Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,50,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, 50, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 50);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 50 \) |
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: | \(15.2066205099\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 27962089502x + 71708842875120 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(165922.\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25719e7 | −0.951336 | −0.475668 | − | 0.879625i | \(-0.657794\pi\) | ||||
−0.475668 | + | 0.879625i | \(0.657794\pi\) | |||||||
\(3\) | 5.57972e11 | 1.14062 | 0.570311 | − | 0.821429i | \(-0.306823\pi\) | ||||
0.570311 | + | 0.821429i | \(0.306823\pi\) | |||||||
\(4\) | −5.34581e13 | −0.0949606 | ||||||||
\(5\) | −1.06460e17 | −0.798768 | −0.399384 | − | 0.916784i | \(-0.630776\pi\) | ||||
−0.399384 | + | 0.916784i | \(0.630776\pi\) | |||||||
\(6\) | −1.25945e19 | −1.08511 | ||||||||
\(7\) | 5.68014e20 | 1.12062 | 0.560308 | − | 0.828284i | \(-0.310683\pi\) | ||||
0.560308 | + | 0.828284i | \(0.310683\pi\) | |||||||
\(8\) | 1.39135e22 | 1.04167 | ||||||||
\(9\) | 7.20337e22 | 0.301019 | ||||||||
\(10\) | 2.40300e24 | 0.759897 | ||||||||
\(11\) | −4.66926e25 | −1.42931 | −0.714656 | − | 0.699476i | \(-0.753417\pi\) | ||||
−0.714656 | + | 0.699476i | \(0.753417\pi\) | |||||||
\(12\) | −2.98281e25 | −0.108314 | ||||||||
\(13\) | 1.95401e27 | 0.998421 | 0.499211 | − | 0.866481i | \(-0.333623\pi\) | ||||
0.499211 | + | 0.866481i | \(0.333623\pi\) | |||||||
\(14\) | −1.28212e28 | −1.06608 | ||||||||
\(15\) | −5.94017e28 | −0.911093 | ||||||||
\(16\) | −2.83961e29 | −0.896022 | ||||||||
\(17\) | −1.59552e30 | −1.13999 | −0.569997 | − | 0.821647i | \(-0.693056\pi\) | ||||
−0.569997 | + | 0.821647i | \(0.693056\pi\) | |||||||
\(18\) | −1.62594e30 | −0.286370 | ||||||||
\(19\) | −3.45099e31 | −1.61614 | −0.808072 | − | 0.589084i | \(-0.799489\pi\) | ||||
−0.808072 | + | 0.589084i | \(0.799489\pi\) | |||||||
\(20\) | 5.69114e30 | 0.0758515 | ||||||||
\(21\) | 3.16936e32 | 1.27820 | ||||||||
\(22\) | 1.05394e33 | 1.35976 | ||||||||
\(23\) | −2.46487e33 | −1.07019 | −0.535096 | − | 0.844791i | \(-0.679725\pi\) | ||||
−0.535096 | + | 0.844791i | \(0.679725\pi\) | |||||||
\(24\) | 7.76336e33 | 1.18816 | ||||||||
\(25\) | −6.42986e33 | −0.361969 | ||||||||
\(26\) | −4.41057e34 | −0.949834 | ||||||||
\(27\) | −9.33296e34 | −0.797273 | ||||||||
\(28\) | −3.03649e34 | −0.106414 | ||||||||
\(29\) | 4.27652e35 | 0.634365 | 0.317183 | − | 0.948364i | \(-0.397263\pi\) | ||||
0.317183 | + | 0.948364i | \(0.397263\pi\) | |||||||
\(30\) | 1.34081e36 | 0.866755 | ||||||||
\(31\) | 2.26555e36 | 0.655861 | 0.327930 | − | 0.944702i | \(-0.393649\pi\) | ||||
0.327930 | + | 0.944702i | \(0.393649\pi\) | |||||||
\(32\) | −1.42307e36 | −0.189258 | ||||||||
\(33\) | −2.60532e37 | −1.63031 | ||||||||
\(34\) | 3.60138e37 | 1.08452 | ||||||||
\(35\) | −6.04707e37 | −0.895113 | ||||||||
\(36\) | −3.85078e36 | −0.0285850 | ||||||||
\(37\) | −1.55810e38 | −0.591088 | −0.295544 | − | 0.955329i | \(-0.595501\pi\) | ||||
−0.295544 | + | 0.955329i | \(0.595501\pi\) | |||||||
\(38\) | 7.78954e38 | 1.53749 | ||||||||
\(39\) | 1.09028e39 | 1.13882 | ||||||||
\(40\) | −1.48123e39 | −0.832057 | ||||||||
\(41\) | −1.49379e39 | −0.458233 | −0.229117 | − | 0.973399i | \(-0.573584\pi\) | ||||
−0.229117 | + | 0.973399i | \(0.573584\pi\) | |||||||
\(42\) | −7.15386e39 | −1.21600 | ||||||||
\(43\) | 5.17800e39 | 0.494521 | 0.247260 | − | 0.968949i | \(-0.420470\pi\) | ||||
0.247260 | + | 0.968949i | \(0.420470\pi\) | |||||||
\(44\) | 2.49610e39 | 0.135728 | ||||||||
\(45\) | −7.66870e39 | −0.240445 | ||||||||
\(46\) | 5.56368e40 | 1.01811 | ||||||||
\(47\) | 5.79235e40 | 0.625831 | 0.312916 | − | 0.949781i | \(-0.398694\pi\) | ||||
0.312916 | + | 0.949781i | \(0.398694\pi\) | |||||||
\(48\) | −1.58442e41 | −1.02202 | ||||||||
\(49\) | 6.57162e40 | 0.255781 | ||||||||
\(50\) | 1.45134e41 | 0.344354 | ||||||||
\(51\) | −8.90253e41 | −1.30030 | ||||||||
\(52\) | −1.04457e41 | −0.0948107 | ||||||||
\(53\) | −5.51356e41 | −0.313815 | −0.156907 | − | 0.987613i | \(-0.550152\pi\) | ||||
−0.156907 | + | 0.987613i | \(0.550152\pi\) | |||||||
\(54\) | 2.10663e42 | 0.758474 | ||||||||
\(55\) | 4.97089e42 | 1.14169 | ||||||||
\(56\) | 7.90307e42 | 1.16732 | ||||||||
\(57\) | −1.92555e43 | −1.84341 | ||||||||
\(58\) | −9.65293e42 | −0.603494 | ||||||||
\(59\) | −1.93125e42 | −0.0794262 | −0.0397131 | − | 0.999211i | \(-0.512644\pi\) | ||||
−0.0397131 | + | 0.999211i | \(0.512644\pi\) | |||||||
\(60\) | 3.17550e42 | 0.0865180 | ||||||||
\(61\) | 2.41153e43 | 0.438239 | 0.219120 | − | 0.975698i | \(-0.429681\pi\) | ||||
0.219120 | + | 0.975698i | \(0.429681\pi\) | |||||||
\(62\) | −5.11377e43 | −0.623943 | ||||||||
\(63\) | 4.09161e43 | 0.337327 | ||||||||
\(64\) | 1.91977e44 | 1.07607 | ||||||||
\(65\) | −2.08023e44 | −0.797507 | ||||||||
\(66\) | 5.88070e44 | 1.55097 | ||||||||
\(67\) | −8.25642e44 | −1.50646 | −0.753232 | − | 0.657755i | \(-0.771506\pi\) | ||||
−0.753232 | + | 0.657755i | \(0.771506\pi\) | |||||||
\(68\) | 8.52932e43 | 0.108254 | ||||||||
\(69\) | −1.37533e45 | −1.22069 | ||||||||
\(70\) | 1.36494e45 | 0.851553 | ||||||||
\(71\) | −1.77228e45 | −0.781094 | −0.390547 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390547 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(72\) | 1.00224e45 | 0.313564 | ||||||||
\(73\) | 6.25517e45 | 1.39582 | 0.697910 | − | 0.716186i | \(-0.254114\pi\) | ||||
0.697910 | + | 0.716186i | \(0.254114\pi\) | |||||||
\(74\) | 3.51693e45 | 0.562323 | ||||||||
\(75\) | −3.58768e45 | −0.412870 | ||||||||
\(76\) | 1.84483e45 | 0.153470 | ||||||||
\(77\) | −2.65220e46 | −1.60171 | ||||||||
\(78\) | −2.46097e46 | −1.08340 | ||||||||
\(79\) | 4.72997e46 | 1.52404 | 0.762018 | − | 0.647556i | \(-0.224209\pi\) | ||||
0.762018 | + | 0.647556i | \(0.224209\pi\) | |||||||
\(80\) | 3.02304e46 | 0.715714 | ||||||||
\(81\) | −6.93129e46 | −1.21041 | ||||||||
\(82\) | 3.37178e46 | 0.435933 | ||||||||
\(83\) | 4.29785e46 | 0.412893 | 0.206447 | − | 0.978458i | \(-0.433810\pi\) | ||||
0.206447 | + | 0.978458i | \(0.433810\pi\) | |||||||
\(84\) | −1.69428e46 | −0.121379 | ||||||||
\(85\) | 1.69858e47 | 0.910591 | ||||||||
\(86\) | −1.16877e47 | −0.470455 | ||||||||
\(87\) | 2.38618e47 | 0.723571 | ||||||||
\(88\) | −6.49658e47 | −1.48888 | ||||||||
\(89\) | −7.42748e47 | −1.29058 | −0.645292 | − | 0.763936i | \(-0.723264\pi\) | ||||
−0.645292 | + | 0.763936i | \(0.723264\pi\) | |||||||
\(90\) | 1.73097e47 | 0.228744 | ||||||||
\(91\) | 1.10990e48 | 1.11885 | ||||||||
\(92\) | 1.31767e47 | 0.101626 | ||||||||
\(93\) | 1.26411e48 | 0.748089 | ||||||||
\(94\) | −1.30744e48 | −0.595375 | ||||||||
\(95\) | 3.67392e48 | 1.29092 | ||||||||
\(96\) | −7.94036e47 | −0.215871 | ||||||||
\(97\) | −5.90631e48 | −1.24569 | −0.622843 | − | 0.782347i | \(-0.714023\pi\) | ||||
−0.622843 | + | 0.782347i | \(0.714023\pi\) | |||||||
\(98\) | −1.48334e48 | −0.243334 | ||||||||
\(99\) | −3.36344e48 | −0.430250 | ||||||||
\(100\) | 3.43728e47 | 0.0343728 | ||||||||
\(101\) | −1.67953e48 | −0.131618 | −0.0658090 | − | 0.997832i | \(-0.520963\pi\) | ||||
−0.0658090 | + | 0.997832i | \(0.520963\pi\) | |||||||
\(102\) | 2.00947e49 | 1.23702 | ||||||||
\(103\) | −9.66426e48 | −0.468443 | −0.234221 | − | 0.972183i | \(-0.575254\pi\) | ||||
−0.234221 | + | 0.972183i | \(0.575254\pi\) | |||||||
\(104\) | 2.71871e49 | 1.04003 | ||||||||
\(105\) | −3.37410e49 | −1.02099 | ||||||||
\(106\) | 1.24452e49 | 0.298543 | ||||||||
