Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,48,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, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 48 \) |
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: | \(13.9907662655\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(901372.\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.30793e7 | 1.94544 | 0.972720 | − | 0.231981i | \(-0.0745207\pi\) | ||||
0.972720 | + | 0.231981i | \(0.0745207\pi\) | |||||||
\(3\) | 1.28510e11 | 0.788109 | 0.394055 | − | 0.919087i | \(-0.371072\pi\) | ||||
0.394055 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(4\) | 3.91917e14 | 2.78474 | ||||||||
\(5\) | −1.15086e16 | −0.431745 | −0.215873 | − | 0.976422i | \(-0.569260\pi\) | ||||
−0.215873 | + | 0.976422i | \(0.569260\pi\) | |||||||
\(6\) | 2.96592e18 | 1.53322 | ||||||||
\(7\) | 1.54211e19 | 0.212966 | 0.106483 | − | 0.994315i | \(-0.466041\pi\) | ||||
0.106483 | + | 0.994315i | \(0.466041\pi\) | |||||||
\(8\) | 5.79706e21 | 3.47211 | ||||||||
\(9\) | −1.00741e22 | −0.378884 | ||||||||
\(10\) | −2.65611e23 | −0.839935 | ||||||||
\(11\) | −3.19474e24 | −1.07574 | −0.537871 | − | 0.843027i | \(-0.680771\pi\) | ||||
−0.537871 | + | 0.843027i | \(0.680771\pi\) | |||||||
\(12\) | 5.03652e25 | 2.19468 | ||||||||
\(13\) | 1.57743e25 | 0.104781 | 0.0523903 | − | 0.998627i | \(-0.483316\pi\) | ||||
0.0523903 | + | 0.998627i | \(0.483316\pi\) | |||||||
\(14\) | 3.55908e26 | 0.414313 | ||||||||
\(15\) | −1.47897e27 | −0.340262 | ||||||||
\(16\) | 7.86346e28 | 3.97004 | ||||||||
\(17\) | −3.42618e28 | −0.416160 | −0.208080 | − | 0.978112i | \(-0.566722\pi\) | ||||
−0.208080 | + | 0.978112i | \(0.566722\pi\) | |||||||
\(18\) | −2.32503e29 | −0.737096 | ||||||||
\(19\) | 1.00019e30 | 0.889961 | 0.444980 | − | 0.895540i | \(-0.353211\pi\) | ||||
0.444980 | + | 0.895540i | \(0.353211\pi\) | |||||||
\(20\) | −4.51042e30 | −1.20230 | ||||||||
\(21\) | 1.98176e30 | 0.167841 | ||||||||
\(22\) | −7.37325e31 | −2.09279 | ||||||||
\(23\) | 5.17765e31 | 0.517045 | 0.258522 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258522 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(24\) | 7.44978e32 | 2.73640 | ||||||||
\(25\) | −5.78095e32 | −0.813596 | ||||||||
\(26\) | 3.64060e32 | 0.203844 | ||||||||
\(27\) | −4.71154e33 | −1.08671 | ||||||||
\(28\) | 6.04378e33 | 0.593055 | ||||||||
\(29\) | −6.90432e33 | −0.297008 | −0.148504 | − | 0.988912i | \(-0.547446\pi\) | ||||
−0.148504 | + | 0.988912i | \(0.547446\pi\) | |||||||
\(30\) | −3.41336e34 | −0.661960 | ||||||||
\(31\) | −1.79630e35 | −1.61205 | −0.806025 | − | 0.591882i | \(-0.798385\pi\) | ||||
−0.806025 | + | 0.591882i | \(0.798385\pi\) | |||||||
\(32\) | 9.98970e35 | 4.25136 | ||||||||
\(33\) | −4.10556e35 | −0.847802 | ||||||||
\(34\) | −7.90739e35 | −0.809615 | ||||||||
\(35\) | −1.77475e35 | −0.0919471 | ||||||||
\(36\) | −3.94820e36 | −1.05509 | ||||||||
\(37\) | −2.68894e36 | −0.377434 | −0.188717 | − | 0.982032i | \(-0.560433\pi\) | ||||
−0.188717 | + | 0.982032i | \(0.560433\pi\) | |||||||
\(38\) | 2.30836e37 | 1.73137 | ||||||||
\(39\) | 2.02715e36 | 0.0825786 | ||||||||
\(40\) | −6.67160e37 | −1.49906 | ||||||||
\(41\) | 1.17249e38 | 1.47465 | 0.737325 | − | 0.675538i | \(-0.236088\pi\) | ||||
0.737325 | + | 0.675538i | \(0.236088\pi\) | |||||||
\(42\) | 4.57376e37 | 0.326524 | ||||||||
\(43\) | 1.58085e38 | 0.649204 | 0.324602 | − | 0.945851i | \(-0.394770\pi\) | ||||
0.324602 | + | 0.945851i | \(0.394770\pi\) | |||||||
\(44\) | −1.25208e39 | −2.99566 | ||||||||
\(45\) | 1.15938e38 | 0.163581 | ||||||||
\(46\) | 1.19497e39 | 1.00588 | ||||||||
\(47\) | −1.34555e39 | −0.683282 | −0.341641 | − | 0.939831i | \(-0.610983\pi\) | ||||
−0.341641 | + | 0.939831i | \(0.610983\pi\) | |||||||
\(48\) | 1.01053e40 | 3.12882 | ||||||||
\(49\) | −5.00553e39 | −0.954645 | ||||||||
\(50\) | −1.33420e40 | −1.58280 | ||||||||
\(51\) | −4.40298e39 | −0.327980 | ||||||||
\(52\) | 6.18221e39 | 0.291787 | ||||||||
\(53\) | 4.68526e40 | 1.41335 | 0.706677 | − | 0.707536i | \(-0.250193\pi\) | ||||
0.706677 | + | 0.707536i | \(0.250193\pi\) | |||||||
\(54\) | −1.08739e41 | −2.11413 | ||||||||
\(55\) | 3.67670e40 | 0.464446 | ||||||||
\(56\) | 8.93968e40 | 0.739440 | ||||||||
\(57\) | 1.28534e41 | 0.701387 | ||||||||
\(58\) | −1.59347e41 | −0.577811 | ||||||||
\(59\) | 3.84916e41 | 0.933993 | 0.466997 | − | 0.884259i | \(-0.345336\pi\) | ||||
0.466997 | + | 0.884259i | \(0.345336\pi\) | |||||||
\(60\) | −5.79633e41 | −0.947542 | ||||||||
\(61\) | 4.37844e41 | 0.485365 | 0.242683 | − | 0.970106i | \(-0.421973\pi\) | ||||
0.242683 | + | 0.970106i | \(0.421973\pi\) | |||||||
\(62\) | −4.14573e42 | −3.13615 | ||||||||
\(63\) | −1.55353e41 | −0.0806893 | ||||||||
\(64\) | 1.19887e43 | 4.30074 | ||||||||
\(65\) | −1.81540e41 | −0.0452385 | ||||||||
\(66\) | −9.47534e42 | −1.64935 | ||||||||
\(67\) | 4.64892e42 | 0.568321 | 0.284161 | − | 0.958777i | \(-0.408285\pi\) | ||||
0.284161 | + | 0.958777i | \(0.408285\pi\) | |||||||
\(68\) | −1.34278e43 | −1.15890 | ||||||||
\(69\) | 6.65378e42 | 0.407488 | ||||||||
\(70\) | −4.09600e42 | −0.178878 | ||||||||
\(71\) | 1.91856e43 | 0.600349 | 0.300175 | − | 0.953884i | \(-0.402955\pi\) | ||||
0.300175 | + | 0.953884i | \(0.402955\pi\) | |||||||
\(72\) | −5.83999e43 | −1.31552 | ||||||||
\(73\) | 8.25143e43 | 1.34413 | 0.672066 | − | 0.740491i | \(-0.265407\pi\) | ||||
0.672066 | + | 0.740491i | \(0.265407\pi\) | |||||||
\(74\) | −6.20589e43 | −0.734275 | ||||||||
\(75\) | −7.42908e43 | −0.641203 | ||||||||
\(76\) | 3.91990e44 | 2.47831 | ||||||||
\(77\) | −4.92663e43 | −0.229096 | ||||||||
\(78\) | 4.67852e43 | 0.160652 | ||||||||
\(79\) | −5.45765e44 | −1.38921 | −0.694607 | − | 0.719389i | \(-0.744422\pi\) | ||||
−0.694607 | + | 0.719389i | \(0.744422\pi\) | |||||||
\(80\) | −9.04975e44 | −1.71404 | ||||||||
\(81\) | −3.37621e44 | −0.477564 | ||||||||
\(82\) | 2.70603e45 | 2.86885 | ||||||||
\(83\) | −1.02727e45 | −0.819125 | −0.409563 | − | 0.912282i | \(-0.634319\pi\) | ||||
−0.409563 | + | 0.912282i | \(0.634319\pi\) | |||||||
\(84\) | 7.76685e44 | 0.467392 | ||||||||
\(85\) | 3.94306e44 | 0.179675 | ||||||||
\(86\) | 3.64849e45 | 1.26299 | ||||||||
\(87\) | −8.87272e44 | −0.234075 | ||||||||
\(88\) | −1.85201e46 | −3.73509 | ||||||||
\(89\) | 1.06667e46 | 1.64954 | 0.824771 | − | 0.565467i | \(-0.191304\pi\) | ||||
0.824771 | + | 0.565467i | \(0.191304\pi\) | |||||||
\(90\) | 2.67578e45 | 0.318237 | ||||||||
\(91\) | 2.43256e44 | 0.0223147 | ||||||||
\(92\) | 2.02921e46 | 1.43984 | ||||||||
\(93\) | −2.30842e46 | −1.27047 | ||||||||
\(94\) | −3.10543e46 | −1.32928 | ||||||||
\(95\) | −1.15107e46 | −0.384236 | ||||||||
\(96\) | 1.28377e47 | 3.35054 | ||||||||
\(97\) | 3.72976e46 | 0.763037 | 0.381518 | − | 0.924361i | \(-0.375401\pi\) | ||||
0.381518 | + | 0.924361i | \(0.375401\pi\) | |||||||
\(98\) | −1.15524e47 | −1.85721 | ||||||||
\(99\) | 3.21841e46 | 0.407581 | ||||||||
\(100\) | −2.26565e47 | −2.26565 | ||||||||
\(101\) | 9.27720e46 | 0.734285 | 0.367142 | − | 0.930165i | \(-0.380336\pi\) | ||||
0.367142 | + | 0.930165i | \(0.380336\pi\) | |||||||
\(102\) | −1.01618e47 | −0.638065 | ||||||||
\(103\) | 1.00960e47 | 0.504051 | 0.252026 | − | 0.967721i | \(-0.418903\pi\) | ||||
0.252026 | + | 0.967721i | \(0.418903\pi\) | |||||||
\(104\) | 9.14444e46 | 0.363809 | ||||||||
\(105\) | −2.28072e46 | −0.0724643 | ||||||||
\(106\) | 1.08133e48 | 2.74960 | ||||||||
\(107\) | 1.99211e47 | 0.406252 | 0.203126 | − | 0.979153i | \(-0.434890\pi\) | ||||
0.203126 | + | 0.979153i | \(0.434890\pi\) | |||||||
