Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.162447943996702457856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1011.6 | ||
Root | \(-0.140577 - 1.40721i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1011 |
Dual form | 1078.2.i.b.901.6 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.559525 | − | 0.323042i | −0.323042 | − | 0.186508i | 0.329706 | − | 0.944084i | \(-0.393050\pi\) |
−0.652748 | + | 0.757575i | \(0.726384\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.68085 | − | 1.54779i | 1.19891 | − | 0.692191i | 0.238598 | − | 0.971118i | \(-0.423312\pi\) |
0.960312 | + | 0.278927i | \(0.0899788\pi\) | |||||||
\(6\) | −0.646084 | −0.263763 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.29129 | − | 2.23658i | −0.430429 | − | 0.745525i | ||||
\(10\) | 1.54779 | − | 2.68085i | 0.489453 | − | 0.847758i | ||||
\(11\) | −1.52168 | − | 2.94694i | −0.458804 | − | 0.888537i | ||||
\(12\) | −0.559525 | + | 0.323042i | −0.161521 | + | 0.0932542i | ||||
\(13\) | −0.646084 | −0.179191 | −0.0895957 | − | 0.995978i | \(-0.528557\pi\) | ||||
−0.0895957 | + | 0.995978i | \(0.528557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.87083 | + | 3.24037i | −0.453743 | + | 0.785905i | −0.998615 | − | 0.0526138i | \(-0.983245\pi\) |
0.544872 | + | 0.838519i | \(0.316578\pi\) | |||||||
\(18\) | −2.23658 | − | 1.29129i | −0.527166 | − | 0.304359i | ||||
\(19\) | −0.901703 | − | 1.56180i | −0.206865 | − | 0.358300i | 0.743860 | − | 0.668335i | \(-0.232993\pi\) |
−0.950725 | + | 0.310035i | \(0.899659\pi\) | |||||||
\(20\) | − | 3.09557i | − | 0.692191i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.79129 | − | 1.79129i | −0.595105 | − | 0.381904i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | −0.323042 | + | 0.559525i | −0.0659407 | + | 0.114213i | ||||
\(25\) | 2.29129 | − | 3.96863i | 0.458258 | − | 0.793725i | ||||
\(26\) | −0.559525 | + | 0.323042i | −0.109732 | + | 0.0633537i | ||||
\(27\) | 3.60681i | 0.694131i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.58258i | − | 0.293877i | −0.989146 | − | 0.146938i | \(-0.953058\pi\) | ||
0.989146 | − | 0.146938i | \(-0.0469419\pi\) | |||||||
\(30\) | −1.73205 | + | 1.00000i | −0.316228 | + | 0.182574i | ||||
\(31\) | 7.48301 | + | 4.32032i | 1.34399 | + | 0.775952i | 0.987390 | − | 0.158306i | \(-0.0506032\pi\) |
0.356598 | + | 0.934258i | \(0.383936\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −0.100567 | + | 2.14046i | −0.0175065 | + | 0.372606i | ||||
\(34\) | 3.74166i | 0.641689i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.58258 | −0.430429 | ||||||||
\(37\) | −1.79129 | − | 3.10260i | −0.294486 | − | 0.510065i | 0.680379 | − | 0.732860i | \(-0.261815\pi\) |
−0.974865 | + | 0.222796i | \(0.928482\pi\) | |||||||
\(38\) | −1.56180 | − | 0.901703i | −0.253357 | − | 0.146276i | ||||
\(39\) | 0.361500 | + | 0.208712i | 0.0578863 | + | 0.0334207i | ||||
\(40\) | −1.54779 | − | 2.68085i | −0.244727 | − | 0.423879i | ||||
\(41\) | 9.93280 | 1.55124 | 0.775622 | − | 0.631198i | \(-0.217436\pi\) | ||||
0.775622 | + | 0.631198i | \(0.217436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16515i | 1.09268i | 0.837565 | + | 0.546338i | \(0.183978\pi\) | ||||
−0.837565 | + | 0.546338i | \(0.816022\pi\) | |||||||
\(44\) | −3.31297 | − | 0.155657i | −0.499449 | − | 0.0234662i | ||||
\(45\) | −6.92349 | − | 3.99728i | −1.03209 | − | 0.595879i | ||||
\(46\) | −3.46410 | − | 2.00000i | −0.510754 | − | 0.294884i | ||||
\(47\) | −8.60206 | + | 4.96640i | −1.25474 | + | 0.724424i | −0.972047 | − | 0.234786i | \(-0.924561\pi\) |
−0.282693 | + | 0.959211i | \(0.591228\pi\) | |||||||
\(48\) | 0.646084i | 0.0932542i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.58258i | − | 0.648074i | ||||||
\(51\) | 2.09355 | − | 1.20871i | 0.293156 | − | 0.169254i | ||||
\(52\) | −0.323042 | + | 0.559525i | −0.0447979 | + | 0.0775922i | ||||
\(53\) | 5.79129 | − | 10.0308i | 0.795495 | − | 1.37784i | −0.127030 | − | 0.991899i | \(-0.540544\pi\) |
0.922525 | − | 0.385938i | \(-0.126122\pi\) | |||||||
\(54\) | 1.80341 | + | 3.12359i | 0.245412 | + | 0.425067i | ||||
\(55\) | −8.64064 | − | 5.54506i | −1.16510 | − | 0.747696i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.16515i | 0.154328i | ||||||||
\(58\) | −0.791288 | − | 1.37055i | −0.103901 | − | 0.179962i | ||||
\(59\) | 0.559525 | + | 0.323042i | 0.0728440 | + | 0.0420565i | 0.535980 | − | 0.844231i | \(-0.319942\pi\) |
−0.463136 | + | 0.886287i | \(0.653276\pi\) | |||||||
\(60\) | −1.00000 | + | 1.73205i | −0.129099 | + | 0.223607i | ||||
\(61\) | 0.969126 | + | 1.67858i | 0.124084 | + | 0.214920i | 0.921374 | − | 0.388676i | \(-0.127067\pi\) |
−0.797291 | + | 0.603596i | \(0.793734\pi\) | |||||||
\(62\) | 8.64064 | 1.09736 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.73205 | + | 1.00000i | −0.214834 | + | 0.124035i | ||||
\(66\) | 0.983134 | + | 1.90397i | 0.121015 | + | 0.234363i | ||||
\(67\) | 3.79129 | − | 6.56670i | 0.463180 | − | 0.802250i | −0.535938 | − | 0.844257i | \(-0.680042\pi\) |
0.999117 | + | 0.0420070i | \(0.0133752\pi\) | |||||||
\(68\) | 1.87083 | + | 3.24037i | 0.226871 | + | 0.392953i | ||||
\(69\) | 2.58434i | 0.311117i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −2.23658 | + | 1.29129i | −0.263583 | + | 0.152180i | ||||
\(73\) | 8.06198 | − | 13.9638i | 0.943583 | − | 1.63433i | 0.185019 | − | 0.982735i | \(-0.440765\pi\) |
0.758564 | − | 0.651599i | \(-0.225901\pi\) | |||||||
\(74\) | −3.10260 | − | 1.79129i | −0.360670 | − | 0.208233i | ||||
\(75\) | −2.56407 | + | 1.48036i | −0.296073 | + | 0.170938i | ||||
\(76\) | −1.80341 | −0.206865 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.417424 | 0.0472640 | ||||||||
\(79\) | 3.46410 | − | 2.00000i | 0.389742 | − | 0.225018i | −0.292306 | − | 0.956325i | \(-0.594423\pi\) |
0.682048 | + | 0.731307i | \(0.261089\pi\) | |||||||
\(80\) | −2.68085 | − | 1.54779i | −0.299728 | − | 0.173048i | ||||
\(81\) | −2.70871 | + | 4.69163i | −0.300968 | + | 0.521292i | ||||
\(82\) | 8.60206 | − | 4.96640i | 0.949939 | − | 0.548447i | ||||
\(83\) | −12.8935 | −1.41525 | −0.707625 | − | 0.706589i | \(-0.750233\pi\) | ||||
−0.707625 | + | 0.706589i | \(0.750233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5826i | 1.25631i | ||||||||
\(86\) | 3.58258 | + | 6.20520i | 0.386319 | + | 0.669124i | ||||
\(87\) | −0.511238 | + | 0.885491i | −0.0548105 | + | 0.0949346i | ||||
\(88\) | −2.94694 | + | 1.52168i | −0.314145 | + | 0.162212i | ||||
\(89\) | 8.48528 | − | 4.89898i | 0.899438 | − | 0.519291i | 0.0224202 | − | 0.999749i | \(-0.492863\pi\) |
0.877018 | + | 0.480458i | \(0.159529\pi\) | |||||||
\(90\) | −7.99455 | −0.842700 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | −2.79129 | − | 4.83465i | −0.289443 | − | 0.501330i | ||||
\(94\) | −4.96640 | + | 8.60206i | −0.512245 | + | 0.887235i | ||||
\(95\) | −4.83465 | − | 2.79129i | −0.496025 | − | 0.286380i | ||||
\(96\) | 0.323042 | + | 0.559525i | 0.0329703 | + | 0.0571063i | ||||
\(97\) | − | 8.50579i | − | 0.863632i | −0.901962 | − | 0.431816i | \(-0.857873\pi\) | ||
0.901962 | − | 0.431816i | \(-0.142127\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.62614 | + | 7.20871i | −0.464944 | + | 0.724503i | ||||
\(100\) | −2.29129 | − | 3.96863i | −0.229129 | − | 0.396863i | ||||
\(101\) | −5.86811 | + | 10.1639i | −0.583898 | + | 1.01134i | 0.411114 | + | 0.911584i | \(0.365140\pi\) |
−0.995012 | + | 0.0997573i | \(0.968193\pi\) | |||||||
\(102\) | 1.20871 | − | 2.09355i | 0.119680 | − | 0.207292i | ||||
\(103\) | 5.24491 | − | 3.02815i | 0.516796 | − | 0.298373i | −0.218827 | − | 0.975764i | \(-0.570223\pi\) |
0.735623 | + | 0.677391i | \(0.236890\pi\) | |||||||
\(104\) | 0.646084i | 0.0633537i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.5826i | − | 1.12500i | ||||||
\(107\) | −15.2270 | + | 8.79129i | −1.47205 | + | 0.849886i | −0.999506 | − | 0.0314237i | \(-0.989996\pi\) |
−0.472539 | + | 0.881310i | \(0.656663\pi\) | |||||||
\(108\) | 3.12359 | + | 1.80341i | 0.300568 | + | 0.173533i | ||||
\(109\) | 14.8655 | + | 8.58258i | 1.42385 | + | 0.822062i | 0.996626 | − | 0.0820827i | \(-0.0261572\pi\) |
0.427227 | + | 0.904144i | \(0.359491\pi\) | |||||||
\(110\) | −10.2555 | − | 0.481847i | −0.977828 | − | 0.0459423i | ||||
\(111\) | 2.31464i | 0.219696i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7477 | 1.01106 | 0.505531 | − | 0.862809i | \(-0.331297\pi\) | ||||
0.505531 | + | 0.862809i | \(0.331297\pi\) | |||||||
\(114\) | 0.582576 | + | 1.00905i | 0.0545632 | + | 0.0945063i | ||||
\(115\) | −10.7234 | − | 6.19115i | −0.999960 | − | 0.577327i | ||||
\(116\) | −1.37055 | − | 0.791288i | −0.127252 | − | 0.0734692i | ||||
\(117\) | 0.834280 | + | 1.44502i | 0.0771292 | + | 0.133592i | ||||
\(118\) | 0.646084 | 0.0594768 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000i | 0.182574i | ||||||||
\(121\) | −6.36897 | + | 8.96863i | −0.578997 | + | 0.815330i | ||||
\(122\) | 1.67858 | + | 0.969126i | 0.151971 | + | 0.0877405i | ||||
