Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,56,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 56, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 56);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 56 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(19.1581467685\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 149272663100531x^{2} + 190291401428579434725x + 325546600176957146615614350 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{9}\cdot 5^{2}\cdot 7\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.14055e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.25888e8 | 1.71690 | 0.858448 | − | 0.512901i | \(-0.171429\pi\) | ||||
0.858448 | + | 0.512901i | \(0.171429\pi\) | |||||||
\(3\) | 5.98183e12 | 0.452897 | 0.226449 | − | 0.974023i | \(-0.427288\pi\) | ||||
0.226449 | + | 0.974023i | \(0.427288\pi\) | |||||||
\(4\) | 7.01743e16 | 1.94773 | ||||||||
\(5\) | 2.73659e19 | 1.64261 | 0.821304 | − | 0.570490i | \(-0.193247\pi\) | ||||
0.821304 | + | 0.570490i | \(0.193247\pi\) | |||||||
\(6\) | 1.94941e21 | 0.777577 | ||||||||
\(7\) | −1.10303e23 | −0.634440 | −0.317220 | − | 0.948352i | \(-0.602749\pi\) | ||||
−0.317220 | + | 0.948352i | \(0.602749\pi\) | |||||||
\(8\) | 1.11276e25 | 1.62715 | ||||||||
\(9\) | −1.38667e26 | −0.794884 | ||||||||
\(10\) | 8.91821e27 | 2.82019 | ||||||||
\(11\) | 4.91412e28 | 1.13018 | 0.565090 | − | 0.825030i | \(-0.308842\pi\) | ||||
0.565090 | + | 0.825030i | \(0.308842\pi\) | |||||||
\(12\) | 4.19771e29 | 0.882121 | ||||||||
\(13\) | −5.50498e30 | −1.28030 | −0.640152 | − | 0.768248i | \(-0.721129\pi\) | ||||
−0.640152 | + | 0.768248i | \(0.721129\pi\) | |||||||
\(14\) | −3.59464e31 | −1.08927 | ||||||||
\(15\) | 1.63698e32 | 0.743933 | ||||||||
\(16\) | 1.09807e33 | 0.845919 | ||||||||
\(17\) | 6.74131e33 | 0.980390 | 0.490195 | − | 0.871613i | \(-0.336926\pi\) | ||||
0.490195 | + | 0.871613i | \(0.336926\pi\) | |||||||
\(18\) | −4.51899e34 | −1.36473 | ||||||||
\(19\) | 4.63069e34 | 0.316171 | 0.158085 | − | 0.987425i | \(-0.449468\pi\) | ||||
0.158085 | + | 0.987425i | \(0.449468\pi\) | |||||||
\(20\) | 1.92038e36 | 3.19936 | ||||||||
\(21\) | −6.59813e35 | −0.287336 | ||||||||
\(22\) | 1.60146e37 | 1.94040 | ||||||||
\(23\) | −2.33537e37 | −0.833376 | −0.416688 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416688 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(24\) | 6.65636e37 | 0.736932 | ||||||||
\(25\) | 4.71335e38 | 1.69816 | ||||||||
\(26\) | −1.79401e39 | −2.19815 | ||||||||
\(27\) | −1.87301e39 | −0.812898 | ||||||||
\(28\) | −7.74043e39 | −1.23572 | ||||||||
\(29\) | 8.29368e39 | 0.504431 | 0.252216 | − | 0.967671i | \(-0.418841\pi\) | ||||
0.252216 | + | 0.967671i | \(0.418841\pi\) | |||||||
\(30\) | 5.33472e40 | 1.27725 | ||||||||
\(31\) | −2.22670e40 | −0.216379 | −0.108189 | − | 0.994130i | \(-0.534505\pi\) | ||||
−0.108189 | + | 0.994130i | \(0.534505\pi\) | |||||||
\(32\) | −4.30685e40 | −0.174797 | ||||||||
\(33\) | 2.93955e41 | 0.511855 | ||||||||
\(34\) | 2.19691e42 | 1.68323 | ||||||||
\(35\) | −3.01853e42 | −1.04214 | ||||||||
\(36\) | −9.73086e42 | −1.54822 | ||||||||
\(37\) | −8.62039e42 | −0.645624 | −0.322812 | − | 0.946463i | \(-0.604628\pi\) | ||||
−0.322812 | + | 0.946463i | \(0.604628\pi\) | |||||||
\(38\) | 1.50909e43 | 0.542832 | ||||||||
\(39\) | −3.29298e43 | −0.579846 | ||||||||
\(40\) | 3.04517e44 | 2.67277 | ||||||||
\(41\) | −1.28503e44 | −0.571951 | −0.285975 | − | 0.958237i | \(-0.592318\pi\) | ||||
−0.285975 | + | 0.958237i | \(0.592318\pi\) | |||||||
\(42\) | −2.15025e44 | −0.493326 | ||||||||
\(43\) | −7.80265e44 | −0.937259 | −0.468629 | − | 0.883395i | \(-0.655252\pi\) | ||||
−0.468629 | + | 0.883395i | \(0.655252\pi\) | |||||||
\(44\) | 3.44845e45 | 2.20128 | ||||||||
\(45\) | −3.79474e45 | −1.30568 | ||||||||
\(46\) | −7.61071e45 | −1.43082 | ||||||||
\(47\) | 2.24956e45 | 0.234103 | 0.117052 | − | 0.993126i | \(-0.462656\pi\) | ||||
0.117052 | + | 0.993126i | \(0.462656\pi\) | |||||||
\(48\) | 6.56844e45 | 0.383114 | ||||||||
\(49\) | −1.80601e46 | −0.597486 | ||||||||
\(50\) | 1.53602e47 | 2.91557 | ||||||||
\(51\) | 4.03254e46 | 0.444016 | ||||||||
\(52\) | −3.86308e47 | −2.49369 | ||||||||
\(53\) | 6.54418e46 | 0.250189 | 0.125095 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125095 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(54\) | −6.10391e47 | −1.39566 | ||||||||
\(55\) | 1.34479e48 | 1.85644 | ||||||||
\(56\) | −1.22741e48 | −1.03233 | ||||||||
\(57\) | 2.77000e47 | 0.143193 | ||||||||
\(58\) | 2.70281e48 | 0.866056 | ||||||||
\(59\) | −4.81860e48 | −0.964918 | −0.482459 | − | 0.875918i | \(-0.660256\pi\) | ||||
−0.482459 | + | 0.875918i | \(0.660256\pi\) | |||||||
\(60\) | 1.14874e49 | 1.44898 | ||||||||
\(61\) | −1.00856e48 | −0.0807480 | −0.0403740 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403740 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(62\) | −7.25655e48 | −0.371500 | ||||||||
\(63\) | 1.52954e49 | 0.504307 | ||||||||
\(64\) | −5.35975e49 | −1.14603 | ||||||||
\(65\) | −1.50648e50 | −2.10304 | ||||||||
\(66\) | 9.57963e49 | 0.878801 | ||||||||
\(67\) | 2.13547e50 | 1.29550 | 0.647749 | − | 0.761854i | \(-0.275711\pi\) | ||||
0.647749 | + | 0.761854i | \(0.275711\pi\) | |||||||
\(68\) | 4.73067e50 | 1.90953 | ||||||||
\(69\) | −1.39698e50 | −0.377434 | ||||||||
\(70\) | −9.83705e50 | −1.78924 | ||||||||
\(71\) | 9.56825e50 | 1.17822 | 0.589112 | − | 0.808051i | \(-0.299478\pi\) | ||||
0.589112 | + | 0.808051i | \(0.299478\pi\) | |||||||
\(72\) | −1.54303e51 | −1.29340 | ||||||||
\(73\) | 1.10863e51 | 0.635926 | 0.317963 | − | 0.948103i | \(-0.397001\pi\) | ||||
0.317963 | + | 0.948103i | \(0.397001\pi\) | |||||||
\(74\) | −2.80928e51 | −1.10847 | ||||||||
\(75\) | 2.81945e51 | 0.769093 | ||||||||
\(76\) | 3.24956e51 | 0.615815 | ||||||||
\(77\) | −5.42042e51 | −0.717031 | ||||||||
\(78\) | −1.07314e52 | −0.995535 | ||||||||
\(79\) | 2.07492e52 | 1.35599 | 0.677995 | − | 0.735067i | \(-0.262849\pi\) | ||||
0.677995 | + | 0.735067i | \(0.262849\pi\) | |||||||
\(80\) | 3.00495e52 | 1.38951 | ||||||||
\(81\) | 1.29863e52 | 0.426725 | ||||||||
\(82\) | −4.18778e52 | −0.981980 | ||||||||
\(83\) | −1.06353e53 | −1.78691 | −0.893456 | − | 0.449150i | \(-0.851727\pi\) | ||||
−0.893456 | + | 0.449150i | \(0.851727\pi\) | |||||||
\(84\) | −4.63019e52 | −0.559653 | ||||||||
\(85\) | 1.84482e53 | 1.61040 | ||||||||
\(86\) | −2.54279e53 | −1.60917 | ||||||||
\(87\) | 4.96114e52 | 0.228456 | ||||||||
\(88\) | 5.46825e53 | 1.83897 | ||||||||
\(89\) | 7.48693e53 | 1.84535 | 0.922675 | − | 0.385578i | \(-0.125998\pi\) | ||||
0.922675 | + | 0.385578i | \(0.125998\pi\) | |||||||
\(90\) | −1.23666e54 | −2.24172 | ||||||||
\(91\) | 6.07215e53 | 0.812277 | ||||||||
\(92\) | −1.63883e54 | −1.62319 | ||||||||
\(93\) | −1.33197e53 | −0.0979974 | ||||||||
\(94\) | 7.33106e53 | 0.401931 | ||||||||
\(95\) | 1.26723e54 | 0.519345 | ||||||||
\(96\) | −2.57628e53 | −0.0791653 | ||||||||
\(97\) | −5.59692e53 | −0.129338 | −0.0646691 | − | 0.997907i | \(-0.520599\pi\) | ||||
−0.0646691 | + | 0.997907i | \(0.520599\pi\) | |||||||
\(98\) | −5.88557e54 | −1.02582 | ||||||||
\(99\) | −6.81426e54 | −0.898361 | ||||||||
\(100\) | 3.30756e55 | 3.30756 | ||||||||
\(101\) | −1.15529e55 | −0.878729 | −0.439364 | − | 0.898309i | \(-0.644796\pi\) | ||||
−0.439364 | + | 0.898309i | \(0.644796\pi\) | |||||||
\(102\) | 1.31416e55 | 0.762329 | ||||||||
\(103\) | 1.27447e55 | 0.565335 | 0.282667 | − | 0.959218i | \(-0.408781\pi\) | ||||
0.282667 | + | 0.959218i | \(0.408781\pi\) | |||||||
