Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(1699,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.z (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-2.21837 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1849 |
Dual form | 1950.2.z.m.1699.1 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | −3.08440 | − | 1.78078i | −1.16579 | − | 0.673070i | −0.213107 | − | 0.977029i | \(-0.568358\pi\) |
−0.952685 | + | 0.303959i | \(0.901692\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.280776 | + | 0.486319i | 0.0846573 | + | 0.146631i | 0.905245 | − | 0.424890i | \(-0.139687\pi\) |
−0.820588 | + | 0.571520i | \(0.806354\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 2.21837 | + | 2.84233i | 0.615265 | + | 0.788320i | ||||
\(14\) | 3.56155 | 0.951865 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.70469 | − | 1.56155i | −0.655983 | − | 0.378732i | 0.134761 | − | 0.990878i | \(-0.456973\pi\) |
−0.790745 | + | 0.612146i | \(0.790307\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.21922 | + | 2.11176i | −0.279709 | + | 0.484470i | −0.971312 | − | 0.237807i | \(-0.923571\pi\) |
0.691603 | + | 0.722278i | \(0.256905\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.56155 | −0.777195 | ||||||||
\(22\) | −0.486319 | − | 0.280776i | −0.103684 | − | 0.0598617i | ||||
\(23\) | −6.65511 | + | 3.84233i | −1.38769 | + | 0.801181i | −0.993054 | − | 0.117658i | \(-0.962461\pi\) |
−0.394632 | + | 0.918839i | \(0.629128\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.34233 | − | 1.35234i | −0.655485 | − | 0.265217i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.08440 | + | 1.78078i | −0.582896 | + | 0.336535i | ||||
\(29\) | 0.561553 | + | 0.972638i | 0.104278 | + | 0.180614i | 0.913443 | − | 0.406967i | \(-0.133414\pi\) |
−0.809165 | + | 0.587581i | \(0.800080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0.486319 | + | 0.280776i | 0.0846573 | + | 0.0488769i | ||||
\(34\) | 3.12311 | 0.535608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −0.486319 | + | 0.280776i | −0.0799504 | + | 0.0461594i | −0.539442 | − | 0.842023i | \(-0.681365\pi\) |
0.459492 | + | 0.888182i | \(0.348032\pi\) | |||||||
\(38\) | − | 2.43845i | − | 0.395568i | ||||||
\(39\) | 3.34233 | + | 1.35234i | 0.535201 | + | 0.216548i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.56155 | + | 2.70469i | 0.243874 | + | 0.422401i | 0.961814 | − | 0.273703i | \(-0.0882485\pi\) |
−0.717941 | + | 0.696104i | \(0.754915\pi\) | |||||||
\(42\) | 3.08440 | − | 1.78078i | 0.475933 | − | 0.274780i | ||||
\(43\) | −0.379706 | − | 0.219224i | −0.0579047 | − | 0.0334313i | 0.470768 | − | 0.882257i | \(-0.343977\pi\) |
−0.528673 | + | 0.848826i | \(0.677310\pi\) | |||||||
\(44\) | 0.561553 | 0.0846573 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.84233 | − | 6.65511i | 0.566521 | − | 0.981242i | ||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 2.84233 | + | 4.92306i | 0.406047 | + | 0.703294i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12311 | −0.437322 | ||||||||
\(52\) | 3.57071 | − | 0.500000i | 0.495169 | − | 0.0693375i | ||||
\(53\) | 4.24621i | 0.583262i | 0.956531 | + | 0.291631i | \(0.0941979\pi\) | ||||
−0.956531 | + | 0.291631i | \(0.905802\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.78078 | − | 3.08440i | 0.237966 | − | 0.412170i | ||||
\(57\) | 2.43845i | 0.322980i | ||||||||
\(58\) | −0.972638 | − | 0.561553i | −0.127714 | − | 0.0737355i | ||||
\(59\) | −5.12311 | + | 8.87348i | −0.666972 | + | 1.15523i | 0.311775 | + | 0.950156i | \(0.399076\pi\) |
−0.978747 | + | 0.205073i | \(0.934257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.842329 | − | 1.45896i | 0.107849 | − | 0.186800i | −0.807050 | − | 0.590484i | \(-0.798937\pi\) |
0.914899 | + | 0.403683i | \(0.132270\pi\) | |||||||
\(62\) | −3.46410 | + | 2.00000i | −0.439941 | + | 0.254000i | ||||
\(63\) | −3.08440 | + | 1.78078i | −0.388597 | + | 0.224357i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.561553 | −0.0691224 | ||||||||
\(67\) | −10.2258 | + | 5.90388i | −1.24928 | + | 0.721274i | −0.970967 | − | 0.239215i | \(-0.923110\pi\) |
−0.278317 | + | 0.960489i | \(0.589776\pi\) | |||||||
\(68\) | −2.70469 | + | 1.56155i | −0.327992 | + | 0.189366i | ||||
\(69\) | −3.84233 | + | 6.65511i | −0.462562 | + | 0.801181i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.28078 | + | 10.8786i | −0.745391 | + | 1.29106i | 0.204621 | + | 0.978841i | \(0.434404\pi\) |
−0.950012 | + | 0.312214i | \(0.898929\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 9.00000i | 1.05337i | 0.850060 | + | 0.526685i | \(0.176565\pi\) | ||||
−0.850060 | + | 0.526685i | \(0.823435\pi\) | |||||||
\(74\) | 0.280776 | − | 0.486319i | 0.0326396 | − | 0.0565334i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21922 | + | 2.11176i | 0.139855 | + | 0.242235i | ||||
\(77\) | − | 2.00000i | − | 0.227921i | ||||||
\(78\) | −3.57071 | + | 0.500000i | −0.404304 | + | 0.0566139i | ||||
\(79\) | 15.8078 | 1.77851 | 0.889256 | − | 0.457409i | \(-0.151223\pi\) | ||||
0.889256 | + | 0.457409i | \(0.151223\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.70469 | − | 1.56155i | −0.298683 | − | 0.172445i | ||||
\(83\) | 6.56155i | 0.720224i | 0.932909 | + | 0.360112i | \(0.117262\pi\) | ||||
−0.932909 | + | 0.360112i | \(0.882738\pi\) | |||||||
\(84\) | −1.78078 | + | 3.08440i | −0.194299 | + | 0.336535i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.438447 | 0.0472790 | ||||||||
\(87\) | 0.972638 | + | 0.561553i | 0.104278 | + | 0.0602048i | ||||
\(88\) | −0.486319 | + | 0.280776i | −0.0518418 | + | 0.0299309i | ||||
\(89\) | 5.12311 | + | 8.87348i | 0.543048 | + | 0.940587i | 0.998727 | + | 0.0504427i | \(0.0160632\pi\) |
−0.455679 | + | 0.890144i | \(0.650603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.78078 | − | 12.7173i | −0.186676 | − | 1.33313i | ||||
\(92\) | 7.68466i | 0.801181i | ||||||||
\(93\) | 3.46410 | − | 2.00000i | 0.359211 | − | 0.207390i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.43160 | − | 1.40388i | −0.246891 | − | 0.142543i | 0.371449 | − | 0.928453i | \(-0.378861\pi\) |
−0.618340 | + | 0.785911i | \(0.712194\pi\) | |||||||
\(98\) | −4.92306 | − | 2.84233i | −0.497304 | − | 0.287119i | ||||
\(99\) | 0.561553 | 0.0564382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.12311 | + | 5.40938i | 0.310761 | + | 0.538253i | 0.978527 | − | 0.206118i | \(-0.0660829\pi\) |
−0.667767 | + | 0.744371i | \(0.732750\pi\) | |||||||
\(102\) | 2.70469 | − | 1.56155i | 0.267804 | − | 0.154617i | ||||
\(103\) | − | 4.43845i | − | 0.437333i | −0.975800 | − | 0.218667i | \(-0.929829\pi\) | ||
0.975800 | − | 0.218667i | \(-0.0701707\pi\) | |||||||
\(104\) | −2.84233 | + | 2.21837i | −0.278713 | + | 0.217529i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.12311 | − | 3.67733i | −0.206214 | − | 0.357174i | ||||
\(107\) | −4.64996 | + | 2.68466i | −0.449529 | + | 0.259536i | −0.707631 | − | 0.706582i | \(-0.750236\pi\) |
0.258102 | + | 0.966118i | \(0.416903\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 2.80776 | 0.268935 | 0.134468 | − | 0.990918i | \(-0.457068\pi\) | ||||
0.134468 | + | 0.990918i | \(0.457068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.280776 | + | 0.486319i | −0.0266501 | + | 0.0461594i | ||||
\(112\) | 3.56155i | 0.336535i | ||||||||
\(113\) | −3.46410 | − | 2.00000i | −0.325875 | − | 0.188144i | 0.328133 | − | 0.944632i | \(-0.393581\pi\) |
−0.654008 | + | 0.756487i | \(0.726914\pi\) | |||||||
\(114\) | −1.21922 | − | 2.11176i | −0.114191 | − | 0.197784i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.12311 | 0.104278 | ||||||||
\(117\) | 3.57071 | − | 0.500000i | 0.330113 | − | 0.0462250i | ||||
\(118\) | − | 10.2462i | − | 0.943240i | ||||||
\(119\) | 5.56155 | + | 9.63289i | 0.509827 | + | 0.883046i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.34233 | − | 9.25319i | 0.485666 | − | 0.841199i | ||||
\(122\) | 1.68466i | 0.152522i | ||||||||
\(123\) | 2.70469 | + | 1.56155i | 0.243874 | + | 0.140800i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.78078 | − | 3.08440i | 0.158644 | − | 0.274780i | ||||
\(127\) | −18.8861 | + | 10.9039i | −1.67587 | + | 0.967563i | −0.711619 | + | 0.702565i | \(0.752038\pi\) |
−0.964249 | + | 0.264998i | \(0.914629\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −0.438447 | −0.0386031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.876894 | 0.0766146 | 0.0383073 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383073 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(132\) | 0.486319 | − | 0.280776i | 0.0423286 | − | 0.0244384i | ||||
