Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,72,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 72, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 72);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 72 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(95.7738481683\) |
Analytic rank: | \(1\) |
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: | \( x^{5} - 2 x^{4} + \cdots - 10\!\cdots\!54 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(6.47992e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05621e10 | −0.423157 | −0.211579 | − | 0.977361i | \(-0.567860\pi\) | ||||
−0.211579 | + | 0.977361i | \(0.567860\pi\) | |||||||
\(3\) | 5.00315e16 | 0.577350 | ||||||||
\(4\) | −1.93838e21 | −0.820938 | ||||||||
\(5\) | −6.43665e24 | −0.989065 | −0.494533 | − | 0.869159i | \(-0.664661\pi\) | ||||
−0.494533 | + | 0.869159i | \(0.664661\pi\) | |||||||
\(6\) | −1.02875e27 | −0.244310 | ||||||||
\(7\) | 4.31786e29 | 0.430812 | 0.215406 | − | 0.976525i | \(-0.430892\pi\) | ||||
0.215406 | + | 0.976525i | \(0.430892\pi\) | |||||||
\(8\) | 8.84080e31 | 0.770543 | ||||||||
\(9\) | 2.50316e33 | 0.333333 | ||||||||
\(10\) | 1.32351e35 | 0.418530 | ||||||||
\(11\) | −1.03462e37 | −1.11005 | −0.555024 | − | 0.831834i | \(-0.687291\pi\) | ||||
−0.555024 | + | 0.831834i | \(0.687291\pi\) | |||||||
\(12\) | −9.69804e37 | −0.473969 | ||||||||
\(13\) | −1.12453e39 | −0.320613 | −0.160307 | − | 0.987067i | \(-0.551248\pi\) | ||||
−0.160307 | + | 0.987067i | \(0.551248\pi\) | |||||||
\(14\) | −8.87841e39 | −0.182301 | ||||||||
\(15\) | −3.22036e41 | −0.571037 | ||||||||
\(16\) | 2.75903e42 | 0.494877 | ||||||||
\(17\) | 2.79729e43 | 0.583177 | 0.291589 | − | 0.956544i | \(-0.405816\pi\) | ||||
0.291589 | + | 0.956544i | \(0.405816\pi\) | |||||||
\(18\) | −5.14700e43 | −0.141052 | ||||||||
\(19\) | 1.59912e45 | 0.642876 | 0.321438 | − | 0.946931i | \(-0.395834\pi\) | ||||
0.321438 | + | 0.946931i | \(0.395834\pi\) | |||||||
\(20\) | 1.24767e46 | 0.811961 | ||||||||
\(21\) | 2.16029e46 | 0.248730 | ||||||||
\(22\) | 2.12740e47 | 0.469725 | ||||||||
\(23\) | 1.17659e48 | 0.536150 | 0.268075 | − | 0.963398i | \(-0.413612\pi\) | ||||
0.268075 | + | 0.963398i | \(0.413612\pi\) | |||||||
\(24\) | 4.42319e48 | 0.444873 | ||||||||
\(25\) | −9.21131e47 | −0.0217496 | ||||||||
\(26\) | 2.31226e49 | 0.135670 | ||||||||
\(27\) | 1.25237e50 | 0.192450 | ||||||||
\(28\) | −8.36967e50 | −0.353670 | ||||||||
\(29\) | 1.13318e52 | 1.37775 | 0.688877 | − | 0.724878i | \(-0.258104\pi\) | ||||
0.688877 | + | 0.724878i | \(0.258104\pi\) | |||||||
\(30\) | 6.62172e51 | 0.241639 | ||||||||
\(31\) | −8.82218e52 | −1.00516 | −0.502581 | − | 0.864530i | \(-0.667616\pi\) | ||||
−0.502581 | + | 0.864530i | \(0.667616\pi\) | |||||||
\(32\) | −2.65479e53 | −0.979954 | ||||||||
\(33\) | −5.17638e53 | −0.640887 | ||||||||
\(34\) | −5.75180e53 | −0.246776 | ||||||||
\(35\) | −2.77926e54 | −0.426101 | ||||||||
\(36\) | −4.85208e54 | −0.273646 | ||||||||
\(37\) | 5.62400e55 | 1.19918 | 0.599590 | − | 0.800308i | \(-0.295330\pi\) | ||||
0.599590 | + | 0.800308i | \(0.295330\pi\) | |||||||
\(38\) | −3.28811e55 | −0.272038 | ||||||||
\(39\) | −5.62619e55 | −0.185106 | ||||||||
\(40\) | −5.69052e56 | −0.762118 | ||||||||
\(41\) | −1.33250e56 | −0.0742743 | −0.0371372 | − | 0.999310i | \(-0.511824\pi\) | ||||
−0.0371372 | + | 0.999310i | \(0.511824\pi\) | |||||||
\(42\) | −4.44201e56 | −0.105252 | ||||||||
\(43\) | 1.13532e58 | 1.16678 | 0.583391 | − | 0.812191i | \(-0.301725\pi\) | ||||
0.583391 | + | 0.812191i | \(0.301725\pi\) | |||||||
\(44\) | 2.00550e58 | 0.911281 | ||||||||
\(45\) | −1.61119e58 | −0.329688 | ||||||||
\(46\) | −2.41931e58 | −0.226876 | ||||||||
\(47\) | 1.12423e59 | 0.491340 | 0.245670 | − | 0.969353i | \(-0.420992\pi\) | ||||
0.245670 | + | 0.969353i | \(0.420992\pi\) | |||||||
\(48\) | 1.38039e59 | 0.285717 | ||||||||
\(49\) | −8.18086e59 | −0.814401 | ||||||||
\(50\) | 1.89403e58 | 0.00920350 | ||||||||
\(51\) | 1.39953e60 | 0.336698 | ||||||||
\(52\) | 2.17977e60 | 0.263203 | ||||||||
\(53\) | 8.51201e60 | 0.522684 | 0.261342 | − | 0.965246i | \(-0.415835\pi\) | ||||
0.261342 | + | 0.965246i | \(0.415835\pi\) | |||||||
\(54\) | −2.57513e60 | −0.0814367 | ||||||||
\(55\) | 6.65951e61 | 1.09791 | ||||||||
\(56\) | 3.81733e61 | 0.331959 | ||||||||
\(57\) | 8.00063e61 | 0.371165 | ||||||||
\(58\) | −2.33006e62 | −0.583007 | ||||||||
\(59\) | −1.21168e62 | −0.165250 | −0.0826252 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826252 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(60\) | 6.24229e62 | 0.468786 | ||||||||
\(61\) | −4.10214e63 | −1.71317 | −0.856586 | − | 0.516004i | \(-0.827419\pi\) | ||||
−0.856586 | + | 0.516004i | \(0.827419\pi\) | |||||||
\(62\) | 1.81402e63 | 0.425342 | ||||||||
\(63\) | 1.08083e63 | 0.143604 | ||||||||
\(64\) | −1.05578e63 | −0.0802022 | ||||||||
\(65\) | 7.23820e63 | 0.317107 | ||||||||
\(66\) | 1.06437e64 | 0.271196 | ||||||||
\(67\) | −5.67761e64 | −0.848223 | −0.424112 | − | 0.905610i | \(-0.639414\pi\) | ||||
−0.424112 | + | 0.905610i | \(0.639414\pi\) | |||||||
\(68\) | −5.42222e64 | −0.478752 | ||||||||
\(69\) | 5.88665e64 | 0.309546 | ||||||||
\(70\) | 5.71472e64 | 0.180308 | ||||||||
\(71\) | −1.78276e65 | −0.339954 | −0.169977 | − | 0.985448i | \(-0.554369\pi\) | ||||
−0.169977 | + | 0.985448i | \(0.554369\pi\) | |||||||
\(72\) | 2.21299e65 | 0.256848 | ||||||||
\(73\) | 1.82157e66 | 1.29564 | 0.647819 | − | 0.761794i | \(-0.275681\pi\) | ||||
0.647819 | + | 0.761794i | \(0.275681\pi\) | |||||||
\(74\) | −1.15641e66 | −0.507442 | ||||||||
\(75\) | −4.60856e64 | −0.0125571 | ||||||||
\(76\) | −3.09970e66 | −0.527761 | ||||||||
\(77\) | −4.46736e66 | −0.478222 | ||||||||
\(78\) | 1.15686e66 | 0.0783290 | ||||||||
\(79\) | 3.72892e67 | 1.60628 | 0.803140 | − | 0.595791i | \(-0.203161\pi\) | ||||
0.803140 | + | 0.595791i | \(0.203161\pi\) | |||||||
\(80\) | −1.77589e67 | −0.489466 | ||||||||
\(81\) | 6.26579e66 | 0.111111 | ||||||||
\(82\) | 2.73989e66 | 0.0314297 | ||||||||
\(83\) | −2.02166e68 | −1.50812 | −0.754060 | − | 0.656806i | \(-0.771907\pi\) | ||||
−0.754060 | + | 0.656806i | \(0.771907\pi\) | |||||||
\(84\) | −4.18748e67 | −0.204192 | ||||||||
\(85\) | −1.80052e68 | −0.576801 | ||||||||
\(86\) | −2.33446e68 | −0.493732 | ||||||||
\(87\) | 5.66950e68 | 0.795447 | ||||||||
\(88\) | −9.14690e68 | −0.855340 | ||||||||
\(89\) | 2.01594e69 | 1.26221 | 0.631105 | − | 0.775697i | \(-0.282602\pi\) | ||||
0.631105 | + | 0.775697i | \(0.282602\pi\) | |||||||
\(90\) | 3.31295e68 | 0.139510 | ||||||||
\(91\) | −4.85555e68 | −0.138124 | ||||||||
\(92\) | −2.28068e69 | −0.440146 | ||||||||
\(93\) | −4.41387e69 | −0.580330 | ||||||||
\(94\) | −2.31165e69 | −0.207914 | ||||||||
\(95\) | −1.02930e70 | −0.635847 | ||||||||
\(96\) | −1.32823e70 | −0.565777 | ||||||||
\(97\) | −4.57132e70 | −1.34786 | −0.673931 | − | 0.738795i | \(-0.735395\pi\) | ||||
−0.673931 | + | 0.738795i | \(0.735395\pi\) | |||||||
\(98\) | 1.68215e70 | 0.344620 | ||||||||
\(99\) | −2.58982e70 | −0.370016 | ||||||||
\(100\) | 1.78551e69 | 0.0178551 | ||||||||
\(101\) | −2.30611e71 | −1.61984 | −0.809919 | − | 0.586542i | \(-0.800489\pi\) | ||||
−0.809919 | + | 0.586542i | \(0.800489\pi\) | |||||||
\(102\) | −2.87772e70 | −0.142476 | ||||||||
\(103\) | −3.04898e71 | −1.06766 | −0.533831 | − | 0.845591i | \(-0.679248\pi\) | ||||
−0.533831 | + | 0.845591i | \(0.679248\pi\) | |||||||
\(104\) | −9.94173e70 | −0.247046 | ||||||||
\(105\) | −1.39050e71 | −0.246010 | ||||||||
\(106\) | −1.75025e71 | −0.221177 | ||||||||
\(107\) | −1.23450e72 | −1.11781 | −0.558903 | − | 0.829233i | \(-0.688778\pi\) | ||||