\(104\) | −6.12573e55 | −2.08325 | ||||||||
\(105\) | −1.80564e55 | −0.471981 | ||||||||
\(106\) | 2.13267e55 | 0.429549 | ||||||||
\(107\) | −3.18160e55 | −0.494984 | −0.247492 | − | 0.968890i | \(-0.579606\pi\) | ||||
−0.247492 | + | 0.968890i | \(0.579606\pi\) | |||||||
\(108\) | −1.31437e56 | −1.58330 | ||||||||
\(109\) | 1.12821e56 | 1.05478 | 0.527388 | − | 0.849625i | \(-0.323171\pi\) | ||||
0.527388 | + | 0.849625i | \(0.323171\pi\) | |||||||
\(110\) | 4.38252e56 | 3.18732 | ||||||||
\(111\) | −5.15657e55 | −0.292401 | ||||||||
\(112\) | −1.21120e56 | −0.536685 | ||||||||
\(113\) | −2.75852e56 | −0.957238 | −0.478619 | − | 0.878023i | \(-0.658862\pi\) | ||||
−0.478619 | + | 0.878023i | \(0.658862\pi\) | |||||||
\(114\) | 9.02711e55 | 0.245847 | ||||||||
\(115\) | −6.39095e56 | −1.36891 | ||||||||
\(116\) | 5.82003e56 | 0.982496 | ||||||||
\(117\) | 7.63358e56 | 1.01769 | ||||||||
\(118\) | −1.57033e57 | −1.65666 | ||||||||
\(119\) | −7.43586e56 | −0.621999 | ||||||||
\(120\) | 1.82157e57 | 1.21049 | ||||||||
\(121\) | 5.24270e56 | 0.277305 | ||||||||
\(122\) | −3.28678e56 | −0.138636 | ||||||||
\(123\) | −7.68686e56 | −0.259035 | ||||||||
\(124\) | −1.56257e57 | −0.421448 | ||||||||
\(125\) | 5.30294e57 | 1.14681 | ||||||||
\(126\) | 4.98458e57 | 0.865841 | ||||||||
\(127\) | 7.27512e57 | 1.01680 | 0.508402 | − | 0.861120i | \(-0.330236\pi\) | ||||
0.508402 | + | 0.861120i | \(0.330236\pi\) | |||||||
\(128\) | −1.59151e58 | −1.79281 | ||||||||
\(129\) | −4.66741e57 | −0.424482 | ||||||||
\(130\) | −4.90946e58 | −3.61070 | ||||||||
\(131\) | 3.20710e58 | 1.91052 | 0.955261 | − | 0.295764i | \(-0.0955743\pi\) | ||||
0.955261 | + | 0.295764i | \(0.0955743\pi\) | |||||||
\(132\) | 2.06281e58 | 0.996955 | ||||||||
\(133\) | −5.10779e57 | −0.200592 | ||||||||
\(134\) | 6.95925e58 | 2.22423 | ||||||||
\(135\) | −5.12565e58 | −1.33527 | ||||||||
\(136\) | 7.50148e58 | 1.59524 | ||||||||
\(137\) | −5.59686e58 | −0.973036 | −0.486518 | − | 0.873671i | \(-0.661733\pi\) | ||||
−0.486518 | + | 0.873671i | \(0.661733\pi\) | |||||||
\(138\) | −4.55260e58 | −0.648014 | ||||||||
\(139\) | 6.10557e58 | 0.712556 | 0.356278 | − | 0.934380i | \(-0.384046\pi\) | ||||
0.356278 | + | 0.934380i | \(0.384046\pi\) | |||||||
\(140\) | −2.11824e59 | −2.02980 | ||||||||
\(141\) | 1.34565e58 | 0.106025 | ||||||||
\(142\) | 3.11818e59 | 2.02289 | ||||||||
\(143\) | −2.70521e59 | −1.44697 | ||||||||
\(144\) | −1.52265e59 | −0.672407 | ||||||||
\(145\) | 2.26964e59 | 0.828584 | ||||||||
\(146\) | 3.61289e59 | 1.09182 | ||||||||
\(147\) | −1.08032e59 | −0.270600 | ||||||||
\(148\) | −6.04930e59 | −1.25750 | ||||||||
\(149\) | −1.00005e59 | −0.172743 | −0.0863713 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863713 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(150\) | 9.18824e59 | 1.32045 | ||||||||
\(151\) | 8.74454e59 | 1.04682 | 0.523409 | − | 0.852082i | \(-0.324660\pi\) | ||||
0.523409 | + | 0.852082i | \(0.324660\pi\) | |||||||
\(152\) | 5.15286e59 | 0.514458 | ||||||||
\(153\) | −9.34796e59 | −0.779296 | ||||||||
\(154\) | −1.76645e60 | −1.23107 | ||||||||
\(155\) | −6.09356e59 | −0.355426 | ||||||||
\(156\) | −2.31083e60 | −1.12938 | ||||||||
\(157\) | −2.34355e60 | −0.960802 | −0.480401 | − | 0.877049i | \(-0.659509\pi\) | ||||
−0.480401 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(158\) | 6.76192e60 | 2.32809 | ||||||||
\(159\) | 3.91462e59 | 0.113310 | ||||||||
\(160\) | −1.17861e60 | −0.287124 | ||||||||
\(161\) | 2.57598e60 | 0.528727 | ||||||||
\(162\) | 4.23209e60 | 0.732642 | ||||||||
\(163\) | 9.54155e60 | 1.39463 | 0.697316 | − | 0.716763i | \(-0.254377\pi\) | ||||
0.697316 | + | 0.716763i | \(0.254377\pi\) | |||||||
\(164\) | −9.01764e60 | −1.11401 | ||||||||
\(165\) | 8.04432e60 | 0.840777 | ||||||||
\(166\) | −3.46593e61 | −3.06794 | ||||||||
\(167\) | −6.27360e60 | −0.470776 | −0.235388 | − | 0.971902i | \(-0.575636\pi\) | ||||
−0.235388 | + | 0.971902i | \(0.575636\pi\) | |||||||
\(168\) | −7.34215e60 | −0.467539 | ||||||||
\(169\) | 1.18170e61 | 0.639179 | ||||||||
\(170\) | 6.01204e61 | 2.76488 | ||||||||
\(171\) | −6.42124e60 | −0.251319 | ||||||||
\(172\) | −5.47546e61 | −1.82553 | ||||||||
\(173\) | 1.23980e61 | 0.352439 | 0.176219 | − | 0.984351i | \(-0.443613\pi\) | ||||
0.176219 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(174\) | 1.61678e61 | 0.392234 | ||||||||
\(175\) | −5.19896e61 | −1.07738 | ||||||||
\(176\) | 5.39603e61 | 0.956040 | ||||||||
\(177\) | −2.88241e61 | −0.437009 | ||||||||
\(178\) | 2.43990e62 | 3.16827 | ||||||||
\(179\) | −6.84198e61 | −0.761594 | −0.380797 | − | 0.924659i | \(-0.624350\pi\) | ||||
−0.380797 | + | 0.924659i | \(0.624350\pi\) | |||||||
\(180\) | −2.66293e62 | −2.54312 | ||||||||
\(181\) | −1.10035e61 | −0.0902340 | −0.0451170 | − | 0.998982i | \(-0.514366\pi\) | ||||
−0.0451170 | + | 0.998982i | \(0.514366\pi\) | |||||||
\(182\) | 1.97884e62 | 1.39459 | ||||||||
\(183\) | −6.03304e60 | −0.0365706 | ||||||||
\(184\) | −2.59872e62 | −1.35603 | ||||||||
\(185\) | −2.35905e62 | −1.06051 | ||||||||
\(186\) | −4.34075e61 | −0.168251 | ||||||||
\(187\) | 3.31276e62 | 1.10802 | ||||||||
\(188\) | 1.57862e62 | 0.455969 | ||||||||
\(189\) | 2.06598e62 | 0.515735 | ||||||||
\(190\) | 4.12975e62 | 0.891661 | ||||||||
\(191\) | 7.90077e62 | 1.47656 | 0.738281 | − | 0.674493i | \(-0.235638\pi\) | ||||
0.738281 | + | 0.674493i | \(0.235638\pi\) | |||||||
\(192\) | −3.20611e62 | −0.519033 | ||||||||
\(193\) | −9.51922e62 | −1.33590 | −0.667952 | − | 0.744204i | \(-0.732829\pi\) | ||||
−0.667952 | + | 0.744204i | \(0.732829\pi\) | |||||||
\(194\) | −1.82397e62 | −0.222060 | ||||||||
\(195\) | −9.01154e62 | −0.952461 | ||||||||
\(196\) | −1.26735e63 | −1.16374 | ||||||||
\(197\) | 1.86380e63 | 1.48791 | 0.743956 | − | 0.668229i | \(-0.232947\pi\) | ||||
0.743956 | + | 0.668229i | \(0.232947\pi\) | |||||||
\(198\) | −2.22069e63 | −1.54239 | ||||||||
\(199\) | −2.70172e62 | −0.163373 | −0.0816866 | − | 0.996658i | \(-0.526031\pi\) | ||||
−0.0816866 | + | 0.996658i | \(0.526031\pi\) | |||||||
\(200\) | 5.24484e63 | 2.76317 | ||||||||
\(201\) | 1.27740e63 | 0.586728 | ||||||||
\(202\) | −3.76497e63 | −1.50869 | ||||||||
\(203\) | −9.14817e62 | −0.320032 | ||||||||
\(204\) | 2.82981e63 | 0.864823 | ||||||||
\(205\) | −3.51661e63 | −0.939491 | ||||||||
\(206\) | 4.15335e63 | 0.970621 | ||||||||
\(207\) | 3.23839e63 | 0.662437 | ||||||||
\(208\) | −6.04482e63 | −1.08303 | ||||||||
\(209\) | 2.27558e63 | 0.357330 | ||||||||
\(210\) | −5.88436e63 | −0.810342 | ||||||||
\(211\) | 3.39112e63 | 0.409804 | 0.204902 | − | 0.978783i | \(-0.434312\pi\) | ||||
0.204902 | + | 0.978783i | \(0.434312\pi\) | |||||||
\(212\) | 4.59233e63 | 0.487301 | ||||||||
\(213\) | 5.72357e63 | 0.533614 | ||||||||
\(214\) | −1.03685e64 | −0.849836 | ||||||||
\(215\) | −2.13526e64 | −1.53955 | ||||||||
\(216\) | −2.08421e64 | −1.32271 | ||||||||
\(217\) | 2.45611e63 | 0.137280 | ||||||||
\(218\) | 3.67669e64 | 1.81094 | ||||||||
\(219\) | 6.63162e63 | 0.288009 | ||||||||
\(220\) | 9.43699e64 | 3.61585 | ||||||||
\(221\) | −3.71107e64 | −1.25520 | ||||||||
\(222\) | −1.68047e64 | −0.502022 | ||||||||
\(223\) | −1.50393e64 | −0.397049 | −0.198524 | − | 0.980096i | \(-0.563615\pi\) | ||||
−0.198524 | + | 0.980096i | \(0.563615\pi\) | |||||||
\(224\) | 4.75058e63 | 0.110899 | ||||||||
\(225\) | −6.53586e64 | −1.34984 | ||||||||
\(226\) | −8.98971e64 | −1.64348 | ||||||||
\(227\) | 6.25379e64 | 1.01259 | 0.506293 | − | 0.862361i | \(-0.331015\pi\) | ||||
0.506293 | + | 0.862361i | \(0.331015\pi\) | |||||||
\(228\) | 1.94383e64 | 0.278901 | ||||||||
