Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,38,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 38, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 38);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 38 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(26.0142114374\) |
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: | \( x^{3} - x^{2} - 2495042360x + 9241471873200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-51708.0\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 516864. | 1.39419 | 0.697094 | − | 0.716980i | \(-0.254476\pi\) | ||||
0.697094 | + | 0.716980i | \(0.254476\pi\) | |||||||
\(3\) | −3.87420e8 | −0.577350 | ||||||||
\(4\) | 1.29709e11 | 0.943758 | ||||||||
\(5\) | 3.13693e12 | 0.367756 | 0.183878 | − | 0.982949i | \(-0.441135\pi\) | ||||
0.183878 | + | 0.982949i | \(0.441135\pi\) | |||||||
\(6\) | −2.00244e14 | −0.804934 | ||||||||
\(7\) | −3.10972e15 | −0.721785 | −0.360892 | − | 0.932608i | \(-0.617528\pi\) | ||||
−0.360892 | + | 0.932608i | \(0.617528\pi\) | |||||||
\(8\) | −3.99525e15 | −0.0784114 | ||||||||
\(9\) | 1.50095e17 | 0.333333 | ||||||||
\(10\) | 1.62136e18 | 0.512721 | ||||||||
\(11\) | 7.50440e18 | 0.406960 | 0.203480 | − | 0.979079i | \(-0.434775\pi\) | ||||
0.203480 | + | 0.979079i | \(0.434775\pi\) | |||||||
\(12\) | −5.02520e19 | −0.544879 | ||||||||
\(13\) | −6.39538e20 | −1.57730 | −0.788650 | − | 0.614843i | \(-0.789219\pi\) | ||||
−0.788650 | + | 0.614843i | \(0.789219\pi\) | |||||||
\(14\) | −1.60730e21 | −1.00630 | ||||||||
\(15\) | −1.21531e21 | −0.212324 | ||||||||
\(16\) | −1.98921e22 | −1.05308 | ||||||||
\(17\) | −5.44751e22 | −0.939492 | −0.469746 | − | 0.882802i | \(-0.655655\pi\) | ||||
−0.469746 | + | 0.882802i | \(0.655655\pi\) | |||||||
\(18\) | 7.75785e22 | 0.464729 | ||||||||
\(19\) | 2.22938e23 | 0.491182 | 0.245591 | − | 0.969374i | \(-0.421018\pi\) | ||||
0.245591 | + | 0.969374i | \(0.421018\pi\) | |||||||
\(20\) | 4.06888e23 | 0.347073 | ||||||||
\(21\) | 1.20477e24 | 0.416722 | ||||||||
\(22\) | 3.87875e24 | 0.567378 | ||||||||
\(23\) | −1.64570e25 | −1.05775 | −0.528877 | − | 0.848698i | \(-0.677387\pi\) | ||||
−0.528877 | + | 0.848698i | \(0.677387\pi\) | |||||||
\(24\) | 1.54784e24 | 0.0452708 | ||||||||
\(25\) | −6.29193e25 | −0.864756 | ||||||||
\(26\) | −3.30554e26 | −2.19905 | ||||||||
\(27\) | −5.81497e25 | −0.192450 | ||||||||
\(28\) | −4.03359e26 | −0.681190 | ||||||||
\(29\) | 1.49927e27 | 1.32287 | 0.661434 | − | 0.750004i | \(-0.269948\pi\) | ||||
0.661434 | + | 0.750004i | \(0.269948\pi\) | |||||||
\(30\) | −6.28150e26 | −0.296019 | ||||||||
\(31\) | −4.99985e27 | −1.28459 | −0.642297 | − | 0.766456i | \(-0.722018\pi\) | ||||
−0.642297 | + | 0.766456i | \(0.722018\pi\) | |||||||
\(32\) | −9.73240e27 | −1.38978 | ||||||||
\(33\) | −2.90736e27 | −0.234958 | ||||||||
\(34\) | −2.81562e28 | −1.30983 | ||||||||
\(35\) | −9.75497e27 | −0.265440 | ||||||||
\(36\) | 1.94686e28 | 0.314586 | ||||||||
\(37\) | 4.47694e28 | 0.435762 | 0.217881 | − | 0.975975i | \(-0.430086\pi\) | ||||
0.217881 | + | 0.975975i | \(0.430086\pi\) | |||||||
\(38\) | 1.15228e29 | 0.684799 | ||||||||
\(39\) | 2.47770e29 | 0.910654 | ||||||||
\(40\) | −1.25328e28 | −0.0288362 | ||||||||
\(41\) | 1.03254e30 | 1.50455 | 0.752275 | − | 0.658849i | \(-0.228956\pi\) | ||||
0.752275 | + | 0.658849i | \(0.228956\pi\) | |||||||
\(42\) | 6.22702e29 | 0.580989 | ||||||||
\(43\) | −2.18835e30 | −1.32114 | −0.660572 | − | 0.750763i | \(-0.729686\pi\) | ||||
−0.660572 | + | 0.750763i | \(0.729686\pi\) | |||||||
\(44\) | 9.73390e29 | 0.384072 | ||||||||
\(45\) | 4.70836e29 | 0.122585 | ||||||||
\(46\) | −8.50601e30 | −1.47471 | ||||||||
\(47\) | 1.06681e31 | 1.24244 | 0.621221 | − | 0.783635i | \(-0.286637\pi\) | ||||
0.621221 | + | 0.783635i | \(0.286637\pi\) | |||||||
\(48\) | 7.70660e30 | 0.607995 | ||||||||
\(49\) | −8.89176e30 | −0.479027 | ||||||||
\(50\) | −3.25207e31 | −1.20563 | ||||||||
\(51\) | 2.11048e31 | 0.542416 | ||||||||
\(52\) | −8.29539e31 | −1.48859 | ||||||||
\(53\) | −2.17162e31 | −0.273956 | −0.136978 | − | 0.990574i | \(-0.543739\pi\) | ||||
−0.136978 | + | 0.990574i | \(0.543739\pi\) | |||||||
\(54\) | −3.00555e31 | −0.268311 | ||||||||
\(55\) | 2.35408e31 | 0.149662 | ||||||||
\(56\) | 1.24241e31 | 0.0565961 | ||||||||
\(57\) | −8.63707e31 | −0.283584 | ||||||||
\(58\) | 7.74917e32 | 1.84433 | ||||||||
\(59\) | 9.25373e32 | 1.60529 | 0.802647 | − | 0.596455i | \(-0.203424\pi\) | ||||
0.802647 | + | 0.596455i | \(0.203424\pi\) | |||||||
\(60\) | −1.57637e32 | −0.200382 | ||||||||
\(61\) | 1.78286e33 | 1.66923 | 0.834615 | − | 0.550833i | \(-0.185690\pi\) | ||||
0.834615 | + | 0.550833i | \(0.185690\pi\) | |||||||
\(62\) | −2.58424e33 | −1.79096 | ||||||||
\(63\) | −4.66752e32 | −0.240595 | ||||||||
\(64\) | −2.29638e33 | −0.884532 | ||||||||
\(65\) | −2.00618e33 | −0.580061 | ||||||||
\(66\) | −1.50271e33 | −0.327576 | ||||||||
\(67\) | 5.16951e33 | 0.853229 | 0.426615 | − | 0.904433i | \(-0.359706\pi\) | ||||
0.426615 | + | 0.904433i | \(0.359706\pi\) | |||||||
\(68\) | −7.06592e33 | −0.886654 | ||||||||
\(69\) | 6.37577e33 | 0.610695 | ||||||||
\(70\) | −5.04199e33 | −0.370074 | ||||||||
\(71\) | 3.92232e33 | 0.221444 | 0.110722 | − | 0.993851i | \(-0.464684\pi\) | ||||
0.110722 | + | 0.993851i | \(0.464684\pi\) | |||||||
\(72\) | −5.99665e32 | −0.0261371 | ||||||||
\(73\) | −3.83796e34 | −1.29607 | −0.648034 | − | 0.761612i | \(-0.724408\pi\) | ||||
−0.648034 | + | 0.761612i | \(0.724408\pi\) | |||||||
\(74\) | 2.31397e34 | 0.607534 | ||||||||
\(75\) | 2.43762e34 | 0.499267 | ||||||||
\(76\) | 2.89171e34 | 0.463557 | ||||||||
\(77\) | −2.33366e34 | −0.293737 | ||||||||
\(78\) | 1.28063e35 | 1.26962 | ||||||||
\(79\) | −5.14706e34 | −0.403142 | −0.201571 | − | 0.979474i | \(-0.564605\pi\) | ||||
−0.201571 | + | 0.979474i | \(0.564605\pi\) | |||||||
\(80\) | −6.24001e34 | −0.387276 | ||||||||
\(81\) | 2.25284e34 | 0.111111 | ||||||||
\(82\) | 5.33684e35 | 2.09763 | ||||||||
\(83\) | −2.76468e35 | −0.868361 | −0.434180 | − | 0.900826i | \(-0.642962\pi\) | ||||
−0.434180 | + | 0.900826i | \(0.642962\pi\) | |||||||
\(84\) | 1.56270e35 | 0.393285 | ||||||||
\(85\) | −1.70885e35 | −0.345504 | ||||||||
\(86\) | −1.13108e36 | −1.84192 | ||||||||
\(87\) | −5.80847e35 | −0.763758 | ||||||||
\(88\) | −2.99820e34 | −0.0319103 | ||||||||
\(89\) | −1.38448e36 | −1.19556 | −0.597780 | − | 0.801661i | \(-0.703950\pi\) | ||||
−0.597780 | + | 0.801661i | \(0.703950\pi\) | |||||||
\(90\) | 2.43358e35 | 0.170907 | ||||||||
\(91\) | 1.98878e36 | 1.13847 | ||||||||
\(92\) | −2.13462e36 | −0.998265 | ||||||||
\(93\) | 1.93704e36 | 0.741660 | ||||||||
\(94\) | 5.51395e36 | 1.73220 | ||||||||
\(95\) | 6.99340e35 | 0.180635 | ||||||||
\(96\) | 3.77053e36 | 0.802388 | ||||||||
\(97\) | 1.68983e36 | 0.296870 | 0.148435 | − | 0.988922i | \(-0.452576\pi\) | ||||
0.148435 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(98\) | −4.59583e36 | −0.667853 | ||||||||
\(99\) | 1.12637e36 | 0.135653 | ||||||||
\(100\) | −8.16120e36 | −0.816120 | ||||||||
\(101\) | −5.62367e36 | −0.467815 | −0.233908 | − | 0.972259i | \(-0.575151\pi\) | ||||
−0.233908 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(102\) | 1.09083e37 | 0.756230 | ||||||||
\(103\) | −1.48424e37 | −0.859046 | −0.429523 | − | 0.903056i | \(-0.641318\pi\) | ||||
−0.429523 | + | 0.903056i | \(0.641318\pi\) | |||||||
\(104\) | 2.55511e36 | 0.123678 | ||||||||
\(105\) | 3.77928e36 | 0.153252 | ||||||||
\(106\) | −1.12243e37 | −0.381945 | ||||||||
\(107\) | 4.70122e36 | 0.134465 | 0.0672327 | − | 0.997737i | \(-0.478583\pi\) | ||||