−0.558903 | + | 0.829233i | \(0.688778\pi\) | |||||||
\(108\) | −2.42757e71 | −0.157990 | ||||||||
\(109\) | −3.68560e72 | −1.72929 | −0.864645 | − | 0.502383i | \(-0.832457\pi\) | ||||
−0.864645 | + | 0.502383i | \(0.832457\pi\) | |||||||
\(110\) | −1.36933e72 | −0.464589 | ||||||||
\(111\) | 2.81377e72 | 0.692347 | ||||||||
\(112\) | 1.19131e72 | 0.213199 | ||||||||
\(113\) | −4.37947e72 | −0.571659 | −0.285829 | − | 0.958281i | \(-0.592269\pi\) | ||||
−0.285829 | + | 0.958281i | \(0.592269\pi\) | |||||||
\(114\) | −1.64509e72 | −0.157061 | ||||||||
\(115\) | −7.57329e72 | −0.530287 | ||||||||
\(116\) | −2.19655e73 | −1.13105 | ||||||||
\(117\) | −2.81487e72 | −0.106871 | ||||||||
\(118\) | 2.49147e72 | 0.0699269 | ||||||||
\(119\) | 1.20783e73 | 0.251240 | ||||||||
\(120\) | −2.84705e73 | −0.440009 | ||||||||
\(121\) | 2.01724e73 | 0.232207 | ||||||||
\(122\) | 8.43484e73 | 0.724941 | ||||||||
\(123\) | −6.66668e72 | −0.0428823 | ||||||||
\(124\) | 1.71008e74 | 0.825175 | ||||||||
\(125\) | 2.78532e74 | 1.01058 | ||||||||
\(126\) | −2.22240e73 | −0.0607671 | ||||||||
\(127\) | 6.93356e73 | 0.143194 | 0.0715968 | − | 0.997434i | \(-0.477190\pi\) | ||||
0.0715968 | + | 0.997434i | \(0.477190\pi\) | |||||||
\(128\) | 6.48553e74 | 1.01389 | ||||||||
\(129\) | 5.68020e74 | 0.673642 | ||||||||
\(130\) | −1.48832e74 | −0.134186 | ||||||||
\(131\) | 7.14182e74 | 0.490544 | 0.245272 | − | 0.969454i | \(-0.421123\pi\) | ||||
0.245272 | + | 0.969454i | \(0.421123\pi\) | |||||||
\(132\) | 1.00338e75 | 0.526128 | ||||||||
\(133\) | 6.90476e74 | 0.276959 | ||||||||
\(134\) | 1.16743e75 | 0.358932 | ||||||||
\(135\) | −8.06106e74 | −0.190346 | ||||||||
\(136\) | 2.47303e75 | 0.449363 | ||||||||
\(137\) | −1.01049e76 | −1.41564 | −0.707820 | − | 0.706392i | \(-0.750321\pi\) | ||||
−0.707820 | + | 0.706392i | \(0.750321\pi\) | |||||||
\(138\) | −1.21042e75 | −0.130987 | ||||||||
\(139\) | 2.20784e75 | 0.184902 | 0.0924510 | − | 0.995717i | \(-0.470530\pi\) | ||||
0.0924510 | + | 0.995717i | \(0.470530\pi\) | |||||||
\(140\) | 5.38727e75 | 0.349803 | ||||||||
\(141\) | 5.62471e75 | 0.283675 | ||||||||
\(142\) | 3.66572e75 | 0.143854 | ||||||||
\(143\) | 1.16346e76 | 0.355896 | ||||||||
\(144\) | 6.90628e75 | 0.164959 | ||||||||
\(145\) | −7.29392e76 | −1.36269 | ||||||||
\(146\) | −3.74552e76 | −0.548259 | ||||||||
\(147\) | −4.09301e76 | −0.470195 | ||||||||
\(148\) | −1.09015e77 | −0.984452 | ||||||||
\(149\) | −1.12055e77 | −0.796746 | −0.398373 | − | 0.917223i | \(-0.630425\pi\) | ||||
−0.398373 | + | 0.917223i | \(0.630425\pi\) | |||||||
\(150\) | 9.47615e74 | 0.00531364 | ||||||||
\(151\) | −2.69028e77 | −1.19156 | −0.595780 | − | 0.803148i | \(-0.703157\pi\) | ||||
−0.595780 | + | 0.803148i | \(0.703157\pi\) | |||||||
\(152\) | 1.41375e77 | 0.495364 | ||||||||
\(153\) | 7.00205e76 | 0.194392 | ||||||||
\(154\) | 9.18581e76 | 0.202363 | ||||||||
\(155\) | 5.67853e77 | 0.994171 | ||||||||
\(156\) | 1.09057e77 | 0.151961 | ||||||||
\(157\) | −1.26925e78 | −1.40964 | −0.704821 | − | 0.709385i | \(-0.748973\pi\) | ||||
−0.704821 | + | 0.709385i | \(0.748973\pi\) | |||||||
\(158\) | −7.66743e77 | −0.679709 | ||||||||
\(159\) | 4.25869e77 | 0.301772 | ||||||||
\(160\) | 1.70880e78 | 0.969239 | ||||||||
\(161\) | 5.08034e77 | 0.230980 | ||||||||
\(162\) | −1.28838e77 | −0.0470175 | ||||||||
\(163\) | 4.30092e78 | 1.26154 | 0.630770 | − | 0.775970i | \(-0.282739\pi\) | ||||
0.630770 | + | 0.775970i | \(0.282739\pi\) | |||||||
\(164\) | 2.58289e77 | 0.0609746 | ||||||||
\(165\) | 3.33186e78 | 0.633879 | ||||||||
\(166\) | 4.15695e78 | 0.638172 | ||||||||
\(167\) | 7.45816e78 | 0.925118 | 0.462559 | − | 0.886589i | \(-0.346931\pi\) | ||||
0.462559 | + | 0.886589i | \(0.346931\pi\) | |||||||
\(168\) | 1.90987e78 | 0.191657 | ||||||||
\(169\) | −1.10375e79 | −0.897207 | ||||||||
\(170\) | 3.70224e78 | 0.244077 | ||||||||
\(171\) | 4.00284e78 | 0.214292 | ||||||||
\(172\) | −2.20070e79 | −0.957856 | ||||||||
\(173\) | 2.93224e79 | 1.03888 | 0.519438 | − | 0.854508i | \(-0.326141\pi\) | ||||
0.519438 | + | 0.854508i | \(0.326141\pi\) | |||||||
\(174\) | −1.16577e79 | −0.336599 | ||||||||
\(175\) | −3.97731e77 | −0.00936999 | ||||||||
\(176\) | −2.85456e79 | −0.549337 | ||||||||
\(177\) | −6.06224e78 | −0.0954074 | ||||||||
\(178\) | −4.14518e79 | −0.534113 | ||||||||
\(179\) | −5.61348e79 | −0.592856 | −0.296428 | − | 0.955055i | \(-0.595795\pi\) | ||||
−0.296428 | + | 0.955055i | \(0.595795\pi\) | |||||||
\(180\) | 3.12312e79 | 0.270654 | ||||||||
\(181\) | 5.40924e79 | 0.385076 | 0.192538 | − | 0.981290i | \(-0.438328\pi\) | ||||
0.192538 | + | 0.981290i | \(0.438328\pi\) | |||||||
\(182\) | 9.98402e78 | 0.0584482 | ||||||||
\(183\) | −2.05236e80 | −0.989100 | ||||||||
\(184\) | 1.04020e80 | 0.413127 | ||||||||
\(185\) | −3.61997e80 | −1.18607 | ||||||||
\(186\) | 9.07584e79 | 0.245571 | ||||||||
\(187\) | −2.89414e80 | −0.647355 | ||||||||
\(188\) | −2.17920e80 | −0.403360 | ||||||||
\(189\) | 5.40755e79 | 0.0829099 | ||||||||
\(190\) | 2.11645e80 | 0.269063 | ||||||||
\(191\) | −4.64288e80 | −0.489895 | −0.244947 | − | 0.969536i | \(-0.578771\pi\) | ||||
−0.244947 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(192\) | −5.28225e79 | −0.0463047 | ||||||||
\(193\) | −2.52043e80 | −0.183734 | −0.0918670 | − | 0.995771i | \(-0.529283\pi\) | ||||
−0.0918670 | + | 0.995771i | \(0.529283\pi\) | |||||||
\(194\) | 9.39958e80 | 0.570357 | ||||||||
\(195\) | 3.62138e80 | 0.183082 | ||||||||
\(196\) | 1.58577e81 | 0.668572 | ||||||||
\(197\) | 2.77270e81 | 0.975780 | 0.487890 | − | 0.872905i | \(-0.337767\pi\) | ||||
0.487890 | + | 0.872905i | \(0.337767\pi\) | |||||||
\(198\) | 5.32521e80 | 0.156575 | ||||||||
\(199\) | 3.83538e81 | 0.943027 | 0.471514 | − | 0.881859i | \(-0.343708\pi\) | ||||
0.471514 | + | 0.881859i | \(0.343708\pi\) | |||||||
\(200\) | −8.14353e79 | −0.0167590 | ||||||||
\(201\) | −2.84060e81 | −0.489722 | ||||||||
\(202\) | 4.74184e81 | 0.685446 | ||||||||
\(203\) | 4.89293e81 | 0.593553 | ||||||||
\(204\) | −2.71282e81 | −0.276408 | ||||||||
\(205\) | 8.57681e80 | 0.0734622 | ||||||||
\(206\) | 6.26934e81 | 0.451789 | ||||||||
\(207\) | 2.94518e81 | 0.178717 | ||||||||
\(208\) | −3.10261e81 | −0.158664 | ||||||||
\(209\) | −1.65448e82 | −0.713624 | ||||||||
\(210\) | 2.85917e81 | 0.104101 | ||||||||
\(211\) | −3.76862e82 | −1.15919 | −0.579596 | − | 0.814904i | \(-0.696789\pi\) | ||||
−0.579596 | + | 0.814904i | \(0.696789\pi\) | |||||||
\(212\) | −1.64996e82 | −0.429091 | ||||||||
\(213\) | −8.91941e81 | −0.196273 | ||||||||
\(214\) | 2.53838e82 | 0.473008 | ||||||||
\(215\) | −7.30769e82 | −1.15402 | ||||||||
\(216\) | 1.10719e82 | 0.148291 | ||||||||
\(217\) | −3.80929e82 | −0.433036 | ||||||||
\(218\) | 7.57836e82 | 0.731762 | ||||||||
\(219\) | 9.11358e82 | 0.748037 | ||||||||
\(220\) | −1.29087e83 | −0.901316 | ||||||||
\(221\) | −3.14563e82 | −0.186974 | ||||||||
\(222\) | −5.78570e82 | −0.292972 | ||||||||
\(223\) | −2.26378e83 | −0.977264 | −0.488632 | − | 0.872490i | \(-0.662504\pi\) | ||||
−0.488632 | + | 0.872490i | \(0.662504\pi\) | |||||||
\(224\) | −1.14630e83 | −0.422176 | ||||||||
\(225\) | −2.30573e81 | −0.00724986 | ||||||||
\(226\) | 9.00509e82 | 0.241902 | ||||||||
\(227\) | 5.11719e83 | 1.17520 | 0.587602 | − | 0.809150i | \(-0.300072\pi\) | ||||
0.587602 | + | 0.809150i | \(0.300072\pi\) | |||||||
\(228\) | −1.55083e83 | −0.304703 | ||||||||
\(229\) | 4.72950e83 | 0.795528 | 0.397764 | − | 0.917488i | \(-0.369786\pi\) | ||||
0.397764 | + | 0.917488i | \(0.369786\pi\) | |||||||
\(230\) | 1.55723e83 | 0.224395 | ||||||||
\(231\) | −2.23509e83 | −0.276102 | ||||||||
