Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,30,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(31.9668254298\) |
Analytic rank: | \(0\) |
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: | \( x^{2} - x - 2722854711072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.65011e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16384.0 | 0.707107 | ||||||||
\(3\) | −4.78297e6 | −0.577350 | ||||||||
\(4\) | 2.68435e8 | 0.500000 | ||||||||
\(5\) | −2.03873e10 | −1.49381 | −0.746903 | − | 0.664933i | \(-0.768460\pi\) | ||||
−0.746903 | + | 0.664933i | \(0.768460\pi\) | |||||||
\(6\) | −7.83642e10 | −0.408248 | ||||||||
\(7\) | −2.52164e12 | −1.40527 | −0.702637 | − | 0.711548i | \(-0.747994\pi\) | ||||
−0.702637 | + | 0.711548i | \(0.747994\pi\) | |||||||
\(8\) | 4.39805e12 | 0.353553 | ||||||||
\(9\) | 2.28768e13 | 0.333333 | ||||||||
\(10\) | −3.34025e14 | −1.05628 | ||||||||
\(11\) | 2.16814e15 | 1.72145 | 0.860725 | − | 0.509070i | \(-0.170011\pi\) | ||||
0.860725 | + | 0.509070i | \(0.170011\pi\) | |||||||
\(12\) | −1.28392e15 | −0.288675 | ||||||||
\(13\) | −1.73173e16 | −1.21984 | −0.609919 | − | 0.792464i | \(-0.708798\pi\) | ||||
−0.609919 | + | 0.792464i | \(0.708798\pi\) | |||||||
\(14\) | −4.13145e16 | −0.993679 | ||||||||
\(15\) | 9.75118e16 | 0.862450 | ||||||||
\(16\) | 7.20576e16 | 0.250000 | ||||||||
\(17\) | 1.09493e18 | 1.57716 | 0.788582 | − | 0.614929i | \(-0.210815\pi\) | ||||
0.788582 | + | 0.614929i | \(0.210815\pi\) | |||||||
\(18\) | 3.74813e17 | 0.235702 | ||||||||
\(19\) | 1.44082e18 | 0.413697 | 0.206849 | − | 0.978373i | \(-0.433679\pi\) | ||||
0.206849 | + | 0.978373i | \(0.433679\pi\) | |||||||
\(20\) | −5.47267e18 | −0.746903 | ||||||||
\(21\) | 1.20609e19 | 0.811336 | ||||||||
\(22\) | 3.55229e19 | 1.21725 | ||||||||
\(23\) | −7.43943e19 | −1.33809 | −0.669046 | − | 0.743221i | \(-0.733297\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(24\) | −2.10357e19 | −0.204124 | ||||||||
\(25\) | 2.29377e20 | 1.23146 | ||||||||
\(26\) | −2.83727e20 | −0.862556 | ||||||||
\(27\) | −1.09419e20 | −0.192450 | ||||||||
\(28\) | −6.76897e20 | −0.702637 | ||||||||
\(29\) | 1.78624e21 | 1.11473 | 0.557364 | − | 0.830268i | \(-0.311813\pi\) | ||||
0.557364 | + | 0.830268i | \(0.311813\pi\) | |||||||
\(30\) | 1.59763e21 | 0.609844 | ||||||||
\(31\) | 1.83689e21 | 0.435852 | 0.217926 | − | 0.975965i | \(-0.430071\pi\) | ||||
0.217926 | + | 0.975965i | \(0.430071\pi\) | |||||||
\(32\) | 1.18059e21 | 0.176777 | ||||||||
\(33\) | −1.03702e22 | −0.993880 | ||||||||
\(34\) | 1.79393e22 | 1.11522 | ||||||||
\(35\) | 5.14094e22 | 2.09921 | ||||||||
\(36\) | 6.14094e21 | 0.166667 | ||||||||
\(37\) | 6.04145e22 | 1.10209 | 0.551044 | − | 0.834476i | \(-0.314230\pi\) | ||||
0.551044 | + | 0.834476i | \(0.314230\pi\) | |||||||
\(38\) | 2.36064e22 | 0.292528 | ||||||||
\(39\) | 8.28282e22 | 0.704274 | ||||||||
\(40\) | −8.96642e22 | −0.528140 | ||||||||
\(41\) | −7.54895e22 | −0.310829 | −0.155414 | − | 0.987849i | \(-0.549671\pi\) | ||||
−0.155414 | + | 0.987849i | \(0.549671\pi\) | |||||||
\(42\) | 1.97606e23 | 0.573701 | ||||||||
\(43\) | 4.59709e23 | 0.948835 | 0.474417 | − | 0.880300i | \(-0.342659\pi\) | ||||
0.474417 | + | 0.880300i | \(0.342659\pi\) | |||||||
\(44\) | 5.82007e23 | 0.860725 | ||||||||
\(45\) | −4.66396e23 | −0.497936 | ||||||||
\(46\) | −1.21888e24 | −0.946174 | ||||||||
\(47\) | 7.22727e23 | 0.410729 | 0.205365 | − | 0.978686i | \(-0.434162\pi\) | ||||
0.205365 | + | 0.978686i | \(0.434162\pi\) | |||||||
\(48\) | −3.44649e23 | −0.144338 | ||||||||
\(49\) | 3.13875e24 | 0.974796 | ||||||||
\(50\) | 3.75811e24 | 0.870773 | ||||||||
\(51\) | −5.23702e24 | −0.910576 | ||||||||
\(52\) | −4.64858e24 | −0.609919 | ||||||||
\(53\) | −5.39412e24 | −0.536933 | −0.268467 | − | 0.963289i | \(-0.586517\pi\) | ||||
−0.268467 | + | 0.963289i | \(0.586517\pi\) | |||||||
\(54\) | −1.79272e24 | −0.136083 | ||||||||
\(55\) | −4.42026e25 | −2.57151 | ||||||||
\(56\) | −1.10903e25 | −0.496840 | ||||||||
\(57\) | −6.89140e24 | −0.238848 | ||||||||
\(58\) | 2.92658e25 | 0.788232 | ||||||||
\(59\) | −6.59432e24 | −0.138617 | −0.0693084 | − | 0.997595i | \(-0.522079\pi\) | ||||
−0.0693084 | + | 0.997595i | \(0.522079\pi\) | |||||||
\(60\) | 2.61756e25 | 0.431225 | ||||||||
\(61\) | 6.51969e24 | 0.0845170 | 0.0422585 | − | 0.999107i | \(-0.486545\pi\) | ||||
0.0422585 | + | 0.999107i | \(0.486545\pi\) | |||||||
\(62\) | 3.00957e25 | 0.308194 | ||||||||
\(63\) | −5.76870e25 | −0.468425 | ||||||||
\(64\) | 1.93428e25 | 0.125000 | ||||||||
\(65\) | 3.53053e26 | 1.82220 | ||||||||
\(66\) | −1.69905e26 | −0.702779 | ||||||||
\(67\) | −1.98903e26 | −0.661541 | −0.330770 | − | 0.943711i | \(-0.607309\pi\) | ||||
−0.330770 | + | 0.943711i | \(0.607309\pi\) | |||||||
\(68\) | 2.93918e26 | 0.788582 | ||||||||
\(69\) | 3.55826e26 | 0.772548 | ||||||||
\(70\) | 8.42291e26 | 1.48436 | ||||||||
\(71\) | −4.25661e26 | −0.610686 | −0.305343 | − | 0.952242i | \(-0.598771\pi\) | ||||
−0.305343 | + | 0.952242i | \(0.598771\pi\) | |||||||
\(72\) | 1.00613e26 | 0.117851 | ||||||||
\(73\) | −4.61216e26 | −0.442306 | −0.221153 | − | 0.975239i | \(-0.570982\pi\) | ||||
−0.221153 | + | 0.975239i | \(0.570982\pi\) | |||||||
\(74\) | 9.89831e26 | 0.779294 | ||||||||
\(75\) | −1.09710e27 | −0.710983 | ||||||||
\(76\) | 3.86767e26 | 0.206849 | ||||||||
\(77\) | −5.46728e27 | −2.41911 | ||||||||
\(78\) | 1.35706e27 | 0.497997 | ||||||||
\(79\) | 5.25329e27 | 1.60265 | 0.801325 | − | 0.598229i | \(-0.204129\pi\) | ||||
0.801325 | + | 0.598229i | \(0.204129\pi\) | |||||||
\(80\) | −1.46906e27 | −0.373452 | ||||||||
\(81\) | 5.23348e26 | 0.111111 | ||||||||
\(82\) | −1.23682e27 | −0.219789 | ||||||||
\(83\) | −4.10278e27 | −0.611569 | −0.305784 | − | 0.952101i | \(-0.598919\pi\) | ||||
−0.305784 | + | 0.952101i | \(0.598919\pi\) | |||||||
\(84\) | 3.23758e27 | 0.405668 | ||||||||
\(85\) | −2.23227e28 | −2.35598 | ||||||||
\(86\) | 7.53188e27 | 0.670928 | ||||||||
\(87\) | −8.54353e27 | −0.643589 | ||||||||
\(88\) | 9.53560e27 | 0.608624 | ||||||||
\(89\) | −5.01761e27 | −0.271858 | −0.135929 | − | 0.990719i | \(-0.543402\pi\) | ||||
−0.135929 | + | 0.990719i | \(0.543402\pi\) | |||||||
\(90\) | −7.64143e27 | −0.352094 | ||||||||
\(91\) | 4.36680e28 | 1.71421 | ||||||||
\(92\) | −1.99701e28 | −0.669046 | ||||||||
\(93\) | −8.78580e27 | −0.251639 | ||||||||
\(94\) | 1.18412e28 | 0.290429 | ||||||||
\(95\) | −2.93744e28 | −0.617984 | ||||||||
\(96\) | −5.64673e27 | −0.102062 | ||||||||
\(97\) | 9.02825e28 | 1.40415 | 0.702075 | − | 0.712103i | \(-0.252257\pi\) | ||||
0.702075 | + | 0.712103i | \(0.252257\pi\) | |||||||
\(98\) | 5.14253e28 | 0.689285 | ||||||||
\(99\) | 4.96002e28 | 0.573817 | ||||||||
\(100\) | 6.15729e28 | 0.615729 | ||||||||
\(101\) | 1.35694e29 | 1.17463 | 0.587316 | − | 0.809358i | \(-0.300185\pi\) | ||||
0.587316 | + | 0.809358i | \(0.300185\pi\) | |||||||
\(102\) | −8.58033e28 | −0.643875 | ||||||||
\(103\) | 6.86763e28 | 0.447370 | 0.223685 | − | 0.974661i | \(-0.428191\pi\) | ||||
0.223685 | + | 0.974661i | \(0.428191\pi\) | |||||||
\(104\) | −7.61624e28 | −0.431278 | ||||||||
\(105\) | −2.45889e29 | −1.21198 | ||||||||
\(106\) | −8.83773e28 | −0.379669 | ||||||||
\(107\) | 1.23781e29 | 0.464075 | 0.232038 | − | 0.972707i | \(-0.425461\pi\) | ||||
0.232038 | + | 0.972707i | \(0.425461\pi\) | |||||||
\(108\) | −2.93719e28 | −0.0962250 | ||||||||
\(109\) | −1.13178e28 | −0.0324396 | −0.0162198 | − | 0.999868i | \(-0.505163\pi\) | ||||
−0.0162198 | + | 0.999868i | \(0.505163\pi\) | |||||||
