Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,80,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, 80, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 80);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 80 \) |
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: | \(79.0474097443\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5157021731103247543589585180x + 141562397820564875200991893221092433132672 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{9}\cdot 5^{4}\cdot 7\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.28584e13\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.49756e11 | 0.707107 | ||||||||
\(3\) | −8.21312e18 | −1.17009 | −0.585044 | − | 0.811002i | \(-0.698923\pi\) | ||||
−0.585044 | + | 0.811002i | \(0.698923\pi\) | |||||||
\(4\) | 3.02231e23 | 0.500000 | ||||||||
\(5\) | −6.30299e27 | −1.54964 | −0.774821 | − | 0.632181i | \(-0.782160\pi\) | ||||
−0.774821 | + | 0.632181i | \(0.782160\pi\) | |||||||
\(6\) | −4.51521e30 | −0.827377 | ||||||||
\(7\) | 3.82944e33 | 1.59134 | 0.795670 | − | 0.605731i | \(-0.207119\pi\) | ||||
0.795670 | + | 0.605731i | \(0.207119\pi\) | |||||||
\(8\) | 1.66153e35 | 0.353553 | ||||||||
\(9\) | 1.81857e37 | 0.369105 | ||||||||
\(10\) | −3.46510e39 | −1.09576 | ||||||||
\(11\) | −8.25322e40 | −0.604801 | −0.302400 | − | 0.953181i | \(-0.597788\pi\) | ||||
−0.302400 | + | 0.953181i | \(0.597788\pi\) | |||||||
\(12\) | −2.48226e42 | −0.585044 | ||||||||
\(13\) | −6.74458e43 | −0.673275 | −0.336638 | − | 0.941634i | \(-0.609290\pi\) | ||||
−0.336638 | + | 0.941634i | \(0.609290\pi\) | |||||||
\(14\) | 2.10526e45 | 1.12525 | ||||||||
\(15\) | 5.17672e46 | 1.81322 | ||||||||
\(16\) | 9.13439e46 | 0.250000 | ||||||||
\(17\) | 2.03217e48 | 0.507256 | 0.253628 | − | 0.967302i | \(-0.418376\pi\) | ||||
0.253628 | + | 0.967302i | \(0.418376\pi\) | |||||||
\(18\) | 9.99767e48 | 0.260997 | ||||||||
\(19\) | 3.74962e50 | 1.15670 | 0.578349 | − | 0.815789i | \(-0.303697\pi\) | ||||
0.578349 | + | 0.815789i | \(0.303697\pi\) | |||||||
\(20\) | −1.90496e51 | −0.774821 | ||||||||
\(21\) | −3.14516e52 | −1.86201 | ||||||||
\(22\) | −4.53726e52 | −0.427659 | ||||||||
\(23\) | 8.53875e53 | 1.39042 | 0.695208 | − | 0.718808i | \(-0.255312\pi\) | ||||
0.695208 | + | 0.718808i | \(0.255312\pi\) | |||||||
\(24\) | −1.36464e54 | −0.413688 | ||||||||
\(25\) | 2.31840e55 | 1.40139 | ||||||||
\(26\) | −3.70787e55 | −0.476078 | ||||||||
\(27\) | 2.55296e56 | 0.738202 | ||||||||
\(28\) | 1.15738e57 | 0.795670 | ||||||||
\(29\) | 7.45811e57 | 1.28206 | 0.641029 | − | 0.767517i | \(-0.278508\pi\) | ||||
0.641029 | + | 0.767517i | \(0.278508\pi\) | |||||||
\(30\) | 2.84593e58 | 1.28214 | ||||||||
\(31\) | −1.19450e59 | −1.47367 | −0.736834 | − | 0.676073i | \(-0.763680\pi\) | ||||
−0.736834 | + | 0.676073i | \(0.763680\pi\) | |||||||
\(32\) | 5.02168e58 | 0.176777 | ||||||||
\(33\) | 6.77847e59 | 0.707670 | ||||||||
\(34\) | 1.11720e60 | 0.358684 | ||||||||
\(35\) | −2.41369e61 | −2.46601 | ||||||||
\(36\) | 5.49628e60 | 0.184553 | ||||||||
\(37\) | −9.28617e61 | −1.05650 | −0.528249 | − | 0.849089i | \(-0.677151\pi\) | ||||
−0.528249 | + | 0.849089i | \(0.677151\pi\) | |||||||
\(38\) | 2.06138e62 | 0.817909 | ||||||||
\(39\) | 5.53941e62 | 0.787791 | ||||||||
\(40\) | −1.04726e63 | −0.547881 | ||||||||
\(41\) | 2.58172e63 | 0.509268 | 0.254634 | − | 0.967037i | \(-0.418045\pi\) | ||||
0.254634 | + | 0.967037i | \(0.418045\pi\) | |||||||
\(42\) | −1.72907e64 | −1.31664 | ||||||||
\(43\) | −5.39380e64 | −1.62140 | −0.810701 | − | 0.585460i | \(-0.800914\pi\) | ||||
−0.810701 | + | 0.585460i | \(0.800914\pi\) | |||||||
\(44\) | −2.49438e64 | −0.302400 | ||||||||
\(45\) | −1.14624e65 | −0.571981 | ||||||||
\(46\) | 4.69423e65 | 0.983173 | ||||||||
\(47\) | −1.50875e66 | −1.35130 | −0.675651 | − | 0.737222i | \(-0.736137\pi\) | ||||
−0.675651 | + | 0.737222i | \(0.736137\pi\) | |||||||
\(48\) | −7.50218e65 | −0.292522 | ||||||||
\(49\) | 8.87373e66 | 1.53236 | ||||||||
\(50\) | 1.27456e67 | 0.990932 | ||||||||
\(51\) | −1.66904e67 | −0.593535 | ||||||||
\(52\) | −2.03843e67 | −0.336638 | ||||||||
\(53\) | −5.02607e67 | −0.391140 | −0.195570 | − | 0.980690i | \(-0.562656\pi\) | ||||
−0.195570 | + | 0.980690i | \(0.562656\pi\) | |||||||
\(54\) | 1.40350e68 | 0.521988 | ||||||||
\(55\) | 5.20200e68 | 0.937225 | ||||||||
\(56\) | 6.36275e68 | 0.562623 | ||||||||
\(57\) | −3.07961e69 | −1.35344 | ||||||||
\(58\) | 4.10014e69 | 0.906552 | ||||||||
\(59\) | −1.39145e70 | −1.56607 | −0.783037 | − | 0.621976i | \(-0.786330\pi\) | ||||
−0.783037 | + | 0.621976i | \(0.786330\pi\) | |||||||
\(60\) | 1.56457e70 | 0.906608 | ||||||||
\(61\) | −3.14906e70 | −0.949843 | −0.474921 | − | 0.880028i | \(-0.657524\pi\) | ||||
−0.474921 | + | 0.880028i | \(0.657524\pi\) | |||||||
\(62\) | −6.56684e70 | −1.04204 | ||||||||
\(63\) | 6.96409e70 | 0.587371 | ||||||||
\(64\) | 2.76070e70 | 0.125000 | ||||||||
\(65\) | 4.25110e71 | 1.04334 | ||||||||
\(66\) | 3.72650e71 | 0.500398 | ||||||||
\(67\) | 8.22074e71 | 0.609475 | 0.304738 | − | 0.952436i | \(-0.401431\pi\) | ||||
0.304738 | + | 0.952436i | \(0.401431\pi\) | |||||||
\(68\) | 6.14186e71 | 0.253628 | ||||||||
\(69\) | −7.01298e72 | −1.62691 | ||||||||
\(70\) | −1.32694e73 | −1.74373 | ||||||||
\(71\) | 7.87577e72 | 0.591001 | 0.295500 | − | 0.955343i | \(-0.404514\pi\) | ||||
0.295500 | + | 0.955343i | \(0.404514\pi\) | |||||||
\(72\) | 3.02161e72 | 0.130498 | ||||||||
\(73\) | 4.25972e73 | 1.06691 | 0.533456 | − | 0.845828i | \(-0.320893\pi\) | ||||
0.533456 | + | 0.845828i | \(0.320893\pi\) | |||||||
\(74\) | −5.10513e73 | −0.747057 | ||||||||
\(75\) | −1.90413e74 | −1.63975 | ||||||||
\(76\) | 1.13325e74 | 0.578349 | ||||||||
\(77\) | −3.16052e74 | −0.962443 | ||||||||
\(78\) | 3.04532e74 | 0.557053 | ||||||||
\(79\) | −3.92382e74 | −0.433949 | −0.216974 | − | 0.976177i | \(-0.569619\pi\) | ||||
−0.216974 | + | 0.976177i | \(0.569619\pi\) | |||||||
\(80\) | −5.75739e74 | −0.387410 | ||||||||
\(81\) | −2.99278e75 | −1.23287 | ||||||||
\(82\) | 1.41931e75 | 0.360107 | ||||||||
\(83\) | −4.63134e75 | −0.727985 | −0.363992 | − | 0.931402i | \(-0.618587\pi\) | ||||
−0.363992 | + | 0.931402i | \(0.618587\pi\) | |||||||
\(84\) | −9.50567e75 | −0.931003 | ||||||||
\(85\) | −1.28087e76 | −0.786066 | ||||||||
\(86\) | −2.96527e76 | −1.14650 | ||||||||
\(87\) | −6.12543e76 | −1.50012 | ||||||||
\(88\) | −1.37130e76 | −0.213829 | ||||||||
\(89\) | −5.55275e76 | −0.554119 | −0.277059 | − | 0.960853i | \(-0.589360\pi\) | ||||
−0.277059 | + | 0.960853i | \(0.589360\pi\) | |||||||
\(90\) | −6.30152e76 | −0.404451 | ||||||||
\(91\) | −2.58280e77 | −1.07141 | ||||||||
\(92\) | 2.58068e77 | 0.695208 | ||||||||
\(93\) | 9.81058e77 | 1.72432 | ||||||||
\(94\) | −8.29445e77 | −0.955515 | ||||||||
\(95\) | −2.36338e78 | −1.79247 | ||||||||
\(96\) | −4.12437e77 | −0.206844 | ||||||||
\(97\) | −3.14342e78 | −1.04693 | −0.523466 | − | 0.852047i | \(-0.675361\pi\) | ||||
−0.523466 | + | 0.852047i | \(0.675361\pi\) | |||||||
\(98\) | 4.87838e78 | 1.08354 | ||||||||
\(99\) | −1.50090e78 | −0.223235 | ||||||||
\(100\) | 7.00695e78 | 0.700695 | ||||||||
\(101\) | 2.63770e79 | 1.78045 | 0.890227 | − | 0.455517i | \(-0.150546\pi\) | ||||
0.890227 | + | 0.455517i | \(0.150546\pi\) | |||||||
\(102\) | −9.17567e78 | −0.419692 | ||||||||
\(103\) | 2.28078e79 | 0.709600 | 0.354800 | − | 0.934942i | \(-0.384549\pi\) | ||||
0.354800 | + | 0.934942i | \(0.384549\pi\) | |||||||
\(104\) | −1.12064e79 | −0.238039 | ||||||||
\(105\) | 1.98239e80 | 2.88544 | ||||||||
\(106\) | −2.76311e79 | −0.276577 | ||||||||
\(107\) | −5.16285e79 | −0.356640 | −0.178320 | − | 0.983973i | \(-0.557066\pi\) | ||||
