Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,122,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, 122, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 122);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 122 \) |
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: | \(92.7173263878\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 2 x^{8} + \cdots + 32\!\cdots\!74 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{145}\cdot 3^{53}\cdot 5^{20}\cdot 7^{8}\cdot 11^{6}\cdot 13^{2}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77468e16\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.07240e18 | −1.27104 | −0.635520 | − | 0.772084i | \(-0.719214\pi\) | ||||
−0.635520 | + | 0.772084i | \(0.719214\pi\) | |||||||
\(3\) | −2.64580e28 | −0.360347 | −0.180174 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180174 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(4\) | 1.63640e36 | 0.615544 | ||||||||
\(5\) | −5.16214e41 | −0.266161 | −0.133081 | − | 0.991105i | \(-0.542487\pi\) | ||||
−0.133081 | + | 0.991105i | \(0.542487\pi\) | |||||||
\(6\) | 5.48316e46 | 0.458016 | ||||||||
\(7\) | −2.39892e51 | −1.78478 | −0.892391 | − | 0.451264i | \(-0.850973\pi\) | ||||
−0.892391 | + | 0.451264i | \(0.850973\pi\) | |||||||
\(8\) | 2.11812e54 | 0.488660 | ||||||||
\(9\) | −4.69101e57 | −0.870150 | ||||||||
\(10\) | 1.06980e60 | 0.338302 | ||||||||
\(11\) | 6.81449e62 | 0.674802 | 0.337401 | − | 0.941361i | \(-0.390452\pi\) | ||||
0.337401 | + | 0.941361i | \(0.390452\pi\) | |||||||
\(12\) | −4.32958e64 | −0.221809 | ||||||||
\(13\) | 2.56774e66 | 0.103748 | 0.0518738 | − | 0.998654i | \(-0.483481\pi\) | ||||
0.0518738 | + | 0.998654i | \(0.483481\pi\) | |||||||
\(14\) | 4.97154e69 | 2.26853 | ||||||||
\(15\) | 1.36580e70 | 0.0959105 | ||||||||
\(16\) | −8.73988e72 | −1.23665 | ||||||||
\(17\) | −1.61699e74 | −0.584180 | −0.292090 | − | 0.956391i | \(-0.594351\pi\) | ||||
−0.292090 | + | 0.956391i | \(0.594351\pi\) | |||||||
\(18\) | 9.72165e75 | 1.10600 | ||||||||
\(19\) | −1.10211e76 | −0.0476028 | −0.0238014 | − | 0.999717i | \(-0.507577\pi\) | ||||
−0.0238014 | + | 0.999717i | \(0.507577\pi\) | |||||||
\(20\) | −8.44731e77 | −0.163834 | ||||||||
\(21\) | 6.34707e79 | 0.643141 | ||||||||
\(22\) | −1.41224e81 | −0.857700 | ||||||||
\(23\) | −5.71167e81 | −0.235629 | −0.117815 | − | 0.993036i | \(-0.537589\pi\) | ||||
−0.117815 | + | 0.993036i | \(0.537589\pi\) | |||||||
\(24\) | −5.60412e82 | −0.176087 | ||||||||
\(25\) | −3.49510e84 | −0.929158 | ||||||||
\(26\) | −5.32139e84 | −0.131867 | ||||||||
\(27\) | 2.66751e86 | 0.673903 | ||||||||
\(28\) | −3.92559e87 | −1.09861 | ||||||||
\(29\) | 5.46451e88 | 1.83009 | 0.915044 | − | 0.403354i | \(-0.132156\pi\) | ||||
0.915044 | + | 0.403354i | \(0.132156\pi\) | |||||||
\(30\) | −2.83049e88 | −0.121906 | ||||||||
\(31\) | −1.61112e90 | −0.954433 | −0.477217 | − | 0.878786i | \(-0.658354\pi\) | ||||
−0.477217 | + | 0.878786i | \(0.658354\pi\) | |||||||
\(32\) | 1.24816e91 | 1.08317 | ||||||||
\(33\) | −1.80298e91 | −0.243163 | ||||||||
\(34\) | 3.35104e92 | 0.742516 | ||||||||
\(35\) | 1.23836e93 | 0.475040 | ||||||||
\(36\) | −7.67634e93 | −0.535615 | ||||||||
\(37\) | −2.70619e94 | −0.359877 | −0.179939 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179939 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(38\) | 2.28402e94 | 0.0605051 | ||||||||
\(39\) | −6.79372e94 | −0.0373851 | ||||||||
\(40\) | −1.09340e96 | −0.130062 | ||||||||
\(41\) | 3.14111e97 | 0.838801 | 0.419401 | − | 0.907801i | \(-0.362240\pi\) | ||||
0.419401 | + | 0.907801i | \(0.362240\pi\) | |||||||
\(42\) | −1.31537e98 | −0.817458 | ||||||||
\(43\) | 7.06608e98 | 1.05764 | 0.528819 | − | 0.848734i | \(-0.322635\pi\) | ||||
0.528819 | + | 0.848734i | \(0.322635\pi\) | |||||||
\(44\) | 1.11512e99 | 0.415370 | ||||||||
\(45\) | 2.42156e99 | 0.231600 | ||||||||
\(46\) | 1.18369e100 | 0.299494 | ||||||||
\(47\) | 1.46831e101 | 1.01134 | 0.505671 | − | 0.862726i | \(-0.331245\pi\) | ||||
0.505671 | + | 0.862726i | \(0.331245\pi\) | |||||||
\(48\) | 2.31240e101 | 0.445623 | ||||||||
\(49\) | 3.94823e102 | 2.18544 | ||||||||
\(50\) | 7.24326e102 | 1.18100 | ||||||||
\(51\) | 4.27822e102 | 0.210507 | ||||||||
\(52\) | 4.20183e102 | 0.0638611 | ||||||||
\(53\) | 3.40087e104 | 1.63267 | 0.816337 | − | 0.577576i | \(-0.196001\pi\) | ||||
0.816337 | + | 0.577576i | \(0.196001\pi\) | |||||||
\(54\) | −5.52814e104 | −0.856558 | ||||||||
\(55\) | −3.51774e104 | −0.179606 | ||||||||
\(56\) | −5.08121e105 | −0.872151 | ||||||||
\(57\) | 2.91597e104 | 0.0171535 | ||||||||
\(58\) | −1.13247e107 | −2.32612 | ||||||||
\(59\) | 1.01537e107 | 0.741444 | 0.370722 | − | 0.928744i | \(-0.379110\pi\) | ||||
0.370722 | + | 0.928744i | \(0.379110\pi\) | |||||||
\(60\) | 2.23499e106 | 0.0590371 | ||||||||
\(61\) | −6.56814e107 | −0.638245 | −0.319122 | − | 0.947713i | \(-0.603388\pi\) | ||||
−0.319122 | + | 0.947713i | \(0.603388\pi\) | |||||||
\(62\) | 3.33889e108 | 1.21312 | ||||||||
\(63\) | 1.12534e109 | 1.55303 | ||||||||
\(64\) | −2.63235e108 | −0.140106 | ||||||||
\(65\) | −1.32550e108 | −0.0276136 | ||||||||
\(66\) | 3.73650e109 | 0.309070 | ||||||||
\(67\) | −3.87624e110 | −1.29088 | −0.645439 | − | 0.763812i | \(-0.723325\pi\) | ||||
−0.645439 | + | 0.763812i | \(0.723325\pi\) | |||||||
\(68\) | −2.64603e110 | −0.359588 | ||||||||
\(69\) | 1.51119e110 | 0.0849084 | ||||||||
\(70\) | −2.56638e111 | −0.603795 | ||||||||
\(71\) | 4.17247e110 | 0.0416163 | 0.0208081 | − | 0.999783i | \(-0.493376\pi\) | ||||
0.0208081 | + | 0.999783i | \(0.493376\pi\) | |||||||
\(72\) | −9.93611e111 | −0.425207 | ||||||||
\(73\) | 8.94067e112 | 1.66088 | 0.830438 | − | 0.557111i | \(-0.188090\pi\) | ||||
0.830438 | + | 0.557111i | \(0.188090\pi\) | |||||||
\(74\) | 5.60832e112 | 0.457419 | ||||||||
\(75\) | 9.24735e112 | 0.334820 | ||||||||
\(76\) | −1.80349e112 | −0.0293016 | ||||||||
\(77\) | −1.63474e114 | −1.20437 | ||||||||
\(78\) | 1.40793e113 | 0.0475180 | ||||||||
\(79\) | −8.25811e114 | −1.28956 | −0.644780 | − | 0.764368i | \(-0.723051\pi\) | ||||
−0.644780 | + | 0.764368i | \(0.723051\pi\) | |||||||
\(80\) | 4.51165e114 | 0.329148 | ||||||||
\(81\) | 1.82317e115 | 0.627311 | ||||||||
\(82\) | −6.50963e115 | −1.06615 | ||||||||
\(83\) | 2.01103e116 | 1.58196 | 0.790979 | − | 0.611843i | \(-0.209572\pi\) | ||||
0.790979 | + | 0.611843i | \(0.209572\pi\) | |||||||
\(84\) | 1.03863e116 | 0.395881 | ||||||||
\(85\) | 8.34711e115 | 0.155486 | ||||||||
\(86\) | −1.46438e117 | −1.34430 | ||||||||
\(87\) | −1.44580e117 | −0.659467 | ||||||||
\(88\) | 1.44339e117 | 0.329748 | ||||||||
\(89\) | −1.38039e118 | −1.59186 | −0.795932 | − | 0.605386i | \(-0.793019\pi\) | ||||
−0.795932 | + | 0.605386i | \(0.793019\pi\) | |||||||
\(90\) | −5.01846e117 | −0.294373 | ||||||||
\(91\) | −6.15981e117 | −0.185167 | ||||||||
\(92\) | −9.34656e117 | −0.145040 | ||||||||
\(93\) | 4.26270e118 | 0.343927 | ||||||||
\(94\) | −3.04293e119 | −1.28546 | ||||||||
\(95\) | 5.68926e117 | 0.0126700 | ||||||||
\(96\) | −3.30239e119 | −0.390318 | ||||||||
\(97\) | −2.29519e120 | −1.44920 | −0.724602 | − | 0.689168i | \(-0.757976\pi\) | ||||
−0.724602 | + | 0.689168i | \(0.757976\pi\) | |||||||
\(98\) | −8.18233e120 | −2.77779 | ||||||||
\(99\) | −3.19668e120 | −0.587179 | ||||||||
\(100\) | −5.71937e120 | −0.571937 | ||||||||
\(101\) | −2.31541e120 | −0.126819 | −0.0634096 | − | 0.997988i | \(-0.520197\pi\) | ||||
−0.0634096 | + | 0.997988i | \(0.520197\pi\) | |||||||
\(102\) | −8.86619e120 | −0.267563 | ||||||||
\(103\) | −3.55655e121 | −0.594809 | −0.297404 | − | 0.954752i | \(-0.596121\pi\) | ||||
−0.297404 | + | 0.954752i | \(0.596121\pi\) | |||||||
\(104\) | 5.43878e120 | 0.0506972 | ||||||||
