Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,70,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, 70, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 70);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 70 \) |
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: | \(30.1514953292\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 94\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.28427e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.33859e10 | 1.37413 | 0.687066 | − | 0.726595i | \(-0.258899\pi\) | ||||
0.687066 | + | 0.726595i | \(0.258899\pi\) | |||||||
\(3\) | −1.33163e16 | −0.460998 | −0.230499 | − | 0.973073i | \(-0.574036\pi\) | ||||
−0.230499 | + | 0.973073i | \(0.574036\pi\) | |||||||
\(4\) | 5.24322e20 | 0.888236 | ||||||||
\(5\) | 1.09328e24 | 0.839971 | 0.419986 | − | 0.907531i | \(-0.362035\pi\) | ||||
0.419986 | + | 0.907531i | \(0.362035\pi\) | |||||||
\(6\) | −4.44575e26 | −0.633472 | ||||||||
\(7\) | −1.48686e29 | −1.03846 | −0.519228 | − | 0.854635i | \(-0.673781\pi\) | ||||
−0.519228 | + | 0.854635i | \(0.673781\pi\) | |||||||
\(8\) | −2.20259e30 | −0.153578 | ||||||||
\(9\) | −6.57062e32 | −0.787481 | ||||||||
\(10\) | 3.65000e34 | 1.15423 | ||||||||
\(11\) | 3.06873e35 | 0.362168 | 0.181084 | − | 0.983468i | \(-0.442039\pi\) | ||||
0.181084 | + | 0.983468i | \(0.442039\pi\) | |||||||
\(12\) | −6.98201e36 | −0.409475 | ||||||||
\(13\) | 1.14858e38 | 0.425712 | 0.212856 | − | 0.977084i | \(-0.431723\pi\) | ||||
0.212856 | + | 0.977084i | \(0.431723\pi\) | |||||||
\(14\) | −4.96402e39 | −1.42698 | ||||||||
\(15\) | −1.45583e40 | −0.387225 | ||||||||
\(16\) | −3.83041e41 | −1.09927 | ||||||||
\(17\) | −4.51308e42 | −1.59950 | −0.799752 | − | 0.600331i | \(-0.795036\pi\) | ||||
−0.799752 | + | 0.600331i | \(0.795036\pi\) | |||||||
\(18\) | −2.19366e43 | −1.08210 | ||||||||
\(19\) | 1.29128e44 | 0.986331 | 0.493165 | − | 0.869936i | \(-0.335840\pi\) | ||||
0.493165 | + | 0.869936i | \(0.335840\pi\) | |||||||
\(20\) | 5.73229e44 | 0.746093 | ||||||||
\(21\) | 1.97994e45 | 0.478726 | ||||||||
\(22\) | 1.02452e46 | 0.497667 | ||||||||
\(23\) | −1.62820e47 | −1.70646 | −0.853232 | − | 0.521531i | \(-0.825361\pi\) | ||||
−0.853232 | + | 0.521531i | \(0.825361\pi\) | |||||||
\(24\) | 2.93302e46 | 0.0707991 | ||||||||
\(25\) | −4.98815e47 | −0.294448 | ||||||||
\(26\) | 3.83464e48 | 0.584984 | ||||||||
\(27\) | 1.98605e49 | 0.824025 | ||||||||
\(28\) | −7.79595e49 | −0.922395 | ||||||||
\(29\) | −5.30666e50 | −1.87107 | −0.935536 | − | 0.353232i | \(-0.885083\pi\) | ||||
−0.935536 | + | 0.353232i | \(0.885083\pi\) | |||||||
\(30\) | −4.86043e50 | −0.532098 | ||||||||
\(31\) | 1.03303e51 | 0.364866 | 0.182433 | − | 0.983218i | \(-0.441603\pi\) | ||||
0.182433 | + | 0.983218i | \(0.441603\pi\) | |||||||
\(32\) | −1.14880e52 | −1.35697 | ||||||||
\(33\) | −4.08640e51 | −0.166959 | ||||||||
\(34\) | −1.50673e53 | −2.19793 | ||||||||
\(35\) | −1.62555e53 | −0.872274 | ||||||||
\(36\) | −3.44512e53 | −0.699469 | ||||||||
\(37\) | 3.96132e53 | 0.312522 | 0.156261 | − | 0.987716i | \(-0.450056\pi\) | ||||
0.156261 | + | 0.987716i | \(0.450056\pi\) | |||||||
\(38\) | 4.31107e54 | 1.35535 | ||||||||
\(39\) | −1.52948e54 | −0.196252 | ||||||||
\(40\) | −2.40804e54 | −0.129001 | ||||||||
\(41\) | 3.97903e55 | 0.909355 | 0.454678 | − | 0.890656i | \(-0.349754\pi\) | ||||
0.454678 | + | 0.890656i | \(0.349754\pi\) | |||||||
\(42\) | 6.61022e55 | 0.657833 | ||||||||
\(43\) | 2.19103e56 | 0.968248 | 0.484124 | − | 0.874999i | \(-0.339138\pi\) | ||||
0.484124 | + | 0.874999i | \(0.339138\pi\) | |||||||
\(44\) | 1.60900e56 | 0.321691 | ||||||||
\(45\) | −7.18350e56 | −0.661461 | ||||||||
\(46\) | −5.43589e57 | −2.34491 | ||||||||
\(47\) | −1.05065e57 | −0.215816 | −0.107908 | − | 0.994161i | \(-0.534415\pi\) | ||||
−0.107908 | + | 0.994161i | \(0.534415\pi\) | |||||||
\(48\) | 5.10067e57 | 0.506762 | ||||||||
\(49\) | 1.60709e57 | 0.0783927 | ||||||||
\(50\) | −1.66534e58 | −0.404610 | ||||||||
\(51\) | 6.00973e58 | 0.737368 | ||||||||
\(52\) | 6.02226e58 | 0.378133 | ||||||||
\(53\) | −7.74716e58 | −0.252130 | −0.126065 | − | 0.992022i | \(-0.540235\pi\) | ||||
−0.126065 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(54\) | 6.63061e59 | 1.13232 | ||||||||
\(55\) | 3.35496e59 | 0.304211 | ||||||||
\(56\) | 3.27495e59 | 0.159484 | ||||||||
\(57\) | −1.71951e60 | −0.454696 | ||||||||
\(58\) | −1.77168e61 | −2.57110 | ||||||||
\(59\) | 4.93714e60 | 0.397266 | 0.198633 | − | 0.980074i | \(-0.436350\pi\) | ||||
0.198633 | + | 0.980074i | \(0.436350\pi\) | |||||||
\(60\) | −7.63326e60 | −0.343947 | ||||||||
\(61\) | 4.27197e61 | 1.08830 | 0.544150 | − | 0.838988i | \(-0.316852\pi\) | ||||
0.544150 | + | 0.838988i | \(0.316852\pi\) | |||||||
\(62\) | 3.44885e61 | 0.501374 | ||||||||
\(63\) | 9.76962e61 | 0.817765 | ||||||||
\(64\) | −1.57429e62 | −0.765378 | ||||||||
\(65\) | 1.25572e62 | 0.357586 | ||||||||
\(66\) | −1.36428e62 | −0.229423 | ||||||||
\(67\) | 1.10432e63 | 1.10539 | 0.552695 | − | 0.833384i | \(-0.313599\pi\) | ||||
0.552695 | + | 0.833384i | \(0.313599\pi\) | |||||||
\(68\) | −2.36631e63 | −1.42074 | ||||||||
\(69\) | 2.16815e63 | 0.786677 | ||||||||
\(70\) | −5.42705e63 | −1.19862 | ||||||||
\(71\) | −1.05763e64 | −1.43192 | −0.715962 | − | 0.698139i | \(-0.754012\pi\) | ||||
−0.715962 | + | 0.698139i | \(0.754012\pi\) | |||||||
\(72\) | 1.44724e63 | 0.120940 | ||||||||
\(73\) | 3.43414e64 | 1.78311 | 0.891556 | − | 0.452910i | \(-0.149614\pi\) | ||||
0.891556 | + | 0.452910i | \(0.149614\pi\) | |||||||
\(74\) | 1.32252e64 | 0.429446 | ||||||||
\(75\) | 6.64234e63 | 0.135740 | ||||||||
\(76\) | 6.77049e64 | 0.876095 | ||||||||
\(77\) | −4.56278e64 | −0.376096 | ||||||||
\(78\) | −5.10631e64 | −0.269676 | ||||||||
\(79\) | −3.22940e65 | −1.09897 | −0.549487 | − | 0.835502i | \(-0.685177\pi\) | ||||
−0.549487 | + | 0.835502i | \(0.685177\pi\) | |||||||
\(80\) | −4.18769e65 | −0.923357 | ||||||||
\(81\) | 2.83776e65 | 0.407607 | ||||||||
\(82\) | 1.32843e66 | 1.24957 | ||||||||
\(83\) | −1.44619e66 | −0.895427 | −0.447714 | − | 0.894177i | \(-0.647762\pi\) | ||||
−0.447714 | + | 0.894177i | \(0.647762\pi\) | |||||||
\(84\) | 1.03813e66 | 0.425222 | ||||||||
\(85\) | −4.93404e66 | −1.34354 | ||||||||
\(86\) | 7.31495e66 | 1.33050 | ||||||||
\(87\) | 7.06649e66 | 0.862560 | ||||||||
\(88\) | −6.75914e65 | −0.0556211 | ||||||||
\(89\) | 1.81631e67 | 1.01213 | 0.506064 | − | 0.862496i | \(-0.331100\pi\) | ||||
0.506064 | + | 0.862496i | \(0.331100\pi\) | |||||||
\(90\) | −2.39828e67 | −0.908935 | ||||||||
\(91\) | −1.70778e67 | −0.442084 | ||||||||
\(92\) | −8.53701e67 | −1.51574 | ||||||||
\(93\) | −1.37561e67 | −0.168202 | ||||||||
\(94\) | −3.50770e67 | −0.296560 | ||||||||
\(95\) | 1.41173e68 | 0.828490 | ||||||||
\(96\) | 1.52977e68 | 0.625559 | ||||||||
\(97\) | 3.55540e68 | 1.01687 | 0.508433 | − | 0.861102i | \(-0.330225\pi\) | ||||
0.508433 | + | 0.861102i | \(0.330225\pi\) | |||||||
\(98\) | 5.36542e67 | 0.107722 | ||||||||
\(99\) | −2.01635e68 | −0.285201 | ||||||||
\(100\) | −2.61540e68 | −0.261540 | ||||||||
\(101\) | −9.36000e68 | −0.664031 | −0.332016 | − | 0.943274i | \(-0.607729\pi\) | ||||
−0.332016 | + | 0.943274i | \(0.607729\pi\) | |||||||
\(102\) | 2.00640e69 | 1.01324 | ||||||||
\(103\) | −3.11841e69 | −1.12473 | −0.562366 | − | 0.826888i | \(-0.690109\pi\) | ||||
−0.562366 | + | 0.826888i | \(0.690109\pi\) | |||||||
\(104\) | −2.52985e68 | −0.0653800 | ||||||||
\(105\) | 2.16463e69 | 0.402116 | ||||||||
\(106\) | −2.58646e69 | −0.346460 | ||||||||
\(107\) | −1.12774e70 | −1.09262 | −0.546311 | − | 0.837583i | \(-0.683968\pi\) | ||||