\(108\) | −1.84653e48 | −3.02621 | ||||||||
\(109\) | −6.24516e47 | −0.824177 | −0.412089 | − | 0.911144i | \(-0.635201\pi\) | ||||
−0.412089 | + | 0.911144i | \(0.635201\pi\) | |||||||
\(110\) | 8.48558e47 | 0.903553 | ||||||||
\(111\) | −3.45555e47 | −0.297459 | ||||||||
\(112\) | 1.21263e48 | 0.845483 | ||||||||
\(113\) | −2.17631e48 | −1.23134 | −0.615669 | − | 0.788005i | \(-0.711114\pi\) | ||||
−0.615669 | + | 0.788005i | \(0.711114\pi\) | |||||||
\(114\) | 2.96647e48 | 1.36451 | ||||||||
\(115\) | −5.95875e47 | −0.223232 | ||||||||
\(116\) | −2.70592e48 | −0.827089 | ||||||||
\(117\) | −1.58911e47 | −0.0396996 | ||||||||
\(118\) | 8.88360e48 | 1.81703 | ||||||||
\(119\) | −5.28354e47 | −0.0886280 | ||||||||
\(120\) | −8.57366e48 | −1.18143 | ||||||||
\(121\) | 1.38664e48 | 0.157220 | ||||||||
\(122\) | 1.01051e49 | 0.944249 | ||||||||
\(123\) | 1.50677e49 | 1.16219 | ||||||||
\(124\) | −7.04000e49 | −4.48914 | ||||||||
\(125\) | 1.48304e49 | 0.783011 | ||||||||
\(126\) | −3.58544e48 | −0.156976 | ||||||||
\(127\) | −1.42624e49 | −0.518568 | −0.259284 | − | 0.965801i | \(-0.583487\pi\) | ||||
−0.259284 | + | 0.965801i | \(0.583487\pi\) | |||||||
\(128\) | 1.36099e50 | 4.11547 | ||||||||
\(129\) | 2.03154e49 | 0.511644 | ||||||||
\(130\) | −4.18982e48 | −0.0880088 | ||||||||
\(131\) | −7.28871e49 | −1.27872 | −0.639359 | − | 0.768908i | \(-0.720800\pi\) | ||||
−0.639359 | + | 0.768908i | \(0.720800\pi\) | |||||||
\(132\) | −1.60904e50 | −2.36091 | ||||||||
\(133\) | 1.54239e49 | 0.189531 | ||||||||
\(134\) | 1.07294e50 | 1.10564 | ||||||||
\(135\) | 5.42232e49 | 0.469182 | ||||||||
\(136\) | −1.98618e50 | −1.44495 | ||||||||
\(137\) | 2.99893e49 | 0.183668 | 0.0918338 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918338 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(138\) | 1.53565e50 | 0.792743 | ||||||||
\(139\) | 1.25821e50 | 0.548159 | 0.274079 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274079 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(140\) | −6.95555e49 | −0.256049 | ||||||||
\(141\) | −1.72916e50 | −0.538501 | ||||||||
\(142\) | 4.42790e50 | 1.16794 | ||||||||
\(143\) | −5.03948e49 | −0.112717 | ||||||||
\(144\) | −7.92171e50 | −1.50418 | ||||||||
\(145\) | 7.94590e49 | 0.128232 | ||||||||
\(146\) | 1.90437e51 | 2.61493 | ||||||||
\(147\) | −6.43259e50 | −0.752365 | ||||||||
\(148\) | −1.05384e51 | −1.05106 | ||||||||
\(149\) | −1.60599e51 | −1.36730 | −0.683652 | − | 0.729809i | \(-0.739609\pi\) | ||||
−0.683652 | + | 0.729809i | \(0.739609\pi\) | |||||||
\(150\) | −1.71458e51 | −1.24742 | ||||||||
\(151\) | 2.76267e49 | 0.0171938 | 0.00859689 | − | 0.999963i | \(-0.497263\pi\) | ||||
0.00859689 | + | 0.999963i | \(0.497263\pi\) | |||||||
\(152\) | 5.79813e51 | 3.09004 | ||||||||
\(153\) | 3.45156e50 | 0.157676 | ||||||||
\(154\) | −1.13703e51 | −0.445693 | ||||||||
\(155\) | 2.06729e51 | 0.695995 | ||||||||
\(156\) | 7.94474e50 | 0.229960 | ||||||||
\(157\) | 3.26071e51 | 0.812214 | 0.406107 | − | 0.913825i | \(-0.366886\pi\) | ||||
0.406107 | + | 0.913825i | \(0.366886\pi\) | |||||||
\(158\) | −1.25959e52 | −2.70263 | ||||||||
\(159\) | 6.02102e51 | 1.11388 | ||||||||
\(160\) | −1.14968e52 | −1.83551 | ||||||||
\(161\) | 7.98448e50 | 0.110113 | ||||||||
\(162\) | −7.79206e51 | −0.929072 | ||||||||
\(163\) | −1.71469e51 | −0.176920 | −0.0884602 | − | 0.996080i | \(-0.528195\pi\) | ||||
−0.0884602 | + | 0.996080i | \(0.528195\pi\) | |||||||
\(164\) | 4.59520e52 | 4.10652 | ||||||||
\(165\) | 4.72492e51 | 0.366034 | ||||||||
\(166\) | −2.37087e52 | −1.59356 | ||||||||
\(167\) | −1.35054e52 | −0.788264 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(168\) | 1.14884e52 | 0.582760 | ||||||||
\(169\) | −2.24152e52 | −0.989021 | ||||||||
\(170\) | 9.10030e51 | 0.349548 | ||||||||
\(171\) | −1.00759e52 | −0.337192 | ||||||||
\(172\) | 6.19562e52 | 1.80787 | ||||||||
\(173\) | 9.07124e51 | 0.230985 | 0.115492 | − | 0.993308i | \(-0.463155\pi\) | ||||
0.115492 | + | 0.993308i | \(0.463155\pi\) | |||||||
\(174\) | −2.04776e52 | −0.455378 | ||||||||
\(175\) | −8.91484e51 | −0.173268 | ||||||||
\(176\) | −2.51218e53 | −4.27073 | ||||||||
\(177\) | 4.94655e52 | 0.736089 | ||||||||
\(178\) | 2.46179e53 | 3.20908 | ||||||||
\(179\) | −2.83103e52 | −0.323518 | −0.161759 | − | 0.986830i | \(-0.551717\pi\) | ||||
−0.161759 | + | 0.986830i | \(0.551717\pi\) | |||||||
\(180\) | 4.54383e52 | 0.455531 | ||||||||
\(181\) | −7.28434e52 | −0.641127 | −0.320563 | − | 0.947227i | \(-0.603872\pi\) | ||||
−0.320563 | + | 0.947227i | \(0.603872\pi\) | |||||||
\(182\) | 5.61418e51 | 0.0434119 | ||||||||
\(183\) | 5.62672e52 | 0.382521 | ||||||||
\(184\) | 3.00151e53 | 1.79523 | ||||||||
\(185\) | 3.09460e52 | 0.162955 | ||||||||
\(186\) | −5.32767e53 | −2.47163 | ||||||||
\(187\) | 1.09458e53 | 0.447681 | ||||||||
\(188\) | −5.27344e53 | −1.90276 | ||||||||
\(189\) | −7.26569e52 | −0.231433 | ||||||||
\(190\) | −2.65660e53 | −0.747509 | ||||||||
\(191\) | 2.15414e53 | 0.535785 | 0.267893 | − | 0.963449i | \(-0.413673\pi\) | ||||
0.267893 | + | 0.963449i | \(0.413673\pi\) | |||||||
\(192\) | 1.54067e54 | 3.38945 | ||||||||
\(193\) | −4.58281e53 | −0.892351 | −0.446175 | − | 0.894946i | \(-0.647214\pi\) | ||||
−0.446175 | + | 0.894946i | \(0.647214\pi\) | |||||||
\(194\) | 8.60804e53 | 1.48444 | ||||||||
\(195\) | −2.33296e52 | −0.0356529 | ||||||||
\(196\) | −1.96175e54 | −2.65844 | ||||||||
\(197\) | 2.29005e53 | 0.275353 | 0.137676 | − | 0.990477i | \(-0.456037\pi\) | ||||
0.137676 | + | 0.990477i | \(0.456037\pi\) | |||||||
\(198\) | 7.42786e53 | 0.792924 | ||||||||
\(199\) | 1.26295e54 | 1.19767 | 0.598835 | − | 0.800872i | \(-0.295630\pi\) | ||||
0.598835 | + | 0.800872i | \(0.295630\pi\) | |||||||
\(200\) | −3.35125e54 | −2.82489 | ||||||||
\(201\) | 5.97431e53 | 0.447899 | ||||||||
\(202\) | 2.14111e54 | 1.42851 | ||||||||
\(203\) | −1.06472e53 | −0.0632525 | ||||||||
\(204\) | −1.72560e54 | −0.913339 | ||||||||
\(205\) | −1.34937e54 | −0.636673 | ||||||||
\(206\) | 2.33009e54 | 0.980602 | ||||||||
\(207\) | −5.21599e53 | −0.195900 | ||||||||
\(208\) | 1.24040e54 | 0.415983 | ||||||||
\(209\) | −3.19534e54 | −0.957368 | ||||||||
\(210\) | −5.26376e53 | −0.140975 | ||||||||
\(211\) | −4.97549e54 | −1.19178 | −0.595892 | − | 0.803064i | \(-0.703201\pi\) | ||||
−0.595892 | + | 0.803064i | \(0.703201\pi\) | |||||||
\(212\) | 1.83624e55 | 3.93582 | ||||||||
\(213\) | 2.46554e54 | 0.473141 | ||||||||
\(214\) | 4.59766e54 | 0.790339 | ||||||||
\(215\) | −1.81934e54 | −0.280291 | ||||||||
\(216\) | −2.73130e55 | −3.77318 | ||||||||
\(217\) | −2.77008e54 | −0.343312 | ||||||||
\(218\) | −1.44134e55 | −1.60339 | ||||||||
\(219\) | 1.06039e55 | 1.05932 | ||||||||
\(220\) | 1.44096e55 | 1.29336 | ||||||||
\(221\) | −5.40455e53 | −0.0436055 | ||||||||
\(222\) | −7.97518e54 | −0.578689 | ||||||||
\(223\) | 2.79892e55 | 1.82737 | 0.913686 | − | 0.406421i | \(-0.133223\pi\) | ||||
0.913686 | + | 0.406421i | \(0.133223\pi\) | |||||||
\(224\) | 1.54052e55 | 0.905396 | ||||||||
\(225\) | 5.82376e54 | 0.308258 | ||||||||
\(226\) | −5.02277e55 | −2.39549 | ||||||||
\(227\) | 1.40478e55 | 0.603949 | 0.301974 | − | 0.953316i | \(-0.402354\pi\) | ||||
0.301974 | + | 0.953316i | \(0.402354\pi\) | |||||||
\(228\) | 5.03745e55 | 1.95318 | ||||||||
\(229\) | −4.09641e55 | −1.43308 | −0.716539 | − | 0.697547i | \(-0.754275\pi\) | ||||
−0.716539 | + | 0.697547i | \(0.754275\pi\) | |||||||
\(230\) | −1.37524e55 | −0.434284 | ||||||||
\(231\) | −6.33120e54 | −0.180553 | ||||||||