\(133\) | 7.52113 | − | 4.34233i | 0.652165 | − | 0.376528i | ||||
\(134\) | 5.90388 | − | 10.2258i | 0.510018 | − | 0.883377i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.56155 | − | 2.70469i | 0.133902 | − | 0.231925i | ||||
\(137\) | 14.2829 | + | 8.24621i | 1.22027 | + | 0.704521i | 0.964975 | − | 0.262343i | \(-0.0844951\pi\) |
0.255292 | + | 0.966864i | \(0.417828\pi\) | |||||||
\(138\) | − | 7.68466i | − | 0.654162i | ||||||
\(139\) | 10.7808 | − | 18.6729i | 0.914414 | − | 1.58381i | 0.106656 | − | 0.994296i | \(-0.465986\pi\) |
0.807758 | − | 0.589515i | \(-0.200681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 3.46410i | −0.168430 | − | 0.291730i | ||||
\(142\) | − | 12.5616i | − | 1.05414i | ||||||
\(143\) | −0.759413 | + | 1.87689i | −0.0635053 | + | 0.156954i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50000 | − | 7.79423i | −0.372423 | − | 0.645055i | ||||
\(147\) | 4.92306 | + | 2.84233i | 0.406047 | + | 0.234431i | ||||
\(148\) | 0.561553i | 0.0461594i | ||||||||
\(149\) | −5.12311 | + | 8.87348i | −0.419701 | + | 0.726944i | −0.995909 | − | 0.0903593i | \(-0.971198\pi\) |
0.576208 | + | 0.817303i | \(0.304532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6847 | −1.35778 | −0.678889 | − | 0.734241i | \(-0.737538\pi\) | ||||
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(152\) | −2.11176 | − | 1.21922i | −0.171286 | − | 0.0988921i | ||||
\(153\) | −2.70469 | + | 1.56155i | −0.218661 | + | 0.126244i | ||||
\(154\) | 1.00000 | + | 1.73205i | 0.0805823 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.84233 | − | 2.21837i | 0.227568 | − | 0.177612i | ||||
\(157\) | − | 17.2462i | − | 1.37640i | −0.725522 | − | 0.688199i | \(-0.758402\pi\) | ||
0.725522 | − | 0.688199i | \(-0.241598\pi\) | |||||||
\(158\) | −13.6899 | + | 7.90388i | −1.08911 | + | 0.628799i | ||||
\(159\) | 2.12311 | + | 3.67733i | 0.168373 | + | 0.291631i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.3693 | 2.15700 | ||||||||
\(162\) | 0.866025 | + | 0.500000i | 0.0680414 | + | 0.0392837i | ||||
\(163\) | 14.2829 | + | 8.24621i | 1.11872 | + | 0.645893i | 0.941074 | − | 0.338201i | \(-0.109818\pi\) |
0.177646 | + | 0.984094i | \(0.443152\pi\) | |||||||
\(164\) | 3.12311 | 0.243874 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.28078 | − | 5.68247i | −0.254638 | − | 0.441045i | ||||
\(167\) | −20.5115 | + | 11.8423i | −1.58723 | + | 0.916387i | −0.593468 | + | 0.804858i | \(0.702241\pi\) |
−0.993761 | + | 0.111529i | \(0.964425\pi\) | |||||||
\(168\) | − | 3.56155i | − | 0.274780i | ||||||
\(169\) | −3.15767 | + | 12.6107i | −0.242898 | + | 0.970052i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.21922 | + | 2.11176i | 0.0932364 | + | 0.161490i | ||||
\(172\) | −0.379706 | + | 0.219224i | −0.0289523 | + | 0.0167156i | ||||
\(173\) | 7.68762 | + | 4.43845i | 0.584479 | + | 0.337449i | 0.762911 | − | 0.646503i | \(-0.223769\pi\) |
−0.178433 | + | 0.983952i | \(0.557103\pi\) | |||||||
\(174\) | −1.12311 | −0.0851424 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.280776 | − | 0.486319i | 0.0211643 | − | 0.0366577i | ||||
\(177\) | 10.2462i | 0.770152i | ||||||||
\(178\) | −8.87348 | − | 5.12311i | −0.665095 | − | 0.383993i | ||||
\(179\) | −7.84233 | − | 13.5833i | −0.586163 | − | 1.01526i | −0.994729 | − | 0.102536i | \(-0.967304\pi\) |
0.408566 | − | 0.912729i | \(-0.366029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4924 | −1.15154 | −0.575771 | − | 0.817611i | \(-0.695298\pi\) | ||||
−0.575771 | + | 0.817611i | \(0.695298\pi\) | |||||||
\(182\) | 7.90084 | + | 10.1231i | 0.585649 | + | 0.750375i | ||||
\(183\) | − | 1.68466i | − | 0.124534i | ||||||
\(184\) | −3.84233 | − | 6.65511i | −0.283260 | − | 0.490621i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | + | 3.46410i | −0.146647 | + | 0.254000i | ||||
\(187\) | − | 1.75379i | − | 0.128250i | ||||||
\(188\) | −3.46410 | − | 2.00000i | −0.252646 | − | 0.145865i | ||||
\(189\) | −1.78078 | + | 3.08440i | −0.129532 | + | 0.224357i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.96543 | + | 13.7965i | −0.576359 | + | 0.998282i | 0.419534 | + | 0.907740i | \(0.362194\pi\) |
−0.995893 | + | 0.0905428i | \(0.971140\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 2.59808 | − | 1.50000i | 0.187014 | − | 0.107972i | −0.403570 | − | 0.914949i | \(-0.632231\pi\) |
0.590584 | + | 0.806976i | \(0.298898\pi\) | |||||||
\(194\) | 2.80776 | 0.201586 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.68466 | 0.406047 | ||||||||
\(197\) | −4.43674 | + | 2.56155i | −0.316105 | + | 0.182503i | −0.649655 | − | 0.760229i | \(-0.725087\pi\) |
0.333550 | + | 0.942732i | \(0.391753\pi\) | |||||||
\(198\) | −0.486319 | + | 0.280776i | −0.0345612 | + | 0.0199539i | ||||
\(199\) | −2.21922 | + | 3.84381i | −0.157317 | + | 0.272480i | −0.933900 | − | 0.357534i | \(-0.883618\pi\) |
0.776584 | + | 0.630014i | \(0.216951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.90388 | + | 10.2258i | −0.416428 | + | 0.721274i | ||||
\(202\) | −5.40938 | − | 3.12311i | −0.380602 | − | 0.219741i | ||||
\(203\) | − | 4.00000i | − | 0.280745i | ||||||
\(204\) | −1.56155 | + | 2.70469i | −0.109331 | + | 0.189366i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.21922 | + | 3.84381i | 0.154621 | + | 0.267811i | ||||
\(207\) | 7.68466i | 0.534121i | ||||||||
\(208\) | 1.35234 | − | 3.34233i | 0.0937682 | − | 0.231749i | ||||
\(209\) | −1.36932 | −0.0947176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.561553 | − | 0.972638i | −0.0386589 | − | 0.0669592i | 0.846049 | − | 0.533106i | \(-0.178975\pi\) |
−0.884707 | + | 0.466147i | \(0.845642\pi\) | |||||||
\(212\) | 3.67733 | + | 2.12311i | 0.252560 | + | 0.145815i | ||||
\(213\) | 12.5616i | 0.860703i | ||||||||
\(214\) | 2.68466 | − | 4.64996i | 0.183519 | − | 0.317865i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −12.3376 | − | 7.12311i | −0.837530 | − | 0.483548i | ||||
\(218\) | −2.43160 | + | 1.40388i | −0.164688 | + | 0.0950829i | ||||
\(219\) | 4.50000 | + | 7.79423i | 0.304082 | + | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56155 | − | 11.1517i | −0.105041 | − | 0.750146i | ||||
\(222\) | − | 0.561553i | − | 0.0376890i | ||||||
\(223\) | −0.379706 | + | 0.219224i | −0.0254270 | + | 0.0146803i | −0.512660 | − | 0.858592i | \(-0.671340\pi\) |
0.487233 | + | 0.873272i | \(0.338006\pi\) | |||||||
\(224\) | −1.78078 | − | 3.08440i | −0.118983 | − | 0.206085i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | 25.7077 | + | 14.8423i | 1.70628 | + | 0.985120i | 0.939073 | + | 0.343718i | \(0.111686\pi\) |
0.767205 | + | 0.641402i | \(0.221647\pi\) | |||||||
\(228\) | 2.11176 | + | 1.21922i | 0.139855 | + | 0.0807451i | ||||
\(229\) | −9.49242 | −0.627277 | −0.313638 | − | 0.949542i | \(-0.601548\pi\) | ||||
−0.313638 | + | 0.949542i | \(0.601548\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | − | 1.73205i | −0.0657952 | − | 0.113961i | ||||
\(232\) | −0.972638 | + | 0.561553i | −0.0638568 | + | 0.0368677i | ||||
\(233\) | − | 25.3693i | − | 1.66200i | −0.556273 | − | 0.831000i | \(-0.687769\pi\) | ||
0.556273 | − | 0.831000i | \(-0.312231\pi\) | |||||||
\(234\) | −2.84233 | + | 2.21837i | −0.185809 | + | 0.145019i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.12311 | + | 8.87348i | 0.333486 | + | 0.577614i | ||||
\(237\) | 13.6899 | − | 7.90388i | 0.889256 | − | 0.513412i | ||||
\(238\) | −9.63289 | − | 5.56155i | −0.624408 | − | 0.360502i | ||||
\(239\) | −27.0540 | −1.74998 | −0.874988 | − | 0.484144i | \(-0.839131\pi\) | ||||
−0.874988 | + | 0.484144i | \(0.839131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.78078 | + | 13.4767i | −0.501204 | + | 0.868111i | 0.498795 | + | 0.866720i | \(0.333776\pi\) |
−0.999999 | + | 0.00139067i | \(0.999557\pi\) | |||||||
\(242\) | 10.6847i | 0.686836i | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −0.842329 | − | 1.45896i | −0.0539246 | − | 0.0934002i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.12311 | −0.199122 | ||||||||
\(247\) | −8.70700 | + | 1.21922i | −0.554013 | + | 0.0775773i | ||||
\(248\) | 4.00000i | 0.254000i | ||||||||
\(249\) | 3.28078 | + | 5.68247i | 0.207911 | + | 0.360112i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9654 | + | 20.7247i | −0.755252 | + | 1.30813i | 0.189998 | + | 0.981785i | \(0.439152\pi\) |
−0.945249 | + | 0.326350i | \(0.894181\pi\) | |||||||
\(252\) | 3.56155i | 0.224357i | ||||||||
\(253\) | −3.73720 | − | 2.15767i | −0.234955 | − | 0.135652i | ||||