−0.546311 | + | 0.837583i | \(0.683968\pi\) | |||||||
\(108\) | 1.04133e70 | 0.731929 | ||||||||
\(109\) | 9.74708e69 | 0.498495 | 0.249247 | − | 0.968440i | \(-0.419817\pi\) | ||||
0.249247 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(110\) | 1.12008e70 | 0.418026 | ||||||||
\(111\) | −5.27500e69 | −0.144072 | ||||||||
\(112\) | 5.69529e70 | 1.14155 | ||||||||
\(113\) | 5.90939e70 | 0.871639 | 0.435819 | − | 0.900034i | \(-0.356459\pi\) | ||||
0.435819 | + | 0.900034i | \(0.356459\pi\) | |||||||
\(114\) | −5.74073e70 | −0.624813 | ||||||||
\(115\) | −1.78007e71 | −1.43338 | ||||||||
\(116\) | −2.78240e71 | −1.66195 | ||||||||
\(117\) | −7.54689e70 | −0.335240 | ||||||||
\(118\) | 1.64831e71 | 0.545895 | ||||||||
\(119\) | 6.71033e71 | 1.66102 | ||||||||
\(120\) | 3.20660e70 | 0.0594692 | ||||||||
\(121\) | −6.23781e71 | −0.868834 | ||||||||
\(122\) | 1.42624e72 | 1.49547 | ||||||||
\(123\) | −5.29857e71 | −0.419211 | ||||||||
\(124\) | 5.41639e71 | 0.324087 | ||||||||
\(125\) | −2.39742e72 | −1.08730 | ||||||||
\(126\) | 3.26167e72 | 1.12372 | ||||||||
\(127\) | −3.53335e72 | −0.926740 | −0.463370 | − | 0.886165i | \(-0.653360\pi\) | ||||
−0.463370 | + | 0.886165i | \(0.653360\pi\) | |||||||
\(128\) | 1.52539e72 | 0.305237 | ||||||||
\(129\) | −2.91763e72 | −0.446360 | ||||||||
\(130\) | 4.19232e72 | 0.491370 | ||||||||
\(131\) | −1.16166e73 | −1.04525 | −0.522624 | − | 0.852563i | \(-0.675047\pi\) | ||||
−0.522624 | + | 0.852563i | \(0.675047\pi\) | |||||||
\(132\) | −2.14259e72 | −0.148299 | ||||||||
\(133\) | −1.91996e73 | −1.02426 | ||||||||
\(134\) | 3.68688e73 | 1.51895 | ||||||||
\(135\) | 2.17130e73 | 0.692157 | ||||||||
\(136\) | 9.94045e72 | 0.245648 | ||||||||
\(137\) | 2.02412e73 | 0.388486 | 0.194243 | − | 0.980953i | \(-0.437775\pi\) | ||||
0.194243 | + | 0.980953i | \(0.437775\pi\) | |||||||
\(138\) | 7.23857e73 | 1.08100 | ||||||||
\(139\) | −7.74542e73 | −0.901643 | −0.450821 | − | 0.892614i | \(-0.648869\pi\) | ||||
−0.450821 | + | 0.892614i | \(0.648869\pi\) | |||||||
\(140\) | −8.52312e73 | −0.774785 | ||||||||
\(141\) | 1.39908e73 | 0.0994908 | ||||||||
\(142\) | −3.53099e74 | −1.96765 | ||||||||
\(143\) | 3.52468e73 | 0.154179 | ||||||||
\(144\) | 2.51682e74 | 0.865656 | ||||||||
\(145\) | −5.80164e74 | −1.57165 | ||||||||
\(146\) | 1.14652e75 | 2.45023 | ||||||||
\(147\) | −2.14004e73 | −0.0361389 | ||||||||
\(148\) | 2.07701e74 | 0.277594 | ||||||||
\(149\) | 3.21877e74 | 0.341007 | 0.170504 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170504 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(150\) | 2.21761e74 | 0.186525 | ||||||||
\(151\) | −2.24095e75 | −1.49874 | −0.749371 | − | 0.662150i | \(-0.769644\pi\) | ||||
−0.749371 | + | 0.662150i | \(0.769644\pi\) | |||||||
\(152\) | −2.84417e74 | −0.151479 | ||||||||
\(153\) | 2.96537e75 | 1.25958 | ||||||||
\(154\) | −1.52332e75 | −0.516806 | ||||||||
\(155\) | 1.12938e75 | 0.306477 | ||||||||
\(156\) | −8.01940e74 | −0.174318 | ||||||||
\(157\) | −3.05508e74 | −0.0532703 | −0.0266351 | − | 0.999645i | \(-0.508479\pi\) | ||||
−0.0266351 | + | 0.999645i | \(0.508479\pi\) | |||||||
\(158\) | −1.07817e76 | −1.51013 | ||||||||
\(159\) | 1.03163e75 | 0.116231 | ||||||||
\(160\) | −1.25595e76 | −1.13981 | ||||||||
\(161\) | 2.42091e76 | 1.77209 | ||||||||
\(162\) | 9.47410e75 | 0.560106 | ||||||||
\(163\) | 1.23091e76 | 0.588510 | 0.294255 | − | 0.955727i | \(-0.404929\pi\) | ||||
0.294255 | + | 0.955727i | \(0.404929\pi\) | |||||||
\(164\) | 2.08629e76 | 0.807722 | ||||||||
\(165\) | −4.46756e75 | −0.140241 | ||||||||
\(166\) | −4.82822e76 | −1.23043 | ||||||||
\(167\) | 5.42598e76 | 1.12398 | 0.561992 | − | 0.827143i | \(-0.310035\pi\) | ||||
0.561992 | + | 0.827143i | \(0.310035\pi\) | |||||||
\(168\) | −4.36100e75 | −0.0735218 | ||||||||
\(169\) | −5.96009e76 | −0.818769 | ||||||||
\(170\) | −1.64727e77 | −1.84620 | ||||||||
\(171\) | −8.48454e76 | −0.776717 | ||||||||
\(172\) | 1.14881e77 | 0.860033 | ||||||||
\(173\) | 8.73350e76 | 0.535301 | 0.267650 | − | 0.963516i | \(-0.413753\pi\) | ||||
0.267650 | + | 0.963516i | \(0.413753\pi\) | |||||||
\(174\) | 2.35921e77 | 1.18527 | ||||||||
\(175\) | 7.41669e76 | 0.305772 | ||||||||
\(176\) | −1.17545e77 | −0.398122 | ||||||||
\(177\) | −6.57442e76 | −0.183139 | ||||||||
\(178\) | 6.06392e77 | 1.39080 | ||||||||
\(179\) | −5.63287e77 | −1.06488 | −0.532439 | − | 0.846468i | \(-0.678725\pi\) | ||||
−0.532439 | + | 0.846468i | \(0.678725\pi\) | |||||||
\(180\) | −3.76647e77 | −0.587534 | ||||||||
\(181\) | 8.30874e77 | 1.07059 | 0.535296 | − | 0.844664i | \(-0.320200\pi\) | ||||
0.535296 | + | 0.844664i | \(0.320200\pi\) | |||||||
\(182\) | −5.70158e77 | −0.607481 | ||||||||
\(183\) | −5.68867e77 | −0.501704 | ||||||||
\(184\) | 3.58625e77 | 0.262075 | ||||||||
\(185\) | 4.33082e77 | 0.262510 | ||||||||
\(186\) | −4.59258e77 | −0.231132 | ||||||||
\(187\) | −1.38494e78 | −0.579290 | ||||||||
\(188\) | −5.50882e77 | −0.191696 | ||||||||
\(189\) | −2.95298e78 | −0.855714 | ||||||||
\(190\) | 4.71319e78 | 1.13845 | ||||||||
\(191\) | −2.30079e78 | −0.463688 | −0.231844 | − | 0.972753i | \(-0.574476\pi\) | ||||
−0.231844 | + | 0.972753i | \(0.574476\pi\) | |||||||
\(192\) | 2.09637e78 | 0.352837 | ||||||||
\(193\) | 8.58446e78 | 1.20777 | 0.603887 | − | 0.797070i | \(-0.293618\pi\) | ||||
0.603887 | + | 0.797070i | \(0.293618\pi\) | |||||||
\(194\) | 1.18700e79 | 1.39731 | ||||||||
\(195\) | −1.67214e78 | −0.164846 | ||||||||
\(196\) | 8.42633e77 | 0.0696312 | ||||||||
\(197\) | −2.11212e79 | −1.46431 | −0.732156 | − | 0.681137i | \(-0.761486\pi\) | ||||
−0.732156 | + | 0.681137i | \(0.761486\pi\) | |||||||
\(198\) | −6.73175e78 | −0.391903 | ||||||||
\(199\) | −2.19954e79 | −1.07622 | −0.538111 | − | 0.842874i | \(-0.680862\pi\) | ||||
−0.538111 | + | 0.842874i | \(0.680862\pi\) | |||||||
\(200\) | 1.09868e78 | 0.0452207 | ||||||||
\(201\) | −1.47055e79 | −0.509583 | ||||||||
\(202\) | −3.12492e79 | −0.912466 | ||||||||
\(203\) | 7.89028e79 | 1.94303 | ||||||||
\(204\) | 3.15104e79 | 0.654957 | ||||||||
\(205\) | 4.35017e79 | 0.763832 | ||||||||
\(206\) | −1.04111e80 | −1.54553 | ||||||||
\(207\) | 1.06983e80 | 1.34381 | ||||||||
\(208\) | −4.39953e79 | −0.467974 | ||||||||
\(209\) | 3.96260e79 | 0.357218 | ||||||||
\(210\) | 7.22679e79 | 0.552561 | ||||||||
\(211\) | −1.54836e80 | −1.00491 | −0.502455 | − | 0.864603i | \(-0.667570\pi\) | ||||
−0.502455 | + | 0.864603i | \(0.667570\pi\) | |||||||
\(212\) | −4.06201e79 | −0.223951 | ||||||||
\(213\) | 1.40837e80 | 0.660114 | ||||||||
\(214\) | −3.76507e80 | −1.50141 | ||||||||
\(215\) | 2.39540e80 | 0.813301 | ||||||||
\(216\) | −4.37445e79 | −0.126552 | ||||||||
\(217\) | −1.53597e80 | −0.378898 | ||||||||
\(218\) | 3.25415e80 | 0.684997 | ||||||||
\(219\) | −4.57298e80 | −0.822011 | ||||||||
\(220\) | 1.75908e80 | 0.270211 | ||||||||
\(221\) | −5.18364e80 | −0.680928 | ||||||||
\(222\) | −1.76111e80 | −0.197974 | ||||||||
\(223\) | 5.11766e80 | 0.492667 | 0.246333 | − | 0.969185i | \(-0.420774\pi\) | ||||
0.246333 | + | 0.969185i | \(0.420774\pi\) | |||||||
\(224\) | 1.70810e81 | 1.40915 | ||||||||
\(225\) | 3.27752e80 | 0.231872 | ||||||||
\(226\) | 1.97290e81 | 1.19775 | ||||||||
\(227\) | −3.41994e80 | −0.178290 | −0.0891450 | − | 0.996019i | \(-0.528413\pi\) | ||||
−0.0891450 | + | 0.996019i | \(0.528413\pi\) | |||||||
\(228\) | −9.01576e80 | −0.403878 | ||||||||
\(229\) | −1.35567e81 | −0.522192 | −0.261096 | − | 0.965313i | \(-0.584084\pi\) | ||||
−0.261096 | + | 0.965313i | \(0.584084\pi\) | |||||||
\(230\) | −5.94293e81 | −1.96965 | ||||||||