\(232\) | −4.00247e55 | −1.03124 | ||||||||
\(233\) | −1.21897e55 | −0.283876 | −0.141938 | − | 0.989876i | \(-0.545333\pi\) | ||||
−0.141938 | + | 0.989876i | \(0.545333\pi\) | |||||||
\(234\) | −3.66756e54 | −0.0772333 | ||||||||
\(235\) | 1.54854e55 | 0.295004 | ||||||||
\(236\) | 1.50855e56 | 2.60093 | ||||||||
\(237\) | −7.01362e55 | −1.09485 | ||||||||
\(238\) | −1.21940e55 | −0.172421 | ||||||||
\(239\) | 6.34948e55 | 0.813556 | 0.406778 | − | 0.913527i | \(-0.366652\pi\) | ||||
0.406778 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(240\) | −1.16298e56 | −1.35085 | ||||||||
\(241\) | −1.11357e56 | −1.17305 | −0.586525 | − | 0.809931i | \(-0.699504\pi\) | ||||
−0.586525 | + | 0.809931i | \(0.699504\pi\) | |||||||
\(242\) | 3.20027e55 | 0.305862 | ||||||||
\(243\) | 8.18866e55 | 0.710339 | ||||||||
\(244\) | 1.71599e56 | 1.35162 | ||||||||
\(245\) | 5.76066e55 | 0.412164 | ||||||||
\(246\) | 3.47751e56 | 2.26096 | ||||||||
\(247\) | 1.57772e55 | 0.0932506 | ||||||||
\(248\) | −1.04132e57 | −5.59721 | ||||||||
\(249\) | −1.32014e56 | −0.645560 | ||||||||
\(250\) | 3.42276e56 | 1.52330 | ||||||||
\(251\) | 1.81960e56 | 0.737299 | 0.368649 | − | 0.929569i | \(-0.379820\pi\) | ||||
0.368649 | + | 0.929569i | \(0.379820\pi\) | |||||||
\(252\) | −6.08854e55 | −0.224699 | ||||||||
\(253\) | −1.65413e56 | −0.556207 | ||||||||
\(254\) | −3.29167e56 | −1.00884 | ||||||||
\(255\) | 5.06721e55 | 0.141604 | ||||||||
\(256\) | 1.45380e57 | 3.70566 | ||||||||
\(257\) | −3.46416e56 | −0.805694 | −0.402847 | − | 0.915267i | \(-0.631979\pi\) | ||||
−0.402847 | + | 0.915267i | \(0.631979\pi\) | |||||||
\(258\) | 4.68866e56 | 0.995373 | ||||||||
\(259\) | −4.14663e55 | −0.0803806 | ||||||||
\(260\) | −7.11486e55 | −0.125977 | ||||||||
\(261\) | 6.95545e55 | 0.112531 | ||||||||
\(262\) | −1.68218e57 | −2.48767 | ||||||||
\(263\) | 1.25535e57 | 1.69748 | 0.848738 | − | 0.528814i | \(-0.177363\pi\) | ||||
0.848738 | + | 0.528814i | \(0.177363\pi\) | |||||||
\(264\) | −2.38001e57 | −2.94366 | ||||||||
\(265\) | −5.39208e56 | −0.610209 | ||||||||
\(266\) | 3.55974e56 | 0.368722 | ||||||||
\(267\) | 1.37077e57 | 1.30002 | ||||||||
\(268\) | 1.82199e57 | 1.58263 | ||||||||
\(269\) | −2.60597e55 | −0.0207391 | −0.0103696 | − | 0.999946i | \(-0.503301\pi\) | ||||
−0.0103696 | + | 0.999946i | \(0.503301\pi\) | |||||||
\(270\) | 1.25143e57 | 0.912766 | ||||||||
\(271\) | −1.42492e57 | −0.952822 | −0.476411 | − | 0.879223i | \(-0.658063\pi\) | ||||
−0.476411 | + | 0.879223i | \(0.658063\pi\) | |||||||
\(272\) | −2.69417e57 | −1.65217 | ||||||||
\(273\) | 3.12608e55 | 0.0175864 | ||||||||
\(274\) | 6.92132e56 | 0.357314 | ||||||||
\(275\) | 1.84686e57 | 0.875219 | ||||||||
\(276\) | 2.60773e57 | 1.13475 | ||||||||
\(277\) | −3.96329e57 | −1.58409 | −0.792047 | − | 0.610461i | \(-0.790984\pi\) | ||||
−0.792047 | + | 0.610461i | \(0.790984\pi\) | |||||||
\(278\) | 2.90387e57 | 1.06641 | ||||||||
\(279\) | 1.80960e57 | 0.610779 | ||||||||
\(280\) | −1.02883e57 | −0.319250 | ||||||||
\(281\) | −4.27684e57 | −1.22046 | −0.610231 | − | 0.792223i | \(-0.708924\pi\) | ||||
−0.610231 | + | 0.792223i | \(0.708924\pi\) | |||||||
\(282\) | −3.99078e57 | −1.04762 | ||||||||
\(283\) | −9.57574e56 | −0.231308 | −0.115654 | − | 0.993290i | \(-0.536896\pi\) | ||||
−0.115654 | + | 0.993290i | \(0.536896\pi\) | |||||||
\(284\) | 7.51917e57 | 1.67182 | ||||||||
\(285\) | −1.47924e57 | −0.302820 | ||||||||
\(286\) | −1.16308e57 | −0.219284 | ||||||||
\(287\) | 1.80811e57 | 0.314050 | ||||||||
\(288\) | −1.00637e58 | −1.61077 | ||||||||
\(289\) | −5.60409e57 | −0.826811 | ||||||||
\(290\) | 1.83386e57 | 0.249467 | ||||||||
\(291\) | 4.79311e57 | 0.601357 | ||||||||
\(292\) | 3.23388e58 | 3.74306 | ||||||||
\(293\) | 1.40107e58 | 1.49648 | 0.748241 | − | 0.663427i | \(-0.230899\pi\) | ||||
0.748241 | + | 0.663427i | \(0.230899\pi\) | |||||||
\(294\) | −1.48460e58 | −1.46368 | ||||||||
\(295\) | −4.42985e57 | −0.403247 | ||||||||
\(296\) | −1.55880e58 | −1.31049 | ||||||||
\(297\) | 1.50522e58 | 1.16902 | ||||||||
\(298\) | −3.70651e58 | −2.66001 | ||||||||
\(299\) | 8.16736e56 | 0.0541762 | ||||||||
\(300\) | −2.91158e58 | −1.78558 | ||||||||
\(301\) | 2.43784e57 | 0.138258 | ||||||||
\(302\) | 6.37606e56 | 0.0334495 | ||||||||
\(303\) | 1.19221e58 | 0.578697 | ||||||||
\(304\) | 7.86492e58 | 3.53318 | ||||||||
\(305\) | −5.03897e57 | −0.209554 | ||||||||
\(306\) | 7.96596e57 | 0.306750 | ||||||||
\(307\) | −4.70339e58 | −1.67749 | −0.838743 | − | 0.544527i | \(-0.816709\pi\) | ||||
−0.838743 | + | 0.544527i | \(0.816709\pi\) | |||||||
\(308\) | −1.93083e58 | −0.637974 | ||||||||
\(309\) | 1.29743e58 | 0.397248 | ||||||||
\(310\) | 4.77116e58 | 1.35402 | ||||||||
\(311\) | −2.66280e58 | −0.700600 | −0.350300 | − | 0.936638i | \(-0.613920\pi\) | ||||
−0.350300 | + | 0.936638i | \(0.613920\pi\) | |||||||
\(312\) | 1.17515e58 | 0.286721 | ||||||||
\(313\) | −5.63252e58 | −1.27471 | −0.637354 | − | 0.770571i | \(-0.719971\pi\) | ||||
−0.637354 | + | 0.770571i | \(0.719971\pi\) | |||||||
\(314\) | 7.52550e58 | 1.58012 | ||||||||
\(315\) | 1.78789e57 | 0.0348372 | ||||||||
\(316\) | −2.13895e59 | −3.86860 | ||||||||
\(317\) | 9.99715e58 | 1.67874 | 0.839371 | − | 0.543560i | \(-0.182924\pi\) | ||||
0.839371 | + | 0.543560i | \(0.182924\pi\) | |||||||
\(318\) | 1.38961e59 | 2.16698 | ||||||||
\(319\) | 2.20575e58 | 0.319503 | ||||||||
\(320\) | −1.37973e59 | −1.85682 | ||||||||
\(321\) | 2.56006e58 | 0.320171 | ||||||||
\(322\) | 1.84276e58 | 0.214218 | ||||||||
\(323\) | −3.42682e58 | −0.370366 | ||||||||
\(324\) | −1.32319e59 | −1.32989 | ||||||||
\(325\) | −9.11903e57 | −0.0852491 | ||||||||
\(326\) | −3.95740e58 | −0.344188 | ||||||||
\(327\) | −8.02563e58 | −0.649542 | ||||||||
\(328\) | 6.79700e59 | 5.12014 | ||||||||
\(329\) | −2.07498e58 | −0.145516 | ||||||||
\(330\) | 1.09048e59 | 0.712098 | ||||||||
\(331\) | −1.86524e58 | −0.113443 | −0.0567215 | − | 0.998390i | \(-0.518065\pi\) | ||||
−0.0567215 | + | 0.998390i | \(0.518065\pi\) | |||||||
\(332\) | −4.02606e59 | −2.28105 | ||||||||
\(333\) | 2.70886e58 | 0.143004 | ||||||||
\(334\) | −3.11696e59 | −1.53352 | ||||||||
\(335\) | −5.35025e58 | −0.245370 | ||||||||
\(336\) | 1.55835e59 | 0.666333 | ||||||||
\(337\) | 2.11425e59 | 0.843050 | 0.421525 | − | 0.906817i | \(-0.361495\pi\) | ||||
0.421525 | + | 0.906817i | \(0.361495\pi\) | |||||||
\(338\) | −5.17328e59 | −1.92408 | ||||||||
\(339\) | −2.79677e59 | −0.970429 | ||||||||
\(340\) | 1.54535e59 | 0.500349 | ||||||||
\(341\) | 5.73871e59 | 1.73415 | ||||||||
\(342\) | −2.32546e59 | −0.655986 | ||||||||
\(343\) | −1.58048e59 | −0.416273 | ||||||||
\(344\) | 9.16427e59 | 2.25411 | ||||||||
\(345\) | −7.65757e58 | −0.175931 | ||||||||
\(346\) | 2.09358e59 | 0.449367 | ||||||||
\(347\) | 1.60147e59 | 0.321200 | 0.160600 | − | 0.987020i | \(-0.448657\pi\) | ||||
0.160600 | + | 0.987020i | \(0.448657\pi\) | |||||||
\(348\) | −3.47737e59 | −0.651837 | ||||||||
\(349\) | 8.79943e59 | 1.54190 | 0.770951 | − | 0.636894i | \(-0.219781\pi\) | ||||
0.770951 | + | 0.636894i | \(0.219781\pi\) | |||||||
\(350\) | −2.05748e59 | −0.337083 | ||||||||
\(351\) | −7.43211e58 | −0.113866 | ||||||||
\(352\) | −3.19145e60 | −4.57337 | ||||||||
\(353\) | −9.28528e59 | −1.24477 | −0.622386 | − | 0.782711i | \(-0.713836\pi\) | ||||
−0.622386 | + | 0.782711i | \(0.713836\pi\) | |||||||
\(354\) | 1.14163e60 | 1.43202 | ||||||||
\(355\) | −2.20799e59 | −0.259198 | ||||||||
\(356\) | 4.18045e60 | 4.59354 | ||||||||
\(357\) | −6.78986e58 | −0.0698486 | ||||||||
\(358\) | −6.53382e59 | −0.629385 | ||||||||