\(254\) | 10.9039 | − | 18.8861i | 0.684170 | − | 1.18502i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.7914 | − | 6.80776i | 0.735527 | − | 0.424657i | −0.0849138 | − | 0.996388i | \(-0.527061\pi\) |
0.820441 | + | 0.571732i | \(0.193728\pi\) | |||||||
\(258\) | 0.379706 | − | 0.219224i | 0.0236395 | − | 0.0136483i | ||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.12311 | 0.0695185 | ||||||||
\(262\) | −0.759413 | + | 0.438447i | −0.0469167 | + | 0.0270874i | ||||
\(263\) | 5.46925 | − | 3.15767i | 0.337248 | − | 0.194710i | −0.321806 | − | 0.946806i | \(-0.604290\pi\) |
0.659054 | + | 0.752095i | \(0.270957\pi\) | |||||||
\(264\) | −0.280776 | + | 0.486319i | −0.0172806 | + | 0.0299309i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.34233 | + | 7.52113i | −0.266245 | + | 0.461150i | ||||
\(267\) | 8.87348 | + | 5.12311i | 0.543048 | + | 0.313529i | ||||
\(268\) | 11.8078i | 0.721274i | ||||||||
\(269\) | −1.68466 | + | 2.91791i | −0.102715 | + | 0.177908i | −0.912803 | − | 0.408401i | \(-0.866086\pi\) |
0.810087 | + | 0.586310i | \(0.199420\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.46543 | − | 7.73436i | −0.271256 | − | 0.469829i | 0.697928 | − | 0.716168i | \(-0.254106\pi\) |
−0.969184 | + | 0.246339i | \(0.920772\pi\) | |||||||
\(272\) | 3.12311i | 0.189366i | ||||||||
\(273\) | −7.90084 | − | 10.1231i | −0.478181 | − | 0.612678i | ||||
\(274\) | −16.4924 | −0.996344 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.84233 | + | 6.65511i | 0.231281 | + | 0.400591i | ||||
\(277\) | 4.33013 | + | 2.50000i | 0.260172 | + | 0.150210i | 0.624413 | − | 0.781094i | \(-0.285338\pi\) |
−0.364241 | + | 0.931305i | \(0.618672\pi\) | |||||||
\(278\) | 21.5616i | 1.29318i | ||||||||
\(279\) | 2.00000 | − | 3.46410i | 0.119737 | − | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75379 | −0.104622 | −0.0523111 | − | 0.998631i | \(-0.516659\pi\) | ||||
−0.0523111 | + | 0.998631i | \(0.516659\pi\) | |||||||
\(282\) | 3.46410 | + | 2.00000i | 0.206284 | + | 0.119098i | ||||
\(283\) | 25.6478 | − | 14.8078i | 1.52460 | − | 0.880230i | 0.525028 | − | 0.851085i | \(-0.324055\pi\) |
0.999575 | − | 0.0291454i | \(-0.00927859\pi\) | |||||||
\(284\) | 6.28078 | + | 10.8786i | 0.372696 | + | 0.645528i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.280776 | − | 2.00514i | −0.0166027 | − | 0.118567i | ||||
\(287\) | − | 11.1231i | − | 0.656576i | ||||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | −3.62311 | − | 6.27540i | −0.213124 | − | 0.369141i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.80776 | −0.164594 | ||||||||
\(292\) | 7.79423 | + | 4.50000i | 0.456123 | + | 0.263343i | ||||
\(293\) | −17.5337 | − | 10.1231i | −1.02433 | − | 0.591398i | −0.108976 | − | 0.994044i | \(-0.534757\pi\) |
−0.915356 | + | 0.402646i | \(0.868090\pi\) | |||||||
\(294\) | −5.68466 | −0.331536 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.280776 | − | 0.486319i | −0.0163198 | − | 0.0282667i | ||||
\(297\) | 0.486319 | − | 0.280776i | 0.0282191 | − | 0.0162923i | ||||
\(298\) | − | 10.2462i | − | 0.593547i | ||||||
\(299\) | −25.6847 | − | 10.3923i | −1.48538 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.780776 | + | 1.35234i | 0.0450032 | + | 0.0779478i | ||||
\(302\) | 14.4493 | − | 8.34233i | 0.831466 | − | 0.480047i | ||||
\(303\) | 5.40938 | + | 3.12311i | 0.310761 | + | 0.179418i | ||||
\(304\) | 2.43845 | 0.139855 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56155 | − | 2.70469i | 0.0892680 | − | 0.154617i | ||||
\(307\) | − | 22.2462i | − | 1.26966i | −0.772653 | − | 0.634829i | \(-0.781070\pi\) | ||
0.772653 | − | 0.634829i | \(-0.218930\pi\) | |||||||
\(308\) | −1.73205 | − | 1.00000i | −0.0986928 | − | 0.0569803i | ||||
\(309\) | −2.21922 | − | 3.84381i | −0.126247 | − | 0.218667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3153 | −0.584929 | −0.292465 | − | 0.956276i | \(-0.594475\pi\) | ||||
−0.292465 | + | 0.956276i | \(0.594475\pi\) | |||||||
\(312\) | −1.35234 | + | 3.34233i | −0.0765614 | + | 0.189222i | ||||
\(313\) | 31.0000i | 1.75222i | 0.482108 | + | 0.876112i | \(0.339871\pi\) | ||||
−0.482108 | + | 0.876112i | \(0.660129\pi\) | |||||||
\(314\) | 8.62311 | + | 14.9357i | 0.486630 | + | 0.842868i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.90388 | − | 13.6899i | 0.444628 | − | 0.770118i | ||||
\(317\) | − | 16.2462i | − | 0.912478i | −0.889857 | − | 0.456239i | \(-0.849196\pi\) | ||
0.889857 | − | 0.456239i | \(-0.150804\pi\) | |||||||
\(318\) | −3.67733 | − | 2.12311i | −0.206214 | − | 0.119058i | ||||
\(319\) | −0.315342 | + | 0.546188i | −0.0176557 | + | 0.0305806i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.68466 | + | 4.64996i | −0.149843 | + | 0.259536i | ||||
\(322\) | −23.7025 | + | 13.6847i | −1.32089 | + | 0.762616i | ||||
\(323\) | 6.59524 | − | 3.80776i | 0.366969 | − | 0.211870i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.4924 | −0.913431 | ||||||||
\(327\) | 2.43160 | − | 1.40388i | 0.134468 | − | 0.0776349i | ||||
\(328\) | −2.70469 | + | 1.56155i | −0.149341 | + | 0.0862223i | ||||
\(329\) | −7.12311 | + | 12.3376i | −0.392710 | + | 0.680193i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.34233 | − | 14.4493i | 0.458536 | − | 0.794207i | −0.540348 | − | 0.841442i | \(-0.681707\pi\) |
0.998884 | + | 0.0472342i | \(0.0150407\pi\) | |||||||
\(332\) | 5.68247 | + | 3.28078i | 0.311866 | + | 0.180056i | ||||
\(333\) | 0.561553i | 0.0307729i | ||||||||
\(334\) | 11.8423 | − | 20.5115i | 0.647983 | − | 1.12234i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.78078 | + | 3.08440i | 0.0971493 | + | 0.168268i | ||||
\(337\) | − | 8.05398i | − | 0.438728i | −0.975643 | − | 0.219364i | \(-0.929602\pi\) | ||
0.975643 | − | 0.219364i | \(-0.0703982\pi\) | |||||||
\(338\) | −3.57071 | − | 12.5000i | −0.194221 | − | 0.679910i | ||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12311 | + | 1.94528i | 0.0608196 | + | 0.105343i | ||||
\(342\) | −2.11176 | − | 1.21922i | −0.114191 | − | 0.0659281i | ||||
\(343\) | 4.68466i | 0.252948i | ||||||||
\(344\) | 0.219224 | − | 0.379706i | 0.0118197 | − | 0.0204724i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.87689 | −0.477225 | ||||||||
\(347\) | −21.4842 | − | 12.4039i | −1.15333 | − | 0.665875i | −0.203633 | − | 0.979047i | \(-0.565275\pi\) |
−0.949696 | + | 0.313172i | \(0.898608\pi\) | |||||||
\(348\) | 0.972638 | − | 0.561553i | 0.0521389 | − | 0.0301024i | ||||
\(349\) | −9.62311 | − | 16.6677i | −0.515113 | − | 0.892202i | −0.999846 | − | 0.0175398i | \(-0.994417\pi\) |
0.484733 | − | 0.874662i | \(-0.338917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.84233 | − | 2.21837i | 0.151712 | − | 0.118408i | ||||
\(352\) | 0.561553i | 0.0299309i | ||||||||
\(353\) | 1.94528 | − | 1.12311i | 0.103537 | − | 0.0597769i | −0.447338 | − | 0.894365i | \(-0.647628\pi\) |
0.550874 | + | 0.834588i | \(0.314294\pi\) | |||||||
\(354\) | −5.12311 | − | 8.87348i | −0.272290 | − | 0.471620i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.2462 | 0.543048 | ||||||||
\(357\) | 9.63289 | + | 5.56155i | 0.509827 | + | 0.294349i | ||||
\(358\) | 13.5833 | + | 7.84233i | 0.717900 | + | 0.414480i | ||||
\(359\) | 4.87689 | 0.257393 | 0.128696 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128696 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.52699 | + | 11.3051i | 0.343526 | + | 0.595004i | ||||
\(362\) | 13.4168 | − | 7.74621i | 0.705173 | − | 0.407132i | ||||
\(363\) | − | 10.6847i | − | 0.560799i | ||||||
\(364\) | −11.9039 | − | 4.81645i | −0.623933 | − | 0.252450i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.842329 | + | 1.45896i | 0.0440293 | + | 0.0762609i | ||||
\(367\) | 8.82674 | − | 5.09612i | 0.460752 | − | 0.266015i | −0.251609 | − | 0.967829i | \(-0.580960\pi\) |
0.712360 | + | 0.701814i | \(0.247626\pi\) | |||||||
\(368\) | 6.65511 | + | 3.84233i | 0.346922 | + | 0.200295i | ||||
\(369\) | 3.12311 | 0.162582 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.56155 | − | 13.0970i | 0.392576 | − | 0.679962i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 8.22068 | + | 4.74621i | 0.425651 | + | 0.245750i | 0.697492 | − | 0.716593i | \(-0.254299\pi\) |
−0.271841 | + | 0.962342i | \(0.587633\pi\) | |||||||
\(374\) | 0.876894 | + | 1.51883i | 0.0453431 | + | 0.0785366i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | −1.51883 | + | 3.75379i | −0.0782235 | + | 0.193330i | ||||
\(378\) | − | 3.56155i | − | 0.183187i | ||||||
\(379\) | −12.0270 | − | 20.8314i | −0.617785 | − | 1.07003i | −0.989889 | − | 0.141844i | \(-0.954697\pi\) |