\(231\) | 6.07591e80 | 0.173380 | ||||||||
\(232\) | 1.16884e81 | 0.287355 | ||||||||
\(233\) | −2.21214e81 | −0.468849 | −0.234425 | − | 0.972134i | \(-0.575321\pi\) | ||||
−0.234425 | + | 0.972134i | \(0.575321\pi\) | |||||||
\(234\) | −2.51960e81 | −0.460664 | ||||||||
\(235\) | −1.14865e81 | −0.181279 | ||||||||
\(236\) | 2.58865e81 | 0.352866 | ||||||||
\(237\) | 4.30036e81 | 0.506625 | ||||||||
\(238\) | 2.24030e82 | 2.28245 | ||||||||
\(239\) | −1.28714e81 | −0.113474 | −0.0567371 | − | 0.998389i | \(-0.518070\pi\) | ||||
−0.0567371 | + | 0.998389i | \(0.518070\pi\) | |||||||
\(240\) | 5.57643e81 | 0.425666 | ||||||||
\(241\) | −5.65464e81 | −0.373953 | −0.186976 | − | 0.982364i | \(-0.559869\pi\) | ||||
−0.186976 | + | 0.982364i | \(0.559869\pi\) | |||||||
\(242\) | −2.08255e82 | −1.19389 | ||||||||
\(243\) | −2.03501e82 | −1.01193 | ||||||||
\(244\) | 2.23989e82 | 0.966668 | ||||||||
\(245\) | 1.75699e81 | 0.0658476 | ||||||||
\(246\) | −1.76898e82 | −0.576051 | ||||||||
\(247\) | 1.48314e82 | 0.419893 | ||||||||
\(248\) | −2.27533e81 | −0.0560354 | ||||||||
\(249\) | 1.92578e82 | 0.412790 | ||||||||
\(250\) | −8.00401e82 | −1.49409 | ||||||||
\(251\) | 2.72558e82 | 0.443319 | 0.221659 | − | 0.975124i | \(-0.428853\pi\) | ||||
0.221659 | + | 0.975124i | \(0.428853\pi\) | |||||||
\(252\) | 5.12243e82 | 0.726369 | ||||||||
\(253\) | −4.99650e82 | −0.618028 | ||||||||
\(254\) | −1.17964e83 | −1.27346 | ||||||||
\(255\) | 6.57029e82 | 0.619368 | ||||||||
\(256\) | 1.43856e83 | 1.18481 | ||||||||
\(257\) | 1.85886e83 | 1.33830 | 0.669151 | − | 0.743126i | \(-0.266658\pi\) | ||||
0.669151 | + | 0.743126i | \(0.266658\pi\) | |||||||
\(258\) | −9.74078e82 | −0.613358 | ||||||||
\(259\) | −5.88994e82 | −0.324541 | ||||||||
\(260\) | 6.58399e82 | 0.317621 | ||||||||
\(261\) | 3.48681e83 | 1.47343 | ||||||||
\(262\) | −3.87830e83 | −1.43631 | ||||||||
\(263\) | −1.49982e83 | −0.487040 | −0.243520 | − | 0.969896i | \(-0.578302\pi\) | ||||
−0.243520 | + | 0.969896i | \(0.578302\pi\) | |||||||
\(264\) | 9.00065e81 | 0.0256412 | ||||||||
\(265\) | −8.46978e82 | −0.211782 | ||||||||
\(266\) | −6.40997e83 | −1.40747 | ||||||||
\(267\) | −2.41865e83 | −0.466589 | ||||||||
\(268\) | 5.79021e83 | 0.981848 | ||||||||
\(269\) | −1.02493e84 | −1.52842 | −0.764210 | − | 0.644968i | \(-0.776871\pi\) | ||||
−0.764210 | + | 0.644968i | \(0.776871\pi\) | |||||||
\(270\) | 7.24908e83 | 0.951115 | ||||||||
\(271\) | 3.51588e83 | 0.406063 | 0.203031 | − | 0.979172i | \(-0.434921\pi\) | ||||
0.203031 | + | 0.979172i | \(0.434921\pi\) | |||||||
\(272\) | 1.72869e84 | 1.75829 | ||||||||
\(273\) | 2.27413e83 | 0.203800 | ||||||||
\(274\) | 6.75769e83 | 0.533831 | ||||||||
\(275\) | −1.53073e83 | −0.106640 | ||||||||
\(276\) | 1.13681e84 | 0.698755 | ||||||||
\(277\) | −2.11779e84 | −1.14903 | −0.574516 | − | 0.818494i | \(-0.694810\pi\) | ||||
−0.574516 | + | 0.818494i | \(0.694810\pi\) | |||||||
\(278\) | −2.58588e84 | −1.23898 | ||||||||
\(279\) | −6.78763e83 | −0.287325 | ||||||||
\(280\) | 3.58042e83 | 0.133962 | ||||||||
\(281\) | −1.81711e84 | −0.601192 | −0.300596 | − | 0.953752i | \(-0.597186\pi\) | ||||
−0.300596 | + | 0.953752i | \(0.597186\pi\) | |||||||
\(282\) | 4.67095e83 | 0.136713 | ||||||||
\(283\) | 7.40610e84 | 1.91848 | 0.959240 | − | 0.282591i | \(-0.0911940\pi\) | ||||
0.959240 | + | 0.282591i | \(0.0911940\pi\) | |||||||
\(284\) | −5.54538e84 | −1.27189 | ||||||||
\(285\) | −1.87990e84 | −0.381932 | ||||||||
\(286\) | 1.17675e84 | 0.211863 | ||||||||
\(287\) | −5.91626e84 | −0.944326 | ||||||||
\(288\) | 7.54832e84 | 1.06859 | ||||||||
\(289\) | 1.24067e85 | 1.55841 | ||||||||
\(290\) | −1.93693e85 | −2.15965 | ||||||||
\(291\) | −4.73446e84 | −0.468773 | ||||||||
\(292\) | 1.80059e85 | 1.58383 | ||||||||
\(293\) | 4.21629e84 | 0.329608 | 0.164804 | − | 0.986326i | \(-0.447301\pi\) | ||||
0.164804 | + | 0.986326i | \(0.447301\pi\) | |||||||
\(294\) | −7.14473e83 | −0.0496595 | ||||||||
\(295\) | 5.39765e84 | 0.333692 | ||||||||
\(296\) | −8.72516e83 | −0.0479965 | ||||||||
\(297\) | 6.09465e84 | 0.298436 | ||||||||
\(298\) | 1.07462e85 | 0.468589 | ||||||||
\(299\) | −1.87012e85 | −0.726463 | ||||||||
\(300\) | 3.48273e84 | 0.120569 | ||||||||
\(301\) | −3.25776e85 | −1.00548 | ||||||||
\(302\) | −7.48161e85 | −2.05947 | ||||||||
\(303\) | 1.24640e85 | 0.306117 | ||||||||
\(304\) | −4.94614e85 | −1.08425 | ||||||||
\(305\) | 4.67044e85 | 0.914141 | ||||||||
\(306\) | 9.90017e85 | 1.73083 | ||||||||
\(307\) | 4.27730e85 | 0.668183 | 0.334092 | − | 0.942541i | \(-0.391571\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(308\) | −2.39236e85 | −0.334062 | ||||||||
\(309\) | 4.15256e85 | 0.518499 | ||||||||
\(310\) | 3.77055e85 | 0.421140 | ||||||||
\(311\) | −9.59066e83 | −0.00958550 | −0.00479275 | − | 0.999989i | \(-0.501526\pi\) | ||||
−0.00479275 | + | 0.999989i | \(0.501526\pi\) | |||||||
\(312\) | 3.36881e84 | 0.0301400 | ||||||||
\(313\) | −9.21743e84 | −0.0738465 | −0.0369233 | − | 0.999318i | \(-0.511756\pi\) | ||||
−0.0369233 | + | 0.999318i | \(0.511756\pi\) | |||||||
\(314\) | −1.01997e85 | −0.0732003 | ||||||||
\(315\) | 1.06809e86 | 0.686899 | ||||||||
\(316\) | −1.69325e86 | −0.976149 | ||||||||
\(317\) | −2.74826e86 | −1.42074 | −0.710368 | − | 0.703831i | \(-0.751471\pi\) | ||||
−0.710368 | + | 0.703831i | \(0.751471\pi\) | |||||||
\(318\) | 3.44419e85 | 0.159717 | ||||||||
\(319\) | −1.62847e86 | −0.677643 | ||||||||
\(320\) | −1.72113e86 | −0.642895 | ||||||||
\(321\) | 1.50173e86 | 0.503696 | ||||||||
\(322\) | 8.08242e86 | 2.43508 | ||||||||
\(323\) | −5.82767e86 | −1.57764 | ||||||||
\(324\) | 1.48790e86 | 0.362052 | ||||||||
\(325\) | −5.72929e85 | −0.125350 | ||||||||
\(326\) | 4.10950e86 | 0.808690 | ||||||||
\(327\) | −1.29795e86 | −0.229805 | ||||||||
\(328\) | −8.76415e85 | −0.139657 | ||||||||
\(329\) | 1.56218e86 | 0.224116 | ||||||||
\(330\) | −1.49153e86 | −0.192709 | ||||||||
\(331\) | 2.93761e86 | 0.341924 | 0.170962 | − | 0.985278i | \(-0.445313\pi\) | ||||
0.170962 | + | 0.985278i | \(0.445313\pi\) | |||||||
\(332\) | −7.58268e86 | −0.795351 | ||||||||
\(333\) | −2.60284e86 | −0.246105 | ||||||||
\(334\) | 1.81151e87 | 1.54450 | ||||||||
\(335\) | 1.20733e87 | 0.928496 | ||||||||
\(336\) | −7.58399e86 | −0.526251 | ||||||||
\(337\) | −9.85960e85 | −0.0617487 | −0.0308743 | − | 0.999523i | \(-0.509829\pi\) | ||||
−0.0308743 | + | 0.999523i | \(0.509829\pi\) | |||||||
\(338\) | −1.98983e87 | −1.12510 | ||||||||
\(339\) | −7.86910e86 | −0.401824 | ||||||||
\(340\) | −2.58703e87 | −1.19338 | ||||||||
\(341\) | 3.17008e86 | 0.132143 | ||||||||
\(342\) | −2.83264e87 | −1.06731 | ||||||||
\(343\) | 2.80919e87 | 0.957049 | ||||||||
\(344\) | −4.82594e86 | −0.148702 | ||||||||
\(345\) | 2.37039e87 | 0.660786 | ||||||||
\(346\) | 2.91576e87 | 0.735573 | ||||||||
\(347\) | 2.16749e87 | 0.494984 | 0.247492 | − | 0.968890i | \(-0.420394\pi\) | ||||
0.247492 | + | 0.968890i | \(0.420394\pi\) | |||||||
\(348\) | 3.70512e87 | 0.766157 | ||||||||
\(349\) | 5.35272e86 | 0.100253 | 0.0501265 | − | 0.998743i | \(-0.484038\pi\) | ||||
0.0501265 | + | 0.998743i | \(0.484038\pi\) | |||||||
\(350\) | 2.47613e87 | 0.420170 | ||||||||
\(351\) | 2.28114e87 | 0.350797 | ||||||||
\(352\) | −3.52535e87 | −0.491451 | ||||||||
\(353\) | −5.11860e87 | −0.647029 | −0.323515 | − | 0.946223i | \(-0.604864\pi\) | ||||
−0.323515 | + | 0.946223i | \(0.604864\pi\) | |||||||
\(354\) | −2.19493e87 | −0.251656 | ||||||||
\(355\) | −1.15628e88 | −1.20278 | ||||||||
\(356\) | 9.52333e87 | 0.899009 | ||||||||
\(357\) | −8.93565e87 | −0.765725 | ||||||||