\(105\) | −3.27645e121 | −0.171179 | ||||||||
\(106\) | −7.04797e122 | −2.07519 | ||||||||
\(107\) | 5.79788e121 | 0.0967277 | 0.0483639 | − | 0.998830i | \(-0.484599\pi\) | ||||
0.0483639 | + | 0.998830i | \(0.484599\pi\) | |||||||
\(108\) | 4.36509e122 | 0.414817 | ||||||||
\(109\) | −6.45454e122 | −0.351206 | −0.175603 | − | 0.984461i | \(-0.556188\pi\) | ||||
−0.175603 | + | 0.984461i | \(0.556188\pi\) | |||||||
\(110\) | 7.29017e122 | 0.228286 | ||||||||
\(111\) | 7.16005e122 | 0.129681 | ||||||||
\(112\) | 2.09663e124 | 2.20715 | ||||||||
\(113\) | 2.20120e124 | 1.35336 | 0.676680 | − | 0.736277i | \(-0.263418\pi\) | ||||
0.676680 | + | 0.736277i | \(0.263418\pi\) | |||||||
\(114\) | −6.04305e122 | −0.0218028 | ||||||||
\(115\) | 2.94845e123 | 0.0627154 | ||||||||
\(116\) | 8.94209e124 | 1.12650 | ||||||||
\(117\) | −1.20453e124 | −0.0902759 | ||||||||
\(118\) | −2.10426e125 | −0.942406 | ||||||||
\(119\) | 3.87903e125 | 1.04263 | ||||||||
\(120\) | 2.89293e124 | 0.0468676 | ||||||||
\(121\) | −5.55427e125 | −0.544643 | ||||||||
\(122\) | 1.36118e126 | 0.811235 | ||||||||
\(123\) | −8.31074e125 | −0.302260 | ||||||||
\(124\) | −2.63643e126 | −0.587495 | ||||||||
\(125\) | 3.74601e126 | 0.513467 | ||||||||
\(126\) | −2.33215e127 | −1.97396 | ||||||||
\(127\) | −2.40916e127 | −1.26398 | −0.631991 | − | 0.774976i | \(-0.717762\pi\) | ||||
−0.631991 | + | 0.774976i | \(0.717762\pi\) | |||||||
\(128\) | −2.77266e127 | −0.905092 | ||||||||
\(129\) | −1.86954e127 | −0.381117 | ||||||||
\(130\) | 2.74698e126 | 0.0350980 | ||||||||
\(131\) | 1.88519e128 | 1.51510 | 0.757550 | − | 0.652778i | \(-0.226396\pi\) | ||||
0.757550 | + | 0.652778i | \(0.226396\pi\) | |||||||
\(132\) | −2.95039e127 | −0.149677 | ||||||||
\(133\) | 2.64388e127 | 0.0849606 | ||||||||
\(134\) | 8.03313e128 | 1.64076 | ||||||||
\(135\) | −1.37700e128 | −0.179367 | ||||||||
\(136\) | −3.42497e128 | −0.285465 | ||||||||
\(137\) | 5.12965e128 | 0.274469 | 0.137235 | − | 0.990539i | \(-0.456179\pi\) | ||||
0.137235 | + | 0.990539i | \(0.456179\pi\) | |||||||
\(138\) | −3.13180e128 | −0.107922 | ||||||||
\(139\) | 5.83869e129 | 1.29993 | 0.649965 | − | 0.759964i | \(-0.274784\pi\) | ||||
0.649965 | + | 0.759964i | \(0.274784\pi\) | |||||||
\(140\) | 2.02644e129 | 0.292408 | ||||||||
\(141\) | −3.88486e129 | −0.364434 | ||||||||
\(142\) | −8.64704e128 | −0.0528960 | ||||||||
\(143\) | 1.74978e129 | 0.0700090 | ||||||||
\(144\) | 4.09988e130 | 1.07607 | ||||||||
\(145\) | −2.82086e130 | −0.487099 | ||||||||
\(146\) | −1.85287e131 | −2.11104 | ||||||||
\(147\) | −1.04462e131 | −0.787519 | ||||||||
\(148\) | −4.42840e130 | −0.221520 | ||||||||
\(149\) | −2.54981e131 | −0.848671 | −0.424335 | − | 0.905505i | \(-0.639492\pi\) | ||||
−0.424335 | + | 0.905505i | \(0.639492\pi\) | |||||||
\(150\) | −1.91642e131 | −0.425569 | ||||||||
\(151\) | 5.59487e131 | 0.831160 | 0.415580 | − | 0.909557i | \(-0.363579\pi\) | ||||
0.415580 | + | 0.909557i | \(0.363579\pi\) | |||||||
\(152\) | −2.33440e130 | −0.0232616 | ||||||||
\(153\) | 7.58529e131 | 0.508324 | ||||||||
\(154\) | 3.38785e132 | 1.53081 | ||||||||
\(155\) | 8.31684e131 | 0.254033 | ||||||||
\(156\) | −1.11172e131 | −0.0230122 | ||||||||
\(157\) | −5.66314e132 | −0.796395 | −0.398198 | − | 0.917300i | \(-0.630364\pi\) | ||||
−0.398198 | + | 0.917300i | \(0.630364\pi\) | |||||||
\(158\) | 1.71141e133 | 1.63908 | ||||||||
\(159\) | −8.99802e132 | −0.588330 | ||||||||
\(160\) | −6.44319e132 | −0.288298 | ||||||||
\(161\) | 1.37019e133 | 0.420547 | ||||||||
\(162\) | −3.77833e133 | −0.797337 | ||||||||
\(163\) | 8.91375e133 | 1.29631 | 0.648157 | − | 0.761506i | \(-0.275540\pi\) | ||||
0.648157 | + | 0.761506i | \(0.275540\pi\) | |||||||
\(164\) | 5.14009e133 | 0.516319 | ||||||||
\(165\) | 9.30723e132 | 0.0647205 | ||||||||
\(166\) | −4.16767e134 | −2.01073 | ||||||||
\(167\) | −3.85090e134 | −1.29186 | −0.645930 | − | 0.763397i | \(-0.723530\pi\) | ||||
−0.645930 | + | 0.763397i | \(0.723530\pi\) | |||||||
\(168\) | 1.34439e134 | 0.314277 | ||||||||
\(169\) | −6.05962e134 | −0.989236 | ||||||||
\(170\) | −1.72986e134 | −0.197629 | ||||||||
\(171\) | 5.17001e133 | 0.0414216 | ||||||||
\(172\) | 1.15629e135 | 0.651023 | ||||||||
\(173\) | 6.93703e134 | 0.275033 | 0.137516 | − | 0.990499i | \(-0.456088\pi\) | ||||
0.137516 | + | 0.990499i | \(0.456088\pi\) | |||||||
\(174\) | 2.99628e135 | 0.838209 | ||||||||
\(175\) | 8.38449e135 | 1.65834 | ||||||||
\(176\) | −5.95579e135 | −0.834493 | ||||||||
\(177\) | −2.68647e135 | −0.267177 | ||||||||
\(178\) | 2.86072e136 | 2.02332 | ||||||||
\(179\) | −1.40783e136 | −0.709482 | −0.354741 | − | 0.934965i | \(-0.615431\pi\) | ||||
−0.354741 | + | 0.934965i | \(0.615431\pi\) | |||||||
\(180\) | 3.96264e135 | 0.142560 | ||||||||
\(181\) | −6.92545e136 | −1.78195 | −0.890973 | − | 0.454057i | \(-0.849976\pi\) | ||||
−0.890973 | + | 0.454057i | \(0.849976\pi\) | |||||||
\(182\) | 1.27656e136 | 0.235354 | ||||||||
\(183\) | 1.73780e136 | 0.229990 | ||||||||
\(184\) | −1.20980e136 | −0.115143 | ||||||||
\(185\) | 1.39698e136 | 0.0957854 | ||||||||
\(186\) | −8.83404e136 | −0.437146 | ||||||||
\(187\) | −1.10189e137 | −0.394205 | ||||||||
\(188\) | 2.40274e137 | 0.622525 | ||||||||
\(189\) | −6.39914e137 | −1.20277 | ||||||||
\(190\) | −1.17904e136 | −0.0161041 | ||||||||
\(191\) | −9.75491e137 | −0.969850 | −0.484925 | − | 0.874556i | \(-0.661153\pi\) | ||||
−0.484925 | + | 0.874556i | \(0.661153\pi\) | |||||||
\(192\) | 6.96468e136 | 0.0504867 | ||||||||
\(193\) | 1.27458e137 | 0.0674762 | 0.0337381 | − | 0.999431i | \(-0.489259\pi\) | ||||
0.0337381 | + | 0.999431i | \(0.489259\pi\) | |||||||
\(194\) | 4.75657e138 | 1.84200 | ||||||||
\(195\) | 3.50702e136 | 0.00995047 | ||||||||
\(196\) | 6.46087e138 | 1.34524 | ||||||||
\(197\) | 8.72607e137 | 0.133540 | 0.0667701 | − | 0.997768i | \(-0.478731\pi\) | ||||
0.0667701 | + | 0.997768i | \(0.478731\pi\) | |||||||
\(198\) | 6.62481e138 | 0.746328 | ||||||||
\(199\) | −5.08881e138 | −0.422674 | −0.211337 | − | 0.977413i | \(-0.567782\pi\) | ||||
−0.211337 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(200\) | −7.40305e138 | −0.454042 | ||||||||
\(201\) | 1.02558e139 | 0.465164 | ||||||||
\(202\) | 4.79846e138 | 0.161192 | ||||||||
\(203\) | −1.31089e140 | −3.26631 | ||||||||
\(204\) | 7.00086e138 | 0.129577 | ||||||||
\(205\) | −1.62148e139 | −0.223256 | ||||||||
\(206\) | 7.37061e139 | 0.756026 | ||||||||
\(207\) | 2.67935e139 | 0.205033 | ||||||||
\(208\) | −2.24417e139 | −0.128299 | ||||||||
\(209\) | −7.51033e138 | −0.0321224 | ||||||||
\(210\) | 6.79012e139 | 0.217576 | ||||||||
\(211\) | −3.22420e140 | −0.775056 | −0.387528 | − | 0.921858i | \(-0.626671\pi\) | ||||
−0.387528 | + | 0.921858i | \(0.626671\pi\) | |||||||
\(212\) | 5.56516e140 | 1.00498 | ||||||||
\(213\) | −1.10395e139 | −0.0149963 | ||||||||
\(214\) | −1.20155e140 | −0.122945 | ||||||||
\(215\) | −3.64761e140 | −0.281502 | ||||||||
\(216\) | 5.65010e140 | 0.329309 | ||||||||
\(217\) | 3.86496e141 | 1.70346 | ||||||||
\(218\) | 1.33764e141 | 0.446397 | ||||||||
\(219\) | −2.36552e141 | −0.598492 | ||||||||
\(220\) | −5.75641e140 | −0.110555 | ||||||||
\(221\) | −4.15199e140 | −0.0606072 | ||||||||
\(222\) | −1.48385e141 | −0.164830 | ||||||||
\(223\) | 8.38698e141 | 0.709842 | 0.354921 | − | 0.934896i | \(-0.384508\pi\) | ||||
0.354921 | + | 0.934896i | \(0.384508\pi\) | |||||||
\(224\) | −2.99425e142 | −1.93323 | ||||||||
\(225\) | 1.63956e142 | 0.808507 | ||||||||
\(226\) | −4.56177e142 | −1.72018 | ||||||||
\(227\) | −5.86880e142 | −1.69428 | −0.847140 | − | 0.531369i | \(-0.821678\pi\) | ||||
−0.847140 | + | 0.531369i | \(0.821678\pi\) | |||||||
\(228\) | 4.77167e140 | 0.0105587 | ||||||||