\(107\) | 1.13270e49 | 0.215879 | 0.107940 | − | 0.994157i | \(-0.465575\pi\) | ||||
0.107940 | + | 0.994157i | \(0.465575\pi\) | |||||||
\(108\) | 4.98922e48 | 0.0757095 | ||||||||
\(109\) | 4.53029e49 | 0.548500 | 0.274250 | − | 0.961658i | \(-0.411570\pi\) | ||||
0.274250 | + | 0.961658i | \(0.411570\pi\) | |||||||
\(110\) | −1.12203e50 | −1.08613 | ||||||||
\(111\) | −8.69375e49 | −0.674208 | ||||||||
\(112\) | −1.61294e50 | −1.00410 | ||||||||
\(113\) | 9.56756e48 | 0.0479048 | 0.0239524 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239524 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(114\) | 4.34635e50 | 1.75370 | ||||||||
\(115\) | 2.62410e50 | 0.854836 | ||||||||
\(116\) | −2.28614e49 | −0.0602397 | ||||||||
\(117\) | 1.40754e50 | 0.300544 | ||||||||
\(118\) | 4.35920e49 | 0.0755609 | ||||||||
\(119\) | −9.06275e50 | −1.27750 | ||||||||
\(120\) | −8.26486e50 | −0.949063 | ||||||||
\(121\) | 1.11301e51 | 1.04293 | ||||||||
\(122\) | −5.44328e50 | −0.416913 | ||||||||
\(123\) | −8.33496e50 | −0.522671 | ||||||||
\(124\) | −1.21112e50 | −0.0622809 | ||||||||
\(125\) | 2.57563e51 | 1.08790 | ||||||||
\(126\) | −9.23556e50 | −0.320911 | ||||||||
\(127\) | 3.33633e51 | 0.955164 | 0.477582 | − | 0.878587i | \(-0.341513\pi\) | ||||
0.477582 | + | 0.878587i | \(0.341513\pi\) | |||||||
\(128\) | −3.53218e51 | −0.834445 | ||||||||
\(129\) | 2.88918e51 | 0.564061 | ||||||||
\(130\) | 4.69549e51 | 0.758697 | ||||||||
\(131\) | −7.56140e51 | −1.01264 | −0.506320 | − | 0.862346i | \(-0.668995\pi\) | ||||
−0.506320 | + | 0.862346i | \(0.668995\pi\) | |||||||
\(132\) | 1.39275e51 | 0.154815 | ||||||||
\(133\) | −1.96021e52 | −1.81108 | ||||||||
\(134\) | 1.86363e52 | 1.43315 | ||||||||
\(135\) | 9.93586e51 | 0.636837 | ||||||||
\(136\) | −2.21992e52 | −1.18750 | ||||||||
\(137\) | −3.63264e52 | −1.62393 | −0.811967 | − | 0.583704i | \(-0.801603\pi\) | ||||
−0.811967 | + | 0.583704i | \(0.801603\pi\) | |||||||
\(138\) | 3.10438e52 | 1.16128 | ||||||||
\(139\) | 4.58875e52 | 1.43824 | 0.719121 | − | 0.694885i | \(-0.244545\pi\) | ||||
0.719121 | + | 0.694885i | \(0.244545\pi\) | |||||||
\(140\) | 3.23265e51 | 0.0850005 | ||||||||
\(141\) | 3.23197e52 | 0.713837 | ||||||||
\(142\) | 4.00038e52 | 0.743082 | ||||||||
\(143\) | −9.12376e52 | −1.42706 | ||||||||
\(144\) | −2.04547e52 | −0.269720 | ||||||||
\(145\) | −4.55278e52 | −0.506711 | ||||||||
\(146\) | −1.41191e53 | −1.32789 | ||||||||
\(147\) | 3.66678e52 | 0.291750 | ||||||||
\(148\) | 8.32929e51 | 0.0561301 | ||||||||
\(149\) | 1.90143e53 | 1.08647 | 0.543233 | − | 0.839582i | \(-0.317200\pi\) | ||||
0.543233 | + | 0.839582i | \(0.317200\pi\) | |||||||
\(150\) | 8.09809e52 | 0.392778 | ||||||||
\(151\) | 2.73658e53 | 1.12791 | 0.563953 | − | 0.825807i | \(-0.309280\pi\) | ||||
0.563953 | + | 0.825807i | \(0.309280\pi\) | |||||||
\(152\) | −4.80153e53 | −1.68350 | ||||||||
\(153\) | −1.14931e53 | −0.343160 | ||||||||
\(154\) | 5.98654e53 | 1.52376 | ||||||||
\(155\) | −2.41190e53 | −0.523881 | ||||||||
\(156\) | −5.82843e52 | −0.108143 | ||||||||
\(157\) | 6.65092e53 | 1.05521 | 0.527607 | − | 0.849489i | \(-0.323090\pi\) | ||||
0.527607 | + | 0.849489i | \(0.323090\pi\) | |||||||
\(158\) | −1.06765e54 | −1.44987 | ||||||||
\(159\) | −3.07642e53 | −0.357944 | ||||||||
\(160\) | 1.51500e53 | 0.151173 | ||||||||
\(161\) | −1.40008e54 | −1.19928 | ||||||||
\(162\) | 1.56453e54 | 1.15150 | ||||||||
\(163\) | −4.80475e53 | −0.304141 | −0.152070 | − | 0.988370i | \(-0.548594\pi\) | ||||
−0.152070 | + | 0.988370i | \(0.548594\pi\) | |||||||
\(164\) | 7.98554e52 | 0.0435141 | ||||||||
\(165\) | 2.77362e54 | 1.30224 | ||||||||
\(166\) | −9.70107e53 | −0.392800 | ||||||||
\(167\) | −5.81006e53 | −0.203061 | −0.101531 | − | 0.994832i | \(-0.532374\pi\) | ||||
−0.101531 | + | 0.994832i | \(0.532374\pi\) | |||||||
\(168\) | 4.40969e54 | 1.33147 | ||||||||
\(169\) | −1.20849e52 | −0.00315515 | ||||||||
\(170\) | −3.83403e54 | −0.866277 | ||||||||
\(171\) | −2.48587e54 | −0.486490 | ||||||||
\(172\) | −2.76806e53 | −0.0469600 | ||||||||
\(173\) | −5.03434e54 | −0.740991 | −0.370496 | − | 0.928834i | \(-0.620812\pi\) | ||||
−0.370496 | + | 0.928834i | \(0.620812\pi\) | |||||||
\(174\) | −5.38606e54 | −0.688359 | ||||||||
\(175\) | −3.65225e54 | −0.405628 | ||||||||
\(176\) | 1.32589e55 | 1.28070 | ||||||||
\(177\) | −1.07758e54 | −0.0905953 | ||||||||
\(178\) | 1.67653e55 | 1.22778 | ||||||||
\(179\) | 1.02146e55 | 0.652114 | 0.326057 | − | 0.945350i | \(-0.394280\pi\) | ||||
0.326057 | + | 0.945350i | \(0.394280\pi\) | |||||||
\(180\) | 4.09954e53 | 0.0228328 | ||||||||
\(181\) | −4.89697e54 | −0.238124 | −0.119062 | − | 0.992887i | \(-0.537989\pi\) | ||||
−0.119062 | + | 0.992887i | \(0.537989\pi\) | |||||||
\(182\) | −2.50526e55 | −1.06440 | ||||||||
\(183\) | 1.34557e55 | 0.499866 | ||||||||
\(184\) | −3.42950e55 | −1.11479 | ||||||||
\(185\) | 1.65875e55 | 0.472143 | ||||||||
\(186\) | −2.85334e55 | −0.711684 | ||||||||
\(187\) | 7.44987e55 | 1.62941 | ||||||||
\(188\) | −3.09648e54 | −0.0594293 | ||||||||
\(189\) | −5.30125e55 | −0.893437 | ||||||||
\(190\) | −8.29273e55 | −1.22810 | ||||||||
\(191\) | −2.57335e55 | −0.335105 | −0.167553 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167553 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(192\) | 1.07118e56 | 1.22739 | ||||||||
\(193\) | 6.57181e55 | 0.663026 | 0.331513 | − | 0.943451i | \(-0.392441\pi\) | ||||
0.331513 | + | 0.943451i | \(0.392441\pi\) | |||||||
\(194\) | 1.33317e56 | 1.18507 | ||||||||
\(195\) | −1.16071e56 | −0.909655 | ||||||||
\(196\) | −3.51306e54 | −0.0242891 | ||||||||
\(197\) | 1.67063e56 | 1.01967 | 0.509833 | − | 0.860273i | \(-0.329707\pi\) | ||||
0.509833 | + | 0.860273i | \(0.329707\pi\) | |||||||
\(198\) | 7.59193e55 | 0.409313 | ||||||||
\(199\) | −2.81794e56 | −1.34286 | −0.671431 | − | 0.741067i | \(-0.734320\pi\) | ||||
−0.671431 | + | 0.741067i | \(0.734320\pi\) | |||||||
\(200\) | −8.94620e55 | −0.377054 | ||||||||
\(201\) | −4.60685e56 | −1.71831 | ||||||||
\(202\) | 3.79103e55 | 0.125213 | ||||||||
\(203\) | 2.42912e56 | 0.710880 | ||||||||
\(204\) | 4.75912e55 | 0.123477 | ||||||||
\(205\) | 1.59029e56 | 0.366022 | ||||||||
\(206\) | 2.18141e56 | 0.445646 | ||||||||
\(207\) | −1.77554e56 | −0.322148 | ||||||||
\(208\) | −5.54861e56 | −0.894607 | ||||||||
\(209\) | 1.61135e57 | 2.30997 | ||||||||
\(210\) | 7.61599e56 | 0.971300 | ||||||||
\(211\) | −1.09882e57 | −1.24741 | −0.623703 | − | 0.781662i | \(-0.714372\pi\) | ||||
−0.623703 | + | 0.781662i | \(0.714372\pi\) | |||||||
\(212\) | 2.94745e55 | 0.0298001 | ||||||||
\(213\) | −9.88884e56 | −0.890933 | ||||||||
\(214\) | −2.55671e56 | −0.205373 | ||||||||
\(215\) | −5.51249e56 | −0.395008 | ||||||||
\(216\) | −1.29854e57 | −0.830499 | ||||||||
\(217\) | 1.28686e57 | 0.734968 | ||||||||
\(218\) | −1.02257e57 | −0.521808 | ||||||||
\(219\) | 3.49021e57 | 1.59210 | ||||||||
\(220\) | −2.65734e56 | −0.108416 | ||||||||
\(221\) | −3.11765e57 | −1.13819 | ||||||||
\(222\) | 1.96235e57 | 0.641398 | ||||||||
\(223\) | 1.62911e57 | 0.476958 | 0.238479 | − | 0.971148i | \(-0.423351\pi\) | ||||
0.238479 | + | 0.971148i | \(0.423351\pi\) | |||||||
\(224\) | −8.08326e56 | −0.212085 | ||||||||
\(225\) | −4.63167e56 | −0.108960 | ||||||||
\(226\) | −2.15958e56 | −0.0455736 | ||||||||
\(227\) | 3.87678e57 | 0.734239 | 0.367120 | − | 0.930174i | \(-0.380344\pi\) | ||||
0.367120 | + | 0.930174i | \(0.380344\pi\) | |||||||
\(228\) | 1.02936e57 | 0.175051 | ||||||||
\(229\) | 6.74432e57 | 1.03031 | 0.515156 | − | 0.857097i | \(-0.327734\pi\) | ||||