\(358\) | −1.88058e88 | −1.46328 | ||||||||
\(359\) | 4.89613e87 | 0.346015 | 0.173007 | − | 0.984921i | \(-0.444652\pi\) | ||||
0.173007 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(360\) | 1.58223e87 | 0.101586 | ||||||||
\(361\) | −4.65361e86 | −0.0271513 | ||||||||
\(362\) | 2.77395e88 | 1.47113 | ||||||||
\(363\) | 8.30643e87 | 0.400531 | ||||||||
\(364\) | −8.95428e87 | −0.392675 | ||||||||
\(365\) | 3.75446e88 | 1.49776 | ||||||||
\(366\) | −1.89921e88 | −0.689407 | ||||||||
\(367\) | −5.99403e88 | −1.98034 | −0.990170 | − | 0.139870i | \(-0.955332\pi\) | ||||
−0.990170 | + | 0.139870i | \(0.955332\pi\) | |||||||
\(368\) | 6.23667e88 | 1.87587 | ||||||||
\(369\) | −2.61447e88 | −0.716100 | ||||||||
\(370\) | 1.44588e88 | 0.360723 | ||||||||
\(371\) | 1.15190e88 | 0.261826 | ||||||||
\(372\) | −7.21261e87 | −0.149404 | ||||||||
\(373\) | 3.54730e88 | 0.669798 | 0.334899 | − | 0.942254i | \(-0.391298\pi\) | ||||
0.334899 | + | 0.942254i | \(0.391298\pi\) | |||||||
\(374\) | −4.62375e88 | −0.796020 | ||||||||
\(375\) | 3.19247e88 | 0.501243 | ||||||||
\(376\) | 2.31416e87 | 0.0331446 | ||||||||
\(377\) | −6.09513e88 | −0.796538 | ||||||||
\(378\) | −9.85880e88 | −1.17586 | ||||||||
\(379\) | 2.22937e88 | 0.242733 | 0.121367 | − | 0.992608i | \(-0.461272\pi\) | ||||
0.121367 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(380\) | 7.40201e88 | 0.735895 | ||||||||
\(381\) | 4.70510e88 | 0.427225 | ||||||||
\(382\) | −7.68140e88 | −0.637168 | ||||||||
\(383\) | −1.24464e89 | −0.943377 | −0.471688 | − | 0.881765i | \(-0.656355\pi\) | ||||
−0.471688 | + | 0.881765i | \(0.656355\pi\) | |||||||
\(384\) | −2.03125e88 | −0.140714 | ||||||||
\(385\) | −4.98837e88 | −0.315910 | ||||||||
\(386\) | 2.86600e89 | 1.65964 | ||||||||
\(387\) | −1.43964e89 | −0.762477 | ||||||||
\(388\) | 1.86418e89 | 0.903217 | ||||||||
\(389\) | 5.53987e88 | 0.245606 | 0.122803 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122803 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(390\) | −5.58260e88 | −0.226521 | ||||||||
\(391\) | 7.34819e89 | 2.72950 | ||||||||
\(392\) | −3.53976e87 | −0.0120394 | ||||||||
\(393\) | 1.54690e89 | 0.481857 | ||||||||
\(394\) | −7.05150e89 | −2.01216 | ||||||||
\(395\) | −3.53063e89 | −0.923107 | ||||||||
\(396\) | −1.05721e89 | −0.253326 | ||||||||
\(397\) | −4.52792e89 | −0.994549 | −0.497275 | − | 0.867593i | \(-0.665666\pi\) | ||||
−0.497275 | + | 0.867593i | \(0.665666\pi\) | |||||||
\(398\) | −7.34338e89 | −1.47887 | ||||||||
\(399\) | 2.55667e89 | 0.472183 | ||||||||
\(400\) | 1.91066e89 | 0.323679 | ||||||||
\(401\) | 8.61105e89 | 1.33837 | 0.669184 | − | 0.743097i | \(-0.266644\pi\) | ||||
0.669184 | + | 0.743097i | \(0.266644\pi\) | |||||||
\(402\) | −4.90955e89 | −0.700233 | ||||||||
\(403\) | 1.18652e89 | 0.155328 | ||||||||
\(404\) | −4.90766e89 | −0.589817 | ||||||||
\(405\) | 3.10245e89 | 0.342378 | ||||||||
\(406\) | 2.63424e90 | 2.66997 | ||||||||
\(407\) | 1.21562e89 | 0.113186 | ||||||||
\(408\) | −1.32370e89 | −0.113243 | ||||||||
\(409\) | −2.16606e90 | −1.70301 | −0.851503 | − | 0.524349i | \(-0.824309\pi\) | ||||
−0.851503 | + | 0.524349i | \(0.824309\pi\) | |||||||
\(410\) | 1.45234e90 | 1.04961 | ||||||||
\(411\) | −2.69537e89 | −0.179091 | ||||||||
\(412\) | −1.63505e90 | −0.999028 | ||||||||
\(413\) | −7.34085e89 | −0.412543 | ||||||||
\(414\) | 3.57172e90 | 1.84657 | ||||||||
\(415\) | −1.58108e90 | −0.752133 | ||||||||
\(416\) | −1.31949e90 | −0.577677 | ||||||||
\(417\) | 1.03140e90 | 0.415656 | ||||||||
\(418\) | 1.32295e90 | 0.490864 | ||||||||
\(419\) | −4.26463e90 | −1.45713 | −0.728564 | − | 0.684978i | \(-0.759812\pi\) | ||||
−0.728564 | + | 0.684978i | \(0.759812\pi\) | |||||||
\(420\) | 1.13496e90 | 0.357174 | ||||||||
\(421\) | 2.14948e90 | 0.623161 | 0.311580 | − | 0.950220i | \(-0.399142\pi\) | ||||
0.311580 | + | 0.950220i | \(0.399142\pi\) | |||||||
\(422\) | −5.16934e90 | −1.38088 | ||||||||
\(423\) | 6.90346e89 | 0.169951 | ||||||||
\(424\) | 1.70638e89 | 0.0387216 | ||||||||
\(425\) | 2.25119e90 | 0.470971 | ||||||||
\(426\) | 4.70195e90 | 0.907083 | ||||||||
\(427\) | −6.35183e90 | −1.13015 | ||||||||
\(428\) | −5.91301e90 | −0.970506 | ||||||||
\(429\) | −4.69356e89 | −0.0710764 | ||||||||
\(430\) | 7.99726e90 | 1.11758 | ||||||||
\(431\) | 1.33305e91 | 1.71942 | 0.859709 | − | 0.510784i | \(-0.170645\pi\) | ||||
0.859709 | + | 0.510784i | \(0.170645\pi\) | |||||||
\(432\) | −7.60738e90 | −0.905828 | ||||||||
\(433\) | 1.51128e91 | 1.66155 | 0.830775 | − | 0.556609i | \(-0.187898\pi\) | ||||
0.830775 | + | 0.556609i | \(0.187898\pi\) | |||||||
\(434\) | −5.12797e90 | −0.520655 | ||||||||
\(435\) | 7.72562e90 | 0.724526 | ||||||||
\(436\) | 5.11061e90 | 0.442781 | ||||||||
\(437\) | −2.10247e91 | −1.68314 | ||||||||
\(438\) | −1.52673e91 | −1.12955 | ||||||||
\(439\) | 2.64868e90 | 0.181135 | 0.0905676 | − | 0.995890i | \(-0.471132\pi\) | ||||
0.0905676 | + | 0.995890i | \(0.471132\pi\) | |||||||
\(440\) | −7.38960e89 | −0.0467201 | ||||||||
\(441\) | −1.05596e90 | −0.0617327 | ||||||||
\(442\) | −1.73060e91 | −0.935684 | ||||||||
\(443\) | −2.29504e91 | −1.14779 | −0.573895 | − | 0.818929i | \(-0.694568\pi\) | ||||
−0.573895 | + | 0.818929i | \(0.694568\pi\) | |||||||
\(444\) | −2.76580e90 | −0.127970 | ||||||||
\(445\) | 1.98573e91 | 0.850158 | ||||||||
\(446\) | 1.70858e91 | 0.676989 | ||||||||
\(447\) | −4.28620e90 | −0.157204 | ||||||||
\(448\) | 2.34075e91 | 0.794812 | ||||||||
\(449\) | 2.43709e90 | 0.0766254 | 0.0383127 | − | 0.999266i | \(-0.487802\pi\) | ||||
0.0383127 | + | 0.999266i | \(0.487802\pi\) | |||||||
\(450\) | 1.09423e91 | 0.318623 | ||||||||
\(451\) | 1.22105e91 | 0.329340 | ||||||||
\(452\) | 3.09842e91 | 0.774221 | ||||||||
\(453\) | 2.98410e91 | 0.690917 | ||||||||
\(454\) | −1.14178e91 | −0.244994 | ||||||||
\(455\) | −1.86708e91 | −0.371338 | ||||||||
\(456\) | 3.78737e90 | 0.0698313 | ||||||||
\(457\) | −1.52668e91 | −0.260999 | −0.130499 | − | 0.991448i | \(-0.541658\pi\) | ||||
−0.130499 | + | 0.991448i | \(0.541658\pi\) | |||||||
\(458\) | −4.52603e91 | −0.717560 | ||||||||
\(459\) | −8.96320e91 | −1.31803 | ||||||||
\(460\) | −9.33331e91 | −1.27318 | ||||||||
\(461\) | 8.38473e91 | 1.06122 | 0.530612 | − | 0.847615i | \(-0.321962\pi\) | ||||
0.530612 | + | 0.847615i | \(0.321962\pi\) | |||||||
\(462\) | 2.02850e91 | 0.238246 | ||||||||
\(463\) | −4.55428e91 | −0.496450 | −0.248225 | − | 0.968702i | \(-0.579847\pi\) | ||||
−0.248225 | + | 0.968702i | \(0.579847\pi\) | |||||||
\(464\) | 2.03267e92 | 2.05682 | ||||||||
\(465\) | −1.50392e91 | −0.141285 | ||||||||
\(466\) | −7.38542e91 | −0.644260 | ||||||||
\(467\) | 8.33552e91 | 0.675306 | 0.337653 | − | 0.941271i | \(-0.390367\pi\) | ||||
0.337653 | + | 0.941271i | \(0.390367\pi\) | |||||||
\(468\) | −3.95700e91 | −0.297772 | ||||||||
\(469\) | −1.64198e92 | −1.14790 | ||||||||
\(470\) | −3.83489e91 | −0.249102 | ||||||||
\(471\) | 4.06823e90 | 0.0245575 | ||||||||
\(472\) | −1.08745e91 | −0.0610112 | ||||||||
\(473\) | 6.72367e91 | 0.350669 | ||||||||
\(474\) | 1.43571e92 | 0.696169 | ||||||||
\(475\) | −6.44111e91 | −0.290423 | ||||||||
\(476\) | 3.51837e92 | 1.47537 | ||||||||
\(477\) | 5.09037e91 | 0.198548 | ||||||||
\(478\) | −4.29722e91 | −0.155928 | ||||||||
\(479\) | −3.70416e91 | −0.125059 | −0.0625294 | − | 0.998043i | \(-0.519917\pi\) | ||||
−0.0625294 | + | 0.998043i | \(0.519917\pi\) | |||||||
\(480\) | 1.67246e92 | 0.525451 | ||||||||
\(481\) | 4.54990e91 | 0.133044 | ||||||||
\(482\) | −1.88785e92 | −0.513860 | ||||||||
\(483\) | −3.22375e92 | −0.816930 | ||||||||
\(484\) | −3.27062e92 | −0.771730 | ||||||||
