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: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1699.3 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.1699 |
Dual form | 1950.2.z.n.1849.3 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 | −0.952685 | − | 0.303959i | \(-0.901692\pi\) |
−0.213107 | + | 0.977029i | \(0.568358\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.06155 | − | 3.57071i | 0.621582 | − | 1.07661i | −0.367610 | − | 0.929980i | \(-0.619824\pi\) |
0.989191 | − | 0.146631i | \(-0.0468429\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.35234 | − | 3.34233i | 0.375073 | − | 0.926995i | ||||
\(14\) | −3.56155 | −0.951865 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.43674 | + | 2.56155i | −1.07607 | + | 0.621268i | −0.929833 | − | 0.367982i | \(-0.880049\pi\) |
−0.146235 | + | 0.989250i | \(0.546715\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.78078 | − | 3.08440i | −0.408538 | − | 0.707609i | 0.586188 | − | 0.810175i | \(-0.300628\pi\) |
−0.994726 | + | 0.102566i | \(0.967295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.56155 | 0.777195 | ||||||||
\(22\) | 3.57071 | − | 2.06155i | 0.761279 | − | 0.439525i | ||||
\(23\) | 6.65511 | + | 3.84233i | 1.38769 | + | 0.801181i | 0.993054 | − | 0.117658i | \(-0.0375387\pi\) |
0.394632 | + | 0.918839i | \(0.370872\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.84233 | − | 2.21837i | 0.557427 | − | 0.435058i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.08440 | − | 1.78078i | −0.582896 | − | 0.336535i | ||||
\(29\) | 3.28078 | − | 5.68247i | 0.609225 | − | 1.05521i | −0.382144 | − | 0.924103i | \(-0.624814\pi\) |
0.991368 | − | 0.131105i | \(-0.0418527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.68466 | 1.02099 | 0.510497 | − | 0.859879i | \(-0.329461\pi\) | ||||
0.510497 | + | 0.859879i | \(0.329461\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | −3.57071 | + | 2.06155i | −0.621582 | + | 0.358870i | ||||
\(34\) | −5.12311 | −0.878605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 3.57071 | + | 2.06155i | 0.587022 | + | 0.338917i | 0.763919 | − | 0.645312i | \(-0.223273\pi\) |
−0.176897 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(38\) | − | 3.56155i | − | 0.577760i | ||||||
\(39\) | −2.84233 | + | 2.21837i | −0.455137 | + | 0.355223i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.12311 | − | 3.67733i | 0.331573 | − | 0.574302i | −0.651247 | − | 0.758866i | \(-0.725754\pi\) |
0.982821 | + | 0.184564i | \(0.0590872\pi\) | |||||||
\(42\) | 3.08440 | + | 1.78078i | 0.475933 | + | 0.274780i | ||||
\(43\) | 3.95042 | − | 2.28078i | 0.602433 | − | 0.347815i | −0.167565 | − | 0.985861i | \(-0.553590\pi\) |
0.769998 | + | 0.638046i | \(0.220257\pi\) | |||||||
\(44\) | 4.12311 | 0.621582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.84233 | + | 6.65511i | 0.566521 | + | 0.981242i | ||||
\(47\) | − | 7.00000i | − | 1.02105i | −0.859861 | − | 0.510527i | \(-0.829450\pi\) | ||
0.859861 | − | 0.510527i | \(-0.170550\pi\) | |||||||
\(48\) | 0.866025 | − | 0.500000i | 0.125000 | − | 0.0721688i | ||||
\(49\) | 2.84233 | − | 4.92306i | 0.406047 | − | 0.703294i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.12311 | 0.717378 | ||||||||
\(52\) | 3.57071 | − | 0.500000i | 0.495169 | − | 0.0693375i | ||||
\(53\) | 4.43845i | 0.609668i | 0.952406 | + | 0.304834i | \(0.0986009\pi\) | ||||
−0.952406 | + | 0.304834i | \(0.901399\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.78078 | − | 3.08440i | −0.237966 | − | 0.412170i | ||||
\(57\) | 3.56155i | 0.471739i | ||||||||
\(58\) | 5.68247 | − | 3.28078i | 0.746145 | − | 0.430787i | ||||
\(59\) | 5.28078 | + | 9.14657i | 0.687499 | + | 1.19078i | 0.972645 | + | 0.232298i | \(0.0746246\pi\) |
−0.285146 | + | 0.958484i | \(0.592042\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 4.92306 | + | 2.84233i | 0.625229 | + | 0.360976i | ||||
\(63\) | −3.08440 | − | 1.78078i | −0.388597 | − | 0.224357i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.12311 | −0.507519 | ||||||||
\(67\) | 12.3376 | + | 7.12311i | 1.50728 | + | 0.870226i | 0.999964 | + | 0.00846293i | \(0.00269387\pi\) |
0.507311 | + | 0.861763i | \(0.330639\pi\) | |||||||
\(68\) | −4.43674 | − | 2.56155i | −0.538034 | − | 0.310634i | ||||
\(69\) | −3.84233 | − | 6.65511i | −0.462562 | − | 0.801181i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.43845 | + | 4.22351i | 0.289390 | + | 0.501239i | 0.973664 | − | 0.227986i | \(-0.0732141\pi\) |
−0.684274 | + | 0.729225i | \(0.739881\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | − | 15.3693i | − | 1.79884i | −0.437083 | − | 0.899421i | \(-0.643988\pi\) | ||
0.437083 | − | 0.899421i | \(-0.356012\pi\) | |||||||
\(74\) | 2.06155 | + | 3.57071i | 0.239651 | + | 0.415087i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.78078 | − | 3.08440i | 0.204269 | − | 0.353804i | ||||
\(77\) | 14.6847i | 1.67347i | ||||||||
\(78\) | −3.57071 | + | 0.500000i | −0.404304 | + | 0.0566139i | ||||
\(79\) | −7.43845 | −0.836891 | −0.418445 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418445 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.67733 | − | 2.12311i | 0.406093 | − | 0.234458i | ||||
\(83\) | 1.12311i | 0.123277i | 0.998099 | + | 0.0616384i | \(0.0196326\pi\) | ||||
−0.998099 | + | 0.0616384i | \(0.980367\pi\) | |||||||
\(84\) | 1.78078 | + | 3.08440i | 0.194299 | + | 0.336535i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.56155 | 0.491885 | ||||||||
\(87\) | −5.68247 | + | 3.28078i | −0.609225 | + | 0.351736i | ||||
\(88\) | 3.57071 | + | 2.06155i | 0.380639 | + | 0.219762i | ||||
\(89\) | 0.903882 | − | 1.56557i | 0.0958113 | − | 0.165950i | −0.814136 | − | 0.580675i | \(-0.802789\pi\) |
0.909947 | + | 0.414725i | \(0.136122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.78078 | + | 12.7173i | 0.186676 | + | 1.33313i | ||||
\(92\) | 7.68466i | 0.801181i | ||||||||
\(93\) | −4.92306 | − | 2.84233i | −0.510497 | − | 0.294736i | ||||
\(94\) | 3.50000 | − | 6.06218i | 0.360997 | − | 0.625266i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.972638 | + | 0.561553i | −0.0987564 | + | 0.0570170i | −0.548565 | − | 0.836108i | \(-0.684826\pi\) |
0.449808 | + | 0.893125i | \(0.351492\pi\) | |||||||
\(98\) | 4.92306 | − | 2.84233i | 0.497304 | − | 0.287119i | ||||
\(99\) | 4.12311 | 0.414388 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.56155 | − | 14.8290i | 0.851906 | − | 1.47555i | −0.0275793 | − | 0.999620i | \(-0.508780\pi\) |
0.879486 | − | 0.475925i | \(-0.157887\pi\) | |||||||
\(102\) | 4.43674 | + | 2.56155i | 0.439303 | + | 0.253632i | ||||
\(103\) | 0.438447i | 0.0432015i | 0.999767 | + | 0.0216007i | \(0.00687626\pi\) | ||||
−0.999767 | + | 0.0216007i | \(0.993124\pi\) | |||||||
\(104\) | 3.34233 | + | 1.35234i | 0.327742 | + | 0.132608i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.21922 | + | 3.84381i | −0.215550 | + | 0.373344i | ||||
\(107\) | 1.73205 | + | 1.00000i | 0.167444 | + | 0.0966736i | 0.581380 | − | 0.813632i | \(-0.302513\pi\) |
−0.413936 | + | 0.910306i | \(0.635846\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 20.2462 | 1.93924 | 0.969618 | − | 0.244625i | \(-0.0786650\pi\) | ||||
0.969618 | + | 0.244625i | \(0.0786650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.06155 | − | 3.57071i | −0.195674 | − | 0.338917i | ||||
\(112\) | − | 3.56155i | − | 0.336535i | ||||||
\(113\) | −3.19101 | + | 1.84233i | −0.300185 | + | 0.173312i | −0.642526 | − | 0.766264i | \(-0.722113\pi\) |
0.342341 | + | 0.939576i | \(0.388780\pi\) | |||||||
\(114\) | −1.78078 | + | 3.08440i | −0.166785 | + | 0.288880i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.56155 | 0.609225 | ||||||||
\(117\) | 3.57071 | − | 0.500000i | 0.330113 | − | 0.0462250i | ||||
\(118\) | 10.5616i | 0.972270i | ||||||||
\(119\) | 9.12311 | − | 15.8017i | 0.836314 | − | 1.44854i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | ||||
\(122\) | − | 6.00000i | − | 0.543214i | ||||||
\(123\) | −3.67733 | + | 2.12311i | −0.331573 | + | 0.191434i | ||||
\(124\) | 2.84233 | + | 4.92306i | 0.255249 | + | 0.442104i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.78078 | − | 3.08440i | −0.158644 | − | 0.274780i | ||||
\(127\) | −3.84381 | − | 2.21922i | −0.341083 | − | 0.196924i | 0.319668 | − | 0.947530i | \(-0.396429\pi\) |
−0.660751 | + | 0.750605i | \(0.729762\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −4.56155 | −0.401622 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.12311 | 0.534978 | 0.267489 | − | 0.963561i | \(-0.413806\pi\) | ||||
0.267489 | + | 0.963561i | \(0.413806\pi\) | |||||||