\(229\) | 1.01653e143 | 1.72613 | 0.863066 | − | 0.505091i | \(-0.168541\pi\) | ||||
0.863066 | + | 0.505091i | \(0.168541\pi\) | |||||||
\(230\) | −6.11037e141 | −0.0797138 | ||||||||
\(231\) | 4.32521e142 | 0.433993 | ||||||||
\(232\) | 1.15745e143 | 0.894290 | ||||||||
\(233\) | 1.52230e143 | 0.906704 | 0.453352 | − | 0.891331i | \(-0.350228\pi\) | ||||
0.453352 | + | 0.891331i | \(0.350228\pi\) | |||||||
\(234\) | 2.49626e142 | 0.114744 | ||||||||
\(235\) | −7.57964e142 | −0.269180 | ||||||||
\(236\) | 1.66155e143 | 0.456391 | ||||||||
\(237\) | 2.18493e143 | 0.464689 | ||||||||
\(238\) | −8.03890e143 | −1.32523 | ||||||||
\(239\) | −4.56142e143 | −0.583481 | −0.291741 | − | 0.956497i | \(-0.594234\pi\) | ||||
−0.291741 | + | 0.956497i | \(0.594234\pi\) | |||||||
\(240\) | −1.19369e143 | −0.118608 | ||||||||
\(241\) | 1.10935e144 | 0.857110 | 0.428555 | − | 0.903516i | \(-0.359023\pi\) | ||||
0.428555 | + | 0.903516i | \(0.359023\pi\) | |||||||
\(242\) | 1.15107e144 | 0.692263 | ||||||||
\(243\) | −1.92043e144 | −0.899953 | ||||||||
\(244\) | −1.07481e144 | −0.392868 | ||||||||
\(245\) | −2.03813e144 | −0.581681 | ||||||||
\(246\) | 1.72232e144 | 0.384184 | ||||||||
\(247\) | −2.82993e142 | −0.00493867 | ||||||||
\(248\) | −3.41255e144 | −0.466393 | ||||||||
\(249\) | −5.32080e144 | −0.570054 | ||||||||
\(250\) | −7.76323e144 | −0.652637 | ||||||||
\(251\) | 1.21642e144 | 0.0803200 | 0.0401600 | − | 0.999193i | \(-0.487213\pi\) | ||||
0.0401600 | + | 0.999193i | \(0.487213\pi\) | |||||||
\(252\) | 1.84150e145 | 0.955956 | ||||||||
\(253\) | −3.89222e144 | −0.159003 | ||||||||
\(254\) | 4.99275e145 | 1.60657 | ||||||||
\(255\) | −2.20848e144 | −0.0560289 | ||||||||
\(256\) | 6.44586e145 | 1.29051 | ||||||||
\(257\) | −3.59155e145 | −0.567973 | −0.283987 | − | 0.958828i | \(-0.591657\pi\) | ||||
−0.283987 | + | 0.958828i | \(0.591657\pi\) | |||||||
\(258\) | 3.87445e145 | 0.484415 | ||||||||
\(259\) | 6.49195e145 | 0.642302 | ||||||||
\(260\) | −2.16905e144 | −0.0169974 | ||||||||
\(261\) | −2.56340e146 | −1.59245 | ||||||||
\(262\) | −3.90687e146 | −1.92575 | ||||||||
\(263\) | 1.64079e146 | 0.642289 | 0.321145 | − | 0.947030i | \(-0.395932\pi\) | ||||
0.321145 | + | 0.947030i | \(0.395932\pi\) | |||||||
\(264\) | −3.81893e145 | −0.118824 | ||||||||
\(265\) | −1.75558e146 | −0.434555 | ||||||||
\(266\) | −5.47918e145 | −0.107988 | ||||||||
\(267\) | 3.65223e146 | 0.573624 | ||||||||
\(268\) | −6.34306e146 | −0.794592 | ||||||||
\(269\) | −1.43687e146 | −0.143683 | −0.0718414 | − | 0.997416i | \(-0.522888\pi\) | ||||
−0.0718414 | + | 0.997416i | \(0.522888\pi\) | |||||||
\(270\) | 2.85371e146 | 0.227983 | ||||||||
\(271\) | 2.23153e147 | 1.42548 | 0.712740 | − | 0.701428i | \(-0.247454\pi\) | ||||
0.712740 | + | 0.701428i | \(0.247454\pi\) | |||||||
\(272\) | 1.41323e147 | 0.722426 | ||||||||
\(273\) | 1.62976e146 | 0.0667243 | ||||||||
\(274\) | −1.06307e147 | −0.348861 | ||||||||
\(275\) | −2.38174e147 | −0.626997 | ||||||||
\(276\) | 2.47291e146 | 0.0522648 | ||||||||
\(277\) | 7.37038e147 | 1.25160 | 0.625798 | − | 0.779985i | \(-0.284774\pi\) | ||||
0.625798 | + | 0.779985i | \(0.284774\pi\) | |||||||
\(278\) | −1.21001e148 | −1.65226 | ||||||||
\(279\) | 7.55778e147 | 0.830500 | ||||||||
\(280\) | 2.62299e147 | 0.232133 | ||||||||
\(281\) | 1.22628e148 | 0.874696 | 0.437348 | − | 0.899292i | \(-0.355918\pi\) | ||||
0.437348 | + | 0.899292i | \(0.355918\pi\) | |||||||
\(282\) | 8.05099e147 | 0.463211 | ||||||||
\(283\) | −3.36601e148 | −1.56328 | −0.781638 | − | 0.623733i | \(-0.785615\pi\) | ||||
−0.781638 | + | 0.623733i | \(0.785615\pi\) | |||||||
\(284\) | 6.82781e146 | 0.0256166 | ||||||||
\(285\) | −1.50526e146 | −0.00456561 | ||||||||
\(286\) | −3.62625e147 | −0.0889843 | ||||||||
\(287\) | −7.53527e148 | −1.49708 | ||||||||
\(288\) | −5.85514e148 | −0.942522 | ||||||||
\(289\) | −5.04696e148 | −0.658734 | ||||||||
\(290\) | 5.84595e148 | 0.619122 | ||||||||
\(291\) | 6.07263e148 | 0.522217 | ||||||||
\(292\) | 1.46305e149 | 1.02234 | ||||||||
\(293\) | 9.89552e148 | 0.562273 | 0.281137 | − | 0.959668i | \(-0.409289\pi\) | ||||
0.281137 | + | 0.959668i | \(0.409289\pi\) | |||||||
\(294\) | 2.16488e149 | 1.00097 | ||||||||
\(295\) | −5.24150e148 | −0.197344 | ||||||||
\(296\) | −5.73204e148 | −0.175858 | ||||||||
\(297\) | 1.81777e149 | 0.454751 | ||||||||
\(298\) | 5.28424e149 | 1.07869 | ||||||||
\(299\) | −1.46661e148 | −0.0244460 | ||||||||
\(300\) | 1.51323e149 | 0.206096 | ||||||||
\(301\) | −1.69510e150 | −1.88765 | ||||||||
\(302\) | −1.15948e150 | −1.05644 | ||||||||
\(303\) | 6.12611e148 | 0.0456989 | ||||||||
\(304\) | 9.63232e148 | 0.0588680 | ||||||||
\(305\) | 3.39057e149 | 0.169876 | ||||||||
\(306\) | −1.57198e150 | −0.646100 | ||||||||
\(307\) | 2.35422e150 | 0.794284 | 0.397142 | − | 0.917757i | \(-0.370002\pi\) | ||||
0.397142 | + | 0.917757i | \(0.370002\pi\) | |||||||
\(308\) | −2.67509e150 | −0.741344 | ||||||||
\(309\) | 9.40993e149 | 0.214338 | ||||||||
\(310\) | −1.72358e150 | −0.322886 | ||||||||
\(311\) | 6.35294e150 | 0.979424 | 0.489712 | − | 0.871884i | \(-0.337102\pi\) | ||||
0.489712 | + | 0.871884i | \(0.337102\pi\) | |||||||
\(312\) | −1.43899e149 | −0.0182686 | ||||||||
\(313\) | −6.10266e150 | −0.638391 | −0.319195 | − | 0.947689i | \(-0.603413\pi\) | ||||
−0.319195 | + | 0.947689i | \(0.603413\pi\) | |||||||
\(314\) | 1.17363e151 | 1.01225 | ||||||||
\(315\) | −5.80915e150 | −0.413356 | ||||||||
\(316\) | −1.35135e151 | −0.793780 | ||||||||
\(317\) | 8.99646e150 | 0.436502 | 0.218251 | − | 0.975893i | \(-0.429965\pi\) | ||||
0.218251 | + | 0.975893i | \(0.429965\pi\) | |||||||
\(318\) | 1.86475e151 | 0.747791 | ||||||||
\(319\) | 3.72378e151 | 1.23495 | ||||||||
\(320\) | 1.35886e150 | 0.0372907 | ||||||||
\(321\) | −1.53400e150 | −0.0348556 | ||||||||
\(322\) | −2.83958e151 | −0.534532 | ||||||||
\(323\) | 1.78210e150 | 0.0278086 | ||||||||
\(324\) | 2.98342e151 | 0.386137 | ||||||||
\(325\) | −8.97451e150 | −0.0963979 | ||||||||
\(326\) | −1.84729e152 | −1.64767 | ||||||||
\(327\) | 1.70774e151 | 0.126556 | ||||||||
\(328\) | 6.65324e151 | 0.409888 | ||||||||
\(329\) | −3.52237e152 | −1.80502 | ||||||||
\(330\) | −1.92883e151 | −0.0822624 | ||||||||
\(331\) | −3.69989e152 | −1.31400 | −0.657000 | − | 0.753890i | \(-0.728175\pi\) | ||||
−0.657000 | + | 0.753890i | \(0.728175\pi\) | |||||||
\(332\) | 3.29085e152 | 0.973764 | ||||||||
\(333\) | 1.26948e152 | 0.313147 | ||||||||
\(334\) | 7.98061e152 | 1.64201 | ||||||||
\(335\) | 2.00097e152 | 0.343582 | ||||||||
\(336\) | −5.54727e152 | −0.795340 | ||||||||
\(337\) | 1.38638e153 | 1.66063 | 0.830316 | − | 0.557292i | \(-0.188160\pi\) | ||||
0.830316 | + | 0.557292i | \(0.188160\pi\) | |||||||
\(338\) | 1.25580e153 | 1.25736 | ||||||||
\(339\) | −5.82393e152 | −0.487680 | ||||||||
\(340\) | 1.36592e152 | 0.0957084 | ||||||||
\(341\) | −1.09790e153 | −0.644053 | ||||||||
\(342\) | −1.07143e152 | −0.0526485 | ||||||||
\(343\) | −5.13760e153 | −2.11576 | ||||||||
\(344\) | 1.49668e153 | 0.516825 | ||||||||
\(345\) | −7.80100e151 | −0.0225993 | ||||||||
\(346\) | −1.43763e153 | −0.349578 | ||||||||
\(347\) | 7.57101e153 | 1.54604 | 0.773020 | − | 0.634382i | \(-0.218745\pi\) | ||||
0.773020 | + | 0.634382i | \(0.218745\pi\) | |||||||
\(348\) | −2.36590e153 | −0.405931 | ||||||||
\(349\) | 1.46318e153 | 0.211037 | 0.105519 | − | 0.994417i | \(-0.466350\pi\) | ||||
0.105519 | + | 0.994417i | \(0.466350\pi\) | |||||||
\(350\) | −1.73760e154 | −2.10782 | ||||||||
\(351\) | 6.84945e152 | 0.0699158 | ||||||||
\(352\) | 8.50559e153 | 0.730926 | ||||||||
\(353\) | 2.50797e153 | 0.181532 | 0.0907660 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907660 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(354\) | 5.56745e153 | 0.339593 | ||||||||
