191\) | −2.67648e83 | −1.47859 | −0.739293 | − | 0.673384i | \(-0.764840\pi\) | ||||
−0.739293 | + | 0.673384i | \(0.764840\pi\) | |||||||
\(192\) | 4.64119e82 | 0.211902 | ||||||||
\(193\) | −1.63168e83 | −0.616300 | −0.308150 | − | 0.951338i | \(-0.599710\pi\) | ||||
−0.308150 | + | 0.951338i | \(0.599710\pi\) | |||||||
\(194\) | −1.61075e83 | −0.503806 | ||||||||
\(195\) | 1.23078e84 | 3.19094 | ||||||||
\(196\) | −2.23615e83 | −0.481011 | ||||||||
\(197\) | 4.78478e83 | 0.854761 | 0.427380 | − | 0.904072i | \(-0.359436\pi\) | ||||
0.427380 | + | 0.904072i | \(0.359436\pi\) | |||||||
\(198\) | 1.02141e84 | 1.51678 | ||||||||
\(199\) | 7.72352e83 | 0.954285 | 0.477143 | − | 0.878826i | \(-0.341673\pi\) | ||||
0.477143 | + | 0.878826i | \(0.341673\pi\) | |||||||
\(200\) | 8.31126e83 | 0.855208 | ||||||||
\(201\) | −3.19686e84 | −2.74200 | ||||||||
\(202\) | 3.82584e83 | 0.273780 | ||||||||
\(203\) | −1.62165e83 | −0.0969065 | ||||||||
\(204\) | 1.54350e84 | 0.770912 | ||||||||
\(205\) | −8.53523e84 | −3.56615 | ||||||||
\(206\) | 5.34749e83 | 0.187067 | ||||||||
\(207\) | 7.06706e84 | 2.07167 | ||||||||
\(208\) | −1.03515e84 | −0.254502 | ||||||||
\(209\) | 4.54221e84 | 0.937406 | ||||||||
\(210\) | −2.49129e84 | −0.431937 | ||||||||
\(211\) | −2.41050e84 | −0.351397 | −0.175698 | − | 0.984444i | \(-0.556218\pi\) | ||||
−0.175698 | + | 0.984444i | \(0.556218\pi\) | |||||||
\(212\) | −2.93183e84 | −0.359650 | ||||||||
\(213\) | −1.23950e85 | −1.28054 | ||||||||
\(214\) | 7.01576e84 | 0.610903 | ||||||||
\(215\) | −1.42277e85 | −1.04504 | ||||||||
\(216\) | 8.44551e84 | 0.523677 | ||||||||
\(217\) | 3.38609e82 | 0.00177386 | ||||||||
\(218\) | 2.84910e84 | 0.126196 | ||||||||
\(219\) | 2.30342e85 | 0.863303 | ||||||||
\(220\) | −3.33478e85 | −1.05837 | ||||||||
\(221\) | −3.44255e85 | −0.925895 | ||||||||
\(222\) | 6.15925e85 | 1.40490 | ||||||||
\(223\) | 2.03817e84 | 0.0394560 | 0.0197280 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197280 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(224\) | 2.09530e84 | 0.0344503 | ||||||||
\(225\) | 3.24332e86 | 4.53239 | ||||||||
\(226\) | −9.23895e85 | −1.09816 | ||||||||
\(227\) | −1.34214e86 | −1.35786 | −0.678929 | − | 0.734204i | \(-0.737556\pi\) | ||||
−0.678929 | + | 0.734204i | \(0.737556\pi\) | |||||||
\(228\) | 8.05411e85 | 0.694058 | ||||||||
\(229\) | −2.03245e85 | −0.149288 | −0.0746438 | − | 0.997210i | \(-0.523782\pi\) | ||||
−0.0746438 | + | 0.997210i | \(0.523782\pi\) | |||||||
\(230\) | −2.30730e86 | −1.44557 | ||||||||
\(231\) | 7.07223e85 | 0.378198 | ||||||||
\(232\) | −3.84903e85 | −0.175808 | ||||||||
\(233\) | −2.65619e86 | −1.03698 | −0.518488 | − | 0.855085i | \(-0.673505\pi\) | ||||
−0.518488 | + | 0.855085i | \(0.673505\pi\) | |||||||
\(234\) | −4.03948e86 | −1.34880 | ||||||||
\(235\) | 4.58378e86 | 1.30993 | ||||||||
\(236\) | 2.23997e86 | 0.548219 | ||||||||
\(237\) | 2.82945e86 | 0.593455 | ||||||||
\(238\) | 6.96824e85 | 0.125333 | ||||||||
\(239\) | −1.21129e87 | −1.86950 | −0.934752 | − | 0.355301i | \(-0.884378\pi\) | ||||
−0.934752 | + | 0.355301i | \(0.884378\pi\) | |||||||
\(240\) | −5.91313e86 | −0.783623 | ||||||||
\(241\) | −5.87394e86 | −0.668817 | −0.334409 | − | 0.942428i | \(-0.608537\pi\) | ||||
−0.334409 | + | 0.942428i | \(0.608537\pi\) | |||||||
\(242\) | 2.24323e86 | 0.219590 | ||||||||
\(243\) | −4.76226e86 | −0.401036 | ||||||||
\(244\) | 3.08220e86 | 0.223425 | ||||||||
\(245\) | 2.84898e87 | 1.77880 | ||||||||
\(246\) | 4.29632e87 | 2.31188 | ||||||||
\(247\) | −1.79635e87 | −0.833590 | ||||||||
\(248\) | 8.03695e84 | 0.00321814 | ||||||||
\(249\) | 6.96860e86 | 0.240918 | ||||||||
\(250\) | −6.21138e87 | −1.85515 | ||||||||
\(251\) | 6.83827e87 | 1.76545 | 0.882726 | − | 0.469889i | \(-0.155706\pi\) | ||||
0.882726 | + | 0.469889i | \(0.155706\pi\) | |||||||
\(252\) | 8.17652e86 | 0.182578 | ||||||||
\(253\) | 6.54992e87 | 1.26572 | ||||||||
\(254\) | 4.72159e87 | 0.790055 | ||||||||
\(255\) | −1.96650e88 | −2.85087 | ||||||||
\(256\) | 4.97323e86 | 0.0625000 | ||||||||
\(257\) | −1.37152e88 | −1.49501 | −0.747504 | − | 0.664257i | \(-0.768748\pi\) | ||||
−0.747504 | + | 0.664257i | \(0.768748\pi\) | |||||||
\(258\) | 7.16171e87 | 0.677481 | ||||||||
\(259\) | 2.78064e87 | 0.228404 | ||||||||
\(260\) | 1.31884e88 | 0.941161 | ||||||||
\(261\) | −1.50201e88 | −0.931740 | ||||||||
\(262\) | −1.12026e88 | −0.604397 | ||||||||
\(263\) | −1.37975e88 | −0.647763 | −0.323881 | − | 0.946098i | \(-0.604988\pi\) | ||||
−0.323881 | + | 0.946098i | \(0.604988\pi\) | |||||||
\(264\) | 1.67861e88 | 0.686128 | ||||||||
\(265\) | 3.73532e88 | 1.33000 | ||||||||
\(266\) | 3.63609e87 | 0.112838 | ||||||||
\(267\) | 1.87447e87 | 0.0507245 | ||||||||
\(268\) | −3.42557e88 | −0.808748 | ||||||||
\(269\) | −5.70510e88 | −1.17572 | −0.587862 | − | 0.808962i | \(-0.700030\pi\) | ||||
−0.587862 | + | 0.808962i | \(0.700030\pi\) | |||||||
\(270\) | −1.07600e89 | −1.93658 | ||||||||
\(271\) | 5.21634e88 | 0.820326 | 0.410163 | − | 0.912012i | \(-0.365472\pi\) | ||||
0.410163 | + | 0.912012i | \(0.365472\pi\) | |||||||
\(272\) | 1.65392e88 | 0.227379 | ||||||||
\(273\) | −2.79692e88 | −0.336313 | ||||||||
\(274\) | −2.22183e88 | −0.233785 | ||||||||
\(275\) | 3.00598e89 | 2.76913 | ||||||||
\(276\) | 1.16141e89 | 0.937141 | ||||||||
\(277\) | 1.77935e89 | 1.25820 | 0.629100 | − | 0.777324i | \(-0.283424\pi\) | ||||
0.629100 | + | 0.777324i | \(0.283424\pi\) | |||||||
\(278\) | 9.20251e88 | 0.570521 | ||||||||
\(279\) | 3.13627e87 | 0.0170553 | ||||||||
\(280\) | −2.66953e88 | −0.127399 | ||||||||
\(281\) | −3.49527e89 | −1.46453 | −0.732267 | − | 0.681017i | \(-0.761538\pi\) | ||||
−0.732267 | + | 0.681017i | \(0.761538\pi\) | |||||||
\(282\) | −2.30731e89 | −0.849206 | ||||||||
\(283\) | 5.88769e89 | 1.90432 | 0.952160 | − | 0.305600i | \(-0.0988571\pi\) | ||||
0.952160 | + | 0.305600i | \(0.0988571\pi\) | |||||||
\(284\) | −1.32818e89 | −0.377692 | ||||||||
\(285\) | −1.02614e90 | −2.56666 | ||||||||
\(286\) | −3.74389e89 | −0.824067 | ||||||||