\(359\) | −1.74133e60 | −1.57095 | −0.785475 | − | 0.618893i | \(-0.787581\pi\) | ||||
−0.785475 | + | 0.618893i | \(0.787581\pi\) | |||||||
\(360\) | 6.72102e59 | 0.567971 | ||||||||
\(361\) | −2.62675e59 | −0.207970 | ||||||||
\(362\) | −1.68118e60 | −1.24727 | ||||||||
\(363\) | 1.78197e59 | 0.123906 | ||||||||
\(364\) | 9.53363e58 | 0.0621406 | ||||||||
\(365\) | −9.49624e59 | −0.580323 | ||||||||
\(366\) | 1.29861e60 | 0.744171 | ||||||||
\(367\) | 2.18975e60 | 1.17691 | 0.588453 | − | 0.808531i | \(-0.299737\pi\) | ||||
0.588453 | + | 0.808531i | \(0.299737\pi\) | |||||||
\(368\) | 4.07142e60 | 2.05269 | ||||||||
\(369\) | −1.18118e60 | −0.558721 | ||||||||
\(370\) | 7.14212e59 | 0.317020 | ||||||||
\(371\) | 7.22517e59 | 0.300996 | ||||||||
\(372\) | −9.04709e60 | −3.53793 | ||||||||
\(373\) | 1.69293e60 | 0.621556 | 0.310778 | − | 0.950482i | \(-0.399410\pi\) | ||||
0.310778 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(374\) | 2.52621e60 | 0.870937 | ||||||||
\(375\) | 1.90585e60 | 0.617099 | ||||||||
\(376\) | −7.80022e60 | −2.37243 | ||||||||
\(377\) | −1.08911e59 | −0.0311206 | ||||||||
\(378\) | −1.67687e60 | −0.450238 | ||||||||
\(379\) | 4.02001e60 | 1.01439 | 0.507196 | − | 0.861831i | \(-0.330682\pi\) | ||||
0.507196 | + | 0.861831i | \(0.330682\pi\) | |||||||
\(380\) | −4.51126e60 | −1.07000 | ||||||||
\(381\) | −1.83286e60 | −0.408688 | ||||||||
\(382\) | 4.97162e60 | 1.04234 | ||||||||
\(383\) | 2.58725e60 | 0.510113 | 0.255057 | − | 0.966926i | \(-0.417906\pi\) | ||||
0.255057 | + | 0.966926i | \(0.417906\pi\) | |||||||
\(384\) | 1.74900e61 | 3.24344 | ||||||||
\(385\) | 5.66987e59 | 0.0989113 | ||||||||
\(386\) | −1.05768e61 | −1.73602 | ||||||||
\(387\) | −1.59256e60 | −0.245973 | ||||||||
\(388\) | 1.46176e61 | 2.12486 | ||||||||
\(389\) | −7.66990e60 | −1.04948 | −0.524740 | − | 0.851263i | \(-0.675837\pi\) | ||||
−0.524740 | + | 0.851263i | \(0.675837\pi\) | |||||||
\(390\) | −5.38432e59 | −0.0693606 | ||||||||
\(391\) | −1.77396e60 | −0.215174 | ||||||||
\(392\) | −2.90173e61 | −3.31463 | ||||||||
\(393\) | −9.36670e60 | −1.00777 | ||||||||
\(394\) | 5.28529e60 | 0.535683 | ||||||||
\(395\) | 6.28100e60 | 0.599787 | ||||||||
\(396\) | 1.26135e61 | 1.13501 | ||||||||
\(397\) | 2.69403e60 | 0.228468 | 0.114234 | − | 0.993454i | \(-0.463559\pi\) | ||||
0.114234 | + | 0.993454i | \(0.463559\pi\) | |||||||
\(398\) | 2.91479e61 | 2.33000 | ||||||||
\(399\) | 1.98212e60 | 0.149372 | ||||||||
\(400\) | −4.54583e61 | −3.23001 | ||||||||
\(401\) | −8.61448e60 | −0.577213 | −0.288607 | − | 0.957448i | \(-0.593192\pi\) | ||||
−0.288607 | + | 0.957448i | \(0.593192\pi\) | |||||||
\(402\) | 1.37883e61 | 0.871362 | ||||||||
\(403\) | −2.83353e60 | −0.168912 | ||||||||
\(404\) | 3.63589e61 | 2.04479 | ||||||||
\(405\) | 3.88554e60 | 0.206186 | ||||||||
\(406\) | −2.45730e60 | −0.123054 | ||||||||
\(407\) | 8.59048e60 | 0.406021 | ||||||||
\(408\) | −2.55243e61 | −1.13878 | ||||||||
\(409\) | −4.89023e60 | −0.205983 | −0.102992 | − | 0.994682i | \(-0.532841\pi\) | ||||
−0.102992 | + | 0.994682i | \(0.532841\pi\) | |||||||
\(410\) | −3.11426e61 | −1.23861 | ||||||||
\(411\) | 3.85391e60 | 0.144750 | ||||||||
\(412\) | 3.95680e61 | 1.40365 | ||||||||
\(413\) | 5.93581e60 | 0.198909 | ||||||||
\(414\) | −1.20382e61 | −0.381111 | ||||||||
\(415\) | 1.18225e61 | 0.353653 | ||||||||
\(416\) | 1.57580e61 | 0.445460 | ||||||||
\(417\) | 1.61693e61 | 0.432009 | ||||||||
\(418\) | −7.37462e61 | −1.86250 | ||||||||
\(419\) | −4.08353e60 | −0.0975003 | −0.0487501 | − | 0.998811i | \(-0.515524\pi\) | ||||
−0.0487501 | + | 0.998811i | \(0.515524\pi\) | |||||||
\(420\) | −8.93855e60 | −0.201794 | ||||||||
\(421\) | −8.09919e61 | −1.72907 | −0.864534 | − | 0.502574i | \(-0.832386\pi\) | ||||
−0.864534 | + | 0.502574i | \(0.832386\pi\) | |||||||
\(422\) | −1.14831e62 | −2.31855 | ||||||||
\(423\) | 1.35551e61 | 0.258884 | ||||||||
\(424\) | 2.71607e62 | 4.90731 | ||||||||
\(425\) | 1.98066e61 | 0.338586 | ||||||||
\(426\) | 5.69029e61 | 0.920468 | ||||||||
\(427\) | 6.75202e60 | 0.103366 | ||||||||
\(428\) | 7.80744e61 | 1.13131 | ||||||||
\(429\) | −6.47622e60 | −0.0888332 | ||||||||
\(430\) | −4.19890e61 | −0.545289 | ||||||||
\(431\) | 5.41910e61 | 0.666364 | 0.333182 | − | 0.942863i | \(-0.391878\pi\) | ||||
0.333182 | + | 0.942863i | \(0.391878\pi\) | |||||||
\(432\) | −3.70490e62 | −4.31428 | ||||||||
\(433\) | 1.10085e62 | 1.21412 | 0.607060 | − | 0.794656i | \(-0.292349\pi\) | ||||
0.607060 | + | 0.794656i | \(0.292349\pi\) | |||||||
\(434\) | −6.39316e61 | −0.667893 | ||||||||
\(435\) | 1.02113e61 | 0.101061 | ||||||||
\(436\) | −2.44758e62 | −2.29512 | ||||||||
\(437\) | 5.17861e61 | 0.460150 | ||||||||
\(438\) | 2.44731e62 | 2.06085 | ||||||||
\(439\) | −1.32013e62 | −1.05366 | −0.526832 | − | 0.849969i | \(-0.676620\pi\) | ||||
−0.526832 | + | 0.849969i | \(0.676620\pi\) | |||||||
\(440\) | 2.13141e62 | 1.61261 | ||||||||
\(441\) | 5.04260e61 | 0.361699 | ||||||||
\(442\) | −1.24733e61 | −0.0848320 | ||||||||
\(443\) | −8.89175e61 | −0.573455 | −0.286728 | − | 0.958012i | \(-0.592567\pi\) | ||||
−0.286728 | + | 0.958012i | \(0.592567\pi\) | |||||||
\(444\) | −1.35429e62 | −0.828346 | ||||||||
\(445\) | −1.22758e62 | −0.712181 | ||||||||
\(446\) | 6.45973e62 | 3.55504 | ||||||||
\(447\) | −2.06385e62 | −1.07758 | ||||||||
\(448\) | 1.84879e62 | 0.915911 | ||||||||
\(449\) | 9.45855e61 | 0.444668 | 0.222334 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222334 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(450\) | 1.34408e62 | 0.599698 | ||||||||
\(451\) | −3.74581e62 | −1.58634 | ||||||||
\(452\) | −8.52933e62 | −3.42896 | ||||||||
\(453\) | 3.55030e60 | 0.0135506 | ||||||||
\(454\) | 3.24213e62 | 1.17495 | ||||||||
\(455\) | −2.79954e60 | −0.00963426 | ||||||||
\(456\) | 7.45116e62 | 2.43529 | ||||||||
\(457\) | 3.37293e62 | 1.04707 | 0.523536 | − | 0.852003i | \(-0.324612\pi\) | ||||
0.523536 | + | 0.852003i | \(0.324612\pi\) | |||||||
\(458\) | −9.45424e62 | −2.78797 | ||||||||
\(459\) | 1.61426e62 | 0.452246 | ||||||||
\(460\) | −2.33534e62 | −0.621642 | ||||||||
\(461\) | 4.97092e62 | 1.25738 | 0.628688 | − | 0.777658i | \(-0.283592\pi\) | ||||
0.628688 | + | 0.777658i | \(0.283592\pi\) | |||||||
\(462\) | −1.46120e62 | −0.351255 | ||||||||
\(463\) | −4.42973e62 | −1.01210 | −0.506051 | − | 0.862504i | \(-0.668895\pi\) | ||||
−0.506051 | + | 0.862504i | \(0.668895\pi\) | |||||||
\(464\) | −5.42918e62 | −1.17913 | ||||||||
\(465\) | 2.65667e62 | 0.548520 | ||||||||
\(466\) | −2.81330e62 | −0.552264 | ||||||||
\(467\) | 7.17000e62 | 1.33836 | 0.669179 | − | 0.743101i | \(-0.266646\pi\) | ||||
0.669179 | + | 0.743101i | \(0.266646\pi\) | |||||||
\(468\) | −6.22800e61 | −0.110553 | ||||||||
\(469\) | 7.16912e61 | 0.121033 | ||||||||
\(470\) | 3.57392e62 | 0.573912 | ||||||||
\(471\) | 4.19033e62 | 0.640114 | ||||||||
\(472\) | 2.23138e63 | 3.24292 | ||||||||
\(473\) | −5.05040e62 | −0.698376 | ||||||||
\(474\) | −1.61869e63 | −2.12997 | ||||||||
\(475\) | −5.78202e62 | −0.724069 | ||||||||
\(476\) | −2.07071e62 | −0.246806 | ||||||||
\(477\) | −4.71996e62 | −0.535497 | ||||||||
\(478\) | 1.46542e63 | 1.58273 | ||||||||
\(479\) | −1.03149e62 | −0.106067 | −0.0530337 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530337 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(480\) | −1.47744e63 | −1.44658 | ||||||||
\(481\) | −4.24161e61 | −0.0395477 | ||||||||
\(482\) | −2.57004e63 | −2.28210 | ||||||||
\(483\) | 1.02608e62 | 0.0867811 | ||||||||
\(484\) | 5.43448e62 | 0.437816 | ||||||||