\(485\) | 3.88703e92 | 0.854138 | ||||||||
\(486\) | −6.79408e92 | −1.39053 | ||||||||
\(487\) | 2.37954e91 | 0.0453674 | 0.0226837 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226837 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(488\) | −9.40939e91 | −0.167139 | ||||||||
\(489\) | −1.63911e92 | −0.271302 | ||||||||
\(490\) | 5.86588e91 | 0.0904833 | ||||||||
\(491\) | −9.67144e92 | −1.39053 | −0.695264 | − | 0.718755i | \(-0.744712\pi\) | ||||
−0.695264 | + | 0.718755i | \(0.744712\pi\) | |||||||
\(492\) | −2.77816e92 | −0.372358 | ||||||||
\(493\) | 2.39494e93 | 2.99279 | ||||||||
\(494\) | 4.95161e92 | 0.576988 | ||||||||
\(495\) | −2.20442e92 | −0.239560 | ||||||||
\(496\) | −3.95691e92 | −0.401087 | ||||||||
\(497\) | 1.57255e93 | 1.48699 | ||||||||
\(498\) | 6.42939e92 | 0.567228 | ||||||||
\(499\) | 4.76253e92 | 0.392075 | 0.196038 | − | 0.980596i | \(-0.437193\pi\) | ||||
0.196038 | + | 0.980596i | \(0.437193\pi\) | |||||||
\(500\) | −1.25702e93 | −0.965779 | ||||||||
\(501\) | −7.22538e92 | −0.518154 | ||||||||
\(502\) | 9.09961e92 | 0.609178 | ||||||||
\(503\) | −1.36831e93 | −0.855241 | −0.427621 | − | 0.903958i | \(-0.640648\pi\) | ||||
−0.427621 | + | 0.903958i | \(0.640648\pi\) | |||||||
\(504\) | −2.15184e92 | −0.125591 | ||||||||
\(505\) | −1.02331e93 | −0.557767 | ||||||||
\(506\) | −1.66813e93 | −0.849251 | ||||||||
\(507\) | 7.93661e92 | 0.377451 | ||||||||
\(508\) | −1.85261e93 | −0.823164 | ||||||||
\(509\) | −1.95379e92 | −0.0811174 | −0.0405587 | − | 0.999177i | \(-0.512914\pi\) | ||||
−0.0405587 | + | 0.999177i | \(0.512914\pi\) | |||||||
\(510\) | 2.19355e93 | 0.851092 | ||||||||
\(511\) | −5.10609e93 | −1.85169 | ||||||||
\(512\) | 3.90234e93 | 1.32285 | ||||||||
\(513\) | 2.56456e93 | 0.812761 | ||||||||
\(514\) | 6.20598e93 | 1.83900 | ||||||||
\(515\) | −3.40928e93 | −0.944743 | ||||||||
\(516\) | −1.52978e93 | −0.396473 | ||||||||
\(517\) | −3.22417e92 | −0.0781618 | ||||||||
\(518\) | −1.96641e93 | −0.445962 | ||||||||
\(519\) | −1.16298e93 | −0.246773 | ||||||||
\(520\) | −2.76582e92 | −0.0549173 | ||||||||
\(521\) | −5.63899e92 | −0.104785 | −0.0523926 | − | 0.998627i | \(-0.516685\pi\) | ||||
−0.0523926 | + | 0.998627i | \(0.516685\pi\) | |||||||
\(522\) | 1.16410e94 | 2.02469 | ||||||||
\(523\) | 3.06121e93 | 0.498408 | 0.249204 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249204 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(524\) | −6.09084e93 | −0.928427 | ||||||||
\(525\) | −9.87625e92 | −0.140960 | ||||||||
\(526\) | −5.00727e93 | −0.669257 | ||||||||
\(527\) | −4.66213e93 | −0.583604 | ||||||||
\(528\) | 1.56526e93 | 0.183533 | ||||||||
\(529\) | 1.74066e94 | 1.91202 | ||||||||
\(530\) | −2.82771e93 | −0.291016 | ||||||||
\(531\) | −3.24401e93 | −0.312839 | ||||||||
\(532\) | −1.00668e94 | −0.909787 | ||||||||
\(533\) | 4.57023e93 | 0.387124 | ||||||||
\(534\) | −8.07487e93 | −0.641154 | ||||||||
\(535\) | −1.23293e94 | −0.917771 | ||||||||
\(536\) | −2.43237e93 | −0.169764 | ||||||||
\(537\) | 7.50087e93 | 0.490907 | ||||||||
\(538\) | −3.42184e94 | −2.10025 | ||||||||
\(539\) | 4.93172e92 | 0.0283914 | ||||||||
\(540\) | 1.13846e94 | 0.614799 | ||||||||
\(541\) | 3.42402e94 | 1.73473 | 0.867363 | − | 0.497676i | \(-0.165813\pi\) | ||||
0.867363 | + | 0.497676i | \(0.165813\pi\) | |||||||
\(542\) | 1.17381e94 | 0.557983 | ||||||||
\(543\) | −1.10641e94 | −0.493541 | ||||||||
\(544\) | 5.18461e94 | 2.17047 | ||||||||
\(545\) | 1.06562e94 | 0.418721 | ||||||||
\(546\) | 7.59238e93 | 0.280047 | ||||||||
\(547\) | −9.21148e93 | −0.318982 | −0.159491 | − | 0.987199i | \(-0.550985\pi\) | ||||
−0.159491 | + | 0.987199i | \(0.550985\pi\) | |||||||
\(548\) | 1.06129e94 | 0.345068 | ||||||||
\(549\) | −2.80695e94 | −0.857016 | ||||||||
\(550\) | −5.11047e93 | −0.146537 | ||||||||
\(551\) | −6.85241e94 | −1.84550 | ||||||||
\(552\) | −4.77555e93 | −0.120816 | ||||||||
\(553\) | 4.80168e94 | 1.14124 | ||||||||
\(554\) | −7.07045e94 | −1.57892 | ||||||||
\(555\) | −5.76703e93 | −0.121016 | ||||||||
\(556\) | −4.06110e94 | −0.800872 | ||||||||
\(557\) | 4.57947e94 | 0.848810 | 0.424405 | − | 0.905472i | \(-0.360483\pi\) | ||||
0.424405 | + | 0.905472i | \(0.360483\pi\) | |||||||
\(558\) | −2.26611e94 | −0.394822 | ||||||||
\(559\) | 2.51658e94 | 0.412195 | ||||||||
\(560\) | 6.22652e94 | 0.958867 | ||||||||
\(561\) | 1.84422e94 | 0.267051 | ||||||||
\(562\) | −6.06659e94 | −0.826117 | ||||||||
\(563\) | −7.69524e94 | −0.985558 | −0.492779 | − | 0.870154i | \(-0.664019\pi\) | ||||
−0.492779 | + | 0.870154i | \(0.664019\pi\) | |||||||
\(564\) | 7.33568e93 | 0.0883713 | ||||||||
\(565\) | 6.46059e94 | 0.732151 | ||||||||
\(566\) | 2.47259e95 | 2.63624 | ||||||||
\(567\) | −4.21935e94 | −0.423282 | ||||||||
\(568\) | 2.32952e94 | 0.219912 | ||||||||
\(569\) | −2.74215e94 | −0.243623 | −0.121811 | − | 0.992553i | \(-0.538870\pi\) | ||||
−0.121811 | + | 0.992553i | \(0.538870\pi\) | |||||||
\(570\) | −6.27620e94 | −0.524825 | ||||||||
\(571\) | −8.73385e94 | −0.687480 | −0.343740 | − | 0.939065i | \(-0.611694\pi\) | ||||
−0.343740 | + | 0.939065i | \(0.611694\pi\) | |||||||
\(572\) | 1.84807e94 | 0.136948 | ||||||||
\(573\) | 3.06379e94 | 0.213759 | ||||||||
\(574\) | −1.97520e95 | −1.29763 | ||||||||
\(575\) | 8.12170e94 | 0.502465 | ||||||||
\(576\) | 1.03441e95 | 0.602720 | ||||||||
\(577\) | −1.84195e95 | −1.01091 | −0.505456 | − | 0.862852i | \(-0.668676\pi\) | ||||
−0.505456 | + | 0.862852i | \(0.668676\pi\) | |||||||
\(578\) | 4.14210e95 | 2.14146 | ||||||||
\(579\) | −1.14313e95 | −0.556781 | ||||||||
\(580\) | −3.04193e95 | −1.39599 | ||||||||
\(581\) | 2.15028e95 | 0.929862 | ||||||||
\(582\) | −1.58064e95 | −0.644156 | ||||||||
\(583\) | −2.37739e94 | −0.0913136 | ||||||||
\(584\) | −7.56399e94 | −0.273847 | ||||||||
\(585\) | −8.25083e94 | −0.281592 | ||||||||
\(586\) | 1.40764e95 | 0.452924 | ||||||||
\(587\) | −4.28656e95 | −1.30045 | −0.650226 | − | 0.759741i | \(-0.725326\pi\) | ||||
−0.650226 | + | 0.759741i | \(0.725326\pi\) | |||||||
\(588\) | −1.12207e94 | −0.0320999 | ||||||||
\(589\) | 1.33393e95 | 0.359879 | ||||||||
\(590\) | 1.80206e95 | 0.458536 | ||||||||
\(591\) | 2.81255e95 | 0.675045 | ||||||||
\(592\) | −1.51735e95 | −0.343547 | ||||||||
\(593\) | 1.24823e95 | 0.266629 | 0.133314 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133314 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(594\) | 2.03475e95 | 0.410090 | ||||||||
\(595\) | 7.33624e95 | 1.39521 | ||||||||
\(596\) | 1.68767e95 | 0.302895 | ||||||||
\(597\) | 2.92897e95 | 0.496136 | ||||||||
\(598\) | −6.24356e95 | −0.998255 | ||||||||
\(599\) | 1.05846e95 | 0.159752 | 0.0798761 | − | 0.996805i | \(-0.474548\pi\) | ||||
0.0798761 | + | 0.996805i | \(0.474548\pi\) | |||||||
\(600\) | −1.46303e94 | −0.0208467 | ||||||||
\(601\) | 8.57967e95 | 1.15425 | 0.577127 | − | 0.816654i | \(-0.304174\pi\) | ||||
0.577127 | + | 0.816654i | \(0.304174\pi\) | |||||||
\(602\) | −1.08763e96 | −1.38167 | ||||||||
\(603\) | −7.25609e95 | −0.870474 | ||||||||
\(604\) | −1.17498e96 | −1.33124 | ||||||||
\(605\) | −6.81964e95 | −0.729796 | ||||||||
\(606\) | 4.16123e95 | 0.420645 | ||||||||
\(607\) | 4.90330e95 | 0.468250 | 0.234125 | − | 0.972206i | \(-0.424777\pi\) | ||||
0.234125 | + | 0.972206i | \(0.424777\pi\) | |||||||
\(608\) | −1.48342e96 | −1.33842 | ||||||||
\(609\) | −1.05069e96 | −0.895732 | ||||||||
\(610\) | 1.55927e96 | 1.25615 | ||||||||
\(611\) | −1.20676e95 | −0.0918755 | ||||||||
\(612\) | 1.55481e96 | 1.11880 | ||||||||
\(613\) | 1.07997e96 | 0.734556 | 0.367278 | − | 0.930111i | \(-0.380290\pi\) | ||||