\(355\) | −2.15389e152 | −0.0110766 | ||||||||
\(356\) | −2.25886e154 | −0.979861 | ||||||||
\(357\) | −1.02631e154 | −0.375710 | ||||||||
\(358\) | 2.91759e154 | 0.901780 | ||||||||
\(359\) | 3.19117e154 | 0.833175 | 0.416587 | − | 0.909096i | \(-0.363226\pi\) | ||||
0.416587 | + | 0.909096i | \(0.363226\pi\) | |||||||
\(360\) | 5.12916e153 | 0.113174 | ||||||||
\(361\) | −5.34811e154 | −0.997734 | ||||||||
\(362\) | 1.43523e155 | 2.26492 | ||||||||
\(363\) | 1.46955e154 | 0.196261 | ||||||||
\(364\) | −1.00799e154 | −0.113978 | ||||||||
\(365\) | −4.61530e154 | −0.442061 | ||||||||
\(366\) | −3.60142e154 | −0.292326 | ||||||||
\(367\) | 4.61606e154 | 0.317669 | 0.158835 | − | 0.987305i | \(-0.449226\pi\) | ||||
0.158835 | + | 0.987305i | \(0.449226\pi\) | |||||||
\(368\) | 4.99194e154 | 0.291391 | ||||||||
\(369\) | −1.47349e155 | −0.729883 | ||||||||
\(370\) | −2.89510e154 | −0.121747 | ||||||||
\(371\) | −8.15842e155 | −2.91397 | ||||||||
\(372\) | 6.97547e154 | 0.211702 | ||||||||
\(373\) | −6.56950e154 | −0.169492 | −0.0847458 | − | 0.996403i | \(-0.527008\pi\) | ||||
−0.0847458 | + | 0.996403i | \(0.527008\pi\) | |||||||
\(374\) | 2.28357e155 | 0.501051 | ||||||||
\(375\) | −9.91118e154 | −0.185026 | ||||||||
\(376\) | 3.11006e155 | 0.494202 | ||||||||
\(377\) | 1.40314e155 | 0.189867 | ||||||||
\(378\) | 1.32616e156 | 1.52877 | ||||||||
\(379\) | −2.34599e155 | −0.230491 | −0.115245 | − | 0.993337i | \(-0.536765\pi\) | ||||
−0.115245 | + | 0.993337i | \(0.536765\pi\) | |||||||
\(380\) | 9.30987e153 | 0.00779895 | ||||||||
\(381\) | 6.37416e155 | 0.455472 | ||||||||
\(382\) | 2.02161e156 | 1.23272 | ||||||||
\(383\) | −1.63444e156 | −0.850830 | −0.425415 | − | 0.904998i | \(-0.639872\pi\) | ||||
−0.425415 | + | 0.904998i | \(0.639872\pi\) | |||||||
\(384\) | 7.33589e155 | 0.326147 | ||||||||
\(385\) | 8.43879e155 | 0.320557 | ||||||||
\(386\) | −2.64145e155 | −0.0857650 | ||||||||
\(387\) | −3.31470e156 | −0.920304 | ||||||||
\(388\) | −3.75585e156 | −0.892048 | ||||||||
\(389\) | −1.85102e156 | −0.376237 | −0.188118 | − | 0.982146i | \(-0.560239\pi\) | ||||
−0.188118 | + | 0.982146i | \(0.560239\pi\) | |||||||
\(390\) | −7.26795e154 | −0.0126475 | ||||||||
\(391\) | 9.23569e155 | 0.137650 | ||||||||
\(392\) | 8.36283e156 | 1.06794 | ||||||||
\(393\) | −4.98783e156 | −0.545962 | ||||||||
\(394\) | −1.80839e156 | −0.169735 | ||||||||
\(395\) | 4.26295e156 | 0.343231 | ||||||||
\(396\) | −5.23104e156 | −0.361434 | ||||||||
\(397\) | −2.01690e157 | −1.19635 | −0.598177 | − | 0.801364i | \(-0.704108\pi\) | ||||
−0.598177 | + | 0.801364i | \(0.704108\pi\) | |||||||
\(398\) | 1.05461e157 | 0.537236 | ||||||||
\(399\) | −6.99518e155 | −0.0306153 | ||||||||
\(400\) | 3.05468e157 | 1.14904 | ||||||||
\(401\) | −3.04168e157 | −0.983738 | −0.491869 | − | 0.870669i | \(-0.663686\pi\) | ||||
−0.491869 | + | 0.870669i | \(0.663686\pi\) | |||||||
\(402\) | −2.12541e157 | −0.591242 | ||||||||
\(403\) | −4.13694e156 | −0.0990201 | ||||||||
\(404\) | −3.78893e156 | −0.0780627 | ||||||||
\(405\) | −9.41145e156 | −0.166966 | ||||||||
\(406\) | 2.71670e158 | 4.15161 | ||||||||
\(407\) | −1.84413e157 | −0.242846 | ||||||||
\(408\) | 9.06179e156 | 0.102867 | ||||||||
\(409\) | −8.33715e157 | −0.816126 | −0.408063 | − | 0.912954i | \(-0.633796\pi\) | ||||
−0.408063 | + | 0.912954i | \(0.633796\pi\) | |||||||
\(410\) | 3.36037e157 | 0.283768 | ||||||||
\(411\) | −1.35720e157 | −0.0989042 | ||||||||
\(412\) | −5.81993e157 | −0.366131 | ||||||||
\(413\) | −2.43580e158 | −1.32332 | ||||||||
\(414\) | −5.55269e157 | −0.260605 | ||||||||
\(415\) | −1.03812e158 | −0.421056 | ||||||||
\(416\) | 3.20495e157 | 0.112376 | ||||||||
\(417\) | −1.54480e158 | −0.468426 | ||||||||
\(418\) | 1.55644e157 | 0.0408289 | ||||||||
\(419\) | −6.42807e158 | −1.45926 | −0.729630 | − | 0.683842i | \(-0.760308\pi\) | ||||
−0.729630 | + | 0.683842i | \(0.760308\pi\) | |||||||
\(420\) | −5.36157e157 | −0.105368 | ||||||||
\(421\) | 7.49095e158 | 1.27488 | 0.637441 | − | 0.770499i | \(-0.279993\pi\) | ||||
0.637441 | + | 0.770499i | \(0.279993\pi\) | |||||||
\(422\) | 6.68183e158 | 0.985128 | ||||||||
\(423\) | −6.88786e158 | −0.880019 | ||||||||
\(424\) | 7.20345e158 | 0.797822 | ||||||||
\(425\) | 5.65153e158 | 0.542795 | ||||||||
\(426\) | 2.28783e157 | 0.0190609 | ||||||||
\(427\) | 1.57565e159 | 1.13913 | ||||||||
\(428\) | 9.48763e157 | 0.0595401 | ||||||||
\(429\) | −4.62958e157 | −0.0252275 | ||||||||
\(430\) | 7.55932e158 | 0.357801 | ||||||||
\(431\) | −1.69880e159 | −0.698664 | −0.349332 | − | 0.936999i | \(-0.613591\pi\) | ||||
−0.349332 | + | 0.936999i | \(0.613591\pi\) | |||||||
\(432\) | −2.33137e159 | −0.833382 | ||||||||
\(433\) | 4.37631e159 | 1.36016 | 0.680080 | − | 0.733138i | \(-0.261945\pi\) | ||||
0.680080 | + | 0.733138i | \(0.261945\pi\) | |||||||
\(434\) | −8.00974e159 | −2.16516 | ||||||||
\(435\) | 7.46342e158 | 0.175525 | ||||||||
\(436\) | −1.05622e159 | −0.216183 | ||||||||
\(437\) | 6.29490e157 | 0.0112166 | ||||||||
\(438\) | 4.90232e159 | 0.760707 | ||||||||
\(439\) | 6.94989e159 | 0.939452 | 0.469726 | − | 0.882812i | \(-0.344353\pi\) | ||||
0.469726 | + | 0.882812i | \(0.344353\pi\) | |||||||
\(440\) | −7.45099e158 | −0.0877662 | ||||||||
\(441\) | −1.85212e160 | −1.90166 | ||||||||
\(442\) | 8.60460e158 | 0.0770342 | ||||||||
\(443\) | −8.71532e158 | −0.0680547 | −0.0340273 | − | 0.999421i | \(-0.510833\pi\) | ||||
−0.0340273 | + | 0.999421i | \(0.510833\pi\) | |||||||
\(444\) | 1.17167e159 | 0.0798242 | ||||||||
\(445\) | 7.12576e159 | 0.423692 | ||||||||
\(446\) | −1.73812e160 | −0.902238 | ||||||||
\(447\) | 6.74630e159 | 0.305816 | ||||||||
\(448\) | 6.31481e159 | 0.250058 | ||||||||
\(449\) | 1.45705e160 | 0.504163 | 0.252082 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252082 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(450\) | −3.39782e160 | −1.02764 | ||||||||
\(451\) | 2.14050e160 | 0.566024 | ||||||||
\(452\) | 3.60203e160 | 0.833052 | ||||||||
\(453\) | −1.48029e160 | −0.299506 | ||||||||
\(454\) | 1.21625e161 | 2.15350 | ||||||||
\(455\) | 3.17978e159 | 0.0492842 | ||||||||
\(456\) | 6.17637e158 | 0.00838224 | ||||||||
\(457\) | 9.72851e160 | 1.15642 | 0.578211 | − | 0.815887i | \(-0.303751\pi\) | ||||
0.578211 | + | 0.815887i | \(0.303751\pi\) | |||||||
\(458\) | −2.10666e161 | −2.19398 | ||||||||
\(459\) | −4.31332e160 | −0.393681 | ||||||||
\(460\) | 4.82483e159 | 0.0386041 | ||||||||
\(461\) | −2.24952e160 | −0.157828 | −0.0789141 | − | 0.996881i | \(-0.525145\pi\) | ||||
−0.0789141 | + | 0.996881i | \(0.525145\pi\) | |||||||
\(462\) | −8.96357e160 | −0.551622 | ||||||||
\(463\) | 1.06518e161 | 0.575141 | 0.287571 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287571 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(464\) | −4.77591e161 | −2.26318 | ||||||||
\(465\) | −2.20047e160 | −0.0915401 | ||||||||
\(466\) | −3.15481e161 | −1.15246 | ||||||||
\(467\) | 9.57907e160 | 0.307363 | 0.153682 | − | 0.988120i | \(-0.450887\pi\) | ||||
0.153682 | + | 0.988120i | \(0.450887\pi\) | |||||||
\(468\) | −1.97108e160 | −0.0555688 | ||||||||
\(469\) | 9.29881e161 | 2.30393 | ||||||||
\(470\) | 1.57081e161 | 0.342139 | ||||||||
\(471\) | 1.49835e161 | 0.286979 | ||||||||
\(472\) | 2.15068e161 | 0.362314 | ||||||||
\(473\) | 4.81518e161 | 0.713696 | ||||||||
\(474\) | −4.52806e161 | −0.590639 | ||||||||
\(475\) | 3.85199e160 | 0.0442305 | ||||||||
\(476\) | 6.34762e161 | 0.641786 | ||||||||
\(477\) | −1.59535e162 | −1.42067 | ||||||||
\(478\) | 9.45310e161 | 0.741629 | ||||||||
\(479\) | 5.22132e161 | 0.360979 | 0.180489 | − | 0.983577i | \(-0.442232\pi\) | ||||
0.180489 | + | 0.983577i | \(0.442232\pi\) | |||||||
\(480\) | 1.70474e161 | 0.103888 | ||||||||
