Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(61,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.i (of order \(3\), degree \(2\), 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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(1.28078 + 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.61 |
Dual form | 390.2.i.g.211.1 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −1.78078 | − | 3.08440i | −0.673070 | − | 1.16579i | −0.977029 | − | 0.213107i | \(-0.931642\pi\) |
0.303959 | − | 0.952685i | \(-0.401692\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 2.06155 | − | 3.57071i | 0.621582 | − | 1.07661i | −0.367610 | − | 0.929980i | \(-0.619824\pi\) |
0.989191 | − | 0.146631i | \(-0.0468429\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.34233 | − | 1.35234i | −0.926995 | − | 0.375073i | ||||
\(14\) | 3.56155 | 0.951865 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.56155 | − | 4.43674i | −0.621268 | − | 1.07607i | −0.989250 | − | 0.146235i | \(-0.953285\pi\) |
0.367982 | − | 0.929833i | \(-0.380049\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.78078 | + | 3.08440i | 0.408538 | + | 0.707609i | 0.994726 | − | 0.102566i | \(-0.0327054\pi\) |
−0.586188 | + | 0.810175i | \(0.699372\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 3.56155 | 0.777195 | ||||||||
\(22\) | 2.06155 | + | 3.57071i | 0.439525 | + | 0.761279i | ||||
\(23\) | 3.84233 | − | 6.65511i | 0.801181 | − | 1.38769i | −0.117658 | − | 0.993054i | \(-0.537539\pi\) |
0.918839 | − | 0.394632i | \(-0.129128\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.84233 | − | 2.21837i | 0.557427 | − | 0.435058i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.78078 | + | 3.08440i | −0.336535 | + | 0.582896i | ||||
\(29\) | −3.28078 | + | 5.68247i | −0.609225 | + | 1.05521i | 0.382144 | + | 0.924103i | \(0.375186\pi\) |
−0.991368 | + | 0.131105i | \(0.958147\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | 5.68466 | 1.02099 | 0.510497 | − | 0.859879i | \(-0.329461\pi\) | ||||
0.510497 | + | 0.859879i | \(0.329461\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 2.06155 | + | 3.57071i | 0.358870 | + | 0.621582i | ||||
\(34\) | 5.12311 | 0.878605 | ||||||||
\(35\) | −1.78078 | − | 3.08440i | −0.301006 | − | 0.521358i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −2.06155 | + | 3.57071i | −0.338917 | + | 0.587022i | −0.984229 | − | 0.176897i | \(-0.943394\pi\) |
0.645312 | + | 0.763919i | \(0.276727\pi\) | |||||||
\(38\) | −3.56155 | −0.577760 | ||||||||
\(39\) | 2.84233 | − | 2.21837i | 0.455137 | − | 0.355223i | ||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.12311 | − | 3.67733i | 0.331573 | − | 0.574302i | −0.651247 | − | 0.758866i | \(-0.725754\pi\) |
0.982821 | + | 0.184564i | \(0.0590872\pi\) | |||||||
\(42\) | −1.78078 | + | 3.08440i | −0.274780 | + | 0.475933i | ||||
\(43\) | −2.28078 | − | 3.95042i | −0.347815 | − | 0.602433i | 0.638046 | − | 0.769998i | \(-0.279743\pi\) |
−0.985861 | + | 0.167565i | \(0.946410\pi\) | |||||||
\(44\) | −4.12311 | −0.621582 | ||||||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 3.84233 | + | 6.65511i | 0.566521 | + | 0.981242i | ||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −2.84233 | + | 4.92306i | −0.406047 | + | 0.703294i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 5.12311 | 0.717378 | ||||||||
\(52\) | 0.500000 | + | 3.57071i | 0.0693375 | + | 0.495169i | ||||
\(53\) | 4.43845 | 0.609668 | 0.304834 | − | 0.952406i | \(-0.401399\pi\) | ||||
0.304834 | + | 0.952406i | \(0.401399\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.06155 | − | 3.57071i | 0.277980 | − | 0.481475i | ||||
\(56\) | −1.78078 | − | 3.08440i | −0.237966 | − | 0.412170i | ||||
\(57\) | −3.56155 | −0.471739 | ||||||||
\(58\) | −3.28078 | − | 5.68247i | −0.430787 | − | 0.746145i | ||||
\(59\) | −5.28078 | − | 9.14657i | −0.687499 | − | 1.19078i | −0.972645 | − | 0.232298i | \(-0.925375\pi\) |
0.285146 | − | 0.958484i | \(-0.407958\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | −2.84233 | + | 4.92306i | −0.360976 | + | 0.625229i | ||||
\(63\) | −1.78078 | + | 3.08440i | −0.224357 | + | 0.388597i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.34233 | − | 1.35234i | −0.414565 | − | 0.167738i | ||||