0.367278 | + | 0.930111i | \(0.380290\pi\) | |||||||
\(614\) | 1.42801e96 | 0.918171 | ||||||||
\(615\) | −5.79280e95 | −0.352125 | ||||||||
\(616\) | 1.00499e95 | 0.0577601 | ||||||||
\(617\) | −6.04192e95 | −0.328350 | −0.164175 | − | 0.986431i | \(-0.552496\pi\) | ||||
−0.164175 | + | 0.986431i | \(0.552496\pi\) | |||||||
\(618\) | 1.38637e96 | 0.712486 | ||||||||
\(619\) | 2.55704e96 | 1.24283 | 0.621413 | − | 0.783483i | \(-0.286559\pi\) | ||||
0.621413 | + | 0.783483i | \(0.286559\pi\) | |||||||
\(620\) | 5.92161e95 | 0.272224 | ||||||||
\(621\) | −3.23369e96 | −1.40617 | ||||||||
\(622\) | −3.20193e94 | −0.0131717 | ||||||||
\(623\) | −2.70061e96 | −1.05105 | ||||||||
\(624\) | 5.85853e95 | 0.215735 | ||||||||
\(625\) | −1.77602e96 | −0.618852 | ||||||||
\(626\) | −3.07732e95 | −0.101475 | ||||||||
\(627\) | −5.27670e95 | −0.164677 | ||||||||
\(628\) | −1.60185e95 | −0.0473166 | ||||||||
\(629\) | −1.78778e96 | −0.499880 | ||||||||
\(630\) | 3.56591e96 | 0.943890 | ||||||||
\(631\) | 4.61934e96 | 1.15762 | 0.578812 | − | 0.815461i | \(-0.303517\pi\) | ||||
0.578812 | + | 0.815461i | \(0.303517\pi\) | |||||||
\(632\) | 7.11304e95 | 0.168778 | ||||||||
\(633\) | 2.06184e96 | 0.463261 | ||||||||
\(634\) | −9.17531e96 | −1.95228 | ||||||||
\(635\) | −3.86292e96 | −0.778435 | ||||||||
\(636\) | 5.40907e95 | 0.103241 | ||||||||
\(637\) | 1.84587e95 | 0.0333727 | ||||||||
\(638\) | −5.43679e96 | −0.931171 | ||||||||
\(639\) | 6.94928e96 | 1.12761 | ||||||||
\(640\) | 1.66767e96 | 0.256391 | ||||||||
\(641\) | −4.05240e96 | −0.590351 | −0.295176 | − | 0.955443i | \(-0.595378\pi\) | ||||
−0.295176 | + | 0.955443i | \(0.595378\pi\) | |||||||
\(642\) | 5.01367e96 | 0.692145 | ||||||||
\(643\) | 6.21130e96 | 0.812650 | 0.406325 | − | 0.913729i | \(-0.366810\pi\) | ||||
0.406325 | + | 0.913729i | \(0.366810\pi\) | |||||||
\(644\) | 1.26934e97 | 1.57403 | ||||||||
\(645\) | −3.18978e96 | −0.374930 | ||||||||
\(646\) | −1.94562e97 | −2.16788 | ||||||||
\(647\) | 1.26722e97 | 1.33861 | 0.669305 | − | 0.742988i | \(-0.266592\pi\) | ||||
0.669305 | + | 0.742988i | \(0.266592\pi\) | |||||||
\(648\) | −6.25041e95 | −0.0625995 | ||||||||
\(649\) | 1.51507e96 | 0.143877 | ||||||||
\(650\) | −1.91277e96 | −0.172248 | ||||||||
\(651\) | 2.04534e96 | 0.174671 | ||||||||
\(652\) | 6.45393e96 | 0.522736 | ||||||||
\(653\) | 1.30200e97 | 1.00024 | 0.500121 | − | 0.865956i | \(-0.333289\pi\) | ||||
0.500121 | + | 0.865956i | \(0.333289\pi\) | |||||||
\(654\) | −4.33331e96 | −0.315782 | ||||||||
\(655\) | −1.27001e97 | −0.877978 | ||||||||
\(656\) | −1.52413e97 | −0.999629 | ||||||||
\(657\) | −2.25644e97 | −1.40417 | ||||||||
\(658\) | 5.21547e96 | 0.307964 | ||||||||
\(659\) | 2.36954e96 | 0.132776 | 0.0663878 | − | 0.997794i | \(-0.478853\pi\) | ||||
0.0663878 | + | 0.997794i | \(0.478853\pi\) | |||||||
\(660\) | −2.34244e96 | −0.124567 | ||||||||
\(661\) | −3.01280e97 | −1.52062 | −0.760309 | − | 0.649561i | \(-0.774953\pi\) | ||||
−0.760309 | + | 0.649561i | \(0.774953\pi\) | |||||||
\(662\) | 9.80749e96 | 0.469848 | ||||||||
\(663\) | 6.90267e96 | 0.313906 | ||||||||
\(664\) | 3.18535e96 | 0.137518 | ||||||||
\(665\) | −2.09905e97 | −0.860351 | ||||||||
\(666\) | −8.68980e96 | −0.338181 | ||||||||
\(667\) | 8.64030e97 | 3.19292 | ||||||||
\(668\) | 2.84496e97 | 0.998364 | ||||||||
\(669\) | −6.81481e96 | −0.227118 | ||||||||
\(670\) | 4.03078e97 | 1.27588 | ||||||||
\(671\) | 1.31095e97 | 0.394148 | ||||||||
\(672\) | −2.27456e97 | −0.649616 | ||||||||
\(673\) | −2.89421e97 | −0.785255 | −0.392628 | − | 0.919698i | \(-0.628434\pi\) | ||||
−0.392628 | + | 0.919698i | \(0.628434\pi\) | |||||||
\(674\) | −3.29172e96 | −0.0848508 | ||||||||
\(675\) | −9.90671e96 | −0.242633 | ||||||||
\(676\) | −3.12501e97 | −0.727261 | ||||||||
\(677\) | 2.23424e97 | 0.494106 | 0.247053 | − | 0.969002i | \(-0.420538\pi\) | ||||
0.247053 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(678\) | −2.62717e97 | −0.552158 | ||||||||
\(679\) | −5.28639e97 | −1.05597 | ||||||||
\(680\) | 1.08677e97 | 0.206338 | ||||||||
\(681\) | 4.55409e96 | 0.0821913 | ||||||||
\(682\) | 1.05836e97 | 0.181582 | ||||||||
\(683\) | −4.84431e97 | −0.790165 | −0.395083 | − | 0.918646i | \(-0.629284\pi\) | ||||
−0.395083 | + | 0.918646i | \(0.629284\pi\) | |||||||
\(684\) | −4.44863e97 | −0.689908 | ||||||||
\(685\) | 2.21292e97 | 0.326318 | ||||||||
\(686\) | 9.37874e97 | 1.31511 | ||||||||
\(687\) | 1.80525e97 | 0.240729 | ||||||||
\(688\) | −8.39253e97 | −1.06437 | ||||||||
\(689\) | −8.89824e96 | −0.107335 | ||||||||
\(690\) | 7.91375e97 | 0.908006 | ||||||||
\(691\) | −6.77284e96 | −0.0739227 | −0.0369614 | − | 0.999317i | \(-0.511768\pi\) | ||||
−0.0369614 | + | 0.999317i | \(0.511768\pi\) | |||||||
\(692\) | 4.57917e97 | 0.475474 | ||||||||
\(693\) | 2.99803e97 | 0.296169 | ||||||||
\(694\) | 7.23637e97 | 0.680173 | ||||||||
\(695\) | −8.46788e97 | −0.757354 | ||||||||
\(696\) | −1.55646e97 | −0.132470 | ||||||||
\(697\) | −1.79577e98 | −1.45452 | ||||||||
\(698\) | 1.78705e97 | 0.137761 | ||||||||
\(699\) | 2.94574e97 | 0.216138 | ||||||||
\(700\) | 3.88873e97 | 0.271598 | ||||||||
\(701\) | 1.99785e98 | 1.32829 | 0.664144 | − | 0.747605i | \(-0.268796\pi\) | ||||
0.664144 | + | 0.747605i | \(0.268796\pi\) | |||||||
\(702\) | 7.61579e97 | 0.482042 | ||||||||
\(703\) | 5.11519e97 | 0.308250 | ||||||||
\(704\) | −4.83107e97 | −0.277196 | ||||||||
\(705\) | 1.52958e97 | 0.0835694 | ||||||||
\(706\) | −1.70889e98 | −0.889103 | ||||||||
\(707\) | 1.39170e98 | 0.689568 | ||||||||
\(708\) | −3.44712e97 | −0.162670 | ||||||||
\(709\) | −2.67263e97 | −0.120128 | −0.0600640 | − | 0.998195i | \(-0.519130\pi\) | ||||
−0.0600640 | + | 0.998195i | \(0.519130\pi\) | |||||||
\(710\) | −3.86034e98 | −1.65277 | ||||||||
\(711\) | 2.12192e98 | 0.865421 | ||||||||
\(712\) | −4.00059e97 | −0.155440 | ||||||||
\(713\) | −1.68197e98 | −0.622631 | ||||||||
\(714\) | −2.98325e98 | −1.05221 | ||||||||
\(715\) | 3.85345e97 | 0.129506 | ||||||||
\(716\) | −2.95344e98 | −0.945864 | ||||||||
\(717\) | 1.71398e97 | 0.0523113 | ||||||||
\(718\) | 1.63462e98 | 0.475470 | ||||||||
\(719\) | 7.00234e97 | 0.194132 | 0.0970659 | − | 0.995278i | \(-0.469054\pi\) | ||||
0.0970659 | + | 0.995278i | \(0.469054\pi\) | |||||||
\(720\) | 2.75157e98 | 0.727126 | ||||||||
\(721\) | 4.63665e98 | 1.16799 | ||||||||
\(722\) | −1.55365e97 | −0.0373095 | ||||||||
\(723\) | 7.52986e97 | 0.172391 | ||||||||
\(724\) | 4.35646e98 | 0.950939 | ||||||||
\(725\) | 2.64704e98 | 0.550934 | ||||||||
\(726\) | 2.77318e98 | 0.550382 | ||||||||
\(727\) | −6.73415e98 | −1.27452 | −0.637259 | − | 0.770650i | \(-0.719932\pi\) | ||||
−0.637259 | + | 0.770650i | \(0.719932\pi\) | |||||||
\(728\) | 3.76154e97 | 0.0678943 | ||||||||
\(729\) | 3.42096e97 | 0.0588909 | ||||||||
\(730\) | 1.25346e99 | 2.05812 | ||||||||
\(731\) | −9.88829e98 | −1.54872 | ||||||||
\(732\) | −2.98269e98 | −0.445632 | ||||||||
\(733\) | −2.73438e98 | −0.389737 | −0.194868 | − | 0.980829i | \(-0.562428\pi\) | ||||
−0.194868 | + | 0.980829i | \(0.562428\pi\) | |||||||
\(734\) | −2.00116e99 | −2.72125 | ||||||||
\(735\) | −2.33966e97 | −0.0303556 | ||||||||
\(736\) | 1.87047e99 | 2.31562 | ||||||||
\(737\) | 3.38887e98 | 0.400338 | ||||||||
\(738\) | −8.72863e98 | −0.984015 | ||||||||
\(739\) | −1.70145e99 | −1.83057 | −0.915286 | − | 0.402804i | \(-0.868036\pi\) | ||||
−0.915286 | + | 0.402804i | \(0.868036\pi\) | |||||||
\(740\) | 2.27074e98 | 0.233171 | ||||||||
\(741\) | −1.97499e98 | −0.193570 | ||||||||
\(742\) | 3.84571e98 | 0.359784 | ||||||||
\(743\) | 1.16332e98 | 0.103893 | 0.0519465 | − | 0.998650i | \(-0.483457\pi\) | ||||