−0.178320 | + | 0.983973i | \(0.557066\pi\) | |||||||
\(108\) | 7.71585e79 | 0.369101 | ||||||||
\(109\) | −4.16854e80 | −1.38560 | −0.692800 | − | 0.721130i | \(-0.743623\pi\) | ||||
−0.692800 | + | 0.721130i | \(0.743623\pi\) | |||||||
\(110\) | 2.85983e80 | 0.662718 | ||||||||
\(111\) | 7.62684e80 | 1.23620 | ||||||||
\(112\) | 3.49796e80 | 0.397835 | ||||||||
\(113\) | −1.74584e80 | −0.139768 | −0.0698838 | − | 0.997555i | \(-0.522263\pi\) | ||||
−0.0698838 | + | 0.997555i | \(0.522263\pi\) | |||||||
\(114\) | −1.69303e81 | −0.957025 | ||||||||
\(115\) | −5.38197e81 | −2.15465 | ||||||||
\(116\) | 2.25408e81 | 0.641029 | ||||||||
\(117\) | −1.22655e81 | −0.248509 | ||||||||
\(118\) | −7.64956e81 | −1.10738 | ||||||||
\(119\) | 7.78207e81 | 0.807217 | ||||||||
\(120\) | 8.60130e81 | 0.641069 | ||||||||
\(121\) | −1.18103e82 | −0.634216 | ||||||||
\(122\) | −1.73121e82 | −0.671640 | ||||||||
\(123\) | −2.12039e82 | −0.595888 | ||||||||
\(124\) | −3.61016e82 | −0.736834 | ||||||||
\(125\) | −4.18546e82 | −0.622010 | ||||||||
\(126\) | 3.82855e82 | 0.415334 | ||||||||
\(127\) | 4.46335e82 | 0.354335 | 0.177167 | − | 0.984181i | \(-0.443307\pi\) | ||||
0.177167 | + | 0.984181i | \(0.443307\pi\) | |||||||
\(128\) | 1.51771e82 | 0.0883883 | ||||||||
\(129\) | 4.42999e83 | 1.89718 | ||||||||
\(130\) | 2.33707e83 | 0.737750 | ||||||||
\(131\) | −2.66669e83 | −0.621952 | −0.310976 | − | 0.950418i | \(-0.600656\pi\) | ||||
−0.310976 | + | 0.950418i | \(0.600656\pi\) | |||||||
\(132\) | 2.04867e83 | 0.353835 | ||||||||
\(133\) | 1.43589e84 | 1.84070 | ||||||||
\(134\) | 4.51940e83 | 0.430964 | ||||||||
\(135\) | −1.60913e84 | −1.14395 | ||||||||
\(136\) | 3.37652e83 | 0.179342 | ||||||||
\(137\) | 2.69740e84 | 1.07271 | 0.536356 | − | 0.843992i | \(-0.319801\pi\) | ||||
0.536356 | + | 0.843992i | \(0.319801\pi\) | |||||||
\(138\) | −3.85542e84 | −1.15040 | ||||||||
\(139\) | −6.92728e84 | −1.55410 | −0.777048 | − | 0.629441i | \(-0.783284\pi\) | ||||
−0.777048 | + | 0.629441i | \(0.783284\pi\) | |||||||
\(140\) | −7.29494e84 | −1.23300 | ||||||||
\(141\) | 1.23915e85 | 1.58114 | ||||||||
\(142\) | 4.32975e84 | 0.417901 | ||||||||
\(143\) | 5.56646e84 | 0.407198 | ||||||||
\(144\) | 1.66115e84 | 0.0922763 | ||||||||
\(145\) | −4.70084e85 | −1.98673 | ||||||||
\(146\) | 2.34181e85 | 0.754420 | ||||||||
\(147\) | −7.28809e85 | −1.79300 | ||||||||
\(148\) | −2.80657e85 | −0.528249 | ||||||||
\(149\) | 8.99610e85 | 1.29777 | 0.648884 | − | 0.760888i | \(-0.275236\pi\) | ||||
0.648884 | + | 0.760888i | \(0.275236\pi\) | |||||||
\(150\) | −1.04681e86 | −1.15948 | ||||||||
\(151\) | 5.00768e85 | 0.426626 | 0.213313 | − | 0.976984i | \(-0.431575\pi\) | ||||
0.213313 | + | 0.976984i | \(0.431575\pi\) | |||||||
\(152\) | 6.23013e85 | 0.408955 | ||||||||
\(153\) | 3.69564e85 | 0.187231 | ||||||||
\(154\) | −1.73752e86 | −0.680550 | ||||||||
\(155\) | 7.52893e86 | 2.28366 | ||||||||
\(156\) | 1.67418e86 | 0.393896 | ||||||||
\(157\) | −2.12281e86 | −0.388039 | −0.194020 | − | 0.980998i | \(-0.562153\pi\) | ||||
−0.194020 | + | 0.980998i | \(0.562153\pi\) | |||||||
\(158\) | −2.15714e86 | −0.306848 | ||||||||
\(159\) | 4.12797e86 | 0.457668 | ||||||||
\(160\) | −3.16516e86 | −0.273941 | ||||||||
\(161\) | 3.26986e87 | 2.21262 | ||||||||
\(162\) | −1.64530e87 | −0.871768 | ||||||||
\(163\) | 1.08655e87 | 0.451483 | 0.225741 | − | 0.974187i | \(-0.427520\pi\) | ||||
0.225741 | + | 0.974187i | \(0.427520\pi\) | |||||||
\(164\) | 7.80276e86 | 0.254634 | ||||||||
\(165\) | −4.27246e87 | −1.09664 | ||||||||
\(166\) | −2.54611e87 | −0.514763 | ||||||||
\(167\) | −1.89691e87 | −0.302515 | −0.151257 | − | 0.988494i | \(-0.548332\pi\) | ||||
−0.151257 | + | 0.988494i | \(0.548332\pi\) | |||||||
\(168\) | −5.22580e87 | −0.658319 | ||||||||
\(169\) | −5.48623e87 | −0.546700 | ||||||||
\(170\) | −7.04168e87 | −0.555832 | ||||||||
\(171\) | 6.81893e87 | 0.426943 | ||||||||
\(172\) | −1.63018e88 | −0.810701 | ||||||||
\(173\) | −8.50105e87 | −0.336242 | −0.168121 | − | 0.985766i | \(-0.553770\pi\) | ||||
−0.168121 | + | 0.985766i | \(0.553770\pi\) | |||||||
\(174\) | −3.36749e88 | −1.06075 | ||||||||
\(175\) | 8.87819e88 | 2.23009 | ||||||||
\(176\) | −7.53881e87 | −0.151200 | ||||||||
\(177\) | 1.14281e89 | 1.83244 | ||||||||
\(178\) | −3.05266e88 | −0.391821 | ||||||||
\(179\) | 1.38245e88 | 0.142218 | 0.0711090 | − | 0.997469i | \(-0.477346\pi\) | ||||
0.0711090 | + | 0.997469i | \(0.477346\pi\) | |||||||
\(180\) | −3.46430e88 | −0.285990 | ||||||||
\(181\) | −2.33673e89 | −1.54990 | −0.774951 | − | 0.632022i | \(-0.782225\pi\) | ||||
−0.774951 | + | 0.632022i | \(0.782225\pi\) | |||||||
\(182\) | −1.41991e89 | −0.757601 | ||||||||
\(183\) | 2.58636e89 | 1.11140 | ||||||||
\(184\) | 1.41874e89 | 0.491587 | ||||||||
\(185\) | 5.85306e89 | 1.63719 | ||||||||
\(186\) | 5.39342e89 | 1.21928 | ||||||||
\(187\) | −1.67719e89 | −0.306789 | ||||||||
\(188\) | −4.55992e89 | −0.675651 | ||||||||
\(189\) | 9.77641e89 | 1.17473 | ||||||||
\(190\) | −1.29928e90 | −1.26747 | ||||||||
\(191\) | −1.09703e90 | −0.869759 | −0.434880 | − | 0.900489i | \(-0.643209\pi\) | ||||
−0.434880 | + | 0.900489i | \(0.643209\pi\) | |||||||
\(192\) | −2.26739e89 | −0.146261 | ||||||||
\(193\) | 1.32482e90 | 0.696054 | 0.348027 | − | 0.937484i | \(-0.386852\pi\) | ||||
0.348027 | + | 0.937484i | \(0.386852\pi\) | |||||||
\(194\) | −1.72811e90 | −0.740292 | ||||||||
\(195\) | −3.49148e90 | −1.22079 | ||||||||
\(196\) | 2.68192e90 | 0.766180 | ||||||||
\(197\) | −6.08806e90 | −1.42253 | −0.711267 | − | 0.702922i | \(-0.751878\pi\) | ||||
−0.711267 | + | 0.702922i | \(0.751878\pi\) | |||||||
\(198\) | −8.25130e89 | −0.157851 | ||||||||
\(199\) | −5.10486e90 | −0.800363 | −0.400182 | − | 0.916436i | \(-0.631053\pi\) | ||||
−0.400182 | + | 0.916436i | \(0.631053\pi\) | |||||||
\(200\) | 3.85211e90 | 0.495466 | ||||||||
\(201\) | −6.75179e90 | −0.713139 | ||||||||
\(202\) | 1.45009e91 | 1.25897 | ||||||||
\(203\) | 2.85604e91 | 2.04019 | ||||||||
\(204\) | −5.04438e90 | −0.296767 | ||||||||
\(205\) | −1.62725e91 | −0.789183 | ||||||||
\(206\) | 1.25387e91 | 0.501763 | ||||||||
\(207\) | 1.55283e91 | 0.513210 | ||||||||
\(208\) | −6.16076e90 | −0.168319 | ||||||||
\(209\) | −3.09465e91 | −0.699572 | ||||||||
\(210\) | 1.08983e92 | 2.04032 | ||||||||
\(211\) | −1.42596e91 | −0.221285 | −0.110642 | − | 0.993860i | \(-0.535291\pi\) | ||||
−0.110642 | + | 0.993860i | \(0.535291\pi\) | |||||||
\(212\) | −1.51904e91 | −0.195570 | ||||||||
\(213\) | −6.46846e91 | −0.691523 | ||||||||
\(214\) | −2.83831e91 | −0.252183 | ||||||||
\(215\) | 3.39971e92 | 2.51259 | ||||||||
\(216\) | 4.24183e91 | 0.260994 | ||||||||
\(217\) | −4.57427e92 | −2.34511 | ||||||||
\(218\) | −2.29168e92 | −0.979767 | ||||||||
\(219\) | −3.49856e92 | −1.24838 | ||||||||
\(220\) | 1.57221e92 | 0.468612 | ||||||||
\(221\) | −1.37061e92 | −0.341523 | ||||||||
\(222\) | 4.19290e92 | 0.874122 | ||||||||
\(223\) | −2.27052e92 | −0.396355 | −0.198177 | − | 0.980166i | \(-0.563502\pi\) | ||||
−0.198177 | + | 0.980166i | \(0.563502\pi\) | |||||||
\(224\) | 1.92302e92 | 0.281312 | ||||||||
\(225\) | 4.21617e92 | 0.517260 | ||||||||
\(226\) | −9.59787e91 | −0.0988306 | ||||||||
\(227\) | −3.35766e92 | −0.290413 | −0.145206 | − | 0.989401i | \(-0.546385\pi\) | ||||
−0.145206 | + | 0.989401i | \(0.546385\pi\) | |||||||
\(228\) | −9.30754e92 | −0.676719 | ||||||||
\(229\) | 4.88971e92 | 0.299076 | 0.149538 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149538 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(230\) | −2.95877e93 | −1.52357 | ||||||||