\(132\) | −3.57071 | − | 2.06155i | −0.310791 | − | 0.179435i | ||||
\(133\) | 10.9852 | + | 6.34233i | 0.952541 | + | 0.549950i | ||||
\(134\) | 7.12311 | + | 12.3376i | 0.615343 | + | 1.06580i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.56155 | − | 4.43674i | −0.219651 | − | 0.380447i | ||||
\(137\) | 7.62775 | − | 4.40388i | 0.651682 | − | 0.376249i | −0.137418 | − | 0.990513i | \(-0.543880\pi\) |
0.789101 | + | 0.614264i | \(0.210547\pi\) | |||||||
\(138\) | − | 7.68466i | − | 0.654162i | ||||||
\(139\) | 4.21922 | + | 7.30791i | 0.357870 | + | 0.619849i | 0.987605 | − | 0.156961i | \(-0.0501698\pi\) |
−0.629735 | + | 0.776810i | \(0.716836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.50000 | + | 6.06218i | −0.294753 | + | 0.510527i | ||||
\(142\) | 4.87689i | 0.409260i | ||||||||
\(143\) | −9.14657 | − | 11.7192i | −0.764875 | − | 0.980011i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.68466 | − | 13.3102i | 0.635987 | − | 1.10156i | ||||
\(147\) | −4.92306 | + | 2.84233i | −0.406047 | + | 0.234431i | ||||
\(148\) | 4.12311i | 0.338917i | ||||||||
\(149\) | −11.4039 | − | 19.7521i | −0.934242 | − | 1.61816i | −0.775979 | − | 0.630758i | \(-0.782744\pi\) |
−0.158263 | − | 0.987397i | \(-0.550589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.36932 | 0.762464 | 0.381232 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381232 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(152\) | 3.08440 | − | 1.78078i | 0.250177 | − | 0.144440i | ||||
\(153\) | −4.43674 | − | 2.56155i | −0.358689 | − | 0.207089i | ||||
\(154\) | −7.34233 | + | 12.7173i | −0.591662 | + | 1.02479i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.34233 | − | 1.35234i | −0.267601 | − | 0.108274i | ||||
\(157\) | − | 22.1231i | − | 1.76562i | −0.469734 | − | 0.882808i | \(-0.655650\pi\) | ||
0.469734 | − | 0.882808i | \(-0.344350\pi\) | |||||||
\(158\) | −6.44188 | − | 3.71922i | −0.512489 | − | 0.295886i | ||||
\(159\) | 2.21922 | − | 3.84381i | 0.175996 | − | 0.304834i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.3693 | −2.15700 | ||||||||
\(162\) | −0.866025 | + | 0.500000i | −0.0680414 | + | 0.0392837i | ||||
\(163\) | −16.0748 | + | 9.28078i | −1.25907 | + | 0.726927i | −0.972894 | − | 0.231250i | \(-0.925719\pi\) |
−0.286179 | + | 0.958176i | \(0.592385\pi\) | |||||||
\(164\) | 4.24621 | 0.331573 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.561553 | + | 0.972638i | −0.0435850 | + | 0.0754913i | ||||
\(167\) | −17.6403 | − | 10.1847i | −1.36505 | − | 0.788113i | −0.374760 | − | 0.927122i | \(-0.622275\pi\) |
−0.990291 | + | 0.139009i | \(0.955608\pi\) | |||||||
\(168\) | 3.56155i | 0.274780i | ||||||||
\(169\) | −9.34233 | − | 9.03996i | −0.718641 | − | 0.695382i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.78078 | − | 3.08440i | 0.136179 | − | 0.235870i | ||||
\(172\) | 3.95042 | + | 2.28078i | 0.301217 | + | 0.173908i | ||||
\(173\) | −21.8040 | + | 12.5885i | −1.65773 | + | 0.957089i | −0.683966 | + | 0.729514i | \(0.739746\pi\) |
−0.973760 | + | 0.227575i | \(0.926920\pi\) | |||||||
\(174\) | −6.56155 | −0.497430 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.06155 | + | 3.57071i | 0.155395 | + | 0.269153i | ||||
\(177\) | − | 10.5616i | − | 0.793855i | ||||||
\(178\) | 1.56557 | − | 0.903882i | 0.117344 | − | 0.0677488i | ||||
\(179\) | −0.157671 | + | 0.273094i | −0.0117849 | + | 0.0204120i | −0.871858 | − | 0.489759i | \(-0.837085\pi\) |
0.860073 | + | 0.510171i | \(0.170418\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1231 | 0.826774 | 0.413387 | − | 0.910555i | \(-0.364346\pi\) | ||||
0.413387 | + | 0.910555i | \(0.364346\pi\) | |||||||
\(182\) | −4.81645 | + | 11.9039i | −0.357019 | + | 0.882374i | ||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | −3.84233 | + | 6.65511i | −0.283260 | + | 0.490621i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.84233 | − | 4.92306i | −0.208410 | − | 0.360976i | ||||
\(187\) | 21.1231i | 1.54467i | ||||||||
\(188\) | 6.06218 | − | 3.50000i | 0.442130 | − | 0.255264i | ||||
\(189\) | 1.78078 | + | 3.08440i | 0.129532 | + | 0.224357i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.56155 | − | 16.5611i | −0.691850 | − | 1.19832i | −0.971231 | − | 0.238139i | \(-0.923463\pi\) |
0.279381 | − | 0.960180i | \(-0.409871\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | −1.12311 | −0.0806343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.68466 | 0.406047 | ||||||||
\(197\) | −6.76172 | − | 3.90388i | −0.481753 | − | 0.278140i | 0.239394 | − | 0.970923i | \(-0.423051\pi\) |
−0.721147 | + | 0.692782i | \(0.756385\pi\) | |||||||
\(198\) | 3.57071 | + | 2.06155i | 0.253760 | + | 0.146508i | ||||
\(199\) | 5.56155 | + | 9.63289i | 0.394248 | + | 0.682858i | 0.993005 | − | 0.118073i | \(-0.0376718\pi\) |
−0.598757 | + | 0.800931i | \(0.704338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.12311 | − | 12.3376i | −0.502425 | − | 0.870226i | ||||
\(202\) | 14.8290 | − | 8.56155i | 1.04337 | − | 0.602389i | ||||
\(203\) | 23.3693i | 1.64020i | ||||||||
\(204\) | 2.56155 | + | 4.43674i | 0.179345 | + | 0.310634i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.219224 | + | 0.379706i | −0.0152740 | + | 0.0264554i | ||||
\(207\) | 7.68466i | 0.534121i | ||||||||
\(208\) | 2.21837 | + | 2.84233i | 0.153816 | + | 0.197080i | ||||
\(209\) | −14.6847 | −1.01576 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.46543 | + | 6.00231i | −0.238570 | + | 0.413216i | −0.960304 | − | 0.278955i | \(-0.910012\pi\) |
0.721734 | + | 0.692171i | \(0.243345\pi\) | |||||||
\(212\) | −3.84381 | + | 2.21922i | −0.263994 | + | 0.152417i | ||||
\(213\) | − | 4.87689i | − | 0.334159i | ||||||
\(214\) | 1.00000 | + | 1.73205i | 0.0683586 | + | 0.118401i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −17.5337 | + | 10.1231i | −1.19027 | + | 0.687201i | ||||
\(218\) | 17.5337 | + | 10.1231i | 1.18753 | + | 0.685623i | ||||
\(219\) | −7.68466 | + | 13.3102i | −0.519281 | + | 0.899421i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.56155 | + | 18.2931i | 0.172309 | + | 1.23053i | ||||
\(222\) | − | 4.12311i | − | 0.276725i | ||||||
\(223\) | 22.7766 | + | 13.1501i | 1.52524 | + | 0.880595i | 0.999552 | + | 0.0299151i | \(0.00952371\pi\) |
0.525683 | + | 0.850680i | \(0.323810\pi\) | |||||||
\(224\) | 1.78078 | − | 3.08440i | 0.118983 | − | 0.206085i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.68466 | −0.245100 | ||||||||
\(227\) | 17.3205 | − | 10.0000i | 1.14960 | − | 0.663723i | 0.200812 | − | 0.979630i | \(-0.435642\pi\) |
0.948790 | + | 0.315906i | \(0.102309\pi\) | |||||||
\(228\) | −3.08440 | + | 1.78078i | −0.204269 | + | 0.117935i | ||||
\(229\) | 7.75379 | 0.512385 | 0.256192 | − | 0.966626i | \(-0.417532\pi\) | ||||
0.256192 | + | 0.966626i | \(0.417532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.34233 | − | 12.7173i | 0.483090 | − | 0.836736i | ||||
\(232\) | 5.68247 | + | 3.28078i | 0.373073 | + | 0.215394i | ||||
\(233\) | − | 17.6847i | − | 1.15856i | −0.815128 | − | 0.579280i | \(-0.803334\pi\) | ||
0.815128 | − | 0.579280i | \(-0.196666\pi\) | |||||||
\(234\) | 3.34233 | + | 1.35234i | 0.218495 | + | 0.0884055i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.28078 | + | 9.14657i | −0.343749 | + | 0.595391i | ||||
\(237\) | 6.44188 | + | 3.71922i | 0.418445 | + | 0.241590i | ||||
\(238\) | 15.8017 | − | 9.12311i | 1.02427 | − | 0.591363i | ||||
\(239\) | −13.3693 | −0.864789 | −0.432395 | − | 0.901684i | \(-0.642331\pi\) | ||||
−0.432395 | + | 0.901684i | \(0.642331\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.93845 | + | 17.2139i | 0.640192 | + | 1.10884i | 0.985390 | + | 0.170315i | \(0.0544784\pi\) |
−0.345198 | + | 0.938530i | \(0.612188\pi\) | |||||||
\(242\) | − | 6.00000i | − | 0.385695i | ||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.00000 | − | 5.19615i | 0.192055 | − | 0.332650i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.24621 | −0.270729 | ||||||||
\(247\) | −12.7173 | + | 1.78078i | −0.809182 | + | 0.113308i | ||||
\(248\) | 5.68466i | 0.360976i | ||||||||
\(249\) | 0.561553 | − | 0.972638i | 0.0355870 | − | 0.0616384i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0615528 | − | 0.106613i | −0.00388518 | − | 0.00672933i | 0.864076 | − | 0.503361i | \(-0.167903\pi\) |
−0.867961 | + | 0.496632i | \(0.834570\pi\) | |||||||
\(252\) | − | 3.56155i | − | 0.224357i | ||||||
\(253\) | 27.4397 | − | 15.8423i | 1.72512 | − | 0.995999i | ||||
\(254\) | −2.21922 | − | 3.84381i | −0.139246 | − | 0.241182i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.24573 | − | 0.719224i | −0.0777066 | − | 0.0448639i | 0.460643 | − | 0.887585i | \(-0.347619\pi\) |