0.0519465 | + | 0.998650i | \(0.483457\pi\) | |||||||
\(744\) | 3.02989e97 | 0.0258322 | ||||||||
\(745\) | 3.51900e98 | 0.286436 | ||||||||
\(746\) | 1.18430e99 | 0.920390 | ||||||||
\(747\) | 9.50235e98 | 0.705132 | ||||||||
\(748\) | −7.26155e98 | −0.514546 | ||||||||
\(749\) | 1.67680e99 | 1.13464 | ||||||||
\(750\) | 1.06583e99 | 0.688773 | ||||||||
\(751\) | 1.48592e98 | 0.0917099 | 0.0458550 | − | 0.998948i | \(-0.485399\pi\) | ||||
0.0458550 | + | 0.998948i | \(0.485399\pi\) | |||||||
\(752\) | 4.02443e98 | 0.237241 | ||||||||
\(753\) | −3.62946e98 | −0.204369 | ||||||||
\(754\) | −2.03491e99 | −1.09455 | ||||||||
\(755\) | −2.44997e99 | −1.25890 | ||||||||
\(756\) | −1.54831e99 | −0.760077 | ||||||||
\(757\) | 7.78263e98 | 0.365021 | 0.182511 | − | 0.983204i | \(-0.441578\pi\) | ||||
0.182511 | + | 0.983204i | \(0.441578\pi\) | |||||||
\(758\) | 7.44295e98 | 0.333548 | ||||||||
\(759\) | 6.65347e98 | 0.284910 | ||||||||
\(760\) | −3.10946e98 | −0.127238 | ||||||||
\(761\) | 3.37753e99 | 1.32077 | 0.660387 | − | 0.750926i | \(-0.270392\pi\) | ||||
0.660387 | + | 0.750926i | \(0.270392\pi\) | |||||||
\(762\) | 1.57084e99 | 0.587064 | ||||||||
\(763\) | −1.44926e99 | −0.517665 | ||||||||
\(764\) | −1.20636e99 | −0.411865 | ||||||||
\(765\) | 3.24197e99 | 1.05801 | ||||||||
\(766\) | −4.15533e99 | −1.29632 | ||||||||
\(767\) | 5.67070e98 | 0.169121 | ||||||||
\(768\) | −1.91563e99 | −0.546197 | ||||||||
\(769\) | −4.43773e99 | −1.20977 | −0.604884 | − | 0.796313i | \(-0.706781\pi\) | ||||
−0.604884 | + | 0.796313i | \(0.706781\pi\) | |||||||
\(770\) | −1.66541e99 | −0.434102 | ||||||||
\(771\) | −2.47531e99 | −0.616955 | ||||||||
\(772\) | 4.50102e99 | 1.07279 | ||||||||
\(773\) | 4.82208e99 | 1.09911 | 0.549556 | − | 0.835457i | \(-0.314797\pi\) | ||||
0.549556 | + | 0.835457i | \(0.314797\pi\) | |||||||
\(774\) | −4.80638e99 | −1.04774 | ||||||||
\(775\) | −5.15289e98 | −0.107434 | ||||||||
\(776\) | −7.83108e98 | −0.156168 | ||||||||
\(777\) | 7.84320e98 | 0.149613 | ||||||||
\(778\) | 1.84954e99 | 0.337494 | ||||||||
\(779\) | 5.13805e99 | 0.896925 | ||||||||
\(780\) | −8.76742e98 | −0.146423 | ||||||||
\(781\) | −3.24557e99 | −0.518598 | ||||||||
\(782\) | 2.45326e100 | 3.75069 | ||||||||
\(783\) | −1.05393e100 | −1.54181 | ||||||||
\(784\) | −6.15581e98 | −0.0861749 | ||||||||
\(785\) | −3.34005e98 | −0.0447455 | ||||||||
\(786\) | 5.16445e99 | 0.662134 | ||||||||
\(787\) | 7.88562e99 | 0.967626 | 0.483813 | − | 0.875171i | \(-0.339252\pi\) | ||||
0.483813 | + | 0.875171i | \(0.339252\pi\) | |||||||
\(788\) | −1.10743e100 | −1.30066 | ||||||||
\(789\) | 1.99719e99 | 0.224524 | ||||||||
\(790\) | −1.17873e100 | −1.26847 | ||||||||
\(791\) | −8.78645e99 | −0.905159 | ||||||||
\(792\) | 4.44118e98 | 0.0438005 | ||||||||
\(793\) | 4.90670e99 | 0.463303 | ||||||||
\(794\) | −1.51169e100 | −1.36664 | ||||||||
\(795\) | 1.12786e99 | 0.0976311 | ||||||||
\(796\) | −1.15327e100 | −0.955939 | ||||||||
\(797\) | −1.25803e100 | −0.998568 | −0.499284 | − | 0.866439i | \(-0.666403\pi\) | ||||
−0.499284 | + | 0.866439i | \(0.666403\pi\) | |||||||
\(798\) | 8.53568e99 | 0.648841 | ||||||||
\(799\) | 4.74169e99 | 0.345199 | ||||||||
\(800\) | 5.73037e99 | 0.399556 | ||||||||
\(801\) | −1.19343e100 | −0.797031 | ||||||||
\(802\) | 2.87488e100 | 1.83909 | ||||||||
\(803\) | 1.05384e100 | 0.645787 | ||||||||
\(804\) | −7.71040e99 | −0.452630 | ||||||||
\(805\) | 2.64672e100 | 1.48850 | ||||||||
\(806\) | 3.96129e99 | 0.213441 | ||||||||
\(807\) | 1.36483e100 | 0.704598 | ||||||||
\(808\) | 2.06162e99 | 0.101981 | ||||||||
\(809\) | −3.84669e100 | −1.82332 | −0.911660 | − | 0.410945i | \(-0.865199\pi\) | ||||
−0.911660 | + | 0.410945i | \(0.865199\pi\) | |||||||
\(810\) | 1.03578e100 | 0.470473 | ||||||||
\(811\) | −3.67612e100 | −1.60018 | −0.800092 | − | 0.599877i | \(-0.795216\pi\) | ||||
−0.800092 | + | 0.599877i | \(0.795216\pi\) | |||||||
\(812\) | 4.13705e100 | 1.72587 | ||||||||
\(813\) | −4.68183e99 | −0.187194 | ||||||||
\(814\) | 4.05846e99 | 0.155532 | ||||||||
\(815\) | 1.34572e100 | 0.494332 | ||||||||
\(816\) | −2.30197e100 | −0.810568 | ||||||||
\(817\) | 2.82924e100 | 0.955013 | ||||||||
\(818\) | −7.23159e100 | −2.34015 | ||||||||
\(819\) | 1.12212e100 | 0.348132 | ||||||||
\(820\) | 2.28089e100 | 0.678464 | ||||||||
\(821\) | −2.26554e100 | −0.646150 | −0.323075 | − | 0.946373i | \(-0.604717\pi\) | ||||
−0.323075 | + | 0.946373i | \(0.604717\pi\) | |||||||
\(822\) | −8.99872e99 | −0.246095 | ||||||||
\(823\) | −9.10937e99 | −0.238888 | −0.119444 | − | 0.992841i | \(-0.538111\pi\) | ||||
−0.119444 | + | 0.992841i | \(0.538111\pi\) | |||||||
\(824\) | 6.86858e99 | 0.172734 | ||||||||
\(825\) | 2.03835e99 | 0.0491607 | ||||||||
\(826\) | −2.45081e100 | −0.566889 | ||||||||
\(827\) | 6.95998e100 | 1.54407 | 0.772036 | − | 0.635579i | \(-0.219238\pi\) | ||||
0.772036 | + | 0.635579i | \(0.219238\pi\) | |||||||
\(828\) | 5.60935e100 | 1.19362 | ||||||||
\(829\) | −8.75117e100 | −1.78622 | −0.893110 | − | 0.449839i | \(-0.851481\pi\) | ||||
−0.893110 | + | 0.449839i | \(0.851481\pi\) | |||||||
\(830\) | −5.27858e100 | −1.03353 | ||||||||
\(831\) | 2.82011e100 | 0.529701 | ||||||||
\(832\) | −1.80820e100 | −0.325830 | ||||||||
\(833\) | −7.25293e99 | −0.125389 | ||||||||
\(834\) | 3.44342e100 | 0.571165 | ||||||||
\(835\) | 5.93210e100 | 0.944115 | ||||||||
\(836\) | 2.07768e100 | 0.317294 | ||||||||
\(837\) | 2.05164e100 | 0.300659 | ||||||||
\(838\) | −1.42379e101 | −2.00228 | ||||||||
\(839\) | −2.45769e100 | −0.331695 | −0.165848 | − | 0.986151i | \(-0.553036\pi\) | ||||
−0.165848 | + | 0.986151i | \(0.553036\pi\) | |||||||
\(840\) | −4.76778e99 | −0.0617562 | ||||||||
\(841\) | 2.01168e101 | 2.50091 | ||||||||
\(842\) | 7.17621e100 | 0.856305 | ||||||||
\(843\) | 2.41971e100 | 0.277148 | ||||||||
\(844\) | −8.11839e100 | −0.892598 | ||||||||
\(845\) | −6.51602e100 | −0.687743 | ||||||||
\(846\) | 2.30478e100 | 0.233535 | ||||||||
\(847\) | 9.27477e100 | 0.902247 | ||||||||
\(848\) | 2.96748e100 | 0.277160 | ||||||||
\(849\) | −9.86215e100 | −0.884416 | ||||||||
\(850\) | 7.51580e100 | 0.647176 | ||||||||
\(851\) | −6.44983e100 | −0.533308 | ||||||||
\(852\) | 7.38437e100 | 0.586337 | ||||||||
\(853\) | −2.04726e101 | −1.56110 | −0.780552 | − | 0.625090i | \(-0.785062\pi\) | ||||
−0.780552 | + | 0.625090i | \(0.785062\pi\) | |||||||
\(854\) | −2.12062e101 | −1.55298 | ||||||||
\(855\) | −9.27594e100 | −0.652420 | ||||||||
\(856\) | 2.48395e100 | 0.167803 | ||||||||
\(857\) | −2.37001e101 | −1.53784 | −0.768922 | − | 0.639342i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639342i | \(0.779207\pi\) | |||||||
\(858\) | −1.56699e100 | −0.0976683 | ||||||||
\(859\) | 4.04034e99 | 0.0241910 | 0.0120955 | − | 0.999927i | \(-0.496150\pi\) | ||||
0.0120955 | + | 0.999927i | \(0.496150\pi\) | |||||||
\(860\) | 1.25596e101 | 0.722403 | ||||||||
\(861\) | 7.87825e100 | 0.435332 | ||||||||
\(862\) | 4.45051e101 | 2.36271 | ||||||||
\(863\) | 1.44294e101 | 0.735998 | 0.367999 | − | 0.929826i | \(-0.380043\pi\) | ||||
0.367999 | + | 0.929826i | \(0.380043\pi\) | |||||||
\(864\) | −2.28157e101 | −1.11817 | ||||||||
\(865\) | 9.54812e100 | 0.449637 | ||||||||
\(866\) | 5.04555e101 | 2.28319 | ||||||||
\(867\) | −1.65211e101 | −0.718424 | ||||||||
\(868\) | −8.05343e100 | −0.336551 | ||||||||
\(869\) | −9.91016e100 | −0.398014 | ||||||||
\(870\) | 2.57927e101 | 0.995593 | ||||||||
\(871\) | 1.26840e101 | 0.470578 | ||||||||
\(872\) | −2.14688e100 | −0.0765577 | ||||||||
\(873\) | −2.33612e101 | −0.800763 | ||||||||
\(874\) | −7.01928e101 | −2.31285 | ||||||||