\(485\) | −4.29244e62 | −0.329438 | ||||||||
\(486\) | 1.88989e63 | 1.38192 | ||||||||
\(487\) | −2.41720e61 | −0.0168415 | −0.00842076 | − | 0.999965i | \(-0.502680\pi\) | ||||
−0.00842076 | + | 0.999965i | \(0.502680\pi\) | |||||||
\(488\) | 2.53821e63 | 1.68524 | ||||||||
\(489\) | −2.20355e62 | −0.139433 | ||||||||
\(490\) | 1.32952e63 | 0.801840 | ||||||||
\(491\) | −1.48334e63 | −0.852760 | −0.426380 | − | 0.904544i | \(-0.640211\pi\) | ||||
−0.426380 | + | 0.904544i | \(0.640211\pi\) | |||||||
\(492\) | 5.90528e63 | 3.23639 | ||||||||
\(493\) | 2.36554e62 | 0.123603 | ||||||||
\(494\) | 3.64127e62 | 0.181414 | ||||||||
\(495\) | −3.70394e62 | −0.175971 | ||||||||
\(496\) | −1.41251e64 | −6.39989 | ||||||||
\(497\) | 2.95862e62 | 0.127854 | ||||||||
\(498\) | −3.04680e63 | −1.25590 | ||||||||
\(499\) | 3.58476e63 | 1.40960 | 0.704802 | − | 0.709404i | \(-0.251036\pi\) | ||||
0.704802 | + | 0.709404i | \(0.251036\pi\) | |||||||
\(500\) | 5.81230e63 | 2.18048 | ||||||||
\(501\) | −1.73558e63 | −0.621238 | ||||||||
\(502\) | 4.19951e63 | 1.43437 | ||||||||
\(503\) | 3.59373e63 | 1.17138 | 0.585691 | − | 0.810535i | \(-0.300823\pi\) | ||||
0.585691 | + | 0.810535i | \(0.300823\pi\) | |||||||
\(504\) | −9.00589e62 | −0.280162 | ||||||||
\(505\) | −1.06768e63 | −0.317024 | ||||||||
\(506\) | −3.81761e63 | −1.08207 | ||||||||
\(507\) | −2.88057e63 | −0.779457 | ||||||||
\(508\) | −5.58969e63 | −1.44408 | ||||||||
\(509\) | 1.51124e63 | 0.372790 | 0.186395 | − | 0.982475i | \(-0.440320\pi\) | ||||
0.186395 | + | 0.982475i | \(0.440320\pi\) | |||||||
\(510\) | 1.16948e63 | 0.275482 | ||||||||
\(511\) | 1.27246e63 | 0.286255 | ||||||||
\(512\) | 1.43986e64 | 3.09368 | ||||||||
\(513\) | −4.71241e63 | −0.967130 | ||||||||
\(514\) | −7.99505e63 | −1.56743 | ||||||||
\(515\) | −1.16191e63 | −0.217622 | ||||||||
\(516\) | 7.96197e63 | 1.42480 | ||||||||
\(517\) | 4.29868e63 | 0.735034 | ||||||||
\(518\) | −9.57015e62 | −0.156376 | ||||||||
\(519\) | 1.16574e63 | 0.182041 | ||||||||
\(520\) | −1.05240e63 | −0.157073 | ||||||||
\(521\) | −5.89563e63 | −0.841093 | −0.420546 | − | 0.907271i | \(-0.638162\pi\) | ||||
−0.420546 | + | 0.907271i | \(0.638162\pi\) | |||||||
\(522\) | 1.60527e63 | 0.218923 | ||||||||
\(523\) | 1.19071e64 | 1.55245 | 0.776224 | − | 0.630457i | \(-0.217132\pi\) | ||||
0.776224 | + | 0.630457i | \(0.217132\pi\) | |||||||
\(524\) | −2.85657e64 | −3.56090 | ||||||||
\(525\) | −1.14564e63 | −0.136554 | ||||||||
\(526\) | 2.89725e64 | 3.30234 | ||||||||
\(527\) | 6.15444e63 | 0.670871 | ||||||||
\(528\) | −3.22839e64 | −3.36580 | ||||||||
\(529\) | −7.34706e63 | −0.732665 | ||||||||
\(530\) | −1.24446e64 | −1.18712 | ||||||||
\(531\) | −3.87767e63 | −0.353875 | ||||||||
\(532\) | 6.04490e63 | 0.527796 | ||||||||
\(533\) | 1.84952e63 | 0.154515 | ||||||||
\(534\) | 3.16364e64 | 2.52911 | ||||||||
\(535\) | −2.29264e63 | −0.175397 | ||||||||
\(536\) | 2.69500e64 | 1.97327 | ||||||||
\(537\) | −3.63815e63 | −0.254968 | ||||||||
\(538\) | −6.01439e62 | −0.0403467 | ||||||||
\(539\) | 1.59914e64 | 1.02695 | ||||||||
\(540\) | 2.12510e64 | 1.30655 | ||||||||
\(541\) | −1.24707e64 | −0.734101 | −0.367051 | − | 0.930201i | \(-0.619632\pi\) | ||||
−0.367051 | + | 0.930201i | \(0.619632\pi\) | |||||||
\(542\) | −3.28861e64 | −1.85366 | ||||||||
\(543\) | −9.36109e63 | −0.505278 | ||||||||
\(544\) | −3.42265e64 | −1.76925 | ||||||||
\(545\) | 7.18730e63 | 0.355835 | ||||||||
\(546\) | 7.21477e62 | 0.0342134 | ||||||||
\(547\) | −3.38744e64 | −1.53876 | −0.769378 | − | 0.638794i | \(-0.779434\pi\) | ||||
−0.769378 | + | 0.638794i | \(0.779434\pi\) | |||||||
\(548\) | 1.17533e64 | 0.511467 | ||||||||
\(549\) | −4.41087e63 | −0.183897 | ||||||||
\(550\) | 4.26244e64 | 1.70269 | ||||||||
\(551\) | −6.90560e63 | −0.264325 | ||||||||
\(552\) | 3.85723e64 | 1.41484 | ||||||||
\(553\) | −8.41628e63 | −0.295856 | ||||||||
\(554\) | −9.14699e64 | −3.08176 | ||||||||
\(555\) | 3.97686e63 | 0.128427 | ||||||||
\(556\) | 4.93115e64 | 1.52648 | ||||||||
\(557\) | 4.80284e64 | 1.42528 | 0.712641 | − | 0.701528i | \(-0.247499\pi\) | ||||
0.712641 | + | 0.701528i | \(0.247499\pi\) | |||||||
\(558\) | 4.17644e64 | 1.18823 | ||||||||
\(559\) | 2.49367e63 | 0.0680240 | ||||||||
\(560\) | −1.39557e64 | −0.365033 | ||||||||
\(561\) | 1.40664e64 | 0.352822 | ||||||||
\(562\) | −9.87066e64 | −2.37434 | ||||||||
\(563\) | 3.05103e64 | 0.703882 | 0.351941 | − | 0.936022i | \(-0.385522\pi\) | ||||
0.351941 | + | 0.936022i | \(0.385522\pi\) | |||||||
\(564\) | −6.77688e64 | −1.49958 | ||||||||
\(565\) | 2.50463e64 | 0.531624 | ||||||||
\(566\) | −2.21002e64 | −0.449997 | ||||||||
\(567\) | −5.20647e63 | −0.101705 | ||||||||
\(568\) | 1.11220e65 | 2.08448 | ||||||||
\(569\) | 7.49437e64 | 1.34771 | 0.673856 | − | 0.738863i | \(-0.264637\pi\) | ||||
0.673856 | + | 0.738863i | \(0.264637\pi\) | |||||||
\(570\) | −3.41399e64 | −0.589119 | ||||||||
\(571\) | −5.47320e64 | −0.906344 | −0.453172 | − | 0.891423i | \(-0.649708\pi\) | ||||
−0.453172 | + | 0.891423i | \(0.649708\pi\) | |||||||
\(572\) | −1.97506e64 | −0.313887 | ||||||||
\(573\) | 2.76828e64 | 0.422257 | ||||||||
\(574\) | 4.17299e64 | 0.610967 | ||||||||
\(575\) | −2.99317e64 | −0.420666 | ||||||||
\(576\) | −1.20775e65 | −1.62948 | ||||||||
\(577\) | −4.19523e63 | −0.0543406 | −0.0271703 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271703 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(578\) | −1.29339e65 | −1.60851 | ||||||||
\(579\) | −5.88936e64 | −0.703270 | ||||||||
\(580\) | 3.11414e64 | 0.357092 | ||||||||
\(581\) | −1.58416e64 | −0.174446 | ||||||||
\(582\) | 1.10622e65 | 1.16990 | ||||||||
\(583\) | −1.49682e65 | −1.52040 | ||||||||
\(584\) | 4.78340e65 | 4.66697 | ||||||||
\(585\) | 1.82884e63 | 0.0171401 | ||||||||
\(586\) | 3.23358e65 | 2.91132 | ||||||||
\(587\) | 3.17978e64 | 0.275043 | 0.137522 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137522 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(588\) | −2.52104e65 | −2.09514 | ||||||||
\(589\) | −1.79663e65 | −1.43466 | ||||||||
\(590\) | −1.02238e65 | −0.784493 | ||||||||
\(591\) | 2.94294e64 | 0.217008 | ||||||||
\(592\) | −2.11444e65 | −1.49843 | ||||||||
\(593\) | 4.66511e64 | 0.317744 | 0.158872 | − | 0.987299i | \(-0.449214\pi\) | ||||
0.158872 | + | 0.987299i | \(0.449214\pi\) | |||||||
\(594\) | 3.47393e65 | 2.27426 | ||||||||
\(595\) | 6.08061e63 | 0.0382647 | ||||||||
\(596\) | −6.29414e65 | −3.80758 | ||||||||
\(597\) | 1.62301e65 | 0.943896 | ||||||||
\(598\) | 1.88497e64 | 0.105397 | ||||||||
\(599\) | 2.50137e65 | 1.34477 | 0.672384 | − | 0.740202i | \(-0.265270\pi\) | ||||
0.672384 | + | 0.740202i | \(0.265270\pi\) | |||||||
\(600\) | −4.30668e65 | −2.22632 | ||||||||
\(601\) | 4.33262e64 | 0.215377 | 0.107689 | − | 0.994185i | \(-0.465655\pi\) | ||||
0.107689 | + | 0.994185i | \(0.465655\pi\) | |||||||
\(602\) | 5.62636e64 | 0.268974 | ||||||||
\(603\) | −4.68335e64 | −0.215328 | ||||||||
\(604\) | 1.08274e64 | 0.0478802 | ||||||||
\(605\) | −1.59583e64 | −0.0678789 | ||||||||
\(606\) | 2.75154e65 | 1.12582 | ||||||||
\(607\) | −2.09462e64 | −0.0824464 | −0.0412232 | − | 0.999150i | \(-0.513125\pi\) | ||||
−0.0412232 | + | 0.999150i | \(0.513125\pi\) | |||||||
\(608\) | 9.99156e65 | 3.78355 | ||||||||
\(609\) | −1.36827e64 | −0.0498499 | ||||||||
\(610\) | −1.16296e65 | −0.407675 | ||||||||
\(611\) | −2.12251e64 | −0.0715946 | ||||||||
\(612\) | 1.35273e65 | 0.439088 | ||||||||
\(613\) | −4.02606e65 | −1.25765 | −0.628824 | − | 0.777548i | \(-0.716463\pi\) | ||||