\(229\) | 9.72208e64 | 1.23675 | 0.618377 | − | 0.785882i | \(-0.287791\pi\) | ||||
0.618377 | + | 0.785882i | \(0.287791\pi\) | |||||||
\(230\) | −2.08274e65 | −2.35028 | ||||||||
\(231\) | −3.24240e64 | −0.324741 | ||||||||
\(232\) | 9.22889e64 | 0.820786 | ||||||||
\(233\) | 1.58206e65 | 1.25007 | 0.625037 | − | 0.780595i | \(-0.285084\pi\) | ||||
0.625037 | + | 0.780595i | \(0.285084\pi\) | |||||||
\(234\) | 2.48769e65 | 1.74727 | ||||||||
\(235\) | 6.15613e64 | 0.384540 | ||||||||
\(236\) | −3.38142e65 | −1.87940 | ||||||||
\(237\) | 1.24118e65 | 0.614124 | ||||||||
\(238\) | −2.42326e65 | −1.06791 | ||||||||
\(239\) | −1.73759e65 | −0.682346 | −0.341173 | − | 0.940000i | \(-0.610824\pi\) | ||||
−0.341173 | + | 0.940000i | \(0.610824\pi\) | |||||||
\(240\) | 1.79751e65 | 0.629307 | ||||||||
\(241\) | −8.77618e64 | −0.274054 | −0.137027 | − | 0.990567i | \(-0.543755\pi\) | ||||
−0.137027 | + | 0.990567i | \(0.543755\pi\) | |||||||
\(242\) | 1.70854e65 | 0.476103 | ||||||||
\(243\) | 4.04427e65 | 1.00616 | ||||||||
\(244\) | −7.07751e64 | −0.157275 | ||||||||
\(245\) | −4.94230e65 | −0.981435 | ||||||||
\(246\) | −2.50506e65 | −0.444736 | ||||||||
\(247\) | −2.54918e65 | −0.404795 | ||||||||
\(248\) | −2.47779e65 | −0.352081 | ||||||||
\(249\) | −6.36187e65 | −0.809288 | ||||||||
\(250\) | 1.72816e66 | 1.96895 | ||||||||
\(251\) | 6.61756e63 | 0.00675570 | 0.00337785 | − | 0.999994i | \(-0.498925\pi\) | ||||
0.00337785 | + | 0.999994i | \(0.498925\pi\) | |||||||
\(252\) | 1.07334e66 | 0.982252 | ||||||||
\(253\) | −1.14763e66 | −0.941864 | ||||||||
\(254\) | 2.37087e66 | 1.74575 | ||||||||
\(255\) | 1.10354e66 | 0.729344 | ||||||||
\(256\) | −3.25548e66 | −1.93204 | ||||||||
\(257\) | 2.05584e66 | 1.09605 | 0.548024 | − | 0.836463i | \(-0.315380\pi\) | ||||
0.548024 | + | 0.836463i | \(0.315380\pi\) | |||||||
\(258\) | −1.52105e66 | −0.728791 | ||||||||
\(259\) | 9.50854e65 | 0.409610 | ||||||||
\(260\) | −1.05717e67 | −4.09615 | ||||||||
\(261\) | −1.15006e66 | −0.400965 | ||||||||
\(262\) | 1.04516e67 | 3.28017 | ||||||||
\(263\) | −5.76788e66 | −1.63017 | −0.815086 | − | 0.579340i | \(-0.803310\pi\) | ||||
−0.815086 | + | 0.579340i | \(0.803310\pi\) | |||||||
\(264\) | 3.27102e66 | 0.832865 | ||||||||
\(265\) | 1.79087e66 | 0.410963 | ||||||||
\(266\) | −1.66457e66 | −0.344395 | ||||||||
\(267\) | 4.47856e66 | 0.835754 | ||||||||
\(268\) | 1.49855e67 | 2.52328 | ||||||||
\(269\) | 3.84467e66 | 0.584348 | 0.292174 | − | 0.956365i | \(-0.405621\pi\) | ||||
0.292174 | + | 0.956365i | \(0.405621\pi\) | |||||||
\(270\) | −1.67039e67 | −2.29252 | ||||||||
\(271\) | −1.55611e67 | −1.92923 | −0.964615 | − | 0.263662i | \(-0.915070\pi\) | ||||
−0.964615 | + | 0.263662i | \(0.915070\pi\) | |||||||
\(272\) | 7.40240e66 | 0.829330 | ||||||||
\(273\) | 3.63226e66 | 0.367878 | ||||||||
\(274\) | −1.82395e67 | −1.67060 | ||||||||
\(275\) | 2.31620e67 | 1.91923 | ||||||||
\(276\) | −9.80322e66 | −0.735138 | ||||||||
\(277\) | 1.29112e65 | 0.00876541 | 0.00438271 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438271 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(278\) | 1.98973e67 | 1.22338 | ||||||||
\(279\) | 3.08770e66 | 0.171996 | ||||||||
\(280\) | −3.35891e67 | −1.69571 | ||||||||
\(281\) | −4.05496e67 | −1.85594 | −0.927968 | − | 0.372661i | \(-0.878446\pi\) | ||||
−0.927968 | + | 0.372661i | \(0.878446\pi\) | |||||||
\(282\) | 4.38532e66 | 0.182033 | ||||||||
\(283\) | 4.16122e67 | 1.56709 | 0.783545 | − | 0.621335i | \(-0.213409\pi\) | ||||
0.783545 | + | 0.621335i | \(0.213409\pi\) | |||||||
\(284\) | 6.71445e67 | 2.29486 | ||||||||
\(285\) | 7.58035e66 | 0.235210 | ||||||||
\(286\) | −8.81597e67 | −2.48430 | ||||||||
\(287\) | 1.41743e67 | 0.362869 | ||||||||
\(288\) | 5.97217e66 | 0.138944 | ||||||||
\(289\) | −1.83619e66 | −0.0388353 | ||||||||
\(290\) | 7.39648e67 | 1.42259 | ||||||||
\(291\) | −3.34798e66 | −0.0585769 | ||||||||
\(292\) | 7.77972e67 | 1.23861 | ||||||||
\(293\) | −7.89264e67 | −1.14383 | −0.571917 | − | 0.820312i | \(-0.693800\pi\) | ||||
−0.571917 | + | 0.820312i | \(0.693800\pi\) | |||||||
\(294\) | −3.52065e67 | −0.464591 | ||||||||
\(295\) | −1.31865e68 | −1.58498 | ||||||||
\(296\) | −9.59245e67 | −1.05053 | ||||||||
\(297\) | −9.20419e67 | −0.918720 | ||||||||
\(298\) | −3.25905e67 | −0.296581 | ||||||||
\(299\) | 1.28562e68 | 1.06697 | ||||||||
\(300\) | 1.97853e68 | 1.49799 | ||||||||
\(301\) | 8.60655e67 | 0.594635 | ||||||||
\(302\) | 2.84974e68 | 1.79728 | ||||||||
\(303\) | −6.91078e67 | −0.397974 | ||||||||
\(304\) | 5.08480e67 | 0.267455 | ||||||||
\(305\) | −2.76002e67 | −0.132637 | ||||||||
\(306\) | −3.04639e68 | −1.33797 | ||||||||
\(307\) | 1.91003e68 | 0.766893 | 0.383446 | − | 0.923563i | \(-0.374737\pi\) | ||||
0.383446 | + | 0.923563i | \(0.374737\pi\) | |||||||
\(308\) | −3.80374e68 | −1.39658 | ||||||||
\(309\) | 7.62366e67 | 0.256039 | ||||||||
\(310\) | −1.98582e68 | −0.610229 | ||||||||
\(311\) | 3.42073e68 | 0.962074 | 0.481037 | − | 0.876700i | \(-0.340260\pi\) | ||||
0.481037 | + | 0.876700i | \(0.340260\pi\) | |||||||
\(312\) | −3.66431e68 | −0.943497 | ||||||||
\(313\) | 7.31342e66 | 0.0172445 | 0.00862227 | − | 0.999963i | \(-0.497255\pi\) | ||||
0.00862227 | + | 0.999963i | \(0.497255\pi\) | |||||||
\(314\) | −7.63735e68 | −1.64960 | ||||||||
\(315\) | 4.18571e68 | 0.828378 | ||||||||
\(316\) | 1.45606e69 | 2.64110 | ||||||||
\(317\) | −5.41902e68 | −0.901137 | −0.450569 | − | 0.892742i | \(-0.648779\pi\) | ||||
−0.450569 | + | 0.892742i | \(0.648779\pi\) | |||||||
\(318\) | 1.27573e68 | 0.194541 | ||||||||
\(319\) | 4.07562e68 | 0.570098 | ||||||||
\(320\) | −1.46674e69 | −1.88247 | ||||||||
\(321\) | −1.90318e68 | −0.224177 | ||||||||
\(322\) | 8.39483e68 | 0.907769 | ||||||||
\(323\) | 3.12169e68 | 0.309971 | ||||||||
\(324\) | 9.11306e68 | 0.831144 | ||||||||
\(325\) | −2.59469e69 | −2.17417 | ||||||||
\(326\) | 3.10948e69 | 2.39444 | ||||||||
\(327\) | 6.74875e68 | 0.477705 | ||||||||
\(328\) | −1.42994e69 | −0.930650 | ||||||||
\(329\) | −2.48133e68 | −0.148524 | ||||||||
\(330\) | 2.62155e69 | 1.44353 | ||||||||
\(331\) | −1.74335e69 | −0.883315 | −0.441658 | − | 0.897184i | \(-0.645609\pi\) | ||||
−0.441658 | + | 0.897184i | \(0.645609\pi\) | |||||||
\(332\) | −7.46327e69 | −3.48042 | ||||||||
\(333\) | 1.19536e69 | 0.513196 | ||||||||
\(334\) | −2.04449e69 | −0.808273 | ||||||||
\(335\) | 5.84390e69 | 2.12800 | ||||||||
\(336\) | −7.24518e68 | −0.243063 | ||||||||
\(337\) | −3.48749e69 | −1.07818 | −0.539090 | − | 0.842248i | \(-0.681232\pi\) | ||||
−0.539090 | + | 0.842248i | \(0.681232\pi\) | |||||||
\(338\) | 3.85102e69 | 1.09740 | ||||||||
\(339\) | −1.65010e69 | −0.433530 | ||||||||
\(340\) | 1.29459e70 | 3.13662 | ||||||||
\(341\) | −1.09423e69 | −0.244547 | ||||||||
\(342\) | −2.09261e69 | −0.431489 | ||||||||
\(343\) | 5.32618e69 | 1.01351 | ||||||||
\(344\) | −8.68249e69 | −1.52506 | ||||||||
\(345\) | −3.82296e69 | −0.619976 | ||||||||
\(346\) | 4.04036e69 | 0.605101 | ||||||||
\(347\) | −3.19386e69 | −0.441830 | −0.220915 | − | 0.975293i | \(-0.570904\pi\) | ||||
−0.220915 | + | 0.975293i | \(0.570904\pi\) | |||||||
\(348\) | 3.48145e69 | 0.444970 | ||||||||
\(349\) | −1.03259e70 | −1.21963 | −0.609813 | − | 0.792545i | \(-0.708755\pi\) | ||||
−0.609813 | + | 0.792545i | \(0.708755\pi\) | |||||||
\(350\) | −1.69428e70 | −1.84975 | ||||||||
\(351\) | 1.03109e70 | 1.04076 | ||||||||
\(352\) | −2.11644e69 | −0.197552 | ||||||||
\(353\) | −6.47303e69 | −0.558860 | −0.279430 | − | 0.960166i | \(-0.590145\pi\) | ||||
−0.279430 | + | 0.960166i | \(0.590145\pi\) | |||||||