\(481\) | −6.94880e160 | −0.0373364 | ||||||||
\(482\) | −2.29901e162 | −1.08942 | ||||||||
\(483\) | −3.62524e161 | −0.151543 | ||||||||
\(484\) | −9.08898e161 | −0.335251 | ||||||||
\(485\) | 1.18481e162 | 0.385722 | ||||||||
\(486\) | 3.97991e162 | 1.14388 | ||||||||
\(487\) | −4.57656e162 | −1.16155 | −0.580774 | − | 0.814065i | \(-0.697250\pi\) | ||||
−0.580774 | + | 0.814065i | \(0.697250\pi\) | |||||||
\(488\) | −1.39121e162 | −0.311885 | ||||||||
\(489\) | −2.35840e162 | −0.467123 | ||||||||
\(490\) | 4.22383e162 | 0.739340 | ||||||||
\(491\) | −8.60617e161 | −0.133162 | −0.0665809 | − | 0.997781i | \(-0.521209\pi\) | ||||
−0.0665809 | + | 0.997781i | \(0.521209\pi\) | |||||||
\(492\) | −1.35997e162 | −0.186054 | ||||||||
\(493\) | −8.83603e162 | −1.06910 | ||||||||
\(494\) | 5.86476e160 | 0.00627725 | ||||||||
\(495\) | 1.65017e162 | 0.156284 | ||||||||
\(496\) | 1.40810e163 | 1.18030 | ||||||||
\(497\) | −1.00094e162 | −0.0742760 | ||||||||
\(498\) | 1.10268e163 | 0.724562 | ||||||||
\(499\) | −2.43499e163 | −1.41715 | −0.708573 | − | 0.705637i | \(-0.750661\pi\) | ||||
−0.708573 | + | 0.705637i | \(0.750661\pi\) | |||||||
\(500\) | 6.12995e162 | 0.316061 | ||||||||
\(501\) | 1.01887e163 | 0.465518 | ||||||||
\(502\) | −2.52091e162 | −0.102090 | ||||||||
\(503\) | 4.06905e163 | 1.46093 | 0.730466 | − | 0.682949i | \(-0.239303\pi\) | ||||
0.730466 | + | 0.682949i | \(0.239303\pi\) | |||||||
\(504\) | 2.38360e163 | 0.758902 | ||||||||
\(505\) | 1.19525e162 | 0.0337543 | ||||||||
\(506\) | 8.06624e162 | 0.202099 | ||||||||
\(507\) | 1.60326e163 | 0.356469 | ||||||||
\(508\) | −3.94234e163 | −0.778036 | ||||||||
\(509\) | −1.84603e163 | −0.323455 | −0.161728 | − | 0.986835i | \(-0.551707\pi\) | ||||
−0.161728 | + | 0.986835i | \(0.551707\pi\) | |||||||
\(510\) | 4.57686e162 | 0.0712150 | ||||||||
\(511\) | −2.14480e164 | −2.96430 | ||||||||
\(512\) | −5.98743e163 | −0.735204 | ||||||||
\(513\) | −2.93989e162 | −0.0320797 | ||||||||
\(514\) | 7.44313e163 | 0.721917 | ||||||||
\(515\) | 1.83594e163 | 0.158315 | ||||||||
\(516\) | −3.05931e163 | −0.234594 | ||||||||
\(517\) | 1.00058e164 | 0.682455 | ||||||||
\(518\) | −1.34539e164 | −0.816392 | ||||||||
\(519\) | −1.83540e163 | −0.0991073 | ||||||||
\(520\) | −2.80758e162 | −0.0134936 | ||||||||
\(521\) | 3.64619e164 | 1.56012 | 0.780058 | − | 0.625708i | \(-0.215190\pi\) | ||||
0.780058 | + | 0.625708i | \(0.215190\pi\) | |||||||
\(522\) | 5.31240e164 | 2.02407 | ||||||||
\(523\) | −2.38094e164 | −0.807971 | −0.403986 | − | 0.914765i | \(-0.632375\pi\) | ||||
−0.403986 | + | 0.914765i | \(0.632375\pi\) | |||||||
\(524\) | 3.08491e164 | 0.932610 | ||||||||
\(525\) | −2.21837e164 | −0.597580 | ||||||||
\(526\) | −3.40038e164 | −0.816376 | ||||||||
\(527\) | 2.60516e164 | 0.557561 | ||||||||
\(528\) | 1.57578e164 | 0.300707 | ||||||||
\(529\) | −5.54958e164 | −0.944479 | ||||||||
\(530\) | 3.63826e164 | 0.552336 | ||||||||
\(531\) | −4.76312e164 | −0.645168 | ||||||||
\(532\) | 4.32643e163 | 0.0522970 | ||||||||
\(533\) | 8.06553e163 | 0.0870236 | ||||||||
\(534\) | −7.56889e164 | −0.729099 | ||||||||
\(535\) | −2.99295e163 | −0.0257452 | ||||||||
\(536\) | −8.21034e164 | −0.630800 | ||||||||
\(537\) | 3.72483e164 | 0.255660 | ||||||||
\(538\) | 2.97778e164 | 0.182627 | ||||||||
\(539\) | 2.69052e165 | 1.47474 | ||||||||
\(540\) | −2.25332e164 | −0.110408 | ||||||||
\(541\) | −9.91470e164 | −0.434355 | −0.217178 | − | 0.976132i | \(-0.569685\pi\) | ||||
−0.217178 | + | 0.976132i | \(0.569685\pi\) | |||||||
\(542\) | −4.62464e165 | −1.81184 | ||||||||
\(543\) | 1.83234e165 | 0.642119 | ||||||||
\(544\) | −2.01826e165 | −0.632767 | ||||||||
\(545\) | 3.33193e164 | 0.0934775 | ||||||||
\(546\) | −3.37752e164 | −0.0848093 | ||||||||
\(547\) | 5.30962e164 | 0.119352 | 0.0596761 | − | 0.998218i | \(-0.480993\pi\) | ||||
0.0596761 | + | 0.998218i | \(0.480993\pi\) | |||||||
\(548\) | 8.39414e164 | 0.168948 | ||||||||
\(549\) | 3.08112e165 | 0.555369 | ||||||||
\(550\) | 4.93592e165 | 0.796939 | ||||||||
\(551\) | −6.02249e164 | −0.0871173 | ||||||||
\(552\) | 3.20089e164 | 0.0414913 | ||||||||
\(553\) | 1.98106e166 | 2.30158 | ||||||||
\(554\) | −1.52744e166 | −1.59083 | ||||||||
\(555\) | −3.69612e164 | −0.0345160 | ||||||||
\(556\) | 9.55440e165 | 0.800163 | ||||||||
\(557\) | 9.51657e165 | 0.714893 | 0.357447 | − | 0.933934i | \(-0.383647\pi\) | ||||
0.357447 | + | 0.933934i | \(0.383647\pi\) | |||||||
\(558\) | −1.56628e166 | −1.05560 | ||||||||
\(559\) | 1.81439e165 | 0.109727 | ||||||||
\(560\) | −1.08231e166 | −0.587458 | ||||||||
\(561\) | 2.91539e165 | 0.142051 | ||||||||
\(562\) | −2.54134e166 | −1.11177 | ||||||||
\(563\) | −3.86845e166 | −1.51977 | −0.759887 | − | 0.650055i | \(-0.774746\pi\) | ||||
−0.759887 | + | 0.650055i | \(0.774746\pi\) | |||||||
\(564\) | −6.35717e165 | −0.224325 | ||||||||
\(565\) | −1.13629e166 | −0.360212 | ||||||||
\(566\) | 6.97572e166 | 1.98699 | ||||||||
\(567\) | −4.37364e166 | −1.11961 | ||||||||
\(568\) | 8.83780e164 | 0.0203362 | ||||||||
\(569\) | −3.35645e166 | −0.694366 | −0.347183 | − | 0.937797i | \(-0.612862\pi\) | ||||
−0.347183 | + | 0.937797i | \(0.612862\pi\) | |||||||
\(570\) | 3.11951e164 | 0.00580307 | ||||||||
\(571\) | 4.30635e166 | 0.720484 | 0.360242 | − | 0.932859i | \(-0.382694\pi\) | ||||
0.360242 | + | 0.932859i | \(0.382694\pi\) | |||||||
\(572\) | 2.86334e165 | 0.0430936 | ||||||||
\(573\) | 2.58095e166 | 0.349483 | ||||||||
\(574\) | 1.56161e167 | 1.90285 | ||||||||
\(575\) | 1.99629e166 | 0.218937 | ||||||||
\(576\) | 1.23484e166 | 0.121913 | ||||||||
\(577\) | 4.03725e166 | 0.358879 | 0.179440 | − | 0.983769i | \(-0.442572\pi\) | ||||
0.179440 | + | 0.983769i | \(0.442572\pi\) | |||||||
\(578\) | 1.04593e167 | 0.837278 | ||||||||
\(579\) | −3.37229e165 | −0.0243149 | ||||||||
\(580\) | −4.61604e166 | −0.299830 | ||||||||
\(581\) | −4.82432e167 | −2.82345 | ||||||||
\(582\) | −1.25849e167 | −0.663758 | ||||||||
\(583\) | 2.31752e167 | 1.10173 | ||||||||
\(584\) | 1.89374e167 | 0.811603 | ||||||||
\(585\) | 6.21794e165 | 0.0240280 | ||||||||
\(586\) | −2.05075e167 | −0.714672 | ||||||||
\(587\) | −8.96368e166 | −0.281761 | −0.140881 | − | 0.990027i | \(-0.544993\pi\) | ||||
−0.140881 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(588\) | −1.70942e167 | −0.484752 | ||||||||
\(589\) | 1.77563e166 | 0.0454337 | ||||||||
\(590\) | 1.08625e167 | 0.250832 | ||||||||
\(591\) | −2.30874e166 | −0.0481208 | ||||||||
\(592\) | 2.36518e167 | 0.445042 | ||||||||
\(593\) | 4.04604e167 | 0.687418 | 0.343709 | − | 0.939076i | \(-0.388317\pi\) | ||||
0.343709 | + | 0.939076i | \(0.388317\pi\) | |||||||
\(594\) | −3.76715e167 | −0.578007 | ||||||||
\(595\) | −2.00241e167 | −0.277508 | ||||||||
\(596\) | −4.17250e167 | −0.522394 | ||||||||
\(597\) | 1.34640e167 | 0.152309 | ||||||||
\(598\) | 3.03940e166 | 0.0310718 | ||||||||
\(599\) | −1.16804e168 | −1.07928 | −0.539640 | − | 0.841896i | \(-0.681440\pi\) | ||||
−0.539640 | + | 0.841896i | \(0.681440\pi\) | |||||||
\(600\) | 1.95870e167 | 0.163613 | ||||||||
\(601\) | −1.51560e168 | −1.14466 | −0.572332 | − | 0.820022i | \(-0.693961\pi\) | ||||
−0.572332 | + | 0.820022i | \(0.693961\pi\) | |||||||
\(602\) | 3.51293e168 | 2.39928 | ||||||||
\(603\) | 1.81835e168 | 1.12326 | ||||||||
\(604\) | 9.15542e167 | 0.511615 | ||||||||
\(605\) | 2.86719e167 | 0.144963 | ||||||||
\(606\) | −1.26958e167 | −0.0580852 | ||||||||
\(607\) | −2.05167e168 | −0.849554 | −0.424777 | − | 0.905298i | \(-0.639648\pi\) | ||||
−0.424777 | + | 0.905298i | \(0.639648\pi\) | |||||||
\(608\) | −1.37561e167 | −0.0515620 | ||||||||
\(609\) | 3.46836e168 | 1.17700 | ||||||||
\(610\) | −7.02662e167 | −0.215919 | ||||||||
\(611\) | 3.77024e167 | 0.104924 | ||||||||