\(66\) | −4.12311 | −0.507519 | ||||||||
\(67\) | −7.12311 | + | 12.3376i | −0.870226 | + | 1.50728i | −0.00846293 | + | 0.999964i | \(0.502694\pi\) |
−0.861763 | + | 0.507311i | \(0.830639\pi\) | |||||||
\(68\) | −2.56155 | + | 4.43674i | −0.310634 | + | 0.538034i | ||||
\(69\) | 3.84233 | + | 6.65511i | 0.462562 | + | 0.801181i | ||||
\(70\) | 3.56155 | 0.425687 | ||||||||
\(71\) | 2.43845 | + | 4.22351i | 0.289390 | + | 0.501239i | 0.973664 | − | 0.227986i | \(-0.0732141\pi\) |
−0.684274 | + | 0.729225i | \(0.739881\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −15.3693 | −1.79884 | −0.899421 | − | 0.437083i | \(-0.856012\pi\) | ||||
−0.899421 | + | 0.437083i | \(0.856012\pi\) | |||||||
\(74\) | −2.06155 | − | 3.57071i | −0.239651 | − | 0.415087i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 1.78078 | − | 3.08440i | 0.204269 | − | 0.353804i | ||||
\(77\) | −14.6847 | −1.67347 | ||||||||
\(78\) | 0.500000 | + | 3.57071i | 0.0566139 | + | 0.404304i | ||||
\(79\) | 7.43845 | 0.836891 | 0.418445 | − | 0.908242i | \(-0.362575\pi\) | ||||
0.418445 | + | 0.908242i | \(0.362575\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.12311 | + | 3.67733i | 0.234458 | + | 0.406093i | ||||
\(83\) | 1.12311 | 0.123277 | 0.0616384 | − | 0.998099i | \(-0.480367\pi\) | ||||
0.0616384 | + | 0.998099i | \(0.480367\pi\) | |||||||
\(84\) | −1.78078 | − | 3.08440i | −0.194299 | − | 0.336535i | ||||
\(85\) | −2.56155 | − | 4.43674i | −0.277839 | − | 0.481232i | ||||
\(86\) | 4.56155 | 0.491885 | ||||||||
\(87\) | −3.28078 | − | 5.68247i | −0.351736 | − | 0.609225i | ||||
\(88\) | 2.06155 | − | 3.57071i | 0.219762 | − | 0.380639i | ||||
\(89\) | −0.903882 | + | 1.56557i | −0.0958113 | + | 0.165950i | −0.909947 | − | 0.414725i | \(-0.863878\pi\) |
0.814136 | + | 0.580675i | \(0.197211\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 1.78078 | + | 12.7173i | 0.186676 | + | 1.33313i | ||||
\(92\) | −7.68466 | −0.801181 | ||||||||
\(93\) | −2.84233 | + | 4.92306i | −0.294736 | + | 0.510497i | ||||
\(94\) | −3.50000 | + | 6.06218i | −0.360997 | + | 0.625266i | ||||
\(95\) | 1.78078 | + | 3.08440i | 0.182704 | + | 0.316452i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.561553 | − | 0.972638i | −0.0570170 | − | 0.0987564i | 0.836108 | − | 0.548565i | \(-0.184826\pi\) |
−0.893125 | + | 0.449808i | \(0.851492\pi\) | |||||||
\(98\) | −2.84233 | − | 4.92306i | −0.287119 | − | 0.497304i | ||||
\(99\) | −4.12311 | −0.414388 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 8.56155 | − | 14.8290i | 0.851906 | − | 1.47555i | −0.0275793 | − | 0.999620i | \(-0.508780\pi\) |
0.879486 | − | 0.475925i | \(-0.157887\pi\) | |||||||
\(102\) | −2.56155 | + | 4.43674i | −0.253632 | + | 0.439303i | ||||
\(103\) | 0.438447 | 0.0432015 | 0.0216007 | − | 0.999767i | \(-0.493124\pi\) | ||||
0.0216007 | + | 0.999767i | \(0.493124\pi\) | |||||||
\(104\) | −3.34233 | − | 1.35234i | −0.327742 | − | 0.132608i | ||||
\(105\) | 3.56155 | 0.347572 | ||||||||
\(106\) | −2.21922 | + | 3.84381i | −0.215550 | + | 0.373344i | ||||
\(107\) | −1.00000 | + | 1.73205i | −0.0966736 | + | 0.167444i | −0.910306 | − | 0.413936i | \(-0.864154\pi\) |
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −20.2462 | −1.93924 | −0.969618 | − | 0.244625i | \(-0.921335\pi\) | ||||
−0.969618 | + | 0.244625i | \(0.921335\pi\) | |||||||
\(110\) | 2.06155 | + | 3.57071i | 0.196561 | + | 0.340454i | ||||
\(111\) | −2.06155 | − | 3.57071i | −0.195674 | − | 0.338917i | ||||
\(112\) | 3.56155 | 0.336535 | ||||||||
\(113\) | 1.84233 | + | 3.19101i | 0.173312 | + | 0.300185i | 0.939576 | − | 0.342341i | \(-0.111220\pi\) |
−0.766264 | + | 0.642526i | \(0.777887\pi\) | |||||||
\(114\) | 1.78078 | − | 3.08440i | 0.166785 | − | 0.288880i | ||||
\(115\) | 3.84233 | − | 6.65511i | 0.358299 | − | 0.620592i | ||||
\(116\) | 6.56155 | 0.609225 | ||||||||
\(117\) | 0.500000 | + | 3.57071i | 0.0462250 | + | 0.330113i | ||||
\(118\) | 10.5616 | 0.972270 | ||||||||
\(119\) | −9.12311 | + | 15.8017i | −0.836314 | + | 1.44854i | ||||
\(120\) | −0.500000 | + | 0.866025i | −0.0456435 | + | 0.0790569i | ||||
\(121\) | −3.00000 | − | 5.19615i | −0.272727 | − | 0.472377i | ||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 2.12311 | + | 3.67733i | 0.191434 | + | 0.331573i | ||||