−0.628824 | + | 0.777548i | \(0.716463\pi\) | |||||||
\(614\) | −1.08551e66 | −3.26345 | ||||||||
\(615\) | −1.73408e65 | −0.501768 | ||||||||
\(616\) | −2.85600e65 | −0.795447 | ||||||||
\(617\) | 4.25894e65 | 1.14183 | 0.570914 | − | 0.821010i | \(-0.306589\pi\) | ||||
0.570914 | + | 0.821010i | \(0.306589\pi\) | |||||||
\(618\) | 2.99439e65 | 0.772821 | ||||||||
\(619\) | 3.05847e65 | 0.759931 | 0.379965 | − | 0.925001i | \(-0.375936\pi\) | ||||
0.379965 | + | 0.925001i | \(0.375936\pi\) | |||||||
\(620\) | 8.10206e65 | 1.93816 | ||||||||
\(621\) | −2.43947e65 | −0.561878 | ||||||||
\(622\) | −6.14557e65 | −1.36298 | ||||||||
\(623\) | 1.64491e65 | 0.351296 | ||||||||
\(624\) | 1.59404e65 | 0.327840 | ||||||||
\(625\) | 2.40084e65 | 0.475535 | ||||||||
\(626\) | −1.29995e66 | −2.47987 | ||||||||
\(627\) | −4.10632e65 | −0.754511 | ||||||||
\(628\) | 1.27793e66 | 2.26181 | ||||||||
\(629\) | 9.21280e64 | 0.157073 | ||||||||
\(630\) | 4.12634e64 | 0.0677738 | ||||||||
\(631\) | 6.21302e65 | 0.983134 | 0.491567 | − | 0.870840i | \(-0.336424\pi\) | ||||
0.491567 | + | 0.870840i | \(0.336424\pi\) | |||||||
\(632\) | −3.16383e66 | −4.82350 | ||||||||
\(633\) | −6.39398e65 | −0.939257 | ||||||||
\(634\) | 2.30727e66 | 3.26589 | ||||||||
\(635\) | 1.64141e65 | 0.223889 | ||||||||
\(636\) | 2.35974e66 | 3.10186 | ||||||||
\(637\) | −7.89586e64 | −0.100028 | ||||||||
\(638\) | 5.09072e65 | 0.621575 | ||||||||
\(639\) | −1.93277e65 | −0.227463 | ||||||||
\(640\) | −1.56631e66 | −1.77683 | ||||||||
\(641\) | −6.05212e65 | −0.661826 | −0.330913 | − | 0.943661i | \(-0.607357\pi\) | ||||
−0.330913 | + | 0.943661i | \(0.607357\pi\) | |||||||
\(642\) | 5.90844e65 | 0.622873 | ||||||||
\(643\) | 8.65041e65 | 0.879183 | 0.439591 | − | 0.898198i | \(-0.355123\pi\) | ||||
0.439591 | + | 0.898198i | \(0.355123\pi\) | |||||||
\(644\) | 3.12926e65 | 0.306636 | ||||||||
\(645\) | −2.33802e65 | −0.220900 | ||||||||
\(646\) | −7.90886e65 | −0.720526 | ||||||||
\(647\) | 2.75625e65 | 0.242141 | 0.121070 | − | 0.992644i | \(-0.461367\pi\) | ||||
0.121070 | + | 0.992644i | \(0.461367\pi\) | |||||||
\(648\) | −1.95721e66 | −1.65815 | ||||||||
\(649\) | −1.22971e66 | −1.00474 | ||||||||
\(650\) | −2.10461e65 | −0.165847 | ||||||||
\(651\) | −3.55982e65 | −0.270567 | ||||||||
\(652\) | −6.72018e65 | −0.492677 | ||||||||
\(653\) | −1.27020e66 | −0.898282 | −0.449141 | − | 0.893461i | \(-0.648270\pi\) | ||||
−0.449141 | + | 0.893461i | \(0.648270\pi\) | |||||||
\(654\) | −1.85226e66 | −1.26365 | ||||||||
\(655\) | 8.38828e65 | 0.552081 | ||||||||
\(656\) | 9.21985e66 | 5.85441 | ||||||||
\(657\) | −8.31254e65 | −0.509270 | ||||||||
\(658\) | −4.78891e65 | −0.283092 | ||||||||
\(659\) | 1.08832e66 | 0.620794 | 0.310397 | − | 0.950607i | \(-0.399538\pi\) | ||||
0.310397 | + | 0.950607i | \(0.399538\pi\) | |||||||
\(660\) | 1.85178e66 | 1.01931 | ||||||||
\(661\) | 1.19166e66 | 0.633020 | 0.316510 | − | 0.948589i | \(-0.397489\pi\) | ||||
0.316510 | + | 0.948589i | \(0.397489\pi\) | |||||||
\(662\) | −4.30485e65 | −0.220697 | ||||||||
\(663\) | −6.94538e64 | −0.0343659 | ||||||||
\(664\) | −5.95515e66 | −2.84409 | ||||||||
\(665\) | −1.77508e65 | −0.0818293 | ||||||||
\(666\) | 6.25186e65 | 0.278205 | ||||||||
\(667\) | −3.57481e65 | −0.153566 | ||||||||
\(668\) | −5.29301e66 | −2.19511 | ||||||||
\(669\) | 3.59689e66 | 1.44017 | ||||||||
\(670\) | −1.23480e66 | −0.477353 | ||||||||
\(671\) | −1.39880e66 | −0.522127 | ||||||||
\(672\) | 1.97972e66 | 0.713551 | ||||||||
\(673\) | 2.35019e66 | 0.817993 | 0.408997 | − | 0.912536i | \(-0.365879\pi\) | ||||
0.408997 | + | 0.912536i | \(0.365879\pi\) | |||||||
\(674\) | 4.87954e66 | 1.64010 | ||||||||
\(675\) | 2.72371e66 | 0.884144 | ||||||||
\(676\) | −8.78491e66 | −2.75417 | ||||||||
\(677\) | −1.35609e66 | −0.410633 | −0.205316 | − | 0.978696i | \(-0.565822\pi\) | ||||
−0.205316 | + | 0.978696i | \(0.565822\pi\) | |||||||
\(678\) | −6.45475e66 | −1.88791 | ||||||||
\(679\) | 5.75169e65 | 0.162501 | ||||||||
\(680\) | 2.28581e66 | 0.623851 | ||||||||
\(681\) | 1.80528e66 | 0.475978 | ||||||||
\(682\) | 1.32446e67 | 3.37368 | ||||||||
\(683\) | −2.30165e66 | −0.566438 | −0.283219 | − | 0.959055i | \(-0.591402\pi\) | ||||
−0.283219 | + | 0.959055i | \(0.591402\pi\) | |||||||
\(684\) | −3.94893e66 | −0.938991 | ||||||||
\(685\) | −3.45135e65 | −0.0792976 | ||||||||
\(686\) | −3.64765e66 | −0.809835 | ||||||||
\(687\) | −5.26429e66 | −1.12942 | ||||||||
\(688\) | 1.24309e67 | 2.57736 | ||||||||
\(689\) | 7.39066e65 | 0.148092 | ||||||||
\(690\) | −1.76731e66 | −0.342263 | ||||||||
\(691\) | −8.06352e66 | −1.50935 | −0.754676 | − | 0.656098i | \(-0.772206\pi\) | ||||
−0.754676 | + | 0.656098i | \(0.772206\pi\) | |||||||
\(692\) | 3.55517e66 | 0.643232 | ||||||||
\(693\) | 4.96312e65 | 0.0868009 | ||||||||
\(694\) | 3.69608e66 | 0.624876 | ||||||||
\(695\) | −1.44803e66 | −0.236665 | ||||||||
\(696\) | −5.14356e66 | −0.812731 | ||||||||
\(697\) | −4.01717e66 | −0.613691 | ||||||||
\(698\) | 2.03085e67 | 2.99968 | ||||||||
\(699\) | −1.56649e66 | −0.223725 | ||||||||
\(700\) | −3.49388e66 | −0.482507 | ||||||||
\(701\) | 5.85991e66 | 0.782560 | 0.391280 | − | 0.920272i | \(-0.372032\pi\) | ||||
0.391280 | + | 0.920272i | \(0.372032\pi\) | |||||||
\(702\) | −1.71528e66 | −0.221520 | ||||||||
\(703\) | −2.68944e66 | −0.335901 | ||||||||
\(704\) | −3.83009e67 | −4.62648 | ||||||||
\(705\) | 1.99002e66 | 0.232495 | ||||||||
\(706\) | −2.14298e67 | −2.42163 | ||||||||
\(707\) | 1.43064e66 | 0.156378 | ||||||||
\(708\) | 1.93864e67 | 2.04982 | ||||||||
\(709\) | 1.17722e67 | 1.20413 | 0.602064 | − | 0.798448i | \(-0.294345\pi\) | ||||
0.602064 | + | 0.798448i | \(0.294345\pi\) | |||||||
\(710\) | −5.09590e66 | −0.504254 | ||||||||
\(711\) | 5.49808e66 | 0.526351 | ||||||||
\(712\) | 6.18352e67 | 5.72738 | ||||||||
\(713\) | −9.30059e66 | −0.833502 | ||||||||
\(714\) | −1.56705e66 | −0.135886 | ||||||||
\(715\) | 5.79974e65 | 0.0486649 | ||||||||
\(716\) | −1.10953e67 | −0.900913 | ||||||||
\(717\) | 8.15970e66 | 0.641171 | ||||||||
\(718\) | −4.01888e67 | −3.05619 | ||||||||
\(719\) | 1.34473e67 | 0.989709 | 0.494854 | − | 0.868976i | \(-0.335221\pi\) | ||||
0.494854 | + | 0.868976i | \(0.335221\pi\) | |||||||
\(720\) | 9.11678e66 | 0.649423 | ||||||||
\(721\) | 1.55691e66 | 0.107346 | ||||||||
\(722\) | −6.06236e66 | −0.404593 | ||||||||
\(723\) | −1.43104e67 | −0.924491 | ||||||||
\(724\) | −2.85486e67 | −1.78537 | ||||||||
\(725\) | 3.99135e66 | 0.241644 | ||||||||
\(726\) | 4.11266e66 | 0.241053 | ||||||||
\(727\) | −6.52974e66 | −0.370542 | −0.185271 | − | 0.982687i | \(-0.559316\pi\) | ||||
−0.185271 | + | 0.982687i | \(0.559316\pi\) | |||||||
\(728\) | 1.41017e66 | 0.0774790 | ||||||||
\(729\) | 1.95002e67 | 1.03739 | ||||||||
\(730\) | −2.19167e67 | −1.12898 | ||||||||
\(731\) | −5.41627e66 | −0.270173 | ||||||||
\(732\) | 2.20521e67 | 1.06522 | ||||||||
\(733\) | −4.16163e67 | −1.94679 | −0.973397 | − | 0.229127i | \(-0.926413\pi\) | ||||
−0.973397 | + | 0.229127i | \(0.926413\pi\) | |||||||
\(734\) | 5.05379e67 | 2.28960 | ||||||||
\(735\) | 7.40301e66 | 0.324830 | ||||||||
\(736\) | 5.17232e67 | 2.19815 | ||||||||
\(737\) | −1.48521e67 | −0.611367 | ||||||||
\(738\) | −2.72607e67 | −1.08696 | ||||||||
\(739\) | 1.83231e67 | 0.707709 | 0.353854 | − | 0.935301i | \(-0.384871\pi\) | ||||
0.353854 | + | 0.935301i | \(0.384871\pi\) | |||||||
\(740\) | 1.21283e67 | 0.453788 | ||||||||
\(741\) | 2.02752e66 | 0.0734917 | ||||||||
\(742\) | 1.66752e67 | 0.585571 | ||||||||