0.372104 | − | 0.928191i | \(-0.378636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9039 | + | 18.8861i | −0.558623 | + | 0.967563i | ||||
\(382\) | − | 15.9309i | − | 0.815094i | ||||||
\(383\) | 4.70983 | + | 2.71922i | 0.240661 | + | 0.138946i | 0.615481 | − | 0.788152i | \(-0.288962\pi\) |
−0.374819 | + | 0.927098i | \(0.622295\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | + | 2.59808i | −0.0763480 | + | 0.132239i | ||||
\(387\) | −0.379706 | + | 0.219224i | −0.0193016 | + | 0.0111438i | ||||
\(388\) | −2.43160 | + | 1.40388i | −0.123446 | + | 0.0712713i | ||||
\(389\) | −11.3693 | −0.576447 | −0.288224 | − | 0.957563i | \(-0.593065\pi\) | ||||
−0.288224 | + | 0.957563i | \(0.593065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −4.92306 | + | 2.84233i | −0.248652 | + | 0.143559i | ||||
\(393\) | 0.759413 | − | 0.438447i | 0.0383073 | − | 0.0221167i | ||||
\(394\) | 2.56155 | − | 4.43674i | 0.129049 | − | 0.223520i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.280776 | − | 0.486319i | 0.0141095 | − | 0.0244384i | ||||
\(397\) | −8.49377 | − | 4.90388i | −0.426290 | − | 0.246119i | 0.271475 | − | 0.962446i | \(-0.412489\pi\) |
−0.697765 | + | 0.716327i | \(0.745822\pi\) | |||||||
\(398\) | − | 4.43845i | − | 0.222479i | ||||||
\(399\) | 4.34233 | − | 7.52113i | 0.217388 | − | 0.376528i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.31534 | + | 10.9385i | 0.315373 | + | 0.546242i | 0.979517 | − | 0.201363i | \(-0.0645370\pi\) |
−0.664144 | + | 0.747605i | \(0.731204\pi\) | |||||||
\(402\) | − | 11.8078i | − | 0.588918i | ||||||
\(403\) | 8.87348 | + | 11.3693i | 0.442019 | + | 0.566346i | ||||
\(404\) | 6.24621 | 0.310761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | + | 3.46410i | 0.0992583 | + | 0.171920i | ||||
\(407\) | −0.273094 | − | 0.157671i | −0.0135368 | − | 0.00781545i | ||||
\(408\) | − | 3.12311i | − | 0.154617i | ||||||
\(409\) | 8.12311 | − | 14.0696i | 0.401662 | − | 0.695699i | −0.592265 | − | 0.805743i | \(-0.701766\pi\) |
0.993927 | + | 0.110045i | \(0.0350994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4924 | 0.813511 | ||||||||
\(412\) | −3.84381 | − | 2.21922i | −0.189371 | − | 0.109333i | ||||
\(413\) | 31.6034 | − | 18.2462i | 1.55510 | − | 0.897837i | ||||
\(414\) | −3.84233 | − | 6.65511i | −0.188840 | − | 0.327081i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 3.57071i | 0.0245145 | + | 0.175069i | ||||
\(417\) | − | 21.5616i | − | 1.05587i | ||||||
\(418\) | 1.18586 | − | 0.684658i | 0.0580025 | − | 0.0334877i | ||||
\(419\) | −5.96543 | − | 10.3324i | −0.291431 | − | 0.504773i | 0.682718 | − | 0.730682i | \(-0.260798\pi\) |
−0.974148 | + | 0.225910i | \(0.927465\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2462 | 1.52285 | 0.761424 | − | 0.648255i | \(-0.224501\pi\) | ||||
0.761424 | + | 0.648255i | \(0.224501\pi\) | |||||||
\(422\) | 0.972638 | + | 0.561553i | 0.0473473 | + | 0.0273360i | ||||
\(423\) | −3.46410 | − | 2.00000i | −0.168430 | − | 0.0972433i | ||||
\(424\) | −4.24621 | −0.206214 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.28078 | − | 10.8786i | −0.304305 | − | 0.527071i | ||||
\(427\) | −5.19615 | + | 3.00000i | −0.251459 | + | 0.145180i | ||||
\(428\) | 5.36932i | 0.259536i | ||||||||
\(429\) | 0.280776 | + | 2.00514i | 0.0135560 | + | 0.0968093i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.15767 | − | 15.8616i | −0.441109 | − | 0.764024i | 0.556663 | − | 0.830739i | \(-0.312082\pi\) |
−0.997772 | + | 0.0667146i | \(0.978748\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 11.8513 | + | 6.84233i | 0.569535 | + | 0.328821i | 0.756964 | − | 0.653457i | \(-0.226682\pi\) |
−0.187428 | + | 0.982278i | \(0.560015\pi\) | |||||||
\(434\) | 14.2462 | 0.683840 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.40388 | − | 2.43160i | 0.0672338 | − | 0.116452i | ||||
\(437\) | − | 18.7386i | − | 0.896390i | ||||||
\(438\) | −7.79423 | − | 4.50000i | −0.372423 | − | 0.215018i | ||||
\(439\) | −3.46543 | − | 6.00231i | −0.165396 | − | 0.286475i | 0.771400 | − | 0.636351i | \(-0.219557\pi\) |
−0.936796 | + | 0.349876i | \(0.886224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.68466 | 0.270698 | ||||||||
\(442\) | 6.92820 | + | 8.87689i | 0.329541 | + | 0.422231i | ||||
\(443\) | − | 2.80776i | − | 0.133401i | −0.997773 | − | 0.0667004i | \(-0.978753\pi\) | ||
0.997773 | − | 0.0667004i | \(-0.0212472\pi\) | |||||||
\(444\) | 0.280776 | + | 0.486319i | 0.0133251 | + | 0.0230797i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.219224 | − | 0.379706i | 0.0103805 | − | 0.0179796i | ||||
\(447\) | 10.2462i | 0.484629i | ||||||||
\(448\) | 3.08440 | + | 1.78078i | 0.145724 | + | 0.0841338i | ||||
\(449\) | −1.56155 | + | 2.70469i | −0.0736942 | + | 0.127642i | −0.900518 | − | 0.434819i | \(-0.856812\pi\) |
0.826823 | + | 0.562462i | \(0.190146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.876894 | + | 1.51883i | −0.0412913 | + | 0.0715187i | ||||
\(452\) | −3.46410 | + | 2.00000i | −0.162938 | + | 0.0940721i | ||||
\(453\) | −14.4493 | + | 8.34233i | −0.678889 | + | 0.391957i | ||||
\(454\) | −29.6847 | −1.39317 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.43845 | −0.114191 | ||||||||
\(457\) | −3.90368 | + | 2.25379i | −0.182606 | + | 0.105428i | −0.588517 | − | 0.808485i | \(-0.700288\pi\) |
0.405910 | + | 0.913913i | \(0.366955\pi\) | |||||||
\(458\) | 8.22068 | − | 4.74621i | 0.384127 | − | 0.221776i | ||||
\(459\) | −1.56155 | + | 2.70469i | −0.0728870 | + | 0.126244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.31534 | + | 9.20644i | −0.247560 | + | 0.428787i | −0.962848 | − | 0.270043i | \(-0.912962\pi\) |
0.715288 | + | 0.698830i | \(0.246295\pi\) | |||||||
\(462\) | 1.73205 | + | 1.00000i | 0.0805823 | + | 0.0465242i | ||||
\(463\) | 27.8078i | 1.29234i | 0.763195 | + | 0.646168i | \(0.223630\pi\) | ||||
−0.763195 | + | 0.646168i | \(0.776370\pi\) | |||||||
\(464\) | 0.561553 | − | 0.972638i | 0.0260694 | − | 0.0451536i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.6847 | + | 21.9705i | 0.587605 | + | 1.01776i | ||||
\(467\) | 3.43845i | 0.159112i | 0.996830 | + | 0.0795562i | \(0.0253503\pi\) | ||||
−0.996830 | + | 0.0795562i | \(0.974650\pi\) | |||||||
\(468\) | 1.35234 | − | 3.34233i | 0.0625121 | − | 0.154499i | ||||
\(469\) | 42.0540 | 1.94187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.62311 | − | 14.9357i | −0.397332 | − | 0.688199i | ||||
\(472\) | −8.87348 | − | 5.12311i | −0.408435 | − | 0.235810i | ||||
\(473\) | − | 0.246211i | − | 0.0113208i | ||||||
\(474\) | −7.90388 | + | 13.6899i | −0.363037 | + | 0.628799i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.1231 | 0.509827 | ||||||||
\(477\) | 3.67733 | + | 2.12311i | 0.168373 | + | 0.0972103i | ||||
\(478\) | 23.4294 | − | 13.5270i | 1.07164 | − | 0.618710i | ||||
\(479\) | −5.80776 | − | 10.0593i | −0.265364 | − | 0.459623i | 0.702295 | − | 0.711886i | \(-0.252159\pi\) |
−0.967659 | + | 0.252263i | \(0.918825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.87689 | − | 0.759413i | −0.0855790 | − | 0.0346262i | ||||
\(482\) | − | 15.5616i | − | 0.708809i | ||||||
\(483\) | 23.7025 | − | 13.6847i | 1.07850 | − | 0.622674i | ||||
\(484\) | −5.34233 | − | 9.25319i | −0.242833 | − | 0.420599i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 36.9660 | + | 21.3423i | 1.67509 | + | 0.967113i | 0.964718 | + | 0.263286i | \(0.0848064\pi\) |
0.710372 | + | 0.703827i | \(0.248527\pi\) | |||||||
\(488\) | 1.45896 | + | 0.842329i | 0.0660439 | + | 0.0381305i | ||||
\(489\) | 16.4924 | 0.745813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6501 | − | 27.1068i | −0.706279 | − | 1.22331i | −0.966228 | − | 0.257689i | \(-0.917039\pi\) |
0.259949 | − | 0.965622i | \(-0.416294\pi\) | |||||||
\(492\) | 2.70469 | − | 1.56155i | 0.121937 | − | 0.0704002i | ||||
\(493\) | − | 3.50758i | − | 0.157973i | ||||||
\(494\) | 6.93087 | − | 5.40938i | 0.311835 | − | 0.243379i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | − | 3.46410i | −0.0898027 | − | 0.155543i | ||||
\(497\) | 38.7448 | − | 22.3693i | 1.73794 | − | 1.00340i | ||||
\(498\) | −5.68247 | − | 3.28078i | −0.254638 | − | 0.147015i | ||||
\(499\) | −6.05398 | −0.271013 | −0.135507 | − | 0.990776i | \(-0.543266\pi\) | ||||
−0.135507 | + | 0.990776i | \(0.543266\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8423 | + | 20.5115i | −0.529076 | + | 0.916387i | ||||
\(502\) | − | 23.9309i | − | 1.06809i | ||||||
\(503\) | 21.0577 | + | 12.1577i | 0.938917 | + | 0.542084i | 0.889621 | − | 0.456700i | \(-0.150969\pi\) |
0.0492961 | + | 0.998784i | \(0.484302\pi\) | |||||||