\(124\) | −2.84233 | − | 4.92306i | −0.255249 | − | 0.442104i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.78078 | − | 3.08440i | −0.158644 | − | 0.274780i | ||||
\(127\) | 2.21922 | − | 3.84381i | 0.196924 | − | 0.341083i | −0.750605 | − | 0.660751i | \(-0.770238\pi\) |
0.947530 | + | 0.319668i | \(0.103571\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.56155 | 0.401622 | ||||||||
\(130\) | 2.84233 | − | 2.21837i | 0.249289 | − | 0.194564i | ||||
\(131\) | 6.12311 | 0.534978 | 0.267489 | − | 0.963561i | \(-0.413806\pi\) | ||||
0.267489 | + | 0.963561i | \(0.413806\pi\) | |||||||
\(132\) | 2.06155 | − | 3.57071i | 0.179435 | − | 0.310791i | ||||
\(133\) | 6.34233 | − | 10.9852i | 0.549950 | − | 0.952541i | ||||
\(134\) | −7.12311 | − | 12.3376i | −0.615343 | − | 1.06580i | ||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −2.56155 | − | 4.43674i | −0.219651 | − | 0.380447i | ||||
\(137\) | 4.40388 | + | 7.62775i | 0.376249 | + | 0.651682i | 0.990513 | − | 0.137418i | \(-0.0438804\pi\) |
−0.614264 | + | 0.789101i | \(0.710547\pi\) | |||||||
\(138\) | −7.68466 | −0.654162 | ||||||||
\(139\) | −4.21922 | − | 7.30791i | −0.357870 | − | 0.619849i | 0.629735 | − | 0.776810i | \(-0.283164\pi\) |
−0.987605 | + | 0.156961i | \(0.949830\pi\) | |||||||
\(140\) | −1.78078 | + | 3.08440i | −0.150503 | + | 0.260679i | ||||
\(141\) | −3.50000 | + | 6.06218i | −0.294753 | + | 0.510527i | ||||
\(142\) | −4.87689 | −0.409260 | ||||||||
\(143\) | −11.7192 | + | 9.14657i | −0.980011 | + | 0.764875i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.28078 | + | 5.68247i | −0.272454 | + | 0.471904i | ||||
\(146\) | 7.68466 | − | 13.3102i | 0.635987 | − | 1.10156i | ||||
\(147\) | −2.84233 | − | 4.92306i | −0.234431 | − | 0.406047i | ||||
\(148\) | 4.12311 | 0.338917 | ||||||||
\(149\) | 11.4039 | + | 19.7521i | 0.934242 | + | 1.61816i | 0.775979 | + | 0.630758i | \(0.217256\pi\) |
0.158263 | + | 0.987397i | \(0.449411\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 9.36932 | 0.762464 | 0.381232 | − | 0.924479i | \(-0.375500\pi\) | ||||
0.381232 | + | 0.924479i | \(0.375500\pi\) | |||||||
\(152\) | 1.78078 | + | 3.08440i | 0.144440 | + | 0.250177i | ||||
\(153\) | −2.56155 | + | 4.43674i | −0.207089 | + | 0.358689i | ||||
\(154\) | 7.34233 | − | 12.7173i | 0.591662 | − | 1.02479i | ||||
\(155\) | 5.68466 | 0.456603 | ||||||||
\(156\) | −3.34233 | − | 1.35234i | −0.267601 | − | 0.108274i | ||||
\(157\) | 22.1231 | 1.76562 | 0.882808 | − | 0.469734i | \(-0.155650\pi\) | ||||
0.882808 | + | 0.469734i | \(0.155650\pi\) | |||||||
\(158\) | −3.71922 | + | 6.44188i | −0.295886 | + | 0.512489i | ||||
\(159\) | −2.21922 | + | 3.84381i | −0.175996 | + | 0.304834i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | −27.3693 | −2.15700 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 9.28078 | + | 16.0748i | 0.726927 | + | 1.25907i | 0.958176 | + | 0.286179i | \(0.0923853\pi\) |
−0.231250 | + | 0.972894i | \(0.574281\pi\) | |||||||
\(164\) | −4.24621 | −0.331573 | ||||||||
\(165\) | 2.06155 | + | 3.57071i | 0.160492 | + | 0.277980i | ||||
\(166\) | −0.561553 | + | 0.972638i | −0.0435850 | + | 0.0754913i | ||||
\(167\) | 10.1847 | − | 17.6403i | 0.788113 | − | 1.36505i | −0.139009 | − | 0.990291i | \(-0.544392\pi\) |
0.927122 | − | 0.374760i | \(-0.122275\pi\) | |||||||
\(168\) | 3.56155 | 0.274780 | ||||||||
\(169\) | 9.34233 | + | 9.03996i | 0.718641 | + | 0.695382i | ||||
\(170\) | 5.12311 | 0.392924 | ||||||||
\(171\) | 1.78078 | − | 3.08440i | 0.136179 | − | 0.235870i | ||||
\(172\) | −2.28078 | + | 3.95042i | −0.173908 | + | 0.301217i | ||||
\(173\) | 12.5885 | + | 21.8040i | 0.957089 | + | 1.65773i | 0.729514 | + | 0.683966i | \(0.239746\pi\) |
0.227575 | + | 0.973760i | \(0.426920\pi\) | |||||||
\(174\) | 6.56155 | 0.497430 | ||||||||
\(175\) | −1.78078 | − | 3.08440i | −0.134614 | − | 0.233158i | ||||
\(176\) | 2.06155 | + | 3.57071i | 0.155395 | + | 0.269153i | ||||
\(177\) | 10.5616 | 0.793855 | ||||||||
\(178\) | −0.903882 | − | 1.56557i | −0.0677488 | − | 0.117344i | ||||
\(179\) | 0.157671 | − | 0.273094i | 0.0117849 | − | 0.0204120i | −0.860073 | − | 0.510171i | \(-0.829582\pi\) |