0.0672327 | + | 0.997737i | \(0.478583\pi\) | |||||||
\(108\) | −7.54255e36 | −0.181626 | ||||||||
\(109\) | −3.33633e36 | −0.0677453 | −0.0338726 | − | 0.999426i | \(-0.510784\pi\) | ||||
−0.0338726 | + | 0.999426i | \(0.510784\pi\) | |||||||
\(110\) | 1.21674e37 | 0.208657 | ||||||||
\(111\) | −1.73446e37 | −0.251587 | ||||||||
\(112\) | 6.18588e37 | 0.760096 | ||||||||
\(113\) | −1.52031e38 | −1.58483 | −0.792414 | − | 0.609984i | \(-0.791176\pi\) | ||||
−0.792414 | + | 0.609984i | \(0.791176\pi\) | |||||||
\(114\) | −4.46419e37 | −0.395369 | ||||||||
\(115\) | −5.16243e37 | −0.388995 | ||||||||
\(116\) | 1.94469e38 | 1.24847 | ||||||||
\(117\) | −9.59912e37 | −0.525766 | ||||||||
\(118\) | 4.78292e38 | 2.23808 | ||||||||
\(119\) | 1.69402e38 | 0.678111 | ||||||||
\(120\) | 4.85547e36 | 0.0166486 | ||||||||
\(121\) | −2.83723e38 | −0.834384 | ||||||||
\(122\) | 9.21498e38 | 2.32722 | ||||||||
\(123\) | −4.00028e38 | −0.868653 | ||||||||
\(124\) | −6.48527e38 | −1.21235 | ||||||||
\(125\) | −4.25615e38 | −0.685775 | ||||||||
\(126\) | −2.41247e38 | −0.335434 | ||||||||
\(127\) | −9.46165e38 | −1.13658 | −0.568288 | − | 0.822830i | \(-0.692394\pi\) | ||||
−0.568288 | + | 0.822830i | \(0.692394\pi\) | |||||||
\(128\) | 1.50697e38 | 0.156575 | ||||||||
\(129\) | 8.47811e38 | 0.762762 | ||||||||
\(130\) | −1.03692e39 | −0.808714 | ||||||||
\(131\) | −7.30262e38 | −0.494265 | −0.247133 | − | 0.968982i | \(-0.579488\pi\) | ||||
−0.247133 | + | 0.968982i | \(0.579488\pi\) | |||||||
\(132\) | −3.77111e38 | −0.221744 | ||||||||
\(133\) | −6.93274e38 | −0.354527 | ||||||||
\(134\) | 2.67193e39 | 1.18956 | ||||||||
\(135\) | −1.82412e38 | −0.0707746 | ||||||||
\(136\) | 2.17642e38 | 0.0736669 | ||||||||
\(137\) | 2.73285e39 | 0.807765 | 0.403883 | − | 0.914811i | \(-0.367660\pi\) | ||||
0.403883 | + | 0.914811i | \(0.367660\pi\) | |||||||
\(138\) | 3.29540e39 | 0.851423 | ||||||||
\(139\) | 5.99229e39 | 1.35462 | 0.677312 | − | 0.735696i | \(-0.263145\pi\) | ||||
0.677312 | + | 0.735696i | \(0.263145\pi\) | |||||||
\(140\) | −1.26531e39 | −0.250512 | ||||||||
\(141\) | −4.13304e39 | −0.717325 | ||||||||
\(142\) | 2.02730e39 | 0.308734 | ||||||||
\(143\) | −4.79935e39 | −0.641897 | ||||||||
\(144\) | −2.98570e39 | −0.351026 | ||||||||
\(145\) | 4.70310e39 | 0.486492 | ||||||||
\(146\) | −1.98370e40 | −1.80696 | ||||||||
\(147\) | 3.44485e39 | 0.276566 | ||||||||
\(148\) | 5.80700e39 | 0.411254 | ||||||||
\(149\) | −1.46862e40 | −0.918255 | −0.459127 | − | 0.888370i | \(-0.651838\pi\) | ||||
−0.459127 | + | 0.888370i | \(0.651838\pi\) | |||||||
\(150\) | 1.25992e40 | 0.696072 | ||||||||
\(151\) | 2.01471e40 | 0.984328 | 0.492164 | − | 0.870503i | \(-0.336206\pi\) | ||||
0.492164 | + | 0.870503i | \(0.336206\pi\) | |||||||
\(152\) | −8.90692e38 | −0.0385142 | ||||||||
\(153\) | −8.17643e39 | −0.313164 | ||||||||
\(154\) | −1.20618e40 | −0.409525 | ||||||||
\(155\) | −1.56842e40 | −0.472417 | ||||||||
\(156\) | 3.21380e40 | 0.859437 | ||||||||
\(157\) | −5.21717e40 | −1.23963 | −0.619815 | − | 0.784748i | \(-0.712792\pi\) | ||||
−0.619815 | + | 0.784748i | \(0.712792\pi\) | |||||||
\(158\) | −2.66033e40 | −0.562056 | ||||||||
\(159\) | 8.41330e39 | 0.158168 | ||||||||
\(160\) | −3.05298e40 | −0.511099 | ||||||||
\(161\) | 5.11766e40 | 0.763471 | ||||||||
\(162\) | 1.16441e40 | 0.154910 | ||||||||
\(163\) | 1.10448e41 | 1.31125 | 0.655625 | − | 0.755086i | \(-0.272405\pi\) | ||||
0.655625 | + | 0.755086i | \(0.272405\pi\) | |||||||
\(164\) | 1.33930e41 | 1.41993 | ||||||||
\(165\) | −9.12018e39 | −0.0864073 | ||||||||
\(166\) | −1.42896e41 | −1.21066 | ||||||||
\(167\) | 8.68066e40 | 0.658109 | 0.329055 | − | 0.944311i | \(-0.393270\pi\) | ||||
0.329055 | + | 0.944311i | \(0.393270\pi\) | |||||||
\(168\) | −4.81335e39 | −0.0326758 | ||||||||
\(169\) | 2.44608e41 | 1.48787 | ||||||||
\(170\) | −8.83241e40 | −0.481697 | ||||||||
\(171\) | 3.34618e40 | 0.163727 | ||||||||
\(172\) | −2.83849e41 | −1.24684 | ||||||||
\(173\) | −2.30699e41 | −0.910316 | −0.455158 | − | 0.890411i | \(-0.650417\pi\) | ||||
−0.455158 | + | 0.890411i | \(0.650417\pi\) | |||||||
\(174\) | −3.00219e41 | −1.06482 | ||||||||
\(175\) | 1.95661e41 | 0.624167 | ||||||||
\(176\) | −1.49278e41 | −0.428561 | ||||||||
\(177\) | −3.58508e41 | −0.926817 | ||||||||
\(178\) | −7.15587e41 | −1.66683 | ||||||||
\(179\) | 4.00112e41 | 0.840235 | 0.420118 | − | 0.907470i | \(-0.361989\pi\) | ||||
0.420118 | + | 0.907470i | \(0.361989\pi\) | |||||||
\(180\) | 6.10718e40 | 0.115691 | ||||||||
\(181\) | 8.60285e41 | 1.47092 | 0.735460 | − | 0.677569i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677569i | \(0.236966\pi\) | |||||||
\(182\) | 1.02793e42 | 1.58724 | ||||||||
\(183\) | −6.90718e41 | −0.963731 | ||||||||
\(184\) | 6.57497e40 | 0.0829400 | ||||||||
\(185\) | 1.40438e41 | 0.160254 | ||||||||
\(186\) | 1.00119e42 | 1.03401 | ||||||||
\(187\) | −4.08803e41 | −0.382336 | ||||||||
\(188\) | 1.38375e42 | 1.17257 | ||||||||
\(189\) | 1.80829e41 | 0.138907 | ||||||||
\(190\) | 3.61464e41 | 0.251839 | ||||||||
\(191\) | −2.36146e42 | −1.49301 | −0.746507 | − | 0.665378i | \(-0.768270\pi\) | ||||
−0.746507 | + | 0.665378i | \(0.768270\pi\) | |||||||
\(192\) | 8.89663e41 | 0.510685 | ||||||||
\(193\) | −2.73448e42 | −1.42582 | −0.712910 | − | 0.701255i | \(-0.752623\pi\) | ||||
−0.712910 | + | 0.701255i | \(0.752623\pi\) | |||||||
\(194\) | 8.73414e41 | 0.413893 | ||||||||
\(195\) | 7.77237e41 | 0.334898 | ||||||||
\(196\) | −1.15334e42 | −0.452086 | ||||||||
\(197\) | −2.24211e42 | −0.799893 | −0.399947 | − | 0.916538i | \(-0.630971\pi\) | ||||
−0.399947 | + | 0.916538i | \(0.630971\pi\) | |||||||
\(198\) | 5.82180e41 | 0.189126 | ||||||||
\(199\) | 4.34264e42 | 1.28520 | 0.642602 | − | 0.766201i | \(-0.277855\pi\) | ||||
0.642602 | + | 0.766201i | \(0.277855\pi\) | |||||||
\(200\) | 2.51378e41 | 0.0678067 | ||||||||
\(201\) | −2.00278e42 | −0.492612 | ||||||||
\(202\) | −2.90667e42 | −0.652222 | ||||||||
\(203\) | −4.66230e42 | −0.954825 | ||||||||
\(204\) | 2.73748e42 | 0.511910 | ||||||||
\(205\) | 3.23901e42 | 0.553307 | ||||||||
\(206\) | −7.67151e42 | −1.19767 | ||||||||
\(207\) | −2.47010e42 | −0.352585 | ||||||||
\(208\) | 1.27217e43 | 1.66102 | ||||||||
\(209\) | 1.67302e42 | 0.199891 | ||||||||
\(210\) | 1.95337e42 | 0.213662 | ||||||||
\(211\) | −1.99383e42 | −0.199739 | −0.0998696 | − | 0.995001i | \(-0.531843\pi\) | ||||
−0.0998696 | + | 0.995001i | \(0.531843\pi\) | |||||||
\(212\) | −2.81679e42 | −0.258548 | ||||||||
\(213\) | −1.51959e42 | −0.127851 | ||||||||
\(214\) | 2.42989e42 | 0.187470 | ||||||||
\(215\) | −6.86469e42 | −0.485858 | ||||||||
\(216\) | 2.32323e41 | 0.0150903 | ||||||||
\(217\) | 1.55481e43 | 0.927200 | ||||||||
\(218\) | −1.72443e42 | −0.0944496 | ||||||||
\(219\) | 1.48690e43 | 0.748285 | ||||||||
\(220\) | 3.05345e42 | 0.141245 | ||||||||
\(221\) | 3.48389e43 | 1.48186 | ||||||||
\(222\) | −8.96478e42 | −0.350760 | ||||||||
\(223\) | −1.45882e43 | −0.525245 | −0.262622 | − | 0.964899i | \(-0.584587\pi\) | ||||
−0.262622 | + | 0.964899i | \(0.584587\pi\) | |||||||
\(224\) | 3.02650e43 | 1.00312 | ||||||||
\(225\) | −9.44384e42 | −0.288252 | ||||||||
\(226\) | −7.85795e43 | −2.20955 | ||||||||
\(227\) | −1.02701e43 | −0.266132 | −0.133066 | − | 0.991107i | \(-0.542482\pi\) | ||||
−0.133066 | + | 0.991107i | \(0.542482\pi\) | |||||||
\(228\) | −1.12031e43 | −0.267635 | ||||||||
\(229\) | −7.93768e43 | −1.74879 | −0.874394 | − | 0.485216i | \(-0.838741\pi\) | ||||
−0.874394 | + | 0.485216i | \(0.838741\pi\) | |||||||
\(230\) | −2.66828e43 | −0.542333 | ||||||||