\(612\) | 1.24125e168 | 0.312895 | ||||||||
\(613\) | −2.50276e168 | −0.571558 | −0.285779 | − | 0.958295i | \(-0.592252\pi\) | ||||
−0.285779 | + | 0.958295i | \(0.592252\pi\) | |||||||
\(614\) | −4.87890e168 | −1.00957 | ||||||||
\(615\) | 4.29012e167 | 0.0804498 | ||||||||
\(616\) | −3.46259e168 | −0.588529 | ||||||||
\(617\) | −6.17889e168 | −0.952046 | −0.476023 | − | 0.879433i | \(-0.657922\pi\) | ||||
−0.476023 | + | 0.879433i | \(0.657922\pi\) | |||||||
\(618\) | −1.95012e168 | −0.272432 | ||||||||
\(619\) | −8.34218e168 | −1.05681 | −0.528403 | − | 0.848994i | \(-0.677209\pi\) | ||||
−0.528403 | + | 0.848994i | \(0.677209\pi\) | |||||||
\(620\) | 1.36096e168 | 0.156368 | ||||||||
\(621\) | −1.52359e168 | −0.158791 | ||||||||
\(622\) | −1.31658e169 | −1.24489 | ||||||||
\(623\) | 3.31145e169 | 2.84113 | ||||||||
\(624\) | 5.93763e167 | 0.0462323 | ||||||||
\(625\) | 1.12134e169 | 0.792493 | ||||||||
\(626\) | 1.26472e169 | 0.811420 | ||||||||
\(627\) | 1.98708e167 | 0.0115752 | ||||||||
\(628\) | −9.26714e168 | −0.490216 | ||||||||
\(629\) | 4.37588e168 | 0.210233 | ||||||||
\(630\) | 1.20389e169 | 0.525392 | ||||||||
\(631\) | 2.07517e169 | 0.822768 | 0.411384 | − | 0.911462i | \(-0.365046\pi\) | ||||
0.411384 | + | 0.911462i | \(0.365046\pi\) | |||||||
\(632\) | −1.74917e169 | −0.630156 | ||||||||
\(633\) | 8.53058e168 | 0.279289 | ||||||||
\(634\) | −1.86443e169 | −0.554812 | ||||||||
\(635\) | 1.24364e169 | 0.336423 | ||||||||
\(636\) | −1.47243e169 | −0.362143 | ||||||||
\(637\) | 1.01380e169 | 0.226735 | ||||||||
\(638\) | −7.71718e169 | −1.56967 | ||||||||
\(639\) | −1.95731e168 | −0.0362124 | ||||||||
\(640\) | 1.43128e169 | 0.240900 | ||||||||
\(641\) | −2.59447e169 | −0.397318 | −0.198659 | − | 0.980069i | \(-0.563659\pi\) | ||||
−0.198659 | + | 0.980069i | \(0.563659\pi\) | |||||||
\(642\) | 3.17907e168 | 0.0443028 | ||||||||
\(643\) | −5.49700e168 | −0.0697207 | −0.0348603 | − | 0.999392i | \(-0.511099\pi\) | ||||
−0.0348603 | + | 0.999392i | \(0.511099\pi\) | |||||||
\(644\) | 2.24217e169 | 0.258865 | ||||||||
\(645\) | 9.65086e168 | 0.101439 | ||||||||
\(646\) | −3.69322e168 | −0.0353458 | ||||||||
\(647\) | −1.23674e170 | −1.07788 | −0.538941 | − | 0.842344i | \(-0.681175\pi\) | ||||
−0.538941 | + | 0.842344i | \(0.681175\pi\) | |||||||
\(648\) | 3.86169e169 | 0.306541 | ||||||||
\(649\) | 6.91925e169 | 0.500328 | ||||||||
\(650\) | 1.85988e169 | 0.122526 | ||||||||
\(651\) | −1.02259e170 | −0.613835 | ||||||||
\(652\) | 1.45864e170 | 0.797938 | ||||||||
\(653\) | 1.99178e170 | 0.993102 | 0.496551 | − | 0.868007i | \(-0.334600\pi\) | ||||
0.496551 | + | 0.868007i | \(0.334600\pi\) | |||||||
\(654\) | −3.53913e169 | −0.160858 | ||||||||
\(655\) | −9.73161e169 | −0.403261 | ||||||||
\(656\) | −2.74529e170 | −1.03730 | ||||||||
\(657\) | −4.19407e170 | −1.44521 | ||||||||
\(658\) | 7.29977e170 | 2.29426 | ||||||||
\(659\) | 6.47582e169 | 0.185664 | 0.0928319 | − | 0.995682i | \(-0.470408\pi\) | ||||
0.0928319 | + | 0.995682i | \(0.470408\pi\) | |||||||
\(660\) | 1.52303e169 | 0.0398383 | ||||||||
\(661\) | −1.46234e170 | −0.349028 | −0.174514 | − | 0.984655i | \(-0.555835\pi\) | ||||
−0.174514 | + | 0.984655i | \(0.555835\pi\) | |||||||
\(662\) | 7.66767e170 | 1.67015 | ||||||||
\(663\) | 1.09853e169 | 0.0218396 | ||||||||
\(664\) | 4.25961e170 | 0.773039 | ||||||||
\(665\) | −1.36481e169 | −0.0226132 | ||||||||
\(666\) | −2.63087e170 | −0.398023 | ||||||||
\(667\) | −3.12115e170 | −0.431222 | ||||||||
\(668\) | −6.30159e170 | −0.795196 | ||||||||
\(669\) | −2.21903e170 | −0.255790 | ||||||||
\(670\) | −4.14682e170 | −0.436706 | ||||||||
\(671\) | −4.47585e170 | −0.430689 | ||||||||
\(672\) | 7.92218e170 | 0.696632 | ||||||||
\(673\) | −4.46853e170 | −0.359131 | −0.179566 | − | 0.983746i | \(-0.557469\pi\) | ||||
−0.179566 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(674\) | −2.87314e171 | −2.11073 | ||||||||
\(675\) | −9.32321e170 | −0.626163 | ||||||||
\(676\) | −9.91594e170 | −0.608918 | ||||||||
\(677\) | −8.54958e169 | −0.0480098 | −0.0240049 | − | 0.999712i | \(-0.507642\pi\) | ||||
−0.0240049 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(678\) | 1.20695e171 | 0.619860 | ||||||||
\(679\) | 5.50600e171 | 2.58651 | ||||||||
\(680\) | 1.76802e170 | 0.0759797 | ||||||||
\(681\) | 1.55277e171 | 0.610529 | ||||||||
\(682\) | 2.27528e171 | 0.818618 | ||||||||
\(683\) | −2.95078e171 | −0.971592 | −0.485796 | − | 0.874072i | \(-0.661470\pi\) | ||||
−0.485796 | + | 0.874072i | \(0.661470\pi\) | |||||||
\(684\) | 8.46018e169 | 0.0254968 | ||||||||
\(685\) | −2.64800e170 | −0.0730530 | ||||||||
\(686\) | 1.06472e172 | 2.68922 | ||||||||
\(687\) | −2.68954e171 | −0.622007 | ||||||||
\(688\) | −6.17568e171 | −1.30793 | ||||||||
\(689\) | 8.73253e170 | 0.169386 | ||||||||
\(690\) | 1.61668e170 | 0.0287246 | ||||||||
\(691\) | −1.96563e171 | −0.319948 | −0.159974 | − | 0.987121i | \(-0.551141\pi\) | ||||
−0.159974 | + | 0.987121i | \(0.551141\pi\) | |||||||
\(692\) | 1.13517e171 | 0.169295 | ||||||||
\(693\) | 7.66860e171 | 1.04799 | ||||||||
\(694\) | −1.56902e172 | −1.96508 | ||||||||
\(695\) | −3.01401e171 | −0.345991 | ||||||||
\(696\) | −3.06238e171 | −0.322255 | ||||||||
\(697\) | −5.07912e171 | −0.490011 | ||||||||
\(698\) | −3.03229e171 | −0.268237 | ||||||||
\(699\) | −4.02769e171 | −0.326728 | ||||||||
\(700\) | 1.37203e172 | 1.02078 | ||||||||
\(701\) | 4.98212e171 | 0.339996 | 0.169998 | − | 0.985444i | \(-0.445624\pi\) | ||||
0.169998 | + | 0.985444i | \(0.445624\pi\) | |||||||
\(702\) | −1.41948e171 | −0.0888658 | ||||||||
\(703\) | 2.98253e170 | 0.0171312 | ||||||||
\(704\) | −1.79382e171 | −0.0945435 | ||||||||
\(705\) | 2.00542e171 | 0.0969983 | ||||||||
\(706\) | −5.19753e171 | −0.230734 | ||||||||
\(707\) | 5.55449e171 | 0.226344 | ||||||||
\(708\) | −4.39613e171 | −0.164459 | ||||||||
\(709\) | −2.82066e171 | −0.0968844 | −0.0484422 | − | 0.998826i | \(-0.515426\pi\) | ||||
−0.0484422 | + | 0.998826i | \(0.515426\pi\) | |||||||
\(710\) | 4.46373e170 | 0.0140789 | ||||||||
\(711\) | 3.87388e172 | 1.12211 | ||||||||
\(712\) | −2.92383e172 | −0.777879 | ||||||||
\(713\) | 9.20220e171 | 0.224892 | ||||||||
\(714\) | 2.12693e172 | 0.477542 | ||||||||
\(715\) | −9.03263e170 | −0.0186337 | ||||||||
\(716\) | −2.30376e172 | −0.436717 | ||||||||
\(717\) | 1.20686e172 | 0.210256 | ||||||||
\(718\) | −6.61339e172 | −1.05900 | ||||||||
\(719\) | 1.34032e173 | 1.97293 | 0.986466 | − | 0.163965i | \(-0.0524285\pi\) | ||||
0.986466 | + | 0.163965i | \(0.0524285\pi\) | |||||||
\(720\) | −2.11642e172 | −0.286408 | ||||||||
\(721\) | 8.53190e172 | 1.06160 | ||||||||
\(722\) | 1.10834e173 | 1.26816 | ||||||||
\(723\) | −2.93511e172 | −0.308857 | ||||||||
\(724\) | −1.13328e173 | −1.09686 | ||||||||
\(725\) | −1.90990e173 | −1.70044 | ||||||||
\(726\) | −3.04549e172 | −0.249455 | ||||||||
\(727\) | −5.97341e172 | −0.450185 | −0.225092 | − | 0.974337i | \(-0.572268\pi\) | ||||
−0.225092 | + | 0.974337i | \(0.572268\pi\) | |||||||
\(728\) | −1.30472e172 | −0.0904835 | ||||||||
\(729\) | −4.74766e172 | −0.303015 | ||||||||
\(730\) | 9.56476e172 | 0.561877 | ||||||||
\(731\) | −1.14258e173 | −0.617851 | ||||||||
\(732\) | 2.84373e172 | 0.141569 | ||||||||
\(733\) | −5.60300e172 | −0.256821 | −0.128410 | − | 0.991721i | \(-0.540987\pi\) | ||||
−0.128410 | + | 0.991721i | \(0.540987\pi\) | |||||||
\(734\) | −9.56634e172 | −0.403770 | ||||||||
\(735\) | 5.39250e172 | 0.209607 | ||||||||
\(736\) | −7.12910e172 | −0.255227 | ||||||||
\(737\) | −2.64146e173 | −0.871086 | ||||||||
\(738\) | 3.05367e173 | 0.927711 | ||||||||
\(739\) | 1.59736e173 | 0.447109 | 0.223555 | − | 0.974691i | \(-0.428234\pi\) | ||||
0.223555 | + | 0.974691i | \(0.428234\pi\) | |||||||