\(231\) | 2.59577e93 | 1.12614 | ||||||||
\(232\) | 1.23919e93 | 0.453276 | ||||||||
\(233\) | 2.60425e92 | 0.0803754 | 0.0401877 | − | 0.999192i | \(-0.487204\pi\) | ||||
0.0401877 | + | 0.999192i | \(0.487204\pi\) | |||||||
\(234\) | −6.74302e92 | −0.175723 | ||||||||
\(235\) | 9.50964e93 | 2.09403 | ||||||||
\(236\) | −4.20539e93 | −0.783037 | ||||||||
\(237\) | 3.22268e93 | 0.507758 | ||||||||
\(238\) | 4.27824e93 | 0.570789 | ||||||||
\(239\) | 6.47603e93 | 0.732136 | 0.366068 | − | 0.930588i | \(-0.380704\pi\) | ||||
0.366068 | + | 0.930588i | \(0.380704\pi\) | |||||||
\(240\) | 4.72861e93 | 0.453304 | ||||||||
\(241\) | −7.71719e93 | −0.627749 | −0.313874 | − | 0.949465i | \(-0.601627\pi\) | ||||
−0.313874 | + | 0.949465i | \(0.601627\pi\) | |||||||
\(242\) | −6.49275e93 | −0.448458 | ||||||||
\(243\) | 1.20017e94 | 0.704359 | ||||||||
\(244\) | −9.51744e93 | −0.474921 | ||||||||
\(245\) | −5.59310e94 | −2.37461 | ||||||||
\(246\) | −1.16570e94 | −0.421357 | ||||||||
\(247\) | −2.52896e94 | −0.778777 | ||||||||
\(248\) | −1.98471e94 | −0.521021 | ||||||||
\(249\) | 3.80378e94 | 0.851806 | ||||||||
\(250\) | −2.30098e94 | −0.439827 | ||||||||
\(251\) | 5.59683e94 | 0.913756 | 0.456878 | − | 0.889529i | \(-0.348968\pi\) | ||||
0.456878 | + | 0.889529i | \(0.348968\pi\) | |||||||
\(252\) | 2.10477e94 | 0.293686 | ||||||||
\(253\) | −7.04722e94 | −0.840925 | ||||||||
\(254\) | 2.45375e94 | 0.250553 | ||||||||
\(255\) | 1.05200e95 | 0.919766 | ||||||||
\(256\) | 8.34370e93 | 0.0625000 | ||||||||
\(257\) | −2.35450e94 | −0.151196 | −0.0755982 | − | 0.997138i | \(-0.524087\pi\) | ||||
−0.0755982 | + | 0.997138i | \(0.524087\pi\) | |||||||
\(258\) | 2.43541e95 | 1.34151 | ||||||||
\(259\) | −3.55608e95 | −1.68125 | ||||||||
\(260\) | 1.28482e95 | 0.521668 | ||||||||
\(261\) | 1.35631e95 | 0.473214 | ||||||||
\(262\) | −1.46603e95 | −0.439786 | ||||||||
\(263\) | 1.52001e94 | 0.0392280 | 0.0196140 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196140 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(264\) | 1.12627e95 | 0.250199 | ||||||||
\(265\) | 3.16793e95 | 0.606126 | ||||||||
\(266\) | 7.89391e95 | 1.30157 | ||||||||
\(267\) | 4.56054e95 | 0.648368 | ||||||||
\(268\) | 2.48457e95 | 0.304738 | ||||||||
\(269\) | −1.48094e96 | −1.56792 | −0.783960 | − | 0.620812i | \(-0.786803\pi\) | ||||
−0.783960 | + | 0.620812i | \(0.786803\pi\) | |||||||
\(270\) | −8.84627e95 | −0.808894 | ||||||||
\(271\) | −2.26883e96 | −1.79273 | −0.896366 | − | 0.443315i | \(-0.853802\pi\) | ||||
−0.896366 | + | 0.443315i | \(0.853802\pi\) | |||||||
\(272\) | 1.85626e95 | 0.126814 | ||||||||
\(273\) | 2.12128e96 | 1.25364 | ||||||||
\(274\) | 1.48291e96 | 0.758521 | ||||||||
\(275\) | −1.91343e96 | −0.847562 | ||||||||
\(276\) | −2.11954e96 | −0.813455 | ||||||||
\(277\) | 4.00584e96 | 1.33273 | 0.666365 | − | 0.745625i | \(-0.267849\pi\) | ||||
0.666365 | + | 0.745625i | \(0.267849\pi\) | |||||||
\(278\) | −3.80831e96 | −1.09891 | ||||||||
\(279\) | −2.17228e96 | −0.543939 | ||||||||
\(280\) | −4.01043e96 | −0.871865 | ||||||||
\(281\) | −2.14515e96 | −0.405095 | −0.202548 | − | 0.979272i | \(-0.564922\pi\) | ||||
−0.202548 | + | 0.979272i | \(0.564922\pi\) | |||||||
\(282\) | 6.81233e96 | 1.11804 | ||||||||
\(283\) | −9.57649e96 | −1.36660 | −0.683301 | − | 0.730136i | \(-0.739456\pi\) | ||||
−0.683301 | + | 0.730136i | \(0.739456\pi\) | |||||||
\(284\) | 2.38031e96 | 0.295500 | ||||||||
\(285\) | 1.94107e97 | 2.09734 | ||||||||
\(286\) | 3.06019e96 | 0.287932 | ||||||||
\(287\) | 9.88653e96 | 0.810418 | ||||||||
\(288\) | 9.13226e95 | 0.0652492 | ||||||||
\(289\) | −1.19199e97 | −0.742691 | ||||||||
\(290\) | −2.58431e97 | −1.40483 | ||||||||
\(291\) | 2.58172e97 | 1.22500 | ||||||||
\(292\) | 1.28742e97 | 0.533456 | ||||||||
\(293\) | 3.05995e97 | 1.10775 | 0.553876 | − | 0.832599i | \(-0.313148\pi\) | ||||
0.553876 | + | 0.832599i | \(0.313148\pi\) | |||||||
\(294\) | −4.00667e97 | −1.26784 | ||||||||
\(295\) | 8.77027e97 | 2.42685 | ||||||||
\(296\) | −1.54293e97 | −0.373528 | ||||||||
\(297\) | −2.10702e97 | −0.446466 | ||||||||
\(298\) | 4.94566e97 | 0.917660 | ||||||||
\(299\) | −5.75903e97 | −0.936133 | ||||||||
\(300\) | −5.75489e97 | −0.819874 | ||||||||
\(301\) | −2.06552e98 | −2.58020 | ||||||||
\(302\) | 2.75300e97 | 0.301670 | ||||||||
\(303\) | −2.16637e98 | −2.08329 | ||||||||
\(304\) | 3.42505e97 | 0.289175 | ||||||||
\(305\) | 1.98485e98 | 1.47192 | ||||||||
\(306\) | 2.03170e97 | 0.132392 | ||||||||
\(307\) | 7.77058e97 | 0.445131 | 0.222565 | − | 0.974918i | \(-0.428557\pi\) | ||||
0.222565 | + | 0.974918i | \(0.428557\pi\) | |||||||
\(308\) | −9.55209e97 | −0.481222 | ||||||||
\(309\) | −1.87323e98 | −0.830294 | ||||||||
\(310\) | 4.13907e98 | 1.61479 | ||||||||
\(311\) | 3.47624e98 | 1.19419 | 0.597097 | − | 0.802169i | \(-0.296321\pi\) | ||||
0.597097 | + | 0.802169i | \(0.296321\pi\) | |||||||
\(312\) | 9.20392e97 | 0.278526 | ||||||||
\(313\) | −2.20496e98 | −0.588029 | −0.294015 | − | 0.955801i | \(-0.594991\pi\) | ||||
−0.294015 | + | 0.955801i | \(0.594991\pi\) | |||||||
\(314\) | −1.16703e98 | −0.274385 | ||||||||
\(315\) | −4.38946e98 | −0.910215 | ||||||||
\(316\) | −1.18590e98 | −0.216974 | ||||||||
\(317\) | 7.00574e98 | 1.13139 | 0.565696 | − | 0.824614i | \(-0.308608\pi\) | ||||
0.565696 | + | 0.824614i | \(0.308608\pi\) | |||||||
\(318\) | 2.26938e98 | 0.323620 | ||||||||
\(319\) | −6.15534e98 | −0.775390 | ||||||||
\(320\) | −1.74006e98 | −0.193705 | ||||||||
\(321\) | 4.24031e98 | 0.417300 | ||||||||
\(322\) | 1.79763e99 | 1.56456 | ||||||||
\(323\) | 7.61987e98 | 0.586743 | ||||||||
\(324\) | −9.04511e98 | −0.616433 | ||||||||
\(325\) | −1.56367e99 | −0.943521 | ||||||||
\(326\) | 5.97340e98 | 0.319246 | ||||||||
\(327\) | 3.42367e99 | 1.62127 | ||||||||
\(328\) | 4.28961e98 | 0.180053 | ||||||||
\(329\) | −5.77767e99 | −2.15038 | ||||||||
\(330\) | −2.34881e99 | −0.775438 | ||||||||
\(331\) | 2.76926e99 | 0.811255 | 0.405628 | − | 0.914038i | \(-0.367053\pi\) | ||||
0.405628 | + | 0.914038i | \(0.367053\pi\) | |||||||
\(332\) | −1.39974e99 | −0.363992 | ||||||||
\(333\) | −1.68875e99 | −0.389959 | ||||||||
\(334\) | −1.04284e99 | −0.213910 | ||||||||
\(335\) | −5.18152e99 | −0.944468 | ||||||||
\(336\) | −2.87291e99 | −0.465502 | ||||||||
\(337\) | 1.60789e99 | 0.231672 | 0.115836 | − | 0.993268i | \(-0.463045\pi\) | ||||
0.115836 | + | 0.993268i | \(0.463045\pi\) | |||||||
\(338\) | −3.01609e99 | −0.386575 | ||||||||
\(339\) | 1.43388e99 | 0.163540 | ||||||||
\(340\) | −3.87120e99 | −0.393033 | ||||||||
\(341\) | 9.85849e99 | 0.891276 | ||||||||
\(342\) | 3.74875e99 | 0.301894 | ||||||||
\(343\) | 1.18055e100 | 0.847165 | ||||||||
\(344\) | −8.96199e99 | −0.573252 | ||||||||
\(345\) | 4.42027e100 | 2.52113 | ||||||||
\(346\) | −4.67350e99 | −0.237759 | ||||||||
\(347\) | −2.28429e100 | −1.03690 | −0.518450 | − | 0.855108i | \(-0.673491\pi\) | ||||
−0.518450 | + | 0.855108i | \(0.673491\pi\) | |||||||
\(348\) | −1.85130e100 | −0.750060 | ||||||||
\(349\) | −4.51784e99 | −0.163428 | −0.0817140 | − | 0.996656i | \(-0.526039\pi\) | ||||
−0.0817140 | + | 0.996656i | \(0.526039\pi\) | |||||||
\(350\) | 4.88084e100 | 1.57691 | ||||||||
\(351\) | −1.72187e100 | −0.497014 | ||||||||
\(352\) | −4.14451e99 | −0.106915 | ||||||||
\(353\) | 5.92330e100 | 1.36604 | 0.683020 | − | 0.730400i | \(-0.260666\pi\) | ||||
0.683020 | + | 0.730400i | \(0.260666\pi\) | |||||||
\(354\) | 6.28267e100 | 1.29573 | ||||||||
\(355\) | −4.96409e100 | −0.915840 | ||||||||
\(356\) | −1.67822e100 | −0.277059 | ||||||||
\(357\) | −6.39151e100 | −0.944515 | ||||||||
\(358\) | 7.60010e99 | 0.100563 | ||||||||