\(743\) | −2.26817e67 | −0.771681 | −0.385840 | − | 0.922566i | \(-0.626088\pi\) | ||||
−0.385840 | + | 0.922566i | \(0.626088\pi\) | |||||||
\(744\) | −1.33820e68 | −4.41121 | ||||||||
\(745\) | 1.84827e67 | 0.590327 | ||||||||
\(746\) | 3.90716e67 | 1.20920 | ||||||||
\(747\) | 1.03488e67 | 0.310353 | ||||||||
\(748\) | 4.28984e67 | 1.24668 | ||||||||
\(749\) | 3.07205e66 | 0.0865178 | ||||||||
\(750\) | 4.39858e67 | 1.20053 | ||||||||
\(751\) | 3.95970e67 | 1.04743 | 0.523713 | − | 0.851895i | \(-0.324546\pi\) | ||||
0.523713 | + | 0.851895i | \(0.324546\pi\) | |||||||
\(752\) | −1.05807e68 | −2.71265 | ||||||||
\(753\) | 2.33836e67 | 0.581072 | ||||||||
\(754\) | −2.51358e66 | −0.0605433 | ||||||||
\(755\) | −3.17945e65 | −0.00742333 | ||||||||
\(756\) | −2.84755e67 | −0.644479 | ||||||||
\(757\) | −3.90670e67 | −0.857149 | −0.428575 | − | 0.903506i | \(-0.640984\pi\) | ||||
−0.428575 | + | 0.903506i | \(0.640984\pi\) | |||||||
\(758\) | 9.27790e67 | 1.97344 | ||||||||
\(759\) | −2.12571e67 | −0.438352 | ||||||||
\(760\) | −6.67284e67 | −1.33411 | ||||||||
\(761\) | −8.64597e67 | −1.67600 | −0.838001 | − | 0.545669i | \(-0.816276\pi\) | ||||
−0.838001 | + | 0.545669i | \(0.816276\pi\) | |||||||
\(762\) | −4.23012e67 | −0.795079 | ||||||||
\(763\) | −9.63069e66 | −0.175522 | ||||||||
\(764\) | 8.44246e67 | 1.49202 | ||||||||
\(765\) | −3.97226e66 | −0.0680760 | ||||||||
\(766\) | 5.97119e67 | 0.992395 | ||||||||
\(767\) | 6.07177e66 | 0.0978643 | ||||||||
\(768\) | 1.86828e68 | 2.92047 | ||||||||
\(769\) | 8.45845e67 | 1.28240 | 0.641198 | − | 0.767376i | \(-0.278438\pi\) | ||||
0.641198 | + | 0.767376i | \(0.278438\pi\) | |||||||
\(770\) | 1.30857e67 | 0.192426 | ||||||||
\(771\) | −4.45179e67 | −0.634975 | ||||||||
\(772\) | −1.79608e68 | −2.48496 | ||||||||
\(773\) | −9.32204e67 | −1.25110 | −0.625551 | − | 0.780183i | \(-0.715126\pi\) | ||||
−0.625551 | + | 0.780183i | \(0.715126\pi\) | |||||||
\(774\) | −3.67551e67 | −0.478526 | ||||||||
\(775\) | 1.03843e68 | 1.31156 | ||||||||
\(776\) | 2.16217e68 | 2.64934 | ||||||||
\(777\) | −5.32883e66 | −0.0633487 | ||||||||
\(778\) | −1.77016e68 | −2.04170 | ||||||||
\(779\) | 1.17271e68 | 1.31238 | ||||||||
\(780\) | −9.14329e66 | −0.0992840 | ||||||||
\(781\) | −6.12931e67 | −0.645821 | ||||||||
\(782\) | −4.09417e67 | −0.418607 | ||||||||
\(783\) | 3.25299e67 | 0.322762 | ||||||||
\(784\) | −3.93608e68 | −3.78998 | ||||||||
\(785\) | −3.75262e67 | −0.350670 | ||||||||
\(786\) | −2.16177e68 | −1.96056 | ||||||||
\(787\) | 1.40543e68 | 1.23709 | 0.618547 | − | 0.785748i | \(-0.287722\pi\) | ||||
0.618547 | + | 0.785748i | \(0.287722\pi\) | |||||||
\(788\) | 8.97512e67 | 0.766786 | ||||||||
\(789\) | 1.61324e68 | 1.33780 | ||||||||
\(790\) | 1.44961e68 | 1.16685 | ||||||||
\(791\) | −3.35610e67 | −0.262233 | ||||||||
\(792\) | 1.86573e68 | 1.41516 | ||||||||
\(793\) | 6.90668e66 | 0.0508568 | ||||||||
\(794\) | 6.21764e67 | 0.444471 | ||||||||
\(795\) | −6.92935e67 | −0.480911 | ||||||||
\(796\) | 4.94970e68 | 3.33520 | ||||||||
\(797\) | −6.41377e67 | −0.419607 | −0.209804 | − | 0.977744i | \(-0.567282\pi\) | ||||
−0.209804 | + | 0.977744i | \(0.567282\pi\) | |||||||
\(798\) | 4.57461e67 | 0.290593 | ||||||||
\(799\) | 4.61009e67 | 0.284355 | ||||||||
\(800\) | −5.77500e68 | −3.45889 | ||||||||
\(801\) | −1.07457e68 | −0.624984 | ||||||||
\(802\) | −1.98816e68 | −1.12293 | ||||||||
\(803\) | −2.63612e68 | −1.44594 | ||||||||
\(804\) | 2.34144e68 | 1.24728 | ||||||||
\(805\) | −9.18902e66 | −0.0475407 | ||||||||
\(806\) | −6.53959e67 | −0.328607 | ||||||||
\(807\) | −3.34892e66 | −0.0163447 | ||||||||
\(808\) | 5.37805e68 | 2.54951 | ||||||||
\(809\) | 7.54417e67 | 0.347393 | 0.173696 | − | 0.984799i | \(-0.444429\pi\) | ||||
0.173696 | + | 0.984799i | \(0.444429\pi\) | |||||||
\(810\) | 8.96757e67 | 0.401122 | ||||||||
\(811\) | −2.25843e68 | −0.981332 | −0.490666 | − | 0.871348i | \(-0.663247\pi\) | ||||
−0.490666 | + | 0.871348i | \(0.663247\pi\) | |||||||
\(812\) | −4.17282e67 | −0.176142 | ||||||||
\(813\) | −1.83116e68 | −0.750928 | ||||||||
\(814\) | 1.98262e68 | 0.789890 | ||||||||
\(815\) | 1.97337e67 | 0.0763845 | ||||||||
\(816\) | −3.46227e68 | −1.30209 | ||||||||
\(817\) | 1.58114e68 | 0.577766 | ||||||||
\(818\) | −1.12863e68 | −0.400728 | ||||||||
\(819\) | −2.45058e66 | −0.00845467 | ||||||||
\(820\) | −5.28843e68 | −1.77297 | ||||||||
\(821\) | 2.57889e68 | 0.840174 | 0.420087 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420087 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(822\) | 8.89457e67 | 0.281603 | ||||||||
\(823\) | −8.83986e67 | −0.271988 | −0.135994 | − | 0.990710i | \(-0.543423\pi\) | ||||
−0.135994 | + | 0.990710i | \(0.543423\pi\) | |||||||
\(824\) | 5.85271e68 | 1.75012 | ||||||||
\(825\) | 2.37340e68 | 0.689768 | ||||||||
\(826\) | 1.36995e68 | 0.386965 | ||||||||
\(827\) | −2.82593e68 | −0.775856 | −0.387928 | − | 0.921690i | \(-0.626809\pi\) | ||||
−0.387928 | + | 0.921690i | \(0.626809\pi\) | |||||||
\(828\) | −2.04424e68 | −0.545530 | ||||||||
\(829\) | 2.91606e68 | 0.756423 | 0.378211 | − | 0.925719i | \(-0.376539\pi\) | ||||
0.378211 | + | 0.925719i | \(0.376539\pi\) | |||||||
\(830\) | 2.72854e68 | 0.688012 | ||||||||
\(831\) | −5.09321e68 | −1.24844 | ||||||||
\(832\) | 1.89113e68 | 0.450634 | ||||||||
\(833\) | 1.71499e68 | 0.397286 | ||||||||
\(834\) | 3.73175e68 | 0.840448 | ||||||||
\(835\) | 1.55429e68 | 0.340329 | ||||||||
\(836\) | −1.25231e69 | −2.66602 | ||||||||
\(837\) | 8.46332e68 | 1.75183 | ||||||||
\(838\) | −9.42450e67 | −0.189681 | ||||||||
\(839\) | 9.42111e68 | 1.84372 | 0.921862 | − | 0.387518i | \(-0.126667\pi\) | ||||
0.921862 | + | 0.387518i | \(0.126667\pi\) | |||||||
\(840\) | −1.32215e68 | −0.251604 | ||||||||
\(841\) | −4.92719e68 | −0.911786 | ||||||||
\(842\) | −1.86924e69 | −3.36380 | ||||||||
\(843\) | −5.49616e68 | −0.961858 | ||||||||
\(844\) | −1.94998e69 | −3.31881 | ||||||||
\(845\) | 2.57968e68 | 0.427005 | ||||||||
\(846\) | 3.12843e68 | 0.503644 | ||||||||
\(847\) | 2.13835e67 | 0.0334825 | ||||||||
\(848\) | 3.68424e69 | 5.61106 | ||||||||
\(849\) | −1.23058e68 | −0.182296 | ||||||||
\(850\) | 4.57122e68 | 0.658700 | ||||||||
\(851\) | −1.39224e68 | −0.195150 | ||||||||
\(852\) | 9.66286e68 | 1.31757 | ||||||||
\(853\) | −1.22430e69 | −1.62400 | −0.811999 | − | 0.583659i | \(-0.801620\pi\) | ||||
−0.811999 | + | 0.583659i | \(0.801620\pi\) | |||||||
\(854\) | 1.55832e68 | 0.201093 | ||||||||
\(855\) | 1.15960e68 | 0.145581 | ||||||||
\(856\) | 1.15484e69 | 1.41055 | ||||||||
\(857\) | −4.45209e68 | −0.529071 | −0.264536 | − | 0.964376i | \(-0.585219\pi\) | ||||
−0.264536 | + | 0.964376i | \(0.585219\pi\) | |||||||
\(858\) | −1.49467e68 | −0.172820 | ||||||||
\(859\) | −2.77149e68 | −0.311799 | −0.155899 | − | 0.987773i | \(-0.549828\pi\) | ||||
−0.155899 | + | 0.987773i | \(0.549828\pi\) | |||||||
\(860\) | −7.13029e68 | −0.780537 | ||||||||
\(861\) | 2.32359e68 | 0.247506 | ||||||||
\(862\) | 1.25069e69 | 1.29637 | ||||||||
\(863\) | 2.86475e68 | 0.288957 | 0.144479 | − | 0.989508i | \(-0.453850\pi\) | ||||
0.144479 | + | 0.989508i | \(0.453850\pi\) | |||||||
\(864\) | −4.70669e69 | −4.62000 | ||||||||
\(865\) | −1.04397e68 | −0.0997265 | ||||||||
\(866\) | 2.54068e69 | 2.36200 | ||||||||
\(867\) | −7.20180e68 | −0.651617 | ||||||||
\(868\) | −1.08564e69 | −0.956034 | ||||||||
\(869\) | 1.74358e69 | 1.49444 | ||||||||
\(870\) | 2.35669e68 | 0.196607 | ||||||||
\(871\) | 7.33333e67 | 0.0595490 | ||||||||
\(872\) | −3.62035e69 | −2.86163 | ||||||||
\(873\) | −3.75739e68 | −0.289102 | ||||||||
