Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,68,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, 68, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 68);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
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: | \(28.4290351930\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 20\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.64845e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.06726e9 | 0.417127 | 0.208563 | − | 0.978009i | \(-0.433121\pi\) | ||||
0.208563 | + | 0.978009i | \(0.433121\pi\) | |||||||
\(3\) | −7.82458e15 | −0.812641 | −0.406321 | − | 0.913731i | \(-0.633188\pi\) | ||||
−0.406321 | + | 0.913731i | \(0.633188\pi\) | |||||||
\(4\) | −1.21897e20 | −0.826005 | ||||||||
\(5\) | −8.33551e22 | −0.320211 | −0.160106 | − | 0.987100i | \(-0.551184\pi\) | ||||
−0.160106 | + | 0.987100i | \(0.551184\pi\) | |||||||
\(6\) | −3.96491e25 | −0.338974 | ||||||||
\(7\) | −1.15070e28 | −0.562570 | −0.281285 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281285 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(8\) | −1.36548e30 | −0.761676 | ||||||||
\(9\) | −3.14854e31 | −0.339614 | ||||||||
\(10\) | −4.22381e32 | −0.133569 | ||||||||
\(11\) | −1.09259e35 | −1.41842 | −0.709208 | − | 0.705000i | \(-0.750947\pi\) | ||||
−0.709208 | + | 0.705000i | \(0.750947\pi\) | |||||||
\(12\) | 9.53792e35 | 0.671246 | ||||||||
\(13\) | 1.54273e37 | 0.743338 | 0.371669 | − | 0.928365i | \(-0.378786\pi\) | ||||
0.371669 | + | 0.928365i | \(0.378786\pi\) | |||||||
\(14\) | −5.83087e37 | −0.234663 | ||||||||
\(15\) | 6.52218e38 | 0.260217 | ||||||||
\(16\) | 1.10696e40 | 0.508290 | ||||||||
\(17\) | 8.24456e40 | 0.496739 | 0.248370 | − | 0.968665i | \(-0.420105\pi\) | ||||
0.248370 | + | 0.968665i | \(0.420105\pi\) | |||||||
\(18\) | −1.59545e41 | −0.141662 | ||||||||
\(19\) | −5.93328e42 | −0.861091 | −0.430546 | − | 0.902569i | \(-0.641679\pi\) | ||||
−0.430546 | + | 0.902569i | \(0.641679\pi\) | |||||||
\(20\) | 1.01607e43 | 0.264496 | ||||||||
\(21\) | 9.00371e43 | 0.457167 | ||||||||
\(22\) | −5.53645e44 | −0.591659 | ||||||||
\(23\) | 2.28489e45 | 0.550785 | 0.275393 | − | 0.961332i | \(-0.411192\pi\) | ||||
0.275393 | + | 0.961332i | \(0.411192\pi\) | |||||||
\(24\) | 1.06843e46 | 0.618969 | ||||||||
\(25\) | −6.08146e46 | −0.897465 | ||||||||
\(26\) | 7.81738e46 | 0.310066 | ||||||||
\(27\) | 9.71773e47 | 1.08863 | ||||||||
\(28\) | 1.40266e48 | 0.464686 | ||||||||
\(29\) | 1.07438e49 | 1.09856 | 0.549281 | − | 0.835638i | \(-0.314902\pi\) | ||||
0.549281 | + | 0.835638i | \(0.314902\pi\) | |||||||
\(30\) | 3.30496e48 | 0.108543 | ||||||||
\(31\) | 1.32534e50 | 1.45114 | 0.725572 | − | 0.688147i | \(-0.241575\pi\) | ||||
0.725572 | + | 0.688147i | \(0.241575\pi\) | |||||||
\(32\) | 2.57601e50 | 0.973697 | ||||||||
\(33\) | 8.54908e50 | 1.15266 | ||||||||
\(34\) | 4.17773e50 | 0.207203 | ||||||||
\(35\) | 9.59164e50 | 0.180141 | ||||||||
\(36\) | 3.83798e51 | 0.280523 | ||||||||
\(37\) | −5.20056e52 | −1.51807 | −0.759037 | − | 0.651048i | \(-0.774330\pi\) | ||||
−0.759037 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(38\) | −3.00655e52 | −0.359184 | ||||||||
\(39\) | −1.20712e53 | −0.604067 | ||||||||
\(40\) | 1.13819e53 | 0.243897 | ||||||||
\(41\) | −1.63973e54 | −1.53643 | −0.768217 | − | 0.640190i | \(-0.778856\pi\) | ||||
−0.768217 | + | 0.640190i | \(0.778856\pi\) | |||||||
\(42\) | 4.56241e53 | 0.190697 | ||||||||
\(43\) | 5.64177e54 | 1.07207 | 0.536034 | − | 0.844197i | \(-0.319922\pi\) | ||||
0.536034 | + | 0.844197i | \(0.319922\pi\) | |||||||
\(44\) | 1.33184e55 | 1.17162 | ||||||||
\(45\) | 2.62447e54 | 0.108748 | ||||||||
\(46\) | 1.15781e55 | 0.229747 | ||||||||
\(47\) | 2.41027e55 | 0.232695 | 0.116347 | − | 0.993209i | \(-0.462881\pi\) | ||||
0.116347 | + | 0.993209i | \(0.462881\pi\) | |||||||
\(48\) | −8.66148e55 | −0.413057 | ||||||||
\(49\) | −2.85968e56 | −0.683515 | ||||||||
\(50\) | −3.08163e56 | −0.374356 | ||||||||
\(51\) | −6.45102e56 | −0.403671 | ||||||||
\(52\) | −1.88053e57 | −0.614001 | ||||||||
\(53\) | 2.84898e57 | 0.491414 | 0.245707 | − | 0.969344i | \(-0.420980\pi\) | ||||
0.245707 | + | 0.969344i | \(0.420980\pi\) | |||||||
\(54\) | 4.92422e57 | 0.454095 | ||||||||
\(55\) | 9.10731e57 | 0.454193 | ||||||||
\(56\) | 1.57125e58 | 0.428496 | ||||||||
\(57\) | 4.64254e58 | 0.699759 | ||||||||
\(58\) | 5.44415e58 | 0.458239 | ||||||||
\(59\) | −3.30680e59 | −1.56987 | −0.784937 | − | 0.619575i | \(-0.787305\pi\) | ||||
−0.784937 | + | 0.619575i | \(0.787305\pi\) | |||||||
\(60\) | −7.95034e58 | −0.214941 | ||||||||
\(61\) | −6.89383e59 | −1.07130 | −0.535650 | − | 0.844440i | \(-0.679933\pi\) | ||||
−0.535650 | + | 0.844440i | \(0.679933\pi\) | |||||||
\(62\) | 6.71583e59 | 0.605311 | ||||||||
\(63\) | 3.62302e59 | 0.191057 | ||||||||
\(64\) | −3.28249e59 | −0.102135 | ||||||||
\(65\) | −1.28594e60 | −0.238025 | ||||||||
\(66\) | 4.33204e60 | 0.480806 | ||||||||
\(67\) | 2.58683e61 | 1.73485 | 0.867424 | − | 0.497569i | \(-0.165774\pi\) | ||||
0.867424 | + | 0.497569i | \(0.165774\pi\) | |||||||
\(68\) | −1.00499e61 | −0.410309 | ||||||||
\(69\) | −1.78783e61 | −0.447591 | ||||||||
\(70\) | 4.86033e60 | 0.0751418 | ||||||||
\(71\) | −1.34953e62 | −1.29726 | −0.648630 | − | 0.761104i | \(-0.724658\pi\) | ||||
−0.648630 | + | 0.761104i | \(0.724658\pi\) | |||||||
\(72\) | 4.29927e61 | 0.258676 | ||||||||
\(73\) | −1.11285e62 | −0.421814 | −0.210907 | − | 0.977506i | \(-0.567642\pi\) | ||||
−0.210907 | + | 0.977506i | \(0.567642\pi\) | |||||||
\(74\) | −2.63526e62 | −0.633229 | ||||||||
\(75\) | 4.75848e62 | 0.729317 | ||||||||
\(76\) | 7.23248e62 | 0.711266 | ||||||||
\(77\) | 1.25724e63 | 0.797958 | ||||||||
\(78\) | −6.11677e62 | −0.251973 | ||||||||
\(79\) | 1.23916e63 | 0.333135 | 0.166568 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166568 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(80\) | −9.22705e62 | −0.162760 | ||||||||
\(81\) | −4.68471e63 | −0.545048 | ||||||||
\(82\) | −8.30894e63 | −0.640887 | ||||||||
\(83\) | 3.41100e63 | 0.175294 | 0.0876468 | − | 0.996152i | \(-0.472065\pi\) | ||||
0.0876468 | + | 0.996152i | \(0.472065\pi\) | |||||||
\(84\) | −1.09752e64 | −0.377623 | ||||||||
\(85\) | −6.87226e63 | −0.159062 | ||||||||
\(86\) | 2.85883e64 | 0.447188 | ||||||||
\(87\) | −8.40656e64 | −0.892736 | ||||||||
\(88\) | 1.49191e65 | 1.08037 | ||||||||
\(89\) | 3.04246e65 | 1.50890 | 0.754448 | − | 0.656360i | \(-0.227905\pi\) | ||||
0.754448 | + | 0.656360i | \(0.227905\pi\) | |||||||
\(90\) | 1.32989e64 | 0.0453618 | ||||||||
\(91\) | −1.77521e65 | −0.418180 | ||||||||
\(92\) | −2.78521e65 | −0.454951 | ||||||||
\(93\) | −1.03702e66 | −1.17926 | ||||||||
\(94\) | 1.22134e65 | 0.0970633 | ||||||||
\(95\) | 4.94569e65 | 0.275731 | ||||||||
\(96\) | −2.01562e66 | −0.791266 | ||||||||
\(97\) | 2.29986e66 | 0.638041 | 0.319021 | − | 0.947748i | \(-0.396646\pi\) | ||||
0.319021 | + | 0.947748i | \(0.396646\pi\) | |||||||
\(98\) | −1.44907e66 | −0.285112 | ||||||||
\(99\) | 3.44008e66 | 0.481714 | ||||||||
\(100\) | 7.41311e66 | 0.741311 | ||||||||
\(101\) | 8.83103e66 | 0.632769 | 0.316385 | − | 0.948631i | \(-0.397531\pi\) | ||||
0.316385 | + | 0.948631i | \(0.397531\pi\) | |||||||
\(102\) | −3.26890e66 | −0.168382 | ||||||||
\(103\) | −1.08466e67 | −0.402947 | −0.201473 | − | 0.979494i | \(-0.564573\pi\) | ||||
−0.201473 | + | 0.979494i | \(0.564573\pi\) | |||||||
\(104\) | −2.10656e67 | −0.566182 | ||||||||
\(105\) | −7.50505e66 | −0.146390 | ||||||||
\(106\) | 1.44365e67 | 0.204982 | ||||||||