\(231\) | 9.04107e42 | 0.169589 | ||||||||
\(232\) | −5.98995e42 | −0.103728 | ||||||||
\(233\) | 3.40755e43 | 0.544951 | 0.272476 | − | 0.962163i | \(-0.412158\pi\) | ||||
0.272476 | + | 0.962163i | \(0.412158\pi\) | |||||||
\(234\) | −4.96144e43 | −0.733017 | ||||||||
\(235\) | 3.34650e43 | 0.456916 | ||||||||
\(236\) | 1.20029e44 | 1.51501 | ||||||||
\(237\) | 1.99408e43 | 0.232754 | ||||||||
\(238\) | 8.75580e43 | 0.945414 | ||||||||
\(239\) | 4.85851e43 | 0.485447 | 0.242724 | − | 0.970095i | \(-0.421959\pi\) | ||||
0.242724 | + | 0.970095i | \(0.421959\pi\) | |||||||
\(240\) | 2.41751e43 | 0.223594 | ||||||||
\(241\) | 1.16789e44 | 1.00020 | 0.500100 | − | 0.865968i | \(-0.333297\pi\) | ||||
0.500100 | + | 0.865968i | \(0.333297\pi\) | |||||||
\(242\) | −1.46646e44 | −1.16329 | ||||||||
\(243\) | −8.72796e42 | −0.0641500 | ||||||||
\(244\) | 2.31254e44 | 1.57535 | ||||||||
\(245\) | −2.78928e43 | −0.176165 | ||||||||
\(246\) | −2.06760e44 | −1.21106 | ||||||||
\(247\) | −1.42577e44 | −0.774741 | ||||||||
\(248\) | 1.99756e43 | 0.100727 | ||||||||
\(249\) | 1.07109e44 | 0.501348 | ||||||||
\(250\) | −2.19985e44 | −0.956098 | ||||||||
\(251\) | 1.50654e44 | 0.608158 | 0.304079 | − | 0.952647i | \(-0.401651\pi\) | ||||
0.304079 | + | 0.952647i | \(0.401651\pi\) | |||||||
\(252\) | −6.05421e43 | −0.227063 | ||||||||
\(253\) | −1.23500e44 | −0.430464 | ||||||||
\(254\) | −4.89039e44 | −1.58460 | ||||||||
\(255\) | 6.62042e43 | 0.199477 | ||||||||
\(256\) | 3.93501e44 | 1.10283 | ||||||||
\(257\) | −2.05457e44 | −0.535746 | −0.267873 | − | 0.963454i | \(-0.586321\pi\) | ||||
−0.267873 | + | 0.963454i | \(0.586321\pi\) | |||||||
\(258\) | 4.38203e44 | 1.06343 | ||||||||
\(259\) | −1.39220e44 | −0.314526 | ||||||||
\(260\) | −2.60220e44 | −0.547437 | ||||||||
\(261\) | 2.25032e44 | 0.440956 | ||||||||
\(262\) | −3.77446e44 | −0.689098 | ||||||||
\(263\) | 3.74763e44 | 0.637639 | 0.318819 | − | 0.947815i | \(-0.396714\pi\) | ||||
0.318819 | + | 0.947815i | \(0.396714\pi\) | |||||||
\(264\) | 1.16156e43 | 0.0184234 | ||||||||
\(265\) | −6.81221e43 | −0.100749 | ||||||||
\(266\) | −3.58328e44 | −0.494278 | ||||||||
\(267\) | 5.36375e44 | 0.690256 | ||||||||
\(268\) | 6.70533e44 | 0.805242 | ||||||||
\(269\) | −6.18015e44 | −0.692758 | −0.346379 | − | 0.938095i | \(-0.612589\pi\) | ||||
−0.346379 | + | 0.938095i | \(0.612589\pi\) | |||||||
\(270\) | −9.42819e43 | −0.0986731 | ||||||||
\(271\) | −8.98660e44 | −0.878342 | −0.439171 | − | 0.898403i | \(-0.644728\pi\) | ||||
−0.439171 | + | 0.898403i | \(0.644728\pi\) | |||||||
\(272\) | 1.08362e45 | 0.989359 | ||||||||
\(273\) | −7.70495e44 | −0.657296 | ||||||||
\(274\) | 1.41251e45 | 1.12618 | ||||||||
\(275\) | −4.72171e44 | −0.351921 | ||||||||
\(276\) | 8.26996e44 | 0.576348 | ||||||||
\(277\) | 5.14897e44 | 0.335617 | 0.167809 | − | 0.985820i | \(-0.446331\pi\) | ||||
0.167809 | + | 0.985820i | \(0.446331\pi\) | |||||||
\(278\) | 3.09719e45 | 1.88860 | ||||||||
\(279\) | −7.50451e44 | −0.428198 | ||||||||
\(280\) | 3.89735e43 | 0.0208135 | ||||||||
\(281\) | −2.48686e45 | −1.24333 | −0.621663 | − | 0.783285i | \(-0.713543\pi\) | ||||
−0.621663 | + | 0.783285i | \(0.713543\pi\) | |||||||
\(282\) | −2.13622e45 | −1.00008 | ||||||||
\(283\) | 1.48025e45 | 0.649062 | 0.324531 | − | 0.945875i | \(-0.394793\pi\) | ||||
0.324531 | + | 0.945875i | \(0.394793\pi\) | |||||||
\(284\) | 5.08761e44 | 0.208989 | ||||||||
\(285\) | −2.70939e44 | −0.104290 | ||||||||
\(286\) | −2.48061e45 | −0.894925 | ||||||||
\(287\) | −3.21092e45 | −1.08596 | ||||||||
\(288\) | −1.46078e45 | −0.463259 | ||||||||
\(289\) | −3.94555e44 | −0.117354 | ||||||||
\(290\) | 2.43086e45 | 0.678261 | ||||||||
\(291\) | −6.54676e44 | −0.171398 | ||||||||
\(292\) | −4.97819e45 | −1.22317 | ||||||||
\(293\) | 1.29229e45 | 0.298064 | 0.149032 | − | 0.988832i | \(-0.452384\pi\) | ||||
0.149032 | + | 0.988832i | \(0.452384\pi\) | |||||||
\(294\) | 1.78052e45 | 0.385585 | ||||||||
\(295\) | 2.90283e45 | 0.590356 | ||||||||
\(296\) | −1.78865e44 | −0.0341687 | ||||||||
\(297\) | −4.36379e44 | −0.0783194 | ||||||||
\(298\) | −7.59076e45 | −1.28022 | ||||||||
\(299\) | 1.05249e46 | 1.66840 | ||||||||
\(300\) | 3.16182e45 | 0.471187 | ||||||||
\(301\) | 6.80515e45 | 0.953581 | ||||||||
\(302\) | 1.04133e46 | 1.37234 | ||||||||
\(303\) | 2.17873e45 | 0.270093 | ||||||||
\(304\) | −4.43470e45 | −0.517253 | ||||||||
\(305\) | 5.59272e45 | 0.613869 | ||||||||
\(306\) | −4.22610e45 | −0.436609 | ||||||||
\(307\) | 3.03724e45 | 0.295406 | 0.147703 | − | 0.989032i | \(-0.452812\pi\) | ||||
0.147703 | + | 0.989032i | \(0.452812\pi\) | |||||||
\(308\) | −3.02697e45 | −0.277217 | ||||||||
\(309\) | 5.75026e45 | 0.495970 | ||||||||
\(310\) | −8.10658e45 | −0.658637 | ||||||||
\(311\) | −2.03519e46 | −1.55789 | −0.778947 | − | 0.627090i | \(-0.784246\pi\) | ||||
−0.778947 | + | 0.627090i | \(0.784246\pi\) | |||||||
\(312\) | −9.89903e44 | −0.0714056 | ||||||||
\(313\) | 1.26896e46 | 0.862736 | 0.431368 | − | 0.902176i | \(-0.358031\pi\) | ||||
0.431368 | + | 0.902176i | \(0.358031\pi\) | |||||||
\(314\) | −2.69657e46 | −1.72828 | ||||||||
\(315\) | −1.46417e45 | −0.0884802 | ||||||||
\(316\) | −6.67621e45 | −0.380469 | ||||||||
\(317\) | −2.19161e46 | −1.17806 | −0.589029 | − | 0.808112i | \(-0.700490\pi\) | ||||
−0.589029 | + | 0.808112i | \(0.700490\pi\) | |||||||
\(318\) | 4.34853e45 | 0.220516 | ||||||||
\(319\) | 1.12511e46 | 0.538354 | ||||||||
\(320\) | −7.20356e45 | −0.325292 | ||||||||
\(321\) | −1.82135e45 | −0.0776336 | ||||||||
\(322\) | 2.64513e46 | 1.06442 | ||||||||
\(323\) | −1.21446e46 | −0.461461 | ||||||||
\(324\) | 2.92214e45 | 0.104862 | ||||||||
\(325\) | 4.02392e46 | 1.36398 | ||||||||
\(326\) | 5.70864e46 | 1.82813 | ||||||||
\(327\) | 1.29256e45 | 0.0391127 | ||||||||
\(328\) | −4.12527e45 | −0.117974 | ||||||||
\(329\) | −3.31748e46 | −0.896776 | ||||||||
\(330\) | −4.71389e45 | −0.120468 | ||||||||
\(331\) | −6.51418e46 | −1.57413 | −0.787067 | − | 0.616867i | \(-0.788402\pi\) | ||||
−0.787067 | + | 0.616867i | \(0.788402\pi\) | |||||||
\(332\) | −3.58604e46 | −0.819523 | ||||||||
\(333\) | 6.71965e45 | 0.145254 | ||||||||
\(334\) | 4.48672e46 | 0.917528 | ||||||||
\(335\) | 1.62164e46 | 0.313780 | ||||||||
\(336\) | −2.39654e46 | −0.438842 | ||||||||
\(337\) | −4.49138e46 | −0.778443 | −0.389221 | − | 0.921144i | \(-0.627256\pi\) | ||||
−0.389221 | + | 0.921144i | \(0.627256\pi\) | |||||||
\(338\) | 1.26429e47 | 2.07437 | ||||||||
\(339\) | 5.89001e46 | 0.915000 | ||||||||
\(340\) | −2.21653e46 | −0.326072 | ||||||||
\(341\) | −3.75209e46 | −0.522778 | ||||||||
\(342\) | 1.72952e46 | 0.228266 | ||||||||
\(343\) | 8.53739e46 | 1.06754 | ||||||||
\(344\) | 8.74299e45 | 0.103593 | ||||||||
\(345\) | 2.00003e46 | 0.224587 | ||||||||
\(346\) | −1.19240e47 | −1.26915 | ||||||||
\(347\) | −3.07449e45 | −0.0310226 | −0.0155113 | − | 0.999880i | \(-0.504938\pi\) | ||||
−0.0155113 | + | 0.999880i | \(0.504938\pi\) | |||||||
\(348\) | −7.53412e46 | −0.720803 | ||||||||
\(349\) | −1.55130e47 | −1.40742 | −0.703711 | − | 0.710487i | \(-0.748475\pi\) | ||||
−0.703711 | + | 0.710487i | \(0.748475\pi\) | |||||||
\(350\) | 1.01130e47 | 0.870206 | ||||||||
\(351\) | 3.71889e46 | 0.303551 | ||||||||
\(352\) | −7.30358e46 | −0.565583 | ||||||||
\(353\) | 1.60772e47 | 1.18135 | 0.590675 | − | 0.806909i | \(-0.298861\pi\) | ||||
0.590675 | + | 0.806909i | \(0.298861\pi\) | |||||||
\(354\) | −1.85300e47 | −1.29216 | ||||||||
\(355\) | 1.23040e46 | 0.0814372 | ||||||||
\(356\) | −1.79580e47 | −1.12832 | ||||||||
\(357\) | −6.56300e46 | −0.391508 | ||||||||