\(287\) | 1.93961e89 | 0.375859 | ||||||||
\(288\) | 1.94071e89 | 0.331234 | ||||||||
\(289\) | −1.14885e89 | −0.172780 | ||||||||
\(290\) | 4.90387e89 | 0.650148 | ||||||||
\(291\) | −1.03299e90 | −1.20782 | ||||||||
\(292\) | 2.46822e89 | 0.254630 | ||||||||
\(293\) | 2.14538e90 | 1.95361 | 0.976803 | − | 0.214141i | \(-0.0686953\pi\) | ||||
0.976803 | + | 0.214141i | \(0.0686953\pi\) | |||||||
\(294\) | −1.43407e90 | −1.15317 | ||||||||
\(295\) | −2.85385e90 | −2.02734 | ||||||||
\(296\) | 6.59991e89 | 0.414372 | ||||||||
\(297\) | 3.05454e90 | 1.69565 | ||||||||
\(298\) | −1.17414e90 | −0.576538 | ||||||||
\(299\) | −2.59036e90 | −1.12554 | ||||||||
\(300\) | 5.33012e90 | 2.05027 | ||||||||
\(301\) | 3.23321e89 | 0.110143 | ||||||||
\(302\) | 3.99547e89 | 0.120591 | ||||||||
\(303\) | 2.45356e90 | 0.656358 | ||||||||
\(304\) | 8.63033e89 | 0.204711 | ||||||||
\(305\) | −3.92690e90 | −0.826239 | ||||||||
\(306\) | 6.45414e90 | 1.20505 | ||||||||
\(307\) | −5.86814e90 | −0.972635 | −0.486317 | − | 0.873782i | \(-0.661660\pi\) | ||||
−0.486317 | + | 0.873782i | \(0.661660\pi\) | |||||||
\(308\) | 7.57820e89 | 0.111549 | ||||||||
\(309\) | 3.42941e90 | 0.448472 | ||||||||
\(310\) | −1.02395e89 | −0.0119008 | ||||||||
\(311\) | 7.44177e90 | 0.768993 | 0.384496 | − | 0.923127i | \(-0.374375\pi\) | ||||
0.384496 | + | 0.923127i | \(0.374375\pi\) | |||||||
\(312\) | −6.63855e90 | −0.610141 | ||||||||
\(313\) | 6.11264e89 | 0.0499874 | 0.0249937 | − | 0.999688i | \(-0.492043\pi\) | ||||
0.0249937 | + | 0.999688i | \(0.492043\pi\) | |||||||
\(314\) | −1.82417e91 | −1.32780 | ||||||||
\(315\) | −1.04173e91 | −0.675183 | ||||||||
\(316\) | 3.03188e90 | 0.175039 | ||||||||
\(317\) | 4.50179e90 | 0.231591 | 0.115796 | − | 0.993273i | \(-0.463058\pi\) | ||||
0.115796 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(318\) | −1.88022e91 | −0.862223 | ||||||||
\(319\) | −1.39210e91 | −0.569260 | ||||||||
\(320\) | −6.33617e90 | −0.231128 | ||||||||
\(321\) | 4.49930e91 | 1.46457 | ||||||||
\(322\) | 5.24328e90 | 0.152358 | ||||||||
\(323\) | 2.87015e91 | 0.744753 | ||||||||
\(324\) | 1.37443e91 | 0.318587 | ||||||||
\(325\) | −1.18881e92 | −2.46245 | ||||||||
\(326\) | 3.56804e91 | 0.660675 | ||||||||
\(327\) | 1.82716e91 | 0.302541 | ||||||||
\(328\) | 4.60370e91 | 0.681886 | ||||||||
\(329\) | −1.04165e91 | −0.138061 | ||||||||
\(330\) | −2.13864e92 | −2.53734 | ||||||||
\(331\) | 4.58554e91 | 0.487157 | 0.243578 | − | 0.969881i | \(-0.421679\pi\) | ||||
0.243578 | + | 0.969881i | \(0.421679\pi\) | |||||||
\(332\) | 7.46716e90 | 0.0710584 | ||||||||
\(333\) | 2.57549e92 | 2.19607 | ||||||||
\(334\) | 1.04561e92 | 0.799138 | ||||||||
\(335\) | 4.36437e92 | 2.99079 | ||||||||
\(336\) | 1.34374e91 | 0.0825910 | ||||||||
\(337\) | −5.44105e91 | −0.300049 | −0.150024 | − | 0.988682i | \(-0.547935\pi\) | ||||
−0.150024 | + | 0.988682i | \(0.547935\pi\) | |||||||
\(338\) | 5.19196e90 | 0.0256964 | ||||||||
\(339\) | −5.92506e92 | −2.63272 | ||||||||
\(340\) | −2.10719e92 | −0.840860 | ||||||||
\(341\) | 2.90677e90 | 0.0104202 | ||||||||
\(342\) | 3.36783e92 | 1.08492 | ||||||||
\(343\) | −1.32041e92 | −0.382360 | ||||||||
\(344\) | 7.67408e91 | 0.199822 | ||||||||
\(345\) | −1.47970e93 | −3.46559 | ||||||||
\(346\) | 1.25293e92 | 0.264027 | ||||||||
\(347\) | 4.82676e92 | 0.915439 | 0.457720 | − | 0.889097i | \(-0.348666\pi\) | ||||
0.457720 | + | 0.889097i | \(0.348666\pi\) | |||||||
\(348\) | −2.46843e92 | −0.421482 | ||||||||
\(349\) | 2.26931e92 | 0.348951 | 0.174476 | − | 0.984661i | \(-0.444177\pi\) | ||||
0.174476 | + | 0.984661i | \(0.444177\pi\) | |||||||
\(350\) | 2.40632e92 | 0.333327 | ||||||||
\(351\) | −1.20801e93 | −1.50786 | ||||||||
\(352\) | 1.79870e92 | 0.202372 | ||||||||
\(353\) | 3.79349e92 | 0.384824 | 0.192412 | − | 0.981314i | \(-0.438369\pi\) | ||||
0.192412 | + | 0.981314i | \(0.438369\pi\) | |||||||
\(354\) | 1.43652e93 | 1.31430 | ||||||||
\(355\) | 1.69218e93 | 1.39673 | ||||||||
\(356\) | 2.00858e91 | 0.0149611 | ||||||||
\(357\) | 4.46882e92 | 0.300471 | ||||||||
\(358\) | −6.66475e91 | −0.0404626 | ||||||||
\(359\) | 4.26527e92 | 0.233883 | 0.116942 | − | 0.993139i | \(-0.462691\pi\) | ||||
0.116942 | + | 0.993139i | \(0.462691\pi\) | |||||||
\(360\) | −2.47258e93 | −1.22492 | ||||||||
\(361\) | −7.35970e92 | −0.329494 | ||||||||
\(362\) | −2.93451e92 | −0.118761 | ||||||||
\(363\) | 1.43861e93 | 0.526444 | ||||||||
\(364\) | −2.99702e92 | −0.0991949 | ||||||||
\(365\) | −3.14465e93 | −0.941634 | ||||||||
\(366\) | 1.97666e93 | 0.535638 | ||||||||
\(367\) | 1.28566e93 | 0.315365 | 0.157683 | − | 0.987490i | \(-0.449598\pi\) | ||||
0.157683 | + | 0.987490i | \(0.449598\pi\) | |||||||
\(368\) | 1.24450e93 | 0.276408 | ||||||||
\(369\) | 1.79651e94 | 3.61382 | ||||||||
\(370\) | −8.40865e93 | −1.53237 | ||||||||
\(371\) | −8.48841e92 | −0.140178 | ||||||||
\(372\) | 5.15420e91 | 0.00771514 | ||||||||
\(373\) | −5.43996e93 | −0.738284 | −0.369142 | − | 0.929373i | \(-0.620348\pi\) | ||||
−0.369142 | + | 0.929373i | \(0.620348\pi\) | |||||||
\(374\) | 5.98185e93 | 0.736244 | ||||||||
\(375\) | −3.98344e94 | −4.44751 | ||||||||
\(376\) | −2.47238e93 | −0.250472 | ||||||||
\(377\) | 5.50548e93 | 0.506216 | ||||||||
\(378\) | 2.44519e93 | 0.204109 | ||||||||
\(379\) | 5.07066e93 | 0.384356 | 0.192178 | − | 0.981360i | \(-0.438445\pi\) | ||||
0.192178 | + | 0.981360i | \(0.438445\pi\) | |||||||
\(380\) | −1.09955e94 | −0.757032 | ||||||||
\(381\) | 3.02802e94 | 1.89407 | ||||||||
\(382\) | −1.83927e94 | −1.04552 | ||||||||
\(383\) | 1.73605e94 | 0.897032 | 0.448516 | − | 0.893775i | \(-0.351953\pi\) | ||||
0.448516 | + | 0.893775i | \(0.351953\pi\) | |||||||
\(384\) | 3.18940e93 | 0.149837 | ||||||||
\(385\) | −9.65504e93 | −0.412513 | ||||||||
\(386\) | −1.12128e94 | −0.435790 | ||||||||
\(387\) | 2.99467e94 | 1.05901 | ||||||||
\(388\) | −1.10690e94 | −0.356245 | ||||||||
\(389\) | −5.19087e94 | −1.52083 | −0.760414 | − | 0.649439i | \(-0.775004\pi\) | ||||
−0.760414 | + | 0.649439i | \(0.775004\pi\) | |||||||