0.871858 | + | 0.489759i | \(0.162915\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | 11.1231 | 0.826774 | 0.413387 | − | 0.910555i | \(-0.364346\pi\) | ||||
0.413387 | + | 0.910555i | \(0.364346\pi\) | |||||||
\(182\) | −11.9039 | − | 4.81645i | −0.882374 | − | 0.357019i | ||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 3.84233 | − | 6.65511i | 0.283260 | − | 0.490621i | ||||
\(185\) | −2.06155 | + | 3.57071i | −0.151568 | + | 0.262524i | ||||
\(186\) | −2.84233 | − | 4.92306i | −0.208410 | − | 0.360976i | ||||
\(187\) | −21.1231 | −1.54467 | ||||||||
\(188\) | −3.50000 | − | 6.06218i | −0.255264 | − | 0.442130i | ||||
\(189\) | −1.78078 | − | 3.08440i | −0.129532 | − | 0.224357i | ||||
\(190\) | −3.56155 | −0.258382 | ||||||||
\(191\) | −9.56155 | − | 16.5611i | −0.691850 | − | 1.19832i | −0.971231 | − | 0.238139i | \(-0.923463\pi\) |
0.279381 | − | 0.960180i | \(-0.409871\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(194\) | 1.12311 | 0.0806343 | ||||||||
\(195\) | 2.84233 | − | 2.21837i | 0.203543 | − | 0.158861i | ||||
\(196\) | 5.68466 | 0.406047 | ||||||||
\(197\) | 3.90388 | − | 6.76172i | 0.278140 | − | 0.481753i | −0.692782 | − | 0.721147i | \(-0.743615\pi\) |
0.970923 | + | 0.239394i | \(0.0769487\pi\) | |||||||
\(198\) | 2.06155 | − | 3.57071i | 0.146508 | − | 0.253760i | ||||
\(199\) | −5.56155 | − | 9.63289i | −0.394248 | − | 0.682858i | 0.598757 | − | 0.800931i | \(-0.295662\pi\) |
−0.993005 | + | 0.118073i | \(0.962328\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −7.12311 | − | 12.3376i | −0.502425 | − | 0.870226i | ||||
\(202\) | 8.56155 | + | 14.8290i | 0.602389 | + | 1.04337i | ||||
\(203\) | 23.3693 | 1.64020 | ||||||||
\(204\) | −2.56155 | − | 4.43674i | −0.179345 | − | 0.310634i | ||||
\(205\) | 2.12311 | − | 3.67733i | 0.148284 | − | 0.256836i | ||||
\(206\) | −0.219224 | + | 0.379706i | −0.0152740 | + | 0.0264554i | ||||
\(207\) | −7.68466 | −0.534121 | ||||||||
\(208\) | 2.84233 | − | 2.21837i | 0.197080 | − | 0.153816i | ||||
\(209\) | 14.6847 | 1.01576 | ||||||||
\(210\) | −1.78078 | + | 3.08440i | −0.122885 | + | 0.212843i | ||||
\(211\) | −3.46543 | + | 6.00231i | −0.238570 | + | 0.413216i | −0.960304 | − | 0.278955i | \(-0.910012\pi\) |
0.721734 | + | 0.692171i | \(0.243345\pi\) | |||||||
\(212\) | −2.21922 | − | 3.84381i | −0.152417 | − | 0.263994i | ||||
\(213\) | −4.87689 | −0.334159 | ||||||||
\(214\) | −1.00000 | − | 1.73205i | −0.0683586 | − | 0.118401i | ||||
\(215\) | −2.28078 | − | 3.95042i | −0.155548 | − | 0.269416i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −10.1231 | − | 17.5337i | −0.687201 | − | 1.19027i | ||||
\(218\) | 10.1231 | − | 17.5337i | 0.685623 | − | 1.18753i | ||||
\(219\) | 7.68466 | − | 13.3102i | 0.519281 | − | 0.899421i | ||||
\(220\) | −4.12311 | −0.277980 | ||||||||
\(221\) | 2.56155 | + | 18.2931i | 0.172309 | + | 1.23053i | ||||
\(222\) | 4.12311 | 0.276725 | ||||||||
\(223\) | 13.1501 | − | 22.7766i | 0.880595 | − | 1.52524i | 0.0299151 | − | 0.999552i | \(-0.490476\pi\) |
0.850680 | − | 0.525683i | \(-0.176190\pi\) | |||||||
\(224\) | −1.78078 | + | 3.08440i | −0.118983 | + | 0.206085i | ||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | −3.68466 | −0.245100 | ||||||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | 1.78078 | + | 3.08440i | 0.117935 | + | 0.204269i | ||||
\(229\) | −7.75379 | −0.512385 | −0.256192 | − | 0.966626i | \(-0.582468\pi\) | ||||
−0.256192 | + | 0.966626i | \(0.582468\pi\) | |||||||
\(230\) | 3.84233 | + | 6.65511i | 0.253356 | + | 0.438825i | ||||
\(231\) | 7.34233 | − | 12.7173i | 0.483090 | − | 0.836736i | ||||
\(232\) | −3.28078 | + | 5.68247i | −0.215394 | + | 0.373073i | ||||
\(233\) | −17.6847 | −1.15856 | −0.579280 | − | 0.815128i | \(-0.696666\pi\) | ||||
−0.579280 | + | 0.815128i | \(0.696666\pi\) | |||||||
\(234\) | −3.34233 | − | 1.35234i | −0.218495 | − | 0.0884055i | ||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | −5.28078 | + | 9.14657i | −0.343749 | + | 0.595391i | ||||
\(237\) | −3.71922 | + | 6.44188i | −0.241590 | + | 0.418445i | ||||
\(238\) | −9.12311 | − | 15.8017i | −0.591363 | − | 1.02427i | ||||
\(239\) | 13.3693 | 0.864789 | 0.432395 | − | 0.901684i | \(-0.357669\pi\) | ||||
0.432395 | + | 0.901684i | \(0.357669\pi\) | |||||||