\(123\) | −5.55765 | − | 3.20871i | −0.501117 | − | 0.289320i | ||||
\(124\) | 7.48301 | − | 4.32032i | 0.671994 | − | 0.387976i | ||||
\(125\) | 1.29217i | 0.115575i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.58258i | 0.317902i | 0.987286 | + | 0.158951i | \(0.0508112\pi\) | ||||
−0.987286 | + | 0.158951i | \(0.949189\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 2.31464 | − | 4.00908i | 0.203793 | − | 0.352980i | ||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | −8.38502 | − | 14.5233i | −0.732602 | − | 1.26890i | −0.955767 | − | 0.294124i | \(-0.904972\pi\) |
0.223165 | − | 0.974781i | \(-0.428361\pi\) | |||||||
\(132\) | 1.80341 | + | 1.15732i | 0.156966 | + | 0.100732i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 7.58258i | − | 0.655035i | ||||||
\(135\) | 5.58258 | + | 9.66930i | 0.480472 | + | 0.832201i | ||||
\(136\) | 3.24037 | + | 1.87083i | 0.277859 | + | 0.160422i | ||||
\(137\) | 1.58258 | − | 2.74110i | 0.135209 | − | 0.234188i | −0.790469 | − | 0.612503i | \(-0.790163\pi\) |
0.925677 | + | 0.378315i | \(0.123496\pi\) | |||||||
\(138\) | 1.29217 | + | 2.23810i | 0.109997 | + | 0.190520i | ||||
\(139\) | 15.4779 | 1.31282 | 0.656408 | − | 0.754406i | \(-0.272075\pi\) | ||||
0.656408 | + | 0.754406i | \(0.272075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.41742 | 0.540445 | ||||||||
\(142\) | 1.73205 | − | 1.00000i | 0.145350 | − | 0.0839181i | ||||
\(143\) | 0.983134 | + | 1.90397i | 0.0822138 | + | 0.159218i | ||||
\(144\) | −1.29129 | + | 2.23658i | −0.107607 | + | 0.186381i | ||||
\(145\) | −2.44949 | − | 4.24264i | −0.203419 | − | 0.352332i | ||||
\(146\) | − | 16.1240i | − | 1.33443i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.58258 | −0.294486 | ||||||||
\(149\) | 12.1244 | − | 7.00000i | 0.993266 | − | 0.573462i | 0.0870170 | − | 0.996207i | \(-0.472267\pi\) |
0.906249 | + | 0.422744i | \(0.138933\pi\) | |||||||
\(150\) | −1.48036 | + | 2.56407i | −0.120871 | + | 0.209355i | ||||
\(151\) | 4.83465 | + | 2.79129i | 0.393438 | + | 0.227152i | 0.683649 | − | 0.729811i | \(-0.260392\pi\) |
−0.290210 | + | 0.956963i | \(0.593725\pi\) | |||||||
\(152\) | −1.56180 | + | 0.901703i | −0.126678 | + | 0.0731378i | ||||
\(153\) | 9.66311 | 0.781216 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.7477 | 2.14843 | ||||||||
\(156\) | 0.361500 | − | 0.208712i | 0.0289432 | − | 0.0167103i | ||||
\(157\) | 11.3997 | + | 6.58161i | 0.909794 | + | 0.525270i | 0.880365 | − | 0.474297i | \(-0.157298\pi\) |
0.0294291 | + | 0.999567i | \(0.490631\pi\) | |||||||
\(158\) | 2.00000 | − | 3.46410i | 0.159111 | − | 0.275589i | ||||
\(159\) | −6.48074 | + | 3.74166i | −0.513956 | + | 0.296733i | ||||
\(160\) | −3.09557 | −0.244727 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.41742i | 0.425633i | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 4.96640 | − | 8.60206i | 0.387811 | − | 0.671708i | ||||
\(165\) | 3.04336 | + | 5.89389i | 0.236926 | + | 0.458839i | ||||
\(166\) | −11.1661 | + | 6.44677i | −0.866660 | + | 0.500366i | ||||
\(167\) | −1.29217 | −0.0999909 | −0.0499955 | − | 0.998749i | \(-0.515921\pi\) | ||||
−0.0499955 | + | 0.998749i | \(0.515921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5826 | −0.967890 | ||||||||
\(170\) | 5.79129 | + | 10.0308i | 0.444172 | + | 0.769328i | ||||
\(171\) | −2.32872 | + | 4.03345i | −0.178081 | + | 0.308446i | ||||
\(172\) | 6.20520 | + | 3.58258i | 0.473142 | + | 0.273169i | ||||
\(173\) | 5.35687 | + | 9.27837i | 0.407275 | + | 0.705421i | 0.994583 | − | 0.103942i | \(-0.0331457\pi\) |
−0.587308 | + | 0.809363i | \(0.699812\pi\) | |||||||
\(174\) | 1.02248i | 0.0775137i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.79129 | + | 2.79129i | −0.135023 | + | 0.210401i | ||||
\(177\) | −0.208712 | − | 0.361500i | −0.0156878 | − | 0.0271720i | ||||
\(178\) | 4.89898 | − | 8.48528i | 0.367194 | − | 0.635999i | ||||
\(179\) | −5.58258 | + | 9.66930i | −0.417261 | + | 0.722718i | −0.995663 | − | 0.0930344i | \(-0.970343\pi\) |
0.578402 | + | 0.815752i | \(0.303677\pi\) | |||||||
\(180\) | −6.92349 | + | 3.99728i | −0.516046 | + | 0.297939i | ||||
\(181\) | 5.41022i | 0.402138i | 0.979577 | + | 0.201069i | \(0.0644416\pi\) | ||||
−0.979577 | + | 0.201069i | \(0.935558\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.25227i | − | 0.0925707i | ||||||
\(184\) | −3.46410 | + | 2.00000i | −0.255377 | + | 0.147442i | ||||
\(185\) | −9.60433 | − | 5.54506i | −0.706124 | − | 0.407681i | ||||
\(186\) | −4.83465 | − | 2.79129i | −0.354494 | − | 0.204667i | ||||
\(187\) | 12.3960 | + | 0.582415i | 0.906485 | + | 0.0425904i | ||||
\(188\) | 9.93280i | 0.724424i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.58258 | −0.405003 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0.559525 | + | 0.323042i | 0.0403802 | + | 0.0233135i | ||||
\(193\) | 14.1425 | + | 8.16515i | 1.01800 | + | 0.587740i | 0.913523 | − | 0.406787i | \(-0.133351\pi\) |
0.104473 | + | 0.994528i | \(0.466684\pi\) | |||||||
\(194\) | −4.25290 | − | 7.36623i | −0.305340 | − | 0.528865i | ||||
\(195\) | 1.29217 | 0.0925340 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 8.74773i | − | 0.623250i | −0.950205 | − | 0.311625i | \(-0.899127\pi\) | ||
0.950205 | − | 0.311625i | \(-0.100873\pi\) | |||||||
\(198\) | −0.401996 | + | 8.55600i | −0.0285686 | + | 0.608048i | ||||
\(199\) | 8.36850 | + | 4.83156i | 0.593227 | + | 0.342500i | 0.766373 | − | 0.642396i | \(-0.222060\pi\) |
−0.173145 | + | 0.984896i | \(0.555393\pi\) | |||||||
\(200\) | −3.96863 | − | 2.29129i | −0.280624 | − | 0.162019i | ||||
\(201\) | −4.24264 | + | 2.44949i | −0.299253 | + | 0.172774i | ||||
\(202\) | 11.7362i | 0.825757i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 2.41742i | − | 0.169254i | ||||||
\(205\) | 26.6283 | − | 15.3739i | 1.85980 | − | 1.07376i | ||||
\(206\) | 3.02815 | − | 5.24491i | 0.210981 | − | 0.365430i | ||||
\(207\) | −5.16515 | + | 8.94630i | −0.359003 | + | 0.621811i | ||||
\(208\) | 0.323042 | + | 0.559525i | 0.0223989 | + | 0.0387961i | ||||
\(209\) | −3.23042 | + | 5.03383i | −0.223453 | + | 0.348197i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.7477i | − | 1.15296i | −0.817111 | − | 0.576481i | \(-0.804426\pi\) | ||
0.817111 | − | 0.576481i | \(-0.195574\pi\) | |||||||
\(212\) | −5.79129 | − | 10.0308i | −0.397747 | − | 0.688919i | ||||
\(213\) | −1.11905 | − | 0.646084i | −0.0766760 | − | 0.0442689i | ||||
\(214\) | −8.79129 | + | 15.2270i | −0.600960 | + | 1.04089i | ||||
\(215\) | 11.0901 | + | 19.2087i | 0.756340 | + | 1.31002i | ||||
\(216\) | 3.60681 | 0.245412 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.1652 | 1.16257 | ||||||||
\(219\) | −9.02175 | + | 5.20871i | −0.609634 | + | 0.351972i | ||||
\(220\) | −9.12248 | + | 4.71048i | −0.615038 | + | 0.317580i | ||||
\(221\) | 1.20871 | − | 2.09355i | 0.0813068 | − | 0.140827i | ||||
\(222\) | 1.15732 | + | 2.00454i | 0.0776744 | + | 0.134536i | ||||
\(223\) | 16.1240i | 1.07974i | 0.841749 | + | 0.539870i | \(0.181527\pi\) | ||||
−0.841749 | + | 0.539870i | \(0.818473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.8348 | −0.788990 | ||||||||
\(226\) | 9.30780 | − | 5.37386i | 0.619146 | − | 0.357464i | ||||
\(227\) | −0.255619 | + | 0.442745i | −0.0169660 | + | 0.0293860i | −0.874384 | − | 0.485235i | \(-0.838734\pi\) |
0.857418 | + | 0.514621i | \(0.172067\pi\) | |||||||
\(228\) | 1.00905 | + | 0.582576i | 0.0668260 | + | 0.0385820i | ||||
\(229\) | −4.91895 | + | 2.83995i | −0.325053 | + | 0.187669i | −0.653643 | − | 0.756803i | \(-0.726760\pi\) |
0.328590 | + | 0.944473i | \(0.393427\pi\) | |||||||
\(230\) | −12.3823 | −0.816464 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.58258 | −0.103901 | ||||||||
\(233\) | 23.5257 | − | 13.5826i | 1.54122 | − | 0.889824i | 0.542458 | − | 0.840083i | \(-0.317494\pi\) |
0.998762 | − | 0.0497415i | \(-0.0158397\pi\) | |||||||
\(234\) | 1.44502 | + | 0.834280i | 0.0944636 | + | 0.0545386i | ||||
\(235\) | −15.3739 | + | 26.6283i | −1.00288 | + | 1.73704i | ||||
\(236\) | 0.559525 | − | 0.323042i | 0.0364220 | − | 0.0210282i | ||||
\(237\) | −2.58434 | −0.167871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.41742i | 0.544478i | 0.962230 | + | 0.272239i | \(0.0877641\pi\) | ||||
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | −1.73598 | + | 3.00681i | −0.111825 | + | 0.193686i | −0.916506 | − | 0.400021i | \(-0.869003\pi\) |
0.804681 | + | 0.593707i | \(0.202336\pi\) | |||||||
\(242\) | −1.03137 | + | 10.9515i | −0.0662992 | + | 0.703992i | ||||
\(243\) | 12.4020 | − | 7.16027i | 0.795586 | − | 0.459332i | ||||
\(244\) | 1.93825 | 0.124084 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.41742 | −0.409160 | ||||||||
\(247\) | 0.582576 | + | 1.00905i | 0.0370684 | + | 0.0642044i | ||||
\(248\) | 4.32032 | − | 7.48301i | 0.274340 | − | 0.475172i | ||||
\(249\) | 7.21425 | + | 4.16515i | 0.457185 | + | 0.263956i | ||||
\(250\) | 0.646084 | + | 1.11905i | 0.0408619 | + | 0.0707749i | ||||
\(251\) | 24.1185i | 1.52235i | 0.648549 | + | 0.761173i | \(0.275376\pi\) | ||||
