Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(379,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.f (of order \(3\), degree \(2\), not 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 757.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.757 |
Dual form | 1134.2.f.i.379.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | −3.00000 | − | 5.19615i | −0.904534 | − | 1.56670i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
−0.0829925 | − | 0.996550i | \(-0.526448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0.500000 | − | 0.866025i | 0.133631 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.50000 | − | 2.59808i | −0.335410 | − | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | − | 5.19615i | 0.639602 | − | 1.10782i | ||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.50000 | − | 7.79423i | −0.835629 | − | 1.44735i | −0.893517 | − | 0.449029i | \(-0.851770\pi\) |
0.0578882 | − | 0.998323i | \(-0.481563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | − | 8.66025i | 0.898027 | − | 1.55543i | 0.0680129 | − | 0.997684i | \(-0.478334\pi\) |
0.830014 | − | 0.557743i | \(-0.188333\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | − | 2.59808i | −0.257248 | − | 0.445566i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.00000 | −1.15079 | −0.575396 | − | 0.817875i | \(-0.695152\pi\) | ||||
−0.575396 | + | 0.817875i | \(0.695152\pi\) | |||||||
\(38\) | 1.00000 | + | 1.73205i | 0.162221 | + | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 6.00000 | 0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 2.00000 | − | 3.46410i | 0.282843 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.0000 | 2.42712 | ||||||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | − | 9.52628i | −0.704203 | − | 1.21972i | −0.966978 | − | 0.254858i | \(-0.917971\pi\) |
0.262776 | − | 0.964857i | \(-0.415362\pi\) | |||||||
\(62\) | 10.0000 | 1.27000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.50000 | + | 2.59808i | 0.186052 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.50000 | + | 2.59808i | 0.179284 | + | 0.310530i | ||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −3.00000 | + | 5.19615i | −0.341882 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | − | 7.79423i | 0.488094 | − | 0.845403i | ||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | + | 5.19615i | 0.319801 | + | 0.553912i | ||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 12.1244i | −0.710742 | − | 1.23104i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | − | 13.8564i | 0.788263 | − | 1.36531i | −0.138767 | − | 0.990325i | \(-0.544314\pi\) |
0.927030 | − | 0.374987i | \(-0.122353\pi\) | |||||||
\(104\) | −0.500000 | + | 0.866025i | −0.0490290 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 9.00000 | + | 15.5885i | 0.858116 | + | 1.48630i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 0.866025i | −0.0472456 | + | 0.0818317i | ||||
\(113\) | −7.50000 | + | 12.9904i | −0.705541 | + | 1.22203i | 0.260955 | + | 0.965351i | \(0.415962\pi\) |
−0.966496 | + | 0.256681i | \(0.917371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | − | 15.5885i | −0.839254 | − | 1.45363i | ||||
\(116\) | 9.00000 | 0.835629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.00000 | −0.552345 | ||||||||
\(119\) | 1.50000 | + | 2.59808i | 0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | 5.50000 | − | 9.52628i | 0.497947 | − | 0.862469i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.00000 | + | 8.66025i | 0.449013 | + | 0.777714i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.50000 | + | 2.59808i | −0.131559 | + | 0.227866i | ||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 1.73205i | −0.0867110 | − | 0.150188i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.00000 | + | 12.1244i | −0.593732 | + | 1.02837i | 0.399992 | + | 0.916519i | \(0.369013\pi\) |
−0.993724 | + | 0.111856i | \(0.964321\pi\) | |||||||
\(140\) | −1.50000 | + | 2.59808i | −0.126773 | + | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | − | 10.3923i | −0.503509 | − | 0.872103i | ||||
\(143\) | −6.00000 | −0.501745 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.0000 | 2.24223 | ||||||||
\(146\) | −3.50000 | − | 6.06218i | −0.289662 | − | 0.501709i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50000 | − | 6.06218i | 0.287698 | − | 0.498308i | ||||
\(149\) | 1.50000 | − | 2.59808i | 0.122885 | − | 0.212843i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) |
0.920904 | + | 0.389789i | \(0.127452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00000 | − | 1.73205i | −0.0813788 | − | 0.140952i | 0.822464 | − | 0.568818i | \(-0.192599\pi\) |
−0.903842 | + | 0.427865i | \(0.859266\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | −0.483494 | ||||||||
\(155\) | 15.0000 | + | 25.9808i | 1.20483 | + | 2.08683i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5000 | + | 19.9186i | −0.917800 | + | 1.58968i | −0.115050 | + | 0.993360i | \(0.536703\pi\) |
−0.802749 | + | 0.596316i | \(0.796630\pi\) | |||||||
\(158\) | 1.00000 | − | 1.73205i | 0.0795557 | − | 0.137795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.50000 | + | 2.59808i | 0.118585 | + | 0.205396i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 3.00000 | − | 5.19615i | 0.232147 | − | 0.402090i | −0.726293 | − | 0.687386i | \(-0.758758\pi\) |
0.958440 | + | 0.285295i | \(0.0920916\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 4.50000 | + | 7.79423i | 0.342129 | + | 0.592584i | 0.984828 | − | 0.173534i | \(-0.0555188\pi\) |
−0.642699 | + | 0.766119i | \(0.722185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | + | 3.46410i | −0.151186 | + | 0.261861i | ||||