\(390\) | 8.45788e94 | 2.25633 | ||||||||
\(391\) | 4.13879e94 | 1.00559 | ||||||||
\(392\) | −1.53667e94 | −0.340126 | ||||||||
\(393\) | −7.18439e94 | −1.44898 | ||||||||
\(394\) | 3.28808e94 | 0.604407 | ||||||||
\(395\) | −3.86279e94 | −0.647302 | ||||||||
\(396\) | 7.01909e94 | 1.07252 | ||||||||
\(397\) | 9.79236e94 | 1.36469 | 0.682345 | − | 0.731030i | \(-0.260960\pi\) | ||||
0.682345 | + | 0.731030i | \(0.260960\pi\) | |||||||
\(398\) | 5.30757e94 | 0.674782 | ||||||||
\(399\) | 2.33187e94 | 0.270517 | ||||||||
\(400\) | 5.71145e94 | 0.604724 | ||||||||
\(401\) | −1.67677e95 | −1.62071 | −0.810354 | − | 0.585941i | \(-0.800725\pi\) | ||||
−0.810354 | + | 0.585941i | \(0.800725\pi\) | |||||||
\(402\) | −2.19686e95 | −1.93889 | ||||||||
\(403\) | −1.14957e93 | −0.00926619 | ||||||||
\(404\) | 2.62910e94 | 0.193592 | ||||||||
\(405\) | −1.75110e95 | −1.17815 | ||||||||
\(406\) | −1.11439e94 | −0.0685232 | ||||||||
\(407\) | 2.38703e95 | 1.34172 | ||||||||
\(408\) | 1.06068e95 | 0.545117 | ||||||||
\(409\) | −1.70027e95 | −0.799127 | −0.399564 | − | 0.916705i | \(-0.630838\pi\) | ||||
−0.399564 | + | 0.916705i | \(0.630838\pi\) | |||||||
\(410\) | −5.86537e95 | −2.52165 | ||||||||
\(411\) | −1.42489e95 | −0.560473 | ||||||||
\(412\) | 3.67476e94 | 0.132276 | ||||||||
\(413\) | 6.48529e94 | 0.213674 | ||||||||
\(414\) | 4.85645e95 | 1.46489 | ||||||||
\(415\) | −9.51357e94 | −0.262777 | ||||||||
\(416\) | −7.11349e94 | −0.179960 | ||||||||
\(417\) | 5.90169e95 | 1.36776 | ||||||||
\(418\) | 3.12138e95 | 0.662846 | ||||||||
\(419\) | 4.66273e95 | 0.907463 | 0.453731 | − | 0.891138i | \(-0.350093\pi\) | ||||
0.453731 | + | 0.891138i | \(0.350093\pi\) | |||||||
\(420\) | −1.71200e95 | −0.305426 | ||||||||
\(421\) | 6.58342e95 | 1.07685 | 0.538425 | − | 0.842674i | \(-0.319020\pi\) | ||||
0.538425 | + | 0.842674i | \(0.319020\pi\) | |||||||
\(422\) | −1.65648e95 | −0.248475 | ||||||||
\(423\) | −9.64801e95 | −1.32744 | ||||||||
\(424\) | −2.01474e95 | −0.254311 | ||||||||
\(425\) | 1.89943e96 | 2.20002 | ||||||||
\(426\) | −8.51780e95 | −0.905477 | ||||||||
\(427\) | 8.92377e94 | 0.0870825 | ||||||||
\(428\) | 4.82120e95 | 0.431974 | ||||||||
\(429\) | −2.40100e96 | −1.97561 | ||||||||
\(430\) | −9.77720e95 | −0.738951 | ||||||||
\(431\) | −1.71148e96 | −1.18837 | −0.594184 | − | 0.804329i | \(-0.702525\pi\) | ||||
−0.594184 | + | 0.804329i | \(0.702525\pi\) | |||||||
\(432\) | 5.80371e95 | 0.370296 | ||||||||
\(433\) | 2.15999e96 | 1.26661 | 0.633306 | − | 0.773901i | \(-0.281697\pi\) | ||||
0.633306 | + | 0.773901i | \(0.281697\pi\) | |||||||
\(434\) | 2.32690e93 | 0.00125431 | ||||||||
\(435\) | 3.14492e96 | 1.55866 | ||||||||
\(436\) | 1.95789e95 | 0.0892340 | ||||||||
\(437\) | 2.15966e96 | 0.905341 | ||||||||
\(438\) | 1.58290e96 | 0.610448 | ||||||||
\(439\) | −3.71212e96 | −1.31725 | −0.658624 | − | 0.752472i | \(-0.728861\pi\) | ||||
−0.658624 | + | 0.752472i | \(0.728861\pi\) | |||||||
\(440\) | −2.29164e96 | −0.748383 | ||||||||
\(441\) | −5.99658e96 | −1.80258 | ||||||||
\(442\) | −2.36570e96 | −0.654707 | ||||||||
\(443\) | −2.95072e96 | −0.751956 | −0.375978 | − | 0.926629i | \(-0.622693\pi\) | ||||
−0.375978 | + | 0.926629i | \(0.622693\pi\) | |||||||
\(444\) | 4.23261e96 | 0.993412 | ||||||||
\(445\) | −2.55904e95 | −0.0553270 | ||||||||
\(446\) | 1.40062e95 | 0.0278996 | ||||||||
\(447\) | −7.52994e96 | −1.38219 | ||||||||
\(448\) | 1.43988e95 | 0.0243601 | ||||||||
\(449\) | −7.64002e96 | −1.19153 | −0.595763 | − | 0.803161i | \(-0.703150\pi\) | ||||
−0.595763 | + | 0.803161i | \(0.703150\pi\) | |||||||
\(450\) | 2.22879e97 | 3.20488 | ||||||||
\(451\) | 1.66505e97 | 2.20792 | ||||||||
\(452\) | −6.34896e96 | −0.776515 | ||||||||
\(453\) | 2.56234e96 | 0.289103 | ||||||||
\(454\) | −9.22313e96 | −0.960151 | ||||||||
\(455\) | 3.81837e96 | 0.366828 | ||||||||
\(456\) | 5.53474e96 | 0.490773 | ||||||||
\(457\) | 5.24571e96 | 0.429401 | 0.214700 | − | 0.976680i | \(-0.431122\pi\) | ||||
0.214700 | + | 0.976680i | \(0.431122\pi\) | |||||||
\(458\) | −1.39669e96 | −0.105562 | ||||||||
\(459\) | 1.93011e97 | 1.34716 | ||||||||
\(460\) | −1.58557e97 | −1.02217 | ||||||||
\(461\) | 1.20990e97 | 0.720550 | 0.360275 | − | 0.932846i | \(-0.382683\pi\) | ||||
0.360275 | + | 0.932846i | \(0.382683\pi\) | |||||||
\(462\) | 4.86000e96 | 0.267426 | ||||||||
\(463\) | −2.83398e97 | −1.44109 | −0.720544 | − | 0.693409i | \(-0.756108\pi\) | ||||
−0.720544 | + | 0.693409i | \(0.756108\pi\) | |||||||
\(464\) | −2.64503e96 | −0.124315 | ||||||||
\(465\) | −6.56674e95 | −0.0285310 | ||||||||
\(466\) | −1.82532e97 | −0.733252 | ||||||||
\(467\) | 2.09309e97 | 0.777537 | 0.388768 | − | 0.921336i | \(-0.372901\pi\) | ||||
0.388768 | + | 0.921336i | \(0.372901\pi\) | |||||||
\(468\) | −2.77591e97 | −0.953744 | ||||||||
\(469\) | −9.91791e96 | −0.315218 | ||||||||
\(470\) | 3.14995e97 | 0.926258 | ||||||||
\(471\) | −1.16986e98 | −3.18325 | ||||||||
\(472\) | 1.53930e97 | 0.387650 | ||||||||
\(473\) | 2.77553e97 | 0.647015 | ||||||||
\(474\) | 1.94439e97 | 0.419636 | ||||||||
\(475\) | 9.91140e97 | 1.98070 | ||||||||
\(476\) | 4.78854e96 | 0.0886235 | ||||||||
\(477\) | −7.86215e97 | −1.34779 | ||||||||
\(478\) | −8.32395e97 | −1.32194 | ||||||||
\(479\) | 9.84743e97 | 1.44903 | 0.724514 | − | 0.689260i | \(-0.242064\pi\) | ||||
0.724514 | + | 0.689260i | \(0.242064\pi\) | |||||||
\(480\) | −4.06347e97 | −0.554105 | ||||||||
\(481\) | −9.44021e97 | −1.19313 | ||||||||
\(482\) | −4.03654e97 | −0.472925 | ||||||||
\(483\) | 3.36259e97 | 0.365261 | ||||||||
\(484\) | 1.54154e97 | 0.155274 | ||||||||
\(485\) | 1.41025e98 | 1.31741 | ||||||||
\(486\) | −3.27260e97 | −0.283576 | ||||||||
\(487\) | 1.79002e98 | 1.43897 | 0.719485 | − | 0.694508i | \(-0.244378\pi\) | ||||
0.719485 | + | 0.694508i | \(0.244378\pi\) | |||||||
\(488\) | 2.11807e97 | 0.157986 | ||||||||
\(489\) | 2.28823e98 | 1.58390 | ||||||||
\(490\) | 1.95781e98 | 1.25780 | ||||||||
\(491\) | −1.44665e98 | −0.862761 | −0.431380 | − | 0.902170i | \(-0.641973\pi\) | ||||