\(504\) | −1.78078 | − | 3.08440i | −0.0793221 | − | 0.137390i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.31534 | 0.191840 | ||||||||
\(507\) | 3.57071 | + | 12.5000i | 0.158581 | + | 0.555144i | ||||
\(508\) | 21.8078i | 0.967563i | ||||||||
\(509\) | −8.12311 | − | 14.0696i | −0.360050 | − | 0.623625i | 0.627918 | − | 0.778279i | \(-0.283907\pi\) |
−0.987969 | + | 0.154654i | \(0.950574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0270 | − | 27.7596i | 0.708992 | − | 1.22801i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.11176 | + | 1.21922i | 0.0932364 | + | 0.0538300i | ||||
\(514\) | −6.80776 | + | 11.7914i | −0.300278 | + | 0.520096i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.219224 | + | 0.379706i | −0.00965078 | + | 0.0167156i | ||||
\(517\) | 1.94528 | − | 1.12311i | 0.0855531 | − | 0.0493941i | ||||
\(518\) | −1.73205 | + | 1.00000i | −0.0761019 | + | 0.0439375i | ||||
\(519\) | 8.87689 | 0.389652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7386 | 1.52193 | 0.760964 | − | 0.648795i | \(-0.224727\pi\) | ||||
0.760964 | + | 0.648795i | \(0.224727\pi\) | |||||||
\(522\) | −0.972638 | + | 0.561553i | −0.0425712 | + | 0.0245785i | ||||
\(523\) | 21.5908 | − | 12.4654i | 0.944098 | − | 0.545075i | 0.0528556 | − | 0.998602i | \(-0.483168\pi\) |
0.891243 | + | 0.453527i | \(0.149834\pi\) | |||||||
\(524\) | 0.438447 | − | 0.759413i | 0.0191537 | − | 0.0331751i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.15767 | + | 5.46925i | −0.137681 | + | 0.238470i | ||||
\(527\) | −10.8188 | − | 6.24621i | −0.471272 | − | 0.272089i | ||||
\(528\) | − | 0.561553i | − | 0.0244384i | ||||||
\(529\) | 18.0270 | − | 31.2237i | 0.783782 | − | 1.35755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.12311 | + | 8.87348i | 0.222324 | + | 0.385076i | ||||
\(532\) | − | 8.68466i | − | 0.376528i | ||||||
\(533\) | −4.22351 | + | 10.4384i | −0.182941 | + | 0.452139i | ||||
\(534\) | −10.2462 | −0.443397 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.90388 | − | 10.2258i | −0.255009 | − | 0.441688i | ||||
\(537\) | −13.5833 | − | 7.84233i | −0.586163 | − | 0.338421i | ||||
\(538\) | − | 3.36932i | − | 0.145262i | ||||||
\(539\) | −1.59612 | + | 2.76456i | −0.0687497 | + | 0.119078i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.3153 | −0.959411 | −0.479706 | − | 0.877429i | \(-0.659257\pi\) | ||||
−0.479706 | + | 0.877429i | \(0.659257\pi\) | |||||||
\(542\) | 7.73436 | + | 4.46543i | 0.332219 | + | 0.191807i | ||||
\(543\) | −13.4168 | + | 7.74621i | −0.575771 | + | 0.332422i | ||||
\(544\) | −1.56155 | − | 2.70469i | −0.0669510 | − | 0.115963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.9039 | + | 4.81645i | 0.509439 | + | 0.206125i | ||||
\(547\) | 30.9309i | 1.32251i | 0.750162 | + | 0.661254i | \(0.229976\pi\) | ||||
−0.750162 | + | 0.661254i | \(0.770024\pi\) | |||||||
\(548\) | 14.2829 | − | 8.24621i | 0.610133 | − | 0.352261i | ||||
\(549\) | −0.842329 | − | 1.45896i | −0.0359497 | − | 0.0622668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.73863 | −0.116670 | ||||||||
\(552\) | −6.65511 | − | 3.84233i | −0.283260 | − | 0.163540i | ||||
\(553\) | −48.7574 | − | 28.1501i | −2.07338 | − | 1.19706i | ||||
\(554\) | −5.00000 | −0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.7808 | − | 18.6729i | −0.457207 | − | 0.791905i | ||||
\(557\) | 27.3799 | − | 15.8078i | 1.16012 | − | 0.669796i | 0.208788 | − | 0.977961i | \(-0.433048\pi\) |
0.951333 | + | 0.308164i | \(0.0997147\pi\) | |||||||
\(558\) | 4.00000i | 0.169334i | ||||||||
\(559\) | −0.219224 | − | 1.56557i | −0.00927217 | − | 0.0662165i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.876894 | − | 1.51883i | −0.0370225 | − | 0.0641249i | ||||
\(562\) | 1.51883 | − | 0.876894i | 0.0640678 | − | 0.0369896i | ||||
\(563\) | −18.0201 | − | 10.4039i | −0.759455 | − | 0.438471i | 0.0696453 | − | 0.997572i | \(-0.477813\pi\) |
−0.829100 | + | 0.559100i | \(0.811147\pi\) | |||||||
\(564\) | −4.00000 | −0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.8078 | + | 25.6478i | −0.622417 | + | 1.07806i | ||||
\(567\) | 3.56155i | 0.149571i | ||||||||
\(568\) | −10.8786 | − | 6.28078i | −0.456457 | − | 0.263536i | ||||
\(569\) | −5.75379 | − | 9.96585i | −0.241211 | − | 0.417790i | 0.719848 | − | 0.694131i | \(-0.244211\pi\) |
−0.961060 | + | 0.276341i | \(0.910878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.4233 | 0.896537 | 0.448268 | − | 0.893899i | \(-0.352041\pi\) | ||||
0.448268 | + | 0.893899i | \(0.352041\pi\) | |||||||
\(572\) | 1.24573 | + | 1.59612i | 0.0520867 | + | 0.0667370i | ||||
\(573\) | 15.9309i | 0.665522i | ||||||||
\(574\) | 5.56155 | + | 9.63289i | 0.232135 | + | 0.402069i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 23.0000i | − | 0.957503i | −0.877951 | − | 0.478751i | \(-0.841090\pi\) | ||
0.877951 | − | 0.478751i | \(-0.158910\pi\) | |||||||
\(578\) | 6.27540 | + | 3.62311i | 0.261022 | + | 0.150701i | ||||
\(579\) | 1.50000 | − | 2.59808i | 0.0623379 | − | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6847 | − | 20.2384i | 0.484761 | − | 0.839631i | ||||
\(582\) | 2.43160 | − | 1.40388i | 0.100793 | − | 0.0581928i | ||||
\(583\) | −2.06501 | + | 1.19224i | −0.0855241 | + | 0.0493774i | ||||
\(584\) | −9.00000 | −0.372423 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.2462 | 0.836363 | ||||||||
\(587\) | 15.5286 | − | 8.96543i | 0.640933 | − | 0.370043i | −0.144041 | − | 0.989572i | \(-0.546010\pi\) |
0.784974 | + | 0.619529i | \(0.212676\pi\) | |||||||
\(588\) | 4.92306 | − | 2.84233i | 0.203024 | − | 0.117216i | ||||
\(589\) | −4.87689 | + | 8.44703i | −0.200949 | + | 0.348054i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.56155 | + | 4.43674i | −0.105368 | + | 0.182503i | ||||
\(592\) | 0.486319 | + | 0.280776i | 0.0199876 | + | 0.0115398i | ||||
\(593\) | − | 38.9848i | − | 1.60092i | −0.599389 | − | 0.800458i | \(-0.704590\pi\) | ||
0.599389 | − | 0.800458i | \(-0.295410\pi\) | |||||||
\(594\) | −0.280776 | + | 0.486319i | −0.0115204 | + | 0.0199539i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.12311 | + | 8.87348i | 0.209851 | + | 0.363472i | ||||
\(597\) | 4.43845i | 0.181654i | ||||||||
\(598\) | 27.4397 | − | 3.84233i | 1.12209 | − | 0.157125i | ||||
\(599\) | 18.3153 | 0.748345 | 0.374172 | − | 0.927359i | \(-0.377927\pi\) | ||||
0.374172 | + | 0.927359i | \(0.377927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.90388 | + | 5.02967i | 0.118452 | + | 0.205165i | 0.919154 | − | 0.393898i | \(-0.128874\pi\) |
−0.800703 | + | 0.599062i | \(0.795540\pi\) | |||||||
\(602\) | −1.35234 | − | 0.780776i | −0.0551174 | − | 0.0318221i | ||||
\(603\) | 11.8078i | 0.480849i | ||||||||
\(604\) | −8.34233 | + | 14.4493i | −0.339445 | + | 0.587935i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.24621 | −0.253735 | ||||||||
\(607\) | −34.0948 | − | 19.6847i | −1.38387 | − | 0.798976i | −0.391252 | − | 0.920284i | \(-0.627958\pi\) |
−0.992615 | + | 0.121308i | \(0.961291\pi\) | |||||||
\(608\) | −2.11176 | + | 1.21922i | −0.0856431 | + | 0.0494460i | ||||
\(609\) | −2.00000 | − | 3.46410i | −0.0810441 | − | 0.140372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3693 | − | 8.87348i | 0.459953 | − | 0.358983i | ||||
\(612\) | 3.12311i | 0.126244i | ||||||||
\(613\) | −31.6501 | + | 18.2732i | −1.27834 | + | 0.738048i | −0.976542 | − | 0.215326i | \(-0.930919\pi\) |
−0.301794 | + | 0.953373i | \(0.597585\pi\) | |||||||
\(614\) | 11.1231 | + | 19.2658i | 0.448892 | + | 0.777504i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | 41.0230 | + | 23.6847i | 1.65153 | + | 0.953508i | 0.976446 | + | 0.215763i | \(0.0692240\pi\) |
0.675079 | + | 0.737745i | \(0.264109\pi\) | |||||||
\(618\) | 3.84381 | + | 2.21922i | 0.154621 | + | 0.0892703i | ||||
\(619\) | 12.3002 | 0.494386 | 0.247193 | − | 0.968966i | \(-0.420492\pi\) | ||||
0.247193 | + | 0.968966i | \(0.420492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.84233 | + | 6.65511i | 0.154187 | + | 0.267060i | ||||
\(622\) | 8.93335 | − | 5.15767i | 0.358195 | − | 0.206804i | ||||
\(623\) | − | 36.4924i | − | 1.46204i | ||||||
\(624\) | −0.500000 | − | 3.57071i | −0.0200160 | − | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5000 | − | 26.8468i | −0.619505 | − | 1.07301i | ||||
\(627\) | −1.18586 | + | 0.684658i | −0.0473588 | + | 0.0273426i | ||||
\(628\) | −14.9357 | − | 8.62311i | −0.595998 | − | 0.344099i | ||||
\(629\) | 1.75379 | 0.0699281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.4654 | + | 28.5190i | −0.655479 | + | 1.13532i | 0.326295 | + | 0.945268i | \(0.394200\pi\) |