−0.538350 | + | 0.842721i | \(0.680952\pi\) | |||||||
\(258\) | −3.95042 | − | 2.28078i | −0.245942 | − | 0.141995i | ||||
\(259\) | −14.6847 | −0.912460 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.56155 | 0.406150 | ||||||||
\(262\) | 5.30277 | + | 3.06155i | 0.327606 | + | 0.189143i | ||||
\(263\) | 11.2583 | + | 6.50000i | 0.694218 | + | 0.400807i | 0.805190 | − | 0.593016i | \(-0.202063\pi\) |
−0.110972 | + | 0.993824i | \(0.535396\pi\) | |||||||
\(264\) | −2.06155 | − | 3.57071i | −0.126880 | − | 0.219762i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.34233 | + | 10.9852i | 0.388873 | + | 0.673548i | ||||
\(267\) | −1.56557 | + | 0.903882i | −0.0958113 | + | 0.0553167i | ||||
\(268\) | 14.2462i | 0.870226i | ||||||||
\(269\) | −1.68466 | − | 2.91791i | −0.102715 | − | 0.177908i | 0.810087 | − | 0.586310i | \(-0.199420\pi\) |
−0.912803 | + | 0.408401i | \(0.866086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0885 | + | 27.8662i | −0.977309 | + | 1.69275i | −0.305215 | + | 0.952283i | \(0.598728\pi\) |
−0.672094 | + | 0.740466i | \(0.734605\pi\) | |||||||
\(272\) | − | 5.12311i | − | 0.310634i | ||||||
\(273\) | 4.81645 | − | 11.9039i | 0.291505 | − | 0.720456i | ||||
\(274\) | 8.80776 | 0.532096 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.84233 | − | 6.65511i | 0.231281 | − | 0.400591i | ||||
\(277\) | 0.866025 | − | 0.500000i | 0.0520344 | − | 0.0300421i | −0.473757 | − | 0.880656i | \(-0.657103\pi\) |
0.525792 | + | 0.850613i | \(0.323769\pi\) | |||||||
\(278\) | 8.43845i | 0.506104i | ||||||||
\(279\) | 2.84233 | + | 4.92306i | 0.170166 | + | 0.294736i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.246211 | −0.0146877 | −0.00734387 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734387 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(282\) | −6.06218 | + | 3.50000i | −0.360997 | + | 0.208422i | ||||
\(283\) | −9.90599 | − | 5.71922i | −0.588850 | − | 0.339973i | 0.175793 | − | 0.984427i | \(-0.443751\pi\) |
−0.764643 | + | 0.644455i | \(0.777084\pi\) | |||||||
\(284\) | −2.43845 | + | 4.22351i | −0.144695 | + | 0.250619i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.06155 | − | 14.7224i | −0.121902 | − | 0.870556i | ||||
\(287\) | 15.1231i | 0.892689i | ||||||||
\(288\) | −0.866025 | − | 0.500000i | −0.0510310 | − | 0.0294628i | ||||
\(289\) | 4.62311 | − | 8.00745i | 0.271947 | − | 0.471027i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.12311 | 0.0658376 | ||||||||
\(292\) | 13.3102 | − | 7.68466i | 0.778922 | − | 0.449711i | ||||
\(293\) | −21.5908 | + | 12.4654i | −1.26135 | + | 0.728238i | −0.973335 | − | 0.229389i | \(-0.926327\pi\) |
−0.288011 | + | 0.957627i | \(0.592994\pi\) | |||||||
\(294\) | −5.68466 | −0.331536 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.06155 | + | 3.57071i | −0.119825 | + | 0.207544i | ||||
\(297\) | −3.57071 | − | 2.06155i | −0.207194 | − | 0.119623i | ||||
\(298\) | − | 22.8078i | − | 1.32122i | ||||||
\(299\) | 21.8423 | − | 17.0474i | 1.26317 | − | 0.985877i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12311 | + | 14.0696i | −0.468208 | + | 0.810960i | ||||
\(302\) | 8.11407 | + | 4.68466i | 0.466912 | + | 0.269572i | ||||
\(303\) | −14.8290 | + | 8.56155i | −0.851906 | + | 0.491848i | ||||
\(304\) | 3.56155 | 0.204269 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.56155 | − | 4.43674i | −0.146434 | − | 0.253632i | ||||
\(307\) | 15.6155i | 0.891225i | 0.895226 | + | 0.445613i | \(0.147014\pi\) | ||||
−0.895226 | + | 0.445613i | \(0.852986\pi\) | |||||||
\(308\) | −12.7173 | + | 7.34233i | −0.724635 | + | 0.418368i | ||||
\(309\) | 0.219224 | − | 0.379706i | 0.0124712 | − | 0.0216007i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.7386 | −1.06257 | −0.531285 | − | 0.847193i | \(-0.678291\pi\) | ||||
−0.531285 | + | 0.847193i | \(0.678291\pi\) | |||||||
\(312\) | −2.21837 | − | 2.84233i | −0.125590 | − | 0.160915i | ||||
\(313\) | 6.63068i | 0.374788i | 0.982285 | + | 0.187394i | \(0.0600042\pi\) | ||||
−0.982285 | + | 0.187394i | \(0.939996\pi\) | |||||||
\(314\) | 11.0616 | − | 19.1592i | 0.624240 | − | 1.08121i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.71922 | − | 6.44188i | −0.209223 | − | 0.362384i | ||||
\(317\) | 4.19224i | 0.235459i | 0.993046 | + | 0.117730i | \(0.0375616\pi\) | ||||
−0.993046 | + | 0.117730i | \(0.962438\pi\) | |||||||
\(318\) | 3.84381 | − | 2.21922i | 0.215550 | − | 0.124448i | ||||
\(319\) | −13.5270 | − | 23.4294i | −0.757366 | − | 1.31180i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.00000 | − | 1.73205i | −0.0558146 | − | 0.0966736i | ||||
\(322\) | −23.7025 | − | 13.6847i | −1.32089 | − | 0.762616i | ||||
\(323\) | 15.8017 | + | 9.12311i | 0.879229 | + | 0.507623i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.5616 | −1.02803 | ||||||||
\(327\) | −17.5337 | − | 10.1231i | −0.969618 | − | 0.559809i | ||||
\(328\) | 3.67733 | + | 2.12311i | 0.203046 | + | 0.117229i | ||||
\(329\) | 12.4654 | + | 21.5908i | 0.687242 | + | 1.19034i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.36932 | + | 16.2281i | 0.514984 | + | 0.891979i | 0.999849 | + | 0.0173896i | \(0.00553556\pi\) |
−0.484865 | + | 0.874589i | \(0.661131\pi\) | |||||||
\(332\) | −0.972638 | + | 0.561553i | −0.0533804 | + | 0.0308192i | ||||
\(333\) | 4.12311i | 0.225945i | ||||||||
\(334\) | −10.1847 | − | 17.6403i | −0.557280 | − | 0.965237i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.78078 | + | 3.08440i | −0.0971493 | + | 0.168268i | ||||
\(337\) | 6.00000i | 0.326841i | 0.986557 | + | 0.163420i | \(0.0522527\pi\) | ||||
−0.986557 | + | 0.163420i | \(0.947747\pi\) | |||||||
\(338\) | −3.57071 | − | 12.5000i | −0.194221 | − | 0.679910i | ||||
\(339\) | 3.68466 | 0.200123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7192 | − | 20.2983i | 0.634632 | − | 1.09921i | ||||
\(342\) | 3.08440 | − | 1.78078i | 0.166785 | − | 0.0962934i | ||||
\(343\) | − | 4.68466i | − | 0.252948i | ||||||
\(344\) | 2.28078 | + | 3.95042i | 0.122971 | + | 0.212992i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.1771 | −1.35353 | ||||||||
\(347\) | −7.90084 | + | 4.56155i | −0.424139 | + | 0.244877i | −0.696847 | − | 0.717220i | \(-0.745414\pi\) |
0.272707 | + | 0.962097i | \(0.412081\pi\) | |||||||
\(348\) | −5.68247 | − | 3.28078i | −0.304612 | − | 0.175868i | ||||
\(349\) | −12.2462 | + | 21.2111i | −0.655525 | + | 1.13540i | 0.326237 | + | 0.945288i | \(0.394219\pi\) |
−0.981762 | + | 0.190114i | \(0.939114\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.34233 | − | 1.35234i | −0.178400 | − | 0.0721828i | ||||
\(352\) | 4.12311i | 0.219762i | ||||||||
\(353\) | −27.5931 | − | 15.9309i | −1.46863 | − | 0.847915i | −0.469249 | − | 0.883066i | \(-0.655475\pi\) |
−0.999382 | + | 0.0351511i | \(0.988809\pi\) | |||||||
\(354\) | 5.28078 | − | 9.14657i | 0.280670 | − | 0.486135i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.80776 | 0.0958113 | ||||||||
\(357\) | −15.8017 | + | 9.12311i | −0.836314 | + | 0.482846i | ||||
\(358\) | −0.273094 | + | 0.157671i | −0.0144335 | + | 0.00833316i | ||||
\(359\) | −4.87689 | −0.257393 | −0.128696 | − | 0.991684i | \(-0.541079\pi\) | ||||
−0.128696 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.15767 | − | 5.46925i | 0.166193 | − | 0.287855i | ||||
\(362\) | 9.63289 | + | 5.56155i | 0.506294 | + | 0.292309i | ||||
\(363\) | 6.00000i | 0.314918i | ||||||||
\(364\) | −10.1231 | + | 7.90084i | −0.530595 | + | 0.414117i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −17.7470 | − | 10.2462i | −0.926384 | − | 0.534848i | −0.0407177 | − | 0.999171i | \(-0.512964\pi\) |
−0.885666 | + | 0.464323i | \(0.846298\pi\) | |||||||
\(368\) | −6.65511 | + | 3.84233i | −0.346922 | + | 0.200295i | ||||
\(369\) | 4.24621 | 0.221049 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90388 | − | 13.6899i | −0.410349 | − | 0.710746i | ||||
\(372\) | − | 5.68466i | − | 0.294736i | ||||||
\(373\) | −4.49661 | + | 2.59612i | −0.232826 | + | 0.134422i | −0.611875 | − | 0.790955i | \(-0.709584\pi\) |
0.379049 | + | 0.925376i | \(0.376251\pi\) | |||||||
\(374\) | −10.5616 | + | 18.2931i | −0.546125 | + | 0.945916i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | −14.5560 | − | 18.6501i | −0.749670 | − | 0.960529i | ||||
\(378\) | 3.56155i | 0.183187i | ||||||||
\(379\) | −2.65767 | + | 4.60322i | −0.136515 | + | 0.236452i | −0.926175 | − | 0.377093i | \(-0.876924\pi\) |
0.789660 | + | 0.613545i | \(0.210257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.21922 | + | 3.84381i | 0.113694 | + | 0.196924i | ||||