\(110\) | −7.24215e29 | −1.81833 | ||||||||
\(111\) | −2.88961e29 | −0.636291 | ||||||||
\(112\) | −1.81703e29 | −0.351319 | ||||||||
\(113\) | −2.65183e29 | −0.450721 | −0.225360 | − | 0.974275i | \(-0.572356\pi\) | ||||
−0.225360 | + | 0.974275i | \(0.572356\pi\) | |||||||
\(114\) | −1.12909e29 | −0.168891 | ||||||||
\(115\) | 1.51670e30 | 1.99885 | ||||||||
\(116\) | 4.79490e29 | 0.557364 | ||||||||
\(117\) | −3.96165e29 | −0.406613 | ||||||||
\(118\) | −1.08041e29 | −0.0980169 | ||||||||
\(119\) | −2.76102e30 | −2.21635 | ||||||||
\(120\) | 4.28861e29 | 0.304922 | ||||||||
\(121\) | 3.11454e30 | 1.96339 | ||||||||
\(122\) | 1.06819e29 | 0.0597626 | ||||||||
\(123\) | 3.61064e29 | 0.179457 | ||||||||
\(124\) | 4.93087e29 | 0.217926 | ||||||||
\(125\) | −8.78946e29 | −0.345754 | ||||||||
\(126\) | −9.45144e29 | −0.331226 | ||||||||
\(127\) | 2.04844e30 | 0.640131 | 0.320066 | − | 0.947395i | \(-0.396295\pi\) | ||||
0.320066 | + | 0.947395i | \(0.396295\pi\) | |||||||
\(128\) | 3.16913e29 | 0.0883883 | ||||||||
\(129\) | −2.19878e30 | −0.547810 | ||||||||
\(130\) | 5.78442e30 | 1.28849 | ||||||||
\(131\) | 3.72567e30 | 0.742626 | 0.371313 | − | 0.928508i | \(-0.378908\pi\) | ||||
0.371313 | + | 0.928508i | \(0.378908\pi\) | |||||||
\(132\) | −2.78372e30 | −0.496940 | ||||||||
\(133\) | −3.63323e30 | −0.581358 | ||||||||
\(134\) | −3.25883e30 | −0.467780 | ||||||||
\(135\) | 2.23076e30 | 0.287483 | ||||||||
\(136\) | 4.81555e30 | 0.557612 | ||||||||
\(137\) | 1.00289e30 | 0.104425 | 0.0522125 | − | 0.998636i | \(-0.483373\pi\) | ||||
0.0522125 | + | 0.998636i | \(0.483373\pi\) | |||||||
\(138\) | 5.82985e30 | 0.546274 | ||||||||
\(139\) | −3.72507e30 | −0.314354 | −0.157177 | − | 0.987570i | \(-0.550239\pi\) | ||||
−0.157177 | + | 0.987570i | \(0.550239\pi\) | |||||||
\(140\) | 1.38001e31 | 1.04960 | ||||||||
\(141\) | −3.45678e30 | −0.237135 | ||||||||
\(142\) | −6.97403e30 | −0.431820 | ||||||||
\(143\) | −3.75465e31 | −2.09989 | ||||||||
\(144\) | 1.64845e30 | 0.0833333 | ||||||||
\(145\) | −3.64166e31 | −1.66519 | ||||||||
\(146\) | −7.55657e30 | −0.312758 | ||||||||
\(147\) | −1.50125e31 | −0.562799 | ||||||||
\(148\) | 1.62174e31 | 0.551044 | ||||||||
\(149\) | 5.39425e31 | 1.66238 | 0.831190 | − | 0.555989i | \(-0.187660\pi\) | ||||
0.831190 | + | 0.555989i | \(0.187660\pi\) | |||||||
\(150\) | −1.79749e31 | −0.502741 | ||||||||
\(151\) | 3.97080e31 | 1.00858 | 0.504292 | − | 0.863533i | \(-0.331754\pi\) | ||||
0.504292 | + | 0.863533i | \(0.331754\pi\) | |||||||
\(152\) | 6.33679e30 | 0.146264 | ||||||||
\(153\) | 2.50485e31 | 0.525721 | ||||||||
\(154\) | −8.95758e31 | −1.71057 | ||||||||
\(155\) | −3.74493e31 | −0.651079 | ||||||||
\(156\) | 2.22340e31 | 0.352137 | ||||||||
\(157\) | −7.76788e31 | −1.12139 | −0.560696 | − | 0.828022i | \(-0.689466\pi\) | ||||
−0.560696 | + | 0.828022i | \(0.689466\pi\) | |||||||
\(158\) | 8.60700e31 | 1.13325 | ||||||||
\(159\) | 2.57999e31 | 0.309999 | ||||||||
\(160\) | −2.40691e31 | −0.264070 | ||||||||
\(161\) | 1.87596e32 | 1.88039 | ||||||||
\(162\) | 8.57453e30 | 0.0785674 | ||||||||
\(163\) | 8.75557e31 | 0.733777 | 0.366888 | − | 0.930265i | \(-0.380423\pi\) | ||||
0.366888 | + | 0.930265i | \(0.380423\pi\) | |||||||
\(164\) | −2.02641e31 | −0.155414 | ||||||||
\(165\) | 2.11420e32 | 1.48466 | ||||||||
\(166\) | −6.72199e31 | −0.432445 | ||||||||
\(167\) | 3.82845e31 | 0.225753 | 0.112877 | − | 0.993609i | \(-0.463994\pi\) | ||||
0.112877 | + | 0.993609i | \(0.463994\pi\) | |||||||
\(168\) | 5.30445e31 | 0.286850 | ||||||||
\(169\) | 9.83515e31 | 0.488005 | ||||||||
\(170\) | −3.65734e32 | −1.66593 | ||||||||
\(171\) | 3.29613e31 | 0.137899 | ||||||||
\(172\) | 1.23402e32 | 0.474417 | ||||||||
\(173\) | −4.47491e32 | −1.58167 | −0.790835 | − | 0.612029i | \(-0.790354\pi\) | ||||
−0.790835 | + | 0.612029i | \(0.790354\pi\) | |||||||
\(174\) | −1.39977e32 | −0.455086 | ||||||||
\(175\) | −5.78406e32 | −1.73054 | ||||||||
\(176\) | 1.56231e32 | 0.430362 | ||||||||
\(177\) | 3.15404e31 | 0.0800305 | ||||||||
\(178\) | −8.22085e31 | −0.192232 | ||||||||
\(179\) | 7.12699e32 | 1.53652 | 0.768258 | − | 0.640141i | \(-0.221124\pi\) | ||||
0.768258 | + | 0.640141i | \(0.221124\pi\) | |||||||
\(180\) | −1.25197e32 | −0.248968 | ||||||||
\(181\) | −1.03470e33 | −1.89879 | −0.949394 | − | 0.314087i | \(-0.898302\pi\) | ||||
−0.949394 | + | 0.314087i | \(0.898302\pi\) | |||||||
\(182\) | 7.15457e32 | 1.21213 | ||||||||
\(183\) | −3.11835e31 | −0.0487959 | ||||||||
\(184\) | −3.27190e32 | −0.473087 | ||||||||
\(185\) | −1.23169e33 | −1.64631 | ||||||||
\(186\) | −1.43947e32 | −0.177936 | ||||||||
\(187\) | 2.37397e33 | 2.71501 | ||||||||
\(188\) | 1.94006e32 | 0.205365 | ||||||||
\(189\) | 2.75915e32 | 0.270445 | ||||||||
\(190\) | −4.81270e32 | −0.436980 | ||||||||
\(191\) | −6.40588e32 | −0.539008 | −0.269504 | − | 0.962999i | \(-0.586860\pi\) | ||||
−0.269504 | + | 0.962999i | \(0.586860\pi\) | |||||||
\(192\) | −9.25161e31 | −0.0721688 | ||||||||
\(193\) | 8.50623e32 | 0.615398 | 0.307699 | − | 0.951484i | \(-0.400441\pi\) | ||||
0.307699 | + | 0.951484i | \(0.400441\pi\) | |||||||
\(194\) | 1.47919e33 | 0.992883 | ||||||||
\(195\) | −1.68864e33 | −1.05205 | ||||||||
\(196\) | 8.42552e32 | 0.487398 | ||||||||
\(197\) | 3.60046e32 | 0.193463 | 0.0967314 | − | 0.995311i | \(-0.469161\pi\) | ||||
0.0967314 | + | 0.995311i | \(0.469161\pi\) | |||||||
\(198\) | 8.12650e32 | 0.405750 | ||||||||
\(199\) | −6.99395e32 | −0.324603 | −0.162302 | − | 0.986741i | \(-0.551892\pi\) | ||||
−0.162302 | + | 0.986741i | \(0.551892\pi\) | |||||||
\(200\) | 1.00881e33 | 0.435386 | ||||||||
\(201\) | 9.51346e32 | 0.381941 | ||||||||
\(202\) | 2.22322e33 | 0.830590 | ||||||||
\(203\) | −4.50425e33 | −1.56650 | ||||||||
\(204\) | −1.40580e33 | −0.455288 | ||||||||
\(205\) | 1.53903e33 | 0.464318 | ||||||||
\(206\) | 1.12519e33 | 0.316338 | ||||||||
\(207\) | −1.70190e33 | −0.446031 | ||||||||
\(208\) | −1.24784e33 | −0.304959 | ||||||||
\(209\) | 3.12391e33 | 0.712159 | ||||||||
\(210\) | −4.02865e33 | −0.856998 | ||||||||
\(211\) | 9.78000e33 | 1.94197 | 0.970987 | − | 0.239133i | \(-0.0768634\pi\) | ||||
0.970987 | + | 0.239133i | \(0.0768634\pi\) | |||||||
\(212\) | −1.44797e33 | −0.268467 | ||||||||
\(213\) | 2.03592e33 | 0.352580 | ||||||||
\(214\) | 2.02802e33 | 0.328151 | ||||||||
\(215\) | −9.37223e33 | −1.41738 | ||||||||
\(216\) | −4.81230e32 | −0.0680414 | ||||||||
\(217\) | −4.63198e33 | −0.612492 | ||||||||
\(218\) | −1.85430e32 | −0.0229383 | ||||||||
\(219\) | 2.20598e33 | 0.255366 | ||||||||
\(220\) | −1.18655e34 | −1.28576 | ||||||||
\(221\) | −1.89613e34 | −1.92388 | ||||||||
\(222\) | −4.73433e33 | −0.449925 | ||||||||
\(223\) | 1.44345e34 | 1.28523 | 0.642615 | − | 0.766189i | \(-0.277849\pi\) | ||||
0.642615 | + | 0.766189i | \(0.277849\pi\) | |||||||
\(224\) | −2.97702e33 | −0.248420 | ||||||||
\(225\) | 5.24741e33 | 0.410486 | ||||||||
\(226\) | −4.34475e33 | −0.318708 | ||||||||
\(227\) | −4.35500e33 | −0.299649 | −0.149825 | − | 0.988713i | \(-0.547871\pi\) | ||||
−0.149825 | + | 0.988713i | \(0.547871\pi\) | |||||||
\(228\) | −1.84990e33 | −0.119424 | ||||||||
\(229\) | −3.53428e33 | −0.214134 | −0.107067 | − | 0.994252i | \(-0.534146\pi\) | ||||
−0.107067 | + | 0.994252i | \(0.534146\pi\) | |||||||
\(230\) | 2.48496e34 | 1.41340 | ||||||||
\(231\) | 2.61498e34 | 1.39667 | ||||||||
\(232\) | 7.85597e33 | 0.394116 | ||||||||
\(233\) | 2.51120e34 | 1.18364 | 0.591820 | − | 0.806070i | \(-0.298410\pi\) | ||||
0.591820 | + | 0.806070i | \(0.298410\pi\) | |||||||