−0.981774 | + | 0.190054i | \(0.939134\pi\) | |||||||
\(632\) | 15.8078i | 0.628799i | ||||||||
\(633\) | −0.972638 | − | 0.561553i | −0.0386589 | − | 0.0223197i | ||||
\(634\) | 8.12311 | + | 14.0696i | 0.322610 | + | 0.558776i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.24621 | 0.168373 | ||||||||
\(637\) | −7.68762 | + | 19.0000i | −0.304594 | + | 0.752807i | ||||
\(638\) | − | 0.630683i | − | 0.0249690i | ||||||
\(639\) | 6.28078 | + | 10.8786i | 0.248464 | + | 0.430352i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1231 | + | 33.1222i | −0.755317 | + | 1.30825i | 0.189899 | + | 0.981804i | \(0.439184\pi\) |
−0.945216 | + | 0.326444i | \(0.894149\pi\) | |||||||
\(642\) | − | 5.36932i | − | 0.211910i | ||||||
\(643\) | −21.2578 | − | 12.2732i | −0.838326 | − | 0.484008i | 0.0183689 | − | 0.999831i | \(-0.494153\pi\) |
−0.856695 | + | 0.515824i | \(0.827486\pi\) | |||||||
\(644\) | 13.6847 | − | 23.7025i | 0.539251 | − | 0.934010i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.80776 | + | 6.59524i | −0.149814 | + | 0.259486i | ||||
\(647\) | −28.0794 | + | 16.2116i | −1.10391 | + | 0.637346i | −0.937247 | − | 0.348667i | \(-0.886634\pi\) |
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −5.75379 | −0.225856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.2462 | −0.558353 | ||||||||
\(652\) | 14.2829 | − | 8.24621i | 0.559360 | − | 0.322947i | ||||
\(653\) | −32.5760 | + | 18.8078i | −1.27480 | + | 0.736005i | −0.975887 | − | 0.218276i | \(-0.929957\pi\) |
−0.298911 | + | 0.954281i | \(0.596623\pi\) | |||||||
\(654\) | −1.40388 | + | 2.43160i | −0.0548961 | + | 0.0950829i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.56155 | − | 2.70469i | 0.0609684 | − | 0.105600i | ||||
\(657\) | 7.79423 | + | 4.50000i | 0.304082 | + | 0.175562i | ||||
\(658\) | − | 14.2462i | − | 0.555375i | ||||||
\(659\) | 9.15767 | − | 15.8616i | 0.356732 | − | 0.617878i | −0.630681 | − | 0.776042i | \(-0.717224\pi\) |
0.987413 | + | 0.158164i | \(0.0505575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.2732 | + | 42.0424i | 0.944118 | + | 1.63526i | 0.757508 | + | 0.652826i | \(0.226417\pi\) |
0.186610 | + | 0.982434i | \(0.440250\pi\) | |||||||
\(662\) | 16.6847i | 0.648468i | ||||||||
\(663\) | −6.92820 | − | 8.87689i | −0.269069 | − | 0.344750i | ||||
\(664\) | −6.56155 | −0.254638 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.280776 | − | 0.486319i | −0.0108799 | − | 0.0188445i | ||||
\(667\) | −7.47439 | − | 4.31534i | −0.289410 | − | 0.167091i | ||||
\(668\) | 23.6847i | 0.916387i | ||||||||
\(669\) | −0.219224 | + | 0.379706i | −0.00847567 | + | 0.0146803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.946025 | 0.0365209 | ||||||||
\(672\) | −3.08440 | − | 1.78078i | −0.118983 | − | 0.0686949i | ||||
\(673\) | 24.9015 | − | 14.3769i | 0.959883 | − | 0.554189i | 0.0637458 | − | 0.997966i | \(-0.479695\pi\) |
0.896137 | + | 0.443778i | \(0.146362\pi\) | |||||||
\(674\) | 4.02699 | + | 6.97495i | 0.155114 | + | 0.268665i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.34233 | + | 9.03996i | 0.359320 | + | 0.347691i | ||||
\(677\) | − | 11.6155i | − | 0.446421i | −0.974770 | − | 0.223211i | \(-0.928346\pi\) | ||
0.974770 | − | 0.223211i | \(-0.0716537\pi\) | |||||||
\(678\) | 3.46410 | − | 2.00000i | 0.133038 | − | 0.0768095i | ||||
\(679\) | 5.00000 | + | 8.66025i | 0.191882 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.6847 | 1.13752 | ||||||||
\(682\) | −1.94528 | − | 1.12311i | −0.0744885 | − | 0.0430059i | ||||
\(683\) | −13.3701 | − | 7.71922i | −0.511592 | − | 0.295368i | 0.221896 | − | 0.975070i | \(-0.428776\pi\) |
−0.733488 | + | 0.679703i | \(0.762109\pi\) | |||||||
\(684\) | 2.43845 | 0.0932364 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.34233 | − | 4.05703i | −0.0894305 | − | 0.154898i | ||||
\(687\) | −8.22068 | + | 4.74621i | −0.313638 | + | 0.181079i | ||||
\(688\) | 0.438447i | 0.0167156i | ||||||||
\(689\) | −12.0691 | + | 9.41967i | −0.459797 | + | 0.358861i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.41146 | + | 4.17677i | 0.0917362 | + | 0.158892i | 0.908242 | − | 0.418446i | \(-0.137425\pi\) |
−0.816506 | + | 0.577338i | \(0.804092\pi\) | |||||||
\(692\) | 7.68762 | − | 4.43845i | 0.292239 | − | 0.168724i | ||||
\(693\) | −1.73205 | − | 1.00000i | −0.0657952 | − | 0.0379869i | ||||
\(694\) | 24.8078 | 0.941690 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.561553 | + | 0.972638i | −0.0212856 | + | 0.0368677i | ||||
\(697\) | − | 9.75379i | − | 0.369451i | ||||||
\(698\) | 16.6677 | + | 9.62311i | 0.630882 | + | 0.364240i | ||||
\(699\) | −12.6847 | − | 21.9705i | −0.479778 | − | 0.831000i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.876894 | −0.0331198 | −0.0165599 | − | 0.999863i | \(-0.505271\pi\) | ||||
−0.0165599 | + | 0.999863i | \(0.505271\pi\) | |||||||
\(702\) | −1.35234 | + | 3.34233i | −0.0510410 | + | 0.126148i | ||||
\(703\) | − | 1.36932i | − | 0.0516448i | ||||||
\(704\) | −0.280776 | − | 0.486319i | −0.0105822 | − | 0.0183288i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.12311 | + | 1.94528i | −0.0422686 | + | 0.0732114i | ||||
\(707\) | − | 22.2462i | − | 0.836655i | ||||||
\(708\) | 8.87348 | + | 5.12311i | 0.333486 | + | 0.192538i | ||||
\(709\) | −14.3769 | + | 24.9015i | −0.539936 | + | 0.935196i | 0.458971 | + | 0.888451i | \(0.348218\pi\) |
−0.998907 | + | 0.0467448i | \(0.985115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.90388 | − | 13.6899i | 0.296419 | − | 0.513412i | ||||
\(712\) | −8.87348 | + | 5.12311i | −0.332548 | + | 0.191997i | ||||
\(713\) | −26.6204 | + | 15.3693i | −0.996943 | + | 0.575585i | ||||
\(714\) | −11.1231 | −0.416272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.6847 | −0.586163 | ||||||||
\(717\) | −23.4294 | + | 13.5270i | −0.874988 | + | 0.505175i | ||||
\(718\) | −4.22351 | + | 2.43845i | −0.157620 | + | 0.0910020i | ||||
\(719\) | −8.71922 | + | 15.1021i | −0.325172 | + | 0.563215i | −0.981547 | − | 0.191220i | \(-0.938756\pi\) |
0.656375 | + | 0.754435i | \(0.272089\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.90388 | + | 13.6899i | −0.294356 | + | 0.509839i | ||||
\(722\) | −11.3051 | − | 6.52699i | −0.420731 | − | 0.242909i | ||||
\(723\) | 15.5616i | 0.578740i | ||||||||
\(724\) | −7.74621 | + | 13.4168i | −0.287886 | + | 0.498633i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.34233 | + | 9.25319i | 0.198272 | + | 0.343418i | ||||
\(727\) | 50.7926i | 1.88379i | 0.335902 | + | 0.941897i | \(0.390959\pi\) | ||||
−0.335902 | + | 0.941897i | \(0.609041\pi\) | |||||||
\(728\) | 12.7173 | − | 1.78078i | 0.471334 | − | 0.0660000i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.684658 | + | 1.18586i | 0.0253230 | + | 0.0438607i | ||||
\(732\) | −1.45896 | − | 0.842329i | −0.0539246 | − | 0.0311334i | ||||
\(733\) | − | 47.9848i | − | 1.77236i | −0.463340 | − | 0.886180i | \(-0.653349\pi\) | ||
0.463340 | − | 0.886180i | \(-0.346651\pi\) | |||||||
\(734\) | −5.09612 | + | 8.82674i | −0.188101 | + | 0.325801i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.68466 | −0.283260 | ||||||||
\(737\) | −5.74234 | − | 3.31534i | −0.211522 | − | 0.122122i | ||||
\(738\) | −2.70469 | + | 1.56155i | −0.0995610 | + | 0.0574816i | ||||
\(739\) | −6.56155 | − | 11.3649i | −0.241371 | − | 0.418066i | 0.719734 | − | 0.694250i | \(-0.244264\pi\) |
−0.961105 | + | 0.276183i | \(0.910930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.93087 | + | 5.40938i | −0.254612 | + | 0.198718i | ||||
\(742\) | 15.1231i | 0.555187i | ||||||||
\(743\) | 9.63289 | − | 5.56155i | 0.353397 | − | 0.204034i | −0.312784 | − | 0.949824i | \(-0.601261\pi\) |
0.666180 | + | 0.745791i | \(0.267928\pi\) | |||||||
\(744\) | 2.00000 | + | 3.46410i | 0.0733236 | + | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.49242 | −0.347542 | ||||||||
\(747\) | 5.68247 | + | 3.28078i | 0.207911 | + | 0.120037i | ||||
\(748\) | −1.51883 | − | 0.876894i | −0.0555338 | − | 0.0320624i | ||||
\(749\) | 19.1231 | 0.698743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.1231 | − | 43.5145i | −0.916755 | − | 1.58787i | −0.804311 | − | 0.594208i | \(-0.797465\pi\) |
−0.112444 | − | 0.993658i | \(-0.535868\pi\) | |||||||
\(752\) | −3.46410 | + | 2.00000i | −0.126323 | + | 0.0729325i | ||||
\(753\) | 23.9309i | 0.872089i | ||||||||
\(754\) | −0.561553 | − | 4.01029i | −0.0204505 | − | 0.146046i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.78078 | + | 3.08440i | 0.0647662 | + | 0.112178i | ||||
\(757\) | 26.5737 | − | 15.3423i | 0.965837 | − | 0.557626i | 0.0678727 | − | 0.997694i | \(-0.478379\pi\) |