\(232\) | 1.00183e84 | 1.06162 | ||||||||
\(233\) | 6.20872e83 | 0.564764 | 0.282382 | − | 0.959302i | \(-0.408875\pi\) | ||||
0.282382 | + | 0.959302i | \(0.408875\pi\) | |||||||
\(234\) | 5.78795e82 | 0.0452233 | ||||||||
\(235\) | −7.23630e83 | −0.485968 | ||||||||
\(236\) | 2.34871e83 | 0.135660 | ||||||||
\(237\) | 1.86564e84 | 0.927386 | ||||||||
\(238\) | −2.48355e83 | −0.106314 | ||||||||
\(239\) | −6.72639e83 | −0.248117 | −0.124059 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124059 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(240\) | −8.88507e83 | −0.282593 | ||||||||
\(241\) | −1.99795e84 | −0.548252 | −0.274126 | − | 0.961694i | \(-0.588389\pi\) | ||||
−0.274126 | + | 0.961694i | \(0.588389\pi\) | |||||||
\(242\) | −4.14785e83 | −0.0982602 | ||||||||
\(243\) | 3.13487e83 | 0.0641500 | ||||||||
\(244\) | 7.95152e84 | 1.40641 | ||||||||
\(245\) | 5.26574e84 | 0.805496 | ||||||||
\(246\) | 1.37081e83 | 0.0181460 | ||||||||
\(247\) | −1.79825e84 | −0.206115 | ||||||||
\(248\) | −7.79951e84 | −0.774521 | ||||||||
\(249\) | −1.01147e85 | −0.870713 | ||||||||
\(250\) | −5.72719e84 | −0.427633 | ||||||||
\(251\) | −2.65267e85 | −1.71896 | −0.859480 | − | 0.511169i | \(-0.829213\pi\) | ||||
−0.859480 | + | 0.511169i | \(0.829213\pi\) | |||||||
\(252\) | −2.09506e84 | −0.117890 | ||||||||
\(253\) | −1.21733e85 | −0.595152 | ||||||||
\(254\) | −1.42568e84 | −0.0605935 | ||||||||
\(255\) | −9.00827e84 | −0.333016 | ||||||||
\(256\) | −1.08427e85 | −0.348834 | ||||||||
\(257\) | 4.24592e85 | 1.18945 | 0.594724 | − | 0.803930i | \(-0.297261\pi\) | ||||
0.594724 | + | 0.803930i | \(0.297261\pi\) | |||||||
\(258\) | −1.16797e85 | −0.285057 | ||||||||
\(259\) | 2.42836e85 | 0.516621 | ||||||||
\(260\) | −1.40304e85 | −0.260325 | ||||||||
\(261\) | 2.83654e85 | 0.459251 | ||||||||
\(262\) | −1.46851e85 | −0.207577 | ||||||||
\(263\) | 1.50287e86 | 1.85563 | 0.927816 | − | 0.373038i | \(-0.121684\pi\) | ||||
0.927816 | + | 0.373038i | \(0.121684\pi\) | |||||||
\(264\) | −4.57633e85 | −0.493831 | ||||||||
\(265\) | −5.47889e85 | −0.516968 | ||||||||
\(266\) | −1.41976e85 | −0.117197 | ||||||||
\(267\) | 1.00860e86 | 0.728737 | ||||||||
\(268\) | 1.10054e86 | 0.696339 | ||||||||
\(269\) | 6.91704e85 | 0.383455 | 0.191727 | − | 0.981448i | \(-0.438591\pi\) | ||||
0.191727 | + | 0.981448i | \(0.438591\pi\) | |||||||
\(270\) | 1.65752e85 | 0.0805462 | ||||||||
\(271\) | −6.25012e85 | −0.266366 | −0.133183 | − | 0.991091i | \(-0.542520\pi\) | ||||
−0.133183 | + | 0.991091i | \(0.542520\pi\) | |||||||
\(272\) | 7.71781e85 | 0.288601 | ||||||||
\(273\) | −2.42931e85 | −0.0797460 | ||||||||
\(274\) | 2.07778e86 | 0.599039 | ||||||||
\(275\) | 9.53023e84 | 0.0241431 | ||||||||
\(276\) | −1.14106e86 | −0.254118 | ||||||||
\(277\) | −3.12921e86 | −0.612918 | −0.306459 | − | 0.951884i | \(-0.599144\pi\) | ||||
−0.306459 | + | 0.951884i | \(0.599144\pi\) | |||||||
\(278\) | −4.53977e85 | −0.0782427 | ||||||||
\(279\) | −2.20833e86 | −0.335054 | ||||||||
\(280\) | −2.45708e86 | −0.328330 | ||||||||
\(281\) | 1.07871e87 | 1.27007 | 0.635037 | − | 0.772482i | \(-0.280985\pi\) | ||||
0.635037 | + | 0.772482i | \(0.280985\pi\) | |||||||
\(282\) | −1.15656e86 | −0.120039 | ||||||||
\(283\) | −1.17930e87 | −1.07946 | −0.539729 | − | 0.841839i | \(-0.681473\pi\) | ||||
−0.539729 | + | 0.841839i | \(0.681473\pi\) | |||||||
\(284\) | 3.45567e86 | 0.279081 | ||||||||
\(285\) | −5.14973e86 | −0.367106 | ||||||||
\(286\) | −2.39232e86 | −0.150600 | ||||||||
\(287\) | −5.75353e85 | −0.0319983 | ||||||||
\(288\) | −6.64535e86 | −0.326651 | ||||||||
\(289\) | −1.51829e87 | −0.659904 | ||||||||
\(290\) | 1.49978e87 | 0.576632 | ||||||||
\(291\) | −2.28710e87 | −0.778188 | ||||||||
\(292\) | −3.53090e87 | −1.06364 | ||||||||
\(293\) | −1.69373e86 | −0.0451901 | −0.0225950 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225950 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(294\) | 8.41608e86 | 0.198966 | ||||||||
\(295\) | 7.79919e86 | 0.163444 | ||||||||
\(296\) | 4.97207e87 | 0.924020 | ||||||||
\(297\) | −1.29573e87 | −0.213629 | ||||||||
\(298\) | 2.30409e87 | 0.337149 | ||||||||
\(299\) | −1.32311e87 | −0.171897 | ||||||||
\(300\) | 8.93316e85 | 0.0103086 | ||||||||
\(301\) | 4.90217e87 | 0.502664 | ||||||||
\(302\) | 5.53177e87 | 0.504217 | ||||||||
\(303\) | −1.15378e88 | −0.935214 | ||||||||
\(304\) | 4.41201e87 | 0.318145 | ||||||||
\(305\) | 2.64040e88 | 1.69444 | ||||||||
\(306\) | −1.43977e87 | −0.0822586 | ||||||||
\(307\) | 1.50981e88 | 0.768264 | 0.384132 | − | 0.923278i | \(-0.374501\pi\) | ||||
0.384132 | + | 0.923278i | \(0.374501\pi\) | |||||||
\(308\) | 8.65946e87 | 0.392591 | ||||||||
\(309\) | −1.52545e88 | −0.616414 | ||||||||
\(310\) | −1.16762e88 | −0.420691 | ||||||||
\(311\) | 3.95108e88 | 1.26976 | 0.634881 | − | 0.772610i | \(-0.281049\pi\) | ||||
0.634881 | + | 0.772610i | \(0.281049\pi\) | |||||||
\(312\) | −4.97400e87 | −0.142632 | ||||||||
\(313\) | −3.96054e88 | −1.01375 | −0.506875 | − | 0.862020i | \(-0.669199\pi\) | ||||
−0.506875 | + | 0.862020i | \(0.669199\pi\) | |||||||
\(314\) | 2.60984e88 | 0.596500 | ||||||||
\(315\) | −6.95691e87 | −0.142034 | ||||||||
\(316\) | −7.22808e88 | −1.31866 | ||||||||
\(317\) | 8.65682e88 | 1.41174 | 0.705869 | − | 0.708342i | \(-0.250557\pi\) | ||||
0.705869 | + | 0.708342i | \(0.250557\pi\) | |||||||
\(318\) | −8.75675e87 | −0.127697 | ||||||||
\(319\) | −1.17242e89 | −1.52937 | ||||||||
\(320\) | 6.79572e87 | 0.0793252 | ||||||||
\(321\) | −6.17638e88 | −0.645365 | ||||||||
\(322\) | −1.04462e88 | −0.0977409 | ||||||||
\(323\) | 4.47319e88 | 0.374911 | ||||||||
\(324\) | −1.21455e88 | −0.0912153 | ||||||||
\(325\) | 1.03584e87 | 0.00697320 | ||||||||
\(326\) | −8.84358e88 | −0.533830 | ||||||||
\(327\) | −1.84396e89 | −0.998406 | ||||||||
\(328\) | −1.17803e88 | −0.0572316 | ||||||||
\(329\) | 4.85428e88 | 0.211675 | ||||||||
\(330\) | −6.85098e88 | −0.268230 | ||||||||
\(331\) | −3.38783e89 | −1.19132 | −0.595660 | − | 0.803237i | \(-0.703109\pi\) | ||||
−0.595660 | + | 0.803237i | \(0.703109\pi\) | |||||||
\(332\) | 3.91876e89 | 1.23807 | ||||||||
\(333\) | 1.40777e89 | 0.399726 | ||||||||
\(334\) | −1.53355e89 | −0.391470 | ||||||||
\(335\) | 3.65448e89 | 0.838948 | ||||||||
\(336\) | 5.96031e88 | 0.123091 | ||||||||
\(337\) | 5.88470e89 | 1.09361 | 0.546805 | − | 0.837260i | \(-0.315844\pi\) | ||||
0.546805 | + | 0.837260i | \(0.315844\pi\) | |||||||
\(338\) | 2.26954e89 | 0.379660 | ||||||||
\(339\) | −2.19112e89 | −0.330047 | ||||||||
\(340\) | 3.49010e89 | 0.473517 | ||||||||
\(341\) | 9.12764e89 | 1.11578 | ||||||||
\(342\) | −8.23066e88 | −0.0906793 | ||||||||
\(343\) | −7.86978e89 | −0.781666 | ||||||||
\(344\) | 1.00372e90 | 0.899056 | ||||||||
\(345\) | −3.78903e89 | −0.306162 | ||||||||
\(346\) | −6.02930e89 | −0.439608 | ||||||||
\(347\) | −6.92123e89 | −0.455498 | −0.227749 | − | 0.973720i | \(-0.573137\pi\) | ||||
−0.227749 | + | 0.973720i | \(0.573137\pi\) | |||||||
\(348\) | −1.09897e90 | −0.653012 | ||||||||
\(349\) | −7.95083e89 | −0.426688 | −0.213344 | − | 0.976977i | \(-0.568435\pi\) | ||||
−0.213344 | + | 0.976977i | \(0.568435\pi\) | |||||||
\(350\) | 8.17817e87 | 0.00396498 | ||||||||
\(351\) | −1.40832e89 | −0.0617020 | ||||||||
\(352\) | 2.74671e90 | 1.08780 | ||||||||
\(353\) | 4.54547e90 | 1.62771 | 0.813854 | − | 0.581070i | \(-0.197366\pi\) | ||||
0.813854 | + | 0.581070i | \(0.197366\pi\) | |||||||
\(354\) | 1.24652e89 | 0.0403723 | ||||||||
\(355\) | 1.14750e90 | 0.336237 | ||||||||
\(356\) | −3.90766e90 | −1.03620 | ||||||||
\(357\) | 6.04296e89 | 0.145053 | ||||||||