\(240\) | −0.500000 | − | 0.866025i | −0.0322749 | − | 0.0559017i | ||||
\(241\) | 9.93845 | + | 17.2139i | 0.640192 | + | 1.10884i | 0.985390 | + | 0.170315i | \(0.0544784\pi\) |
−0.345198 | + | 0.938530i | \(0.612188\pi\) | |||||||
\(242\) | 6.00000 | 0.385695 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −3.00000 | + | 5.19615i | −0.192055 | + | 0.332650i | ||||
\(245\) | −2.84233 | + | 4.92306i | −0.181590 | + | 0.314523i | ||||
\(246\) | −4.24621 | −0.270729 | ||||||||
\(247\) | −1.78078 | − | 12.7173i | −0.113308 | − | 0.809182i | ||||
\(248\) | 5.68466 | 0.360976 | ||||||||
\(249\) | −0.561553 | + | 0.972638i | −0.0355870 | + | 0.0616384i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −0.0615528 | − | 0.106613i | −0.00388518 | − | 0.00672933i | 0.864076 | − | 0.503361i | \(-0.167903\pi\) |
−0.867961 | + | 0.496632i | \(0.834570\pi\) | |||||||
\(252\) | 3.56155 | 0.224357 | ||||||||
\(253\) | −15.8423 | − | 27.4397i | −0.995999 | − | 1.72512i | ||||
\(254\) | 2.21922 | + | 3.84381i | 0.139246 | + | 0.241182i | ||||
\(255\) | 5.12311 | 0.320821 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.719224 | − | 1.24573i | 0.0448639 | − | 0.0777066i | −0.842721 | − | 0.538350i | \(-0.819048\pi\) |
0.887585 | + | 0.460643i | \(0.152381\pi\) | |||||||
\(258\) | −2.28078 | + | 3.95042i | −0.141995 | + | 0.245942i | ||||
\(259\) | 14.6847 | 0.912460 | ||||||||
\(260\) | 0.500000 | + | 3.57071i | 0.0310087 | + | 0.221446i | ||||
\(261\) | 6.56155 | 0.406150 | ||||||||
\(262\) | −3.06155 | + | 5.30277i | −0.189143 | + | 0.327606i | ||||
\(263\) | 6.50000 | − | 11.2583i | 0.400807 | − | 0.694218i | −0.593016 | − | 0.805190i | \(-0.702063\pi\) |
0.993824 | + | 0.110972i | \(0.0353964\pi\) | |||||||
\(264\) | 2.06155 | + | 3.57071i | 0.126880 | + | 0.219762i | ||||
\(265\) | 4.43845 | 0.272652 | ||||||||
\(266\) | 6.34233 | + | 10.9852i | 0.388873 | + | 0.673548i | ||||
\(267\) | −0.903882 | − | 1.56557i | −0.0553167 | − | 0.0958113i | ||||
\(268\) | 14.2462 | 0.870226 | ||||||||
\(269\) | 1.68466 | + | 2.91791i | 0.102715 | + | 0.177908i | 0.912803 | − | 0.408401i | \(-0.133914\pi\) |
−0.810087 | + | 0.586310i | \(0.800580\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −16.0885 | + | 27.8662i | −0.977309 | + | 1.69275i | −0.305215 | + | 0.952283i | \(0.598728\pi\) |
−0.672094 | + | 0.740466i | \(0.734605\pi\) | |||||||
\(272\) | 5.12311 | 0.310634 | ||||||||
\(273\) | −11.9039 | − | 4.81645i | −0.720456 | − | 0.291505i | ||||
\(274\) | −8.80776 | −0.532096 | ||||||||
\(275\) | 2.06155 | − | 3.57071i | 0.124316 | − | 0.215322i | ||||
\(276\) | 3.84233 | − | 6.65511i | 0.231281 | − | 0.400591i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 8.43845 | 0.506104 | ||||||||
\(279\) | −2.84233 | − | 4.92306i | −0.170166 | − | 0.294736i | ||||
\(280\) | −1.78078 | − | 3.08440i | −0.106422 | − | 0.184328i | ||||
\(281\) | −0.246211 | −0.0146877 | −0.00734387 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734387 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(282\) | −3.50000 | − | 6.06218i | −0.208422 | − | 0.360997i | ||||
\(283\) | −5.71922 | + | 9.90599i | −0.339973 | + | 0.588850i | −0.984427 | − | 0.175793i | \(-0.943751\pi\) |
0.644455 | + | 0.764643i | \(0.277084\pi\) | |||||||
\(284\) | 2.43845 | − | 4.22351i | 0.144695 | − | 0.250619i | ||||
\(285\) | −3.56155 | −0.210968 | ||||||||
\(286\) | −2.06155 | − | 14.7224i | −0.121902 | − | 0.870556i | ||||
\(287\) | −15.1231 | −0.892689 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −4.62311 | + | 8.00745i | −0.271947 | + | 0.471027i | ||||
\(290\) | −3.28078 | − | 5.68247i | −0.192654 | − | 0.333686i | ||||
\(291\) | 1.12311 | 0.0658376 | ||||||||
\(292\) | 7.68466 | + | 13.3102i | 0.449711 | + | 0.778922i | ||||
\(293\) | 12.4654 | + | 21.5908i | 0.728238 | + | 1.26135i | 0.957627 | + | 0.288011i | \(0.0929940\pi\) |
−0.229389 | + | 0.973335i | \(0.573673\pi\) | |||||||
\(294\) | 5.68466 | 0.331536 | ||||||||
\(295\) | −5.28078 | − | 9.14657i | −0.307459 | − | 0.532534i | ||||
\(296\) | −2.06155 | + | 3.57071i | −0.119825 | + | 0.207544i | ||||
\(297\) | 2.06155 | − | 3.57071i | 0.119623 | − | 0.207194i | ||||
\(298\) | −22.8078 | −1.32122 | ||||||||