\(382\) | − | 19.1231i | − | 0.978423i | ||||||
\(383\) | 18.0201 | − | 10.4039i | 0.920782 | − | 0.531614i | 0.0368973 | − | 0.999319i | \(-0.488253\pi\) |
0.883884 | + | 0.467706i | \(0.154919\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.95042 | + | 2.28078i | 0.200811 | + | 0.115938i | ||||
\(388\) | −0.972638 | − | 0.561553i | −0.0493782 | − | 0.0285085i | ||||
\(389\) | −19.0540 | −0.966075 | −0.483037 | − | 0.875600i | \(-0.660467\pi\) | ||||
−0.483037 | + | 0.875600i | \(0.660467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.3693 | −1.99099 | ||||||||
\(392\) | 4.92306 | + | 2.84233i | 0.248652 | + | 0.143559i | ||||
\(393\) | −5.30277 | − | 3.06155i | −0.267489 | − | 0.154435i | ||||
\(394\) | −3.90388 | − | 6.76172i | −0.196675 | − | 0.340651i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.06155 | + | 3.57071i | 0.103597 | + | 0.179435i | ||||
\(397\) | 10.2857 | − | 5.93845i | 0.516224 | − | 0.298042i | −0.219164 | − | 0.975688i | \(-0.570333\pi\) |
0.735388 | + | 0.677646i | \(0.237000\pi\) | |||||||
\(398\) | 11.1231i | 0.557551i | ||||||||
\(399\) | −6.34233 | − | 10.9852i | −0.317514 | − | 0.549950i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.34233 | + | 10.9852i | −0.316721 | + | 0.548577i | −0.979802 | − | 0.199971i | \(-0.935915\pi\) |
0.663081 | + | 0.748548i | \(0.269248\pi\) | |||||||
\(402\) | − | 14.2462i | − | 0.710536i | ||||||
\(403\) | 7.68762 | − | 19.0000i | 0.382947 | − | 0.946457i | ||||
\(404\) | 17.1231 | 0.851906 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.6847 | + | 20.2384i | −0.579900 | + | 1.00442i | ||||
\(407\) | 14.7224 | − | 8.50000i | 0.729764 | − | 0.421329i | ||||
\(408\) | 5.12311i | 0.253632i | ||||||||
\(409\) | 0.903882 | + | 1.56557i | 0.0446941 | + | 0.0774124i | 0.887507 | − | 0.460794i | \(-0.152435\pi\) |
−0.842813 | + | 0.538207i | \(0.819102\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.80776 | −0.434455 | ||||||||
\(412\) | −0.379706 | + | 0.219224i | −0.0187068 | + | 0.0108004i | ||||
\(413\) | −32.5760 | − | 18.8078i | −1.60296 | − | 0.925470i | ||||
\(414\) | −3.84233 | + | 6.65511i | −0.188840 | + | 0.327081i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 3.57071i | 0.0245145 | + | 0.175069i | ||||
\(417\) | − | 8.43845i | − | 0.413233i | ||||||
\(418\) | −12.7173 | − | 7.34233i | −0.622023 | − | 0.359125i | ||||
\(419\) | −0.246211 | + | 0.426450i | −0.0120282 | + | 0.0208335i | −0.871977 | − | 0.489547i | \(-0.837162\pi\) |
0.859949 | + | 0.510381i | \(0.170495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.492423 | 0.0239992 | 0.0119996 | − | 0.999928i | \(-0.496180\pi\) | ||||
0.0119996 | + | 0.999928i | \(0.496180\pi\) | |||||||
\(422\) | −6.00231 | + | 3.46543i | −0.292188 | + | 0.168695i | ||||
\(423\) | 6.06218 | − | 3.50000i | 0.294753 | − | 0.170176i | ||||
\(424\) | −4.43845 | −0.215550 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.43845 | − | 4.22351i | 0.118143 | − | 0.204630i | ||||
\(427\) | 18.5064 | + | 10.6847i | 0.895586 | + | 0.517067i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 2.06155 | + | 14.7224i | 0.0995327 | + | 0.710806i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3693 | + | 23.1563i | −0.643977 | + | 1.11540i | 0.340559 | + | 0.940223i | \(0.389384\pi\) |
−0.984537 | + | 0.175178i | \(0.943950\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 26.6204 | − | 15.3693i | 1.27930 | − | 0.738602i | 0.302578 | − | 0.953125i | \(-0.402153\pi\) |
0.976719 | + | 0.214523i | \(0.0688195\pi\) | |||||||
\(434\) | −20.2462 | −0.971849 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1231 | + | 17.5337i | 0.484809 | + | 0.839714i | ||||
\(437\) | − | 27.3693i | − | 1.30925i | ||||||
\(438\) | −13.3102 | + | 7.68466i | −0.635987 | + | 0.367187i | ||||
\(439\) | 8.43845 | − | 14.6158i | 0.402745 | − | 0.697575i | −0.591311 | − | 0.806444i | \(-0.701389\pi\) |
0.994056 | + | 0.108869i | \(0.0347228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.68466 | 0.270698 | ||||||||
\(442\) | −6.92820 | + | 17.1231i | −0.329541 | + | 0.814463i | ||||
\(443\) | − | 4.87689i | − | 0.231708i | −0.993266 | − | 0.115854i | \(-0.963039\pi\) | ||
0.993266 | − | 0.115854i | \(-0.0369605\pi\) | |||||||
\(444\) | 2.06155 | − | 3.57071i | 0.0978370 | − | 0.169459i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.1501 | + | 22.7766i | 0.622675 | + | 1.07850i | ||||
\(447\) | 22.8078i | 1.07877i | ||||||||
\(448\) | 3.08440 | − | 1.78078i | 0.145724 | − | 0.0841338i | ||||
\(449\) | 12.5885 | + | 21.8040i | 0.594090 | + | 1.02899i | 0.993675 | + | 0.112298i | \(0.0358210\pi\) |
−0.399585 | + | 0.916696i | \(0.630846\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.75379 | − | 15.1620i | −0.412200 | − | 0.713951i | ||||
\(452\) | −3.19101 | − | 1.84233i | −0.150092 | − | 0.0866559i | ||||
\(453\) | −8.11407 | − | 4.68466i | −0.381232 | − | 0.220104i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.56155 | −0.166785 | ||||||||
\(457\) | 3.25088 | + | 1.87689i | 0.152070 | + | 0.0877974i | 0.574104 | − | 0.818782i | \(-0.305351\pi\) |
−0.422034 | + | 0.906580i | \(0.638684\pi\) | |||||||
\(458\) | 6.71498 | + | 3.87689i | 0.313770 | + | 0.181155i | ||||
\(459\) | 2.56155 | + | 4.43674i | 0.119563 | + | 0.207089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.52699 | − | 6.10892i | −0.164268 | − | 0.284521i | 0.772127 | − | 0.635468i | \(-0.219193\pi\) |
−0.936395 | + | 0.350947i | \(0.885860\pi\) | |||||||
\(462\) | 12.7173 | − | 7.34233i | 0.591662 | − | 0.341596i | ||||
\(463\) | 33.6155i | 1.56225i | 0.624377 | + | 0.781123i | \(0.285353\pi\) | ||||
−0.624377 | + | 0.781123i | \(0.714647\pi\) | |||||||
\(464\) | 3.28078 | + | 5.68247i | 0.152306 | + | 0.263802i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.84233 | − | 15.3154i | 0.409613 | − | 0.709471i | ||||
\(467\) | − | 39.8617i | − | 1.84458i | −0.386497 | − | 0.922291i | \(-0.626315\pi\) | ||
0.386497 | − | 0.922291i | \(-0.373685\pi\) | |||||||
\(468\) | 2.21837 | + | 2.84233i | 0.102544 | + | 0.131387i | ||||
\(469\) | −50.7386 | −2.34289 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.0616 | + | 19.1592i | −0.509689 | + | 0.882808i | ||||
\(472\) | −9.14657 | + | 5.28078i | −0.421005 | + | 0.243067i | ||||
\(473\) | − | 18.8078i | − | 0.864782i | ||||||
\(474\) | 3.71922 | + | 6.44188i | 0.170830 | + | 0.295886i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 18.2462 | 0.836314 | ||||||||
\(477\) | −3.84381 | + | 2.21922i | −0.175996 | + | 0.101611i | ||||
\(478\) | −11.5782 | − | 6.68466i | −0.529573 | − | 0.305749i | ||||
\(479\) | −10.8769 | + | 18.8393i | −0.496978 | + | 0.860791i | −0.999994 | − | 0.00348601i | \(-0.998890\pi\) |
0.503016 | + | 0.864277i | \(0.332224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7192 | − | 9.14657i | 0.534351 | − | 0.417048i | ||||
\(482\) | 19.8769i | 0.905368i | ||||||||
\(483\) | 23.7025 | + | 13.6847i | 1.07850 | + | 0.622674i | ||||
\(484\) | 3.00000 | − | 5.19615i | 0.136364 | − | 0.236189i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.8314 | − | 12.0270i | 0.943959 | − | 0.544995i | 0.0527597 | − | 0.998607i | \(-0.483198\pi\) |
0.891199 | + | 0.453612i | \(0.149865\pi\) | |||||||
\(488\) | 5.19615 | − | 3.00000i | 0.235219 | − | 0.135804i | ||||
\(489\) | 18.5616 | 0.839382 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7808 | − | 18.6729i | 0.486530 | − | 0.842694i | −0.513350 | − | 0.858179i | \(-0.671596\pi\) |
0.999880 | + | 0.0154850i | \(0.00492923\pi\) | |||||||
\(492\) | −3.67733 | − | 2.12311i | −0.165787 | − | 0.0957170i | ||||
\(493\) | 33.6155i | 1.51397i | ||||||||
\(494\) | −11.9039 | − | 4.81645i | −0.535581 | − | 0.216702i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.84233 | + | 4.92306i | −0.127624 | + | 0.221052i | ||||
\(497\) | −15.0423 | − | 8.68466i | −0.674738 | − | 0.389560i | ||||
\(498\) | 0.972638 | − | 0.561553i | 0.0435850 | − | 0.0251638i | ||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1847 | + | 17.6403i | 0.455017 | + | 0.788113i | ||||
\(502\) | − | 0.123106i | − | 0.00549447i | ||||||
\(503\) | −5.14941 | + | 2.97301i | −0.229601 | + | 0.132560i | −0.610388 | − | 0.792103i | \(-0.708986\pi\) |
0.380787 | + | 0.924663i | \(0.375653\pi\) | |||||||
\(504\) | 1.78078 | − | 3.08440i | 0.0793221 | − | 0.137390i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.6847 | 1.40855 | ||||||||
\(507\) | 3.57071 | + | 12.5000i | 0.158581 | + | 0.555144i | ||||
\(508\) | − | 4.43845i | − | 0.196924i | ||||||
\(509\) | −14.7732 | + | 25.5879i | −0.654811 | + | 1.13417i | 0.327131 | + | 0.944979i | \(0.393918\pi\) |