\(358\) | 1.15425e90 | 0.250871 | ||||||||
\(359\) | −9.02810e90 | −1.77723 | −0.888615 | − | 0.458654i | \(-0.848332\pi\) | ||||
−0.888615 | + | 0.458654i | \(0.848332\pi\) | |||||||
\(360\) | −1.42442e90 | −0.254039 | ||||||||
\(361\) | −3.63019e90 | −0.586710 | ||||||||
\(362\) | −1.11225e90 | −0.162948 | ||||||||
\(363\) | 1.00925e90 | 0.134065 | ||||||||
\(364\) | 9.41193e89 | 0.113391 | ||||||||
\(365\) | −1.17248e91 | −1.28147 | ||||||||
\(366\) | 4.22008e90 | 0.418545 | ||||||||
\(367\) | −1.36021e91 | −1.22450 | −0.612251 | − | 0.790663i | \(-0.709736\pi\) | ||||
−0.612251 | + | 0.790663i | \(0.709736\pi\) | |||||||
\(368\) | 3.24624e90 | 0.265328 | ||||||||
\(369\) | −3.33544e89 | −0.0247581 | ||||||||
\(370\) | 7.44342e90 | 0.501893 | ||||||||
\(371\) | 3.67537e90 | 0.225179 | ||||||||
\(372\) | 8.55579e90 | 0.476415 | ||||||||
\(373\) | 1.01818e90 | 0.0515422 | 0.0257711 | − | 0.999668i | \(-0.491796\pi\) | ||||
0.0257711 | + | 0.999668i | \(0.491796\pi\) | |||||||
\(374\) | 5.95095e90 | 0.273933 | ||||||||
\(375\) | 1.39354e91 | 0.583457 | ||||||||
\(376\) | 9.93912e90 | 0.378599 | ||||||||
\(377\) | −1.27430e91 | −0.441726 | ||||||||
\(378\) | −1.11190e90 | −0.0350839 | ||||||||
\(379\) | 2.51275e91 | 0.721868 | 0.360934 | − | 0.932591i | \(-0.382458\pi\) | ||||
0.360934 | + | 0.932591i | \(0.382458\pi\) | |||||||
\(380\) | 1.99517e91 | 0.521991 | ||||||||
\(381\) | 3.46896e90 | 0.0826729 | ||||||||
\(382\) | 9.54672e90 | 0.207303 | ||||||||
\(383\) | −3.74261e91 | −0.740658 | −0.370329 | − | 0.928901i | \(-0.620755\pi\) | ||||
−0.370329 | + | 0.928901i | \(0.620755\pi\) | |||||||
\(384\) | 3.24481e91 | 0.585371 | ||||||||
\(385\) | 2.87548e91 | 0.472993 | ||||||||
\(386\) | 5.18252e90 | 0.0777484 | ||||||||
\(387\) | 2.84189e91 | 0.388927 | ||||||||
\(388\) | 8.86098e91 | 1.10651 | ||||||||
\(389\) | −1.01443e92 | −1.15615 | −0.578073 | − | 0.815985i | \(-0.696195\pi\) | ||||
−0.578073 | + | 0.815985i | \(0.696195\pi\) | |||||||
\(390\) | −7.44631e90 | −0.0774725 | ||||||||
\(391\) | 3.29126e91 | 0.312671 | ||||||||
\(392\) | −7.23254e91 | −0.627531 | ||||||||
\(393\) | 3.57316e91 | 0.283216 | ||||||||
\(394\) | −5.70125e91 | −0.412909 | ||||||||
\(395\) | −2.40018e92 | −1.58872 | ||||||||
\(396\) | 5.02007e91 | 0.303760 | ||||||||
\(397\) | −1.02196e92 | −0.565419 | −0.282709 | − | 0.959206i | \(-0.591233\pi\) | ||||
−0.282709 | + | 0.959206i | \(0.591233\pi\) | |||||||
\(398\) | −7.88633e91 | −0.399049 | ||||||||
\(399\) | 3.45456e91 | 0.159902 | ||||||||
\(400\) | −2.54143e90 | −0.0107634 | ||||||||
\(401\) | −2.77072e92 | −1.07391 | −0.536954 | − | 0.843612i | \(-0.680425\pi\) | ||||
−0.536954 | + | 0.843612i | \(0.680425\pi\) | |||||||
\(402\) | 5.84085e91 | 0.207229 | ||||||||
\(403\) | 9.92079e91 | 0.322268 | ||||||||
\(404\) | 4.47013e92 | 1.32979 | ||||||||
\(405\) | −4.03307e91 | −0.109896 | ||||||||
\(406\) | −1.00609e92 | −0.251166 | ||||||||
\(407\) | −5.81872e92 | −1.33115 | ||||||||
\(408\) | 1.23729e92 | 0.259440 | ||||||||
\(409\) | −7.85763e91 | −0.151048 | −0.0755239 | − | 0.997144i | \(-0.524063\pi\) | ||||
−0.0755239 | + | 0.997144i | \(0.524063\pi\) | |||||||
\(410\) | −1.76357e91 | −0.0310861 | ||||||||
\(411\) | −5.05565e92 | −0.817321 | ||||||||
\(412\) | 5.91010e92 | 0.876483 | ||||||||
\(413\) | −5.23188e91 | −0.0711919 | ||||||||
\(414\) | −6.05590e91 | −0.0756253 | ||||||||
\(415\) | 1.30127e93 | 1.49163 | ||||||||
\(416\) | 2.98538e92 | 0.314186 | ||||||||
\(417\) | 1.10462e92 | 0.106753 | ||||||||
\(418\) | 3.40196e92 | 0.301975 | ||||||||
\(419\) | 1.53284e93 | 1.24997 | 0.624984 | − | 0.780638i | \(-0.285106\pi\) | ||||
0.624984 | + | 0.780638i | \(0.285106\pi\) | |||||||
\(420\) | 2.69533e92 | 0.201959 | ||||||||
\(421\) | −2.73838e93 | −1.88573 | −0.942864 | − | 0.333179i | \(-0.891879\pi\) | ||||
−0.942864 | + | 0.333179i | \(0.891879\pi\) | |||||||
\(422\) | 7.74906e92 | 0.490520 | ||||||||
\(423\) | 2.81413e92 | 0.163780 | ||||||||
\(424\) | 7.52530e92 | 0.402750 | ||||||||
\(425\) | −2.57667e91 | −0.0126839 | ||||||||
\(426\) | 1.83401e92 | 0.0830543 | ||||||||
\(427\) | −1.77124e93 | −0.738055 | ||||||||
\(428\) | 2.39293e93 | 0.917649 | ||||||||
\(429\) | 5.82098e92 | 0.205477 | ||||||||
\(430\) | 1.50261e93 | 0.488334 | ||||||||
\(431\) | −1.97815e93 | −0.591994 | −0.295997 | − | 0.955189i | \(-0.595652\pi\) | ||||
−0.295997 | + | 0.955189i | \(0.595652\pi\) | |||||||
\(432\) | 3.45532e92 | 0.0952391 | ||||||||
\(433\) | −5.62822e93 | −1.42906 | −0.714530 | − | 0.699605i | \(-0.753359\pi\) | ||||
−0.714530 | + | 0.699605i | \(0.753359\pi\) | |||||||
\(434\) | 7.83269e92 | 0.183242 | ||||||||
\(435\) | −3.64926e93 | −0.786749 | ||||||||
\(436\) | 7.14412e93 | 1.41964 | ||||||||
\(437\) | 1.88150e93 | 0.344678 | ||||||||
\(438\) | −1.87394e93 | −0.316537 | ||||||||
\(439\) | −1.12111e94 | −1.74646 | −0.873229 | − | 0.487310i | \(-0.837978\pi\) | ||||
−0.873229 | + | 0.487310i | \(0.837978\pi\) | |||||||
\(440\) | 5.88754e93 | 0.845987 | ||||||||
\(441\) | −2.04780e93 | −0.271467 | ||||||||
\(442\) | 6.46807e92 | 0.0791196 | ||||||||
\(443\) | 7.36596e92 | 0.0831566 | 0.0415783 | − | 0.999135i | \(-0.486761\pi\) | ||||
0.0415783 | + | 0.999135i | \(0.486761\pi\) | |||||||
\(444\) | −5.45418e93 | −0.568374 | ||||||||
\(445\) | −1.29759e94 | −1.24841 | ||||||||
\(446\) | 4.65480e93 | 0.413537 | ||||||||
\(447\) | −5.60630e93 | −0.460002 | ||||||||
\(448\) | −4.55873e92 | −0.0345521 | ||||||||
\(449\) | 5.66884e93 | 0.396962 | 0.198481 | − | 0.980105i | \(-0.436399\pi\) | ||||
0.198481 | + | 0.980105i | \(0.436399\pi\) | |||||||
\(450\) | 4.74106e91 | 0.00306783 | ||||||||
\(451\) | 1.37863e93 | 0.0824481 | ||||||||
\(452\) | 8.48910e93 | 0.469296 | ||||||||
\(453\) | −1.34599e94 | −0.687948 | ||||||||
\(454\) | −1.05220e94 | −0.497297 | ||||||||
\(455\) | 3.12535e93 | 0.136614 | ||||||||
\(456\) | 7.07319e93 | 0.285998 | ||||||||
\(457\) | 2.57670e94 | 0.963916 | 0.481958 | − | 0.876194i | \(-0.339926\pi\) | ||||
0.481958 | + | 0.876194i | \(0.339926\pi\) | |||||||
\(458\) | −9.72482e93 | −0.336633 | ||||||||
\(459\) | 3.50323e93 | 0.112233 | ||||||||
\(460\) | 1.46800e94 | 0.435333 | ||||||||
\(461\) | 4.29540e94 | 1.17929 | 0.589645 | − | 0.807663i | \(-0.299268\pi\) | ||||
0.589645 | + | 0.807663i | \(0.299268\pi\) | |||||||
\(462\) | 4.59580e93 | 0.116835 | ||||||||
\(463\) | 4.18743e94 | 0.985876 | 0.492938 | − | 0.870065i | \(-0.335923\pi\) | ||||
0.492938 | + | 0.870065i | \(0.335923\pi\) | |||||||
\(464\) | 3.12649e94 | 0.681819 | ||||||||
\(465\) | 2.84106e94 | 0.573985 | ||||||||
\(466\) | −1.27664e94 | −0.238984 | ||||||||
\(467\) | −3.31055e93 | −0.0574315 | −0.0287158 | − | 0.999588i | \(-0.509142\pi\) | ||||
−0.0287158 | + | 0.999588i | \(0.509142\pi\) | |||||||
\(468\) | 5.45630e93 | 0.0877345 | ||||||||
\(469\) | −2.45151e94 | −0.365425 | ||||||||
\(470\) | 1.48793e94 | 0.205641 | ||||||||
\(471\) | −6.35024e94 | −0.813857 | ||||||||
\(472\) | −1.07122e94 | −0.127333 | ||||||||
\(473\) | −1.17463e95 | −1.29518 | ||||||||
\(474\) | −3.83613e94 | −0.392430 | ||||||||
\(475\) | −1.47300e93 | −0.0139823 | ||||||||
\(476\) | −2.34124e94 | −0.206252 | ||||||||
\(477\) | 2.13069e94 | 0.174228 | ||||||||
\(478\) | 1.38309e94 | 0.104993 | ||||||||
\(479\) | −1.85594e95 | −1.30814 | −0.654069 | − | 0.756435i | \(-0.726939\pi\) | ||||
−0.654069 | + | 0.756435i | \(0.726939\pi\) | |||||||
\(480\) | 8.54937e94 | 0.559590 | ||||||||
\(481\) | −6.32435e94 | −0.384473 | ||||||||
\(482\) | 4.10820e94 | 0.231997 | ||||||||
\(483\) | 2.54177e94 | 0.133356 | ||||||||
\(484\) | −3.91018e94 | −0.190628 | ||||||||
\(485\) | 2.94240e95 | 1.33312 | ||||||||