\(740\) | 2.28601e172 | 0.0589601 | ||||||||
\(741\) | 7.48744e170 | 0.00177964 | ||||||||
\(742\) | 1.69075e174 | 3.70377 | ||||||||
\(743\) | −1.32421e173 | −0.267382 | −0.133691 | − | 0.991023i | \(-0.542683\pi\) | ||||
−0.133691 | + | 0.991023i | \(0.542683\pi\) | |||||||
\(744\) | 9.02892e172 | 0.168063 | ||||||||
\(745\) | 1.31625e173 | 0.225883 | ||||||||
\(746\) | 1.36147e173 | 0.215431 | ||||||||
\(747\) | −9.43377e173 | −1.37654 | ||||||||
\(748\) | −1.80313e173 | −0.242651 | ||||||||
\(749\) | −1.39087e173 | −0.172638 | ||||||||
\(750\) | 2.05400e173 | 0.235176 | ||||||||
\(751\) | −4.83823e173 | −0.511058 | −0.255529 | − | 0.966801i | \(-0.582250\pi\) | ||||
−0.255529 | + | 0.966801i | \(0.582250\pi\) | |||||||
\(752\) | −1.28329e174 | −1.25068 | ||||||||
\(753\) | −3.21841e172 | −0.0289431 | ||||||||
\(754\) | −2.90787e173 | −0.241329 | ||||||||
\(755\) | −2.88815e173 | −0.221223 | ||||||||
\(756\) | −1.04715e174 | −0.740357 | ||||||||
\(757\) | −1.03035e173 | −0.0672486 | −0.0336243 | − | 0.999435i | \(-0.510705\pi\) | ||||
−0.0336243 | + | 0.999435i | \(0.510705\pi\) | |||||||
\(758\) | 4.86183e173 | 0.292963 | ||||||||
\(759\) | 1.02980e173 | 0.0572963 | ||||||||
\(760\) | 1.20505e172 | 0.00619133 | ||||||||
\(761\) | 3.07415e174 | 1.45866 | 0.729328 | − | 0.684164i | \(-0.239833\pi\) | ||||
0.729328 | + | 0.684164i | \(0.239833\pi\) | |||||||
\(762\) | −1.32098e174 | −0.578924 | ||||||||
\(763\) | 1.54839e174 | 0.626826 | ||||||||
\(764\) | −1.59629e174 | −0.596985 | ||||||||
\(765\) | −3.91563e173 | −0.135296 | ||||||||
\(766\) | 3.38722e174 | 1.08144 | ||||||||
\(767\) | 2.60721e173 | 0.0769230 | ||||||||
\(768\) | −1.70545e174 | −0.465033 | ||||||||
\(769\) | −2.09468e174 | −0.527927 | −0.263963 | − | 0.964533i | \(-0.585030\pi\) | ||||
−0.263963 | + | 0.964533i | \(0.585030\pi\) | |||||||
\(770\) | −1.74886e174 | −0.407442 | ||||||||
\(771\) | 9.50252e173 | 0.204668 | ||||||||
\(772\) | 2.08572e173 | 0.0415346 | ||||||||
\(773\) | 3.16270e173 | 0.0582370 | 0.0291185 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291185 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(774\) | 6.86940e174 | 1.16974 | ||||||||
\(775\) | 5.63104e174 | 0.886820 | ||||||||
\(776\) | −4.86150e174 | −0.708168 | ||||||||
\(777\) | −1.71764e174 | −0.231452 | ||||||||
\(778\) | 3.83607e174 | 0.478212 | ||||||||
\(779\) | −3.46185e173 | −0.0399293 | ||||||||
\(780\) | 5.73887e172 | 0.00612495 | ||||||||
\(781\) | 2.84333e173 | 0.0280827 | ||||||||
\(782\) | −1.91401e174 | −0.174958 | ||||||||
\(783\) | 1.45766e175 | 1.23330 | ||||||||
\(784\) | −3.45071e175 | −2.70263 | ||||||||
\(785\) | 2.92340e174 | 0.211969 | ||||||||
\(786\) | 1.03368e175 | 0.693939 | ||||||||
\(787\) | 5.09657e173 | 0.0316816 | 0.0158408 | − | 0.999875i | \(-0.494958\pi\) | ||||
0.0158408 | + | 0.999875i | \(0.494958\pi\) | |||||||
\(788\) | 1.42793e174 | 0.0821998 | ||||||||
\(789\) | −4.34121e174 | −0.231447 | ||||||||
\(790\) | −8.83456e174 | −0.436260 | ||||||||
\(791\) | −5.28051e175 | −2.41545 | ||||||||
\(792\) | −6.77096e174 | −0.286930 | ||||||||
\(793\) | −1.68653e174 | −0.0662163 | ||||||||
\(794\) | 4.17984e175 | 1.52061 | ||||||||
\(795\) | 4.64490e174 | 0.156591 | ||||||||
\(796\) | −8.32731e174 | −0.260174 | ||||||||
\(797\) | 4.71982e175 | 1.36677 | 0.683387 | − | 0.730056i | \(-0.260506\pi\) | ||||
0.683387 | + | 0.730056i | \(0.260506\pi\) | |||||||
\(798\) | 1.44968e174 | 0.0389133 | ||||||||
\(799\) | −2.37424e175 | −0.590805 | ||||||||
\(800\) | −4.36246e175 | −1.00644 | ||||||||
\(801\) | 6.47541e175 | 1.38516 | ||||||||
\(802\) | 6.30359e175 | 1.25037 | ||||||||
\(803\) | 6.09261e175 | 1.12076 | ||||||||
\(804\) | 1.67825e175 | 0.286329 | ||||||||
\(805\) | −7.07310e174 | −0.111933 | ||||||||
\(806\) | 8.57340e174 | 0.125859 | ||||||||
\(807\) | 3.80167e174 | 0.0517757 | ||||||||
\(808\) | −4.90432e174 | −0.0619714 | ||||||||
\(809\) | −4.53797e175 | −0.532079 | −0.266039 | − | 0.963962i | \(-0.585715\pi\) | ||||
−0.266039 | + | 0.963962i | \(0.585715\pi\) | |||||||
\(810\) | 1.95043e175 | 0.212220 | ||||||||
\(811\) | −6.54588e175 | −0.661007 | −0.330504 | − | 0.943805i | \(-0.607219\pi\) | ||||
−0.330504 | + | 0.943805i | \(0.607219\pi\) | |||||||
\(812\) | −2.14514e176 | −2.01055 | ||||||||
\(813\) | −5.90419e175 | −0.513668 | ||||||||
\(814\) | 3.82179e175 | 0.308667 | ||||||||
\(815\) | −4.60141e175 | −0.345029 | ||||||||
\(816\) | −3.73911e175 | −0.260324 | ||||||||
\(817\) | −7.78761e174 | −0.0503466 | ||||||||
\(818\) | 1.72779e176 | 1.03733 | ||||||||
\(819\) | 2.88957e175 | 0.161123 | ||||||||
\(820\) | −2.65339e175 | −0.137424 | ||||||||
\(821\) | −3.47295e176 | −1.67085 | −0.835425 | − | 0.549604i | \(-0.814779\pi\) | ||||
−0.835425 | + | 0.549604i | \(0.814779\pi\) | |||||||
\(822\) | 2.81267e175 | 0.125711 | ||||||||
\(823\) | 1.97889e176 | 0.821736 | 0.410868 | − | 0.911695i | \(-0.365226\pi\) | ||||
0.410868 | + | 0.911695i | \(0.365226\pi\) | |||||||
\(824\) | −7.53321e175 | −0.290659 | ||||||||
\(825\) | 6.30160e175 | 0.225937 | ||||||||
\(826\) | 5.04796e176 | 1.68199 | ||||||||
\(827\) | 1.70660e176 | 0.528503 | 0.264252 | − | 0.964454i | \(-0.414875\pi\) | ||||
0.264252 | + | 0.964454i | \(0.414875\pi\) | |||||||
\(828\) | 4.38447e175 | 0.126207 | ||||||||
\(829\) | −1.27004e176 | −0.339834 | −0.169917 | − | 0.985458i | \(-0.554350\pi\) | ||||
−0.169917 | + | 0.985458i | \(0.554350\pi\) | |||||||
\(830\) | 2.15141e176 | 0.535179 | ||||||||
\(831\) | −1.95006e176 | −0.451009 | ||||||||
\(832\) | −6.75919e174 | −0.0145356 | ||||||||
\(833\) | −6.38423e176 | −1.27669 | ||||||||
\(834\) | 3.20145e176 | 0.595388 | ||||||||
\(835\) | 1.98789e176 | 0.343843 | ||||||||
\(836\) | −1.22899e175 | −0.0197728 | ||||||||
\(837\) | −4.29767e176 | −0.643196 | ||||||||
\(838\) | 1.33216e177 | 1.85478 | ||||||||
\(839\) | −1.39765e177 | −1.81051 | −0.905254 | − | 0.424870i | \(-0.860320\pi\) | ||||
−0.905254 | + | 0.424870i | \(0.860320\pi\) | |||||||
\(840\) | −6.93992e175 | −0.0836484 | ||||||||
\(841\) | 2.09451e177 | 2.34922 | ||||||||
\(842\) | −1.55243e177 | −1.62043 | ||||||||
\(843\) | −3.24449e176 | −0.315194 | ||||||||
\(844\) | −5.27606e176 | −0.477081 | ||||||||
\(845\) | 3.12807e176 | 0.263296 | ||||||||
\(846\) | 1.42744e177 | 1.11854 | ||||||||
\(847\) | 1.33243e177 | 0.972068 | ||||||||
\(848\) | −2.97232e177 | −2.01905 | ||||||||
\(849\) | 8.90578e176 | 0.563322 | ||||||||
\(850\) | −1.17123e177 | −0.689915 | ||||||||
\(851\) | 1.54569e176 | 0.0847977 | ||||||||
\(852\) | −1.80650e175 | −0.00923088 | ||||||||
\(853\) | −3.49520e177 | −1.66363 | −0.831813 | − | 0.555057i | \(-0.812697\pi\) | ||||
−0.831813 | + | 0.555057i | \(0.812697\pi\) | |||||||
\(854\) | −3.26537e177 | −1.44788 | ||||||||
\(855\) | −2.66883e175 | −0.0110248 | ||||||||
\(856\) | 1.22806e176 | 0.0472669 | ||||||||
\(857\) | 4.28472e177 | 1.53668 | 0.768339 | − | 0.640043i | \(-0.221083\pi\) | ||||
0.768339 | + | 0.640043i | \(0.221083\pi\) | |||||||
\(858\) | 9.59434e175 | 0.0320652 | ||||||||
\(859\) | 1.98589e177 | 0.618542 | 0.309271 | − | 0.950974i | \(-0.399915\pi\) | ||||
0.309271 | + | 0.950974i | \(0.399915\pi\) | |||||||
\(860\) | −5.96894e176 | −0.173277 | ||||||||
\(861\) | 1.99368e177 | 0.539468 | ||||||||
\(862\) | 3.52061e177 | 0.888030 | ||||||||
\(863\) | 6.91411e177 | 1.62586 | 0.812930 | − | 0.582361i | \(-0.197871\pi\) | ||||
0.812930 | + | 0.582361i | \(0.197871\pi\) | |||||||
\(864\) | 3.32948e177 | 0.729953 | ||||||||
\(865\) | −3.58100e176 | −0.0732031 | ||||||||
\(866\) | −9.06947e177 | −1.72882 | ||||||||
\(867\) | 1.33532e177 | 0.237373 | ||||||||
\(868\) | 6.32460e177 | 1.04855 | ||||||||
\(869\) | −5.62748e177 | −0.870197 | ||||||||
\(870\) | −1.54672e177 | −0.223099 | ||||||||