−0.431380 | + | 0.902170i | \(0.641973\pi\) | |||||||
\(492\) | 2.95241e98 | 1.63475 | ||||||||
\(493\) | −8.79646e97 | −0.452267 | ||||||||
\(494\) | −1.23444e98 | −0.589437 | ||||||||
\(495\) | −8.94272e98 | −3.96625 | ||||||||
\(496\) | 5.52295e95 | 0.00227557 | ||||||||
\(497\) | −3.84543e97 | −0.147210 | ||||||||
\(498\) | 4.78879e97 | 0.170355 | ||||||||
\(499\) | 2.56109e97 | 0.0846749 | 0.0423374 | − | 0.999103i | \(-0.486520\pi\) | ||||
0.0423374 | + | 0.999103i | \(0.486520\pi\) | |||||||
\(500\) | −4.26843e98 | −1.31179 | ||||||||
\(501\) | 6.70560e98 | 1.91585 | ||||||||
\(502\) | 4.69923e98 | 1.24836 | ||||||||
\(503\) | −5.69558e98 | −1.40704 | −0.703520 | − | 0.710675i | \(-0.748389\pi\) | ||||
−0.703520 | + | 0.710675i | \(0.748389\pi\) | |||||||
\(504\) | 5.61886e97 | 0.129102 | ||||||||
\(505\) | −3.34961e98 | −0.715912 | ||||||||
\(506\) | 4.50107e98 | 0.894998 | ||||||||
\(507\) | 3.32967e97 | 0.0616043 | ||||||||
\(508\) | 3.24465e98 | 0.558653 | ||||||||
\(509\) | −1.31519e97 | −0.0210761 | −0.0105381 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105381 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(510\) | −1.35137e99 | −2.01587 | ||||||||
\(511\) | 7.14612e97 | 0.0992448 | ||||||||
\(512\) | 3.41758e97 | 0.0441942 | ||||||||
\(513\) | 1.00715e99 | 1.21286 | ||||||||
\(514\) | −9.42503e98 | −1.05713 | ||||||||
\(515\) | −4.68185e98 | −0.489163 | ||||||||
\(516\) | 4.92149e98 | 0.479051 | ||||||||
\(517\) | −8.94201e98 | −0.811018 | ||||||||
\(518\) | 1.91084e98 | 0.161506 | ||||||||
\(519\) | 8.03520e98 | 0.632977 | ||||||||
\(520\) | 9.06298e98 | 0.665501 | ||||||||
\(521\) | 9.33703e98 | 0.639193 | 0.319596 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319596 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(522\) | −1.03217e99 | −0.658840 | ||||||||
\(523\) | 1.72766e99 | 1.02837 | 0.514183 | − | 0.857681i | \(-0.328095\pi\) | ||||
0.514183 | + | 0.857681i | \(0.328095\pi\) | |||||||
\(524\) | −7.69838e98 | −0.427373 | ||||||||
\(525\) | 1.54321e99 | 0.799115 | ||||||||
\(526\) | −9.48158e98 | −0.458038 | ||||||||
\(527\) | 1.83674e97 | 0.00827867 | ||||||||
\(528\) | 1.15353e99 | 0.485166 | ||||||||
\(529\) | 5.66646e98 | 0.222423 | ||||||||
\(530\) | 2.56689e99 | 0.940455 | ||||||||
\(531\) | 6.00682e99 | 2.05445 | ||||||||
\(532\) | 2.49870e98 | 0.0797884 | ||||||||
\(533\) | −6.58492e99 | −1.96339 | ||||||||
\(534\) | 1.28813e98 | 0.0358677 | ||||||||
\(535\) | −6.14247e99 | −1.59746 | ||||||||
\(536\) | −2.35403e99 | −0.571871 | ||||||||
\(537\) | −4.27419e98 | −0.0970047 | ||||||||
\(538\) | −3.92052e99 | −0.831362 | ||||||||
\(539\) | −5.55778e99 | −1.10131 | ||||||||
\(540\) | −7.39424e99 | −1.36937 | ||||||||
\(541\) | 5.02383e99 | 0.869631 | 0.434816 | − | 0.900520i | \(-0.356814\pi\) | ||||
0.434816 | + | 0.900520i | \(0.356814\pi\) | |||||||
\(542\) | 3.58464e99 | 0.580058 | ||||||||
\(543\) | −1.88194e99 | −0.284716 | ||||||||
\(544\) | 1.13657e99 | 0.160781 | ||||||||
\(545\) | −2.49446e99 | −0.329992 | ||||||||
\(546\) | −1.92203e99 | −0.237809 | ||||||||
\(547\) | 7.38676e99 | 0.854902 | 0.427451 | − | 0.904038i | \(-0.359412\pi\) | ||||
0.427451 | + | 0.904038i | \(0.359412\pi\) | |||||||
\(548\) | −1.52683e99 | −0.165311 | ||||||||
\(549\) | 8.26540e99 | 0.837285 | ||||||||
\(550\) | 2.06570e100 | 1.95807 | ||||||||
\(551\) | −4.59007e99 | −0.407180 | ||||||||
\(552\) | 7.98116e99 | 0.662659 | ||||||||
\(553\) | 8.77808e98 | 0.0682233 | ||||||||
\(554\) | 1.22276e100 | 0.889682 | ||||||||
\(555\) | −5.39258e100 | −3.67369 | ||||||||
\(556\) | 6.32392e99 | 0.403419 | ||||||||
\(557\) | 2.60182e100 | 1.55440 | 0.777200 | − | 0.629254i | \(-0.216639\pi\) | ||||
0.777200 | + | 0.629254i | \(0.216639\pi\) | |||||||
\(558\) | 2.15523e98 | 0.0120599 | ||||||||
\(559\) | −1.09767e100 | −0.575359 | ||||||||
\(560\) | −1.83449e99 | −0.0900847 | ||||||||
\(561\) | 3.83624e100 | 1.76507 | ||||||||
\(562\) | −2.40193e100 | −1.03558 | ||||||||
\(563\) | −3.27071e100 | −1.32156 | −0.660778 | − | 0.750582i | \(-0.729773\pi\) | ||||
−0.660778 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(564\) | −1.58557e100 | −0.600479 | ||||||||
\(565\) | 8.08893e100 | 2.87159 | ||||||||
\(566\) | 4.04599e100 | 1.34656 | ||||||||
\(567\) | 3.97932e99 | 0.124173 | ||||||||
\(568\) | −9.12720e99 | −0.267069 | ||||||||
\(569\) | 1.42662e100 | 0.391480 | 0.195740 | − | 0.980656i | \(-0.437289\pi\) | ||||
0.195740 | + | 0.980656i | \(0.437289\pi\) | |||||||
\(570\) | −7.05157e100 | −1.81490 | ||||||||
\(571\) | −4.71485e100 | −1.13828 | −0.569141 | − | 0.822240i | \(-0.692724\pi\) | ||||
−0.569141 | + | 0.822240i | \(0.692724\pi\) | |||||||
\(572\) | −2.57278e100 | −0.582703 | ||||||||
\(573\) | −1.17954e101 | −2.50652 | ||||||||
\(574\) | 1.33289e100 | 0.265772 | ||||||||
\(575\) | 1.42924e101 | 2.67441 | ||||||||
\(576\) | 1.33365e100 | 0.234218 | ||||||||
\(577\) | −5.71235e100 | −0.941668 | −0.470834 | − | 0.882222i | \(-0.656047\pi\) | ||||
−0.470834 | + | 0.882222i | \(0.656047\pi\) | |||||||
\(578\) | −7.89484e99 | −0.122174 | ||||||||
\(579\) | −7.19091e100 | −1.04476 | ||||||||
\(580\) | 3.36992e100 | 0.459724 | ||||||||
\(581\) | 2.16193e99 | 0.0276958 | ||||||||
\(582\) | −7.09867e100 | −0.854059 | ||||||||
\(583\) | −7.28683e100 | −0.823449 | ||||||||
\(584\) | 1.69615e100 | 0.180050 | ||||||||
\(585\) | 3.53666e101 | 3.52699 | ||||||||
\(586\) | 1.47430e101 | 1.38141 | ||||||||
\(587\) | −1.41978e101 | −1.25006 | −0.625030 | − | 0.780601i | \(-0.714913\pi\) | ||||
−0.625030 | + | 0.780601i | \(0.714913\pi\) | |||||||
\(588\) | −9.85488e100 | −0.815415 | ||||||||
\(589\) | 9.58428e98 | 0.00745335 | ||||||||
\(590\) | −1.96115e101 | −1.43355 | ||||||||
\(591\) | 2.10869e101 | 1.44900 | ||||||||
\(592\) | 4.53542e100 | 0.293005 | ||||||||
\(593\) | −1.84307e101 | −1.11956 | −0.559778 | − | 0.828642i | \(-0.689114\pi\) | ||||
−0.559778 | + | 0.828642i | \(0.689114\pi\) | |||||||
\(594\) | 2.09906e101 | 1.19900 | ||||||||
\(595\) | −6.10086e100 | −0.327734 | ||||||||