\(486\) | −6.44594e93 | −0.0271456 | ||||||||
\(487\) | −1.18747e95 | −0.464885 | −0.232443 | − | 0.972610i | \(-0.574672\pi\) | ||||
−0.232443 | + | 0.972610i | \(0.574672\pi\) | |||||||
\(488\) | −3.62662e95 | −1.32007 | ||||||||
\(489\) | 2.15182e95 | 0.728351 | ||||||||
\(490\) | −1.08274e95 | −0.340851 | ||||||||
\(491\) | −4.61391e95 | −1.35107 | −0.675533 | − | 0.737330i | \(-0.736086\pi\) | ||||
−0.675533 | + | 0.737330i | \(0.736086\pi\) | |||||||
\(492\) | 1.29226e94 | 0.0352037 | ||||||||
\(493\) | 3.16985e95 | 0.803475 | ||||||||
\(494\) | 3.69758e94 | 0.0872189 | ||||||||
\(495\) | 1.66698e95 | 0.365970 | ||||||||
\(496\) | −2.43407e95 | −0.497431 | ||||||||
\(497\) | −7.69769e94 | −0.146457 | ||||||||
\(498\) | 2.07979e95 | 0.368449 | ||||||||
\(499\) | 7.10119e95 | 1.17155 | 0.585777 | − | 0.810473i | \(-0.300790\pi\) | ||||
0.585777 | + | 0.810473i | \(0.300790\pi\) | |||||||
\(500\) | −5.39902e95 | −0.829621 | ||||||||
\(501\) | 3.73143e95 | 0.534117 | ||||||||
\(502\) | 5.45443e95 | 0.727391 | ||||||||
\(503\) | 2.17519e95 | 0.270292 | 0.135146 | − | 0.990826i | \(-0.456850\pi\) | ||||
0.135146 | + | 0.990826i | \(0.456850\pi\) | |||||||
\(504\) | 9.55538e94 | 0.110653 | ||||||||
\(505\) | 1.48436e96 | 1.60213 | ||||||||
\(506\) | 2.50307e95 | 0.251843 | ||||||||
\(507\) | −5.52223e95 | −0.518003 | ||||||||
\(508\) | −1.34399e95 | −0.117553 | ||||||||
\(509\) | −1.18373e96 | −0.965539 | −0.482769 | − | 0.875748i | \(-0.660369\pi\) | ||||
−0.482769 | + | 0.875748i | \(0.660369\pi\) | |||||||
\(510\) | 1.85229e95 | 0.140918 | ||||||||
\(511\) | 7.86527e95 | 0.558177 | ||||||||
\(512\) | −1.30840e96 | −0.866281 | ||||||||
\(513\) | 2.00268e95 | 0.123722 | ||||||||
\(514\) | −8.73048e95 | −0.503324 | ||||||||
\(515\) | 1.96252e96 | 1.05599 | ||||||||
\(516\) | −1.10104e96 | −0.553018 | ||||||||
\(517\) | −1.16316e96 | −0.545411 | ||||||||
\(518\) | −4.99322e95 | −0.218612 | ||||||||
\(519\) | 1.46705e96 | 0.599795 | ||||||||
\(520\) | 6.39915e95 | 0.244345 | ||||||||
\(521\) | 2.20858e96 | 0.787724 | 0.393862 | − | 0.919170i | \(-0.371139\pi\) | ||||
0.393862 | + | 0.919170i | \(0.371139\pi\) | |||||||
\(522\) | −5.83251e95 | −0.194336 | ||||||||
\(523\) | −1.71963e96 | −0.535333 | −0.267667 | − | 0.963512i | \(-0.586253\pi\) | ||||
−0.267667 | + | 0.963512i | \(0.586253\pi\) | |||||||
\(524\) | −1.38436e96 | −0.402706 | ||||||||
\(525\) | −1.98991e94 | −0.00540976 | ||||||||
\(526\) | −3.09021e96 | −0.785224 | ||||||||
\(527\) | −2.46782e96 | −0.586188 | ||||||||
\(528\) | −1.42818e96 | −0.317160 | ||||||||
\(529\) | −3.43153e96 | −0.712543 | ||||||||
\(530\) | 1.12657e96 | 0.218759 | ||||||||
\(531\) | −3.03303e95 | −0.0550835 | ||||||||
\(532\) | −1.33841e96 | −0.227366 | ||||||||
\(533\) | 1.49843e95 | 0.0238133 | ||||||||
\(534\) | −2.07390e96 | −0.308371 | ||||||||
\(535\) | 7.94604e96 | 1.10558 | ||||||||
\(536\) | −5.01946e96 | −0.653593 | ||||||||
\(537\) | −2.80851e96 | −0.342286 | ||||||||
\(538\) | −1.42229e96 | −0.162262 | ||||||||
\(539\) | 8.46411e96 | 0.904024 | ||||||||
\(540\) | 1.56254e96 | 0.156262 | ||||||||
\(541\) | 4.62986e96 | 0.433575 | 0.216788 | − | 0.976219i | \(-0.430442\pi\) | ||||
0.216788 | + | 0.976219i | \(0.430442\pi\) | |||||||
\(542\) | 1.28515e96 | 0.112715 | ||||||||
\(543\) | 2.70632e96 | 0.222324 | ||||||||
\(544\) | −7.42621e96 | −0.571487 | ||||||||
\(545\) | 2.37230e97 | 1.71038 | ||||||||
\(546\) | 4.99516e95 | 0.0337451 | ||||||||
\(547\) | −1.88303e97 | −1.19209 | −0.596043 | − | 0.802953i | \(-0.703261\pi\) | ||||
−0.596043 | + | 0.802953i | \(0.703261\pi\) | |||||||
\(548\) | 1.95872e97 | 1.16215 | ||||||||
\(549\) | −1.02683e97 | −0.571057 | ||||||||
\(550\) | −1.95961e95 | −0.0102163 | ||||||||
\(551\) | 1.81209e97 | 0.885726 | ||||||||
\(552\) | 5.20427e96 | 0.238519 | ||||||||
\(553\) | 1.61009e97 | 0.692005 | ||||||||
\(554\) | 6.43430e96 | 0.259361 | ||||||||
\(555\) | −1.81113e97 | −0.684776 | ||||||||
\(556\) | −4.27964e96 | −0.151793 | ||||||||
\(557\) | 3.83468e97 | 1.27605 | 0.638027 | − | 0.770014i | \(-0.279751\pi\) | ||||
0.638027 | + | 0.770014i | \(0.279751\pi\) | |||||||
\(558\) | 4.54078e96 | 0.141781 | ||||||||
\(559\) | −1.27670e97 | −0.374086 | ||||||||
\(560\) | −7.66805e96 | −0.210868 | ||||||||
\(561\) | −1.44798e97 | −0.373751 | ||||||||
\(562\) | −2.21804e97 | −0.537441 | ||||||||
\(563\) | −5.42588e97 | −1.23430 | −0.617152 | − | 0.786844i | \(-0.711714\pi\) | ||||
−0.617152 | + | 0.786844i | \(0.711714\pi\) | |||||||
\(564\) | −1.09029e97 | −0.232880 | ||||||||
\(565\) | 2.81891e97 | 0.565408 | ||||||||
\(566\) | 2.42488e97 | 0.456780 | ||||||||
\(567\) | 2.70548e96 | 0.0478680 | ||||||||
\(568\) | −1.57610e97 | −0.261950 | ||||||||
\(569\) | −1.17545e98 | −1.83535 | −0.917677 | − | 0.397328i | \(-0.869937\pi\) | ||||
−0.917677 | + | 0.397328i | \(0.869937\pi\) | |||||||
\(570\) | 1.05889e97 | 0.155344 | ||||||||
\(571\) | −8.24006e97 | −1.13592 | −0.567961 | − | 0.823056i | \(-0.692267\pi\) | ||||
−0.567961 | + | 0.823056i | \(0.692267\pi\) | |||||||
\(572\) | −2.25524e97 | −0.292169 | ||||||||
\(573\) | −2.32290e97 | −0.282841 | ||||||||
\(574\) | 1.18304e96 | 0.0135403 | ||||||||
\(575\) | −1.08379e96 | −0.0116610 | ||||||||
\(576\) | −2.64279e96 | −0.0267341 | ||||||||
\(577\) | 1.61133e98 | 1.53265 | 0.766326 | − | 0.642452i | \(-0.222083\pi\) | ||||
0.766326 | + | 0.642452i | \(0.222083\pi\) | |||||||
\(578\) | 3.12191e97 | 0.279243 | ||||||||
\(579\) | −1.26101e97 | −0.106079 | ||||||||
\(580\) | 1.41384e98 | 1.11868 | ||||||||
\(581\) | −8.72924e97 | −0.649717 | ||||||||
\(582\) | 4.70276e97 | 0.329296 | ||||||||
\(583\) | −8.80673e97 | −0.580204 | ||||||||
\(584\) | 1.61041e98 | 0.998345 | ||||||||
\(585\) | 1.81183e97 | 0.105702 | ||||||||
\(586\) | 3.48265e96 | 0.0191225 | ||||||||
\(587\) | −2.32660e98 | −1.20246 | −0.601228 | − | 0.799078i | \(-0.705322\pi\) | ||||
−0.601228 | + | 0.799078i | \(0.705322\pi\) | |||||||
\(588\) | 7.93383e97 | 0.386001 | ||||||||
\(589\) | −1.41077e98 | −0.646195 | ||||||||
\(590\) | −1.60367e97 | −0.0691623 | ||||||||
\(591\) | 1.38723e98 | 0.563367 | ||||||||
\(592\) | 1.55168e98 | 0.593446 | ||||||||
\(593\) | 2.35123e98 | 0.846940 | 0.423470 | − | 0.905910i | \(-0.360812\pi\) | ||||
0.423470 | + | 0.905910i | \(0.360812\pi\) | |||||||
\(594\) | 2.66428e97 | 0.0903986 | ||||||||
\(595\) | −7.77438e97 | −0.248493 | ||||||||
\(596\) | 2.17206e98 | 0.654079 | ||||||||
\(597\) | 1.91890e98 | 0.544457 | ||||||||
\(598\) | 2.72058e97 | 0.0727394 | ||||||||
\(599\) | −5.98305e98 | −1.50754 | −0.753772 | − | 0.657136i | \(-0.771768\pi\) | ||||
−0.753772 | + | 0.657136i | \(0.771768\pi\) | |||||||
\(600\) | −4.07433e96 | −0.00967581 | ||||||||
\(601\) | 2.46247e98 | 0.551222 | 0.275611 | − | 0.961269i | \(-0.411120\pi\) | ||||
0.275611 | + | 0.961269i | \(0.411120\pi\) | |||||||
\(602\) | −1.00799e98 | −0.212706 | ||||||||
\(603\) | −1.42119e98 | −0.282741 | ||||||||
\(604\) | 5.21480e98 | 0.978197 | ||||||||
\(605\) | −1.29842e98 | −0.229668 | ||||||||
\(606\) | 2.37242e98 | 0.395743 | ||||||||
\(607\) | 3.58896e98 | 0.564638 | 0.282319 | − | 0.959321i | \(-0.408896\pi\) | ||||
0.282319 | + | 0.959321i | \(0.408896\pi\) | |||||||
\(608\) | −4.24532e98 | −0.629989 | ||||||||
\(609\) | 2.44801e98 | 0.342688 | ||||||||
\(610\) | −5.42921e98 | −0.717014 | ||||||||
\(611\) | −1.26423e98 | −0.157530 | ||||||||
\(612\) | −1.35727e98 | −0.159584 | ||||||||
\(613\) | 2.98052e98 | 0.330708 | 0.165354 | − | 0.986234i | \(-0.447123\pi\) | ||||
0.165354 | + | 0.986234i | \(0.447123\pi\) | |||||||
\(614\) | −3.10448e98 | −0.325097 | ||||||||
\(615\) | 4.29111e97 | 0.0424134 | ||||||||