\(875\) | 3.56464e101 | 1.12911 | ||||||||
\(876\) | −2.39772e101 | −0.730140 | ||||||||
\(877\) | 1.03367e101 | 0.302618 | 0.151309 | − | 0.988486i | \(-0.451651\pi\) | ||||
0.151309 | + | 0.988486i | \(0.451651\pi\) | |||||||
\(878\) | 8.84284e100 | 0.248904 | ||||||||
\(879\) | −5.61452e100 | −0.151948 | ||||||||
\(880\) | −1.28509e101 | −0.334411 | ||||||||
\(881\) | −1.84554e100 | −0.0461801 | −0.0230900 | − | 0.999733i | \(-0.507350\pi\) | ||||
−0.0230900 | + | 0.999733i | \(0.507350\pi\) | |||||||
\(882\) | −3.52541e100 | −0.0848289 | ||||||||
\(883\) | 2.67901e100 | 0.0619911 | 0.0309956 | − | 0.999520i | \(-0.490132\pi\) | ||||
0.0309956 | + | 0.999520i | \(0.490132\pi\) | |||||||
\(884\) | −2.71790e101 | −0.604825 | ||||||||
\(885\) | −7.18766e100 | −0.153831 | ||||||||
\(886\) | −7.66221e101 | −1.57721 | ||||||||
\(887\) | 5.27008e101 | 1.04340 | 0.521701 | − | 0.853128i | \(-0.325297\pi\) | ||||
0.521701 | + | 0.853128i | \(0.325297\pi\) | |||||||
\(888\) | 1.16187e100 | 0.0221263 | ||||||||
\(889\) | 5.25360e101 | 0.962380 | ||||||||
\(890\) | 6.62954e101 | 1.16823 | ||||||||
\(891\) | 8.70830e100 | 0.147622 | ||||||||
\(892\) | 2.68330e101 | 0.437605 | ||||||||
\(893\) | −1.35669e101 | −0.212866 | ||||||||
\(894\) | −1.43099e101 | −0.216019 | ||||||||
\(895\) | −6.15828e101 | −0.894467 | ||||||||
\(896\) | −2.26805e101 | −0.316976 | ||||||||
\(897\) | 2.49030e101 | 0.334898 | ||||||||
\(898\) | 8.13644e100 | 0.105293 | ||||||||
\(899\) | −5.48193e101 | −0.682690 | ||||||||
\(900\) | 1.71848e101 | 0.205957 | ||||||||
\(901\) | 3.49635e101 | 0.403283 | ||||||||
\(902\) | 4.07660e101 | 0.452556 | ||||||||
\(903\) | 4.33812e101 | 0.463526 | ||||||||
\(904\) | −1.30160e101 | −0.133864 | ||||||||
\(905\) | 9.08374e101 | 0.899267 | ||||||||
\(906\) | 9.96270e101 | 0.949411 | ||||||||
\(907\) | −1.42836e102 | −1.31035 | −0.655173 | − | 0.755479i | \(-0.727404\pi\) | ||||
−0.655173 | + | 0.755479i | \(0.727404\pi\) | |||||||
\(908\) | −1.79315e101 | −0.158364 | ||||||||
\(909\) | 6.15011e101 | 0.522912 | ||||||||
\(910\) | −6.23340e101 | −0.510267 | ||||||||
\(911\) | −1.37535e102 | −1.08400 | −0.542000 | − | 0.840378i | \(-0.682333\pi\) | ||||
−0.542000 | + | 0.840378i | \(0.682333\pi\) | |||||||
\(912\) | 6.58641e101 | 0.499835 | ||||||||
\(913\) | −4.43795e101 | −0.324295 | ||||||||
\(914\) | −5.09695e101 | −0.358646 | ||||||||
\(915\) | −6.21928e101 | −0.421417 | ||||||||
\(916\) | −7.10809e101 | −0.463830 | ||||||||
\(917\) | 1.72723e102 | 1.08544 | ||||||||
\(918\) | −2.99245e102 | −1.81115 | ||||||||
\(919\) | −2.81280e101 | −0.163966 | −0.0819829 | − | 0.996634i | \(-0.526125\pi\) | ||||
−0.0819829 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(920\) | 3.92076e101 | 0.220136 | ||||||||
\(921\) | −5.69576e101 | −0.308031 | ||||||||
\(922\) | 2.79932e102 | 1.45826 | ||||||||
\(923\) | −1.21477e102 | −0.609587 | ||||||||
\(924\) | 3.18573e101 | 0.154002 | ||||||||
\(925\) | −1.97597e101 | −0.0920216 | ||||||||
\(926\) | −1.52049e102 | −0.682188 | ||||||||
\(927\) | 2.04899e102 | 0.885705 | ||||||||
\(928\) | 6.09628e102 | 2.53898 | ||||||||
\(929\) | 6.85921e101 | 0.275253 | 0.137626 | − | 0.990484i | \(-0.456053\pi\) | ||||
0.137626 | + | 0.990484i | \(0.456053\pi\) | |||||||
\(930\) | −5.02096e101 | −0.194144 | ||||||||
\(931\) | 2.07521e101 | 0.0773211 | ||||||||
\(932\) | −1.15987e102 | −0.416449 | ||||||||
\(933\) | 1.27712e100 | 0.00441890 | ||||||||
\(934\) | 2.78289e102 | 0.927958 | ||||||||
\(935\) | −1.51412e102 | −0.486587 | ||||||||
\(936\) | 1.66227e101 | 0.0514855 | ||||||||
\(937\) | 4.17633e102 | 1.24675 | 0.623375 | − | 0.781923i | \(-0.285761\pi\) | ||||
0.623375 | + | 0.781923i | \(0.285761\pi\) | |||||||
\(938\) | −5.48189e102 | −1.57737 | ||||||||
\(939\) | 1.22742e101 | 0.0340431 | ||||||||
\(940\) | −6.02265e101 | −0.161019 | ||||||||
\(941\) | −6.90927e102 | −1.78070 | −0.890349 | − | 0.455280i | \(-0.849539\pi\) | ||||
−0.890349 | + | 0.455280i | \(0.849539\pi\) | |||||||
\(942\) | 1.35821e101 | 0.0337452 | ||||||||
\(943\) | −6.47865e102 | −1.55178 | ||||||||
\(944\) | −1.89112e102 | −0.436703 | ||||||||
\(945\) | −3.22842e102 | −0.718776 | ||||||||
\(946\) | 2.24476e102 | 0.481865 | ||||||||
\(947\) | 2.68653e102 | 0.556055 | 0.278028 | − | 0.960573i | \(-0.410319\pi\) | ||||
0.278028 | + | 0.960573i | \(0.410319\pi\) | |||||||
\(948\) | 2.25477e102 | 0.450003 | ||||||||
\(949\) | 3.94438e102 | 0.759093 | ||||||||
\(950\) | −2.15042e102 | −0.399080 | ||||||||
\(951\) | 3.65965e102 | 0.654956 | ||||||||
\(952\) | −1.47801e102 | −0.255095 | ||||||||
\(953\) | 1.09155e103 | 1.81694 | 0.908470 | − | 0.417950i | \(-0.137251\pi\) | ||||
0.908470 | + | 0.417950i | \(0.137251\pi\) | |||||||
\(954\) | 1.69946e102 | 0.272831 | ||||||||
\(955\) | −2.51540e102 | −0.389485 | ||||||||
\(956\) | −6.74874e101 | −0.100792 | ||||||||
\(957\) | 2.16851e102 | 0.312392 | ||||||||
\(958\) | −1.23667e102 | −0.171847 | ||||||||
\(959\) | −3.00958e102 | −0.403426 | ||||||||
\(960\) | 2.29191e102 | 0.296373 | ||||||||
\(961\) | −6.94884e102 | −0.866873 | ||||||||
\(962\) | 1.51902e102 | 0.182821 | ||||||||
\(963\) | 7.40998e102 | 0.860419 | ||||||||
\(964\) | −2.96485e102 | −0.332158 | ||||||||
\(965\) | 9.38518e102 | 1.01450 | ||||||||
\(966\) | −1.07628e103 | −1.12257 | ||||||||
\(967\) | −1.75819e103 | −1.76950 | −0.884751 | − | 0.466063i | \(-0.845672\pi\) | ||||
−0.884751 | + | 0.466063i | \(0.845672\pi\) | |||||||
\(968\) | 1.37393e102 | 0.133434 | ||||||||
\(969\) | 7.76027e102 | 0.727289 | ||||||||
\(970\) | 1.29772e103 | 1.17370 | ||||||||
\(971\) | 6.68592e102 | 0.583576 | 0.291788 | − | 0.956483i | \(-0.405750\pi\) | ||||
0.291788 | + | 0.956483i | \(0.405750\pi\) | |||||||
\(972\) | −1.06700e103 | −0.898834 | ||||||||
\(973\) | 1.15164e103 | 0.936317 | ||||||||
\(974\) | 7.94430e101 | 0.0623407 | ||||||||
\(975\) | 7.62927e101 | 0.0577862 | ||||||||
\(976\) | −1.63634e103 | −1.19634 | ||||||||
\(977\) | −9.63413e102 | −0.679908 | −0.339954 | − | 0.940442i | \(-0.610411\pi\) | ||||
−0.339954 | + | 0.940442i | \(0.610411\pi\) | |||||||
\(978\) | −5.47232e102 | −0.372804 | ||||||||
\(979\) | 5.57377e102 | 0.366561 | ||||||||
\(980\) | 9.21230e101 | 0.0584882 | ||||||||
\(981\) | −6.40444e102 | −0.392555 | ||||||||
\(982\) | −3.22890e103 | −1.91077 | ||||||||
\(983\) | 5.82748e102 | 0.332954 | 0.166477 | − | 0.986045i | \(-0.446761\pi\) | ||||
0.166477 | + | 0.986045i | \(0.446761\pi\) | |||||||
\(984\) | 1.16706e102 | 0.0643815 | ||||||||
\(985\) | −2.30913e103 | −1.22998 | ||||||||
\(986\) | 7.99572e103 | 4.11248 | ||||||||
\(987\) | −2.08024e102 | −0.103317 | ||||||||
\(988\) | 7.77646e102 | 0.372964 | ||||||||
\(989\) | −3.56743e103 | −1.65228 | ||||||||
\(990\) | −7.35966e102 | −0.329187 | ||||||||
\(991\) | 2.95358e103 | 1.27587 | 0.637936 | − | 0.770090i | \(-0.279789\pi\) | ||||
0.637936 | + | 0.770090i | \(0.279789\pi\) | |||||||
\(992\) | −1.18674e103 | −0.495111 | ||||||||
\(993\) | −3.91180e102 | −0.157626 | ||||||||
\(994\) | 5.25009e103 | 2.04332 | ||||||||
\(995\) | −2.40471e103 | −0.903995 | ||||||||
\(996\) | 1.00973e103 | 0.366655 | ||||||||
\(997\) | 1.27987e103 | 0.448933 | 0.224467 | − | 0.974482i | \(-0.427936\pi\) | ||||
0.224467 | + | 0.974482i | \(0.427936\pi\) | |||||||
\(998\) | 1.59001e103 | 0.538763 | ||||||||
\(999\) | 7.86739e102 | 0.257526 |
(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 | 1.70.a.a.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 9.70.a.b.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.70.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.70.a.b.1.1 | 5 | 3.2 | odd | 2 |