0.897965 | + | 0.440068i | \(0.145046\pi\) | |||||||
\(758\) | 20.8314 | + | 12.0270i | 0.756629 | + | 0.436840i | ||||
\(759\) | −4.31534 | −0.156637 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4924 | − | 19.9055i | 0.416600 | − | 0.721572i | −0.578995 | − | 0.815331i | \(-0.696555\pi\) |
0.995595 | + | 0.0937588i | \(0.0298882\pi\) | |||||||
\(762\) | − | 21.8078i | − | 0.790012i | ||||||
\(763\) | −8.66025 | − | 5.00000i | −0.313522 | − | 0.181012i | ||||
\(764\) | 7.96543 | + | 13.7965i | 0.288179 | + | 0.499141i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.43845 | −0.196499 | ||||||||
\(767\) | −36.5863 | + | 5.12311i | −1.32105 | + | 0.184985i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −4.65767 | − | 8.06732i | −0.167960 | − | 0.290915i | 0.769743 | − | 0.638354i | \(-0.220385\pi\) |
−0.937702 | + | 0.347439i | \(0.887051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.80776 | − | 11.7914i | 0.245176 | − | 0.424657i | ||||
\(772\) | − | 3.00000i | − | 0.107972i | ||||||
\(773\) | 25.6478 | + | 14.8078i | 0.922487 | + | 0.532598i | 0.884428 | − | 0.466677i | \(-0.154549\pi\) |
0.0380595 | + | 0.999275i | \(0.487882\pi\) | |||||||
\(774\) | 0.219224 | − | 0.379706i | 0.00787983 | − | 0.0136483i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.40388 | − | 2.43160i | 0.0503964 | − | 0.0872892i | ||||
\(777\) | 1.73205 | − | 1.00000i | 0.0621370 | − | 0.0358748i | ||||
\(778\) | 9.84612 | − | 5.68466i | 0.353000 | − | 0.203805i | ||||
\(779\) | −7.61553 | −0.272855 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.05398 | −0.252411 | ||||||||
\(782\) | −20.7846 | + | 12.0000i | −0.743256 | + | 0.429119i | ||||
\(783\) | 0.972638 | − | 0.561553i | 0.0347592 | − | 0.0200683i | ||||
\(784\) | 2.84233 | − | 4.92306i | 0.101512 | − | 0.175824i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.438447 | + | 0.759413i | −0.0156389 | + | 0.0270874i | ||||
\(787\) | −10.3923 | − | 6.00000i | −0.370446 | − | 0.213877i | 0.303207 | − | 0.952925i | \(-0.401942\pi\) |
−0.673653 | + | 0.739048i | \(0.735276\pi\) | |||||||
\(788\) | 5.12311i | 0.182503i | ||||||||
\(789\) | 3.15767 | − | 5.46925i | 0.112416 | − | 0.194710i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.12311 | + | 12.3376i | 0.253268 | + | 0.438674i | ||||
\(792\) | 0.561553i | 0.0199539i | ||||||||
\(793\) | 6.01543 | − | 0.842329i | 0.213614 | − | 0.0299120i | ||||
\(794\) | 9.80776 | 0.348065 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.21922 | + | 3.84381i | 0.0786583 | + | 0.136240i | ||||
\(797\) | −22.7299 | − | 13.1231i | −0.805134 | − | 0.464844i | 0.0401293 | − | 0.999194i | \(-0.487223\pi\) |
−0.845263 | + | 0.534350i | \(0.820556\pi\) | |||||||
\(798\) | 8.68466i | 0.307434i | ||||||||
\(799\) | −6.24621 | + | 10.8188i | −0.220975 | + | 0.382740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2462 | 0.362032 | ||||||||
\(802\) | −10.9385 | − | 6.31534i | −0.386252 | − | 0.223002i | ||||
\(803\) | −4.37687 | + | 2.52699i | −0.154456 | + | 0.0891755i | ||||
\(804\) | 5.90388 | + | 10.2258i | 0.208214 | + | 0.360637i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.3693 | − | 5.40938i | −0.470914 | − | 0.190537i | ||||
\(807\) | 3.36932i | 0.118606i | ||||||||
\(808\) | −5.40938 | + | 3.12311i | −0.190301 | + | 0.109870i | ||||
\(809\) | 15.8078 | + | 27.3799i | 0.555771 | + | 0.962624i | 0.997843 | + | 0.0656446i | \(0.0209103\pi\) |
−0.442072 | + | 0.896980i | \(0.645756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9309 | −0.594523 | −0.297262 | − | 0.954796i | \(-0.596073\pi\) | ||||
−0.297262 | + | 0.954796i | \(0.596073\pi\) | |||||||
\(812\) | −3.46410 | − | 2.00000i | −0.121566 | − | 0.0701862i | ||||
\(813\) | −7.73436 | − | 4.46543i | −0.271256 | − | 0.156610i | ||||
\(814\) | 0.315342 | 0.0110527 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.56155 | + | 2.70469i | 0.0546653 | + | 0.0946830i | ||||
\(817\) | 0.925894 | − | 0.534565i | 0.0323929 | − | 0.0187021i | ||||
\(818\) | 16.2462i | 0.568035i | ||||||||
\(819\) | −11.9039 | − | 4.81645i | −0.415955 | − | 0.168300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.4924 | − | 33.7619i | −0.680290 | − | 1.17830i | −0.974892 | − | 0.222677i | \(-0.928520\pi\) |
0.294602 | − | 0.955620i | \(-0.404813\pi\) | |||||||
\(822\) | −14.2829 | + | 8.24621i | −0.498172 | + | 0.287620i | ||||
\(823\) | −43.9877 | − | 25.3963i | −1.53331 | − | 0.885260i | −0.999206 | − | 0.0398436i | \(-0.987314\pi\) |
−0.534109 | − | 0.845416i | \(-0.679353\pi\) | |||||||
\(824\) | 4.43845 | 0.154621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.2462 | + | 31.6034i | −0.634867 | + | 1.09962i | ||||
\(827\) | − | 6.06913i | − | 0.211044i | −0.994417 | − | 0.105522i | \(-0.966349\pi\) | ||
0.994417 | − | 0.105522i | \(-0.0336514\pi\) | |||||||
\(828\) | 6.65511 | + | 3.84233i | 0.231281 | + | 0.133530i | ||||
\(829\) | 6.27320 | + | 10.8655i | 0.217877 | + | 0.377374i | 0.954159 | − | 0.299301i | \(-0.0967534\pi\) |
−0.736282 | + | 0.676675i | \(0.763420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | 0.173448 | ||||||||
\(832\) | −2.21837 | − | 2.84233i | −0.0769081 | − | 0.0985400i | ||||
\(833\) | − | 17.7538i | − | 0.615132i | ||||||
\(834\) | 10.7808 | + | 18.6729i | 0.373308 | + | 0.646588i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.684658 | + | 1.18586i | −0.0236794 | + | 0.0410139i | ||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | 10.3324 | + | 5.96543i | 0.356928 | + | 0.206073i | ||||
\(839\) | 6.84233 | − | 11.8513i | 0.236223 | − | 0.409151i | −0.723404 | − | 0.690425i | \(-0.757424\pi\) |
0.959628 | + | 0.281274i | \(0.0907569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8693 | − | 24.0224i | 0.478252 | − | 0.828357i | ||||
\(842\) | −27.0600 | + | 15.6231i | −0.932550 | + | 0.538408i | ||||
\(843\) | −1.51883 | + | 0.876894i | −0.0523111 | + | 0.0302018i | ||||
\(844\) | −1.12311 | −0.0386589 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | −32.9557 | + | 19.0270i | −1.13237 | + | 0.653775i | ||||
\(848\) | 3.67733 | − | 2.12311i | 0.126280 | − | 0.0729077i | ||||
\(849\) | 14.8078 | − | 25.6478i | 0.508201 | − | 0.880230i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.15767 | − | 3.73720i | 0.0739640 | − | 0.128109i | ||||
\(852\) | 10.8786 | + | 6.28078i | 0.372696 | + | 0.215176i | ||||
\(853\) | 18.9848i | 0.650029i | 0.945709 | + | 0.325014i | \(0.105369\pi\) | ||||
−0.945709 | + | 0.325014i | \(0.894631\pi\) | |||||||
\(854\) | 3.00000 | − | 5.19615i | 0.102658 | − | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.68466 | − | 4.64996i | −0.0917597 | − | 0.158933i | ||||
\(857\) | 56.2462i | 1.92133i | 0.277703 | + | 0.960667i | \(0.410427\pi\) | ||||
−0.277703 | + | 0.960667i | \(0.589573\pi\) | |||||||
\(858\) | −1.24573 | − | 1.59612i | −0.0425286 | − | 0.0544906i | ||||
\(859\) | −27.4233 | −0.935671 | −0.467835 | − | 0.883816i | \(-0.654966\pi\) | ||||
−0.467835 | + | 0.883816i | \(0.654966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.56155 | − | 9.63289i | −0.189537 | − | 0.328288i | ||||
\(862\) | 15.8616 | + | 9.15767i | 0.540247 | + | 0.311912i | ||||
\(863\) | 2.06913i | 0.0704340i | 0.999380 | + | 0.0352170i | \(0.0112122\pi\) | ||||
−0.999380 | + | 0.0352170i | \(0.988788\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.6847 | −0.465024 | ||||||||
\(867\) | −6.27540 | − | 3.62311i | −0.213124 | − | 0.123047i | ||||
\(868\) | −12.3376 | + | 7.12311i | −0.418765 | + | 0.241774i | ||||
\(869\) | 4.43845 | + | 7.68762i | 0.150564 | + | 0.260785i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.4654 | − | 15.9682i | −1.33724 | − | 0.541061i | ||||
\(872\) | 2.80776i | 0.0950829i | ||||||||
\(873\) | −2.43160 | + | 1.40388i | −0.0822970 | + | 0.0475142i | ||||
\(874\) | 9.36932 | + | 16.2281i | 0.316922 | + | 0.548925i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | 37.6655 | + | 21.7462i | 1.27188 | + | 0.734317i | 0.975341 | − | 0.220705i | \(-0.0708357\pi\) |
0.296534 | + | 0.955022i | \(0.404169\pi\) | |||||||
\(878\) | 6.00231 | + | 3.46543i | 0.202568 | + | 0.116953i | ||||
\(879\) | −20.2462 | −0.682888 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5616 | − | 42.5419i | −0.827500 | − | 1.43327i | −0.899994 | − | 0.435903i | \(-0.856429\pi\) |
0.0724940 | − | 0.997369i | \(-0.476904\pi\) | |||||||
\(882\) | −4.92306 | + | 2.84233i | −0.165768 | + | 0.0957062i | ||||
\(883\) | 34.2462i | 1.15248i | 0.817282 | + | 0.576238i | \(0.195480\pi\) | ||||
−0.817282 | + | 0.576238i | \(0.804520\pi\) | |||||||