\(596\) | −8.06866e100 | −0.407674 | ||||||||
\(597\) | 3.40381e101 | 1.61772 | ||||||||
\(598\) | −1.78008e101 | −0.795879 | ||||||||
\(599\) | −3.83951e100 | −0.161509 | −0.0807546 | − | 0.996734i | \(-0.525733\pi\) | ||||
−0.0807546 | + | 0.996734i | \(0.525733\pi\) | |||||||
\(600\) | 3.66283e101 | 1.44976 | ||||||||
\(601\) | 2.44570e101 | 0.910929 | 0.455465 | − | 0.890254i | \(-0.349473\pi\) | ||||
0.455465 | + | 0.890254i | \(0.349473\pi\) | |||||||
\(602\) | 2.22184e100 | 0.0778828 | ||||||||
\(603\) | −9.18619e101 | −3.03077 | ||||||||
\(604\) | 2.74566e100 | 0.0852705 | ||||||||
\(605\) | −1.96400e101 | −0.574210 | ||||||||
\(606\) | 1.68607e101 | 0.464115 | ||||||||
\(607\) | 7.40100e101 | 1.91824 | 0.959120 | − | 0.283000i | \(-0.0913297\pi\) | ||||
0.959120 | + | 0.283000i | \(0.0913297\pi\) | |||||||
\(608\) | 5.93072e100 | 0.144753 | ||||||||
\(609\) | −7.14674e100 | −0.164277 | ||||||||
\(610\) | −2.69854e101 | −0.584239 | ||||||||
\(611\) | 3.53638e101 | 0.721199 | ||||||||
\(612\) | 4.43525e101 | 0.852101 | ||||||||
\(613\) | 1.17887e101 | 0.213382 | 0.106691 | − | 0.994292i | \(-0.465974\pi\) | ||||
0.106691 | + | 0.994292i | \(0.465974\pi\) | |||||||
\(614\) | −4.03256e101 | −0.687757 | ||||||||
\(615\) | −3.76154e102 | −6.04538 | ||||||||
\(616\) | 5.20770e100 | 0.0788769 | ||||||||
\(617\) | −8.71142e101 | −1.24360 | −0.621799 | − | 0.783177i | \(-0.713598\pi\) | ||||
−0.621799 | + | 0.783177i | \(0.713598\pi\) | |||||||
\(618\) | 2.35667e101 | 0.317117 | ||||||||
\(619\) | 7.46816e101 | 0.947339 | 0.473669 | − | 0.880703i | \(-0.342929\pi\) | ||||
0.473669 | + | 0.880703i | \(0.342929\pi\) | |||||||
\(620\) | −7.03654e99 | −0.00841517 | ||||||||
\(621\) | 1.45232e102 | 1.63764 | ||||||||
\(622\) | 5.11395e101 | 0.543760 | ||||||||
\(623\) | 5.81535e99 | 0.00583126 | ||||||||
\(624\) | −4.56197e101 | −0.431435 | ||||||||
\(625\) | 2.72654e102 | 2.43216 | ||||||||
\(626\) | 4.20057e100 | 0.0353464 | ||||||||
\(627\) | 2.00178e102 | 1.58910 | ||||||||
\(628\) | −1.25356e102 | −0.938895 | ||||||||
\(629\) | 1.50832e102 | 1.06597 | ||||||||
\(630\) | −7.15874e101 | −0.477427 | ||||||||
\(631\) | 1.75887e102 | 1.10704 | 0.553518 | − | 0.832837i | \(-0.313285\pi\) | ||||
0.553518 | + | 0.832837i | \(0.313285\pi\) | |||||||
\(632\) | 2.08349e101 | 0.123771 | ||||||||
\(633\) | −1.06232e102 | −0.595692 | ||||||||
\(634\) | 3.09360e101 | 0.163760 | ||||||||
\(635\) | −4.13386e102 | −2.06593 | ||||||||
\(636\) | −1.29208e102 | −0.609683 | ||||||||
\(637\) | 2.19799e102 | 0.979346 | ||||||||
\(638\) | −9.56645e101 | −0.402528 | ||||||||
\(639\) | −3.56172e102 | −1.41540 | ||||||||
\(640\) | −4.35419e101 | −0.163432 | ||||||||
\(641\) | 5.11680e102 | 1.81418 | 0.907091 | − | 0.420935i | \(-0.138298\pi\) | ||||
0.907091 | + | 0.420935i | \(0.138298\pi\) | |||||||
\(642\) | 3.09190e102 | 1.03561 | ||||||||
\(643\) | −2.35088e101 | −0.0743925 | −0.0371963 | − | 0.999308i | \(-0.511843\pi\) | ||||
−0.0371963 | + | 0.999308i | \(0.511843\pi\) | |||||||
\(644\) | 3.60316e101 | 0.107733 | ||||||||
\(645\) | −6.27025e102 | −1.77156 | ||||||||
\(646\) | 1.97235e102 | 0.526620 | ||||||||
\(647\) | −5.13307e102 | −1.29530 | −0.647651 | − | 0.761937i | \(-0.724249\pi\) | ||||
−0.647651 | + | 0.761937i | \(0.724249\pi\) | |||||||
\(648\) | 9.44499e101 | 0.225275 | ||||||||
\(649\) | 5.56727e102 | 1.25519 | ||||||||
\(650\) | −8.16941e102 | −1.74122 | ||||||||
\(651\) | 1.49227e100 | 0.00300706 | ||||||||
\(652\) | 2.45194e102 | 0.467168 | ||||||||
\(653\) | −1.01178e103 | −1.82286 | −0.911430 | − | 0.411454i | \(-0.865021\pi\) | ||||
−0.911430 | + | 0.411454i | \(0.865021\pi\) | |||||||
\(654\) | 1.25562e102 | 0.213929 | ||||||||
\(655\) | 9.80816e102 | 1.58045 | ||||||||
\(656\) | 3.16364e102 | 0.482166 | ||||||||
\(657\) | 6.61890e102 | 0.954223 | ||||||||
\(658\) | −7.15818e101 | −0.0976241 | ||||||||
\(659\) | 1.89029e102 | 0.243900 | 0.121950 | − | 0.992536i | \(-0.461085\pi\) | ||||
0.121950 | + | 0.992536i | \(0.461085\pi\) | |||||||
\(660\) | −1.46966e103 | −1.79417 | ||||||||
\(661\) | 9.13646e100 | 0.0105542 | 0.00527709 | − | 0.999986i | \(-0.498320\pi\) | ||||
0.00527709 | + | 0.999986i | \(0.498320\pi\) | |||||||
\(662\) | 3.15116e102 | 0.344472 | ||||||||
\(663\) | −1.51715e103 | −1.56959 | ||||||||
\(664\) | 5.13139e101 | 0.0502459 | ||||||||
\(665\) | −3.18348e102 | −0.295062 | ||||||||
\(666\) | 1.76987e103 | 1.55285 | ||||||||
\(667\) | −6.61894e102 | −0.549788 | ||||||||
\(668\) | 7.18535e102 | 0.565076 | ||||||||
\(669\) | 8.98236e101 | 0.0668863 | ||||||||
\(670\) | 2.99917e103 | 2.11481 | ||||||||
\(671\) | 7.66057e102 | 0.511551 | ||||||||
\(672\) | 9.23413e101 | 0.0584006 | ||||||||
\(673\) | −2.13125e103 | −1.27669 | −0.638344 | − | 0.769751i | \(-0.720380\pi\) | ||||
−0.638344 | + | 0.769751i | \(0.720380\pi\) | |||||||
\(674\) | −3.73906e102 | −0.212166 | ||||||||
\(675\) | 6.66520e103 | 3.58283 | ||||||||
\(676\) | 3.56789e101 | 0.0181701 | ||||||||
\(677\) | −5.31475e102 | −0.256446 | −0.128223 | − | 0.991745i | \(-0.540927\pi\) | ||||
−0.128223 | + | 0.991745i | \(0.540927\pi\) | |||||||
\(678\) | −4.07167e103 | −1.86161 | ||||||||
\(679\) | −3.20475e102 | −0.138850 | ||||||||
\(680\) | −1.44805e103 | −0.594578 | ||||||||
\(681\) | −5.91491e103 | −2.30186 | ||||||||
\(682\) | 1.99752e101 | 0.00736820 | ||||||||
\(683\) | −5.72510e102 | −0.200183 | −0.100092 | − | 0.994978i | \(-0.531914\pi\) | ||||
−0.100092 | + | 0.994978i | \(0.531914\pi\) | |||||||
\(684\) | 2.31435e103 | 0.767153 | ||||||||
\(685\) | 1.94527e103 | 0.611327 | ||||||||
\(686\) | −9.07376e102 | −0.270369 | ||||||||
\(687\) | −8.95713e102 | −0.253074 | ||||||||
\(688\) | 5.27359e102 | 0.141295 | ||||||||
\(689\) | 2.88179e103 | 0.732254 | ||||||||
\(690\) | −1.01684e104 | −2.45055 | ||||||||
\(691\) | 4.29996e103 | 0.982914 | 0.491457 | − | 0.870902i | \(-0.336464\pi\) | ||||
0.491457 | + | 0.870902i | \(0.336464\pi\) | |||||||
\(692\) | 8.61006e102 | 0.186695 | ||||||||
\(693\) | 2.03221e103 | 0.418028 | ||||||||