−0.981941 | + | 0.189186i | \(0.939415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3693 | + | 47.4050i | 1.21075 | + | 2.09708i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −3.08440 | + | 1.78078i | −0.136179 | + | 0.0786232i | ||||
\(514\) | −0.719224 | − | 1.24573i | −0.0317236 | − | 0.0549469i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.28078 | − | 3.95042i | −0.100406 | − | 0.173908i | ||||
\(517\) | −24.9950 | − | 14.4309i | −1.09928 | − | 0.634669i | ||||
\(518\) | −12.7173 | − | 7.34233i | −0.558766 | − | 0.322603i | ||||
\(519\) | 25.1771 | 1.10515 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.6847 | −0.818590 | −0.409295 | − | 0.912402i | \(-0.634225\pi\) | ||||
−0.409295 | + | 0.912402i | \(0.634225\pi\) | |||||||
\(522\) | 5.68247 | + | 3.28078i | 0.248715 | + | 0.143596i | ||||
\(523\) | 7.96071 | + | 4.59612i | 0.348098 | + | 0.200974i | 0.663847 | − | 0.747868i | \(-0.268923\pi\) |
−0.315749 | + | 0.948843i | \(0.602256\pi\) | |||||||
\(524\) | 3.06155 | + | 5.30277i | 0.133745 | + | 0.231652i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.50000 | + | 11.2583i | 0.283413 | + | 0.490887i | ||||
\(527\) | −25.2213 | + | 14.5616i | −1.09866 | + | 0.634311i | ||||
\(528\) | − | 4.12311i | − | 0.179435i | ||||||
\(529\) | 18.0270 | + | 31.2237i | 0.783782 | + | 1.35755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.28078 | + | 9.14657i | −0.229166 | + | 0.396927i | ||||
\(532\) | 12.6847i | 0.549950i | ||||||||
\(533\) | −9.41967 | − | 12.0691i | −0.408011 | − | 0.522772i | ||||
\(534\) | −1.80776 | −0.0782296 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.12311 | + | 12.3376i | −0.307671 | + | 0.532902i | ||||
\(537\) | 0.273094 | − | 0.157671i | 0.0117849 | − | 0.00680400i | ||||
\(538\) | − | 3.36932i | − | 0.145262i | ||||||
\(539\) | −11.7192 | − | 20.2983i | −0.504783 | − | 0.874309i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.63068 | −0.113102 | −0.0565510 | − | 0.998400i | \(-0.518010\pi\) | ||||
−0.0565510 | + | 0.998400i | \(0.518010\pi\) | |||||||
\(542\) | −27.8662 | + | 16.0885i | −1.19695 | + | 0.691062i | ||||
\(543\) | −9.63289 | − | 5.56155i | −0.413387 | − | 0.238669i | ||||
\(544\) | 2.56155 | − | 4.43674i | 0.109826 | − | 0.190224i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.1231 | − | 7.90084i | 0.433229 | − | 0.338125i | ||||
\(547\) | − | 35.6155i | − | 1.52281i | −0.648276 | − | 0.761405i | \(-0.724510\pi\) | ||
0.648276 | − | 0.761405i | \(-0.275490\pi\) | |||||||
\(548\) | 7.62775 | + | 4.40388i | 0.325841 | + | 0.188125i | ||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.3693 | −0.995566 | ||||||||
\(552\) | 6.65511 | − | 3.84233i | 0.283260 | − | 0.163540i | ||||
\(553\) | 22.9431 | − | 13.2462i | 0.975640 | − | 0.563286i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.21922 | + | 7.30791i | −0.178935 | + | 0.309924i | ||||
\(557\) | −3.84381 | − | 2.21922i | −0.162867 | − | 0.0940315i | 0.416351 | − | 0.909204i | \(-0.363309\pi\) |
−0.579218 | + | 0.815172i | \(0.696642\pi\) | |||||||
\(558\) | 5.68466i | 0.240651i | ||||||||
\(559\) | −2.28078 | − | 16.2880i | −0.0964666 | − | 0.688909i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.5616 | − | 18.2931i | 0.445909 | − | 0.772337i | ||||
\(562\) | −0.213225 | − | 0.123106i | −0.00899436 | − | 0.00519290i | ||||
\(563\) | 28.5657 | − | 16.4924i | 1.20390 | − | 0.695073i | 0.242481 | − | 0.970156i | \(-0.422039\pi\) |
0.961420 | + | 0.275083i | \(0.0887055\pi\) | |||||||
\(564\) | −7.00000 | −0.294753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.71922 | − | 9.90599i | −0.240397 | − | 0.416380i | ||||
\(567\) | − | 3.56155i | − | 0.149571i | ||||||
\(568\) | −4.22351 | + | 2.43845i | −0.177215 | + | 0.102315i | ||||
\(569\) | −9.58854 | + | 16.6078i | −0.401973 | + | 0.696237i | −0.993964 | − | 0.109707i | \(-0.965009\pi\) |
0.591991 | + | 0.805944i | \(0.298342\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3153 | 0.473532 | 0.236766 | − | 0.971567i | \(-0.423912\pi\) | ||||
0.236766 | + | 0.971567i | \(0.423912\pi\) | |||||||
\(572\) | 5.57586 | − | 13.7808i | 0.233138 | − | 0.576203i | ||||
\(573\) | 19.1231i | 0.798879i | ||||||||
\(574\) | −7.56155 | + | 13.0970i | −0.315613 | + | 0.546658i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | − | 8.73863i | − | 0.363794i | −0.983318 | − | 0.181897i | \(-0.941776\pi\) | ||
0.983318 | − | 0.181897i | \(-0.0582238\pi\) | |||||||
\(578\) | 8.00745 | − | 4.62311i | 0.333066 | − | 0.192296i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.00000 | − | 3.46410i | −0.0829740 | − | 0.143715i | ||||
\(582\) | 0.972638 | + | 0.561553i | 0.0403171 | + | 0.0232771i | ||||
\(583\) | 15.8484 | + | 9.15009i | 0.656375 | + | 0.378958i | ||||
\(584\) | 15.3693 | 0.635987 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.9309 | −1.02988 | ||||||||
\(587\) | −20.5714 | − | 11.8769i | −0.849072 | − | 0.490212i | 0.0112657 | − | 0.999937i | \(-0.496414\pi\) |
−0.860338 | + | 0.509725i | \(0.829747\pi\) | |||||||
\(588\) | −4.92306 | − | 2.84233i | −0.203024 | − | 0.117216i | ||||
\(589\) | −10.1231 | − | 17.5337i | −0.417115 | − | 0.722465i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.90388 | + | 6.76172i | 0.160584 | + | 0.278140i | ||||
\(592\) | −3.57071 | + | 2.06155i | −0.146755 | + | 0.0847293i | ||||
\(593\) | − | 12.1771i | − | 0.500053i | −0.968239 | − | 0.250026i | \(-0.919561\pi\) | ||
0.968239 | − | 0.250026i | \(-0.0804393\pi\) | |||||||
\(594\) | −2.06155 | − | 3.57071i | −0.0845865 | − | 0.146508i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.4039 | − | 19.7521i | 0.467121 | − | 0.809078i | ||||
\(597\) | − | 11.1231i | − | 0.455238i | ||||||
\(598\) | 27.4397 | − | 3.84233i | 1.12209 | − | 0.157125i | ||||
\(599\) | 14.0000 | 0.572024 | 0.286012 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286012 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9924 | − | 31.1638i | 0.733926 | − | 1.27120i | −0.221267 | − | 0.975213i | \(-0.571019\pi\) |
0.955193 | − | 0.295984i | \(-0.0956476\pi\) | |||||||
\(602\) | −14.0696 | + | 8.12311i | −0.573435 | + | 0.331073i | ||||
\(603\) | 14.2462i | 0.580151i | ||||||||
\(604\) | 4.68466 | + | 8.11407i | 0.190616 | + | 0.330157i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.1231 | −0.695579 | ||||||||
\(607\) | 25.4813 | − | 14.7116i | 1.03425 | − | 0.597127i | 0.116054 | − | 0.993243i | \(-0.462975\pi\) |
0.918201 | + | 0.396116i | \(0.129642\pi\) | |||||||
\(608\) | 3.08440 | + | 1.78078i | 0.125089 | + | 0.0722200i | ||||
\(609\) | 11.6847 | − | 20.2384i | 0.473486 | − | 0.820102i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.3963 | − | 9.46641i | −0.946513 | − | 0.382970i | ||||
\(612\) | − | 5.12311i | − | 0.207089i | ||||||
\(613\) | −24.3553 | − | 14.0616i | −0.983702 | − | 0.567941i | −0.0803164 | − | 0.996769i | \(-0.525593\pi\) |
−0.903386 | + | 0.428829i | \(0.858926\pi\) | |||||||
\(614\) | −7.80776 | + | 13.5234i | −0.315096 | + | 0.545762i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.6847 | −0.591662 | ||||||||
\(617\) | 36.1000 | − | 20.8423i | 1.45333 | − | 0.839081i | 0.454662 | − | 0.890664i | \(-0.349760\pi\) |
0.998669 | + | 0.0515837i | \(0.0164269\pi\) | |||||||
\(618\) | 0.379706 | − | 0.219224i | 0.0152740 | − | 0.00881847i | ||||
\(619\) | 16.4384 | 0.660717 | 0.330358 | − | 0.943856i | \(-0.392830\pi\) | ||||
0.330358 | + | 0.943856i | \(0.392830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.84233 | − | 6.65511i | 0.154187 | − | 0.267060i | ||||
\(622\) | −16.2281 | − | 9.36932i | −0.650689 | − | 0.375675i | ||||
\(623\) | 6.43845i | 0.257951i | ||||||||
\(624\) | −0.500000 | − | 3.57071i | −0.0200160 | − | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.31534 | + | 5.74234i | −0.132508 | + | 0.229510i | ||||
\(627\) | 12.7173 | + | 7.34233i | 0.507880 | + | 0.293224i | ||||
\(628\) | 19.1592 | − | 11.0616i | 0.764534 | − | 0.441404i | ||||
\(629\) | −21.1231 | −0.842233 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.1231 | + | 26.1940i | 0.602041 | + | 1.04277i | 0.992512 | + | 0.122151i | \(0.0389791\pi\) |
−0.390470 | + | 0.920616i | \(0.627688\pi\) | |||||||
\(632\) | − | 7.43845i | − | 0.295886i | ||||||
\(633\) | 6.00231 | − | 3.46543i | 0.238570 | − | 0.137739i | ||||
\(634\) | −2.09612 | + | 3.63058i | −0.0832475 | + | 0.144189i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.43845 | 0.175996 | ||||||||
\(637\) | −12.6107 | − | 16.1577i | −0.499653 | − | 0.640190i | ||||
\(638\) | − | 27.0540i | − | 1.07108i | ||||||