\(874\) | 1.19519e69 | 0.895194 | ||||||||
\(875\) | 2.28701e68 | 0.166755 | ||||||||
\(876\) | 4.15585e69 | 2.94994 | ||||||||
\(877\) | −6.75109e68 | −0.466534 | −0.233267 | − | 0.972413i | \(-0.574942\pi\) | ||||
−0.233267 | + | 0.972413i | \(0.574942\pi\) | |||||||
\(878\) | −3.04678e69 | −2.04984 | ||||||||
\(879\) | 1.80052e69 | 1.17939 | ||||||||
\(880\) | 2.89116e69 | 1.84387 | ||||||||
\(881\) | −2.56812e67 | −0.0159471 | −0.00797354 | − | 0.999968i | \(-0.502538\pi\) | ||||
−0.00797354 | + | 0.999968i | \(0.502538\pi\) | |||||||
\(882\) | 1.16380e69 | 0.703665 | ||||||||
\(883\) | −1.81395e69 | −1.06794 | −0.533972 | − | 0.845502i | \(-0.679301\pi\) | ||||
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(884\) | −2.11814e68 | −0.121430 | ||||||||
\(885\) | −5.69278e68 | −0.317803 | ||||||||
\(886\) | −2.05215e69 | −1.11562 | ||||||||
\(887\) | 1.74355e68 | 0.0923059 | 0.0461529 | − | 0.998934i | \(-0.485304\pi\) | ||||
0.0461529 | + | 0.998934i | \(0.485304\pi\) | |||||||
\(888\) | −2.00320e69 | −1.03281 | ||||||||
\(889\) | −2.19942e68 | −0.110437 | ||||||||
\(890\) | −2.83318e69 | −1.38551 | ||||||||
\(891\) | 1.07861e69 | 0.513735 | ||||||||
\(892\) | 1.09695e70 | 5.08875 | ||||||||
\(893\) | −1.34580e69 | −0.608094 | ||||||||
\(894\) | −4.76322e69 | −2.09638 | ||||||||
\(895\) | 3.25812e68 | 0.139677 | ||||||||
\(896\) | 2.09879e69 | 0.876455 | ||||||||
\(897\) | 1.04959e68 | 0.0426968 | ||||||||
\(898\) | 2.18297e69 | 0.865074 | ||||||||
\(899\) | 1.24022e69 | 0.478791 | ||||||||
\(900\) | 2.28243e69 | 0.858419 | ||||||||
\(901\) | −1.60526e69 | −0.588182 | ||||||||
\(902\) | −8.64507e69 | −3.08614 | ||||||||
\(903\) | 3.13286e68 | 0.108963 | ||||||||
\(904\) | −1.26162e70 | −4.27533 | ||||||||
\(905\) | 8.38326e68 | 0.276803 | ||||||||
\(906\) | 8.19386e67 | 0.0263618 | ||||||||
\(907\) | −7.97555e68 | −0.250028 | −0.125014 | − | 0.992155i | \(-0.539898\pi\) | ||||
−0.125014 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(908\) | 5.50557e69 | 1.68184 | ||||||||
\(909\) | −9.34591e68 | −0.278208 | ||||||||
\(910\) | −6.46114e67 | −0.0187429 | ||||||||
\(911\) | 6.39008e69 | 1.80644 | 0.903222 | − | 0.429173i | \(-0.141195\pi\) | ||||
0.903222 | + | 0.429173i | \(0.141195\pi\) | |||||||
\(912\) | 1.01072e70 | 2.78453 | ||||||||
\(913\) | 3.28187e69 | 0.881167 | ||||||||
\(914\) | 7.78449e69 | 2.03702 | ||||||||
\(915\) | −6.47557e68 | −0.165151 | ||||||||
\(916\) | −1.60546e70 | −3.99075 | ||||||||
\(917\) | −1.12400e69 | −0.272324 | ||||||||
\(918\) | 3.72560e69 | 0.879818 | ||||||||
\(919\) | 3.86963e69 | 0.890747 | 0.445373 | − | 0.895345i | \(-0.353071\pi\) | ||||
0.445373 | + | 0.895345i | \(0.353071\pi\) | |||||||
\(920\) | −3.45432e69 | −0.775084 | ||||||||
\(921\) | −6.04431e69 | −1.32204 | ||||||||
\(922\) | 1.14725e70 | 2.44615 | ||||||||
\(923\) | 3.02639e68 | 0.0629050 | ||||||||
\(924\) | −2.48131e69 | −0.502793 | ||||||||
\(925\) | 1.55446e69 | 0.307079 | ||||||||
\(926\) | −1.02235e70 | −1.96898 | ||||||||
\(927\) | −1.01708e69 | −0.190977 | ||||||||
\(928\) | −6.89721e69 | −1.26269 | ||||||||
\(929\) | −4.53114e69 | −0.808795 | −0.404398 | − | 0.914583i | \(-0.632519\pi\) | ||||
−0.404398 | + | 0.914583i | \(0.632519\pi\) | |||||||
\(930\) | 6.13140e69 | 1.06711 | ||||||||
\(931\) | −5.00646e69 | −0.849597 | ||||||||
\(932\) | −4.77735e69 | −0.790520 | ||||||||
\(933\) | −3.42196e69 | −0.552149 | ||||||||
\(934\) | 1.65479e70 | 2.60370 | ||||||||
\(935\) | −1.25971e69 | −0.193284 | ||||||||
\(936\) | −9.21217e68 | −0.137841 | ||||||||
\(937\) | 2.69082e69 | 0.392648 | 0.196324 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196324 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(938\) | 1.65458e69 | 0.235463 | ||||||||
\(939\) | −7.23833e69 | −1.00461 | ||||||||
\(940\) | 6.06899e69 | 0.821508 | ||||||||
\(941\) | −3.38983e69 | −0.447530 | −0.223765 | − | 0.974643i | \(-0.571835\pi\) | ||||
−0.223765 | + | 0.974643i | \(0.571835\pi\) | |||||||
\(942\) | 9.67100e69 | 1.24530 | ||||||||
\(943\) | 6.07075e69 | 0.762460 | ||||||||
\(944\) | 3.02677e70 | 3.70799 | ||||||||
\(945\) | 8.36179e68 | 0.0999199 | ||||||||
\(946\) | −1.16560e70 | −1.35865 | ||||||||
\(947\) | −1.24658e70 | −1.41742 | −0.708708 | − | 0.705502i | \(-0.750721\pi\) | ||||
−0.708708 | + | 0.705502i | \(0.750721\pi\) | |||||||
\(948\) | −2.74876e70 | −3.04888 | ||||||||
\(949\) | 1.30160e69 | 0.140839 | ||||||||
\(950\) | −1.33445e70 | −1.40863 | ||||||||
\(951\) | 1.28473e70 | 1.32303 | ||||||||
\(952\) | −3.06290e69 | −0.307726 | ||||||||
\(953\) | 1.47472e70 | 1.44553 | 0.722766 | − | 0.691093i | \(-0.242870\pi\) | ||||
0.722766 | + | 0.691093i | \(0.242870\pi\) | |||||||
\(954\) | −1.08934e70 | −1.04178 | ||||||||
\(955\) | −2.47912e69 | −0.231323 | ||||||||
\(956\) | 2.48847e70 | 2.26554 | ||||||||
\(957\) | 2.83461e69 | 0.251804 | ||||||||
\(958\) | −2.38062e69 | −0.206348 | ||||||||
\(959\) | 4.62466e68 | 0.0391150 | ||||||||
\(960\) | −1.77309e70 | −1.46338 | ||||||||
\(961\) | 1.98503e70 | 1.59871 | ||||||||
\(962\) | −9.78935e68 | −0.0769378 | ||||||||
\(963\) | −2.00687e69 | −0.153922 | ||||||||
\(964\) | −4.36427e70 | −3.26664 | ||||||||
\(965\) | 5.27418e69 | 0.385268 | ||||||||
\(966\) | 2.36813e69 | 0.168827 | ||||||||
\(967\) | 9.72062e69 | 0.676351 | 0.338175 | − | 0.941083i | \(-0.390190\pi\) | ||||
0.338175 | + | 0.941083i | \(0.390190\pi\) | |||||||
\(968\) | 8.03843e69 | 0.545884 | ||||||||
\(969\) | −4.40379e69 | −0.291889 | ||||||||
\(970\) | −9.90665e69 | −0.640901 | ||||||||
\(971\) | −2.15826e70 | −1.36286 | −0.681431 | − | 0.731883i | \(-0.738642\pi\) | ||||
−0.681431 | + | 0.731883i | \(0.738642\pi\) | |||||||
\(972\) | 3.20928e70 | 1.97811 | ||||||||
\(973\) | 1.94030e69 | 0.116739 | ||||||||
\(974\) | −5.57872e68 | −0.0327642 | ||||||||
\(975\) | −1.17188e69 | −0.0671856 | ||||||||
\(976\) | 3.44297e70 | 1.92692 | ||||||||
\(977\) | −1.11352e69 | −0.0608384 | −0.0304192 | − | 0.999537i | \(-0.509684\pi\) | ||||
−0.0304192 | + | 0.999537i | \(0.509684\pi\) | |||||||
\(978\) | −5.08564e69 | −0.271258 | ||||||||
\(979\) | −3.40772e70 | −1.77448 | ||||||||
\(980\) | 2.25770e70 | 1.14777 | ||||||||
\(981\) | 6.29141e69 | 0.312267 | ||||||||
\(982\) | −3.42345e70 | −1.65899 | ||||||||
\(983\) | −3.46672e69 | −0.164025 | −0.0820127 | − | 0.996631i | \(-0.526135\pi\) | ||||
−0.0820127 | + | 0.996631i | \(0.526135\pi\) | |||||||
\(984\) | 8.73481e70 | 4.03523 | ||||||||
\(985\) | −2.63553e69 | −0.118882 | ||||||||
\(986\) | 5.45951e69 | 0.240462 | ||||||||
\(987\) | −2.66655e69 | −0.114682 | ||||||||
\(988\) | 6.18336e69 | 0.259679 | ||||||||
\(989\) | 8.18507e69 | 0.335668 | ||||||||
\(990\) | −8.54843e69 | −0.342341 | ||||||||
\(991\) | 1.50226e70 | 0.587510 | 0.293755 | − | 0.955881i | \(-0.405095\pi\) | ||||
0.293755 | + | 0.955881i | \(0.405095\pi\) | |||||||
\(992\) | −1.79445e71 | −6.85341 | ||||||||
\(993\) | −2.39702e69 | −0.0894055 | ||||||||
\(994\) | 6.82830e69 | 0.248732 | ||||||||
\(995\) | −1.45347e70 | −0.517089 | ||||||||
\(996\) | −5.17387e70 | −1.79772 | ||||||||
\(997\) | −9.94591e69 | −0.337527 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(998\) | 8.27338e70 | 2.74230 | ||||||||
\(999\) | 1.26690e70 | 0.410162 |
(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 | 1.48.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 9.48.a.c.1.1 | 4 | |||
4.3 | odd | 2 | 16.48.a.d.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.48.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.48.a.c.1.1 | 4 | 3.2 | odd | 2 | |||
16.48.a.d.1.2 | 4 | 4.3 | odd | 2 |