0.515156 | + | 0.857097i | \(0.327734\pi\) | |||||||
\(230\) | −5.92309e57 | −0.813236 | ||||||||
\(231\) | −1.47986e58 | −1.82695 | ||||||||
\(232\) | 5.95014e57 | 0.660802 | ||||||||
\(233\) | −1.07268e58 | −1.07214 | −0.536069 | − | 0.844174i | \(-0.680091\pi\) | ||||
−0.536069 | + | 0.844174i | \(0.680091\pi\) | |||||||
\(234\) | −3.17709e57 | −0.285918 | ||||||||
\(235\) | −6.16653e57 | −0.499894 | ||||||||
\(236\) | 1.03241e56 | 0.00754236 | ||||||||
\(237\) | 2.63919e58 | 1.73835 | ||||||||
\(238\) | 2.04564e58 | 1.21533 | ||||||||
\(239\) | −6.84695e57 | −0.367070 | −0.183535 | − | 0.983013i | \(-0.558754\pi\) | ||||
−0.183535 | + | 0.983013i | \(0.558754\pi\) | |||||||
\(240\) | 1.68677e58 | 0.816359 | ||||||||
\(241\) | 6.43851e57 | 0.281429 | 0.140714 | − | 0.990050i | \(-0.455060\pi\) | ||||
0.140714 | + | 0.990050i | \(0.455060\pi\) | |||||||
\(242\) | −2.51227e58 | −0.992180 | ||||||||
\(243\) | −1.63410e58 | −0.583344 | ||||||||
\(244\) | −1.28916e57 | −0.0416155 | ||||||||
\(245\) | −6.99614e57 | −0.204310 | ||||||||
\(246\) | 1.88136e58 | 0.497235 | ||||||||
\(247\) | −6.74325e58 | −1.61359 | ||||||||
\(248\) | 3.15217e58 | 0.683193 | ||||||||
\(249\) | 2.39808e58 | 0.470955 | ||||||||
\(250\) | −5.81369e58 | −1.03496 | ||||||||
\(251\) | 4.88114e57 | 0.0787980 | 0.0393990 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393990 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(252\) | −2.18730e57 | −0.0320328 | ||||||||
\(253\) | 1.15091e59 | 1.52964 | ||||||||
\(254\) | −7.53074e58 | −0.908682 | ||||||||
\(255\) | 9.47762e58 | 1.03864 | ||||||||
\(256\) | −2.83455e58 | −0.282232 | ||||||||
\(257\) | 9.71196e58 | 0.878912 | 0.439456 | − | 0.898264i | \(-0.355171\pi\) | ||||
0.439456 | + | 0.898264i | \(0.355171\pi\) | |||||||
\(258\) | −6.52143e58 | −0.536612 | ||||||||
\(259\) | −8.85021e58 | −0.662383 | ||||||||
\(260\) | 1.11205e58 | 0.0757318 | ||||||||
\(261\) | 3.08053e58 | 0.190956 | ||||||||
\(262\) | 1.70675e59 | 0.963361 | ||||||||
\(263\) | −1.69871e59 | −0.873381 | −0.436690 | − | 0.899612i | \(-0.643849\pi\) | ||||
−0.436690 | + | 0.899612i | \(0.643849\pi\) | |||||||
\(264\) | −3.62491e59 | −1.69825 | ||||||||
\(265\) | 5.86973e58 | 0.250666 | ||||||||
\(266\) | 4.42457e59 | 1.72294 | ||||||||
\(267\) | −4.14433e59 | −1.47207 | ||||||||
\(268\) | 4.41372e58 | 0.143055 | ||||||||
\(269\) | 3.89211e58 | 0.115148 | 0.0575738 | − | 0.998341i | \(-0.481664\pi\) | ||||
0.0575738 | + | 0.998341i | \(0.481664\pi\) | |||||||
\(270\) | −2.24271e59 | −0.605845 | ||||||||
\(271\) | −2.42138e59 | −0.597468 | −0.298734 | − | 0.954336i | \(-0.596564\pi\) | ||||
−0.298734 | + | 0.954336i | \(0.596564\pi\) | |||||||
\(272\) | 4.53064e59 | 1.02146 | ||||||||
\(273\) | 6.19295e59 | 1.27618 | ||||||||
\(274\) | 8.19956e59 | 1.54491 | ||||||||
\(275\) | 3.00227e59 | 0.517367 | ||||||||
\(276\) | 7.35224e58 | 0.115917 | ||||||||
\(277\) | −1.36745e60 | −1.97313 | −0.986566 | − | 0.163363i | \(-0.947766\pi\) | ||||
−0.986566 | + | 0.163363i | \(0.947766\pi\) | |||||||
\(278\) | −1.03577e60 | −1.36825 | ||||||||
\(279\) | 1.63196e59 | 0.197427 | ||||||||
\(280\) | −8.41360e59 | −0.932417 | ||||||||
\(281\) | 1.32527e60 | 1.34585 | 0.672927 | − | 0.739709i | \(-0.265037\pi\) | ||||
0.672927 | + | 0.739709i | \(0.265037\pi\) | |||||||
\(282\) | −7.29518e59 | −0.679098 | ||||||||
\(283\) | −1.55414e60 | −1.32655 | −0.663273 | − | 0.748378i | \(-0.730833\pi\) | ||||
−0.663273 | + | 0.748378i | \(0.730833\pi\) | |||||||
\(284\) | 9.47427e58 | 0.0741731 | ||||||||
\(285\) | 2.04994e60 | 1.47246 | ||||||||
\(286\) | 2.05941e60 | 1.35761 | ||||||||
\(287\) | −8.48496e59 | −0.513504 | ||||||||
\(288\) | −1.02509e59 | −0.0569701 | ||||||||
\(289\) | 5.86836e59 | 0.299585 | ||||||||
\(290\) | 1.02765e60 | 0.482052 | ||||||||
\(291\) | −3.29556e60 | −1.42086 | ||||||||
\(292\) | −3.34389e59 | −0.132548 | ||||||||
\(293\) | 3.60920e60 | 1.31569 | 0.657846 | − | 0.753152i | \(-0.271468\pi\) | ||||
0.657846 | + | 0.753152i | \(0.271468\pi\) | |||||||
\(294\) | −8.27664e59 | −0.277552 | ||||||||
\(295\) | 2.05600e59 | 0.0634431 | ||||||||
\(296\) | −2.16786e60 | −0.615722 | ||||||||
\(297\) | 4.35780e60 | 1.13955 | ||||||||
\(298\) | −4.29189e60 | −1.03359 | ||||||||
\(299\) | −4.81637e60 | −1.06850 | ||||||||
\(300\) | 1.91791e59 | 0.0392064 | ||||||||
\(301\) | 2.94117e60 | 0.554168 | ||||||||
\(302\) | −6.17699e60 | −1.07302 | ||||||||
\(303\) | −9.37133e59 | −0.150126 | ||||||||
\(304\) | 9.79944e60 | 1.44810 | ||||||||
\(305\) | −2.56731e60 | −0.350052 | ||||||||
\(306\) | 2.59421e60 | 0.326460 | ||||||||
\(307\) | 6.56165e60 | 0.762295 | 0.381147 | − | 0.924514i | \(-0.375529\pi\) | ||||
0.381147 | + | 0.924514i | \(0.375529\pi\) | |||||||
\(308\) | 1.41782e60 | 0.152099 | ||||||||
\(309\) | −5.39239e60 | −0.534316 | ||||||||
\(310\) | 5.44412e60 | 0.498386 | ||||||||
\(311\) | −4.77277e60 | −0.403776 | −0.201888 | − | 0.979409i | \(-0.564708\pi\) | ||||
−0.201888 | + | 0.979409i | \(0.564708\pi\) | |||||||
\(312\) | 1.51696e61 | 1.18628 | ||||||||
\(313\) | −9.64049e59 | −0.0697048 | −0.0348524 | − | 0.999392i | \(-0.511096\pi\) | ||||
−0.0348524 | + | 0.999392i | \(0.511096\pi\) | |||||||
\(314\) | −1.50124e61 | −1.00386 | ||||||||
\(315\) | −4.35593e60 | −0.269446 | ||||||||
\(316\) | −2.52855e60 | −0.144723 | ||||||||
\(317\) | −1.84778e61 | −0.978809 | −0.489405 | − | 0.872057i | \(-0.662786\pi\) | ||||
−0.489405 | + | 0.872057i | \(0.662786\pi\) | |||||||
\(318\) | 6.94406e60 | 0.340525 | ||||||||
\(319\) | −1.99682e61 | −0.906706 | ||||||||
\(320\) | −2.04379e61 | −0.859530 | ||||||||
\(321\) | 6.32013e60 | 0.246237 | ||||||||
\(322\) | 3.16025e61 | 1.14091 | ||||||||
\(323\) | 5.50610e61 | 1.84239 | ||||||||
\(324\) | 3.70534e60 | 0.114941 | ||||||||
\(325\) | −1.25640e61 | −0.361397 | ||||||||
\(326\) | 1.08452e61 | 0.289340 | ||||||||
\(327\) | 2.52778e61 | 0.625631 | ||||||||
\(328\) | −2.07839e61 | −0.477330 | ||||||||
\(329\) | 3.29013e61 | 0.701317 | ||||||||
\(330\) | −6.26059e61 | −1.23886 | ||||||||
\(331\) | −6.60491e61 | −1.21361 | −0.606807 | − | 0.794849i | \(-0.707550\pi\) | ||||
−0.606807 | + | 0.794849i | \(0.707550\pi\) | |||||||
\(332\) | −2.29755e60 | −0.0392086 | ||||||||
\(333\) | −1.12235e61 | −0.177929 | ||||||||
\(334\) | 1.31144e61 | 0.193179 | ||||||||
\(335\) | 8.78977e61 | 1.20332 | ||||||||
\(336\) | −8.99974e61 | −1.14530 | ||||||||
\(337\) | 5.02594e61 | 0.594682 | 0.297341 | − | 0.954771i | \(-0.403900\pi\) | ||||
0.297341 | + | 0.954771i | \(0.403900\pi\) | |||||||
\(338\) | 2.72780e59 | 0.00300160 | ||||||||
\(339\) | 5.33843e60 | 0.0546413 | ||||||||
\(340\) | −9.08030e60 | −0.0864703 | ||||||||
\(341\) | −1.05784e62 | −0.937430 | ||||||||
\(342\) | 5.61109e61 | 0.462815 | ||||||||
\(343\) | −1.08608e62 | −0.833984 | ||||||||
\(344\) | 7.20441e61 | 0.515130 | ||||||||
\(345\) | 1.46417e62 | 0.975045 | ||||||||
\(346\) | 1.13635e62 | 0.704931 | ||||||||
\(347\) | 2.35153e62 | 1.35919 | 0.679594 | − | 0.733589i | \(-0.262156\pi\) | ||||
0.679594 | + | 0.733589i | \(0.262156\pi\) | |||||||
\(348\) | −1.27561e61 | −0.0687108 | ||||||||
\(349\) | −2.73741e62 | −1.37441 | −0.687206 | − | 0.726463i | \(-0.741163\pi\) | ||||
−0.687206 | + | 0.726463i | \(0.741163\pi\) | |||||||
\(350\) | 8.24383e61 | 0.385889 | ||||||||
\(351\) | −1.82367e62 | −0.796014 | ||||||||
\(352\) | 6.64470e61 | 0.270508 | ||||||||
\(353\) | −3.98901e62 | −1.51490 | −0.757452 | − | 0.652891i | \(-0.773556\pi\) | ||||
−0.757452 | + | 0.652891i | \(0.773556\pi\) | |||||||
\(354\) | 2.43231e61 | 0.0861865 | ||||||||