\(359\) | −1.17034e101 | −1.38702 | −0.693508 | − | 0.720449i | \(-0.743936\pi\) | ||||
−0.693508 | + | 0.720449i | \(0.743936\pi\) | |||||||
\(360\) | −1.90452e100 | −0.202226 | ||||||||
\(361\) | 3.55130e100 | 0.337951 | ||||||||
\(362\) | −1.28463e101 | −1.09595 | ||||||||
\(363\) | 9.69990e100 | 0.742088 | ||||||||
\(364\) | −7.80603e100 | −0.535705 | ||||||||
\(365\) | −2.68490e101 | −1.65333 | ||||||||
\(366\) | 1.42186e101 | 0.785878 | ||||||||
\(367\) | 1.67047e100 | 0.0828951 | 0.0414475 | − | 0.999141i | \(-0.486803\pi\) | ||||
0.0414475 | + | 0.999141i | \(0.486803\pi\) | |||||||
\(368\) | 7.79963e100 | 0.347604 | ||||||||
\(369\) | 4.69502e100 | 0.187973 | ||||||||
\(370\) | 3.21776e101 | 1.15767 | ||||||||
\(371\) | −1.92470e101 | −0.622436 | ||||||||
\(372\) | 2.96507e101 | 0.862161 | ||||||||
\(373\) | −1.64281e100 | −0.0429624 | −0.0214812 | − | 0.999769i | \(-0.506838\pi\) | ||||
−0.0214812 | + | 0.999769i | \(0.506838\pi\) | |||||||
\(374\) | −9.22048e100 | −0.216933 | ||||||||
\(375\) | 3.43756e101 | 0.727806 | ||||||||
\(376\) | −2.50684e101 | −0.477757 | ||||||||
\(377\) | −5.03018e101 | −0.863178 | ||||||||
\(378\) | 5.37464e101 | 0.830660 | ||||||||
\(379\) | 1.18470e102 | 1.64953 | 0.824763 | − | 0.565478i | \(-0.191308\pi\) | ||||
0.824763 | + | 0.565478i | \(0.191308\pi\) | |||||||
\(380\) | −7.14288e101 | −0.896234 | ||||||||
\(381\) | −3.66580e101 | −0.414603 | ||||||||
\(382\) | −6.03096e101 | −0.615013 | ||||||||
\(383\) | 4.39756e101 | 0.404446 | 0.202223 | − | 0.979340i | \(-0.435183\pi\) | ||||
0.202223 | + | 0.979340i | \(0.435183\pi\) | |||||||
\(384\) | −1.24651e101 | −0.103422 | ||||||||
\(385\) | 1.99207e102 | 1.49144 | ||||||||
\(386\) | 7.28327e101 | 0.492185 | ||||||||
\(387\) | −9.80898e101 | −0.598468 | ||||||||
\(388\) | −9.50039e101 | −0.523466 | ||||||||
\(389\) | −1.30405e102 | −0.649063 | −0.324531 | − | 0.945875i | \(-0.605207\pi\) | ||||
−0.324531 | + | 0.945875i | \(0.605207\pi\) | |||||||
\(390\) | −1.91946e102 | −0.863232 | ||||||||
\(391\) | 1.73522e102 | 0.705298 | ||||||||
\(392\) | 1.47440e102 | 0.541771 | ||||||||
\(393\) | 2.19019e102 | 0.727738 | ||||||||
\(394\) | −3.34694e102 | −1.00588 | ||||||||
\(395\) | 2.47318e102 | 0.672465 | ||||||||
\(396\) | −4.53620e101 | −0.111618 | ||||||||
\(397\) | −7.99431e102 | −1.78056 | −0.890278 | − | 0.455417i | \(-0.849490\pi\) | ||||
−0.890278 | + | 0.455417i | \(0.849490\pi\) | |||||||
\(398\) | −2.80642e102 | −0.565942 | ||||||||
\(399\) | −1.17932e103 | −2.15378 | ||||||||
\(400\) | 2.11772e102 | 0.350347 | ||||||||
\(401\) | −2.55804e102 | −0.383447 | −0.191724 | − | 0.981449i | \(-0.561408\pi\) | ||||
−0.191724 | + | 0.981449i | \(0.561408\pi\) | |||||||
\(402\) | −3.71183e102 | −0.504266 | ||||||||
\(403\) | 8.05642e102 | 0.992185 | ||||||||
\(404\) | 7.97195e102 | 0.890227 | ||||||||
\(405\) | 1.88634e103 | 1.91050 | ||||||||
\(406\) | 1.57012e103 | 1.44263 | ||||||||
\(407\) | 7.66409e102 | 0.638971 | ||||||||
\(408\) | −2.77318e102 | −0.209846 | ||||||||
\(409\) | 2.16051e103 | 1.48418 | 0.742090 | − | 0.670300i | \(-0.233835\pi\) | ||||
0.742090 | + | 0.670300i | \(0.233835\pi\) | |||||||
\(410\) | −8.94592e102 | −0.558037 | ||||||||
\(411\) | −2.21541e103 | −1.25517 | ||||||||
\(412\) | 6.89324e102 | 0.354800 | ||||||||
\(413\) | −5.32846e103 | −2.49215 | ||||||||
\(414\) | 8.53677e102 | 0.362894 | ||||||||
\(415\) | 2.91913e103 | 1.12812 | ||||||||
\(416\) | −3.38692e102 | −0.119019 | ||||||||
\(417\) | 5.68945e103 | 1.81843 | ||||||||
\(418\) | −1.70130e103 | −0.494672 | ||||||||
\(419\) | −5.50337e103 | −1.45604 | −0.728022 | − | 0.685554i | \(-0.759560\pi\) | ||||
−0.728022 | + | 0.685554i | \(0.759560\pi\) | |||||||
\(420\) | 5.99141e103 | 1.44272 | ||||||||
\(421\) | −6.95144e103 | −1.52381 | −0.761907 | − | 0.647686i | \(-0.775737\pi\) | ||||
−0.761907 | + | 0.647686i | \(0.775737\pi\) | |||||||
\(422\) | −7.83932e102 | −0.156472 | ||||||||
\(423\) | −2.74376e103 | −0.498772 | ||||||||
\(424\) | −8.35099e102 | −0.138289 | ||||||||
\(425\) | 4.71139e103 | 0.710864 | ||||||||
\(426\) | −3.55607e103 | −0.488981 | ||||||||
\(427\) | −1.20591e104 | −1.51152 | ||||||||
\(428\) | −1.56038e103 | −0.178320 | ||||||||
\(429\) | −4.57179e103 | −0.476457 | ||||||||
\(430\) | 1.86901e104 | 1.77667 | ||||||||
\(431\) | 3.22243e103 | 0.279468 | 0.139734 | − | 0.990189i | \(-0.455375\pi\) | ||||
0.139734 | + | 0.990189i | \(0.455375\pi\) | |||||||
\(432\) | 2.33197e103 | 0.184551 | ||||||||
\(433\) | −1.40100e104 | −1.01196 | −0.505982 | − | 0.862544i | \(-0.668870\pi\) | ||||
−0.505982 | + | 0.862544i | \(0.668870\pi\) | |||||||
\(434\) | −2.51473e104 | −1.65824 | ||||||||
\(435\) | 3.86085e104 | 2.32465 | ||||||||
\(436\) | −1.25987e104 | −0.692800 | ||||||||
\(437\) | 3.20171e104 | 1.60829 | ||||||||
\(438\) | −1.92335e104 | −0.882738 | ||||||||
\(439\) | 6.97672e103 | 0.292619 | 0.146310 | − | 0.989239i | \(-0.453260\pi\) | ||||
0.146310 | + | 0.989239i | \(0.453260\pi\) | |||||||
\(440\) | 8.64330e103 | 0.331359 | ||||||||
\(441\) | 1.61375e104 | 0.565602 | ||||||||
\(442\) | −7.53503e103 | −0.241493 | ||||||||
\(443\) | 7.02654e103 | 0.205965 | 0.102983 | − | 0.994683i | \(-0.467161\pi\) | ||||
0.102983 | + | 0.994683i | \(0.467161\pi\) | |||||||
\(444\) | 2.30507e104 | 0.618098 | ||||||||
\(445\) | 3.49989e104 | 0.858686 | ||||||||
\(446\) | −1.24823e104 | −0.280265 | ||||||||
\(447\) | −7.38860e104 | −1.51850 | ||||||||
\(448\) | 1.05719e104 | 0.198917 | ||||||||
\(449\) | 2.55988e103 | 0.0441052 | 0.0220526 | − | 0.999757i | \(-0.492980\pi\) | ||||
0.0220526 | + | 0.999757i | \(0.492980\pi\) | |||||||
\(450\) | 2.31786e104 | 0.365758 | ||||||||
\(451\) | −2.13075e104 | −0.308006 | ||||||||
\(452\) | −5.27648e103 | −0.0698838 | ||||||||
\(453\) | −4.11287e104 | −0.499190 | ||||||||
\(454\) | −1.84589e104 | −0.205353 | ||||||||
\(455\) | 1.62793e105 | 1.66030 | ||||||||
\(456\) | −5.11687e104 | −0.478513 | ||||||||
\(457\) | −1.40981e105 | −1.20912 | −0.604562 | − | 0.796558i | \(-0.706652\pi\) | ||||
−0.604562 | + | 0.796558i | \(0.706652\pi\) | |||||||
\(458\) | 2.68814e104 | 0.211479 | ||||||||
\(459\) | 5.18805e104 | 0.374458 | ||||||||
\(460\) | −1.62660e105 | −1.07732 | ||||||||
\(461\) | −8.17494e104 | −0.496933 | −0.248467 | − | 0.968640i | \(-0.579927\pi\) | ||||
−0.248467 | + | 0.968640i | \(0.579927\pi\) | |||||||
\(462\) | 1.42704e105 | 0.796303 | ||||||||
\(463\) | 1.15708e105 | 0.592809 | 0.296405 | − | 0.955062i | \(-0.404212\pi\) | ||||
0.296405 | + | 0.955062i | \(0.404212\pi\) | |||||||
\(464\) | 6.81252e104 | 0.320515 | ||||||||
\(465\) | −6.18360e105 | −2.67208 | ||||||||
\(466\) | 1.43170e104 | 0.0568340 | ||||||||
\(467\) | −3.86650e105 | −1.41027 | −0.705133 | − | 0.709075i | \(-0.749113\pi\) | ||||
−0.705133 | + | 0.709075i | \(0.749113\pi\) | |||||||
\(468\) | −3.70701e104 | −0.124255 | ||||||||
\(469\) | 3.14808e105 | 0.969882 | ||||||||
\(470\) | 5.22798e105 | 1.48071 | ||||||||
\(471\) | 1.74349e105 | 0.454040 | ||||||||
\(472\) | −2.31194e105 | −0.553690 | ||||||||
\(473\) | 4.45162e105 | 0.980626 | ||||||||
\(474\) | 1.77168e105 | 0.359039 | ||||||||
\(475\) | 8.69314e105 | 1.62098 | ||||||||
\(476\) | 2.35199e105 | 0.403609 | ||||||||
\(477\) | −9.14024e104 | −0.144372 | ||||||||
\(478\) | 3.56023e105 | 0.517698 | ||||||||
\(479\) | −4.66249e105 | −0.624260 | −0.312130 | − | 0.950039i | \(-0.601042\pi\) | ||||
−0.312130 | + | 0.950039i | \(0.601042\pi\) | |||||||
\(480\) | 2.59958e105 | 0.320534 | ||||||||
\(481\) | 6.26314e105 | 0.711314 | ||||||||
\(482\) | −4.24257e105 | −0.443885 | ||||||||
\(483\) | −2.68558e106 | −2.58896 | ||||||||
\(484\) | −3.56943e105 | −0.317108 | ||||||||