\(299\) | −21.8423 | + | 17.0474i | −1.26317 | + | 0.985877i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −8.12311 | + | 14.0696i | −0.468208 | + | 0.810960i | ||||
\(302\) | −4.68466 | + | 8.11407i | −0.269572 | + | 0.466912i | ||||
\(303\) | 8.56155 | + | 14.8290i | 0.491848 | + | 0.851906i | ||||
\(304\) | −3.56155 | −0.204269 | ||||||||
\(305\) | −3.00000 | − | 5.19615i | −0.171780 | − | 0.297531i | ||||
\(306\) | −2.56155 | − | 4.43674i | −0.146434 | − | 0.253632i | ||||
\(307\) | −15.6155 | −0.891225 | −0.445613 | − | 0.895226i | \(-0.647014\pi\) | ||||
−0.445613 | + | 0.895226i | \(0.647014\pi\) | |||||||
\(308\) | 7.34233 | + | 12.7173i | 0.418368 | + | 0.724635i | ||||
\(309\) | −0.219224 | + | 0.379706i | −0.0124712 | + | 0.0216007i | ||||
\(310\) | −2.84233 | + | 4.92306i | −0.161433 | + | 0.279611i | ||||
\(311\) | −18.7386 | −1.06257 | −0.531285 | − | 0.847193i | \(-0.678291\pi\) | ||||
−0.531285 | + | 0.847193i | \(0.678291\pi\) | |||||||
\(312\) | 2.84233 | − | 2.21837i | 0.160915 | − | 0.125590i | ||||
\(313\) | 6.63068 | 0.374788 | 0.187394 | − | 0.982285i | \(-0.439996\pi\) | ||||
0.187394 | + | 0.982285i | \(0.439996\pi\) | |||||||
\(314\) | −11.0616 | + | 19.1592i | −0.624240 | + | 1.08121i | ||||
\(315\) | −1.78078 | + | 3.08440i | −0.100335 | + | 0.173786i | ||||
\(316\) | −3.71922 | − | 6.44188i | −0.209223 | − | 0.362384i | ||||
\(317\) | −4.19224 | −0.235459 | −0.117730 | − | 0.993046i | \(-0.537562\pi\) | ||||
−0.117730 | + | 0.993046i | \(0.537562\pi\) | |||||||
\(318\) | −2.21922 | − | 3.84381i | −0.124448 | − | 0.215550i | ||||
\(319\) | 13.5270 | + | 23.4294i | 0.757366 | + | 1.31180i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.00000 | − | 1.73205i | −0.0558146 | − | 0.0966736i | ||||
\(322\) | 13.6847 | − | 23.7025i | 0.762616 | − | 1.32089i | ||||
\(323\) | 9.12311 | − | 15.8017i | 0.507623 | − | 0.879229i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −3.34233 | − | 1.35234i | −0.185399 | − | 0.0750146i | ||||
\(326\) | −18.5616 | −1.02803 | ||||||||
\(327\) | 10.1231 | − | 17.5337i | 0.559809 | − | 0.969618i | ||||
\(328\) | 2.12311 | − | 3.67733i | 0.117229 | − | 0.203046i | ||||
\(329\) | −12.4654 | − | 21.5908i | −0.687242 | − | 1.19034i | ||||
\(330\) | −4.12311 | −0.226969 | ||||||||
\(331\) | 9.36932 | + | 16.2281i | 0.514984 | + | 0.891979i | 0.999849 | + | 0.0173896i | \(0.00553556\pi\) |
−0.484865 | + | 0.874589i | \(0.661131\pi\) | |||||||
\(332\) | −0.561553 | − | 0.972638i | −0.0308192 | − | 0.0533804i | ||||
\(333\) | 4.12311 | 0.225945 | ||||||||
\(334\) | 10.1847 | + | 17.6403i | 0.557280 | + | 0.965237i | ||||
\(335\) | −7.12311 | + | 12.3376i | −0.389177 | + | 0.674074i | ||||
\(336\) | −1.78078 | + | 3.08440i | −0.0971493 | + | 0.168268i | ||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | −12.5000 | + | 3.57071i | −0.679910 | + | 0.194221i | ||||
\(339\) | −3.68466 | −0.200123 | ||||||||
\(340\) | −2.56155 | + | 4.43674i | −0.138920 | + | 0.240616i | ||||
\(341\) | 11.7192 | − | 20.2983i | 0.634632 | − | 1.09921i | ||||
\(342\) | 1.78078 | + | 3.08440i | 0.0962934 | + | 0.166785i | ||||
\(343\) | −4.68466 | −0.252948 | ||||||||
\(344\) | −2.28078 | − | 3.95042i | −0.122971 | − | 0.212992i | ||||
\(345\) | 3.84233 | + | 6.65511i | 0.206864 | + | 0.358299i | ||||
\(346\) | −25.1771 | −1.35353 | ||||||||
\(347\) | −4.56155 | − | 7.90084i | −0.244877 | − | 0.424139i | 0.717220 | − | 0.696847i | \(-0.245414\pi\) |
−0.962097 | + | 0.272707i | \(0.912081\pi\) | |||||||
\(348\) | −3.28078 | + | 5.68247i | −0.175868 | + | 0.304612i | ||||
\(349\) | 12.2462 | − | 21.2111i | 0.655525 | − | 1.13540i | −0.326237 | − | 0.945288i | \(-0.605781\pi\) |
0.981762 | − | 0.190114i | \(-0.0608858\pi\) | |||||||
\(350\) | 3.56155 | 0.190373 | ||||||||
\(351\) | −3.34233 | − | 1.35234i | −0.178400 | − | 0.0721828i | ||||
\(352\) | −4.12311 | −0.219762 | ||||||||
\(353\) | −15.9309 | + | 27.5931i | −0.847915 | + | 1.46863i | 0.0351511 | + | 0.999382i | \(0.488809\pi\) |
−0.883066 | + | 0.469249i | \(0.844525\pi\) | |||||||
\(354\) | −5.28078 | + | 9.14657i | −0.280670 | + | 0.486135i | ||||
\(355\) | 2.43845 | + | 4.22351i | 0.129419 | + | 0.224161i | ||||
\(356\) | 1.80776 | 0.0958113 | ||||||||