\(355\) | 1.88677e62 | 0.623913 | ||||||||
\(356\) | 3.97059e61 | 0.122555 | ||||||||
\(357\) | −5.05676e62 | −1.45714 | ||||||||
\(358\) | −2.30564e62 | −0.620379 | ||||||||
\(359\) | 3.99475e62 | 1.00387 | 0.501933 | − | 0.864906i | \(-0.332622\pi\) | ||||
0.501933 | + | 0.864906i | \(0.332622\pi\) | |||||||
\(360\) | −1.06699e62 | −0.250465 | ||||||||
\(361\) | 7.34970e62 | 1.61192 | ||||||||
\(362\) | 1.10534e62 | 0.226536 | ||||||||
\(363\) | 6.21028e62 | 1.18959 | ||||||||
\(364\) | −5.93333e61 | −0.106246 | ||||||||
\(365\) | −6.65925e62 | −1.11494 | ||||||||
\(366\) | −3.03720e62 | −0.475540 | ||||||||
\(367\) | 4.47176e62 | 0.654878 | 0.327439 | − | 0.944872i | \(-0.393814\pi\) | ||||
0.327439 | + | 0.944872i | \(0.393814\pi\) | |||||||
\(368\) | 6.99926e62 | 0.958916 | ||||||||
\(369\) | −1.07604e62 | −0.137937 | ||||||||
\(370\) | −3.74412e62 | −0.449166 | ||||||||
\(371\) | −3.13178e62 | −0.351666 | ||||||||
\(372\) | −6.75770e61 | −0.0710390 | ||||||||
\(373\) | −1.90519e63 | −1.87531 | −0.937654 | − | 0.347569i | \(-0.887007\pi\) | ||||
−0.937654 | + | 0.347569i | \(0.887007\pi\) | |||||||
\(374\) | −1.68158e63 | −1.55011 | ||||||||
\(375\) | 1.43713e63 | 1.24088 | ||||||||
\(376\) | 8.05919e62 | 0.651913 | ||||||||
\(377\) | 8.35634e62 | 0.633364 | ||||||||
\(378\) | 1.19659e63 | 0.849959 | ||||||||
\(379\) | −1.10306e63 | −0.734408 | −0.367204 | − | 0.930140i | \(-0.619685\pi\) | ||||
−0.367204 | + | 0.930140i | \(0.619685\pi\) | |||||||
\(380\) | −1.96400e62 | −0.122587 | ||||||||
\(381\) | 1.86158e63 | 1.08948 | ||||||||
\(382\) | 5.80855e62 | 0.318798 | ||||||||
\(383\) | −1.13569e63 | −0.584643 | −0.292321 | − | 0.956320i | \(-0.594428\pi\) | ||||
−0.292321 | + | 0.956320i | \(0.594428\pi\) | |||||||
\(384\) | −1.97086e63 | −0.951787 | ||||||||
\(385\) | 2.82353e63 | 1.27940 | ||||||||
\(386\) | −1.48338e63 | −0.630760 | ||||||||
\(387\) | 3.72990e62 | 0.148860 | ||||||||
\(388\) | 3.15740e62 | 0.118291 | ||||||||
\(389\) | −2.42232e63 | −0.852053 | −0.426026 | − | 0.904711i | \(-0.640087\pi\) | ||||
−0.426026 | + | 0.904711i | \(0.640087\pi\) | |||||||
\(390\) | 2.61995e63 | 0.865387 | ||||||||
\(391\) | 3.93273e63 | 1.22001 | ||||||||
\(392\) | 9.14344e62 | 0.266441 | ||||||||
\(393\) | −4.21905e63 | −1.15504 | ||||||||
\(394\) | −3.77094e63 | −0.970045 | ||||||||
\(395\) | −5.03552e63 | −1.21735 | ||||||||
\(396\) | 1.79803e62 | 0.0408568 | ||||||||
\(397\) | −2.38482e62 | −0.0509434 | −0.0254717 | − | 0.999676i | \(-0.508109\pi\) | ||||
−0.0254717 | + | 0.999676i | \(0.508109\pi\) | |||||||
\(398\) | 6.36064e63 | 1.27751 | ||||||||
\(399\) | −1.09374e64 | −2.06575 | ||||||||
\(400\) | 1.82583e63 | 0.324332 | ||||||||
\(401\) | 3.76821e63 | 0.629649 | 0.314824 | − | 0.949150i | \(-0.398054\pi\) | ||||
0.314824 | + | 0.949150i | \(0.398054\pi\) | |||||||
\(402\) | 1.03986e64 | 1.63469 | ||||||||
\(403\) | 4.42689e63 | 0.654825 | ||||||||
\(404\) | 8.97846e61 | 0.0124985 | ||||||||
\(405\) | 7.37905e63 | 0.966835 | ||||||||
\(406\) | −5.48300e63 | −0.676286 | ||||||||
\(407\) | 7.27516e63 | 0.844850 | ||||||||
\(408\) | −1.23866e64 | −1.35449 | ||||||||
\(409\) | 4.86604e63 | 0.501135 | 0.250567 | − | 0.968099i | \(-0.419383\pi\) | ||||
0.250567 | + | 0.968099i | \(0.419383\pi\) | |||||||
\(410\) | −3.58960e63 | −0.348210 | ||||||||
\(411\) | −2.02691e64 | −1.85229 | ||||||||
\(412\) | 5.16633e62 | 0.0444836 | ||||||||
\(413\) | −1.09698e63 | −0.0890063 | ||||||||
\(414\) | 4.00773e63 | 0.306471 | ||||||||
\(415\) | −4.57548e63 | −0.329806 | ||||||||
\(416\) | −2.78070e63 | −0.188959 | ||||||||
\(417\) | 2.56040e64 | 1.64049 | ||||||||
\(418\) | −3.63714e64 | −2.19756 | ||||||||
\(419\) | 2.47515e64 | 1.41045 | 0.705225 | − | 0.708983i | \(-0.250846\pi\) | ||||
0.705225 | + | 0.708983i | \(0.250846\pi\) | |||||||
\(420\) | 1.80373e63 | 0.0969535 | ||||||||
\(421\) | −1.56805e64 | −0.795149 | −0.397575 | − | 0.917570i | \(-0.630148\pi\) | ||||
−0.397575 | + | 0.917570i | \(0.630148\pi\) | |||||||
\(422\) | 2.48026e64 | 1.18670 | ||||||||
\(423\) | 4.17244e63 | 0.188387 | ||||||||
\(424\) | −7.67131e63 | −0.326893 | ||||||||
\(425\) | 1.02589e64 | 0.412642 | ||||||||
\(426\) | 2.23210e64 | 0.847576 | ||||||||
\(427\) | 1.36978e64 | 0.491098 | ||||||||
\(428\) | −6.05517e62 | −0.0205000 | ||||||||
\(429\) | −5.09080e64 | −1.62773 | ||||||||
\(430\) | 1.24427e64 | 0.375785 | ||||||||
\(431\) | −5.26924e64 | −1.50333 | −0.751666 | − | 0.659544i | \(-0.770749\pi\) | ||||
−0.751666 | + | 0.659544i | \(0.770749\pi\) | |||||||
\(432\) | 2.65019e64 | 0.714374 | ||||||||
\(433\) | 3.37012e64 | 0.858405 | 0.429202 | − | 0.903208i | \(-0.358795\pi\) | ||||
0.429202 | + | 0.903208i | \(0.358795\pi\) | |||||||
\(434\) | −2.90470e64 | −0.699201 | ||||||||
\(435\) | −2.54032e64 | −0.577966 | ||||||||
\(436\) | −2.42181e63 | −0.0520859 | ||||||||
\(437\) | 8.50623e64 | 1.72958 | ||||||||
\(438\) | −7.87808e64 | −1.51462 | ||||||||
\(439\) | −7.18240e64 | −1.30584 | −0.652918 | − | 0.757428i | \(-0.726456\pi\) | ||||
−0.652918 | + | 0.757428i | \(0.726456\pi\) | |||||||
\(440\) | 6.91625e64 | 1.18927 | ||||||||
\(441\) | 4.73378e63 | 0.0769951 | ||||||||
\(442\) | 7.03713e64 | 1.08280 | ||||||||
\(443\) | −1.13418e65 | −1.65116 | −0.825582 | − | 0.564282i | \(-0.809153\pi\) | ||||
−0.825582 | + | 0.564282i | \(0.809153\pi\) | |||||||
\(444\) | 4.64751e63 | 0.0640232 | ||||||||
\(445\) | 7.90729e64 | 1.03088 | ||||||||
\(446\) | −3.67720e64 | −0.453747 | ||||||||
\(447\) | 1.06094e65 | 1.23925 | ||||||||
\(448\) | 1.09046e65 | 1.20586 | ||||||||
\(449\) | −1.35648e65 | −1.42030 | −0.710148 | − | 0.704053i | \(-0.751372\pi\) | ||||
−0.710148 | + | 0.704053i | \(0.751372\pi\) | |||||||
\(450\) | 1.04546e64 | 0.103657 | ||||||||
\(451\) | 6.97491e64 | 0.654958 | ||||||||
\(452\) | −5.11463e62 | −0.00454907 | ||||||||
\(453\) | 1.52694e65 | 1.28652 | ||||||||
\(454\) | −8.75064e64 | −0.698508 | ||||||||
\(455\) | −1.18160e65 | −0.893700 | ||||||||
\(456\) | −2.67912e65 | −1.92023 | ||||||||
\(457\) | −2.05883e65 | −1.39854 | −0.699268 | − | 0.714859i | \(-0.746491\pi\) | ||||
−0.699268 | + | 0.714859i | \(0.746491\pi\) | |||||||
\(458\) | −1.52232e65 | −0.980172 | ||||||||
\(459\) | 1.48909e65 | 0.908886 | ||||||||
\(460\) | −1.40279e64 | −0.0811757 | ||||||||
\(461\) | 2.18282e65 | 1.19769 | 0.598847 | − | 0.800863i | \(-0.295626\pi\) | ||||
0.598847 | + | 0.800863i | \(0.295626\pi\) | |||||||
\(462\) | 3.34032e65 | 1.73804 | ||||||||
\(463\) | 9.59055e64 | 0.473270 | 0.236635 | − | 0.971599i | \(-0.423955\pi\) | ||||
0.236635 | + | 0.971599i | \(0.423955\pi\) | |||||||
\(464\) | −1.21436e65 | −0.568405 | ||||||||
\(465\) | −1.34577e65 | −0.597550 | ||||||||
\(466\) | 2.42125e65 | 1.01996 | ||||||||
\(467\) | 1.86197e65 | 0.744234 | 0.372117 | − | 0.928186i | \(-0.378632\pi\) | ||||
0.372117 | + | 0.928186i | \(0.378632\pi\) | |||||||
\(468\) | −7.52445e63 | −0.0285398 | ||||||||
\(469\) | −4.68976e65 | −1.68817 | ||||||||
\(470\) | 1.39190e65 | 0.475567 | ||||||||
\(471\) | 3.71103e65 | 1.20360 | ||||||||
\(472\) | −2.68704e64 | −0.0827363 | ||||||||
\(473\) | −2.41774e65 | −0.706825 | ||||||||
\(474\) | −5.95717e65 | −1.65375 | ||||||||
\(475\) | 2.21894e65 | 0.584994 | ||||||||
\(476\) | 4.84477e64 | 0.121312 | ||||||||
\(477\) | −3.97162e64 | −0.0944643 | ||||||||
\(478\) | 1.54549e65 | 0.349207 | ||||||||
\(479\) | 9.86762e64 | 0.211832 | 0.105916 | − | 0.994375i | \(-0.466222\pi\) | ||||
0.105916 | + | 0.994375i | \(0.466222\pi\) | |||||||
\(480\) | 8.45330e64 | 0.172431 | ||||||||
\(481\) | −3.04453e65 | −0.590155 | ||||||||
\(482\) | −1.45330e65 | −0.267733 | ||||||||