\(485\) | 1.98129e106 | 1.62237 | ||||||||
\(486\) | 6.59800e105 | 0.498057 | ||||||||
\(487\) | −1.15665e106 | −0.805026 | −0.402513 | − | 0.915414i | \(-0.631863\pi\) | ||||
−0.402513 | + | 0.915414i | \(0.631863\pi\) | |||||||
\(488\) | −5.23227e105 | −0.335820 | ||||||||
\(489\) | −8.92400e105 | −0.528274 | ||||||||
\(490\) | −3.07484e106 | −1.67910 | ||||||||
\(491\) | 3.67125e105 | 0.184967 | 0.0924836 | − | 0.995714i | \(-0.470519\pi\) | ||||
0.0924836 | + | 0.995714i | \(0.470519\pi\) | |||||||
\(492\) | −6.40850e105 | −0.297944 | ||||||||
\(493\) | 1.51561e106 | 0.650332 | ||||||||
\(494\) | −1.39031e106 | −0.550678 | ||||||||
\(495\) | 9.46017e105 | 0.345934 | ||||||||
\(496\) | −1.09110e106 | −0.368417 | ||||||||
\(497\) | 3.01598e106 | 0.940483 | ||||||||
\(498\) | 2.09115e106 | 0.602318 | ||||||||
\(499\) | −2.49648e106 | −0.664287 | −0.332144 | − | 0.943229i | \(-0.607772\pi\) | ||||
−0.332144 | + | 0.943229i | \(0.607772\pi\) | |||||||
\(500\) | −1.26498e106 | −0.311005 | ||||||||
\(501\) | 1.55796e106 | 0.353969 | ||||||||
\(502\) | 3.07689e106 | 0.646123 | ||||||||
\(503\) | 8.98748e106 | 1.74463 | 0.872313 | − | 0.488948i | \(-0.162619\pi\) | ||||
0.872313 | + | 0.488948i | \(0.162619\pi\) | |||||||
\(504\) | 1.15711e106 | 0.207667 | ||||||||
\(505\) | −1.66254e107 | −2.75907 | ||||||||
\(506\) | −3.87425e106 | −0.594624 | ||||||||
\(507\) | 4.50590e106 | 0.639687 | ||||||||
\(508\) | 1.34896e106 | 0.177167 | ||||||||
\(509\) | −6.54652e106 | −0.795533 | −0.397767 | − | 0.917487i | \(-0.630215\pi\) | ||||
−0.397767 | + | 0.917487i | \(0.630215\pi\) | |||||||
\(510\) | 5.78341e106 | 0.650373 | ||||||||
\(511\) | 1.63124e107 | 1.69782 | ||||||||
\(512\) | 4.58700e105 | 0.0441942 | ||||||||
\(513\) | 9.57263e106 | 0.853877 | ||||||||
\(514\) | −1.29440e106 | −0.106912 | ||||||||
\(515\) | −1.43757e107 | −1.09963 | ||||||||
\(516\) | 1.33888e107 | 0.948591 | ||||||||
\(517\) | 1.24521e107 | 0.817269 | ||||||||
\(518\) | −1.95498e107 | −1.18882 | ||||||||
\(519\) | 6.98201e106 | 0.393432 | ||||||||
\(520\) | 7.06336e106 | 0.368875 | ||||||||
\(521\) | −3.19837e106 | −0.154824 | −0.0774122 | − | 0.996999i | \(-0.524666\pi\) | ||||
−0.0774122 | + | 0.996999i | \(0.524666\pi\) | |||||||
\(522\) | 7.45637e106 | 0.334613 | ||||||||
\(523\) | −1.84452e107 | −0.767480 | −0.383740 | − | 0.923441i | \(-0.625364\pi\) | ||||
−0.383740 | + | 0.923441i | \(0.625364\pi\) | |||||||
\(524\) | −8.05958e106 | −0.310976 | ||||||||
\(525\) | −7.29176e107 | −2.60940 | ||||||||
\(526\) | 8.35637e105 | 0.0277384 | ||||||||
\(527\) | −2.42743e107 | −0.747528 | ||||||||
\(528\) | 6.19171e106 | 0.176918 | ||||||||
\(529\) | 3.51966e107 | 0.933258 | ||||||||
\(530\) | 1.74159e107 | 0.428596 | ||||||||
\(531\) | −2.53044e107 | −0.578046 | ||||||||
\(532\) | 4.33973e107 | 0.920350 | ||||||||
\(533\) | −1.74126e107 | −0.342878 | ||||||||
\(534\) | 2.50718e107 | 0.458465 | ||||||||
\(535\) | 3.25414e107 | 0.552665 | ||||||||
\(536\) | 1.36590e107 | 0.215482 | ||||||||
\(537\) | −1.13542e107 | −0.166408 | ||||||||
\(538\) | −8.14158e107 | −1.10869 | ||||||||
\(539\) | −7.32368e107 | −0.926773 | ||||||||
\(540\) | −4.86329e107 | −0.571975 | ||||||||
\(541\) | 4.78952e107 | 0.523600 | 0.261800 | − | 0.965122i | \(-0.415684\pi\) | ||||
0.261800 | + | 0.965122i | \(0.415684\pi\) | |||||||
\(542\) | −1.24730e108 | −1.26765 | ||||||||
\(543\) | 1.91918e108 | 1.81352 | ||||||||
\(544\) | 1.02049e107 | 0.0896711 | ||||||||
\(545\) | 2.62743e108 | 2.14718 | ||||||||
\(546\) | 1.16619e108 | 0.886460 | ||||||||
\(547\) | 4.04694e107 | 0.286172 | 0.143086 | − | 0.989710i | \(-0.454297\pi\) | ||||
0.143086 | + | 0.989710i | \(0.454297\pi\) | |||||||
\(548\) | 8.15239e107 | 0.536356 | ||||||||
\(549\) | −5.72677e107 | −0.350592 | ||||||||
\(550\) | −1.05192e108 | −0.599317 | ||||||||
\(551\) | 2.79651e108 | 1.48295 | ||||||||
\(552\) | −1.16523e108 | −0.575199 | ||||||||
\(553\) | −1.50260e108 | −0.690560 | ||||||||
\(554\) | 2.20223e108 | 0.942383 | ||||||||
\(555\) | −4.80719e108 | −1.91566 | ||||||||
\(556\) | −2.09364e108 | −0.777048 | ||||||||
\(557\) | −1.61844e108 | −0.559521 | −0.279760 | − | 0.960070i | \(-0.590255\pi\) | ||||
−0.279760 | + | 0.960070i | \(0.590255\pi\) | |||||||
\(558\) | −1.19422e108 | −0.384623 | ||||||||
\(559\) | 3.63789e108 | 1.09165 | ||||||||
\(560\) | −2.20476e108 | −0.616501 | ||||||||
\(561\) | 1.37750e108 | 0.358970 | ||||||||
\(562\) | −1.17931e108 | −0.286446 | ||||||||
\(563\) | −4.79605e108 | −1.08593 | −0.542965 | − | 0.839755i | \(-0.682698\pi\) | ||||
−0.542965 | + | 0.839755i | \(0.682698\pi\) | |||||||
\(564\) | 3.74512e108 | 0.790571 | ||||||||
\(565\) | 1.10040e108 | 0.216590 | ||||||||
\(566\) | −5.26473e108 | −0.966334 | ||||||||
\(567\) | −1.14607e109 | −1.96191 | ||||||||
\(568\) | 1.30859e108 | 0.208950 | ||||||||
\(569\) | −4.57641e108 | −0.681695 | −0.340847 | − | 0.940119i | \(-0.610714\pi\) | ||||
−0.340847 | + | 0.940119i | \(0.610714\pi\) | |||||||
\(570\) | 1.06712e109 | 1.48305 | ||||||||
\(571\) | 5.56713e108 | 0.721947 | 0.360973 | − | 0.932576i | \(-0.382445\pi\) | ||||
0.360973 | + | 0.932576i | \(0.382445\pi\) | |||||||
\(572\) | 1.68236e108 | 0.203599 | ||||||||
\(573\) | 9.01000e108 | 1.01769 | ||||||||
\(574\) | 5.43518e108 | 0.573052 | ||||||||
\(575\) | 1.97963e109 | 1.94852 | ||||||||
\(576\) | 5.02051e107 | 0.0461381 | ||||||||
\(577\) | −2.39008e108 | −0.205101 | −0.102551 | − | 0.994728i | \(-0.532700\pi\) | ||||
−0.102551 | + | 0.994728i | \(0.532700\pi\) | |||||||
\(578\) | −6.55304e108 | −0.525162 | ||||||||
\(579\) | −1.08809e109 | −0.814444 | ||||||||
\(580\) | −1.42074e109 | −0.993366 | ||||||||
\(581\) | −1.77355e109 | −1.15847 | ||||||||
\(582\) | 1.41932e109 | 0.866207 | ||||||||
\(583\) | 4.14813e108 | 0.236562 | ||||||||
\(584\) | 7.07768e108 | 0.377210 | ||||||||
\(585\) | 7.73091e108 | 0.385101 | ||||||||
\(586\) | 1.68222e109 | 0.783300 | ||||||||
\(587\) | 5.56169e108 | 0.242104 | 0.121052 | − | 0.992646i | \(-0.461373\pi\) | ||||
0.121052 | + | 0.992646i | \(0.461373\pi\) | |||||||
\(588\) | −2.20269e109 | −0.896498 | ||||||||
\(589\) | −4.47893e109 | −1.70459 | ||||||||
\(590\) | 4.82151e109 | 1.71604 | ||||||||
\(591\) | 5.00019e109 | 1.66449 | ||||||||
\(592\) | −8.48235e108 | −0.264125 | ||||||||
\(593\) | −1.68614e109 | −0.491172 | −0.245586 | − | 0.969375i | \(-0.578980\pi\) | ||||
−0.245586 | + | 0.969375i | \(0.578980\pi\) | |||||||
\(594\) | −1.15834e109 | −0.315699 | ||||||||
\(595\) | −4.90503e109 | −1.25090 | ||||||||
\(596\) | 2.71891e109 | 0.648884 | ||||||||
\(597\) | 4.19268e109 | 0.936495 | ||||||||
\(598\) | −3.16606e109 | −0.661946 | ||||||||
\(599\) | 1.24027e109 | 0.242748 | 0.121374 | − | 0.992607i | \(-0.461270\pi\) | ||||
0.121374 | + | 0.992607i | \(0.461270\pi\) | |||||||
\(600\) | −3.16378e109 | −0.579739 | ||||||||
\(601\) | −5.87933e109 | −1.00876 | −0.504378 | − | 0.863483i | \(-0.668278\pi\) | ||||
−0.504378 | + | 0.863483i | \(0.668278\pi\) | |||||||
\(602\) | −1.13553e110 | −1.82448 | ||||||||
\(603\) | 1.49500e109 | 0.224960 | ||||||||
\(604\) | 1.51348e109 | 0.213313 | ||||||||
\(605\) | 7.44399e109 | 0.982807 | ||||||||
\(606\) | −1.19098e110 | −1.47311 | ||||||||
\(607\) | 1.04727e110 | 1.21368 | 0.606841 | − | 0.794823i | \(-0.292436\pi\) | ||||
0.606841 | + | 0.794823i | \(0.292436\pi\) | |||||||
\(608\) | 1.88294e109 | 0.204477 | ||||||||
\(609\) | −2.34570e110 | −2.38720 | ||||||||
\(610\) | 1.09118e110 | 1.04080 | ||||||||
\(611\) | 1.01759e110 | 0.909798 | ||||||||
\(612\) | 1.11694e109 | 0.0936155 | ||||||||
\(613\) | 1.00038e110 | 0.786095 | 0.393048 | − | 0.919518i | \(-0.371421\pi\) | ||||