\(358\) | 2.06804e47 | 1.17145 | ||||||||
\(359\) | −3.06245e47 | −1.64749 | −0.823743 | − | 0.566963i | \(-0.808118\pi\) | ||||
−0.823743 | + | 0.566963i | \(0.808118\pi\) | |||||||
\(360\) | −1.88111e45 | −0.00961208 | ||||||||
\(361\) | −1.56306e47 | −0.758741 | ||||||||
\(362\) | 4.44650e47 | 2.05074 | ||||||||
\(363\) | 1.09920e47 | 0.481732 | ||||||||
\(364\) | 2.57963e47 | 1.07444 | ||||||||
\(365\) | −1.20394e47 | −0.476636 | ||||||||
\(366\) | −3.57007e47 | −1.34362 | ||||||||
\(367\) | 3.11125e47 | 1.11330 | 0.556651 | − | 0.830746i | \(-0.312086\pi\) | ||||
0.556651 | + | 0.830746i | \(0.312086\pi\) | |||||||
\(368\) | 3.27364e47 | 1.11390 | ||||||||
\(369\) | 1.54979e47 | 0.501517 | ||||||||
\(370\) | 7.25875e46 | 0.223424 | ||||||||
\(371\) | 6.75313e46 | 0.197737 | ||||||||
\(372\) | 2.51252e47 | 0.699948 | ||||||||
\(373\) | 2.77220e47 | 0.734872 | 0.367436 | − | 0.930049i | \(-0.380236\pi\) | ||||
0.367436 | + | 0.930049i | \(0.380236\pi\) | |||||||
\(374\) | −2.11296e47 | −0.533047 | ||||||||
\(375\) | 1.64892e47 | 0.395932 | ||||||||
\(376\) | −4.26217e46 | −0.0974216 | ||||||||
\(377\) | −9.58838e47 | −2.08656 | ||||||||
\(378\) | 9.34642e46 | 0.193663 | ||||||||
\(379\) | −3.61039e47 | −0.712408 | −0.356204 | − | 0.934408i | \(-0.615929\pi\) | ||||
−0.356204 | + | 0.934408i | \(0.615929\pi\) | |||||||
\(380\) | 9.07108e46 | 0.170476 | ||||||||
\(381\) | 3.66564e47 | 0.656202 | ||||||||
\(382\) | −1.22055e48 | −2.08154 | ||||||||
\(383\) | 3.07589e47 | 0.499797 | 0.249898 | − | 0.968272i | \(-0.419603\pi\) | ||||
0.249898 | + | 0.968272i | \(0.419603\pi\) | |||||||
\(384\) | −5.83833e46 | −0.0903984 | ||||||||
\(385\) | −7.32052e46 | −0.108024 | ||||||||
\(386\) | −1.41335e48 | −1.98786 | ||||||||
\(387\) | −3.28459e47 | −0.440381 | ||||||||
\(388\) | 2.19187e47 | 0.280174 | ||||||||
\(389\) | 8.01241e47 | 0.976552 | 0.488276 | − | 0.872689i | \(-0.337626\pi\) | ||||
0.488276 | + | 0.872689i | \(0.337626\pi\) | |||||||
\(390\) | 4.01725e47 | 0.466911 | ||||||||
\(391\) | 8.96496e47 | 0.993753 | ||||||||
\(392\) | 3.55248e46 | 0.0375612 | ||||||||
\(393\) | 2.82919e47 | 0.285364 | ||||||||
\(394\) | −1.15887e48 | −1.11520 | ||||||||
\(395\) | −1.61460e47 | −0.148258 | ||||||||
\(396\) | 1.46101e47 | 0.128024 | ||||||||
\(397\) | 5.55598e47 | 0.464661 | 0.232331 | − | 0.972637i | \(-0.425365\pi\) | ||||
0.232331 | + | 0.972637i | \(0.425365\pi\) | |||||||
\(398\) | 2.24455e48 | 1.79181 | ||||||||
\(399\) | 2.68589e47 | 0.204686 | ||||||||
\(400\) | 1.25160e48 | 0.910656 | ||||||||
\(401\) | −2.52389e48 | −1.75347 | −0.876736 | − | 0.480972i | \(-0.840284\pi\) | ||||
−0.876736 | + | 0.480972i | \(0.840284\pi\) | |||||||
\(402\) | −1.03516e48 | −0.686794 | ||||||||
\(403\) | 3.19759e48 | 2.02619 | ||||||||
\(404\) | −7.29442e47 | −0.441505 | ||||||||
\(405\) | 7.06700e46 | 0.0408618 | ||||||||
\(406\) | −2.40978e48 | −1.33121 | ||||||||
\(407\) | 3.35968e47 | 0.177338 | ||||||||
\(408\) | −8.43188e46 | −0.0425316 | ||||||||
\(409\) | 1.92635e48 | 0.928653 | 0.464326 | − | 0.885664i | \(-0.346296\pi\) | ||||
0.464326 | + | 0.885664i | \(0.346296\pi\) | |||||||
\(410\) | 1.67413e48 | 0.771414 | ||||||||
\(411\) | −1.05876e48 | −0.466363 | ||||||||
\(412\) | −1.92520e48 | −0.810731 | ||||||||
\(413\) | −2.87765e48 | −1.15868 | ||||||||
\(414\) | −1.27671e48 | −0.491569 | ||||||||
\(415\) | −8.67260e47 | −0.319345 | ||||||||
\(416\) | 6.22423e48 | 2.19209 | ||||||||
\(417\) | −2.32153e48 | −0.782092 | ||||||||
\(418\) | 8.64721e47 | 0.278686 | ||||||||
\(419\) | 1.97665e48 | 0.609494 | 0.304747 | − | 0.952433i | \(-0.401428\pi\) | ||||
0.304747 | + | 0.952433i | \(0.401428\pi\) | |||||||
\(420\) | 4.90207e47 | 0.144633 | ||||||||
\(421\) | −3.96618e48 | −1.11983 | −0.559916 | − | 0.828549i | \(-0.689167\pi\) | ||||
−0.559916 | + | 0.828549i | \(0.689167\pi\) | |||||||
\(422\) | −1.03054e48 | −0.278474 | ||||||||
\(423\) | 1.60122e48 | 0.414148 | ||||||||
\(424\) | 8.67616e46 | 0.0214812 | ||||||||
\(425\) | 3.42753e48 | 0.812431 | ||||||||
\(426\) | −7.85419e47 | −0.178248 | ||||||||
\(427\) | −5.54421e48 | −1.20482 | ||||||||
\(428\) | 6.09791e47 | 0.126903 | ||||||||
\(429\) | 1.85937e48 | 0.370600 | ||||||||
\(430\) | −3.54811e48 | −0.677377 | ||||||||
\(431\) | −9.76026e48 | −1.78497 | −0.892487 | − | 0.451074i | \(-0.851041\pi\) | ||||
−0.892487 | + | 0.451074i | \(0.851041\pi\) | |||||||
\(432\) | 1.15672e48 | 0.202665 | ||||||||
\(433\) | −4.50754e48 | −0.756683 | −0.378341 | − | 0.925666i | \(-0.623505\pi\) | ||||
−0.378341 | + | 0.925666i | \(0.623505\pi\) | |||||||
\(434\) | 8.03627e48 | 1.29269 | ||||||||
\(435\) | −1.82208e48 | −0.280876 | ||||||||
\(436\) | −4.32753e47 | −0.0639352 | ||||||||
\(437\) | −3.66888e48 | −0.519550 | ||||||||
\(438\) | 7.68527e48 | 1.04325 | ||||||||
\(439\) | 1.11863e49 | 1.45577 | 0.727886 | − | 0.685699i | \(-0.240503\pi\) | ||||
0.727886 | + | 0.685699i | \(0.240503\pi\) | |||||||
\(440\) | −9.40512e46 | −0.0117352 | ||||||||
\(441\) | −1.33460e48 | −0.159676 | ||||||||
\(442\) | 1.80070e49 | 2.06599 | ||||||||
\(443\) | 1.43677e49 | 1.58095 | 0.790474 | − | 0.612496i | \(-0.209834\pi\) | ||||
0.790474 | + | 0.612496i | \(0.209834\pi\) | |||||||
\(444\) | −2.24975e48 | −0.237438 | ||||||||
\(445\) | −4.34301e48 | −0.439674 | ||||||||
\(446\) | −7.54011e48 | −0.732290 | ||||||||
\(447\) | 5.68973e48 | 0.530155 | ||||||||
\(448\) | 7.14108e48 | 0.638441 | ||||||||
\(449\) | −9.50078e48 | −0.815084 | −0.407542 | − | 0.913187i | \(-0.633614\pi\) | ||||
−0.407542 | + | 0.913187i | \(0.633614\pi\) | |||||||
\(450\) | −4.88118e48 | −0.401877 | ||||||||
\(451\) | 7.74862e48 | 0.612292 | ||||||||
\(452\) | −1.97199e49 | −1.49569 | ||||||||
\(453\) | −7.80541e48 | −0.568302 | ||||||||
\(454\) | −5.30824e48 | −0.371037 | ||||||||
\(455\) | 6.23867e48 | 0.418679 | ||||||||
\(456\) | 3.45072e47 | 0.0222362 | ||||||||
\(457\) | −1.14567e49 | −0.708941 | −0.354471 | − | 0.935067i | \(-0.615339\pi\) | ||||
−0.354471 | + | 0.935067i | \(0.615339\pi\) | |||||||
\(458\) | −4.10270e49 | −2.43814 | ||||||||
\(459\) | 3.16771e48 | 0.180805 | ||||||||
\(460\) | −6.69615e48 | −0.367118 | ||||||||
\(461\) | 1.13686e49 | 0.598741 | 0.299370 | − | 0.954137i | \(-0.403223\pi\) | ||||
0.299370 | + | 0.954137i | \(0.403223\pi\) | |||||||
\(462\) | 4.67300e48 | 0.236439 | ||||||||
\(463\) | 1.21451e49 | 0.590409 | 0.295204 | − | 0.955434i | \(-0.404612\pi\) | ||||
0.295204 | + | 0.955434i | \(0.404612\pi\) | |||||||
\(464\) | −2.98236e49 | −1.39308 | ||||||||
\(465\) | 6.07637e48 | 0.272750 | ||||||||
\(466\) | 1.76124e49 | 0.759764 | ||||||||
\(467\) | 4.37721e49 | 1.81483 | 0.907414 | − | 0.420237i | \(-0.138053\pi\) | ||||
0.907414 | + | 0.420237i | \(0.138053\pi\) | |||||||
\(468\) | −1.24509e49 | −0.496196 | ||||||||
\(469\) | −1.60757e49 | −0.615848 | ||||||||
\(470\) | 1.72969e49 | 0.637026 | ||||||||
\(471\) | 2.02124e49 | 0.715700 | ||||||||
\(472\) | −3.69709e48 | −0.125873 | ||||||||
\(473\) | −1.64222e49 | −0.537652 | ||||||||
\(474\) | 1.03067e49 | 0.324503 | ||||||||
\(475\) | −1.40271e49 | −0.424752 | ||||||||
\(476\) | 2.19730e49 | 0.639973 | ||||||||
\(477\) | −3.25948e48 | −0.0913185 | ||||||||
\(478\) | 2.51119e49 | 0.676805 | ||||||||
\(479\) | 3.52297e49 | 0.913486 | 0.456743 | − | 0.889599i | \(-0.349016\pi\) | ||||
0.456743 | + | 0.889599i | \(0.349016\pi\) | |||||||
\(480\) | 1.18279e49 | 0.295083 | ||||||||
\(481\) | −2.86317e49 | −0.687327 | ||||||||
\(482\) | 6.03640e49 | 1.39447 | ||||||||
\(483\) | −1.98269e49 | −0.440790 | ||||||||
\(484\) | −3.68015e49 | −0.787457 | ||||||||