\(694\) | 3.31692e103 | 0.647313 | ||||||||
\(695\) | −8.05702e103 | −1.49186 | ||||||||
\(696\) | −1.69629e103 | −0.298032 | ||||||||
\(697\) | 1.05212e104 | 1.75415 | ||||||||
\(698\) | 1.55946e103 | 0.246746 | ||||||||
\(699\) | −1.17060e104 | −1.75789 | ||||||||
\(700\) | 1.65361e103 | 0.235698 | ||||||||
\(701\) | −1.07964e104 | −1.46074 | −0.730369 | − | 0.683053i | \(-0.760652\pi\) | ||||
−0.730369 | + | 0.683053i | \(0.760652\pi\) | |||||||
\(702\) | −8.30136e103 | −1.06622 | ||||||||
\(703\) | 7.87057e103 | 0.959703 | ||||||||
\(704\) | 1.23606e103 | 0.143099 | ||||||||
\(705\) | 2.02010e104 | 2.22060 | ||||||||
\(706\) | 2.60687e103 | 0.272112 | ||||||||
\(707\) | 7.61191e102 | 0.0754545 | ||||||||
\(708\) | 9.87171e103 | 0.929348 | ||||||||
\(709\) | −4.86603e103 | −0.435098 | −0.217549 | − | 0.976049i | \(-0.569806\pi\) | ||||
−0.217549 | + | 0.976049i | \(0.569806\pi\) | |||||||
\(710\) | 1.16286e104 | 0.987634 | ||||||||
\(711\) | 8.13046e103 | 0.655956 | ||||||||
\(712\) | 1.38028e102 | 0.0105791 | ||||||||
\(713\) | 1.38207e102 | 0.0100638 | ||||||||
\(714\) | 3.07095e103 | 0.212465 | ||||||||
\(715\) | 3.27786e104 | 2.15487 | ||||||||
\(716\) | −4.57998e102 | −0.0286114 | ||||||||
\(717\) | −5.33826e104 | −3.16921 | ||||||||
\(718\) | 2.93107e103 | 0.165381 | ||||||||
\(719\) | −2.92832e103 | −0.157041 | −0.0785207 | − | 0.996912i | \(-0.525020\pi\) | ||||
−0.0785207 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(720\) | −1.69914e104 | −0.866150 | ||||||||
\(721\) | 1.06394e103 | 0.0515560 | ||||||||
\(722\) | −5.05755e103 | −0.232987 | ||||||||
\(723\) | −2.58869e104 | −1.13379 | ||||||||
\(724\) | −2.01658e103 | −0.0839765 | ||||||||
\(725\) | −3.03766e104 | −1.20282 | ||||||||
\(726\) | 9.88607e103 | 0.372252 | ||||||||
\(727\) | 2.53306e104 | 0.907069 | 0.453534 | − | 0.891239i | \(-0.350163\pi\) | ||||
0.453534 | + | 0.891239i | \(0.350163\pi\) | |||||||
\(728\) | −2.05954e103 | −0.0701414 | ||||||||
\(729\) | −4.06580e104 | −1.31702 | ||||||||
\(730\) | −2.16098e104 | −0.665836 | ||||||||
\(731\) | 1.75381e104 | 0.514042 | ||||||||
\(732\) | 1.35835e104 | 0.378754 | ||||||||
\(733\) | −9.16740e103 | −0.243193 | −0.121596 | − | 0.992580i | \(-0.538801\pi\) | ||||
−0.121596 | + | 0.992580i | \(0.538801\pi\) | |||||||
\(734\) | 8.83497e103 | 0.222997 | ||||||||
\(735\) | 1.25557e105 | 3.01545 | ||||||||
\(736\) | 8.55216e103 | 0.195450 | ||||||||
\(737\) | −8.51398e104 | −1.85169 | ||||||||
\(738\) | 1.23455e105 | 2.55536 | ||||||||
\(739\) | −5.93173e104 | −1.16858 | −0.584292 | − | 0.811544i | \(-0.698628\pi\) | ||||
−0.584292 | + | 0.811544i | \(0.698628\pi\) | |||||||
\(740\) | −5.77838e104 | −1.08355 | ||||||||
\(741\) | −7.91665e104 | −1.41311 | ||||||||
\(742\) | −5.83319e103 | −0.0991205 | ||||||||
\(743\) | 1.03004e105 | 1.66633 | 0.833167 | − | 0.553021i | \(-0.186525\pi\) | ||||
0.833167 | + | 0.553021i | \(0.186525\pi\) | |||||||
\(744\) | 3.54194e102 | 0.00545543 | ||||||||
\(745\) | 1.02799e105 | 1.50760 | ||||||||
\(746\) | −3.73831e104 | −0.522046 | ||||||||
\(747\) | 2.00243e104 | 0.266291 | ||||||||
\(748\) | 4.11070e104 | 0.520603 | ||||||||
\(749\) | 1.39586e104 | 0.168366 | ||||||||
\(750\) | −2.73740e105 | −3.14487 | ||||||||
\(751\) | −1.02419e105 | −1.12078 | −0.560392 | − | 0.828228i | \(-0.689349\pi\) | ||||
−0.560392 | + | 0.828228i | \(0.689349\pi\) | |||||||
\(752\) | −1.69901e104 | −0.177110 | ||||||||
\(753\) | 3.01368e105 | 2.99281 | ||||||||
\(754\) | 3.78334e104 | 0.357949 | ||||||||
\(755\) | −3.49813e104 | −0.315335 | ||||||||
\(756\) | 1.68032e104 | 0.144327 | ||||||||
\(757\) | −1.34912e104 | −0.110421 | −0.0552103 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552103 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(758\) | 3.48453e104 | 0.271781 | ||||||||
\(759\) | 2.88660e105 | 2.14566 | ||||||||
\(760\) | −7.55606e104 | −0.535303 | ||||||||
\(761\) | 1.84315e104 | 0.124458 | 0.0622288 | − | 0.998062i | \(-0.480179\pi\) | ||||
0.0622288 | + | 0.998062i | \(0.480179\pi\) | |||||||
\(762\) | 2.08084e105 | 1.33931 | ||||||||
\(763\) | 5.66858e103 | 0.0347799 | ||||||||
\(764\) | −1.26393e105 | −0.739293 | ||||||||
\(765\) | −5.65075e105 | −3.15111 | ||||||||
\(766\) | 1.19301e105 | 0.634298 | ||||||||
\(767\) | −2.20174e105 | −1.11618 | ||||||||
\(768\) | 2.19174e104 | 0.105951 | ||||||||
\(769\) | 1.37771e104 | 0.0635107 | 0.0317554 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317554 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(770\) | −6.63489e104 | −0.291691 | ||||||||
\(771\) | −6.04439e105 | −2.53436 | ||||||||
\(772\) | −7.70537e104 | −0.308150 | ||||||||
\(773\) | 1.82843e105 | 0.697472 | 0.348736 | − | 0.937221i | \(-0.386611\pi\) | ||||
0.348736 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(774\) | 2.05792e105 | 0.748830 | ||||||||
\(775\) | 6.34277e103 | 0.0220174 | ||||||||
\(776\) | −7.60653e104 | −0.251903 | ||||||||
\(777\) | 1.22545e105 | 0.387193 | ||||||||
\(778\) | −3.56714e105 | −1.07539 | ||||||||
\(779\) | 5.49004e105 | 1.57928 | ||||||||
\(780\) | 5.81221e105 | 1.59547 | ||||||||
\(781\) | −3.30109e105 | −0.864758 | ||||||||
\(782\) | 2.84415e105 | 0.711060 | ||||||||
\(783\) | −3.08672e105 | −0.736535 | ||||||||
\(784\) | −1.05599e105 | −0.240505 | ||||||||
\(785\) | 1.59710e106 | 3.47208 | ||||||||
\(786\) | −4.93707e105 | −1.02458 | ||||||||
\(787\) | −3.90064e105 | −0.772784 | −0.386392 | − | 0.922335i | \(-0.626279\pi\) | ||||
−0.386392 | + | 0.922335i | \(0.626279\pi\) | |||||||
\(788\) | 2.25955e105 | 0.427380 | ||||||||
\(789\) | −6.08066e105 | −1.09810 | ||||||||
\(790\) | −2.65449e105 | −0.457712 | ||||||||
\(791\) | −1.83819e105 | −0.302655 | ||||||||
\(792\) | 4.82348e105 | 0.758389 | ||||||||
\(793\) | −3.02960e105 | −0.454898 | ||||||||
\(794\) | 6.72926e105 | 0.964981 | ||||||||
\(795\) | 1.64618e106 | 2.25464 | ||||||||
\(796\) | 3.64733e105 | 0.477143 | ||||||||
\(797\) | −8.67794e105 | −1.08440 | −0.542198 | − | 0.840251i | \(-0.682408\pi\) | ||||
−0.542198 | + | 0.840251i | \(0.682408\pi\) | |||||||