\(483\) | −7.81206e65 | −1.36792 | ||||||||
\(484\) | −5.94993e64 | −0.0990376 | ||||||||
\(485\) | 6.28785e65 | 0.995015 | ||||||||
\(486\) | 3.68847e65 | 0.554956 | ||||||||
\(487\) | 3.74023e65 | 0.535104 | 0.267552 | − | 0.963543i | \(-0.413785\pi\) | ||||
0.267552 | + | 0.963543i | \(0.413785\pi\) | |||||||
\(488\) | 3.35528e65 | 0.456503 | ||||||||
\(489\) | −2.68092e65 | −0.346910 | ||||||||
\(490\) | 1.57916e65 | 0.194367 | ||||||||
\(491\) | 1.40013e65 | 0.163935 | 0.0819676 | − | 0.996635i | \(-0.473880\pi\) | ||||
0.0819676 | + | 0.996635i | \(0.473880\pi\) | |||||||
\(492\) | 4.45571e64 | 0.0496331 | ||||||||
\(493\) | −6.82325e65 | −0.723172 | ||||||||
\(494\) | 1.52208e66 | 1.53507 | ||||||||
\(495\) | 3.58071e65 | 0.343670 | ||||||||
\(496\) | −6.43326e65 | −0.587665 | ||||||||
\(497\) | −1.00668e66 | −0.875306 | ||||||||
\(498\) | −5.41293e65 | −0.448036 | ||||||||
\(499\) | 2.84241e65 | 0.223987 | 0.111994 | − | 0.993709i | \(-0.464276\pi\) | ||||
0.111994 | + | 0.993709i | \(0.464276\pi\) | |||||||
\(500\) | −1.37688e65 | −0.103307 | ||||||||
\(501\) | −3.24185e65 | −0.231616 | ||||||||
\(502\) | −1.10177e65 | −0.0749634 | ||||||||
\(503\) | −9.62685e65 | −0.623833 | −0.311917 | − | 0.950109i | \(-0.600971\pi\) | ||||
−0.311917 | + | 0.950109i | \(0.600971\pi\) | |||||||
\(504\) | 5.69287e65 | 0.351385 | ||||||||
\(505\) | 1.78803e65 | 0.105132 | ||||||||
\(506\) | −2.59783e66 | −1.45520 | ||||||||
\(507\) | −6.74305e63 | −0.00359883 | ||||||||
\(508\) | −1.78354e65 | −0.0907030 | ||||||||
\(509\) | 3.05352e66 | 1.47984 | 0.739921 | − | 0.672694i | \(-0.234863\pi\) | ||||
0.739921 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(510\) | −2.13928e66 | −0.988095 | ||||||||
\(511\) | 3.55303e66 | 1.56418 | ||||||||
\(512\) | 2.62825e66 | 1.10294 | ||||||||
\(513\) | 3.22079e66 | 1.28851 | ||||||||
\(514\) | −2.19218e66 | −0.836140 | ||||||||
\(515\) | 1.02886e66 | 0.374177 | ||||||||
\(516\) | −1.54450e65 | −0.0535636 | ||||||||
\(517\) | −2.70460e66 | −0.894508 | ||||||||
\(518\) | 1.99766e66 | 0.630149 | ||||||||
\(519\) | −2.80902e66 | −0.845191 | ||||||||
\(520\) | −2.89434e66 | −0.830743 | ||||||||
\(521\) | −4.02652e66 | −1.10257 | −0.551284 | − | 0.834318i | \(-0.685862\pi\) | ||||
−0.551284 | + | 0.834318i | \(0.685862\pi\) | |||||||
\(522\) | −6.95336e65 | −0.181663 | ||||||||
\(523\) | 6.70243e65 | 0.167086 | 0.0835431 | − | 0.996504i | \(-0.473376\pi\) | ||||
0.0835431 | + | 0.996504i | \(0.473376\pi\) | |||||||
\(524\) | 4.04218e65 | 0.0961609 | ||||||||
\(525\) | −2.03785e66 | −0.462669 | ||||||||
\(526\) | 3.83432e66 | 0.830878 | ||||||||
\(527\) | −3.61471e66 | −0.747677 | ||||||||
\(528\) | 7.39807e66 | 1.46079 | ||||||||
\(529\) | 7.70839e65 | 0.145311 | ||||||||
\(530\) | −1.32491e66 | −0.238467 | ||||||||
\(531\) | −1.39115e65 | −0.0239088 | ||||||||
\(532\) | 1.04789e66 | 0.171981 | ||||||||
\(533\) | −2.91888e66 | −0.457510 | ||||||||
\(534\) | 9.35455e66 | 1.40043 | ||||||||
\(535\) | −1.20587e66 | −0.172437 | ||||||||
\(536\) | −1.14876e67 | −1.56925 | ||||||||
\(537\) | 5.69948e66 | 0.743816 | ||||||||
\(538\) | −8.78525e65 | −0.109544 | ||||||||
\(539\) | −3.06846e66 | −0.365591 | ||||||||
\(540\) | −5.31152e65 | −0.0604744 | ||||||||
\(541\) | 1.63687e67 | 1.78107 | 0.890536 | − | 0.454913i | \(-0.150330\pi\) | ||||
0.890536 | + | 0.454913i | \(0.150330\pi\) | |||||||
\(542\) | 5.46552e66 | 0.568393 | ||||||||
\(543\) | −2.73238e66 | −0.271609 | ||||||||
\(544\) | 2.27054e66 | 0.215752 | ||||||||
\(545\) | −4.82294e66 | −0.438125 | ||||||||
\(546\) | −1.39787e67 | −1.21408 | ||||||||
\(547\) | −1.21163e67 | −1.00619 | −0.503095 | − | 0.864231i | \(-0.667805\pi\) | ||||
−0.503095 | + | 0.864231i | \(0.667805\pi\) | |||||||
\(548\) | 1.94194e66 | 0.154210 | ||||||||
\(549\) | 1.73711e66 | 0.131918 | ||||||||
\(550\) | −6.77670e66 | −0.492189 | ||||||||
\(551\) | −1.47582e67 | −1.02523 | ||||||||
\(552\) | −1.91357e67 | −1.27156 | ||||||||
\(553\) | 2.68669e67 | 1.70786 | ||||||||
\(554\) | 3.08659e67 | 1.87711 | ||||||||
\(555\) | 9.25536e66 | 0.538536 | ||||||||
\(556\) | −2.45306e66 | −0.136576 | ||||||||
\(557\) | −2.42193e67 | −1.29035 | −0.645177 | − | 0.764033i | \(-0.723217\pi\) | ||||
−0.645177 | + | 0.764033i | \(0.723217\pi\) | |||||||
\(558\) | −3.68364e66 | −0.187819 | ||||||||
\(559\) | 1.01178e67 | 0.493740 | ||||||||
\(560\) | 1.71713e67 | 0.802041 | ||||||||
\(561\) | 4.15682e67 | 1.85854 | ||||||||
\(562\) | −2.99138e67 | −1.28036 | ||||||||
\(563\) | 3.00539e66 | 0.123153 | 0.0615764 | − | 0.998102i | \(-0.480387\pi\) | ||||
0.0615764 | + | 0.998102i | \(0.480387\pi\) | |||||||
\(564\) | −1.72775e66 | −0.0677864 | ||||||||
\(565\) | −1.01856e66 | −0.0382649 | ||||||||
\(566\) | 3.50799e67 | 1.26199 | ||||||||
\(567\) | −3.93707e67 | −1.35640 | ||||||||
\(568\) | −2.46587e67 | −0.813646 | ||||||||
\(569\) | 1.27892e67 | 0.404197 | 0.202099 | − | 0.979365i | \(-0.435224\pi\) | ||||
0.202099 | + | 0.979365i | \(0.435224\pi\) | |||||||
\(570\) | −4.62712e67 | −1.40080 | ||||||||
\(571\) | −1.78328e67 | −0.517172 | −0.258586 | − | 0.965988i | \(-0.583257\pi\) | ||||
−0.258586 | + | 0.965988i | \(0.583257\pi\) | |||||||
\(572\) | 4.87739e66 | 0.135514 | ||||||||
\(573\) | −1.43586e67 | −0.382229 | ||||||||
\(574\) | 1.91522e67 | 0.488514 | ||||||||
\(575\) | 1.58488e67 | 0.387376 | ||||||||
\(576\) | 1.38288e67 | 0.323917 | ||||||||
\(577\) | −4.00078e67 | −0.898127 | −0.449064 | − | 0.893500i | \(-0.648242\pi\) | ||||
−0.449064 | + | 0.893500i | \(0.648242\pi\) | |||||||
\(578\) | −1.32460e67 | −0.285006 | ||||||||
\(579\) | 3.66688e67 | 0.756262 | ||||||||
\(580\) | 2.43383e66 | 0.0481176 | ||||||||
\(581\) | 2.44124e67 | 0.462695 | ||||||||
\(582\) | 7.43871e67 | 1.35171 | ||||||||
\(583\) | 2.57443e67 | 0.448540 | ||||||||
\(584\) | 8.70315e67 | 1.45399 | ||||||||
\(585\) | −1.49847e67 | −0.240065 | ||||||||
\(586\) | −8.14666e67 | −1.25167 | ||||||||
\(587\) | −9.20452e67 | −1.35634 | −0.678168 | − | 0.734907i | \(-0.737226\pi\) | ||||
−0.678168 | + | 0.734907i | \(0.737226\pi\) | |||||||
\(588\) | −1.96019e66 | −0.0277047 | ||||||||
\(589\) | −7.81837e67 | −1.05996 | ||||||||
\(590\) | −4.64080e66 | −0.0603557 | ||||||||
\(591\) | 9.32166e67 | 1.16305 | ||||||||
\(592\) | 4.42438e67 | 0.529628 | ||||||||
\(593\) | −3.70854e66 | −0.0425954 | −0.0212977 | − | 0.999773i | \(-0.506780\pi\) | ||||
−0.0212977 | + | 0.999773i | \(0.506780\pi\) | |||||||
\(594\) | −9.83639e67 | −1.08410 | ||||||||
\(595\) | 9.64819e67 | 1.02042 | ||||||||
\(596\) | −1.01647e67 | −0.103171 | ||||||||
\(597\) | −1.57233e68 | −1.53170 | ||||||||
\(598\) | 1.08715e68 | 1.01650 | ||||||||
\(599\) | 1.91162e67 | 0.171571 | 0.0857857 | − | 0.996314i | \(-0.472660\pi\) | ||||
0.0857857 | + | 0.996314i | \(0.472660\pi\) | |||||||
\(600\) | −4.99173e67 | −0.430076 | ||||||||
\(601\) | 3.78925e67 | 0.313421 | 0.156711 | − | 0.987645i | \(-0.449911\pi\) | ||||
0.156711 | + | 0.987645i | \(0.449911\pi\) | |||||||
\(602\) | −6.63879e67 | −0.527200 | ||||||||
\(603\) | −5.94740e67 | −0.453475 | ||||||||
\(604\) | −1.46292e67 | −0.107107 | ||||||||
\(605\) | −1.18491e68 | −0.833063 | ||||||||
\(606\) | 2.11529e67 | 0.142821 | ||||||||
\(607\) | 2.02918e68 | 1.31582 | 0.657910 | − | 0.753096i | \(-0.271441\pi\) | ||||
0.657910 | + | 0.753096i | \(0.271441\pi\) | |||||||
\(608\) | 4.91101e67 | 0.305867 | ||||||||
\(609\) | 1.35538e68 | 0.810846 | ||||||||
\(610\) | 5.79491e67 | 0.333017 | ||||||||
\(611\) | 1.13183e68 | 0.624843 | ||||||||
\(612\) | 6.14398e66 | 0.0325867 | ||||||||
\(613\) | 2.45514e68 | 1.25111 | 0.625553 | − | 0.780182i | \(-0.284874\pi\) | ||||
0.625553 | + | 0.780182i | \(0.284874\pi\) | |||||||
\(614\) | −1.48109e68 | −0.725198 | ||||||||
\(615\) | 8.87339e67 | 0.417493 | ||||||||
\(616\) | −3.69015e68 | −1.66846 | ||||||||
\(617\) | −2.87337e68 | −1.24855 | −0.624274 | − | 0.781205i | \(-0.714605\pi\) | ||||
−0.624274 | + | 0.781205i | \(0.714605\pi\) | |||||||
\(618\) | 1.21717e68 | 0.508314 | ||||||||
\(619\) | −3.11706e68 | −1.25119 | −0.625596 | − | 0.780147i | \(-0.715144\pi\) | ||||
−0.625596 | + | 0.780147i | \(0.715144\pi\) | |||||||
\(620\) | 1.28935e67 | 0.0497480 | ||||||||
\(621\) | 2.30045e68 | 0.853236 | ||||||||
\(622\) | 1.07731e68 | 0.384127 | ||||||||
\(623\) | −4.21891e68 | −1.44625 | ||||||||
\(624\) | −3.09597e68 | −1.02041 | ||||||||
\(625\) | −1.59984e68 | −0.507010 | ||||||||
\(626\) | 2.17604e67 | 0.0663127 | ||||||||
\(627\) | 8.99091e68 | 2.63481 | ||||||||
\(628\) | −3.55545e67 | −0.100204 | ||||||||
\(629\) | 2.48597e68 | 0.673837 | ||||||||
\(630\) | 9.83217e67 | 0.256334 | ||||||||
\(631\) | −2.97792e68 | −0.746781 | −0.373391 | − | 0.927674i | \(-0.621805\pi\) | ||||
−0.373391 | + | 0.927674i | \(0.621805\pi\) | |||||||
\(632\) | 6.58106e68 | 1.58755 | ||||||||
\(633\) | −6.13113e68 | −1.42282 | ||||||||
\(634\) | 4.17079e68 | 0.931176 | ||||||||
\(635\) | −3.55185e68 | −0.762955 | ||||||||
\(636\) | 1.64459e67 | 0.0339906 | ||||||||
\(637\) | 1.28410e68 | 0.255377 | ||||||||
\(638\) | 4.50720e68 | 0.862582 | ||||||||
\(639\) | −1.27664e68 | −0.235124 | ||||||||
\(640\) | 3.76035e68 | 0.666529 | ||||||||
\(641\) | −9.83451e68 | −1.67776 | −0.838882 | − | 0.544314i | \(-0.816790\pi\) | ||||
−0.838882 | + | 0.544314i | \(0.816790\pi\) | |||||||
\(642\) | −1.42657e68 | −0.234254 | ||||||||
\(643\) | 2.53725e68 | 0.401046 | 0.200523 | − | 0.979689i | \(-0.435736\pi\) | ||||
0.200523 | + | 0.979689i | \(0.435736\pi\) | |||||||
\(644\) | 7.48456e67 | 0.113884 | ||||||||
\(645\) | −3.07582e68 | −0.450554 | ||||||||
\(646\) | −1.24283e69 | −1.75273 | ||||||||
\(647\) | 8.46297e68 | 1.14913 | 0.574563 | − | 0.818460i | \(-0.305172\pi\) | ||||
0.574563 | + | 0.818460i | \(0.305172\pi\) | |||||||
\(648\) | −9.64387e68 | −1.26085 | ||||||||
\(649\) | 9.01749e67 | 0.113525 | ||||||||
\(650\) | 2.83593e68 | 0.343810 | ||||||||
\(651\) | 7.18033e68 | 0.838321 | ||||||||
\(652\) | 2.56853e67 | 0.0288814 | ||||||||
\(653\) | 5.94791e68 | 0.644157 | 0.322079 | − | 0.946713i | \(-0.395618\pi\) | ||||
0.322079 | + | 0.946713i | \(0.395618\pi\) | |||||||
\(654\) | −5.70568e68 | −0.595185 | ||||||||
\(655\) | 8.04985e68 | 0.808865 | ||||||||
\(656\) | 4.24179e68 | 0.410587 | ||||||||
\(657\) | 4.50583e68 | 0.420168 | ||||||||
\(658\) | −7.42647e68 | −0.667187 | ||||||||
\(659\) | −1.75187e69 | −1.51638 | −0.758190 | − | 0.652034i | \(-0.773916\pi\) | ||||
−0.758190 | + | 0.652034i | \(0.773916\pi\) | |||||||
\(660\) | −1.48272e68 | −0.123661 | ||||||||
\(661\) | 1.24865e69 | 1.00347 | 0.501736 | − | 0.865021i | \(-0.332695\pi\) | ||||
0.501736 | + | 0.865021i | \(0.332695\pi\) | |||||||
\(662\) | 1.49085e69 | 1.15455 | ||||||||
\(663\) | −1.73956e69 | −1.29825 | ||||||||
\(664\) | 5.97982e68 | 0.430101 | ||||||||
\(665\) | 2.08683e69 | 1.44663 | ||||||||
\(666\) | 2.53337e68 | 0.169270 | ||||||||
\(667\) | −1.05411e69 | −0.678893 | ||||||||
\(668\) | 3.10595e67 | 0.0192828 | ||||||||
\(669\) | 9.08996e68 | 0.544029 | ||||||||
\(670\) | −1.98402e69 | −1.14476 | ||||||||
\(671\) | −1.12600e69 | −0.626381 | ||||||||
\(672\) | −4.51023e68 | −0.241909 | ||||||||
\(673\) | 2.09516e68 | 0.108355 | 0.0541773 | − | 0.998531i | \(-0.482746\pi\) | ||||
0.0541773 | + | 0.998531i | \(0.482746\pi\) | |||||||
\(674\) | −1.13445e69 | −0.565742 | ||||||||
\(675\) | 6.00096e68 | 0.288588 | ||||||||
\(676\) | 6.46037e65 | 0.000299615 0 | ||||||||
\(677\) | −2.83899e69 | −1.26982 | −0.634910 | − | 0.772586i | \(-0.718963\pi\) | ||||
−0.634910 | + | 0.772586i | \(0.718963\pi\) | |||||||
\(678\) | −1.20499e68 | −0.0519822 | ||||||||
\(679\) | −3.35487e69 | −1.39594 | ||||||||
\(680\) | 2.36333e69 | 0.948540 | ||||||||
\(681\) | 2.16314e69 | 0.837490 | ||||||||
\(682\) | 2.38775e69 | 0.891810 | ||||||||
\(683\) | 1.06976e69 | 0.385460 | 0.192730 | − | 0.981252i | \(-0.438266\pi\) | ||||
0.192730 | + | 0.981252i | \(0.438266\pi\) | |||||||
\(684\) | 1.32890e68 | 0.0461974 | ||||||||
\(685\) | 3.86730e69 | 1.29715 | ||||||||
\(686\) | 2.45150e69 | 0.793398 | ||||||||
\(687\) | 3.76314e69 | 1.17520 | ||||||||
\(688\) | −1.47035e69 | −0.443101 | ||||||||
\(689\) | −1.07735e69 | −0.313320 | ||||||||
\(690\) | −3.30492e69 | −0.927595 | ||||||||
\(691\) | −2.08108e69 | −0.563738 | −0.281869 | − | 0.959453i | \(-0.590954\pi\) | ||||
−0.281869 | + | 0.959453i | \(0.590954\pi\) | |||||||
\(692\) | 2.69126e68 | 0.0703650 | ||||||||
\(693\) | −1.91048e69 | −0.482146 | ||||||||
\(694\) | −5.30787e69 | −1.29304 | ||||||||
\(695\) | −4.88518e69 | −1.14882 | ||||||||
\(696\) | 3.32001e69 | 0.753726 | ||||||||
\(697\) | 2.38337e69 | 0.522383 | ||||||||
\(698\) | 6.17886e69 | 1.30753 | ||||||||
\(699\) | −5.98527e69 | −1.22290 | ||||||||
\(700\) | 1.95242e68 | 0.0385187 | ||||||||
\(701\) | −4.28863e69 | −0.817010 | −0.408505 | − | 0.912756i | \(-0.633950\pi\) | ||||
−0.408505 | + | 0.912756i | \(0.633950\pi\) | |||||||
\(702\) | 4.11637e69 | 0.757277 | ||||||||
\(703\) | 5.37697e69 | 0.955283 | ||||||||
\(704\) | −8.96391e69 | −1.53804 | ||||||||
\(705\) | −3.44075e69 | −0.570190 | ||||||||
\(706\) | 9.00397e69 | 1.44118 | ||||||||
\(707\) | −9.53998e68 | −0.147493 | ||||||||
\(708\) | 5.76055e67 | 0.00860298 | ||||||||
\(709\) | 1.06701e70 | 1.53935 | 0.769673 | − | 0.638438i | \(-0.220419\pi\) | ||||
0.769673 | + | 0.638438i | \(0.220419\pi\) | |||||||
\(710\) | −4.25880e69 | −0.593551 | ||||||||
\(711\) | 3.40717e69 | 0.458764 | ||||||||
\(712\) | −1.03342e70 | −1.34437 | ||||||||
\(713\) | −5.58427e69 | −0.701897 | ||||||||
\(714\) | 1.14141e70 | 1.38623 | ||||||||
\(715\) | 9.71314e69 | 1.13989 | ||||||||
\(716\) | −5.46055e68 | −0.0619251 | ||||||||
\(717\) | −3.82041e69 | −0.418688 | ||||||||
\(718\) | −9.01693e69 | −0.955014 | ||||||||
\(719\) | 1.57271e70 | 1.60987 | 0.804936 | − | 0.593362i | \(-0.202200\pi\) | ||||
0.804936 | + | 0.593362i | \(0.202200\pi\) | |||||||
\(720\) | 2.17761e69 | 0.215444 | ||||||||
\(721\) | −5.48943e69 | −0.524945 | ||||||||
\(722\) | −1.65897e70 | −1.53348 | ||||||||
\(723\) | 3.59251e69 | 0.321004 | ||||||||
\(724\) | 2.61783e68 | 0.0226124 | ||||||||
\(725\) | −2.74974e69 | −0.229621 | ||||||||
\(726\) | −1.40178e70 | −1.13170 | ||||||||
\(727\) | −1.05830e70 | −0.826067 | −0.413033 | − | 0.910716i | \(-0.635531\pi\) | ||||
−0.413033 | + | 0.910716i | \(0.635531\pi\) | |||||||
\(728\) | 1.54426e70 | 1.16548 | ||||||||
\(729\) | 7.46872e69 | 0.545032 | ||||||||
\(730\) | 1.50312e70 | 1.06068 | ||||||||
\(731\) | −8.26157e69 | −0.563750 | ||||||||
\(732\) | −7.19313e68 | −0.0474675 | ||||||||
\(733\) | −2.28917e70 | −1.46093 | −0.730466 | − | 0.682949i | \(-0.760697\pi\) | ||||
−0.730466 | + | 0.682949i | \(0.760697\pi\) | |||||||
\(734\) | −1.00936e70 | −0.623008 | ||||||||
\(735\) | −3.90365e69 | −0.233041 | ||||||||
\(736\) | 3.50769e69 | 0.202542 | ||||||||
\(737\) | 3.85513e70 | 2.15321 | ||||||||
\(738\) | 2.42882e69 | 0.131224 | ||||||||
\(739\) | 2.74741e70 | 1.43594 | 0.717968 | − | 0.696076i | \(-0.245072\pi\) | ||||
0.717968 | + | 0.696076i | \(0.245072\pi\) | |||||||
\(740\) | −8.86735e68 | −0.0448350 | ||||||||
\(741\) | −3.76254e70 | −1.84050 | ||||||||
\(742\) | 7.06903e69 | 0.334553 | ||||||||
\(743\) | 1.03737e70 | 0.475017 | 0.237508 | − | 0.971386i | \(-0.423669\pi\) | ||||
0.237508 | + | 0.971386i | \(0.423669\pi\) | |||||||
\(744\) | 1.75882e70 | 0.779266 | ||||||||
\(745\) | −2.02426e70 | −0.867834 | ||||||||
\(746\) | 4.30039e70 | 1.78405 | ||||||||
\(747\) | 3.09590e69 | 0.124289 | ||||||||
\(748\) | −3.98256e69 | −0.154729 | ||||||||
\(749\) | 6.43387e69 | 0.241918 | ||||||||
\(750\) | −3.24388e70 | −1.18049 | ||||||||
\(751\) | −5.36589e70 | −1.89001 | −0.945003 | − | 0.327062i | \(-0.893941\pi\) | ||||
−0.945003 | + | 0.327062i | \(0.893941\pi\) | |||||||
\(752\) | −1.64480e70 | −0.560758 | ||||||||
\(753\) | 2.72354e69 | 0.0898788 | ||||||||
\(754\) | −1.88619e70 | −0.602541 | ||||||||
\(755\) | −2.91336e70 | −0.900936 | ||||||||
\(756\) | 2.83395e69 | 0.0848414 | ||||||||
\(757\) | −3.78086e70 | −1.09583 | −0.547913 | − | 0.836535i | \(-0.684578\pi\) | ||||
−0.547913 | + | 0.836535i | \(0.684578\pi\) | |||||||
\(758\) | 2.48981e70 | 0.698668 | ||||||||
\(759\) | 6.42176e70 | 1.74474 | ||||||||
\(760\) | 5.11171e70 | 1.34472 | ||||||||
\(761\) | 3.04475e70 | 0.775581 | 0.387791 | − | 0.921748i | \(-0.373238\pi\) | ||||
0.387791 | + | 0.921748i | \(0.373238\pi\) | |||||||
\(762\) | −4.20195e70 | −1.03646 | ||||||||
\(763\) | 2.57327e70 | 0.614658 | ||||||||
\(764\) | 1.37566e69 | 0.0318218 | ||||||||
\(765\) | 1.22355e70 | 0.274105 | ||||||||
\(766\) | 2.56348e70 | 0.556192 | ||||||||
\(767\) | −3.77367e69 | −0.0793008 | ||||||||
\(768\) | −1.58160e70 | −0.321920 | ||||||||
\(769\) | −1.49566e70 | −0.294874 | −0.147437 | − | 0.989071i | \(-0.547102\pi\) | ||||
−0.147437 | + | 0.989071i | \(0.547102\pi\) | |||||||
\(770\) | −6.37326e70 | −1.21714 | ||||||||
\(771\) | 5.41900e70 | 1.00251 | ||||||||
\(772\) | −3.51316e69 | −0.0629614 | ||||||||
\(773\) | 3.62206e70 | 0.628866 | 0.314433 | − | 0.949280i | \(-0.398186\pi\) | ||||
0.314433 | + | 0.949280i | \(0.398186\pi\) | |||||||
\(774\) | −8.41910e69 | −0.141616 | ||||||||
\(775\) | −1.45671e70 | −0.237401 | ||||||||
\(776\) | −8.21776e70 | −1.29760 | ||||||||
\(777\) | −4.93817e70 | −0.755529 | ||||||||
\(778\) | 5.46765e70 | 0.810588 | ||||||||
\(779\) | 5.15506e70 | 0.740570 | ||||||||
\(780\) | 6.20494e69 | 0.0863814 | ||||||||
\(781\) | 8.27524e70 | 1.11643 | ||||||||
\(782\) | −8.87694e70 | −1.16064 | ||||||||
\(783\) | −3.99126e70 | −0.505762 | ||||||||
\(784\) | −1.86608e70 | −0.229186 | ||||||||
\(785\) | −7.08056e70 | −0.842871 | ||||||||
\(786\) | 9.52321e70 | 1.09883 | ||||||||
\(787\) | −5.90448e70 | −0.660391 | −0.330195 | − | 0.943913i | \(-0.607115\pi\) | ||||
−0.330195 | + | 0.943913i | \(0.607115\pi\) | |||||||
\(788\) | −8.93087e69 | −0.0968282 | ||||||||
\(789\) | −9.47834e70 | −0.996198 | ||||||||
\(790\) | 1.13662e71 | 1.15811 | ||||||||
\(791\) | 5.43451e69 | 0.0536829 | ||||||||
\(792\) | −4.67973e70 | −0.448181 | ||||||||
\(793\) | 4.71214e70 | 0.437547 | ||||||||
\(794\) | 5.38299e69 | 0.0484642 | ||||||||
\(795\) | 3.27515e70 | 0.285915 | ||||||||
\(796\) | 1.50642e70 | 0.127519 | ||||||||
\(797\) | 1.73928e71 | 1.42771 | 0.713856 | − | 0.700292i | \(-0.246947\pi\) | ||||
0.713856 | + | 0.700292i | \(0.246947\pi\) | |||||||
\(798\) | 2.46879e71 | 1.96523 | ||||||||
\(799\) | −9.24178e70 | −0.713443 | ||||||||
\(800\) | 9.15017e69 | 0.0685053 | ||||||||
\(801\) | −5.35029e70 | −0.388491 | ||||||||
\(802\) | −8.50558e70 | −0.599007 | ||||||||
\(803\) | −2.92070e71 | −1.99506 | ||||||||
\(804\) | 2.46273e70 | 0.163171 | ||||||||
\(805\) | 1.49052e71 | 0.957943 | ||||||||
\(806\) | −9.99235e70 | −0.622958 | ||||||||
\(807\) | 2.17169e70 | 0.131340 | ||||||||
\(808\) | −2.33682e70 | −0.137103 | ||||||||
\(809\) | 1.56081e71 | 0.888403 | 0.444202 | − | 0.895927i | \(-0.353487\pi\) | ||||
0.444202 | + | 0.895927i | \(0.353487\pi\) | |||||||
\(810\) | −1.66559e71 | −0.919784 | ||||||||
\(811\) | −9.44857e70 | −0.506238 | −0.253119 | − | 0.967435i | \(-0.581456\pi\) | ||||
−0.253119 | + | 0.967435i | \(0.581456\pi\) | |||||||
\(812\) | −1.29856e70 | −0.0675056 | ||||||||
\(813\) | −1.35106e71 | −0.681486 | ||||||||
\(814\) | −1.64214e71 | −0.803736 | ||||||||
\(815\) | 5.11513e70 | 0.242938 | ||||||||
\(816\) | 2.52797e71 | 1.16510 | ||||||||
\(817\) | −1.78692e71 | −0.799216 | ||||||||
\(818\) | −1.09836e71 | −0.476747 | ||||||||
\(819\) | 7.99504e70 | 0.336794 | ||||||||
\(820\) | −8.50140e69 | −0.0347577 | ||||||||
\(821\) | 4.10899e71 | 1.63053 | 0.815263 | − | 0.579091i | \(-0.196592\pi\) | ||||
0.815263 | + | 0.579091i | \(0.196592\pi\) | |||||||
\(822\) | 4.57513e71 | 1.76215 | ||||||||
\(823\) | −7.73454e70 | −0.289160 | −0.144580 | − | 0.989493i | \(-0.546183\pi\) | ||||
−0.144580 | + | 0.989493i | \(0.546183\pi\) | |||||||
\(824\) | −1.34464e71 | −0.487965 | ||||||||
\(825\) | 1.67518e71 | 0.590120 | ||||||||
\(826\) | 2.47608e70 | 0.0846748 | ||||||||
\(827\) | −2.26640e71 | −0.752404 | −0.376202 | − | 0.926538i | \(-0.622770\pi\) | ||||
−0.376202 | + | 0.926538i | \(0.622770\pi\) | |||||||
\(828\) | 9.49167e69 | 0.0305914 | ||||||||
\(829\) | 4.51215e71 | 1.41188 | 0.705939 | − | 0.708273i | \(-0.250525\pi\) | ||||
0.705939 | + | 0.708273i | \(0.250525\pi\) | |||||||
\(830\) | 1.03277e71 | 0.313756 | ||||||||
\(831\) | −7.62997e71 | −2.25060 | ||||||||
\(832\) | 3.75125e71 | 1.07437 | ||||||||
\(833\) | −1.04851e71 | −0.291589 | ||||||||
\(834\) | −5.77931e71 | −1.56066 | ||||||||
\(835\) | 6.18538e70 | 0.162199 | ||||||||
\(836\) | −8.61399e70 | −0.219357 | ||||||||
\(837\) | −2.11443e71 | −0.522900 | ||||||||
\(838\) | −5.58689e71 | −1.34181 | ||||||||
\(839\) | 7.26480e71 | 1.69456 | 0.847278 | − | 0.531150i | \(-0.178240\pi\) | ||||
0.847278 | + | 0.531150i | \(0.178240\pi\) | |||||||
\(840\) | −4.69456e71 | −1.06354 | ||||||||
\(841\) | −2.71580e71 | −0.597581 | ||||||||
\(842\) | 3.53939e71 | 0.756454 | ||||||||
\(843\) | 7.39461e71 | 1.53511 | ||||||||
\(844\) | 5.87410e70 | 0.118454 | ||||||||
\(845\) | 1.28656e69 | 0.00252023 | ||||||||
\(846\) | −9.41800e70 | −0.179219 | ||||||||
\(847\) | 6.32204e71 | 1.16873 | ||||||||
\(848\) | 1.56564e71 | 0.281185 | ||||||||
\(849\) | −8.67166e71 | −1.51309 | ||||||||
\(850\) | −2.31564e71 | −0.392561 | ||||||||
\(851\) | 3.84050e71 | 0.632578 | ||||||||
\(852\) | 5.28638e70 | 0.0846035 | ||||||||
\(853\) | −5.90172e71 | −0.917757 | −0.458878 | − | 0.888499i | \(-0.651749\pi\) | ||||
−0.458878 | + | 0.888499i | \(0.651749\pi\) | |||||||
\(854\) | −3.09186e71 | −0.467199 | ||||||||
\(855\) | 2.64646e71 | 0.388593 | ||||||||
\(856\) | 1.57598e71 | 0.224876 | ||||||||
\(857\) | 7.99787e71 | 1.10903 | 0.554516 | − | 0.832173i | \(-0.312903\pi\) | ||||
0.554516 | + | 0.832173i | \(0.312903\pi\) | |||||||
\(858\) | 1.14909e72 | 1.54852 | ||||||||
\(859\) | −6.56838e71 | −0.860252 | −0.430126 | − | 0.902769i | \(-0.641531\pi\) | ||||
−0.430126 | + | 0.902769i | \(0.641531\pi\) | |||||||
\(860\) | 2.94687e70 | 0.0375102 | ||||||||
\(861\) | −4.73437e71 | −0.585714 | ||||||||
\(862\) | 1.18937e72 | 1.43017 | ||||||||
\(863\) | −1.10305e72 | −1.28924 | −0.644618 | − | 0.764505i | \(-0.722984\pi\) | ||||
−0.644618 | + | 0.764505i | \(0.722984\pi\) | |||||||
\(864\) | 1.32815e71 | 0.150890 | ||||||||
\(865\) | 5.35955e71 | 0.591880 | ||||||||
\(866\) | −7.60701e71 | −0.816631 | ||||||||
\(867\) | 3.27438e71 | 0.341713 | ||||||||
\(868\) | −6.87932e70 | −0.0697930 | ||||||||
\(869\) | −2.20855e72 | −2.17832 | ||||||||
\(870\) | 5.73400e71 | 0.549839 | ||||||||
\(871\) | −1.61331e72 | −1.50409 | ||||||||
\(872\) | 6.30323e71 | 0.571359 | ||||||||
\(873\) | −4.25453e71 | −0.374976 | ||||||||