\(234\) | −6.49076e33 | −0.287519 | ||||||||
\(235\) | −1.47345e34 | −0.613550 | ||||||||
\(236\) | −1.77015e33 | −0.0693084 | ||||||||
\(237\) | −2.51263e34 | −0.925291 | ||||||||
\(238\) | −4.52365e34 | −1.56720 | ||||||||
\(239\) | 5.36225e34 | 1.74815 | 0.874073 | − | 0.485794i | \(-0.161470\pi\) | ||||
0.874073 | + | 0.485794i | \(0.161470\pi\) | |||||||
\(240\) | 7.02646e33 | 0.215612 | ||||||||
\(241\) | 5.55366e34 | 1.60447 | 0.802236 | − | 0.597007i | \(-0.203644\pi\) | ||||
0.802236 | + | 0.597007i | \(0.203644\pi\) | |||||||
\(242\) | 5.10287e34 | 1.38833 | ||||||||
\(243\) | −2.50316e33 | −0.0641500 | ||||||||
\(244\) | 1.75012e33 | 0.0422585 | ||||||||
\(245\) | −6.39906e34 | −1.45616 | ||||||||
\(246\) | 5.91568e33 | 0.126895 | ||||||||
\(247\) | −2.49511e34 | −0.504643 | ||||||||
\(248\) | 8.07874e33 | 0.154097 | ||||||||
\(249\) | 1.96234e34 | 0.353089 | ||||||||
\(250\) | −1.44007e34 | −0.244485 | ||||||||
\(251\) | −3.45099e34 | −0.552936 | −0.276468 | − | 0.961023i | \(-0.589164\pi\) | ||||
−0.276468 | + | 0.961023i | \(0.589164\pi\) | |||||||
\(252\) | −1.54852e34 | −0.234212 | ||||||||
\(253\) | −1.61298e35 | −2.30346 | ||||||||
\(254\) | 3.35616e34 | 0.452641 | ||||||||
\(255\) | 1.06769e35 | 1.36022 | ||||||||
\(256\) | 5.19230e33 | 0.0625000 | ||||||||
\(257\) | −7.35858e34 | −0.837074 | −0.418537 | − | 0.908200i | \(-0.637457\pi\) | ||||
−0.418537 | + | 0.908200i | \(0.637457\pi\) | |||||||
\(258\) | −3.60247e34 | −0.387360 | ||||||||
\(259\) | −1.52343e35 | −1.54874 | ||||||||
\(260\) | 9.47720e34 | 0.911101 | ||||||||
\(261\) | 4.08635e34 | 0.371576 | ||||||||
\(262\) | 6.10413e34 | 0.525116 | ||||||||
\(263\) | −1.05848e35 | −0.861640 | −0.430820 | − | 0.902438i | \(-0.641776\pi\) | ||||
−0.430820 | + | 0.902438i | \(0.641776\pi\) | |||||||
\(264\) | −4.56085e34 | −0.351389 | ||||||||
\(265\) | 1.09971e35 | 0.802075 | ||||||||
\(266\) | −5.95268e34 | −0.411082 | ||||||||
\(267\) | 2.39991e34 | 0.156957 | ||||||||
\(268\) | −5.33926e34 | −0.330770 | ||||||||
\(269\) | −8.17172e34 | −0.479629 | −0.239815 | − | 0.970819i | \(-0.577087\pi\) | ||||
−0.239815 | + | 0.970819i | \(0.577087\pi\) | |||||||
\(270\) | 3.65487e34 | 0.203281 | ||||||||
\(271\) | 2.70296e35 | 1.42490 | 0.712450 | − | 0.701723i | \(-0.247585\pi\) | ||||
0.712450 | + | 0.701723i | \(0.247585\pi\) | |||||||
\(272\) | 7.88980e34 | 0.394291 | ||||||||
\(273\) | −2.08863e35 | −0.989698 | ||||||||
\(274\) | 1.64313e34 | 0.0738396 | ||||||||
\(275\) | 4.97323e35 | 2.11989 | ||||||||
\(276\) | 9.55163e34 | 0.386274 | ||||||||
\(277\) | −9.35727e34 | −0.359081 | −0.179541 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179541 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(278\) | −6.10315e34 | −0.222282 | ||||||||
\(279\) | 4.20222e34 | 0.145284 | ||||||||
\(280\) | 2.26101e35 | 0.742182 | ||||||||
\(281\) | −4.90540e35 | −1.52909 | −0.764544 | − | 0.644571i | \(-0.777036\pi\) | ||||
−0.764544 | + | 0.644571i | \(0.777036\pi\) | |||||||
\(282\) | −5.66359e34 | −0.167679 | ||||||||
\(283\) | 6.11272e35 | 1.71922 | 0.859609 | − | 0.510953i | \(-0.170707\pi\) | ||||
0.859609 | + | 0.510953i | \(0.170707\pi\) | |||||||
\(284\) | −1.14263e35 | −0.305343 | ||||||||
\(285\) | 1.40497e35 | 0.356793 | ||||||||
\(286\) | −6.15161e35 | −1.48485 | ||||||||
\(287\) | 1.90357e35 | 0.436799 | ||||||||
\(288\) | 2.70081e34 | 0.0589256 | ||||||||
\(289\) | 7.16903e35 | 1.48745 | ||||||||
\(290\) | −5.96650e35 | −1.17747 | ||||||||
\(291\) | −4.31818e35 | −0.810686 | ||||||||
\(292\) | −1.23807e35 | −0.221153 | ||||||||
\(293\) | −4.44214e35 | −0.755113 | −0.377557 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377557 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(294\) | −2.45966e35 | −0.397959 | ||||||||
\(295\) | 1.34440e35 | 0.207067 | ||||||||
\(296\) | 2.65706e35 | 0.389647 | ||||||||
\(297\) | −2.37236e35 | −0.331293 | ||||||||
\(298\) | 8.83794e35 | 1.17548 | ||||||||
\(299\) | 1.28831e36 | 1.63226 | ||||||||
\(300\) | −2.94501e35 | −0.355491 | ||||||||
\(301\) | −1.15922e36 | −1.33337 | ||||||||
\(302\) | 6.50575e35 | 0.713176 | ||||||||
\(303\) | −6.49022e35 | −0.678174 | ||||||||
\(304\) | 1.03822e35 | 0.103424 | ||||||||
\(305\) | −1.32919e35 | −0.126252 | ||||||||
\(306\) | 4.10394e35 | 0.371741 | ||||||||
\(307\) | −1.08810e36 | −0.940078 | −0.470039 | − | 0.882646i | \(-0.655760\pi\) | ||||
−0.470039 | + | 0.882646i | \(0.655760\pi\) | |||||||
\(308\) | −1.46761e36 | −1.20955 | ||||||||
\(309\) | −3.28476e35 | −0.258289 | ||||||||
\(310\) | −6.13569e35 | −0.460382 | ||||||||
\(311\) | −1.31602e36 | −0.942402 | −0.471201 | − | 0.882026i | \(-0.656179\pi\) | ||||
−0.471201 | + | 0.882026i | \(0.656179\pi\) | |||||||
\(312\) | 3.64282e35 | 0.248998 | ||||||||
\(313\) | −9.80838e35 | −0.640036 | −0.320018 | − | 0.947411i | \(-0.603689\pi\) | ||||
−0.320018 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(314\) | −1.27269e36 | −0.792944 | ||||||||
\(315\) | 1.17608e36 | 0.699736 | ||||||||
\(316\) | 1.41017e36 | 0.801325 | ||||||||
\(317\) | 2.03796e36 | 1.10621 | 0.553104 | − | 0.833112i | \(-0.313443\pi\) | ||||
0.553104 | + | 0.833112i | \(0.313443\pi\) | |||||||
\(318\) | 4.22706e35 | 0.219202 | ||||||||
\(319\) | 3.87283e36 | 1.91895 | ||||||||
\(320\) | −3.94347e35 | −0.186726 | ||||||||
\(321\) | −5.92040e35 | −0.267934 | ||||||||
\(322\) | 3.07357e36 | 1.32963 | ||||||||
\(323\) | 1.57760e36 | 0.652468 | ||||||||
\(324\) | 1.40485e35 | 0.0555556 | ||||||||
\(325\) | −3.97220e36 | −1.50218 | ||||||||
\(326\) | 1.43451e36 | 0.518859 | ||||||||
\(327\) | 5.41325e34 | 0.0187290 | ||||||||
\(328\) | −3.32007e35 | −0.109894 | ||||||||
\(329\) | −1.82246e36 | −0.577187 | ||||||||
\(330\) | 3.46390e36 | 1.04982 | ||||||||
\(331\) | 1.12914e35 | 0.0327522 | 0.0163761 | − | 0.999866i | \(-0.494787\pi\) | ||||
0.0163761 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(332\) | −1.10133e36 | −0.305784 | ||||||||
\(333\) | 1.38209e36 | 0.367363 | ||||||||
\(334\) | 6.27253e35 | 0.159632 | ||||||||
\(335\) | 4.05509e36 | 0.988214 | ||||||||
\(336\) | 8.69081e35 | 0.202834 | ||||||||
\(337\) | −8.08762e36 | −1.80795 | −0.903977 | − | 0.427581i | \(-0.859366\pi\) | ||||
−0.903977 | + | 0.427581i | \(0.859366\pi\) | |||||||
\(338\) | 1.61139e36 | 0.345071 | ||||||||
\(339\) | 1.26836e36 | 0.260224 | ||||||||
\(340\) | −5.99219e36 | −1.17799 | ||||||||
\(341\) | 3.98265e36 | 0.750298 | ||||||||
\(342\) | 5.40039e35 | 0.0975093 | ||||||||
\(343\) | 2.04643e35 | 0.0354186 | ||||||||
\(344\) | 2.02182e36 | 0.335464 | ||||||||
\(345\) | −7.25432e36 | −1.15404 | ||||||||
\(346\) | −7.33170e36 | −1.11841 | ||||||||
\(347\) | −5.00016e36 | −0.731487 | −0.365744 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365744 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(348\) | −2.29339e36 | −0.321794 | ||||||||
\(349\) | −7.92228e36 | −1.06630 | −0.533152 | − | 0.846019i | \(-0.678993\pi\) | ||||
−0.533152 | + | 0.846019i | \(0.678993\pi\) | |||||||
\(350\) | −9.47660e36 | −1.22367 | ||||||||
\(351\) | 1.89484e36 | 0.234758 | ||||||||
\(352\) | 2.55969e36 | 0.304312 | ||||||||
\(353\) | 7.39537e35 | 0.0843775 | 0.0421888 | − | 0.999110i | \(-0.486567\pi\) | ||||
0.0421888 | + | 0.999110i | \(0.486567\pi\) | |||||||
\(354\) | 5.16759e35 | 0.0565901 | ||||||||
\(355\) | 8.67807e36 | 0.912247 | ||||||||
\(356\) | −1.34690e36 | −0.135929 | ||||||||
\(357\) | 1.32059e37 | 1.27961 | ||||||||
\(358\) | 1.16769e37 | 1.08648 | ||||||||
\(359\) | 1.81161e37 | 1.61881 | 0.809403 | − | 0.587254i | \(-0.199791\pi\) | ||||