\(639\) | −2.43845 | + | 4.22351i | −0.0964635 | + | 0.167080i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.78078 | + | 13.4767i | 0.307322 | + | 0.532298i | 0.977776 | − | 0.209654i | \(-0.0672337\pi\) |
−0.670453 | + | 0.741952i | \(0.733900\pi\) | |||||||
\(642\) | − | 2.00000i | − | 0.0789337i | ||||||
\(643\) | 33.1222 | − | 19.1231i | 1.30621 | − | 0.754142i | 0.324750 | − | 0.945800i | \(-0.394720\pi\) |
0.981462 | + | 0.191658i | \(0.0613865\pi\) | |||||||
\(644\) | −13.6847 | − | 23.7025i | −0.539251 | − | 0.934010i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.12311 | + | 15.8017i | 0.358944 | + | 0.621709i | ||||
\(647\) | −1.77879 | − | 1.02699i | −0.0699316 | − | 0.0403751i | 0.464626 | − | 0.885507i | \(-0.346189\pi\) |
−0.534558 | + | 0.845132i | \(0.679522\pi\) | |||||||
\(648\) | −0.866025 | − | 0.500000i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | 43.5464 | 1.70935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.2462 | 0.793512 | ||||||||
\(652\) | −16.0748 | − | 9.28078i | −0.629537 | − | 0.363463i | ||||
\(653\) | 35.0207 | + | 20.2192i | 1.37047 | + | 0.791239i | 0.990987 | − | 0.133961i | \(-0.0427695\pi\) |
0.379480 | + | 0.925200i | \(0.376103\pi\) | |||||||
\(654\) | −10.1231 | − | 17.5337i | −0.395845 | − | 0.685623i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.12311 | + | 3.67733i | 0.0828933 | + | 0.143575i | ||||
\(657\) | 13.3102 | − | 7.68466i | 0.519281 | − | 0.299807i | ||||
\(658\) | 24.9309i | 0.971906i | ||||||||
\(659\) | 15.5270 | + | 26.8935i | 0.604846 | + | 1.04762i | 0.992076 | + | 0.125640i | \(0.0400985\pi\) |
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.80776 | − | 10.0593i | 0.225896 | − | 0.391263i | −0.730692 | − | 0.682707i | \(-0.760802\pi\) |
0.956588 | + | 0.291444i | \(0.0941358\pi\) | |||||||
\(662\) | 18.7386i | 0.728298i | ||||||||
\(663\) | 6.92820 | − | 17.1231i | 0.269069 | − | 0.665006i | ||||
\(664\) | −1.12311 | −0.0435850 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.06155 | + | 3.57071i | −0.0798835 | + | 0.138362i | ||||
\(667\) | 43.6679 | − | 25.2116i | 1.69083 | − | 0.976199i | ||||
\(668\) | − | 20.3693i | − | 0.788113i | ||||||
\(669\) | −13.1501 | − | 22.7766i | −0.508412 | − | 0.880595i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.7386 | −0.955024 | ||||||||
\(672\) | −3.08440 | + | 1.78078i | −0.118983 | + | 0.0686949i | ||||
\(673\) | −36.5863 | − | 21.1231i | −1.41030 | − | 0.814236i | −0.414882 | − | 0.909875i | \(-0.636177\pi\) |
−0.995416 | + | 0.0956394i | \(0.969510\pi\) | |||||||
\(674\) | −3.00000 | + | 5.19615i | −0.115556 | + | 0.200148i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.15767 | − | 12.6107i | 0.121449 | − | 0.485026i | ||||
\(677\) | 28.8769i | 1.10983i | 0.831907 | + | 0.554915i | \(0.187249\pi\) | ||||
−0.831907 | + | 0.554915i | \(0.812751\pi\) | |||||||
\(678\) | 3.19101 | + | 1.84233i | 0.122550 | + | 0.0707542i | ||||
\(679\) | 2.00000 | − | 3.46410i | 0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 20.2983 | − | 11.7192i | 0.777262 | − | 0.448752i | ||||
\(683\) | 7.68762 | − | 4.43845i | 0.294158 | − | 0.169832i | −0.345657 | − | 0.938361i | \(-0.612344\pi\) |
0.639816 | + | 0.768528i | \(0.279011\pi\) | |||||||
\(684\) | 3.56155 | 0.136179 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.34233 | − | 4.05703i | 0.0894305 | − | 0.154898i | ||||
\(687\) | −6.71498 | − | 3.87689i | −0.256192 | − | 0.147913i | ||||
\(688\) | 4.56155i | 0.173908i | ||||||||
\(689\) | 14.8348 | + | 6.00231i | 0.565159 | + | 0.228670i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.21922 | − | 14.2361i | 0.312674 | − | 0.541567i | −0.666266 | − | 0.745714i | \(-0.732109\pi\) |
0.978940 | + | 0.204147i | \(0.0654419\pi\) | |||||||
\(692\) | −21.8040 | − | 12.5885i | −0.828863 | − | 0.478545i | ||||
\(693\) | −12.7173 | + | 7.34233i | −0.483090 | + | 0.278912i | ||||
\(694\) | −9.12311 | −0.346308 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.28078 | − | 5.68247i | −0.124358 | − | 0.215394i | ||||
\(697\) | 21.7538i | 0.823984i | ||||||||
\(698\) | −21.2111 | + | 12.2462i | −0.802850 | + | 0.463526i | ||||
\(699\) | −8.84233 | + | 15.3154i | −0.334448 | + | 0.579280i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3002 | 0.653419 | 0.326710 | − | 0.945125i | \(-0.394060\pi\) | ||||
0.326710 | + | 0.945125i | \(0.394060\pi\) | |||||||
\(702\) | −2.21837 | − | 2.84233i | −0.0837270 | − | 0.107277i | ||||
\(703\) | − | 14.6847i | − | 0.553842i | ||||||
\(704\) | −2.06155 | + | 3.57071i | −0.0776977 | + | 0.134576i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.9309 | − | 27.5931i | −0.599566 | − | 1.03848i | ||||
\(707\) | 60.9848i | 2.29357i | ||||||||
\(708\) | 9.14657 | − | 5.28078i | 0.343749 | − | 0.198464i | ||||
\(709\) | 8.87689 | + | 15.3752i | 0.333379 | + | 0.577429i | 0.983172 | − | 0.182682i | \(-0.0584779\pi\) |
−0.649793 | + | 0.760111i | \(0.725145\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71922 | − | 6.44188i | −0.139482 | − | 0.241590i | ||||
\(712\) | 1.56557 | + | 0.903882i | 0.0586722 | + | 0.0338744i | ||||
\(713\) | 37.8320 | + | 21.8423i | 1.41682 | + | 0.818002i | ||||
\(714\) | −18.2462 | −0.682847 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.315342 | −0.0117849 | ||||||||
\(717\) | 11.5782 | + | 6.68466i | 0.432395 | + | 0.249643i | ||||
\(718\) | −4.22351 | − | 2.43845i | −0.157620 | − | 0.0910020i | ||||
\(719\) | −10.4924 | − | 18.1734i | −0.391301 | − | 0.677754i | 0.601320 | − | 0.799008i | \(-0.294642\pi\) |
−0.992621 | + | 0.121254i | \(0.961308\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.780776 | − | 1.35234i | −0.0290776 | − | 0.0503639i | ||||
\(722\) | 5.46925 | − | 3.15767i | 0.203544 | − | 0.117516i | ||||
\(723\) | − | 19.8769i | − | 0.739230i | ||||||
\(724\) | 5.56155 | + | 9.63289i | 0.206693 | + | 0.358004i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.00000 | + | 5.19615i | −0.111340 | + | 0.192847i | ||||
\(727\) | 23.4233i | 0.868722i | 0.900739 | + | 0.434361i | \(0.143026\pi\) | ||||
−0.900739 | + | 0.434361i | \(0.856974\pi\) | |||||||
\(728\) | −12.7173 | + | 1.78078i | −0.471334 | + | 0.0660000i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6847 | + | 20.2384i | −0.432173 | + | 0.748545i | ||||
\(732\) | −5.19615 | + | 3.00000i | −0.192055 | + | 0.110883i | ||||
\(733\) | 48.9309i | 1.80730i | 0.428269 | + | 0.903651i | \(0.359124\pi\) | ||||
−0.428269 | + | 0.903651i | \(0.640876\pi\) | |||||||
\(734\) | −10.2462 | − | 17.7470i | −0.378195 | − | 0.655052i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.68466 | −0.283260 | ||||||||
\(737\) | 50.8691 | − | 29.3693i | 1.87379 | − | 1.08183i | ||||
\(738\) | 3.67733 | + | 2.12311i | 0.135364 | + | 0.0781526i | ||||
\(739\) | 21.2732 | − | 36.8463i | 0.782547 | − | 1.35541i | −0.147906 | − | 0.989001i | \(-0.547253\pi\) |
0.930453 | − | 0.366410i | \(-0.119413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.9039 | + | 4.81645i | 0.437300 | + | 0.176937i | ||||
\(742\) | − | 15.8078i | − | 0.580321i | ||||||
\(743\) | 27.8662 | + | 16.0885i | 1.02231 | + | 0.590231i | 0.914772 | − | 0.403970i | \(-0.132370\pi\) |
0.107538 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(744\) | 2.84233 | − | 4.92306i | 0.104205 | − | 0.180488i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.19224 | −0.190101 | ||||||||
\(747\) | −0.972638 | + | 0.561553i | −0.0355870 | + | 0.0205461i | ||||
\(748\) | −18.2931 | + | 10.5616i | −0.668864 | + | 0.386169i | ||||
\(749\) | −7.12311 | −0.260273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.59612 | − | 2.76456i | 0.0582432 | − | 0.100880i | −0.835434 | − | 0.549591i | \(-0.814783\pi\) |
0.893677 | + | 0.448711i | \(0.148117\pi\) | |||||||
\(752\) | 6.06218 | + | 3.50000i | 0.221065 | + | 0.127632i | ||||
\(753\) | 0.123106i | 0.00448622i | ||||||||
\(754\) | −3.28078 | − | 23.4294i | −0.119479 | − | 0.853250i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.78078 | + | 3.08440i | −0.0647662 | + | 0.112178i | ||||
\(757\) | 28.9454 | + | 16.7116i | 1.05204 | + | 0.607395i | 0.923220 | − | 0.384273i | \(-0.125548\pi\) |
0.128820 | + | 0.991668i | \(0.458881\pi\) | |||||||
\(758\) | −4.60322 | + | 2.65767i | −0.167197 | + | 0.0965309i | ||||
\(759\) | −31.6847 | −1.15008 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.46543 | − | 9.46641i | −0.198122 | − | 0.343157i | 0.749798 | − | 0.661667i | \(-0.230151\pi\) |
−0.947919 | + | 0.318510i | \(0.896818\pi\) | |||||||
\(762\) | 4.43845i | 0.160788i | ||||||||
\(763\) | −62.4473 | + | 36.0540i | −2.26074 | + | 1.30524i | ||||