\(884\) | −10.4384 | − | 4.22351i | −0.351083 | − | 0.142052i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.40388 | + | 2.43160i | 0.0471643 | + | 0.0816910i | ||||
\(887\) | 35.8269 | − | 20.6847i | 1.20295 | − | 0.694523i | 0.241739 | − | 0.970341i | \(-0.422282\pi\) |
0.961210 | + | 0.275818i | \(0.0889488\pi\) | |||||||
\(888\) | −0.486319 | − | 0.280776i | −0.0163198 | − | 0.00942224i | ||||
\(889\) | 77.6695 | 2.60495 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.280776 | − | 0.486319i | 0.00940636 | − | 0.0162923i | ||||
\(892\) | 0.438447i | 0.0146803i | ||||||||
\(893\) | 8.44703 | + | 4.87689i | 0.282669 | + | 0.163199i | ||||
\(894\) | −5.12311 | − | 8.87348i | −0.171342 | − | 0.296774i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.56155 | −0.118983 | ||||||||
\(897\) | −27.4397 | + | 3.84233i | −0.916186 | + | 0.128292i | ||||
\(898\) | − | 3.12311i | − | 0.104219i | ||||||
\(899\) | 2.24621 | + | 3.89055i | 0.0749153 | + | 0.129757i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.63068 | − | 11.4847i | 0.220900 | − | 0.382610i | ||||
\(902\) | − | 1.75379i | − | 0.0583948i | ||||||
\(903\) | 1.35234 | + | 0.780776i | 0.0450032 | + | 0.0259826i | ||||
\(904\) | 2.00000 | − | 3.46410i | 0.0665190 | − | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.34233 | − | 14.4493i | 0.277155 | − | 0.480047i | ||||
\(907\) | 3.34436 | − | 1.93087i | 0.111048 | − | 0.0641135i | −0.443447 | − | 0.896300i | \(-0.646245\pi\) |
0.554495 | + | 0.832187i | \(0.312911\pi\) | |||||||
\(908\) | 25.7077 | − | 14.8423i | 0.853139 | − | 0.492560i | ||||
\(909\) | 6.24621 | 0.207174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.6847 | 1.31481 | 0.657406 | − | 0.753537i | \(-0.271654\pi\) | ||||
0.657406 | + | 0.753537i | \(0.271654\pi\) | |||||||
\(912\) | 2.11176 | − | 1.21922i | 0.0699273 | − | 0.0403725i | ||||
\(913\) | −3.19101 | + | 1.84233i | −0.105607 | + | 0.0609722i | ||||
\(914\) | 2.25379 | − | 3.90368i | 0.0745487 | − | 0.129122i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.74621 | + | 8.22068i | −0.156819 | + | 0.271619i | ||||
\(917\) | −2.70469 | − | 1.56155i | −0.0893167 | − | 0.0515670i | ||||
\(918\) | − | 3.12311i | − | 0.103078i | ||||||
\(919\) | 13.6577 | − | 23.6558i | 0.450525 | − | 0.780332i | −0.547894 | − | 0.836548i | \(-0.684570\pi\) |
0.998419 | + | 0.0562158i | \(0.0179035\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1231 | − | 19.2658i | −0.366519 | − | 0.634829i | ||||
\(922\) | − | 10.6307i | − | 0.350103i | ||||||
\(923\) | −44.8537 | + | 6.28078i | −1.47638 | + | 0.206734i | ||||
\(924\) | −2.00000 | −0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.9039 | − | 24.0822i | −0.456910 | − | 0.791391i | ||||
\(927\) | −3.84381 | − | 2.21922i | −0.126247 | − | 0.0728889i | ||||
\(928\) | 1.12311i | 0.0368677i | ||||||||
\(929\) | −24.9309 | + | 43.1815i | −0.817955 | + | 1.41674i | 0.0892310 | + | 0.996011i | \(0.471559\pi\) |
−0.907186 | + | 0.420729i | \(0.861774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8617 | −0.454300 | ||||||||
\(932\) | −21.9705 | − | 12.6847i | −0.719667 | − | 0.415500i | ||||
\(933\) | −8.93335 | + | 5.15767i | −0.292465 | + | 0.168855i | ||||
\(934\) | −1.71922 | − | 2.97778i | −0.0562547 | − | 0.0974360i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 3.57071i | 0.0163430 | + | 0.116712i | ||||
\(937\) | 11.2462i | 0.367398i | 0.982983 | + | 0.183699i | \(0.0588071\pi\) | ||||
−0.982983 | + | 0.183699i | \(0.941193\pi\) | |||||||
\(938\) | −36.4198 | + | 21.0270i | −1.18915 | + | 0.686555i | ||||
\(939\) | 15.5000 | + | 26.8468i | 0.505823 | + | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6307 | 1.12893 | 0.564464 | − | 0.825458i | \(-0.309083\pi\) | ||||
0.564464 | + | 0.825458i | \(0.309083\pi\) | |||||||
\(942\) | 14.9357 | + | 8.62311i | 0.486630 | + | 0.280956i | ||||
\(943\) | −20.7846 | − | 12.0000i | −0.676840 | − | 0.390774i | ||||
\(944\) | 10.2462 | 0.333486 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.123106 | + | 0.213225i | 0.00400251 | + | 0.00693255i | ||||
\(947\) | −40.4170 | + | 23.3348i | −1.31338 | + | 0.758278i | −0.982654 | − | 0.185451i | \(-0.940625\pi\) |
−0.330722 | + | 0.943728i | \(0.607292\pi\) | |||||||
\(948\) | − | 15.8078i | − | 0.513412i | ||||||
\(949\) | −25.5810 | + | 19.9653i | −0.830393 | + | 0.648102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.12311 | − | 14.0696i | −0.263410 | − | 0.456239i | ||||
\(952\) | −9.63289 | + | 5.56155i | −0.312204 | + | 0.180251i | ||||
\(953\) | 7.14143 | + | 4.12311i | 0.231334 | + | 0.133560i | 0.611187 | − | 0.791486i | \(-0.290692\pi\) |
−0.379854 | + | 0.925047i | \(0.624026\pi\) | |||||||
\(954\) | −4.24621 | −0.137476 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.5270 | + | 23.4294i | −0.437494 | + | 0.757762i | ||||
\(957\) | 0.630683i | 0.0203871i | ||||||||
\(958\) | 10.0593 | + | 5.80776i | 0.325003 | + | 0.187640i | ||||
\(959\) | −29.3693 | − | 50.8691i | −0.948385 | − | 1.64265i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 2.00514 | − | 0.280776i | 0.0646485 | − | 0.00905259i | ||||
\(963\) | 5.36932i | 0.173024i | ||||||||
\(964\) | 7.78078 | + | 13.4767i | 0.250602 | + | 0.434055i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.6847 | + | 23.7025i | −0.440297 | + | 0.762616i | ||||
\(967\) | − | 16.6307i | − | 0.534807i | −0.963585 | − | 0.267403i | \(-0.913834\pi\) | ||
0.963585 | − | 0.267403i | \(-0.0861656\pi\) | |||||||
\(968\) | 9.25319 | + | 5.34233i | 0.297409 | + | 0.171709i | ||||
\(969\) | 3.80776 | − | 6.59524i | 0.122323 | − | 0.211870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.31534 | + | 12.6705i | −0.234760 | + | 0.406617i | −0.959203 | − | 0.282718i | \(-0.908764\pi\) |
0.724443 | + | 0.689335i | \(0.242097\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | −66.5044 | + | 38.3963i | −2.13203 | + | 1.23093i | ||||
\(974\) | −42.6847 | −1.36770 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.68466 | −0.0539246 | ||||||||
\(977\) | 40.0504 | − | 23.1231i | 1.28133 | − | 0.739774i | 0.304235 | − | 0.952597i | \(-0.401599\pi\) |
0.977091 | + | 0.212823i | \(0.0682659\pi\) | |||||||
\(978\) | −14.2829 | + | 8.24621i | −0.456715 | + | 0.263685i | ||||
\(979\) | −2.87689 | + | 4.98293i | −0.0919459 | + | 0.159255i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40388 | − | 2.43160i | 0.0448225 | − | 0.0776349i | ||||
\(982\) | 27.1068 | + | 15.6501i | 0.865011 | + | 0.499415i | ||||
\(983\) | − | 22.2462i | − | 0.709544i | −0.934953 | − | 0.354772i | \(-0.884559\pi\) | ||
0.934953 | − | 0.354772i | \(-0.115441\pi\) | |||||||
\(984\) | −1.56155 | + | 2.70469i | −0.0497805 | + | 0.0862223i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.75379 | + | 3.03765i | 0.0558520 | + | 0.0967385i | ||||
\(987\) | 14.2462i | 0.453462i | ||||||||
\(988\) | −3.29762 | + | 8.15009i | −0.104911 | + | 0.259289i | ||||
\(989\) | 3.36932 | 0.107138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.97301 | + | 17.2738i | 0.316803 | + | 0.548719i | 0.979819 | − | 0.199886i | \(-0.0640572\pi\) |
−0.663016 | + | 0.748605i | \(0.730724\pi\) | |||||||
\(992\) | 3.46410 | + | 2.00000i | 0.109985 | + | 0.0635001i | ||||
\(993\) | − | 16.6847i | − | 0.529472i | ||||||
\(994\) | −22.3693 | + | 38.7448i | −0.709512 | + | 1.22891i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.56155 | 0.207911 | ||||||||
\(997\) | 23.9625 | + | 13.8348i | 0.758900 | + | 0.438151i | 0.828901 | − | 0.559396i | \(-0.188967\pi\) |
−0.0700008 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(998\) | 5.24290 | − | 3.02699i | 0.165961 | − | 0.0958176i | ||||
\(999\) | 0.280776 | + | 0.486319i | 0.00888337 | + | 0.0153865i |
(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 | 1950.2.z.m.1849.1 | 8 | ||
5.2 | odd | 4 | 1950.2.i.z.601.2 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.i.bg.601.1 | yes | 4 | ||
5.4 | even | 2 | inner | 1950.2.z.m.1849.4 | 8 | ||
13.9 | even | 3 | inner | 1950.2.z.m.1699.4 | 8 | ||
65.9 | even | 6 | inner | 1950.2.z.m.1699.1 | 8 | ||
65.22 | odd | 12 | 1950.2.i.z.451.2 | ✓ | 4 | ||
65.48 | odd | 12 | 1950.2.i.bg.451.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.z.451.2 | ✓ | 4 | 65.22 | odd | 12 | ||
1950.2.i.z.601.2 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.i.bg.451.1 | yes | 4 | 65.48 | odd | 12 | ||
1950.2.i.bg.601.1 | yes | 4 | 5.3 | odd | 4 | ||
1950.2.z.m.1699.1 | 8 | 65.9 | even | 6 | inner | ||
1950.2.z.m.1699.4 | 8 | 13.9 | even | 3 | inner | ||
1950.2.z.m.1849.1 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.m.1849.4 | 8 | 5.4 | even | 2 | inner |