\(485\) | 5.30089e48 | 0.109176 | ||||||||
\(486\) | −4.51117e48 | −0.0894372 | ||||||||
\(487\) | −3.72470e49 | −0.710894 | −0.355447 | − | 0.934696i | \(-0.615671\pi\) | ||||
−0.355447 | + | 0.934696i | \(0.615671\pi\) | |||||||
\(488\) | −7.12299e48 | −0.130887 | ||||||||
\(489\) | −4.27897e49 | −0.757051 | ||||||||
\(490\) | −1.44168e49 | −0.245607 | ||||||||
\(491\) | 6.86626e49 | 1.12645 | 0.563226 | − | 0.826303i | \(-0.309560\pi\) | ||||
0.563226 | + | 0.826303i | \(0.309560\pi\) | |||||||
\(492\) | −5.18873e49 | −0.819798 | ||||||||
\(493\) | −8.16728e49 | −1.24282 | ||||||||
\(494\) | −7.36930e49 | −1.08013 | ||||||||
\(495\) | 3.53334e48 | 0.0498873 | ||||||||
\(496\) | 9.94575e49 | 1.35278 | ||||||||
\(497\) | −1.21973e49 | −0.159835 | ||||||||
\(498\) | 5.53610e49 | 0.698973 | ||||||||
\(499\) | 1.17556e50 | 1.43016 | 0.715080 | − | 0.699042i | \(-0.246390\pi\) | ||||
0.715080 | + | 0.699042i | \(0.246390\pi\) | |||||||
\(500\) | −5.52061e49 | −0.647206 | ||||||||
\(501\) | −3.36307e49 | −0.379960 | ||||||||
\(502\) | 7.78675e49 | 0.847886 | ||||||||
\(503\) | −1.53249e49 | −0.160838 | −0.0804191 | − | 0.996761i | \(-0.525626\pi\) | ||||
−0.0804191 | + | 0.996761i | \(0.525626\pi\) | |||||||
\(504\) | 1.86479e48 | 0.0188654 | ||||||||
\(505\) | −1.76411e49 | −0.172042 | ||||||||
\(506\) | −6.38325e49 | −0.600147 | ||||||||
\(507\) | −9.47660e49 | −0.859024 | ||||||||
\(508\) | −1.22726e50 | −1.07265 | ||||||||
\(509\) | −7.32055e49 | −0.616971 | −0.308486 | − | 0.951229i | \(-0.599822\pi\) | ||||
−0.308486 | + | 0.951229i | \(0.599822\pi\) | |||||||
\(510\) | 3.42185e49 | 0.278108 | ||||||||
\(511\) | 1.19350e50 | 0.935481 | ||||||||
\(512\) | 1.82675e50 | 1.38097 | ||||||||
\(513\) | −1.29638e49 | −0.0945280 | ||||||||
\(514\) | −1.06193e50 | −0.746930 | ||||||||
\(515\) | −4.65596e49 | −0.315919 | ||||||||
\(516\) | 1.09969e50 | 0.719863 | ||||||||
\(517\) | 8.00577e49 | 0.505624 | ||||||||
\(518\) | −7.19579e49 | −0.438508 | ||||||||
\(519\) | 8.93774e49 | 0.525571 | ||||||||
\(520\) | 8.01520e48 | 0.0454834 | ||||||||
\(521\) | 1.44081e50 | 0.789061 | 0.394530 | − | 0.918883i | \(-0.370907\pi\) | ||||
0.394530 | + | 0.918883i | \(0.370907\pi\) | |||||||
\(522\) | 1.16311e50 | 0.614775 | ||||||||
\(523\) | −1.41522e50 | −0.722007 | −0.361003 | − | 0.932564i | \(-0.617566\pi\) | ||||
−0.361003 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(524\) | −9.47217e49 | −0.466467 | ||||||||
\(525\) | −7.58032e49 | −0.360363 | ||||||||
\(526\) | 1.93701e50 | 0.888988 | ||||||||
\(527\) | 2.72368e50 | 1.20687 | ||||||||
\(528\) | 5.78335e49 | 0.247430 | ||||||||
\(529\) | 2.87681e49 | 0.118845 | ||||||||
\(530\) | −3.52099e49 | −0.140463 | ||||||||
\(531\) | 1.38893e50 | 0.535098 | ||||||||
\(532\) | −8.99240e49 | −0.334588 | ||||||||
\(533\) | −6.60350e50 | −2.37313 | ||||||||
\(534\) | 2.77233e50 | 0.962347 | ||||||||
\(535\) | 1.47474e49 | 0.0494504 | ||||||||
\(536\) | −2.06535e49 | −0.0669029 | ||||||||
\(537\) | −1.55012e50 | −0.485110 | ||||||||
\(538\) | −3.19429e50 | −0.965835 | ||||||||
\(539\) | −6.67273e49 | −0.194945 | ||||||||
\(540\) | −2.36605e49 | −0.0667942 | ||||||||
\(541\) | −3.29954e50 | −0.900127 | −0.450064 | − | 0.892997i | \(-0.648599\pi\) | ||||
−0.450064 | + | 0.892997i | \(0.648599\pi\) | |||||||
\(542\) | −4.64485e50 | −1.22457 | ||||||||
\(543\) | −3.33292e50 | −0.849236 | ||||||||
\(544\) | 5.30174e50 | 1.30569 | ||||||||
\(545\) | −1.04658e49 | −0.0249137 | ||||||||
\(546\) | −3.98241e50 | −0.916394 | ||||||||
\(547\) | 9.95610e49 | 0.221474 | 0.110737 | − | 0.993850i | \(-0.464679\pi\) | ||||
0.110737 | + | 0.993850i | \(0.464679\pi\) | |||||||
\(548\) | 3.54475e50 | 0.762335 | ||||||||
\(549\) | 2.67598e50 | 0.556410 | ||||||||
\(550\) | −2.44048e50 | −0.490643 | ||||||||
\(551\) | 3.34244e50 | 0.649768 | ||||||||
\(552\) | −2.54728e49 | −0.0478854 | ||||||||
\(553\) | 1.60059e50 | 0.290982 | ||||||||
\(554\) | 2.66131e50 | 0.467913 | ||||||||
\(555\) | −5.44087e49 | −0.0925227 | ||||||||
\(556\) | 7.77254e50 | 1.27844 | ||||||||
\(557\) | 9.57323e50 | 1.52313 | 0.761565 | − | 0.648088i | \(-0.224431\pi\) | ||||
0.761565 | + | 0.648088i | \(0.224431\pi\) | |||||||
\(558\) | −3.87881e50 | −0.596988 | ||||||||
\(559\) | 1.39953e51 | 2.08384 | ||||||||
\(560\) | 1.94047e50 | 0.279530 | ||||||||
\(561\) | 1.58379e50 | 0.220742 | ||||||||
\(562\) | −1.28537e51 | −1.73343 | ||||||||
\(563\) | 3.20639e50 | 0.418419 | 0.209209 | − | 0.977871i | \(-0.432911\pi\) | ||||
0.209209 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(564\) | −5.36093e50 | −0.676981 | ||||||||
\(565\) | −4.76911e50 | −0.582829 | ||||||||
\(566\) | 7.65088e50 | 0.904914 | ||||||||
\(567\) | −7.00570e49 | −0.0801983 | ||||||||
\(568\) | −1.56706e49 | −0.0173637 | ||||||||
\(569\) | −1.54737e51 | −1.65966 | −0.829829 | − | 0.558018i | \(-0.811562\pi\) | ||||
−0.829829 | + | 0.558018i | \(0.811562\pi\) | |||||||
\(570\) | −1.40038e50 | −0.145399 | ||||||||
\(571\) | −8.82178e50 | −0.886723 | −0.443362 | − | 0.896343i | \(-0.646214\pi\) | ||||
−0.443362 | + | 0.896343i | \(0.646214\pi\) | |||||||
\(572\) | −6.22519e50 | −0.605796 | ||||||||
\(573\) | 9.14879e50 | 0.861992 | ||||||||
\(574\) | −1.65961e51 | −1.51403 | ||||||||
\(575\) | 1.03546e51 | 0.914699 | ||||||||
\(576\) | −3.44674e50 | −0.294844 | ||||||||
\(577\) | −4.93183e50 | −0.408560 | −0.204280 | − | 0.978913i | \(-0.565485\pi\) | ||||
−0.204280 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(578\) | −2.03931e50 | −0.163613 | ||||||||
\(579\) | 1.05939e51 | 0.823198 | ||||||||
\(580\) | 6.10035e50 | 0.459131 | ||||||||
\(581\) | 8.59738e50 | 0.626769 | ||||||||
\(582\) | −3.38378e50 | −0.238961 | ||||||||
\(583\) | −1.62967e50 | −0.111489 | ||||||||
\(584\) | 1.53336e50 | 0.101626 | ||||||||
\(585\) | −3.01117e50 | −0.193354 | ||||||||
\(586\) | 6.67939e50 | 0.415557 | ||||||||
\(587\) | −1.61018e51 | −0.970666 | −0.485333 | − | 0.874330i | \(-0.661302\pi\) | ||||
−0.485333 | + | 0.874330i | \(0.661302\pi\) | |||||||
\(588\) | 4.46828e50 | 0.261012 | ||||||||
\(589\) | −1.11466e51 | −0.630969 | ||||||||
\(590\) | 1.50037e51 | 0.823067 | ||||||||
\(591\) | 8.68640e50 | 0.461819 | ||||||||
\(592\) | −8.90557e50 | −0.458892 | ||||||||
\(593\) | 8.02157e49 | 0.0400634 | 0.0200317 | − | 0.999799i | \(-0.493623\pi\) | ||||
0.0200317 | + | 0.999799i | \(0.493623\pi\) | |||||||
\(594\) | −2.25549e50 | −0.109192 | ||||||||
\(595\) | 5.31403e50 | 0.249379 | ||||||||
\(596\) | −1.90493e51 | −0.866611 | ||||||||
\(597\) | −1.68243e51 | −0.742012 | ||||||||
\(598\) | 5.43991e51 | 2.32606 | ||||||||
\(599\) | −4.13904e51 | −1.71595 | −0.857973 | − | 0.513694i | \(-0.828276\pi\) | ||||
−0.857973 | + | 0.513694i | \(0.828276\pi\) | |||||||
\(600\) | −9.73890e49 | −0.0391482 | ||||||||
\(601\) | 1.01480e51 | 0.395551 | 0.197776 | − | 0.980247i | \(-0.436628\pi\) | ||||
0.197776 | + | 0.980247i | \(0.436628\pi\) | |||||||
\(602\) | 3.51733e51 | 1.32947 | ||||||||
\(603\) | 7.75916e50 | 0.284410 | ||||||||
\(604\) | 2.61327e51 | 0.928968 | ||||||||
\(605\) | −8.90020e50 | −0.306849 | ||||||||
\(606\) | 1.12610e51 | 0.376561 | ||||||||
\(607\) | −1.59854e51 | −0.518482 | −0.259241 | − | 0.965813i | \(-0.583472\pi\) | ||||
−0.259241 | + | 0.965813i | \(0.583472\pi\) | |||||||
\(608\) | −2.16972e51 | −0.682633 | ||||||||
\(609\) | 1.80627e51 | 0.551269 | ||||||||
\(610\) | 2.89067e51 | 0.855849 | ||||||||
\(611\) | −6.82265e51 | −1.95970 | ||||||||
\(612\) | −1.06056e51 | −0.295551 | ||||||||
\(613\) | 3.62477e51 | 0.980081 | 0.490041 | − | 0.871700i | \(-0.336982\pi\) | ||||