\(764\) | 9.56155 | − | 16.5611i | 0.345925 | − | 0.599159i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.8078 | 0.751815 | ||||||||
\(767\) | 37.7123 | − | 5.28078i | 1.36171 | − | 0.190678i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −22.8423 | + | 39.5641i | −0.823715 | + | 1.42672i | 0.0791816 | + | 0.996860i | \(0.474769\pi\) |
−0.902897 | + | 0.429857i | \(0.858564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.719224 | + | 1.24573i | 0.0259022 | + | 0.0448639i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3399 | + | 10.5885i | −0.659640 | + | 0.380843i | −0.792140 | − | 0.610340i | \(-0.791033\pi\) |
0.132500 | + | 0.991183i | \(0.457700\pi\) | |||||||
\(774\) | 2.28078 | + | 3.95042i | 0.0819808 | + | 0.141995i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.561553 | − | 0.972638i | −0.0201586 | − | 0.0349157i | ||||
\(777\) | 12.7173 | + | 7.34233i | 0.456230 | + | 0.263405i | ||||
\(778\) | −16.5012 | − | 9.52699i | −0.591598 | − | 0.341559i | ||||
\(779\) | −15.1231 | −0.541841 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1080 | 0.719519 | ||||||||
\(782\) | −34.0948 | − | 19.6847i | −1.21923 | − | 0.703922i | ||||
\(783\) | −5.68247 | − | 3.28078i | −0.203075 | − | 0.117245i | ||||
\(784\) | 2.84233 | + | 4.92306i | 0.101512 | + | 0.175824i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.06155 | − | 5.30277i | −0.109202 | − | 0.189143i | ||||
\(787\) | −37.8320 | + | 21.8423i | −1.34857 | + | 0.778595i | −0.988046 | − | 0.154157i | \(-0.950734\pi\) |
−0.360520 | + | 0.932752i | \(0.617401\pi\) | |||||||
\(788\) | − | 7.80776i | − | 0.278140i | ||||||
\(789\) | −6.50000 | − | 11.2583i | −0.231406 | − | 0.400807i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.56155 | − | 11.3649i | 0.233302 | − | 0.404091i | ||||
\(792\) | 4.12311i | 0.146508i | ||||||||
\(793\) | −21.4243 | + | 3.00000i | −0.760799 | + | 0.106533i | ||||
\(794\) | 11.8769 | 0.421495 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.56155 | + | 9.63289i | −0.197124 | + | 0.341429i | ||||
\(797\) | −4.22351 | + | 2.43845i | −0.149605 | + | 0.0863742i | −0.572934 | − | 0.819602i | \(-0.694195\pi\) |
0.423329 | + | 0.905976i | \(0.360861\pi\) | |||||||
\(798\) | − | 12.6847i | − | 0.449032i | ||||||
\(799\) | 17.9309 | + | 31.0572i | 0.634349 | + | 1.09872i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.80776 | 0.0638742 | ||||||||
\(802\) | −10.9852 | + | 6.34233i | −0.387902 | + | 0.223955i | ||||
\(803\) | −54.8794 | − | 31.6847i | −1.93665 | − | 1.11813i | ||||
\(804\) | 7.12311 | − | 12.3376i | 0.251213 | − | 0.435113i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.1577 | − | 12.6107i | 0.569130 | − | 0.444192i | ||||
\(807\) | 3.36932i | 0.118606i | ||||||||
\(808\) | 14.8290 | + | 8.56155i | 0.521684 | + | 0.301194i | ||||
\(809\) | 9.24621 | − | 16.0149i | 0.325079 | − | 0.563054i | −0.656449 | − | 0.754370i | \(-0.727942\pi\) |
0.981528 | + | 0.191316i | \(0.0612756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.5464 | −0.791711 | −0.395856 | − | 0.918313i | \(-0.629552\pi\) | ||||
−0.395856 | + | 0.918313i | \(0.629552\pi\) | |||||||
\(812\) | −20.2384 | + | 11.6847i | −0.710229 | + | 0.410051i | ||||
\(813\) | 27.8662 | − | 16.0885i | 0.977309 | − | 0.564250i | ||||
\(814\) | 17.0000 | 0.595850 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.56155 | + | 4.43674i | −0.0896723 | + | 0.155317i | ||||
\(817\) | −14.0696 | − | 8.12311i | −0.492234 | − | 0.284191i | ||||
\(818\) | 1.80776i | 0.0632070i | ||||||||
\(819\) | −10.1231 | + | 7.90084i | −0.353730 | + | 0.276078i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.28078 | − | 10.8786i | 0.219201 | − | 0.379667i | −0.735363 | − | 0.677673i | \(-0.762988\pi\) |
0.954564 | + | 0.298007i | \(0.0963217\pi\) | |||||||
\(822\) | −7.62775 | − | 4.40388i | −0.266048 | − | 0.153603i | ||||
\(823\) | −27.7596 | + | 16.0270i | −0.967637 | + | 0.558666i | −0.898515 | − | 0.438943i | \(-0.855353\pi\) |
−0.0691222 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(824\) | −0.438447 | −0.0152740 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.8078 | − | 32.5760i | −0.654406 | − | 1.13346i | ||||
\(827\) | 11.7538i | 0.408719i | 0.978896 | + | 0.204360i | \(0.0655112\pi\) | ||||
−0.978896 | + | 0.204360i | \(0.934489\pi\) | |||||||
\(828\) | −6.65511 | + | 3.84233i | −0.231281 | + | 0.133530i | ||||
\(829\) | 26.8078 | − | 46.4324i | 0.931072 | − | 1.61266i | 0.149580 | − | 0.988750i | \(-0.452208\pi\) |
0.781493 | − | 0.623915i | \(-0.214459\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | −1.35234 | + | 3.34233i | −0.0468841 | + | 0.115874i | ||||
\(833\) | 29.1231i | 1.00906i | ||||||||
\(834\) | 4.21922 | − | 7.30791i | 0.146100 | − | 0.253052i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.34233 | − | 12.7173i | −0.253940 | − | 0.439837i | ||||
\(837\) | − | 5.68466i | − | 0.196491i | ||||||
\(838\) | −0.426450 | + | 0.246211i | −0.0147315 | + | 0.00850523i | ||||
\(839\) | −6.36932 | − | 11.0320i | −0.219893 | − | 0.380866i | 0.734882 | − | 0.678195i | \(-0.237238\pi\) |
−0.954775 | + | 0.297329i | \(0.903904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.02699 | − | 12.1711i | −0.242310 | − | 0.419693i | ||||
\(842\) | 0.426450 | + | 0.246211i | 0.0146965 | + | 0.00848500i | ||||
\(843\) | 0.213225 | + | 0.123106i | 0.00734387 | + | 0.00423998i | ||||
\(844\) | −6.93087 | −0.238570 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | 18.5064 | + | 10.6847i | 0.635886 | + | 0.367129i | ||||
\(848\) | −3.84381 | − | 2.21922i | −0.131997 | − | 0.0762085i | ||||
\(849\) | 5.71922 | + | 9.90599i | 0.196283 | + | 0.339973i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8423 | + | 27.4397i | 0.543068 | + | 0.940621i | ||||
\(852\) | 4.22351 | − | 2.43845i | 0.144695 | − | 0.0835398i | ||||
\(853\) | − | 51.3002i | − | 1.75648i | −0.478216 | − | 0.878242i | \(-0.658716\pi\) | ||
0.478216 | − | 0.878242i | \(-0.341284\pi\) | |||||||
\(854\) | 10.6847 | + | 18.5064i | 0.365621 | + | 0.633275i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.00000 | + | 1.73205i | −0.0341793 | + | 0.0592003i | ||||
\(857\) | 26.8078i | 0.915736i | 0.889020 | + | 0.457868i | \(0.151387\pi\) | ||||
−0.889020 | + | 0.457868i | \(0.848613\pi\) | |||||||
\(858\) | −5.57586 | + | 13.7808i | −0.190357 | + | 0.470468i | ||||
\(859\) | 46.7926 | 1.59654 | 0.798272 | − | 0.602298i | \(-0.205748\pi\) | ||||
0.798272 | + | 0.602298i | \(0.205748\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.56155 | − | 13.0970i | 0.257697 | − | 0.446344i | ||||
\(862\) | −23.1563 | + | 13.3693i | −0.788708 | + | 0.455361i | ||||
\(863\) | 6.56155i | 0.223358i | 0.993744 | + | 0.111679i | \(0.0356228\pi\) | ||||
−0.993744 | + | 0.111679i | \(0.964377\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 30.7386 | 1.04454 | ||||||||
\(867\) | −8.00745 | + | 4.62311i | −0.271947 | + | 0.157009i | ||||
\(868\) | −17.5337 | − | 10.1231i | −0.595134 | − | 0.343601i | ||||
\(869\) | −15.3348 | + | 26.5606i | −0.520196 | + | 0.901006i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.4924 | − | 31.6034i | 1.37203 | − | 1.07084i | ||||
\(872\) | 20.2462i | 0.685623i | ||||||||
\(873\) | −0.972638 | − | 0.561553i | −0.0329188 | − | 0.0190057i | ||||
\(874\) | 13.6847 | − | 23.7025i | 0.462890 | − | 0.801750i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −15.3693 | −0.519281 | ||||||||
\(877\) | −10.8786 | + | 6.28078i | −0.367345 | + | 0.212087i | −0.672298 | − | 0.740281i | \(-0.734693\pi\) |
0.304953 | + | 0.952367i | \(0.401359\pi\) | |||||||
\(878\) | 14.6158 | − | 8.43845i | 0.493260 | − | 0.284784i | ||||
\(879\) | 24.9309 | 0.840897 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2192 | − | 17.7002i | 0.344294 | − | 0.596335i | −0.640931 | − | 0.767599i | \(-0.721452\pi\) |
0.985225 | + | 0.171263i | \(0.0547848\pi\) | |||||||
\(882\) | 4.92306 | + | 2.84233i | 0.165768 | + | 0.0957062i | ||||
\(883\) | 26.1771i | 0.880929i | 0.897770 | + | 0.440464i | \(0.145186\pi\) | ||||
−0.897770 | + | 0.440464i | \(0.854814\pi\) | |||||||
\(884\) | −14.5616 | + | 11.3649i | −0.489758 | + | 0.382244i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.43845 | − | 4.22351i | 0.0819212 | − | 0.141892i | ||||
\(887\) | 35.6005 | + | 20.5540i | 1.19535 | + | 0.690135i | 0.959515 | − | 0.281658i | \(-0.0908845\pi\) |
0.235834 | + | 0.971793i | \(0.424218\pi\) | |||||||
\(888\) | 3.57071 | − | 2.06155i | 0.119825 | − | 0.0691812i | ||||
\(889\) | 15.8078 | 0.530175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.06155 | + | 3.57071i | 0.0690646 | + | 0.119623i | ||||