\(616\) | −3.94950e98 | −0.368491 | ||||||||
\(617\) | −1.51606e99 | −1.33534 | −0.667670 | − | 0.744457i | \(-0.732708\pi\) | ||||
−0.667670 | + | 0.744457i | \(0.732708\pi\) | |||||||
\(618\) | 3.13665e98 | 0.260840 | ||||||||
\(619\) | −9.30578e98 | −0.730693 | −0.365346 | − | 0.930872i | \(-0.619049\pi\) | ||||
−0.365346 | + | 0.930872i | \(0.619049\pi\) | |||||||
\(620\) | −1.10072e99 | −0.816152 | ||||||||
\(621\) | 1.47352e98 | 0.103182 | ||||||||
\(622\) | −8.12424e98 | −0.537309 | ||||||||
\(623\) | 8.70453e98 | 0.543776 | ||||||||
\(624\) | −1.55228e98 | −0.0916047 | ||||||||
\(625\) | −1.75380e99 | −0.977777 | ||||||||
\(626\) | 8.14370e98 | 0.428976 | ||||||||
\(627\) | −8.27764e98 | −0.412011 | ||||||||
\(628\) | 2.46029e99 | 1.15723 | ||||||||
\(629\) | 1.57320e99 | 0.699334 | ||||||||
\(630\) | 1.43048e98 | 0.0601027 | ||||||||
\(631\) | 2.74731e99 | 1.09110 | 0.545550 | − | 0.838078i | \(-0.316321\pi\) | ||||
0.545550 | + | 0.838078i | \(0.316321\pi\) | |||||||
\(632\) | 3.29666e99 | 1.23771 | ||||||||
\(633\) | −1.88550e99 | −0.669259 | ||||||||
\(634\) | −1.78002e99 | −0.597388 | ||||||||
\(635\) | −4.46289e98 | −0.141628 | ||||||||
\(636\) | −8.25498e98 | −0.247736 | ||||||||
\(637\) | 9.19961e98 | 0.261108 | ||||||||
\(638\) | 2.41074e99 | 0.647166 | ||||||||
\(639\) | −4.46252e98 | −0.113318 | ||||||||
\(640\) | −4.17451e99 | −1.00281 | ||||||||
\(641\) | 1.25416e99 | 0.285032 | 0.142516 | − | 0.989793i | \(-0.454481\pi\) | ||||
0.142516 | + | 0.989793i | \(0.454481\pi\) | |||||||
\(642\) | 1.26999e99 | 0.273091 | ||||||||
\(643\) | 9.41159e99 | 1.91502 | 0.957510 | − | 0.288400i | \(-0.0931233\pi\) | ||||
0.957510 | + | 0.288400i | \(0.0931233\pi\) | |||||||
\(644\) | −9.84766e98 | −0.189620 | ||||||||
\(645\) | −3.65615e99 | −0.666276 | ||||||||
\(646\) | −9.19781e98 | −0.158646 | ||||||||
\(647\) | 5.81388e99 | 0.949215 | 0.474607 | − | 0.880198i | \(-0.342590\pi\) | ||||
0.474607 | + | 0.880198i | \(0.342590\pi\) | |||||||
\(648\) | 5.53946e98 | 0.0856159 | ||||||||
\(649\) | 1.25364e99 | 0.183436 | ||||||||
\(650\) | −2.12990e97 | −0.00295076 | ||||||||
\(651\) | −1.90585e99 | −0.250013 | ||||||||
\(652\) | −8.33684e99 | −1.03565 | ||||||||
\(653\) | 1.14795e100 | 1.35054 | 0.675268 | − | 0.737573i | \(-0.264028\pi\) | ||||
0.675268 | + | 0.737573i | \(0.264028\pi\) | |||||||
\(654\) | 3.79157e99 | 0.422483 | ||||||||
\(655\) | −4.59694e99 | −0.485180 | ||||||||
\(656\) | −3.67640e98 | −0.0367566 | ||||||||
\(657\) | 4.55967e99 | 0.431879 | ||||||||
\(658\) | −9.98140e98 | −0.0895720 | ||||||||
\(659\) | −1.28525e100 | −1.09283 | −0.546417 | − | 0.837514i | \(-0.684008\pi\) | ||||
−0.546417 | + | 0.837514i | \(0.684008\pi\) | |||||||
\(660\) | −6.45842e99 | −0.520375 | ||||||||
\(661\) | −2.50553e100 | −1.91314 | −0.956571 | − | 0.291501i | \(-0.905845\pi\) | ||||
−0.956571 | + | 0.291501i | \(0.905845\pi\) | |||||||
\(662\) | 6.96608e99 | 0.504116 | ||||||||
\(663\) | −1.57381e99 | −0.107950 | ||||||||
\(664\) | −1.78731e100 | −1.16207 | ||||||||
\(665\) | −4.44436e99 | −0.273930 | ||||||||
\(666\) | −2.89468e99 | −0.169147 | ||||||||
\(667\) | 1.33329e100 | 0.738683 | ||||||||
\(668\) | −1.44568e100 | −0.759464 | ||||||||
\(669\) | −1.13261e100 | −0.564224 | ||||||||
\(670\) | −7.51437e99 | −0.355007 | ||||||||
\(671\) | 4.24417e100 | 1.90170 | ||||||||
\(672\) | −5.73512e99 | −0.243744 | ||||||||
\(673\) | 2.51439e100 | 1.01367 | 0.506837 | − | 0.862042i | \(-0.330814\pi\) | ||||
0.506837 | + | 0.862042i | \(0.330814\pi\) | |||||||
\(674\) | −1.21002e100 | −0.462769 | ||||||||
\(675\) | −1.15359e98 | −0.00418571 | ||||||||
\(676\) | 2.13949e100 | 0.736551 | ||||||||
\(677\) | 1.83479e100 | 0.599360 | 0.299680 | − | 0.954040i | \(-0.403120\pi\) | ||||
0.299680 | + | 0.954040i | \(0.403120\pi\) | |||||||
\(678\) | 4.50539e99 | 0.139662 | ||||||||
\(679\) | −1.97383e100 | −0.580675 | ||||||||
\(680\) | −1.59180e100 | −0.444450 | ||||||||
\(681\) | 2.56021e100 | 0.678505 | ||||||||
\(682\) | −1.87683e100 | −0.472150 | ||||||||
\(683\) | −3.84076e100 | −0.917237 | −0.458619 | − | 0.888633i | \(-0.651656\pi\) | ||||
−0.458619 | + | 0.888633i | \(0.651656\pi\) | |||||||
\(684\) | −7.75904e99 | −0.175920 | ||||||||
\(685\) | 6.50419e100 | 1.40016 | ||||||||
\(686\) | 1.61819e100 | 0.330768 | ||||||||
\(687\) | 2.36624e100 | 0.459298 | ||||||||
\(688\) | 3.13240e100 | 0.577414 | ||||||||
\(689\) | −9.57200e99 | −0.167579 | ||||||||
\(690\) | 7.79104e99 | 0.129555 | ||||||||
\(691\) | 4.41005e100 | 0.696583 | 0.348292 | − | 0.937386i | \(-0.386762\pi\) | ||||
0.348292 | + | 0.937386i | \(0.386762\pi\) | |||||||
\(692\) | −5.68382e100 | −0.852852 | ||||||||
\(693\) | −1.11825e100 | −0.159407 | ||||||||
\(694\) | 1.42315e100 | 0.192747 | ||||||||
\(695\) | −1.42111e100 | −0.182880 | ||||||||
\(696\) | 5.01229e100 | 0.612926 | ||||||||
\(697\) | −3.72737e99 | −0.0433151 | ||||||||
\(698\) | 1.63486e100 | 0.180556 | ||||||||
\(699\) | 3.10632e100 | 0.326067 | ||||||||
\(700\) | 7.70956e98 | 0.00769218 | ||||||||
\(701\) | −1.21602e101 | −1.15333 | −0.576663 | − | 0.816982i | \(-0.695645\pi\) | ||||
−0.576663 | + | 0.816982i | \(0.695645\pi\) | |||||||
\(702\) | 2.89580e99 | 0.0261097 | ||||||||
\(703\) | 8.99343e100 | 0.770924 | ||||||||
\(704\) | 1.09234e100 | 0.0890283 | ||||||||
\(705\) | −3.62043e100 | −0.280574 | ||||||||
\(706\) | −9.34642e100 | −0.688776 | ||||||||
\(707\) | −9.95747e100 | −0.697846 | ||||||||
\(708\) | 1.17510e100 | 0.0783235 | ||||||||
\(709\) | −1.60637e101 | −1.01837 | −0.509184 | − | 0.860657i | \(-0.670053\pi\) | ||||
−0.509184 | + | 0.860657i | \(0.670053\pi\) | |||||||
\(710\) | −2.35949e100 | −0.142281 | ||||||||
\(711\) | 9.33406e100 | 0.535427 | ||||||||
\(712\) | 1.78225e101 | 0.972587 | ||||||||
\(713\) | −1.03801e101 | −0.538917 | ||||||||
\(714\) | −1.24256e100 | −0.0613804 | ||||||||
\(715\) | −7.48881e100 | −0.352005 | ||||||||
\(716\) | 1.08811e101 | 0.486698 | ||||||||
\(717\) | −3.36532e100 | −0.143251 | ||||||||
\(718\) | 1.85636e101 | 0.752048 | ||||||||
\(719\) | −3.09787e101 | −1.19450 | −0.597252 | − | 0.802054i | \(-0.703741\pi\) | ||||
−0.597252 | + | 0.802054i | \(0.703741\pi\) | |||||||
\(720\) | −4.44534e100 | −0.163155 | ||||||||
\(721\) | −1.31651e101 | −0.459961 | ||||||||
\(722\) | 7.46442e100 | 0.248271 | ||||||||
\(723\) | −9.99606e100 | −0.316533 | ||||||||
\(724\) | −1.04852e101 | −0.316124 | ||||||||
\(725\) | −1.04381e100 | −0.0299656 | ||||||||
\(726\) | −2.07523e100 | −0.0567306 | ||||||||
\(727\) | −4.73980e101 | −1.23392 | −0.616962 | − | 0.786993i | \(-0.711637\pi\) | ||||
−0.616962 | + | 0.786993i | \(0.711637\pi\) | |||||||
\(728\) | −4.29270e100 | −0.106431 | ||||||||
\(729\) | 1.56842e100 | 0.0370370 | ||||||||
\(730\) | 2.41086e101 | 0.542264 | ||||||||
\(731\) | 3.17583e101 | 0.680441 | ||||||||
\(732\) | 3.97827e101 | 0.811990 | ||||||||
\(733\) | −2.17449e100 | −0.0422831 | −0.0211416 | − | 0.999776i | \(-0.506730\pi\) | ||||
−0.0211416 | + | 0.999776i | \(0.506730\pi\) | |||||||
\(734\) | 2.79687e101 | 0.518157 | ||||||||
\(735\) | 2.63453e101 | 0.465053 | ||||||||
\(736\) | −3.12359e101 | −0.525402 | ||||||||
\(737\) | 5.87419e101 | 0.941569 | ||||||||
\(738\) | 6.85836e99 | 0.0104766 | ||||||||
\(739\) | 8.53447e101 | 1.24251 | 0.621254 | − | 0.783609i | \(-0.286624\pi\) | ||||
0.621254 | + | 0.783609i | \(0.286624\pi\) | |||||||
\(740\) | 7.01690e101 | 0.973687 | ||||||||
\(741\) | −8.99693e100 | −0.119000 | ||||||||
\(742\) | −7.55731e100 | −0.0952859 | ||||||||
\(743\) | −9.28234e99 | −0.0111572 | −0.00557859 | − | 0.999984i | \(-0.501776\pi\) | ||||
−0.00557859 | + | 0.999984i | \(0.501776\pi\) | |||||||