\(354\) | −9.39342e69 | −0.750298 | ||||||||
\(355\) | 2.61843e70 | 1.93536 | ||||||||
\(356\) | 5.25391e70 | 3.59424 | ||||||||
\(357\) | −4.44801e69 | −0.281702 | ||||||||
\(358\) | −2.22972e70 | −1.30758 | ||||||||
\(359\) | 1.06064e70 | 0.576063 | 0.288031 | − | 0.957621i | \(-0.406999\pi\) | ||||
0.288031 | + | 0.957621i | \(0.406999\pi\) | |||||||
\(360\) | −4.22264e70 | −2.12454 | ||||||||
\(361\) | −1.93067e70 | −0.900036 | ||||||||
\(362\) | −3.58591e69 | −0.154922 | ||||||||
\(363\) | 3.13610e69 | 0.125591 | ||||||||
\(364\) | 4.26109e70 | 1.58209 | ||||||||
\(365\) | 3.03385e70 | 1.04458 | ||||||||
\(366\) | −1.96610e69 | −0.0627878 | ||||||||
\(367\) | 5.03481e69 | 0.149165 | 0.0745824 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745824 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(368\) | −2.56439e70 | −0.704968 | ||||||||
\(369\) | 1.78192e70 | 0.454635 | ||||||||
\(370\) | −7.68785e70 | −1.82078 | ||||||||
\(371\) | −7.21842e69 | −0.158730 | ||||||||
\(372\) | −9.34704e69 | −0.190872 | ||||||||
\(373\) | −9.67049e70 | −1.83424 | −0.917119 | − | 0.398613i | \(-0.869492\pi\) | ||||
−0.917119 | + | 0.398613i | \(0.869492\pi\) | |||||||
\(374\) | 1.07959e71 | 1.90235 | ||||||||
\(375\) | 3.17213e70 | 0.519386 | ||||||||
\(376\) | 2.50323e70 | 0.380921 | ||||||||
\(377\) | −4.56565e70 | −0.645826 | ||||||||
\(378\) | 6.73279e70 | 0.885463 | ||||||||
\(379\) | −1.49089e71 | −1.82333 | −0.911667 | − | 0.410930i | \(-0.865204\pi\) | ||||
−0.911667 | + | 0.410930i | \(0.865204\pi\) | |||||||
\(380\) | 8.89269e70 | 1.01154 | ||||||||
\(381\) | 4.35185e70 | 0.460508 | ||||||||
\(382\) | 2.57477e71 | 2.53510 | ||||||||
\(383\) | 1.32996e71 | 1.21863 | 0.609317 | − | 0.792927i | \(-0.291444\pi\) | ||||
0.609317 | + | 0.792927i | \(0.291444\pi\) | |||||||
\(384\) | −9.52013e70 | −0.811959 | ||||||||
\(385\) | −1.48335e71 | −1.17780 | ||||||||
\(386\) | −3.10220e71 | −2.29361 | ||||||||
\(387\) | 1.08197e71 | 0.745012 | ||||||||
\(388\) | −3.92760e70 | −0.251916 | ||||||||
\(389\) | 1.84119e70 | 0.110023 | 0.0550115 | − | 0.998486i | \(-0.482480\pi\) | ||||
0.0550115 | + | 0.998486i | \(0.482480\pi\) | |||||||
\(390\) | −2.93675e71 | −1.63527 | ||||||||
\(391\) | −1.57435e71 | −0.817033 | ||||||||
\(392\) | −2.00966e71 | −0.972199 | ||||||||
\(393\) | 1.91843e71 | 0.865270 | ||||||||
\(394\) | 6.07389e71 | 2.55459 | ||||||||
\(395\) | 5.67820e71 | 2.22736 | ||||||||
\(396\) | −4.78186e71 | −1.74976 | ||||||||
\(397\) | 2.35772e70 | 0.0804922 | 0.0402461 | − | 0.999190i | \(-0.487186\pi\) | ||||
0.0402461 | + | 0.999190i | \(0.487186\pi\) | |||||||
\(398\) | −8.80459e70 | −0.280495 | ||||||||
\(399\) | −3.05539e70 | −0.0908473 | ||||||||
\(400\) | 5.17556e71 | 1.43651 | ||||||||
\(401\) | −5.55389e71 | −1.43922 | −0.719610 | − | 0.694378i | \(-0.755679\pi\) | ||||
−0.719610 | + | 0.694378i | \(0.755679\pi\) | |||||||
\(402\) | 4.16291e71 | 1.00735 | ||||||||
\(403\) | 1.22579e71 | 0.277031 | ||||||||
\(404\) | −8.10720e71 | −1.71153 | ||||||||
\(405\) | 3.55382e71 | 0.700942 | ||||||||
\(406\) | −2.98128e71 | −0.549461 | ||||||||
\(407\) | −4.23617e71 | −0.729671 | ||||||||
\(408\) | 4.48726e71 | 0.722481 | ||||||||
\(409\) | 5.98705e71 | 0.901201 | 0.450600 | − | 0.892726i | \(-0.351210\pi\) | ||||
0.450600 | + | 0.892726i | \(0.351210\pi\) | |||||||
\(410\) | −1.14602e72 | −1.61301 | ||||||||
\(411\) | −3.34795e71 | −0.440685 | ||||||||
\(412\) | 8.94350e71 | 1.10112 | ||||||||
\(413\) | 5.31506e71 | 0.612183 | ||||||||
\(414\) | 1.05535e72 | 1.13734 | ||||||||
\(415\) | −2.91045e72 | −2.93520 | ||||||||
\(416\) | 2.37091e71 | 0.223794 | ||||||||
\(417\) | 3.65225e71 | 0.322715 | ||||||||
\(418\) | 7.41584e71 | 0.613498 | ||||||||
\(419\) | 1.73387e71 | 0.134317 | 0.0671585 | − | 0.997742i | \(-0.478607\pi\) | ||||
0.0671585 | + | 0.997742i | \(0.478607\pi\) | |||||||
\(420\) | −1.26709e72 | −0.919291 | ||||||||
\(421\) | 6.27129e71 | 0.426186 | 0.213093 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213093 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(422\) | 1.10513e72 | 0.703590 | ||||||||
\(423\) | −3.11940e71 | −0.186085 | ||||||||
\(424\) | 7.28212e71 | 0.407096 | ||||||||
\(425\) | 3.17741e72 | 1.66486 | ||||||||
\(426\) | 1.86524e72 | 0.916160 | ||||||||
\(427\) | 1.11247e71 | 0.0512298 | ||||||||
\(428\) | −2.23267e72 | −0.964095 | ||||||||
\(429\) | −1.61821e72 | −0.655330 | ||||||||
\(430\) | −6.95857e72 | −2.64324 | ||||||||
\(431\) | 3.86872e71 | 0.137861 | 0.0689306 | − | 0.997621i | \(-0.478041\pi\) | ||||
0.0689306 | + | 0.997621i | \(0.478041\pi\) | |||||||
\(432\) | −2.05668e72 | −0.687646 | ||||||||
\(433\) | −3.85260e72 | −1.20875 | −0.604376 | − | 0.796699i | \(-0.706578\pi\) | ||||
−0.604376 | + | 0.796699i | \(0.706578\pi\) | |||||||
\(434\) | 8.00419e71 | 0.235695 | ||||||||
\(435\) | 1.35766e72 | 0.375263 | ||||||||
\(436\) | 7.91712e72 | 2.05442 | ||||||||
\(437\) | −1.08144e72 | −0.263489 | ||||||||
\(438\) | 2.16117e72 | 0.494482 | ||||||||
\(439\) | −7.04112e71 | −0.151310 | −0.0756550 | − | 0.997134i | \(-0.524105\pi\) | ||||
−0.0756550 | + | 0.997134i | \(0.524105\pi\) | |||||||
\(440\) | 1.49643e73 | 3.02071 | ||||||||
\(441\) | 2.50433e72 | 0.474932 | ||||||||
\(442\) | −1.20940e73 | −2.15504 | ||||||||
\(443\) | −1.05429e73 | −1.76545 | −0.882727 | − | 0.469887i | \(-0.844295\pi\) | ||||
−0.882727 | + | 0.469887i | \(0.844295\pi\) | |||||||
\(444\) | −3.61859e72 | −0.569518 | ||||||||
\(445\) | 2.04886e73 | 3.03119 | ||||||||
\(446\) | −4.90113e72 | −0.681691 | ||||||||
\(447\) | −5.98213e71 | −0.0782347 | ||||||||
\(448\) | 5.91196e72 | 0.727086 | ||||||||
\(449\) | −5.83745e71 | −0.0675226 | −0.0337613 | − | 0.999430i | \(-0.510749\pi\) | ||||
−0.0337613 | + | 0.999430i | \(0.510749\pi\) | |||||||
\(450\) | −2.12996e73 | −2.31754 | ||||||||
\(451\) | −6.31482e72 | −0.646407 | ||||||||
\(452\) | −1.93578e73 | −1.86444 | ||||||||
\(453\) | 5.23084e72 | 0.474101 | ||||||||
\(454\) | 2.03804e73 | 1.73850 | ||||||||
\(455\) | 1.66170e73 | 1.33425 | ||||||||
\(456\) | 3.08235e72 | 0.232996 | ||||||||
\(457\) | −9.08985e72 | −0.646936 | −0.323468 | − | 0.946239i | \(-0.604849\pi\) | ||||
−0.323468 | + | 0.946239i | \(0.604849\pi\) | |||||||
\(458\) | 3.16831e73 | 2.12338 | ||||||||
\(459\) | −1.26265e73 | −0.796957 | ||||||||
\(460\) | −4.48481e73 | −2.66627 | ||||||||
\(461\) | 1.94861e73 | 1.09131 | 0.545656 | − | 0.838009i | \(-0.316281\pi\) | ||||
0.545656 | + | 0.838009i | \(0.316281\pi\) | |||||||
\(462\) | −1.05666e73 | −0.557547 | ||||||||
\(463\) | −5.72642e72 | −0.284712 | −0.142356 | − | 0.989816i | \(-0.545468\pi\) | ||||
−0.142356 | + | 0.989816i | \(0.545468\pi\) | |||||||
\(464\) | 9.10700e72 | 0.426708 | ||||||||
\(465\) | −3.64506e72 | −0.160971 | ||||||||
\(466\) | 5.15575e73 | 2.14624 | ||||||||
\(467\) | −2.64935e73 | −1.03974 | −0.519871 | − | 0.854245i | \(-0.674020\pi\) | ||||
−0.519871 | + | 0.854245i | \(0.674020\pi\) | |||||||
\(468\) | 5.35681e73 | 1.98219 | ||||||||
\(469\) | −2.35549e73 | −0.821916 | ||||||||
\(470\) | 2.00621e73 | 0.660215 | ||||||||
\(471\) | −1.40187e73 | −0.435144 | ||||||||
\(472\) | −5.36196e73 | −1.57007 | ||||||||
\(473\) | −3.83432e73 | −1.05927 | ||||||||
\(474\) | 4.04487e73 | 1.05439 | ||||||||
\(475\) | 2.18261e73 | 0.536910 | ||||||||
\(476\) | −5.21806e73 | −1.21149 | ||||||||
\(477\) | −9.07461e72 | −0.198871 | ||||||||
\(478\) | −5.66260e73 | −1.17152 | ||||||||
\(479\) | 2.29697e73 | 0.448672 | 0.224336 | − | 0.974512i | \(-0.427979\pi\) | ||||
0.224336 | + | 0.974512i | \(0.427979\pi\) | |||||||
\(480\) | −7.05022e72 | −0.130038 | ||||||||
\(481\) | 4.74551e73 | 0.826595 | ||||||||
\(482\) | −2.86005e73 | −0.470523 | ||||||||
\(483\) | 1.54091e73 | 0.239459 | ||||||||
\(484\) | 3.67903e73 | 0.540115 | ||||||||
\(485\) | −1.53165e73 | −0.212452 | ||||||||
\(486\) | 1.31798e74 | 1.72747 | ||||||||
\(487\) | 1.57576e74 | 1.95184 | 0.975920 | − | 0.218128i | \(-0.0699951\pi\) | ||||
0.975920 | + | 0.218128i | \(0.0699951\pi\) | |||||||
\(488\) | −1.12229e73 | −0.131389 | ||||||||
\(489\) | 5.70760e73 | 0.631625 | ||||||||
\(490\) | −1.61064e74 | −1.68502 | ||||||||
\(491\) | −9.33302e73 | −0.923168 | −0.461584 | − | 0.887096i | \(-0.652719\pi\) | ||||
−0.461584 | + | 0.887096i | \(0.652719\pi\) | |||||||
\(492\) | −5.39420e73 | −0.504530 | ||||||||
\(493\) | 5.59102e73 | 0.494540 | ||||||||
\(494\) | −8.30749e73 | −0.694990 | ||||||||
\(495\) | −1.86478e74 | −1.47566 | ||||||||
\(496\) | −2.44506e73 | −0.183039 | ||||||||
\(497\) | −1.05541e74 | −0.747513 | ||||||||
\(498\) | −2.07326e74 | −1.38946 | ||||||||
\(499\) | 2.92720e74 | 1.85647 | 0.928235 | − | 0.371994i | \(-0.121326\pi\) | ||||
0.928235 | + | 0.371994i | \(0.121326\pi\) | |||||||
\(500\) | 3.72130e74 | 2.23367 | ||||||||
\(501\) | −3.75276e73 | −0.213213 | ||||||||
\(502\) | 2.15658e72 | 0.0115988 | ||||||||
\(503\) | 1.72201e74 | 0.876833 | 0.438417 | − | 0.898772i | \(-0.355539\pi\) | ||||
0.438417 | + | 0.898772i | \(0.355539\pi\) | |||||||
\(504\) | 1.70201e74 | 0.820583 | ||||||||
\(505\) | −3.16156e74 | −1.44341 | ||||||||
\(506\) | −3.74000e74 | −1.61708 | ||||||||
\(507\) | 7.06873e73 | 0.289483 | ||||||||
\(508\) | 5.10526e74 | 1.98046 | ||||||||
\(509\) | −3.58739e74 | −1.31838 | −0.659188 | − | 0.751978i | \(-0.729100\pi\) | ||||
−0.659188 | + | 0.751978i | \(0.729100\pi\) | |||||||
\(510\) | 3.59630e74 | 1.25221 | ||||||||
\(511\) | −1.22285e74 | −0.403457 | ||||||||
\(512\) | −4.87523e74 | −1.52430 | ||||||||
\(513\) | −8.67332e73 | −0.257015 | ||||||||
\(514\) | 6.69975e74 | 1.88180 | ||||||||
\(515\) | 3.48770e74 | 0.928624 | ||||||||
\(516\) | −3.27533e74 | −0.826776 | ||||||||
\(517\) | 1.10546e74 | 0.264578 | ||||||||
\(518\) | 3.09872e74 | 0.703257 | ||||||||
\(519\) | 7.41628e73 | 0.159619 | ||||||||
\(520\) | −1.67636e75 | −3.42196 | ||||||||
\(521\) | −2.44717e74 | −0.473834 | −0.236917 | − | 0.971530i | \(-0.576137\pi\) | ||||
−0.236917 | + | 0.971530i | \(0.576137\pi\) | |||||||
\(522\) | −3.74791e74 | −0.688414 | ||||||||
\(523\) | 4.08574e74 | 0.711990 | 0.355995 | − | 0.934488i | \(-0.384142\pi\) | ||||
0.355995 | + | 0.934488i | \(0.384142\pi\) | |||||||
\(524\) | 2.25056e75 | 3.72118 | ||||||||
\(525\) | −3.10993e74 | −0.487944 | ||||||||
\(526\) | −1.87969e75 | −2.79883 | ||||||||
\(527\) | −1.50109e74 | −0.212136 | ||||||||
\(528\) | 3.22781e74 | 0.432988 | ||||||||
\(529\) | −2.39895e74 | −0.305485 | ||||||||
\(530\) | 5.83624e74 | 0.705580 | ||||||||
\(531\) | 6.68180e74 | 0.766998 | ||||||||
\(532\) | −3.58435e74 | −0.390698 | ||||||||
\(533\) | 7.07408e74 | 0.732271 | ||||||||
\(534\) | 1.45951e75 | 1.43490 | ||||||||
\(535\) | −8.70672e74 | −0.813066 | ||||||||
\(536\) | 2.37627e75 | 2.10797 | ||||||||
\(537\) | −4.09276e74 | −0.344924 | ||||||||
\(538\) | 1.25293e75 | 1.00326 | ||||||||
\(539\) | −8.87495e74 | −0.675266 | ||||||||
\(540\) | −3.59689e75 | −2.60075 | ||||||||
\(541\) | −1.21945e74 | −0.0837988 | −0.0418994 | − | 0.999122i | \(-0.513341\pi\) | ||||
−0.0418994 | + | 0.999122i | \(0.513341\pi\) | |||||||
\(542\) | −5.07117e75 | −3.31229 | ||||||||
\(543\) | −6.58211e73 | −0.0408667 | ||||||||
\(544\) | −2.90338e74 | −0.171370 | ||||||||
\(545\) | 3.08744e75 | 1.73258 | ||||||||
\(546\) | 1.18371e75 | 0.631608 | ||||||||
\(547\) | 1.44748e75 | 0.734446 | 0.367223 | − | 0.930133i | \(-0.380309\pi\) | ||||
0.367223 | + | 0.930133i | \(0.380309\pi\) | |||||||
\(548\) | −3.92756e75 | −1.89521 | ||||||||
\(549\) | 1.39854e74 | 0.0641853 | ||||||||
\(550\) | 7.54822e75 | 3.29511 | ||||||||
\(551\) | 3.84055e74 | 0.159487 | ||||||||
\(552\) | −1.55451e75 | −0.614141 | ||||||||
\(553\) | −2.28870e75 | −0.860295 | ||||||||
\(554\) | 4.20760e73 | 0.0150493 | ||||||||
\(555\) | −1.41114e75 | −0.480301 | ||||||||
\(556\) | 4.28454e75 | 1.38787 | ||||||||
\(557\) | 2.32271e74 | 0.0716104 | 0.0358052 | − | 0.999359i | \(-0.488600\pi\) | ||||
0.0358052 | + | 0.999359i | \(0.488600\pi\) | |||||||
\(558\) | 1.00624e75 | 0.295299 | ||||||||
\(559\) | 4.29534e75 | 1.19998 | ||||||||
\(560\) | −3.31455e75 | −0.881563 | ||||||||
\(561\) | 1.98164e75 | 0.501818 | ||||||||
\(562\) | −1.32146e76 | −3.18645 | ||||||||
\(563\) | −2.67933e75 | −0.615242 | −0.307621 | − | 0.951509i | \(-0.599533\pi\) | ||||
−0.307621 | + | 0.951509i | \(0.599533\pi\) | |||||||
\(564\) | 9.44302e74 | 0.206507 | ||||||||
\(565\) | −7.54894e75 | −1.57237 | ||||||||
\(566\) | 1.35609e76 | 2.69053 | ||||||||
\(567\) | −1.43243e75 | −0.270731 | ||||||||
\(568\) | 1.06472e76 | 1.91715 | ||||||||
\(569\) | 1.95670e75 | 0.335688 | 0.167844 | − | 0.985814i | \(-0.446319\pi\) | ||||
0.167844 | + | 0.985814i | \(0.446319\pi\) | |||||||
\(570\) | 2.47035e75 | 0.403831 | ||||||||
\(571\) | −6.00217e75 | −0.935008 | −0.467504 | − | 0.883991i | \(-0.654847\pi\) | ||||
−0.467504 | + | 0.883991i | \(0.654847\pi\) | |||||||
\(572\) | −1.89837e76 | −2.81831 | ||||||||
\(573\) | 4.72611e75 | 0.668731 | ||||||||
\(574\) | 4.61924e75 | 0.623007 | ||||||||
\(575\) | −1.10074e76 | −1.41521 | ||||||||
\(576\) | 7.43219e75 | 0.910959 | ||||||||
\(577\) | −1.73805e75 | −0.203108 | −0.101554 | − | 0.994830i | \(-0.532382\pi\) | ||||
−0.101554 | + | 0.994830i | \(0.532382\pi\) | |||||||
\(578\) | −5.98393e74 | −0.0666762 | ||||||||
\(579\) | −5.69424e75 | −0.605027 | ||||||||
\(580\) | 1.59270e76 | 1.61386 | ||||||||
\(581\) | 1.17311e76 | 1.13369 | ||||||||
\(582\) | −1.09107e75 | −0.100570 | ||||||||
\(583\) | 3.21589e75 | 0.282759 | ||||||||
\(584\) | 1.23364e76 | 1.03475 | ||||||||
\(585\) | 2.08900e76 | 1.67167 | ||||||||
\(586\) | −2.57212e76 | −1.96384 | ||||||||
\(587\) | −2.45150e75 | −0.178601 | −0.0893006 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0893006 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(588\) | −7.58110e75 | −0.527054 | ||||||||
\(589\) | −1.03112e75 | −0.0684127 | ||||||||
\(590\) | −4.29733e76 | −2.72125 | ||||||||
\(591\) | 1.11489e76 | 0.673871 | ||||||||
\(592\) | −9.46575e75 | −0.546145 | ||||||||
\(593\) | 3.41502e76 | 1.88100 | 0.940500 | − | 0.339794i | \(-0.110357\pi\) | ||||
0.940500 | + | 0.339794i | \(0.110357\pi\) | |||||||
\(594\) | −2.99954e76 | −1.57735 | ||||||||
\(595\) | −2.03489e76 | −1.02170 | ||||||||
\(596\) | −7.01779e75 | −0.336456 | ||||||||
\(597\) | −1.61612e75 | −0.0739913 | ||||||||
\(598\) | 4.18968e76 | 1.83188 | ||||||||
\(599\) | 4.74508e75 | 0.198155 | 0.0990777 | − | 0.995080i | \(-0.468411\pi\) | ||||
0.0990777 | + | 0.995080i | \(0.468411\pi\) | |||||||
\(600\) | 3.13737e76 | 1.25143 | ||||||||
\(601\) | −3.25978e76 | −1.24205 | −0.621027 | − | 0.783789i | \(-0.713284\pi\) | ||||
−0.621027 | + | 0.783789i | \(0.713284\pi\) | |||||||
\(602\) | 2.80477e76 | 1.02093 | ||||||||
\(603\) | −2.96119e76 | −1.02977 | ||||||||
\(604\) | 6.13642e76 | 2.03892 | ||||||||
\(605\) | 1.43471e76 | 0.455503 | ||||||||
\(606\) | −2.25214e76 | −0.683279 | ||||||||
\(607\) | 2.76963e76 | 0.803031 | 0.401515 | − | 0.915852i | \(-0.368484\pi\) | ||||
0.401515 | + | 0.915852i | \(0.368484\pi\) | |||||||
\(608\) | −1.99437e75 | −0.0552658 | ||||||||
\(609\) | −5.47228e75 | −0.144941 | ||||||||
\(610\) | −8.99457e75 | −0.227724 | ||||||||
\(611\) | −1.23838e76 | −0.299723 | ||||||||
\(612\) | −6.55987e76 | −1.51786 | ||||||||
\(613\) | −7.08667e76 | −1.56776 | −0.783879 | − | 0.620913i | \(-0.786762\pi\) | ||||
−0.783879 | + | 0.620913i | \(0.786762\pi\) | |||||||
\(614\) | 6.22456e76 | 1.31667 | ||||||||
\(615\) | −2.10358e76 | −0.425493 | ||||||||
\(616\) | −6.03164e76 | −1.16672 | ||||||||
\(617\) | −5.00063e75 | −0.0925087 | −0.0462543 | − | 0.998930i | \(-0.514728\pi\) | ||||
−0.0462543 | + | 0.998930i | \(0.514728\pi\) | |||||||
\(618\) | 2.48446e76 | 0.439591 | ||||||||
\(619\) | 1.09383e77 | 1.85121 | 0.925604 | − | 0.378494i | \(-0.123558\pi\) | ||||
0.925604 | + | 0.378494i | \(0.123558\pi\) | |||||||
\(620\) | −4.27611e76 | −0.692273 | ||||||||
\(621\) | 4.37417e76 | 0.677450 | ||||||||
\(622\) | 1.11478e77 | 1.65178 | ||||||||
\(623\) | −8.25830e76 | −1.17076 | ||||||||
\(624\) | −3.61591e76 | −0.490503 | ||||||||
\(625\) | 1.42977e76 | 0.185595 | ||||||||
\(626\) | 2.38336e75 | 0.0296070 | ||||||||
\(627\) | 1.36121e76 | 0.161834 | ||||||||
\(628\) | −1.64457e77 | −1.87138 | ||||||||
\(629\) | −5.81127e76 | −0.632963 | ||||||||
\(630\) | 1.36407e77 | 1.42224 | ||||||||
\(631\) | −6.03396e76 | −0.602276 | −0.301138 | − | 0.953581i | \(-0.597366\pi\) | ||||
−0.301138 | + | 0.953581i | \(0.597366\pi\) | |||||||
\(632\) | 2.30889e77 | 2.20640 | ||||||||
\(633\) | 2.02851e76 | 0.185599 | ||||||||
\(634\) | −1.76599e77 | −1.54716 | ||||||||
\(635\) | 1.99090e77 | 1.67021 | ||||||||
\(636\) | 2.74706e76 | 0.220697 | ||||||||
\(637\) | 9.94203e76 | 0.764963 | ||||||||
\(638\) | 1.32820e77 | 0.978798 | ||||||||
\(639\) | −1.32680e77 | −0.936552 | ||||||||
\(640\) | −4.35530e77 | −2.94489 | ||||||||
\(641\) | −1.24358e77 | −0.805522 | −0.402761 | − | 0.915305i | \(-0.631949\pi\) | ||||
−0.402761 | + | 0.915305i | \(0.631949\pi\) | |||||||
\(642\) | −6.20224e76 | −0.384889 | ||||||||
\(643\) | 1.52782e77 | 0.908385 | 0.454192 | − | 0.890904i | \(-0.349928\pi\) | ||||
0.454192 | + | 0.890904i | \(0.349928\pi\) | |||||||
\(644\) | 1.80768e77 | 1.02982 | ||||||||
\(645\) | −1.27728e77 | −0.697258 | ||||||||
\(646\) | 1.01732e77 | 0.532187 | ||||||||
\(647\) | −8.10455e76 | −0.406313 | −0.203157 | − | 0.979146i | \(-0.565120\pi\) | ||||
−0.203157 | + | 0.979146i | \(0.565120\pi\) | |||||||
\(648\) | 1.44507e77 | 0.694346 | ||||||||
\(649\) | −2.36792e77 | −1.09053 | ||||||||
\(650\) | −8.45578e77 | −3.73281 | ||||||||
\(651\) | 1.46921e76 | 0.0621735 | ||||||||
\(652\) | 6.69572e77 | 2.71637 | ||||||||
\(653\) | 2.22340e77 | 0.864778 | 0.432389 | − | 0.901687i | \(-0.357671\pi\) | ||||
0.432389 | + | 0.901687i | \(0.357671\pi\) | |||||||
\(654\) | 2.19934e77 | 0.820170 | ||||||||
\(655\) | 8.77651e77 | 3.13824 | ||||||||
\(656\) | −1.41105e77 | −0.483824 | ||||||||
\(657\) | −1.53730e77 | −0.505488 | ||||||||
\(658\) | −8.08637e76 | −0.255001 | ||||||||
\(659\) | 1.77062e77 | 0.535520 | 0.267760 | − | 0.963486i | \(-0.413717\pi\) | ||||
0.267760 | + | 0.963486i | \(0.413717\pi\) | |||||||
\(660\) | 5.64505e77 | 1.63761 | ||||||||
\(661\) | −3.47431e77 | −0.966782 | −0.483391 | − | 0.875405i | \(-0.660595\pi\) | ||||
−0.483391 | + | 0.875405i | \(0.660595\pi\) | |||||||
\(662\) | −5.68138e77 | −1.51656 | ||||||||
\(663\) | −2.21990e77 | −0.568476 | ||||||||
\(664\) | −1.18346e78 | −2.90758 | ||||||||
\(665\) | −1.39779e77 | −0.329493 | ||||||||
\(666\) | 3.89555e77 | 0.881104 | ||||||||
\(667\) | −1.93688e77 | −0.420381 | ||||||||
\(668\) | −4.40246e77 | −0.916943 | ||||||||
\(669\) | −8.99625e76 | −0.179822 | ||||||||
\(670\) | 1.90446e78 | 3.65355 | ||||||||
\(671\) | −4.95620e76 | −0.0912597 | ||||||||
\(672\) | 2.84171e76 | 0.0502256 | ||||||||
\(673\) | 3.53476e77 | 0.599716 | 0.299858 | − | 0.953984i | \(-0.403061\pi\) | ||||
0.299858 | + | 0.953984i | \(0.403061\pi\) | |||||||
\(674\) | −1.13653e78 | −1.85112 | ||||||||
\(675\) | −8.82814e77 | −1.38043 | ||||||||
\(676\) | 8.29250e77 | 1.24495 | ||||||||
\(677\) | 3.06962e77 | 0.442482 | 0.221241 | − | 0.975219i | \(-0.428989\pi\) | ||||
0.221241 | + | 0.975219i | \(0.428989\pi\) | |||||||
\(678\) | −5.37749e77 | −0.744326 | ||||||||
\(679\) | 6.17357e76 | 0.0820573 | ||||||||
\(680\) | 2.05284e78 | 2.62036 | ||||||||
\(681\) | 3.74091e77 | 0.458598 | ||||||||
\(682\) | −3.56596e77 | −0.419862 | ||||||||
\(683\) | −6.23098e77 | −0.704672 | −0.352336 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352336 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(684\) | −4.50606e77 | −0.489502 | ||||||||
\(685\) | −1.53163e78 | −1.59832 | ||||||||
\(686\) | 1.73574e78 | 1.74009 | ||||||||
\(687\) | 5.81558e77 | 0.560122 | ||||||||
\(688\) | −8.56782e77 | −0.792845 | ||||||||
\(689\) | −3.60255e77 | −0.320318 | ||||||||
\(690\) | −1.24586e78 | −1.06443 | ||||||||
\(691\) | 5.11269e77 | 0.419762 | 0.209881 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209881 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(692\) | 8.70021e77 | 0.686455 | ||||||||
\(693\) | 7.51633e77 | 0.569957 | ||||||||
\(694\) | −1.04084e78 | −0.758575 | ||||||||
\(695\) | 1.67084e78 | 1.17045 | ||||||||
\(696\) | 5.52057e77 | 0.371732 | ||||||||
\(697\) | −8.66282e77 | −0.560735 | ||||||||
\(698\) | −3.36507e78 | −2.09397 | ||||||||
\(699\) | 9.46362e77 | 0.566155 | ||||||||
\(700\) | −3.64834e78 | −2.09845 | ||||||||
\(701\) | 1.90874e78 | 1.05561 | 0.527804 | − | 0.849366i | \(-0.323016\pi\) | ||||
0.527804 | + | 0.849366i | \(0.323016\pi\) | |||||||
\(702\) | 3.36019e78 | 1.78687 | ||||||||
\(703\) | −3.99184e77 | −0.204127 | ||||||||
\(704\) | −2.63385e78 | −1.29522 | ||||||||
\(705\) | 3.68249e77 | 0.174157 | ||||||||
\(706\) | −2.10948e78 | −0.959504 | ||||||||
\(707\) | 1.27432e78 | 0.557501 | ||||||||
\(708\) | −2.02271e78 | −0.851175 | ||||||||
\(709\) | 3.69220e78 | 1.49456 | 0.747280 | − | 0.664509i | \(-0.231359\pi\) | ||||
0.747280 | + | 0.664509i | \(0.231359\pi\) | |||||||
\(710\) | 8.53317e78 | 3.32281 | ||||||||
\(711\) | −2.87723e78 | −1.07785 | ||||||||
\(712\) | 8.33118e78 | 3.00266 | ||||||||
\(713\) | 5.20018e77 | 0.180325 | ||||||||
\(714\) | −1.44955e78 | −0.483652 | ||||||||
\(715\) | −7.40305e78 | −2.37681 | ||||||||
\(716\) | −4.80131e78 | −1.48338 | ||||||||
\(717\) | −1.03940e78 | −0.309033 | ||||||||
\(718\) | 3.45649e78 | 0.989039 | ||||||||
\(719\) | −8.48236e77 | −0.233600 | −0.116800 | − | 0.993155i | \(-0.537264\pi\) | ||||
−0.116800 | + | 0.993155i | \(0.537264\pi\) | |||||||
\(720\) | −4.16687e78 | −1.10450 | ||||||||
\(721\) | −1.40578e78 | −0.358671 | ||||||||
\(722\) | −6.29182e78 | −1.54527 | ||||||||
\(723\) | −5.24976e77 | −0.124118 | ||||||||
\(724\) | −7.72163e77 | −0.175751 | ||||||||
\(725\) | 3.90910e78 | 0.856607 | ||||||||
\(726\) | 1.02202e78 | 0.215626 | ||||||||
\(727\) | −1.05653e78 | −0.214628 | −0.107314 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107314 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(728\) | 6.75686e78 | 1.32170 | ||||||||
\(729\) | 1.53760e77 | 0.0289625 | ||||||||
\(730\) | 9.88697e78 | 1.79343 | ||||||||
\(731\) | −5.26001e78 | −0.918879 | ||||||||
\(732\) | −4.23365e77 | −0.0712295 | ||||||||
\(733\) | 7.22141e77 | 0.117021 | 0.0585104 | − | 0.998287i | \(-0.481365\pi\) | ||||
0.0585104 | + | 0.998287i | \(0.481365\pi\) | |||||||
\(734\) | 1.64079e78 | 0.256100 | ||||||||
\(735\) | −2.95640e78 | −0.444489 | ||||||||
\(736\) | 1.00581e78 | 0.145672 | ||||||||
\(737\) | 1.04940e79 | 1.46415 | ||||||||
\(738\) | 5.80706e78 | 0.780560 | ||||||||
\(739\) | −6.27071e76 | −0.00812073 | −0.00406036 | − | 0.999992i | \(-0.501292\pi\) | ||||
−0.00406036 | + | 0.999992i | \(0.501292\pi\) | |||||||
\(740\) | −1.65544e79 | −2.06558 | ||||||||
\(741\) | −1.52488e78 | −0.183330 | ||||||||
\(742\) | −2.35240e78 | −0.272523 | ||||||||
\(743\) | 2.11611e77 | 0.0236236 | 0.0118118 | − | 0.999930i | \(-0.496240\pi\) | ||||
0.0118118 | + | 0.999930i | \(0.496240\pi\) | |||||||
\(744\) | −1.48217e78 | −0.159457 | ||||||||
\(745\) | −2.73673e78 | −0.283749 | ||||||||
\(746\) | −3.15150e79 | −3.14919 | ||||||||
\(747\) | 1.47477e79 | 1.42039 | ||||||||
\(748\) | 2.32471e79 | 2.15812 | ||||||||
\(749\) | 3.50940e78 | 0.314038 | ||||||||
\(750\) | 1.03376e79 | 0.891732 | ||||||||
\(751\) | −1.43216e79 | −1.19095 | −0.595474 | − | 0.803374i | \(-0.703036\pi\) | ||||
−0.595474 | + | 0.803374i | \(0.703036\pi\) | |||||||
\(752\) | 2.47017e78 | 0.198032 | ||||||||
\(753\) | 3.95851e76 | 0.00305964 | ||||||||
\(754\) | −1.48789e79 | −1.10882 | ||||||||
\(755\) | 2.39302e79 | 1.71951 | ||||||||
\(756\) | 1.44979e79 | 1.00451 | ||||||||
\(757\) | −2.38175e79 | −1.59132 | −0.795662 | − | 0.605741i | \(-0.792877\pi\) | ||||
−0.795662 | + | 0.605741i | \(0.792877\pi\) | |||||||
\(758\) | −4.85862e79 | −3.13047 | ||||||||
\(759\) | −6.86494e78 | −0.426568 | ||||||||
\(760\) | 1.41012e79 | 0.845053 | ||||||||
\(761\) | 1.24548e79 | 0.719879 | 0.359940 | − | 0.932976i | \(-0.382797\pi\) | ||||
0.359940 | + | 0.932976i | \(0.382797\pi\) | |||||||
\(762\) | 1.41822e79 | 0.790644 | ||||||||
\(763\) | −1.24445e79 | −0.669192 | ||||||||
\(764\) | 5.54431e79 | 2.87594 | ||||||||
\(765\) | −2.55815e79 | −1.28008 | ||||||||
\(766\) | 4.33419e79 | 2.09227 | ||||||||
\(767\) | 2.65263e79 | 1.23539 | ||||||||
\(768\) | −1.94738e79 | −0.875016 | ||||||||
\(769\) | 1.10483e79 | 0.478984 | 0.239492 | − | 0.970898i | \(-0.423019\pi\) | ||||
0.239492 | + | 0.970898i | \(0.423019\pi\) | |||||||
\(770\) | −4.83405e79 | −2.02216 | ||||||||
\(771\) | 1.22977e79 | 0.496397 | ||||||||
\(772\) | −6.68005e79 | −2.60198 | ||||||||
\(773\) | 1.34251e79 | 0.504640 | 0.252320 | − | 0.967644i | \(-0.418806\pi\) | ||||
0.252320 | + | 0.967644i | \(0.418806\pi\) | |||||||
\(774\) | 3.52601e79 | 1.27911 | ||||||||
\(775\) | −1.04952e79 | −0.367447 | ||||||||
\(776\) | −6.22804e78 | −0.210453 | ||||||||
\(777\) | 5.68785e78 | 0.185511 | ||||||||
\(778\) | 6.00021e78 | 0.188898 | ||||||||
\(779\) | −5.95060e78 | −0.180834 | ||||||||
\(780\) | −6.32378e79 | −1.85513 | ||||||||
\(781\) | 4.70196e79 | 1.33160 | ||||||||
\(782\) | −5.13061e79 | −1.40276 | ||||||||
\(783\) | −1.55341e79 | −0.410051 | ||||||||
\(784\) | −1.98311e79 | −0.505424 | ||||||||
\(785\) | −6.41333e79 | −1.57822 | ||||||||
\(786\) | 6.25195e79 | 1.48558 | ||||||||
\(787\) | −9.76349e78 | −0.224027 | −0.112013 | − | 0.993707i | \(-0.535730\pi\) | ||||
−0.112013 | + | 0.993707i | \(0.535730\pi\) | |||||||
\(788\) | 1.30791e80 | 2.89805 | ||||||||
\(789\) | −3.45025e79 | −0.738300 | ||||||||
\(790\) | 1.85046e80 | 3.82414 | ||||||||
\(791\) | 3.04273e79 | 0.607310 | ||||||||
\(792\) | −7.58266e79 | −1.46177 | ||||||||
\(793\) | 5.55211e78 | 0.103382 | ||||||||
\(794\) | 7.68354e78 | 0.138197 | ||||||||
\(795\) | 1.07127e79 | 0.186124 | ||||||||
\(796\) | −1.89591e79 | −0.318207 | ||||||||
\(797\) | −9.76352e79 | −1.58308 | −0.791539 | − | 0.611118i | \(-0.790720\pi\) | ||||
−0.791539 | + | 0.611118i | \(0.790720\pi\) | |||||||
\(798\) | −9.95716e78 | −0.155975 | ||||||||
\(799\) | 1.51650e79 | 0.229512 | ||||||||
\(800\) | −2.02997e79 | −0.296834 | ||||||||
\(801\) | −1.03819e80 | −1.46684 | ||||||||
\(802\) | −1.80995e80 | −2.47099 | ||||||||
\(803\) | 5.44793e79 | 0.718711 | ||||||||
\(804\) | 8.96409e79 | 1.14279 | ||||||||
\(805\) | 7.04941e79 | 0.868492 | ||||||||
\(806\) | 3.99471e79 | 0.475633 | ||||||||
\(807\) | 2.29982e79 | 0.264650 | ||||||||
\(808\) | −1.28557e80 | −1.42982 | ||||||||
\(809\) | 1.16511e80 | 1.25252 | 0.626259 | − | 0.779615i | \(-0.284585\pi\) | ||||
0.626259 | + | 0.779615i | \(0.284585\pi\) | |||||||
\(810\) | 1.15815e80 | 1.20344 | ||||||||
\(811\) | −4.92243e79 | −0.494432 | −0.247216 | − | 0.968960i | \(-0.579516\pi\) | ||||
−0.247216 | + | 0.968960i | \(0.579516\pi\) | |||||||
\(812\) | −6.41966e79 | −0.623335 | ||||||||
\(813\) | −9.30837e79 | −0.873743 | ||||||||
\(814\) | −1.38052e80 | −1.25277 | ||||||||
\(815\) | 2.61113e80 | 2.29084 | ||||||||
\(816\) | 4.42799e79 | 0.375601 | ||||||||
\(817\) | −3.61317e79 | −0.296334 | ||||||||
\(818\) | 1.95111e80 | 1.54727 | ||||||||
\(819\) | −8.42006e79 | −0.645666 | ||||||||
\(820\) | −2.46776e80 | −1.82987 | ||||||||
\(821\) | −6.21015e79 | −0.445313 | −0.222656 | − | 0.974897i | \(-0.571473\pi\) | ||||
−0.222656 | + | 0.974897i | \(0.571473\pi\) | |||||||
\(822\) | −1.09106e80 | −0.756610 | ||||||||
\(823\) | 1.15377e80 | 0.773789 | 0.386894 | − | 0.922124i | \(-0.373548\pi\) | ||||
0.386894 | + | 0.922124i | \(0.373548\pi\) | |||||||
\(824\) | 1.41818e80 | 0.919885 | ||||||||
\(825\) | 1.38551e80 | 0.869213 | ||||||||
\(826\) | 1.73211e80 | 1.05105 | ||||||||
\(827\) | 3.20884e79 | 0.188342 | 0.0941708 | − | 0.995556i | \(-0.469980\pi\) | ||||
0.0941708 | + | 0.995556i | \(0.469980\pi\) | |||||||
\(828\) | 2.27252e80 | 1.29025 | ||||||||
\(829\) | 1.48156e80 | 0.813711 | 0.406855 | − | 0.913493i | \(-0.366625\pi\) | ||||
0.406855 | + | 0.913493i | \(0.366625\pi\) | |||||||
\(830\) | −9.48481e80 | −5.03943 | ||||||||
\(831\) | 7.72325e77 | 0.00396983 | ||||||||
\(832\) | 2.95053e80 | 1.46726 | ||||||||
\(833\) | −1.21749e80 | −0.585769 | ||||||||
\(834\) | 1.19022e80 | 0.554067 | ||||||||
\(835\) | −1.71683e80 | −0.773300 | ||||||||
\(836\) | 1.59687e80 | 0.695981 | ||||||||
\(837\) | 4.17063e79 | 0.175894 | ||||||||
\(838\) | 5.65048e79 | 0.230608 | ||||||||
\(839\) | −4.75921e80 | −1.87967 | −0.939835 | − | 0.341630i | \(-0.889021\pi\) | ||||
−0.939835 | + | 0.341630i | \(0.889021\pi\) | |||||||
\(840\) | −2.00924e80 | −0.767984 | ||||||||
\(841\) | −2.01542e80 | −0.745549 | ||||||||
\(842\) | 2.04374e80 | 0.731717 | ||||||||
\(843\) | −2.42561e80 | −0.840548 | ||||||||
\(844\) | 2.37970e80 | 0.798187 | ||||||||
\(845\) | 3.23382e80 | 1.04992 | ||||||||
\(846\) | −1.01658e80 | −0.319488 | ||||||||
\(847\) | −5.78285e79 | −0.175933 | ||||||||
\(848\) | 7.18593e79 | 0.211640 | ||||||||
\(849\) | 2.48917e80 | 0.709731 | ||||||||
\(850\) | 1.03548e81 | 2.85839 | ||||||||
\(851\) | 2.01318e80 | 0.538047 | ||||||||
\(852\) | 4.01647e80 | 1.03934 | ||||||||
\(853\) | −4.08457e80 | −1.02341 | −0.511703 | − | 0.859162i | \(-0.670985\pi\) | ||||
−0.511703 | + | 0.859162i | \(0.670985\pi\) | |||||||
\(854\) | 3.62542e79 | 0.0879562 | ||||||||
\(855\) | −1.75723e80 | −0.412819 | ||||||||
\(856\) | −3.54036e80 | −0.805414 | ||||||||
\(857\) | −1.70584e80 | −0.375807 | −0.187904 | − | 0.982187i | \(-0.560169\pi\) | ||||
−0.187904 | + | 0.982187i | \(0.560169\pi\) | |||||||
\(858\) | −5.27357e80 | −1.12513 | ||||||||
\(859\) | 3.33842e80 | 0.689809 | 0.344905 | − | 0.938638i | \(-0.387911\pi\) | ||||
0.344905 | + | 0.938638i | \(0.387911\pi\) | |||||||
\(860\) | −1.49841e81 | −2.99862 | ||||||||
\(861\) | 8.47883e79 | 0.164342 | ||||||||
\(862\) | 1.26077e80 | 0.236693 | ||||||||
\(863\) | 4.33083e80 | 0.787543 | 0.393771 | − | 0.919208i | \(-0.371170\pi\) | ||||
0.393771 | + | 0.919208i | \(0.371170\pi\) | |||||||
\(864\) | 8.06676e79 | 0.142092 | ||||||||
\(865\) | 3.39282e80 | 0.578919 | ||||||||
\(866\) | −1.25552e81 | −2.07530 | ||||||||
\(867\) | −1.09838e79 | −0.0175884 | ||||||||
\(868\) | 1.72356e80 | 0.267383 | ||||||||
\(869\) | 1.01964e81 | 1.53251 | ||||||||
\(870\) | 4.42445e80 | 0.644288 | ||||||||
\(871\) | −1.17557e81 | −1.65863 | ||||||||
\(872\) | 1.25543e81 | 1.71628 | ||||||||
\(873\) | 7.76108e79 | 0.102809 | ||||||||
\(874\) | −3.52428e80 | −0.452383 | ||||||||
\(875\) | −5.84929e80 | −0.727582 | ||||||||
\(876\) | 4.65370e80 | 0.560964 | ||||||||
\(877\) | 6.55585e80 | 0.765844 | 0.382922 | − | 0.923781i | \(-0.374918\pi\) | ||||
0.382922 | + | 0.923781i | \(0.374918\pi\) | |||||||
\(878\) | −2.29462e80 | −0.259783 | ||||||||
\(879\) | −4.72125e80 | −0.518039 | ||||||||
\(880\) | 1.47667e81 | 1.57040 | ||||||||
\(881\) | 9.94877e80 | 1.02549 | 0.512746 | − | 0.858541i | \(-0.328628\pi\) | ||||
0.512746 | + | 0.858541i | \(0.328628\pi\) | |||||||
\(882\) | 8.16133e80 | 0.815408 | ||||||||
\(883\) | 7.57548e80 | 0.733653 | 0.366827 | − | 0.930289i | \(-0.380444\pi\) | ||||
0.366827 | + | 0.930289i | \(0.380444\pi\) | |||||||
\(884\) | −2.60422e81 | −2.44478 | ||||||||
\(885\) | −7.88795e80 | −0.717835 | ||||||||
\(886\) | −3.43580e81 | −3.03110 | ||||||||
\(887\) | −4.64982e80 | −0.397683 | −0.198841 | − | 0.980032i | \(-0.563718\pi\) | ||||
−0.198841 | + | 0.980032i | \(0.563718\pi\) | |||||||
\(888\) | −5.73804e80 | −0.475781 | ||||||||
\(889\) | −8.02466e80 | −0.645102 | ||||||||
\(890\) | 6.67701e81 | 5.20423 | ||||||||
\(891\) | 6.38164e80 | 0.482276 | ||||||||
\(892\) | −1.05537e81 | −0.773343 | ||||||||
\(893\) | 1.04170e80 | 0.0740166 | ||||||||
\(894\) | −1.94951e80 | −0.134321 | ||||||||
\(895\) | −1.87237e81 | −1.25100 | ||||||||
\(896\) | 1.75548e81 | 1.13743 | ||||||||
\(897\) | 7.69035e80 | 0.483230 | ||||||||
\(898\) | −1.90236e80 | −0.115929 | ||||||||
\(899\) | −1.84675e80 | −0.109148 | ||||||||
\(900\) | −4.58649e81 | −2.62913 | ||||||||
\(901\) | 4.41163e80 | 0.245283 | ||||||||
\(902\) | −2.05793e81 | −1.10981 | ||||||||
\(903\) | 5.14829e80 | 0.269308 | ||||||||
\(904\) | −3.06958e81 | −1.55757 | ||||||||
\(905\) | −3.01120e80 | −0.148219 | ||||||||
\(906\) | 1.70467e81 | 0.813981 | ||||||||
\(907\) | 1.49725e81 | 0.693577 | 0.346788 | − | 0.937943i | \(-0.387272\pi\) | ||||
0.346788 | + | 0.937943i | \(0.387272\pi\) | |||||||
\(908\) | 4.38855e81 | 1.97224 | ||||||||
\(909\) | 1.60201e81 | 0.698488 | ||||||||
\(910\) | 5.41527e81 | 2.29077 | ||||||||
\(911\) | 2.12167e81 | 0.870807 | 0.435404 | − | 0.900235i | \(-0.356606\pi\) | ||||
0.435404 | + | 0.900235i | \(0.356606\pi\) | |||||||
\(912\) | 3.04164e80 | 0.121130 | ||||||||
\(913\) | −5.22633e81 | −2.01953 | ||||||||
\(914\) | −2.96227e81 | −1.11072 | ||||||||
\(915\) | −1.65099e80 | −0.0600711 | ||||||||
\(916\) | 6.82240e81 | 2.40886 | ||||||||
\(917\) | −3.53753e81 | −1.21211 | ||||||||
\(918\) | −4.11484e81 | −1.36829 | ||||||||
\(919\) | 4.79467e81 | 1.54733 | 0.773664 | − | 0.633596i | \(-0.218422\pi\) | ||||
0.773664 | + | 0.633596i | \(0.218422\pi\) | |||||||
\(920\) | −7.11161e81 | −2.22742 | ||||||||
\(921\) | 1.14255e81 | 0.347324 | ||||||||
\(922\) | 6.35028e81 | 1.87367 | ||||||||
\(923\) | −5.26730e81 | −1.50849 | ||||||||
\(924\) | −2.27534e81 | −0.632508 | ||||||||
\(925\) | −4.06309e81 | −1.09637 | ||||||||
\(926\) | −1.86617e81 | −0.488821 | ||||||||
\(927\) | −1.76727e81 | −0.449376 | ||||||||
\(928\) | −3.57196e80 | −0.0881733 | ||||||||
\(929\) | −8.73325e80 | −0.209288 | −0.104644 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104644 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(930\) | −1.18788e81 | −0.276371 | ||||||||
\(931\) | −8.36306e80 | −0.188907 | ||||||||
\(932\) | 1.11020e82 | 2.43480 | ||||||||
\(933\) | 2.04623e81 | 0.435721 | ||||||||
\(934\) | −8.63393e81 | −1.78513 | ||||||||
\(935\) | 9.06566e81 | 1.82004 | ||||||||
\(936\) | 8.49436e81 | 1.65594 | ||||||||
\(937\) | 2.20940e81 | 0.418250 | 0.209125 | − | 0.977889i | \(-0.432938\pi\) | ||||
0.209125 | + | 0.977889i | \(0.432938\pi\) | |||||||
\(938\) | −7.67626e81 | −1.41114 | ||||||||
\(939\) | 4.37477e79 | 0.00781000 | ||||||||
\(940\) | 4.32002e81 | 0.748979 | ||||||||
\(941\) | 7.24578e81 | 1.22003 | 0.610015 | − | 0.792390i | \(-0.291163\pi\) | ||||
0.610015 | + | 0.792390i | \(0.291163\pi\) | |||||||
\(942\) | −4.56853e81 | −0.747097 | ||||||||
\(943\) | 3.00104e81 | 0.476650 | ||||||||
\(944\) | −5.29114e81 | −0.816242 | ||||||||
\(945\) | 5.65374e81 | 0.847151 | ||||||||
\(946\) | −1.24956e82 | −1.81866 | ||||||||
\(947\) | −1.07373e82 | −1.51800 | −0.759000 | − | 0.651090i | \(-0.774312\pi\) | ||||
−0.759000 | + | 0.651090i | \(0.774312\pi\) | |||||||
\(948\) | 8.70991e81 | 1.19615 | ||||||||
\(949\) | −6.10297e81 | −0.814179 | ||||||||
\(950\) | 7.11286e81 | 0.921817 | ||||||||
\(951\) | −3.24157e81 | −0.408123 | ||||||||
\(952\) | −8.27434e81 | −1.01209 | ||||||||
\(953\) | −2.80192e81 | −0.332966 | −0.166483 | − | 0.986044i | \(-0.553241\pi\) | ||||
−0.166483 | + | 0.986044i | \(0.553241\pi\) | |||||||
\(954\) | −2.95731e81 | −0.341441 | ||||||||
\(955\) | 2.16211e82 | 2.42541 | ||||||||
\(956\) | −1.21934e82 | −1.32903 | ||||||||
\(957\) | 2.43796e81 | 0.258196 | ||||||||
\(958\) | 7.48556e81 | 0.770322 | ||||||||
\(959\) | 6.17350e81 | 0.617333 | ||||||||
\(960\) | −8.77380e81 | −0.852567 | ||||||||
\(961\) | −1.00941e82 | −0.953180 | ||||||||
\(962\) | 1.54650e82 | 1.41918 | ||||||||
\(963\) | 4.41182e81 | 0.393455 | ||||||||
\(964\) | −6.15862e81 | −0.533784 | ||||||||
\(965\) | −2.60502e82 | −2.19437 | ||||||||
\(966\) | 5.02165e81 | 0.411126 | ||||||||
\(967\) | 6.52535e81 | 0.519249 | 0.259624 | − | 0.965710i | \(-0.416401\pi\) | ||||
0.259624 | + | 0.965710i | \(0.416401\pi\) | |||||||
\(968\) | 5.83388e81 | 0.451217 | ||||||||
\(969\) | 1.86734e81 | 0.140385 | ||||||||
\(970\) | −4.99145e81 | −0.364758 | ||||||||
\(971\) | −2.42379e82 | −1.72173 | −0.860866 | − | 0.508833i | \(-0.830077\pi\) | ||||
−0.860866 | + | 0.508833i | \(0.830077\pi\) | |||||||
\(972\) | 2.83804e82 | 1.95973 | ||||||||
\(973\) | −6.73462e81 | −0.452074 | ||||||||
\(974\) | 5.13522e82 | 3.35110 | ||||||||
\(975\) | −1.55210e82 | −0.984674 | ||||||||
\(976\) | −1.10747e81 | −0.0683063 | ||||||||
\(977\) | −1.29199e82 | −0.774744 | −0.387372 | − | 0.921923i | \(-0.626617\pi\) | ||||
−0.387372 | + | 0.921923i | \(0.626617\pi\) | |||||||
\(978\) | 1.86004e82 | 1.08443 | ||||||||
\(979\) | 3.67917e82 | 2.08558 | ||||||||
\(980\) | −3.46822e82 | −1.91157 | ||||||||
\(981\) | −1.56445e82 | −0.838425 | ||||||||
\(982\) | −3.04152e82 | −1.58498 | ||||||||
\(983\) | −1.06339e82 | −0.538854 | −0.269427 | − | 0.963021i | \(-0.586834\pi\) | ||||
−0.269427 | + | 0.963021i | \(0.586834\pi\) | |||||||
\(984\) | −8.55365e81 | −0.421489 | ||||||||
\(985\) | 5.10044e82 | 2.44406 | ||||||||
\(986\) | 1.82205e82 | 0.849073 | ||||||||
\(987\) | −1.48429e81 | −0.0672663 | ||||||||
\(988\) | −1.78887e82 | −0.788431 | ||||||||
\(989\) | 1.82221e82 | 0.781089 | ||||||||
\(990\) | −6.07711e82 | −2.53355 | ||||||||
\(991\) | −2.78037e82 | −1.12740 | −0.563699 | − | 0.825980i | \(-0.690622\pi\) | ||||
−0.563699 | + | 0.825980i | \(0.690622\pi\) | |||||||
\(992\) | 9.59005e80 | 0.0378225 | ||||||||
\(993\) | −1.04284e82 | −0.400051 | ||||||||
\(994\) | −3.43944e82 | −1.28340 | ||||||||
\(995\) | −7.39349e81 | −0.268358 | ||||||||
\(996\) | −4.46440e82 | −1.57627 | ||||||||
\(997\) | 4.12474e82 | 1.41671 | 0.708353 | − | 0.705858i | \(-0.249438\pi\) | ||||
0.708353 | + | 0.705858i | \(0.249438\pi\) | |||||||
\(998\) | 9.53941e82 | 3.18736 | ||||||||
\(999\) | 1.61461e82 | 0.524826 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.56.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 9.56.a.a.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.56.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.56.a.a.1.1 | 4 | 3.2 | odd | 2 |