\(798\) | 1.60245e105 | 0.191284 | ||||||||
\(799\) | −5.65031e105 | −0.644339 | ||||||||
\(800\) | 3.92488e105 | 0.427604 | ||||||||
\(801\) | 5.38631e104 | 0.0560666 | ||||||||
\(802\) | −1.15227e106 | −1.14601 | ||||||||
\(803\) | 6.13455e105 | 0.582996 | ||||||||
\(804\) | −1.50967e106 | −1.37100 | ||||||||
\(805\) | −4.59062e105 | −0.398402 | ||||||||
\(806\) | −7.89978e103 | −0.00655218 | ||||||||
\(807\) | −2.51428e106 | −1.99310 | ||||||||
\(808\) | 1.80670e105 | 0.136890 | ||||||||
\(809\) | 1.18602e106 | 0.858955 | 0.429478 | − | 0.903077i | \(-0.358698\pi\) | ||||
0.429478 | + | 0.903077i | \(0.358698\pi\) | |||||||
\(810\) | −1.20334e106 | −0.833079 | ||||||||
\(811\) | 1.04206e106 | 0.689653 | 0.344826 | − | 0.938666i | \(-0.387938\pi\) | ||||
0.344826 | + | 0.938666i | \(0.387938\pi\) | |||||||
\(812\) | −7.65805e104 | −0.0484532 | ||||||||
\(813\) | 2.29888e106 | 1.39063 | ||||||||
\(814\) | 1.64035e106 | 0.948739 | ||||||||
\(815\) | −3.12391e106 | −1.72761 | ||||||||
\(816\) | 7.28896e105 | 0.385456 | ||||||||
\(817\) | 9.15155e105 | 0.462796 | ||||||||
\(818\) | −1.16841e106 | −0.565068 | ||||||||
\(819\) | −8.03697e105 | −0.371732 | ||||||||
\(820\) | −4.03065e106 | −1.78307 | ||||||||
\(821\) | −3.06697e106 | −1.29773 | −0.648864 | − | 0.760904i | \(-0.724756\pi\) | ||||
−0.648864 | + | 0.760904i | \(0.724756\pi\) | |||||||
\(822\) | −9.79177e105 | −0.396315 | ||||||||
\(823\) | −6.90406e105 | −0.267307 | −0.133654 | − | 0.991028i | \(-0.542671\pi\) | ||||
−0.133654 | + | 0.991028i | \(0.542671\pi\) | |||||||
\(824\) | 2.52528e105 | 0.0935333 | ||||||||
\(825\) | 1.32476e107 | 4.69426 | ||||||||
\(826\) | 4.45666e105 | 0.151091 | ||||||||
\(827\) | 4.71629e106 | 1.52985 | 0.764926 | − | 0.644119i | \(-0.222776\pi\) | ||||
0.764926 | + | 0.644119i | \(0.222776\pi\) | |||||||
\(828\) | 3.33733e106 | 1.03584 | ||||||||
\(829\) | −6.66879e106 | −1.98065 | −0.990323 | − | 0.138781i | \(-0.955682\pi\) | ||||
−0.990323 | + | 0.138781i | \(0.955682\pi\) | |||||||
\(830\) | −6.53768e105 | −0.185812 | ||||||||
\(831\) | 7.84172e106 | 2.13292 | ||||||||
\(832\) | −4.88835e105 | −0.127251 | ||||||||
\(833\) | −3.51187e106 | −0.874975 | ||||||||
\(834\) | 4.05561e106 | 0.967154 | ||||||||
\(835\) | −9.15453e106 | −2.08968 | ||||||||
\(836\) | 2.14500e106 | 0.468703 | ||||||||
\(837\) | 6.44522e104 | 0.0134821 | ||||||||
\(838\) | 3.20421e106 | 0.641673 | ||||||||
\(839\) | −3.53926e106 | −0.678579 | −0.339290 | − | 0.940682i | \(-0.610187\pi\) | ||||
−0.339290 | + | 0.940682i | \(0.610187\pi\) | |||||||
\(840\) | −1.17648e106 | −0.215968 | ||||||||
\(841\) | −4.28247e106 | −0.752731 | ||||||||
\(842\) | 4.52409e106 | 0.761447 | ||||||||
\(843\) | −1.54039e107 | −2.48270 | ||||||||
\(844\) | −1.13833e106 | −0.175698 | ||||||||
\(845\) | −4.54569e105 | −0.0671939 | ||||||||
\(846\) | −6.63006e106 | −0.938641 | ||||||||
\(847\) | 4.46314e105 | 0.0605196 | ||||||||
\(848\) | −1.38452e106 | −0.179825 | ||||||||
\(849\) | 2.59474e107 | 3.22823 | ||||||||
\(850\) | 1.30528e107 | 1.55565 | ||||||||
\(851\) | 1.13495e107 | 1.29582 | ||||||||
\(852\) | −5.85339e106 | −0.640269 | ||||||||
\(853\) | −9.52082e105 | −0.0997780 | −0.0498890 | − | 0.998755i | \(-0.515887\pi\) | ||||
−0.0498890 | + | 0.998755i | \(0.515887\pi\) | |||||||
\(854\) | 6.13237e105 | 0.0615766 | ||||||||
\(855\) | −2.94861e107 | −2.83697 | ||||||||
\(856\) | 3.31310e106 | 0.305452 | ||||||||
\(857\) | 6.55956e106 | 0.579529 | 0.289764 | − | 0.957098i | \(-0.406423\pi\) | ||||
0.289764 | + | 0.957098i | \(0.406423\pi\) | |||||||
\(858\) | −1.64996e107 | −1.39697 | ||||||||
\(859\) | −1.41476e107 | −1.14798 | −0.573989 | − | 0.818863i | \(-0.694605\pi\) | ||||
−0.573989 | + | 0.818863i | \(0.694605\pi\) | |||||||
\(860\) | −6.71884e106 | −0.522518 | ||||||||
\(861\) | 8.54799e106 | 0.637161 | ||||||||
\(862\) | −1.17612e107 | −0.840304 | ||||||||
\(863\) | 4.99653e105 | 0.0342195 | 0.0171098 | − | 0.999854i | \(-0.494554\pi\) | ||||
0.0171098 | + | 0.999854i | \(0.494554\pi\) | |||||||
\(864\) | 3.98828e106 | 0.261839 | ||||||||
\(865\) | −1.09697e107 | −0.690409 | ||||||||
\(866\) | 1.48434e107 | 0.895631 | ||||||||
\(867\) | −5.06306e106 | −0.292898 | ||||||||
\(868\) | 1.59904e104 | 0.000886928 0 | ||||||||
\(869\) | 7.53550e106 | 0.400766 | ||||||||
\(870\) | 2.16117e107 | 1.10214 | ||||||||
\(871\) | 3.36711e107 | 1.64662 | ||||||||
\(872\) | 1.34545e106 | 0.0630980 | ||||||||
\(873\) | −2.96831e107 | −1.33502 | ||||||||
\(874\) | 1.48410e107 | 0.640173 | ||||||||
\(875\) | −1.23582e107 | −0.511283 | ||||||||
\(876\) | 1.08776e107 | 0.431652 | ||||||||
\(877\) | 2.87704e107 | 1.09512 | 0.547558 | − | 0.836767i | \(-0.315557\pi\) | ||||
0.547558 | + | 0.836767i | \(0.315557\pi\) | |||||||
\(878\) | −2.55095e107 | −0.931435 | ||||||||
\(879\) | 9.45486e107 | 3.31178 | ||||||||
\(880\) | −1.57480e107 | −0.529187 | ||||||||
\(881\) | 5.29762e107 | 1.70789 | 0.853946 | − | 0.520362i | \(-0.174203\pi\) | ||||
0.853946 | + | 0.520362i | \(0.174203\pi\) | |||||||
\(882\) | −4.12082e107 | −1.27462 | ||||||||
\(883\) | 5.20945e107 | 1.54606 | 0.773030 | − | 0.634369i | \(-0.218740\pi\) | ||||
0.773030 | + | 0.634369i | \(0.218740\pi\) | |||||||
\(884\) | −1.62570e107 | −0.462948 | ||||||||
\(885\) | −1.25771e108 | −3.43678 | ||||||||
\(886\) | −2.02772e107 | −0.531713 | ||||||||
\(887\) | −6.50483e107 | −1.63691 | −0.818453 | − | 0.574574i | \(-0.805168\pi\) | ||||
−0.818453 | + | 0.574574i | \(0.805168\pi\) | |||||||
\(888\) | 2.90863e107 | 0.702448 | ||||||||
\(889\) | 9.39410e106 | 0.217741 | ||||||||
\(890\) | −1.75856e106 | −0.0391221 | ||||||||
\(891\) | 3.41603e107 | 0.729432 | ||||||||
\(892\) | 9.62499e105 | 0.0197280 | ||||||||
\(893\) | −2.94838e107 | −0.580103 | ||||||||
\(894\) | −5.17453e107 | −0.977354 | ||||||||
\(895\) | 5.83515e106 | 0.105806 | ||||||||
\(896\) | 9.89477e105 | 0.0172252 | ||||||||
\(897\) | −1.14159e108 | −1.90803 | ||||||||
\(898\) | −5.25018e107 | −0.842535 | ||||||||
\(899\) | −2.93740e105 | −0.00452621 | ||||||||