0.393048 | + | 0.919518i | \(0.371421\pi\) | |||||||
\(614\) | 4.27192e109 | 0.314755 | ||||||||
\(615\) | 1.33648e110 | 0.923413 | ||||||||
\(616\) | −5.25132e109 | −0.340275 | ||||||||
\(617\) | 6.42669e109 | 0.390592 | 0.195296 | − | 0.980744i | \(-0.437433\pi\) | ||||
0.195296 | + | 0.980744i | \(0.437433\pi\) | |||||||
\(618\) | −1.02982e110 | −0.587107 | ||||||||
\(619\) | −8.63865e109 | −0.462025 | −0.231012 | − | 0.972951i | \(-0.574204\pi\) | ||||
−0.231012 | + | 0.972951i | \(0.574204\pi\) | |||||||
\(620\) | 2.27548e110 | 1.14183 | ||||||||
\(621\) | 2.17991e110 | 1.02641 | ||||||||
\(622\) | 1.91109e110 | 0.844423 | ||||||||
\(623\) | −2.12639e110 | −0.881791 | ||||||||
\(624\) | 5.05991e109 | 0.196948 | ||||||||
\(625\) | −1.19739e110 | −0.437497 | ||||||||
\(626\) | −1.21219e110 | −0.415800 | ||||||||
\(627\) | 2.54167e110 | 0.818561 | ||||||||
\(628\) | −6.41581e109 | −0.194020 | ||||||||
\(629\) | −1.88711e110 | −0.535915 | ||||||||
\(630\) | −2.41313e110 | −0.643619 | ||||||||
\(631\) | −4.06248e110 | −1.01773 | −0.508864 | − | 0.860847i | \(-0.669935\pi\) | ||||
−0.508864 | + | 0.860847i | \(0.669935\pi\) | |||||||
\(632\) | −6.51956e109 | −0.153424 | ||||||||
\(633\) | 1.17116e110 | 0.258923 | ||||||||
\(634\) | 3.85144e110 | 0.800015 | ||||||||
\(635\) | −2.81324e110 | −0.549092 | ||||||||
\(636\) | 1.24760e110 | 0.228834 | ||||||||
\(637\) | −5.98496e110 | −1.03170 | ||||||||
\(638\) | −3.38394e110 | −0.548284 | ||||||||
\(639\) | 1.43226e110 | 0.218141 | ||||||||
\(640\) | −9.56611e109 | −0.136970 | ||||||||
\(641\) | 1.85524e110 | 0.249752 | 0.124876 | − | 0.992172i | \(-0.460147\pi\) | ||||
0.124876 | + | 0.992172i | \(0.460147\pi\) | |||||||
\(642\) | 2.33114e110 | 0.295076 | ||||||||
\(643\) | 1.40624e110 | 0.167389 | 0.0836946 | − | 0.996491i | \(-0.473328\pi\) | ||||
0.0836946 | + | 0.996491i | \(0.473328\pi\) | |||||||
\(644\) | 9.88256e110 | 1.10631 | ||||||||
\(645\) | −2.79222e111 | −2.93995 | ||||||||
\(646\) | 4.18907e110 | 0.414890 | ||||||||
\(647\) | −7.93419e110 | −0.739237 | −0.369618 | − | 0.929184i | \(-0.620512\pi\) | ||||
−0.369618 | + | 0.929184i | \(0.620512\pi\) | |||||||
\(648\) | −4.97260e110 | −0.435884 | ||||||||
\(649\) | 1.14839e111 | 0.947163 | ||||||||
\(650\) | −8.59635e110 | −0.667170 | ||||||||
\(651\) | 3.75690e111 | 2.74398 | ||||||||
\(652\) | 3.28391e110 | 0.225741 | ||||||||
\(653\) | 1.35943e110 | 0.0879602 | 0.0439801 | − | 0.999032i | \(-0.485996\pi\) | ||||
0.0439801 | + | 0.999032i | \(0.485996\pi\) | |||||||
\(654\) | 1.88218e111 | 1.14641 | ||||||||
\(655\) | 1.68081e111 | 0.963802 | ||||||||
\(656\) | 2.35824e110 | 0.127317 | ||||||||
\(657\) | 7.74659e110 | 0.393802 | ||||||||
\(658\) | −3.17631e111 | −1.52055 | ||||||||
\(659\) | 3.54015e111 | 1.59605 | 0.798027 | − | 0.602621i | \(-0.205877\pi\) | ||||
0.798027 | + | 0.602621i | \(0.205877\pi\) | |||||||
\(660\) | −1.29127e111 | −0.548318 | ||||||||
\(661\) | −4.21617e111 | −1.68640 | −0.843199 | − | 0.537602i | \(-0.819330\pi\) | ||||
−0.843199 | + | 0.537602i | \(0.819330\pi\) | |||||||
\(662\) | 1.52242e111 | 0.573644 | ||||||||
\(663\) | 1.12570e111 | 0.399612 | ||||||||
\(664\) | −7.69514e110 | −0.257381 | ||||||||
\(665\) | −9.05043e111 | −2.85242 | ||||||||
\(666\) | −9.28401e110 | −0.275742 | ||||||||
\(667\) | 6.36830e111 | 1.78260 | ||||||||
\(668\) | −5.73307e110 | −0.151257 | ||||||||
\(669\) | 1.86481e111 | 0.463770 | ||||||||
\(670\) | −2.84857e111 | −0.667840 | ||||||||
\(671\) | 2.59899e111 | 0.574466 | ||||||||
\(672\) | −1.57940e111 | −0.329159 | ||||||||
\(673\) | −2.68247e110 | −0.0527157 | −0.0263578 | − | 0.999653i | \(-0.508391\pi\) | ||||
−0.0263578 | + | 0.999653i | \(0.508391\pi\) | |||||||
\(674\) | 8.83945e110 | 0.163817 | ||||||||
\(675\) | 5.91880e111 | 1.03451 | ||||||||
\(676\) | −1.65811e111 | −0.273350 | ||||||||
\(677\) | 1.61023e111 | 0.250400 | 0.125200 | − | 0.992132i | \(-0.460043\pi\) | ||||
0.125200 | + | 0.992132i | \(0.460043\pi\) | |||||||
\(678\) | 7.88284e110 | 0.115640 | ||||||||
\(679\) | −1.20375e112 | −1.66602 | ||||||||
\(680\) | −2.12822e111 | −0.277916 | ||||||||
\(681\) | 2.75768e111 | 0.339808 | ||||||||
\(682\) | 5.41976e111 | 0.630227 | ||||||||
\(683\) | −1.41196e112 | −1.54955 | −0.774773 | − | 0.632240i | \(-0.782136\pi\) | ||||
−0.774773 | + | 0.632240i | \(0.782136\pi\) | |||||||
\(684\) | 2.06090e111 | 0.213472 | ||||||||
\(685\) | −1.70017e112 | −1.66232 | ||||||||
\(686\) | 6.49017e111 | 0.599036 | ||||||||
\(687\) | −4.01597e111 | −0.349945 | ||||||||
\(688\) | −4.92690e111 | −0.405351 | ||||||||
\(689\) | 3.38988e111 | 0.263345 | ||||||||
\(690\) | 2.43007e112 | 1.78271 | ||||||||
\(691\) | 1.55517e112 | 1.07744 | 0.538722 | − | 0.842483i | \(-0.318907\pi\) | ||||
0.538722 | + | 0.842483i | \(0.318907\pi\) | |||||||
\(692\) | −2.56929e111 | −0.168121 | ||||||||
\(693\) | −5.74762e111 | −0.355243 | ||||||||
\(694\) | −1.25580e112 | −0.733199 | ||||||||
\(695\) | 4.36625e112 | 2.40829 | ||||||||
\(696\) | −1.01776e112 | −0.530373 | ||||||||
\(697\) | 5.24649e111 | 0.258330 | ||||||||
\(698\) | −2.48371e111 | −0.115561 | ||||||||
\(699\) | −2.13890e111 | −0.0940463 | ||||||||
\(700\) | 2.68327e112 | 1.11504 | ||||||||
\(701\) | 3.52460e112 | 1.38436 | 0.692178 | − | 0.721727i | \(-0.256651\pi\) | ||||
0.692178 | + | 0.721727i | \(0.256651\pi\) | |||||||
\(702\) | −9.46606e111 | −0.351442 | ||||||||
\(703\) | −3.48196e112 | −1.22205 | ||||||||
\(704\) | −2.27847e111 | −0.0756001 | ||||||||
\(705\) | −7.81038e112 | −2.45020 | ||||||||
\(706\) | 3.25637e112 | 0.965936 | ||||||||
\(707\) | 1.01009e113 | 2.83331 | ||||||||
\(708\) | 3.45393e112 | 0.916221 | ||||||||
\(709\) | −7.33733e112 | −1.84082 | −0.920412 | − | 0.390951i | \(-0.872146\pi\) | ||||
−0.920412 | + | 0.390951i | \(0.872146\pi\) | |||||||
\(710\) | −2.72904e112 | −0.647596 | ||||||||
\(711\) | −7.13572e111 | −0.160173 | ||||||||
\(712\) | −9.22609e111 | −0.195911 | ||||||||
\(713\) | −1.01996e113 | −2.04901 | ||||||||
\(714\) | −3.51377e112 | −0.667873 | ||||||||
\(715\) | −3.50853e112 | −0.631011 | ||||||||
\(716\) | 4.17820e111 | 0.0711090 | ||||||||
\(717\) | −5.31884e112 | −0.856663 | ||||||||
\(718\) | −6.43401e112 | −0.980768 | ||||||||
\(719\) | 1.11527e113 | 1.60913 | 0.804564 | − | 0.593866i | \(-0.202399\pi\) | ||||
0.804564 | + | 0.593866i | \(0.202399\pi\) | |||||||
\(720\) | −1.04702e112 | −0.142995 | ||||||||
\(721\) | 8.73412e112 | 1.12921 | ||||||||
\(722\) | 1.95235e112 | 0.238967 | ||||||||
\(723\) | 6.33821e112 | 0.734521 | ||||||||
\(724\) | −7.06232e112 | −0.774951 | ||||||||
\(725\) | 1.72909e113 | 1.79666 | ||||||||
\(726\) | 5.33257e112 | 0.524735 | ||||||||
\(727\) | −3.69443e112 | −0.344301 | −0.172151 | − | 0.985071i | \(-0.555072\pi\) | ||||
−0.172151 | + | 0.985071i | \(0.555072\pi\) | |||||||
\(728\) | −4.29141e112 | −0.378800 | ||||||||
\(729\) | 4.88817e112 | 0.408704 | ||||||||
\(730\) | −1.47604e113 | −1.16908 | ||||||||
\(731\) | −1.09611e113 | −0.822467 | ||||||||
\(732\) | 7.81678e112 | 0.555700 | ||||||||
\(733\) | −2.41435e113 | −1.62628 | −0.813138 | − | 0.582072i | \(-0.802242\pi\) | ||||
−0.813138 | + | 0.582072i | \(0.802242\pi\) | |||||||
\(734\) | 9.18350e111 | 0.0586157 | ||||||||
\(735\) | 4.59368e113 | 2.77850 | ||||||||
\(736\) | 4.28789e112 | 0.245793 | ||||||||
\(737\) | −6.78476e112 | −0.368611 | ||||||||
\(738\) | 2.58112e112 | 0.132917 | ||||||||
\(739\) | 2.42273e113 | 1.18263 | 0.591315 | − | 0.806441i | \(-0.298609\pi\) | ||||
0.591315 | + | 0.806441i | \(0.298609\pi\) | |||||||
\(740\) | 1.76898e113 | 0.818597 | ||||||||
\(741\) | 2.07707e113 | 0.911237 | ||||||||
\(742\) | −1.05812e113 | −0.440128 | ||||||||