0.809403 | + | 0.587254i | \(0.199791\pi\) | |||||||
\(360\) | −2.05123e36 | −0.176047 | ||||||||
\(361\) | −1.00539e37 | −0.828855 | ||||||||
\(362\) | −1.69526e37 | −1.34265 | ||||||||
\(363\) | −1.48968e37 | −1.13356 | ||||||||
\(364\) | 1.17220e37 | 0.857103 | ||||||||
\(365\) | 9.40295e36 | 0.660720 | ||||||||
\(366\) | −5.10910e35 | −0.0345039 | ||||||||
\(367\) | 1.51023e37 | 0.980362 | 0.490181 | − | 0.871621i | \(-0.336931\pi\) | ||||
0.490181 | + | 0.871621i | \(0.336931\pi\) | |||||||
\(368\) | −5.36068e36 | −0.334523 | ||||||||
\(369\) | −1.72696e36 | −0.103610 | ||||||||
\(370\) | −2.01800e37 | −1.16411 | ||||||||
\(371\) | 1.36020e37 | 0.754539 | ||||||||
\(372\) | −2.35842e36 | −0.125820 | ||||||||
\(373\) | 1.54624e37 | 0.793414 | 0.396707 | − | 0.917945i | \(-0.370153\pi\) | ||||
0.396707 | + | 0.917945i | \(0.370153\pi\) | |||||||
\(374\) | 3.88951e37 | 1.91980 | ||||||||
\(375\) | 4.20397e36 | 0.199621 | ||||||||
\(376\) | 3.17859e36 | 0.145215 | ||||||||
\(377\) | −3.09329e37 | −1.35979 | ||||||||
\(378\) | 4.52059e36 | 0.191234 | ||||||||
\(379\) | −1.50980e37 | −0.614684 | −0.307342 | − | 0.951599i | \(-0.599440\pi\) | ||||
−0.307342 | + | 0.951599i | \(0.599440\pi\) | |||||||
\(380\) | −7.88513e36 | −0.308992 | ||||||||
\(381\) | −9.79762e36 | −0.369580 | ||||||||
\(382\) | −1.04954e37 | −0.381136 | ||||||||
\(383\) | −2.64946e37 | −0.926351 | −0.463175 | − | 0.886267i | \(-0.653290\pi\) | ||||
−0.463175 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(384\) | −1.51578e36 | −0.0510310 | ||||||||
\(385\) | 1.11463e38 | 3.61368 | ||||||||
\(386\) | 1.39366e37 | 0.435152 | ||||||||
\(387\) | 1.05167e37 | 0.316278 | ||||||||
\(388\) | 2.42350e37 | 0.702075 | ||||||||
\(389\) | −5.09411e37 | −1.42167 | −0.710836 | − | 0.703358i | \(-0.751683\pi\) | ||||
−0.710836 | + | 0.703358i | \(0.751683\pi\) | |||||||
\(390\) | −2.76667e37 | −0.743911 | ||||||||
\(391\) | −8.14566e37 | −2.11039 | ||||||||
\(392\) | 1.38044e37 | 0.344642 | ||||||||
\(393\) | −1.78198e37 | −0.428755 | ||||||||
\(394\) | 5.89899e36 | 0.136799 | ||||||||
\(395\) | −1.07100e38 | −2.39405 | ||||||||
\(396\) | 1.33145e37 | 0.286908 | ||||||||
\(397\) | 6.75019e37 | 1.40234 | 0.701171 | − | 0.712994i | \(-0.252661\pi\) | ||||
0.701171 | + | 0.712994i | \(0.252661\pi\) | |||||||
\(398\) | −1.14589e37 | −0.229529 | ||||||||
\(399\) | 1.73776e37 | 0.335647 | ||||||||
\(400\) | 1.65284e37 | 0.307865 | ||||||||
\(401\) | −1.90835e37 | −0.342819 | −0.171410 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171410 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(402\) | 1.55869e37 | 0.270073 | ||||||||
\(403\) | −3.18101e37 | −0.531669 | ||||||||
\(404\) | 3.64252e37 | 0.587316 | ||||||||
\(405\) | −1.06696e37 | −0.165979 | ||||||||
\(406\) | −7.37977e37 | −1.10768 | ||||||||
\(407\) | 1.30987e38 | 1.89719 | ||||||||
\(408\) | −2.30326e37 | −0.321937 | ||||||||
\(409\) | −9.02898e37 | −1.21801 | −0.609005 | − | 0.793167i | \(-0.708431\pi\) | ||||
−0.609005 | + | 0.793167i | \(0.708431\pi\) | |||||||
\(410\) | 2.52154e37 | 0.328322 | ||||||||
\(411\) | −4.79679e36 | −0.0602898 | ||||||||
\(412\) | 1.84351e37 | 0.223685 | ||||||||
\(413\) | 1.66285e37 | 0.194795 | ||||||||
\(414\) | −2.78840e37 | −0.315391 | ||||||||
\(415\) | 8.36445e37 | 0.913566 | ||||||||
\(416\) | −2.04447e37 | −0.215639 | ||||||||
\(417\) | 1.78169e37 | 0.181493 | ||||||||
\(418\) | 5.11821e37 | 0.503572 | ||||||||
\(419\) | −1.07363e38 | −1.02036 | −0.510179 | − | 0.860068i | \(-0.670421\pi\) | ||||
−0.510179 | + | 0.860068i | \(0.670421\pi\) | |||||||
\(420\) | −6.60054e37 | −0.605989 | ||||||||
\(421\) | −1.26637e38 | −1.12323 | −0.561616 | − | 0.827398i | \(-0.689820\pi\) | ||||
−0.561616 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(422\) | 1.60236e38 | 1.37318 | ||||||||
\(423\) | 1.65337e37 | 0.136910 | ||||||||
\(424\) | −2.37236e37 | −0.189835 | ||||||||
\(425\) | 2.51152e38 | 1.94221 | ||||||||
\(426\) | 3.33566e37 | 0.249311 | ||||||||
\(427\) | −1.64403e37 | −0.118770 | ||||||||
\(428\) | 3.32272e37 | 0.232038 | ||||||||
\(429\) | 1.79584e38 | 1.21237 | ||||||||
\(430\) | −1.53555e38 | −1.00224 | ||||||||
\(431\) | 6.83365e37 | 0.431253 | 0.215627 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215627 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(432\) | −7.88447e36 | −0.0481125 | ||||||||
\(433\) | 1.64537e38 | 0.970933 | 0.485467 | − | 0.874255i | \(-0.338650\pi\) | ||||
0.485467 | + | 0.874255i | \(0.338650\pi\) | |||||||
\(434\) | −7.58903e37 | −0.433097 | ||||||||
\(435\) | 1.74179e38 | 0.961397 | ||||||||
\(436\) | −3.03809e36 | −0.0162198 | ||||||||
\(437\) | −1.07189e38 | −0.553565 | ||||||||
\(438\) | 3.61428e37 | 0.180571 | ||||||||
\(439\) | −6.20787e37 | −0.300059 | −0.150030 | − | 0.988681i | \(-0.547937\pi\) | ||||
−0.150030 | + | 0.988681i | \(0.547937\pi\) | |||||||
\(440\) | −1.94405e38 | −0.909167 | ||||||||
\(441\) | 7.18046e37 | 0.324932 | ||||||||
\(442\) | −3.10661e38 | −1.36039 | ||||||||
\(443\) | −2.81830e38 | −1.19435 | −0.597177 | − | 0.802110i | \(-0.703711\pi\) | ||||
−0.597177 | + | 0.802110i | \(0.703711\pi\) | |||||||
\(444\) | −7.75673e37 | −0.318145 | ||||||||
\(445\) | 1.02295e38 | 0.406103 | ||||||||
\(446\) | 2.36495e38 | 0.908796 | ||||||||
\(447\) | −2.58005e38 | −0.959775 | ||||||||
\(448\) | −4.87756e37 | −0.175659 | ||||||||
\(449\) | 4.33351e38 | 1.51101 | 0.755506 | − | 0.655141i | \(-0.227391\pi\) | ||||
0.755506 | + | 0.655141i | \(0.227391\pi\) | |||||||
\(450\) | 8.59736e37 | 0.290258 | ||||||||
\(451\) | −1.63672e38 | −0.535076 | ||||||||
\(452\) | −7.11844e37 | −0.225360 | ||||||||
\(453\) | −1.89922e38 | −0.582306 | ||||||||
\(454\) | −7.13523e37 | −0.211884 | ||||||||
\(455\) | −8.90272e38 | −2.56069 | ||||||||
\(456\) | −3.03087e37 | −0.0844456 | ||||||||
\(457\) | −2.39766e38 | −0.647147 | −0.323574 | − | 0.946203i | \(-0.604884\pi\) | ||||
−0.323574 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(458\) | −5.79056e37 | −0.151416 | ||||||||
\(459\) | −1.19806e38 | −0.303525 | ||||||||
\(460\) | 4.07136e38 | 0.999426 | ||||||||
\(461\) | −1.00404e38 | −0.238828 | −0.119414 | − | 0.992845i | \(-0.538102\pi\) | ||||
−0.119414 | + | 0.992845i | \(0.538102\pi\) | |||||||
\(462\) | 4.28439e38 | 0.987597 | ||||||||
\(463\) | −2.18695e38 | −0.488556 | −0.244278 | − | 0.969705i | \(-0.578551\pi\) | ||||
−0.244278 | + | 0.969705i | \(0.578551\pi\) | |||||||
\(464\) | 1.28712e38 | 0.278682 | ||||||||
\(465\) | 1.79119e38 | 0.375901 | ||||||||
\(466\) | 4.11434e38 | 0.836960 | ||||||||
\(467\) | 7.59341e38 | 1.49741 | 0.748707 | − | 0.662901i | \(-0.230675\pi\) | ||||
0.748707 | + | 0.662901i | \(0.230675\pi\) | |||||||
\(468\) | −1.06345e38 | −0.203306 | ||||||||
\(469\) | 5.01561e38 | 0.929646 | ||||||||
\(470\) | −2.41409e38 | −0.433845 | ||||||||
\(471\) | 3.71535e38 | 0.647436 | ||||||||
\(472\) | −2.90021e37 | −0.0490085 | ||||||||
\(473\) | 9.96716e38 | 1.63337 | ||||||||
\(474\) | −4.11670e38 | −0.654279 | ||||||||
\(475\) | 3.30491e38 | 0.509451 | ||||||||
\(476\) | −7.41155e38 | −1.10817 | ||||||||
\(477\) | −1.23400e38 | −0.178978 | ||||||||
\(478\) | 8.78552e38 | 1.23613 | ||||||||
\(479\) | −9.71497e37 | −0.132610 | −0.0663050 | − | 0.997799i | \(-0.521121\pi\) | ||||
−0.0663050 | + | 0.997799i | \(0.521121\pi\) | |||||||
\(480\) | 1.15122e38 | 0.152461 | ||||||||
\(481\) | −1.04622e39 | −1.34437 | ||||||||
\(482\) | 9.09911e38 | 1.13453 | ||||||||
\(483\) | −8.97264e38 | −1.08564 | ||||||||
\(484\) | 8.36054e38 | 0.981695 | ||||||||