\(107\) | −2.87086e67 | −0.297616 | −0.148808 | − | 0.988866i | \(-0.547544\pi\) | ||||
−0.148808 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(108\) | −1.18456e68 | −0.899211 | ||||||||
\(109\) | 5.52911e66 | 0.0308225 | 0.0154112 | − | 0.999881i | \(-0.495094\pi\) | ||||
0.0154112 | + | 0.999881i | \(0.495094\pi\) | |||||||
\(110\) | 4.61491e67 | 0.189456 | ||||||||
\(111\) | 4.06922e68 | 1.23365 | ||||||||
\(112\) | −1.27377e68 | −0.285949 | ||||||||
\(113\) | 5.97000e68 | 0.995054 | 0.497527 | − | 0.867449i | \(-0.334242\pi\) | ||||
0.497527 | + | 0.867449i | \(0.334242\pi\) | |||||||
\(114\) | 2.35250e68 | 0.291888 | ||||||||
\(115\) | −1.90457e68 | −0.176368 | ||||||||
\(116\) | −1.30963e69 | −0.907418 | ||||||||
\(117\) | −4.85734e68 | −0.252448 | ||||||||
\(118\) | −1.67564e69 | −0.654837 | ||||||||
\(119\) | −9.48698e68 | −0.279451 | ||||||||
\(120\) | −8.90589e68 | −0.198201 | ||||||||
\(121\) | 6.00410e69 | 1.01190 | ||||||||
\(122\) | −3.49328e69 | −0.446868 | ||||||||
\(123\) | 1.28302e70 | 1.24857 | ||||||||
\(124\) | −1.61555e70 | −1.19865 | ||||||||
\(125\) | 1.07176e70 | 0.607590 | ||||||||
\(126\) | 1.83588e69 | 0.0796948 | ||||||||
\(127\) | 5.53532e70 | 1.84382 | 0.921909 | − | 0.387406i | \(-0.126629\pi\) | ||||
0.921909 | + | 0.387406i | \(0.126629\pi\) | |||||||
\(128\) | −3.96786e70 | −1.01630 | ||||||||
\(129\) | −4.41445e70 | −0.871206 | ||||||||
\(130\) | −6.51619e69 | −0.0992867 | ||||||||
\(131\) | −3.42212e70 | −0.403373 | −0.201687 | − | 0.979450i | \(-0.564642\pi\) | ||||
−0.201687 | + | 0.979450i | \(0.564642\pi\) | |||||||
\(132\) | −1.04211e71 | −0.952106 | ||||||||
\(133\) | 6.82741e70 | 0.484424 | ||||||||
\(134\) | 1.31081e71 | 0.723652 | ||||||||
\(135\) | −8.10022e70 | −0.348590 | ||||||||
\(136\) | −1.12578e71 | −0.378354 | ||||||||
\(137\) | 4.32164e71 | 1.13634 | 0.568171 | − | 0.822910i | \(-0.307651\pi\) | ||||
0.568171 | + | 0.822910i | \(0.307651\pi\) | |||||||
\(138\) | −9.05938e70 | −0.186702 | ||||||||
\(139\) | 8.25204e71 | 1.33526 | 0.667629 | − | 0.744494i | \(-0.267309\pi\) | ||||
0.667629 | + | 0.744494i | \(0.267309\pi\) | |||||||
\(140\) | −1.16919e71 | −0.148798 | ||||||||
\(141\) | −1.88593e71 | −0.189098 | ||||||||
\(142\) | −6.83840e71 | −0.541122 | ||||||||
\(143\) | −1.68557e72 | −1.05436 | ||||||||
\(144\) | −3.48530e71 | −0.172622 | ||||||||
\(145\) | −8.95549e71 | −0.351772 | ||||||||
\(146\) | −5.63910e71 | −0.175950 | ||||||||
\(147\) | 2.23758e72 | 0.555453 | ||||||||
\(148\) | 6.33932e72 | 1.25394 | ||||||||
\(149\) | −6.68758e72 | −1.05567 | −0.527836 | − | 0.849346i | \(-0.676997\pi\) | ||||
−0.527836 | + | 0.849346i | \(0.676997\pi\) | |||||||
\(150\) | 2.41125e72 | 0.304218 | ||||||||
\(151\) | 2.60779e72 | 0.263357 | 0.131679 | − | 0.991292i | \(-0.457963\pi\) | ||||
0.131679 | + | 0.991292i | \(0.457963\pi\) | |||||||
\(152\) | 8.10176e72 | 0.655872 | ||||||||
\(153\) | −2.59584e72 | −0.168700 | ||||||||
\(154\) | 6.37077e72 | 0.332849 | ||||||||
\(155\) | −1.10474e73 | −0.464673 | ||||||||
\(156\) | 1.47144e73 | 0.498963 | ||||||||
\(157\) | −4.90233e73 | −1.34204 | −0.671018 | − | 0.741441i | \(-0.734143\pi\) | ||||
−0.671018 | + | 0.741441i | \(0.734143\pi\) | |||||||
\(158\) | 6.27915e72 | 0.138960 | ||||||||
\(159\) | −2.22921e73 | −0.399344 | ||||||||
\(160\) | −2.14724e73 | −0.311789 | ||||||||
\(161\) | −2.62921e73 | −0.309855 | ||||||||
\(162\) | −2.37386e73 | −0.227354 | ||||||||
\(163\) | 1.63101e74 | 1.27108 | 0.635538 | − | 0.772069i | \(-0.280778\pi\) | ||||
0.635538 | + | 0.772069i | \(0.280778\pi\) | |||||||
\(164\) | 1.99878e74 | 1.26910 | ||||||||
\(165\) | −7.12609e73 | −0.369096 | ||||||||
\(166\) | 1.72844e73 | 0.0731196 | ||||||||
\(167\) | 8.02398e73 | 0.277580 | 0.138790 | − | 0.990322i | \(-0.455679\pi\) | ||||
0.138790 | + | 0.990322i | \(0.455679\pi\) | |||||||
\(168\) | −1.22944e74 | −0.348213 | ||||||||
\(169\) | −1.92729e74 | −0.447449 | ||||||||
\(170\) | −3.48235e73 | −0.0663489 | ||||||||
\(171\) | 1.86812e74 | 0.292439 | ||||||||
\(172\) | −6.87714e74 | −0.885533 | ||||||||
\(173\) | −4.19257e74 | −0.444566 | −0.222283 | − | 0.974982i | \(-0.571351\pi\) | ||||
−0.222283 | + | 0.974982i | \(0.571351\pi\) | |||||||
\(174\) | −4.25982e74 | −0.372384 | ||||||||
\(175\) | 6.99791e74 | 0.504887 | ||||||||
\(176\) | −1.20945e75 | −0.720966 | ||||||||
\(177\) | 2.58743e75 | 1.27574 | ||||||||
\(178\) | 1.54169e75 | 0.629401 | ||||||||
\(179\) | 2.46277e75 | 0.833389 | 0.416695 | − | 0.909046i | \(-0.363188\pi\) | ||||
0.416695 | + | 0.909046i | \(0.363188\pi\) | |||||||
\(180\) | −3.19915e74 | −0.0898267 | ||||||||
\(181\) | −5.01874e75 | −1.17048 | −0.585238 | − | 0.810862i | \(-0.698999\pi\) | ||||
−0.585238 | + | 0.810862i | \(0.698999\pi\) | |||||||
\(182\) | −8.99544e74 | −0.174434 | ||||||||
\(183\) | 5.39413e75 | 0.870583 | ||||||||
\(184\) | −3.11996e75 | −0.419520 | ||||||||
\(185\) | 4.33493e75 | 0.486104 | ||||||||
\(186\) | −5.25486e75 | −0.491900 | ||||||||
\(187\) | −9.00795e75 | −0.704583 | ||||||||
\(188\) | −2.93804e75 | −0.192207 | ||||||||
\(189\) | −1.11822e76 | −0.612428 | ||||||||
\(190\) | 2.50611e75 | 0.115015 | ||||||||
\(191\) | −1.28809e75 | −0.0495825 | −0.0247912 | − | 0.999693i | \(-0.507892\pi\) | ||||
−0.0247912 | + | 0.999693i | \(0.507892\pi\) | |||||||
\(192\) | 2.56841e75 | 0.0829991 | ||||||||
\(193\) | 5.85943e76 | 1.59106 | 0.795528 | − | 0.605916i | \(-0.207193\pi\) | ||||
0.795528 | + | 0.605916i | \(0.207193\pi\) | |||||||
\(194\) | 1.16540e76 | 0.266144 | ||||||||
\(195\) | 1.00619e76 | 0.193429 | ||||||||
\(196\) | 3.48586e76 | 0.564587 | ||||||||
\(197\) | −6.37062e76 | −0.870087 | −0.435044 | − | 0.900409i | \(-0.643267\pi\) | ||||
−0.435044 | + | 0.900409i | \(0.643267\pi\) | |||||||
\(198\) | 1.74317e76 | 0.200936 | ||||||||
\(199\) | −9.92421e76 | −0.966313 | −0.483157 | − | 0.875534i | \(-0.660510\pi\) | ||||
−0.483157 | + | 0.875534i | \(0.660510\pi\) | |||||||
\(200\) | 8.30409e76 | 0.683577 | ||||||||
\(201\) | −2.02408e77 | −1.40981 | ||||||||
\(202\) | 4.47491e76 | 0.263945 | ||||||||
\(203\) | −1.23628e77 | −0.618018 | ||||||||
\(204\) | 7.86359e76 | 0.333434 | ||||||||
\(205\) | 1.36680e77 | 0.491984 | ||||||||
\(206\) | −5.49626e76 | −0.168080 | ||||||||
\(207\) | −7.19407e76 | −0.187054 | ||||||||
\(208\) | 1.70773e77 | 0.377831 | ||||||||
\(209\) | 6.48266e77 | 1.22139 | ||||||||
\(210\) | −3.80300e76 | −0.0610633 | ||||||||
\(211\) | −2.29628e77 | −0.314459 | −0.157229 | − | 0.987562i | \(-0.550256\pi\) | ||||
−0.157229 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(212\) | −3.47282e77 | −0.405911 | ||||||||
\(213\) | 1.05595e78 | 1.05421 | ||||||||
\(214\) | −1.45474e77 | −0.124144 | ||||||||
\(215\) | −4.70270e77 | −0.343288 | ||||||||
\(216\) | −1.32693e78 | −0.829180 | ||||||||
\(217\) | −1.52506e78 | −0.816369 | ||||||||
\(218\) | 2.80174e76 | 0.0128569 | ||||||||
\(219\) | 8.70759e77 | 0.342784 | ||||||||
\(220\) | −1.11015e78 | −0.375166 | ||||||||
\(221\) | 1.27191e78 | 0.369245 | ||||||||
\(222\) | 2.06198e78 | 0.514588 | ||||||||
\(223\) | −3.32066e77 | −0.0712871 | −0.0356436 | − | 0.999365i | \(-0.511348\pi\) | ||||
−0.0356436 | + | 0.999365i | \(0.511348\pi\) | |||||||
\(224\) | −2.96421e78 | −0.547773 | ||||||||
\(225\) | 1.91477e78 | 0.304792 | ||||||||
\(226\) | 3.02515e78 | 0.415064 | ||||||||
\(227\) | 1.36540e79 | 1.61582 | 0.807909 | − | 0.589307i | \(-0.200599\pi\) | ||||
0.807909 | + | 0.589307i | \(0.200599\pi\) | |||||||
\(228\) | −5.65911e78 | −0.578004 | ||||||||
\(229\) | 4.64291e78 | 0.409545 | 0.204773 | − | 0.978810i | \(-0.434354\pi\) | ||||
0.204773 | + | 0.978810i | \(0.434354\pi\) | |||||||
\(230\) | −9.65094e77 | −0.0735677 | ||||||||
\(231\) | −9.83739e78 | −0.648453 | ||||||||
\(232\) | −1.46704e79 | −0.836747 | ||||||||
\(233\) | −2.73417e79 | −1.35021 | −0.675105 | − | 0.737721i | \(-0.735902\pi\) | ||||
−0.675105 | + | 0.737721i | \(0.735902\pi\) | |||||||
\(234\) | −2.46134e78 | −0.105303 | ||||||||
\(235\) | −2.00908e78 | −0.0745116 | ||||||||
\(236\) | 4.03088e79 | 1.29672 | ||||||||
\(237\) | −9.69591e78 | −0.270719 | ||||||||
\(238\) | −4.80730e78 | −0.116566 | ||||||||
\(239\) | 5.49826e79 | 1.15850 | 0.579249 | − | 0.815150i | \(-0.303346\pi\) | ||||
0.579249 | + | 0.815150i | \(0.303346\pi\) | |||||||
\(240\) | 7.21978e78 | 0.132266 | ||||||||
\(241\) | −3.38224e79 | −0.539056 | −0.269528 | − | 0.962993i | \(-0.586868\pi\) | ||||
−0.269528 | + | 0.962993i | \(0.586868\pi\) | |||||||
\(242\) | 3.04243e79 | 0.422091 | ||||||||
\(243\) | −5.34366e79 | −0.645697 | ||||||||
\(244\) | 8.40336e79 | 0.884900 | ||||||||
\(245\) | 2.38368e79 | 0.218869 | ||||||||
\(246\) | 6.50140e79 | 0.520812 | ||||||||
\(247\) | −9.15342e79 | −0.640082 | ||||||||
\(248\) | −1.80972e80 | −1.10530 | ||||||||
\(249\) | −2.66897e79 | −0.142451 | ||||||||
\(250\) | 5.43086e79 | 0.253442 | ||||||||
\(251\) | −8.54919e79 | −0.349024 | −0.174512 | − | 0.984655i | \(-0.555835\pi\) | ||||
−0.174512 | + | 0.984655i | \(0.555835\pi\) | |||||||
\(252\) | −4.41635e79 | −0.157814 | ||||||||
\(253\) | −2.49645e80 | −0.781242 | ||||||||
\(254\) | 2.80489e80 | 0.769106 | ||||||||
\(255\) | 5.37725e79 | 0.129260 | ||||||||
\(256\) | −1.52620e80 | −0.321791 | ||||||||
\(257\) | 7.14436e80 | 1.32191 | 0.660957 | − | 0.750423i | \(-0.270150\pi\) | ||||
0.660957 | + | 0.750423i | \(0.270150\pi\) | |||||||
\(258\) | −2.23691e80 | −0.363403 | ||||||||
\(259\) | 5.98427e80 | 0.854022 | ||||||||
\(260\) | 1.56752e80 | 0.196610 | ||||||||
\(261\) | −3.38273e80 | −0.373087 | ||||||||
\(262\) | −1.73408e80 | −0.168258 | ||||||||
\(263\) | 8.76506e80 | 0.748578 | 0.374289 | − | 0.927312i | \(-0.377887\pi\) | ||||
0.374289 | + | 0.927312i | \(0.377887\pi\) | |||||||
\(264\) | −1.16736e81 | −0.877955 | ||||||||
\(265\) | −2.37477e80 | −0.157357 | ||||||||
\(266\) | 3.45962e80 | 0.202066 | ||||||||
\(267\) | −2.38059e81 | −1.22619 | ||||||||
\(268\) | −3.15326e81 | −1.43299 | ||||||||
\(269\) | 4.76354e81 | 1.91086 | 0.955428 | − | 0.295223i | \(-0.0953940\pi\) | ||||
0.955428 | + | 0.295223i | \(0.0953940\pi\) | |||||||
\(270\) | −4.10459e80 | −0.145406 | ||||||||
\(271\) | −3.02040e81 | −0.945352 | −0.472676 | − | 0.881236i | \(-0.656712\pi\) | ||||
−0.472676 | + | 0.881236i | \(0.656712\pi\) | |||||||
\(272\) | 9.12638e80 | 0.252488 | ||||||||
\(273\) | 1.38903e81 | 0.339830 | ||||||||
\(274\) | 2.18988e81 | 0.473999 | ||||||||
\(275\) | 6.64456e81 | 1.27298 | ||||||||
\(276\) | 2.17931e81 | 0.369712 | ||||||||
\(277\) | −3.30476e81 | −0.496670 | −0.248335 | − | 0.968674i | \(-0.579883\pi\) | ||||
−0.248335 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(278\) | 4.18152e81 | 0.556972 | ||||||||
\(279\) | −4.17289e81 | −0.492829 | ||||||||
\(280\) | −1.30972e81 | −0.137209 | ||||||||
\(281\) | −9.67683e81 | −0.899645 | −0.449823 | − | 0.893118i | \(-0.648513\pi\) | ||||
−0.449823 | + | 0.893118i | \(0.648513\pi\) | |||||||
\(282\) | −9.55650e80 | −0.0788776 | ||||||||
\(283\) | −1.18626e82 | −0.869630 | −0.434815 | − | 0.900520i | \(-0.643186\pi\) | ||||
−0.434815 | + | 0.900520i | \(0.643186\pi\) | |||||||
\(284\) | 1.64503e82 | 1.07154 | ||||||||
\(285\) | −3.86979e81 | −0.224071 | ||||||||
\(286\) | −8.54122e81 | −0.439802 | ||||||||
\(287\) | 1.88683e82 | 0.864351 | ||||||||
\(288\) | −8.11069e81 | −0.330681 | ||||||||
\(289\) | −2.07499e82 | −0.753250 | ||||||||
\(290\) | −4.53798e81 | −0.146733 | ||||||||
\(291\) | −1.79954e82 | −0.518499 | ||||||||
\(292\) | 1.35653e82 | 0.348421 | ||||||||
\(293\) | 7.50510e82 | 1.71906 | 0.859530 | − | 0.511085i | \(-0.170756\pi\) | ||||
0.859530 | + | 0.511085i | \(0.170756\pi\) | |||||||
\(294\) | 1.13384e82 | 0.231694 | ||||||||
\(295\) | 2.75638e82 | 0.502692 | ||||||||
\(296\) | 7.10125e82 | 1.15628 | ||||||||
\(297\) | −1.06175e83 | −1.54412 | ||||||||
\(298\) | −3.38877e82 | −0.440349 | ||||||||
\(299\) | 3.52495e82 | 0.409419 | ||||||||
\(300\) | −5.80044e82 | −0.602420 | ||||||||
\(301\) | −6.49196e82 | −0.603113 | ||||||||
\(302\) | 1.32144e82 | 0.109853 | ||||||||
\(303\) | −6.90991e82 | −0.514214 | ||||||||
\(304\) | −6.56789e82 | −0.437684 | ||||||||
\(305\) | 5.74636e82 | 0.343043 | ||||||||
\(306\) | −1.31538e82 | −0.0703691 | ||||||||
\(307\) | 1.38135e83 | 0.662475 | 0.331237 | − | 0.943547i | \(-0.392534\pi\) | ||||
0.331237 | + | 0.943547i | \(0.392534\pi\) | |||||||
\(308\) | −1.53254e83 | −0.659117 | ||||||||
\(309\) | 8.48703e82 | 0.327451 | ||||||||
\(310\) | −5.59799e82 | −0.193827 | ||||||||
\(311\) | 3.94064e83 | 1.22488 | 0.612441 | − | 0.790516i | \(-0.290188\pi\) | ||||
0.612441 | + | 0.790516i | \(0.290188\pi\) | |||||||
\(312\) | 1.64829e83 | 0.460103 | ||||||||
\(313\) | 2.68725e83 | 0.673864 | 0.336932 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336932 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(314\) | −2.48414e83 | −0.559799 | ||||||||
\(315\) | −3.01997e82 | −0.0611785 | ||||||||
\(316\) | −1.51050e83 | −0.275171 | ||||||||
\(317\) | 2.06813e83 | 0.338917 | 0.169458 | − | 0.985537i | \(-0.445798\pi\) | ||||
0.169458 | + | 0.985537i | \(0.445798\pi\) | |||||||
\(318\) | −1.12960e83 | −0.166577 | ||||||||
\(319\) | −1.17386e84 | −1.55822 | ||||||||
\(320\) | 2.73612e82 | 0.0327048 | ||||||||
\(321\) | 2.24633e83 | 0.241855 | ||||||||
\(322\) | −1.33229e83 | −0.129249 | ||||||||
\(323\) | −4.89173e83 | −0.427738 | ||||||||
\(324\) | 5.71052e83 | 0.450213 | ||||||||
\(325\) | −9.38202e83 | −0.667120 | ||||||||
\(326\) | 8.26474e83 | 0.530200 | ||||||||
\(327\) | −4.32629e82 | −0.0250476 | ||||||||
\(328\) | 2.23902e84 | 1.17026 | ||||||||
\(329\) | −2.77349e83 | −0.130907 | ||||||||
\(330\) | −3.61097e83 | −0.153960 | ||||||||
\(331\) | 5.77944e83 | 0.222663 | 0.111332 | − | 0.993783i | \(-0.464488\pi\) | ||||
0.111332 | + | 0.993783i | \(0.464488\pi\) | |||||||
\(332\) | −4.15791e83 | −0.144793 | ||||||||
\(333\) | 1.63742e84 | 0.515559 | ||||||||
\(334\) | 4.06596e83 | 0.115786 | ||||||||
\(335\) | −2.15625e84 | −0.555518 | ||||||||
\(336\) | 9.96673e83 | 0.232374 | ||||||||
\(337\) | 3.23409e84 | 0.682576 | 0.341288 | − | 0.939959i | \(-0.389137\pi\) | ||||
0.341288 | + | 0.939959i | \(0.389137\pi\) | |||||||
\(338\) | −9.76609e83 | −0.186643 | ||||||||
\(339\) | −4.67127e84 | −0.808622 | ||||||||
\(340\) | 8.37707e83 | 0.131386 | ||||||||
\(341\) | −1.44806e85 | −2.05832 | ||||||||
\(342\) | 9.46624e83 | 0.121984 | ||||||||
\(343\) | 8.10488e84 | 0.947095 | ||||||||
\(344\) | −7.70371e84 | −0.816568 | ||||||||
\(345\) | 1.49024e84 | 0.143324 | ||||||||
\(346\) | −2.12448e84 | −0.185440 | ||||||||
\(347\) | 7.38268e84 | 0.585028 | 0.292514 | − | 0.956261i | \(-0.405508\pi\) | ||||
0.292514 | + | 0.956261i | \(0.405508\pi\) | |||||||
\(348\) | 1.02473e85 | 0.737405 | ||||||||
\(349\) | 2.25397e85 | 1.47331 | 0.736657 | − | 0.676266i | \(-0.236403\pi\) | ||||
0.736657 | + | 0.676266i | \(0.236403\pi\) | |||||||
\(350\) | 3.54602e84 | 0.210602 | ||||||||
\(351\) | 1.49918e85 | 0.809217 | ||||||||
\(352\) | −2.81453e85 | −1.38111 | ||||||||
\(353\) | −2.28605e85 | −1.02008 | −0.510038 | − | 0.860152i | \(-0.670369\pi\) | ||||
−0.510038 | + | 0.860152i | \(0.670369\pi\) | |||||||
\(354\) | 1.31112e85 | 0.532147 | ||||||||
\(355\) | 1.12490e85 | 0.415397 | ||||||||
\(356\) | −3.70866e85 | −1.24636 | ||||||||
\(357\) | 7.42317e84 | 0.227093 | ||||||||
\(358\) | 1.24795e85 | 0.347629 | ||||||||
\(359\) | −7.82216e84 | −0.198455 | −0.0992276 | − | 0.995065i | \(-0.531637\pi\) | ||||
−0.0992276 | + | 0.995065i | \(0.531637\pi\) | |||||||
\(360\) | −3.58366e84 | −0.0828309 | ||||||||
\(361\) | −1.22740e85 | −0.258521 | ||||||||
\(362\) | −2.54312e85 | −0.488237 | ||||||||
\(363\) | −4.69796e85 | −0.822313 | ||||||||
\(364\) | 2.16392e85 | 0.345418 | ||||||||
\(365\) | 9.27618e84 | 0.135070 | ||||||||
\(366\) | 2.73335e85 | 0.363143 | ||||||||
\(367\) | 6.12079e85 | 0.742155 | 0.371077 | − | 0.928602i | \(-0.378988\pi\) | ||||
0.371077 | + | 0.928602i | \(0.378988\pi\) | |||||||
\(368\) | 2.52927e85 | 0.279959 | ||||||||
\(369\) | 5.16277e85 | 0.521794 | ||||||||
\(370\) | 2.19662e85 | 0.202767 | ||||||||
\(371\) | −3.27831e85 | −0.276455 | ||||||||
\(372\) | 1.26410e86 | 0.974074 | ||||||||
\(373\) | −1.28610e86 | −0.905791 | −0.452895 | − | 0.891564i | \(-0.649609\pi\) | ||||
−0.452895 | + | 0.891564i | \(0.649609\pi\) | |||||||
\(374\) | −4.56456e85 | −0.293900 | ||||||||
\(375\) | −8.38604e85 | −0.493753 | ||||||||
\(376\) | −3.29117e85 | −0.177238 | ||||||||
\(377\) | 1.65747e86 | 0.816602 | ||||||||
\(378\) | −5.66628e85 | −0.255460 | ||||||||
\(379\) | 5.21083e85 | 0.215027 | 0.107514 | − | 0.994204i | \(-0.465711\pi\) | ||||
0.107514 | + | 0.994204i | \(0.465711\pi\) | |||||||
\(380\) | −6.02864e85 | −0.227756 | ||||||||
\(381\) | −4.33115e86 | −1.49836 | ||||||||
\(382\) | −6.52708e84 | −0.0206822 | ||||||||
\(383\) | −1.33278e86 | −0.386901 | −0.193451 | − | 0.981110i | \(-0.561968\pi\) | ||||
−0.193451 | + | 0.981110i | \(0.561968\pi\) | |||||||
\(384\) | 3.10468e86 | 0.825888 | ||||||||
\(385\) | −1.04798e86 | −0.255515 | ||||||||
\(386\) | 2.96912e86 | 0.663672 | ||||||||
\(387\) | −1.77634e86 | −0.364089 | ||||||||
\(388\) | −2.80346e86 | −0.527025 | ||||||||
\(389\) | 9.94670e86 | 1.71541 | 0.857704 | − | 0.514144i | \(-0.171890\pi\) | ||||
0.857704 | + | 0.514144i | \(0.171890\pi\) | |||||||
\(390\) | 5.09864e85 | 0.0806845 | ||||||||
\(391\) | 1.88379e86 | 0.273597 | ||||||||
\(392\) | 3.90482e86 | 0.520617 | ||||||||
\(393\) | 2.67766e86 | 0.327798 | ||||||||
\(394\) | −3.22815e86 | −0.362937 | ||||||||
\(395\) | −1.03290e86 | −0.106674 | ||||||||
\(396\) | −4.19335e86 | −0.397898 | ||||||||
\(397\) | −5.37440e86 | −0.468649 | −0.234325 | − | 0.972158i | \(-0.575288\pi\) | ||||
−0.234325 | + | 0.972158i | \(0.575288\pi\) | |||||||
\(398\) | −5.02885e86 | −0.403075 | ||||||||
\(399\) | −5.34216e86 | −0.393663 | ||||||||
\(400\) | −6.73192e86 | −0.456172 | ||||||||
\(401\) | −4.13165e86 | −0.257506 | −0.128753 | − | 0.991677i | \(-0.541097\pi\) | ||||
−0.128753 | + | 0.991677i | \(0.541097\pi\) | |||||||
\(402\) | −1.02565e87 | −0.588069 | ||||||||
\(403\) | 2.04463e87 | 1.07869 | ||||||||
\(404\) | −1.07647e87 | −0.522671 | ||||||||
\(405\) | 3.90495e86 | 0.174531 | ||||||||
\(406\) | −6.26456e86 | −0.257792 | ||||||||
\(407\) | 5.68210e87 | 2.15326 | ||||||||
\(408\) | 8.80872e86 | 0.307466 | ||||||||
\(409\) | −2.75139e87 | −0.884753 | −0.442376 | − | 0.896830i | \(-0.645864\pi\) | ||||
−0.442376 | + | 0.896830i | \(0.645864\pi\) | |||||||
\(410\) | 6.92592e86 | 0.205219 | ||||||||
\(411\) | −3.38150e87 | −0.923439 | ||||||||
\(412\) | 1.32217e87 | 0.332836 | ||||||||
\(413\) | 3.80512e87 | 0.883164 | ||||||||
\(414\) | −3.64542e86 | −0.0780254 | ||||||||
\(415\) | −2.84324e86 | −0.0561310 | ||||||||
\(416\) | 3.97408e87 | 0.723786 | ||||||||
\(417\) | −6.45687e87 | −1.08509 | ||||||||
\(418\) | 3.28493e87 | 0.509472 | ||||||||
\(419\) | −1.09982e87 | −0.157454 | −0.0787268 | − | 0.996896i | \(-0.525085\pi\) | ||||
−0.0787268 | + | 0.996896i | \(0.525085\pi\) | |||||||
\(420\) | 9.14842e86 | 0.120919 | ||||||||
\(421\) | −1.24851e88 | −1.52385 | −0.761923 | − | 0.647668i | \(-0.775744\pi\) | ||||
−0.761923 | + | 0.647668i | \(0.775744\pi\) | |||||||
\(422\) | −1.16359e87 | −0.131169 | ||||||||
\(423\) | −7.58883e86 | −0.0790265 | ||||||||
\(424\) | −3.89022e87 | −0.374298 | ||||||||
\(425\) | −5.01389e87 | −0.445806 | ||||||||
\(426\) | 5.35076e87 | 0.439738 | ||||||||
\(427\) | 7.93271e87 | 0.602681 | ||||||||
\(428\) | 3.49949e87 | 0.245832 | ||||||||
\(429\) | 1.31889e88 | 0.856818 | ||||||||
\(430\) | −2.38298e87 | −0.143195 | ||||||||
\(431\) | −2.68649e87 | −0.149347 | −0.0746736 | − | 0.997208i | \(-0.523791\pi\) | ||||
−0.0746736 | + | 0.997208i | \(0.523791\pi\) | |||||||
\(432\) | 1.07571e88 | 0.553338 | ||||||||
\(433\) | 6.74157e87 | 0.320934 | 0.160467 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160467 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(434\) | −7.72789e87 | −0.340530 | ||||||||
\(435\) | 7.00729e87 | 0.285864 | ||||||||
\(436\) | −6.73981e86 | −0.0254595 | ||||||||
\(437\) | −1.35569e88 | −0.474276 | ||||||||
\(438\) | 4.41236e87 | 0.142984 | ||||||||
\(439\) | 1.55673e88 | 0.467360 | 0.233680 | − | 0.972314i | \(-0.424923\pi\) | ||||
0.233680 | + | 0.972314i | \(0.424923\pi\) | |||||||
\(440\) | −1.24358e88 | −0.345948 | ||||||||
\(441\) | 9.00382e87 | 0.232131 | ||||||||
\(442\) | 6.44509e87 | 0.154022 | ||||||||
\(443\) | −7.64486e88 | −1.69373 | −0.846866 | − | 0.531806i | \(-0.821513\pi\) | ||||
−0.846866 | + | 0.531806i | \(0.821513\pi\) | |||||||
\(444\) | −4.96025e88 | −1.01900 | ||||||||
\(445\) | −2.53604e88 | −0.483166 | ||||||||
\(446\) | −1.68266e87 | −0.0297358 | ||||||||
\(447\) | 5.23275e88 | 0.857883 | ||||||||
\(448\) | 3.77715e87 | 0.0574581 | ||||||||
\(449\) | 3.05563e88 | 0.431368 | 0.215684 | − | 0.976463i | \(-0.430802\pi\) | ||||
0.215684 | + | 0.976463i | \(0.430802\pi\) | |||||||
\(450\) | 9.70265e87 | 0.127137 | ||||||||
\(451\) | 1.79156e89 | 2.17930 | ||||||||
\(452\) | −7.27724e88 | −0.821920 | ||||||||
\(453\) | −2.04049e88 | −0.214015 | ||||||||
\(454\) | 6.91882e88 | 0.674001 | ||||||||
\(455\) | 1.47973e88 | 0.133906 | ||||||||
\(456\) | −6.33929e88 | −0.532989 | ||||||||
\(457\) | −4.84706e88 | −0.378692 | −0.189346 | − | 0.981910i | \(-0.560637\pi\) | ||||
−0.189346 | + | 0.981910i | \(0.560637\pi\) | |||||||
\(458\) | 2.35268e88 | 0.170832 | ||||||||
\(459\) | 8.01184e88 | 0.540763 | ||||||||
\(460\) | 2.32161e88 | 0.145681 | ||||||||
\(461\) | −2.17512e89 | −1.26912 | −0.634560 | − | 0.772874i | \(-0.718818\pi\) | ||||
−0.634560 | + | 0.772874i | \(0.718818\pi\) | |||||||
\(462\) | −4.98486e88 | −0.270487 | ||||||||
\(463\) | −7.57996e88 | −0.382564 | −0.191282 | − | 0.981535i | \(-0.561264\pi\) | ||||
−0.191282 | + | 0.981535i | \(0.561264\pi\) | |||||||
\(464\) | 1.18929e89 | 0.558388 | ||||||||
\(465\) | 8.64410e88 | 0.377612 | ||||||||
\(466\) | −1.38547e89 | −0.563209 | ||||||||
\(467\) | −1.00599e89 | −0.380607 | −0.190304 | − | 0.981725i | \(-0.560947\pi\) | ||||
−0.190304 | + | 0.981725i | \(0.560947\pi\) | |||||||
\(468\) | 5.92094e88 | 0.208523 | ||||||||
\(469\) | −2.97665e89 | −0.975973 | ||||||||
\(470\) | −1.01805e88 | −0.0310808 | ||||||||
\(471\) | 3.83587e89 | 1.09059 | ||||||||
\(472\) | 4.51536e89 | 1.19574 | ||||||||
\(473\) | −6.16416e89 | −1.52064 | ||||||||
\(474\) | −4.91317e88 | −0.112924 | ||||||||
\(475\) | 3.60830e89 | 0.772799 | ||||||||
\(476\) | 1.15643e89 | 0.230828 | ||||||||
\(477\) | −8.97014e88 | −0.166891 | ||||||||
\(478\) | 2.78611e89 | 0.483241 | ||||||||
\(479\) | 9.96571e89 | 1.61164 | 0.805821 | − | 0.592159i | \(-0.201724\pi\) | ||||
0.805821 | + | 0.592159i | \(0.201724\pi\) | |||||||
\(480\) | 1.68012e89 | 0.253373 | ||||||||
\(481\) | −8.02304e89 | −1.12844 | ||||||||
\(482\) | −1.71387e89 | −0.224855 | ||||||||
\(483\) | 2.05725e89 | 0.251801 | ||||||||
\(484\) | −7.31881e89 | −0.835836 | ||||||||
\(485\) | −1.91705e89 | −0.204308 | ||||||||
\(486\) | −2.70777e89 | −0.269337 | ||||||||
\(487\) | −1.58587e90 | −1.47247 | −0.736236 | − | 0.676725i | \(-0.763399\pi\) | ||||
−0.736236 | + | 0.676725i | \(0.763399\pi\) | |||||||
\(488\) | 9.41337e89 | 0.815983 | ||||||||
\(489\) | −1.27620e90 | −1.03293 | ||||||||
\(490\) | 1.20787e89 | 0.0912963 | ||||||||
\(491\) | 2.42050e90 | 1.70874 | 0.854369 | − | 0.519668i | \(-0.173944\pi\) | ||||
0.854369 | + | 0.519668i | \(0.173944\pi\) | |||||||
\(492\) | −1.56396e90 | −1.03132 | ||||||||
\(493\) | 8.85778e89 | 0.545699 | ||||||||
\(494\) | −4.63827e89 | −0.266995 | ||||||||
\(495\) | −2.86748e89 | −0.154250 | ||||||||
\(496\) | 1.46709e90 | 0.737602 | ||||||||
\(497\) | 1.55290e90 | 0.729799 | ||||||||
\(498\) | −1.35243e89 | −0.0594200 | ||||||||
\(499\) | 1.18042e90 | 0.484918 | 0.242459 | − | 0.970162i | \(-0.422046\pi\) | ||||
0.242459 | + | 0.970162i | \(0.422046\pi\) | |||||||
\(500\) | −1.30644e90 | −0.501872 | ||||||||
\(501\) | −6.27843e89 | −0.225573 | ||||||||
\(502\) | −4.33210e89 | −0.145587 | ||||||||
\(503\) | 5.26757e90 | 1.65609 | 0.828043 | − | 0.560665i | \(-0.189455\pi\) | ||||
0.828043 | + | 0.560665i | \(0.189455\pi\) | |||||||
\(504\) | −4.94715e89 | −0.145523 | ||||||||
\(505\) | −7.36111e89 | −0.202620 | ||||||||
\(506\) | −1.26502e90 | −0.325877 | ||||||||
\(507\) | 1.50803e90 | 0.363615 | ||||||||
\(508\) | −6.74738e90 | −1.52300 | ||||||||
\(509\) | −7.88037e90 | −1.66533 | −0.832666 | − | 0.553776i | \(-0.813186\pi\) | ||||
−0.832666 | + | 0.553776i | \(0.813186\pi\) | |||||||
\(510\) | 2.72479e89 | 0.0539178 | ||||||||
\(511\) | 1.28055e90 | 0.237300 | ||||||||
\(512\) | 5.08216e90 | 0.882073 | ||||||||
\(513\) | −5.76580e90 | −0.937406 | ||||||||
\(514\) | 3.62023e90 | 0.551406 | ||||||||
\(515\) | 9.04121e89 | 0.129028 | ||||||||
\(516\) | 5.38107e90 | 0.719621 | ||||||||
\(517\) | −2.63344e90 | −0.330058 | ||||||||
\(518\) | 3.03238e90 | 0.356235 | ||||||||
\(519\) | 3.28051e90 | 0.361273 | ||||||||
\(520\) | 1.75592e90 | 0.181298 | ||||||||
\(521\) | −1.48169e90 | −0.143448 | −0.0717239 | − | 0.997425i | \(-0.522850\pi\) | ||||
−0.0717239 | + | 0.997425i | \(0.522850\pi\) | |||||||
\(522\) | −1.71411e90 | −0.155625 | ||||||||
\(523\) | −1.36105e90 | −0.115896 | −0.0579481 | − | 0.998320i | \(-0.518456\pi\) | ||||
−0.0579481 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(524\) | 4.17146e90 | 0.333188 | ||||||||
\(525\) | −5.47557e90 | −0.410292 | ||||||||
\(526\) | 4.44148e90 | 0.312252 | ||||||||
\(527\) | 1.09268e91 | 0.720840 | ||||||||
\(528\) | 9.46347e90 | 0.585887 | ||||||||
\(529\) | −1.19887e91 | −0.696636 | ||||||||
\(530\) | −1.20336e90 | −0.0656376 | ||||||||
\(531\) | 1.04116e91 | 0.533151 | ||||||||
\(532\) | −8.32239e90 | −0.400137 | ||||||||
\(533\) | −2.52966e91 | −1.14209 | ||||||||
\(534\) | −1.20631e91 | −0.511477 | ||||||||
\(535\) | 2.39301e90 | 0.0953000 | ||||||||
\(536\) | −3.53226e91 | −1.32139 | ||||||||
\(537\) | −1.92702e91 | −0.677247 | ||||||||
\(538\) | 2.41381e91 | 0.797069 | ||||||||
\(539\) | 3.12446e91 | 0.969508 | ||||||||
\(540\) | 9.87391e90 | 0.287938 | ||||||||
\(541\) | −2.07523e90 | −0.0568797 | −0.0284399 | − | 0.999596i | \(-0.509054\pi\) | ||||
−0.0284399 | + | 0.999596i | \(0.509054\pi\) | |||||||
\(542\) | −1.53052e91 | −0.394332 | ||||||||
\(543\) | 3.92695e91 | 0.951177 | ||||||||
\(544\) | 2.12381e91 | 0.483674 | ||||||||
\(545\) | −4.60879e89 | −0.00986971 | ||||||||
\(546\) | 7.03855e90 | 0.141752 | ||||||||
\(547\) | 5.89842e91 | 1.11728 | 0.558638 | − | 0.829412i | \(-0.311324\pi\) | ||||
0.558638 | + | 0.829412i | \(0.311324\pi\) | |||||||
\(548\) | −5.26794e91 | −0.938625 | ||||||||
\(549\) | 2.17055e91 | 0.363829 | ||||||||
\(550\) | 3.36697e91 | 0.530993 | ||||||||
\(551\) | −6.37459e91 | −0.945962 | ||||||||
\(552\) | 2.44124e91 | 0.340919 | ||||||||
\(553\) | −1.42590e91 | −0.187412 | ||||||||
\(554\) | −1.67461e91 | −0.207174 | ||||||||
\(555\) | −3.39190e91 | −0.395029 | ||||||||
\(556\) | −1.00590e92 | −1.10293 | ||||||||
\(557\) | −5.36319e91 | −0.553700 | −0.276850 | − | 0.960913i | \(-0.589290\pi\) | ||||
−0.276850 | + | 0.960913i | \(0.589290\pi\) | |||||||
\(558\) | −2.11451e91 | −0.205572 | ||||||||
\(559\) | 8.70370e91 | 0.796908 | ||||||||
\(560\) | 1.06175e91 | 0.0915640 | ||||||||
\(561\) | 7.04834e91 | 0.572573 | ||||||||
\(562\) | −4.90350e91 | −0.375266 | ||||||||
\(563\) | −2.64660e91 | −0.190835 | −0.0954174 | − | 0.995437i | \(-0.530419\pi\) | ||||
−0.0954174 | + | 0.995437i | \(0.530419\pi\) | |||||||
\(564\) | 2.29889e91 | 0.156196 | ||||||||
\(565\) | −4.97630e91 | −0.318628 | ||||||||
\(566\) | −6.01108e91 | −0.362746 | ||||||||
\(567\) | 5.39068e91 | 0.306628 | ||||||||
\(568\) | 1.84275e92 | 0.988091 | ||||||||
\(569\) | 1.56640e92 | 0.791848 | 0.395924 | − | 0.918283i | \(-0.370424\pi\) | ||||
0.395924 | + | 0.918283i | \(0.370424\pi\) | |||||||
\(570\) | −1.96092e91 | −0.0934659 | ||||||||
\(571\) | −1.15568e92 | −0.519433 | −0.259717 | − | 0.965685i | \(-0.583629\pi\) | ||||
−0.259717 | + | 0.965685i | \(0.583629\pi\) | |||||||
\(572\) | 2.05466e92 | 0.870908 | ||||||||
\(573\) | 1.00788e91 | 0.0402928 | ||||||||
\(574\) | 9.56107e91 | 0.360544 | ||||||||
\(575\) | −1.38954e92 | −0.494310 | ||||||||
\(576\) | 1.03351e91 | 0.0346865 | ||||||||
\(577\) | −2.87114e90 | −0.00909210 | −0.00454605 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454605 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(578\) | −1.05145e92 | −0.314201 | ||||||||
\(579\) | −4.58476e92 | −1.29296 | ||||||||
\(580\) | 1.09165e92 | 0.290565 | ||||||||
\(581\) | −3.92503e91 | −0.0986149 | ||||||||
\(582\) | −9.11875e91 | −0.216280 | ||||||||
\(583\) | −3.11278e92 | −0.697030 | ||||||||
\(584\) | 1.51957e92 | 0.321286 | ||||||||
\(585\) | 4.04884e91 | 0.0808367 | ||||||||
\(586\) | 3.80303e92 | 0.717066 | ||||||||
\(587\) | 2.33816e92 | 0.416387 | 0.208194 | − | 0.978088i | \(-0.433242\pi\) | ||||
0.208194 | + | 0.978088i | \(0.433242\pi\) | |||||||
\(588\) | −2.72753e92 | −0.458807 | ||||||||
\(589\) | −7.86361e92 | −1.24957 | ||||||||
\(590\) | 1.39673e92 | 0.209686 | ||||||||
\(591\) | 4.98474e92 | 0.707069 | ||||||||
\(592\) | −5.75680e92 | −0.771621 | ||||||||
\(593\) | 1.19409e93 | 1.51253 | 0.756267 | − | 0.654263i | \(-0.227021\pi\) | ||||
0.756267 | + | 0.654263i | \(0.227021\pi\) | |||||||
\(594\) | −5.38017e92 | −0.644095 | ||||||||
\(595\) | 7.90788e91 | 0.0894833 | ||||||||
\(596\) | 8.15196e92 | 0.871991 | ||||||||
\(597\) | 7.76528e92 | 0.785266 | ||||||||
\(598\) | 1.78618e92 | 0.170780 | ||||||||
\(599\) | 1.02253e93 | 0.924434 | 0.462217 | − | 0.886767i | \(-0.347054\pi\) | ||||
0.462217 | + | 0.886767i | \(0.347054\pi\) | |||||||
\(600\) | −6.49760e92 | −0.555503 | ||||||||
\(601\) | −3.89386e92 | −0.314837 | −0.157418 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157418 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(602\) | −3.28964e92 | −0.251574 | ||||||||
\(603\) | −8.14474e92 | −0.589179 | ||||||||
\(604\) | −3.17882e92 | −0.217535 | ||||||||
\(605\) | −5.00472e92 | −0.324022 | ||||||||
\(606\) | −3.50143e92 | −0.214493 | ||||||||
\(607\) | −2.57597e93 | −1.49321 | −0.746603 | − | 0.665270i | \(-0.768317\pi\) | ||||
−0.746603 | + | 0.665270i | \(0.768317\pi\) | |||||||
\(608\) | −1.52842e93 | −0.838442 | ||||||||
\(609\) | 9.67340e92 | 0.502227 | ||||||||
\(610\) | 2.91183e92 | 0.143092 | ||||||||
\(611\) | 3.71838e92 | 0.172971 | ||||||||
\(612\) | 3.16424e92 | 0.139347 | ||||||||
\(613\) | 4.23652e93 | 1.76638 | 0.883189 | − | 0.469017i | \(-0.155392\pi\) | ||||
0.883189 | + | 0.469017i | \(0.155392\pi\) | |||||||
\(614\) | 6.99967e92 | 0.276336 | ||||||||
\(615\) | −1.06946e93 | −0.399806 | ||||||||
\(616\) | −1.71674e93 | −0.607785 | ||||||||
\(617\) | 8.17102e92 | 0.273983 | 0.136991 | − | 0.990572i | \(-0.456257\pi\) | ||||
0.136991 | + | 0.990572i | \(0.456257\pi\) | |||||||
\(618\) | 4.30060e92 | 0.136589 | ||||||||
\(619\) | −2.52814e92 | −0.0760613 | −0.0380306 | − | 0.999277i | \(-0.512108\pi\) | ||||
−0.0380306 | + | 0.999277i | \(0.512108\pi\) | |||||||
\(620\) | 1.34664e93 | 0.383822 | ||||||||
\(621\) | 2.22039e93 | 0.599599 | ||||||||
\(622\) | 1.99683e93 | 0.510931 | ||||||||
\(623\) | −3.50095e93 | −0.848859 | ||||||||
\(624\) | −1.33623e93 | −0.307041 | ||||||||
\(625\) | 3.22759e93 | 0.702907 | ||||||||
\(626\) | 1.36170e93 | 0.281087 | ||||||||
\(627\) | −5.07241e93 | −0.992548 | ||||||||
\(628\) | 5.97579e93 | 1.10853 | ||||||||
\(629\) | −4.28764e93 | −0.754087 | ||||||||
\(630\) | −1.53030e92 | −0.0255192 | ||||||||
\(631\) | −7.14064e93 | −1.12915 | −0.564577 | − | 0.825380i | \(-0.690961\pi\) | ||||
−0.564577 | + | 0.825380i | \(0.690961\pi\) | |||||||
\(632\) | −1.69205e93 | −0.253741 | ||||||||
\(633\) | 1.79675e93 | 0.255542 | ||||||||
\(634\) | 1.04798e93 | 0.141371 | ||||||||
\(635\) | −4.61397e93 | −0.590412 | ||||||||
\(636\) | 2.71733e93 | 0.329860 | ||||||||
\(637\) | −4.41169e93 | −0.508083 | ||||||||
\(638\) | −5.94824e93 | −0.649974 | ||||||||
\(639\) | 4.24905e93 | 0.440568 | ||||||||
\(640\) | 3.30741e93 | 0.325431 | ||||||||
\(641\) | 1.19515e94 | 1.11603 | 0.558017 | − | 0.829830i | \(-0.311563\pi\) | ||||
0.558017 | + | 0.829830i | \(0.311563\pi\) | |||||||
\(642\) | 1.13827e93 | 0.100884 | ||||||||
\(643\) | −3.95521e93 | −0.332738 | −0.166369 | − | 0.986064i | \(-0.553204\pi\) | ||||
−0.166369 | + | 0.986064i | \(0.553204\pi\) | |||||||
\(644\) | 3.20493e93 | 0.255942 | ||||||||
\(645\) | 3.67966e93 | 0.278970 | ||||||||
\(646\) | −2.47876e93 | −0.178421 | ||||||||
\(647\) | −9.68870e93 | −0.662174 | −0.331087 | − | 0.943600i | \(-0.607415\pi\) | ||||
−0.331087 | + | 0.943600i | \(0.607415\pi\) | |||||||
\(648\) | 6.39687e93 | 0.415150 | ||||||||
\(649\) | 3.61298e94 | 2.22673 | ||||||||
\(650\) | −4.75411e93 | −0.278273 | ||||||||
\(651\) | 1.19330e94 | 0.663416 | ||||||||
\(652\) | −1.98815e94 | −1.04992 | ||||||||
\(653\) | −2.58186e94 | −1.29522 | −0.647608 | − | 0.761974i | \(-0.724230\pi\) | ||||
−0.647608 | + | 0.761974i | \(0.724230\pi\) | |||||||
\(654\) | −2.19224e92 | −0.0104480 | ||||||||
\(655\) | 2.85251e93 | 0.129165 | ||||||||
\(656\) | −1.81511e94 | −0.780954 | ||||||||
\(657\) | 3.50386e93 | 0.143254 | ||||||||
\(658\) | −1.40540e93 | −0.0546049 | ||||||||
\(659\) | −5.02240e92 | −0.0185460 | −0.00927300 | − | 0.999957i | \(-0.502952\pi\) | ||||
−0.00927300 | + | 0.999957i | \(0.502952\pi\) | |||||||
\(660\) | 8.68648e93 | 0.304875 | ||||||||
\(661\) | −2.75448e94 | −0.918948 | −0.459474 | − | 0.888191i | \(-0.651962\pi\) | ||||
−0.459474 | + | 0.888191i | \(0.651962\pi\) | |||||||
\(662\) | 2.92859e93 | 0.0928787 | ||||||||
\(663\) | −9.95215e93 | −0.300064 | ||||||||
\(664\) | −4.65765e93 | −0.133517 | ||||||||
\(665\) | −5.69099e93 | −0.155118 | ||||||||
\(666\) | 8.29723e93 | 0.215053 | ||||||||
\(667\) | 2.45483e94 | 0.605071 | ||||||||
\(668\) | −9.78098e93 | −0.229282 | ||||||||
\(669\) | 2.59827e93 | 0.0579309 | ||||||||
\(670\) | −1.09263e94 | −0.231722 | ||||||||
\(671\) | 7.53215e94 | 1.51955 | ||||||||
\(672\) | 2.31937e94 | 0.445143 | ||||||||
\(673\) | 7.54513e94 | 1.37772 | 0.688862 | − | 0.724893i | \(-0.258111\pi\) | ||||
0.688862 | + | 0.724893i | \(0.258111\pi\) | |||||||
\(674\) | 1.63880e94 | 0.284721 | ||||||||
\(675\) | −5.90979e94 | −0.977003 | ||||||||
\(676\) | 2.34931e94 | 0.369595 | ||||||||
\(677\) | −4.57696e94 | −0.685262 | −0.342631 | − | 0.939470i | \(-0.611318\pi\) | ||||
−0.342631 | + | 0.939470i | \(0.611318\pi\) | |||||||
\(678\) | −2.36705e94 | −0.337298 | ||||||||
\(679\) | −2.64644e94 | −0.358943 | ||||||||
\(680\) | 9.38391e93 | 0.121153 | ||||||||
\(681\) | −1.06837e95 | −1.31308 | ||||||||
\(682\) | −7.33767e94 | −0.858582 | ||||||||
\(683\) | 9.77094e94 | 1.08854 | 0.544268 | − | 0.838911i | \(-0.316807\pi\) | ||||
0.544268 | + | 0.838911i | \(0.316807\pi\) | |||||||
\(684\) | −2.27718e94 | −0.241556 | ||||||||
\(685\) | −3.60230e94 | −0.363870 | ||||||||
\(686\) | 4.10695e94 | 0.395059 | ||||||||
\(687\) | −3.63288e94 | −0.332813 | ||||||||
\(688\) | 6.24520e94 | 0.544921 | ||||||||
\(689\) | 4.39519e94 | 0.365287 | ||||||||
\(690\) | 7.55145e93 | 0.0597841 | ||||||||
\(691\) | −1.14117e95 | −0.860669 | −0.430334 | − | 0.902670i | \(-0.641604\pi\) | ||||
−0.430334 | + | 0.902670i | \(0.641604\pi\) | |||||||
\(692\) | 5.11061e94 | 0.367214 | ||||||||
\(693\) | −3.95848e94 | −0.270998 | ||||||||
\(694\) | 3.74099e94 | 0.244031 | ||||||||
\(695\) | −6.87849e94 | −0.427565 | ||||||||
\(696\) | 1.14790e95 | 0.679976 | ||||||||
\(697\) | −1.35189e95 | −0.763207 | ||||||||
\(698\) | 1.14214e95 | 0.614559 | ||||||||
\(699\) | 2.13937e95 | 1.09724 | ||||||||
\(700\) | −8.53023e94 | −0.417039 | ||||||||
\(701\) | −7.36200e92 | −0.00343117 | −0.00171558 | − | 0.999999i | \(-0.500546\pi\) | ||||
−0.00171558 | + | 0.999999i | \(0.500546\pi\) | |||||||
\(702\) | 7.59672e94 | 0.337546 | ||||||||
\(703\) | 3.08564e95 | 1.30720 | ||||||||
\(704\) | 3.58643e94 | 0.144870 | ||||||||
\(705\) | 1.57202e94 | 0.0605512 | ||||||||
\(706\) | −1.15840e95 | −0.425501 | ||||||||
\(707\) | −1.01618e95 | −0.355977 | ||||||||
\(708\) | −3.15399e95 | −1.05377 | ||||||||
\(709\) | −2.42896e95 | −0.774053 | −0.387027 | − | 0.922069i | \(-0.626498\pi\) | ||||
−0.387027 | + | 0.922069i | \(0.626498\pi\) | |||||||
\(710\) | 5.70015e94 | 0.173273 | ||||||||
\(711\) | −3.90155e94 | −0.113137 | ||||||||
\(712\) | −4.15441e95 | −1.14929 | ||||||||
\(713\) | 3.02825e95 | 0.799268 | ||||||||
\(714\) | 3.76151e94 | 0.0947266 | ||||||||
\(715\) | 1.40501e95 | 0.337619 | ||||||||
\(716\) | −3.00204e95 | −0.688384 | ||||||||
\(717\) | −4.30216e95 | −0.941444 | ||||||||
\(718\) | −3.96369e94 | −0.0827810 | ||||||||
\(719\) | 6.97731e95 | 1.39082 | 0.695409 | − | 0.718614i | \(-0.255223\pi\) | ||||
0.695409 | + | 0.718614i | \(0.255223\pi\) | |||||||
\(720\) | 2.90518e94 | 0.0552757 | ||||||||
\(721\) | 1.24812e95 | 0.226686 | ||||||||
\(722\) | −6.21957e94 | −0.107836 | ||||||||
\(723\) | 2.64646e95 | 0.438059 | ||||||||
\(724\) | 6.11769e95 | 0.966819 | ||||||||
\(725\) | −6.53379e95 | −0.985920 | ||||||||
\(726\) | −2.38058e95 | −0.343009 | ||||||||
\(727\) | 5.00262e95 | 0.688327 | 0.344164 | − | 0.938910i | \(-0.388162\pi\) | ||||
0.344164 | + | 0.938910i | \(0.388162\pi\) | |||||||
\(728\) | 2.42401e95 | 0.318517 | ||||||||
\(729\) | 8.52436e95 | 1.06977 | ||||||||
\(730\) | 4.70048e94 | 0.0563412 | ||||||||
\(731\) | 4.65139e95 | 0.532538 | ||||||||
\(732\) | −6.57528e95 | −0.719106 | ||||||||
\(733\) | −8.92678e95 | −0.932634 | −0.466317 | − | 0.884618i | \(-0.654419\pi\) | ||||
−0.466317 | + | 0.884618i | \(0.654419\pi\) | |||||||
\(734\) | 3.10156e95 | 0.309573 | ||||||||
\(735\) | −1.86513e95 | −0.177862 | ||||||||
\(736\) | 5.88590e95 | 0.536298 | ||||||||
\(737\) | −2.82635e96 | −2.46074 | ||||||||
\(738\) | 2.61611e95 | 0.217654 | ||||||||
\(739\) | 3.28768e95 | 0.261397 | 0.130699 | − | 0.991422i | \(-0.458278\pi\) | ||||
0.130699 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(740\) | −5.28415e95 | −0.401525 | ||||||||
\(741\) | 7.16217e95 | 0.520157 | ||||||||
\(742\) | −1.66120e95 | −0.115317 | ||||||||
\(743\) | −1.93595e96 | −1.28460 | −0.642301 | − | 0.766453i | \(-0.722020\pi\) | ||||
−0.642301 | + | 0.766453i | \(0.722020\pi\) | |||||||
\(744\) | 1.41603e96 | 0.898213 | ||||||||
\(745\) | 5.57444e95 | 0.338038 | ||||||||
\(746\) | −6.51698e95 | −0.377830 | ||||||||
\(747\) | −1.07397e95 | −0.0595322 | ||||||||
\(748\) | 1.09804e96 | 0.581989 | ||||||||
\(749\) | 3.30349e95 | 0.167430 | ||||||||
\(750\) | −4.24942e95 | −0.205957 | ||||||||
\(751\) | 2.33056e96 | 1.08025 | 0.540123 | − | 0.841586i | \(-0.318378\pi\) | ||||
0.540123 | + | 0.841586i | \(0.318378\pi\) | |||||||
\(752\) | 2.66806e95 | 0.118277 | ||||||||
\(753\) | 6.68938e95 | 0.283631 | ||||||||
\(754\) | 8.39883e95 | 0.340627 | ||||||||
\(755\) | −2.17373e95 | −0.0843301 | ||||||||
\(756\) | 1.36307e96 | 0.505869 | ||||||||
\(757\) | −3.90449e96 | −1.38628 | −0.693141 | − | 0.720802i | \(-0.743774\pi\) | ||||
−0.693141 | + | 0.720802i | \(0.743774\pi\) | |||||||
\(758\) | 2.64046e95 | 0.0896936 | ||||||||
\(759\) | 1.95337e96 | 0.634869 | ||||||||
\(760\) | −6.75323e95 | −0.210018 | ||||||||
\(761\) | 4.58353e95 | 0.136400 | 0.0681999 | − | 0.997672i | \(-0.478274\pi\) | ||||
0.0681999 | + | 0.997672i | \(0.478274\pi\) | |||||||
\(762\) | −2.19471e96 | −0.625007 | ||||||||
\(763\) | −6.36232e94 | −0.0173398 | ||||||||
\(764\) | 1.57014e95 | 0.0409554 | ||||||||
\(765\) | 2.16376e95 | 0.0540196 | ||||||||
\(766\) | −6.75355e95 | −0.161387 | ||||||||
\(767\) | −5.10148e96 | −1.16695 | ||||||||
\(768\) | 1.19419e96 | 0.261501 | ||||||||
\(769\) | 6.37251e96 | 1.33591 | 0.667956 | − | 0.744201i | \(-0.267169\pi\) | ||||
0.667956 | + | 0.744201i | \(0.267169\pi\) | |||||||
\(770\) | −5.31036e95 | −0.106582 | ||||||||
\(771\) | −5.59016e96 | −1.07424 | ||||||||
\(772\) | −7.14246e96 | −1.31422 | ||||||||
\(773\) | 1.01535e97 | 1.78897 | 0.894486 | − | 0.447096i | \(-0.147542\pi\) | ||||
0.894486 | + | 0.447096i | \(0.147542\pi\) | |||||||
\(774\) | −9.00115e95 | −0.151871 | ||||||||
\(775\) | −8.05999e96 | −1.30235 | ||||||||
\(776\) | −3.14041e96 | −0.485980 | ||||||||
\(777\) | −4.68244e96 | −0.694014 | ||||||||
\(778\) | 5.04025e96 | 0.715542 | ||||||||
\(779\) | 9.72899e96 | 1.32301 | ||||||||
\(780\) | −1.22652e96 | −0.159774 | ||||||||
\(781\) | 1.47448e97 | 1.84005 | ||||||||
\(782\) | 9.54564e95 | 0.114124 | ||||||||
\(783\) | 1.04405e97 | 1.19592 | ||||||||
\(784\) | −3.16554e96 | −0.347424 | ||||||||
\(785\) | 4.08634e96 | 0.429735 | ||||||||
\(786\) | 1.35684e96 | 0.136733 | ||||||||
\(787\) | −1.79495e97 | −1.73340 | −0.866699 | − | 0.498832i | \(-0.833762\pi\) | ||||
−0.866699 | + | 0.498832i | \(0.833762\pi\) | |||||||
\(788\) | 7.76558e96 | 0.718697 | ||||||||
\(789\) | −6.85829e96 | −0.608326 | ||||||||
\(790\) | −5.23399e95 | −0.0444964 | ||||||||
\(791\) | −6.86966e96 | −0.559787 | ||||||||
\(792\) | −4.69735e96 | −0.366910 | ||||||||
\(793\) | −1.06353e97 | −0.796338 | ||||||||
\(794\) | −2.72334e96 | −0.195486 | ||||||||
\(795\) | 1.85816e96 | 0.127874 | ||||||||
\(796\) | 1.20973e97 | 0.798180 | ||||||||
\(797\) | −2.24378e96 | −0.141947 | −0.0709737 | − | 0.997478i | \(-0.522611\pi\) | ||||
−0.0709737 | + | 0.997478i | \(0.522611\pi\) | |||||||
\(798\) | −2.70701e96 | −0.164207 | ||||||||
\(799\) | 1.98716e96 | 0.115589 | ||||||||
\(800\) | −1.56659e97 | −0.873859 | ||||||||
\(801\) | −9.57931e96 | −0.512442 | ||||||||
\(802\) | −2.09361e96 | −0.107413 | ||||||||
\(803\) | 1.21589e97 | 0.598308 | ||||||||
\(804\) | 2.46729e97 | 1.16451 | ||||||||
\(805\) | 2.19158e96 | 0.0992191 | ||||||||
\(806\) | 1.03607e97 | 0.449950 | ||||||||
\(807\) | −3.72727e97 | −1.55284 | ||||||||
\(808\) | −1.20586e97 | −0.481965 | ||||||||
\(809\) | 4.98406e97 | 1.91121 | 0.955603 | − | 0.294658i | \(-0.0952057\pi\) | ||||
0.955603 | + | 0.294658i | \(0.0952057\pi\) | |||||||
\(810\) | 1.97874e96 | 0.0728014 | ||||||||
\(811\) | −6.56249e96 | −0.231670 | −0.115835 | − | 0.993268i | \(-0.536954\pi\) | ||||
−0.115835 | + | 0.993268i | \(0.536954\pi\) | |||||||
\(812\) | 1.50699e97 | 0.510486 | ||||||||
\(813\) | 2.36334e97 | 0.768232 | ||||||||
\(814\) | 2.87926e97 | 0.898181 | ||||||||
\(815\) | −1.35953e97 | −0.407013 | ||||||||
\(816\) | −7.14101e96 | −0.205182 | ||||||||
\(817\) | −3.34742e97 | −0.923148 | ||||||||
\(818\) | −1.39420e97 | −0.369054 | ||||||||
\(819\) | 5.58932e96 | 0.142020 | ||||||||
\(820\) | −1.66609e97 | −0.406381 | ||||||||
\(821\) | −1.14583e96 | −0.0268302 | −0.0134151 | − | 0.999910i | \(-0.504270\pi\) | ||||
−0.0134151 | + | 0.999910i | \(0.504270\pi\) | |||||||
\(822\) | −1.71349e97 | −0.385191 | ||||||||
\(823\) | −4.59764e95 | −0.00992295 | −0.00496147 | − | 0.999988i | \(-0.501579\pi\) | ||||
−0.00496147 | + | 0.999988i | \(0.501579\pi\) | |||||||
\(824\) | 1.48108e97 | 0.306915 | ||||||||
\(825\) | −5.19908e97 | −1.03447 | ||||||||
\(826\) | 1.92815e97 | 0.368391 | ||||||||
\(827\) | −7.95450e97 | −1.45941 | −0.729707 | − | 0.683760i | \(-0.760343\pi\) | ||||
−0.729707 | + | 0.683760i | \(0.760343\pi\) | |||||||
\(828\) | 8.76934e96 | 0.154508 | ||||||||
\(829\) | 9.08914e97 | 1.53796 | 0.768982 | − | 0.639271i | \(-0.220764\pi\) | ||||
0.768982 | + | 0.639271i | \(0.220764\pi\) | |||||||
\(830\) | −1.44074e96 | −0.0234137 | ||||||||
\(831\) | 2.58584e97 | 0.403614 | ||||||||
\(832\) | −5.06398e96 | −0.0759208 | ||||||||
\(833\) | −2.35768e97 | −0.339529 | ||||||||
\(834\) | −3.27186e97 | −0.452619 | ||||||||
\(835\) | −6.68839e96 | −0.0888843 | ||||||||
\(836\) | −7.90216e97 | −1.00887 | ||||||||
\(837\) | 1.28793e98 | 1.57975 | ||||||||
\(838\) | −5.57308e96 | −0.0656781 | ||||||||
\(839\) | 8.73266e97 | 0.988828 | 0.494414 | − | 0.869227i | \(-0.335383\pi\) | ||||
0.494414 | + | 0.869227i | \(0.335383\pi\) | |||||||
\(840\) | 1.02480e97 | 0.111502 | ||||||||
\(841\) | 1.97831e97 | 0.206837 | ||||||||
\(842\) | −6.32651e97 | −0.635636 | ||||||||
\(843\) | 7.57171e97 | 0.731089 | ||||||||
\(844\) | 2.79910e97 | 0.259744 | ||||||||
\(845\) | 1.60650e97 | 0.143278 | ||||||||
\(846\) | −3.84546e96 | −0.0329641 | ||||||||
\(847\) | −6.90890e97 | −0.569265 | ||||||||
\(848\) | 3.15370e97 | 0.249781 | ||||||||
\(849\) | 9.28198e97 | 0.706697 | ||||||||
\(850\) | −2.54067e97 | −0.185958 | ||||||||
\(851\) | −1.18827e98 | −0.836132 | ||||||||
\(852\) | −1.28717e98 | −0.870780 | ||||||||
\(853\) | −5.65226e97 | −0.367646 | −0.183823 | − | 0.982959i | \(-0.558847\pi\) | ||||
−0.183823 | + | 0.982959i | \(0.558847\pi\) | |||||||
\(854\) | 4.01971e97 | 0.251394 | ||||||||
\(855\) | −1.55717e97 | −0.0936422 | ||||||||
\(856\) | 3.92010e97 | 0.226687 | ||||||||
\(857\) | −3.44343e98 | −1.91484 | −0.957422 | − | 0.288692i | \(-0.906780\pi\) | ||||
−0.957422 | + | 0.288692i | \(0.906780\pi\) | |||||||
\(858\) | 6.68314e97 | 0.357402 | ||||||||
\(859\) | 1.63520e97 | 0.0841008 | 0.0420504 | − | 0.999115i | \(-0.486611\pi\) | ||||
0.0420504 | + | 0.999115i | \(0.486611\pi\) | |||||||
\(860\) | 5.73244e97 | 0.283558 | ||||||||
\(861\) | −1.47637e98 | −0.702407 | ||||||||
\(862\) | −1.36131e97 | −0.0622967 | ||||||||
\(863\) | 1.28936e98 | 0.567559 | 0.283779 | − | 0.958890i | \(-0.408412\pi\) | ||||
0.283779 | + | 0.958890i | \(0.408412\pi\) | |||||||
\(864\) | 2.50330e98 | 1.05999 | ||||||||
\(865\) | 3.49472e97 | 0.142355 | ||||||||
\(866\) | 3.41612e97 | 0.133870 | ||||||||
\(867\) | 1.62360e98 | 0.612122 | ||||||||
\(868\) | 1.85900e98 | 0.674326 | ||||||||
\(869\) | −1.35390e98 | −0.472524 | ||||||||
\(870\) | 3.55077e97 | 0.119242 | ||||||||
\(871\) | 3.99076e98 | 1.28958 | ||||||||
\(872\) | −7.54987e96 | −0.0234767 | ||||||||