−0.648549 | + | 0.761173i | \(0.724624\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.16515 | + | 11.1652i | −0.450469 | + | 0.701947i | ||||
\(254\) | 1.79129 | + | 3.10260i | 0.112395 | + | 0.194675i | ||||
\(255\) | 3.74166 | − | 6.48074i | 0.234312 | − | 0.405840i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −4.24264 | + | 2.44949i | −0.264649 | + | 0.152795i | −0.626453 | − | 0.779459i | \(-0.715494\pi\) |
0.361805 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(258\) | − | 4.62929i | − | 0.288207i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.00000i | 0.124035i | ||||||||
\(261\) | −3.53955 | + | 2.04356i | −0.219093 | + | 0.126493i | ||||
\(262\) | −14.5233 | − | 8.38502i | −0.897251 | − | 0.518028i | ||||
\(263\) | −7.21425 | − | 4.16515i | −0.444850 | − | 0.256834i | 0.260803 | − | 0.965392i | \(-0.416013\pi\) |
−0.705653 | + | 0.708558i | \(0.749346\pi\) | |||||||
\(264\) | 2.14046 | + | 0.100567i | 0.131736 | + | 0.00618949i | ||||
\(265\) | − | 35.8547i | − | 2.20254i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.33030 | −0.387408 | ||||||||
\(268\) | −3.79129 | − | 6.56670i | −0.231590 | − | 0.401125i | ||||
\(269\) | 14.2897 | + | 8.25017i | 0.871259 | + | 0.503022i | 0.867767 | − | 0.496972i | \(-0.165555\pi\) |
0.00349288 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(270\) | 9.66930 | + | 5.58258i | 0.588455 | + | 0.339745i | ||||
\(271\) | −2.44949 | − | 4.24264i | −0.148796 | − | 0.257722i | 0.781987 | − | 0.623295i | \(-0.214206\pi\) |
−0.930783 | + | 0.365573i | \(0.880873\pi\) | |||||||
\(272\) | 3.74166 | 0.226871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.16515i | − | 0.191214i | ||||||
\(275\) | −15.1819 | − | 0.713309i | −0.915505 | − | 0.0430142i | ||||
\(276\) | 2.23810 | + | 1.29217i | 0.134718 | + | 0.0777794i | ||||
\(277\) | 1.73205 | + | 1.00000i | 0.104069 | + | 0.0600842i | 0.551131 | − | 0.834419i | \(-0.314196\pi\) |
−0.447062 | + | 0.894503i | \(0.647530\pi\) | |||||||
\(278\) | 13.4042 | − | 7.73893i | 0.803932 | − | 0.464150i | ||||
\(279\) | − | 22.3151i | − | 1.33597i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.1652i | − | 0.666057i | −0.942917 | − | 0.333029i | \(-0.891929\pi\) | ||
0.942917 | − | 0.333029i | \(-0.108071\pi\) | |||||||
\(282\) | 5.55765 | − | 3.20871i | 0.330953 | − | 0.191076i | ||||
\(283\) | −9.03110 | + | 15.6423i | −0.536843 | + | 0.929840i | 0.462228 | + | 0.886761i | \(0.347050\pi\) |
−0.999072 | + | 0.0430789i | \(0.986283\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 1.80341 | + | 3.12359i | 0.106825 | + | 0.185026i | ||||
\(286\) | 1.80341 | + | 1.15732i | 0.106638 | + | 0.0684339i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.58258i | 0.152180i | ||||||||
\(289\) | 1.50000 | + | 2.59808i | 0.0882353 | + | 0.152828i | ||||
\(290\) | −4.24264 | − | 2.44949i | −0.249136 | − | 0.143839i | ||||
\(291\) | −2.74773 | + | 4.75920i | −0.161075 | + | 0.278989i | ||||
\(292\) | −8.06198 | − | 13.9638i | −0.471791 | − | 0.817167i | ||||
\(293\) | −25.1410 | −1.46875 | −0.734376 | − | 0.678743i | \(-0.762525\pi\) | ||||
−0.734376 | + | 0.678743i | \(0.762525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | −3.10260 | + | 1.79129i | −0.180335 | + | 0.104116i | ||||
\(297\) | 10.6291 | − | 5.48842i | 0.616761 | − | 0.318471i | ||||
\(298\) | 7.00000 | − | 12.1244i | 0.405499 | − | 0.702345i | ||||
\(299\) | 1.29217 | + | 2.23810i | 0.0747280 | + | 0.129433i | ||||
\(300\) | 2.96073i | 0.170938i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.58258 | 0.321241 | ||||||||
\(303\) | 6.56670 | − | 3.79129i | 0.377247 | − | 0.217804i | ||||
\(304\) | −0.901703 | + | 1.56180i | −0.0517162 | + | 0.0895751i | ||||
\(305\) | 5.19615 | + | 3.00000i | 0.297531 | + | 0.171780i | ||||
\(306\) | 8.36850 | − | 4.83156i | 0.478395 | − | 0.276202i | ||||
\(307\) | 10.5789 | 0.603769 | 0.301885 | − | 0.953344i | \(-0.402384\pi\) | ||||
0.301885 | + | 0.953344i | \(0.402384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.91288 | −0.222596 | ||||||||
\(310\) | 23.1642 | − | 13.3739i | 1.31564 | − | 0.759584i | ||||
\(311\) | −4.35942 | − | 2.51691i | −0.247200 | − | 0.142721i | 0.371281 | − | 0.928520i | \(-0.378919\pi\) |
−0.618482 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(312\) | 0.208712 | − | 0.361500i | 0.0118160 | − | 0.0204659i | ||||
\(313\) | −20.3277 | + | 11.7362i | −1.14899 | + | 0.663370i | −0.948641 | − | 0.316355i | \(-0.897541\pi\) |
−0.200349 | + | 0.979725i | \(0.564208\pi\) | |||||||
\(314\) | 13.1632 | 0.742844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | −4.58258 | − | 7.93725i | −0.257383 | − | 0.445801i | 0.708157 | − | 0.706055i | \(-0.249527\pi\) |
−0.965540 | + | 0.260254i | \(0.916194\pi\) | |||||||
\(318\) | −3.74166 | + | 6.48074i | −0.209822 | + | 0.363422i | ||||
\(319\) | −4.66376 | + | 2.40818i | −0.261121 | + | 0.134832i | ||||
\(320\) | −2.68085 | + | 1.54779i | −0.149864 | + | 0.0865239i | ||||
\(321\) | 11.3598 | 0.634043 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.74773 | 0.375454 | ||||||||
\(324\) | 2.70871 | + | 4.69163i | 0.150484 | + | 0.260646i | ||||
\(325\) | −1.48036 | + | 2.56407i | −0.0821158 | + | 0.142229i | ||||
\(326\) | −3.46410 | − | 2.00000i | −0.191859 | − | 0.110770i | ||||
\(327\) | −5.54506 | − | 9.60433i | −0.306643 | − | 0.531121i | ||||
\(328\) | − | 9.93280i | − | 0.548447i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.58258 | + | 3.58258i | 0.307311 | + | 0.197214i | ||||
\(331\) | 11.7913 | + | 20.4231i | 0.648108 | + | 1.12256i | 0.983574 | + | 0.180504i | \(0.0577727\pi\) |
−0.335467 | + | 0.942052i | \(0.608894\pi\) | |||||||
\(332\) | −6.44677 | + | 11.1661i | −0.353812 | + | 0.612821i | ||||
\(333\) | −4.62614 | + | 8.01270i | −0.253511 | + | 0.439093i | ||||
\(334\) | −1.11905 | + | 0.646084i | −0.0612317 | + | 0.0353521i | ||||
\(335\) | − | 23.4724i | − | 1.28244i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.8348i | − | 0.590212i | −0.955465 | − | 0.295106i | \(-0.904645\pi\) | ||
0.955465 | − | 0.295106i | \(-0.0953549\pi\) | |||||||
\(338\) | −10.8968 | + | 6.29129i | −0.592709 | + | 0.342201i | ||||
\(339\) | −6.01362 | − | 3.47197i | −0.326615 | − | 0.188571i | ||||
\(340\) | 10.0308 | + | 5.79129i | 0.543997 | + | 0.314077i | ||||
\(341\) | 1.34497 | − | 28.6262i | 0.0728344 | − | 1.55019i | ||||
\(342\) | 4.65743i | 0.251845i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.16515 | 0.386319 | ||||||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | 9.27837 | + | 5.35687i | 0.498808 | + | 0.287987i | ||||
\(347\) | −16.5975 | − | 9.58258i | −0.891001 | − | 0.514420i | −0.0167312 | − | 0.999860i | \(-0.505326\pi\) |
−0.874270 | + | 0.485440i | \(0.838659\pi\) | |||||||
\(348\) | 0.511238 | + | 0.885491i | 0.0274052 | + | 0.0474673i | ||||
\(349\) | −24.1185 | −1.29103 | −0.645517 | − | 0.763746i | \(-0.723358\pi\) | ||||
−0.645517 | + | 0.763746i | \(0.723358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.33030i | − | 0.124382i | ||||||
\(352\) | −0.155657 | + | 3.31297i | −0.00829654 | + | 0.176582i | ||||
\(353\) | −6.48074 | − | 3.74166i | −0.344935 | − | 0.199148i | 0.317517 | − | 0.948253i | \(-0.397151\pi\) |
−0.662452 | + | 0.749104i | \(0.730484\pi\) | |||||||
\(354\) | −0.361500 | − | 0.208712i | −0.0192135 | − | 0.0110929i | ||||
\(355\) | 5.36169 | − | 3.09557i | 0.284569 | − | 0.164296i | ||||
\(356\) | − | 9.79796i | − | 0.519291i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1652i | 0.590097i | ||||||||
\(359\) | 8.29875 | − | 4.79129i | 0.437991 | − | 0.252875i | −0.264754 | − | 0.964316i | \(-0.585291\pi\) |
0.702745 | + | 0.711442i | \(0.251957\pi\) | |||||||
\(360\) | −3.99728 | + | 6.92349i | −0.210675 | + | 0.364900i | ||||
\(361\) | 7.87386 | − | 13.6379i | 0.414414 | − | 0.717786i | ||||
\(362\) | 2.70511 | + | 4.68539i | 0.142177 | + | 0.246258i | ||||
\(363\) | 6.46084 | − | 2.96073i | 0.339106 | − | 0.155398i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 49.9129i | − | 2.61256i | ||||||
\(366\) | −0.626136 | − | 1.08450i | −0.0327287 | − | 0.0566877i | ||||
\(367\) | −18.2064 | − | 10.5115i | −0.950366 | − | 0.548694i | −0.0571714 | − | 0.998364i | \(-0.518208\pi\) |
−0.893195 | + | 0.449670i | \(0.851541\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | −12.8261 | − | 22.2155i | −0.667701 | − | 1.15649i | ||||
\(370\) | −11.0901 | −0.576548 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.58258 | −0.289443 | ||||||||
\(373\) | −8.29875 | + | 4.79129i | −0.429693 | + | 0.248083i | −0.699216 | − | 0.714911i | \(-0.746467\pi\) |
0.269523 | + | 0.962994i | \(0.413134\pi\) | |||||||
\(374\) | 11.0265 | − | 5.69361i | 0.570165 | − | 0.294410i | ||||
\(375\) | 0.417424 | − | 0.723000i | 0.0215557 | − | 0.0373356i | ||||
\(376\) | 4.96640 | + | 8.60206i | 0.256123 | + | 0.443617i | ||||
\(377\) | 1.02248i | 0.0526602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3303 | −1.14703 | −0.573515 | − | 0.819195i | \(-0.694421\pi\) | ||||
−0.573515 | + | 0.819195i | \(0.694421\pi\) | |||||||
\(380\) | −4.83465 | + | 2.79129i | −0.248012 | + | 0.143190i | ||||
\(381\) | 1.15732 | − | 2.00454i | 0.0592914 | − | 0.102696i | ||||
\(382\) | 15.5885 | + | 9.00000i | 0.797575 | + | 0.460480i | ||||
\(383\) | 17.0873 | − | 9.86538i | 0.873122 | − | 0.504097i | 0.00473782 | − | 0.999989i | \(-0.498492\pi\) |
0.868385 | + | 0.495891i | \(0.165159\pi\) | |||||||
\(384\) | 0.646084 | 0.0329703 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.3303 | 0.831191 | ||||||||
\(387\) | 16.0254 | − | 9.25227i | 0.814617 | − | 0.470319i | ||||
\(388\) | −7.36623 | − | 4.25290i | −0.373964 | − | 0.215908i | ||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 1.11905 | − | 0.646084i | 0.0566653 | − | 0.0327157i | ||||
\(391\) | 14.9666 | 0.756895 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.8348i | 0.546546i | ||||||||
\(394\) | −4.37386 | − | 7.57575i | −0.220352 | − | 0.381661i | ||||
\(395\) | 6.19115 | − | 10.7234i | 0.311510 | − | 0.539552i | ||||
\(396\) | 3.92986 | + | 7.61071i | 0.197483 | + | 0.382452i | ||||
\(397\) | −23.8940 | + | 13.7952i | −1.19921 | + | 0.692363i | −0.960379 | − | 0.278699i | \(-0.910097\pi\) |
−0.238829 | + | 0.971062i | \(0.576764\pi\) | |||||||
\(398\) | 9.66311 | 0.484368 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.58258 | −0.229129 | ||||||||
\(401\) | −3.79129 | − | 6.56670i | −0.189328 | − | 0.327926i | 0.755698 | − | 0.654920i | \(-0.227298\pi\) |
−0.945026 | + | 0.326994i | \(0.893964\pi\) | |||||||
\(402\) | −2.44949 | + | 4.24264i | −0.122169 | + | 0.211604i | ||||
\(403\) | −4.83465 | − | 2.79129i | −0.240831 | − | 0.139044i | ||||
\(404\) | 5.86811 | + | 10.1639i | 0.291949 | + | 0.505671i | ||||
\(405\) | 16.7700i | 0.833310i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.41742 | + | 10.0000i | −0.318100 | + | 0.495682i | ||||
\(408\) | −1.20871 | − | 2.09355i | −0.0598402 | − | 0.103646i | ||||
\(409\) | −2.51691 | + | 4.35942i | −0.124453 | + | 0.215559i | −0.921519 | − | 0.388333i | \(-0.873051\pi\) |
0.797066 | + | 0.603892i | \(0.206384\pi\) | |||||||
\(410\) | 15.3739 | − | 26.6283i | 0.759261 | − | 1.31508i | ||||
\(411\) | −1.77098 | + | 1.02248i | −0.0873561 | + | 0.0504350i | ||||
\(412\) | − | 6.05630i | − | 0.298373i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.3303i | 0.507707i | ||||||||
\(415\) | −34.5656 | + | 19.9564i | −1.69676 | + | 0.979623i | ||||
\(416\) | 0.559525 | + | 0.323042i | 0.0274330 | + | 0.0158384i | ||||
\(417\) | −8.66025 | − | 5.00000i | −0.424094 | − | 0.244851i | ||||
\(418\) | −0.280712 | + | 5.97463i | −0.0137301 | + | 0.292229i | ||||
\(419\) | 13.0284i | 0.636478i | 0.948011 | + | 0.318239i | \(0.103091\pi\) | ||||
−0.948011 | + | 0.318239i | \(0.896909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.58258 | 0.369552 | 0.184776 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184776 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(422\) | −8.37386 | − | 14.5040i | −0.407633 | − | 0.706042i | ||||
\(423\) | 22.2155 | + | 12.8261i | 1.08015 | + | 0.623627i | ||||
\(424\) | −10.0308 | − | 5.79129i | −0.487139 | − | 0.281250i | ||||
\(425\) | 8.57321 | + | 14.8492i | 0.415862 | + | 0.720294i | ||||
\(426\) | −1.29217 | −0.0626057 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17.5826i | 0.849886i | ||||||||
\(429\) | 0.0649750 | − | 1.38291i | 0.00313702 | − | 0.0667677i | ||||
\(430\) | 19.2087 | + | 11.0901i | 0.926324 | + | 0.534813i | ||||
\(431\) | −24.1733 | − | 13.9564i | −1.16439 | − | 0.672258i | −0.212034 | − | 0.977262i | \(-0.568009\pi\) |
−0.952351 | + | 0.305004i | \(0.901342\pi\) | |||||||
\(432\) | 3.12359 | − | 1.80341i | 0.150284 | − | 0.0867664i | ||||
\(433\) | 35.5850i | 1.71011i | 0.518540 | + | 0.855054i | \(0.326476\pi\) | ||||
−0.518540 | + | 0.855054i | \(0.673524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.16515i | 0.151757i | ||||||||
\(436\) | 14.8655 | − | 8.58258i | 0.711926 | − | 0.411031i | ||||
\(437\) | −3.60681 | + | 6.24718i | −0.172537 | + | 0.298843i | ||||
\(438\) | −5.20871 | + | 9.02175i | −0.248882 | + | 0.431076i | ||||
\(439\) | 8.64064 | + | 14.9660i | 0.412395 | + | 0.714289i | 0.995151 | − | 0.0983579i | \(-0.0313590\pi\) |
−0.582756 | + | 0.812647i | \(0.698026\pi\) | |||||||
\(440\) | −5.54506 | + | 8.64064i | −0.264351 | + | 0.411926i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.41742i | − | 0.114985i | ||||||
\(443\) | −7.58258 | − | 13.1334i | −0.360259 | − | 0.623987i | 0.627744 | − | 0.778420i | \(-0.283978\pi\) |
−0.988003 | + | 0.154433i | \(0.950645\pi\) | |||||||
\(444\) | 2.00454 | + | 1.15732i | 0.0951313 | + | 0.0549241i | ||||
\(445\) | 15.1652 | − | 26.2668i | 0.718897 | − | 1.24517i | ||||
\(446\) | 8.06198 | + | 13.9638i | 0.381746 | + | 0.661203i | ||||
\(447\) | −9.04517 | −0.427822 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1652 | 1.47077 | 0.735387 | − | 0.677647i | \(-0.237000\pi\) | ||||
0.735387 | + | 0.677647i | \(0.237000\pi\) | |||||||
\(450\) | −10.2493 | + | 5.91742i | −0.483156 | + | 0.278950i | ||||
\(451\) | −15.1146 | − | 29.2714i | −0.711717 | − | 1.37834i | ||||
\(452\) | 5.37386 | − | 9.30780i | 0.252765 | − | 0.437802i | ||||
\(453\) | −1.80341 | − | 3.12359i | −0.0847314 | − | 0.146759i | ||||
\(454\) | 0.511238i | 0.0239936i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.16515 | 0.0545632 | ||||||||
\(457\) | −28.7219 | + | 16.5826i | −1.34355 | + | 0.775700i | −0.987327 | − | 0.158700i | \(-0.949270\pi\) |
−0.356225 | + | 0.934400i | \(0.615936\pi\) | |||||||
\(458\) | −2.83995 | + | 4.91895i | −0.132702 | + | 0.229847i | ||||
\(459\) | −11.6874 | − | 6.74773i | −0.545521 | − | 0.314957i | ||||
\(460\) | −10.7234 | + | 6.19115i | −0.499980 | + | 0.288664i | ||||
\(461\) | −30.0400 | −1.39910 | −0.699550 | − | 0.714583i | \(-0.746616\pi\) | ||||
−0.699550 | + | 0.714583i | \(0.746616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.16515 | 0.240045 | 0.120022 | − | 0.992771i | \(-0.461703\pi\) | ||||
0.120022 | + | 0.992771i | \(0.461703\pi\) | |||||||
\(464\) | −1.37055 | + | 0.791288i | −0.0636262 | + | 0.0367346i | ||||
\(465\) | −14.9660 | − | 8.64064i | −0.694033 | − | 0.400700i | ||||
\(466\) | 13.5826 | − | 23.5257i | 0.629201 | − | 1.08981i | ||||
\(467\) | −10.1639 | + | 5.86811i | −0.470327 | + | 0.271544i | −0.716377 | − | 0.697714i | \(-0.754201\pi\) |
0.246049 | + | 0.969257i | \(0.420867\pi\) | |||||||
\(468\) | 1.66856 | 0.0771292 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 30.7477i | 1.41829i | ||||||||
\(471\) | −4.25227 | − | 7.36515i | −0.195934 | − | 0.339368i | ||||
\(472\) | 0.323042 | − | 0.559525i | 0.0148692 | − | 0.0257542i | ||||
\(473\) | 21.1153 | − | 10.9031i | 0.970883 | − | 0.501324i | ||||
\(474\) | −2.23810 | + | 1.29217i | −0.102799 | + | 0.0593512i | ||||
\(475\) | −8.26424 | −0.379190 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.9129 | −1.36962 | ||||||||
\(478\) | 4.20871 | + | 7.28970i | 0.192502 | + | 0.333423i | ||||
\(479\) | 15.4779 | − | 26.8085i | 0.707202 | − | 1.22491i | −0.258689 | − | 0.965961i | \(-0.583291\pi\) |
0.965891 | − | 0.258949i | \(-0.0833761\pi\) | |||||||
\(480\) | 1.73205 | + | 1.00000i | 0.0790569 | + | 0.0456435i | ||||
\(481\) | 1.15732 | + | 2.00454i | 0.0527693 | + | 0.0913992i | ||||
\(482\) | 3.47197i | 0.158144i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.58258 | + | 10.0000i | 0.208299 | + | 0.454545i | ||||
\(485\) | −13.1652 | − | 22.8027i | −0.597799 | − | 1.03542i | ||||
\(486\) | 7.16027 | − | 12.4020i | 0.324797 | − | 0.562564i | ||||
\(487\) | −10.7477 | + | 18.6156i | −0.487026 | + | 0.843554i | −0.999889 | − | 0.0149168i | \(-0.995252\pi\) |
0.512863 | + | 0.858471i | \(0.328585\pi\) | |||||||
\(488\) | 1.67858 | − | 0.969126i | 0.0759855 | − | 0.0438703i | ||||
\(489\) | 2.58434i | 0.116868i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 33.4955i | − | 1.51163i | −0.654786 | − | 0.755814i | \(-0.727241\pi\) | ||
0.654786 | − | 0.755814i | \(-0.272759\pi\) | |||||||
\(492\) | −5.55765 | + | 3.20871i | −0.250558 | + | 0.144660i | ||||
\(493\) | 5.12813 | + | 2.96073i | 0.230959 | + | 0.133344i | ||||
\(494\) | 1.00905 | + | 0.582576i | 0.0453993 | + | 0.0262113i | ||||
\(495\) | −1.24441 | + | 26.4857i | −0.0559319 | + | 1.19044i | ||||
\(496\) | − | 8.64064i | − | 0.387976i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.33030 | 0.373290 | ||||||||
\(499\) | 8.95644 | + | 15.5130i | 0.400945 | + | 0.694458i | 0.993840 | − | 0.110822i | \(-0.0353484\pi\) |
−0.592895 | + | 0.805280i | \(0.702015\pi\) | |||||||
\(500\) | 1.11905 | + | 0.646084i | 0.0500454 | + | 0.0288937i | ||||
\(501\) | 0.723000 | + | 0.417424i | 0.0323013 | + | 0.0186491i | ||||
\(502\) | 12.0593 | + | 20.8872i | 0.538231 | + | 0.932243i | ||||
\(503\) | 17.0116 | 0.758509 | 0.379254 | − | 0.925292i | \(-0.376180\pi\) | ||||
0.379254 | + | 0.925292i | \(0.376180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.3303i | 1.61668i | ||||||||
\(506\) | −0.622627 | + | 13.2519i | −0.0276792 | + | 0.589118i | ||||
\(507\) | 7.04027 | + | 4.06470i | 0.312669 | + | 0.180520i | ||||
\(508\) | 3.10260 | + | 1.79129i | 0.137656 | + | 0.0794755i | ||||
\(509\) | 0.676305 | − | 0.390465i | 0.0299767 | − | 0.0173070i | −0.484937 | − | 0.874549i | \(-0.661157\pi\) |
0.514913 | + | 0.857242i | \(0.327824\pi\) | |||||||
\(510\) | − | 7.48331i | − | 0.331367i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.63310 | − | 3.25227i | 0.248708 | − | 0.143591i | ||||
\(514\) | −2.44949 | + | 4.24264i | −0.108042 | + | 0.187135i | ||||
\(515\) | 9.37386 | − | 16.2360i | 0.413062 | − | 0.715444i | ||||
\(516\) | −2.31464 | − | 4.00908i | −0.101897 | − | 0.176490i | ||||
\(517\) | 27.7253 | + | 17.7925i | 1.21936 | + | 0.782514i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 6.92197i | − | 0.303841i | ||||||
\(520\) | 1.00000 | + | 1.73205i | 0.0438529 | + | 0.0759555i | ||||
\(521\) | 24.3368 | + | 14.0509i | 1.06621 | + | 0.615579i | 0.927145 | − | 0.374703i | \(-0.122255\pi\) |
0.139070 | + | 0.990283i | \(0.455589\pi\) | |||||||
\(522\) | −2.04356 | + | 3.53955i | −0.0894442 | + | 0.154922i | ||||
\(523\) | −7.22770 | − | 12.5187i | −0.316045 | − | 0.547406i | 0.663614 | − | 0.748075i | \(-0.269022\pi\) |
−0.979659 | + | 0.200669i | \(0.935688\pi\) | |||||||
\(524\) | −16.7700 | −0.732602 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.33030 | −0.363218 | ||||||||
\(527\) | −27.9989 | + | 16.1652i | −1.21965 | + | 0.704165i | ||||
\(528\) | 1.90397 | − | 0.983134i | 0.0828598 | − | 0.0427854i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −17.9274 | − | 31.0511i | −0.778715 | − | 1.34877i | ||||
\(531\) | − | 1.66856i | − | 0.0724094i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.41742 | −0.277970 | ||||||||
\(534\) | −5.48220 | + | 3.16515i | −0.237238 | + | 0.136969i | ||||
\(535\) | −27.2141 | + | 47.1362i | −1.17657 | + | 2.03787i | ||||
\(536\) | −6.56670 | − | 3.79129i | −0.283638 | − | 0.163759i | ||||
\(537\) | 6.24718 | − | 3.60681i | 0.269586 | − | 0.155645i | ||||
\(538\) | 16.5003 | 0.711380 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.1652 | 0.480472 | ||||||||
\(541\) | 31.8245 | − | 18.3739i | 1.36824 | − | 0.789954i | 0.377537 | − | 0.925994i | \(-0.376771\pi\) |
0.990703 | + | 0.136040i | \(0.0434377\pi\) | |||||||
\(542\) | −4.24264 | − | 2.44949i | −0.182237 | − | 0.105215i | ||||
\(543\) | 1.74773 | − | 3.02715i | 0.0750021 | − | 0.129908i | ||||
\(544\) | 3.24037 | − | 1.87083i | 0.138930 | − | 0.0802111i | ||||
\(545\) | 53.1360 | 2.27610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.7477i | 1.05814i | 0.848579 | + | 0.529068i | \(0.177458\pi\) | ||||
−0.848579 | + | 0.529068i | \(0.822542\pi\) | |||||||
\(548\) | −1.58258 | − | 2.74110i | −0.0676043 | − | 0.117094i | ||||
\(549\) | 2.50284 | − | 4.33505i | 0.106819 | − | 0.185015i | ||||
\(550\) | −13.5046 | + | 6.97322i | −0.575838 | + | 0.297339i | ||||
\(551\) | −2.47166 | + | 1.42701i | −0.105296 | + | 0.0607928i | ||||
\(552\) | 2.58434 | 0.109997 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 3.58258 | + | 6.20520i | 0.152072 | + | 0.263396i | ||||
\(556\) | 7.73893 | − | 13.4042i | 0.328204 | − | 0.568466i | ||||
\(557\) | −31.1015 | − | 17.9564i | −1.31781 | − | 0.760839i | −0.334435 | − | 0.942419i | \(-0.608546\pi\) |
−0.983376 | + | 0.181580i | \(0.941879\pi\) | |||||||
\(558\) | −11.1575 | − | 19.3254i | −0.472337 | − | 0.818111i | ||||
\(559\) | − | 4.62929i | − | 0.195798i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.74773 | − | 4.33030i | −0.284889 | − | 0.182826i | ||||
\(562\) | −5.58258 | − | 9.66930i | −0.235487 | − | 0.407875i | ||||
\(563\) | 11.8570 | − | 20.5369i | 0.499712 | − | 0.865527i | −0.500288 | − | 0.865859i | \(-0.666772\pi\) |
1.00000 | 0.000332178i | \(0.000105736\pi\) | ||||||||
\(564\) | 3.20871 | − | 5.55765i | 0.135111 | − | 0.234019i | ||||
\(565\) | 28.8130 | − | 16.6352i | 1.21217 | − | 0.699848i | ||||
\(566\) | 18.0622i | 0.759211i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | −34.2041 | + | 19.7477i | −1.43391 | + | 0.827868i | −0.997416 | − | 0.0718399i | \(-0.977113\pi\) |
−0.436493 | + | 0.899708i | \(0.643780\pi\) | |||||||
\(570\) | 3.12359 | + | 1.80341i | 0.130833 | + | 0.0755364i | ||||
\(571\) | −4.83465 | − | 2.79129i | −0.202324 | − | 0.116812i | 0.395415 | − | 0.918503i | \(-0.370601\pi\) |
−0.597739 | + | 0.801691i | \(0.703934\pi\) | |||||||
\(572\) | 2.14046 | + | 0.100567i | 0.0894970 | + | 0.00420493i | ||||
\(573\) | − | 11.6295i | − | 0.485830i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.3303 | −0.764426 | ||||||||
\(576\) | 1.29129 | + | 2.23658i | 0.0538037 | + | 0.0931907i | ||||
\(577\) | −25.6894 | − | 14.8318i | −1.06946 | − | 0.617455i | −0.141429 | − | 0.989948i | \(-0.545170\pi\) |
−0.928035 | + | 0.372493i | \(0.878503\pi\) | |||||||
\(578\) | 2.59808 | + | 1.50000i | 0.108066 | + | 0.0623918i | ||||
\(579\) | −5.27537 | − | 9.13721i | −0.219237 | − | 0.379730i | ||||
\(580\) | −4.89898 | −0.203419 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.49545i | 0.227794i | ||||||||
\(583\) | −38.3727 | − | 1.80291i | −1.58924 | − | 0.0746688i | ||||
\(584\) | −13.9638 | − | 8.06198i | −0.577824 | − | 0.333607i | ||||
\(585\) | 4.47315 | + | 2.58258i | 0.184942 | + | 0.106776i | ||||
\(586\) | −21.7727 | + | 12.5705i | −0.899423 | + | 0.519282i | ||||
\(587\) | − | 39.0851i | − | 1.61322i | −0.591087 | − | 0.806608i | \(-0.701301\pi\) | ||
0.591087 | − | 0.806608i | \(-0.298699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15.5826i | − | 0.642069i | ||||||
\(590\) | 1.73205 | − | 1.00000i | 0.0713074 | − | 0.0411693i | ||||
\(591\) | −2.82588 | + | 4.89457i | −0.116241 | + | 0.201336i | ||||
\(592\) | −1.79129 | + | 3.10260i | −0.0736215 | + | 0.127516i | ||||
\(593\) | −7.41589 | − | 12.8447i | −0.304534 | − | 0.527469i | 0.672623 | − | 0.739985i | \(-0.265167\pi\) |
−0.977158 | + | 0.212516i | \(0.931834\pi\) | |||||||
\(594\) | 6.46084 | − | 10.0677i | 0.265091 | − | 0.413081i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.0000i | − | 0.573462i | ||||||
\(597\) | −3.12159 | − | 5.40675i | −0.127758 | − | 0.221284i | ||||
\(598\) | 2.23810 | + | 1.29217i | 0.0915227 | + | 0.0528407i | ||||
\(599\) | 10.5826 | − | 18.3296i | 0.432392 | − | 0.748925i | −0.564686 | − | 0.825306i | \(-0.691003\pi\) |
0.997079 | + | 0.0763801i | \(0.0243362\pi\) | |||||||
\(600\) | 1.48036 | + | 2.56407i | 0.0604356 | + | 0.104678i | ||||
\(601\) | −21.0229 | −0.857543 | −0.428772 | − | 0.903413i | \(-0.641053\pi\) | ||||
−0.428772 | + | 0.903413i | \(0.641053\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.5826 | −0.797464 | ||||||||
\(604\) | 4.83465 | − | 2.79129i | 0.196719 | − | 0.113576i | ||||
\(605\) | −3.19269 | + | 33.9013i | −0.129801 | + | 1.37828i | ||||
\(606\) | 3.79129 | − | 6.56670i | 0.154011 | − | 0.266754i | ||||
\(607\) | 1.02248 | + | 1.77098i | 0.0415010 | + | 0.0718819i | 0.886030 | − | 0.463628i | \(-0.153453\pi\) |
−0.844529 | + | 0.535510i | \(0.820119\pi\) | |||||||
\(608\) | 1.80341i | 0.0731378i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 5.55765 | − | 3.20871i | 0.224839 | − | 0.129811i | ||||
\(612\) | 4.83156 | − | 8.36850i | 0.195304 | − | 0.338277i | ||||
\(613\) | 27.6374 | + | 15.9564i | 1.11626 | + | 0.644475i | 0.940444 | − | 0.339948i | \(-0.110410\pi\) |
0.175818 | + | 0.984423i | \(0.443743\pi\) | |||||||
\(614\) | 9.16159 | − | 5.28944i | 0.369732 | − | 0.213465i | ||||
\(615\) | −19.8656 | −0.801059 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.9129 | −0.801662 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(618\) | −3.38865 | + | 1.95644i | −0.136312 | + | 0.0786995i | ||||
\(619\) | 15.5255 | + | 8.96368i | 0.624024 | + | 0.360281i | 0.778434 | − | 0.627726i | \(-0.216014\pi\) |
−0.154410 | + | 0.988007i | \(0.549348\pi\) | |||||||
\(620\) | 13.3739 | − | 23.1642i | 0.537107 | − | 0.930297i | ||||
\(621\) | 12.4944 | − | 7.21362i | 0.501382 | − | 0.289473i | ||||
\(622\) | −5.03383 | −0.201838 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.417424i | − | 0.0167103i | ||||||
\(625\) | 13.4564 | + | 23.3072i | 0.538258 | + | 0.932289i | ||||
\(626\) | −11.7362 | + | 20.3277i | −0.469073 | + | 0.812459i | ||||
\(627\) | 3.43364 | − | 1.77299i | 0.137126 | − | 0.0708064i | ||||
\(628\) | 11.3997 | − | 6.58161i | 0.454897 | − | 0.262635i | ||||
\(629\) | 13.4048 | 0.534483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1652 | 0.524096 | 0.262048 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262048 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(632\) | −2.00000 | − | 3.46410i | −0.0795557 | − | 0.137795i | ||||
\(633\) | −5.41022 | + | 9.37077i | −0.215037 | + | 0.372455i | ||||
\(634\) | −7.93725 | − | 4.58258i | −0.315229 | − | 0.181997i | ||||
\(635\) | 5.54506 | + | 9.60433i | 0.220049 | + | 0.381136i | ||||
\(636\) | 7.48331i | 0.296733i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.83485 | + | 4.41742i | −0.112233 | + | 0.174888i | ||||
\(639\) | −2.58258 | − | 4.47315i | −0.102165 | − | 0.176955i | ||||
\(640\) | −1.54779 | + | 2.68085i | −0.0611816 | + | 0.105970i | ||||
\(641\) | 7.95644 | − | 13.7810i | 0.314260 | − | 0.544315i | −0.665020 | − | 0.746826i | \(-0.731577\pi\) |
0.979280 | + | 0.202511i | \(0.0649101\pi\) | |||||||
\(642\) | 9.83789 | − | 5.67991i | 0.388271 | − | 0.224168i | ||||
\(643\) | − | 9.42157i | − | 0.371550i | −0.982592 | − | 0.185775i | \(-0.940520\pi\) | ||
0.982592 | − | 0.185775i | \(-0.0594796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 14.3303i | − | 0.564255i | ||||||
\(646\) | 5.84370 | − | 3.37386i | 0.229917 | − | 0.132743i | ||||
\(647\) | 26.0397 | + | 15.0341i | 1.02373 | + | 0.591050i | 0.915182 | − | 0.403042i | \(-0.132047\pi\) |
0.108546 | + | 0.994091i | \(0.465380\pi\) | |||||||
\(648\) | 4.69163 | + | 2.70871i | 0.184305 | + | 0.106408i | ||||
\(649\) | 0.100567 | − | 2.14046i | 0.00394761 | − | 0.0840203i | ||||
\(650\) | 2.96073i | 0.116129i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | −9.60433 | − | 5.54506i | −0.375559 | − | 0.216829i | ||||
\(655\) | −44.9579 | − | 25.9564i | −1.75665 | − | 1.01420i | ||||
\(656\) | −4.96640 | − | 8.60206i | −0.193905 | − | 0.335854i | ||||
\(657\) | −41.6413 | −1.62458 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.33030i | 0.246594i | 0.992370 | + | 0.123297i | \(0.0393467\pi\) | ||||
−0.992370 | + | 0.123297i | \(0.960653\pi\) | |||||||
\(660\) | 6.62594 | + | 0.311314i | 0.257914 | + | 0.0121179i | ||||
\(661\) | −7.15705 | − | 4.13212i | −0.278377 | − | 0.160721i | 0.354312 | − | 0.935127i | \(-0.384715\pi\) |
−0.632688 | + | 0.774407i | \(0.718049\pi\) | |||||||
\(662\) | 20.4231 | + | 11.7913i | 0.793767 | + | 0.458281i | ||||
\(663\) | −1.35261 | + | 0.780929i | −0.0525310 | + | 0.0303288i | ||||
\(664\) | 12.8935i | 0.500366i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.25227i | 0.358518i | ||||||||
\(667\) | −5.48220 | + | 3.16515i | −0.212272 | + | 0.122555i | ||||
\(668\) | −0.646084 | + | 1.11905i | −0.0249977 | + | 0.0432973i | ||||
\(669\) | 5.20871 | − | 9.02175i | 0.201380 | − | 0.348801i | ||||
\(670\) | −11.7362 | − | 20.3277i | −0.453409 | − | 0.785328i | ||||
\(671\) | 3.47197 | − | 5.41022i | 0.134034 | − | 0.208859i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3303i | 0.706581i | 0.935514 | + | 0.353291i | \(0.114937\pi\) | ||||
−0.935514 | + | 0.353291i | \(0.885063\pi\) | |||||||
\(674\) | −5.41742 | − | 9.38325i | −0.208671 | − | 0.361429i | ||||
\(675\) | 14.3141 | + | 8.26424i | 0.550950 | + | 0.318091i | ||||
\(676\) | −6.29129 | + | 10.8968i | −0.241973 | + | 0.419109i | ||||
\(677\) | 2.63769 | + | 4.56861i | 0.101375 | + | 0.175586i | 0.912251 | − | 0.409631i | \(-0.134343\pi\) |
−0.810877 | + | 0.585217i | \(0.801009\pi\) | |||||||
\(678\) | −6.94393 | −0.266680 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11.5826 | 0.444172 | ||||||||
\(681\) | 0.286051 | − | 0.165151i | 0.0109615 | − | 0.00632862i | ||||
\(682\) | −13.1483 | − | 25.4635i | −0.503475 | − | 0.975047i | ||||
\(683\) | 4.74773 | − | 8.22330i | 0.181667 | − | 0.314656i | −0.760782 | − | 0.649008i | \(-0.775184\pi\) |
0.942448 | + | 0.334352i | \(0.108517\pi\) | |||||||
\(684\) | 2.32872 | + | 4.03345i | 0.0890407 | + | 0.154223i | ||||
\(685\) | − | 9.79796i | − | 0.374361i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.66970 | 0.140008 | ||||||||
\(688\) | 6.20520 | − | 3.58258i | 0.236571 | − | 0.136584i | ||||
\(689\) | −3.74166 | + | 6.48074i | −0.142546 | + | 0.246897i | ||||
\(690\) | 6.92820 | + | 4.00000i | 0.263752 | + | 0.152277i | ||||
\(691\) | −3.44956 | + | 1.99160i | −0.131227 | + | 0.0757641i | −0.564177 | − | 0.825654i | \(-0.690806\pi\) |
0.432949 | + | 0.901418i | \(0.357473\pi\) | |||||||
\(692\) | 10.7137 | 0.407275 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1652 | −0.727499 | ||||||||
\(695\) | 41.4938 | − | 23.9564i | 1.57395 | − | 0.908720i | ||||
\(696\) | 0.885491 | + | 0.511238i | 0.0335644 | + | 0.0193784i | ||||
\(697\) | −18.5826 | + | 32.1860i | −0.703865 | + | 1.21913i | ||||
\(698\) | −20.8872 | + | 12.0593i | −0.790594 | + | 0.456449i | ||||
\(699\) | −17.5510 | −0.663838 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.3303i | − | 0.465709i | −0.972512 | − | 0.232855i | \(-0.925193\pi\) | ||
0.972512 | − | 0.232855i | \(-0.0748066\pi\) | |||||||
\(702\) | −1.16515 | − | 2.01810i | −0.0439758 | − | 0.0761683i | ||||
\(703\) | −3.23042 | + | 5.59525i | −0.121838 | + | 0.211029i | ||||
\(704\) | 1.52168 | + | 2.94694i | 0.0573506 | + | 0.111067i | ||||
\(705\) | 17.2041 | − | 9.93280i | 0.647945 | − | 0.374091i | ||||
\(706\) | −7.48331 | −0.281638 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.417424 | −0.0156878 | ||||||||
\(709\) | −26.1652 | − | 45.3194i | −0.982653 | − | 1.70200i | −0.651935 | − | 0.758275i | \(-0.726042\pi\) |
−0.330718 | − | 0.943730i | \(-0.607291\pi\) | |||||||
\(710\) | 3.09557 | − | 5.36169i | 0.116175 | − | 0.201221i | ||||
\(711\) | −8.94630 | − | 5.16515i | −0.335513 | − | 0.193708i | ||||
\(712\) | −4.89898 | − | 8.48528i | −0.183597 | − | 0.317999i | ||||
\(713\) | − | 34.5625i | − | 1.29438i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.58258 | + | 3.58258i | 0.208776 | + | 0.133981i | ||||
\(716\) | 5.58258 | + | 9.66930i | 0.208631 | + | 0.361359i | ||||
\(717\) | 2.71918 | − | 4.70976i | 0.101550 | − | 0.175889i | ||||
\(718\) | 4.79129 | − | 8.29875i | 0.178809 | − | 0.309707i | ||||
\(719\) | −20.2109 | + | 11.6688i | −0.753741 | + | 0.435172i | −0.827044 | − | 0.562137i | \(-0.809979\pi\) |
0.0733033 | + | 0.997310i | \(0.476646\pi\) | |||||||
\(720\) | 7.99455i | 0.297939i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 15.7477i | − | 0.586070i | ||||||
\(723\) | 1.94265 | − | 1.12159i | 0.0722480 | − | 0.0417124i | ||||
\(724\) | 4.68539 | + | 2.70511i | 0.174131 | + | 0.100535i | ||||
\(725\) | −6.28065 | − | 3.62614i | −0.233258 | − | 0.134671i | ||||
\(726\) | 4.11489 | − | 5.79448i | 0.152718 | − | 0.215054i | ||||
\(727\) | 37.5514i | 1.39271i | 0.717700 | + | 0.696353i | \(0.245195\pi\) | ||||
−0.717700 | + | 0.696353i | \(0.754805\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | −24.9564 | − | 43.2258i | −0.923679 | − | 1.59986i | ||||
\(731\) | −23.2177 | − | 13.4048i | −0.858739 | − | 0.495793i | ||||
\(732\) | −1.08450 | − | 0.626136i | −0.0400843 | − | 0.0231427i | ||||
\(733\) | 5.35687 | + | 9.27837i | 0.197860 | + | 0.342704i | 0.947834 | − | 0.318763i | \(-0.103267\pi\) |
−0.749974 | + | 0.661467i | \(0.769934\pi\) | |||||||
\(734\) | −21.0229 | −0.775971 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | −25.1208 | − | 1.18028i | −0.925338 | − | 0.0434762i | ||||
\(738\) | −22.2155 | − | 12.8261i | −0.817763 | − | 0.472136i | ||||
\(739\) | 1.37055 | + | 0.791288i | 0.0504165 | + | 0.0291080i | 0.524996 | − | 0.851104i | \(-0.324067\pi\) |
−0.474580 | + | 0.880212i | \(0.657400\pi\) | |||||||
\(740\) | −9.60433 | + | 5.54506i | −0.353062 | + | 0.203841i | ||||
\(741\) | − | 0.752785i | − | 0.0276543i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.91288i | − | 0.0701767i | −0.999384 | − | 0.0350884i | \(-0.988829\pi\) | ||
0.999384 | − | 0.0350884i | \(-0.0111713\pi\) | |||||||
\(744\) | −4.83465 | + | 2.79129i | −0.177247 | + | 0.102334i | ||||
\(745\) | 21.6690 | − | 37.5318i | 0.793891 | − | 1.37506i | ||||
\(746\) | −4.79129 | + | 8.29875i | −0.175422 | + | 0.303839i | ||||
\(747\) | 16.6493 | + | 28.8374i | 0.609165 | + | 1.05510i | ||||
\(748\) | 6.70239 | − | 10.4440i | 0.245063 | − | 0.381872i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 0.834849i | − | 0.0304844i | ||||||
\(751\) | 20.7477 | + | 35.9361i | 0.757095 | + | 1.31133i | 0.944326 | + | 0.329012i | \(0.106716\pi\) |
−0.187231 | + | 0.982316i | \(0.559951\pi\) | |||||||
\(752\) | 8.60206 | + | 4.96640i | 0.313685 | + | 0.181106i | ||||
\(753\) | 7.79129 | − | 13.4949i | 0.283930 | − | 0.491782i | ||||
\(754\) | 0.511238 | + | 0.885491i | 0.0186182 | + | 0.0322477i | ||||
\(755\) | 17.2813 | 0.628930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.8348 | −1.12071 | −0.560356 | − | 0.828252i | \(-0.689336\pi\) | ||||
−0.560356 | + | 0.828252i | \(0.689336\pi\) | |||||||
\(758\) | −19.3386 | + | 11.1652i | −0.702410 | + | 0.405537i | ||||
\(759\) | 7.61589 | − | 3.93254i | 0.276439 | − | 0.142742i | ||||
\(760\) | −2.79129 | + | 4.83465i | −0.101251 | + | 0.175371i | ||||
\(761\) | 14.1183 | + | 24.4536i | 0.511787 | + | 0.886441i | 0.999907 | + | 0.0136645i | \(0.00434969\pi\) |
−0.488119 | + | 0.872777i | \(0.662317\pi\) | |||||||
\(762\) | − | 2.31464i | − | 0.0838507i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 25.9053 | − | 14.9564i | 0.936609 | − | 0.540751i | ||||
\(766\) | 9.86538 | − | 17.0873i | 0.356451 | − | 0.617391i | ||||
\(767\) | −0.361500 | − | 0.208712i | −0.0130530 | − | 0.00753616i | ||||
\(768\) | 0.559525 | − | 0.323042i | 0.0201901 | − | 0.0116568i | ||||
\(769\) | 15.1015 | 0.544573 | 0.272287 | − | 0.962216i | \(-0.412220\pi\) | ||||
0.272287 | + | 0.962216i | \(0.412220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.16515 | 0.113990 | ||||||||
\(772\) | 14.1425 | − | 8.16515i | 0.508998 | − | 0.293870i | ||||
\(773\) | −8.69447 | − | 5.01975i | −0.312718 | − | 0.180548i | 0.335424 | − | 0.942067i | \(-0.391120\pi\) |
−0.648142 | + | 0.761519i | \(0.724454\pi\) | |||||||
\(774\) | 9.25227 | − | 16.0254i | 0.332566 | − | 0.576021i | ||||
\(775\) | 34.2915 | − | 19.7982i | 1.23179 | − | 0.711172i | ||||
\(776\) | −8.50579 | −0.305340 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0000i | 0.358517i | ||||||||
\(779\) | −8.95644 | − | 15.5130i | −0.320898 | − | 0.555811i | ||||
\(780\) | 0.646084 | − | 1.11905i | 0.0231335 | − | 0.0400684i | ||||
\(781\) | −3.04336 | − | 5.89389i | −0.108900 | − | 0.210900i | ||||
\(782\) | 12.9615 | − | 7.48331i | 0.463502 | − | 0.267603i | ||||
\(783\) | 5.70805 | 0.203989 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.7477 | 1.45435 | ||||||||
\(786\) | 5.41742 | + | 9.38325i | 0.193233 | + | 0.334690i | ||||
\(787\) | 11.6154 | − | 20.1185i | 0.414046 | − | 0.717148i | −0.581282 | − | 0.813702i | \(-0.697449\pi\) |
0.995328 | + | 0.0965541i | \(0.0307821\pi\) | |||||||
\(788\) | −7.57575 | − | 4.37386i | −0.269875 | − | 0.155812i | ||||
\(789\) | 2.69104 | + | 4.66101i | 0.0958035 | + | 0.165936i | ||||
\(790\) | − | 12.3823i | − | 0.440542i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.20871 | + | 4.62614i | 0.256150 | + | 0.164383i | ||||
\(793\) | −0.626136 | − | 1.08450i | −0.0222348 | − | 0.0385117i | ||||
\(794\) | −13.7952 | + | 23.8940i | −0.489575 | + | 0.847968i | ||||
\(795\) | −11.5826 | + | 20.0616i | −0.410792 | + | 0.711512i | ||||
\(796\) | 8.36850 | − | 4.83156i | 0.296614 | − | 0.171250i | ||||
\(797\) | 25.0061i | 0.885763i | 0.896580 | + | 0.442881i | \(0.146044\pi\) | ||||
−0.896580 | + | 0.442881i | \(0.853956\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 37.1652i | − | 1.31481i | ||||||
\(800\) | −3.96863 | + | 2.29129i | −0.140312 | + | 0.0810093i | ||||
\(801\) | −21.9139 | − | 12.6520i | −0.774289 | − | 0.447036i | ||||
\(802\) | −6.56670 | − | 3.79129i | −0.231878 | − | 0.133875i | ||||
\(803\) | −53.4182 | − | 2.50980i | −1.88509 | − | 0.0885690i | ||||
\(804\) | 4.89898i | 0.172774i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.58258 | −0.196638 | ||||||||
\(807\) | −5.33030 | − | 9.23236i | −0.187636 | − | 0.324994i | ||||
\(808\) | 10.1639 | + | 5.86811i | 0.357563 | + | 0.206439i | ||||
\(809\) | 12.8474 | + | 7.41742i | 0.451689 | + | 0.260783i | 0.708543 | − | 0.705667i | \(-0.249353\pi\) |
−0.256854 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(810\) | 8.38502 | + | 14.5233i | 0.294619 | + | 0.510296i | ||||
\(811\) | −3.36526 | −0.118170 | −0.0590852 | − | 0.998253i | \(-0.518818\pi\) | ||||
−0.0590852 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.16515i | 0.111007i | ||||||||
\(814\) | −0.557652 | + | 11.8690i | −0.0195457 | + | 0.416007i | ||||
\(815\) | −10.7234 | − | 6.19115i | −0.375624 | − | 0.216866i | ||||
\(816\) | −2.09355 | − | 1.20871i | −0.0732889 | − | 0.0423134i | ||||
\(817\) | 11.1905 | − | 6.46084i | 0.391506 | − | 0.226036i | ||||
\(818\) | 5.03383i | 0.176004i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 30.7477i | − | 1.07376i | ||||||
\(821\) | 37.6682 | − | 21.7477i | 1.31463 | − | 0.759001i | 0.331769 | − | 0.943361i | \(-0.392354\pi\) |
0.982859 | + | 0.184360i | \(0.0590211\pi\) | |||||||
\(822\) | −1.02248 | + | 1.77098i | −0.0356630 | + | 0.0617701i | ||||
\(823\) | 1.83485 | − | 3.17805i | 0.0639588 | − | 0.110780i | −0.832273 | − | 0.554366i | \(-0.812961\pi\) |
0.896232 | + | 0.443586i | \(0.146294\pi\) | |||||||
\(824\) | −3.02815 | − | 5.24491i | −0.105491 | − | 0.182715i | ||||
\(825\) | 8.26424 | + | 5.30352i | 0.287724 | + | 0.184645i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 3.16515i | − | 0.110063i | −0.998485 | − | 0.0550315i | \(-0.982474\pi\) | ||
0.998485 | − | 0.0550315i | \(-0.0175259\pi\) | |||||||
\(828\) | 5.16515 | + | 8.94630i | 0.179501 | + | 0.310906i | ||||
\(829\) | −6.92349 | − | 3.99728i | −0.240463 | − | 0.138831i | 0.374927 | − | 0.927054i | \(-0.377668\pi\) |
−0.615389 | + | 0.788223i | \(0.711001\pi\) | |||||||
\(830\) | −19.9564 | + | 34.5656i | −0.692698 | + | 1.19979i | ||||
\(831\) | −0.646084 | − | 1.11905i | −0.0224124 | − | 0.0388194i | ||||
\(832\) | 0.646084 | 0.0223989 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.0000 | −0.346272 | ||||||||
\(835\) | −3.46410 | + | 2.00000i | −0.119880 | + | 0.0692129i | ||||
\(836\) | 2.74421 | + | 5.31454i | 0.0949105 | + | 0.183807i | ||||
\(837\) | −15.5826 | + | 26.9898i | −0.538613 | + | 0.932904i | ||||
\(838\) | 6.51419 | + | 11.2829i | 0.225029 | + | 0.389762i | ||||
\(839\) | − | 9.66311i | − | 0.333608i | −0.985990 | − | 0.166804i | \(-0.946655\pi\) | ||
0.985990 | − | 0.166804i | \(-0.0533447\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4955 | 0.913636 | ||||||||
\(842\) | 6.56670 | − | 3.79129i | 0.226304 | − | 0.130656i | ||||
\(843\) | −3.60681 | + | 6.24718i | −0.124225 | + | 0.215164i | ||||
\(844\) | −14.5040 | − | 8.37386i | −0.499247 | − | 0.288240i | ||||
\(845\) | −33.7319 | + | 19.4751i | −1.16041 | + | 0.669965i | ||||
\(846\) | 25.6522 | 0.881941 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.5826 | −0.397747 | ||||||||
\(849\) | 10.1063 | − | 5.83485i | 0.346846 | − | 0.200251i | ||||
\(850\) | 14.8492 | + | 8.57321i | 0.509325 | + | 0.294059i | ||||
\(851\) | −7.16515 | + | 12.4104i | −0.245618 | + | 0.425423i | ||||
\(852\) | −1.11905 | + | 0.646084i | −0.0383380 | + | 0.0221345i | ||||
\(853\) | −11.4665 | −0.392606 | −0.196303 | − | 0.980543i | \(-0.562894\pi\) | ||||
−0.196303 | + | 0.980543i | \(0.562894\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.4174i | 0.493066i | ||||||||
\(856\) | 8.79129 | + | 15.2270i | 0.300480 | + | 0.520447i | ||||
\(857\) | −15.5453 | + | 26.9252i | −0.531017 | + | 0.919748i | 0.468328 | + | 0.883555i | \(0.344857\pi\) |
−0.999345 | + | 0.0361936i | \(0.988477\pi\) | |||||||
\(858\) | −0.635187 | − | 1.23013i | −0.0216849 | − | 0.0419958i | ||||
\(859\) | −21.1208 | + | 12.1941i | −0.720632 | + | 0.416057i | −0.814985 | − | 0.579482i | \(-0.803255\pi\) |
0.0943531 | + | 0.995539i | \(0.469922\pi\) | |||||||
\(860\) | 22.1803 | 0.756340 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.9129 | −0.950716 | ||||||||
\(863\) | 7.41742 | + | 12.8474i | 0.252492 | + | 0.437329i | 0.964211 | − | 0.265135i | \(-0.0854165\pi\) |
−0.711719 | + | 0.702464i | \(0.752083\pi\) | |||||||
\(864\) | 1.80341 | − | 3.12359i | 0.0613531 | − | 0.106267i | ||||
\(865\) | 28.7219 | + | 16.5826i | 0.976573 | + | 0.563824i | ||||
\(866\) | 17.7925 | + | 30.8175i | 0.604614 | + | 1.04722i | ||||
\(867\) | − | 1.93825i | − | 0.0658265i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.1652 | − | 7.16515i | −0.378752 | − | 0.243061i | ||||
\(870\) | 1.58258 | + | 2.74110i | 0.0536543 | + | 0.0929320i | ||||
\(871\) | −2.44949 | + | 4.24264i | −0.0829978 | + | 0.143756i | ||||
\(872\) | 8.58258 | − | 14.8655i | 0.290643 | − | 0.503408i | ||||
\(873\) | −19.0239 | + | 10.9834i | −0.643860 | + | 0.371733i | ||||
\(874\) | 7.21362i | 0.244004i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.4174i | 0.351972i | ||||||||
\(877\) | 5.91915 | − | 3.41742i | 0.199876 | − | 0.115398i | −0.396722 | − | 0.917939i | \(-0.629852\pi\) |
0.596597 | + | 0.802541i | \(0.296519\pi\) | |||||||
\(878\) | 14.9660 | + | 8.64064i | 0.505079 | + | 0.291607i | ||||
\(879\) | 14.0670 | + | 8.12159i | 0.474468 | + | 0.273934i | ||||
\(880\) | −0.481847 | + | 10.2555i | −0.0162431 | + | 0.345714i | ||||
\(881\) | 7.21362i | 0.243033i | 0.992589 | + | 0.121517i | \(0.0387758\pi\) | ||||
−0.992589 | + | 0.121517i | \(0.961224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8348 | 0.431927 | 0.215964 | − | 0.976401i | \(-0.430711\pi\) | ||||
0.215964 | + | 0.976401i | \(0.430711\pi\) | |||||||
\(884\) | −1.20871 | − | 2.09355i | −0.0406534 | − | 0.0704137i | ||||
\(885\) | −1.11905 | − | 0.646084i | −0.0376165 | − | 0.0217179i | ||||
\(886\) | −13.1334 | − | 7.58258i | −0.441225 | − | 0.254742i | ||||
\(887\) | −26.7028 | − | 46.2507i | −0.896594 | − | 1.55295i | −0.831820 | − | 0.555046i | \(-0.812701\pi\) |
−0.0647738 | − | 0.997900i | \(-0.520633\pi\) | |||||||
\(888\) | 2.31464 | 0.0776744 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 30.3303i | − | 1.01667i | ||||||
\(891\) | 17.9478 | + | 0.843259i | 0.601273 | + | 0.0282502i | ||||
\(892\) | 13.9638 | + | 8.06198i | 0.467541 | + | 0.269935i | ||||
\(893\) | 15.5130 | + | 8.95644i | 0.519123 | + | 0.299716i | ||||
\(894\) | −7.83335 | + | 4.52259i | −0.261986 | + | 0.151258i | ||||
\(895\) | 34.5625i | 1.15530i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 1.66970i | − | 0.0557496i | ||||||
\(898\) | 26.9898 | − | 15.5826i | 0.900662 | − | 0.519997i | ||||
\(899\) | 6.83723 | − | 11.8424i | 0.228034 | − | 0.394967i | ||||
\(900\) | −5.91742 | + | 10.2493i | −0.197247 | + | 0.341643i | ||||
\(901\) | 21.6690 | + | 37.5318i | 0.721900 | + | 1.25037i | ||||
\(902\) | −27.7253 | − | 17.7925i | −0.923152 | − | 0.592426i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 10.7477i | − | 0.357464i | ||||||
\(905\) | 8.37386 | + | 14.5040i | 0.278357 | + | 0.482128i | ||||
\(906\) | −3.12359 | − | 1.80341i | −0.103774 | − | 0.0599141i | ||||
\(907\) | −2.95644 | + | 5.12070i | −0.0981670 | + | 0.170030i | −0.910926 | − | 0.412570i | \(-0.864631\pi\) |
0.812759 | + | 0.582600i | \(0.197965\pi\) | |||||||
\(908\) | 0.255619 | + | 0.442745i | 0.00848302 | + | 0.0146930i | ||||
\(909\) | 30.3097 | 1.00531 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.16515 | 0.104866 | 0.0524331 | − | 0.998624i | \(-0.483302\pi\) | ||||
0.0524331 | + | 0.998624i | \(0.483302\pi\) | |||||||
\(912\) | 1.00905 | − | 0.582576i | 0.0334130 | − | 0.0192910i | ||||
\(913\) | 19.6199 | + | 37.9965i | 0.649323 | + | 1.25750i | ||||
\(914\) | −16.5826 | + | 28.7219i | −0.548503 | + | 0.950035i | ||||
\(915\) | −1.93825 | − | 3.35715i | −0.0640766 | − | 0.110984i | ||||
\(916\) | 5.67991i | 0.187669i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.4955 | −0.445416 | ||||||||
\(919\) | −16.8836 | + | 9.74773i | −0.556937 | + | 0.321548i | −0.751915 | − | 0.659260i | \(-0.770870\pi\) |
0.194978 | + | 0.980808i | \(0.437536\pi\) | |||||||
\(920\) | −6.19115 | + | 10.7234i | −0.204116 | + | 0.353539i | ||||
\(921\) | −5.91915 | − | 3.41742i | −0.195043 | − | 0.112608i | ||||
\(922\) | −26.0154 | + | 15.0200i | −0.856771 | + | 0.494657i | ||||
\(923\) | −1.29217 | −0.0425322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4174 | −0.539802 | ||||||||
\(926\) | 4.47315 | − | 2.58258i | 0.146997 | − | 0.0848687i | ||||
\(927\) | −13.5454 | − | 7.82043i | −0.444889 | − | 0.256857i | ||||
\(928\) | −0.791288 | + | 1.37055i | −0.0259753 | + | 0.0449905i | ||||
\(929\) | 37.7654 | − | 21.8039i | 1.23904 | − | 0.715361i | 0.270144 | − | 0.962820i | \(-0.412929\pi\) |
0.968898 | + | 0.247459i | \(0.0795954\pi\) | |||||||
\(930\) | −17.2813 | −0.566675 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 27.1652i | − | 0.889824i | ||||||
\(933\) | 1.62614 | + | 2.81655i | 0.0532373 | + | 0.0922097i | ||||
\(934\) | −5.86811 | + | 10.1639i | −0.192010 | + | 0.332572i | ||||
\(935\) | 34.1332 | − | 17.6250i | 1.11628 | − | 0.576399i | ||||
\(936\) | 1.44502 | − | 0.834280i | 0.0472318 | − | 0.0272693i | ||||
\(937\) | −30.0681 | −0.982282 | −0.491141 | − | 0.871080i | \(-0.663420\pi\) | ||||
−0.491141 | + | 0.871080i | \(0.663420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.1652 | 0.494896 | ||||||||
\(940\) | 15.3739 | + | 26.6283i | 0.501440 | + | 0.868520i | ||||
\(941\) | −2.63769 | + | 4.56861i | −0.0859861 | + | 0.148932i | −0.905811 | − | 0.423682i | \(-0.860737\pi\) |
0.819825 | + | 0.572614i | \(0.194071\pi\) | |||||||
\(942\) | −7.36515 | − | 4.25227i | −0.239970 | − | 0.138547i | ||||
\(943\) | −19.8656 | − | 34.4082i | −0.646913 | − | 1.12049i | ||||
\(944\) | − | 0.646084i | − | 0.0210282i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.8348 | − | 20.0000i | 0.417297 | − | 0.650256i | ||||
\(947\) | −1.79129 | − | 3.10260i | −0.0582090 | − | 0.100821i | 0.835452 | − | 0.549563i | \(-0.185206\pi\) |
−0.893662 | + | 0.448742i | \(0.851872\pi\) | |||||||
\(948\) | −1.29217 | + | 2.23810i | −0.0419677 | + | 0.0726901i | ||||
\(949\) | −5.20871 | + | 9.02175i | −0.169082 | + | 0.292859i | ||||
\(950\) | −7.15705 | + | 4.13212i | −0.232205 | + | 0.134064i | ||||
\(951\) | 5.92146i | 0.192016i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.3303i | 0.593777i | 0.954912 | + | 0.296888i | \(0.0959489\pi\) | ||||
−0.954912 | + | 0.296888i | \(0.904051\pi\) | |||||||
\(954\) | −25.9053 | + | 14.9564i | −0.838715 | + | 0.484233i | ||||
\(955\) | 48.2552 | + | 27.8602i | 1.56150 | + | 0.901534i | ||||
\(956\) | 7.28970 | + | 4.20871i | 0.235766 | + | 0.136119i | ||||
\(957\) | 3.38743 | + | 0.159155i | 0.109500 | + | 0.00514477i | ||||
\(958\) | − | 30.9557i | − | 1.00013i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | 21.8303 | + | 37.8112i | 0.704203 | + | 1.21972i | ||||
\(962\) | 2.00454 | + | 1.15732i | 0.0646290 | + | 0.0373136i | ||||
\(963\) | 39.3248 | + | 22.7042i | 1.26722 | + | 0.731632i | ||||
\(964\) | 1.73598 | + | 3.00681i | 0.0559123 | + | 0.0968429i | ||||
\(965\) | 50.5517 | 1.62732 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.4174i | 0.720896i | 0.932779 | + | 0.360448i | \(0.117376\pi\) | ||||
−0.932779 | + | 0.360448i | \(0.882624\pi\) | |||||||
\(968\) | 8.96863 | + | 6.36897i | 0.288263 | + | 0.204706i | ||||
\(969\) | −3.77552 | − | 2.17980i | −0.121287 | − | 0.0700252i | ||||
\(970\) | −22.8027 | − | 13.1652i | −0.732151 | − | 0.422708i | ||||
\(971\) | 12.1684 | − | 7.02543i | 0.390502 | − | 0.225457i | −0.291875 | − | 0.956456i | \(-0.594279\pi\) |
0.682378 | + | 0.731000i | \(0.260946\pi\) | |||||||
\(972\) | − | 14.3205i | − | 0.459332i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.4955i | 0.688759i | ||||||||
\(975\) | 1.65660 | − | 0.956439i | 0.0530537 | − | 0.0306306i | ||||
\(976\) | 0.969126 | − | 1.67858i | 0.0310210 | − | 0.0537299i | ||||
\(977\) | −4.58258 | + | 7.93725i | −0.146610 | + | 0.253935i | −0.929972 | − | 0.367630i | \(-0.880169\pi\) |
0.783363 | + | 0.621565i | \(0.213503\pi\) | |||||||
\(978\) | 1.29217 | + | 2.23810i | 0.0413190 | + | 0.0715665i | ||||
\(979\) | −27.3489 | − | 17.5510i | −0.874075 | − | 0.560931i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 44.3303i | − | 1.41536i | ||||||
\(982\) | −16.7477 | − | 29.0079i | −0.534441 | − | 0.925680i | ||||
\(983\) | −43.8958 | − | 25.3432i | −1.40006 | − | 0.808324i | −0.405660 | − | 0.914024i | \(-0.632958\pi\) |
−0.994398 | + | 0.105700i | \(0.966292\pi\) | |||||||
\(984\) | −3.20871 | + | 5.55765i | −0.102290 | + | 0.177171i | ||||
\(985\) | −13.5396 | − | 23.4513i | −0.431408 | − | 0.747221i | ||||
\(986\) | 5.92146 | 0.188578 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.16515 | 0.0370684 | ||||||||
\(989\) | 24.8208 | − | 14.3303i | 0.789256 | − | 0.455677i | ||||
\(990\) | 12.1652 | + | 23.5595i | 0.386634 | + | 0.748770i | ||||
\(991\) | −23.3303 | + | 40.4093i | −0.741111 | + | 1.28364i | 0.210878 | + | 0.977512i | \(0.432368\pi\) |
−0.951990 | + | 0.306130i | \(0.900966\pi\) | |||||||
\(992\) | −4.32032 | − | 7.48301i | −0.137170 | − | 0.237586i | ||||
\(993\) | − | 15.2363i | − | 0.483510i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.9129 | 0.948302 | ||||||||
\(996\) | 7.21425 | − | 4.16515i | 0.228592 | − | 0.131978i | ||||
\(997\) | 11.2783 | − | 19.5346i | 0.357188 | − | 0.618668i | −0.630302 | − | 0.776350i | \(-0.717069\pi\) |
0.987490 | + | 0.157682i | \(0.0504022\pi\) | |||||||
\(998\) | 15.5130 | + | 8.95644i | 0.491056 | + | 0.283511i | ||||
\(999\) | 11.1905 | − | 6.46084i | 0.354052 | − | 0.204412i |
(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 | 1078.2.i.b.1011.6 | 16 | ||
7.2 | even | 3 | inner | 1078.2.i.b.901.3 | 16 | ||
7.3 | odd | 6 | 154.2.c.a.153.6 | yes | 8 | ||
7.4 | even | 3 | 154.2.c.a.153.7 | yes | 8 | ||
7.5 | odd | 6 | inner | 1078.2.i.b.901.2 | 16 | ||
7.6 | odd | 2 | inner | 1078.2.i.b.1011.7 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.b.1011.2 | 16 | ||
21.11 | odd | 6 | 1386.2.e.b.307.1 | 8 | |||
21.17 | even | 6 | 1386.2.e.b.307.4 | 8 | |||
28.3 | even | 6 | 1232.2.e.e.769.5 | 8 | |||
28.11 | odd | 6 | 1232.2.e.e.769.4 | 8 | |||
77.10 | even | 6 | 154.2.c.a.153.2 | ✓ | 8 | ||
77.32 | odd | 6 | 154.2.c.a.153.3 | yes | 8 | ||
77.54 | even | 6 | inner | 1078.2.i.b.901.6 | 16 | ||
77.65 | odd | 6 | inner | 1078.2.i.b.901.7 | 16 | ||
77.76 | even | 2 | inner | 1078.2.i.b.1011.3 | 16 | ||
231.32 | even | 6 | 1386.2.e.b.307.5 | 8 | |||
231.164 | odd | 6 | 1386.2.e.b.307.8 | 8 | |||
308.87 | odd | 6 | 1232.2.e.e.769.6 | 8 | |||
308.263 | even | 6 | 1232.2.e.e.769.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.c.a.153.2 | ✓ | 8 | 77.10 | even | 6 | ||
154.2.c.a.153.3 | yes | 8 | 77.32 | odd | 6 | ||
154.2.c.a.153.6 | yes | 8 | 7.3 | odd | 6 | ||
154.2.c.a.153.7 | yes | 8 | 7.4 | even | 3 | ||
1078.2.i.b.901.2 | 16 | 7.5 | odd | 6 | inner | ||
1078.2.i.b.901.3 | 16 | 7.2 | even | 3 | inner | ||
1078.2.i.b.901.6 | 16 | 77.54 | even | 6 | inner | ||
1078.2.i.b.901.7 | 16 | 77.65 | odd | 6 | inner | ||
1078.2.i.b.1011.2 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.b.1011.3 | 16 | 77.76 | even | 2 | inner | ||
1078.2.i.b.1011.6 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.b.1011.7 | 16 | 7.6 | odd | 2 | inner | ||
1232.2.e.e.769.3 | 8 | 308.263 | even | 6 | |||
1232.2.e.e.769.4 | 8 | 28.11 | odd | 6 | |||
1232.2.e.e.769.5 | 8 | 28.3 | even | 6 | |||
1232.2.e.e.769.6 | 8 | 308.87 | odd | 6 | |||
1386.2.e.b.307.1 | 8 | 21.11 | odd | 6 | |||
1386.2.e.b.307.4 | 8 | 21.17 | even | 6 | |||
1386.2.e.b.307.5 | 8 | 231.32 | even | 6 | |||
1386.2.e.b.307.8 | 8 | 231.164 | odd | 6 |