\(485\) | −1.84061e39 | −2.09753 | ||||||||
\(486\) | −4.10117e37 | −0.0453609 | ||||||||
\(487\) | 9.86090e38 | 1.05864 | 0.529318 | − | 0.848423i | \(-0.322448\pi\) | ||||
0.529318 | + | 0.848423i | \(0.322448\pi\) | |||||||
\(488\) | 2.86739e37 | 0.0298813 | ||||||||
\(489\) | −4.18776e38 | −0.423646 | ||||||||
\(490\) | −1.04842e39 | −1.02966 | ||||||||
\(491\) | 2.46794e38 | 0.235317 | 0.117658 | − | 0.993054i | \(-0.462461\pi\) | ||||
0.117658 | + | 0.993054i | \(0.462461\pi\) | |||||||
\(492\) | 9.69224e37 | 0.0897285 | ||||||||
\(493\) | 1.95581e39 | 1.75811 | ||||||||
\(494\) | −4.08800e38 | −0.356837 | ||||||||
\(495\) | −1.01121e39 | −0.857171 | ||||||||
\(496\) | 1.32362e38 | 0.108963 | ||||||||
\(497\) | 1.07336e39 | 0.858181 | ||||||||
\(498\) | 3.21511e38 | 0.249672 | ||||||||
\(499\) | −1.20983e39 | −0.912567 | −0.456283 | − | 0.889835i | \(-0.650820\pi\) | ||||
−0.456283 | + | 0.889835i | \(0.650820\pi\) | |||||||
\(500\) | −2.35940e38 | −0.172877 | ||||||||
\(501\) | −1.83114e38 | −0.130339 | ||||||||
\(502\) | −5.65410e38 | −0.390985 | ||||||||
\(503\) | 1.96508e39 | 1.32021 | 0.660107 | − | 0.751171i | \(-0.270511\pi\) | ||||
0.660107 | + | 0.751171i | \(0.270511\pi\) | |||||||
\(504\) | −2.53710e38 | −0.165613 | ||||||||
\(505\) | −2.76644e39 | −1.75467 | ||||||||
\(506\) | −2.64270e39 | −1.62879 | ||||||||
\(507\) | −4.70412e38 | −0.281750 | ||||||||
\(508\) | 5.49874e38 | 0.320066 | ||||||||
\(509\) | 4.54640e38 | 0.257194 | 0.128597 | − | 0.991697i | \(-0.458953\pi\) | ||||
0.128597 | + | 0.991697i | \(0.458953\pi\) | |||||||
\(510\) | 1.74930e39 | 0.961824 | ||||||||
\(511\) | 1.16302e39 | 0.621562 | ||||||||
\(512\) | 8.50706e37 | 0.0441942 | ||||||||
\(513\) | −1.57653e38 | −0.0796160 | ||||||||
\(514\) | −1.20563e39 | −0.591901 | ||||||||
\(515\) | −1.40012e39 | −0.668284 | ||||||||
\(516\) | −5.90229e38 | −0.273905 | ||||||||
\(517\) | 1.56698e39 | 0.707050 | ||||||||
\(518\) | −2.49600e39 | −1.09512 | ||||||||
\(519\) | 2.14034e39 | 0.913178 | ||||||||
\(520\) | 1.55274e39 | 0.644246 | ||||||||
\(521\) | −2.06563e39 | −0.833500 | −0.416750 | − | 0.909021i | \(-0.636831\pi\) | ||||
−0.416750 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(522\) | 6.69507e38 | 0.262744 | ||||||||
\(523\) | −9.08640e38 | −0.346830 | −0.173415 | − | 0.984849i | \(-0.555480\pi\) | ||||
−0.173415 | + | 0.984849i | \(0.555480\pi\) | |||||||
\(524\) | 1.00010e39 | 0.371313 | ||||||||
\(525\) | 2.76650e39 | 0.999126 | ||||||||
\(526\) | −1.73422e39 | −0.609271 | ||||||||
\(527\) | 2.01127e39 | 0.687411 | ||||||||
\(528\) | −7.47249e38 | −0.248470 | ||||||||
\(529\) | 2.44346e39 | 0.790492 | ||||||||
\(530\) | 1.80177e39 | 0.567153 | ||||||||
\(531\) | −1.50857e38 | −0.0462056 | ||||||||
\(532\) | −9.75287e38 | −0.290679 | ||||||||
\(533\) | 1.30728e39 | 0.379160 | ||||||||
\(534\) | 3.93201e38 | 0.110985 | ||||||||
\(535\) | −2.52356e39 | −0.693239 | ||||||||
\(536\) | −8.74784e38 | −0.233890 | ||||||||
\(537\) | −3.40882e39 | −0.887108 | ||||||||
\(538\) | −1.33886e39 | −0.339149 | ||||||||
\(539\) | 6.80527e39 | 1.67806 | ||||||||
\(540\) | 5.98814e38 | 0.143742 | ||||||||
\(541\) | −6.44804e39 | −1.50684 | −0.753421 | − | 0.657539i | \(-0.771598\pi\) | ||||
−0.753421 | + | 0.657539i | \(0.771598\pi\) | |||||||
\(542\) | 4.42853e39 | 1.00756 | ||||||||
\(543\) | 4.94895e39 | 1.09627 | ||||||||
\(544\) | 1.29267e39 | 0.278806 | ||||||||
\(545\) | 2.30738e38 | 0.0484585 | ||||||||
\(546\) | −3.42201e39 | −0.699822 | ||||||||
\(547\) | 5.73505e39 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(548\) | 2.69211e38 | 0.0522125 | ||||||||
\(549\) | 1.49150e38 | 0.0281723 | ||||||||
\(550\) | 8.14813e39 | 1.49899 | ||||||||
\(551\) | 2.57365e39 | 0.461160 | ||||||||
\(552\) | 1.56494e39 | 0.273137 | ||||||||
\(553\) | −1.32469e40 | −2.25216 | ||||||||
\(554\) | −1.53310e39 | −0.253909 | ||||||||
\(555\) | 5.89112e39 | 0.950495 | ||||||||
\(556\) | −9.99940e38 | −0.157177 | ||||||||
\(557\) | −1.13157e40 | −1.73293 | −0.866466 | − | 0.499236i | \(-0.833614\pi\) | ||||
−0.866466 | + | 0.499236i | \(0.833614\pi\) | |||||||
\(558\) | 6.88492e38 | 0.102731 | ||||||||
\(559\) | −7.96093e39 | −1.15742 | ||||||||
\(560\) | 3.70443e39 | 0.524802 | ||||||||
\(561\) | −1.13546e40 | −1.56751 | ||||||||
\(562\) | −8.03700e39 | −1.08123 | ||||||||
\(563\) | −7.41757e39 | −0.972500 | −0.486250 | − | 0.873820i | \(-0.661636\pi\) | ||||
−0.486250 | + | 0.873820i | \(0.661636\pi\) | |||||||
\(564\) | −9.27923e38 | −0.118567 | ||||||||
\(565\) | 5.40636e39 | 0.673290 | ||||||||
\(566\) | 1.00151e40 | 1.21567 | ||||||||
\(567\) | −1.31969e39 | −0.156142 | ||||||||
\(568\) | −1.87208e39 | −0.215910 | ||||||||
\(569\) | −4.64228e38 | −0.0521920 | −0.0260960 | − | 0.999659i | \(-0.508308\pi\) | ||||
−0.0260960 | + | 0.999659i | \(0.508308\pi\) | |||||||
\(570\) | 2.30190e39 | 0.252291 | ||||||||
\(571\) | 1.12973e40 | 1.20712 | 0.603559 | − | 0.797318i | \(-0.293749\pi\) | ||||
0.603559 | + | 0.797318i | \(0.293749\pi\) | |||||||
\(572\) | −1.00788e40 | −1.04994 | ||||||||
\(573\) | 3.06391e39 | 0.311196 | ||||||||
\(574\) | 3.11881e39 | 0.308864 | ||||||||
\(575\) | −1.70643e40 | −1.64781 | ||||||||
\(576\) | 4.42502e38 | 0.0416667 | ||||||||
\(577\) | 1.57562e40 | 1.44678 | 0.723388 | − | 0.690441i | \(-0.242584\pi\) | ||||
0.723388 | + | 0.690441i | \(0.242584\pi\) | |||||||
\(578\) | 1.17457e40 | 1.05178 | ||||||||
\(579\) | −4.06850e39 | −0.355300 | ||||||||
\(580\) | −9.77551e39 | −0.832594 | ||||||||
\(581\) | 1.03457e40 | 0.859422 | ||||||||
\(582\) | −7.07491e39 | −0.573241 | ||||||||
\(583\) | −1.16952e40 | −0.924304 | ||||||||
\(584\) | −2.02845e39 | −0.156379 | ||||||||
\(585\) | 8.07673e39 | 0.607401 | ||||||||
\(586\) | −7.27801e39 | −0.533946 | ||||||||
\(587\) | 1.71498e39 | 0.122745 | 0.0613727 | − | 0.998115i | \(-0.480452\pi\) | ||||
0.0613727 | + | 0.998115i | \(0.480452\pi\) | |||||||
\(588\) | −4.02990e39 | −0.281399 | ||||||||
\(589\) | 2.64663e39 | 0.180311 | ||||||||
\(590\) | 2.20267e39 | 0.146418 | ||||||||
\(591\) | −1.72209e39 | −0.111696 | ||||||||
\(592\) | 4.35332e39 | 0.275522 | ||||||||
\(593\) | 2.06799e39 | 0.127719 | 0.0638595 | − | 0.997959i | \(-0.479659\pi\) | ||||
0.0638595 | + | 0.997959i | \(0.479659\pi\) | |||||||
\(594\) | −3.88688e39 | −0.234260 | ||||||||
\(595\) | 5.62896e40 | 3.31080 | ||||||||
\(596\) | 1.44801e40 | 0.831190 | ||||||||
\(597\) | 3.34518e39 | 0.187410 | ||||||||
\(598\) | 2.11077e40 | 1.15418 | ||||||||
\(599\) | 1.00136e40 | 0.534444 | 0.267222 | − | 0.963635i | \(-0.413894\pi\) | ||||
0.267222 | + | 0.963635i | \(0.413894\pi\) | |||||||
\(600\) | −4.82511e39 | −0.251370 | ||||||||
\(601\) | 2.26586e40 | 1.15227 | 0.576134 | − | 0.817355i | \(-0.304560\pi\) | ||||
0.576134 | + | 0.817355i | \(0.304560\pi\) | |||||||
\(602\) | −1.89927e40 | −0.942837 | ||||||||
\(603\) | −4.55026e39 | −0.220514 | ||||||||
\(604\) | 1.06590e40 | 0.504292 | ||||||||
\(605\) | −6.34971e40 | −2.93292 | ||||||||
\(606\) | −1.06336e40 | −0.479541 | ||||||||
\(607\) | −4.06471e39 | −0.178975 | −0.0894877 | − | 0.995988i | \(-0.528523\pi\) | ||||
−0.0894877 | + | 0.995988i | \(0.528523\pi\) | |||||||
\(608\) | 1.70102e39 | 0.0731320 | ||||||||
\(609\) | 2.15437e40 | 0.904418 | ||||||||
\(610\) | −2.17774e39 | −0.0892737 | ||||||||
\(611\) | −1.25157e40 | −0.501023 | ||||||||
\(612\) | 6.72390e39 | 0.262861 | ||||||||
\(613\) | −2.69964e40 | −1.03069 | −0.515345 | − | 0.856983i | \(-0.672336\pi\) | ||||
−0.515345 | + | 0.856983i | \(0.672336\pi\) | |||||||
\(614\) | −1.78275e40 | −0.664736 | ||||||||
\(615\) | −7.36112e39 | −0.268074 | ||||||||
\(616\) | −2.40453e40 | −0.855284 | ||||||||
\(617\) | 4.15838e40 | 1.44474 | 0.722369 | − | 0.691508i | \(-0.243053\pi\) | ||||
0.722369 | + | 0.691508i | \(0.243053\pi\) | |||||||
\(618\) | −5.38176e39 | −0.182638 | ||||||||
\(619\) | −3.52546e40 | −1.16870 | −0.584348 | − | 0.811503i | \(-0.698650\pi\) | ||||
−0.584348 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(620\) | −1.00527e40 | −0.325539 | ||||||||
\(621\) | 8.14015e39 | 0.257516 | ||||||||
\(622\) | −2.15616e40 | −0.666379 | ||||||||
\(623\) | 1.26526e40 | 0.382035 | ||||||||
\(624\) | 5.96840e39 | 0.176068 | ||||||||
\(625\) | −2.48055e40 | −0.714969 | ||||||||
\(626\) | −1.60700e40 | −0.452574 | ||||||||
\(627\) | −1.49415e40 | −0.411165 | ||||||||
\(628\) | −2.08517e40 | −0.560696 | ||||||||
\(629\) | 6.61496e40 | 1.73817 | ||||||||
\(630\) | 1.92689e40 | 0.494788 | ||||||||
\(631\) | 3.55952e40 | 0.893234 | 0.446617 | − | 0.894725i | \(-0.352629\pi\) | ||||
0.446617 | + | 0.894725i | \(0.352629\pi\) | |||||||
\(632\) | 2.31042e40 | 0.566623 | ||||||||
\(633\) | −4.67774e40 | −1.12120 | ||||||||
\(634\) | 3.33900e40 | 0.782207 | ||||||||
\(635\) | −4.17621e40 | −0.956232 | ||||||||
\(636\) | 6.92561e39 | 0.154999 | ||||||||
\(637\) | −5.43548e40 | −1.18909 | ||||||||
\(638\) | 6.34524e40 | 1.35690 | ||||||||
\(639\) | −9.73776e39 | −0.203562 | ||||||||
\(640\) | −6.46099e39 | −0.132035 | ||||||||
\(641\) | −1.32448e40 | −0.264608 | −0.132304 | − | 0.991209i | \(-0.542237\pi\) | ||||
−0.132304 | + | 0.991209i | \(0.542237\pi\) | |||||||
\(642\) | −9.69998e39 | −0.189458 | ||||||||
\(643\) | −1.90296e39 | −0.0363389 | −0.0181694 | − | 0.999835i | \(-0.505784\pi\) | ||||
−0.0181694 | + | 0.999835i | \(0.505784\pi\) | |||||||
\(644\) | 5.03573e40 | 0.940194 | ||||||||
\(645\) | 4.48271e40 | 0.818322 | ||||||||
\(646\) | 2.58473e40 | 0.461365 | ||||||||
\(647\) | −1.09747e40 | −0.191549 | −0.0957743 | − | 0.995403i | \(-0.530533\pi\) | ||||
−0.0957743 | + | 0.995403i | \(0.530533\pi\) | |||||||
\(648\) | 2.30171e39 | 0.0392837 | ||||||||
\(649\) | −1.42975e40 | −0.238622 | ||||||||
\(650\) | −6.50804e40 | −1.06220 | ||||||||
\(651\) | 2.21546e40 | 0.353622 | ||||||||
\(652\) | 2.35030e40 | 0.366888 | ||||||||
\(653\) | 3.22859e40 | 0.492914 | 0.246457 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246457 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(654\) | 8.86906e38 | 0.0132434 | ||||||||
\(655\) | −7.59563e40 | −1.10934 | ||||||||
\(656\) | −5.43959e39 | −0.0777071 | ||||||||
\(657\) | −1.05511e40 | −0.147435 | ||||||||
\(658\) | −2.98591e40 | −0.408133 | ||||||||
\(659\) | 8.02727e39 | 0.107332 | 0.0536660 | − | 0.998559i | \(-0.482909\pi\) | ||||
0.0536660 | + | 0.998559i | \(0.482909\pi\) | |||||||
\(660\) | 5.67525e40 | 0.742332 | ||||||||
\(661\) | 5.89261e40 | 0.754026 | 0.377013 | − | 0.926208i | \(-0.376951\pi\) | ||||
0.377013 | + | 0.926208i | \(0.376951\pi\) | |||||||
\(662\) | 1.84998e39 | 0.0231593 | ||||||||
\(663\) | 9.06911e40 | 1.11076 | ||||||||
\(664\) | −1.80442e40 | −0.216222 | ||||||||
\(665\) | 7.40716e40 | 0.868436 | ||||||||
\(666\) | 2.26442e40 | 0.259765 | ||||||||
\(667\) | −1.32886e41 | −1.49161 | ||||||||
\(668\) | 1.02769e40 | 0.112877 | ||||||||
\(669\) | −6.90398e40 | −0.742028 | ||||||||
\(670\) | 6.64386e40 | 0.698773 | ||||||||
\(671\) | 1.41356e40 | 0.145492 | ||||||||
\(672\) | 1.42390e40 | 0.143425 | ||||||||
\(673\) | 1.83445e41 | 1.80838 | 0.904188 | − | 0.427135i | \(-0.140477\pi\) | ||||
0.904188 | + | 0.427135i | \(0.140477\pi\) | |||||||
\(674\) | −1.32508e41 | −1.27842 | ||||||||
\(675\) | −2.50982e40 | −0.236994 | ||||||||
\(676\) | 2.64010e40 | 0.244002 | ||||||||
\(677\) | 1.27839e41 | 1.15645 | 0.578227 | − | 0.815876i | \(-0.303745\pi\) | ||||
0.578227 | + | 0.815876i | \(0.303745\pi\) | |||||||
\(678\) | 2.07808e40 | 0.184006 | ||||||||
\(679\) | −2.27660e41 | −1.97321 | ||||||||
\(680\) | −9.81761e40 | −0.832964 | ||||||||
\(681\) | 2.08298e40 | 0.173003 | ||||||||
\(682\) | 6.52517e40 | 0.530541 | ||||||||
\(683\) | −1.25940e41 | −1.00245 | −0.501227 | − | 0.865316i | \(-0.667118\pi\) | ||||
−0.501227 | + | 0.865316i | \(0.667118\pi\) | |||||||
\(684\) | 8.84799e39 | 0.0689495 | ||||||||
\(685\) | −2.04462e40 | −0.155991 | ||||||||
\(686\) | 3.35287e39 | 0.0250447 | ||||||||
\(687\) | 1.69043e40 | 0.123630 | ||||||||
\(688\) | 3.31255e40 | 0.237209 | ||||||||
\(689\) | 9.34117e40 | 0.654972 | ||||||||
\(690\) | −1.18855e41 | −0.816028 | ||||||||
\(691\) | 1.19626e41 | 0.804254 | 0.402127 | − | 0.915584i | \(-0.368271\pi\) | ||||
0.402127 | + | 0.915584i | \(0.368271\pi\) | |||||||
\(692\) | −1.20123e41 | −0.790835 | ||||||||
\(693\) | −1.25074e41 | −0.806370 | ||||||||
\(694\) | −8.19227e40 | −0.517240 | ||||||||
\(695\) | 7.59440e40 | 0.469585 | ||||||||
\(696\) | −3.75749e40 | −0.227543 | ||||||||
\(697\) | −8.26558e40 | −0.490228 | ||||||||
\(698\) | −1.29799e41 | −0.753991 | ||||||||
\(699\) | −1.20110e41 | −0.683375 | ||||||||
\(700\) | −1.55265e41 | −0.865268 | ||||||||
\(701\) | 4.85810e39 | 0.0265189 | 0.0132594 | − | 0.999912i | \(-0.495779\pi\) | ||||
0.0132594 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(702\) | 3.10451e40 | 0.165999 | ||||||||
\(703\) | 8.70464e40 | 0.455931 | ||||||||
\(704\) | 4.19380e40 | 0.215181 | ||||||||
\(705\) | 7.04744e40 | 0.354233 | ||||||||
\(706\) | 1.21166e40 | 0.0596639 | ||||||||
\(707\) | −3.42172e41 | −1.65068 | ||||||||
\(708\) | 8.46657e39 | 0.0400152 | ||||||||
\(709\) | 2.51260e41 | 1.16346 | 0.581732 | − | 0.813381i | \(-0.302375\pi\) | ||||
0.581732 | + | 0.813381i | \(0.302375\pi\) | |||||||
\(710\) | 1.42182e41 | 0.645056 | ||||||||
\(711\) | 1.20179e41 | 0.534217 | ||||||||
\(712\) | −2.20677e40 | −0.0961162 | ||||||||
\(713\) | −1.36654e41 | −0.583211 | ||||||||
\(714\) | 2.16365e41 | 0.904821 | ||||||||
\(715\) | 7.65471e41 | 3.13683 | ||||||||
\(716\) | 1.91314e41 | 0.768258 | ||||||||
\(717\) | −2.56475e41 | −1.00929 | ||||||||
\(718\) | 2.96814e41 | 1.14467 | ||||||||
\(719\) | 4.13486e40 | 0.156276 | 0.0781379 | − | 0.996943i | \(-0.475103\pi\) | ||||
0.0781379 | + | 0.996943i | \(0.475103\pi\) | |||||||
\(720\) | −3.36074e40 | −0.124484 | ||||||||
\(721\) | −1.73177e41 | −0.628678 | ||||||||
\(722\) | −1.64722e41 | −0.586089 | ||||||||
\(723\) | −2.65630e41 | −0.926342 | ||||||||
\(724\) | −2.77751e41 | −0.949394 | ||||||||
\(725\) | 4.09722e41 | 1.37274 | ||||||||
\(726\) | −2.44069e41 | −0.801550 | ||||||||
\(727\) | −4.16011e41 | −1.33923 | −0.669617 | − | 0.742707i | \(-0.733542\pi\) | ||||
−0.669617 | + | 0.742707i | \(0.733542\pi\) | |||||||
\(728\) | 1.92054e41 | 0.606064 | ||||||||
\(729\) | 1.19725e40 | 0.0370370 | ||||||||
\(730\) | 1.54058e41 | 0.467200 | ||||||||
\(731\) | 5.03349e41 | 1.49647 | ||||||||
\(732\) | −8.37075e39 | −0.0243980 | ||||||||
\(733\) | 3.88242e41 | 1.10942 | 0.554709 | − | 0.832045i | \(-0.312830\pi\) | ||||
0.554709 | + | 0.832045i | \(0.312830\pi\) | |||||||
\(734\) | 2.47437e41 | 0.693220 | ||||||||
\(735\) | 3.06065e41 | 0.840712 | ||||||||
\(736\) | −8.78293e40 | −0.236544 | ||||||||
\(737\) | −4.31250e41 | −1.13881 | ||||||||
\(738\) | −2.82945e40 | −0.0732630 | ||||||||
\(739\) | 1.83417e38 | 0.000465689 0 | 0.000232845 | − | 1.00000i | \(-0.499926\pi\) | ||||
0.000232845 | 1.00000i | \(0.499926\pi\) | ||||||||
\(740\) | −3.30629e41 | −0.823153 | ||||||||
\(741\) | 1.19341e41 | 0.291356 | ||||||||
\(742\) | 2.22855e41 | 0.533540 | ||||||||
\(743\) | −1.07841e41 | −0.253189 | −0.126595 | − | 0.991955i | \(-0.540405\pi\) | ||||
−0.126595 | + | 0.991955i | \(0.540405\pi\) | |||||||
\(744\) | −3.86404e40 | −0.0889680 | ||||||||
\(745\) | −1.09974e42 | −2.48327 | ||||||||
\(746\) | 2.53337e41 | 0.561029 | ||||||||
\(747\) | −9.38583e40 | −0.203856 | ||||||||
\(748\) | 6.37257e41 | 1.35750 | ||||||||
\(749\) | −3.12130e41 | −0.652153 | ||||||||
\(750\) | 6.88779e40 | 0.141153 | ||||||||
\(751\) | −7.12460e40 | −0.143213 | −0.0716064 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716064 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(752\) | 5.20780e40 | 0.102682 | ||||||||
\(753\) | 1.65060e41 | 0.319238 | ||||||||
\(754\) | −5.06805e41 | −0.961515 | ||||||||
\(755\) | −8.09538e41 | −1.50663 | ||||||||
\(756\) | 7.40654e40 | 0.135223 | ||||||||
\(757\) | −5.86689e41 | −1.05079 | −0.525397 | − | 0.850857i | \(-0.676083\pi\) | ||||
−0.525397 | + | 0.850857i | \(0.676083\pi\) | |||||||
\(758\) | −2.47366e41 | −0.434647 | ||||||||
\(759\) | 7.71482e41 | 1.32990 | ||||||||
\(760\) | −1.29190e41 | −0.218490 | ||||||||
\(761\) | −9.15709e41 | −1.51943 | −0.759713 | − | 0.650258i | \(-0.774661\pi\) | ||||
−0.759713 | + | 0.650258i | \(0.774661\pi\) | |||||||
\(762\) | −1.60524e41 | −0.261333 | ||||||||
\(763\) | 2.85393e40 | 0.0455866 | ||||||||
\(764\) | −1.71957e41 | −0.269504 | ||||||||
\(765\) | −5.10671e41 | −0.785326 | ||||||||
\(766\) | −4.34088e41 | −0.655029 | ||||||||
\(767\) | 1.14196e41 | 0.169090 | ||||||||
\(768\) | −2.48346e40 | −0.0360844 | ||||||||
\(769\) | 9.68491e41 | 1.38091 | 0.690453 | − | 0.723378i | \(-0.257411\pi\) | ||||
0.690453 | + | 0.723378i | \(0.257411\pi\) | |||||||
\(770\) | 1.82621e42 | 2.55526 | ||||||||
\(771\) | 3.51959e41 | 0.483285 | ||||||||
\(772\) | 2.28337e41 | 0.307699 | ||||||||
\(773\) | 6.46643e40 | 0.0855188 | 0.0427594 | − | 0.999085i | \(-0.486385\pi\) | ||||
0.0427594 | + | 0.999085i | \(0.486385\pi\) | |||||||
\(774\) | 1.72305e41 | 0.223643 | ||||||||
\(775\) | 4.21341e41 | 0.536734 | ||||||||
\(776\) | 3.97066e41 | 0.496442 | ||||||||
\(777\) | 7.28654e41 | 0.894163 | ||||||||
\(778\) | −8.34619e41 | −1.00527 | ||||||||
\(779\) | −1.08767e41 | −0.128589 | ||||||||
\(780\) | −4.53292e41 | −0.526024 | ||||||||
\(781\) | −9.22895e41 | −1.05127 | ||||||||
\(782\) | −1.33458e42 | −1.49227 | ||||||||
\(783\) | −1.95449e41 | −0.214530 | ||||||||
\(784\) | 2.26171e41 | 0.243699 | ||||||||
\(785\) | 1.58366e42 | 1.67514 | ||||||||
\(786\) | −2.91959e41 | −0.303176 | ||||||||
\(787\) | 1.04389e42 | 1.06419 | 0.532097 | − | 0.846684i | \(-0.321404\pi\) | ||||
0.532097 | + | 0.846684i | \(0.321404\pi\) | |||||||
\(788\) | 9.66491e40 | 0.0967314 | ||||||||
\(789\) | 5.06269e41 | 0.497468 | ||||||||
\(790\) | −1.75473e42 | −1.69285 | ||||||||
\(791\) | 6.68695e41 | 0.633387 | ||||||||
\(792\) | 2.18144e41 | 0.202875 | ||||||||
\(793\) | −1.12904e41 | −0.103097 | ||||||||
\(794\) | 1.10595e42 | 0.991605 | ||||||||
\(795\) | −5.25990e41 | −0.463078 | ||||||||
\(796\) | −1.87742e41 | −0.162302 | ||||||||
\(797\) | 2.34985e42 | 1.99477 | 0.997387 | − | 0.0722472i | \(-0.0230170\pi\) | ||||
0.997387 | + | 0.0722472i | \(0.0230170\pi\) | |||||||
\(798\) | 2.84715e41 | 0.237338 | ||||||||
\(799\) | 7.91336e41 | 0.647787 | ||||||||
\(800\) | 2.70801e41 | 0.217693 | ||||||||
\(801\) | −1.14787e41 | −0.0906192 | ||||||||
\(802\) | −3.12665e41 | −0.242410 | ||||||||
\(803\) | −9.99984e41 | −0.761408 | ||||||||
\(804\) | 2.55375e41 | 0.190970 | ||||||||
\(805\) | −3.82456e42 | −2.80894 | ||||||||
\(806\) | −5.21176e41 | −0.375947 | ||||||||
\(807\) | 3.90851e41 | 0.276914 | ||||||||
\(808\) | 5.96790e41 | 0.415295 | ||||||||
\(809\) | 9.95001e40 | 0.0680096 | 0.0340048 | − | 0.999422i | \(-0.489174\pi\) | ||||
0.0340048 | + | 0.999422i | \(0.489174\pi\) | |||||||
\(810\) | −1.74811e41 | −0.117365 | ||||||||
\(811\) | 2.99801e42 | 1.97711 | 0.988554 | − | 0.150869i | \(-0.0482073\pi\) | ||||
0.988554 | + | 0.150869i | \(0.0482073\pi\) | |||||||
\(812\) | −1.20910e42 | −0.783249 | ||||||||
\(813\) | −1.29282e42 | −0.822667 | ||||||||
\(814\) | 2.14610e42 | 1.34152 | ||||||||
\(815\) | −1.78502e42 | −1.09612 | ||||||||
\(816\) | −3.77367e41 | −0.227644 | ||||||||
\(817\) | 6.62358e41 | 0.392530 | ||||||||
\(818\) | −1.47931e42 | −0.861263 | ||||||||
\(819\) | 9.98984e41 | 0.571402 | ||||||||
\(820\) | 4.13129e41 | 0.232159 | ||||||||
\(821\) | −2.38487e42 | −1.31671 | −0.658353 | − | 0.752709i | \(-0.728747\pi\) | ||||
−0.658353 | + | 0.752709i | \(0.728747\pi\) | |||||||
\(822\) | −7.85905e40 | −0.0426313 | ||||||||
\(823\) | 1.50489e42 | 0.802062 | 0.401031 | − | 0.916065i | \(-0.368652\pi\) | ||||
0.401031 | + | 0.916065i | \(0.368652\pi\) | |||||||
\(824\) | 3.02041e41 | 0.158169 | ||||||||
\(825\) | −2.37868e42 | −1.22392 | ||||||||
\(826\) | 2.72441e41 | 0.137741 | ||||||||
\(827\) | −2.46131e42 | −1.22275 | −0.611374 | − | 0.791342i | \(-0.709383\pi\) | ||||
−0.611374 | + | 0.791342i | \(0.709383\pi\) | |||||||
\(828\) | −4.56851e41 | −0.223015 | ||||||||
\(829\) | −5.65741e40 | −0.0271379 | −0.0135690 | − | 0.999908i | \(-0.504319\pi\) | ||||
−0.0135690 | + | 0.999908i | \(0.504319\pi\) | |||||||
\(830\) | 1.37043e42 | 0.645989 | ||||||||
\(831\) | 4.47555e41 | 0.207316 | ||||||||
\(832\) | −3.34966e41 | −0.152480 | ||||||||
\(833\) | 3.43671e42 | 1.53741 | ||||||||
\(834\) | 2.91912e41 | 0.128335 | ||||||||
\(835\) | −7.80517e41 | −0.337232 | ||||||||
\(836\) | 8.38567e41 | 0.356079 | ||||||||
\(837\) | −2.00991e41 | −0.0838798 | ||||||||
\(838\) | −1.75904e42 | −0.721502 | ||||||||
\(839\) | 1.68024e42 | 0.677365 | 0.338682 | − | 0.940901i | \(-0.390019\pi\) | ||||
0.338682 | + | 0.940901i | \(0.390019\pi\) | |||||||
\(840\) | −1.08143e42 | −0.428499 | ||||||||
\(841\) | 6.22969e41 | 0.242619 | ||||||||
\(842\) | −2.07482e42 | −0.794245 | ||||||||
\(843\) | 2.34624e42 | 0.882820 | ||||||||
\(844\) | 2.62530e42 | 0.970987 | ||||||||
\(845\) | −2.00512e42 | −0.728985 | ||||||||
\(846\) | 2.70888e41 | 0.0968098 | ||||||||
\(847\) | −7.85375e42 | −2.75910 | ||||||||
\(848\) | −3.88687e41 | −0.134233 | ||||||||
\(849\) | −2.92369e42 | −0.992591 | ||||||||
\(850\) | 4.11487e42 | 1.37335 | ||||||||
\(851\) | −4.49450e42 | −1.47470 | ||||||||
\(852\) | 5.46514e41 | 0.176290 | ||||||||
\(853\) | 2.99042e42 | 0.948355 | 0.474178 | − | 0.880429i | \(-0.342745\pi\) | ||||
0.474178 | + | 0.880429i | \(0.342745\pi\) | |||||||
\(854\) | −2.69358e41 | −0.0839828 | ||||||||
\(855\) | −6.71992e41 | −0.205995 | ||||||||
\(856\) | 5.44394e41 | 0.164075 | ||||||||
\(857\) | 4.29729e41 | 0.127342 | 0.0636712 | − | 0.997971i | \(-0.479719\pi\) | ||||
0.0636712 | + | 0.997971i | \(0.479719\pi\) | |||||||
\(858\) | 2.94230e42 | 0.857276 | ||||||||
\(859\) | 2.06742e42 | 0.592280 | 0.296140 | − | 0.955145i | \(-0.404301\pi\) | ||||
0.296140 | + | 0.955145i | \(0.404301\pi\) | |||||||
\(860\) | −2.51584e42 | −0.708688 | ||||||||
\(861\) | −9.10473e41 | −0.252186 | ||||||||
\(862\) | 1.11963e42 | 0.304942 | ||||||||
\(863\) | −7.05431e40 | −0.0188929 | −0.00944644 | − | 0.999955i | \(-0.503007\pi\) | ||||
−0.00944644 | + | 0.999955i | \(0.503007\pi\) | |||||||
\(864\) | −1.29179e41 | −0.0340207 | ||||||||
\(865\) | 9.12313e42 | 2.36271 | ||||||||
\(866\) | 2.69578e42 | 0.686554 | ||||||||
\(867\) | −3.42892e42 | −0.858778 | ||||||||
\(868\) | −1.24339e42 | −0.306246 | ||||||||
\(869\) | 1.13899e43 | 2.75888 | ||||||||
\(870\) | 2.85376e42 | 0.679810 | ||||||||
\(871\) | 3.44447e42 | 0.806972 | ||||||||
\(872\) | −4.97760e40 | −0.0114691 | ||||||||
\(873\) | 2.06537e42 | 0.468050 | ||||||||
\(874\) | −1.75618e42 | −0.391430 | ||||||||
\(875\) | 2.21638e42 | 0.485879 | ||||||||
\(876\) | 5.92164e41 | 0.127683 | ||||||||
\(877\) | −4.82633e42 | −1.02358 | −0.511791 | − | 0.859110i | \(-0.671018\pi\) | ||||
−0.511791 | + | 0.859110i | \(0.671018\pi\) | |||||||
\(878\) | −1.01710e42 | −0.212174 | ||||||||
\(879\) | 2.12466e42 | 0.435965 | ||||||||
\(880\) | −3.18513e42 | −0.642878 | ||||||||
\(881\) | −5.13974e42 | −1.02045 | −0.510224 | − | 0.860042i | \(-0.670437\pi\) | ||||
−0.510224 | + | 0.860042i | \(0.670437\pi\) | |||||||
\(882\) | 1.17645e42 | 0.229762 | ||||||||
\(883\) | −2.99814e42 | −0.575999 | −0.287999 | − | 0.957631i | \(-0.592990\pi\) | ||||
−0.287999 | + | 0.957631i | \(0.592990\pi\) | |||||||
\(884\) | −5.08987e42 | −0.961942 | ||||||||
\(885\) | −6.43024e41 | −0.119550 | ||||||||
\(886\) | −4.61750e42 | −0.844535 | ||||||||
\(887\) | 2.70966e42 | 0.487553 | 0.243777 | − | 0.969831i | \(-0.421614\pi\) | ||||
0.243777 | + | 0.969831i | \(0.421614\pi\) | |||||||
\(888\) | −1.27086e42 | −0.224963 | ||||||||
\(889\) | −5.16542e42 | −0.899560 | ||||||||
\(890\) | 1.67601e42 | 0.287158 | ||||||||
\(891\) | 1.13469e42 | 0.191272 | ||||||||
\(892\) | 3.87473e42 | 0.642615 | ||||||||
\(893\) | 1.04132e42 | 0.169917 | ||||||||
\(894\) | −4.22716e42 | −0.678664 | ||||||||
\(895\) | −1.45300e43 | −2.29526 | ||||||||
\(896\) | −7.99139e41 | −0.124210 | ||||||||
\(897\) | −6.16195e42 | −0.942384 | ||||||||
\(898\) | 7.10003e42 | 1.06845 | ||||||||
\(899\) | 3.28113e42 | 0.485857 | ||||||||
\(900\) | 1.40859e42 | 0.205243 | ||||||||
\(901\) | −5.90618e42 | −0.846832 | ||||||||
\(902\) | −2.68161e42 | −0.378356 | ||||||||
\(903\) | 5.54451e42 | 0.769823 | ||||||||
\(904\) | −1.16629e42 | −0.159354 | ||||||||
\(905\) | 2.10948e43 | 2.83642 | ||||||||
\(906\) | −3.11168e42 | −0.411752 | ||||||||
\(907\) | 3.49446e42 | 0.455067 | 0.227533 | − | 0.973770i | \(-0.426934\pi\) | ||||
0.227533 | + | 0.973770i | \(0.426934\pi\) | |||||||
\(908\) | −1.16904e42 | −0.149825 | ||||||||
\(909\) | 3.10425e42 | 0.391544 | ||||||||
\(910\) | −1.45862e43 | −1.81068 | ||||||||
\(911\) | −1.22703e43 | −1.49913 | −0.749564 | − | 0.661932i | \(-0.769737\pi\) | ||||
−0.749564 | + | 0.661932i | \(0.769737\pi\) | |||||||
\(912\) | −4.96577e41 | −0.0597120 | ||||||||
\(913\) | −8.89541e42 | −1.05279 | ||||||||
\(914\) | −3.92833e42 | −0.457602 | ||||||||
\(915\) | 6.35746e41 | 0.0728917 | ||||||||
\(916\) | −9.48726e41 | −0.107067 | ||||||||
\(917\) | −9.39478e42 | −1.04359 | ||||||||
\(918\) | −1.96290e42 | −0.214625 | ||||||||
\(919\) | 1.04604e43 | 1.12583 | 0.562915 | − | 0.826515i | \(-0.309680\pi\) | ||||
0.562915 | + | 0.826515i | \(0.309680\pi\) | |||||||
\(920\) | 6.67051e42 | 0.706701 | ||||||||
\(921\) | 5.20437e42 | 0.542754 | ||||||||
\(922\) | −1.64501e42 | −0.168877 | ||||||||
\(923\) | 7.37131e42 | 0.744938 | ||||||||
\(924\) | 7.01954e42 | 0.698337 | ||||||||
\(925\) | 1.38577e43 | 1.35718 | ||||||||
\(926\) | −3.58310e42 | −0.345461 | ||||||||
\(927\) | 1.57109e42 | 0.149123 | ||||||||
\(928\) | 2.10882e42 | 0.197058 | ||||||||
\(929\) | 1.61978e43 | 1.49014 | 0.745072 | − | 0.666984i | \(-0.232415\pi\) | ||||
0.745072 | + | 0.666984i | \(0.232415\pi\) | |||||||
\(930\) | 2.93468e42 | 0.265802 | ||||||||
\(931\) | 4.52238e42 | 0.403270 | ||||||||
\(932\) | 6.74094e42 | 0.591820 | ||||||||
\(933\) | 6.29447e42 | 0.544096 | ||||||||
\(934\) | 1.24410e43 | 1.05883 | ||||||||
\(935\) | −4.83987e43 | −4.05570 | ||||||||
\(936\) | −1.74235e42 | −0.143759 | ||||||||
\(937\) | −1.42722e43 | −1.15949 | −0.579746 | − | 0.814797i | \(-0.696848\pi\) | ||||
−0.579746 | + | 0.814797i | \(0.696848\pi\) | |||||||
\(938\) | 8.21758e42 | 0.657359 | ||||||||
\(939\) | 4.69132e42 | 0.369525 | ||||||||
\(940\) | −3.95525e42 | −0.306775 | ||||||||
\(941\) | 2.07537e43 | 1.58506 | 0.792532 | − | 0.609830i | \(-0.208762\pi\) | ||||
0.792532 | + | 0.609830i | \(0.208762\pi\) | |||||||
\(942\) | 6.08723e42 | 0.457806 | ||||||||
\(943\) | 5.61599e42 | 0.415917 | ||||||||
\(944\) | −4.75171e41 | −0.0346542 | ||||||||
\(945\) | −5.62516e42 | −0.403993 | ||||||||
\(946\) | 1.63302e43 | 1.15497 | ||||||||
\(947\) | −2.86659e43 | −1.99660 | −0.998298 | − | 0.0583198i | \(-0.981426\pi\) | ||||
−0.998298 | + | 0.0583198i | \(0.981426\pi\) | |||||||
\(948\) | −6.74480e42 | −0.462645 | ||||||||
\(949\) | 7.98703e42 | 0.539542 | ||||||||
\(950\) | 5.41476e42 | 0.360236 | ||||||||
\(951\) | −9.74750e42 | −0.638669 | ||||||||
\(952\) | −1.21431e43 | −0.783598 | ||||||||
\(953\) | 2.73174e43 | 1.73617 | 0.868086 | − | 0.496414i | \(-0.165350\pi\) | ||||
0.868086 | + | 0.496414i | \(0.165350\pi\) | |||||||
\(954\) | −2.02179e42 | −0.126556 | ||||||||
\(955\) | 1.30599e43 | 0.805173 | ||||||||
\(956\) | 1.43942e43 | 0.874073 | ||||||||
\(957\) | −1.85236e43 | −1.10791 | ||||||||
\(958\) | −1.59170e42 | −0.0937695 | ||||||||
\(959\) | −2.52892e42 | −0.146746 | ||||||||
\(960\) | 1.88615e42 | 0.107806 | ||||||||
\(961\) | −1.43877e43 | −0.810033 | ||||||||
\(962\) | −1.71412e43 | −0.950612 | ||||||||
\(963\) | 2.83171e42 | 0.154692 | ||||||||
\(964\) | 1.49080e43 | 0.802236 | ||||||||
\(965\) | −1.73419e43 | −0.919286 | ||||||||
\(966\) | −1.47008e43 | −0.767665 | ||||||||
\(967\) | 3.08479e43 | 1.58687 | 0.793436 | − | 0.608654i | \(-0.208290\pi\) | ||||
0.793436 | + | 0.608654i | \(0.208290\pi\) | |||||||
\(968\) | 1.36979e43 | 0.694163 | ||||||||
\(969\) | −7.54560e42 | −0.376703 | ||||||||
\(970\) | −3.01566e43 | −1.48318 | ||||||||
\(971\) | −2.71805e43 | −1.31698 | −0.658490 | − | 0.752590i | \(-0.728804\pi\) | ||||
−0.658490 | + | 0.752590i | \(0.728804\pi\) | |||||||
\(972\) | −6.71936e41 | −0.0320750 | ||||||||
\(973\) | 9.39327e42 | 0.441754 | ||||||||
\(974\) | 1.61561e43 | 0.748569 | ||||||||
\(975\) | 1.89989e43 | 0.867284 | ||||||||
\(976\) | 4.69793e41 | 0.0211293 | ||||||||
\(977\) | −4.30767e43 | −1.90885 | −0.954423 | − | 0.298457i | \(-0.903528\pi\) | ||||
−0.954423 | + | 0.298457i | \(0.903528\pi\) | |||||||
\(978\) | −6.86123e42 | −0.299563 | ||||||||
\(979\) | −1.08789e43 | −0.467989 | ||||||||
\(980\) | −1.71774e43 | −0.728078 | ||||||||
\(981\) | −2.58914e41 | −0.0108132 | ||||||||
\(982\) | 4.04347e42 | 0.166394 | ||||||||
\(983\) | 2.56694e43 | 1.04085 | 0.520427 | − | 0.853906i | \(-0.325773\pi\) | ||||
0.520427 | + | 0.853906i | \(0.325773\pi\) | |||||||
\(984\) | 1.58798e42 | 0.0634476 | ||||||||
\(985\) | −7.34036e42 | −0.288996 | ||||||||
\(986\) | 3.20440e43 | 1.24317 | ||||||||
\(987\) | 8.71675e42 | 0.333239 | ||||||||
\(988\) | −6.69777e42 | −0.252322 | ||||||||
\(989\) | −3.41998e43 | −1.26963 | ||||||||
\(990\) | −1.65677e43 | −0.606111 | ||||||||
\(991\) | 2.59767e43 | 0.936518 | 0.468259 | − | 0.883591i | \(-0.344881\pi\) | ||||
0.468259 | + | 0.883591i | \(0.344881\pi\) | |||||||
\(992\) | 2.16862e42 | 0.0770485 | ||||||||
\(993\) | −5.40062e41 | −0.0189095 | ||||||||
\(994\) | 1.75860e43 | 0.606826 | ||||||||
\(995\) | 1.42588e43 | 0.484894 | ||||||||
\(996\) | 5.26763e42 | 0.176545 | ||||||||
\(997\) | −5.01714e43 | −1.65721 | −0.828603 | − | 0.559837i | \(-0.810864\pi\) | ||||
−0.828603 | + | 0.559837i | \(0.810864\pi\) | |||||||
\(998\) | −1.98218e43 | −0.645282 | ||||||||
\(999\) | −6.61049e42 | −0.212097 |
(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 | 6.30.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 18.30.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.30.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
18.30.a.f.1.2 | 2 | 3.2 | odd | 2 |