\(900\) | 1.53161e108 | 2.26620 | ||||||||
\(901\) | −4.60443e107 | −0.654216 | ||||||||
\(902\) | 1.14421e108 | 1.56123 | ||||||||
\(903\) | 1.42490e107 | 0.186716 | ||||||||
\(904\) | −4.36297e107 | −0.549079 | ||||||||
\(905\) | 2.56924e107 | 0.310549 | ||||||||
\(906\) | 1.76083e107 | 0.204427 | ||||||||
\(907\) | −5.23703e107 | −0.584008 | −0.292004 | − | 0.956417i | \(-0.594322\pi\) | ||||
−0.292004 | + | 0.956417i | \(0.594322\pi\) | |||||||
\(908\) | −6.33809e107 | −0.678929 | ||||||||
\(909\) | 7.05032e107 | 0.725483 | ||||||||
\(910\) | 2.62397e107 | 0.259387 | ||||||||
\(911\) | 6.95039e107 | 0.660067 | 0.330034 | − | 0.943969i | \(-0.392940\pi\) | ||||
0.330034 | + | 0.943969i | \(0.392940\pi\) | |||||||
\(912\) | 3.80344e107 | 0.347029 | ||||||||
\(913\) | 1.85590e107 | 0.162694 | ||||||||
\(914\) | 3.60482e107 | 0.303632 | ||||||||
\(915\) | −1.73061e108 | −1.40065 | ||||||||
\(916\) | −9.59795e106 | −0.0746438 | ||||||||
\(917\) | −2.22888e107 | −0.166573 | ||||||||
\(918\) | 1.32636e108 | 0.952586 | ||||||||
\(919\) | 1.60470e108 | 1.10759 | 0.553794 | − | 0.832654i | \(-0.313179\pi\) | ||||
0.553794 | + | 0.832654i | \(0.313179\pi\) | |||||||
\(920\) | −1.08959e108 | −0.722784 | ||||||||
\(921\) | −2.58613e108 | −1.64882 | ||||||||
\(922\) | 8.31434e107 | 0.509506 | ||||||||
\(923\) | 1.30551e108 | 0.768988 | ||||||||
\(924\) | 3.33976e107 | 0.189099 | ||||||||
\(925\) | 5.20865e108 | 2.83500 | ||||||||
\(926\) | −1.94750e108 | −1.01900 | ||||||||
\(927\) | 9.85444e107 | 0.495703 | ||||||||
\(928\) | −1.81765e107 | −0.0879042 | ||||||||
\(929\) | −1.44798e108 | −0.673268 | −0.336634 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336634 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(930\) | −4.51263e106 | −0.0201745 | ||||||||
\(931\) | −1.83252e108 | −0.787746 | ||||||||
\(932\) | −1.25435e108 | −0.518488 | ||||||||
\(933\) | 3.27964e108 | 1.30361 | ||||||||
\(934\) | 1.43836e108 | 0.549802 | ||||||||
\(935\) | −5.23725e108 | −1.92522 | ||||||||
\(936\) | −1.90759e108 | −0.674399 | ||||||||
\(937\) | −4.06681e108 | −1.38280 | −0.691400 | − | 0.722472i | \(-0.743006\pi\) | ||||
−0.691400 | + | 0.722472i | \(0.743006\pi\) | |||||||
\(938\) | −6.81554e107 | −0.222893 | ||||||||
\(939\) | 2.69388e107 | 0.0847392 | ||||||||
\(940\) | 2.16463e108 | 0.654963 | ||||||||
\(941\) | −1.02707e108 | −0.298935 | −0.149468 | − | 0.988767i | \(-0.547756\pi\) | ||||
−0.149468 | + | 0.988767i | \(0.547756\pi\) | |||||||
\(942\) | −8.03922e108 | −2.25090 | ||||||||
\(943\) | 7.91670e108 | 2.13239 | ||||||||
\(944\) | 1.05780e108 | 0.274110 | ||||||||
\(945\) | −2.14082e108 | −0.533728 | ||||||||
\(946\) | 1.90733e108 | 0.457509 | ||||||||
\(947\) | 4.82553e107 | 0.111371 | 0.0556853 | − | 0.998448i | \(-0.482266\pi\) | ||||
0.0556853 | + | 0.998448i | \(0.482266\pi\) | |||||||
\(948\) | 1.33617e108 | 0.296728 | ||||||||
\(949\) | −2.42609e108 | −0.518430 | ||||||||
\(950\) | 6.81106e108 | 1.40057 | ||||||||
\(951\) | 1.98397e108 | 0.392596 | ||||||||
\(952\) | 3.29066e107 | 0.0626663 | ||||||||
\(953\) | −7.60641e108 | −1.39408 | −0.697041 | − | 0.717031i | \(-0.745501\pi\) | ||||
−0.697041 | + | 0.717031i | \(0.745501\pi\) | |||||||
\(954\) | −5.40283e108 | −0.953028 | ||||||||
\(955\) | 1.61032e109 | 2.73394 | ||||||||
\(956\) | −5.72018e108 | −0.934752 | ||||||||
\(957\) | −6.13509e108 | −0.965017 | ||||||||
\(958\) | 6.76710e108 | 1.02462 | ||||||||
\(959\) | −4.42057e107 | −0.0644317 | ||||||||
\(960\) | −2.79240e108 | −0.391811 | ||||||||
\(961\) | −7.40232e108 | −0.999917 | ||||||||
\(962\) | −6.48727e108 | −0.843668 | ||||||||
\(963\) | 1.29288e109 | 1.61882 | ||||||||
\(964\) | −2.77389e108 | −0.334409 | ||||||||
\(965\) | 9.81707e108 | 1.13955 | ||||||||
\(966\) | 2.31075e108 | 0.258278 | ||||||||
\(967\) | −2.33112e108 | −0.250899 | −0.125449 | − | 0.992100i | \(-0.540037\pi\) | ||||
−0.125449 | + | 0.992100i | \(0.540037\pi\) | |||||||
\(968\) | 1.05933e108 | 0.109795 | ||||||||
\(969\) | 1.26489e109 | 1.26251 | ||||||||
\(970\) | 9.69114e108 | 0.931551 | ||||||||
\(971\) | 3.57624e108 | 0.331074 | 0.165537 | − | 0.986204i | \(-0.447064\pi\) | ||||
0.165537 | + | 0.986204i | \(0.447064\pi\) | |||||||
\(972\) | −2.24891e108 | −0.200518 | ||||||||
\(973\) | 1.83094e108 | 0.157237 | ||||||||
\(974\) | 1.23010e109 | 1.01751 | ||||||||
\(975\) | −5.23915e109 | −4.17438 | ||||||||
\(976\) | 1.45553e108 | 0.111713 | ||||||||
\(977\) | −3.42553e108 | −0.253266 | −0.126633 | − | 0.991950i | \(-0.540417\pi\) | ||||
−0.126633 | + | 0.991950i | \(0.540417\pi\) | |||||||
\(978\) | 1.57246e109 | 1.11998 | ||||||||
\(979\) | 4.99216e107 | 0.0342547 | ||||||||
\(980\) | 1.34539e109 | 0.889401 | ||||||||
\(981\) | 5.25037e108 | 0.334404 | ||||||||
\(982\) | −9.94134e108 | −0.610064 | ||||||||
\(983\) | −1.73690e108 | −0.102700 | −0.0513502 | − | 0.998681i | \(-0.516352\pi\) | ||||
−0.0513502 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(984\) | 2.02888e109 | 1.15594 | ||||||||
\(985\) | −2.87879e109 | −1.58047 | ||||||||
\(986\) | −6.04488e108 | −0.319801 | ||||||||
\(987\) | −4.59063e108 | −0.234043 | ||||||||
\(988\) | −8.48303e108 | −0.416795 | ||||||||
\(989\) | 1.31966e109 | 0.624883 | ||||||||
\(990\) | −6.14539e109 | −2.80456 | ||||||||
\(991\) | −1.78550e109 | −0.785363 | −0.392682 | − | 0.919675i | \(-0.628453\pi\) | ||||
−0.392682 | + | 0.919675i | \(0.628453\pi\) | |||||||
\(992\) | 3.79534e106 | 0.00160907 | ||||||||
\(993\) | 2.02088e109 | 0.825834 | ||||||||
\(994\) | −2.64256e108 | −0.104093 | ||||||||
\(995\) | −4.64690e109 | −1.76450 | ||||||||
\(996\) | 3.29083e108 | 0.120459 | ||||||||
\(997\) | 6.27538e108 | 0.221446 | 0.110723 | − | 0.993851i | \(-0.464683\pi\) | ||||
0.110723 | + | 0.993851i | \(0.464683\pi\) | |||||||
\(998\) | 1.75997e108 | 0.0598742 | ||||||||
\(999\) | 5.29279e109 | 1.73598 |
(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 | 2.74.a.b.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.74.a.b.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |