Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,46,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 46, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 46);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 46 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(25.6511452149\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 163774578 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(12797.9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.19430e6 | −0.707107 | ||||||||
\(3\) | −1.07859e11 | −1.98440 | −0.992200 | − | 0.124657i | \(-0.960217\pi\) | ||||
−0.992200 | + | 0.124657i | \(0.960217\pi\) | |||||||
\(4\) | 1.75922e13 | 0.500000 | ||||||||
\(5\) | −5.35098e15 | −1.00371 | −0.501855 | − | 0.864952i | \(-0.667349\pi\) | ||||
−0.501855 | + | 0.864952i | \(0.667349\pi\) | |||||||
\(6\) | 4.52394e17 | 1.40318 | ||||||||
\(7\) | −5.31551e18 | −0.513853 | −0.256927 | − | 0.966431i | \(-0.582710\pi\) | ||||
−0.256927 | + | 0.966431i | \(0.582710\pi\) | |||||||
\(8\) | −7.37870e19 | −0.353553 | ||||||||
\(9\) | 8.67930e21 | 2.93784 | ||||||||
\(10\) | 2.24436e22 | 0.709730 | ||||||||
\(11\) | 3.01022e23 | 1.11497 | 0.557485 | − | 0.830187i | \(-0.311766\pi\) | ||||
0.557485 | + | 0.830187i | \(0.311766\pi\) | |||||||
\(12\) | −1.89748e24 | −0.992200 | ||||||||
\(13\) | −3.58553e24 | −0.309619 | −0.154810 | − | 0.987944i | \(-0.549476\pi\) | ||||
−0.154810 | + | 0.987944i | \(0.549476\pi\) | |||||||
\(14\) | 2.22949e25 | 0.363349 | ||||||||
\(15\) | 5.77153e26 | 1.99176 | ||||||||
\(16\) | 3.09485e26 | 0.250000 | ||||||||
\(17\) | 2.22752e26 | 0.0459961 | 0.0229981 | − | 0.999736i | \(-0.492679\pi\) | ||||
0.0229981 | + | 0.999736i | \(0.492679\pi\) | |||||||
\(18\) | −3.64036e28 | −2.07737 | ||||||||
\(19\) | 4.98355e28 | 0.842525 | 0.421262 | − | 0.906939i | \(-0.361587\pi\) | ||||
0.421262 | + | 0.906939i | \(0.361587\pi\) | |||||||
\(20\) | −9.41355e28 | −0.501855 | ||||||||
\(21\) | 5.73327e29 | 1.01969 | ||||||||
\(22\) | −1.26258e30 | −0.788403 | ||||||||
\(23\) | −4.72970e30 | −1.08632 | −0.543160 | − | 0.839629i | \(-0.682772\pi\) | ||||
−0.543160 | + | 0.839629i | \(0.682772\pi\) | |||||||
\(24\) | 7.95861e30 | 0.701591 | ||||||||
\(25\) | 2.11308e29 | 0.00743474 | ||||||||
\(26\) | 1.50388e31 | 0.218934 | ||||||||
\(27\) | −6.17493e32 | −3.84545 | ||||||||
\(28\) | −9.35114e31 | −0.256927 | ||||||||
\(29\) | 6.15404e32 | 0.767725 | 0.383862 | − | 0.923390i | \(-0.374594\pi\) | ||||
0.383862 | + | 0.923390i | \(0.374594\pi\) | |||||||
\(30\) | −2.42076e33 | −1.40839 | ||||||||
\(31\) | 5.25156e32 | 0.146100 | 0.0730500 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730500 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(32\) | −1.29807e33 | −0.176777 | ||||||||
\(33\) | −3.24681e34 | −2.21255 | ||||||||
\(34\) | −9.34291e32 | −0.0325242 | ||||||||
\(35\) | 2.84432e34 | 0.515760 | ||||||||
\(36\) | 1.52688e35 | 1.46892 | ||||||||
\(37\) | 2.05864e35 | 1.06916 | 0.534579 | − | 0.845119i | \(-0.320470\pi\) | ||||
0.534579 | + | 0.845119i | \(0.320470\pi\) | |||||||
\(38\) | −2.09025e35 | −0.595755 | ||||||||
\(39\) | 3.86732e35 | 0.614408 | ||||||||
\(40\) | 3.94833e35 | 0.354865 | ||||||||
\(41\) | 1.88067e36 | 0.969787 | 0.484894 | − | 0.874573i | \(-0.338858\pi\) | ||||
0.484894 | + | 0.874573i | \(0.338858\pi\) | |||||||
\(42\) | −2.40471e36 | −0.721030 | ||||||||
\(43\) | −1.70766e36 | −0.301551 | −0.150776 | − | 0.988568i | \(-0.548177\pi\) | ||||
−0.150776 | + | 0.988568i | \(0.548177\pi\) | |||||||
\(44\) | 5.29564e36 | 0.557485 | ||||||||
\(45\) | −4.64428e37 | −2.94874 | ||||||||
\(46\) | 1.98378e37 | 0.768144 | ||||||||
\(47\) | 3.61985e37 | 0.863951 | 0.431976 | − | 0.901885i | \(-0.357817\pi\) | ||||
0.431976 | + | 0.901885i | \(0.357817\pi\) | |||||||
\(48\) | −3.33808e37 | −0.496100 | ||||||||
\(49\) | −7.87523e37 | −0.735955 | ||||||||
\(50\) | −8.86290e35 | −0.00525716 | ||||||||
\(51\) | −2.40259e37 | −0.0912747 | ||||||||
\(52\) | −6.30773e37 | −0.154810 | ||||||||
\(53\) | 9.38248e38 | 1.50007 | 0.750033 | − | 0.661400i | \(-0.230038\pi\) | ||||
0.750033 | + | 0.661400i | \(0.230038\pi\) | |||||||
\(54\) | 2.58995e39 | 2.71915 | ||||||||
\(55\) | −1.61077e39 | −1.11911 | ||||||||
\(56\) | 3.92215e38 | 0.181674 | ||||||||
\(57\) | −5.37522e39 | −1.67191 | ||||||||
\(58\) | −2.58119e39 | −0.542863 | ||||||||
\(59\) | −4.98073e39 | −0.713054 | −0.356527 | − | 0.934285i | \(-0.616039\pi\) | ||||
−0.356527 | + | 0.934285i | \(0.616039\pi\) | |||||||
\(60\) | 1.01534e40 | 0.995881 | ||||||||
\(61\) | 2.73039e39 | 0.184631 | 0.0923153 | − | 0.995730i | \(-0.470573\pi\) | ||||
0.0923153 | + | 0.995730i | \(0.470573\pi\) | |||||||
\(62\) | −2.20267e39 | −0.103308 | ||||||||
\(63\) | −4.61349e40 | −1.50962 | ||||||||
\(64\) | 5.44452e39 | 0.125000 | ||||||||
\(65\) | 1.91861e40 | 0.310768 | ||||||||
\(66\) | 1.36181e41 | 1.56451 | ||||||||
\(67\) | −1.07891e41 | −0.883698 | −0.441849 | − | 0.897089i | \(-0.645677\pi\) | ||||
−0.441849 | + | 0.897089i | \(0.645677\pi\) | |||||||
\(68\) | 3.91870e39 | 0.0229981 | ||||||||
\(69\) | 5.10142e41 | 2.15569 | ||||||||
\(70\) | −1.19299e41 | −0.364697 | ||||||||
\(71\) | −9.82494e40 | −0.218282 | −0.109141 | − | 0.994026i | \(-0.534810\pi\) | ||||
−0.109141 | + | 0.994026i | \(0.534810\pi\) | |||||||
\(72\) | −6.40420e41 | −1.03868 | ||||||||
\(73\) | 2.35740e41 | 0.280330 | 0.140165 | − | 0.990128i | \(-0.455237\pi\) | ||||
0.140165 | + | 0.990128i | \(0.455237\pi\) | |||||||
\(74\) | −8.63456e41 | −0.756008 | ||||||||
\(75\) | −2.27915e40 | −0.0147535 | ||||||||
\(76\) | 8.76715e41 | 0.421262 | ||||||||
\(77\) | −1.60009e42 | −0.572931 | ||||||||
\(78\) | −1.62207e42 | −0.434452 | ||||||||
\(79\) | −9.11195e42 | −1.83232 | −0.916161 | − | 0.400810i | \(-0.868729\pi\) | ||||
−0.916161 | + | 0.400810i | \(0.868729\pi\) | |||||||
\(80\) | −1.65605e42 | −0.250928 | ||||||||
\(81\) | 4.09610e43 | 4.69308 | ||||||||
\(82\) | −7.88811e42 | −0.685743 | ||||||||
\(83\) | −3.78507e42 | −0.250505 | −0.125253 | − | 0.992125i | \(-0.539974\pi\) | ||||
−0.125253 | + | 0.992125i | \(0.539974\pi\) | |||||||
\(84\) | 1.00861e43 | 0.509845 | ||||||||
\(85\) | −1.19194e42 | −0.0461668 | ||||||||
\(86\) | 7.16245e42 | 0.213229 | ||||||||
\(87\) | −6.63771e43 | −1.52347 | ||||||||
\(88\) | −2.22115e43 | −0.394202 | ||||||||
\(89\) | −8.23878e43 | −1.13393 | −0.566967 | − | 0.823740i | \(-0.691883\pi\) | ||||
−0.566967 | + | 0.823740i | \(0.691883\pi\) | |||||||
\(90\) | 1.94795e44 | 2.08508 | ||||||||
\(91\) | 1.90589e43 | 0.159099 | ||||||||
\(92\) | −8.32058e43 | −0.543160 | ||||||||
\(93\) | −5.66430e43 | −0.289921 | ||||||||
\(94\) | −1.51828e44 | −0.610906 | ||||||||
\(95\) | −2.66669e44 | −0.845651 | ||||||||
\(96\) | 1.40009e44 | 0.350796 | ||||||||
\(97\) | −1.69418e44 | −0.336198 | −0.168099 | − | 0.985770i | \(-0.553763\pi\) | ||||
−0.168099 | + | 0.985770i | \(0.553763\pi\) | |||||||
\(98\) | 3.30311e44 | 0.520399 | ||||||||
\(99\) | 2.61267e45 | 3.27561 | ||||||||
\(100\) | 3.71737e42 | 0.00371737 | ||||||||
\(101\) | −1.33894e45 | −1.07036 | −0.535182 | − | 0.844737i | \(-0.679757\pi\) | ||||
−0.535182 | + | 0.844737i | \(0.679757\pi\) | |||||||
\(102\) | 1.00772e44 | 0.0645410 | ||||||||
\(103\) | −8.91708e44 | −0.458548 | −0.229274 | − | 0.973362i | \(-0.573635\pi\) | ||||
−0.229274 | + | 0.973362i | \(0.573635\pi\) | |||||||
\(104\) | 2.64565e44 | 0.109467 | ||||||||
\(105\) | −3.06786e45 | −1.02347 | ||||||||
\(106\) | −3.93530e45 | −1.06071 | ||||||||
\(107\) | 8.16657e45 | 1.78199 | 0.890994 | − | 0.454015i | \(-0.150009\pi\) | ||||
0.890994 | + | 0.454015i | \(0.150009\pi\) | |||||||
\(108\) | −1.08631e46 | −1.92273 | ||||||||
\(109\) | 6.73063e45 | 0.968187 | 0.484093 | − | 0.875016i | \(-0.339149\pi\) | ||||
0.484093 | + | 0.875016i | \(0.339149\pi\) | |||||||
\(110\) | 6.75604e45 | 0.791329 | ||||||||
\(111\) | −2.22043e46 | −2.12164 | ||||||||
\(112\) | −1.64507e45 | −0.128463 | ||||||||
\(113\) | 1.22826e46 | 0.785283 | 0.392642 | − | 0.919692i | \(-0.371561\pi\) | ||||
0.392642 | + | 0.919692i | \(0.371561\pi\) | |||||||
\(114\) | 2.25453e46 | 1.18222 | ||||||||
\(115\) | 2.53086e46 | 1.09035 | ||||||||
\(116\) | 1.08263e46 | 0.383862 | ||||||||
\(117\) | −3.11199e46 | −0.909612 | ||||||||
\(118\) | 2.08907e46 | 0.504206 | ||||||||
\(119\) | −1.18404e45 | −0.0236353 | ||||||||
\(120\) | −4.25864e46 | −0.704195 | ||||||||
\(121\) | 1.77240e46 | 0.243160 | ||||||||
\(122\) | −1.14521e46 | −0.130554 | ||||||||
\(123\) | −2.02848e47 | −1.92445 | ||||||||
\(124\) | 9.23865e45 | 0.0730500 | ||||||||
\(125\) | 1.50953e47 | 0.996248 | ||||||||
\(126\) | 1.93504e47 | 1.06746 | ||||||||
\(127\) | −3.00310e47 | −1.38671 | −0.693356 | − | 0.720595i | \(-0.743869\pi\) | ||||
−0.693356 | + | 0.720595i | \(0.743869\pi\) | |||||||
\(128\) | −2.28360e46 | −0.0883883 | ||||||||
\(129\) | 1.84187e47 | 0.598399 | ||||||||
\(130\) | −8.04723e46 | −0.219746 | ||||||||
\(131\) | −9.92430e45 | −0.0228085 | −0.0114042 | − | 0.999935i | \(-0.503630\pi\) | ||||
−0.0114042 | + | 0.999935i | \(0.503630\pi\) | |||||||
\(132\) | −5.71184e47 | −1.10627 | ||||||||
\(133\) | −2.64901e47 | −0.432934 | ||||||||
\(134\) | 4.52529e47 | 0.624869 | ||||||||
\(135\) | 3.30420e48 | 3.85972 | ||||||||
\(136\) | −1.64362e46 | −0.0162621 | ||||||||
\(137\) | 8.57379e47 | 0.719383 | 0.359691 | − | 0.933071i | \(-0.382882\pi\) | ||||
0.359691 | + | 0.933071i | \(0.382882\pi\) | |||||||
\(138\) | −2.13969e48 | −1.52430 | ||||||||
\(139\) | −2.50782e48 | −1.51867 | −0.759335 | − | 0.650699i | \(-0.774476\pi\) | ||||
−0.759335 | + | 0.650699i | \(0.774476\pi\) | |||||||
\(140\) | 5.00378e47 | 0.257880 | ||||||||
\(141\) | −3.90435e48 | −1.71442 | ||||||||
\(142\) | 4.12088e47 | 0.154348 | ||||||||
\(143\) | −1.07932e48 | −0.345216 | ||||||||
\(144\) | 2.68611e48 | 0.734461 | ||||||||
\(145\) | −3.29302e48 | −0.770574 | ||||||||
\(146\) | −9.88766e47 | −0.198223 | ||||||||
\(147\) | 8.49416e48 | 1.46043 | ||||||||
\(148\) | 3.62160e48 | 0.534579 | ||||||||
\(149\) | −1.24099e48 | −0.157427 | −0.0787133 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787133 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(150\) | 9.55946e46 | 0.0104323 | ||||||||
\(151\) | 6.70853e47 | 0.0630443 | 0.0315222 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315222 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(152\) | −3.67721e48 | −0.297878 | ||||||||
\(153\) | 1.93333e48 | 0.135129 | ||||||||
\(154\) | 6.71125e48 | 0.405124 | ||||||||
\(155\) | −2.81010e48 | −0.146642 | ||||||||
\(156\) | 6.80347e48 | 0.307204 | ||||||||
\(157\) | 2.27753e49 | 0.890682 | 0.445341 | − | 0.895361i | \(-0.353082\pi\) | ||||
0.445341 | + | 0.895361i | \(0.353082\pi\) | |||||||
\(158\) | 3.82183e49 | 1.29565 | ||||||||
\(159\) | −1.01199e50 | −2.97673 | ||||||||
\(160\) | 6.94597e48 | 0.177433 | ||||||||
\(161\) | 2.51408e49 | 0.558209 | ||||||||
\(162\) | −1.71803e50 | −3.31851 | ||||||||
\(163\) | 2.89919e49 | 0.487590 | 0.243795 | − | 0.969827i | \(-0.421608\pi\) | ||||
0.243795 | + | 0.969827i | \(0.421608\pi\) | |||||||
\(164\) | 3.30852e49 | 0.484894 | ||||||||
\(165\) | 1.73736e50 | 2.22076 | ||||||||
\(166\) | 1.58757e49 | 0.177134 | ||||||||
\(167\) | −7.10968e49 | −0.692994 | −0.346497 | − | 0.938051i | \(-0.612629\pi\) | ||||
−0.346497 | + | 0.938051i | \(0.612629\pi\) | |||||||
\(168\) | −4.23041e49 | −0.360515 | ||||||||
\(169\) | −1.21251e50 | −0.904136 | ||||||||
\(170\) | 4.99937e48 | 0.0326449 | ||||||||
\(171\) | 4.32537e50 | 2.47521 | ||||||||
\(172\) | −3.00415e49 | −0.150776 | ||||||||
\(173\) | −4.08899e50 | −1.80127 | −0.900634 | − | 0.434578i | \(-0.856897\pi\) | ||||
−0.900634 | + | 0.434578i | \(0.856897\pi\) | |||||||
\(174\) | 2.78406e50 | 1.07726 | ||||||||
\(175\) | −1.12321e48 | −0.00382036 | ||||||||
\(176\) | 9.31619e49 | 0.278743 | ||||||||
\(177\) | 5.37218e50 | 1.41498 | ||||||||
\(178\) | 3.45560e50 | 0.801813 | ||||||||
\(179\) | −4.98693e50 | −1.02009 | −0.510047 | − | 0.860147i | \(-0.670372\pi\) | ||||
−0.510047 | + | 0.860147i | \(0.670372\pi\) | |||||||
\(180\) | −8.17031e50 | −1.47437 | ||||||||
\(181\) | −8.16176e50 | −1.30022 | −0.650109 | − | 0.759841i | \(-0.725277\pi\) | ||||
−0.650109 | + | 0.759841i | \(0.725277\pi\) | |||||||
\(182\) | −7.99388e49 | −0.112500 | ||||||||
\(183\) | −2.94498e50 | −0.366381 | ||||||||
\(184\) | 3.48991e50 | 0.384072 | ||||||||
\(185\) | −1.10157e51 | −1.07312 | ||||||||
\(186\) | 2.37578e50 | 0.205005 | ||||||||
\(187\) | 6.70534e49 | 0.0512843 | ||||||||
\(188\) | 6.36812e50 | 0.431976 | ||||||||
\(189\) | 3.28229e51 | 1.97600 | ||||||||
\(190\) | 1.11849e51 | 0.597966 | ||||||||
\(191\) | 1.24243e51 | 0.590229 | 0.295114 | − | 0.955462i | \(-0.404642\pi\) | ||||
0.295114 | + | 0.955462i | \(0.404642\pi\) | |||||||
\(192\) | −5.87242e50 | −0.248050 | ||||||||
\(193\) | −1.67929e51 | −0.631082 | −0.315541 | − | 0.948912i | \(-0.602186\pi\) | ||||
−0.315541 | + | 0.948912i | \(0.602186\pi\) | |||||||
\(194\) | 7.10590e50 | 0.237728 | ||||||||
\(195\) | −2.06940e51 | −0.616688 | ||||||||
\(196\) | −1.38542e51 | −0.367978 | ||||||||
\(197\) | 6.97671e51 | 1.65257 | 0.826287 | − | 0.563250i | \(-0.190449\pi\) | ||||
0.826287 | + | 0.563250i | \(0.190449\pi\) | |||||||
\(198\) | −1.09583e52 | −2.31620 | ||||||||
\(199\) | −3.27895e51 | −0.618785 | −0.309393 | − | 0.950934i | \(-0.600126\pi\) | ||||
−0.309393 | + | 0.950934i | \(0.600126\pi\) | |||||||
\(200\) | −1.55918e49 | −0.00262858 | ||||||||
\(201\) | 1.16371e52 | 1.75361 | ||||||||
\(202\) | 5.61594e51 | 0.756862 | ||||||||
\(203\) | −3.27119e51 | −0.394498 | ||||||||
\(204\) | −4.22668e50 | −0.0456374 | ||||||||
\(205\) | −1.00634e52 | −0.973386 | ||||||||
\(206\) | 3.74009e51 | 0.324242 | ||||||||
\(207\) | −4.10505e52 | −3.19144 | ||||||||
\(208\) | −1.10967e51 | −0.0774048 | ||||||||
\(209\) | 1.50016e52 | 0.939391 | ||||||||
\(210\) | 1.28675e52 | 0.723705 | ||||||||
\(211\) | 3.10810e52 | 1.57087 | 0.785434 | − | 0.618946i | \(-0.212440\pi\) | ||||
0.785434 | + | 0.618946i | \(0.212440\pi\) | |||||||
\(212\) | 1.65058e52 | 0.750033 | ||||||||
\(213\) | 1.05971e52 | 0.433158 | ||||||||
\(214\) | −3.42531e52 | −1.26006 | ||||||||
\(215\) | 9.13767e51 | 0.302670 | ||||||||
\(216\) | 4.55630e52 | 1.35957 | ||||||||
\(217\) | −2.79147e51 | −0.0750740 | ||||||||
\(218\) | −2.82303e52 | −0.684612 | ||||||||
\(219\) | −2.54268e52 | −0.556286 | ||||||||
\(220\) | −2.83369e52 | −0.559554 | ||||||||
\(221\) | −7.98684e50 | −0.0142413 | ||||||||
\(222\) | 9.31317e52 | 1.50022 | ||||||||
\(223\) | −9.83175e52 | −1.43143 | −0.715717 | − | 0.698390i | \(-0.753900\pi\) | ||||
−0.715717 | + | 0.698390i | \(0.753900\pi\) | |||||||
\(224\) | 6.89993e51 | 0.0908372 | ||||||||
\(225\) | 1.83401e51 | 0.0218421 | ||||||||
\(226\) | −5.15171e52 | −0.555279 | ||||||||
\(227\) | 6.71123e51 | 0.0654969 | 0.0327484 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327484 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(228\) | −9.45618e52 | −0.835953 | ||||||||
\(229\) | 3.17367e51 | 0.0254251 | 0.0127126 | − | 0.999919i | \(-0.495953\pi\) | ||||
0.0127126 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(230\) | −1.06152e53 | −0.770994 | ||||||||
\(231\) | 1.72584e53 | 1.13692 | ||||||||
\(232\) | −4.54088e52 | −0.271432 | ||||||||
\(233\) | 5.76404e52 | 0.312766 | 0.156383 | − | 0.987697i | \(-0.450017\pi\) | ||||
0.156383 | + | 0.987697i | \(0.450017\pi\) | |||||||
\(234\) | 1.30526e53 | 0.643193 | ||||||||
\(235\) | −1.93698e53 | −0.867157 | ||||||||
\(236\) | −8.76219e52 | −0.356527 | ||||||||
\(237\) | 9.82808e53 | 3.63606 | ||||||||
\(238\) | 4.96623e51 | 0.0167126 | ||||||||
\(239\) | 3.11836e52 | 0.0954934 | 0.0477467 | − | 0.998859i | \(-0.484796\pi\) | ||||
0.0477467 | + | 0.998859i | \(0.484796\pi\) | |||||||
\(240\) | 1.78620e53 | 0.497941 | ||||||||
\(241\) | 1.25122e53 | 0.317652 | 0.158826 | − | 0.987307i | \(-0.449229\pi\) | ||||
0.158826 | + | 0.987307i | \(0.449229\pi\) | |||||||
\(242\) | −7.43400e52 | −0.171940 | ||||||||
\(243\) | −2.59375e54 | −5.46748 | ||||||||
\(244\) | 4.80336e52 | 0.0923153 | ||||||||
\(245\) | 4.21402e53 | 0.738686 | ||||||||
\(246\) | 8.50806e53 | 1.36079 | ||||||||
\(247\) | −1.78687e53 | −0.260862 | ||||||||
\(248\) | −3.87497e52 | −0.0516542 | ||||||||
\(249\) | 4.08255e53 | 0.497103 | ||||||||
\(250\) | −6.33144e53 | −0.704454 | ||||||||
\(251\) | 1.51663e54 | 1.54249 | 0.771245 | − | 0.636539i | \(-0.219634\pi\) | ||||
0.771245 | + | 0.636539i | \(0.219634\pi\) | |||||||
\(252\) | −8.11614e53 | −0.754810 | ||||||||
\(253\) | −1.42375e54 | −1.21121 | ||||||||
\(254\) | 1.25959e54 | 0.980554 | ||||||||
\(255\) | 1.28562e53 | 0.0916134 | ||||||||
\(256\) | 9.57810e52 | 0.0625000 | ||||||||
\(257\) | −5.72779e53 | −0.342367 | −0.171183 | − | 0.985239i | \(-0.554759\pi\) | ||||
−0.171183 | + | 0.985239i | \(0.554759\pi\) | |||||||
\(258\) | −7.72537e53 | −0.423132 | ||||||||
\(259\) | −1.09427e54 | −0.549390 | ||||||||
\(260\) | 3.37525e53 | 0.155384 | ||||||||
\(261\) | 5.34128e54 | 2.25545 | ||||||||
\(262\) | 4.16255e52 | 0.0161280 | ||||||||
\(263\) | −2.41909e53 | −0.0860295 | −0.0430147 | − | 0.999074i | \(-0.513696\pi\) | ||||
−0.0430147 | + | 0.999074i | \(0.513696\pi\) | |||||||
\(264\) | 2.39572e54 | 0.782254 | ||||||||
\(265\) | −5.02055e54 | −1.50563 | ||||||||
\(266\) | 1.11108e54 | 0.306131 | ||||||||
\(267\) | 8.88629e54 | 2.25018 | ||||||||
\(268\) | −1.89805e54 | −0.441849 | ||||||||
\(269\) | 2.64339e54 | 0.565894 | 0.282947 | − | 0.959136i | \(-0.408688\pi\) | ||||
0.282947 | + | 0.959136i | \(0.408688\pi\) | |||||||
\(270\) | −1.38588e55 | −2.72924 | ||||||||
\(271\) | −8.54630e54 | −1.54871 | −0.774353 | − | 0.632754i | \(-0.781924\pi\) | ||||
−0.774353 | + | 0.632754i | \(0.781924\pi\) | |||||||
\(272\) | 6.89385e52 | 0.0114990 | ||||||||
\(273\) | −2.05568e54 | −0.315715 | ||||||||
\(274\) | −3.59611e54 | −0.508681 | ||||||||
\(275\) | 6.36085e52 | 0.00828952 | ||||||||
\(276\) | 8.97452e54 | 1.07785 | ||||||||
\(277\) | −5.04059e54 | −0.558067 | −0.279033 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279033 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(278\) | 1.05186e55 | 1.07386 | ||||||||
\(279\) | 4.55799e54 | 0.429219 | ||||||||
\(280\) | −2.09874e54 | −0.182349 | ||||||||
\(281\) | 4.09835e54 | 0.328637 | 0.164318 | − | 0.986407i | \(-0.447458\pi\) | ||||
0.164318 | + | 0.986407i | \(0.447458\pi\) | |||||||
\(282\) | 1.63760e55 | 1.21228 | ||||||||
\(283\) | −2.06696e55 | −1.41298 | −0.706491 | − | 0.707722i | \(-0.749723\pi\) | ||||
−0.706491 | + | 0.707722i | \(0.749723\pi\) | |||||||
\(284\) | −1.72842e54 | −0.109141 | ||||||||
\(285\) | 2.87627e55 | 1.67811 | ||||||||
\(286\) | 4.52702e54 | 0.244105 | ||||||||
\(287\) | −9.99673e54 | −0.498328 | ||||||||
\(288\) | −1.12664e55 | −0.519342 | ||||||||
\(289\) | −2.34035e55 | −0.997884 | ||||||||
\(290\) | 1.38119e55 | 0.544878 | ||||||||
\(291\) | 1.82733e55 | 0.667152 | ||||||||
\(292\) | 4.14719e54 | 0.140165 | ||||||||
\(293\) | 4.39999e55 | 1.37699 | 0.688494 | − | 0.725242i | \(-0.258272\pi\) | ||||
0.688494 | + | 0.725242i | \(0.258272\pi\) | |||||||
\(294\) | −3.56271e55 | −1.03268 | ||||||||
\(295\) | 2.66518e55 | 0.715700 | ||||||||
\(296\) | −1.51901e55 | −0.378004 | ||||||||
\(297\) | −1.85879e56 | −4.28757 | ||||||||
\(298\) | 5.20510e54 | 0.111317 | ||||||||
\(299\) | 1.69585e55 | 0.336345 | ||||||||
\(300\) | −4.00953e53 | −0.00737675 | ||||||||
\(301\) | 9.07709e54 | 0.154953 | ||||||||
\(302\) | −2.81376e54 | −0.0445791 | ||||||||
\(303\) | 1.44418e56 | 2.12403 | ||||||||
\(304\) | 1.54233e55 | 0.210631 | ||||||||
\(305\) | −1.46103e55 | −0.185316 | ||||||||
\(306\) | −8.10899e54 | −0.0955509 | ||||||||
\(307\) | 8.99516e55 | 0.984907 | 0.492453 | − | 0.870339i | \(-0.336100\pi\) | ||||
0.492453 | + | 0.870339i | \(0.336100\pi\) | |||||||
\(308\) | −2.81490e55 | −0.286466 | ||||||||
\(309\) | 9.61789e55 | 0.909943 | ||||||||
\(310\) | 1.17864e55 | 0.103692 | ||||||||
\(311\) | −1.48938e56 | −1.21870 | −0.609350 | − | 0.792901i | \(-0.708570\pi\) | ||||
−0.609350 | + | 0.792901i | \(0.708570\pi\) | |||||||
\(312\) | −2.85358e55 | −0.217226 | ||||||||
\(313\) | −9.05220e55 | −0.641220 | −0.320610 | − | 0.947211i | \(-0.603888\pi\) | ||||
−0.320610 | + | 0.947211i | \(0.603888\pi\) | |||||||
\(314\) | −9.55267e55 | −0.629807 | ||||||||
\(315\) | 2.46867e56 | 1.51522 | ||||||||
\(316\) | −1.60299e56 | −0.916161 | ||||||||
\(317\) | 5.63393e55 | 0.299901 | 0.149951 | − | 0.988693i | \(-0.452089\pi\) | ||||
0.149951 | + | 0.988693i | \(0.452089\pi\) | |||||||
\(318\) | 4.24458e56 | 2.10487 | ||||||||
\(319\) | 1.85251e56 | 0.855991 | ||||||||
\(320\) | −2.91335e55 | −0.125464 | ||||||||
\(321\) | −8.80840e56 | −3.53618 | ||||||||
\(322\) | −1.05448e56 | −0.394713 | ||||||||
\(323\) | 1.11010e55 | 0.0387529 | ||||||||
\(324\) | 7.20593e56 | 2.34654 | ||||||||
\(325\) | −7.57651e53 | −0.00230194 | ||||||||
\(326\) | −1.21601e56 | −0.344779 | ||||||||
\(327\) | −7.25960e56 | −1.92127 | ||||||||
\(328\) | −1.38769e56 | −0.342872 | ||||||||
\(329\) | −1.92414e56 | −0.443944 | ||||||||
\(330\) | −7.28702e56 | −1.57031 | ||||||||
\(331\) | 3.85197e55 | 0.0775448 | 0.0387724 | − | 0.999248i | \(-0.487655\pi\) | ||||
0.0387724 | + | 0.999248i | \(0.487655\pi\) | |||||||
\(332\) | −6.65877e55 | −0.125253 | ||||||||
\(333\) | 1.78676e57 | 3.14102 | ||||||||
\(334\) | 2.98202e56 | 0.490021 | ||||||||
\(335\) | 5.77325e56 | 0.886977 | ||||||||
\(336\) | 1.77436e56 | 0.254922 | ||||||||
\(337\) | 1.10153e57 | 1.48021 | 0.740104 | − | 0.672492i | \(-0.234776\pi\) | ||||
0.740104 | + | 0.672492i | \(0.234776\pi\) | |||||||
\(338\) | 5.08563e56 | 0.639321 | ||||||||
\(339\) | −1.32480e57 | −1.55832 | ||||||||
\(340\) | −2.09689e55 | −0.0230834 | ||||||||
\(341\) | 1.58084e56 | 0.162897 | ||||||||
\(342\) | −1.81419e57 | −1.75023 | ||||||||
\(343\) | 9.87405e56 | 0.892026 | ||||||||
\(344\) | 1.26003e56 | 0.106615 | ||||||||
\(345\) | −2.72976e57 | −2.16369 | ||||||||
\(346\) | 1.71505e57 | 1.27369 | ||||||||
\(347\) | −1.58911e57 | −1.10596 | −0.552981 | − | 0.833194i | \(-0.686510\pi\) | ||||
−0.552981 | + | 0.833194i | \(0.686510\pi\) | |||||||
\(348\) | −1.16772e57 | −0.761737 | ||||||||
\(349\) | 1.31112e57 | 0.801806 | 0.400903 | − | 0.916121i | \(-0.368696\pi\) | ||||
0.400903 | + | 0.916121i | \(0.368696\pi\) | |||||||
\(350\) | 4.71108e54 | 0.00270141 | ||||||||
\(351\) | 2.21404e57 | 1.19063 | ||||||||
\(352\) | −3.90750e56 | −0.197101 | ||||||||
\(353\) | −8.53713e56 | −0.404000 | −0.202000 | − | 0.979386i | \(-0.564744\pi\) | ||||
−0.202000 | + | 0.979386i | \(0.564744\pi\) | |||||||
\(354\) | −2.25325e57 | −1.00055 | ||||||||
\(355\) | 5.25731e56 | 0.219092 | ||||||||
\(356\) | −1.44938e57 | −0.566967 | ||||||||
\(357\) | 1.27710e56 | 0.0469018 | ||||||||
\(358\) | 2.09167e57 | 0.721315 | ||||||||
\(359\) | −2.26719e56 | −0.0734281 | −0.0367141 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367141 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(360\) | 3.42687e57 | 1.04254 | ||||||||
\(361\) | −1.01517e57 | −0.290152 | ||||||||
\(362\) | 3.42329e57 | 0.919392 | ||||||||
\(363\) | −1.91170e57 | −0.482527 | ||||||||
\(364\) | 3.35288e56 | 0.0795494 | ||||||||
\(365\) | −1.26144e57 | −0.281370 | ||||||||
\(366\) | 1.23521e57 | 0.259071 | ||||||||
\(367\) | −3.47667e57 | −0.685768 | −0.342884 | − | 0.939378i | \(-0.611404\pi\) | ||||
−0.342884 | + | 0.939378i | \(0.611404\pi\) | |||||||
\(368\) | −1.46377e57 | −0.271580 | ||||||||
\(369\) | 1.63229e58 | 2.84908 | ||||||||
\(370\) | 4.62034e57 | 0.758814 | ||||||||
\(371\) | −4.98726e57 | −0.770814 | ||||||||
\(372\) | −9.96474e56 | −0.144960 | ||||||||
\(373\) | −7.80953e57 | −1.06949 | −0.534744 | − | 0.845014i | \(-0.679592\pi\) | ||||
−0.534744 | + | 0.845014i | \(0.679592\pi\) | |||||||
\(374\) | −2.81242e56 | −0.0362635 | ||||||||
\(375\) | −1.62817e58 | −1.97695 | ||||||||
\(376\) | −2.67098e57 | −0.305453 | ||||||||
\(377\) | −2.20655e57 | −0.237702 | ||||||||
\(378\) | −1.37669e58 | −1.39724 | ||||||||
\(379\) | 1.79759e58 | 1.71913 | 0.859565 | − | 0.511026i | \(-0.170735\pi\) | ||||
0.859565 | + | 0.511026i | \(0.170735\pi\) | |||||||
\(380\) | −4.69129e57 | −0.422826 | ||||||||
\(381\) | 3.23912e58 | 2.75179 | ||||||||
\(382\) | −5.21112e57 | −0.417355 | ||||||||
\(383\) | −2.20965e58 | −1.66859 | −0.834297 | − | 0.551315i | \(-0.814126\pi\) | ||||
−0.834297 | + | 0.551315i | \(0.814126\pi\) | |||||||
\(384\) | 2.46307e57 | 0.175398 | ||||||||
\(385\) | 8.56204e57 | 0.575057 | ||||||||
\(386\) | 7.04344e57 | 0.446242 | ||||||||
\(387\) | −1.48213e58 | −0.885911 | ||||||||
\(388\) | −2.98043e57 | −0.168099 | ||||||||
\(389\) | −5.18043e57 | −0.275740 | −0.137870 | − | 0.990450i | \(-0.544026\pi\) | ||||
−0.137870 | + | 0.990450i | \(0.544026\pi\) | |||||||
\(390\) | 8.67969e57 | 0.436064 | ||||||||
\(391\) | −1.05355e57 | −0.0499665 | ||||||||
\(392\) | 5.81089e57 | 0.260199 | ||||||||
\(393\) | 1.07043e57 | 0.0452611 | ||||||||
\(394\) | −2.92624e58 | −1.16855 | ||||||||
\(395\) | 4.87579e58 | 1.83912 | ||||||||
\(396\) | 4.59625e58 | 1.63780 | ||||||||
\(397\) | −2.60130e58 | −0.875797 | −0.437898 | − | 0.899024i | \(-0.644277\pi\) | ||||
−0.437898 | + | 0.899024i | \(0.644277\pi\) | |||||||
\(398\) | 1.37529e58 | 0.437547 | ||||||||
\(399\) | 2.85720e58 | 0.859114 | ||||||||
\(400\) | 6.53967e55 | 0.00185869 | ||||||||
\(401\) | 5.24055e58 | 1.40808 | 0.704042 | − | 0.710159i | \(-0.251377\pi\) | ||||
0.704042 | + | 0.710159i | \(0.251377\pi\) | |||||||
\(402\) | −4.88095e58 | −1.23999 | ||||||||
\(403\) | −1.88296e57 | −0.0452354 | ||||||||
\(404\) | −2.35550e58 | −0.535182 | ||||||||
\(405\) | −2.19182e59 | −4.71049 | ||||||||
\(406\) | 1.37204e58 | 0.278952 | ||||||||
\(407\) | 6.19697e58 | 1.19208 | ||||||||
\(408\) | 1.77280e57 | 0.0322705 | ||||||||
\(409\) | −5.81978e58 | −1.00261 | −0.501305 | − | 0.865270i | \(-0.667147\pi\) | ||||
−0.501305 | + | 0.865270i | \(0.667147\pi\) | |||||||
\(410\) | 4.22092e58 | 0.688288 | ||||||||
\(411\) | −9.24763e58 | −1.42754 | ||||||||
\(412\) | −1.56871e58 | −0.229274 | ||||||||
\(413\) | 2.64751e58 | 0.366405 | ||||||||
\(414\) | 1.72178e59 | 2.25669 | ||||||||
\(415\) | 2.02538e58 | 0.251435 | ||||||||
\(416\) | 4.65428e57 | 0.0547334 | ||||||||
\(417\) | 2.70492e59 | 3.01365 | ||||||||
\(418\) | −6.29213e58 | −0.664250 | ||||||||
\(419\) | −1.08479e58 | −0.108525 | −0.0542623 | − | 0.998527i | \(-0.517281\pi\) | ||||
−0.0542623 | + | 0.998527i | \(0.517281\pi\) | |||||||
\(420\) | −5.39704e58 | −0.511737 | ||||||||
\(421\) | −1.99082e59 | −1.78930 | −0.894652 | − | 0.446763i | \(-0.852577\pi\) | ||||
−0.894652 | + | 0.446763i | \(0.852577\pi\) | |||||||
\(422\) | −1.30363e59 | −1.11077 | ||||||||
\(423\) | 3.14178e59 | 2.53815 | ||||||||
\(424\) | −6.92305e58 | −0.530354 | ||||||||
\(425\) | 4.70693e55 | 0.000341969 0 | ||||||||
\(426\) | −4.44475e58 | −0.306289 | ||||||||
\(427\) | −1.45134e58 | −0.0948730 | ||||||||
\(428\) | 1.43668e59 | 0.890994 | ||||||||
\(429\) | 1.16415e59 | 0.685047 | ||||||||
\(430\) | −3.83261e58 | −0.214020 | ||||||||
\(431\) | −2.82963e59 | −1.49965 | −0.749826 | − | 0.661635i | \(-0.769863\pi\) | ||||
−0.749826 | + | 0.661635i | \(0.769863\pi\) | |||||||
\(432\) | −1.91105e59 | −0.961363 | ||||||||
\(433\) | 7.60858e58 | 0.363350 | 0.181675 | − | 0.983359i | \(-0.441848\pi\) | ||||
0.181675 | + | 0.983359i | \(0.441848\pi\) | |||||||
\(434\) | 1.17083e58 | 0.0530853 | ||||||||
\(435\) | 3.55182e59 | 1.52913 | ||||||||
\(436\) | 1.18406e59 | 0.484093 | ||||||||
\(437\) | −2.35707e59 | −0.915251 | ||||||||
\(438\) | 1.06648e59 | 0.393354 | ||||||||
\(439\) | −2.36220e59 | −0.827685 | −0.413843 | − | 0.910348i | \(-0.635814\pi\) | ||||
−0.413843 | + | 0.910348i | \(0.635814\pi\) | |||||||
\(440\) | 1.18854e59 | 0.395664 | ||||||||
\(441\) | −6.83515e59 | −2.16212 | ||||||||
\(442\) | 3.34993e57 | 0.0100701 | ||||||||
\(443\) | −2.46091e59 | −0.703091 | −0.351546 | − | 0.936171i | \(-0.614344\pi\) | ||||
−0.351546 | + | 0.936171i | \(0.614344\pi\) | |||||||
\(444\) | −3.90623e59 | −1.06082 | ||||||||
\(445\) | 4.40856e59 | 1.13814 | ||||||||
\(446\) | 4.12374e59 | 1.01218 | ||||||||
\(447\) | 1.33852e59 | 0.312397 | ||||||||
\(448\) | −2.89404e58 | −0.0642316 | ||||||||
\(449\) | 4.92131e59 | 1.03881 | 0.519407 | − | 0.854527i | \(-0.326153\pi\) | ||||
0.519407 | + | 0.854527i | \(0.326153\pi\) | |||||||
\(450\) | −7.69238e57 | −0.0154447 | ||||||||
\(451\) | 5.66125e59 | 1.08128 | ||||||||
\(452\) | 2.16078e59 | 0.392642 | ||||||||
\(453\) | −7.23577e58 | −0.125105 | ||||||||
\(454\) | −2.81490e58 | −0.0463133 | ||||||||
\(455\) | −1.01984e59 | −0.159689 | ||||||||
\(456\) | 3.96621e59 | 0.591108 | ||||||||
\(457\) | −6.04235e59 | −0.857218 | −0.428609 | − | 0.903490i | \(-0.640996\pi\) | ||||
−0.428609 | + | 0.903490i | \(0.640996\pi\) | |||||||
\(458\) | −1.33113e58 | −0.0179783 | ||||||||
\(459\) | −1.37548e59 | −0.176876 | ||||||||
\(460\) | 4.45233e59 | 0.545175 | ||||||||
\(461\) | −1.23009e60 | −1.43439 | −0.717195 | − | 0.696873i | \(-0.754574\pi\) | ||||
−0.717195 | + | 0.696873i | \(0.754574\pi\) | |||||||
\(462\) | −7.23871e59 | −0.803927 | ||||||||
\(463\) | 1.58815e60 | 1.68004 | 0.840020 | − | 0.542556i | \(-0.182543\pi\) | ||||
0.840020 | + | 0.542556i | \(0.182543\pi\) | |||||||
\(464\) | 1.90458e59 | 0.191931 | ||||||||
\(465\) | 3.03096e59 | 0.290997 | ||||||||
\(466\) | −2.41762e59 | −0.221159 | ||||||||
\(467\) | −1.01307e60 | −0.883103 | −0.441551 | − | 0.897236i | \(-0.645572\pi\) | ||||
−0.441551 | + | 0.897236i | \(0.645572\pi\) | |||||||
\(468\) | −5.47467e59 | −0.454806 | ||||||||
\(469\) | 5.73498e59 | 0.454091 | ||||||||
\(470\) | 8.12427e59 | 0.613173 | ||||||||
\(471\) | −2.45653e60 | −1.76747 | ||||||||
\(472\) | 3.67513e59 | 0.252103 | ||||||||
\(473\) | −5.14044e59 | −0.336221 | ||||||||
\(474\) | −4.12220e60 | −2.57108 | ||||||||
\(475\) | 1.05306e58 | 0.00626395 | ||||||||
\(476\) | −2.08299e58 | −0.0118176 | ||||||||
\(477\) | 8.14334e60 | 4.40696 | ||||||||
\(478\) | −1.30794e59 | −0.0675241 | ||||||||
\(479\) | −2.68469e59 | −0.132234 | −0.0661172 | − | 0.997812i | \(-0.521061\pi\) | ||||
−0.0661172 | + | 0.997812i | \(0.521061\pi\) | |||||||
\(480\) | −7.49187e59 | −0.352097 | ||||||||
\(481\) | −7.38131e59 | −0.331031 | ||||||||
\(482\) | −5.24801e59 | −0.224614 | ||||||||
\(483\) | −2.71167e60 | −1.10771 | ||||||||
\(484\) | 3.11805e59 | 0.121580 | ||||||||
\(485\) | 9.06552e59 | 0.337446 | ||||||||
\(486\) | 1.08790e61 | 3.86609 | ||||||||
\(487\) | 4.16113e60 | 1.41192 | 0.705960 | − | 0.708252i | \(-0.250516\pi\) | ||||
0.705960 | + | 0.708252i | \(0.250516\pi\) | |||||||
\(488\) | −2.01467e59 | −0.0652768 | ||||||||
\(489\) | −3.12704e60 | −0.967574 | ||||||||
\(490\) | −1.76749e60 | −0.522330 | ||||||||
\(491\) | −2.11553e60 | −0.597154 | −0.298577 | − | 0.954386i | \(-0.596512\pi\) | ||||
−0.298577 | + | 0.954386i | \(0.596512\pi\) | |||||||
\(492\) | −3.56854e60 | −0.962223 | ||||||||
\(493\) | 1.37083e59 | 0.0353124 | ||||||||
\(494\) | 7.49466e59 | 0.184457 | ||||||||
\(495\) | −1.39803e61 | −3.28776 | ||||||||
\(496\) | 1.62528e59 | 0.0365250 | ||||||||
\(497\) | 5.22246e59 | 0.112165 | ||||||||
\(498\) | −1.71234e60 | −0.351505 | ||||||||
\(499\) | 1.98362e60 | 0.389222 | 0.194611 | − | 0.980881i | \(-0.437656\pi\) | ||||
0.194611 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(500\) | 2.65560e60 | 0.498124 | ||||||||
\(501\) | 7.66845e60 | 1.37518 | ||||||||
\(502\) | −6.36123e60 | −1.09070 | ||||||||
\(503\) | −5.05113e60 | −0.828150 | −0.414075 | − | 0.910243i | \(-0.635895\pi\) | ||||
−0.414075 | + | 0.910243i | \(0.635895\pi\) | |||||||
\(504\) | 3.40416e60 | 0.533731 | ||||||||
\(505\) | 7.16467e60 | 1.07434 | ||||||||
\(506\) | 5.97163e60 | 0.856458 | ||||||||
\(507\) | 1.30780e61 | 1.79417 | ||||||||
\(508\) | −5.28311e60 | −0.693356 | ||||||||
\(509\) | −1.02093e61 | −1.28188 | −0.640939 | − | 0.767592i | \(-0.721455\pi\) | ||||
−0.640939 | + | 0.767592i | \(0.721455\pi\) | |||||||
\(510\) | −5.39229e59 | −0.0647804 | ||||||||
\(511\) | −1.25308e60 | −0.144048 | ||||||||
\(512\) | −4.01735e59 | −0.0441942 | ||||||||
\(513\) | −3.07731e61 | −3.23989 | ||||||||
\(514\) | 2.40241e60 | 0.242090 | ||||||||
\(515\) | 4.77151e60 | 0.460250 | ||||||||
\(516\) | 3.24025e60 | 0.299199 | ||||||||
\(517\) | 1.08966e61 | 0.963281 | ||||||||
\(518\) | 4.58971e60 | 0.388477 | ||||||||
\(519\) | 4.41035e61 | 3.57444 | ||||||||
\(520\) | −1.41568e60 | −0.109873 | ||||||||
\(521\) | −3.62888e60 | −0.269727 | −0.134863 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134863 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(522\) | −2.24030e61 | −1.59485 | ||||||||
\(523\) | 9.71059e60 | 0.662152 | 0.331076 | − | 0.943604i | \(-0.392588\pi\) | ||||
0.331076 | + | 0.943604i | \(0.392588\pi\) | |||||||
\(524\) | −1.74590e59 | −0.0114042 | ||||||||
\(525\) | 1.21149e59 | 0.00758113 | ||||||||
\(526\) | 1.01464e60 | 0.0608320 | ||||||||
\(527\) | 1.16980e59 | 0.00672004 | ||||||||
\(528\) | −1.00484e61 | −0.553137 | ||||||||
\(529\) | 3.41384e60 | 0.180090 | ||||||||
\(530\) | 2.10577e61 | 1.06464 | ||||||||
\(531\) | −4.32293e61 | −2.09484 | ||||||||
\(532\) | −4.66019e60 | −0.216467 | ||||||||
\(533\) | −6.74321e60 | −0.300265 | ||||||||
\(534\) | −3.72718e61 | −1.59112 | ||||||||
\(535\) | −4.36992e61 | −1.78860 | ||||||||
\(536\) | 7.96098e60 | 0.312434 | ||||||||
\(537\) | 5.37886e61 | 2.02427 | ||||||||
\(538\) | −1.10872e61 | −0.400148 | ||||||||
\(539\) | −2.37062e61 | −0.820568 | ||||||||
\(540\) | 5.81280e61 | 1.92986 | ||||||||
\(541\) | −5.23091e61 | −1.66586 | −0.832931 | − | 0.553377i | \(-0.813339\pi\) | ||||
−0.832931 | + | 0.553377i | \(0.813339\pi\) | |||||||
\(542\) | 3.58458e61 | 1.09510 | ||||||||
\(543\) | 8.80321e61 | 2.58015 | ||||||||
\(544\) | −2.89149e59 | −0.00813104 | ||||||||
\(545\) | −3.60155e61 | −0.971779 | ||||||||
\(546\) | 8.62214e60 | 0.223245 | ||||||||
\(547\) | −5.85485e61 | −1.45479 | −0.727396 | − | 0.686218i | \(-0.759270\pi\) | ||||
−0.727396 | + | 0.686218i | \(0.759270\pi\) | |||||||
\(548\) | 1.50832e61 | 0.359691 | ||||||||
\(549\) | 2.36979e61 | 0.542416 | ||||||||
\(550\) | −2.66793e59 | −0.00586158 | ||||||||
\(551\) | 3.06690e61 | 0.646827 | ||||||||
\(552\) | −3.76419e61 | −0.762152 | ||||||||
\(553\) | 4.84347e61 | 0.941544 | ||||||||
\(554\) | 2.11418e61 | 0.394613 | ||||||||
\(555\) | 1.18815e62 | 2.12951 | ||||||||
\(556\) | −4.41181e61 | −0.759335 | ||||||||
\(557\) | −1.16829e62 | −1.93111 | −0.965556 | − | 0.260196i | \(-0.916213\pi\) | ||||
−0.965556 | + | 0.260196i | \(0.916213\pi\) | |||||||
\(558\) | −1.91176e61 | −0.303504 | ||||||||
\(559\) | 6.12287e60 | 0.0933661 | ||||||||
\(560\) | 8.80274e60 | 0.128940 | ||||||||
\(561\) | −7.23233e60 | −0.101769 | ||||||||
\(562\) | −1.71897e61 | −0.232381 | ||||||||
\(563\) | 1.02917e62 | 1.33675 | 0.668374 | − | 0.743825i | \(-0.266991\pi\) | ||||
0.668374 | + | 0.743825i | \(0.266991\pi\) | |||||||
\(564\) | −6.86860e61 | −0.857212 | ||||||||
\(565\) | −6.57242e61 | −0.788197 | ||||||||
\(566\) | 8.66944e61 | 0.999129 | ||||||||
\(567\) | −2.17729e62 | −2.41155 | ||||||||
\(568\) | 7.24953e60 | 0.0771742 | ||||||||
\(569\) | 7.76715e61 | 0.794760 | 0.397380 | − | 0.917654i | \(-0.369920\pi\) | ||||
0.397380 | + | 0.917654i | \(0.369920\pi\) | |||||||
\(570\) | −1.20640e62 | −1.18660 | ||||||||
\(571\) | 3.25317e61 | 0.307606 | 0.153803 | − | 0.988102i | \(-0.450848\pi\) | ||||
0.153803 | + | 0.988102i | \(0.450848\pi\) | |||||||
\(572\) | −1.89877e61 | −0.172608 | ||||||||
\(573\) | −1.34007e62 | −1.17125 | ||||||||
\(574\) | 4.19293e61 | 0.352371 | ||||||||
\(575\) | −9.99424e59 | −0.00807650 | ||||||||
\(576\) | 4.72546e61 | 0.367230 | ||||||||
\(577\) | 1.39990e62 | 1.04626 | 0.523131 | − | 0.852252i | \(-0.324764\pi\) | ||||
0.523131 | + | 0.852252i | \(0.324764\pi\) | |||||||
\(578\) | 9.81616e61 | 0.705611 | ||||||||
\(579\) | 1.81127e62 | 1.25232 | ||||||||
\(580\) | −5.79314e61 | −0.385287 | ||||||||
\(581\) | 2.01196e61 | 0.128723 | ||||||||
\(582\) | −7.66437e61 | −0.471747 | ||||||||
\(583\) | 2.82434e62 | 1.67253 | ||||||||
\(584\) | −1.73946e61 | −0.0991116 | ||||||||
\(585\) | 1.66522e62 | 0.912987 | ||||||||
\(586\) | −1.84549e62 | −0.973677 | ||||||||
\(587\) | −1.67424e62 | −0.850083 | −0.425042 | − | 0.905174i | \(-0.639741\pi\) | ||||
−0.425042 | + | 0.905174i | \(0.639741\pi\) | |||||||
\(588\) | 1.49431e62 | 0.730214 | ||||||||
\(589\) | 2.61714e61 | 0.123093 | ||||||||
\(590\) | −1.11786e62 | −0.506076 | ||||||||
\(591\) | −7.52503e62 | −3.27937 | ||||||||
\(592\) | 6.37118e61 | 0.267289 | ||||||||
\(593\) | −2.09278e62 | −0.845266 | −0.422633 | − | 0.906301i | \(-0.638894\pi\) | ||||
−0.422633 | + | 0.906301i | \(0.638894\pi\) | |||||||
\(594\) | 7.79635e62 | 3.03177 | ||||||||
\(595\) | 6.33579e60 | 0.0237230 | ||||||||
\(596\) | −2.18318e61 | −0.0787133 | ||||||||
\(597\) | 3.53665e62 | 1.22792 | ||||||||
\(598\) | −7.11290e61 | −0.237832 | ||||||||
\(599\) | −2.68603e62 | −0.864983 | −0.432492 | − | 0.901638i | \(-0.642366\pi\) | ||||
−0.432492 | + | 0.901638i | \(0.642366\pi\) | |||||||
\(600\) | 1.68172e60 | 0.00521615 | ||||||||
\(601\) | 5.99608e62 | 1.79140 | 0.895699 | − | 0.444661i | \(-0.146676\pi\) | ||||
0.895699 | + | 0.444661i | \(0.146676\pi\) | |||||||
\(602\) | −3.80721e61 | −0.109568 | ||||||||
\(603\) | −9.36423e62 | −2.59617 | ||||||||
\(604\) | 1.18018e61 | 0.0315222 | ||||||||
\(605\) | −9.48411e61 | −0.244062 | ||||||||
\(606\) | −6.05731e62 | −1.50192 | ||||||||
\(607\) | 3.35261e62 | 0.801009 | 0.400504 | − | 0.916295i | \(-0.368835\pi\) | ||||
0.400504 | + | 0.916295i | \(0.368835\pi\) | |||||||
\(608\) | −6.46902e61 | −0.148939 | ||||||||
\(609\) | 3.52828e62 | 0.782841 | ||||||||
\(610\) | 6.12800e61 | 0.131038 | ||||||||
\(611\) | −1.29791e62 | −0.267496 | ||||||||
\(612\) | 3.40116e61 | 0.0675647 | ||||||||
\(613\) | −8.00170e62 | −1.53222 | −0.766111 | − | 0.642708i | \(-0.777811\pi\) | ||||
−0.766111 | + | 0.642708i | \(0.777811\pi\) | |||||||
\(614\) | −3.77284e62 | −0.696434 | ||||||||
\(615\) | 1.08544e63 | 1.93159 | ||||||||
\(616\) | 1.18066e62 | 0.202562 | ||||||||
\(617\) | −6.47534e62 | −1.07114 | −0.535570 | − | 0.844491i | \(-0.679903\pi\) | ||||
−0.535570 | + | 0.844491i | \(0.679903\pi\) | |||||||
\(618\) | −4.03404e62 | −0.643427 | ||||||||
\(619\) | 6.57187e62 | 1.01076 | 0.505382 | − | 0.862896i | \(-0.331352\pi\) | ||||
0.505382 | + | 0.862896i | \(0.331352\pi\) | |||||||
\(620\) | −4.94358e61 | −0.0733211 | ||||||||
\(621\) | 2.92056e63 | 4.17739 | ||||||||
\(622\) | 6.24691e62 | 0.861751 | ||||||||
\(623\) | 4.37933e62 | 0.582676 | ||||||||
\(624\) | 1.19688e62 | 0.153602 | ||||||||
\(625\) | −8.13755e62 | −1.00738 | ||||||||
\(626\) | 3.79677e62 | 0.453411 | ||||||||
\(627\) | −1.61806e63 | −1.86413 | ||||||||
\(628\) | 4.00668e62 | 0.445341 | ||||||||
\(629\) | 4.58567e61 | 0.0491771 | ||||||||
\(630\) | −1.03544e63 | −1.07142 | ||||||||
\(631\) | −3.17698e62 | −0.317216 | −0.158608 | − | 0.987342i | \(-0.550701\pi\) | ||||
−0.158608 | + | 0.987342i | \(0.550701\pi\) | |||||||
\(632\) | 6.72343e62 | 0.647824 | ||||||||
\(633\) | −3.35237e63 | −3.11723 | ||||||||
\(634\) | −2.36304e62 | −0.212062 | ||||||||
\(635\) | 1.60696e63 | 1.39186 | ||||||||
\(636\) | −1.78031e63 | −1.48837 | ||||||||
\(637\) | 2.82368e62 | 0.227866 | ||||||||
\(638\) | −7.76997e62 | −0.605277 | ||||||||
\(639\) | −8.52737e62 | −0.641277 | ||||||||
\(640\) | 1.22195e62 | 0.0887163 | ||||||||
\(641\) | 8.07272e62 | 0.565867 | 0.282933 | − | 0.959140i | \(-0.408692\pi\) | ||||
0.282933 | + | 0.959140i | \(0.408692\pi\) | |||||||
\(642\) | 3.69451e63 | 2.50045 | ||||||||
\(643\) | 1.81867e63 | 1.18852 | 0.594261 | − | 0.804273i | \(-0.297445\pi\) | ||||
0.594261 | + | 0.804273i | \(0.297445\pi\) | |||||||
\(644\) | 4.42281e62 | 0.279104 | ||||||||
\(645\) | −9.85582e62 | −0.600619 | ||||||||
\(646\) | −4.65608e61 | −0.0274024 | ||||||||
\(647\) | −6.55772e62 | −0.372741 | −0.186370 | − | 0.982480i | \(-0.559672\pi\) | ||||
−0.186370 | + | 0.982480i | \(0.559672\pi\) | |||||||
\(648\) | −3.02239e63 | −1.65925 | ||||||||
\(649\) | −1.49931e63 | −0.795035 | ||||||||
\(650\) | 3.17782e60 | 0.00162772 | ||||||||
\(651\) | 3.01086e62 | 0.148977 | ||||||||
\(652\) | 5.10030e62 | 0.243795 | ||||||||
\(653\) | −5.28862e62 | −0.244228 | −0.122114 | − | 0.992516i | \(-0.538967\pi\) | ||||
−0.122114 | + | 0.992516i | \(0.538967\pi\) | |||||||
\(654\) | 3.04490e63 | 1.35854 | ||||||||
\(655\) | 5.31048e61 | 0.0228931 | ||||||||
\(656\) | 5.82040e62 | 0.242447 | ||||||||
\(657\) | 2.04606e63 | 0.823565 | ||||||||
\(658\) | 8.07042e62 | 0.313916 | ||||||||
\(659\) | 1.82135e63 | 0.684653 | 0.342327 | − | 0.939581i | \(-0.388785\pi\) | ||||
0.342327 | + | 0.939581i | \(0.388785\pi\) | |||||||
\(660\) | 3.05640e63 | 1.11038 | ||||||||
\(661\) | −2.93115e63 | −1.02921 | −0.514607 | − | 0.857426i | \(-0.672062\pi\) | ||||
−0.514607 | + | 0.857426i | \(0.672062\pi\) | |||||||
\(662\) | −1.61563e62 | −0.0548324 | ||||||||
\(663\) | 8.61455e61 | 0.0282604 | ||||||||
\(664\) | 2.79289e62 | 0.0885670 | ||||||||
\(665\) | 1.41748e63 | 0.434540 | ||||||||
\(666\) | −7.49420e63 | −2.22103 | ||||||||
\(667\) | −2.91068e63 | −0.833995 | ||||||||
\(668\) | −1.25075e63 | −0.346497 | ||||||||
\(669\) | 1.06045e64 | 2.84054 | ||||||||
\(670\) | −2.42148e63 | −0.627187 | ||||||||
\(671\) | 8.21910e62 | 0.205858 | ||||||||
\(672\) | −7.44221e62 | −0.180257 | ||||||||
\(673\) | −7.82685e63 | −1.83336 | −0.916681 | − | 0.399620i | \(-0.869142\pi\) | ||||
−0.916681 | + | 0.399620i | \(0.869142\pi\) | |||||||
\(674\) | −4.62014e63 | −1.04667 | ||||||||
\(675\) | −1.30481e62 | −0.0285900 | ||||||||
\(676\) | −2.13307e63 | −0.452068 | ||||||||
\(677\) | −7.03892e62 | −0.144298 | −0.0721491 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721491 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(678\) | 5.55659e63 | 1.10190 | ||||||||
\(679\) | 9.00543e62 | 0.172756 | ||||||||
\(680\) | 8.79499e61 | 0.0163224 | ||||||||
\(681\) | −7.23869e62 | −0.129972 | ||||||||
\(682\) | −6.63052e62 | −0.115186 | ||||||||
\(683\) | 5.76408e63 | 0.968866 | 0.484433 | − | 0.874828i | \(-0.339026\pi\) | ||||
0.484433 | + | 0.874828i | \(0.339026\pi\) | |||||||
\(684\) | 7.60928e63 | 1.23760 | ||||||||
\(685\) | −4.58782e63 | −0.722052 | ||||||||
\(686\) | −4.14147e63 | −0.630757 | ||||||||
\(687\) | −3.42310e62 | −0.0504536 | ||||||||
\(688\) | −5.28496e62 | −0.0753879 | ||||||||
\(689\) | −3.36411e63 | −0.464449 | ||||||||
\(690\) | 1.14495e64 | 1.52996 | ||||||||
\(691\) | 2.79477e63 | 0.361485 | 0.180742 | − | 0.983530i | \(-0.442150\pi\) | ||||
0.180742 | + | 0.983530i | \(0.442150\pi\) | |||||||
\(692\) | −7.19342e63 | −0.900634 | ||||||||
\(693\) | −1.38876e64 | −1.68318 | ||||||||
\(694\) | 6.66520e63 | 0.782033 | ||||||||
\(695\) | 1.34193e64 | 1.52431 | ||||||||
\(696\) | 4.89776e63 | 0.538629 | ||||||||
\(697\) | 4.18924e62 | 0.0446065 | ||||||||
\(698\) | −5.49922e63 | −0.566962 | ||||||||
\(699\) | −6.21705e63 | −0.620652 | ||||||||
\(700\) | −1.97597e61 | −0.00191018 | ||||||||
\(701\) | 6.93963e63 | 0.649652 | 0.324826 | − | 0.945774i | \(-0.394694\pi\) | ||||
0.324826 | + | 0.945774i | \(0.394694\pi\) | |||||||
\(702\) | −9.28636e63 | −0.841900 | ||||||||
\(703\) | 1.02593e64 | 0.900792 | ||||||||
\(704\) | 1.63892e63 | 0.139371 | ||||||||
\(705\) | 2.08921e64 | 1.72079 | ||||||||
\(706\) | 3.58073e63 | 0.285671 | ||||||||
\(707\) | 7.11717e63 | 0.550010 | ||||||||
\(708\) | 9.45083e63 | 0.707492 | ||||||||
\(709\) | −1.01767e64 | −0.738019 | −0.369009 | − | 0.929426i | \(-0.620303\pi\) | ||||
−0.369009 | + | 0.929426i | \(0.620303\pi\) | |||||||
\(710\) | −2.20508e63 | −0.154921 | ||||||||
\(711\) | −7.90854e64 | −5.38307 | ||||||||
\(712\) | 6.07915e63 | 0.400906 | ||||||||
\(713\) | −2.48383e63 | −0.158711 | ||||||||
\(714\) | −5.35654e62 | −0.0331646 | ||||||||
\(715\) | 5.77545e63 | 0.346497 | ||||||||
\(716\) | −8.77310e63 | −0.510047 | ||||||||
\(717\) | −3.36344e63 | −0.189497 | ||||||||
\(718\) | 9.50928e62 | 0.0519215 | ||||||||
\(719\) | 1.82743e64 | 0.967031 | 0.483516 | − | 0.875336i | \(-0.339360\pi\) | ||||
0.483516 | + | 0.875336i | \(0.339360\pi\) | |||||||
\(720\) | −1.43734e64 | −0.737186 | ||||||||
\(721\) | 4.73988e63 | 0.235626 | ||||||||
\(722\) | 4.25792e63 | 0.205168 | ||||||||
\(723\) | −1.34956e64 | −0.630348 | ||||||||
\(724\) | −1.43583e64 | −0.650109 | ||||||||
\(725\) | 1.30040e62 | 0.00570784 | ||||||||
\(726\) | 8.01826e63 | 0.341198 | ||||||||
\(727\) | 6.92061e63 | 0.285509 | 0.142755 | − | 0.989758i | \(-0.454404\pi\) | ||||
0.142755 | + | 0.989758i | \(0.454404\pi\) | |||||||
\(728\) | −1.40630e63 | −0.0562499 | ||||||||
\(729\) | 1.58749e65 | 6.15660 | ||||||||
\(730\) | 5.29087e63 | 0.198959 | ||||||||
\(731\) | −3.80385e62 | −0.0138702 | ||||||||
\(732\) | −5.18087e63 | −0.183191 | ||||||||
\(733\) | −2.71099e64 | −0.929585 | −0.464793 | − | 0.885420i | \(-0.653871\pi\) | ||||
−0.464793 | + | 0.885420i | \(0.653871\pi\) | |||||||
\(734\) | 1.45822e64 | 0.484911 | ||||||||
\(735\) | −4.54521e64 | −1.46585 | ||||||||
\(736\) | 6.13951e63 | 0.192036 | ||||||||
\(737\) | −3.24777e64 | −0.985298 | ||||||||
\(738\) | −6.84634e64 | −2.01461 | ||||||||
\(739\) | 1.02173e64 | 0.291632 | 0.145816 | − | 0.989312i | \(-0.453419\pi\) | ||||
0.145816 | + | 0.989312i | \(0.453419\pi\) | |||||||
\(740\) | −1.93791e64 | −0.536562 | ||||||||
\(741\) | 1.92730e64 | 0.517654 | ||||||||
\(742\) | 2.09181e64 | 0.545048 | ||||||||
\(743\) | −5.09461e63 | −0.128784 | −0.0643921 | − | 0.997925i | \(-0.520511\pi\) | ||||
−0.0643921 | + | 0.997925i | \(0.520511\pi\) | |||||||
\(744\) | 4.17951e63 | 0.102503 | ||||||||
\(745\) | 6.64053e63 | 0.158011 | ||||||||
\(746\) | 3.27555e64 | 0.756243 | ||||||||
\(747\) | −3.28518e64 | −0.735945 | ||||||||
\(748\) | 1.17962e63 | 0.0256422 | ||||||||
\(749\) | −4.34095e64 | −0.915680 | ||||||||
\(750\) | 6.82905e64 | 1.39792 | ||||||||
\(751\) | 2.78830e64 | 0.553911 | 0.276956 | − | 0.960883i | \(-0.410674\pi\) | ||||
0.276956 | + | 0.960883i | \(0.410674\pi\) | |||||||
\(752\) | 1.12029e64 | 0.215988 | ||||||||
\(753\) | −1.63583e65 | −3.06092 | ||||||||
\(754\) | 9.25494e63 | 0.168081 | ||||||||
\(755\) | −3.58972e63 | −0.0632782 | ||||||||
\(756\) | 5.77427e64 | 0.987999 | ||||||||
\(757\) | 2.39252e64 | 0.397372 | 0.198686 | − | 0.980063i | \(-0.436333\pi\) | ||||
0.198686 | + | 0.980063i | \(0.436333\pi\) | |||||||
\(758\) | −7.53964e64 | −1.21561 | ||||||||
\(759\) | 1.53564e65 | 2.40353 | ||||||||
\(760\) | 1.96767e64 | 0.298983 | ||||||||
\(761\) | −9.78797e64 | −1.44390 | −0.721951 | − | 0.691944i | \(-0.756755\pi\) | ||||
−0.721951 | + | 0.691944i | \(0.756755\pi\) | |||||||
\(762\) | −1.35859e65 | −1.94581 | ||||||||
\(763\) | −3.57767e64 | −0.497506 | ||||||||
\(764\) | 2.18570e64 | 0.295114 | ||||||||
\(765\) | −1.03452e64 | −0.135631 | ||||||||
\(766\) | 9.26794e64 | 1.17987 | ||||||||
\(767\) | 1.78585e64 | 0.220775 | ||||||||
\(768\) | −1.03309e64 | −0.124025 | ||||||||
\(769\) | 1.03162e65 | 1.20276 | 0.601380 | − | 0.798963i | \(-0.294618\pi\) | ||||
0.601380 | + | 0.798963i | \(0.294618\pi\) | |||||||
\(770\) | −3.59118e64 | −0.406627 | ||||||||
\(771\) | 6.17795e64 | 0.679392 | ||||||||
\(772\) | −2.95423e64 | −0.315541 | ||||||||
\(773\) | 5.42578e64 | 0.562891 | 0.281445 | − | 0.959577i | \(-0.409186\pi\) | ||||
0.281445 | + | 0.959577i | \(0.409186\pi\) | |||||||
\(774\) | 6.21651e64 | 0.626433 | ||||||||
\(775\) | 1.10970e62 | 0.00108622 | ||||||||
\(776\) | 1.25008e64 | 0.118864 | ||||||||
\(777\) | 1.18027e65 | 1.09021 | ||||||||
\(778\) | 2.17283e64 | 0.194978 | ||||||||
\(779\) | 9.37243e64 | 0.817070 | ||||||||
\(780\) | −3.64052e64 | −0.308344 | ||||||||
\(781\) | −2.95753e64 | −0.243378 | ||||||||
\(782\) | 4.41892e63 | 0.0353316 | ||||||||
\(783\) | −3.80008e65 | −2.95225 | ||||||||
\(784\) | −2.43726e64 | −0.183989 | ||||||||
\(785\) | −1.21870e65 | −0.893987 | ||||||||
\(786\) | −4.48970e63 | −0.0320044 | ||||||||
\(787\) | 6.58146e64 | 0.455922 | 0.227961 | − | 0.973670i | \(-0.426794\pi\) | ||||
0.227961 | + | 0.973670i | \(0.426794\pi\) | |||||||
\(788\) | 1.22736e65 | 0.826287 | ||||||||
\(789\) | 2.60921e64 | 0.170717 | ||||||||
\(790\) | −2.04505e65 | −1.30045 | ||||||||
\(791\) | −6.52884e64 | −0.403520 | ||||||||
\(792\) | −1.92781e65 | −1.15810 | ||||||||
\(793\) | −9.78990e63 | −0.0571652 | ||||||||
\(794\) | 1.09106e65 | 0.619282 | ||||||||
\(795\) | 5.41512e65 | 2.98778 | ||||||||
\(796\) | −5.76838e64 | −0.309393 | ||||||||
\(797\) | 2.53956e65 | 1.32418 | 0.662089 | − | 0.749425i | \(-0.269670\pi\) | ||||
0.662089 | + | 0.749425i | \(0.269670\pi\) | |||||||
\(798\) | −1.19840e65 | −0.607485 | ||||||||
\(799\) | 8.06331e63 | 0.0397384 | ||||||||
\(800\) | −2.74294e62 | −0.00131429 | ||||||||
\(801\) | −7.15069e65 | −3.33132 | ||||||||
\(802\) | −2.19805e65 | −0.995665 | ||||||||
\(803\) | 7.09631e64 | 0.312560 | ||||||||
\(804\) | 2.04722e65 | 0.876805 | ||||||||
\(805\) | −1.34528e65 | −0.560280 | ||||||||
\(806\) | 7.89772e63 | 0.0319862 | ||||||||
\(807\) | −2.85114e65 | −1.12296 | ||||||||
\(808\) | 9.87967e64 | 0.378431 | ||||||||
\(809\) | −6.75007e64 | −0.251459 | −0.125729 | − | 0.992065i | \(-0.540127\pi\) | ||||
−0.125729 | + | 0.992065i | \(0.540127\pi\) | |||||||
\(810\) | 9.19314e65 | 3.33082 | ||||||||
\(811\) | 1.13300e65 | 0.399266 | 0.199633 | − | 0.979871i | \(-0.436025\pi\) | ||||
0.199633 | + | 0.979871i | \(0.436025\pi\) | |||||||
\(812\) | −5.75473e64 | −0.197249 | ||||||||
\(813\) | 9.21797e65 | 3.07325 | ||||||||
\(814\) | −2.59920e65 | −0.842927 | ||||||||
\(815\) | −1.55135e65 | −0.489400 | ||||||||
\(816\) | −7.43565e63 | −0.0228187 | ||||||||
\(817\) | −8.51021e64 | −0.254065 | ||||||||
\(818\) | 2.44099e65 | 0.708953 | ||||||||
\(819\) | 1.65418e65 | 0.467407 | ||||||||
\(820\) | −1.77038e65 | −0.486693 | ||||||||
\(821\) | −3.62842e65 | −0.970502 | −0.485251 | − | 0.874375i | \(-0.661272\pi\) | ||||
−0.485251 | + | 0.874375i | \(0.661272\pi\) | |||||||
\(822\) | 3.87874e65 | 1.00943 | ||||||||
\(823\) | −3.21071e65 | −0.813025 | −0.406513 | − | 0.913645i | \(-0.633255\pi\) | ||||
−0.406513 | + | 0.913645i | \(0.633255\pi\) | |||||||
\(824\) | 6.57964e64 | 0.162121 | ||||||||
\(825\) | −6.86076e63 | −0.0164497 | ||||||||
\(826\) | −1.11045e65 | −0.259088 | ||||||||
\(827\) | −2.23466e65 | −0.507386 | −0.253693 | − | 0.967285i | \(-0.581645\pi\) | ||||
−0.253693 | + | 0.967285i | \(0.581645\pi\) | |||||||
\(828\) | −7.22169e65 | −1.59572 | ||||||||
\(829\) | −6.35722e65 | −1.36707 | −0.683535 | − | 0.729918i | \(-0.739558\pi\) | ||||
−0.683535 | + | 0.729918i | \(0.739558\pi\) | |||||||
\(830\) | −8.49508e64 | −0.177791 | ||||||||
\(831\) | 5.43674e65 | 1.10743 | ||||||||
\(832\) | −1.95215e64 | −0.0387024 | ||||||||
\(833\) | −1.75422e64 | −0.0338511 | ||||||||
\(834\) | −1.13452e66 | −2.13097 | ||||||||
\(835\) | 3.80438e65 | 0.695565 | ||||||||
\(836\) | 2.63911e65 | 0.469695 | ||||||||
\(837\) | −3.24281e65 | −0.561821 | ||||||||
\(838\) | 4.54992e64 | 0.0767385 | ||||||||
\(839\) | 7.86587e65 | 1.29152 | 0.645762 | − | 0.763538i | \(-0.276540\pi\) | ||||
0.645762 | + | 0.763538i | \(0.276540\pi\) | |||||||
\(840\) | 2.26368e65 | 0.361853 | ||||||||
\(841\) | −2.63832e65 | −0.410599 | ||||||||
\(842\) | 8.35009e65 | 1.26523 | ||||||||
\(843\) | −4.42045e65 | −0.652147 | ||||||||
\(844\) | 5.46782e65 | 0.785434 | ||||||||
\(845\) | 6.48811e65 | 0.907491 | ||||||||
\(846\) | −1.31776e66 | −1.79475 | ||||||||
\(847\) | −9.42123e64 | −0.124948 | ||||||||
\(848\) | 2.90374e65 | 0.375017 | ||||||||
\(849\) | 2.22940e66 | 2.80392 | ||||||||
\(850\) | −1.97423e62 | −0.000241809 0 | ||||||||
\(851\) | −9.73676e65 | −1.16145 | ||||||||
\(852\) | 1.86426e65 | 0.216579 | ||||||||
\(853\) | 7.20063e65 | 0.814736 | 0.407368 | − | 0.913264i | \(-0.366447\pi\) | ||||
0.407368 | + | 0.913264i | \(0.366447\pi\) | |||||||
\(854\) | 6.08737e64 | 0.0670854 | ||||||||
\(855\) | −2.31450e66 | −2.48439 | ||||||||
\(856\) | −6.02587e65 | −0.630028 | ||||||||
\(857\) | −3.35470e64 | −0.0341653 | −0.0170826 | − | 0.999854i | \(-0.505438\pi\) | ||||
−0.0170826 | + | 0.999854i | \(0.505438\pi\) | |||||||
\(858\) | −4.88280e65 | −0.484401 | ||||||||
\(859\) | −3.58672e65 | −0.346619 | −0.173309 | − | 0.984867i | \(-0.555446\pi\) | ||||
−0.173309 | + | 0.984867i | \(0.555446\pi\) | |||||||
\(860\) | 1.60752e65 | 0.151335 | ||||||||
\(861\) | 1.07824e66 | 0.988882 | ||||||||
\(862\) | 1.18683e66 | 1.06041 | ||||||||
\(863\) | −8.48055e65 | −0.738212 | −0.369106 | − | 0.929387i | \(-0.620336\pi\) | ||||
−0.369106 | + | 0.929387i | \(0.620336\pi\) | |||||||
\(864\) | 8.01552e65 | 0.679787 | ||||||||
\(865\) | 2.18801e66 | 1.80795 | ||||||||
\(866\) | −3.19127e65 | −0.256928 | ||||||||
\(867\) | 2.52429e66 | 1.98020 | ||||||||
\(868\) | −4.91081e64 | −0.0375370 | ||||||||
\(869\) | −2.74290e66 | −2.04299 | ||||||||
\(870\) | −1.48974e66 | −1.08126 | ||||||||
\(871\) | 3.86848e65 | 0.273610 | ||||||||
\(872\) | −4.96633e65 | −0.342306 | ||||||||
\(873\) | −1.47043e66 | −0.987697 | ||||||||
\(874\) | 9.88627e65 | 0.647180 | ||||||||
\(875\) | −8.02394e65 | −0.511925 | ||||||||
\(876\) | −4.47312e65 | −0.278143 | ||||||||
\(877\) | −8.34705e64 | −0.0505874 | −0.0252937 | − | 0.999680i | \(-0.508052\pi\) | ||||
−0.0252937 | + | 0.999680i | \(0.508052\pi\) | |||||||
\(878\) | 9.90779e65 | 0.585262 | ||||||||
\(879\) | −4.74579e66 | −2.73249 | ||||||||
\(880\) | −4.98508e65 | −0.279777 | ||||||||
\(881\) | 1.29862e66 | 0.710432 | 0.355216 | − | 0.934784i | \(-0.384407\pi\) | ||||
0.355216 | + | 0.934784i | \(0.384407\pi\) | |||||||
\(882\) | 2.86687e66 | 1.52885 | ||||||||
\(883\) | −1.41183e66 | −0.733950 | −0.366975 | − | 0.930231i | \(-0.619607\pi\) | ||||
−0.366975 | + | 0.930231i | \(0.619607\pi\) | |||||||
\(884\) | −1.40506e64 | −0.00712064 | ||||||||
\(885\) | −2.87464e66 | −1.42024 | ||||||||
\(886\) | 1.03218e66 | 0.497161 | ||||||||
\(887\) | −3.71572e66 | −1.74487 | −0.872433 | − | 0.488735i | \(-0.837459\pi\) | ||||
−0.872433 | + | 0.488735i | \(0.837459\pi\) | |||||||
\(888\) | 1.63839e66 | 0.750111 | ||||||||
\(889\) | 1.59630e66 | 0.712567 | ||||||||
\(890\) | −1.84908e66 | −0.804788 | ||||||||
\(891\) | 1.23302e67 | 5.23264 | ||||||||
\(892\) | −1.72962e66 | −0.715717 | ||||||||
\(893\) | 1.80397e66 | 0.727901 | ||||||||
\(894\) | −5.61418e65 | −0.220898 | ||||||||
\(895\) | 2.66850e66 | 1.02388 | ||||||||
\(896\) | 1.21385e65 | 0.0454186 | ||||||||
\(897\) | −1.82913e66 | −0.667443 | ||||||||
\(898\) | −2.06415e66 | −0.734553 | ||||||||
\(899\) | 3.23183e65 | 0.112165 | ||||||||
\(900\) | 3.22642e64 | 0.0109210 | ||||||||
\(901\) | 2.08997e65 | 0.0689972 | ||||||||
\(902\) | −2.37450e66 | −0.764584 | ||||||||
\(903\) | −9.79048e65 | −0.307489 | ||||||||
\(904\) | −9.06298e65 | −0.277640 | ||||||||
\(905\) | 4.36734e66 | 1.30504 | ||||||||
\(906\) | 3.03490e65 | 0.0884627 | ||||||||
\(907\) | 2.68518e66 | 0.763500 | 0.381750 | − | 0.924266i | \(-0.375322\pi\) | ||||
0.381750 | + | 0.924266i | \(0.375322\pi\) | |||||||
\(908\) | 1.18065e65 | 0.0327484 | ||||||||
\(909\) | −1.16211e67 | −3.14456 | ||||||||
\(910\) | 4.27751e65 | 0.112917 | ||||||||
\(911\) | 3.66119e66 | 0.942886 | 0.471443 | − | 0.881897i | \(-0.343733\pi\) | ||||
0.471443 | + | 0.881897i | \(0.343733\pi\) | |||||||
\(912\) | −1.66355e66 | −0.417977 | ||||||||
\(913\) | −1.13939e66 | −0.279306 | ||||||||
\(914\) | 2.53435e66 | 0.606145 | ||||||||
\(915\) | 1.57585e66 | 0.367741 | ||||||||
\(916\) | 5.58318e64 | 0.0127126 | ||||||||
\(917\) | 5.27527e64 | 0.0117202 | ||||||||
\(918\) | 5.76918e65 | 0.125070 | ||||||||
\(919\) | −2.41366e66 | −0.510595 | −0.255298 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255298 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(920\) | −1.86744e66 | −0.385497 | ||||||||
\(921\) | −9.70211e66 | −1.95445 | ||||||||
\(922\) | 5.15938e66 | 1.01427 | ||||||||
\(923\) | 3.52276e65 | 0.0675841 | ||||||||
\(924\) | 3.03613e66 | 0.568462 | ||||||||
\(925\) | 4.35007e64 | 0.00794891 | ||||||||
\(926\) | −6.66119e66 | −1.18797 | ||||||||
\(927\) | −7.73940e66 | −1.34714 | ||||||||
\(928\) | −7.98841e65 | −0.135716 | ||||||||
\(929\) | 5.90852e66 | 0.979772 | 0.489886 | − | 0.871786i | \(-0.337038\pi\) | ||||
0.489886 | + | 0.871786i | \(0.337038\pi\) | |||||||
\(930\) | −1.27127e66 | −0.205766 | ||||||||
\(931\) | −3.92466e66 | −0.620060 | ||||||||
\(932\) | 1.01402e66 | 0.156383 | ||||||||
\(933\) | 1.60643e67 | 2.41839 | ||||||||
\(934\) | 4.24914e66 | 0.624448 | ||||||||
\(935\) | −3.58802e65 | −0.0514746 | ||||||||
\(936\) | 2.29624e66 | 0.321596 | ||||||||
\(937\) | 5.01170e66 | 0.685243 | 0.342621 | − | 0.939474i | \(-0.388685\pi\) | ||||
0.342621 | + | 0.939474i | \(0.388685\pi\) | |||||||
\(938\) | −2.40542e66 | −0.321091 | ||||||||
\(939\) | 9.76364e66 | 1.27244 | ||||||||
\(940\) | −3.40757e66 | −0.433579 | ||||||||
\(941\) | 4.09627e66 | 0.508888 | 0.254444 | − | 0.967088i | \(-0.418108\pi\) | ||||
0.254444 | + | 0.967088i | \(0.418108\pi\) | |||||||
\(942\) | 1.03034e67 | 1.24979 | ||||||||
\(943\) | −8.89503e66 | −1.05350 | ||||||||
\(944\) | −1.54146e66 | −0.178264 | ||||||||
\(945\) | −1.75635e67 | −1.98333 | ||||||||
\(946\) | 2.15606e66 | 0.237744 | ||||||||
\(947\) | 4.36909e66 | 0.470453 | 0.235226 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235226 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(948\) | 1.72897e67 | 1.81803 | ||||||||
\(949\) | −8.45253e65 | −0.0867955 | ||||||||
\(950\) | −4.41687e64 | −0.00442928 | ||||||||
\(951\) | −6.07672e66 | −0.595124 | ||||||||
\(952\) | 8.73668e64 | 0.00835632 | ||||||||
\(953\) | 3.02105e66 | 0.282207 | 0.141104 | − | 0.989995i | \(-0.454935\pi\) | ||||
0.141104 | + | 0.989995i | \(0.454935\pi\) | |||||||
\(954\) | −3.41556e67 | −3.11619 | ||||||||
\(955\) | −6.64821e66 | −0.592419 | ||||||||
\(956\) | 5.48588e65 | 0.0477467 | ||||||||
\(957\) | −1.99810e67 | −1.69863 | ||||||||
\(958\) | 1.12604e66 | 0.0935039 | ||||||||
\(959\) | −4.55741e66 | −0.369657 | ||||||||
\(960\) | 3.14232e66 | 0.248970 | ||||||||
\(961\) | −1.26446e67 | −0.978655 | ||||||||
\(962\) | 3.09595e66 | 0.234075 | ||||||||
\(963\) | 7.08802e67 | 5.23520 | ||||||||
\(964\) | 2.20118e66 | 0.158826 | ||||||||
\(965\) | 8.98584e66 | 0.633424 | ||||||||
\(966\) | 1.13736e67 | 0.783269 | ||||||||
\(967\) | −1.34618e67 | −0.905749 | −0.452875 | − | 0.891574i | \(-0.649601\pi\) | ||||
−0.452875 | + | 0.891574i | \(0.649601\pi\) | |||||||
\(968\) | −1.30780e66 | −0.0859700 | ||||||||
\(969\) | −1.19734e66 | −0.0769012 | ||||||||
\(970\) | −3.80236e66 | −0.238610 | ||||||||
\(971\) | −1.81545e67 | −1.11315 | −0.556573 | − | 0.830799i | \(-0.687884\pi\) | ||||
−0.556573 | + | 0.830799i | \(0.687884\pi\) | |||||||
\(972\) | −4.56298e67 | −2.73374 | ||||||||
\(973\) | 1.33303e67 | 0.780374 | ||||||||
\(974\) | −1.74531e67 | −0.998378 | ||||||||
\(975\) | 8.17197e64 | 0.00456796 | ||||||||
\(976\) | 8.45016e65 | 0.0461577 | ||||||||
\(977\) | −7.06118e66 | −0.376920 | −0.188460 | − | 0.982081i | \(-0.560350\pi\) | ||||
−0.188460 | + | 0.982081i | \(0.560350\pi\) | |||||||
\(978\) | 1.31158e67 | 0.684178 | ||||||||
\(979\) | −2.48006e67 | −1.26430 | ||||||||
\(980\) | 7.41338e66 | 0.369343 | ||||||||
\(981\) | 5.84172e67 | 2.84438 | ||||||||
\(982\) | 8.87319e66 | 0.422252 | ||||||||
\(983\) | 5.04041e66 | 0.234429 | 0.117215 | − | 0.993107i | \(-0.462603\pi\) | ||||
0.117215 | + | 0.993107i | \(0.462603\pi\) | |||||||
\(984\) | 1.49675e67 | 0.680394 | ||||||||
\(985\) | −3.73323e67 | −1.65870 | ||||||||
\(986\) | −5.74966e65 | −0.0249696 | ||||||||
\(987\) | 2.07536e67 | 0.880963 | ||||||||
\(988\) | −3.14349e66 | −0.130431 | ||||||||
\(989\) | 8.07673e66 | 0.327581 | ||||||||
\(990\) | 5.86378e67 | 2.32480 | ||||||||
\(991\) | −1.58623e67 | −0.614763 | −0.307381 | − | 0.951586i | \(-0.599453\pi\) | ||||
−0.307381 | + | 0.951586i | \(0.599453\pi\) | |||||||
\(992\) | −6.81692e65 | −0.0258271 | ||||||||
\(993\) | −4.15470e66 | −0.153880 | ||||||||
\(994\) | −2.19046e66 | −0.0793124 | ||||||||
\(995\) | 1.75456e67 | 0.621081 | ||||||||
\(996\) | 7.18210e66 | 0.248551 | ||||||||
\(997\) | 5.10990e67 | 1.72890 | 0.864452 | − | 0.502715i | \(-0.167665\pi\) | ||||
0.864452 | + | 0.502715i | \(0.167665\pi\) | |||||||
\(998\) | −8.31992e66 | −0.275221 | ||||||||
\(999\) | −1.27120e68 | −4.11139 |
(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 | 2.46.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 18.46.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 16.46.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.46.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.46.a.b.1.2 | 2 | 4.3 | odd | 2 | |||
18.46.a.f.1.2 | 2 | 3.2 | odd | 2 |