\(176\) | −3.00000 | + | 5.19615i | −0.226134 | + | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.50000 | − | 2.59808i | −0.112430 | − | 0.194734i | ||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −0.500000 | − | 0.866025i | −0.0370625 | − | 0.0641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | + | 15.5885i | 0.658145 | + | 1.13994i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.50000 | + | 9.52628i | −0.395899 | + | 0.685717i | −0.993215 | − | 0.116289i | \(-0.962900\pi\) |
0.597317 | + | 0.802005i | \(0.296234\pi\) | |||||||
\(194\) | 7.00000 | − | 12.1244i | 0.502571 | − | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | − | 0.866025i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0000 | −0.708881 | −0.354441 | − | 0.935079i | \(-0.615329\pi\) | ||||
−0.354441 | + | 0.935079i | \(0.615329\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.00000 | − | 15.5885i | 0.633238 | − | 1.09680i | ||||
\(203\) | −4.50000 | + | 7.79423i | −0.315838 | + | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | + | 15.5885i | 0.628587 | + | 1.08875i | ||||
\(206\) | 16.0000 | 1.11477 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −6.00000 | − | 10.3923i | −0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | + | 1.73205i | −0.0688428 | + | 0.119239i | −0.898392 | − | 0.439194i | \(-0.855264\pi\) |
0.829549 | + | 0.558433i | \(0.188597\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.0000 | −0.818393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0000 | −0.678844 | ||||||||
\(218\) | 2.50000 | + | 4.33013i | 0.169321 | + | 0.293273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.00000 | + | 15.5885i | −0.606780 | + | 1.05097i | ||||
\(221\) | −1.50000 | + | 2.59808i | −0.100901 | + | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000 | + | 24.2487i | 0.937509 | + | 1.62381i | 0.770097 | + | 0.637927i | \(0.220208\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | −12.0000 | − | 20.7846i | −0.796468 | − | 1.37952i | −0.921903 | − | 0.387421i | \(-0.873366\pi\) |
0.125435 | − | 0.992102i | \(-0.459967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5000 | − | 21.6506i | 0.826023 | − | 1.43071i | −0.0751115 | − | 0.997175i | \(-0.523931\pi\) |
0.901135 | − | 0.433539i | \(-0.142735\pi\) | |||||||
\(230\) | 9.00000 | − | 15.5885i | 0.593442 | − | 1.02787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50000 | + | 7.79423i | 0.295439 | + | 0.511716i | ||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | −1.17419 | ||||||||
\(236\) | −3.00000 | − | 5.19615i | −0.195283 | − | 0.338241i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.50000 | + | 2.59808i | −0.0972306 | + | 0.168408i | ||||
\(239\) | 9.00000 | − | 15.5885i | 0.582162 | − | 1.00833i | −0.413061 | − | 0.910703i | \(-0.635540\pi\) |
0.995223 | − | 0.0976302i | \(-0.0311262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.50000 | + | 16.4545i | 0.611949 | + | 1.05993i | 0.990912 | + | 0.134515i | \(0.0429475\pi\) |
−0.378963 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(242\) | −25.0000 | −1.60706 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.0000 | 0.704203 | ||||||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | − | 1.73205i | 0.0636285 | − | 0.110208i | ||||
\(248\) | −5.00000 | + | 8.66025i | −0.317500 | + | 0.549927i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | 6.00000 | 0.378717 | 0.189358 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189358 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.0000 | 2.26330 | ||||||||
\(254\) | −2.00000 | − | 3.46410i | −0.125491 | − | 0.217357i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 13.5000 | − | 23.3827i | 0.842107 | − | 1.45857i | −0.0460033 | − | 0.998941i | \(-0.514648\pi\) |
0.888110 | − | 0.459631i | \(-0.152018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | + | 6.06218i | 0.217479 | + | 0.376685i | ||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.00000 | + | 5.19615i | 0.184988 | + | 0.320408i | 0.943572 | − | 0.331166i | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | + | 15.5885i | −0.552866 | + | 0.957591i | ||||
\(266\) | 1.00000 | − | 1.73205i | 0.0613139 | − | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | − | 1.73205i | −0.0610847 | − | 0.105802i | ||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | 1.50000 | + | 2.59808i | 0.0909509 | + | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | −12.0000 | + | 20.7846i | −0.723627 | + | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | − | 12.1244i | −0.420589 | − | 0.728482i | 0.575408 | − | 0.817867i | \(-0.304843\pi\) |
−0.995997 | + | 0.0893846i | \(0.971510\pi\) | |||||||
\(278\) | −14.0000 | −0.839664 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | 10.5000 | + | 18.1865i | 0.626377 | + | 1.08492i | 0.988273 | + | 0.152699i | \(0.0487965\pi\) |
−0.361895 | + | 0.932219i | \(0.617870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.00000 | − | 5.19615i | −0.177394 | − | 0.307255i | ||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 13.5000 | + | 23.3827i | 0.792747 | + | 1.37308i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.50000 | − | 6.06218i | 0.204822 | − | 0.354762i | ||||
\(293\) | 10.5000 | − | 18.1865i | 0.613417 | − | 1.06247i | −0.377244 | − | 0.926114i | \(-0.623128\pi\) |
0.990660 | − | 0.136355i | \(-0.0435386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | − | 15.5885i | −0.524000 | − | 0.907595i | ||||
\(296\) | 7.00000 | 0.406867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | 0.173785 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 3.46410i | 0.115278 | − | 0.199667i | ||||
\(302\) | 1.00000 | − | 1.73205i | 0.0575435 | − | 0.0996683i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | − | 1.73205i | −0.0573539 | − | 0.0993399i | ||||
\(305\) | 33.0000 | 1.88957 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.0000 | −0.913168 | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −3.00000 | − | 5.19615i | −0.170941 | − | 0.296078i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.0000 | + | 25.9808i | −0.851943 | + | 1.47561i | ||||
\(311\) | −15.0000 | + | 25.9808i | −0.850572 | + | 1.47323i | 0.0301210 | + | 0.999546i | \(0.490411\pi\) |
−0.880693 | + | 0.473688i | \(0.842923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.50000 | + | 16.4545i | 0.536972 | + | 0.930062i | 0.999065 | + | 0.0432311i | \(0.0137652\pi\) |
−0.462093 | + | 0.886831i | \(0.652902\pi\) | |||||||
\(314\) | −23.0000 | −1.29797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −10.5000 | − | 18.1865i | −0.589739 | − | 1.02146i | −0.994266 | − | 0.106932i | \(-0.965897\pi\) |
0.404528 | − | 0.914526i | \(-0.367436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.0000 | + | 46.7654i | −1.51171 | + | 2.61836i | ||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.00000 | + | 5.19615i | 0.167183 | + | 0.289570i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | −8.00000 | − | 13.8564i | −0.443079 | − | 0.767435i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | 3.00000 | − | 5.19615i | 0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | + | 24.2487i | 0.769510 | + | 1.33283i | 0.937829 | + | 0.347097i | \(0.112833\pi\) |
−0.168320 | + | 0.985732i | \(0.553834\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | −3.00000 | − | 5.19615i | −0.163908 | − | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | + | 12.1244i | −0.381314 | + | 0.660456i | −0.991250 | − | 0.131995i | \(-0.957862\pi\) |
0.609936 | + | 0.792451i | \(0.291195\pi\) | |||||||
\(338\) | −6.00000 | + | 10.3923i | −0.326357 | + | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.50000 | + | 7.79423i | 0.244047 | + | 0.422701i | ||||
\(341\) | −60.0000 | −3.24918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.00000 | − | 3.46410i | −0.107833 | − | 0.186772i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.50000 | + | 7.79423i | −0.241921 | + | 0.419020i | ||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0000 | − | 22.5167i | −0.695874 | − | 1.20529i | −0.969885 | − | 0.243563i | \(-0.921684\pi\) |
0.274011 | − | 0.961727i | \(-0.411649\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.00000 | −0.319801 | ||||||||
\(353\) | 9.00000 | + | 15.5885i | 0.479022 | + | 0.829690i | 0.999711 | − | 0.0240566i | \(-0.00765819\pi\) |
−0.520689 | + | 0.853746i | \(0.674325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 31.1769i | 0.955341 | − | 1.65470i | ||||
\(356\) | 1.50000 | − | 2.59808i | 0.0794998 | − | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | − | 5.19615i | −0.158555 | − | 0.274625i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500000 | − | 0.866025i | 0.0262071 | − | 0.0453921i | ||||
\(365\) | 10.5000 | − | 18.1865i | 0.549595 | − | 0.951927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | 6.00000 | 0.312772 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.0000 | 1.09174 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | −9.00000 | + | 15.5885i | −0.465379 | + | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | −3.00000 | − | 5.19615i | −0.153897 | − | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.00000 | − | 15.5885i | −0.458682 | − | 0.794461i | ||||
\(386\) | −11.0000 | −0.559885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.0000 | 0.710742 | ||||||||
\(389\) | −15.0000 | − | 25.9808i | −0.760530 | − | 1.31728i | −0.942578 | − | 0.333987i | \(-0.891606\pi\) |
0.182047 | − | 0.983290i | \(-0.441728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | 0.500000 | − | 0.866025i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.50000 | + | 7.79423i | 0.226707 | + | 0.392668i | ||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | −0.652451 | −0.326226 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326226 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(398\) | −5.00000 | − | 8.66025i | −0.250627 | − | 0.434099i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 10.5000 | − | 18.1865i | 0.524345 | − | 0.908192i | −0.475253 | − | 0.879849i | \(-0.657644\pi\) |
0.999598 | − | 0.0283431i | \(-0.00902310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.00000 | − | 8.66025i | −0.249068 | − | 0.431398i | ||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.00000 | −0.446663 | ||||||||
\(407\) | 21.0000 | + | 36.3731i | 1.04093 | + | 1.80295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50000 | + | 4.33013i | −0.123617 | + | 0.214111i | −0.921192 | − | 0.389109i | \(-0.872783\pi\) |
0.797574 | + | 0.603220i | \(0.206116\pi\) | |||||||
\(410\) | −9.00000 | + | 15.5885i | −0.444478 | + | 0.769859i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | + | 13.8564i | 0.394132 | + | 0.682656i | ||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0000 | −0.883585 | ||||||||
\(416\) | −0.500000 | − | 0.866025i | −0.0245145 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | − | 10.3923i | 0.293470 | − | 0.508304i | ||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.50000 | − | 14.7224i | −0.414265 | − | 0.717527i | 0.581086 | − | 0.813842i | \(-0.302628\pi\) |
−0.995351 | + | 0.0963145i | \(0.969295\pi\) | |||||||
\(422\) | −2.00000 | −0.0973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.50000 | + | 9.52628i | −0.266164 | + | 0.461009i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | − | 10.3923i | −0.289346 | − | 0.501161i | ||||
\(431\) | 36.0000 | 1.73406 | 0.867029 | − | 0.498257i | \(-0.166026\pi\) | ||||
0.867029 | + | 0.498257i | \(0.166026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | −5.00000 | − | 8.66025i | −0.240008 | − | 0.415705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.50000 | + | 4.33013i | −0.119728 | + | 0.207375i | ||||
\(437\) | −6.00000 | + | 10.3923i | −0.287019 | + | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | + | 24.2487i | 0.668184 | + | 1.15733i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | −18.0000 | −0.858116 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00000 | −0.142695 | ||||||||
\(443\) | −15.0000 | − | 25.9808i | −0.712672 | − | 1.23438i | −0.963851 | − | 0.266443i | \(-0.914152\pi\) |
0.251179 | − | 0.967941i | \(-0.419182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | −14.0000 | + | 24.2487i | −0.662919 | + | 1.14821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.0000 | −1.69517 | ||||||||
\(452\) | −7.50000 | − | 12.9904i | −0.352770 | − | 0.611016i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000 | − | 20.7846i | 0.563188 | − | 0.975470i | ||||
\(455\) | 1.50000 | − | 2.59808i | 0.0703211 | − | 0.121800i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | − | 19.9186i | −0.537947 | − | 0.931752i | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | 25.0000 | 1.16817 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.0000 | 0.839254 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | −4.50000 | + | 7.79423i | −0.208907 | + | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.5000 | − | 18.1865i | −0.486403 | − | 0.842475i | ||||
\(467\) | 30.0000 | 1.38823 | 0.694117 | − | 0.719862i | \(-0.255795\pi\) | ||||
0.694117 | + | 0.719862i | \(0.255795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | −9.00000 | − | 15.5885i | −0.415139 | − | 0.719042i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 12.0000 | − | 20.7846i | 0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | − | 6.92820i | −0.183533 | − | 0.317888i | ||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | −3.00000 | − | 5.19615i | −0.137073 | − | 0.237418i | 0.789314 | − | 0.613990i | \(-0.210436\pi\) |
−0.926388 | + | 0.376571i | \(0.877103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50000 | + | 6.06218i | −0.159586 | + | 0.276412i | ||||
\(482\) | −9.50000 | + | 16.4545i | −0.432713 | + | 0.749481i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | 42.0000 | 1.90712 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | 5.50000 | + | 9.52628i | 0.248973 | + | 0.431234i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.50000 | − | 2.59808i | 0.0677631 | − | 0.117369i | ||||
\(491\) | −6.00000 | + | 10.3923i | −0.270776 | + | 0.468998i | −0.969061 | − | 0.246822i | \(-0.920614\pi\) |
0.698285 | + | 0.715820i | \(0.253947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5000 | + | 23.3827i | 0.608009 | + | 1.05310i | ||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | 6.00000 | + | 10.3923i | 0.269137 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.00000 | + | 12.1244i | −0.313363 | + | 0.542761i | −0.979088 | − | 0.203436i | \(-0.934789\pi\) |
0.665725 | + | 0.746197i | \(0.268122\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.00000 | + | 5.19615i | 0.133897 | + | 0.231916i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.0000 | 2.40297 | ||||||||
\(506\) | 18.0000 | + | 31.1769i | 0.800198 | + | 1.38598i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | − | 3.46410i | 0.0887357 | − | 0.153695i | ||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.50000 | + | 6.06218i | 0.154831 | + | 0.268175i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27.0000 | 1.19092 | ||||||||
\(515\) | 24.0000 | + | 41.5692i | 1.05757 | + | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | − | 31.1769i | 0.791639 | − | 1.37116i | ||||
\(518\) | −3.50000 | + | 6.06218i | −0.153781 | + | 0.266357i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50000 | − | 2.59808i | −0.0657794 | − | 0.113933i | ||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000 | 1.92399 | 0.961993 | − | 0.273075i | \(-0.0880406\pi\) | ||||
0.961993 | + | 0.273075i | \(0.0880406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.00000 | + | 5.19615i | −0.130806 | + | 0.226563i | ||||
\(527\) | −15.0000 | + | 25.9808i | −0.653410 | + | 1.13174i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | −18.0000 | −0.781870 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | 0.0867110 | ||||||||
\(533\) | −3.00000 | − | 5.19615i | −0.129944 | − | 0.225070i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.50000 | + | 2.59808i | 0.0646696 | + | 0.112011i | ||||
\(539\) | 6.00000 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.0000 | −1.84871 | −0.924357 | − | 0.381528i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | 7.00000 | + | 12.1244i | 0.300676 | + | 0.520786i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 2.59808i | −0.0643120 | + | 0.111392i | ||||
\(545\) | −7.50000 | + | 12.9904i | −0.321265 | + | 0.556447i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | − | 1.73205i | −0.0427569 | − | 0.0740571i | 0.843855 | − | 0.536571i | \(-0.180281\pi\) |
−0.886612 | + | 0.462514i | \(0.846947\pi\) | |||||||
\(548\) | 3.00000 | 0.128154 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.0000 | −1.02336 | ||||||||
\(551\) | −9.00000 | − | 15.5885i | −0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.00000 | + | 1.73205i | −0.0425243 | + | 0.0736543i | ||||
\(554\) | 7.00000 | − | 12.1244i | 0.297402 | − | 0.515115i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.00000 | − | 12.1244i | −0.296866 | − | 0.514187i | ||||
\(557\) | 9.00000 | 0.381342 | 0.190671 | − | 0.981654i | \(-0.438934\pi\) | ||||
0.190671 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | −1.50000 | − | 2.59808i | −0.0633866 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5000 | + | 18.1865i | −0.442916 | + | 0.767153i | ||||
\(563\) | 12.0000 | − | 20.7846i | 0.505740 | − | 0.875967i | −0.494238 | − | 0.869326i | \(-0.664553\pi\) |
0.999978 | − | 0.00664037i | \(-0.00211371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.5000 | − | 38.9711i | −0.946582 | − | 1.63953i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | 3.00000 | − | 5.19615i | 0.125436 | − | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.00000 | − | 5.19615i | −0.125218 | − | 0.216883i | ||||
\(575\) | 24.0000 | 1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.0000 | 0.707719 | 0.353860 | − | 0.935299i | \(-0.384869\pi\) | ||||
0.353860 | + | 0.935299i | \(0.384869\pi\) | |||||||
\(578\) | −4.00000 | − | 6.92820i | −0.166378 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.5000 | + | 23.3827i | −0.560557 | + | 0.970913i | ||||
\(581\) | 3.00000 | − | 5.19615i | 0.124461 | − | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | − | 31.1769i | −0.745484 | − | 1.29122i | ||||
\(584\) | 7.00000 | 0.289662 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0000 | 0.867502 | ||||||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000 | − | 17.3205i | 0.412043 | − | 0.713679i | ||||
\(590\) | 9.00000 | − | 15.5885i | 0.370524 | − | 0.641767i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.50000 | + | 6.06218i | 0.143849 | + | 0.249154i | ||||
\(593\) | −3.00000 | −0.123195 | −0.0615976 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615976 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | −0.368964 | ||||||||
\(596\) | 1.50000 | + | 2.59808i | 0.0614424 | + | 0.106421i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.00000 | + | 5.19615i | −0.122679 | + | 0.212486i | ||||
\(599\) | −15.0000 | + | 25.9808i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.50000 | + | 6.06218i | 0.142768 | + | 0.247281i | 0.928538 | − | 0.371237i | \(-0.121066\pi\) |
−0.785770 | + | 0.618519i | \(0.787733\pi\) | |||||||
\(602\) | 4.00000 | 0.163028 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.00000 | 0.0813788 | ||||||||
\(605\) | −37.5000 | − | 64.9519i | −1.52459 | − | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | 1.00000 | − | 1.73205i | 0.0405554 | − | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.5000 | + | 28.5788i | 0.668065 | + | 1.15712i | ||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | −8.00000 | − | 13.8564i | −0.322854 | − | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | − | 5.19615i | 0.120873 | − | 0.209359i | ||||
\(617\) | −7.50000 | + | 12.9904i | −0.301939 | + | 0.522973i | −0.976575 | − | 0.215177i | \(-0.930967\pi\) |
0.674636 | + | 0.738150i | \(0.264300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.00000 | + | 3.46410i | 0.0803868 | + | 0.139234i | 0.903416 | − | 0.428765i | \(-0.141051\pi\) |
−0.823029 | + | 0.567999i | \(0.807718\pi\) | |||||||
\(620\) | −30.0000 | −1.20483 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.0000 | −1.20289 | ||||||||
\(623\) | 1.50000 | + | 2.59808i | 0.0600962 | + | 0.104090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −9.50000 | + | 16.4545i | −0.379696 | + | 0.657653i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.5000 | − | 19.9186i | −0.458900 | − | 0.794838i | ||||
\(629\) | 21.0000 | 0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 1.00000 | + | 1.73205i | 0.0397779 | + | 0.0688973i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.5000 | − | 18.1865i | 0.417008 | − | 0.722280i | ||||
\(635\) | 6.00000 | − | 10.3923i | 0.238103 | − | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.500000 | + | 0.866025i | 0.0198107 | + | 0.0343132i | ||||
\(638\) | −54.0000 | −2.13788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | 4.50000 | + | 7.79423i | 0.177739 | + | 0.307854i | 0.941106 | − | 0.338112i | \(-0.109788\pi\) |
−0.763367 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0000 | − | 19.0526i | 0.433798 | − | 0.751360i | −0.563399 | − | 0.826185i | \(-0.690507\pi\) |
0.997197 | + | 0.0748254i | \(0.0238399\pi\) | |||||||
\(644\) | −3.00000 | + | 5.19615i | −0.118217 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | − | 5.19615i | −0.118033 | − | 0.204440i | ||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0000 | 1.41312 | ||||||||
\(650\) | −2.00000 | − | 3.46410i | −0.0784465 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.00000 | − | 13.8564i | 0.313304 | − | 0.542659i | ||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.00000 | 0.233904 | ||||||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.50000 | − | 11.2583i | 0.252821 | − | 0.437898i | −0.711481 | − | 0.702706i | \(-0.751975\pi\) |
0.964301 | + | 0.264807i | \(0.0853084\pi\) | |||||||
\(662\) | −14.0000 | + | 24.2487i | −0.544125 | + | 0.942453i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.00000 | − | 5.19615i | −0.116423 | − | 0.201650i | ||||
\(665\) | 6.00000 | 0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 54.0000 | 2.09089 | ||||||||
\(668\) | 3.00000 | + | 5.19615i | 0.116073 | + | 0.201045i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.00000 | − | 5.19615i | 0.115900 | − | 0.200745i | ||||
\(671\) | −33.0000 | + | 57.1577i | −1.27395 | + | 2.20655i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | −14.0000 | −0.539260 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −3.00000 | − | 5.19615i | −0.115299 | − | 0.199704i | 0.802600 | − | 0.596518i | \(-0.203449\pi\) |
−0.917899 | + | 0.396813i | \(0.870116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00000 | + | 12.1244i | −0.268635 | + | 0.465290i | ||||
\(680\) | −4.50000 | + | 7.79423i | −0.172567 | + | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30.0000 | − | 51.9615i | −1.14876 | − | 1.98971i | ||||
\(683\) | −36.0000 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | 3.00000 | − | 5.19615i | 0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | + | 3.46410i | 0.0760836 | + | 0.131781i | 0.901557 | − | 0.432660i | \(-0.142425\pi\) |
−0.825473 | + | 0.564441i | \(0.809092\pi\) | |||||||
\(692\) | −9.00000 | −0.342129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −21.0000 | − | 36.3731i | −0.796575 | − | 1.37971i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.00000 | + | 15.5885i | −0.340899 | + | 0.590455i | ||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 3.46410i | −0.0755929 | − | 0.130931i | ||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | −3.00000 | − | 5.19615i | −0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | −9.00000 | + | 15.5885i | −0.338480 | + | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50000 | − | 4.33013i | −0.0938895 | − | 0.162621i | 0.815255 | − | 0.579102i | \(-0.196597\pi\) |
−0.909145 | + | 0.416481i | \(0.863263\pi\) | |||||||
\(710\) | 36.0000 | 1.35106 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | 0.112430 | ||||||||
\(713\) | 30.0000 | + | 51.9615i | 1.12351 | + | 1.94597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.00000 | − | 15.5885i | 0.336581 | − | 0.582975i | ||||
\(716\) | 3.00000 | − | 5.19615i | 0.112115 | − | 0.194189i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.0000 | −0.595871 | ||||||||
\(722\) | −7.50000 | − | 12.9904i | −0.279121 | − | 0.483452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | − | 6.92820i | −0.148352 | − | 0.256953i | 0.782267 | − | 0.622944i | \(-0.214063\pi\) |
−0.930618 | + | 0.365991i | \(0.880730\pi\) | |||||||
\(728\) | 1.00000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.0000 | 0.777245 | ||||||||
\(731\) | −6.00000 | − | 10.3923i | −0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.0000 | + | 22.5167i | −0.480166 | + | 0.831672i | −0.999741 | − | 0.0227529i | \(-0.992757\pi\) |
0.519575 | + | 0.854425i | \(0.326090\pi\) | |||||||
\(734\) | −5.00000 | + | 8.66025i | −0.184553 | + | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 12.0000 | 0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.0000 | 1.83928 | 0.919640 | − | 0.392763i | \(-0.128481\pi\) | ||||
0.919640 | + | 0.392763i | \(0.128481\pi\) | |||||||
\(740\) | 10.5000 | + | 18.1865i | 0.385988 | + | 0.668550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.00000 | − | 5.19615i | 0.110133 | − | 0.190757i | ||||
\(743\) | 12.0000 | − | 20.7846i | 0.440237 | − | 0.762513i | −0.557470 | − | 0.830197i | \(-0.688228\pi\) |
0.997707 | + | 0.0676840i | \(0.0215610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 7.79423i | 0.164867 | + | 0.285558i | ||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18.0000 | −0.658145 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000 | − | 3.46410i | 0.0729810 | − | 0.126407i | −0.827225 | − | 0.561870i | \(-0.810082\pi\) |
0.900207 | + | 0.435463i | \(0.143415\pi\) | |||||||
\(752\) | 3.00000 | − | 5.19615i | 0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.50000 | − | 7.79423i | −0.163880 | − | 0.283849i | ||||
\(755\) | 6.00000 | 0.218362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 1.00000 | + | 1.73205i | 0.0363216 | + | 0.0629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.00000 | − | 5.19615i | 0.108821 | − | 0.188484i | ||||
\(761\) | −16.5000 | + | 28.5788i | −0.598125 | + | 1.03598i | 0.394973 | + | 0.918693i | \(0.370754\pi\) |
−0.993098 | + | 0.117289i | \(0.962579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.50000 | − | 4.33013i | −0.0905061 | − | 0.156761i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.00000 | + | 5.19615i | 0.108324 | + | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.50000 | + | 4.33013i | −0.0901523 | + | 0.156148i | −0.907575 | − | 0.419890i | \(-0.862069\pi\) |
0.817423 | + | 0.576038i | \(0.195402\pi\) | |||||||
\(770\) | 9.00000 | − | 15.5885i | 0.324337 | − | 0.561769i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50000 | − | 9.52628i | −0.197949 | − | 0.342858i | ||||
\(773\) | −9.00000 | −0.323708 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.0000 | −1.43684 | ||||||||
\(776\) | 7.00000 | + | 12.1244i | 0.251285 | + | 0.435239i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0000 | − | 25.9808i | 0.537776 | − | 0.931455i | ||||
\(779\) | 6.00000 | − | 10.3923i | 0.214972 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | + | 62.3538i | 1.28818 | + | 2.23120i | ||||
\(782\) | 18.0000 | 0.643679 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −34.5000 | − | 59.7558i | −1.23136 | − | 2.13277i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.00000 | + | 6.92820i | −0.142585 | + | 0.246964i | −0.928469 | − | 0.371409i | \(-0.878875\pi\) |
0.785885 | + | 0.618373i | \(0.212208\pi\) | |||||||
\(788\) | −4.50000 | + | 7.79423i | −0.160306 | + | 0.277658i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.00000 | + | 5.19615i | 0.106735 | + | 0.184871i | ||||
\(791\) | 15.0000 | 0.533339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0000 | −0.390621 | ||||||||
\(794\) | −6.50000 | − | 11.2583i | −0.230676 | − | 0.399543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | − | 8.66025i | 0.177220 | − | 0.306955i | ||||
\(797\) | 4.50000 | − | 7.79423i | 0.159398 | − | 0.276086i | −0.775254 | − | 0.631650i | \(-0.782378\pi\) |
0.934652 | + | 0.355564i | \(0.115711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | − | 15.5885i | −0.318397 | − | 0.551480i | ||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.0000 | 0.741536 | ||||||||
\(803\) | 21.0000 | + | 36.3731i | 0.741074 | + | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.00000 | + | 15.5885i | −0.317208 | + | 0.549421i | ||||
\(806\) | 5.00000 | − | 8.66025i | 0.176117 | − | 0.305044i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.00000 | + | 15.5885i | 0.316619 | + | 0.548400i | ||||
\(809\) | 15.0000 | 0.527372 | 0.263686 | − | 0.964609i | \(-0.415062\pi\) | ||||
0.263686 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | −4.50000 | − | 7.79423i | −0.157919 | − | 0.273524i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.0000 | + | 36.3731i | −0.736050 | + | 1.27488i | ||||
\(815\) | 24.0000 | − | 41.5692i | 0.840683 | − | 1.45611i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | + | 6.92820i | 0.139942 | + | 0.242387i | ||||
\(818\) | −5.00000 | −0.174821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.0000 | −0.628587 | ||||||||
\(821\) | −22.5000 | − | 38.9711i | −0.785255 | − | 1.36010i | −0.928846 | − | 0.370465i | \(-0.879198\pi\) |
0.143591 | − | 0.989637i | \(-0.454135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | −8.00000 | + | 13.8564i | −0.278693 | + | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | + | 5.19615i | 0.104383 | + | 0.180797i | ||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | −9.00000 | − | 15.5885i | −0.312395 | − | 0.541083i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.500000 | − | 0.866025i | 0.0173344 | − | 0.0300240i | ||||
\(833\) | 1.50000 | − | 2.59808i | 0.0519719 | − | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.00000 | + | 15.5885i | 0.311458 | + | 0.539461i | ||||
\(836\) | 12.0000 | 0.415029 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | 24.0000 | + | 41.5692i | 0.828572 | + | 1.43513i | 0.899158 | + | 0.437623i | \(0.144180\pi\) |
−0.0705865 | + | 0.997506i | \(0.522487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 8.50000 | − | 14.7224i | 0.292929 | − | 0.507369i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | −36.0000 | −1.23844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | 0.859010 | ||||||||
\(848\) | −3.00000 | − | 5.19615i | −0.103020 | − | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | + | 10.3923i | −0.205798 | + | 0.356453i | ||||
\(851\) | 21.0000 | − | 36.3731i | 0.719871 | − | 1.24685i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | + | 8.66025i | 0.171197 | + | 0.296521i | 0.938839 | − | 0.344358i | \(-0.111903\pi\) |
−0.767642 | + | 0.640879i | \(0.778570\pi\) | |||||||
\(854\) | −11.0000 | −0.376412 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.50000 | − | 7.79423i | −0.153717 | − | 0.266246i | 0.778874 | − | 0.627180i | \(-0.215791\pi\) |
−0.932591 | + | 0.360935i | \(0.882458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000 | − | 3.46410i | 0.0682391 | − | 0.118194i | −0.829887 | − | 0.557931i | \(-0.811595\pi\) |
0.898126 | + | 0.439738i | \(0.144929\pi\) | |||||||
\(860\) | 6.00000 | − | 10.3923i | 0.204598 | − | 0.354375i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.0000 | + | 31.1769i | 0.613082 | + | 1.06189i | ||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0000 | −0.918028 | ||||||||
\(866\) | 8.50000 | + | 14.7224i | 0.288842 | + | 0.500289i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.00000 | − | 8.66025i | 0.169711 | − | 0.293948i | ||||
\(869\) | −6.00000 | + | 10.3923i | −0.203536 | + | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.00000 | + | 1.73205i | 0.0338837 | + | 0.0586883i | ||||
\(872\) | −5.00000 | −0.169321 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5000 | + | 35.5070i | −0.692236 | + | 1.19899i | 0.278868 | + | 0.960329i | \(0.410041\pi\) |
−0.971104 | + | 0.238658i | \(0.923292\pi\) | |||||||
\(878\) | −14.0000 | + | 24.2487i | −0.472477 | + | 0.818354i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.00000 | − | 15.5885i | −0.303390 | − | 0.525487i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0000 | −1.14419 | −0.572096 | − | 0.820187i | \(-0.693869\pi\) | ||||
−0.572096 | + | 0.820187i | \(0.693869\pi\) | |||||||
\(884\) | −1.50000 | − | 2.59808i | −0.0504505 | − | 0.0873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.0000 | − | 25.9808i | 0.503935 | − | 0.872841i | ||||
\(887\) | 21.0000 | − | 36.3731i | 0.705111 | − | 1.22129i | −0.261540 | − | 0.965193i | \(-0.584230\pi\) |
0.966651 | − | 0.256096i | \(-0.0824362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | + | 3.46410i | 0.0670778 | + | 0.116182i | ||||
\(890\) | 9.00000 | 0.301681 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.0000 | −0.937509 | ||||||||
\(893\) | 6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.00000 | − | 15.5885i | 0.300837 | − | 0.521065i | ||||
\(896\) | 0.500000 | − | 0.866025i | 0.0167038 | − | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0000 | + | 25.9808i | 0.500556 | + | 0.866989i | ||||
\(899\) | −90.0000 | −3.00167 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | −0.599667 | ||||||||
\(902\) | −18.0000 | − | 31.1769i | −0.599334 | − | 1.03808i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.50000 | − | 12.9904i | 0.249446 | − | 0.432054i | ||||
\(905\) | −3.00000 | + | 5.19615i | −0.0997234 | + | 0.172726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.0000 | − | 17.3205i | −0.332045 | − | 0.575118i | 0.650868 | − | 0.759191i | \(-0.274405\pi\) |
−0.982913 | + | 0.184073i | \(0.941072\pi\) | |||||||
\(908\) | 24.0000 | 0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.00000 | 0.0994490 | ||||||||
\(911\) | −18.0000 | − | 31.1769i | −0.596367 | − | 1.03294i | −0.993352 | − | 0.115113i | \(-0.963277\pi\) |
0.396986 | − | 0.917825i | \(-0.370056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 11.5000 | − | 19.9186i | 0.380386 | − | 0.658848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.5000 | + | 21.6506i | 0.413012 | + | 0.715357i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.00000 | 0.0659739 | 0.0329870 | − | 0.999456i | \(-0.489498\pi\) | ||||
0.0329870 | + | 0.999456i | \(0.489498\pi\) | |||||||
\(920\) | 9.00000 | + | 15.5885i | 0.296721 | + | 0.513936i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.00000 | + | 5.19615i | −0.0987997 | + | 0.171126i | ||||
\(923\) | −6.00000 | + | 10.3923i | −0.197492 | + | 0.342067i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | + | 24.2487i | 0.460317 | + | 0.797293i | ||||
\(926\) | 22.0000 | 0.722965 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.00000 | −0.295439 | ||||||||
\(929\) | −10.5000 | − | 18.1865i | −0.344494 | − | 0.596681i | 0.640768 | − | 0.767735i | \(-0.278616\pi\) |
−0.985262 | + | 0.171054i | \(0.945283\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | + | 1.73205i | −0.0327737 | + | 0.0567657i | ||||
\(932\) | 10.5000 | − | 18.1865i | 0.343939 | − | 0.595720i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.0000 | + | 25.9808i | 0.490815 | + | 0.850117i | ||||
\(935\) | −54.0000 | −1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.00000 | −0.228680 | −0.114340 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114340 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(938\) | 1.00000 | + | 1.73205i | 0.0326512 | + | 0.0565535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.00000 | − | 15.5885i | 0.293548 | − | 0.508439i | ||||
\(941\) | −1.50000 | + | 2.59808i | −0.0488986 | + | 0.0846949i | −0.889439 | − | 0.457054i | \(-0.848904\pi\) |
0.840540 | + | 0.541749i | \(0.182238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | + | 31.1769i | 0.586161 | + | 1.01526i | ||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0000 | 0.780307 | ||||||||
\(947\) | 18.0000 | + | 31.1769i | 0.584921 | + | 1.01311i | 0.994885 | + | 0.101012i | \(0.0322080\pi\) |
−0.409964 | + | 0.912102i | \(0.634459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.50000 | + | 6.06218i | −0.113615 | + | 0.196787i | ||||
\(950\) | 4.00000 | − | 6.92820i | 0.129777 | − | 0.224781i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.50000 | − | 2.59808i | −0.0486153 | − | 0.0842041i | ||||
\(953\) | 3.00000 | 0.0971795 | 0.0485898 | − | 0.998819i | \(-0.484527\pi\) | ||||
0.0485898 | + | 0.998819i | \(0.484527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | −0.582466 | ||||||||
\(956\) | 9.00000 | + | 15.5885i | 0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.00000 | − | 5.19615i | 0.0969256 | − | 0.167880i | ||||
\(959\) | −1.50000 | + | 2.59808i | −0.0484375 | + | 0.0838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −34.5000 | − | 59.7558i | −1.11290 | − | 1.92760i | ||||
\(962\) | −7.00000 | −0.225689 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.0000 | −0.611949 | ||||||||
\(965\) | −16.5000 | − | 28.5788i | −0.531154 | − | 0.919985i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | + | 1.73205i | −0.0321578 | + | 0.0556990i | −0.881656 | − | 0.471892i | \(-0.843571\pi\) |
0.849499 | + | 0.527591i | \(0.176905\pi\) | |||||||
\(968\) | 12.5000 | − | 21.6506i | 0.401765 | − | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.0000 | + | 36.3731i | 0.674269 | + | 1.16787i | ||||
\(971\) | −6.00000 | −0.192549 | −0.0962746 | − | 0.995355i | \(-0.530693\pi\) | ||||
−0.0962746 | + | 0.995355i | \(0.530693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | 0.448819 | ||||||||
\(974\) | −17.0000 | − | 29.4449i | −0.544715 | − | 0.943474i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.50000 | + | 9.52628i | −0.176051 | + | 0.304929i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.00000 | + | 15.5885i | 0.287641 | + | 0.498209i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.0000 | −0.382935 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.5000 | + | 23.3827i | −0.430146 | + | 0.745034i | ||||
\(986\) | −13.5000 | + | 23.3827i | −0.429928 | + | 0.744656i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.00000 | + | 1.73205i | 0.0318142 | + | 0.0551039i | ||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0000 | −0.317660 | −0.158830 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158830 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(992\) | −5.00000 | − | 8.66025i | −0.158750 | − | 0.274963i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | + | 10.3923i | −0.190308 | + | 0.329624i | ||||
\(995\) | 15.0000 | − | 25.9808i | 0.475532 | − | 0.823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5000 | + | 32.0429i | 0.585901 | + | 1.01481i | 0.994762 | + | 0.102214i | \(0.0325925\pi\) |
−0.408862 | + | 0.912596i | \(0.634074\pi\) | |||||||
\(998\) | −14.0000 | −0.443162 | ||||||||
\(999\) | 0 | 0 |
(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 | 1134.2.f.i.757.1 | 2 | ||
3.2 | odd | 2 | 1134.2.f.h.757.1 | 2 | |||
9.2 | odd | 6 | 1134.2.f.h.379.1 | 2 | |||
9.4 | even | 3 | 1134.2.a.d.1.1 | ✓ | 1 | ||
9.5 | odd | 6 | 1134.2.a.e.1.1 | yes | 1 | ||
9.7 | even | 3 | inner | 1134.2.f.i.379.1 | 2 | ||
36.23 | even | 6 | 9072.2.a.b.1.1 | 1 | |||
36.31 | odd | 6 | 9072.2.a.v.1.1 | 1 | |||
63.13 | odd | 6 | 7938.2.a.d.1.1 | 1 | |||
63.41 | even | 6 | 7938.2.a.bc.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.d.1.1 | ✓ | 1 | 9.4 | even | 3 | ||
1134.2.a.e.1.1 | yes | 1 | 9.5 | odd | 6 | ||
1134.2.f.h.379.1 | 2 | 9.2 | odd | 6 | |||
1134.2.f.h.757.1 | 2 | 3.2 | odd | 2 | |||
1134.2.f.i.379.1 | 2 | 9.7 | even | 3 | inner | ||
1134.2.f.i.757.1 | 2 | 1.1 | even | 1 | trivial | ||
7938.2.a.d.1.1 | 1 | 63.13 | odd | 6 | |||
7938.2.a.bc.1.1 | 1 | 63.41 | even | 6 | |||
9072.2.a.b.1.1 | 1 | 36.23 | even | 6 | |||
9072.2.a.v.1.1 | 1 | 36.31 | odd | 6 |