\(892\) | 26.3002i | 0.880595i | ||||||||
\(893\) | −21.5908 | + | 12.4654i | −0.722507 | + | 0.417140i | ||||
\(894\) | −11.4039 | + | 19.7521i | −0.381403 | + | 0.660609i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.56155 | 0.118983 | ||||||||
\(897\) | −27.4397 | + | 3.84233i | −0.916186 | + | 0.128292i | ||||
\(898\) | 25.1771i | 0.840170i | ||||||||
\(899\) | 18.6501 | − | 32.3029i | 0.622015 | − | 1.07736i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3693 | − | 19.6922i | −0.378767 | − | 0.656043i | ||||
\(902\) | − | 17.5076i | − | 0.582939i | ||||||
\(903\) | 14.0696 | − | 8.12311i | 0.468208 | − | 0.270320i | ||||
\(904\) | −1.84233 | − | 3.19101i | −0.0612750 | − | 0.106131i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.68466 | − | 8.11407i | −0.155637 | − | 0.269572i | ||||
\(907\) | 35.4340 | + | 20.4579i | 1.17657 | + | 0.679292i | 0.955218 | − | 0.295902i | \(-0.0956203\pi\) |
0.221350 | + | 0.975194i | \(0.428954\pi\) | |||||||
\(908\) | 17.3205 | + | 10.0000i | 0.574801 | + | 0.331862i | ||||
\(909\) | 17.1231 | 0.567938 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.3693 | −1.43689 | −0.718445 | − | 0.695584i | \(-0.755146\pi\) | ||||
−0.718445 | + | 0.695584i | \(0.755146\pi\) | |||||||
\(912\) | −3.08440 | − | 1.78078i | −0.102135 | − | 0.0589674i | ||||
\(913\) | 4.01029 | + | 2.31534i | 0.132721 | + | 0.0766266i | ||||
\(914\) | 1.87689 | + | 3.25088i | 0.0620821 | + | 0.107529i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.87689 | + | 6.71498i | 0.128096 | + | 0.221869i | ||||
\(917\) | −18.8861 | + | 10.9039i | −0.623673 | + | 0.360078i | ||||
\(918\) | 5.12311i | 0.169088i | ||||||||
\(919\) | 20.6847 | + | 35.8269i | 0.682324 | + | 1.18182i | 0.974270 | + | 0.225385i | \(0.0723639\pi\) |
−0.291946 | + | 0.956435i | \(0.594303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.80776 | − | 13.5234i | 0.257275 | − | 0.445613i | ||||
\(922\) | − | 7.05398i | − | 0.232310i | ||||||
\(923\) | 17.4140 | − | 2.43845i | 0.573189 | − | 0.0802625i | ||||
\(924\) | 14.6847 | 0.483090 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.8078 | + | 29.1119i | −0.552337 | + | 0.956676i | ||||
\(927\) | −0.379706 | + | 0.219224i | −0.0124712 | + | 0.00720025i | ||||
\(928\) | 6.56155i | 0.215394i | ||||||||
\(929\) | −8.43845 | − | 14.6158i | −0.276856 | − | 0.479529i | 0.693745 | − | 0.720220i | \(-0.255959\pi\) |
−0.970602 | + | 0.240691i | \(0.922626\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2462 | −0.663543 | ||||||||
\(932\) | 15.3154 | − | 8.84233i | 0.501671 | − | 0.289640i | ||||
\(933\) | 16.2281 | + | 9.36932i | 0.531285 | + | 0.306738i | ||||
\(934\) | 19.9309 | − | 34.5213i | 0.652158 | − | 1.12957i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 3.57071i | 0.0163430 | + | 0.116712i | ||||
\(937\) | 29.2311i | 0.954937i | 0.878649 | + | 0.477468i | \(0.158446\pi\) | ||||
−0.878649 | + | 0.477468i | \(0.841554\pi\) | |||||||
\(938\) | −43.9409 | − | 25.3693i | −1.43472 | − | 0.828338i | ||||
\(939\) | 3.31534 | − | 5.74234i | 0.108192 | − | 0.187394i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.630683 | −0.0205597 | −0.0102798 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102798 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(942\) | −19.1592 | + | 11.0616i | −0.624240 | + | 0.360405i | ||||
\(943\) | 28.2590 | − | 16.3153i | 0.920240 | − | 0.531301i | ||||
\(944\) | −10.5616 | −0.343749 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.40388 | − | 16.2880i | 0.305747 | − | 0.529569i | ||||
\(947\) | 12.0046 | + | 6.93087i | 0.390098 | + | 0.225223i | 0.682202 | − | 0.731163i | \(-0.261022\pi\) |
−0.292105 | + | 0.956386i | \(0.594356\pi\) | |||||||
\(948\) | 7.43845i | 0.241590i | ||||||||
\(949\) | −51.3693 | − | 20.7846i | −1.66752 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.09612 | − | 3.63058i | 0.0679713 | − | 0.117730i | ||||
\(952\) | 15.8017 | + | 9.12311i | 0.512135 | + | 0.295682i | ||||
\(953\) | 5.04280 | − | 2.91146i | 0.163352 | − | 0.0943114i | −0.416095 | − | 0.909321i | \(-0.636602\pi\) |
0.579447 | + | 0.815010i | \(0.303268\pi\) | |||||||
\(954\) | −4.43845 | −0.143700 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.68466 | − | 11.5782i | −0.216197 | − | 0.374465i | ||||
\(957\) | 27.0540i | 0.874531i | ||||||||
\(958\) | −18.8393 | + | 10.8769i | −0.608671 | + | 0.351417i | ||||
\(959\) | −15.6847 | + | 27.1666i | −0.506484 | + | 0.877256i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.31534 | 0.0424304 | ||||||||
\(962\) | 14.7224 | − | 2.06155i | 0.474670 | − | 0.0664671i | ||||
\(963\) | 2.00000i | 0.0644491i | ||||||||
\(964\) | −9.93845 | + | 17.2139i | −0.320096 | + | 0.554422i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.6847 | + | 23.7025i | 0.440297 | + | 0.762616i | ||||
\(967\) | − | 3.31534i | − | 0.106614i | −0.998578 | − | 0.0533071i | \(-0.983024\pi\) | ||
0.998578 | − | 0.0533071i | \(-0.0169762\pi\) | |||||||
\(968\) | 5.19615 | − | 3.00000i | 0.167011 | − | 0.0964237i | ||||
\(969\) | −9.12311 | − | 15.8017i | −0.293076 | − | 0.507623i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.34233 | + | 14.4493i | 0.267718 | + | 0.463701i | 0.968272 | − | 0.249898i | \(-0.0803971\pi\) |
−0.700554 | + | 0.713599i | \(0.747064\pi\) | |||||||
\(972\) | 0.866025 | + | 0.500000i | 0.0277778 | + | 0.0160375i | ||||
\(973\) | −26.0275 | − | 15.0270i | −0.834404 | − | 0.481743i | ||||
\(974\) | 24.0540 | 0.770739 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 4.59010 | + | 2.65009i | 0.146850 | + | 0.0847840i | 0.571625 | − | 0.820515i | \(-0.306313\pi\) |
−0.424775 | + | 0.905299i | \(0.639647\pi\) | |||||||
\(978\) | 16.0748 | + | 9.28078i | 0.514015 | + | 0.296767i | ||||
\(979\) | −3.72680 | − | 6.45501i | −0.119109 | − | 0.206303i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.1231 | + | 17.5337i | 0.323206 | + | 0.559809i | ||||
\(982\) | 18.6729 | − | 10.7808i | 0.595875 | − | 0.344028i | ||||
\(983\) | 23.8769i | 0.761555i | 0.924667 | + | 0.380777i | \(0.124344\pi\) | ||||
−0.924667 | + | 0.380777i | \(0.875656\pi\) | |||||||
\(984\) | −2.12311 | − | 3.67733i | −0.0676821 | − | 0.117229i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.8078 | + | 29.1119i | −0.535268 | + | 0.927112i | ||||
\(987\) | − | 24.9309i | − | 0.793558i | ||||||
\(988\) | −7.90084 | − | 10.1231i | −0.251359 | − | 0.322059i | ||||
\(989\) | 35.0540 | 1.11465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.21165 | − | 10.7589i | 0.197319 | − | 0.341767i | −0.750339 | − | 0.661053i | \(-0.770110\pi\) |
0.947658 | + | 0.319286i | \(0.103443\pi\) | |||||||
\(992\) | −4.92306 | + | 2.84233i | −0.156307 | + | 0.0902440i | ||||
\(993\) | − | 18.7386i | − | 0.594653i | ||||||
\(994\) | −8.68466 | − | 15.0423i | −0.275461 | − | 0.477112i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.12311 | 0.0355870 | ||||||||
\(997\) | −28.1860 | + | 16.2732i | −0.892660 | + | 0.515377i | −0.874812 | − | 0.484463i | \(-0.839015\pi\) |
−0.0178482 | + | 0.999841i | \(0.505682\pi\) | |||||||
\(998\) | −3.46410 | − | 2.00000i | −0.109654 | − | 0.0633089i | ||||
\(999\) | 2.06155 | − | 3.57071i | 0.0652246 | − | 0.112972i |
(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.n.1699.3 | 8 | ||
5.2 | odd | 4 | 390.2.i.g.61.1 | ✓ | 4 | ||
5.3 | odd | 4 | 1950.2.i.bi.451.2 | 4 | |||
5.4 | even | 2 | inner | 1950.2.z.n.1699.2 | 8 | ||
13.3 | even | 3 | inner | 1950.2.z.n.1849.2 | 8 | ||
15.2 | even | 4 | 1170.2.i.o.451.1 | 4 | |||
65.3 | odd | 12 | 1950.2.i.bi.601.2 | 4 | |||
65.7 | even | 12 | 5070.2.b.r.1351.3 | 4 | |||
65.17 | odd | 12 | 5070.2.a.bb.1.1 | 2 | |||
65.22 | odd | 12 | 5070.2.a.bi.1.2 | 2 | |||
65.29 | even | 6 | inner | 1950.2.z.n.1849.3 | 8 | ||
65.32 | even | 12 | 5070.2.b.r.1351.2 | 4 | |||
65.42 | odd | 12 | 390.2.i.g.211.1 | yes | 4 | ||
195.107 | even | 12 | 1170.2.i.o.991.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.1 | ✓ | 4 | 5.2 | odd | 4 | ||
390.2.i.g.211.1 | yes | 4 | 65.42 | odd | 12 | ||
1170.2.i.o.451.1 | 4 | 15.2 | even | 4 | |||
1170.2.i.o.991.1 | 4 | 195.107 | even | 12 | |||
1950.2.i.bi.451.2 | 4 | 5.3 | odd | 4 | |||
1950.2.i.bi.601.2 | 4 | 65.3 | odd | 12 | |||
1950.2.z.n.1699.2 | 8 | 5.4 | even | 2 | inner | ||
1950.2.z.n.1699.3 | 8 | 1.1 | even | 1 | trivial | ||
1950.2.z.n.1849.2 | 8 | 13.3 | even | 3 | inner | ||
1950.2.z.n.1849.3 | 8 | 65.29 | even | 6 | inner | ||
5070.2.a.bb.1.1 | 2 | 65.17 | odd | 12 | |||
5070.2.a.bi.1.2 | 2 | 65.22 | odd | 12 | |||
5070.2.b.r.1351.2 | 4 | 65.32 | even | 12 | |||
5070.2.b.r.1351.3 | 4 | 65.7 | even | 12 |