Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,33,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(32.4333275711\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.11 | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.33.c.a.2.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32395.0 | − | 32395.0i | 0.494308 | − | 0.494308i | −0.415353 | − | 0.909660i | \(-0.636342\pi\) |
0.909660 | + | 0.415353i | \(0.136342\pi\) | |||||||
\(3\) | 1.63684e7 | + | 1.63684e7i | 0.380247 | + | 0.380247i | 0.871191 | − | 0.490944i | \(-0.163348\pi\) |
−0.490944 | + | 0.871191i | \(0.663348\pi\) | |||||||
\(4\) | 2.19610e9i | 0.511319i | ||||||||
\(5\) | 5.30856e10 | − | 1.43056e11i | 0.347902 | − | 0.937531i | ||||
\(6\) | 1.06051e12 | 0.375918 | ||||||||
\(7\) | −2.79912e13 | + | 2.79912e13i | −0.842273 | + | 0.842273i | −0.989154 | − | 0.146881i | \(-0.953076\pi\) |
0.146881 | + | 0.989154i | \(0.453076\pi\) | |||||||
\(8\) | 2.10278e14 | + | 2.10278e14i | 0.747057 | + | 0.747057i | ||||
\(9\) | − | 1.31717e15i | − | 0.710825i | ||||||
\(10\) | −2.91458e15 | − | 6.35400e15i | −0.291458 | − | 0.635400i | ||||
\(11\) | 6.58116e16 | 1.43225 | 0.716126 | − | 0.697971i | \(-0.245914\pi\) | ||||
0.716126 | + | 0.697971i | \(0.245914\pi\) | |||||||
\(12\) | −3.59466e16 | + | 3.59466e16i | −0.194428 | + | 0.194428i | ||||
\(13\) | −2.99215e16 | − | 2.99215e16i | −0.0449666 | − | 0.0449666i | 0.684266 | − | 0.729233i | \(-0.260123\pi\) |
−0.729233 | + | 0.684266i | \(0.760123\pi\) | |||||||
\(14\) | 1.81355e18i | 0.832684i | ||||||||
\(15\) | 3.21052e18 | − | 1.47267e18i | 0.488782 | − | 0.224205i | ||||
\(16\) | 4.19171e18 | 0.227233 | ||||||||
\(17\) | −1.92770e19 | + | 1.92770e19i | −0.396148 | + | 0.396148i | −0.876872 | − | 0.480724i | \(-0.840374\pi\) |
0.480724 | + | 0.876872i | \(0.340374\pi\) | |||||||
\(18\) | −4.26698e19 | − | 4.26698e19i | −0.351366 | − | 0.351366i | ||||
\(19\) | 5.51904e20i | 1.91340i | 0.291073 | + | 0.956701i | \(0.405988\pi\) | ||||
−0.291073 | + | 0.956701i | \(0.594012\pi\) | |||||||
\(20\) | 3.14165e20 | + | 1.16581e20i | 0.479378 | + | 0.177889i | ||||
\(21\) | −9.16341e20 | −0.640543 | ||||||||
\(22\) | 2.13196e21 | − | 2.13196e21i | 0.707973 | − | 0.707973i | ||||
\(23\) | 3.28869e21 | + | 3.28869e21i | 0.536263 | + | 0.536263i | 0.922429 | − | 0.386166i | \(-0.126201\pi\) |
−0.386166 | + | 0.922429i | \(0.626201\pi\) | |||||||
\(24\) | 6.88382e21i | 0.568132i | ||||||||
\(25\) | −1.76469e22 | − | 1.51884e22i | −0.757929 | − | 0.652337i | ||||
\(26\) | −1.93861e21 | −0.0444547 | ||||||||
\(27\) | 5.18909e22 | − | 5.18909e22i | 0.650536 | − | 0.650536i | ||||
\(28\) | −6.14715e22 | − | 6.14715e22i | −0.430670 | − | 0.430670i | ||||
\(29\) | 3.10854e23i | 1.24219i | 0.783734 | + | 0.621096i | \(0.213312\pi\) | ||||
−0.783734 | + | 0.621096i | \(0.786688\pi\) | |||||||
\(30\) | 5.62976e22 | − | 1.51712e23i | 0.130782 | − | 0.352435i | ||||
\(31\) | 1.32479e24 | 1.82121 | 0.910606 | − | 0.413275i | \(-0.135615\pi\) | ||||
0.910606 | + | 0.413275i | \(0.135615\pi\) | |||||||
\(32\) | −7.67346e23 | + | 7.67346e23i | −0.634734 | + | 0.634734i | ||||
\(33\) | 1.07723e24 | + | 1.07723e24i | 0.544609 | + | 0.544609i | ||||
\(34\) | 1.24896e24i | 0.391638i | ||||||||
\(35\) | 2.51838e24 | + | 5.49023e24i | 0.496629 | + | 1.08269i | ||||
\(36\) | 2.89264e24 | 0.363459 | ||||||||
\(37\) | 2.81341e24 | − | 2.81341e24i | 0.228037 | − | 0.228037i | −0.583835 | − | 0.811872i | \(-0.698449\pi\) |
0.811872 | + | 0.583835i | \(0.198449\pi\) | |||||||
\(38\) | 1.78789e25 | + | 1.78789e25i | 0.945810 | + | 0.945810i | ||||
\(39\) | − | 9.79533e23i | − | 0.0341968i | ||||||
\(40\) | 4.12442e25 | − | 1.89188e25i | 0.960292 | − | 0.440487i | ||||
\(41\) | 3.62740e25 | 0.568923 | 0.284462 | − | 0.958687i | \(-0.408185\pi\) | ||||
0.284462 | + | 0.958687i | \(0.408185\pi\) | |||||||
\(42\) | −2.96848e25 | + | 2.96848e25i | −0.316625 | + | 0.316625i | ||||
\(43\) | 1.14542e26 | + | 1.14542e26i | 0.838433 | + | 0.838433i | 0.988653 | − | 0.150219i | \(-0.0479980\pi\) |
−0.150219 | + | 0.988653i | \(0.547998\pi\) | |||||||
\(44\) | 1.44529e26i | 0.732338i | ||||||||
\(45\) | −1.88429e26 | − | 6.99229e25i | −0.666420 | − | 0.247297i | ||||
\(46\) | 2.13074e26 | 0.530158 | ||||||||
\(47\) | −7.62585e24 | + | 7.62585e24i | −0.0134500 | + | 0.0134500i | −0.713800 | − | 0.700350i | \(-0.753027\pi\) |
0.700350 | + | 0.713800i | \(0.253027\pi\) | |||||||
\(48\) | 6.86115e25 | + | 6.86115e25i | 0.0864046 | + | 0.0864046i | ||||
\(49\) | − | 4.62586e26i | − | 0.418847i | ||||||
\(50\) | −1.06370e27 | + | 7.96429e25i | −0.697106 | + | 0.0521948i | ||||
\(51\) | −6.31068e26 | −0.301268 | ||||||||
\(52\) | 6.57107e25 | − | 6.57107e25i | 0.0229923 | − | 0.0229923i | ||||
\(53\) | −4.02727e27 | − | 4.02727e27i | −1.03896 | − | 1.03896i | −0.999210 | − | 0.0397458i | \(-0.987345\pi\) |
−0.0397458 | − | 0.999210i | \(-0.512655\pi\) | |||||||
\(54\) | − | 3.36201e27i | − | 0.643130i | ||||||
\(55\) | 3.49364e27 | − | 9.41473e27i | 0.498283 | − | 1.34278i | ||||
\(56\) | −1.17719e28 | −1.25845 | ||||||||
\(57\) | −9.03378e27 | + | 9.03378e27i | −0.727565 | + | 0.727565i | ||||
\(58\) | 1.00701e28 | + | 1.00701e28i | 0.614025 | + | 0.614025i | ||||
\(59\) | 3.60554e27i | 0.167239i | 0.996498 | + | 0.0836195i | \(0.0266480\pi\) | ||||
−0.996498 | + | 0.0836195i | \(0.973352\pi\) | |||||||
\(60\) | 3.23413e27 | + | 7.05062e27i | 0.114640 | + | 0.249924i | ||||
\(61\) | −1.10442e28 | −0.300509 | −0.150255 | − | 0.988647i | \(-0.548009\pi\) | ||||
−0.150255 | + | 0.988647i | \(0.548009\pi\) | |||||||
\(62\) | 4.29166e28 | − | 4.29166e28i | 0.900240 | − | 0.900240i | ||||
\(63\) | 3.68692e28 | + | 3.68692e28i | 0.598708 | + | 0.598708i | ||||
\(64\) | 6.77196e28i | 0.854741i | ||||||||
\(65\) | −5.86885e27 | + | 2.69205e27i | −0.0578015 | + | 0.0265136i | ||||
\(66\) | 6.97935e28 | 0.538409 | ||||||||
\(67\) | 5.94357e27 | − | 5.94357e27i | 0.0360455 | − | 0.0360455i | −0.688854 | − | 0.724900i | \(-0.741886\pi\) |
0.724900 | + | 0.688854i | \(0.241886\pi\) | |||||||
\(68\) | −4.23343e28 | − | 4.23343e28i | −0.202558 | − | 0.202558i | ||||
\(69\) | 1.07661e29i | 0.407825i | ||||||||
\(70\) | 2.59439e29 | + | 9.62732e28i | 0.780667 | + | 0.289692i | ||||
\(71\) | −2.05516e29 | −0.492847 | −0.246423 | − | 0.969162i | \(-0.579255\pi\) | ||||
−0.246423 | + | 0.969162i | \(0.579255\pi\) | |||||||
\(72\) | 2.76972e29 | − | 2.76972e29i | 0.531027 | − | 0.531027i | ||||
\(73\) | 4.18908e29 | + | 4.18908e29i | 0.644100 | + | 0.644100i | 0.951561 | − | 0.307461i | \(-0.0994793\pi\) |
−0.307461 | + | 0.951561i | \(0.599479\pi\) | |||||||
\(74\) | − | 1.82281e29i | − | 0.225441i | ||||||
\(75\) | −4.02416e28 | − | 5.37461e29i | −0.0401509 | − | 0.536249i | ||||
\(76\) | −1.21204e30 | −0.978359 | ||||||||
\(77\) | −1.84214e30 | + | 1.84214e30i | −1.20635 | + | 1.20635i | ||||
\(78\) | −3.17319e28 | − | 3.17319e28i | −0.0169038 | − | 0.0169038i | ||||
\(79\) | − | 2.78732e30i | − | 1.21103i | −0.795835 | − | 0.605513i | \(-0.792968\pi\) | ||
0.795835 | − | 0.605513i | \(-0.207032\pi\) | |||||||
\(80\) | 2.22519e29 | − | 5.99649e29i | 0.0790548 | − | 0.213038i | ||||
\(81\) | −7.42008e29 | −0.216097 | ||||||||
\(82\) | 1.17510e30 | − | 1.17510e30i | 0.281223 | − | 0.281223i | ||||
\(83\) | −6.45873e30 | − | 6.45873e30i | −1.27320 | − | 1.27320i | −0.944398 | − | 0.328804i | \(-0.893355\pi\) |
−0.328804 | − | 0.944398i | \(-0.606645\pi\) | |||||||
\(84\) | − | 2.01238e30i | − | 0.327522i | ||||||
\(85\) | 1.73436e30 | + | 3.78103e30i | 0.233581 | + | 0.509222i | ||||
\(86\) | 7.42115e30 | 0.828889 | ||||||||
\(87\) | −5.08818e30 | + | 5.08818e30i | −0.472340 | + | 0.472340i | ||||
\(88\) | 1.38387e31 | + | 1.38387e31i | 1.06997 | + | 1.06997i | ||||
\(89\) | − | 7.48910e30i | − | 0.483270i | −0.970367 | − | 0.241635i | \(-0.922316\pi\) | ||
0.970367 | − | 0.241635i | \(-0.0776836\pi\) | |||||||
\(90\) | −8.36931e30 | + | 3.83901e30i | −0.451658 | + | 0.207176i | ||||
\(91\) | 1.67508e30 | 0.0757483 | ||||||||
\(92\) | −7.22230e30 | + | 7.22230e30i | −0.274202 | + | 0.274202i | ||||
\(93\) | 2.16847e31 | + | 2.16847e31i | 0.692510 | + | 0.692510i | ||||
\(94\) | 4.94078e29i | 0.0132969i | ||||||||
\(95\) | 7.89532e31 | + | 2.92982e31i | 1.79387 | + | 0.665676i | ||||
\(96\) | −2.51204e31 | −0.482711 | ||||||||
\(97\) | −1.14137e31 | + | 1.14137e31i | −0.185814 | + | 0.185814i | −0.793884 | − | 0.608070i | \(-0.791944\pi\) |
0.608070 | + | 0.793884i | \(0.291944\pi\) | |||||||
\(98\) | −1.49855e31 | − | 1.49855e31i | −0.207039 | − | 0.207039i | ||||
\(99\) | − | 8.66852e31i | − | 1.01808i | ||||||
\(100\) | 3.33553e31 | − | 3.87544e31i | 0.333553 | − | 0.387544i | ||||
\(101\) | −3.34720e31 | −0.285456 | −0.142728 | − | 0.989762i | \(-0.545587\pi\) | ||||
−0.142728 | + | 0.989762i | \(0.545587\pi\) | |||||||
\(102\) | −2.04434e31 | + | 2.04434e31i | −0.148919 | + | 0.148919i | ||||
\(103\) | −1.15323e32 | − | 1.15323e32i | −0.718655 | − | 0.718655i | 0.249675 | − | 0.968330i | \(-0.419676\pi\) |
−0.968330 | + | 0.249675i | \(0.919676\pi\) | |||||||
\(104\) | − | 1.25837e31i | − | 0.0671852i | ||||||
\(105\) | −4.86445e31 | + | 1.31088e32i | −0.222846 | + | 0.600529i | ||||
\(106\) | −2.60927e32 | −1.02713 | ||||||||
\(107\) | 1.08124e31 | − | 1.08124e31i | 0.0366255 | − | 0.0366255i | −0.688557 | − | 0.725182i | \(-0.741755\pi\) |
0.725182 | + | 0.688557i | \(0.241755\pi\) | |||||||
\(108\) | 1.13958e32 | + | 1.13958e32i | 0.332631 | + | 0.332631i | ||||
\(109\) | − | 2.08454e32i | − | 0.525033i | −0.964928 | − | 0.262516i | \(-0.915448\pi\) | ||
0.964928 | − | 0.262516i | \(-0.0845523\pi\) | |||||||
\(110\) | −1.91813e32 | − | 4.18166e32i | −0.417442 | − | 0.910052i | ||||
\(111\) | 9.21020e31 | 0.173421 | ||||||||
\(112\) | −1.17331e32 | + | 1.17331e32i | −0.191392 | + | 0.191392i | ||||
\(113\) | 3.30218e32 | + | 3.30218e32i | 0.467246 | + | 0.467246i | 0.901021 | − | 0.433775i | \(-0.142819\pi\) |
−0.433775 | + | 0.901021i | \(0.642819\pi\) | |||||||
\(114\) | 5.85298e32i | 0.719282i | ||||||||
\(115\) | 6.45049e32 | − | 2.95885e32i | 0.689330 | − | 0.316196i | ||||
\(116\) | −6.82667e32 | −0.635157 | ||||||||
\(117\) | −3.94118e31 | + | 3.94118e31i | −0.0319634 | + | 0.0319634i | ||||
\(118\) | 1.16801e32 | + | 1.16801e32i | 0.0826676 | + | 0.0826676i | ||||
\(119\) | − | 1.07918e33i | − | 0.667330i | ||||||
\(120\) | 9.84770e32 | + | 3.65431e32i | 0.532641 | + | 0.197654i | ||||
\(121\) | 2.21978e33 | 1.05134 | ||||||||
\(122\) | −3.57777e32 | + | 3.57777e32i | −0.148544 | + | 0.148544i | ||||
\(123\) | 5.93747e32 | + | 5.93747e32i | 0.216331 | + | 0.216331i | ||||
\(124\) | 2.90938e33i | 0.931221i | ||||||||
\(125\) | −3.10959e33 | + | 1.71821e33i | −0.875271 | + | 0.483633i | ||||
\(126\) | 2.38876e33 | 0.591893 | ||||||||
\(127\) | 2.24034e33 | − | 2.24034e33i | 0.489163 | − | 0.489163i | −0.418879 | − | 0.908042i | \(-0.637577\pi\) |
0.908042 | + | 0.418879i | \(0.137577\pi\) | |||||||
\(128\) | −1.10195e33 | − | 1.10195e33i | −0.212229 | − | 0.212229i | ||||
\(129\) | 3.74973e33i | 0.637623i | ||||||||
\(130\) | −1.02912e32 | + | 2.77330e32i | −0.0154659 | + | 0.0416776i | ||||
\(131\) | 2.85785e33 | 0.379926 | 0.189963 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189963 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(132\) | −2.36570e33 | + | 2.36570e33i | −0.278469 | + | 0.278469i | ||||
\(133\) | −1.54485e34 | − | 1.54485e34i | −1.61161 | − | 1.61161i | ||||
\(134\) | − | 3.85083e32i | − | 0.0356351i | ||||||
\(135\) | −4.66864e33 | − | 1.01780e34i | −0.383575 | − | 0.836220i | ||||
\(136\) | −8.10707e33 | −0.591891 | ||||||||
\(137\) | 8.84854e33 | − | 8.84854e33i | 0.574570 | − | 0.574570i | −0.358832 | − | 0.933402i | \(-0.616825\pi\) |
0.933402 | + | 0.358832i | \(0.116825\pi\) | |||||||
\(138\) | 3.48768e33 | + | 3.48768e33i | 0.201591 | + | 0.201591i | ||||
\(139\) | 2.75003e33i | 0.141612i | 0.997490 | + | 0.0708062i | \(0.0225572\pi\) | ||||
−0.997490 | + | 0.0708062i | \(0.977443\pi\) | |||||||
\(140\) | −1.20571e34 | + | 5.53061e33i | −0.553598 | + | 0.253936i | ||||
\(141\) | −2.49646e32 | −0.0102286 | ||||||||
\(142\) | −6.65768e33 | + | 6.65768e33i | −0.243618 | + | 0.243618i | ||||
\(143\) | −1.96918e33 | − | 1.96918e33i | −0.0644035 | − | 0.0644035i | ||||
\(144\) | − | 5.52121e33i | − | 0.161523i | ||||||
\(145\) | 4.44695e34 | + | 1.65019e34i | 1.16459 | + | 0.432161i | ||||
\(146\) | 2.71410e34 | 0.636767 | ||||||||
\(147\) | 7.57179e33 | − | 7.57179e33i | 0.159265 | − | 0.159265i | ||||
\(148\) | 6.17854e33 | + | 6.17854e33i | 0.116600 | + | 0.116600i | ||||
\(149\) | 5.11997e34i | 0.867535i | 0.901025 | + | 0.433768i | \(0.142816\pi\) | ||||
−0.901025 | + | 0.433768i | \(0.857184\pi\) | |||||||
\(150\) | −1.87146e34 | − | 1.61074e34i | −0.284919 | − | 0.245225i | ||||
\(151\) | 6.98984e34 | 0.956834 | 0.478417 | − | 0.878133i | \(-0.341211\pi\) | ||||
0.478417 | + | 0.878133i | \(0.341211\pi\) | |||||||
\(152\) | −1.16053e35 | + | 1.16053e35i | −1.42942 | + | 1.42942i | ||||
\(153\) | 2.53912e34 | + | 2.53912e34i | 0.281592 | + | 0.281592i | ||||
\(154\) | 1.19352e35i | 1.19261i | ||||||||
\(155\) | 7.03274e34 | − | 1.89519e35i | 0.633603 | − | 1.70744i | ||||
\(156\) | 2.15115e33 | 0.0174855 | ||||||||
\(157\) | 1.38018e35 | − | 1.38018e35i | 1.01284 | − | 1.01284i | 0.0129212 | − | 0.999917i | \(-0.495887\pi\) |
0.999917 | − | 0.0129212i | \(-0.00411308\pi\) | |||||||
\(158\) | −9.02952e34 | − | 9.02952e34i | −0.598620 | − | 0.598620i | ||||
\(159\) | − | 1.31840e35i | − | 0.790119i | ||||||
\(160\) | 6.90384e34 | + | 1.50508e35i | 0.374258 | + | 0.815908i | ||||
\(161\) | −1.84109e35 | −0.903360 | ||||||||
\(162\) | −2.40373e34 | + | 2.40373e34i | −0.106818 | + | 0.106818i | ||||
\(163\) | −4.45237e34 | − | 4.45237e34i | −0.179304 | − | 0.179304i | 0.611748 | − | 0.791052i | \(-0.290466\pi\) |
−0.791052 | + | 0.611748i | \(0.790466\pi\) | |||||||
\(164\) | 7.96614e34i | 0.290902i | ||||||||
\(165\) | 2.11289e35 | − | 9.69185e34i | 0.700058 | − | 0.321117i | ||||
\(166\) | −4.18460e35 | −1.25871 | ||||||||
\(167\) | −4.43644e35 | + | 4.43644e35i | −1.21219 | + | 1.21219i | −0.241885 | + | 0.970305i | \(0.577766\pi\) |
−0.970305 | + | 0.241885i | \(0.922234\pi\) | |||||||
\(168\) | −1.92686e35 | − | 1.92686e35i | −0.478522 | − | 0.478522i | ||||
\(169\) | − | 4.40989e35i | − | 0.995956i | ||||||
\(170\) | 1.78671e35 | + | 6.63017e34i | 0.367173 | + | 0.136252i | ||||
\(171\) | 7.26953e35 | 1.36009 | ||||||||
\(172\) | −2.51545e35 | + | 2.51545e35i | −0.428707 | + | 0.428707i | ||||
\(173\) | −6.34231e35 | − | 6.34231e35i | −0.985166 | − | 0.985166i | 0.0147254 | − | 0.999892i | \(-0.495313\pi\) |
−0.999892 | + | 0.0147254i | \(0.995313\pi\) | |||||||
\(174\) | 3.29663e35i | 0.466962i | ||||||||
\(175\) | 9.19100e35 | − | 6.88163e34i | 1.18783 | − | 0.0889370i | ||||
\(176\) | 2.75863e35 | 0.325455 | ||||||||
\(177\) | −5.90168e34 | + | 5.90168e34i | −0.0635921 | + | 0.0635921i | ||||
\(178\) | −2.42609e35 | − | 2.42609e35i | −0.238884 | − | 0.238884i | ||||
\(179\) | 1.03505e36i | 0.931778i | 0.884843 | + | 0.465889i | \(0.154265\pi\) | ||||
−0.884843 | + | 0.465889i | \(0.845735\pi\) | |||||||
\(180\) | 1.53558e35 | − | 4.13810e35i | 0.126448 | − | 0.340754i | ||||
\(181\) | 1.07795e36 | 0.812345 | 0.406173 | − | 0.913796i | \(-0.366863\pi\) | ||||
0.406173 | + | 0.913796i | \(0.366863\pi\) | |||||||
\(182\) | 5.42641e34 | − | 5.42641e34i | 0.0374430 | − | 0.0374430i | ||||
\(183\) | −1.80776e35 | − | 1.80776e35i | −0.114268 | − | 0.114268i | ||||
\(184\) | 1.38308e36i | 0.801238i | ||||||||
\(185\) | −2.53124e35 | − | 5.51827e35i | −0.134457 | − | 0.293127i | ||||
\(186\) | 1.40495e36 | 0.684627 | ||||||||
\(187\) | −1.26865e36 | + | 1.26865e36i | −0.567384 | + | 0.567384i | ||||
\(188\) | −1.67471e34 | − | 1.67471e34i | −0.00687725 | − | 0.00687725i | ||||
\(189\) | 2.90498e36i | 1.09586i | ||||||||
\(190\) | 3.50680e36 | − | 1.60857e36i | 1.21577 | − | 0.557677i | ||||
\(191\) | 8.12751e35 | 0.259074 | 0.129537 | − | 0.991575i | \(-0.458651\pi\) | ||||
0.129537 | + | 0.991575i | \(0.458651\pi\) | |||||||
\(192\) | −1.10846e36 | + | 1.10846e36i | −0.325013 | + | 0.325013i | ||||
\(193\) | −4.31422e36 | − | 4.31422e36i | −1.16409 | − | 1.16409i | −0.983573 | − | 0.180513i | \(-0.942224\pi\) |
−0.180513 | − | 0.983573i | \(-0.557776\pi\) | |||||||
\(194\) | 7.39492e35i | 0.183699i | ||||||||
\(195\) | −1.40128e35 | − | 5.19991e34i | −0.0320606 | − | 0.0118971i | ||||
\(196\) | 1.01589e36 | 0.214165 | ||||||||
\(197\) | −1.43332e36 | + | 1.43332e36i | −0.278537 | + | 0.278537i | −0.832525 | − | 0.553988i | \(-0.813105\pi\) |
0.553988 | + | 0.832525i | \(0.313105\pi\) | |||||||
\(198\) | −2.80816e36 | − | 2.80816e36i | −0.503245 | − | 0.503245i | ||||
\(199\) | 1.40811e36i | 0.232803i | 0.993202 | + | 0.116401i | \(0.0371359\pi\) | ||||
−0.993202 | + | 0.116401i | \(0.962864\pi\) | |||||||
\(200\) | −5.16967e35 | − | 6.90454e36i | −0.0788830 | − | 1.05355i | ||||
\(201\) | 1.94573e35 | 0.0274123 | ||||||||
\(202\) | −1.08432e36 | + | 1.08432e36i | −0.141103 | + | 0.141103i | ||||
\(203\) | −8.70118e36 | − | 8.70118e36i | −1.04626 | − | 1.04626i | ||||
\(204\) | − | 1.38589e36i | − | 0.154044i | ||||||
\(205\) | 1.92563e36 | − | 5.18921e36i | 0.197929 | − | 0.533383i | ||||
\(206\) | −7.47177e36 | −0.710474 | ||||||||
\(207\) | 4.33178e36 | − | 4.33178e36i | 0.381189 | − | 0.381189i | ||||
\(208\) | −1.25422e35 | − | 1.25422e35i | −0.0102179 | − | 0.0102179i | ||||
\(209\) | 3.63217e37i | 2.74047i | ||||||||
\(210\) | 2.67075e36 | + | 5.82243e36i | 0.186692 | + | 0.407001i | ||||
\(211\) | 1.39821e37 | 0.905843 | 0.452922 | − | 0.891550i | \(-0.350382\pi\) | ||||
0.452922 | + | 0.891550i | \(0.350382\pi\) | |||||||
\(212\) | 8.84429e36 | − | 8.84429e36i | 0.531238 | − | 0.531238i | ||||
\(213\) | −3.36396e36 | − | 3.36396e36i | −0.187403 | − | 0.187403i | ||||
\(214\) | − | 7.00537e35i | − | 0.0362085i | ||||||
\(215\) | 2.24664e37 | − | 1.03054e37i | 1.07775 | − | 0.494365i | ||||
\(216\) | 2.18230e37 | 0.971974 | ||||||||
\(217\) | −3.70825e37 | + | 3.70825e37i | −1.53396 | + | 1.53396i | ||||
\(218\) | −6.75286e36 | − | 6.75286e36i | −0.259528 | − | 0.259528i | ||||
\(219\) | 1.37137e37i | 0.489834i | ||||||||
\(220\) | 2.06757e37 | + | 7.67239e36i | 0.686589 | + | 0.254782i | ||||
\(221\) | 1.15360e36 | 0.0356269 | ||||||||
\(222\) | 2.98364e36 | − | 2.98364e36i | 0.0857233 | − | 0.0857233i | ||||
\(223\) | 8.71285e36 | + | 8.71285e36i | 0.232961 | + | 0.232961i | 0.813927 | − | 0.580967i | \(-0.197325\pi\) |
−0.580967 | + | 0.813927i | \(0.697325\pi\) | |||||||
\(224\) | − | 4.29579e37i | − | 1.06924i | ||||||
\(225\) | −2.00058e37 | + | 2.32440e37i | −0.463697 | + | 0.538755i | ||||
\(226\) | 2.13948e37 | 0.461927 | ||||||||
\(227\) | −1.47224e36 | + | 1.47224e36i | −0.0296187 | + | 0.0296187i | −0.721761 | − | 0.692142i | \(-0.756667\pi\) |
0.692142 | + | 0.721761i | \(0.256667\pi\) | |||||||
\(228\) | −1.98391e37 | − | 1.98391e37i | −0.372018 | − | 0.372018i | ||||
\(229\) | − | 9.78900e37i | − | 1.71147i | −0.517411 | − | 0.855737i | \(-0.673104\pi\) | ||
0.517411 | − | 0.855737i | \(-0.326896\pi\) | |||||||
\(230\) | 1.13112e37 | − | 3.04815e37i | 0.184443 | − | 0.497040i | ||||
\(231\) | −6.03058e37 | −0.917419 | ||||||||
\(232\) | −6.53658e37 | + | 6.53658e37i | −0.927988 | + | 0.927988i | ||||
\(233\) | 3.72355e37 | + | 3.72355e37i | 0.493472 | + | 0.493472i | 0.909398 | − | 0.415926i | \(-0.136543\pi\) |
−0.415926 | + | 0.909398i | \(0.636543\pi\) | |||||||
\(234\) | 2.55349e36i | 0.0315995i | ||||||||
\(235\) | 6.86100e35 | + | 1.49575e36i | 0.00793052 | + | 0.0172891i | ||||
\(236\) | −7.91812e36 | −0.0855126 | ||||||||
\(237\) | 4.56240e37 | − | 4.56240e37i | 0.460489 | − | 0.460489i | ||||
\(238\) | −3.49598e37 | − | 3.49598e37i | −0.329866 | − | 0.329866i | ||||
\(239\) | 1.42634e38i | 1.25851i | 0.777200 | + | 0.629254i | \(0.216639\pi\) | ||||
−0.777200 | + | 0.629254i | \(0.783361\pi\) | |||||||
\(240\) | 1.34576e37 | − | 6.17300e36i | 0.111067 | − | 0.0509467i | ||||
\(241\) | −1.34374e38 | −1.03763 | −0.518816 | − | 0.854886i | \(-0.673627\pi\) | ||||
−0.518816 | + | 0.854886i | \(0.673627\pi\) | |||||||
\(242\) | 7.19098e37 | − | 7.19098e37i | 0.519687 | − | 0.519687i | ||||
\(243\) | −1.08300e38 | − | 1.08300e38i | −0.732706 | − | 0.732706i | ||||
\(244\) | − | 2.42542e37i | − | 0.153656i | ||||||
\(245\) | −6.61757e37 | − | 2.45567e37i | −0.392682 | − | 0.145718i | ||||
\(246\) | 3.84688e37 | 0.213869 | ||||||||
\(247\) | 1.65138e37 | − | 1.65138e37i | 0.0860392 | − | 0.0860392i | ||||
\(248\) | 2.78575e38 | + | 2.78575e38i | 1.36055 | + | 1.36055i | ||||
\(249\) | − | 2.11438e38i | − | 0.968262i | ||||||
\(250\) | −4.50737e37 | + | 1.56396e38i | −0.193590 | + | 0.671717i | ||||
\(251\) | 1.65643e38 | 0.667412 | 0.333706 | − | 0.942677i | \(-0.391701\pi\) | ||||
0.333706 | + | 0.942677i | \(0.391701\pi\) | |||||||
\(252\) | −8.09685e37 | + | 8.09685e37i | −0.306131 | + | 0.306131i | ||||
\(253\) | 2.16434e38 | + | 2.16434e38i | 0.768063 | + | 0.768063i | ||||
\(254\) | − | 1.45151e38i | − | 0.483594i | ||||||
\(255\) | −3.35006e37 | + | 9.02780e37i | −0.104812 | + | 0.282448i | ||||
\(256\) | −3.62249e38 | −1.06455 | ||||||||
\(257\) | 4.24543e38 | − | 4.24543e38i | 1.17217 | − | 1.17217i | 0.190481 | − | 0.981691i | \(-0.438995\pi\) |
0.981691 | − | 0.190481i | \(-0.0610047\pi\) | |||||||
\(258\) | 1.21472e38 | + | 1.21472e38i | 0.315182 | + | 0.315182i | ||||
\(259\) | 1.57502e38i | 0.384139i | ||||||||
\(260\) | −5.91201e36 | − | 1.28886e37i | −0.0135569 | − | 0.0295550i | ||||
\(261\) | 4.09449e38 | 0.882981 | ||||||||
\(262\) | 9.25799e37 | − | 9.25799e37i | 0.187800 | − | 0.187800i | ||||
\(263\) | 1.35866e38 | + | 1.35866e38i | 0.259310 | + | 0.259310i | 0.824774 | − | 0.565463i | \(-0.191303\pi\) |
−0.565463 | + | 0.824774i | \(0.691303\pi\) | |||||||
\(264\) | 4.53035e38i | 0.813708i | ||||||||
\(265\) | −7.89915e38 | + | 3.62335e38i | −1.33551 | + | 0.612599i | ||||
\(266\) | −1.00090e39 | −1.59326 | ||||||||
\(267\) | 1.22584e38 | − | 1.22584e38i | 0.183762 | − | 0.183762i | ||||
\(268\) | 1.30527e37 | + | 1.30527e37i | 0.0184307 | + | 0.0184307i | ||||
\(269\) | − | 5.16100e38i | − | 0.686589i | −0.939228 | − | 0.343295i | \(-0.888457\pi\) | ||
0.939228 | − | 0.343295i | \(-0.111543\pi\) | |||||||
\(270\) | −4.80955e38 | − | 1.78474e38i | −0.602954 | − | 0.223746i | ||||
\(271\) | 9.80770e38 | 1.15893 | 0.579467 | − | 0.814996i | \(-0.303261\pi\) | ||||
0.579467 | + | 0.814996i | \(0.303261\pi\) | |||||||
\(272\) | −8.08038e37 | + | 8.08038e37i | −0.0900180 | + | 0.0900180i | ||||
\(273\) | 2.74183e37 | + | 2.74183e37i | 0.0288030 | + | 0.0288030i | ||||
\(274\) | − | 5.73297e38i | − | 0.568029i | ||||||
\(275\) | −1.16137e39 | − | 9.99573e38i | −1.08554 | − | 0.934311i | ||||
\(276\) | −2.36435e38 | −0.208529 | ||||||||
\(277\) | 8.24199e38 | − | 8.24199e38i | 0.686050 | − | 0.686050i | −0.275306 | − | 0.961357i | \(-0.588779\pi\) |
0.961357 | + | 0.275306i | \(0.0887793\pi\) | |||||||
\(278\) | 8.90873e37 | + | 8.90873e37i | 0.0700001 | + | 0.0700001i | ||||
\(279\) | − | 1.74498e39i | − | 1.29456i | ||||||
\(280\) | −6.24916e38 | + | 1.68403e39i | −0.437818 | + | 1.17984i | ||||
\(281\) | −3.51609e38 | −0.232680 | −0.116340 | − | 0.993209i | \(-0.537116\pi\) | ||||
−0.116340 | + | 0.993209i | \(0.537116\pi\) | |||||||
\(282\) | −8.08726e36 | + | 8.08726e36i | −0.00505610 | + | 0.00505610i | ||||
\(283\) | −2.64479e38 | − | 2.64479e38i | −0.156246 | − | 0.156246i | 0.624655 | − | 0.780901i | \(-0.285240\pi\) |
−0.780901 | + | 0.624655i | \(0.785240\pi\) | |||||||
\(284\) | − | 4.51333e38i | − | 0.252002i | ||||||
\(285\) | 8.12772e38 | + | 1.77190e39i | 0.428994 | + | 0.935236i | ||||
\(286\) | −1.27583e38 | −0.0636703 | ||||||||
\(287\) | −1.01535e39 | + | 1.01535e39i | −0.479189 | + | 0.479189i | ||||
\(288\) | 1.01073e39 | + | 1.01073e39i | 0.451185 | + | 0.451185i | ||||
\(289\) | 1.62470e39i | 0.686133i | ||||||||
\(290\) | 1.97517e39 | − | 9.06011e38i | 0.789288 | − | 0.362047i | ||||
\(291\) | −3.73647e38 | −0.141310 | ||||||||
\(292\) | −9.19965e38 | + | 9.19965e38i | −0.329341 | + | 0.329341i | ||||
\(293\) | 2.42303e39 | + | 2.42303e39i | 0.821252 | + | 0.821252i | 0.986288 | − | 0.165036i | \(-0.0527740\pi\) |
−0.165036 | + | 0.986288i | \(0.552774\pi\) | |||||||
\(294\) | − | 4.90576e38i | − | 0.157452i | ||||||
\(295\) | 5.15793e38 | + | 1.91402e38i | 0.156792 | + | 0.0581828i | ||||
\(296\) | 1.18320e39 | 0.340714 | ||||||||
\(297\) | 3.41502e39 | − | 3.41502e39i | 0.931730 | − | 0.931730i | ||||
\(298\) | 1.65861e39 | + | 1.65861e39i | 0.428830 | + | 0.428830i | ||||
\(299\) | − | 1.96805e38i | − | 0.0482279i | ||||||
\(300\) | 1.18032e39 | − | 8.83746e37i | 0.274195 | − | 0.0205299i | ||||
\(301\) | −6.41232e39 | −1.41238 | ||||||||
\(302\) | 2.26436e39 | − | 2.26436e39i | 0.472970 | − | 0.472970i | ||||
\(303\) | −5.47882e38 | − | 5.47882e38i | −0.108544 | − | 0.108544i | ||||
\(304\) | 2.31342e39i | 0.434788i | ||||||||
\(305\) | −5.86289e38 | + | 1.57994e39i | −0.104548 | + | 0.281737i | ||||
\(306\) | 1.64509e39 | 0.278386 | ||||||||
\(307\) | −6.42505e39 | + | 6.42505e39i | −1.03196 | + | 1.03196i | −0.0324874 | + | 0.999472i | \(0.510343\pi\) |
−0.999472 | + | 0.0324874i | \(0.989657\pi\) | |||||||
\(308\) | −4.04553e39 | − | 4.04553e39i | −0.616828 | − | 0.616828i | ||||
\(309\) | − | 3.77530e39i | − | 0.546532i | ||||||
\(310\) | −3.86122e39 | − | 8.41772e39i | −0.530808 | − | 1.15720i | ||||
\(311\) | −3.91789e38 | −0.0511547 | −0.0255773 | − | 0.999673i | \(-0.508142\pi\) | ||||
−0.0255773 | + | 0.999673i | \(0.508142\pi\) | |||||||
\(312\) | 2.05974e38 | − | 2.05974e38i | 0.0255470 | − | 0.0255470i | ||||
\(313\) | −3.75829e39 | − | 3.75829e39i | −0.442875 | − | 0.442875i | 0.450102 | − | 0.892977i | \(-0.351388\pi\) |
−0.892977 | + | 0.450102i | \(0.851388\pi\) | |||||||
\(314\) | − | 8.94215e39i | − | 1.00131i | ||||||
\(315\) | 7.23159e39 | − | 3.31714e39i | 0.769599 | − | 0.353016i | ||||
\(316\) | 6.12124e39 | 0.619222 | ||||||||
\(317\) | −8.45248e39 | + | 8.45248e39i | −0.812897 | + | 0.812897i | −0.985067 | − | 0.172170i | \(-0.944922\pi\) |
0.172170 | + | 0.985067i | \(0.444922\pi\) | |||||||
\(318\) | −4.27095e39 | − | 4.27095e39i | −0.390562 | − | 0.390562i | ||||
\(319\) | 2.04578e40i | 1.77913i | ||||||||
\(320\) | 9.68768e39 | + | 3.59493e39i | 0.801346 | + | 0.297366i | ||||
\(321\) | 3.53964e38 | 0.0278534 | ||||||||
\(322\) | −5.96420e39 | + | 5.96420e39i | −0.446538 | + | 0.446538i | ||||
\(323\) | −1.06391e40 | − | 1.06391e40i | −0.757991 | − | 0.757991i | ||||
\(324\) | − | 1.62952e39i | − | 0.110494i | ||||||
\(325\) | 7.35620e37 | + | 9.82483e38i | 0.00474810 | + | 0.0634149i | ||||
\(326\) | −2.88469e39 | −0.177263 | ||||||||
\(327\) | 3.41205e39 | − | 3.41205e39i | 0.199642 | − | 0.199642i | ||||
\(328\) | 7.62762e39 | + | 7.62762e39i | 0.425018 | + | 0.425018i | ||||
\(329\) | − | 4.26913e38i | − | 0.0226571i | ||||||
\(330\) | 3.70503e39 | − | 9.98438e39i | 0.187313 | − | 0.504775i | ||||
\(331\) | 2.00066e40 | 0.963664 | 0.481832 | − | 0.876264i | \(-0.339972\pi\) | ||||
0.481832 | + | 0.876264i | \(0.339972\pi\) | |||||||
\(332\) | 1.41840e40 | − | 1.41840e40i | 0.651013 | − | 0.651013i | ||||
\(333\) | −3.70575e39 | − | 3.70575e39i | −0.162095 | − | 0.162095i | ||||
\(334\) | 2.87436e40i | 1.19839i | ||||||||
\(335\) | −5.34745e38 | − | 1.16578e39i | −0.0212535 | − | 0.0463340i | ||||
\(336\) | −3.84103e39 | −0.145553 | ||||||||
\(337\) | −2.16825e40 | + | 2.16825e40i | −0.783484 | + | 0.783484i | −0.980417 | − | 0.196933i | \(-0.936902\pi\) |
0.196933 | + | 0.980417i | \(0.436902\pi\) | |||||||
\(338\) | −1.42858e40 | − | 1.42858e40i | −0.492309 | − | 0.492309i | ||||
\(339\) | 1.08103e40i | 0.355338i | ||||||||
\(340\) | −8.30352e39 | + | 3.80883e39i | −0.260375 | + | 0.119434i | ||||
\(341\) | 8.71866e40 | 2.60843 | ||||||||
\(342\) | 2.35496e40 | − | 2.35496e40i | 0.672305 | − | 0.672305i | ||||
\(343\) | −1.79659e40 | − | 1.79659e40i | −0.489489 | − | 0.489489i | ||||
\(344\) | 4.81712e40i | 1.25272i | ||||||||
\(345\) | 1.54016e40 | + | 5.71525e39i | 0.382348 | + | 0.141883i | ||||
\(346\) | −4.10917e40 | −0.973951 | ||||||||
\(347\) | −5.54293e39 | + | 5.54293e39i | −0.125449 | + | 0.125449i | −0.767044 | − | 0.641595i | \(-0.778273\pi\) |
0.641595 | + | 0.767044i | \(0.278273\pi\) | |||||||
\(348\) | −1.11741e40 | − | 1.11741e40i | −0.241516 | − | 0.241516i | ||||
\(349\) | 7.66016e39i | 0.158136i | 0.996869 | + | 0.0790681i | \(0.0251944\pi\) | ||||
−0.996869 | + | 0.0790681i | \(0.974806\pi\) | |||||||
\(350\) | 2.75449e40 | − | 3.20035e40i | 0.543191 | − | 0.631115i | ||||
\(351\) | −3.10531e39 | −0.0585047 | ||||||||
\(352\) | −5.05003e40 | + | 5.05003e40i | −0.909099 | + | 0.909099i | ||||
\(353\) | −5.44550e40 | − | 5.44550e40i | −0.936791 | − | 0.936791i | 0.0613271 | − | 0.998118i | \(-0.480467\pi\) |
−0.998118 | + | 0.0613271i | \(0.980467\pi\) | |||||||
\(354\) | 3.82369e39i | 0.0628682i | ||||||||
\(355\) | −1.09099e40 | + | 2.94003e40i | −0.171462 | + | 0.462059i | ||||
\(356\) | 1.64468e40 | 0.247105 | ||||||||
\(357\) | 1.76643e40 | − | 1.76643e40i | 0.253750 | − | 0.253750i | ||||
\(358\) | 3.35304e40 | + | 3.35304e40i | 0.460585 | + | 0.460585i | ||||
\(359\) | − | 1.11374e41i | − | 1.46310i | −0.681788 | − | 0.731549i | \(-0.738798\pi\) | ||
0.681788 | − | 0.731549i | \(-0.261202\pi\) | |||||||
\(360\) | −2.49193e40 | − | 5.43257e40i | −0.313109 | − | 0.682599i | ||||
\(361\) | −2.21400e41 | −2.66111 | ||||||||
\(362\) | 3.49201e40 | − | 3.49201e40i | 0.401549 | − | 0.401549i | ||||
\(363\) | 3.63342e40 | + | 3.63342e40i | 0.399770 | + | 0.399770i | ||||
\(364\) | 3.67864e39i | 0.0387316i | ||||||||
\(365\) | 8.21653e40 | − | 3.76893e40i | 0.827947 | − | 0.379780i | ||||
\(366\) | −1.17125e40 | −0.112967 | ||||||||
\(367\) | −2.71316e40 | + | 2.71316e40i | −0.250506 | + | 0.250506i | −0.821178 | − | 0.570672i | \(-0.806683\pi\) |
0.570672 | + | 0.821178i | \(0.306683\pi\) | |||||||
\(368\) | 1.37852e40 | + | 1.37852e40i | 0.121857 | + | 0.121857i | ||||
\(369\) | − | 4.77791e40i | − | 0.404405i | ||||||
\(370\) | −2.60763e40 | − | 9.67648e39i | −0.211358 | − | 0.0784314i | ||||
\(371\) | 2.25456e41 | 1.75017 | ||||||||
\(372\) | −4.76218e40 | + | 4.76218e40i | −0.354094 | + | 0.354094i | ||||
\(373\) | 4.57036e40 | + | 4.57036e40i | 0.325544 | + | 0.325544i | 0.850889 | − | 0.525345i | \(-0.176064\pi\) |
−0.525345 | + | 0.850889i | \(0.676064\pi\) | |||||||
\(374\) | 8.21959e40i | 0.560925i | ||||||||
\(375\) | −7.90232e40 | − | 2.27746e40i | −0.516719 | − | 0.148919i | ||||
\(376\) | −3.20709e39 | −0.0200958 | ||||||||
\(377\) | 9.30123e39 | − | 9.30123e39i | 0.0558572 | − | 0.0558572i | ||||
\(378\) | 9.41066e40 | + | 9.41066e40i | 0.541691 | + | 0.541691i | ||||
\(379\) | − | 2.82235e40i | − | 0.155734i | −0.996964 | − | 0.0778670i | \(-0.975189\pi\) | ||
0.996964 | − | 0.0778670i | \(-0.0248110\pi\) | |||||||
\(380\) | −6.43417e40 | + | 1.73389e41i | −0.340373 | + | 0.917242i | ||||
\(381\) | 7.33413e40 | 0.372005 | ||||||||
\(382\) | 2.63290e40 | − | 2.63290e40i | 0.128062 | − | 0.128062i | ||||
\(383\) | 1.47851e41 | + | 1.47851e41i | 0.689672 | + | 0.689672i | 0.962159 | − | 0.272488i | \(-0.0878464\pi\) |
−0.272488 | + | 0.962159i | \(0.587846\pi\) | |||||||
\(384\) | − | 3.60744e40i | − | 0.161399i | ||||||
\(385\) | 1.65738e41 | + | 3.61321e41i | 0.711297 | + | 1.55068i | ||||
\(386\) | −2.79518e41 | −1.15083 | ||||||||
\(387\) | 1.50871e41 | − | 1.50871e41i | 0.595979 | − | 0.595979i | ||||
\(388\) | −2.50656e40 | − | 2.50656e40i | −0.0950103 | − | 0.0950103i | ||||
\(389\) | − | 4.07964e41i | − | 1.48398i | −0.670411 | − | 0.741990i | \(-0.733882\pi\) | ||
0.670411 | − | 0.741990i | \(-0.266118\pi\) | |||||||
\(390\) | −6.22395e39 | + | 2.85493e39i | −0.0217286 | + | 0.00996695i | ||||
\(391\) | −1.26793e41 | −0.424879 | ||||||||
\(392\) | 9.72717e40 | − | 9.72717e40i | 0.312903 | − | 0.312903i | ||||
\(393\) | 4.67784e40 | + | 4.67784e40i | 0.144466 | + | 0.144466i | ||||
\(394\) | 9.28645e40i | 0.275366i | ||||||||
\(395\) | −3.98743e41 | − | 1.47967e41i | −1.13538 | − | 0.421318i | ||||
\(396\) | 1.90369e41 | 0.520564 | ||||||||
\(397\) | −7.65956e40 | + | 7.65956e40i | −0.201166 | + | 0.201166i | −0.800500 | − | 0.599333i | \(-0.795432\pi\) |
0.599333 | + | 0.800500i | \(0.295432\pi\) | |||||||
\(398\) | 4.56158e40 | + | 4.56158e40i | 0.115076 | + | 0.115076i | ||||
\(399\) | − | 5.05732e41i | − | 1.22562i | ||||||
\(400\) | −7.39707e40 | − | 6.36654e40i | −0.172226 | − | 0.148233i | ||||
\(401\) | −2.61119e41 | −0.584156 | −0.292078 | − | 0.956394i | \(-0.594347\pi\) | ||||
−0.292078 | + | 0.956394i | \(0.594347\pi\) | |||||||
\(402\) | 6.30319e39 | − | 6.30319e39i | 0.0135501 | − | 0.0135501i | ||||
\(403\) | −3.96398e40 | − | 3.96398e40i | −0.0818937 | − | 0.0818937i | ||||
\(404\) | − | 7.35078e40i | − | 0.145959i | ||||||
\(405\) | −3.93899e40 | + | 1.06149e41i | −0.0751804 | + | 0.202597i | ||||
\(406\) | −5.63749e41 | −1.03435 | ||||||||
\(407\) | 1.85155e41 | − | 1.85155e41i | 0.326607 | − | 0.326607i | ||||
\(408\) | −1.32700e41 | − | 1.32700e41i | −0.225065 | − | 0.225065i | ||||
\(409\) | 4.82412e41i | 0.786765i | 0.919375 | + | 0.393382i | \(0.128695\pi\) | ||||
−0.919375 | + | 0.393382i | \(0.871305\pi\) | |||||||
\(410\) | −1.05724e41 | − | 2.30485e41i | −0.165818 | − | 0.361494i | ||||
\(411\) | 2.89673e41 | 0.436957 | ||||||||
\(412\) | 2.53261e41 | − | 2.53261e41i | 0.367462 | − | 0.367462i | ||||
\(413\) | −1.00923e41 | − | 1.00923e41i | −0.140861 | − | 0.140861i | ||||
\(414\) | − | 2.80655e41i | − | 0.376850i | ||||||
\(415\) | −1.26682e42 | + | 5.81093e41i | −1.63662 | + | 0.750717i | ||||
\(416\) | 4.59203e40 | 0.0570837 | ||||||||
\(417\) | −4.50136e40 | + | 4.50136e40i | −0.0538477 | + | 0.0538477i | ||||
\(418\) | 1.17664e42 | + | 1.17664e42i | 1.35464 | + | 1.35464i | ||||
\(419\) | 1.61600e42i | 1.79068i | 0.445382 | + | 0.895340i | \(0.353068\pi\) | ||||
−0.445382 | + | 0.895340i | \(0.646932\pi\) | |||||||
\(420\) | −2.87882e41 | − | 1.06828e41i | −0.307062 | − | 0.113945i | ||||
\(421\) | 1.66314e42 | 1.70771 | 0.853855 | − | 0.520510i | \(-0.174258\pi\) | ||||
0.853855 | + | 0.520510i | \(0.174258\pi\) | |||||||
\(422\) | 4.52950e41 | − | 4.52950e41i | 0.447766 | − | 0.447766i | ||||
\(423\) | 1.00446e40 | + | 1.00446e40i | 0.00956060 | + | 0.00956060i | ||||
\(424\) | − | 1.69369e42i | − | 1.55232i | ||||||
\(425\) | 6.32968e41 | − | 4.73925e40i | 0.558674 | − | 0.0418299i | ||||
\(426\) | −2.17951e41 | −0.185270 | ||||||||
\(427\) | 3.09141e41 | − | 3.09141e41i | 0.253111 | − | 0.253111i | ||||
\(428\) | 2.37452e40 | + | 2.37452e40i | 0.0187273 | + | 0.0187273i | ||||
\(429\) | − | 6.44646e40i | − | 0.0489784i | ||||||
\(430\) | 3.93956e41 | − | 1.06164e42i | 0.288372 | − | 0.777109i | ||||
\(431\) | −1.67697e42 | −1.18274 | −0.591371 | − | 0.806400i | \(-0.701413\pi\) | ||||
−0.591371 | + | 0.806400i | \(0.701413\pi\) | |||||||
\(432\) | 2.17512e41 | − | 2.17512e41i | 0.147823 | − | 0.147823i | ||||
\(433\) | −1.80217e41 | − | 1.80217e41i | −0.118029 | − | 0.118029i | 0.645625 | − | 0.763654i | \(-0.276597\pi\) |
−0.763654 | + | 0.645625i | \(0.776597\pi\) | |||||||
\(434\) | 2.40257e42i | 1.51650i | ||||||||
\(435\) | 4.57785e41 | + | 9.98003e41i | 0.278505 | + | 0.607161i | ||||
\(436\) | 4.57786e41 | 0.268459 | ||||||||
\(437\) | −1.81504e42 | + | 1.81504e42i | −1.02609 | + | 1.02609i | ||||
\(438\) | 4.44255e41 | + | 4.44255e41i | 0.242129 | + | 0.242129i | ||||
\(439\) | − | 1.16767e41i | − | 0.0613602i | −0.999529 | − | 0.0306801i | \(-0.990233\pi\) | ||
0.999529 | − | 0.0306801i | \(-0.00976731\pi\) | |||||||
\(440\) | 2.71435e42 | − | 1.24507e42i | 1.37538 | − | 0.630888i | ||||
\(441\) | −6.09306e41 | −0.297727 | ||||||||
\(442\) | 3.73707e40 | − | 3.73707e40i | 0.0176106 | − | 0.0176106i | ||||
\(443\) | −1.81550e42 | − | 1.81550e42i | −0.825157 | − | 0.825157i | 0.161685 | − | 0.986842i | \(-0.448307\pi\) |
−0.986842 | + | 0.161685i | \(0.948307\pi\) | |||||||
\(444\) | 2.02265e41i | 0.0886735i | ||||||||
\(445\) | −1.07136e42 | − | 3.97563e41i | −0.453080 | − | 0.168130i | ||||
\(446\) | 5.64505e41 | 0.230308 | ||||||||
\(447\) | −8.38056e41 | + | 8.38056e41i | −0.329878 | + | 0.329878i | ||||
\(448\) | −1.89555e42 | − | 1.89555e42i | −0.719925 | − | 0.719925i | ||||
\(449\) | − | 3.40343e42i | − | 1.24731i | −0.781699 | − | 0.623656i | \(-0.785647\pi\) | ||
0.781699 | − | 0.623656i | \(-0.214353\pi\) | |||||||
\(450\) | 1.04903e41 | + | 1.40108e42i | 0.0371013 | + | 0.495520i | ||||
\(451\) | 2.38725e42 | 0.814841 | ||||||||
\(452\) | −7.25192e41 | + | 7.25192e41i | −0.238912 | + | 0.238912i | ||||
\(453\) | 1.14412e42 | + | 1.14412e42i | 0.363833 | + | 0.363833i | ||||
\(454\) | 9.53864e40i | 0.0292815i | ||||||||
\(455\) | 8.89225e40 | − | 2.39630e41i | 0.0263530 | − | 0.0710164i | ||||
\(456\) | −3.79921e42 | −1.08707 | ||||||||
\(457\) | 1.14100e42 | − | 1.14100e42i | 0.315228 | − | 0.315228i | −0.531703 | − | 0.846931i | \(-0.678448\pi\) |
0.846931 | + | 0.531703i | \(0.178448\pi\) | |||||||
\(458\) | −3.17114e42 | − | 3.17114e42i | −0.845995 | − | 0.845995i | ||||
\(459\) | 2.00061e42i | 0.515417i | ||||||||
\(460\) | 6.49792e41 | + | 1.41659e42i | 0.161677 | + | 0.352468i | ||||
\(461\) | 1.04524e42 | 0.251190 | 0.125595 | − | 0.992082i | \(-0.459916\pi\) | ||||
0.125595 | + | 0.992082i | \(0.459916\pi\) | |||||||
\(462\) | −1.95360e42 | + | 1.95360e42i | −0.453487 | + | 0.453487i | ||||
\(463\) | −5.26250e42 | − | 5.26250e42i | −1.18004 | − | 1.18004i | −0.979734 | − | 0.200305i | \(-0.935807\pi\) |
−0.200305 | − | 0.979734i | \(-0.564193\pi\) | |||||||
\(464\) | 1.30301e42i | 0.282267i | ||||||||
\(465\) | 4.25327e42 | − | 1.95098e42i | 0.890175 | − | 0.408324i | ||||
\(466\) | 2.41249e42 | 0.487854 | ||||||||
\(467\) | −1.41690e42 | + | 1.41690e42i | −0.276866 | + | 0.276866i | −0.831857 | − | 0.554990i | \(-0.812722\pi\) |
0.554990 | + | 0.831857i | \(0.312722\pi\) | |||||||
\(468\) | −8.65523e40 | − | 8.65523e40i | −0.0163435 | − | 0.0163435i | ||||
\(469\) | 3.32735e41i | 0.0607202i | ||||||||
\(470\) | 7.06808e40 | + | 2.62284e40i | 0.0124662 | + | 0.00462601i | ||||
\(471\) | 4.51825e42 | 0.770257 | ||||||||
\(472\) | −7.58165e41 | + | 7.58165e41i | −0.124937 | + | 0.124937i | ||||
\(473\) | 7.53817e42 | + | 7.53817e42i | 1.20085 | + | 1.20085i | ||||
\(474\) | − | 2.95597e42i | − | 0.455247i | ||||||
\(475\) | 8.38255e42 | − | 9.73940e42i | 1.24818 | − | 1.45022i | ||||
\(476\) | 2.36998e42 | 0.341219 | ||||||||
\(477\) | −5.30461e42 | + | 5.30461e42i | −0.738515 | + | 0.738515i | ||||
\(478\) | 4.62061e42 | + | 4.62061e42i | 0.622090 | + | 0.622090i | ||||
\(479\) | 1.08890e43i | 1.41782i | 0.705298 | + | 0.708910i | \(0.250813\pi\) | ||||
−0.705298 | + | 0.708910i | \(0.749187\pi\) | |||||||
\(480\) | −1.33353e42 | + | 3.59363e42i | −0.167936 | + | 0.452557i | ||||
\(481\) | −1.68363e41 | −0.0205081 | ||||||||
\(482\) | −4.35305e42 | + | 4.35305e42i | −0.512910 | + | 0.512910i | ||||
\(483\) | −3.01356e42 | − | 3.01356e42i | −0.343500 | − | 0.343500i | ||||
\(484\) | 4.87487e42i | 0.537572i | ||||||||
\(485\) | 1.02689e42 | + | 2.23870e42i | 0.109561 | + | 0.238851i | ||||
\(486\) | −7.01677e42 | −0.724364 | ||||||||
\(487\) | 1.16822e43 | − | 1.16822e43i | 1.16698 | − | 1.16698i | 0.184065 | − | 0.982914i | \(-0.441074\pi\) |
0.982914 | − | 0.184065i | \(-0.0589256\pi\) | |||||||
\(488\) | −2.32235e42 | − | 2.32235e42i | −0.224497 | − | 0.224497i | ||||
\(489\) | − | 1.45756e42i | − | 0.136359i | ||||||
\(490\) | −2.93927e42 | + | 1.34825e42i | −0.266135 | + | 0.122077i | ||||
\(491\) | 4.36824e42 | 0.382827 | 0.191414 | − | 0.981509i | \(-0.438693\pi\) | ||||
0.191414 | + | 0.981509i | \(0.438693\pi\) | |||||||
\(492\) | −1.30393e42 | + | 1.30393e42i | −0.110614 | + | 0.110614i | ||||
\(493\) | −5.99235e42 | − | 5.99235e42i | −0.492092 | − | 0.492092i | ||||
\(494\) | − | 1.06993e42i | − | 0.0850597i | ||||||
\(495\) | −1.24008e43 | − | 4.60173e42i | −0.954481 | − | 0.354192i | ||||
\(496\) | 5.55314e42 | 0.413840 | ||||||||
\(497\) | 5.75264e42 | − | 5.75264e42i | 0.415111 | − | 0.415111i | ||||
\(498\) | −6.84952e42 | − | 6.84952e42i | −0.478620 | − | 0.478620i | ||||
\(499\) | − | 4.23299e42i | − | 0.286443i | −0.989691 | − | 0.143221i | \(-0.954254\pi\) | ||
0.989691 | − | 0.143221i | \(-0.0457461\pi\) | |||||||
\(500\) | −3.77336e42 | − | 6.82897e42i | −0.247291 | − | 0.447543i | ||||
\(501\) | −1.45235e43 | −0.921863 | ||||||||
\(502\) | 5.36600e42 | − | 5.36600e42i | 0.329907 | − | 0.329907i | ||||
\(503\) | −1.40581e43 | − | 1.40581e43i | −0.837221 | − | 0.837221i | 0.151271 | − | 0.988492i | \(-0.451663\pi\) |
−0.988492 | + | 0.151271i | \(0.951663\pi\) | |||||||
\(504\) | 1.55056e43i | 0.894539i | ||||||||
\(505\) | −1.77688e42 | + | 4.78836e42i | −0.0993106 | + | 0.267624i | ||||
\(506\) | 1.40227e43 | 0.759320 | ||||||||
\(507\) | 7.21827e42 | − | 7.21827e42i | 0.378709 | − | 0.378709i | ||||
\(508\) | 4.92000e42 | + | 4.92000e42i | 0.250118 | + | 0.250118i | ||||
\(509\) | 3.07292e42i | 0.151379i | 0.997131 | + | 0.0756897i | \(0.0241159\pi\) | ||||
−0.997131 | + | 0.0756897i | \(0.975884\pi\) | |||||||
\(510\) | 1.83930e42 | + | 4.00980e42i | 0.0878072 | + | 0.191426i | ||||
\(511\) | −2.34515e43 | −1.08502 | ||||||||
\(512\) | −7.00218e42 | + | 7.00218e42i | −0.313989 | + | 0.313989i | ||||
\(513\) | 2.86388e43 | + | 2.86388e43i | 1.24474 | + | 1.24474i | ||||
\(514\) | − | 2.75061e43i | − | 1.15883i | ||||||
\(515\) | −2.26196e43 | + | 1.03756e43i | −0.923782 | + | 0.423740i | ||||
\(516\) | −8.23477e42 | −0.326029 | ||||||||
\(517\) | −5.01869e41 | + | 5.01869e41i | −0.0192638 | + | 0.0192638i | ||||
\(518\) | 5.10226e42 | + | 5.10226e42i | 0.189883 | + | 0.189883i | ||||
\(519\) | − | 2.07626e43i | − | 0.749213i | ||||||
\(520\) | −1.80017e42 | − | 6.68011e41i | −0.0629882 | − | 0.0233739i | ||||
\(521\) | 1.37840e43 | 0.467704 | 0.233852 | − | 0.972272i | \(-0.424867\pi\) | ||||
0.233852 | + | 0.972272i | \(0.424867\pi\) | |||||||
\(522\) | 1.32641e43 | − | 1.32641e43i | 0.436464 | − | 0.436464i | ||||
\(523\) | 3.41632e43 | + | 3.41632e43i | 1.09026 | + | 1.09026i | 0.995500 | + | 0.0947622i | \(0.0302091\pi\) |
0.0947622 | + | 0.995500i | \(0.469791\pi\) | |||||||
\(524\) | 6.27612e42i | 0.194263i | ||||||||
\(525\) | 1.61706e43 | + | 1.39178e43i | 0.485486 | + | 0.417850i | ||||
\(526\) | 8.80277e42 | 0.256358 | ||||||||
\(527\) | −2.55381e43 | + | 2.55381e43i | −0.721470 | + | 0.721470i | ||||
\(528\) | 4.51543e42 | + | 4.51543e42i | 0.123753 | + | 0.123753i | ||||
\(529\) | − | 1.59779e43i | − | 0.424844i | ||||||
\(530\) | −1.38514e43 | + | 3.73271e43i | −0.357340 | + | 0.962964i | ||||
\(531\) | 4.74911e42 | 0.118878 | ||||||||
\(532\) | 3.39264e43 | − | 3.39264e43i | 0.824046 | − | 0.824046i | ||||
\(533\) | −1.08537e42 | − | 1.08537e42i | −0.0255826 | − | 0.0255826i | ||||
\(534\) | − | 7.94224e42i | − | 0.181670i | ||||||
\(535\) | −9.72798e41 | − | 2.12077e42i | −0.0215954 | − | 0.0470796i | ||||
\(536\) | 2.49960e42 | 0.0538560 | ||||||||
\(537\) | −1.69421e43 | + | 1.69421e43i | −0.354305 | + | 0.354305i | ||||
\(538\) | −1.67190e43 | − | 1.67190e43i | −0.339387 | − | 0.339387i | ||||
\(539\) | − | 3.04435e43i | − | 0.599894i | ||||||
\(540\) | 2.23518e43 | − | 1.02528e43i | 0.427575 | − | 0.196129i | ||||
\(541\) | 2.05483e43 | 0.381610 | 0.190805 | − | 0.981628i | \(-0.438890\pi\) | ||||
0.190805 | + | 0.981628i | \(0.438890\pi\) | |||||||
\(542\) | 3.17720e43 | − | 3.17720e43i | 0.572870 | − | 0.572870i | ||||
\(543\) | 1.76443e43 | + | 1.76443e43i | 0.308892 | + | 0.308892i | ||||
\(544\) | − | 2.95843e43i | − | 0.502898i | ||||||
\(545\) | −2.98206e43 | − | 1.10659e43i | −0.492234 | − | 0.182660i | ||||
\(546\) | 1.77643e42 | 0.0284751 | ||||||||
\(547\) | −4.56259e43 | + | 4.56259e43i | −0.710256 | + | 0.710256i | −0.966589 | − | 0.256333i | \(-0.917486\pi\) |
0.256333 | + | 0.966589i | \(0.417486\pi\) | |||||||
\(548\) | 1.94323e43 | + | 1.94323e43i | 0.293789 | + | 0.293789i | ||||
\(549\) | 1.45471e43i | 0.213609i | ||||||||
\(550\) | −7.00037e43 | + | 5.24142e42i | −0.998430 | + | 0.0747560i | ||||
\(551\) | −1.71562e44 | −2.37681 | ||||||||
\(552\) | −2.26388e43 | + | 2.26388e43i | −0.304668 | + | 0.304668i | ||||
\(553\) | 7.80205e43 | + | 7.80205e43i | 1.02002 | + | 1.02002i | ||||
\(554\) | − | 5.33998e43i | − | 0.678240i | ||||||
\(555\) | 4.88929e42 | − | 1.31757e43i | 0.0603334 | − | 0.162587i | ||||
\(556\) | −6.03935e42 | −0.0724092 | ||||||||
\(557\) | 9.27187e43 | − | 9.27187e43i | 1.08015 | − | 1.08015i | 0.0836558 | − | 0.996495i | \(-0.473340\pi\) |
0.996495 | − | 0.0836558i | \(-0.0266596\pi\) | |||||||
\(558\) | −5.65286e43 | − | 5.65286e43i | −0.639913 | − | 0.639913i | ||||
\(559\) | − | 6.85453e42i | − | 0.0754030i | ||||||
\(560\) | 1.05563e43 | + | 2.30135e43i | 0.112850 | + | 0.246022i | ||||
\(561\) | −4.15316e43 | −0.431492 | ||||||||
\(562\) | −1.13904e43 | + | 1.13904e43i | −0.115015 | + | 0.115015i | ||||
\(563\) | −3.66109e42 | − | 3.66109e42i | −0.0359315 | − | 0.0359315i | 0.688913 | − | 0.724844i | \(-0.258088\pi\) |
−0.724844 | + | 0.688913i | \(0.758088\pi\) | |||||||
\(564\) | − | 5.48247e41i | − | 0.00523010i | ||||||
\(565\) | 6.47695e43 | − | 2.97098e43i | 0.600614 | − | 0.275502i | ||||
\(566\) | −1.71356e43 | −0.154467 | ||||||||
\(567\) | 2.07697e43 | − | 2.07697e43i | 0.182012 | − | 0.182012i | ||||
\(568\) | −4.32154e43 | − | 4.32154e43i | −0.368185 | − | 0.368185i | ||||
\(569\) | 5.86131e43i | 0.485510i | 0.970088 | + | 0.242755i | \(0.0780512\pi\) | ||||
−0.970088 | + | 0.242755i | \(0.921949\pi\) | |||||||
\(570\) | 8.37303e43 | + | 3.10709e43i | 0.674349 | + | 0.250239i | ||||
\(571\) | −2.82631e43 | −0.221331 | −0.110666 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110666 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(572\) | 4.32452e42 | − | 4.32452e42i | 0.0329307 | − | 0.0329307i | ||||
\(573\) | 1.33034e43 | + | 1.33034e43i | 0.0985120 | + | 0.0985120i | ||||
\(574\) | 6.57846e43i | 0.473734i | ||||||||
\(575\) | −8.08524e42 | − | 1.07985e44i | −0.0566249 | − | 0.756274i | ||||
\(576\) | 8.91984e43 | 0.607571 | ||||||||
\(577\) | −1.16346e44 | + | 1.16346e44i | −0.770793 | + | 0.770793i | −0.978245 | − | 0.207452i | \(-0.933483\pi\) |
0.207452 | + | 0.978245i | \(0.433483\pi\) | |||||||
\(578\) | 5.26322e43 | + | 5.26322e43i | 0.339161 | + | 0.339161i | ||||
\(579\) | − | 1.41233e44i | − | 0.885279i | ||||||
\(580\) | −3.62398e43 | + | 9.76595e43i | −0.220972 | + | 0.595479i | ||||
\(581\) | 3.61575e44 | 2.14477 | ||||||||
\(582\) | −1.21043e43 | + | 1.21043e43i | −0.0698508 | + | 0.0698508i | ||||
\(583\) | −2.65041e44 | − | 2.65041e44i | −1.48805 | − | 1.48805i | ||||
\(584\) | 1.76174e44i | 0.962359i | ||||||||
\(585\) | 3.54589e42 | + | 7.73029e42i | 0.0188465 | + | 0.0410868i | ||||
\(586\) | 1.56988e44 | 0.811902 | ||||||||
\(587\) | 9.20335e43 | − | 9.20335e43i | 0.463166 | − | 0.463166i | −0.436526 | − | 0.899692i | \(-0.643791\pi\) |
0.899692 | + | 0.436526i | \(0.143791\pi\) | |||||||
\(588\) | 1.66284e43 | + | 1.66284e43i | 0.0814354 | + | 0.0814354i | ||||
\(589\) | 7.31159e44i | 3.48471i | ||||||||
\(590\) | 2.29096e43 | − | 1.05086e43i | 0.106264 | − | 0.0487432i | ||||
\(591\) | −4.69221e43 | −0.211825 | ||||||||
\(592\) | 1.17930e43 | − | 1.17930e43i | 0.0518176 | − | 0.0518176i | ||||
\(593\) | 8.88158e43 | + | 8.88158e43i | 0.379853 | + | 0.379853i | 0.871049 | − | 0.491196i | \(-0.163440\pi\) |
−0.491196 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(594\) | − | 2.21259e44i | − | 0.921123i | ||||||
\(595\) | −1.54382e44 | − | 5.72886e43i | −0.625642 | − | 0.232165i | ||||
\(596\) | −1.12440e44 | −0.443588 | ||||||||
\(597\) | −2.30485e43 | + | 2.30485e43i | −0.0885225 | + | 0.0885225i | ||||
\(598\) | −6.37550e42 | − | 6.37550e42i | −0.0238394 | − | 0.0238394i | ||||
\(599\) | − | 3.08997e44i | − | 1.12493i | −0.826822 | − | 0.562464i | \(-0.809854\pi\) | ||
0.826822 | − | 0.562464i | \(-0.190146\pi\) | |||||||
\(600\) | 1.04554e44 | − | 1.21478e44i | 0.370614 | − | 0.430604i | ||||
\(601\) | 2.85700e44 | 0.986096 | 0.493048 | − | 0.870002i | \(-0.335883\pi\) | ||||
0.493048 | + | 0.870002i | \(0.335883\pi\) | |||||||
\(602\) | −2.07727e44 | + | 2.07727e44i | −0.698150 | + | 0.698150i | ||||
\(603\) | −7.82871e42 | − | 7.82871e42i | −0.0256220 | − | 0.0256220i | ||||
\(604\) | 1.53504e44i | 0.489248i | ||||||||
\(605\) | 1.17838e44 | − | 3.17553e44i | 0.365764 | − | 0.985667i | ||||
\(606\) | −3.54972e43 | −0.107308 | ||||||||
\(607\) | −1.73660e44 | + | 1.73660e44i | −0.511306 | + | 0.511306i | −0.914926 | − | 0.403621i | \(-0.867752\pi\) |
0.403621 | + | 0.914926i | \(0.367752\pi\) | |||||||
\(608\) | −4.23502e44 | − | 4.23502e44i | −1.21450 | − | 1.21450i | ||||
\(609\) | − | 2.84848e44i | − | 0.795678i | ||||||
\(610\) | 3.21893e43 | + | 7.01749e43i | 0.0875859 | + | 0.190943i | ||||
\(611\) | 4.56354e41 | 0.00120960 | ||||||||
\(612\) | −5.57616e43 | + | 5.57616e43i | −0.143983 | + | 0.143983i | ||||
\(613\) | −4.23986e44 | − | 4.23986e44i | −1.06656 | − | 1.06656i | −0.997621 | − | 0.0689348i | \(-0.978040\pi\) |
−0.0689348 | − | 0.997621i | \(-0.521960\pi\) | |||||||
\(614\) | 4.16279e44i | 1.02021i | ||||||||
\(615\) | 1.16458e44 | − | 5.34196e43i | 0.278079 | − | 0.127555i | ||||
\(616\) | −7.74724e44 | −1.80242 | ||||||||
\(617\) | 2.57719e44 | − | 2.57719e44i | 0.584230 | − | 0.584230i | −0.351833 | − | 0.936063i | \(-0.614442\pi\) |
0.936063 | + | 0.351833i | \(0.114442\pi\) | |||||||
\(618\) | −1.22301e44 | − | 1.22301e44i | −0.270155 | − | 0.270155i | ||||
\(619\) | − | 3.74778e44i | − | 0.806722i | −0.915041 | − | 0.403361i | \(-0.867842\pi\) | ||
0.915041 | − | 0.403361i | \(-0.132158\pi\) | |||||||
\(620\) | 4.16203e44 | + | 1.54446e44i | 0.873049 | + | 0.323974i | ||||
\(621\) | 3.41307e44 | 0.697717 | ||||||||
\(622\) | −1.26920e43 | + | 1.26920e43i | −0.0252862 | + | 0.0252862i | ||||
\(623\) | 2.09629e44 | + | 2.09629e44i | 0.407045 | + | 0.407045i | ||||
\(624\) | − | 4.10592e42i | − | 0.00777064i | ||||||
\(625\) | 8.07255e43 | + | 5.36057e44i | 0.148912 | + | 0.988850i | ||||
\(626\) | −2.43499e44 | −0.437833 | ||||||||
\(627\) | −5.94527e44 | + | 5.94527e44i | −1.04206 | + | 1.04206i | ||||
\(628\) | 3.03100e44 | + | 3.03100e44i | 0.517884 | + | 0.517884i | ||||
\(629\) | 1.08469e44i | 0.180673i | ||||||||
\(630\) | 1.26808e44 | − | 3.41725e44i | 0.205920 | − | 0.554918i | ||||
\(631\) | 4.45822e44 | 0.705816 | 0.352908 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352908 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(632\) | 5.86112e44 | − | 5.86112e44i | 0.904706 | − | 0.904706i | ||||
\(633\) | 2.28864e44 | + | 2.28864e44i | 0.344444 | + | 0.344444i | ||||
\(634\) | 5.47635e44i | 0.803643i | ||||||||
\(635\) | −2.01564e44 | − | 4.39423e44i | −0.288425 | − | 0.628786i | ||||
\(636\) | 2.89533e44 | 0.404003 | ||||||||
\(637\) | −1.38413e43 | + | 1.38413e43i | −0.0188341 | + | 0.0188341i | ||||
\(638\) | 6.62730e44 | + | 6.62730e44i | 0.879439 | + | 0.879439i | ||||
\(639\) | 2.70700e44i | 0.350328i | ||||||||
\(640\) | −2.16139e44 | + | 9.91432e43i | −0.272806 | + | 0.125136i | ||||
\(641\) | 2.48191e44 | 0.305533 | 0.152766 | − | 0.988262i | \(-0.451182\pi\) | ||||
0.152766 | + | 0.988262i | \(0.451182\pi\) | |||||||
\(642\) | 1.14666e43 | − | 1.14666e43i | 0.0137682 | − | 0.0137682i | ||||
\(643\) | −2.90141e44 | − | 2.90141e44i | −0.339808 | − | 0.339808i | 0.516487 | − | 0.856295i | \(-0.327239\pi\) |
−0.856295 | + | 0.516487i | \(0.827239\pi\) | |||||||
\(644\) | − | 4.04322e44i | − | 0.461905i | ||||||
\(645\) | 5.36420e44 | + | 1.99056e44i | 0.597792 | + | 0.221830i | ||||
\(646\) | −6.89306e44 | −0.749362 | ||||||||
\(647\) | −3.75746e44 | + | 3.75746e44i | −0.398497 | + | 0.398497i | −0.877703 | − | 0.479205i | \(-0.840925\pi\) |
0.479205 | + | 0.877703i | \(0.340925\pi\) | |||||||
\(648\) | −1.56028e44 | − | 1.56028e44i | −0.161437 | − | 0.161437i | ||||
\(649\) | 2.37286e44i | 0.239528i | ||||||||
\(650\) | 3.42105e43 | + | 2.94444e43i | 0.0336935 | + | 0.0289994i | ||||
\(651\) | −1.21396e45 | −1.16657 | ||||||||
\(652\) | 9.77786e43 | − | 9.77786e43i | 0.0916816 | − | 0.0916816i | ||||
\(653\) | 7.84913e44 | + | 7.84913e44i | 0.718142 | + | 0.718142i | 0.968225 | − | 0.250082i | \(-0.0804577\pi\) |
−0.250082 | + | 0.968225i | \(0.580458\pi\) | |||||||
\(654\) | − | 2.21067e44i | − | 0.197369i | ||||||
\(655\) | 1.51711e44 | − | 4.08832e44i | 0.132177 | − | 0.356192i | ||||
\(656\) | 1.52050e44 | 0.129278 | ||||||||
\(657\) | 5.51775e44 | − | 5.51775e44i | 0.457842 | − | 0.457842i | ||||
\(658\) | −1.38298e43 | − | 1.38298e43i | −0.0111996 | − | 0.0111996i | ||||
\(659\) | − | 1.73887e45i | − | 1.37436i | −0.726488 | − | 0.687179i | \(-0.758849\pi\) | ||
0.726488 | − | 0.687179i | \(-0.241151\pi\) | |||||||
\(660\) | 2.12843e44 | + | 4.64012e44i | 0.164194 | + | 0.357953i | ||||
\(661\) | 6.70839e44 | 0.505120 | 0.252560 | − | 0.967581i | \(-0.418727\pi\) | ||||
0.252560 | + | 0.967581i | \(0.418727\pi\) | |||||||
\(662\) | 6.48113e44 | − | 6.48113e44i | 0.476347 | − | 0.476347i | ||||
\(663\) | 1.88825e43 | + | 1.88825e43i | 0.0135470 | + | 0.0135470i | ||||
\(664\) | − | 2.71625e45i | − | 1.90231i | ||||||
\(665\) | −3.03008e45 | + | 1.38990e45i | −2.07161 | + | 0.950250i | ||||
\(666\) | −2.40095e44 | −0.160249 | ||||||||
\(667\) | −1.02230e45 | + | 1.02230e45i | −0.666142 | + | 0.666142i | ||||
\(668\) | −9.74286e44 | − | 9.74286e44i | −0.619816 | − | 0.619816i | ||||
\(669\) | 2.85230e44i | 0.177165i | ||||||||
\(670\) | −5.50884e43 | − | 2.04424e43i | −0.0334090 | − | 0.0123975i | ||||
\(671\) | −7.26837e44 | −0.430404 | ||||||||
\(672\) | 7.03151e44 | − | 7.03151e44i | 0.406574 | − | 0.406574i | ||||
\(673\) | 2.20853e45 | + | 2.20853e45i | 1.24699 | + | 1.24699i | 0.957043 | + | 0.289946i | \(0.0936374\pi\) |
0.289946 | + | 0.957043i | \(0.406363\pi\) | |||||||
\(674\) | 1.40481e45i | 0.774565i | ||||||||
\(675\) | −1.70385e45 | + | 1.27574e44i | −0.917428 | + | 0.0686911i | ||||
\(676\) | 9.68455e44 | 0.509252 | ||||||||
\(677\) | −1.87843e45 | + | 1.87843e45i | −0.964663 | + | 0.964663i | −0.999397 | − | 0.0347338i | \(-0.988942\pi\) |
0.0347338 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(678\) | 3.50198e44 | + | 3.50198e44i | 0.175646 | + | 0.175646i | ||||
\(679\) | − | 6.38966e44i | − | 0.313012i | ||||||
\(680\) | −4.30369e44 | + | 1.15976e45i | −0.205920 | + | 0.554916i | ||||
\(681\) | −4.81964e43 | −0.0225248 | ||||||||
\(682\) | 2.82441e45 | − | 2.82441e45i | 1.28937 | − | 1.28937i | ||||
\(683\) | −2.77659e45 | − | 2.77659e45i | −1.23817 | − | 1.23817i | −0.960749 | − | 0.277421i | \(-0.910520\pi\) |
−0.277421 | − | 0.960749i | \(-0.589480\pi\) | |||||||
\(684\) | 1.59646e45i | 0.695442i | ||||||||
\(685\) | −7.96106e44 | − | 1.73557e45i | −0.338783 | − | 0.738571i | ||||
\(686\) | −1.16401e45 | −0.483917 | ||||||||
\(687\) | 1.60230e45 | − | 1.60230e45i | 0.650783 | − | 0.650783i | ||||
\(688\) | 4.80126e44 | + | 4.80126e44i | 0.190520 | + | 0.190520i | ||||
\(689\) | 2.41004e44i | 0.0934366i | ||||||||
\(690\) | 6.84078e44 | − | 3.13787e44i | 0.259132 | − | 0.118864i | ||||
\(691\) | 2.77231e45 | 1.02611 | 0.513055 | − | 0.858356i | \(-0.328514\pi\) | ||||
0.513055 | + | 0.858356i | \(0.328514\pi\) | |||||||
\(692\) | 1.39283e45 | − | 1.39283e45i | 0.503735 | − | 0.503735i | ||||
\(693\) | 2.42642e45 | + | 2.42642e45i | 0.857501 | + | 0.857501i | ||||
\(694\) | 3.59126e44i | 0.124021i | ||||||||
\(695\) | 3.93409e44 | + | 1.45987e44i | 0.132766 | + | 0.0492672i | ||||
\(696\) | −2.13986e45 | −0.705729 | ||||||||
\(697\) | −6.99256e44 | + | 6.99256e44i | −0.225378 | + | 0.225378i | ||||
\(698\) | 2.48151e44 | + | 2.48151e44i | 0.0781679 | + | 0.0781679i | ||||
\(699\) | 1.21897e45i | 0.375282i | ||||||||
\(700\) | 1.51127e44 | + | 2.01844e45i | 0.0454752 | + | 0.607360i | ||||
\(701\) | 3.55564e45 | 1.04575 | 0.522877 | − | 0.852408i | \(-0.324859\pi\) | ||||
0.522877 | + | 0.852408i | \(0.324859\pi\) | |||||||
\(702\) | −1.00596e44 | + | 1.00596e44i | −0.0289194 | + | 0.0289194i | ||||
\(703\) | 1.55273e45 | + | 1.55273e45i | 0.436327 | + | 0.436327i | ||||
\(704\) | 4.45673e45i | 1.22420i | ||||||||
\(705\) | −1.32526e43 | + | 3.57133e43i | −0.00355856 | + | 0.00958967i | ||||
\(706\) | −3.52814e45 | −0.926126 | ||||||||
\(707\) | 9.36920e44 | − | 9.36920e44i | 0.240432 | − | 0.240432i | ||||
\(708\) | −1.29607e44 | − | 1.29607e44i | −0.0325159 | − | 0.0325159i | ||||
\(709\) | − | 6.93421e45i | − | 1.70082i | −0.526124 | − | 0.850408i | \(-0.676355\pi\) | ||
0.526124 | − | 0.850408i | \(-0.323645\pi\) | |||||||
\(710\) | 5.98993e44 | + | 1.30585e45i | 0.143644 | + | 0.313155i | ||||
\(711\) | −3.67139e45 | −0.860828 | ||||||||
\(712\) | 1.57479e45 | − | 1.57479e45i | 0.361030 | − | 0.361030i | ||||
\(713\) | 4.35684e45 | + | 4.35684e45i | 0.976649 | + | 0.976649i | ||||
\(714\) | − | 1.14447e45i | − | 0.250861i | ||||||
\(715\) | −3.86238e44 | + | 1.77168e44i | −0.0827863 | + | 0.0379742i | ||||
\(716\) | −2.27307e45 | −0.476436 | ||||||||
\(717\) | −2.33468e45 | + | 2.33468e45i | −0.478543 | + | 0.478543i | ||||
\(718\) | −3.60796e45 | − | 3.60796e45i | −0.723221 | − | 0.723221i | ||||
\(719\) | − | 2.13337e45i | − | 0.418219i | −0.977892 | − | 0.209109i | \(-0.932944\pi\) | ||
0.977892 | − | 0.209109i | \(-0.0670564\pi\) | |||||||
\(720\) | −7.89841e44 | − | 2.93096e44i | −0.151433 | − | 0.0561941i | ||||
\(721\) | 6.45606e45 | 1.21061 | ||||||||
\(722\) | −7.17224e45 | + | 7.17224e45i | −1.31541 | + | 1.31541i | ||||
\(723\) | −2.19949e45 | − | 2.19949e45i | −0.394557 | − | 0.394557i | ||||
\(724\) | 2.36728e45i | 0.415368i | ||||||||
\(725\) | 4.72138e45 | − | 5.48561e45i | 0.810328 | − | 0.941493i | ||||
\(726\) | 2.35409e45 | 0.395219 | ||||||||
\(727\) | −1.76532e45 | + | 1.76532e45i | −0.289917 | + | 0.289917i | −0.837047 | − | 0.547131i | \(-0.815720\pi\) |
0.547131 | + | 0.837047i | \(0.315720\pi\) | |||||||
\(728\) | 3.52232e44 | + | 3.52232e44i | 0.0565883 | + | 0.0565883i | ||||
\(729\) | − | 2.17045e45i | − | 0.341121i | ||||||
\(730\) | 1.44080e45 | − | 3.88269e45i | 0.221532 | − | 0.596989i | ||||
\(731\) | −4.41605e45 | −0.664288 | ||||||||
\(732\) | 3.97002e44 | − | 3.97002e44i | 0.0584272 | − | 0.0584272i | ||||
\(733\) | −8.48221e45 | − | 8.48221e45i | −1.22136 | − | 1.22136i | −0.967147 | − | 0.254217i | \(-0.918182\pi\) |
−0.254217 | − | 0.967147i | \(-0.581818\pi\) | |||||||
\(734\) | 1.75786e45i | 0.247655i | ||||||||
\(735\) | −6.81236e44 | − | 1.48514e45i | −0.0939075 | − | 0.204725i | ||||
\(736\) | −5.04713e45 | −0.680769 | ||||||||
\(737\) | 3.91156e44 | − | 3.91156e44i | 0.0516261 | − | 0.0516261i | ||||
\(738\) | −1.54780e45 | − | 1.54780e45i | −0.199901 | − | 0.199901i | ||||
\(739\) | − | 2.67862e45i | − | 0.338532i | −0.985570 | − | 0.169266i | \(-0.945860\pi\) | ||
0.985570 | − | 0.169266i | \(-0.0541397\pi\) | |||||||
\(740\) | 1.21187e45 | − | 5.55885e44i | 0.149881 | − | 0.0687507i | ||||
\(741\) | 5.40609e44 | 0.0654322 | ||||||||
\(742\) | 7.30365e45 | − | 7.30365e45i | 0.865122 | − | 0.865122i | ||||
\(743\) | −2.49646e44 | − | 2.49646e44i | −0.0289404 | − | 0.0289404i | 0.692489 | − | 0.721429i | \(-0.256514\pi\) |
−0.721429 | + | 0.692489i | \(0.756514\pi\) | |||||||
\(744\) | 9.11963e45i | 1.03469i | ||||||||
\(745\) | 7.32442e45 | + | 2.71797e45i | 0.813341 | + | 0.301817i | ||||
\(746\) | 2.96113e45 | 0.321838 | ||||||||
\(747\) | −8.50726e45 | + | 8.50726e45i | −0.905024 | + | 0.905024i | ||||
\(748\) | −2.78609e45 | − | 2.78609e45i | −0.290114 | − | 0.290114i | ||||
\(749\) | 6.05306e44i | 0.0616972i | ||||||||
\(750\) | −3.29774e45 | + | 1.82217e45i | −0.329030 | + | 0.181806i | ||||
\(751\) | 1.63680e46 | 1.59866 | 0.799332 | − | 0.600889i | \(-0.205187\pi\) | ||||
0.799332 | + | 0.600889i | \(0.205187\pi\) | |||||||
\(752\) | −3.19653e43 | + | 3.19653e43i | −0.00305629 | + | 0.00305629i | ||||
\(753\) | 2.71131e45 | + | 2.71131e45i | 0.253781 | + | 0.253781i | ||||
\(754\) | − | 6.02626e44i | − | 0.0552213i | ||||||
\(755\) | 3.71060e45 | − | 9.99938e45i | 0.332884 | − | 0.897061i | ||||
\(756\) | −6.37962e45 | −0.560333 | ||||||||
\(757\) | −1.19494e46 | + | 1.19494e46i | −1.02757 | + | 1.02757i | −0.0279650 | + | 0.999609i | \(0.508903\pi\) |
−0.999609 | + | 0.0279650i | \(0.991097\pi\) | |||||||
\(758\) | −9.14299e44 | − | 9.14299e44i | −0.0769806 | − | 0.0769806i | ||||
\(759\) | 7.08535e45i | 0.584107i | ||||||||
\(760\) | 1.04413e46 | + | 2.27629e46i | 0.842828 | + | 1.83742i | ||||
\(761\) | 1.29949e45 | 0.102712 | 0.0513558 | − | 0.998680i | \(-0.483646\pi\) | ||||
0.0513558 | + | 0.998680i | \(0.483646\pi\) | |||||||
\(762\) | 2.37589e45 | − | 2.37589e45i | 0.183885 | − | 0.183885i | ||||
\(763\) | 5.83488e45 | + | 5.83488e45i | 0.442221 | + | 0.442221i | ||||
\(764\) | 1.78488e45i | 0.132469i | ||||||||
\(765\) | 4.98027e45 | − | 2.28445e45i | 0.361968 | − | 0.166035i | ||||
\(766\) | 9.57922e45 | 0.681820 | ||||||||
\(767\) | 1.07883e44 | − | 1.07883e44i | 0.00752017 | − | 0.00752017i | ||||
\(768\) | −5.92943e45 | − | 5.92943e45i | −0.404793 | − | 0.404793i | ||||
\(769\) | 4.79274e45i | 0.320452i | 0.987080 | + | 0.160226i | \(0.0512222\pi\) | ||||
−0.987080 | + | 0.160226i | \(0.948778\pi\) | |||||||
\(770\) | 1.70741e46 | + | 6.33589e45i | 1.11811 | + | 0.414912i | ||||
\(771\) | 1.38981e46 | 0.891429 | ||||||||
\(772\) | 9.47445e45 | − | 9.47445e45i | 0.595220 | − | 0.595220i | ||||
\(773\) | −1.12693e46 | − | 1.12693e46i | −0.693466 | − | 0.693466i | 0.269527 | − | 0.962993i | \(-0.413133\pi\) |
−0.962993 | + | 0.269527i | \(0.913133\pi\) | |||||||
\(774\) | − | 9.77494e45i | − | 0.589195i | ||||||
\(775\) | −2.33785e46 | − | 2.01215e46i | −1.38035 | − | 1.18804i | ||||
\(776\) | −4.80009e45 | −0.277627 | ||||||||
\(777\) | −2.57805e45 | + | 2.57805e45i | −0.146068 | + | 0.146068i | ||||
\(778\) | −1.32160e46 | − | 1.32160e46i | −0.733543 | − | 0.733543i | ||||
\(779\) | 2.00198e46i | 1.08858i | ||||||||
\(780\) | 1.14195e44 | − | 3.07735e44i | 0.00608323 | − | 0.0163932i | ||||
\(781\) | −1.35253e46 | −0.705880 | ||||||||
\(782\) | −4.10744e45 | + | 4.10744e45i | −0.210021 | + | 0.210021i | ||||
\(783\) | 1.61305e46 | + | 1.61305e46i | 0.808090 | + | 0.808090i | ||||
\(784\) | − | 1.93903e45i | − | 0.0951759i | ||||||
\(785\) | −1.24175e46 | − | 2.70710e46i | −0.597199 | − | 1.30193i | ||||
\(786\) | 3.03077e45 | 0.142821 | ||||||||
\(787\) | 4.43229e45 | − | 4.43229e45i | 0.204660 | − | 0.204660i | −0.597333 | − | 0.801993i | \(-0.703773\pi\) |
0.801993 | + | 0.597333i | \(0.203773\pi\) | |||||||
\(788\) | −3.14771e45 | − | 3.14771e45i | −0.142421 | − | 0.142421i | ||||
\(789\) | 4.44782e45i | 0.197204i | ||||||||
\(790\) | −1.77106e46 | + | 8.12389e45i | −0.769486 | + | 0.352964i | ||||
\(791\) | −1.84864e46 | −0.787098 | ||||||||
\(792\) | 1.82280e46 | − | 1.82280e46i | 0.760564 | − | 0.760564i | ||||
\(793\) | 3.30460e44 | + | 3.30460e44i | 0.0135129 | + | 0.0135129i | ||||
\(794\) | 4.96262e45i | 0.198876i | ||||||||
\(795\) | −1.88605e46 | − | 6.99879e45i | −0.740761 | − | 0.274884i | ||||
\(796\) | −3.09236e45 | −0.119037 | ||||||||
\(797\) | 1.64194e45 | − | 1.64194e45i | 0.0619474 | − | 0.0619474i | −0.675454 | − | 0.737402i | \(-0.736052\pi\) |
0.737402 | + | 0.675454i | \(0.236052\pi\) | |||||||
\(798\) | −1.63832e46 | − | 1.63832e46i | −0.605832 | − | 0.605832i | ||||
\(799\) | − | 2.94008e44i | − | 0.0106564i | ||||||
\(800\) | 2.51961e46 | − | 1.88652e45i | 0.895144 | − | 0.0670226i | ||||
\(801\) | −9.86444e45 | −0.343520 | ||||||||
\(802\) | −8.45895e45 | + | 8.45895e45i | −0.288753 | + | 0.288753i | ||||
\(803\) | 2.75690e46 | + | 2.75690e46i | 0.922513 | + | 0.922513i | ||||
\(804\) | 4.27302e44i | 0.0140165i | ||||||||
\(805\) | −9.77353e45 | + | 2.63379e46i | −0.314280 | + | 0.846928i | ||||
\(806\) | −2.56826e45 | −0.0809615 | ||||||||
\(807\) | 8.44771e45 | − | 8.44771e45i | 0.261073 | − | 0.261073i | ||||
\(808\) | −7.03841e45 | − | 7.03841e45i | −0.213252 | − | 0.213252i | ||||
\(809\) | − | 1.45230e46i | − | 0.431401i | −0.976460 | − | 0.215700i | \(-0.930797\pi\) | ||
0.976460 | − | 0.215700i | \(-0.0692035\pi\) | |||||||
\(810\) | 2.16264e45 | + | 4.71471e45i | 0.0629832 | + | 0.137308i | ||||
\(811\) | 3.78001e46 | 1.07934 | 0.539672 | − | 0.841876i | \(-0.318548\pi\) | ||||
0.539672 | + | 0.841876i | \(0.318548\pi\) | |||||||
\(812\) | 1.91087e46 | − | 1.91087e46i | 0.534975 | − | 0.534975i | ||||
\(813\) | 1.60536e46 | + | 1.60536e46i | 0.440681 | + | 0.440681i | ||||
\(814\) | − | 1.19962e46i | − | 0.322889i | ||||||
\(815\) | −8.73295e45 | + | 4.00581e45i | −0.230483 | + | 0.105723i | ||||
\(816\) | −2.64525e45 | −0.0684581 | ||||||||
\(817\) | −6.32161e46 | + | 6.32161e46i | −1.60426 | + | 1.60426i | ||||
\(818\) | 1.56277e46 | + | 1.56277e46i | 0.388904 | + | 0.388904i | ||||
\(819\) | − | 2.20637e45i | − | 0.0538438i | ||||||
\(820\) | 1.13960e46 | + | 4.22887e45i | 0.272729 | + | 0.101205i | ||||
\(821\) | −8.53495e45 | −0.200314 | −0.100157 | − | 0.994972i | \(-0.531934\pi\) | ||||
−0.100157 | + | 0.994972i | \(0.531934\pi\) | |||||||
\(822\) | 9.38393e45 | − | 9.38393e45i | 0.215991 | − | 0.215991i | ||||
\(823\) | 2.87037e46 | + | 2.87037e46i | 0.647949 | + | 0.647949i | 0.952497 | − | 0.304548i | \(-0.0985054\pi\) |
−0.304548 | + | 0.952497i | \(0.598505\pi\) | |||||||
\(824\) | − | 4.84998e46i | − | 1.07375i | ||||||
\(825\) | −2.64836e45 | − | 3.53711e46i | −0.0575061 | − | 0.768043i | ||||
\(826\) | −6.53881e45 | −0.139257 | ||||||||
\(827\) | 2.23236e46 | − | 2.23236e46i | 0.466311 | − | 0.466311i | −0.434406 | − | 0.900717i | \(-0.643042\pi\) |
0.900717 | + | 0.434406i | \(0.143042\pi\) | |||||||
\(828\) | 9.51302e45 | + | 9.51302e45i | 0.194909 | + | 0.194909i | ||||
\(829\) | − | 6.26867e46i | − | 1.25980i | −0.776675 | − | 0.629902i | \(-0.783095\pi\) | ||
0.776675 | − | 0.629902i | \(-0.216905\pi\) | |||||||
\(830\) | −2.22142e46 | + | 5.98632e46i | −0.437907 | + | 1.18008i | ||||
\(831\) | 2.69816e46 | 0.521737 | ||||||||
\(832\) | 2.02627e45 | − | 2.02627e45i | 0.0384348 | − | 0.0384348i | ||||
\(833\) | 8.91730e45 | + | 8.91730e45i | 0.165926 | + | 0.165926i | ||||
\(834\) | 2.91643e45i | 0.0532347i | ||||||||
\(835\) | 3.99147e46 | + | 8.70169e46i | 0.714743 | + | 1.55819i | ||||
\(836\) | −7.97660e46 | −1.40126 | ||||||||
\(837\) | 6.87447e46 | − | 6.87447e46i | 1.18476 | − | 1.18476i | ||||
\(838\) | 5.23504e46 | + | 5.23504e46i | 0.885148 | + | 0.885148i | ||||
\(839\) | 2.20324e46i | 0.365486i | 0.983161 | + | 0.182743i | \(0.0584977\pi\) | ||||
−0.983161 | + | 0.182743i | \(0.941502\pi\) | |||||||
\(840\) | −3.77938e46 | + | 1.73360e46i | −0.615108 | + | 0.282151i | ||||
\(841\) | −3.40070e46 | −0.543041 | ||||||||
\(842\) | 5.38772e46 | − | 5.38772e46i | 0.844135 | − | 0.844135i | ||||
\(843\) | −5.75527e45 | − | 5.75527e45i | −0.0884758 | − | 0.0884758i | ||||
\(844\) | 3.07061e46i | 0.463175i | ||||||||
\(845\) | −6.30860e46 | − | 2.34101e46i | −0.933740 | − | 0.346495i | ||||
\(846\) | 6.50786e44 | 0.00945176 | ||||||||
\(847\) | −6.21344e46 | + | 6.21344e46i | −0.885518 | + | 0.885518i | ||||
\(848\) | −1.68812e46 | − | 1.68812e46i | −0.236085 | − | 0.236085i | ||||
\(849\) | − | 8.65819e45i | − | 0.118824i | ||||||
\(850\) | 1.89697e46 | − | 2.20403e46i | 0.255480 | − | 0.296834i | ||||
\(851\) | 1.85049e46 | 0.244576 | ||||||||
\(852\) | 7.38760e45 | − | 7.38760e45i | 0.0958230 | − | 0.0958230i | ||||
\(853\) | −4.64283e46 | − | 4.64283e46i | −0.591014 | − | 0.591014i | 0.346891 | − | 0.937905i | \(-0.387237\pi\) |
−0.937905 | + | 0.346891i | \(0.887237\pi\) | |||||||
\(854\) | − | 2.00292e46i | − | 0.250229i | ||||||
\(855\) | 3.85907e46 | − | 1.03995e47i | 0.473179 | − | 1.27513i | ||||
\(856\) | 4.54723e45 | 0.0547226 | ||||||||
\(857\) | −6.40762e46 | + | 6.40762e46i | −0.756839 | + | 0.756839i | −0.975746 | − | 0.218907i | \(-0.929751\pi\) |
0.218907 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(858\) | −2.08833e45 | − | 2.08833e45i | −0.0242104 | − | 0.0242104i | ||||
\(859\) | − | 1.22377e47i | − | 1.39255i | −0.717777 | − | 0.696273i | \(-0.754840\pi\) | ||
0.717777 | − | 0.696273i | \(-0.245160\pi\) | |||||||
\(860\) | 2.26316e46 | + | 4.93384e46i | 0.252778 | + | 0.551074i | ||||
\(861\) | −3.32394e46 | −0.364420 | ||||||||
\(862\) | −5.43255e46 | + | 5.43255e46i | −0.584639 | + | 0.584639i | ||||
\(863\) | 2.84599e46 | + | 2.84599e46i | 0.300650 | + | 0.300650i | 0.841268 | − | 0.540618i | \(-0.181810\pi\) |
−0.540618 | + | 0.841268i | \(0.681810\pi\) | |||||||
\(864\) | 7.96366e46i | 0.825834i | ||||||||
\(865\) | −1.24399e47 | + | 5.70619e46i | −1.26636 | + | 0.580883i | ||||
\(866\) | −1.16762e46 | −0.116685 | ||||||||
\(867\) | −2.65937e46 | + | 2.65937e46i | −0.260900 | + | 0.260900i | ||||
\(868\) | −8.14369e46 | − | 8.14369e46i | −0.784343 | − | 0.784343i | ||||
\(869\) | − | 1.83438e47i | − | 1.73449i | ||||||
\(870\) | 4.71602e46 | + | 1.75003e46i | 0.437792 | + | 0.162457i | ||||
\(871\) | −3.55681e44 | −0.00324168 | ||||||||
\(872\) | 4.38333e46 | − | 4.38333e46i | 0.392229 | − | 0.392229i | ||||
\(873\) | 1.50338e46 | + | 1.50338e46i | 0.132081 | + | 0.132081i | ||||
\(874\) | 1.17597e47i | 1.01441i | ||||||||
\(875\) | 3.89464e46 | − | 1.35136e47i | 0.329866 | − | 1.14457i | ||||
\(876\) | −3.01167e46 | −0.250462 | ||||||||
\(877\) | 1.39784e47 | − | 1.39784e47i | 1.14147 | − | 1.14147i | 0.153284 | − | 0.988182i | \(-0.451015\pi\) |
0.988182 | − | 0.153284i | \(-0.0489850\pi\) | |||||||
\(878\) | −3.78265e45 | − | 3.78265e45i | −0.0303308 | − | 0.0303308i | ||||
\(879\) | 7.93220e46i | 0.624556i | ||||||||
\(880\) | 1.46443e46 | − | 3.94638e46i | 0.113226 | − | 0.305124i | ||||
\(881\) | 2.28136e47 | 1.73213 | 0.866064 | − | 0.499933i | \(-0.166642\pi\) | ||||
0.866064 | + | 0.499933i | \(0.166642\pi\) | |||||||
\(882\) | −1.97384e46 | + | 1.97384e46i | −0.147169 | + | 0.147169i | ||||
\(883\) | 1.49257e47 | + | 1.49257e47i | 1.09286 | + | 1.09286i | 0.995222 | + | 0.0976337i | \(0.0311274\pi\) |
0.0976337 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(884\) | 2.53341e45i | 0.0182167i | ||||||||
\(885\) | 5.30976e45 | + | 1.15756e46i | 0.0374958 | + | 0.0817434i | ||||
\(886\) | −1.17626e47 | −0.815764 | ||||||||
\(887\) | −7.03649e46 | + | 7.03649e46i | −0.479268 | + | 0.479268i | −0.904897 | − | 0.425630i | \(-0.860053\pi\) |
0.425630 | + | 0.904897i | \(0.360053\pi\) | |||||||
\(888\) | 1.93670e46 | + | 1.93670e46i | 0.129555 | + | 0.129555i | ||||
\(889\) | 1.25419e47i | 0.824017i | ||||||||
\(890\) | −4.75857e46 | + | 2.18276e46i | −0.307069 | + | 0.140853i | ||||
\(891\) | −4.88327e46 | −0.309505 | ||||||||
\(892\) | −1.91343e46 | + | 1.91343e46i | −0.119117 | + | 0.119117i | ||||
\(893\) | −4.20874e45 | − | 4.20874e45i | −0.0257353 | − | 0.0257353i | ||||
\(894\) | 5.42976e46i | 0.326122i | ||||||||
\(895\) | 1.48070e47 | + | 5.49462e46i | 0.873571 | + | 0.324167i | ||||
\(896\) | 6.16901e46 | 0.357509 | ||||||||
\(897\) | 3.22138e45 | − | 3.22138e45i | 0.0183385 | − | 0.0183385i | ||||
\(898\) | −1.10254e47 | − | 1.10254e47i | −0.616556 | − | 0.616556i | ||||
\(899\) | 4.11817e47i | 2.26230i | ||||||||
\(900\) | −5.10462e46 | − | 4.39346e46i | −0.275476 | − | 0.237098i | ||||
\(901\) | 1.55268e47 | 0.823161 | ||||||||
\(902\) | 7.73348e46 | − | 7.73348e46i | 0.402782 | − | 0.402782i | ||||
\(903\) | −1.04959e47 | − | 1.04959e47i | −0.537053 | − | 0.537053i | ||||
\(904\) | 1.38875e47i | 0.698119i | ||||||||
\(905\) | 5.72235e46 | − | 1.54207e47i | 0.282616 | − | 0.761599i | ||||
\(906\) | 7.41277e46 | 0.359691 | ||||||||
\(907\) | −1.17549e46 | + | 1.17549e46i | −0.0560406 | + | 0.0560406i | −0.734572 | − | 0.678531i | \(-0.762617\pi\) |
0.678531 | + | 0.734572i | \(0.262617\pi\) | |||||||
\(908\) | −3.23319e45 | − | 3.23319e45i | −0.0151446 | − | 0.0151446i | ||||
\(909\) | 4.40883e46i | 0.202909i | ||||||||
\(910\) | −4.88216e45 | − | 1.06434e46i | −0.0220775 | − | 0.0481304i | ||||
\(911\) | 1.01453e47 | 0.450788 | 0.225394 | − | 0.974268i | \(-0.427633\pi\) | ||||
0.225394 | + | 0.974268i | \(0.427633\pi\) | |||||||
\(912\) | −3.78670e46 | + | 3.78670e46i | −0.165327 | + | 0.165327i | ||||
\(913\) | −4.25059e47 | − | 4.25059e47i | −1.82355 | − | 1.82355i | ||||
\(914\) | − | 7.39251e46i | − | 0.311640i | ||||||
\(915\) | −3.54576e46 | + | 1.62645e46i | −0.146883 | + | 0.0673755i | ||||
\(916\) | 2.14976e47 | 0.875110 | ||||||||
\(917\) | −7.99946e46 | + | 7.99946e46i | −0.320001 | + | 0.320001i | ||||
\(918\) | 6.48096e46 | + | 6.48096e46i | 0.254775 | + | 0.254775i | ||||
\(919\) | − | 4.48499e47i | − | 1.73266i | −0.499472 | − | 0.866330i | \(-0.666472\pi\) | ||
0.499472 | − | 0.866330i | \(-0.333528\pi\) | |||||||
\(920\) | 1.97858e47 | + | 7.34215e46i | 0.751186 | + | 0.278752i | ||||
\(921\) | −2.10335e47 | −0.784799 | ||||||||
\(922\) | 3.38606e46 | − | 3.38606e46i | 0.124165 | − | 0.124165i | ||||
\(923\) | 6.14935e45 | + | 6.14935e45i | 0.0221616 | + | 0.0221616i | ||||
\(924\) | − | 1.32438e47i | − | 0.469094i | ||||||
\(925\) | −9.23793e46 | + | 6.91677e45i | −0.321593 | + | 0.0240788i | ||||
\(926\) | −3.40957e47 | −1.16660 | ||||||||
\(927\) | −1.51900e47 | + | 1.51900e47i | −0.510838 | + | 0.510838i | ||||
\(928\) | −2.38533e47 | − | 2.38533e47i | −0.788462 | − | 0.788462i | ||||
\(929\) | 2.74322e46i | 0.0891270i | 0.999007 | + | 0.0445635i | \(0.0141897\pi\) | ||||
−0.999007 | + | 0.0445635i | \(0.985810\pi\) | |||||||
\(930\) | 7.45826e46 | − | 2.00986e47i | 0.238183 | − | 0.641859i | ||||
\(931\) | 2.55303e47 | 0.801423 | ||||||||
\(932\) | −8.17729e46 | + | 8.17729e46i | −0.252322 | + | 0.252322i | ||||
\(933\) | −6.41294e45 | − | 6.41294e45i | −0.0194514 | − | 0.0194514i | ||||
\(934\) | 9.18010e46i | 0.273714i | ||||||||
\(935\) | 1.14141e47 | + | 2.48835e47i | 0.334546 | + | 0.729334i | ||||
\(936\) | −1.65749e46 | −0.0477569 | ||||||||
\(937\) | −3.92906e47 | + | 3.92906e47i | −1.11290 | + | 1.11290i | −0.120140 | + | 0.992757i | \(0.538334\pi\) |
−0.992757 | + | 0.120140i | \(0.961666\pi\) | |||||||
\(938\) | 1.07789e46 | + | 1.07789e46i | 0.0300145 | + | 0.0300145i | ||||
\(939\) | − | 1.23034e47i | − | 0.336804i | ||||||
\(940\) | −3.28481e45 | + | 1.50674e45i | −0.00884024 | + | 0.00405503i | ||||
\(941\) | −4.45564e47 | −1.17890 | −0.589448 | − | 0.807806i | \(-0.700655\pi\) | ||||
−0.589448 | + | 0.807806i | \(0.700655\pi\) | |||||||
\(942\) | 1.46368e47 | − | 1.46368e47i | 0.380744 | − | 0.380744i | ||||
\(943\) | 1.19294e47 | + | 1.19294e47i | 0.305093 | + | 0.305093i | ||||
\(944\) | 1.51134e46i | 0.0380022i | ||||||||
\(945\) | 4.15574e47 | + | 1.54212e47i | 1.02740 | + | 0.381250i | ||||
\(946\) | 4.88398e47 | 1.18718 | ||||||||
\(947\) | 1.12887e47 | − | 1.12887e47i | 0.269802 | − | 0.269802i | −0.559218 | − | 0.829020i | \(-0.688899\pi\) |
0.829020 | + | 0.559218i | \(0.188899\pi\) | |||||||
\(948\) | 1.00195e47 | + | 1.00195e47i | 0.235457 | + | 0.235457i | ||||
\(949\) | − | 2.50687e46i | − | 0.0579260i | ||||||
\(950\) | −4.39553e46 | − | 5.87060e47i | −0.0998696 | − | 1.33384i | ||||
\(951\) | −2.76707e47 | −0.618203 | ||||||||
\(952\) | 2.26927e47 | − | 2.26927e47i | 0.498534 | − | 0.498534i | ||||
\(953\) | 1.72739e47 | + | 1.72739e47i | 0.373167 | + | 0.373167i | 0.868629 | − | 0.495462i | \(-0.165001\pi\) |
−0.495462 | + | 0.868629i | \(0.665001\pi\) | |||||||
\(954\) | 3.43685e47i | 0.730108i | ||||||||
\(955\) | 4.31454e46 | − | 1.16269e47i | 0.0901322 | − | 0.242890i | ||||
\(956\) | −3.13238e47 | −0.643499 | ||||||||
\(957\) | −3.34861e47 | + | 3.34861e47i | −0.676509 | + | 0.676509i | ||||
\(958\) | 3.52750e47 | + | 3.52750e47i | 0.700840 | + | 0.700840i | ||||
\(959\) | 4.95363e47i | 0.967889i | ||||||||
\(960\) | 9.97284e46 | + | 2.17415e47i | 0.191637 | + | 0.417782i | ||||
\(961\) | 1.22593e48 | 2.31682 | ||||||||
\(962\) | −5.45412e45 | + | 5.45412e45i | −0.0101373 | + | 0.0101373i | ||||
\(963\) | −1.42418e46 | − | 1.42418e46i | −0.0260343 | − | 0.0260343i | ||||
\(964\) | − | 2.95100e47i | − | 0.530562i | ||||||
\(965\) | −8.46197e47 | + | 3.88151e47i | −1.49635 | + | 0.686379i | ||||
\(966\) | −1.95249e47 | −0.339589 | ||||||||
\(967\) | 2.78006e47 | − | 2.78006e47i | 0.475588 | − | 0.475588i | −0.428129 | − | 0.903718i | \(-0.640827\pi\) |
0.903718 | + | 0.428129i | \(0.140827\pi\) | |||||||
\(968\) | 4.66771e47 | + | 4.66771e47i | 0.785413 | + | 0.785413i | ||||
\(969\) | − | 3.48289e47i | − | 0.576447i | ||||||
\(970\) | 1.05789e47 | + | 3.92564e46i | 0.172223 | + | 0.0639091i | ||||
\(971\) | −6.25598e47 | −1.00182 | −0.500908 | − | 0.865501i | \(-0.667000\pi\) | ||||
−0.500908 | + | 0.865501i | \(0.667000\pi\) | |||||||
\(972\) | 2.37838e47 | − | 2.37838e47i | 0.374647 | − | 0.374647i | ||||
\(973\) | −7.69768e46 | − | 7.69768e46i | −0.119276 | − | 0.119276i | ||||
\(974\) | − | 7.56892e47i | − | 1.15369i | ||||||
\(975\) | −1.48776e46 | + | 1.72857e46i | −0.0223079 | + | 0.0259187i | ||||
\(976\) | −4.62942e46 | −0.0682856 | ||||||||
\(977\) | 1.93304e47 | − | 1.93304e47i | 0.280496 | − | 0.280496i | −0.552811 | − | 0.833307i | \(-0.686445\pi\) |
0.833307 | + | 0.552811i | \(0.186445\pi\) | |||||||
\(978\) | −4.72177e46 | − | 4.72177e46i | −0.0674036 | − | 0.0674036i | ||||
\(979\) | − | 4.92869e47i | − | 0.692164i | ||||||
\(980\) | 5.39289e46 | − | 1.45328e47i | 0.0745082 | − | 0.200786i | ||||
\(981\) | −2.74570e47 | −0.373206 | ||||||||
\(982\) | 1.41509e47 | − | 1.41509e47i | 0.189235 | − | 0.189235i | ||||
\(983\) | −1.12896e47 | − | 1.12896e47i | −0.148533 | − | 0.148533i | 0.628929 | − | 0.777463i | \(-0.283494\pi\) |
−0.777463 | + | 0.628929i | \(0.783494\pi\) | |||||||
\(984\) | 2.49704e47i | 0.323224i | ||||||||
\(985\) | 1.28956e47 | + | 2.81133e47i | 0.164233 | + | 0.358040i | ||||
\(986\) | −3.88244e47 | −0.486490 | ||||||||
\(987\) | 6.98788e45 | − | 6.98788e45i | 0.00861531 | − | 0.00861531i | ||||
\(988\) | 3.62660e46 | + | 3.62660e46i | 0.0439935 | + | 0.0439935i | ||||
\(989\) | 7.53385e47i | 0.899242i | ||||||||
\(990\) | −5.50797e47 | + | 2.52651e47i | −0.646887 | + | 0.296728i | ||||
\(991\) | −7.47487e47 | −0.863824 | −0.431912 | − | 0.901916i | \(-0.642161\pi\) | ||||
−0.431912 | + | 0.901916i | \(0.642161\pi\) | |||||||
\(992\) | −1.01657e48 | + | 1.01657e48i | −1.15599 | + | 1.15599i | ||||
\(993\) | 3.27476e47 | + | 3.27476e47i | 0.366430 | + | 0.366430i | ||||
\(994\) | − | 3.72713e47i | − | 0.410386i | ||||||
\(995\) | 2.01439e47 | + | 7.47505e46i | 0.218260 | + | 0.0809925i | ||||
\(996\) | 4.64338e47 | 0.495091 | ||||||||
\(997\) | 1.10528e48 | − | 1.10528e48i | 1.15971 | − | 1.15971i | 0.175172 | − | 0.984538i | \(-0.443952\pi\) |
0.984538 | − | 0.175172i | \(-0.0560481\pi\) | |||||||
\(998\) | −1.37127e47 | − | 1.37127e47i | −0.141591 | − | 0.141591i | ||||
\(999\) | − | 2.91981e47i | − | 0.296693i |
(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 | 5.33.c.a.3.11 | yes | 30 | |
5.2 | odd | 4 | inner | 5.33.c.a.2.11 | ✓ | 30 | |
5.3 | odd | 4 | 25.33.c.b.7.5 | 30 | |||
5.4 | even | 2 | 25.33.c.b.18.5 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.33.c.a.2.11 | ✓ | 30 | 5.2 | odd | 4 | inner | |
5.33.c.a.3.11 | yes | 30 | 1.1 | even | 1 | trivial | |
25.33.c.b.7.5 | 30 | 5.3 | odd | 4 | |||
25.33.c.b.18.5 | 30 | 5.4 | even | 2 |