\(874\) | −1.92002e72 | −1.64541 | ||||||||
\(875\) | 1.46299e72 | 1.21912 | ||||||||
\(876\) | −1.86580e71 | −0.151187 | ||||||||
\(877\) | 1.55281e72 | 1.22357 | 0.611783 | − | 0.791026i | \(-0.290453\pi\) | ||||
0.611783 | + | 0.791026i | \(0.290453\pi\) | |||||||
\(878\) | 1.62121e72 | 1.24229 | ||||||||
\(879\) | 2.01383e72 | 1.50071 | ||||||||
\(880\) | −1.41154e72 | −1.02298 | ||||||||
\(881\) | 6.02597e71 | 0.424734 | 0.212367 | − | 0.977190i | \(-0.431883\pi\) | ||||
0.212367 | + | 0.977190i | \(0.431883\pi\) | |||||||
\(882\) | −1.06851e71 | −0.0732482 | ||||||||
\(883\) | −3.02172e71 | −0.201473 | −0.100737 | − | 0.994913i | \(-0.532120\pi\) | ||||
−0.100737 | + | 0.994913i | \(0.532120\pi\) | |||||||
\(884\) | 1.66663e71 | 0.108084 | ||||||||
\(885\) | 1.14719e71 | 0.0723646 | ||||||||
\(886\) | 2.56006e72 | 1.57081 | ||||||||
\(887\) | −1.92132e72 | −1.14675 | −0.573377 | − | 0.819291i | \(-0.694367\pi\) | ||||
−0.573377 | + | 0.819291i | \(0.694367\pi\) | |||||||
\(888\) | −1.20961e72 | −0.702306 | ||||||||
\(889\) | 1.89508e72 | 1.07037 | ||||||||
\(890\) | −1.78483e72 | −0.980711 | ||||||||
\(891\) | 3.23640e72 | 1.73005 | ||||||||
\(892\) | −8.70888e70 | −0.0452922 | ||||||||
\(893\) | −1.99893e72 | −1.01143 | ||||||||
\(894\) | −2.39475e72 | −1.17894 | ||||||||
\(895\) | −1.08745e72 | −0.520888 | ||||||||
\(896\) | −2.00632e72 | −0.935093 | ||||||||
\(897\) | −2.68740e72 | −1.21876 | ||||||||
\(898\) | 3.06184e72 | 1.35118 | ||||||||
\(899\) | 9.68865e71 | 0.416055 | ||||||||
\(900\) | 2.47600e70 | 0.0103469 | ||||||||
\(901\) | 8.79698e71 | 0.357747 | ||||||||
\(902\) | −1.57437e72 | −0.623085 | ||||||||
\(903\) | 1.64109e72 | 0.632096 | ||||||||
\(904\) | 1.33118e71 | 0.0499013 | ||||||||
\(905\) | 5.21331e71 | 0.190206 | ||||||||
\(906\) | −3.44659e72 | −1.22391 | ||||||||
\(907\) | 5.55555e71 | 0.192021 | 0.0960105 | − | 0.995380i | \(-0.469392\pi\) | ||||
0.0960105 | + | 0.995380i | \(0.469392\pi\) | |||||||
\(908\) | −2.07245e71 | −0.0697238 | ||||||||
\(909\) | −1.20983e71 | −0.0396195 | ||||||||
\(910\) | 2.66710e72 | 0.850208 | ||||||||
\(911\) | 2.02494e72 | 0.628365 | 0.314182 | − | 0.949363i | \(-0.398270\pi\) | ||||
0.314182 | + | 0.949363i | \(0.398270\pi\) | |||||||
\(912\) | 5.46782e72 | 1.65173 | ||||||||
\(913\) | −2.00678e72 | −0.590153 | ||||||||
\(914\) | 4.64718e72 | 1.33048 | ||||||||
\(915\) | −1.43249e72 | −0.399277 | ||||||||
\(916\) | −3.60538e71 | −0.0978390 | ||||||||
\(917\) | −4.29498e72 | −1.13478 | ||||||||
\(918\) | −3.36116e72 | −0.864656 | ||||||||
\(919\) | −1.46950e72 | −0.368077 | −0.184038 | − | 0.982919i | \(-0.558917\pi\) | ||||
−0.184038 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(920\) | 3.65104e72 | 0.890461 | ||||||||
\(921\) | 3.66122e72 | 0.869490 | ||||||||
\(922\) | −4.92706e72 | −1.13941 | ||||||||
\(923\) | −3.46305e72 | −0.779861 | ||||||||
\(924\) | 7.91103e71 | 0.173488 | ||||||||
\(925\) | 1.00183e72 | 0.213956 | ||||||||
\(926\) | −2.16477e72 | −0.450239 | ||||||||
\(927\) | −6.96152e71 | −0.141010 | ||||||||
\(928\) | −6.08580e71 | −0.120058 | ||||||||
\(929\) | 7.04427e72 | 1.35348 | 0.676739 | − | 0.736223i | \(-0.263393\pi\) | ||||
0.676739 | + | 0.736223i | \(0.263393\pi\) | |||||||
\(930\) | 3.03767e72 | 0.568471 | ||||||||
\(931\) | −2.26786e72 | −0.413379 | ||||||||
\(932\) | 5.73435e71 | 0.101811 | ||||||||
\(933\) | −2.66307e72 | −0.460556 | ||||||||
\(934\) | −4.20283e72 | −0.708016 | ||||||||
\(935\) | −7.93113e72 | −1.30152 | ||||||||
\(936\) | 1.95839e72 | 0.313069 | ||||||||
\(937\) | −9.24309e72 | −1.43945 | −0.719726 | − | 0.694258i | \(-0.755733\pi\) | ||||
−0.719726 | + | 0.694258i | \(0.755733\pi\) | |||||||
\(938\) | 1.05857e73 | 1.60602 | ||||||||
\(939\) | −5.37912e71 | −0.0795068 | ||||||||
\(940\) | 3.29651e71 | 0.0474702 | ||||||||
\(941\) | 8.82463e72 | 1.23809 | 0.619043 | − | 0.785357i | \(-0.287521\pi\) | ||||
0.619043 | + | 0.785357i | \(0.287521\pi\) | |||||||
\(942\) | −8.37651e72 | −1.14503 | ||||||||
\(943\) | 3.68201e72 | 0.490397 | ||||||||
\(944\) | 5.48398e71 | 0.0711676 | ||||||||
\(945\) | 5.64371e72 | 0.713650 | ||||||||
\(946\) | 5.45730e72 | 0.672427 | ||||||||
\(947\) | 1.12021e73 | 1.34501 | 0.672504 | − | 0.740093i | \(-0.265219\pi\) | ||||
0.672504 | + | 0.740093i | \(0.265219\pi\) | |||||||
\(948\) | −1.41086e72 | −0.165075 | ||||||||
\(949\) | 1.22226e73 | 1.39362 | ||||||||
\(950\) | −5.00856e72 | −0.556525 | ||||||||
\(951\) | −1.03101e73 | −1.11645 | ||||||||
\(952\) | −1.26095e73 | −1.33073 | ||||||||
\(953\) | 8.31437e72 | 0.855172 | 0.427586 | − | 0.903975i | \(-0.359364\pi\) | ||||
0.427586 | + | 0.903975i | \(0.359364\pi\) | |||||||
\(954\) | 8.96472e71 | 0.0898673 | ||||||||
\(955\) | 2.73959e72 | 0.267672 | ||||||||
\(956\) | 3.66025e71 | 0.0348572 | ||||||||
\(957\) | −1.11417e73 | −1.03421 | ||||||||
\(958\) | −2.22731e72 | −0.201524 | ||||||||
\(959\) | −2.06339e73 | −1.81981 | ||||||||
\(960\) | −1.14038e73 | −0.980399 | ||||||||
\(961\) | −6.79957e72 | −0.569847 | ||||||||
\(962\) | 6.87209e72 | 0.561435 | ||||||||
\(963\) | 8.15922e71 | 0.0649837 | ||||||||
\(964\) | −3.44191e71 | −0.0267246 | ||||||||
\(965\) | −6.99634e72 | −0.529604 | ||||||||
\(966\) | 1.76333e73 | 1.30135 | ||||||||
\(967\) | 1.19977e73 | 0.863277 | 0.431639 | − | 0.902047i | \(-0.357936\pi\) | ||||
0.431639 | + | 0.902047i | \(0.357936\pi\) | |||||||
\(968\) | 1.54859e73 | 1.08640 | ||||||||
\(969\) | 3.07225e73 | 2.10147 | ||||||||
\(970\) | −1.41929e73 | −0.946593 | ||||||||
\(971\) | −2.62188e73 | −1.70507 | −0.852535 | − | 0.522671i | \(-0.824936\pi\) | ||||
−0.852535 | + | 0.522671i | \(0.824936\pi\) | |||||||
\(972\) | 8.73557e71 | 0.0553947 | ||||||||
\(973\) | 2.60648e73 | 1.61172 | ||||||||
\(974\) | −8.44242e72 | −0.509064 | ||||||||
\(975\) | −7.01036e72 | −0.412218 | ||||||||
\(976\) | −6.84779e72 | −0.392672 | ||||||||
\(977\) | −1.17201e73 | −0.655413 | −0.327706 | − | 0.944780i | \(-0.606276\pi\) | ||||
−0.327706 | + | 0.944780i | \(0.606276\pi\) | |||||||
\(978\) | 6.05135e72 | 0.330027 | ||||||||
\(979\) | 3.46808e73 | 1.84465 | ||||||||
\(980\) | 3.74000e71 | 0.0194014 | ||||||||
\(981\) | 3.26333e72 | 0.165109 | ||||||||
\(982\) | −3.16037e72 | −0.155957 | ||||||||
\(983\) | −2.13585e73 | −1.02804 | −0.514019 | − | 0.857779i | \(-0.671844\pi\) | ||||
−0.514019 | + | 0.857779i | \(0.671844\pi\) | |||||||
\(984\) | −1.15969e73 | −0.544453 | ||||||||
\(985\) | −1.77855e73 | −0.814477 | ||||||||
\(986\) | 1.54014e73 | 0.687979 | ||||||||
\(987\) | 1.83580e73 | 0.799937 | ||||||||
\(988\) | 3.60481e72 | 0.153228 | ||||||||
\(989\) | −1.27631e73 | −0.529232 | ||||||||
\(990\) | −8.08236e72 | −0.326946 | ||||||||
\(991\) | −2.03182e73 | −0.801827 | −0.400913 | − | 0.916116i | \(-0.631307\pi\) | ||||
−0.400913 | + | 0.916116i | \(0.631307\pi\) | |||||||
\(992\) | −3.22404e72 | −0.124127 | ||||||||
\(993\) | −3.68535e73 | −1.38428 | ||||||||
\(994\) | 2.27227e73 | 0.832710 | ||||||||
\(995\) | 2.99998e73 | 1.07264 | ||||||||
\(996\) | −1.28197e72 | −0.0447222 | ||||||||
\(997\) | −1.66206e73 | −0.565739 | −0.282869 | − | 0.959158i | \(-0.591286\pi\) | ||||
−0.282869 | + | 0.959158i | \(0.591286\pi\) | |||||||
\(998\) | −6.41587e72 | −0.213087 | ||||||||
\(999\) | 1.45417e73 | 0.471259 |
(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 | 1.50.a.a.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 9.50.a.a.1.2 | 3 | |||
4.3 | odd | 2 | 16.50.a.c.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.50.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.50.a.a.1.2 | 3 | 3.2 | odd | 2 | |||
16.50.a.c.1.1 | 3 | 4.3 | odd | 2 |