\(873\) | −7.24122e97 | −0.216688 | ||||||||
\(874\) | −6.86962e97 | −0.197833 | ||||||||
\(875\) | −1.23327e98 | −0.341812 | ||||||||
\(876\) | −1.06143e98 | −0.283141 | ||||||||
\(877\) | −3.61956e98 | −0.929329 | −0.464665 | − | 0.885487i | \(-0.653825\pi\) | ||||
−0.464665 | + | 0.885487i | \(0.653825\pi\) | |||||||
\(878\) | 7.88834e97 | 0.194948 | ||||||||
\(879\) | −5.87242e98 | −1.39698 | ||||||||
\(880\) | 1.00814e98 | 0.230862 | ||||||||
\(881\) | 2.86429e98 | 0.631428 | 0.315714 | − | 0.948854i | \(-0.397756\pi\) | ||||
0.315714 | + | 0.948854i | \(0.397756\pi\) | |||||||
\(882\) | 4.56246e97 | 0.0968282 | ||||||||
\(883\) | 4.85729e98 | 0.992454 | 0.496227 | − | 0.868193i | \(-0.334718\pi\) | ||||
0.496227 | + | 0.868193i | \(0.334718\pi\) | |||||||
\(884\) | −1.55042e98 | −0.304998 | ||||||||
\(885\) | −2.15675e98 | −0.408508 | ||||||||
\(886\) | −3.87385e98 | −0.706501 | ||||||||
\(887\) | 5.57320e98 | 0.978730 | 0.489365 | − | 0.872079i | \(-0.337229\pi\) | ||||
0.489365 | + | 0.872079i | \(0.337229\pi\) | |||||||
\(888\) | −5.55643e98 | −0.939640 | ||||||||
\(889\) | −6.36947e98 | −1.03728 | ||||||||
\(890\) | −1.28508e98 | −0.201541 | ||||||||
\(891\) | 5.11848e98 | 0.773105 | ||||||||
\(892\) | 4.04778e97 | 0.0588835 | ||||||||
\(893\) | −1.43008e98 | −0.200372 | ||||||||
\(894\) | 2.65157e98 | 0.357846 | ||||||||
\(895\) | −2.05285e98 | −0.266861 | ||||||||
\(896\) | 4.56580e98 | 0.571740 | ||||||||
\(897\) | −2.75813e98 | −0.332711 | ||||||||
\(898\) | 1.54836e98 | 0.179935 | ||||||||
\(899\) | 1.42392e99 | 1.59417 | ||||||||
\(900\) | −2.33405e98 | −0.251759 | ||||||||
\(901\) | 2.34886e98 | 0.244105 | ||||||||
\(902\) | 9.07829e98 | 0.909044 | ||||||||
\(903\) | 5.07969e98 | 0.490114 | ||||||||
\(904\) | −8.15190e98 | −0.757908 | ||||||||
\(905\) | 4.18337e98 | 0.374800 | ||||||||
\(906\) | −1.03397e98 | −0.0892714 | ||||||||
\(907\) | −1.07550e99 | −0.894882 | −0.447441 | − | 0.894313i | \(-0.647665\pi\) | ||||
−0.447441 | + | 0.894313i | \(0.647665\pi\) | |||||||
\(908\) | −1.66438e99 | −1.33467 | ||||||||
\(909\) | −2.78049e98 | −0.214897 | ||||||||
\(910\) | 7.49815e97 | 0.0558557 | ||||||||
\(911\) | 9.91254e98 | 0.711737 | 0.355868 | − | 0.934536i | \(-0.384185\pi\) | ||||
0.355868 | + | 0.934536i | \(0.384185\pi\) | |||||||
\(912\) | 5.13910e98 | 0.355680 | ||||||||
\(913\) | −3.72684e98 | −0.248639 | ||||||||
\(914\) | −2.45613e98 | −0.157962 | ||||||||
\(915\) | −4.49628e98 | −0.278771 | ||||||||
\(916\) | −5.65957e98 | −0.338287 | ||||||||
\(917\) | 3.93782e98 | 0.226926 | ||||||||
\(918\) | 4.05980e98 | 0.225567 | ||||||||
\(919\) | −1.32361e99 | −0.709073 | −0.354537 | − | 0.935042i | \(-0.615361\pi\) | ||||
−0.354537 | + | 0.935042i | \(0.615361\pi\) | |||||||
\(920\) | 2.60065e98 | 0.134335 | ||||||||
\(921\) | −1.08085e99 | −0.538354 | ||||||||
\(922\) | −1.10219e99 | −0.529383 | ||||||||
\(923\) | −2.08195e99 | −0.964302 | ||||||||
\(924\) | 1.19915e99 | 0.535626 | ||||||||
\(925\) | 3.16270e99 | 1.36242 | ||||||||
\(926\) | −3.84096e98 | −0.159578 | ||||||||
\(927\) | 3.41511e98 | 0.136846 | ||||||||
\(928\) | 2.76761e99 | 1.06967 | ||||||||
\(929\) | −1.24297e98 | −0.0463377 | −0.0231688 | − | 0.999732i | \(-0.507376\pi\) | ||||
−0.0231688 | + | 0.999732i | \(0.507376\pi\) | |||||||
\(930\) | 4.38019e98 | 0.157512 | ||||||||
\(931\) | 1.69673e99 | 0.588569 | ||||||||
\(932\) | 3.33286e99 | 1.11528 | ||||||||
\(933\) | −3.08339e99 | −0.995389 | ||||||||
\(934\) | −5.09760e98 | −0.158761 | ||||||||
\(935\) | 7.50858e98 | 0.225615 | ||||||||
\(936\) | 6.63259e98 | 0.192284 | ||||||||
\(937\) | 4.03865e99 | 1.12969 | 0.564846 | − | 0.825197i | \(-0.308936\pi\) | ||||
0.564846 | + | 0.825197i | \(0.308936\pi\) | |||||||
\(938\) | −1.50835e99 | −0.407105 | ||||||||
\(939\) | −2.10266e99 | −0.547610 | ||||||||
\(940\) | 2.44901e98 | 0.0615470 | ||||||||
\(941\) | −7.13430e99 | −1.73021 | −0.865105 | − | 0.501591i | \(-0.832748\pi\) | ||||
−0.865105 | + | 0.501591i | \(0.832748\pi\) | |||||||
\(942\) | 1.94373e99 | 0.454916 | ||||||||
\(943\) | −3.74660e99 | −0.846244 | ||||||||
\(944\) | −3.66048e99 | −0.797952 | ||||||||
\(945\) | 9.32089e98 | 0.196106 | ||||||||
\(946\) | −3.12354e99 | −0.634298 | ||||||||
\(947\) | 3.01348e99 | 0.590668 | 0.295334 | − | 0.955394i | \(-0.404569\pi\) | ||||
0.295334 | + | 0.955394i | \(0.404569\pi\) | |||||||
\(948\) | 1.18190e99 | 0.223616 | ||||||||
\(949\) | −1.71682e99 | −0.313551 | ||||||||
\(950\) | 1.82842e99 | 0.322355 | ||||||||
\(951\) | −1.61823e99 | −0.275418 | ||||||||
\(952\) | 1.29543e99 | 0.212851 | ||||||||
\(953\) | 4.15491e99 | 0.659097 | 0.329549 | − | 0.944139i | \(-0.393103\pi\) | ||||
0.329549 | + | 0.944139i | \(0.393103\pi\) | |||||||
\(954\) | −4.54540e98 | −0.0696148 | ||||||||
\(955\) | 1.07369e98 | 0.0158769 | ||||||||
\(956\) | −6.70220e99 | −0.956926 | ||||||||
\(957\) | 9.18494e99 | 1.26627 | ||||||||
\(958\) | 5.04988e99 | 0.672259 | ||||||||
\(959\) | −4.97289e99 | −0.639272 | ||||||||
\(960\) | −2.14090e98 | −0.0265773 | ||||||||
\(961\) | 9.22395e99 | 1.10582 | ||||||||
\(962\) | −4.06548e99 | −0.470703 | ||||||||
\(963\) | 9.03904e98 | 0.101075 | ||||||||
\(964\) | 4.12285e99 | 0.445263 | ||||||||
\(965\) | −4.88413e99 | −0.509475 | ||||||||
\(966\) | 1.04246e99 | 0.105033 | ||||||||
\(967\) | 4.64253e99 | 0.451823 | 0.225911 | − | 0.974148i | \(-0.427464\pi\) | ||||
0.225911 | + | 0.974148i | \(0.427464\pi\) | |||||||
\(968\) | −8.19847e99 | −0.770741 | ||||||||
\(969\) | 3.82757e99 | 0.347598 | ||||||||
\(970\) | −9.71419e98 | −0.0852224 | ||||||||
\(971\) | 1.49343e99 | 0.126573 | 0.0632863 | − | 0.997995i | \(-0.479842\pi\) | ||||
0.0632863 | + | 0.997995i | \(0.479842\pi\) | |||||||
\(972\) | 6.51376e99 | 0.533349 | ||||||||
\(973\) | −9.49559e99 | −0.751176 | ||||||||
\(974\) | −8.03600e99 | −0.614207 | ||||||||
\(975\) | 7.34103e99 | 0.542129 | ||||||||
\(976\) | −7.63118e99 | −0.544531 | ||||||||
\(977\) | 1.94135e100 | 1.33855 | 0.669275 | − | 0.743014i | \(-0.266605\pi\) | ||||
0.669275 | + | 0.743014i | \(0.266605\pi\) | |||||||
\(978\) | −6.46681e99 | −0.430862 | ||||||||
\(979\) | −3.32417e100 | −2.14024 | ||||||||
\(980\) | −2.90564e99 | −0.180787 | ||||||||
\(981\) | −1.74086e98 | −0.0104677 | ||||||||
\(982\) | 1.22653e100 | 0.712760 | ||||||||
\(983\) | −7.70721e99 | −0.432867 | −0.216433 | − | 0.976297i | \(-0.569442\pi\) | ||||
−0.216433 | + | 0.976297i | \(0.569442\pi\) | |||||||
\(984\) | −1.75194e100 | −0.951005 | ||||||||
\(985\) | 5.31023e99 | 0.278612 | ||||||||
\(986\) | 4.48846e99 | 0.227625 | ||||||||
\(987\) | 2.17014e99 | 0.106381 | ||||||||
\(988\) | 1.11577e100 | 0.528711 | ||||||||
\(989\) | 1.28908e100 | 0.590479 | ||||||||
\(990\) | −1.45302e99 | −0.0643419 | ||||||||
\(991\) | 4.23472e99 | 0.181283 | 0.0906415 | − | 0.995884i | \(-0.471108\pi\) | ||||
0.0906415 | + | 0.995884i | \(0.471108\pi\) | |||||||
\(992\) | 3.41409e100 | 1.41297 | ||||||||
\(993\) | −4.52217e99 | −0.180945 | ||||||||
\(994\) | 7.86892e99 | 0.304419 | ||||||||
\(995\) | 8.27233e99 | 0.309425 | ||||||||
\(996\) | 3.25339e99 | 0.117665 | ||||||||
\(997\) | 1.09542e100 | 0.383082 | 0.191541 | − | 0.981485i | \(-0.438652\pi\) | ||||
0.191541 | + | 0.981485i | \(0.438652\pi\) | |||||||
\(998\) | 5.98149e99 | 0.202272 | ||||||||
\(999\) | −5.05377e100 | −1.65261 |
(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 | 1.68.a.a.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 9.68.a.a.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.68.a.a.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.68.a.a.1.3 | 5 | 3.2 | odd | 2 |