0.490041 | + | 0.871700i | \(0.336982\pi\) | |||||||
\(614\) | 1.56984e51 | 0.411851 | ||||||||
\(615\) | −1.25486e51 | −0.319452 | ||||||||
\(616\) | 9.32355e49 | 0.0230323 | ||||||||
\(617\) | 2.49598e51 | 0.598364 | 0.299182 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299182 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(618\) | 2.97210e51 | 0.691475 | ||||||||
\(619\) | −2.35643e51 | −0.532080 | −0.266040 | − | 0.963962i | \(-0.585715\pi\) | ||||
−0.266040 | + | 0.963962i | \(0.585715\pi\) | |||||||
\(620\) | −2.03438e51 | −0.445847 | ||||||||
\(621\) | 9.56969e50 | 0.203565 | ||||||||
\(622\) | −1.05192e52 | −2.17200 | ||||||||
\(623\) | 4.30534e51 | 0.862936 | ||||||||
\(624\) | −4.92866e51 | −0.958990 | ||||||||
\(625\) | 3.24286e51 | 0.612558 | ||||||||
\(626\) | 6.55880e51 | 1.20282 | ||||||||
\(627\) | −6.48160e50 | −0.115407 | ||||||||
\(628\) | −6.76715e51 | −1.16991 | ||||||||
\(629\) | −2.43882e51 | −0.409395 | ||||||||
\(630\) | −7.56776e50 | −0.123358 | ||||||||
\(631\) | −4.78740e51 | −0.757804 | −0.378902 | − | 0.925437i | \(-0.623698\pi\) | ||||
−0.378902 | + | 0.925437i | \(0.623698\pi\) | |||||||
\(632\) | 2.05638e50 | 0.0316109 | ||||||||
\(633\) | 7.72451e50 | 0.115319 | ||||||||
\(634\) | −1.13276e52 | −1.64243 | ||||||||
\(635\) | −2.96805e51 | −0.417982 | ||||||||
\(636\) | 1.09128e51 | 0.149273 | ||||||||
\(637\) | 5.68661e51 | 0.755569 | ||||||||
\(638\) | 5.81529e51 | 0.750566 | ||||||||
\(639\) | 5.88719e50 | 0.0738146 | ||||||||
\(640\) | 4.72727e50 | 0.0575813 | ||||||||
\(641\) | 5.92335e51 | 0.700961 | 0.350480 | − | 0.936570i | \(-0.386018\pi\) | ||||
0.350480 | + | 0.936570i | \(0.386018\pi\) | |||||||
\(642\) | −9.41389e50 | −0.108236 | ||||||||
\(643\) | 1.23332e52 | 1.37776 | 0.688879 | − | 0.724877i | \(-0.258103\pi\) | ||||
0.688879 | + | 0.724877i | \(0.258103\pi\) | |||||||
\(644\) | 6.63807e51 | 0.720532 | ||||||||
\(645\) | 2.65952e51 | 0.280510 | ||||||||
\(646\) | −6.27709e51 | −0.643364 | ||||||||
\(647\) | 2.91813e51 | 0.290654 | 0.145327 | − | 0.989384i | \(-0.453577\pi\) | ||||
0.145327 | + | 0.989384i | \(0.453577\pi\) | |||||||
\(648\) | −9.00065e49 | −0.00871237 | ||||||||
\(649\) | 6.94437e51 | 0.653290 | ||||||||
\(650\) | 2.07982e52 | 1.90164 | ||||||||
\(651\) | −6.02367e51 | −0.535319 | ||||||||
\(652\) | 1.43261e52 | 1.23750 | ||||||||
\(653\) | 1.85059e51 | 0.155387 | 0.0776936 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776936 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(654\) | 6.68079e50 | 0.0545305 | ||||||||
\(655\) | −2.29078e51 | −0.181769 | ||||||||
\(656\) | −2.05394e52 | −1.58441 | ||||||||
\(657\) | −5.76057e51 | −0.432022 | ||||||||
\(658\) | −1.71468e52 | −1.25027 | ||||||||
\(659\) | −5.04387e51 | −0.357588 | −0.178794 | − | 0.983886i | \(-0.557220\pi\) | ||||
−0.178794 | + | 0.983886i | \(0.557220\pi\) | |||||||
\(660\) | −1.18297e51 | −0.0815476 | ||||||||
\(661\) | 1.90856e52 | 1.27932 | 0.639659 | − | 0.768659i | \(-0.279075\pi\) | ||||
0.639659 | + | 0.768659i | \(0.279075\pi\) | |||||||
\(662\) | −3.36694e52 | −2.19464 | ||||||||
\(663\) | −1.34973e52 | −0.855553 | ||||||||
\(664\) | 1.10456e51 | 0.0680894 | ||||||||
\(665\) | −2.17475e51 | −0.130380 | ||||||||
\(666\) | 3.47314e51 | 0.202511 | ||||||||
\(667\) | −2.46734e52 | −1.39927 | ||||||||
\(668\) | 1.12596e52 | 0.621096 | ||||||||
\(669\) | 5.65177e51 | 0.303250 | ||||||||
\(670\) | 8.38167e51 | 0.437468 | ||||||||
\(671\) | 1.33793e52 | 0.679310 | ||||||||
\(672\) | −1.17253e52 | −0.579151 | ||||||||
\(673\) | −7.73202e51 | −0.371548 | −0.185774 | − | 0.982593i | \(-0.559479\pi\) | ||||
−0.185774 | + | 0.982593i | \(0.559479\pi\) | |||||||
\(674\) | −2.32143e52 | −1.08529 | ||||||||
\(675\) | 3.65874e51 | 0.166422 | ||||||||
\(676\) | 3.17278e52 | 1.40419 | ||||||||
\(677\) | −4.47773e50 | −0.0192827 | −0.00964135 | − | 0.999954i | \(-0.503069\pi\) | ||||
−0.00964135 | + | 0.999954i | \(0.503069\pi\) | |||||||
\(678\) | 3.04433e52 | 1.27568 | ||||||||
\(679\) | −5.25491e51 | −0.214276 | ||||||||
\(680\) | 6.82726e50 | 0.0270914 | ||||||||
\(681\) | 3.97885e51 | 0.153651 | ||||||||
\(682\) | −1.93932e52 | −0.728850 | ||||||||
\(683\) | −3.49109e52 | −1.27696 | −0.638481 | − | 0.769637i | \(-0.720437\pi\) | ||||
−0.638481 | + | 0.769637i | \(0.720437\pi\) | |||||||
\(684\) | 4.34030e51 | 0.154519 | ||||||||
\(685\) | 8.57275e51 | 0.297060 | ||||||||
\(686\) | 4.41267e52 | 1.48835 | ||||||||
\(687\) | 3.07522e52 | 1.00966 | ||||||||
\(688\) | 4.35308e52 | 1.39127 | ||||||||
\(689\) | 1.38883e52 | 0.432110 | ||||||||
\(690\) | 1.03374e52 | 0.313116 | ||||||||
\(691\) | −4.18261e52 | −1.23340 | −0.616700 | − | 0.787198i | \(-0.711531\pi\) | ||||
−0.616700 | + | 0.787198i | \(0.711531\pi\) | |||||||
\(692\) | −2.99237e52 | −0.859118 | ||||||||
\(693\) | −3.50270e51 | −0.0979124 | ||||||||
\(694\) | −1.58909e51 | −0.0432513 | ||||||||
\(695\) | 1.87974e52 | 0.498171 | ||||||||
\(696\) | 2.32063e51 | 0.0598873 | ||||||||
\(697\) | −5.62479e52 | −1.41351 | ||||||||
\(698\) | −8.01808e52 | −1.96221 | ||||||||
\(699\) | −1.32015e52 | −0.314628 | ||||||||
\(700\) | 2.53791e52 | 0.589063 | ||||||||
\(701\) | 5.92287e52 | 1.33890 | 0.669452 | − | 0.742856i | \(-0.266529\pi\) | ||||
0.669452 | + | 0.742856i | \(0.266529\pi\) | |||||||
\(702\) | 1.92216e52 | 0.423207 | ||||||||
\(703\) | 9.98079e51 | 0.214038 | ||||||||
\(704\) | −1.72329e52 | −0.359969 | ||||||||
\(705\) | −1.29650e52 | −0.263800 | ||||||||
\(706\) | 8.30973e52 | 1.64702 | ||||||||
\(707\) | 1.74880e52 | 0.337662 | ||||||||
\(708\) | −4.65018e52 | −0.874691 | ||||||||
\(709\) | −9.83617e51 | −0.180248 | −0.0901241 | − | 0.995931i | \(-0.528726\pi\) | ||||
−0.0901241 | + | 0.995931i | \(0.528726\pi\) | |||||||
\(710\) | 6.35951e51 | 0.113539 | ||||||||
\(711\) | −7.72546e51 | −0.134381 | ||||||||
\(712\) | 5.53134e51 | 0.0937454 | ||||||||
\(713\) | 8.22824e52 | 1.35878 | ||||||||
\(714\) | −3.39218e52 | −0.545835 | ||||||||
\(715\) | −1.50552e52 | −0.236061 | ||||||||
\(716\) | 5.18982e52 | 0.792979 | ||||||||
\(717\) | −1.88229e52 | −0.280273 | ||||||||
\(718\) | −1.58287e53 | −2.29690 | ||||||||
\(719\) | −8.07338e52 | −1.14175 | −0.570875 | − | 0.821037i | \(-0.693396\pi\) | ||||
−0.570875 | + | 0.821037i | \(0.693396\pi\) | |||||||
\(720\) | −9.36592e51 | −0.129092 | ||||||||
\(721\) | 4.61558e52 | 0.620046 | ||||||||
\(722\) | −8.07891e52 | −1.05783 | ||||||||
\(723\) | −4.52465e52 | −0.577466 | ||||||||
\(724\) | 1.11587e53 | 1.38819 | ||||||||
\(725\) | −9.43328e52 | −1.14396 | ||||||||
\(726\) | 5.68138e52 | 0.671624 | ||||||||
\(727\) | 9.90481e51 | 0.114146 | 0.0570728 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570728 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(728\) | −7.94568e51 | −0.0892690 | ||||||||
\(729\) | 3.38139e51 | 0.0370370 | ||||||||
\(730\) | −6.22273e52 | −0.664520 | ||||||||
\(731\) | 1.19211e53 | 1.24120 | ||||||||
\(732\) | −8.95925e52 | −0.909529 | ||||||||
\(733\) | −8.81869e52 | −0.872932 | −0.436466 | − | 0.899721i | \(-0.643770\pi\) | ||||
−0.436466 | + | 0.899721i | \(0.643770\pi\) | |||||||
\(734\) | 1.60809e53 | 1.55215 | ||||||||
\(735\) | 1.08062e52 | 0.101709 | ||||||||
\(736\) | 1.60166e53 | 1.47004 | ||||||||
\(737\) | 3.87941e52 | 0.347230 | ||||||||
\(738\) | 8.01031e52 | 0.699209 | ||||||||
\(739\) | −1.03605e53 | −0.881978 | −0.440989 | − | 0.897513i | \(-0.645372\pi\) | ||||
−0.440989 | + | 0.897513i | \(0.645372\pi\) | |||||||
\(740\) | 1.82161e52 | 0.151241 | ||||||||
\(741\) | 5.52373e52 | 0.447297 | ||||||||
\(742\) | 3.49045e52 | 0.275682 | ||||||||
\(743\) | 1.35827e53 | 1.04639 | 0.523195 | − | 0.852213i | \(-0.324740\pi\) | ||||
0.523195 | + | 0.852213i | \(0.324740\pi\) | |||||||
\(744\) | −7.73897e51 | −0.0581546 | ||||||||
\(745\) | −4.60695e52 | −0.337694 | ||||||||
\(746\) | 1.43285e53 | 1.02455 | ||||||||
\(747\) | −4.14964e52 | −0.289454 | ||||||||
\(748\) | −5.30255e52 | −0.360832 | ||||||||
\(749\) | −1.46195e52 | −0.0970550 | ||||||||
\(750\) | 8.52266e52 | 0.552004 | ||||||||
\(751\) | 2.26512e53 | 1.43137 | 0.715687 | − | 0.698421i | \(-0.246114\pi\) | ||||
0.715687 | + | 0.698421i | \(0.246114\pi\) | |||||||
\(752\) | −2.12211e53 | −1.30839 | ||||||||
\(753\) | −5.83664e52 | −0.351120 | ||||||||
\(754\) | −4.95589e53 | −2.90905 | ||||||||
\(755\) | 6.32001e52 | 0.361992 | ||||||||
\(756\) | 2.34552e52 | 0.131095 | ||||||||
\(757\) | 2.91830e52 | 0.159168 | 0.0795841 | − | 0.996828i | \(-0.474641\pi\) | ||||
0.0795841 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(758\) | −1.86608e53 | −0.993230 | ||||||||
\(759\) | 4.78463e52 | 0.248528 | ||||||||
\(760\) | −2.79404e51 | −0.0141638 | ||||||||
\(761\) | 2.49523e52 | 0.123451 | 0.0617256 | − | 0.998093i | \(-0.480340\pi\) | ||||
0.0617256 | + | 0.998093i | \(0.480340\pi\) | |||||||
\(762\) | 1.89464e53 | 0.914868 | ||||||||
\(763\) | 1.03751e52 | 0.0488975 | ||||||||
\(764\) | −3.06303e53 | −1.40904 | ||||||||
\(765\) | −2.56489e52 | −0.115168 | ||||||||
\(766\) | 1.58982e53 | 0.696810 | ||||||||
\(767\) | −5.91811e53 | −2.53203 | ||||||||
\(768\) | −1.52451e53 | −0.636717 | ||||||||
\(769\) | 3.98900e53 | 1.62640 | 0.813199 | − | 0.581986i | \(-0.197724\pi\) | ||||
0.813199 | + | 0.581986i | \(0.197724\pi\) | |||||||
\(770\) | −3.78371e52 | −0.150605 | ||||||||
\(771\) | 7.95983e52 | 0.309313 | ||||||||
\(772\) | −3.54687e53 | −1.34563 | ||||||||
\(773\) | −1.73601e52 | −0.0643029 | −0.0321515 | − | 0.999483i | \(-0.510236\pi\) | ||||
−0.0321515 | + | 0.999483i | \(0.510236\pi\) | |||||||
\(774\) | −1.69769e53 | −0.613974 | ||||||||
\(775\) | 3.14587e53 | 1.11086 | ||||||||
\(776\) | −6.75130e51 | −0.0232780 | ||||||||
\(777\) | 5.39368e52 | 0.181592 | ||||||||
\(778\) | 4.14132e53 | 1.36150 | ||||||||
\(779\) | 2.30193e53 | 0.739008 | ||||||||
\(780\) | 1.00815e53 | 0.316063 | ||||||||
\(781\) | 2.94347e52 | 0.0901187 | ||||||||
\(782\) | 4.63366e53 | 1.38548 | ||||||||
\(783\) | −8.71821e52 | −0.254586 | ||||||||
\(784\) | 1.76876e53 | 0.504453 | ||||||||
\(785\) | −1.63659e53 | −0.455881 | ||||||||
\(786\) | 1.46230e53 | 0.397851 | ||||||||
\(787\) | 6.17560e53 | 1.64114 | 0.820572 | − | 0.571544i | \(-0.193655\pi\) | ||||
0.820572 | + | 0.571544i | \(0.193655\pi\) | |||||||
\(788\) | −2.90822e53 | −0.754906 | ||||||||
\(789\) | −1.45191e53 | −0.368141 | ||||||||
\(790\) | −8.34526e52 | −0.206699 | ||||||||
\(791\) | 4.72775e53 | 1.14390 | ||||||||
\(792\) | −4.50013e51 | −0.0106368 | ||||||||
\(793\) | −1.14021e54 | −2.63288 | ||||||||
\(794\) | 2.87169e53 | 0.647825 | ||||||||
\(795\) | 2.63919e52 | 0.0581673 | ||||||||
\(796\) | 5.63280e53 | 1.21292 | ||||||||
\(797\) | −8.27498e53 | −1.74096 | −0.870478 | − | 0.492207i | \(-0.836190\pi\) | ||||
−0.870478 | + | 0.492207i | \(0.836190\pi\) | |||||||
\(798\) | 1.38824e53 | 0.285371 | ||||||||
\(799\) | −5.81146e53 | −1.16727 | ||||||||
\(800\) | 6.12355e53 | 1.20182 | ||||||||
\(801\) | −2.07803e53 | −0.398520 | ||||||||
\(802\) | −1.30450e54 | −2.44467 | ||||||||
\(803\) | −2.88016e53 | −0.527447 | ||||||||
\(804\) | −2.59778e53 | −0.464907 | ||||||||
\(805\) | 1.60537e53 | 0.280771 | ||||||||
\(806\) | 1.65272e54 | 2.82489 | ||||||||
\(807\) | 2.39432e53 | 0.399964 | ||||||||
\(808\) | 2.24680e52 | 0.0366821 | ||||||||
\(809\) | −4.25983e53 | −0.679742 | −0.339871 | − | 0.940472i | \(-0.610383\pi\) | ||||
−0.339871 | + | 0.940472i | \(0.610383\pi\) | |||||||
\(810\) | 3.65267e52 | 0.0569689 | ||||||||
\(811\) | 3.53733e52 | 0.0539249 | 0.0269625 | − | 0.999636i | \(-0.491417\pi\) | ||||
0.0269625 | + | 0.999636i | \(0.491417\pi\) | |||||||
\(812\) | −6.04744e53 | −0.901124 | ||||||||
\(813\) | 3.48159e53 | 0.507111 | ||||||||
\(814\) | 1.73649e53 | 0.247242 | ||||||||
\(815\) | 3.46466e53 | 0.482220 | ||||||||
\(816\) | −4.19818e53 | −0.571207 | ||||||||
\(817\) | −4.87865e53 | −0.648921 | ||||||||
\(818\) | 9.95659e53 | 1.29472 | ||||||||
\(819\) | 2.98506e53 | 0.379490 | ||||||||
\(820\) | 4.20130e53 | 0.522188 | ||||||||
\(821\) | −1.14147e54 | −1.38713 | −0.693566 | − | 0.720393i | \(-0.743961\pi\) | ||||
−0.693566 | + | 0.720393i | \(0.743961\pi\) | |||||||
\(822\) | −5.47235e53 | −0.650198 | ||||||||
\(823\) | −4.03065e52 | −0.0468250 | −0.0234125 | − | 0.999726i | \(-0.507453\pi\) | ||||
−0.0234125 | + | 0.999726i | \(0.507453\pi\) | |||||||
\(824\) | 5.92992e52 | 0.0673589 | ||||||||
\(825\) | 1.82929e53 | 0.203182 | ||||||||
\(826\) | −1.48735e54 | −1.61541 | ||||||||
\(827\) | 6.45322e53 | 0.685369 | 0.342685 | − | 0.939450i | \(-0.388664\pi\) | ||||
0.342685 | + | 0.939450i | \(0.388664\pi\) | |||||||
\(828\) | −3.20395e53 | −0.332755 | ||||||||
\(829\) | 2.31995e52 | 0.0235625 | 0.0117812 | − | 0.999931i | \(-0.496250\pi\) | ||||
0.0117812 | + | 0.999931i | \(0.496250\pi\) | |||||||
\(830\) | −4.48255e53 | −0.445226 | ||||||||
\(831\) | −1.99482e53 | −0.193769 | ||||||||
\(832\) | 1.46862e54 | 1.39517 | ||||||||
\(833\) | 4.84380e53 | 0.450042 | ||||||||
\(834\) | −1.19992e54 | −1.09038 | ||||||||
\(835\) | 2.72306e53 | 0.242023 | ||||||||
\(836\) | 2.17005e53 | 0.188649 | ||||||||
\(837\) | 2.90740e53 | 0.247220 | ||||||||
\(838\) | 1.02166e54 | 0.849749 | ||||||||
\(839\) | 8.80747e53 | 0.716564 | 0.358282 | − | 0.933613i | \(-0.383363\pi\) | ||||
0.358282 | + | 0.933613i | \(0.383363\pi\) | |||||||
\(840\) | −1.50991e52 | −0.0120167 | ||||||||
\(841\) | 9.63330e53 | 0.749979 | ||||||||
\(842\) | −2.04997e54 | −1.56126 | ||||||||
\(843\) | 9.63462e53 | 0.717835 | ||||||||
\(844\) | −2.58618e53 | −0.188506 | ||||||||
\(845\) | 7.67316e53 | 0.547174 | ||||||||
\(846\) | 8.27614e53 | 0.577399 | ||||||||
\(847\) | 8.82300e53 | 0.602245 | ||||||||
\(848\) | 4.31980e53 | 0.288497 | ||||||||
\(849\) | −5.73480e53 | −0.374736 | ||||||||
\(850\) | 1.77157e54 | 1.13268 | ||||||||
\(851\) | −7.36769e53 | −0.460929 | ||||||||
\(852\) | −1.97104e53 | −0.120660 | ||||||||
\(853\) | 5.96791e53 | 0.357491 | 0.178745 | − | 0.983895i | \(-0.442796\pi\) | ||||
0.178745 | + | 0.983895i | \(0.442796\pi\) | |||||||
\(854\) | −2.86560e54 | −1.67975 | ||||||||
\(855\) | 1.04967e53 | 0.0602116 | ||||||||
\(856\) | −1.87825e52 | −0.0105436 | ||||||||
\(857\) | −5.15514e52 | −0.0283202 | −0.0141601 | − | 0.999900i | \(-0.504507\pi\) | ||||
−0.0141601 | + | 0.999900i | \(0.504507\pi\) | |||||||
\(858\) | 9.61039e53 | 0.516685 | ||||||||
\(859\) | −1.99312e53 | −0.104872 | −0.0524360 | − | 0.998624i | \(-0.516699\pi\) | ||||
−0.0524360 | + | 0.998624i | \(0.516699\pi\) | |||||||
\(860\) | −8.90413e53 | −0.458533 | ||||||||
\(861\) | 1.24398e54 | 0.626980 | ||||||||
\(862\) | −5.04472e54 | −2.48859 | ||||||||
\(863\) | −1.31893e54 | −0.636829 | −0.318415 | − | 0.947952i | \(-0.603150\pi\) | ||||
−0.318415 | + | 0.947952i | \(0.603150\pi\) | |||||||
\(864\) | 5.65936e53 | 0.267463 | ||||||||
\(865\) | −7.23685e53 | −0.334774 | ||||||||
\(866\) | −2.32979e54 | −1.05496 | ||||||||
\(867\) | 1.52859e53 | 0.0677544 | ||||||||
\(868\) | 2.01674e54 | 0.875053 | ||||||||
\(869\) | −3.86256e53 | −0.164063 | ||||||||
\(870\) | −9.41765e53 | −0.391594 | ||||||||
\(871\) | −3.30610e54 | −1.34580 | ||||||||
\(872\) | 1.33295e52 | 0.00531200 | ||||||||
\(873\) | 2.53635e53 | 0.0989568 | ||||||||