\(744\) | −3.90222e101 | −0.447170 | ||||||||
\(745\) | 7.21262e101 | 0.788034 | ||||||||
\(746\) | −2.09360e100 | −0.0218105 | ||||||||
\(747\) | −5.06053e101 | −0.502707 | ||||||||
\(748\) | 5.60996e101 | 0.531438 | ||||||||
\(749\) | −5.33039e101 | −0.481564 | ||||||||
\(750\) | −2.86540e101 | −0.246894 | ||||||||
\(751\) | −1.57728e102 | −1.29625 | −0.648127 | − | 0.761532i | \(-0.724447\pi\) | ||||
−0.648127 | + | 0.761532i | \(0.724447\pi\) | |||||||
\(752\) | 3.10179e101 | 0.243153 | ||||||||
\(753\) | −1.32717e102 | −0.992442 | ||||||||
\(754\) | 2.62022e101 | 0.186920 | ||||||||
\(755\) | 1.73164e102 | 1.17853 | ||||||||
\(756\) | −1.04819e101 | −0.0680638 | ||||||||
\(757\) | −1.02229e102 | −0.633387 | −0.316693 | − | 0.948528i | \(-0.602573\pi\) | ||||
−0.316693 | + | 0.948528i | \(0.602573\pi\) | |||||||
\(758\) | −5.16674e101 | −0.305464 | ||||||||
\(759\) | −6.09047e101 | −0.343611 | ||||||||
\(760\) | −9.09980e101 | −0.489947 | ||||||||
\(761\) | 6.40901e100 | 0.0329333 | 0.0164667 | − | 0.999864i | \(-0.494758\pi\) | ||||
0.0164667 | + | 0.999864i | \(0.494758\pi\) | |||||||
\(762\) | −7.13291e100 | −0.0349837 | ||||||||
\(763\) | −1.59139e102 | −0.744999 | ||||||||
\(764\) | 8.99969e101 | 0.402173 | ||||||||
\(765\) | −4.50698e101 | −0.192267 | ||||||||
\(766\) | 7.69557e101 | 0.313415 | ||||||||
\(767\) | 1.36257e101 | 0.0529815 | ||||||||
\(768\) | −5.42477e101 | −0.201399 | ||||||||
\(769\) | −2.93171e102 | −1.03929 | −0.519645 | − | 0.854382i | \(-0.673936\pi\) | ||||
−0.519645 | + | 0.854382i | \(0.673936\pi\) | |||||||
\(770\) | −5.91259e101 | −0.200151 | ||||||||
\(771\) | 2.12430e102 | 0.686728 | ||||||||
\(772\) | 4.88556e101 | 0.150834 | ||||||||
\(773\) | 1.62052e102 | 0.477840 | 0.238920 | − | 0.971039i | \(-0.423207\pi\) | ||||
0.238920 | + | 0.971039i | \(0.423207\pi\) | |||||||
\(774\) | −5.84352e101 | −0.164577 | ||||||||
\(775\) | 8.12638e100 | 0.0218618 | ||||||||
\(776\) | −4.04141e102 | −1.03859 | ||||||||
\(777\) | 1.21495e102 | 0.298271 | ||||||||
\(778\) | 2.08589e102 | 0.489232 | ||||||||
\(779\) | −2.13082e101 | −0.0477492 | ||||||||
\(780\) | −7.01963e101 | −0.150299 | ||||||||
\(781\) | 1.84448e102 | 0.377366 | ||||||||
\(782\) | −6.76751e101 | −0.132309 | ||||||||
\(783\) | 1.41916e102 | 0.265149 | ||||||||
\(784\) | −2.25712e102 | −0.403028 | ||||||||
\(785\) | 8.16971e102 | 1.39423 | ||||||||
\(786\) | −7.34716e101 | −0.119845 | ||||||||
\(787\) | 5.77893e102 | 0.901041 | 0.450521 | − | 0.892766i | \(-0.351238\pi\) | ||||
0.450521 | + | 0.892766i | \(0.351238\pi\) | |||||||
\(788\) | −5.37456e102 | −0.801055 | ||||||||
\(789\) | 7.51908e102 | 1.07135 | ||||||||
\(790\) | 4.93526e102 | 0.672277 | ||||||||
\(791\) | −1.89099e102 | −0.246277 | ||||||||
\(792\) | −2.28961e102 | −0.285113 | ||||||||
\(793\) | 4.61297e102 | 0.549265 | ||||||||
\(794\) | 2.10136e102 | 0.239261 | ||||||||
\(795\) | −2.74117e102 | −0.298472 | ||||||||
\(796\) | −7.43444e102 | −0.774167 | ||||||||
\(797\) | 4.03612e102 | 0.401970 | 0.200985 | − | 0.979594i | \(-0.435586\pi\) | ||||
0.200985 | + | 0.979594i | \(0.435586\pi\) | |||||||
\(798\) | −7.10329e101 | −0.0676638 | ||||||||
\(799\) | 3.14480e102 | 0.286539 | ||||||||
\(800\) | 2.44541e101 | 0.0213136 | ||||||||
\(801\) | 5.04620e102 | 0.420737 | ||||||||
\(802\) | 5.69717e102 | 0.454432 | ||||||||
\(803\) | −1.88464e103 | −1.43822 | ||||||||
\(804\) | 5.50617e102 | 0.402031 | ||||||||
\(805\) | −3.27004e102 | −0.228454 | ||||||||
\(806\) | −2.03992e102 | −0.136370 | ||||||||
\(807\) | 3.46070e102 | 0.221388 | ||||||||
\(808\) | −2.03879e103 | −1.24816 | ||||||||
\(809\) | −3.10627e102 | −0.181998 | −0.0909990 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909990 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(810\) | 8.29283e101 | 0.0465034 | ||||||||
\(811\) | −4.60707e102 | −0.247277 | −0.123639 | − | 0.992327i | \(-0.539456\pi\) | ||||
−0.123639 | + | 0.992327i | \(0.539456\pi\) | |||||||
\(812\) | −9.48438e102 | −0.487271 | ||||||||
\(813\) | −3.12703e102 | −0.153786 | ||||||||
\(814\) | 1.19645e103 | 0.563285 | ||||||||
\(815\) | −2.76835e103 | −1.24775 | ||||||||
\(816\) | 3.86134e102 | 0.166624 | ||||||||
\(817\) | 1.81552e103 | 0.750097 | ||||||||
\(818\) | 1.61569e102 | 0.0639170 | ||||||||
\(819\) | −1.21542e102 | −0.0460414 | ||||||||
\(820\) | −1.66252e102 | −0.0603079 | ||||||||
\(821\) | −8.27269e102 | −0.287386 | −0.143693 | − | 0.989622i | \(-0.545898\pi\) | ||||
−0.143693 | + | 0.989622i | \(0.545898\pi\) | |||||||
\(822\) | 1.03955e103 | 0.345855 | ||||||||
\(823\) | 2.47530e103 | 0.788741 | 0.394370 | − | 0.918952i | \(-0.370963\pi\) | ||||
0.394370 | + | 0.918952i | \(0.370963\pi\) | |||||||
\(824\) | −2.69554e103 | −0.822679 | ||||||||
\(825\) | 4.76812e101 | 0.0139390 | ||||||||
\(826\) | 1.07578e102 | 0.0301254 | ||||||||
\(827\) | 1.18072e103 | 0.316739 | 0.158370 | − | 0.987380i | \(-0.449376\pi\) | ||||
0.158370 | + | 0.987380i | \(0.449376\pi\) | |||||||
\(828\) | −5.70890e102 | −0.146715 | ||||||||
\(829\) | 1.03978e103 | 0.256009 | 0.128004 | − | 0.991774i | \(-0.459143\pi\) | ||||
0.128004 | + | 0.991774i | \(0.459143\pi\) | |||||||
\(830\) | −2.67569e103 | −0.631194 | ||||||||
\(831\) | −1.56559e103 | −0.353869 | ||||||||
\(832\) | 1.18726e102 | 0.0257139 | ||||||||
\(833\) | −2.28842e103 | −0.474940 | ||||||||
\(834\) | −2.27132e102 | −0.0451734 | ||||||||
\(835\) | −4.80056e103 | −0.915002 | ||||||||
\(836\) | 3.20703e103 | 0.585841 | ||||||||
\(837\) | −1.10486e103 | −0.193443 | ||||||||
\(838\) | −3.15183e103 | −0.528933 | ||||||||
\(839\) | 8.89695e103 | 1.43117 | 0.715586 | − | 0.698525i | \(-0.246160\pi\) | ||||
0.715586 | + | 0.698525i | \(0.246160\pi\) | |||||||
\(840\) | −1.22932e103 | −0.189561 | ||||||||
\(841\) | 6.07623e103 | 0.898207 | ||||||||
\(842\) | 5.63067e103 | 0.797959 | ||||||||
\(843\) | 5.39694e103 | 0.733278 | ||||||||
\(844\) | 7.30503e103 | 0.951624 | ||||||||
\(845\) | 7.10446e103 | 0.887397 | ||||||||
\(846\) | −5.78643e102 | −0.0693047 | ||||||||
\(847\) | 8.71014e102 | 0.100038 | ||||||||
\(848\) | 2.34849e103 | 0.258664 | ||||||||
\(849\) | −5.90022e103 | −0.623225 | ||||||||
\(850\) | 5.29816e101 | 0.00536727 | ||||||||
\(851\) | 6.61713e103 | 0.642940 | ||||||||
\(852\) | 1.72892e103 | 0.161128 | ||||||||
\(853\) | −1.37178e104 | −1.22629 | −0.613146 | − | 0.789970i | \(-0.710096\pi\) | ||||
−0.613146 | + | 0.789970i | \(0.710096\pi\) | |||||||
\(854\) | 3.64204e103 | 0.312314 | ||||||||
\(855\) | −2.57649e103 | −0.211949 | ||||||||
\(856\) | −1.09139e104 | −0.861318 | ||||||||
\(857\) | −3.43783e103 | −0.260294 | −0.130147 | − | 0.991495i | \(-0.541545\pi\) | ||||
−0.130147 | + | 0.991495i | \(0.541545\pi\) | |||||||
\(858\) | −1.19691e103 | −0.0869490 | ||||||||
\(859\) | −1.63637e104 | −1.14057 | −0.570287 | − | 0.821446i | \(-0.693168\pi\) | ||||
−0.570287 | + | 0.821446i | \(0.693168\pi\) | |||||||
\(860\) | 1.41651e104 | 0.947382 | ||||||||
\(861\) | −2.87858e102 | −0.0184742 | ||||||||
\(862\) | 4.06749e103 | 0.250506 | ||||||||
\(863\) | 3.60240e103 | 0.212916 | 0.106458 | − | 0.994317i | \(-0.466049\pi\) | ||||
0.106458 | + | 0.994317i | \(0.466049\pi\) | |||||||
\(864\) | −3.32477e103 | −0.188592 | ||||||||
\(865\) | −1.88738e104 | −1.02752 | ||||||||
\(866\) | 1.15728e104 | 0.604717 | ||||||||
\(867\) | −7.59623e103 | −0.380996 | ||||||||
\(868\) | 7.38388e103 | 0.355496 | ||||||||
\(869\) | −3.85803e104 | −1.78305 | ||||||||
\(870\) | 7.50363e103 | 0.332919 | ||||||||
\(871\) | 6.38463e103 | 0.271952 | ||||||||
\(872\) | −3.25837e104 | −1.33249 | ||||||||
\(873\) | −1.14427e104 | −0.449287 | ||||||||
\(874\) | −3.86876e103 | −0.145853 | ||||||||