\(871\) | −9.95317e176 | −0.133925 | ||||||||
\(872\) | −1.36715e177 | −0.171620 | ||||||||
\(873\) | 1.07668e178 | 1.26102 | ||||||||
\(874\) | −1.30456e176 | −0.0142568 | ||||||||
\(875\) | −8.98638e177 | −0.916427 | ||||||||
\(876\) | −3.87093e177 | −0.368398 | ||||||||
\(877\) | −2.22632e178 | −1.97748 | −0.988740 | − | 0.149645i | \(-0.952187\pi\) | ||||
−0.988740 | + | 0.149645i | \(0.952187\pi\) | |||||||
\(878\) | −1.44030e178 | −1.19408 | ||||||||
\(879\) | −2.61816e177 | −0.202614 | ||||||||
\(880\) | 3.07446e177 | 0.222110 | ||||||||
\(881\) | −8.76614e177 | −0.591243 | −0.295621 | − | 0.955305i | \(-0.595527\pi\) | ||||
−0.295621 | + | 0.955305i | \(0.595527\pi\) | |||||||
\(882\) | 3.83833e178 | 2.41709 | ||||||||
\(883\) | −3.56005e177 | −0.209331 | −0.104666 | − | 0.994507i | \(-0.533377\pi\) | ||||
−0.104666 | + | 0.994507i | \(0.533377\pi\) | |||||||
\(884\) | −6.79431e176 | −0.0373064 | ||||||||
\(885\) | 1.38680e177 | 0.0711123 | ||||||||
\(886\) | 1.80617e177 | 0.0865002 | ||||||||
\(887\) | −2.22560e178 | −0.995562 | −0.497781 | − | 0.867303i | \(-0.665852\pi\) | ||||
−0.497781 | + | 0.867303i | \(0.665852\pi\) | |||||||
\(888\) | 1.51658e177 | 0.0633698 | ||||||||
\(889\) | 5.77940e178 | 2.25593 | ||||||||
\(890\) | −1.47674e178 | −0.538530 | ||||||||
\(891\) | 1.24240e178 | 0.423310 | ||||||||
\(892\) | 1.37244e178 | 0.436939 | ||||||||
\(893\) | −1.61824e177 | −0.0481427 | ||||||||
\(894\) | −1.39810e178 | −0.388705 | ||||||||
\(895\) | 7.26741e177 | 0.188837 | ||||||||
\(896\) | 6.65139e178 | 1.61539 | ||||||||
\(897\) | 3.88035e176 | 0.00880903 | ||||||||
\(898\) | −3.01960e178 | −0.640812 | ||||||||
\(899\) | −8.80398e178 | −1.74670 | ||||||||
\(900\) | 2.68296e178 | 0.497671 | ||||||||
\(901\) | −5.49915e178 | −0.953775 | ||||||||
\(902\) | −4.43599e178 | −0.719440 | ||||||||
\(903\) | 4.48490e178 | 0.680211 | ||||||||
\(904\) | 4.66240e178 | 0.661333 | ||||||||
\(905\) | 3.57502e178 | 0.474285 | ||||||||
\(906\) | 3.06776e178 | 0.380685 | ||||||||
\(907\) | 1.67040e178 | 0.193900 | 0.0969501 | − | 0.995289i | \(-0.469091\pi\) | ||||
0.0969501 | + | 0.995289i | \(0.469091\pi\) | |||||||
\(908\) | −9.60369e178 | −1.04290 | ||||||||
\(909\) | 1.08616e178 | 0.110352 | ||||||||
\(910\) | −6.58979e177 | −0.0626422 | ||||||||
\(911\) | −5.90627e178 | −0.525354 | −0.262677 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262677 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(912\) | −2.54852e177 | −0.0212129 | ||||||||
\(913\) | 1.37042e179 | 1.06751 | ||||||||
\(914\) | −2.01614e179 | −1.46986 | ||||||||
\(915\) | −8.97077e177 | −0.0612144 | ||||||||
\(916\) | 1.66345e179 | 1.06251 | ||||||||
\(917\) | −4.52242e179 | −2.70412 | ||||||||
\(918\) | 8.93893e178 | 0.500384 | ||||||||
\(919\) | 1.92508e179 | 1.00893 | 0.504464 | − | 0.863433i | \(-0.331690\pi\) | ||||
0.504464 | + | 0.863433i | \(0.331690\pi\) | |||||||
\(920\) | 6.24517e177 | 0.0306465 | ||||||||
\(921\) | −6.22881e178 | −0.286218 | ||||||||
\(922\) | 4.66192e178 | 0.200606 | ||||||||
\(923\) | 1.07138e177 | 0.00431759 | ||||||||
\(924\) | 7.07775e178 | 0.267141 | ||||||||
\(925\) | 9.45843e178 | 0.334383 | ||||||||
\(926\) | −2.20749e179 | −0.731028 | ||||||||
\(927\) | 1.66838e179 | 0.517573 | ||||||||
\(928\) | 6.82059e179 | 1.98230 | ||||||||
\(929\) | 1.82038e179 | 0.495692 | 0.247846 | − | 0.968799i | \(-0.420277\pi\) | ||||
0.247846 | + | 0.968799i | \(0.420277\pi\) | |||||||
\(930\) | 4.56026e178 | 0.116351 | ||||||||
\(931\) | −4.35139e178 | −0.104033 | ||||||||
\(932\) | 2.49108e179 | 0.558116 | ||||||||
\(933\) | −1.68086e179 | −0.352933 | ||||||||
\(934\) | −1.98517e179 | −0.390671 | ||||||||
\(935\) | 5.68813e178 | 0.104922 | ||||||||
\(936\) | −2.55133e178 | −0.0441142 | ||||||||
\(937\) | 8.01956e179 | 1.29989 | 0.649943 | − | 0.759983i | \(-0.274793\pi\) | ||||
0.649943 | + | 0.759983i | \(0.274793\pi\) | |||||||
\(938\) | −1.92709e180 | −2.92839 | ||||||||
\(939\) | 1.61464e179 | 0.230042 | ||||||||
\(940\) | −1.24033e179 | −0.165692 | ||||||||
\(941\) | −7.73694e179 | −0.969163 | −0.484582 | − | 0.874746i | \(-0.661028\pi\) | ||||
−0.484582 | + | 0.874746i | \(0.661028\pi\) | |||||||
\(942\) | −3.10519e179 | −0.364762 | ||||||||
\(943\) | −1.79410e179 | −0.197646 | ||||||||
\(944\) | −8.87424e179 | −0.916907 | ||||||||
\(945\) | 3.30333e179 | 0.320131 | ||||||||
\(946\) | −9.97899e179 | −0.907137 | ||||||||
\(947\) | 7.33813e179 | 0.625766 | 0.312883 | − | 0.949792i | \(-0.398705\pi\) | ||||
0.312883 | + | 0.949792i | \(0.398705\pi\) | |||||||
\(948\) | 3.57541e179 | 0.286037 | ||||||||
\(949\) | 2.29573e179 | 0.172312 | ||||||||
\(950\) | −7.98288e178 | −0.0562188 | ||||||||
\(951\) | −2.38028e179 | −0.157292 | ||||||||
\(952\) | 8.21624e179 | 0.509493 | ||||||||
\(953\) | 2.98138e180 | 1.73499 | 0.867494 | − | 0.497447i | \(-0.165729\pi\) | ||||
0.867494 | + | 0.497447i | \(0.165729\pi\) | |||||||
\(954\) | 3.30620e180 | 1.80573 | ||||||||
\(955\) | 5.03562e179 | 0.258136 | ||||||||
\(956\) | −7.46429e179 | −0.359158 | ||||||||
\(957\) | −9.85239e179 | −0.445009 | ||||||||
\(958\) | −1.08207e180 | −0.458818 | ||||||||
\(959\) | −1.23056e180 | −0.489867 | ||||||||
\(960\) | −3.59527e178 | −0.0134376 | ||||||||
\(961\) | −2.53765e179 | −0.0890568 | ||||||||
\(962\) | 1.44007e179 | 0.0474561 | ||||||||
\(963\) | −2.71979e179 | −0.0841676 | ||||||||
\(964\) | 1.81533e180 | 0.527589 | ||||||||
\(965\) | −6.57958e178 | −0.0179596 | ||||||||
\(966\) | 7.51296e179 | 0.192617 | ||||||||
\(967\) | −2.21131e180 | −0.532536 | −0.266268 | − | 0.963899i | \(-0.585791\pi\) | ||||
−0.266268 | + | 0.963899i | \(0.585791\pi\) | |||||||
\(968\) | −1.17646e180 | −0.266145 | ||||||||
\(969\) | −4.71507e178 | −0.0100207 | ||||||||
\(970\) | −2.45541e180 | −0.490268 | ||||||||
\(971\) | 5.37812e180 | 1.00894 | 0.504472 | − | 0.863428i | \(-0.331687\pi\) | ||||
0.504472 | + | 0.863428i | \(0.331687\pi\) | |||||||
\(972\) | −3.14259e180 | −0.553960 | ||||||||
\(973\) | −1.40066e181 | −2.32009 | ||||||||
\(974\) | 9.48448e180 | 1.47638 | ||||||||
\(975\) | 2.37448e179 | 0.0347367 | ||||||||
\(976\) | 5.74048e180 | 0.789285 | ||||||||
\(977\) | −3.49022e180 | −0.451058 | −0.225529 | − | 0.974236i | \(-0.572411\pi\) | ||||
−0.225529 | + | 0.974236i | \(0.572411\pi\) | |||||||
\(978\) | 4.88756e180 | 0.593733 | ||||||||
\(979\) | −9.40664e180 | −1.07419 | ||||||||
\(980\) | −3.33519e180 | −0.358050 | ||||||||
\(981\) | 3.02783e180 | 0.305602 | ||||||||
\(982\) | 1.78354e180 | 0.169254 | ||||||||
\(983\) | −1.07879e181 | −0.962610 | −0.481305 | − | 0.876553i | \(-0.659837\pi\) | ||||
−0.481305 | + | 0.876553i | \(0.659837\pi\) | |||||||
\(984\) | −1.76031e180 | −0.147702 | ||||||||
\(985\) | −4.50452e179 | −0.0355432 | ||||||||
\(986\) | 1.83118e181 | 1.35887 | ||||||||
\(987\) | 9.31949e180 | 0.650435 | ||||||||
\(988\) | −4.63089e178 | −0.00303997 | ||||||||
\(989\) | −4.03592e180 | −0.249211 | ||||||||
\(990\) | −3.41982e180 | −0.198643 | ||||||||
\(991\) | 7.09661e180 | 0.387789 | 0.193894 | − | 0.981022i | \(-0.437888\pi\) | ||||
0.193894 | + | 0.981022i | \(0.437888\pi\) | |||||||
\(992\) | −2.01094e181 | −1.03382 | ||||||||
\(993\) | 9.78918e180 | 0.473496 | ||||||||
\(994\) | 2.07436e180 | 0.0944077 | ||||||||
\(995\) | 2.62692e180 | 0.112499 | ||||||||
\(996\) | −8.70693e180 | −0.350893 | ||||||||
\(997\) | 3.75837e181 | 1.42542 | 0.712709 | − | 0.701460i | \(-0.247468\pi\) | ||||
0.712709 | + | 0.701460i | \(0.247468\pi\) | |||||||
\(998\) | 5.04629e181 | 1.80125 | ||||||||
\(999\) | −7.21879e180 | −0.242523 |
(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 | 1.122.a.a.1.2 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.122.a.a.1.2 | ✓ | 9 | 1.1 | even | 1 | trivial |