\(743\) | −3.00886e113 | −1.18671 | −0.593354 | − | 0.804941i | \(-0.702197\pi\) | ||||
−0.593354 | + | 0.804941i | \(0.702197\pi\) | |||||||
\(744\) | 1.63006e113 | 0.609640 | ||||||||
\(745\) | −5.67023e113 | −2.01107 | ||||||||
\(746\) | −9.03145e111 | −0.0303790 | ||||||||
\(747\) | −8.42240e112 | −0.268703 | ||||||||
\(748\) | −5.06901e112 | −0.153395 | ||||||||
\(749\) | −1.97708e113 | −0.567536 | ||||||||
\(750\) | 1.88982e113 | 0.514637 | ||||||||
\(751\) | 5.94779e113 | 1.53666 | 0.768330 | − | 0.640054i | \(-0.221088\pi\) | ||||
0.768330 | + | 0.640054i | \(0.221088\pi\) | |||||||
\(752\) | −1.37815e113 | −0.337825 | ||||||||
\(753\) | −4.59674e113 | −1.06917 | ||||||||
\(754\) | −2.76537e113 | −0.610359 | ||||||||
\(755\) | −3.15634e113 | −0.661118 | ||||||||
\(756\) | 2.95474e113 | 0.587365 | ||||||||
\(757\) | −8.35816e113 | −1.57697 | −0.788485 | − | 0.615053i | \(-0.789134\pi\) | ||||
−0.788485 | + | 0.615053i | \(0.789134\pi\) | |||||||
\(758\) | 6.51295e113 | 1.16639 | ||||||||
\(759\) | 5.78797e113 | 0.983956 | ||||||||
\(760\) | −3.92684e113 | −0.633733 | ||||||||
\(761\) | 8.03890e113 | 1.23169 | 0.615847 | − | 0.787866i | \(-0.288814\pi\) | ||||
0.615847 | + | 0.787866i | \(0.288814\pi\) | |||||||
\(762\) | −2.01530e113 | −0.293169 | ||||||||
\(763\) | −1.59632e114 | −2.20496 | ||||||||
\(764\) | −3.31556e113 | −0.434880 | ||||||||
\(765\) | −2.32935e113 | −0.290141 | ||||||||
\(766\) | 2.41758e113 | 0.285986 | ||||||||
\(767\) | 9.38473e113 | 1.05440 | ||||||||
\(768\) | −6.85278e112 | −0.0731305 | ||||||||
\(769\) | 9.45083e113 | 0.958031 | 0.479015 | − | 0.877806i | \(-0.340994\pi\) | ||||
0.479015 | + | 0.877806i | \(0.340994\pi\) | |||||||
\(770\) | 1.09515e114 | 1.05461 | ||||||||
\(771\) | 1.93378e113 | 0.176913 | ||||||||
\(772\) | 4.00402e113 | 0.348027 | ||||||||
\(773\) | 1.29252e113 | 0.106745 | 0.0533724 | − | 0.998575i | \(-0.483003\pi\) | ||||
0.0533724 | + | 0.998575i | \(0.483003\pi\) | |||||||
\(774\) | −5.39254e113 | −0.423181 | ||||||||
\(775\) | −2.76934e114 | −2.06518 | ||||||||
\(776\) | −5.22289e113 | −0.370146 | ||||||||
\(777\) | 2.92065e114 | 1.96721 | ||||||||
\(778\) | −7.16912e113 | −0.458957 | ||||||||
\(779\) | 9.68046e113 | 0.589069 | ||||||||
\(780\) | −1.05524e114 | −0.610397 | ||||||||
\(781\) | −6.50005e113 | −0.357438 | ||||||||
\(782\) | 9.53947e113 | 0.498721 | ||||||||
\(783\) | 1.90403e114 | 0.946419 | ||||||||
\(784\) | 8.10560e113 | 0.383090 | ||||||||
\(785\) | 1.33801e114 | 0.601322 | ||||||||
\(786\) | 1.20407e114 | 0.514589 | ||||||||
\(787\) | −3.27904e113 | −0.133274 | −0.0666368 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666368 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(788\) | −1.84000e114 | −0.711267 | ||||||||
\(789\) | −1.24841e113 | −0.0459002 | ||||||||
\(790\) | 1.35964e114 | 0.475505 | ||||||||
\(791\) | −6.68560e113 | −0.222418 | ||||||||
\(792\) | −2.49380e113 | −0.0789255 | ||||||||
\(793\) | 2.12391e114 | 0.639506 | ||||||||
\(794\) | −4.39492e114 | −1.25904 | ||||||||
\(795\) | −2.60185e114 | −0.709221 | ||||||||
\(796\) | −1.54285e114 | −0.400182 | ||||||||
\(797\) | 3.20452e114 | 0.790968 | 0.395484 | − | 0.918473i | \(-0.370577\pi\) | ||||
0.395484 | + | 0.918473i | \(0.370577\pi\) | |||||||
\(798\) | −6.48336e114 | −1.52295 | ||||||||
\(799\) | −3.06604e114 | −0.685456 | ||||||||
\(800\) | 1.16423e114 | 0.247733 | ||||||||
\(801\) | −1.00980e114 | −0.204528 | ||||||||
\(802\) | −1.40630e114 | −0.271138 | ||||||||
\(803\) | −3.51564e114 | −0.645269 | ||||||||
\(804\) | −2.04060e114 | −0.356570 | ||||||||
\(805\) | −2.06099e115 | −3.42877 | ||||||||
\(806\) | 4.42906e114 | 0.701581 | ||||||||
\(807\) | 1.21632e115 | 1.83460 | ||||||||
\(808\) | 4.38263e114 | 0.629486 | ||||||||
\(809\) | 6.00066e114 | 0.820791 | 0.410395 | − | 0.911908i | \(-0.365391\pi\) | ||||
0.410395 | + | 0.911908i | \(0.365391\pi\) | |||||||
\(810\) | 1.03703e115 | 1.35093 | ||||||||
\(811\) | 1.44248e114 | 0.178973 | 0.0894865 | − | 0.995988i | \(-0.471477\pi\) | ||||
0.0894865 | + | 0.995988i | \(0.471477\pi\) | |||||||
\(812\) | 8.63185e114 | 1.02009 | ||||||||
\(813\) | 1.86342e115 | 2.09765 | ||||||||
\(814\) | 4.21338e114 | 0.451821 | ||||||||
\(815\) | −6.84854e114 | −0.699636 | ||||||||
\(816\) | −1.52457e114 | −0.148384 | ||||||||
\(817\) | −2.02247e115 | −1.87547 | ||||||||
\(818\) | 1.18776e115 | 1.04947 | ||||||||
\(819\) | −4.69699e114 | −0.395463 | ||||||||
\(820\) | −4.91807e114 | −0.394591 | ||||||||
\(821\) | 2.34612e115 | 1.79389 | 0.896945 | − | 0.442143i | \(-0.145781\pi\) | ||||
0.896945 | + | 0.442143i | \(0.145781\pi\) | |||||||
\(822\) | −1.21793e115 | −0.887536 | ||||||||
\(823\) | −1.74822e115 | −1.21423 | −0.607116 | − | 0.794613i | \(-0.707674\pi\) | ||||
−0.607116 | + | 0.794613i | \(0.707674\pi\) | |||||||
\(824\) | 3.78960e114 | 0.250881 | ||||||||
\(825\) | 1.57152e115 | 0.991721 | ||||||||
\(826\) | −2.92935e115 | −1.76222 | ||||||||
\(827\) | 1.49217e115 | 0.855756 | 0.427878 | − | 0.903837i | \(-0.359261\pi\) | ||||
0.427878 | + | 0.903837i | \(0.359261\pi\) | |||||||
\(828\) | 4.69314e114 | 0.256605 | ||||||||
\(829\) | −6.82432e114 | −0.355759 | −0.177879 | − | 0.984052i | \(-0.556924\pi\) | ||||
−0.177879 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(830\) | 1.60481e115 | 0.797698 | ||||||||
\(831\) | −3.29004e115 | −1.55941 | ||||||||
\(832\) | −1.86198e114 | −0.0841594 | ||||||||
\(833\) | 1.80329e115 | 0.777300 | ||||||||
\(834\) | 3.12781e115 | 1.28582 | ||||||||
\(835\) | 1.19562e115 | 0.468790 | ||||||||
\(836\) | −9.35299e114 | −0.349786 | ||||||||
\(837\) | −3.04952e115 | −1.08787 | ||||||||
\(838\) | −3.02551e115 | −1.02958 | ||||||||
\(839\) | −5.82530e115 | −1.89113 | −0.945565 | − | 0.325434i | \(-0.894489\pi\) | ||||
−0.945565 | + | 0.325434i | \(0.894489\pi\) | |||||||
\(840\) | 3.29382e115 | 1.02016 | ||||||||
\(841\) | 2.17825e115 | 0.643674 | ||||||||
\(842\) | −3.82159e115 | −1.07750 | ||||||||
\(843\) | 1.76183e115 | 0.473997 | ||||||||
\(844\) | −4.30971e114 | −0.110642 | ||||||||
\(845\) | 3.45796e115 | 0.847189 | ||||||||
\(846\) | −1.50840e115 | −0.352685 | ||||||||
\(847\) | −4.52267e115 | −1.00925 | ||||||||
\(848\) | −4.59101e114 | −0.0977849 | ||||||||
\(849\) | 7.86528e115 | 1.59904 | ||||||||
\(850\) | 2.59011e115 | 0.502657 | ||||||||
\(851\) | −7.92923e115 | −1.46897 | ||||||||
\(852\) | −1.95497e115 | −0.345761 | ||||||||
\(853\) | 1.07883e116 | 1.82165 | 0.910827 | − | 0.412789i | \(-0.135445\pi\) | ||||
0.910827 | + | 0.412789i | \(0.135445\pi\) | |||||||
\(854\) | −6.62957e115 | −1.06881 | ||||||||
\(855\) | −4.29797e115 | −0.661609 | ||||||||
\(856\) | −8.57826e114 | −0.126091 | ||||||||
\(857\) | 6.82144e115 | 0.957488 | 0.478744 | − | 0.877955i | \(-0.341092\pi\) | ||||
0.478744 | + | 0.877955i | \(0.341092\pi\) | |||||||
\(858\) | −2.51337e115 | −0.336906 | ||||||||
\(859\) | 4.27541e114 | 0.0547329 | 0.0273664 | − | 0.999625i | \(-0.491288\pi\) | ||||
0.0273664 | + | 0.999625i | \(0.491288\pi\) | |||||||
\(860\) | 1.02750e116 | 1.25630 | ||||||||
\(861\) | −8.11992e115 | −0.948260 | ||||||||
\(862\) | 1.77155e115 | 0.197614 | ||||||||
\(863\) | 1.47735e116 | 1.57419 | 0.787093 | − | 0.616835i | \(-0.211585\pi\) | ||||
0.787093 | + | 0.616835i | \(0.211585\pi\) | |||||||
\(864\) | 1.28202e115 | 0.130497 | ||||||||
\(865\) | 5.35820e115 | 0.521054 | ||||||||
\(866\) | −7.70206e115 | −0.715566 | ||||||||
\(867\) | 9.78996e115 | 0.869013 | ||||||||
\(868\) | −1.38249e116 | −1.17255 | ||||||||
\(869\) | 3.23841e115 | 0.262453 | ||||||||
\(870\) | 2.12253e116 | 1.64378 | ||||||||
\(871\) | −5.54455e115 | −0.410345 | ||||||||