\(874\) | −1.89631e54 | −0.724350 | ||||||||
\(875\) | 1.32354e54 | 0.494982 | ||||||||
\(876\) | 1.92865e54 | 0.706200 | ||||||||
\(877\) | −1.88243e54 | −0.674880 | −0.337440 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337440 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(878\) | 5.78180e54 | 2.02962 | ||||||||
\(879\) | −5.00660e53 | −0.172087 | ||||||||
\(880\) | −4.68275e53 | −0.157606 | ||||||||
\(881\) | 1.05207e54 | 0.346728 | 0.173364 | − | 0.984858i | \(-0.444536\pi\) | ||||
0.173364 | + | 0.984858i | \(0.444536\pi\) | |||||||
\(882\) | −6.89809e53 | −0.222618 | ||||||||
\(883\) | 3.19393e54 | 1.00937 | 0.504687 | − | 0.863303i | \(-0.331608\pi\) | ||||
0.504687 | + | 0.863303i | \(0.331608\pi\) | |||||||
\(884\) | 4.51892e54 | 1.39852 | ||||||||
\(885\) | −1.12462e54 | −0.340842 | ||||||||
\(886\) | 7.42613e54 | 2.20414 | ||||||||
\(887\) | −1.83622e54 | −0.533751 | −0.266875 | − | 0.963731i | \(-0.585991\pi\) | ||||
−0.266875 | + | 0.963731i | \(0.585991\pi\) | |||||||
\(888\) | 6.92959e52 | 0.0197273 | ||||||||
\(889\) | 2.94231e54 | 0.820362 | ||||||||
\(890\) | −2.24474e54 | −0.612988 | ||||||||
\(891\) | 1.69062e53 | 0.0452178 | ||||||||
\(892\) | −1.89222e54 | −0.495704 | ||||||||
\(893\) | 2.37832e54 | 0.610265 | ||||||||
\(894\) | 2.94082e54 | 0.739135 | ||||||||
\(895\) | 1.25512e54 | 0.309001 | ||||||||
\(896\) | −4.68627e53 | −0.113013 | ||||||||
\(897\) | −4.07754e54 | −0.963249 | ||||||||
\(898\) | −4.91061e54 | −1.13638 | ||||||||
\(899\) | −7.49612e54 | −1.69935 | ||||||||
\(900\) | −1.22495e54 | −0.272040 | ||||||||
\(901\) | 1.18299e54 | 0.257379 | ||||||||
\(902\) | 4.00498e54 | 0.853649 | ||||||||
\(903\) | −2.63645e54 | −0.550550 | ||||||||
\(904\) | 6.07403e53 | 0.124268 | ||||||||
\(905\) | 2.69865e54 | 0.540939 | ||||||||
\(906\) | −4.03433e54 | −0.792319 | ||||||||
\(907\) | −8.28761e52 | −0.0159476 | −0.00797379 | − | 0.999968i | \(-0.502538\pi\) | ||||
−0.00797379 | + | 0.999968i | \(0.502538\pi\) | |||||||
\(908\) | −1.33213e54 | −0.251164 | ||||||||
\(909\) | −8.44083e53 | −0.155938 | ||||||||
\(910\) | 3.22454e54 | 0.583717 | ||||||||
\(911\) | 4.90694e54 | 0.870404 | 0.435202 | − | 0.900333i | \(-0.356677\pi\) | ||||
0.435202 | + | 0.900333i | \(0.356677\pi\) | |||||||
\(912\) | 1.71809e54 | 0.298636 | ||||||||
\(913\) | −2.07473e54 | −0.353388 | ||||||||
\(914\) | −5.92156e54 | −0.988397 | ||||||||
\(915\) | −2.16673e54 | −0.354418 | ||||||||
\(916\) | −1.02959e55 | −1.65043 | ||||||||
\(917\) | 2.27091e54 | 0.356753 | ||||||||
\(918\) | 1.63728e54 | 0.252077 | ||||||||
\(919\) | −4.20928e53 | −0.0635142 | −0.0317571 | − | 0.999496i | \(-0.510110\pi\) | ||||
−0.0317571 | + | 0.999496i | \(0.510110\pi\) | |||||||
\(920\) | 2.06252e53 | 0.0305017 | ||||||||
\(921\) | −1.17669e54 | −0.170553 | ||||||||
\(922\) | 5.87600e54 | 0.834757 | ||||||||
\(923\) | −2.50847e54 | −0.349283 | ||||||||
\(924\) | 1.17271e54 | 0.160051 | ||||||||
\(925\) | −2.81686e54 | −0.376828 | ||||||||
\(926\) | 6.27736e54 | 0.823140 | ||||||||
\(927\) | −2.22777e54 | −0.286349 | ||||||||
\(928\) | −1.45915e55 | −1.83849 | ||||||||
\(929\) | 8.91667e54 | 1.10132 | 0.550658 | − | 0.834731i | \(-0.314377\pi\) | ||||
0.550658 | + | 0.834731i | \(0.314377\pi\) | |||||||
\(930\) | 3.14066e54 | 0.380265 | ||||||||
\(931\) | −1.98231e54 | −0.235289 | ||||||||
\(932\) | 4.41990e54 | 0.514302 | ||||||||
\(933\) | 7.88474e54 | 0.899450 | ||||||||
\(934\) | 2.26242e55 | 2.53021 | ||||||||
\(935\) | −1.28239e54 | −0.140606 | ||||||||
\(936\) | 3.83509e53 | 0.0412261 | ||||||||
\(937\) | −4.22934e54 | −0.445749 | −0.222874 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222874 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(938\) | −8.30897e54 | −0.858607 | ||||||||
\(939\) | −4.91621e54 | −0.498101 | ||||||||
\(940\) | 4.34072e54 | 0.431218 | ||||||||
\(941\) | −3.94717e54 | −0.384484 | −0.192242 | − | 0.981348i | \(-0.561576\pi\) | ||||
−0.192242 | + | 0.981348i | \(0.561576\pi\) | |||||||
\(942\) | 1.04471e55 | 0.997820 | ||||||||
\(943\) | −1.69925e55 | −1.59145 | ||||||||
\(944\) | −1.84076e55 | −1.69050 | ||||||||
\(945\) | 5.67249e53 | 0.0510840 | ||||||||
\(946\) | −8.48806e54 | −0.749588 | ||||||||
\(947\) | 1.89235e55 | 1.63881 | 0.819403 | − | 0.573218i | \(-0.194305\pi\) | ||||
0.819403 | + | 0.573218i | \(0.194305\pi\) | |||||||
\(948\) | 2.58650e54 | 0.219664 | ||||||||
\(949\) | 2.45452e55 | 2.04429 | ||||||||
\(950\) | −7.25009e54 | −0.592184 | ||||||||
\(951\) | 8.49074e54 | 0.680152 | ||||||||
\(952\) | −6.76805e53 | −0.0531716 | ||||||||
\(953\) | −8.10408e54 | −0.624432 | −0.312216 | − | 0.950011i | \(-0.601071\pi\) | ||||
−0.312216 | + | 0.950011i | \(0.601071\pi\) | |||||||
\(954\) | −1.68471e54 | −0.127315 | ||||||||
\(955\) | −7.40774e54 | −0.549064 | ||||||||
\(956\) | 6.30194e54 | 0.458145 | ||||||||
\(957\) | −4.35891e54 | −0.310819 | ||||||||
\(958\) | 1.82089e55 | 1.27357 | ||||||||
\(959\) | −8.49839e54 | −0.583032 | ||||||||
\(960\) | 2.79081e54 | 0.187807 | ||||||||
\(961\) | 9.84956e54 | 0.650181 | ||||||||
\(962\) | −1.47987e55 | −0.958263 | ||||||||
\(963\) | 7.05628e53 | 0.0448218 | ||||||||
\(964\) | 1.51486e55 | 0.943947 | ||||||||
\(965\) | −8.57787e54 | −0.524354 | ||||||||
\(966\) | −1.02478e55 | −0.614544 | ||||||||
\(967\) | 5.03527e54 | 0.296233 | 0.148116 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148116 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(968\) | 1.13355e54 | 0.0654252 | ||||||||
\(969\) | 4.70506e54 | 0.266425 | ||||||||
\(970\) | 2.73984e54 | 0.152212 | ||||||||
\(971\) | 3.61276e54 | 0.196917 | 0.0984585 | − | 0.995141i | \(-0.468609\pi\) | ||||
0.0984585 | + | 0.995141i | \(0.468609\pi\) | |||||||
\(972\) | −1.13210e54 | −0.0605421 | ||||||||
\(973\) | −1.86343e55 | −0.977746 | ||||||||
\(974\) | −1.92516e55 | −0.991120 | ||||||||
\(975\) | −1.55895e55 | −0.787493 | ||||||||
\(976\) | −3.54649e55 | −1.75783 | ||||||||
\(977\) | 3.31889e55 | 1.61415 | 0.807075 | − | 0.590449i | \(-0.201049\pi\) | ||||
0.807075 | + | 0.590449i | \(0.201049\pi\) | |||||||
\(978\) | −2.21164e55 | −1.05547 | ||||||||
\(979\) | −1.03897e55 | −0.486544 | ||||||||
\(980\) | −3.61795e54 | −0.166257 | ||||||||
\(981\) | −5.00765e53 | −0.0225818 | ||||||||
\(982\) | 3.54892e55 | 1.57048 | ||||||||
\(983\) | −2.95416e55 | −1.28290 | −0.641451 | − | 0.767164i | \(-0.721667\pi\) | ||||
−0.641451 | + | 0.767164i | \(0.721667\pi\) | |||||||
\(984\) | 1.59821e54 | 0.0681123 | ||||||||
\(985\) | −7.03334e54 | −0.294165 | ||||||||
\(986\) | −4.22137e55 | −1.73273 | ||||||||
\(987\) | 1.28526e55 | 0.517754 | ||||||||
\(988\) | −1.84936e55 | −0.731168 | ||||||||
\(989\) | 3.60136e55 | 1.39745 | ||||||||
\(990\) | 1.82626e54 | 0.0695522 | ||||||||
\(991\) | 3.55938e55 | 1.33049 | 0.665245 | − | 0.746625i | \(-0.268327\pi\) | ||||
0.665245 | + | 0.746625i | \(0.268327\pi\) | |||||||
\(992\) | 4.86605e55 | 1.78530 | ||||||||
\(993\) | 2.52373e55 | 0.908827 | ||||||||
\(994\) | −6.30435e54 | −0.222839 | ||||||||
\(995\) | 1.36225e55 | 0.472641 | ||||||||
\(996\) | 1.38931e55 | 0.473152 | ||||||||
\(997\) | 9.42016e54 | 0.314918 | 0.157459 | − | 0.987526i | \(-0.449670\pi\) | ||||
0.157459 | + | 0.987526i | \(0.449670\pi\) | |||||||
\(998\) | 6.07605e55 | 1.99391 | ||||||||
\(999\) | −2.60333e54 | −0.0838624 |
(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 | 3.38.a.a.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 9.38.a.b.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.38.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.38.a.b.1.1 | 3 | 3.2 | odd | 2 |