\(875\) | 1.20266e104 | 0.435369 | ||||||||
\(876\) | −1.76656e104 | −0.614092 | ||||||||
\(877\) | 3.01223e104 | 1.00555 | 0.502774 | − | 0.864418i | \(-0.332313\pi\) | ||||
0.502774 | + | 0.864418i | \(0.332313\pi\) | |||||||
\(878\) | 2.30524e104 | 0.739027 | ||||||||
\(879\) | −8.47398e102 | −0.0260905 | ||||||||
\(880\) | 1.83738e104 | 0.543330 | ||||||||
\(881\) | −3.21497e104 | −0.913130 | −0.456565 | − | 0.889690i | \(-0.650920\pi\) | ||||
−0.456565 | + | 0.889690i | \(0.650920\pi\) | |||||||
\(882\) | 4.21069e103 | 0.114873 | ||||||||
\(883\) | −5.75696e104 | −1.50865 | −0.754324 | − | 0.656502i | \(-0.772035\pi\) | ||||
−0.754324 | + | 0.656502i | \(0.772035\pi\) | |||||||
\(884\) | 6.09744e103 | 0.153494 | ||||||||
\(885\) | 3.90205e103 | 0.0943642 | ||||||||
\(886\) | −1.51459e103 | −0.0351883 | ||||||||
\(887\) | 8.00577e104 | 1.78696 | 0.893479 | − | 0.449104i | \(-0.148257\pi\) | ||||
0.893479 | + | 0.449104i | \(0.148257\pi\) | |||||||
\(888\) | 2.48760e104 | 0.533483 | ||||||||
\(889\) | 2.99381e103 | 0.0616896 | ||||||||
\(890\) | 2.66811e104 | 0.528273 | ||||||||
\(891\) | −6.48273e103 | −0.123339 | ||||||||
\(892\) | 4.38808e104 | 0.802273 | ||||||||
\(893\) | 1.79778e104 | 0.315871 | ||||||||
\(894\) | 1.15277e104 | 0.194653 | ||||||||
\(895\) | 3.61320e104 | 0.586373 | ||||||||
\(896\) | 2.80036e104 | 0.436797 | ||||||||
\(897\) | −6.61971e103 | −0.0992446 | ||||||||
\(898\) | −1.16563e104 | −0.167978 | ||||||||
\(899\) | −9.99716e104 | −1.38487 | ||||||||
\(900\) | 4.46940e102 | 0.00595169 | ||||||||
\(901\) | 2.38106e104 | 0.304817 | ||||||||
\(902\) | −2.83475e103 | −0.0348885 | ||||||||
\(903\) | 2.45263e104 | 0.290213 | ||||||||
\(904\) | −3.87180e104 | −0.440488 | ||||||||
\(905\) | −3.48174e104 | −0.380865 | ||||||||
\(906\) | 2.76763e104 | 0.291110 | ||||||||
\(907\) | 1.24094e105 | 1.25514 | 0.627571 | − | 0.778559i | \(-0.284049\pi\) | ||||
0.627571 | + | 0.778559i | \(0.284049\pi\) | |||||||
\(908\) | −9.91908e104 | −0.964770 | ||||||||
\(909\) | −5.77256e104 | −0.539946 | ||||||||
\(910\) | −6.42637e103 | −0.0578091 | ||||||||
\(911\) | −1.45373e105 | −1.25771 | −0.628857 | − | 0.777521i | \(-0.716477\pi\) | ||||
−0.628857 | + | 0.777521i | \(0.716477\pi\) | |||||||
\(912\) | 2.20740e104 | 0.183681 | ||||||||
\(913\) | 2.09166e105 | 1.67409 | ||||||||
\(914\) | −5.29823e104 | −0.407888 | ||||||||
\(915\) | 1.32103e105 | 0.978285 | ||||||||
\(916\) | −9.16759e104 | −0.653079 | ||||||||
\(917\) | 3.08374e104 | 0.211332 | ||||||||
\(918\) | −7.20337e103 | −0.0474920 | ||||||||
\(919\) | −6.50781e104 | −0.412795 | −0.206397 | − | 0.978468i | \(-0.566174\pi\) | ||||
−0.206397 | + | 0.978468i | \(0.566174\pi\) | |||||||
\(920\) | −6.69540e104 | −0.408609 | ||||||||
\(921\) | 7.55382e104 | 0.443557 | ||||||||
\(922\) | −8.83222e104 | −0.499025 | ||||||||
\(923\) | 2.00476e104 | 0.108994 | ||||||||
\(924\) | 4.33246e104 | 0.226662 | ||||||||
\(925\) | −5.18044e103 | −0.0260817 | ||||||||
\(926\) | −8.61022e104 | −0.417181 | ||||||||
\(927\) | −7.63208e104 | −0.355887 | ||||||||
\(928\) | −3.00837e105 | −1.35014 | ||||||||
\(929\) | −1.71049e105 | −0.738861 | −0.369431 | − | 0.929258i | \(-0.620447\pi\) | ||||
−0.369431 | + | 0.929258i | \(0.620447\pi\) | |||||||
\(930\) | −5.84180e104 | −0.242886 | ||||||||
\(931\) | −1.30822e105 | −0.523559 | ||||||||
\(932\) | −1.20349e105 | −0.463636 | ||||||||
\(933\) | 1.97679e105 | 0.733097 | ||||||||
\(934\) | 6.80717e103 | 0.0243026 | ||||||||
\(935\) | 1.86286e105 | 0.640277 | ||||||||
\(936\) | −2.48857e104 | −0.0823488 | ||||||||
\(937\) | 2.03025e105 | 0.646835 | 0.323417 | − | 0.946256i | \(-0.395168\pi\) | ||||
0.323417 | + | 0.946256i | \(0.395168\pi\) | |||||||
\(938\) | 5.04082e104 | 0.154632 | ||||||||
\(939\) | −1.98152e105 | −0.585289 | ||||||||
\(940\) | 1.40267e105 | 0.398949 | ||||||||
\(941\) | 3.53562e105 | 0.968352 | 0.484176 | − | 0.874971i | \(-0.339119\pi\) | ||||
0.484176 | + | 0.874971i | \(0.339119\pi\) | |||||||
\(942\) | 1.30574e105 | 0.344390 | ||||||||
\(943\) | −1.56780e104 | −0.0398222 | ||||||||
\(944\) | −3.34307e104 | −0.0817786 | ||||||||
\(945\) | −3.48065e104 | −0.0820033 | ||||||||
\(946\) | 2.41529e105 | 0.548067 | ||||||||
\(947\) | 2.88782e105 | 0.631170 | 0.315585 | − | 0.948897i | \(-0.397799\pi\) | ||||
0.315585 | + | 0.948897i | \(0.397799\pi\) | |||||||
\(948\) | −3.61632e105 | −0.761326 | ||||||||
\(949\) | −2.04840e105 | −0.415399 | ||||||||
\(950\) | 3.02878e103 | 0.00591671 | ||||||||
\(951\) | 4.33114e105 | 0.815068 | ||||||||
\(952\) | 1.06782e105 | 0.193591 | ||||||||
\(953\) | 3.65620e105 | 0.638604 | 0.319302 | − | 0.947653i | \(-0.396552\pi\) | ||||
0.319302 | + | 0.947653i | \(0.396552\pi\) | |||||||
\(954\) | −4.38114e104 | −0.0737258 | ||||||||
\(955\) | 2.98846e105 | 0.484538 | ||||||||
\(956\) | 1.30383e105 | 0.203689 | ||||||||
\(957\) | −5.86579e105 | −0.882985 | ||||||||
\(958\) | 3.81620e105 | 0.553548 | ||||||||
\(959\) | −4.36316e105 | −0.609875 | ||||||||
\(960\) | 3.40000e104 | 0.0457984 | ||||||||
\(961\) | 7.97302e103 | 0.0103501 | ||||||||
\(962\) | 1.30042e105 | 0.162692 | ||||||||
\(963\) | −3.09014e105 | −0.372602 | ||||||||
\(964\) | 3.87280e105 | 0.450081 | ||||||||
\(965\) | 1.62231e105 | 0.181725 | ||||||||
\(966\) | −5.22641e104 | −0.0564307 | ||||||||
\(967\) | −5.40345e105 | −0.562382 | −0.281191 | − | 0.959652i | \(-0.590729\pi\) | ||||
−0.281191 | + | 0.959652i | \(0.590729\pi\) | |||||||
\(968\) | 1.78340e105 | 0.178926 | ||||||||
\(969\) | 2.23801e105 | 0.216455 | ||||||||
\(970\) | −6.05018e105 | −0.564121 | ||||||||
\(971\) | 1.95441e106 | 1.75684 | 0.878420 | − | 0.477889i | \(-0.158598\pi\) | ||||
0.878420 | + | 0.477889i | \(0.158598\pi\) | |||||||
\(972\) | −6.07658e104 | −0.0526632 | ||||||||
\(973\) | 9.53313e104 | 0.0796581 | ||||||||
\(974\) | 2.44169e105 | 0.196720 | ||||||||
\(975\) | 5.18245e103 | 0.00402598 | ||||||||
\(976\) | −1.13179e106 | −0.847809 | ||||||||
\(977\) | −1.44045e106 | −1.04050 | −0.520248 | − | 0.854015i | \(-0.674161\pi\) | ||||
−0.520248 | + | 0.854015i | \(0.674161\pi\) | |||||||
\(978\) | −4.42458e105 | −0.308207 | ||||||||
\(979\) | −2.08573e106 | −1.40111 | ||||||||
\(980\) | −1.02070e106 | −0.661262 | ||||||||
\(981\) | −9.22564e105 | −0.576430 | ||||||||
\(982\) | 9.48716e105 | 0.571713 | ||||||||
\(983\) | 1.17402e106 | 0.682382 | 0.341191 | − | 0.939994i | \(-0.389170\pi\) | ||||
0.341191 | + | 0.939994i | \(0.389170\pi\) | |||||||
\(984\) | −5.89388e104 | −0.0330427 | ||||||||
\(985\) | −1.78469e106 | −0.965110 | ||||||||
\(986\) | −6.51786e105 | −0.339996 | ||||||||
\(987\) | 2.42867e105 | 0.122211 | ||||||||
\(988\) | 3.48570e105 | 0.169207 | ||||||||
\(989\) | 1.33581e106 | 0.625570 | ||||||||
\(990\) | −3.42765e105 | −0.154863 | ||||||||
\(991\) | −2.56434e106 | −1.11779 | −0.558897 | − | 0.829237i | \(-0.688775\pi\) | ||||
−0.558897 | + | 0.829237i | \(0.688775\pi\) | |||||||
\(992\) | 2.34210e106 | 0.985012 | ||||||||
\(993\) | −1.69499e106 | −0.687809 | ||||||||
\(994\) | 1.58280e105 | 0.0619742 | ||||||||
\(995\) | −2.46870e106 | −0.932716 | ||||||||
\(996\) | 1.96061e106 | 0.714802 | ||||||||
\(997\) | 3.02413e106 | 1.06395 | 0.531976 | − | 0.846759i | \(-0.321450\pi\) | ||||
0.531976 | + | 0.846759i | \(0.321450\pi\) | |||||||
\(998\) | −1.46015e106 | −0.495751 | ||||||||
\(999\) | 7.04332e105 | 0.230782 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3.72.a.a.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 9.72.a.a.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.72.a.a.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.72.a.a.1.3 | 5 | 3.2 | odd | 2 |