\(872\) | −6.92618e115 | −0.489883 | ||||||||
\(873\) | −5.71651e115 | −0.386428 | ||||||||
\(874\) | 1.76016e116 | 1.13723 | ||||||||
\(875\) | −1.60280e116 | −0.989829 | ||||||||
\(876\) | −1.05737e116 | −0.624190 | ||||||||
\(877\) | −1.63499e116 | −0.922640 | −0.461320 | − | 0.887234i | \(-0.652624\pi\) | ||||
−0.461320 | + | 0.887234i | \(0.652624\pi\) | |||||||
\(878\) | 3.83549e115 | 0.206913 | ||||||||
\(879\) | −2.51317e116 | −1.29617 | ||||||||
\(880\) | 4.75170e115 | 0.234306 | ||||||||
\(881\) | 1.32327e116 | 0.623881 | 0.311940 | − | 0.950102i | \(-0.399021\pi\) | ||||
0.311940 | + | 0.950102i | \(0.399021\pi\) | |||||||
\(882\) | 8.87166e115 | 0.399941 | ||||||||
\(883\) | 1.91608e116 | 0.825975 | 0.412987 | − | 0.910737i | \(-0.364485\pi\) | ||||
0.412987 | + | 0.910737i | \(0.364485\pi\) | |||||||
\(884\) | −4.14243e115 | −0.170762 | ||||||||
\(885\) | −7.20312e116 | −2.83963 | ||||||||
\(886\) | 3.86288e115 | 0.145640 | ||||||||
\(887\) | 2.58557e115 | 0.0932339 | 0.0466169 | − | 0.998913i | \(-0.485156\pi\) | ||||
0.0466169 | + | 0.998913i | \(0.485156\pi\) | |||||||
\(888\) | 1.26723e116 | 0.437061 | ||||||||
\(889\) | 1.70921e116 | 0.563867 | ||||||||
\(890\) | 1.92409e116 | 0.607182 | ||||||||
\(891\) | 2.47001e116 | 0.745639 | ||||||||
\(892\) | −6.86224e115 | −0.198177 | ||||||||
\(893\) | −5.65724e116 | −1.56305 | ||||||||
\(894\) | −4.06193e116 | −1.07374 | ||||||||
\(895\) | −8.71357e115 | −0.220387 | ||||||||
\(896\) | 5.81198e115 | 0.140656 | ||||||||
\(897\) | 4.72996e116 | 1.09536 | ||||||||
\(898\) | 1.40731e115 | 0.0311871 | ||||||||
\(899\) | −8.90872e116 | −1.88933 | ||||||||
\(900\) | 1.27426e116 | 0.258630 | ||||||||
\(901\) | −1.02138e116 | −0.198408 | ||||||||
\(902\) | −1.17139e116 | −0.217793 | ||||||||
\(903\) | 1.69644e117 | 3.01906 | ||||||||
\(904\) | −2.90078e115 | −0.0494153 | ||||||||
\(905\) | 1.47284e117 | 2.40179 | ||||||||
\(906\) | −2.26107e116 | −0.352981 | ||||||||
\(907\) | 4.93689e116 | 0.737846 | 0.368923 | − | 0.929460i | \(-0.379727\pi\) | ||||
0.368923 | + | 0.929460i | \(0.379727\pi\) | |||||||
\(908\) | −1.01479e116 | −0.145206 | ||||||||
\(909\) | 4.79683e116 | 0.657175 | ||||||||
\(910\) | 8.94967e116 | 1.17401 | ||||||||
\(911\) | −7.50189e116 | −0.942312 | −0.471156 | − | 0.882050i | \(-0.656163\pi\) | ||||
−0.471156 | + | 0.882050i | \(0.656163\pi\) | |||||||
\(912\) | −2.81303e116 | −0.338360 | ||||||||
\(913\) | 3.82235e116 | 0.440286 | ||||||||
\(914\) | −7.75052e116 | −0.854980 | ||||||||
\(915\) | −1.63018e117 | −1.72227 | ||||||||
\(916\) | 1.47782e116 | 0.149538 | ||||||||
\(917\) | −1.02119e117 | −0.989736 | ||||||||
\(918\) | 2.85216e116 | 0.264782 | ||||||||
\(919\) | 1.40402e117 | 1.24857 | 0.624283 | − | 0.781198i | \(-0.285391\pi\) | ||||
0.624283 | + | 0.781198i | \(0.285391\pi\) | |||||||
\(920\) | −8.94232e116 | −0.761783 | ||||||||
\(921\) | −6.38207e116 | −0.520842 | ||||||||
\(922\) | −4.49422e116 | −0.351385 | ||||||||
\(923\) | −5.31188e116 | −0.397906 | ||||||||
\(924\) | 7.84524e116 | 0.563072 | ||||||||
\(925\) | −2.15291e117 | −1.48057 | ||||||||
\(926\) | 6.36112e116 | 0.419179 | ||||||||
\(927\) | 4.14775e116 | 0.261917 | ||||||||
\(928\) | 3.74522e116 | 0.226638 | ||||||||
\(929\) | 3.32782e116 | 0.192992 | 0.0964960 | − | 0.995333i | \(-0.469237\pi\) | ||||
0.0964960 | + | 0.995333i | \(0.469237\pi\) | |||||||
\(930\) | −3.39947e117 | −1.88945 | ||||||||
\(931\) | 3.32731e117 | 1.77248 | ||||||||
\(932\) | 7.87085e115 | 0.0401877 | ||||||||
\(933\) | −2.85508e117 | −1.39731 | ||||||||
\(934\) | −2.12563e117 | −0.997208 | ||||||||
\(935\) | 1.05713e117 | 0.475413 | ||||||||
\(936\) | −2.03795e116 | −0.0878613 | ||||||||
\(937\) | 1.14649e117 | 0.473866 | 0.236933 | − | 0.971526i | \(-0.423858\pi\) | ||||
0.236933 | + | 0.971526i | \(0.423858\pi\) | |||||||
\(938\) | 1.73068e117 | 0.685810 | ||||||||
\(939\) | 1.81096e117 | 0.688046 | ||||||||
\(940\) | 2.87411e117 | 1.04702 | ||||||||
\(941\) | 2.64667e117 | 0.924507 | 0.462253 | − | 0.886748i | \(-0.347041\pi\) | ||||
0.462253 | + | 0.886748i | \(0.347041\pi\) | |||||||
\(942\) | 9.58494e116 | 0.321055 | ||||||||
\(943\) | 2.20447e117 | 0.708095 | ||||||||
\(944\) | −1.27100e117 | −0.391518 | ||||||||
\(945\) | −6.16206e117 | −1.82041 | ||||||||
\(946\) | 2.44731e117 | 0.693407 | ||||||||
\(947\) | −6.09833e117 | −1.65724 | −0.828622 | − | 0.559809i | \(-0.810875\pi\) | ||||
−0.828622 | + | 0.559809i | \(0.810875\pi\) | |||||||
\(948\) | 9.73994e116 | 0.253879 | ||||||||
\(949\) | −2.87301e117 | −0.718325 | ||||||||
\(950\) | 4.77910e117 | 1.14621 | ||||||||
\(951\) | −5.75389e117 | −1.32383 | ||||||||
\(952\) | 1.29302e117 | 0.285394 | ||||||||
\(953\) | −2.86861e117 | −0.607438 | −0.303719 | − | 0.952762i | \(-0.598228\pi\) | ||||
−0.303719 | + | 0.952762i | \(0.598228\pi\) | |||||||
\(954\) | −5.02490e116 | −0.102086 | ||||||||
\(955\) | 6.91454e117 | 1.34781 | ||||||||
\(956\) | 1.95726e117 | 0.366068 | ||||||||
\(957\) | 5.05545e117 | 0.907274 | ||||||||
\(958\) | −2.56323e117 | −0.441419 | ||||||||
\(959\) | 1.03295e118 | 1.70705 | ||||||||
\(960\) | 1.42914e117 | 0.226652 | ||||||||
\(961\) | 7.69821e117 | 1.17170 | ||||||||
\(962\) | 3.44320e117 | 0.502975 | ||||||||
\(963\) | −9.38899e116 | −0.131638 | ||||||||
\(964\) | −2.33238e117 | −0.313874 | ||||||||
\(965\) | −8.35032e117 | −1.07863 | ||||||||
\(966\) | −1.47641e118 | −1.83067 | ||||||||
\(967\) | 4.09752e117 | 0.487725 | 0.243862 | − | 0.969810i | \(-0.421585\pi\) | ||||
0.243862 | + | 0.969810i | \(0.421585\pi\) | |||||||
\(968\) | −1.96231e117 | −0.224229 | ||||||||
\(969\) | −6.25828e117 | −0.686540 | ||||||||
\(970\) | 1.08923e118 | 1.14719 | ||||||||
\(971\) | −9.47250e117 | −0.957867 | −0.478933 | − | 0.877851i | \(-0.658976\pi\) | ||||
−0.478933 | + | 0.877851i | \(0.658976\pi\) | |||||||
\(972\) | 3.62729e117 | 0.352180 | ||||||||
\(973\) | −2.65276e118 | −2.47309 | ||||||||
\(974\) | −6.35877e117 | −0.569239 | ||||||||
\(975\) | 1.28426e118 | 1.10400 | ||||||||
\(976\) | −2.87647e117 | −0.237461 | ||||||||
\(977\) | 8.95310e117 | 0.709804 | 0.354902 | − | 0.934904i | \(-0.384514\pi\) | ||||
0.354902 | + | 0.934904i | \(0.384514\pi\) | |||||||
\(978\) | −4.90602e117 | −0.373546 | ||||||||
\(979\) | 4.58281e117 | 0.335132 | ||||||||
\(980\) | −1.69041e118 | −1.18730 | ||||||||
\(981\) | −7.58077e117 | −0.511432 | ||||||||
\(982\) | 2.01829e117 | 0.130792 | ||||||||
\(983\) | −1.68447e118 | −1.04857 | −0.524287 | − | 0.851542i | \(-0.675668\pi\) | ||||
−0.524287 | + | 0.851542i | \(0.675668\pi\) | |||||||
\(984\) | −3.52311e117 | −0.210678 | ||||||||
\(985\) | 3.83729e118 | 2.20442 | ||||||||
\(986\) | 8.33218e117 | 0.459854 | ||||||||
\(987\) | 4.74527e118 | 2.51613 | ||||||||
\(988\) | −7.64332e117 | −0.389388 | ||||||||
\(989\) | −4.60563e118 | −2.25442 | ||||||||
\(990\) | 5.20079e117 | 0.244613 | ||||||||
\(991\) | 1.36583e118 | 0.617287 | 0.308643 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308643 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(992\) | −5.99841e117 | −0.260510 | ||||||||
\(993\) | −2.27442e118 | −0.949240 | ||||||||
\(994\) | 1.65805e118 | 0.665022 | ||||||||
\(995\) | 3.21759e118 | 1.24028 | ||||||||
\(996\) | 1.14962e118 | 0.425903 | ||||||||
\(997\) | 2.34775e118 | 0.835973 | 0.417987 | − | 0.908453i | \(-0.362736\pi\) | ||||
0.417987 | + | 0.908453i | \(0.362736\pi\) | |||||||
\(998\) | −1.37245e118 | −0.469722 | ||||||||
\(999\) | −2.37072e118 | −0.779909 |
(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 | 2.80.a.a.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.80.a.a.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial |