Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,43,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 43, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 43);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 43 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), 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: | \(44.6910828688\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + \cdots + 58\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.12 | ||
Root | \(0.500000 - 1.25309e9i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.43.b.a.3.11 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 232318. | + | 2.08424e6i | 0.110778 | + | 0.993845i | ||||
\(3\) | 2.00495e10i | 1.91671i | 0.285575 | + | 0.958356i | \(0.407815\pi\) | ||||
−0.285575 | + | 0.958356i | \(0.592185\pi\) | |||||||
\(4\) | −4.29010e12 | + | 9.68414e11i | −0.975457 | + | 0.220192i | ||||
\(5\) | −5.01114e14 | −1.05091 | −0.525456 | − | 0.850821i | \(-0.676105\pi\) | ||||
−0.525456 | + | 0.850821i | \(0.676105\pi\) | |||||||
\(6\) | −4.17880e16 | + | 4.65785e15i | −1.90492 | + | 0.212329i | ||||
\(7\) | 9.07936e16i | 0.162553i | 0.996692 | + | 0.0812767i | \(0.0258998\pi\) | ||||
−0.996692 | + | 0.0812767i | \(0.974100\pi\) | |||||||
\(8\) | −3.01508e18 | − | 8.71664e18i | −0.326896 | − | 0.945060i | ||||
\(9\) | −2.92563e20 | −2.67379 | ||||||||
\(10\) | −1.16418e20 | − | 1.04444e21i | −0.116418 | − | 1.04444i | ||||
\(11\) | 1.06683e22i | 1.44161i | 0.693138 | + | 0.720805i | \(0.256228\pi\) | ||||
−0.693138 | + | 0.720805i | \(0.743772\pi\) | |||||||
\(12\) | −1.94162e22 | − | 8.60144e22i | −0.422045 | − | 1.86967i | ||||
\(13\) | −1.14000e23 | −0.461420 | −0.230710 | − | 0.973023i | \(-0.574105\pi\) | ||||
−0.230710 | + | 0.973023i | \(0.574105\pi\) | |||||||
\(14\) | −1.89236e23 | + | 2.10930e22i | −0.161553 | + | 0.0180073i | ||||
\(15\) | − | 1.00471e25i | − | 2.01430i | ||||||
\(16\) | 1.74672e25 | − | 8.30920e24i | 0.903031 | − | 0.429575i | ||||
\(17\) | 4.41888e25 | 0.639566 | 0.319783 | − | 0.947491i | \(-0.396390\pi\) | ||||
0.319783 | + | 0.947491i | \(0.396390\pi\) | |||||||
\(18\) | −6.79676e25 | − | 6.09773e26i | −0.296196 | − | 2.65733i | ||||
\(19\) | 9.90347e25i | 0.138663i | 0.997594 | + | 0.0693317i | \(0.0220867\pi\) | ||||
−0.997594 | + | 0.0693317i | \(0.977913\pi\) | |||||||
\(20\) | 2.14983e27 | − | 4.85286e26i | 1.02512 | − | 0.231402i | ||||
\(21\) | −1.82036e27 | −0.311568 | ||||||||
\(22\) | −2.22353e28 | + | 2.47843e27i | −1.43274 | + | 0.159698i | ||||
\(23\) | 3.40290e28i | 0.862113i | 0.902325 | + | 0.431056i | \(0.141859\pi\) | ||||
−0.902325 | + | 0.431056i | \(0.858141\pi\) | |||||||
\(24\) | 1.74764e29 | − | 6.04508e28i | 1.81141 | − | 0.626565i | ||||
\(25\) | 2.37415e28 | 0.104416 | ||||||||
\(26\) | −2.64843e28 | − | 2.37605e29i | −0.0511151 | − | 0.458580i | ||||
\(27\) | − | 3.67195e30i | − | 3.20817i | ||||||
\(28\) | −8.79258e28 | − | 3.89514e29i | −0.0357930 | − | 0.158564i | ||||
\(29\) | −5.31418e30 | −1.03533 | −0.517664 | − | 0.855584i | \(-0.673198\pi\) | ||||
−0.517664 | + | 0.855584i | \(0.673198\pi\) | |||||||
\(30\) | 2.09406e31 | − | 2.33412e30i | 2.00190 | − | 0.223139i | ||||
\(31\) | 3.57390e31i | 1.71612i | 0.513553 | + | 0.858058i | \(0.328329\pi\) | ||||
−0.513553 | + | 0.858058i | \(0.671671\pi\) | |||||||
\(32\) | 2.13763e31 | + | 3.44755e31i | 0.526967 | + | 0.849886i | ||||
\(33\) | −2.13893e32 | −2.76315 | ||||||||
\(34\) | 1.02659e31 | + | 9.21003e31i | 0.0708497 | + | 0.635629i | ||||
\(35\) | − | 4.54979e31i | − | 0.170829i | ||||||
\(36\) | 1.25513e33 | − | 2.83322e32i | 2.60816 | − | 0.588746i | ||||
\(37\) | −9.70417e32 | −1.13429 | −0.567143 | − | 0.823620i | \(-0.691951\pi\) | ||||
−0.567143 | + | 0.823620i | \(0.691951\pi\) | |||||||
\(38\) | −2.06412e32 | + | 2.30075e31i | −0.137810 | + | 0.0153608i | ||||
\(39\) | − | 2.28565e33i | − | 0.884409i | ||||||
\(40\) | 1.51090e33 | + | 4.36803e33i | 0.343539 | + | 0.993175i | ||||
\(41\) | 5.96887e33 | 0.808037 | 0.404019 | − | 0.914751i | \(-0.367613\pi\) | ||||
0.404019 | + | 0.914751i | \(0.367613\pi\) | |||||||
\(42\) | −4.22903e32 | − | 3.79409e33i | −0.0345148 | − | 0.309651i | ||||
\(43\) | 1.94992e34i | 0.970912i | 0.874261 | + | 0.485456i | \(0.161346\pi\) | ||||
−0.874261 | + | 0.485456i | \(0.838654\pi\) | |||||||
\(44\) | −1.03313e34 | − | 4.57680e34i | −0.317431 | − | 1.40623i | ||||
\(45\) | 1.46607e35 | 2.80992 | ||||||||
\(46\) | −7.09247e34 | + | 7.90554e33i | −0.856807 | + | 0.0955030i | ||||
\(47\) | − | 2.30373e34i | − | 0.177165i | −0.996069 | − | 0.0885823i | \(-0.971766\pi\) | ||
0.996069 | − | 0.0885823i | \(-0.0282336\pi\) | |||||||
\(48\) | 1.66595e35 | + | 3.50208e35i | 0.823372 | + | 1.73085i | ||||
\(49\) | 3.03730e35 | 0.973576 | ||||||||
\(50\) | 5.51557e33 | + | 4.94830e34i | 0.0115670 | + | 0.103773i | ||||
\(51\) | 8.85963e35i | 1.22586i | ||||||||
\(52\) | 4.89074e35 | − | 1.10400e35i | 0.450095 | − | 0.101601i | ||||
\(53\) | 1.67526e35 | 0.103345 | 0.0516723 | − | 0.998664i | \(-0.483545\pi\) | ||||
0.0516723 | + | 0.998664i | \(0.483545\pi\) | |||||||
\(54\) | 7.65323e36 | − | 8.53059e35i | 3.18842 | − | 0.355394i | ||||
\(55\) | − | 5.34602e36i | − | 1.51500i | ||||||
\(56\) | 7.91415e35 | − | 2.73750e35i | 0.153623 | − | 0.0531380i | ||||
\(57\) | −1.98559e36 | −0.265778 | ||||||||
\(58\) | −1.23458e36 | − | 1.10760e37i | −0.114691 | − | 1.02896i | ||||
\(59\) | 2.06438e37i | 1.33936i | 0.742651 | + | 0.669679i | \(0.233568\pi\) | ||||
−0.742651 | + | 0.669679i | \(0.766432\pi\) | |||||||
\(60\) | 9.72974e36 | + | 4.31030e37i | 0.443532 | + | 1.96486i | ||||
\(61\) | 2.37447e37 | 0.764962 | 0.382481 | − | 0.923963i | \(-0.375070\pi\) | ||||
0.382481 | + | 0.923963i | \(0.375070\pi\) | |||||||
\(62\) | −7.44887e37 | + | 8.30280e36i | −1.70555 | + | 0.190107i | ||||
\(63\) | − | 2.65628e37i | − | 0.434633i | ||||||
\(64\) | −6.68892e37 | + | 5.25628e37i | −0.786279 | + | 0.617872i | ||||
\(65\) | 5.71272e37 | 0.484912 | ||||||||
\(66\) | −4.96913e37 | − | 4.45806e38i | −0.306096 | − | 2.74614i | ||||
\(67\) | − | 4.39373e37i | − | 0.197362i | −0.995119 | − | 0.0986808i | \(-0.968538\pi\) | ||
0.995119 | − | 0.0986808i | \(-0.0314623\pi\) | |||||||
\(68\) | −1.89575e38 | + | 4.27931e37i | −0.623868 | + | 0.140827i | ||||
\(69\) | −6.82263e38 | −1.65242 | ||||||||
\(70\) | 9.48288e37 | − | 1.05700e37i | 0.169778 | − | 0.0189241i | ||||
\(71\) | − | 5.38649e38i | − | 0.715946i | −0.933732 | − | 0.357973i | \(-0.883468\pi\) | ||
0.933732 | − | 0.357973i | \(-0.116532\pi\) | |||||||
\(72\) | 8.82101e38 | + | 2.55017e39i | 0.874049 | + | 2.52689i | ||||
\(73\) | −1.46894e39 | −1.08949 | −0.544744 | − | 0.838602i | \(-0.683373\pi\) | ||||
−0.544744 | + | 0.838602i | \(0.683373\pi\) | |||||||
\(74\) | −2.25445e38 | − | 2.02259e39i | −0.125654 | − | 1.12730i | ||||
\(75\) | 4.76005e38i | 0.200136i | ||||||||
\(76\) | −9.59066e37 | − | 4.24869e38i | −0.0305325 | − | 0.135260i | ||||
\(77\) | −9.68610e38 | −0.234339 | ||||||||
\(78\) | 4.76386e39 | − | 5.30998e38i | 0.878966 | − | 0.0979729i | ||||
\(79\) | − | 1.90750e39i | − | 0.269337i | −0.990891 | − | 0.134669i | \(-0.957003\pi\) | ||
0.990891 | − | 0.134669i | \(-0.0429970\pi\) | |||||||
\(80\) | −8.75304e39 | + | 4.16385e39i | −0.949006 | + | 0.451446i | ||||
\(81\) | 4.16087e40 | 3.47535 | ||||||||
\(82\) | 1.38668e39 | + | 1.24406e40i | 0.0895125 | + | 0.803064i | ||||
\(83\) | 3.93683e39i | 0.197018i | 0.995136 | + | 0.0985092i | \(0.0314074\pi\) | ||||
−0.995136 | + | 0.0985092i | \(0.968593\pi\) | |||||||
\(84\) | 7.80955e39 | − | 1.76287e39i | 0.303921 | − | 0.0686048i | ||||
\(85\) | −2.21436e40 | −0.672127 | ||||||||
\(86\) | −4.06411e40 | + | 4.53002e39i | −0.964936 | + | 0.107555i | ||||
\(87\) | − | 1.06547e41i | − | 1.98443i | ||||||
\(88\) | 9.29915e40 | − | 3.21657e40i | 1.36241 | − | 0.471256i | ||||
\(89\) | 4.67965e40 | 0.540784 | 0.270392 | − | 0.962750i | \(-0.412847\pi\) | ||||
0.270392 | + | 0.962750i | \(0.412847\pi\) | |||||||
\(90\) | 3.40595e40 | + | 3.05566e41i | 0.311276 | + | 2.79262i | ||||
\(91\) | − | 1.03505e40i | − | 0.0750054i | ||||||
\(92\) | −3.29541e40 | − | 1.45988e41i | −0.189830 | − | 0.840954i | ||||
\(93\) | −7.16548e41 | −3.28930 | ||||||||
\(94\) | 4.80154e40 | − | 5.35198e39i | 0.176074 | − | 0.0196259i | ||||
\(95\) | − | 4.96276e40i | − | 0.145723i | ||||||
\(96\) | −6.91215e41 | + | 4.28584e41i | −1.62899 | + | 1.01004i | ||||
\(97\) | 8.04950e41 | 1.52603 | 0.763014 | − | 0.646382i | \(-0.223719\pi\) | ||||
0.763014 | + | 0.646382i | \(0.223719\pi\) | |||||||
\(98\) | 7.05619e40 | + | 6.33048e41i | 0.107851 | + | 0.967584i | ||||
\(99\) | − | 3.12114e42i | − | 3.85456i | ||||||
\(100\) | −1.01853e41 | + | 2.29916e40i | −0.101853 | + | 0.0229916i | ||||
\(101\) | 1.16934e42 | 0.948835 | 0.474418 | − | 0.880300i | \(-0.342659\pi\) | ||||
0.474418 | + | 0.880300i | \(0.342659\pi\) | |||||||
\(102\) | −1.84656e42 | + | 2.05825e41i | −1.21832 | + | 0.135798i | ||||
\(103\) | 5.76793e41i | 0.310055i | 0.987910 | + | 0.155027i | \(0.0495466\pi\) | ||||
−0.987910 | + | 0.155027i | \(0.950453\pi\) | |||||||
\(104\) | 3.43721e41 | + | 9.93702e41i | 0.150836 | + | 0.436070i | ||||
\(105\) | 9.12210e41 | 0.327431 | ||||||||
\(106\) | 3.89192e40 | + | 3.49164e41i | 0.0114483 | + | 0.102709i | ||||
\(107\) | 6.93458e41i | 0.167479i | 0.996488 | + | 0.0837395i | \(0.0266864\pi\) | ||||
−0.996488 | + | 0.0837395i | \(0.973314\pi\) | |||||||
\(108\) | 3.55597e42 | + | 1.57530e43i | 0.706413 | + | 3.12943i | ||||
\(109\) | −8.22711e41 | −0.134676 | −0.0673381 | − | 0.997730i | \(-0.521451\pi\) | ||||
−0.0673381 | + | 0.997730i | \(0.521451\pi\) | |||||||
\(110\) | 1.11424e43 | − | 1.24198e42i | 1.50568 | − | 0.167829i | ||||
\(111\) | − | 1.94564e43i | − | 2.17410i | ||||||
\(112\) | 7.54422e41 | + | 1.58591e42i | 0.0698290 | + | 0.146791i | ||||
\(113\) | −6.47037e42 | −0.496915 | −0.248457 | − | 0.968643i | \(-0.579924\pi\) | ||||
−0.248457 | + | 0.968643i | \(0.579924\pi\) | |||||||
\(114\) | −4.61289e41 | − | 4.13846e42i | −0.0294423 | − | 0.264142i | ||||
\(115\) | − | 1.70524e43i | − | 0.906005i | ||||||
\(116\) | 2.27984e43 | − | 5.14632e42i | 1.00992 | − | 0.227971i | ||||
\(117\) | 3.33523e43 | 1.23374 | ||||||||
\(118\) | −4.30267e43 | + | 4.79592e42i | −1.33111 | + | 0.148371i | ||||
\(119\) | 4.01206e42i | 0.103964i | ||||||||
\(120\) | −8.75768e43 | + | 3.02927e43i | −1.90363 | + | 0.658465i | ||||
\(121\) | −5.90483e43 | −1.07824 | ||||||||
\(122\) | 5.51632e42 | + | 4.94898e43i | 0.0847408 | + | 0.760254i | ||||
\(123\) | 1.19673e44i | 1.54877i | ||||||||
\(124\) | −3.46101e43 | − | 1.53324e44i | −0.377875 | − | 1.67400i | ||||
\(125\) | 1.02043e44 | 0.941180 | ||||||||
\(126\) | 5.53635e43 | − | 6.17102e42i | 0.431958 | − | 0.0481477i | ||||
\(127\) | − | 7.41564e43i | − | 0.490084i | −0.969512 | − | 0.245042i | \(-0.921198\pi\) | ||
0.969512 | − | 0.245042i | \(-0.0788018\pi\) | |||||||
\(128\) | −1.25093e44 | − | 1.27202e44i | −0.701172 | − | 0.712993i | ||||
\(129\) | −3.90950e44 | −1.86096 | ||||||||
\(130\) | 1.32717e43 | + | 1.19067e44i | 0.0537174 | + | 0.481927i | ||||
\(131\) | − | 1.72311e44i | − | 0.593767i | −0.954914 | − | 0.296883i | \(-0.904053\pi\) | ||
0.954914 | − | 0.296883i | \(-0.0959472\pi\) | |||||||
\(132\) | 9.17625e44 | − | 2.07137e44i | 2.69533 | − | 0.608424i | ||||
\(133\) | −8.99171e42 | −0.0225402 | ||||||||
\(134\) | 9.15761e43 | − | 1.02074e43i | 0.196147 | − | 0.0218633i | ||||
\(135\) | 1.84006e45i | 3.37150i | ||||||||
\(136\) | −1.33233e44 | − | 3.85178e44i | −0.209071 | − | 0.604428i | ||||
\(137\) | 8.30206e44 | 1.11700 | 0.558501 | − | 0.829504i | \(-0.311377\pi\) | ||||
0.558501 | + | 0.829504i | \(0.311377\pi\) | |||||||
\(138\) | −1.58502e44 | − | 1.42200e45i | −0.183052 | − | 1.64225i | ||||
\(139\) | 2.54122e44i | 0.252192i | 0.992018 | + | 0.126096i | \(0.0402448\pi\) | ||||
−0.992018 | + | 0.126096i | \(0.959755\pi\) | |||||||
\(140\) | 4.40608e43 | + | 1.95191e44i | 0.0376153 | + | 0.166637i | ||||
\(141\) | 4.61887e44 | 0.339574 | ||||||||
\(142\) | 1.12268e45 | − | 1.25138e44i | 0.711540 | − | 0.0793109i | ||||
\(143\) | − | 1.21619e45i | − | 0.665187i | ||||||
\(144\) | −5.11025e45 | + | 2.43096e45i | −2.41451 | + | 1.14859i | ||||
\(145\) | 2.66301e45 | 1.08804 | ||||||||
\(146\) | −3.41260e44 | − | 3.06162e45i | −0.120691 | − | 1.08278i | ||||
\(147\) | 6.08963e45i | 1.86607i | ||||||||
\(148\) | 4.16319e45 | − | 9.39766e44i | 1.10645 | − | 0.249760i | ||||
\(149\) | −6.75311e45 | −1.55809 | −0.779044 | − | 0.626969i | \(-0.784295\pi\) | ||||
−0.779044 | + | 0.626969i | \(0.784295\pi\) | |||||||
\(150\) | −9.92110e44 | + | 1.10584e44i | −0.198904 | + | 0.0221706i | ||||
\(151\) | − | 5.62745e45i | − | 0.981286i | −0.871361 | − | 0.490643i | \(-0.836762\pi\) | ||
0.871361 | − | 0.490643i | \(-0.163238\pi\) | |||||||
\(152\) | 8.63250e44 | − | 2.98597e44i | 0.131045 | − | 0.0453284i | ||||
\(153\) | −1.29280e46 | −1.71006 | ||||||||
\(154\) | −2.25025e44 | − | 2.01882e45i | −0.0259595 | − | 0.232896i | ||||
\(155\) | − | 1.79093e46i | − | 1.80349i | ||||||
\(156\) | 2.21346e45 | + | 9.80568e45i | 0.194740 | + | 0.862703i | ||||
\(157\) | 8.41119e45 | 0.647090 | 0.323545 | − | 0.946213i | \(-0.395125\pi\) | ||||
0.323545 | + | 0.946213i | \(0.395125\pi\) | |||||||
\(158\) | 3.97570e45 | − | 4.43147e44i | 0.267679 | − | 0.0298366i | ||||
\(159\) | 3.35880e45i | 0.198082i | ||||||||
\(160\) | −1.07120e46 | − | 1.72761e46i | −0.553796 | − | 0.893155i | ||||
\(161\) | −3.08961e45 | −0.140139 | ||||||||
\(162\) | 9.66644e45 | + | 8.67227e46i | 0.384992 | + | 3.45396i | ||||
\(163\) | 3.69588e45i | 0.129354i | 0.997906 | + | 0.0646768i | \(0.0206016\pi\) | ||||
−0.997906 | + | 0.0646768i | \(0.979398\pi\) | |||||||
\(164\) | −2.56071e46 | + | 5.78034e45i | −0.788205 | + | 0.177923i | ||||
\(165\) | 1.07185e47 | 2.90383 | ||||||||
\(166\) | −8.20531e45 | + | 9.14596e44i | −0.195806 | + | 0.0218253i | ||||
\(167\) | − | 7.00626e46i | − | 1.47381i | −0.675999 | − | 0.736903i | \(-0.736287\pi\) | ||
0.675999 | − | 0.736903i | \(-0.263713\pi\) | |||||||
\(168\) | 5.48855e45 | + | 1.58675e46i | 0.101850 | + | 0.294451i | ||||
\(169\) | −4.80448e46 | −0.787092 | ||||||||
\(170\) | −5.14436e45 | − | 4.61527e46i | −0.0744568 | − | 0.667990i | ||||
\(171\) | − | 2.89739e46i | − | 0.370756i | ||||||
\(172\) | −1.88833e46 | − | 8.36537e46i | −0.213787 | − | 0.947082i | ||||
\(173\) | 1.00803e47 | 1.01043 | 0.505214 | − | 0.862994i | \(-0.331414\pi\) | ||||
0.505214 | + | 0.862994i | \(0.331414\pi\) | |||||||
\(174\) | 2.22069e47 | − | 2.47527e46i | 1.97221 | − | 0.219830i | ||||
\(175\) | 2.15557e45i | 0.0169732i | ||||||||
\(176\) | 8.86448e46 | + | 1.86344e47i | 0.619280 | + | 1.30182i | ||||
\(177\) | −4.13897e47 | −2.56716 | ||||||||
\(178\) | 1.08717e46 | + | 9.75354e46i | 0.0599068 | + | 0.537455i | ||||
\(179\) | − | 7.07171e46i | − | 0.346426i | −0.984884 | − | 0.173213i | \(-0.944585\pi\) | ||
0.984884 | − | 0.173213i | \(-0.0554150\pi\) | |||||||
\(180\) | −6.28961e47 | + | 1.41977e47i | −2.74095 | + | 0.618721i | ||||
\(181\) | −2.70962e47 | −1.05113 | −0.525567 | − | 0.850752i | \(-0.676147\pi\) | ||||
−0.525567 | + | 0.850752i | \(0.676147\pi\) | |||||||
\(182\) | 2.15730e46 | − | 2.40461e45i | 0.0745438 | − | 0.00830893i | ||||
\(183\) | 4.76069e47i | 1.46621i | ||||||||
\(184\) | 2.96618e47 | − | 1.02600e47i | 0.814749 | − | 0.281821i | ||||
\(185\) | 4.86290e47 | 1.19203 | ||||||||
\(186\) | −1.66467e47 | − | 1.49346e48i | −0.364381 | − | 3.26905i | ||||
\(187\) | 4.71418e47i | 0.922004i | ||||||||
\(188\) | 2.23097e46 | + | 9.88325e46i | 0.0390102 | + | 0.172816i | ||||
\(189\) | 3.33389e47 | 0.521499 | ||||||||
\(190\) | 1.03436e47 | − | 1.15294e46i | 0.144826 | − | 0.0161429i | ||||
\(191\) | − | 5.08885e47i | − | 0.638145i | −0.947730 | − | 0.319072i | \(-0.896629\pi\) | ||
0.947730 | − | 0.319072i | \(-0.103371\pi\) | |||||||
\(192\) | −1.05386e48 | − | 1.34109e48i | −1.18428 | − | 1.50707i | ||||
\(193\) | 1.06856e48 | 1.07671 | 0.538353 | − | 0.842720i | \(-0.319047\pi\) | ||||
0.538353 | + | 0.842720i | \(0.319047\pi\) | |||||||
\(194\) | 1.87004e47 | + | 1.67771e48i | 0.169050 | + | 1.51664i | ||||
\(195\) | 1.14537e48i | 0.929436i | ||||||||
\(196\) | −1.30303e48 | + | 2.94137e47i | −0.949681 | + | 0.214374i | ||||
\(197\) | −1.83912e48 | −1.20453 | −0.602267 | − | 0.798295i | \(-0.705736\pi\) | ||||
−0.602267 | + | 0.798295i | \(0.705736\pi\) | |||||||
\(198\) | 6.50522e48 | − | 7.25097e47i | 3.83083 | − | 0.426999i | ||||
\(199\) | 2.99003e48i | 1.58402i | 0.610507 | + | 0.792011i | \(0.290966\pi\) | ||||
−0.610507 | + | 0.792011i | \(0.709034\pi\) | |||||||
\(200\) | −7.15825e46 | − | 2.06946e47i | −0.0341332 | − | 0.0986796i | ||||
\(201\) | 8.80921e47 | 0.378285 | ||||||||
\(202\) | 2.71658e47 | + | 2.43718e48i | 0.105110 | + | 0.942995i | ||||
\(203\) | − | 4.82493e47i | − | 0.168296i | ||||||
\(204\) | −8.57980e47 | − | 3.80087e48i | −0.269925 | − | 1.19578i | ||||
\(205\) | −2.99108e48 | −0.849176 | ||||||||
\(206\) | −1.20218e48 | + | 1.33999e47i | −0.308147 | + | 0.0343472i | ||||
\(207\) | − | 9.95562e48i | − | 2.30511i | ||||||
\(208\) | −1.99126e48 | + | 9.47252e47i | −0.416676 | + | 0.198215i | ||||
\(209\) | −1.05653e48 | −0.199898 | ||||||||
\(210\) | 2.11923e47 | + | 1.90127e48i | 0.0362721 | + | 0.325416i | ||||
\(211\) | 8.39996e48i | 1.30120i | 0.759419 | + | 0.650602i | \(0.225483\pi\) | ||||
−0.759419 | + | 0.650602i | \(0.774517\pi\) | |||||||
\(212\) | −7.18702e47 | + | 1.62234e47i | −0.100808 | + | 0.0227556i | ||||
\(213\) | 1.07996e49 | 1.37226 | ||||||||
\(214\) | −1.44534e48 | + | 1.61103e47i | −0.166448 | + | 0.0185530i | ||||
\(215\) | − | 9.77133e48i | − | 1.02034i | ||||||
\(216\) | −3.20071e49 | + | 1.10712e49i | −3.03191 | + | 1.04874i | ||||
\(217\) | −3.24487e48 | −0.278960 | ||||||||
\(218\) | −1.91131e47 | − | 1.71473e48i | −0.0149191 | − | 0.133847i | ||||
\(219\) | − | 2.94514e49i | − | 2.08824i | ||||||
\(220\) | 5.17716e48 | + | 2.29350e49i | 0.333592 | + | 1.47782i | ||||
\(221\) | −5.03755e48 | −0.295108 | ||||||||
\(222\) | 4.05518e49 | − | 4.52006e48i | 2.16072 | − | 0.240842i | ||||
\(223\) | 5.23935e48i | 0.254024i | 0.991901 | + | 0.127012i | \(0.0405387\pi\) | ||||
−0.991901 | + | 0.127012i | \(0.959461\pi\) | |||||||
\(224\) | −3.13015e48 | + | 1.94083e48i | −0.138152 | + | 0.0856603i | ||||
\(225\) | −6.94588e48 | −0.279187 | ||||||||
\(226\) | −1.50318e48 | − | 1.34858e49i | −0.0550471 | − | 0.493856i | ||||
\(227\) | 3.25773e49i | 1.08736i | 0.839294 | + | 0.543678i | \(0.182969\pi\) | ||||
−0.839294 | + | 0.543678i | \(0.817031\pi\) | |||||||
\(228\) | 8.51841e48 | − | 1.92288e48i | 0.259255 | − | 0.0585221i | ||||
\(229\) | −2.80755e49 | −0.779440 | −0.389720 | − | 0.920933i | \(-0.627428\pi\) | ||||
−0.389720 | + | 0.920933i | \(0.627428\pi\) | |||||||
\(230\) | 3.55413e49 | − | 3.96157e48i | 0.900429 | − | 0.100365i | ||||
\(231\) | − | 1.94201e49i | − | 0.449160i | ||||||
\(232\) | 1.60227e49 | + | 4.63218e49i | 0.338444 | + | 0.978448i | ||||
\(233\) | 7.31107e49 | 1.41093 | 0.705467 | − | 0.708743i | \(-0.250737\pi\) | ||||
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(234\) | 7.74834e48 | + | 6.95144e49i | 0.136671 | + | 1.22615i | ||||
\(235\) | 1.15443e49i | 0.186184i | ||||||||
\(236\) | −1.99917e49 | − | 8.85639e49i | −0.294916 | − | 1.30649i | ||||
\(237\) | 3.82445e49 | 0.516242 | ||||||||
\(238\) | −8.36212e48 | + | 9.32073e47i | −0.103324 | + | 0.0115169i | ||||
\(239\) | − | 1.20229e50i | − | 1.36036i | −0.733044 | − | 0.680181i | \(-0.761901\pi\) | ||
0.733044 | − | 0.680181i | \(-0.238099\pi\) | |||||||
\(240\) | −8.34831e49 | − | 1.75494e50i | −0.865292 | − | 1.81897i | ||||
\(241\) | 4.41627e49 | 0.419467 | 0.209734 | − | 0.977759i | \(-0.432740\pi\) | ||||
0.209734 | + | 0.977759i | \(0.432740\pi\) | |||||||
\(242\) | −1.37180e49 | − | 1.23071e50i | −0.119445 | − | 1.07160i | ||||
\(243\) | 4.32453e50i | 3.45308i | ||||||||
\(244\) | −1.01867e50 | + | 2.29947e49i | −0.746188 | + | 0.168439i | ||||
\(245\) | −1.52203e50 | −1.02314 | ||||||||
\(246\) | −2.49427e50 | + | 2.78021e49i | −1.53924 | + | 0.171570i | ||||
\(247\) | − | 1.12900e49i | − | 0.0639820i | ||||||
\(248\) | 3.11524e50 | − | 1.07756e50i | 1.62183 | − | 0.560991i | ||||
\(249\) | −7.89314e49 | −0.377628 | ||||||||
\(250\) | 2.37064e49 | + | 2.12682e50i | 0.104262 | + | 0.935387i | ||||
\(251\) | 2.23778e50i | 0.905044i | 0.891753 | + | 0.452522i | \(0.149476\pi\) | ||||
−0.891753 | + | 0.452522i | \(0.850524\pi\) | |||||||
\(252\) | 2.57238e49 | + | 1.13957e50i | 0.0957028 | + | 0.423966i | ||||
\(253\) | −3.63030e50 | −1.24283 | ||||||||
\(254\) | 1.54560e50 | − | 1.72279e49i | 0.487068 | − | 0.0542904i | ||||
\(255\) | − | 4.43969e50i | − | 1.28827i | ||||||
\(256\) | 2.36059e50 | − | 2.90276e50i | 0.630930 | − | 0.775840i | ||||
\(257\) | −4.76780e50 | −1.17415 | −0.587074 | − | 0.809533i | \(-0.699720\pi\) | ||||
−0.587074 | + | 0.809533i | \(0.699720\pi\) | |||||||
\(258\) | −9.08245e49 | − | 8.14834e50i | −0.206153 | − | 1.84950i | ||||
\(259\) | − | 8.81076e49i | − | 0.184382i | ||||||
\(260\) | −2.45082e50 | + | 5.53228e49i | −0.473010 | + | 0.106774i | ||||
\(261\) | 1.55473e51 | 2.76825 | ||||||||
\(262\) | 3.59138e50 | − | 4.00309e49i | 0.590112 | − | 0.0657761i | ||||
\(263\) | − | 4.31487e50i | − | 0.654481i | −0.944941 | − | 0.327240i | \(-0.893881\pi\) | ||
0.944941 | − | 0.327240i | \(-0.106119\pi\) | |||||||
\(264\) | 6.44906e50 | + | 1.86443e51i | 0.903262 | + | 2.61135i | ||||
\(265\) | −8.39494e49 | −0.108606 | ||||||||
\(266\) | −2.08893e48 | − | 1.87409e49i | −0.00249695 | − | 0.0224015i | ||||
\(267\) | 9.38247e50i | 1.03653i | ||||||||
\(268\) | 4.25495e49 | + | 1.88496e50i | 0.0434574 | + | 0.192518i | ||||
\(269\) | 1.32027e51 | 1.24700 | 0.623499 | − | 0.781824i | \(-0.285710\pi\) | ||||
0.623499 | + | 0.781824i | \(0.285710\pi\) | |||||||
\(270\) | −3.83514e51 | + | 4.27480e50i | −3.35075 | + | 0.373488i | ||||
\(271\) | − | 1.45627e50i | − | 0.117730i | −0.998266 | − | 0.0588648i | \(-0.981252\pi\) | ||
0.998266 | − | 0.0588648i | \(-0.0187481\pi\) | |||||||
\(272\) | 7.71853e50 | − | 3.67174e50i | 0.577548 | − | 0.274742i | ||||
\(273\) | 2.07522e50 | 0.143764 | ||||||||
\(274\) | 1.92872e50 | + | 1.73035e51i | 0.123739 | + | 1.11013i | ||||
\(275\) | 2.53281e50i | 0.150527i | ||||||||
\(276\) | 2.92698e51 | − | 6.60714e50i | 1.61187 | − | 0.363850i | ||||
\(277\) | −1.50520e51 | −0.768277 | −0.384138 | − | 0.923276i | \(-0.625501\pi\) | ||||
−0.384138 | + | 0.923276i | \(0.625501\pi\) | |||||||
\(278\) | −5.29653e50 | + | 5.90371e49i | −0.250640 | + | 0.0279373i | ||||
\(279\) | − | 1.04559e52i | − | 4.58853i | ||||||
\(280\) | −3.96589e50 | + | 1.37180e50i | −0.161444 | + | 0.0558434i | ||||
\(281\) | −4.06078e51 | −1.53383 | −0.766913 | − | 0.641751i | \(-0.778208\pi\) | ||||
−0.766913 | + | 0.641751i | \(0.778208\pi\) | |||||||
\(282\) | 1.07305e50 | + | 9.62685e50i | 0.0376172 | + | 0.337484i | ||||
\(283\) | 4.23627e51i | 1.37870i | 0.724430 | + | 0.689348i | \(0.242103\pi\) | ||||
−0.724430 | + | 0.689348i | \(0.757897\pi\) | |||||||
\(284\) | 5.21635e50 | + | 2.31086e51i | 0.157646 | + | 0.698375i | ||||
\(285\) | 9.95009e50 | 0.279309 | ||||||||
\(286\) | 2.53483e51 | − | 2.82542e50i | 0.661093 | − | 0.0736880i | ||||
\(287\) | 5.41935e50i | 0.131349i | ||||||||
\(288\) | −6.25392e51 | − | 1.00862e52i | −1.40900 | − | 2.27241i | ||||
\(289\) | −2.82104e51 | −0.590956 | ||||||||
\(290\) | 6.18664e50 | + | 5.55036e51i | 0.120531 | + | 1.08134i | ||||
\(291\) | 1.61388e52i | 2.92496i | ||||||||
\(292\) | 6.30188e51 | − | 1.42254e51i | 1.06275 | − | 0.239897i | ||||
\(293\) | −1.06303e52 | −1.66850 | −0.834249 | − | 0.551388i | \(-0.814098\pi\) | ||||
−0.834249 | + | 0.551388i | \(0.814098\pi\) | |||||||
\(294\) | −1.26923e52 | + | 1.41473e51i | −1.85458 | + | 0.206719i | ||||
\(295\) | − | 1.03449e52i | − | 1.40755i | ||||||
\(296\) | 2.92589e51 | + | 8.45878e51i | 0.370793 | + | 1.07197i | ||||
\(297\) | 3.91733e52 | 4.62493 | ||||||||
\(298\) | −1.56887e51 | − | 1.40751e52i | −0.172602 | − | 1.54850i | ||||
\(299\) | − | 3.87932e51i | − | 0.397796i | ||||||
\(300\) | −4.60970e50 | − | 2.04211e51i | −0.0440683 | − | 0.195224i | ||||
\(301\) | −1.77040e51 | −0.157825 | ||||||||
\(302\) | 1.17290e52 | − | 1.30736e51i | 0.975247 | − | 0.108705i | ||||
\(303\) | 2.34446e52i | 1.81864i | ||||||||
\(304\) | 8.22898e50 | + | 1.72985e51i | 0.0595663 | + | 0.125217i | ||||
\(305\) | −1.18988e52 | −0.803908 | ||||||||
\(306\) | −3.00341e51 | − | 2.69452e52i | −0.189437 | − | 1.69954i | ||||
\(307\) | 9.76203e51i | 0.574956i | 0.957787 | + | 0.287478i | \(0.0928168\pi\) | ||||
−0.957787 | + | 0.287478i | \(0.907183\pi\) | |||||||
\(308\) | 4.15544e51 | − | 9.38016e50i | 0.228587 | − | 0.0515995i | ||||
\(309\) | −1.15644e52 | −0.594286 | ||||||||
\(310\) | 3.73273e52 | − | 4.16065e51i | 1.79239 | − | 0.199786i | ||||
\(311\) | 2.43319e50i | 0.0109196i | 0.999985 | + | 0.00545981i | \(0.00173792\pi\) | ||||
−0.999985 | + | 0.00545981i | \(0.998262\pi\) | |||||||
\(312\) | −1.99232e52 | + | 6.89142e51i | −0.835820 | + | 0.289110i | ||||
\(313\) | −3.06916e52 | −1.20389 | −0.601947 | − | 0.798536i | \(-0.705608\pi\) | ||||
−0.601947 | + | 0.798536i | \(0.705608\pi\) | |||||||
\(314\) | 1.95407e51 | + | 1.75310e52i | 0.0716832 | + | 0.643107i | ||||
\(315\) | 1.33110e52i | 0.456761i | ||||||||
\(316\) | 1.84725e51 | + | 8.18338e51i | 0.0593059 | + | 0.262727i | ||||
\(317\) | 1.02516e52 | 0.307997 | 0.153998 | − | 0.988071i | \(-0.450785\pi\) | ||||
0.153998 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(318\) | −7.00057e51 | + | 7.80310e50i | −0.196863 | + | 0.0219431i | ||||
\(319\) | − | 5.66931e52i | − | 1.49254i | ||||||
\(320\) | 3.35191e52 | − | 2.63399e52i | 0.826310 | − | 0.649329i | ||||
\(321\) | −1.39035e52 | −0.321009 | ||||||||
\(322\) | −7.17772e50 | − | 6.43950e51i | −0.0155243 | − | 0.139277i | ||||
\(323\) | 4.37623e51i | 0.0886843i | ||||||||
\(324\) | −1.78506e53 | + | 4.02945e52i | −3.39005 | + | 0.765244i | ||||
\(325\) | −2.70654e51 | −0.0481797 | ||||||||
\(326\) | −7.70313e51 | + | 8.58620e50i | −0.128557 | + | 0.0143295i | ||||
\(327\) | − | 1.64949e52i | − | 0.258136i | ||||||
\(328\) | −1.79966e52 | − | 5.20285e52i | −0.264144 | − | 0.763644i | ||||
\(329\) | 2.09164e51 | 0.0287987 | ||||||||
\(330\) | 2.49010e52 | + | 2.23400e53i | 0.321680 | + | 2.88596i | ||||
\(331\) | − | 8.40636e52i | − | 1.01911i | −0.860439 | − | 0.509554i | \(-0.829810\pi\) | ||
0.860439 | − | 0.509554i | \(-0.170190\pi\) | |||||||
\(332\) | −3.81248e51 | − | 1.68894e52i | −0.0433818 | − | 0.192183i | ||||
\(333\) | 2.83908e53 | 3.03284 | ||||||||
\(334\) | 1.46028e53 | − | 1.62768e52i | 1.46473 | − | 0.163265i | ||||
\(335\) | 2.20176e52i | 0.207410i | ||||||||
\(336\) | −3.17966e52 | + | 1.51258e52i | −0.281356 | + | 0.133842i | ||||
\(337\) | −1.09100e53 | −0.906975 | −0.453488 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453488 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(338\) | −1.11617e52 | − | 1.00137e53i | −0.0871923 | − | 0.782247i | ||||
\(339\) | − | 1.29728e53i | − | 0.952443i | ||||||
\(340\) | 9.49985e52 | − | 2.14442e52i | 0.655631 | − | 0.147997i | ||||
\(341\) | −3.81273e53 | −2.47397 | ||||||||
\(342\) | 6.03887e52 | − | 6.73115e51i | 0.368474 | − | 0.0410716i | ||||
\(343\) | 5.59019e52i | 0.320812i | ||||||||
\(344\) | 1.69968e53 | − | 5.87917e52i | 0.917570 | − | 0.317387i | ||||
\(345\) | 3.41892e53 | 1.73655 | ||||||||
\(346\) | 2.34183e52 | + | 2.10098e53i | 0.111933 | + | 1.00421i | ||||
\(347\) | − | 2.35925e53i | − | 1.06134i | −0.847578 | − | 0.530671i | \(-0.821940\pi\) | ||
0.847578 | − | 0.530671i | \(-0.178060\pi\) | |||||||
\(348\) | 1.03181e53 | + | 4.57096e53i | 0.436955 | + | 1.93572i | ||||
\(349\) | 2.01321e52 | 0.0802704 | 0.0401352 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401352 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(350\) | −4.49274e51 | + | 5.00778e50i | −0.0168687 | + | 0.00188025i | ||||
\(351\) | 4.18604e53i | 1.48031i | ||||||||
\(352\) | −3.67794e53 | + | 2.28048e53i | −1.22520 | + | 0.759681i | ||||
\(353\) | −2.95364e53 | −0.927018 | −0.463509 | − | 0.886092i | \(-0.653410\pi\) | ||||
−0.463509 | + | 0.886092i | \(0.653410\pi\) | |||||||
\(354\) | −9.61557e52 | − | 8.62663e53i | −0.284385 | − | 2.55136i | ||||
\(355\) | 2.69924e53i | 0.752397i | ||||||||
\(356\) | −2.00762e53 | + | 4.53184e52i | −0.527511 | + | 0.119076i | ||||
\(357\) | −8.04398e52 | −0.199268 | ||||||||
\(358\) | 1.47392e53 | − | 1.64289e52i | 0.344294 | − | 0.0383763i | ||||
\(359\) | 6.96302e53i | 1.53396i | 0.641671 | + | 0.766980i | \(0.278241\pi\) | ||||
−0.641671 | + | 0.766980i | \(0.721759\pi\) | |||||||
\(360\) | −4.42033e53 | − | 1.27792e54i | −0.918549 | − | 2.65554i | ||||
\(361\) | 5.00287e53 | 0.980772 | ||||||||
\(362\) | −6.29493e52 | − | 5.64751e53i | −0.116442 | − | 1.04466i | ||||
\(363\) | − | 1.18389e54i | − | 2.06667i | ||||||
\(364\) | 1.00236e52 | + | 4.44048e52i | 0.0165156 | + | 0.0731645i | ||||
\(365\) | 7.36104e53 | 1.14496 | ||||||||
\(366\) | −9.92244e53 | + | 1.10599e53i | −1.45719 | + | 0.162424i | ||||
\(367\) | 5.65502e53i | 0.784236i | 0.919915 | + | 0.392118i | \(0.128258\pi\) | ||||
−0.919915 | + | 0.392118i | \(0.871742\pi\) | |||||||
\(368\) | 2.82753e53 | + | 5.94389e53i | 0.370342 | + | 0.778515i | ||||
\(369\) | −1.74627e54 | −2.16052 | ||||||||
\(370\) | 1.12974e53 | + | 1.01355e54i | 0.132051 | + | 1.18470i | ||||
\(371\) | 1.52102e52i | 0.0167990i | ||||||||
\(372\) | 3.07407e54 | − | 6.93915e53i | 3.20857 | − | 0.724277i | ||||
\(373\) | −1.04035e54 | −1.02634 | −0.513172 | − | 0.858286i | \(-0.671530\pi\) | ||||
−0.513172 | + | 0.858286i | \(0.671530\pi\) | |||||||
\(374\) | −9.82551e53 | + | 1.09519e53i | −0.916329 | + | 0.102138i | ||||
\(375\) | 2.04591e54i | 1.80397i | ||||||||
\(376\) | −2.00808e53 | + | 6.94594e52i | −0.167431 | + | 0.0579143i | ||||
\(377\) | 6.05819e53 | 0.477721 | ||||||||
\(378\) | 7.74522e52 | + | 6.94864e53i | 0.0577705 | + | 0.518289i | ||||
\(379\) | 1.05506e54i | 0.744485i | 0.928136 | + | 0.372242i | \(0.121411\pi\) | ||||
−0.928136 | + | 0.372242i | \(0.878589\pi\) | |||||||
\(380\) | 4.80601e52 | + | 2.12908e53i | 0.0320870 | + | 0.142146i | ||||
\(381\) | 1.48680e54 | 0.939351 | ||||||||
\(382\) | 1.06064e54 | − | 1.18223e53i | 0.634217 | − | 0.0706923i | ||||
\(383\) | − | 2.43091e54i | − | 1.37593i | −0.725745 | − | 0.687963i | \(-0.758505\pi\) | ||
0.725745 | − | 0.687963i | \(-0.241495\pi\) | |||||||
\(384\) | 2.55034e54 | − | 2.50805e54i | 1.36660 | − | 1.34394i | ||||
\(385\) | 4.85384e53 | 0.246269 | ||||||||
\(386\) | 2.48246e53 | + | 2.22715e54i | 0.119275 | + | 1.07008i | ||||
\(387\) | − | 5.70475e54i | − | 2.59601i | ||||||
\(388\) | −3.45332e54 | + | 7.79525e53i | −1.48857 | + | 0.336019i | ||||
\(389\) | 6.59971e53 | 0.269515 | 0.134758 | − | 0.990879i | \(-0.456974\pi\) | ||||
0.134758 | + | 0.990879i | \(0.456974\pi\) | |||||||
\(390\) | −2.38723e54 | + | 2.66090e53i | −0.923716 | + | 0.102961i | ||||
\(391\) | 1.50370e54i | 0.551378i | ||||||||
\(392\) | −9.15770e53 | − | 2.64751e54i | −0.318258 | − | 0.920089i | ||||
\(393\) | 3.45475e54 | 1.13808 | ||||||||
\(394\) | −4.27260e53 | − | 3.83317e54i | −0.133436 | − | 1.19712i | ||||
\(395\) | 9.55876e53i | 0.283050i | ||||||||
\(396\) | 3.02256e54 | + | 1.33900e55i | 0.848742 | + | 3.75995i | ||||
\(397\) | 2.59913e54 | 0.692194 | 0.346097 | − | 0.938199i | \(-0.387507\pi\) | ||||
0.346097 | + | 0.938199i | \(0.387507\pi\) | |||||||
\(398\) | −6.23196e54 | + | 6.94638e53i | −1.57427 | + | 0.175474i | ||||
\(399\) | − | 1.80279e53i | − | 0.0432031i | ||||||
\(400\) | 4.14696e53 | − | 1.97273e53i | 0.0942910 | − | 0.0448546i | ||||
\(401\) | −4.81985e54 | −1.03993 | −0.519963 | − | 0.854189i | \(-0.674054\pi\) | ||||
−0.519963 | + | 0.854189i | \(0.674054\pi\) | |||||||
\(402\) | 2.04654e53 | + | 1.83605e54i | 0.0419056 | + | 0.375957i | ||||
\(403\) | − | 4.07426e54i | − | 0.791850i | ||||||
\(404\) | −5.01657e54 | + | 1.13240e54i | −0.925547 | + | 0.208926i | ||||
\(405\) | −2.08507e55 | −3.65229 | ||||||||
\(406\) | 1.00563e54 | − | 1.12092e53i | 0.167260 | − | 0.0186435i | ||||
\(407\) | − | 1.03527e55i | − | 1.63520i | ||||||
\(408\) | 7.72263e54 | − | 2.67125e54i | 1.15852 | − | 0.400729i | ||||
\(409\) | 1.31322e55 | 1.87132 | 0.935661 | − | 0.352899i | \(-0.114804\pi\) | ||||
0.935661 | + | 0.352899i | \(0.114804\pi\) | |||||||
\(410\) | −6.94882e53 | − | 6.23415e54i | −0.0940698 | − | 0.843949i | ||||
\(411\) | 1.66452e55i | 2.14097i | ||||||||
\(412\) | −5.58575e53 | − | 2.47450e54i | −0.0682716 | − | 0.302445i | ||||
\(413\) | −1.87432e54 | −0.217717 | ||||||||
\(414\) | 2.07499e55 | − | 2.31287e54i | 2.29092 | − | 0.255355i | ||||
\(415\) | − | 1.97280e54i | − | 0.207049i | ||||||
\(416\) | −2.43691e54 | − | 3.93022e54i | −0.243153 | − | 0.392154i | ||||
\(417\) | −5.09502e54 | −0.483380 | ||||||||
\(418\) | −2.45450e53 | − | 2.20206e54i | −0.0221443 | − | 0.198668i | ||||
\(419\) | 2.86152e54i | 0.245529i | 0.992436 | + | 0.122764i | \(0.0391760\pi\) | ||||
−0.992436 | + | 0.122764i | \(0.960824\pi\) | |||||||
\(420\) | −3.91348e54 | + | 8.83397e53i | −0.319395 | + | 0.0720976i | ||||
\(421\) | 2.20771e55 | 1.71403 | 0.857013 | − | 0.515295i | \(-0.172318\pi\) | ||||
0.857013 | + | 0.515295i | \(0.172318\pi\) | |||||||
\(422\) | −1.75076e55 | + | 1.95146e54i | −1.29320 | + | 0.144145i | ||||
\(423\) | 6.73987e54i | 0.473701i | ||||||||
\(424\) | −5.05103e53 | − | 1.46026e54i | −0.0337829 | − | 0.0976669i | ||||
\(425\) | 1.04911e54 | 0.0667810 | ||||||||
\(426\) | 2.50895e54 | + | 2.25091e55i | 0.152016 | + | 1.36382i | ||||
\(427\) | 2.15587e54i | 0.124347i | ||||||||
\(428\) | −6.71554e53 | − | 2.97500e54i | −0.0368775 | − | 0.163369i | ||||
\(429\) | 2.43840e55 | 1.27497 | ||||||||
\(430\) | 2.03658e55 | − | 2.27005e54i | 1.01406 | − | 0.113031i | ||||
\(431\) | 2.23228e55i | 1.05859i | 0.848439 | + | 0.529293i | \(0.177543\pi\) | ||||
−0.848439 | + | 0.529293i | \(0.822457\pi\) | |||||||
\(432\) | −3.05109e55 | − | 6.41385e55i | −1.37815 | − | 2.89708i | ||||
\(433\) | 1.16815e54 | 0.0502634 | 0.0251317 | − | 0.999684i | \(-0.491999\pi\) | ||||
0.0251317 | + | 0.999684i | \(0.491999\pi\) | |||||||
\(434\) | −7.53841e53 | − | 6.76310e54i | −0.0309026 | − | 0.277244i | ||||
\(435\) | 5.33919e55i | 2.08546i | ||||||||
\(436\) | 3.52952e54 | − | 7.96726e53i | 0.131371 | − | 0.0296546i | ||||
\(437\) | −3.37005e54 | −0.119543 | ||||||||
\(438\) | 6.13839e55 | − | 6.84209e54i | 2.07538 | − | 0.231330i | ||||
\(439\) | − | 5.62221e55i | − | 1.81197i | −0.423306 | − | 0.905987i | \(-0.639131\pi\) | ||
0.423306 | − | 0.905987i | \(-0.360869\pi\) | |||||||
\(440\) | −4.65993e55 | + | 1.61187e55i | −1.43177 | + | 0.495248i | ||||
\(441\) | −8.88602e55 | −2.60314 | ||||||||
\(442\) | −1.17031e54 | − | 1.04995e55i | −0.0326914 | − | 0.293292i | ||||
\(443\) | 3.30478e55i | 0.880369i | 0.897907 | + | 0.440185i | \(0.145087\pi\) | ||||
−0.897907 | + | 0.440185i | \(0.854913\pi\) | |||||||
\(444\) | 1.88418e55 | + | 8.34698e55i | 0.478719 | + | 2.12074i | ||||
\(445\) | −2.34504e55 | −0.568316 | ||||||||
\(446\) | −1.09201e55 | + | 1.21719e54i | −0.252461 | + | 0.0281402i | ||||
\(447\) | − | 1.35396e56i | − | 2.98641i | ||||||
\(448\) | −4.77236e54 | − | 6.07311e54i | −0.100437 | − | 0.127812i | ||||
\(449\) | −4.46249e55 | −0.896198 | −0.448099 | − | 0.893984i | \(-0.647899\pi\) | ||||
−0.448099 | + | 0.893984i | \(0.647899\pi\) | |||||||
\(450\) | −1.61365e54 | − | 1.44769e55i | −0.0309277 | − | 0.277468i | ||||
\(451\) | 6.36775e55i | 1.16487i | ||||||||
\(452\) | 2.77586e55 | − | 6.26600e54i | 0.484719 | − | 0.109417i | ||||
\(453\) | 1.12828e56 | 1.88084 | ||||||||
\(454\) | −6.78990e55 | + | 7.56828e54i | −1.08066 | + | 0.120455i | ||||
\(455\) | 5.18678e54i | 0.0788241i | ||||||||
\(456\) | 5.98673e54 | + | 1.73077e55i | 0.0868816 | + | 0.251176i | ||||
\(457\) | 4.64937e55 | 0.644398 | 0.322199 | − | 0.946672i | \(-0.395578\pi\) | ||||
0.322199 | + | 0.946672i | \(0.395578\pi\) | |||||||
\(458\) | −6.52244e54 | − | 5.85162e55i | −0.0863446 | − | 0.774643i | ||||
\(459\) | − | 1.62259e56i | − | 2.05183i | ||||||
\(460\) | 1.65138e55 | + | 7.31565e55i | 0.199495 | + | 0.883768i | ||||
\(461\) | −1.28726e56 | −1.48575 | −0.742877 | − | 0.669427i | \(-0.766540\pi\) | ||||
−0.742877 | + | 0.669427i | \(0.766540\pi\) | |||||||
\(462\) | 4.04763e55 | − | 4.51165e54i | 0.446395 | − | 0.0497569i | ||||
\(463\) | 5.41494e55i | 0.570680i | 0.958426 | + | 0.285340i | \(0.0921066\pi\) | ||||
−0.958426 | + | 0.285340i | \(0.907893\pi\) | |||||||
\(464\) | −9.28236e55 | + | 4.41565e55i | −0.934933 | + | 0.444751i | ||||
\(465\) | 3.59072e56 | 3.45676 | ||||||||
\(466\) | 1.69849e55 | + | 1.52381e56i | 0.156300 | + | 1.40225i | ||||
\(467\) | − | 2.30411e55i | − | 0.202698i | −0.994851 | − | 0.101349i | \(-0.967684\pi\) | ||
0.994851 | − | 0.101349i | \(-0.0323159\pi\) | |||||||
\(468\) | −1.43085e56 | + | 3.22989e55i | −1.20346 | + | 0.271659i | ||||
\(469\) | 3.98923e54 | 0.0320818 | ||||||||
\(470\) | −2.40612e55 | + | 2.68195e54i | −0.185039 | + | 0.0206251i | ||||
\(471\) | 1.68640e56i | 1.24029i | ||||||||
\(472\) | 1.79944e56 | − | 6.22426e55i | 1.26577 | − | 0.437830i | ||||
\(473\) | −2.08023e56 | −1.39968 | ||||||||
\(474\) | 8.88487e54 | + | 7.97108e55i | 0.0571881 | + | 0.513065i | ||||
\(475\) | 2.35123e54i | 0.0144787i | ||||||||
\(476\) | −3.88534e54 | − | 1.72122e55i | −0.0228919 | − | 0.101412i | ||||
\(477\) | −4.90118e55 | −0.276322 | ||||||||
\(478\) | 2.50587e56 | − | 2.79314e55i | 1.35199 | − | 0.150698i | ||||
\(479\) | − | 3.25556e56i | − | 1.68105i | −0.541773 | − | 0.840525i | \(-0.682247\pi\) | ||
0.541773 | − | 0.840525i | \(-0.317753\pi\) | |||||||
\(480\) | 3.46378e56 | − | 2.14770e56i | 1.71192 | − | 1.06147i | ||||
\(481\) | 1.10628e56 | 0.523382 | ||||||||
\(482\) | 1.02598e55 | + | 9.20459e55i | 0.0464676 | + | 0.416885i | ||||
\(483\) | − | 6.19451e55i | − | 0.268607i | ||||||
\(484\) | 2.53323e56 | − | 5.71832e55i | 1.05177 | − | 0.237419i | ||||
\(485\) | −4.03372e56 | −1.60372 | ||||||||
\(486\) | −9.01337e56 | + | 1.00466e56i | −3.43183 | + | 0.382525i | ||||
\(487\) | 9.03410e55i | 0.329440i | 0.986340 | + | 0.164720i | \(0.0526721\pi\) | ||||
−0.986340 | + | 0.164720i | \(0.947328\pi\) | |||||||
\(488\) | −7.15922e55 | − | 2.06974e56i | −0.250063 | − | 0.722936i | ||||
\(489\) | −7.41006e55 | −0.247934 | ||||||||
\(490\) | −3.53596e55 | − | 3.17229e56i | −0.113342 | − | 1.01685i | ||||
\(491\) | 2.45159e53i | 0.000752898i | 1.00000 | 0.000376449i | \(0.000119827\pi\) | |||||
−1.00000 | 0.000376449i | \(0.999880\pi\) | ||||||||
\(492\) | −1.15893e56 | − | 5.13409e56i | −0.341028 | − | 1.51076i | ||||
\(493\) | −2.34827e56 | −0.662160 | ||||||||
\(494\) | 2.35311e55 | − | 2.62287e54i | 0.0635882 | − | 0.00708778i | ||||
\(495\) | 1.56405e57i | 4.05080i | ||||||||
\(496\) | 2.96962e56 | + | 6.24258e56i | 0.737201 | + | 1.54971i | ||||
\(497\) | 4.89059e55 | 0.116380 | ||||||||
\(498\) | −1.83372e55 | − | 1.64512e56i | −0.0418327 | − | 0.375303i | ||||
\(499\) | 4.50764e56i | 0.985910i | 0.870055 | + | 0.492955i | \(0.164083\pi\) | ||||
−0.870055 | + | 0.492955i | \(0.835917\pi\) | |||||||
\(500\) | −4.37775e56 | + | 9.88198e55i | −0.918080 | + | 0.207240i | ||||
\(501\) | 1.40472e57 | 2.82486 | ||||||||
\(502\) | −4.66409e56 | + | 5.19877e55i | −0.899474 | + | 0.100259i | ||||
\(503\) | − | 9.17401e56i | − | 1.69680i | −0.529354 | − | 0.848401i | \(-0.677566\pi\) | ||
0.529354 | − | 0.848401i | \(-0.322434\pi\) | |||||||
\(504\) | −2.31539e56 | + | 8.00891e55i | −0.410755 | + | 0.142080i | ||||
\(505\) | −5.85971e56 | −0.997142 | ||||||||
\(506\) | −8.43384e55 | − | 7.56644e56i | −0.137678 | − | 1.23518i | ||||
\(507\) | − | 9.63273e56i | − | 1.50863i | ||||||
\(508\) | 7.18142e55 | + | 3.18139e56i | 0.107913 | + | 0.478056i | ||||
\(509\) | −2.90868e56 | −0.419394 | −0.209697 | − | 0.977766i | \(-0.567248\pi\) | ||||
−0.209697 | + | 0.977766i | \(0.567248\pi\) | |||||||
\(510\) | 9.25339e56 | − | 1.03142e56i | 1.28035 | − | 0.142712i | ||||
\(511\) | − | 1.33370e56i | − | 0.177100i | ||||||
\(512\) | 6.59847e56 | + | 4.24568e56i | 0.840958 | + | 0.541101i | ||||
\(513\) | 3.63650e56 | 0.444855 | ||||||||
\(514\) | −1.10765e56 | − | 9.93727e56i | −0.130070 | − | 1.16692i | ||||
\(515\) | − | 2.89039e56i | − | 0.325840i | ||||||
\(516\) | 1.67721e57 | − | 3.78601e56i | 1.81528 | − | 0.409768i | ||||
\(517\) | 2.45768e56 | 0.255402 | ||||||||
\(518\) | 1.83638e56 | − | 2.04690e55i | 0.183247 | − | 0.0204254i | ||||
\(519\) | 2.02105e57i | 1.93670i | ||||||||
\(520\) | −1.72243e56 | − | 4.97958e56i | −0.158516 | − | 0.458271i | ||||
\(521\) | −1.08917e57 | −0.962724 | −0.481362 | − | 0.876522i | \(-0.659858\pi\) | ||||
−0.481362 | + | 0.876522i | \(0.659858\pi\) | |||||||
\(522\) | 3.61192e56 | + | 3.24044e57i | 0.306660 | + | 2.75121i | ||||
\(523\) | − | 1.14867e57i | − | 0.936832i | −0.883508 | − | 0.468416i | \(-0.844825\pi\) | ||
0.883508 | − | 0.468416i | \(-0.155175\pi\) | |||||||
\(524\) | 1.66868e56 | + | 7.39232e56i | 0.130743 | + | 0.579193i | ||||
\(525\) | −4.32182e55 | −0.0325328 | ||||||||
\(526\) | 8.99324e56 | − | 1.00242e56i | 0.650452 | − | 0.0725019i | ||||
\(527\) | 1.57926e57i | 1.09757i | ||||||||
\(528\) | −3.73611e57 | + | 1.77728e57i | −2.49521 | + | 1.18698i | ||||
\(529\) | 4.00036e56 | 0.256761 | ||||||||
\(530\) | −1.95029e55 | − | 1.74971e56i | −0.0120311 | − | 0.107938i | ||||
\(531\) | − | 6.03960e57i | − | 3.58116i | ||||||
\(532\) | 3.85754e55 | − | 8.70770e54i | 0.0219870 | − | 0.00496317i | ||||
\(533\) | −6.80454e56 | −0.372844 | ||||||||
\(534\) | −1.95554e57 | + | 2.17971e56i | −1.03015 | + | 0.114824i | ||||
\(535\) | − | 3.47501e56i | − | 0.176006i | ||||||
\(536\) | −3.82986e56 | + | 1.32475e56i | −0.186519 | + | 0.0645166i | ||||
\(537\) | 1.41784e57 | 0.664000 | ||||||||
\(538\) | 3.06723e56 | + | 2.75177e57i | 0.138140 | + | 1.23932i | ||||
\(539\) | 3.24027e57i | 1.40352i | ||||||||
\(540\) | −1.78194e57 | − | 7.89406e57i | −0.742378 | − | 3.28876i | ||||
\(541\) | 2.50169e57 | 1.00251 | 0.501257 | − | 0.865298i | \(-0.332871\pi\) | ||||
0.501257 | + | 0.865298i | \(0.332871\pi\) | |||||||
\(542\) | 3.03522e56 | − | 3.38317e55i | 0.117005 | − | 0.0130418i | ||||
\(543\) | − | 5.43265e57i | − | 2.01472i | ||||||
\(544\) | 9.44595e56 | + | 1.52343e57i | 0.337030 | + | 0.543558i | ||||
\(545\) | 4.12272e56 | 0.141533 | ||||||||
\(546\) | 4.82112e55 | + | 4.32528e56i | 0.0159258 | + | 0.142879i | ||||
\(547\) | 2.49088e57i | 0.791807i | 0.918292 | + | 0.395904i | \(0.129569\pi\) | ||||
−0.918292 | + | 0.395904i | \(0.870431\pi\) | |||||||
\(548\) | −3.56167e57 | + | 8.03984e56i | −1.08959 | + | 0.245955i | ||||
\(549\) | −6.94682e57 | −2.04535 | ||||||||
\(550\) | −5.27899e56 | + | 5.88416e55i | −0.149601 | + | 0.0166751i | ||||
\(551\) | − | 5.26288e56i | − | 0.143562i | ||||||
\(552\) | 2.05708e57 | + | 5.94705e57i | 0.540170 | + | 1.56164i | ||||
\(553\) | 1.73189e56 | 0.0437817 | ||||||||
\(554\) | −3.49684e56 | − | 3.13719e57i | −0.0851080 | − | 0.763548i | ||||
\(555\) | 9.74986e57i | 2.28479i | ||||||||
\(556\) | −2.46096e56 | − | 1.09021e57i | −0.0555307 | − | 0.246003i | ||||
\(557\) | 3.87716e57 | 0.842471 | 0.421235 | − | 0.906951i | \(-0.361597\pi\) | ||||
0.421235 | + | 0.906951i | \(0.361597\pi\) | |||||||
\(558\) | 2.17927e58 | − | 2.42909e57i | 4.56029 | − | 0.508307i | ||||
\(559\) | − | 2.22292e57i | − | 0.447998i | ||||||
\(560\) | −3.78051e56 | − | 7.94719e56i | −0.0733841 | − | 0.154264i | ||||
\(561\) | −9.45170e57 | −1.76722 | ||||||||
\(562\) | −9.43391e56 | − | 8.46365e57i | −0.169914 | − | 1.52439i | ||||
\(563\) | 3.22760e57i | 0.560019i | 0.959997 | + | 0.280010i | \(0.0903377\pi\) | ||||
−0.959997 | + | 0.280010i | \(0.909662\pi\) | |||||||
\(564\) | −1.98154e57 | + | 4.47298e56i | −0.331239 | + | 0.0747714i | ||||
\(565\) | 3.24239e57 | 0.522214 | ||||||||
\(566\) | −8.82943e57 | + | 9.84161e56i | −1.37021 | + | 0.152729i | ||||
\(567\) | 3.77780e57i | 0.564930i | ||||||||
\(568\) | −4.69521e57 | + | 1.62407e57i | −0.676613 | + | 0.234040i | ||||
\(569\) | 9.08852e57 | 1.26222 | 0.631110 | − | 0.775693i | \(-0.282599\pi\) | ||||
0.631110 | + | 0.775693i | \(0.282599\pi\) | |||||||
\(570\) | 2.31158e56 | + | 2.07384e57i | 0.0309412 | + | 0.277590i | ||||
\(571\) | − | 6.34725e57i | − | 0.818893i | −0.912334 | − | 0.409447i | \(-0.865722\pi\) | ||
0.912334 | − | 0.409447i | \(-0.134278\pi\) | |||||||
\(572\) | 1.17777e57 | + | 5.21757e57i | 0.146469 | + | 0.648861i | ||||
\(573\) | 1.02029e58 | 1.22314 | ||||||||
\(574\) | −1.12953e57 | + | 1.25901e56i | −0.130541 | + | 0.0145506i | ||||
\(575\) | 8.07898e56i | 0.0900185i | ||||||||
\(576\) | 1.95693e58 | − | 1.53779e58i | 2.10234 | − | 1.65206i | ||||
\(577\) | −1.41714e57 | −0.146798 | −0.0733990 | − | 0.997303i | \(-0.523385\pi\) | ||||
−0.0733990 | + | 0.997303i | \(0.523385\pi\) | |||||||
\(578\) | −6.55379e56 | − | 5.87974e57i | −0.0654648 | − | 0.587319i | ||||
\(579\) | 2.14242e58i | 2.06373i | ||||||||
\(580\) | −1.14246e58 | + | 2.57889e57i | −1.06133 | + | 0.239577i | ||||
\(581\) | −3.57439e56 | −0.0320260 | ||||||||
\(582\) | −3.36373e58 | + | 3.74934e57i | −2.90695 | + | 0.324020i | ||||
\(583\) | 1.78721e57i | 0.148983i | ||||||||
\(584\) | 4.42896e57 | + | 1.28042e58i | 0.356149 | + | 1.02963i | ||||
\(585\) | −1.67133e58 | −1.29655 | ||||||||
\(586\) | −2.46961e57 | − | 2.21561e58i | −0.184832 | − | 1.65823i | ||||
\(587\) | − | 6.78157e57i | − | 0.489700i | −0.969561 | − | 0.244850i | \(-0.921261\pi\) | ||
0.969561 | − | 0.244850i | \(-0.0787387\pi\) | |||||||
\(588\) | −5.89729e57 | − | 2.61252e58i | −0.410893 | − | 1.82027i | ||||
\(589\) | −3.53940e57 | −0.237962 | ||||||||
\(590\) | 2.15613e58 | − | 2.40330e57i | 1.39888 | − | 0.155925i | ||||
\(591\) | − | 3.68734e58i | − | 2.30874i | ||||||
\(592\) | −1.69504e58 | + | 8.06339e57i | −1.02429 | + | 0.487261i | ||||
\(593\) | 1.90720e58 | 1.11237 | 0.556184 | − | 0.831059i | \(-0.312265\pi\) | ||||
0.556184 | + | 0.831059i | \(0.312265\pi\) | |||||||
\(594\) | 9.10066e57 | + | 8.16468e58i | 0.512339 | + | 4.59646i | ||||
\(595\) | − | 2.01050e57i | − | 0.109257i | ||||||
\(596\) | 2.89715e58 | − | 6.53981e57i | 1.51985 | − | 0.343078i | ||||
\(597\) | −5.99486e58 | −3.03612 | ||||||||
\(598\) | 8.08545e57 | − | 9.01235e56i | 0.395348 | − | 0.0440670i | ||||
\(599\) | − | 2.55855e58i | − | 1.20790i | −0.797022 | − | 0.603950i | \(-0.793593\pi\) | ||
0.797022 | − | 0.603950i | \(-0.206407\pi\) | |||||||
\(600\) | 4.14916e57 | − | 1.43519e57i | 0.189140 | − | 0.0654235i | ||||
\(601\) | 5.28475e57 | 0.232627 | 0.116314 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116314 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(602\) | −4.11296e56 | − | 3.68995e57i | −0.0174835 | − | 0.156854i | ||||
\(603\) | 1.28544e58i | 0.527703i | ||||||||
\(604\) | 5.44970e57 | + | 2.41423e58i | 0.216071 | + | 0.957202i | ||||
\(605\) | 2.95899e58 | 1.13313 | ||||||||
\(606\) | −4.88643e58 | + | 5.44660e57i | −1.80745 | + | 0.201465i | ||||
\(607\) | 3.04614e58i | 1.08840i | 0.838956 | + | 0.544199i | \(0.183166\pi\) | ||||
−0.838956 | + | 0.544199i | \(0.816834\pi\) | |||||||
\(608\) | −3.41427e57 | + | 2.11700e57i | −0.117848 | + | 0.0730710i | ||||
\(609\) | 9.67374e57 | 0.322575 | ||||||||
\(610\) | −2.76430e57 | − | 2.48000e58i | −0.0890552 | − | 0.798960i | ||||
\(611\) | 2.62627e57i | 0.0817473i | ||||||||
\(612\) | 5.54625e58 | − | 1.25197e58i | 1.66809 | − | 0.376542i | ||||
\(613\) | −4.50881e57 | −0.131036 | −0.0655182 | − | 0.997851i | \(-0.520870\pi\) | ||||
−0.0655182 | + | 0.997851i | \(0.520870\pi\) | |||||||
\(614\) | −2.03465e58 | + | 2.26789e57i | −0.571417 | + | 0.0636923i | ||||
\(615\) | − | 5.99697e58i | − | 1.62763i | ||||||
\(616\) | 2.92044e57 | + | 8.44303e57i | 0.0766043 | + | 0.221464i | ||||
\(617\) | 6.11538e58 | 1.55037 | 0.775184 | − | 0.631736i | \(-0.217657\pi\) | ||||
0.775184 | + | 0.631736i | \(0.217657\pi\) | |||||||
\(618\) | −2.68662e57 | − | 2.41031e58i | −0.0658337 | − | 0.590628i | ||||
\(619\) | − | 1.56809e58i | − | 0.371421i | −0.982604 | − | 0.185711i | \(-0.940541\pi\) | ||
0.982604 | − | 0.185711i | \(-0.0594587\pi\) | |||||||
\(620\) | 1.73436e58 | + | 7.68327e58i | 0.397113 | + | 1.75922i | ||||
\(621\) | 1.24953e59 | 2.76580 | ||||||||
\(622\) | −5.07136e56 | + | 5.65273e55i | −0.0108524 | + | 0.00120965i | ||||
\(623\) | 4.24882e57i | 0.0879062i | ||||||||
\(624\) | −1.89919e58 | − | 3.99238e58i | −0.379920 | − | 0.798649i | ||||
\(625\) | −5.65333e58 | −1.09351 | ||||||||
\(626\) | −7.13020e57 | − | 6.39687e58i | −0.133365 | − | 1.19648i | ||||
\(627\) | − | 2.11829e58i | − | 0.383148i | ||||||
\(628\) | −3.60849e58 | + | 8.14552e57i | −0.631208 | + | 0.142484i | ||||
\(629\) | −4.28816e58 | −0.725450 | ||||||||
\(630\) | −2.77434e58 | + | 3.09239e57i | −0.453950 | + | 0.0505990i | ||||
\(631\) | 1.20668e59i | 1.90975i | 0.297015 | + | 0.954873i | \(0.404009\pi\) | ||||
−0.297015 | + | 0.954873i | \(0.595991\pi\) | |||||||
\(632\) | −1.66270e58 | + | 5.75127e57i | −0.254540 | + | 0.0880451i | ||||
\(633\) | −1.68415e59 | −2.49403 | ||||||||
\(634\) | 2.38163e57 | + | 2.13668e58i | 0.0341192 | + | 0.306101i | ||||
\(635\) | 3.71608e58i | 0.515035i | ||||||||
\(636\) | −3.25271e57 | − | 1.44096e58i | −0.0436160 | − | 0.193220i | ||||
\(637\) | −3.46254e58 | −0.449227 | ||||||||
\(638\) | 1.18162e59 | − | 1.31708e58i | 1.48335 | − | 0.165340i | ||||
\(639\) | 1.57589e59i | 1.91429i | ||||||||
\(640\) | 6.26859e58 | + | 6.37428e58i | 0.736870 | + | 0.749293i | ||||
\(641\) | −1.06420e59 | −1.21061 | −0.605307 | − | 0.795992i | \(-0.706950\pi\) | ||||
−0.605307 | + | 0.795992i | \(0.706950\pi\) | |||||||
\(642\) | −3.23002e57 | − | 2.89782e58i | −0.0355607 | − | 0.319034i | ||||
\(643\) | − | 1.46456e59i | − | 1.56055i | −0.625440 | − | 0.780273i | \(-0.715080\pi\) | ||
0.625440 | − | 0.780273i | \(-0.284920\pi\) | |||||||
\(644\) | 1.32548e58 | − | 2.99202e57i | 0.136700 | − | 0.0308576i | ||||
\(645\) | 1.95910e59 | 1.95570 | ||||||||
\(646\) | −9.12112e57 | + | 1.01668e57i | −0.0881385 | + | 0.00982425i | ||||
\(647\) | 1.31825e58i | 0.123313i | 0.998097 | + | 0.0616563i | \(0.0196383\pi\) | ||||
−0.998097 | + | 0.0616563i | \(0.980362\pi\) | |||||||
\(648\) | −1.25454e59 | − | 3.62688e59i | −1.13608 | − | 3.28442i | ||||
\(649\) | −2.20233e59 | −1.93083 | ||||||||
\(650\) | −6.28778e56 | − | 5.64109e57i | −0.00533724 | − | 0.0478831i | ||||
\(651\) | − | 6.50580e58i | − | 0.534687i | ||||||
\(652\) | −3.57915e57 | − | 1.58557e58i | −0.0284826 | − | 0.126179i | ||||
\(653\) | 2.30675e58 | 0.177756 | 0.0888780 | − | 0.996043i | \(-0.471672\pi\) | ||||
0.0888780 | + | 0.996043i | \(0.471672\pi\) | |||||||
\(654\) | 3.43795e58 | − | 3.83207e57i | 0.256547 | − | 0.0285957i | ||||
\(655\) | 8.63474e58i | 0.623996i | ||||||||
\(656\) | 1.04259e59 | − | 4.95965e58i | 0.729683 | − | 0.347113i | ||||
\(657\) | 4.29756e59 | 2.91306 | ||||||||
\(658\) | 4.85926e56 | + | 4.35949e57i | 0.00319026 | + | 0.0286215i | ||||
\(659\) | 1.27850e59i | 0.813029i | 0.913644 | + | 0.406514i | \(0.133256\pi\) | ||||
−0.913644 | + | 0.406514i | \(0.866744\pi\) | |||||||
\(660\) | −4.59835e59 | + | 1.03799e59i | −2.83256 | + | 0.639400i | ||||
\(661\) | 2.65202e58 | 0.158251 | 0.0791254 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791254 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(662\) | 1.75209e59 | − | 1.95295e58i | 1.01284 | − | 0.112895i | ||||
\(663\) | − | 1.01000e59i | − | 0.565638i | ||||||
\(664\) | 3.43159e58 | − | 1.18699e58i | 0.186194 | − | 0.0644044i | ||||
\(665\) | 4.50587e57 | 0.0236878 | ||||||||
\(666\) | 6.59570e58 | + | 5.91734e59i | 0.335971 | + | 3.01417i | ||||
\(667\) | − | 1.80836e59i | − | 0.892570i | ||||||
\(668\) | 6.78496e58 | + | 3.00576e59i | 0.324520 | + | 1.43763i | ||||
\(669\) | −1.05046e59 | −0.486892 | ||||||||
\(670\) | −4.58901e58 | + | 5.11508e57i | −0.206133 | + | 0.0229764i | ||||
\(671\) | 2.53315e59i | 1.10278i | ||||||||
\(672\) | −3.89127e58 | − | 6.27579e58i | −0.164186 | − | 0.264797i | ||||
\(673\) | 4.00339e59 | 1.63724 | 0.818619 | − | 0.574337i | \(-0.194740\pi\) | ||||
0.818619 | + | 0.574337i | \(0.194740\pi\) | |||||||
\(674\) | −2.53458e58 | − | 2.27390e59i | −0.100473 | − | 0.901393i | ||||
\(675\) | − | 8.71774e58i | − | 0.334985i | ||||||
\(676\) | 2.06117e59 | − | 4.65272e58i | 0.767774 | − | 0.173311i | ||||
\(677\) | −6.90456e58 | −0.249330 | −0.124665 | − | 0.992199i | \(-0.539786\pi\) | ||||
−0.124665 | + | 0.992199i | \(0.539786\pi\) | |||||||
\(678\) | 2.70384e59 | − | 3.01380e58i | 0.946581 | − | 0.105509i | ||||
\(679\) | 7.30843e58i | 0.248061i | ||||||||
\(680\) | 6.67648e58 | + | 1.93018e59i | 0.219715 | + | 0.635201i | ||||
\(681\) | −6.53158e59 | −2.08415 | ||||||||
\(682\) | −8.85765e58 | − | 7.94666e59i | −0.274061 | − | 2.45874i | ||||
\(683\) | − | 6.41644e59i | − | 1.92513i | −0.271059 | − | 0.962563i | \(-0.587374\pi\) | ||
0.271059 | − | 0.962563i | \(-0.412626\pi\) | |||||||
\(684\) | 2.80587e58 | + | 1.24301e59i | 0.0816375 | + | 0.361657i | ||||
\(685\) | −4.16028e59 | −1.17387 | ||||||||
\(686\) | −1.16513e59 | + | 1.29870e58i | −0.318837 | + | 0.0355388i | ||||
\(687\) | − | 5.62900e59i | − | 1.49396i | ||||||
\(688\) | 1.62023e59 | + | 3.40596e59i | 0.417080 | + | 0.876763i | ||||
\(689\) | −1.90980e58 | −0.0476853 | ||||||||
\(690\) | 7.94275e58 | + | 7.12586e59i | 0.192371 | + | 1.72586i | ||||
\(691\) | − | 3.42914e59i | − | 0.805651i | −0.915277 | − | 0.402825i | \(-0.868028\pi\) | ||
0.915277 | − | 0.402825i | \(-0.131972\pi\) | |||||||
\(692\) | −4.32455e59 | + | 9.76191e58i | −0.985628 | + | 0.222488i | ||||
\(693\) | 2.83380e59 | 0.626572 | ||||||||
\(694\) | 4.91726e59 | − | 5.48097e58i | 1.05481 | − | 0.117573i | ||||
\(695\) | − | 1.27344e59i | − | 0.265032i | ||||||
\(696\) | −9.28728e59 | + | 3.21246e59i | −1.87540 | + | 0.648700i | ||||
\(697\) | 2.63757e59 | 0.516793 | ||||||||
\(698\) | 4.67705e57 | + | 4.19602e58i | 0.00889217 | + | 0.0797763i | ||||
\(699\) | 1.46583e60i | 2.70435i | ||||||||
\(700\) | −2.08749e57 | − | 9.24763e57i | −0.00373736 | − | 0.0165566i | ||||
\(701\) | 2.98694e59 | 0.518977 | 0.259488 | − | 0.965746i | \(-0.416446\pi\) | ||||
0.259488 | + | 0.965746i | \(0.416446\pi\) | |||||||
\(702\) | −8.72472e59 | + | 9.72491e58i | −1.47120 | + | 0.163986i | ||||
\(703\) | − | 9.61049e58i | − | 0.157284i | ||||||
\(704\) | −5.60754e59 | − | 7.13592e59i | −0.890731 | − | 1.13351i | ||||
\(705\) | −2.31458e59 | −0.356862 | ||||||||
\(706\) | −6.86182e58 | − | 6.15610e59i | −0.102693 | − | 0.921312i | ||||
\(707\) | 1.06168e59i | 0.154236i | ||||||||
\(708\) | 1.77566e60 | − | 4.00824e59i | 2.50416 | − | 0.565269i | ||||
\(709\) | 4.15997e59 | 0.569533 | 0.284766 | − | 0.958597i | \(-0.408084\pi\) | ||||
0.284766 | + | 0.958597i | \(0.408084\pi\) | |||||||
\(710\) | −5.62589e59 | + | 6.27083e58i | −0.747766 | + | 0.0833488i | ||||
\(711\) | 5.58065e59i | 0.720150i | ||||||||
\(712\) | −1.41095e59 | − | 4.07909e59i | −0.176780 | − | 0.511073i | ||||
\(713\) | −1.21616e60 | −1.47949 | ||||||||
\(714\) | −1.86876e58 | − | 1.67656e59i | −0.0220745 | − | 0.198042i | ||||
\(715\) | 6.09449e59i | 0.699053i | ||||||||
\(716\) | 6.84835e58 | + | 3.03384e59i | 0.0762803 | + | 0.337924i | ||||
\(717\) | 2.41054e60 | 2.60742 | ||||||||
\(718\) | −1.45126e60 | + | 1.61763e59i | −1.52452 | + | 0.169929i | ||||
\(719\) | − | 1.48006e60i | − | 1.50999i | −0.655732 | − | 0.754993i | \(-0.727640\pi\) | ||
0.655732 | − | 0.754993i | \(-0.272360\pi\) | |||||||
\(720\) | 2.56082e60 | − | 1.21819e60i | 2.53744 | − | 1.20707i | ||||
\(721\) | −5.23691e58 | −0.0504005 | ||||||||
\(722\) | 1.16226e59 | + | 1.04272e60i | 0.108648 | + | 0.974736i | ||||
\(723\) | 8.85440e59i | 0.803998i | ||||||||
\(724\) | 1.16245e60 | − | 2.62403e59i | 1.02534 | − | 0.231451i | ||||
\(725\) | −1.26166e59 | −0.108105 | ||||||||
\(726\) | 2.46751e60 | − | 2.75038e59i | 2.05395 | − | 0.228941i | ||||
\(727\) | 2.23220e60i | 1.80514i | 0.430543 | + | 0.902570i | \(0.358322\pi\) | ||||
−0.430543 | + | 0.902570i | \(0.641678\pi\) | |||||||
\(728\) | −9.02217e58 | + | 3.12076e58i | −0.0708846 | + | 0.0245189i | ||||
\(729\) | −4.11767e60 | −3.14321 | ||||||||
\(730\) | 1.71010e59 | + | 1.53422e60i | 0.126836 | + | 1.13791i | ||||
\(731\) | 8.61648e59i | 0.620962i | ||||||||
\(732\) | −4.61032e59 | − | 2.04239e60i | −0.322848 | − | 1.43023i | ||||
\(733\) | 1.06594e60 | 0.725350 | 0.362675 | − | 0.931916i | \(-0.381864\pi\) | ||||
0.362675 | + | 0.931916i | \(0.381864\pi\) | |||||||
\(734\) | −1.17864e60 | + | 1.31376e59i | −0.779409 | + | 0.0868759i | ||||
\(735\) | − | 3.05160e60i | − | 1.96107i | ||||||
\(736\) | −1.17316e60 | + | 7.27414e59i | −0.732697 | + | 0.454305i | ||||
\(737\) | 4.68735e59 | 0.284518 | ||||||||
\(738\) | −4.05690e59 | − | 3.63966e60i | −0.239338 | − | 2.14722i | ||||
\(739\) | 1.42564e60i | 0.817479i | 0.912651 | + | 0.408739i | \(0.134031\pi\) | ||||
−0.912651 | + | 0.408739i | \(0.865969\pi\) | |||||||
\(740\) | −2.08623e60 | + | 4.70930e59i | −1.16278 | + | 0.262476i | ||||
\(741\) | 2.26359e59 | 0.122635 | ||||||||
\(742\) | −3.17019e58 | + | 3.53361e57i | −0.0166956 | + | 0.00186096i | ||||
\(743\) | − | 1.50905e60i | − | 0.772570i | −0.922379 | − | 0.386285i | \(-0.873758\pi\) | ||
0.922379 | − | 0.386285i | \(-0.126242\pi\) | |||||||
\(744\) | 2.16045e60 | + | 6.24589e60i | 1.07526 | + | 3.10859i | ||||
\(745\) | 3.38408e60 | 1.63741 | ||||||||
\(746\) | −2.41691e59 | − | 2.16834e60i | −0.113696 | − | 1.02003i | ||||
\(747\) | − | 1.15177e60i | − | 0.526785i | ||||||
\(748\) | −4.56528e59 | − | 2.02243e60i | −0.203018 | − | 0.899375i | ||||
\(749\) | −6.29615e58 | −0.0272243 | ||||||||
\(750\) | −4.26417e60 | + | 4.75301e59i | −1.79287 | + | 0.199840i | ||||
\(751\) | 2.05038e60i | 0.838292i | 0.907919 | + | 0.419146i | \(0.137670\pi\) | ||||
−0.907919 | + | 0.419146i | \(0.862330\pi\) | |||||||
\(752\) | −1.91422e59 | − | 4.02397e59i | −0.0761056 | − | 0.159985i | ||||
\(753\) | −4.48664e60 | −1.73471 | ||||||||
\(754\) | 1.40742e59 | + | 1.26267e60i | 0.0529209 | + | 0.474781i | ||||
\(755\) | 2.81999e60i | 1.03125i | ||||||||
\(756\) | −1.43027e60 | + | 3.22859e59i | −0.508700 | + | 0.114830i | ||||
\(757\) | −3.68995e59 | −0.127646 | −0.0638229 | − | 0.997961i | \(-0.520329\pi\) | ||||
−0.0638229 | + | 0.997961i | \(0.520329\pi\) | |||||||
\(758\) | −2.19901e60 | + | 2.45110e59i | −0.739903 | + | 0.0824724i | ||||
\(759\) | − | 7.27857e60i | − | 2.38215i | ||||||
\(760\) | −4.32587e59 | + | 1.49631e59i | −0.137717 | + | 0.0476362i | ||||
\(761\) | 1.81491e60 | 0.562054 | 0.281027 | − | 0.959700i | \(-0.409325\pi\) | ||||
0.281027 | + | 0.959700i | \(0.409325\pi\) | |||||||
\(762\) | 3.45410e59 | + | 3.09885e60i | 0.104059 | + | 0.933569i | ||||
\(763\) | − | 7.46969e58i | − | 0.0218921i | ||||||
\(764\) | 4.92812e59 | + | 2.18317e60i | 0.140514 | + | 0.622483i | ||||
\(765\) | 6.47841e60 | 1.79713 | ||||||||
\(766\) | 5.06662e60 | − | 5.64745e59i | 1.36746 | − | 0.152422i | ||||
\(767\) | − | 2.35340e60i | − | 0.618006i | ||||||
\(768\) | 5.81989e60 | + | 4.73286e60i | 1.48706 | + | 1.20931i | ||||
\(769\) | −6.24685e60 | −1.55313 | −0.776565 | − | 0.630037i | \(-0.783040\pi\) | ||||
−0.776565 | + | 0.630037i | \(0.783040\pi\) | |||||||
\(770\) | 1.12763e59 | + | 1.01166e60i | 0.0272812 | + | 0.244754i | ||||
\(771\) | − | 9.55921e60i | − | 2.25050i | ||||||
\(772\) | −4.58425e60 | + | 1.03481e60i | −1.05028 | + | 0.237082i | ||||
\(773\) | −4.60999e60 | −1.02785 | −0.513926 | − | 0.857835i | \(-0.671809\pi\) | ||||
−0.513926 | + | 0.857835i | \(0.671809\pi\) | |||||||
\(774\) | 1.18901e61 | − | 1.32532e60i | 2.58003 | − | 0.287580i | ||||
\(775\) | 8.48496e59i | 0.179190i | ||||||||
\(776\) | −2.42699e60 | − | 7.01646e60i | −0.498852 | − | 1.44219i | ||||
\(777\) | 1.76651e60 | 0.353407 | ||||||||
\(778\) | 1.53323e59 | + | 1.37554e60i | 0.0298563 | + | 0.267856i | ||||
\(779\) | 5.91125e59i | 0.112045i | ||||||||
\(780\) | −1.10919e60 | − | 4.91376e60i | −0.204654 | − | 0.906625i | ||||
\(781\) | 5.74645e60 | 1.03212 | ||||||||
\(782\) | −3.13408e60 | + | 3.49336e59i | −0.547984 | + | 0.0610804i | ||||
\(783\) | 1.95134e61i | 3.32151i | ||||||||
\(784\) | 5.30530e60 | − | 2.52375e60i | 0.879170 | − | 0.418224i | ||||
\(785\) | −4.21497e60 | −0.680035 | ||||||||
\(786\) | 8.02599e59 | + | 7.20054e60i | 0.126074 | + | 1.13108i | ||||
\(787\) | 1.83379e60i | 0.280467i | 0.990118 | + | 0.140233i | \(0.0447853\pi\) | ||||
−0.990118 | + | 0.140233i | \(0.955215\pi\) | |||||||
\(788\) | 7.89001e60 | − | 1.78103e60i | 1.17497 | − | 0.265229i | ||||
\(789\) | 8.65109e60 | 1.25445 | ||||||||
\(790\) | −1.99228e60 | + | 2.22067e59i | −0.281308 | + | 0.0313556i | ||||
\(791\) | − | 5.87468e59i | − | 0.0807752i | ||||||
\(792\) | −2.72059e61 | + | 9.41049e60i | −3.64279 | + | 1.26004i | ||||
\(793\) | −2.70691e60 | −0.352969 | ||||||||
\(794\) | 6.03825e59 | + | 5.41722e60i | 0.0766797 | + | 0.687933i | ||||
\(795\) | − | 1.68314e60i | − | 0.208167i | ||||||
\(796\) | −2.89559e60 | − | 1.28275e61i | −0.348789 | − | 1.54514i | ||||
\(797\) | 1.27706e61 | 1.49826 | 0.749131 | − | 0.662422i | \(-0.230471\pi\) | ||||
0.749131 | + | 0.662422i | \(0.230471\pi\) | |||||||
\(798\) | 3.75746e59 | − | 4.18821e58i | 0.0429372 | − | 0.00478594i | ||||
\(799\) | − | 1.01799e60i | − | 0.113308i | ||||||
\(800\) | 5.07506e59 | + | 8.18498e59i | 0.0550239 | + | 0.0887418i | ||||
\(801\) | −1.36909e61 | −1.44594 | ||||||||
\(802\) | −1.11974e60 | − | 1.00458e61i | −0.115201 | − | 1.03352i | ||||
\(803\) | − | 1.56710e61i | − | 1.57062i | ||||||
\(804\) | −3.77924e60 | + | 8.53096e59i | −0.369001 | + | 0.0832954i | ||||
\(805\) | 1.54825e60 | 0.147274 | ||||||||
\(806\) | 8.49175e60 | − | 9.46523e59i | 0.786976 | − | 0.0877193i | ||||
\(807\) | 2.64708e61i | 2.39014i | ||||||||
\(808\) | −3.52564e60 | − | 1.01927e61i | −0.310170 | − | 0.896706i | ||||
\(809\) | −1.47711e61 | −1.26618 | −0.633089 | − | 0.774079i | \(-0.718213\pi\) | ||||
−0.633089 | + | 0.774079i | \(0.718213\pi\) | |||||||
\(810\) | −4.84399e60 | − | 4.34580e61i | −0.404592 | − | 3.62981i | ||||
\(811\) | − | 1.59635e60i | − | 0.129924i | −0.997888 | − | 0.0649622i | \(-0.979307\pi\) | ||
0.997888 | − | 0.0649622i | \(-0.0206927\pi\) | |||||||
\(812\) | 4.67253e59 | + | 2.06994e60i | 0.0370575 | + | 0.164166i | ||||
\(813\) | 2.91974e60 | 0.225654 | ||||||||
\(814\) | 2.15775e61 | − | 2.40511e60i | 1.62513 | − | 0.181143i | ||||
\(815\) | − | 1.85206e60i | − | 0.135939i | ||||||
\(816\) | 7.36164e60 | + | 1.54753e61i | 0.526601 | + | 1.10699i | ||||
\(817\) | −1.93110e60 | −0.134630 | ||||||||
\(818\) | 3.05085e60 | + | 2.73708e61i | 0.207301 | + | 1.85981i | ||||
\(819\) | 3.02818e60i | 0.200548i | ||||||||
\(820\) | 1.28321e61 | − | 2.89661e60i | 0.828334 | − | 0.186982i | ||||
\(821\) | −1.45072e61 | −0.912806 | −0.456403 | − | 0.889773i | \(-0.650863\pi\) | ||||
−0.456403 | + | 0.889773i | \(0.650863\pi\) | |||||||
\(822\) | −3.46927e61 | + | 3.86698e60i | −2.12780 | + | 0.237172i | ||||
\(823\) | 1.10912e61i | 0.663105i | 0.943437 | + | 0.331552i | \(0.107572\pi\) | ||||
−0.943437 | + | 0.331552i | \(0.892428\pi\) | |||||||
\(824\) | 5.02770e60 | − | 1.73908e60i | 0.293021 | − | 0.101356i | ||||
\(825\) | −5.07815e60 | −0.288518 | ||||||||
\(826\) | −4.35438e59 | − | 3.90654e60i | −0.0241182 | − | 0.216377i | ||||
\(827\) | 8.97394e60i | 0.484582i | 0.970204 | + | 0.242291i | \(0.0778989\pi\) | ||||
−0.970204 | + | 0.242291i | \(0.922101\pi\) | |||||||
\(828\) | 9.64116e60 | + | 4.27106e61i | 0.507566 | + | 2.24853i | ||||
\(829\) | −3.71513e61 | −1.90690 | −0.953452 | − | 0.301546i | \(-0.902497\pi\) | ||||
−0.953452 | + | 0.301546i | \(0.902497\pi\) | |||||||
\(830\) | 4.11180e60 | − | 4.58317e59i | 0.205775 | − | 0.0229364i | ||||
\(831\) | − | 3.01784e61i | − | 1.47257i | ||||||
\(832\) | 7.62540e60 | − | 5.99218e60i | 0.362805 | − | 0.285099i | ||||
\(833\) | 1.34215e61 | 0.622666 | ||||||||
\(834\) | −1.18366e60 | − | 1.06193e61i | −0.0535478 | − | 0.480405i | ||||
\(835\) | 3.51093e61i | 1.54884i | ||||||||
\(836\) | 4.53262e60 | − | 1.02316e60i | 0.194992 | − | 0.0440160i | ||||
\(837\) | 1.31232e62 | 5.50559 | ||||||||
\(838\) | −5.96411e60 | + | 6.64783e59i | −0.244018 | + | 0.0271992i | ||||
\(839\) | − | 1.59908e61i | − | 0.638072i | −0.947743 | − | 0.319036i | \(-0.896641\pi\) | ||
0.947743 | − | 0.319036i | \(-0.103359\pi\) | |||||||
\(840\) | −2.75039e60 | − | 7.95141e60i | −0.107036 | − | 0.309442i | ||||
\(841\) | 1.89439e60 | 0.0719041 | ||||||||
\(842\) | 5.12890e60 | + | 4.60140e61i | 0.189876 | + | 1.70348i | ||||
\(843\) | − | 8.14165e61i | − | 2.93990i | ||||||
\(844\) | −8.13464e60 | − | 3.60367e61i | −0.286515 | − | 1.26927i | ||||
\(845\) | 2.40759e61 | 0.827164 | ||||||||
\(846\) | −1.40475e61 | + | 1.56579e60i | −0.470785 | + | 0.0524755i | ||||
\(847\) | − | 5.36121e60i | − | 0.175271i | ||||||
\(848\) | 2.92620e60 | − | 1.39200e60i | 0.0933234 | − | 0.0443943i | ||||
\(849\) | −8.49351e61 | −2.64256 | ||||||||
\(850\) | 2.43727e59 | + | 2.18660e60i | 0.00739785 | + | 0.0663699i | ||||
\(851\) | − | 3.30223e61i | − | 0.977882i | ||||||
\(852\) | −4.63316e61 | + | 1.04585e61i | −1.33858 | + | 0.302161i | ||||
\(853\) | −1.96123e61 | −0.552838 | −0.276419 | − | 0.961037i | \(-0.589148\pi\) | ||||
−0.276419 | + | 0.961037i | \(0.589148\pi\) | |||||||
\(854\) | −4.49335e60 | + | 5.00846e59i | −0.123582 | + | 0.0137749i | ||||
\(855\) | 1.45192e61i | 0.389632i | ||||||||
\(856\) | 6.04462e60 | − | 2.09083e60i | 0.158278 | − | 0.0547482i | ||||
\(857\) | 3.35638e61 | 0.857577 | 0.428789 | − | 0.903405i | \(-0.358940\pi\) | ||||
0.428789 | + | 0.903405i | \(0.358940\pi\) | |||||||
\(858\) | 5.66483e60 | + | 5.08221e61i | 0.141239 | + | 1.26713i | ||||
\(859\) | 6.73112e61i | 1.63769i | 0.574017 | + | 0.818843i | \(0.305384\pi\) | ||||
−0.574017 | + | 0.818843i | \(0.694616\pi\) | |||||||
\(860\) | 9.46270e60 | + | 4.19200e61i | 0.224671 | + | 0.995300i | ||||
\(861\) | −1.08655e61 | −0.251759 | ||||||||
\(862\) | −4.65262e61 | + | 5.18598e60i | −1.05207 | + | 0.117268i | ||||
\(863\) | 4.00076e61i | 0.882908i | 0.897284 | + | 0.441454i | \(0.145537\pi\) | ||||
−0.897284 | + | 0.441454i | \(0.854463\pi\) | |||||||
\(864\) | 1.26592e62 | − | 7.84927e61i | 2.72658 | − | 1.69060i | ||||
\(865\) | −5.05138e61 | −1.06187 | ||||||||
\(866\) | 2.71382e59 | + | 2.43471e60i | 0.00556807 | + | 0.0499541i | ||||
\(867\) | − | 5.65605e61i | − | 1.13269i | ||||||
\(868\) | 1.39208e61 | − | 3.14238e60i | 0.272114 | − | 0.0614248i | ||||
\(869\) | 2.03498e61 | 0.388279 | ||||||||
\(870\) | −1.11282e62 | + | 1.24039e61i | −2.07262 | + | 0.231022i | ||||
\(871\) | 5.00888e60i | 0.0910666i | ||||||||
\(872\) | 2.48054e60 | + | 7.17128e60i | 0.0440251 | + | 0.127277i | ||||
\(873\) | −2.35499e62 | −4.08027 | ||||||||
\(874\) | −7.82922e59 | − | 7.02400e60i | −0.0132428 | − | 0.118808i | ||||
\(875\) | 9.26484e60i | 0.152992i | ||||||||
\(876\) | 2.85212e61 | + | 1.26350e62i | 0.459813 | + | 2.03698i | ||||
\(877\) | 6.73875e61 | 1.06069 | 0.530344 | − | 0.847782i | \(-0.322063\pi\) | ||||
0.530344 | + | 0.847782i | \(0.322063\pi\) | |||||||
\(878\) | 1.17181e62 | − | 1.30614e61i | 1.80082 | − | 0.200726i | ||||
\(879\) | − | 2.13132e62i | − | 3.19803i | ||||||
\(880\) | −4.44211e61 | − | 9.33798e61i | −0.650809 | − | 1.36810i | ||||
\(881\) | 5.22171e61 | 0.746997 | 0.373498 | − | 0.927631i | \(-0.378158\pi\) | ||||
0.373498 | + | 0.927631i | \(0.378158\pi\) | |||||||
\(882\) | −2.06438e61 | − | 1.85206e62i | −0.288370 | − | 2.58711i | ||||
\(883\) | 1.34300e62i | 1.83190i | 0.401290 | + | 0.915951i | \(0.368562\pi\) | ||||
−0.401290 | + | 0.915951i | \(0.631438\pi\) | |||||||
\(884\) | 2.16116e61 | − | 4.87843e60i | 0.287865 | − | 0.0649805i | ||||
\(885\) | 2.07410e62 | 2.69786 | ||||||||
\(886\) | −6.88798e61 | + | 7.67760e60i | −0.874951 | + | 0.0975254i | ||||
\(887\) | 2.43070e60i | 0.0301533i | 0.999886 | + | 0.0150766i | \(0.00479923\pi\) | ||||
−0.999886 | + | 0.0150766i | \(0.995201\pi\) | |||||||
\(888\) | −1.69594e62 | + | 5.86625e61i | −2.05465 | + | 0.710703i | ||||
\(889\) | 6.73293e60 | 0.0796649 | ||||||||
\(890\) | −5.44794e60 | − | 4.88763e61i | −0.0629568 | − | 0.564818i | ||||
\(891\) | 4.43893e62i | 5.01010i | ||||||||
\(892\) | −5.07386e60 | − | 2.24774e61i | −0.0559341 | − | 0.247790i | ||||
\(893\) | 2.28149e60 | 0.0245662 | ||||||||
\(894\) | 2.82199e62 | − | 3.14550e61i | 2.96803 | − | 0.330828i | ||||
\(895\) | 3.54373e61i | 0.364064i | ||||||||
\(896\) | 1.15491e61 | − | 1.13577e61i | 0.115899 | − | 0.113978i | ||||
\(897\) | 7.77784e61 | 0.762461 | ||||||||
\(898\) | −1.03672e61 | − | 9.30091e61i | −0.0992788 | − | 0.890682i | ||||
\(899\) | − | 1.89923e62i | − | 1.77674i | ||||||
\(900\) | 2.97985e61 | − | 6.72649e60i | 0.272334 | − | 0.0614746i | ||||
\(901\) | 7.40276e60 | 0.0660957 | ||||||||
\(902\) | −1.32720e62 | + | 1.47934e61i | −1.15770 | + | 0.129042i | ||||
\(903\) | − | 3.54957e61i | − | 0.302505i | ||||||
\(904\) | 1.95087e61 | + | 5.63999e61i | 0.162439 | + | 0.469614i | ||||
\(905\) | 1.35783e62 | 1.10465 | ||||||||
\(906\) | 2.62118e61 | + | 2.35160e62i | 0.208356 | + | 1.86927i | ||||
\(907\) | 3.52578e61i | 0.273843i | 0.990582 | + | 0.136922i | \(0.0437208\pi\) | ||||
−0.990582 | + | 0.136922i | \(0.956279\pi\) | |||||||
\(908\) | −3.15483e61 | − | 1.39760e62i | −0.239427 | − | 1.06067i | ||||
\(909\) | −3.42105e62 | −2.53698 | ||||||||
\(910\) | −1.08105e61 | + | 1.20498e60i | −0.0783389 | + | 0.00873196i | ||||
\(911\) | − | 8.28978e61i | − | 0.587026i | −0.955955 | − | 0.293513i | \(-0.905176\pi\) | ||
0.955955 | − | 0.293513i | \(-0.0948244\pi\) | |||||||
\(912\) | −3.46827e61 | + | 1.64987e61i | −0.240006 | + | 0.114172i | ||||
\(913\) | −4.19992e61 | −0.284024 | ||||||||
\(914\) | 1.08013e61 | + | 9.69043e61i | 0.0713850 | + | 0.640432i | ||||
\(915\) | − | 2.38565e62i | − | 1.54086i | ||||||
\(916\) | 1.20447e62 | − | 2.71887e61i | 0.760310 | − | 0.171626i | ||||
\(917\) | 1.56447e61 | 0.0965188 | ||||||||
\(918\) | 3.38187e62 | − | 3.76957e61i | 2.03921 | − | 0.227298i | ||||
\(919\) | 2.59016e62i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(920\) | −1.48640e62 | + | 5.14143e61i | −0.856229 | + | 0.296169i | ||||
\(921\) | −1.95724e62 | −1.10202 | ||||||||
\(922\) | −2.99054e61 | − | 2.68297e62i | −0.164589 | − | 1.47661i | ||||
\(923\) | 6.14062e61i | 0.330352i | ||||||||
\(924\) | 1.88067e61 | + | 8.33144e61i | 0.0989014 | + | 0.438136i | ||||
\(925\) | −2.30391e61 | −0.118438 | ||||||||
\(926\) | −1.12861e62 | + | 1.25799e61i | −0.567168 | + | 0.0632187i | ||||
\(927\) | − | 1.68748e62i | − | 0.829021i | ||||||
\(928\) | −1.13598e62 | − | 1.83209e62i | −0.545584 | − | 0.879910i | ||||
\(929\) | −1.65713e62 | −0.778083 | −0.389042 | − | 0.921220i | \(-0.627194\pi\) | ||||
−0.389042 | + | 0.921220i | \(0.627194\pi\) | |||||||
\(930\) | 8.34189e61 | + | 7.48394e62i | 0.382933 | + | 3.43549i | ||||
\(931\) | 3.00798e61i | 0.134999i | ||||||||
\(932\) | −3.13652e62 | + | 7.08014e61i | −1.37630 | + | 0.310676i | ||||
\(933\) | −4.87842e60 | −0.0209298 | ||||||||
\(934\) | 4.80234e61 | − | 5.35287e60i | 0.201450 | − | 0.0224544i | ||||
\(935\) | − | 2.36234e62i | − | 0.968945i | ||||||
\(936\) | −1.00560e62 | − | 2.90720e62i | −0.403304 | − | 1.16596i | ||||
\(937\) | 4.29406e62 | 1.68398 | 0.841989 | − | 0.539494i | \(-0.181385\pi\) | ||||
0.841989 | + | 0.539494i | \(0.181385\pi\) | |||||||
\(938\) | 9.26768e59 | + | 8.31452e60i | 0.00355395 | + | 0.0318844i | ||||
\(939\) | − | 6.15350e62i | − | 2.30752i | ||||||
\(940\) | −1.11797e61 | − | 4.95263e61i | −0.0409963 | − | 0.181615i | ||||
\(941\) | 3.52900e62 | 1.26552 | 0.632761 | − | 0.774348i | \(-0.281922\pi\) | ||||
0.632761 | + | 0.774348i | \(0.281922\pi\) | |||||||
\(942\) | −3.51487e62 | + | 3.91781e61i | −1.23265 | + | 0.137396i | ||||
\(943\) | 2.03115e62i | 0.696619i | ||||||||
\(944\) | 1.71533e62 | + | 3.60588e62i | 0.575355 | + | 1.20948i | ||||
\(945\) | −1.67066e62 | −0.548050 | ||||||||
\(946\) | −4.83275e61 | − | 4.33571e62i | −0.155053 | − | 1.39106i | ||||
\(947\) | − | 1.61719e62i | − | 0.507470i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) | ||
0.967274 | − | 0.253735i | \(-0.0816591\pi\) | |||||||
\(948\) | −1.64073e62 | + | 3.70365e61i | −0.503572 | + | 0.113672i | ||||
\(949\) | 1.67459e62 | 0.502711 | ||||||||
\(950\) | −4.90054e60 | + | 5.46233e59i | −0.0143896 | + | 0.00160392i | ||||
\(951\) | 2.05539e62i | 0.590342i | ||||||||
\(952\) | 3.49717e61 | − | 1.20967e61i | 0.0982519 | − | 0.0339852i | ||||
\(953\) | −2.29979e62 | −0.632029 | −0.316014 | − | 0.948754i | \(-0.602345\pi\) | ||||
−0.316014 | + | 0.948754i | \(0.602345\pi\) | |||||||
\(954\) | −1.13863e61 | − | 1.02153e62i | −0.0306103 | − | 0.274621i | ||||
\(955\) | 2.55010e62i | 0.670634i | ||||||||
\(956\) | 1.16432e62 | + | 5.15797e62i | 0.299541 | + | 1.32697i | ||||
\(957\) | 1.13667e63 | 2.86077 | ||||||||
\(958\) | 6.78539e62 | − | 7.56326e61i | 1.67070 | − | 0.186223i | ||||
\(959\) | 7.53774e61i | 0.181573i | ||||||||
\(960\) | 5.28102e62 | + | 6.72041e62i | 1.24458 | + | 1.58380i | ||||
\(961\) | −8.43572e62 | −1.94505 | ||||||||
\(962\) | 2.57009e61 | + | 2.30576e62i | 0.0579791 | + | 0.520160i | ||||
\(963\) | − | 2.02880e62i | − | 0.447803i | ||||||
\(964\) | −1.89463e62 | + | 4.27678e61i | −0.409172 | + | 0.0923633i | ||||
\(965\) | −5.35472e62 | −1.13152 | ||||||||
\(966\) | 1.29109e62 | − | 1.43910e61i | 0.266954 | − | 0.0297557i | ||||
\(967\) | 8.52208e62i | 1.72421i | 0.506731 | + | 0.862104i | \(0.330854\pi\) | ||||
−0.506731 | + | 0.862104i | \(0.669146\pi\) | |||||||
\(968\) | 1.78035e62 | + | 5.14703e62i | 0.352471 | + | 1.01900i | ||||
\(969\) | −8.77411e61 | −0.169982 | ||||||||
\(970\) | −9.37104e61 | − | 8.40725e62i | −0.177657 | − | 1.59385i | ||||
\(971\) | − | 1.89088e62i | − | 0.350801i | −0.984497 | − | 0.175400i | \(-0.943878\pi\) | ||
0.984497 | − | 0.175400i | \(-0.0561220\pi\) | |||||||
\(972\) | −4.18793e62 | − | 1.85527e63i | −0.760341 | − | 3.36833i | ||||
\(973\) | −2.30727e61 | −0.0409947 | ||||||||
\(974\) | −1.88293e62 | + | 2.09878e61i | −0.327413 | + | 0.0364947i | ||||
\(975\) | − | 5.42648e61i | − | 0.0923466i | ||||||
\(976\) | 4.14752e62 | − | 1.97299e62i | 0.690785 | − | 0.328609i | ||||
\(977\) | −7.00263e62 | −1.14150 | −0.570750 | − | 0.821124i | \(-0.693347\pi\) | ||||
−0.570750 | + | 0.821124i | \(0.693347\pi\) | |||||||
\(978\) | −1.72149e61 | − | 1.54444e62i | −0.0274655 | − | 0.246408i | ||||
\(979\) | 4.99238e62i | 0.779599i | ||||||||
\(980\) | 6.52968e62 | − | 1.47396e62i | 0.998032 | − | 0.225288i | ||||
\(981\) | 2.40695e62 | 0.360096 | ||||||||
\(982\) | −5.10971e59 | + | 5.69547e58i | −0.000748264 | + | 8.34043e-5i | ||||
\(983\) | − | 2.81918e61i | − | 0.0404110i | −0.999796 | − | 0.0202055i | \(-0.993568\pi\) | ||
0.999796 | − | 0.0202055i | \(-0.00643204\pi\) | |||||||
\(984\) | 1.04315e63 | − | 3.60823e62i | 1.46369 | − | 0.506288i | ||||
\(985\) | 9.21608e62 | 1.26586 | ||||||||
\(986\) | −5.45545e61 | − | 4.89437e62i | −0.0733526 | − | 0.658085i | ||||
\(987\) | 4.19363e61i | 0.0551989i | ||||||||
\(988\) | 1.09334e61 | + | 4.84353e61i | 0.0140883 | + | 0.0624117i | ||||
\(989\) | −6.63538e62 | −0.837036 | ||||||||
\(990\) | −3.25986e63 | + | 3.63356e62i | −4.02587 | + | 0.448739i | ||||
\(991\) | − | 4.32880e62i | − | 0.523384i | −0.965151 | − | 0.261692i | \(-0.915720\pi\) | ||
0.965151 | − | 0.261692i | \(-0.0842805\pi\) | |||||||
\(992\) | −1.23212e63 | + | 7.63968e62i | −1.45850 | + | 0.904336i | ||||
\(993\) | 1.68543e63 | 1.95334 | ||||||||
\(994\) | 1.13617e61 | + | 1.01932e62i | 0.0128923 | + | 0.115663i | ||||
\(995\) | − | 1.49835e63i | − | 1.66467i | ||||||
\(996\) | 3.38624e62 | − | 7.64383e61i | 0.368359 | − | 0.0831505i | ||||
\(997\) | −1.51374e63 | −1.61232 | −0.806162 | − | 0.591695i | \(-0.798459\pi\) | ||||
−0.806162 | + | 0.591695i | \(0.798459\pi\) | |||||||
\(998\) | −9.39502e62 | + | 1.04720e62i | −0.979842 | + | 0.109217i | ||||
\(999\) | 3.56332e63i | 3.63898i |
(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 | 4.43.b.a.3.12 | yes | 20 | |
4.3 | odd | 2 | inner | 4.43.b.a.3.11 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.43.b.a.3.11 | ✓ | 20 | 4.3 | odd | 2 | inner | |
4.43.b.a.3.12 | yes | 20 | 1.1 | even | 1 | trivial |