\(357\) | −9.12311 | − | 15.8017i | −0.482846 | − | 0.836314i | ||||
\(358\) | 0.157671 | + | 0.273094i | 0.00833316 | + | 0.0144335i | ||||
\(359\) | 4.87689 | 0.257393 | 0.128696 | − | 0.991684i | \(-0.458921\pi\) | ||||
0.128696 | + | 0.991684i | \(0.458921\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 3.15767 | − | 5.46925i | 0.166193 | − | 0.287855i | ||||
\(362\) | −5.56155 | + | 9.63289i | −0.292309 | + | 0.506294i | ||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 10.1231 | − | 7.90084i | 0.530595 | − | 0.414117i | ||||
\(365\) | −15.3693 | −0.804467 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | 10.2462 | − | 17.7470i | 0.534848 | − | 0.926384i | −0.464323 | − | 0.885666i | \(-0.653702\pi\) |
0.999171 | − | 0.0407177i | \(-0.0129644\pi\) | |||||||
\(368\) | 3.84233 | + | 6.65511i | 0.200295 | + | 0.346922i | ||||
\(369\) | −4.24621 | −0.221049 | ||||||||
\(370\) | −2.06155 | − | 3.57071i | −0.107175 | − | 0.185633i | ||||
\(371\) | −7.90388 | − | 13.6899i | −0.410349 | − | 0.710746i | ||||
\(372\) | 5.68466 | 0.294736 | ||||||||
\(373\) | 2.59612 | + | 4.49661i | 0.134422 | + | 0.232826i | 0.925376 | − | 0.379049i | \(-0.123749\pi\) |
−0.790955 | + | 0.611875i | \(0.790416\pi\) | |||||||
\(374\) | 10.5616 | − | 18.2931i | 0.546125 | − | 0.945916i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 18.6501 | − | 14.5560i | 0.960529 | − | 0.749670i | ||||
\(378\) | 3.56155 | 0.183187 | ||||||||
\(379\) | 2.65767 | − | 4.60322i | 0.136515 | − | 0.236452i | −0.789660 | − | 0.613545i | \(-0.789743\pi\) |
0.926175 | + | 0.377093i | \(0.123076\pi\) | |||||||
\(380\) | 1.78078 | − | 3.08440i | 0.0913519 | − | 0.158226i | ||||
\(381\) | 2.21922 | + | 3.84381i | 0.113694 | + | 0.196924i | ||||
\(382\) | 19.1231 | 0.978423 | ||||||||
\(383\) | −10.4039 | − | 18.0201i | −0.531614 | − | 0.920782i | −0.999319 | − | 0.0368973i | \(-0.988253\pi\) |
0.467706 | − | 0.883884i | \(-0.345081\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | −14.6847 | −0.748399 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.28078 | + | 3.95042i | −0.115938 | + | 0.200811i | ||||
\(388\) | −0.561553 | + | 0.972638i | −0.0285085 | + | 0.0493782i | ||||
\(389\) | 19.0540 | 0.966075 | 0.483037 | − | 0.875600i | \(-0.339533\pi\) | ||||
0.483037 | + | 0.875600i | \(0.339533\pi\) | |||||||
\(390\) | 0.500000 | + | 3.57071i | 0.0253185 | + | 0.180810i | ||||
\(391\) | −39.3693 | −1.99099 | ||||||||
\(392\) | −2.84233 | + | 4.92306i | −0.143559 | + | 0.248652i | ||||
\(393\) | −3.06155 | + | 5.30277i | −0.154435 | + | 0.267489i | ||||
\(394\) | 3.90388 | + | 6.76172i | 0.196675 | + | 0.340651i | ||||
\(395\) | 7.43845 | 0.374269 | ||||||||
\(396\) | 2.06155 | + | 3.57071i | 0.103597 | + | 0.179435i | ||||
\(397\) | 5.93845 | + | 10.2857i | 0.298042 | + | 0.516224i | 0.975688 | − | 0.219164i | \(-0.0703331\pi\) |
−0.677646 | + | 0.735388i | \(0.737000\pi\) | |||||||
\(398\) | 11.1231 | 0.557551 | ||||||||
\(399\) | 6.34233 | + | 10.9852i | 0.317514 | + | 0.549950i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −6.34233 | + | 10.9852i | −0.316721 | + | 0.548577i | −0.979802 | − | 0.199971i | \(-0.935915\pi\) |
0.663081 | + | 0.748548i | \(0.269248\pi\) | |||||||
\(402\) | 14.2462 | 0.710536 | ||||||||
\(403\) | −19.0000 | − | 7.68762i | −0.946457 | − | 0.382947i | ||||
\(404\) | −17.1231 | −0.851906 | ||||||||
\(405\) | −0.500000 | + | 0.866025i | −0.0248452 | + | 0.0430331i | ||||
\(406\) | −11.6847 | + | 20.2384i | −0.579900 | + | 1.00442i | ||||
\(407\) | 8.50000 | + | 14.7224i | 0.421329 | + | 0.729764i | ||||
\(408\) | 5.12311 | 0.253632 | ||||||||
\(409\) | −0.903882 | − | 1.56557i | −0.0446941 | − | 0.0774124i | 0.842813 | − | 0.538207i | \(-0.180898\pi\) |
−0.887507 | + | 0.460794i | \(0.847565\pi\) | |||||||
\(410\) | 2.12311 | + | 3.67733i | 0.104853 | + | 0.181610i | ||||
\(411\) | −8.80776 | −0.434455 | ||||||||
\(412\) | −0.219224 | − | 0.379706i | −0.0108004 | − | 0.0187068i | ||||
\(413\) | −18.8078 | + | 32.5760i | −0.925470 | + | 1.60296i | ||||
\(414\) | 3.84233 | − | 6.65511i | 0.188840 | − | 0.327081i | ||||
\(415\) | 1.12311 | 0.0551311 | ||||||||
\(416\) | 0.500000 | + | 3.57071i | 0.0245145 | + | 0.175069i | ||||
\(417\) | 8.43845 | 0.413233 | ||||||||
\(418\) | −7.34233 | + | 12.7173i | −0.359125 | + | 0.622023i | ||||
\(419\) | 0.246211 | − | 0.426450i | 0.0120282 | − | 0.0208335i | −0.859949 | − | 0.510381i | \(-0.829505\pi\) |
0.871977 | + | 0.489547i | \(0.162838\pi\) | |||||||
\(420\) | −1.78078 | − | 3.08440i | −0.0868930 | − | 0.150503i | ||||
\(421\) | 0.492423 | 0.0239992 | 0.0119996 | − | 0.999928i | \(-0.496180\pi\) | ||||
0.0119996 | + | 0.999928i | \(0.496180\pi\) | |||||||
\(422\) | −3.46543 | − | 6.00231i | −0.168695 | − | 0.292188i | ||||
\(423\) | −3.50000 | − | 6.06218i | −0.170176 | − | 0.294753i | ||||
\(424\) | 4.43845 | 0.215550 | ||||||||
\(425\) | −2.56155 | − | 4.43674i | −0.124254 | − | 0.215213i | ||||
\(426\) | 2.43845 | − | 4.22351i | 0.118143 | − | 0.204630i | ||||
\(427\) | −10.6847 | + | 18.5064i | −0.517067 | + | 0.895586i | ||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | −2.06155 | − | 14.7224i | −0.0995327 | − | 0.710806i | ||||
\(430\) | 4.56155 | 0.219978 | ||||||||
\(431\) | −13.3693 | + | 23.1563i | −0.643977 | + | 1.11540i | 0.340559 | + | 0.940223i | \(0.389384\pi\) |
−0.984537 | + | 0.175178i | \(0.943950\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −15.3693 | − | 26.6204i | −0.738602 | − | 1.27930i | −0.953125 | − | 0.302578i | \(-0.902153\pi\) |
0.214523 | − | 0.976719i | \(-0.431180\pi\) | |||||||
\(434\) | 20.2462 | 0.971849 | ||||||||
\(435\) | −3.28078 | − | 5.68247i | −0.157301 | − | 0.272454i | ||||
\(436\) | 10.1231 | + | 17.5337i | 0.484809 | + | 0.839714i | ||||
\(437\) | 27.3693 | 1.30925 | ||||||||
\(438\) | 7.68466 | + | 13.3102i | 0.367187 | + | 0.635987i | ||||
\(439\) | −8.43845 | + | 14.6158i | −0.402745 | + | 0.697575i | −0.994056 | − | 0.108869i | \(-0.965277\pi\) |
0.591311 | + | 0.806444i | \(0.298611\pi\) | |||||||
\(440\) | 2.06155 | − | 3.57071i | 0.0982807 | − | 0.170227i | ||||
\(441\) | 5.68466 | 0.270698 | ||||||||
\(442\) | −17.1231 | − | 6.92820i | −0.814463 | − | 0.329541i | ||||
\(443\) | −4.87689 | −0.231708 | −0.115854 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115854 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(444\) | −2.06155 | + | 3.57071i | −0.0978370 | + | 0.169459i | ||||
\(445\) | −0.903882 | + | 1.56557i | −0.0428481 | + | 0.0742151i | ||||
\(446\) | 13.1501 | + | 22.7766i | 0.622675 | + | 1.07850i | ||||
\(447\) | −22.8078 | −1.07877 | ||||||||
\(448\) | −1.78078 | − | 3.08440i | −0.0841338 | − | 0.145724i | ||||
\(449\) | −12.5885 | − | 21.8040i | −0.594090 | − | 1.02899i | −0.993675 | − | 0.112298i | \(-0.964179\pi\) |
0.399585 | − | 0.916696i | \(-0.369154\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −8.75379 | − | 15.1620i | −0.412200 | − | 0.713951i | ||||
\(452\) | 1.84233 | − | 3.19101i | 0.0866559 | − | 0.150092i | ||||
\(453\) | −4.68466 | + | 8.11407i | −0.220104 | + | 0.381232i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 1.78078 | + | 12.7173i | 0.0834841 | + | 0.596196i | ||||
\(456\) | −3.56155 | −0.166785 | ||||||||
\(457\) | −1.87689 | + | 3.25088i | −0.0877974 | + | 0.152070i | −0.906580 | − | 0.422034i | \(-0.861316\pi\) |
0.818782 | + | 0.574104i | \(0.194649\pi\) | |||||||
\(458\) | 3.87689 | − | 6.71498i | 0.181155 | − | 0.313770i | ||||
\(459\) | −2.56155 | − | 4.43674i | −0.119563 | − | 0.207089i | ||||
\(460\) | −7.68466 | −0.358299 | ||||||||
\(461\) | −3.52699 | − | 6.10892i | −0.164268 | − | 0.284521i | 0.772127 | − | 0.635468i | \(-0.219193\pi\) |
−0.936395 | + | 0.350947i | \(0.885860\pi\) | |||||||
\(462\) | 7.34233 | + | 12.7173i | 0.341596 | + | 0.591662i | ||||
\(463\) | 33.6155 | 1.56225 | 0.781123 | − | 0.624377i | \(-0.214647\pi\) | ||||
0.781123 | + | 0.624377i | \(0.214647\pi\) | |||||||
\(464\) | −3.28078 | − | 5.68247i | −0.152306 | − | 0.263802i | ||||
\(465\) | −2.84233 | + | 4.92306i | −0.131810 | + | 0.228301i | ||||
\(466\) | 8.84233 | − | 15.3154i | 0.409613 | − | 0.709471i | ||||
\(467\) | 39.8617 | 1.84458 | 0.922291 | − | 0.386497i | \(-0.126315\pi\) | ||||
0.922291 | + | 0.386497i | \(0.126315\pi\) | |||||||
\(468\) | 2.84233 | − | 2.21837i | 0.131387 | − | 0.102544i | ||||
\(469\) | 50.7386 | 2.34289 | ||||||||
\(470\) | −3.50000 | + | 6.06218i | −0.161443 | + | 0.279627i | ||||
\(471\) | −11.0616 | + | 19.1592i | −0.509689 | + | 0.882808i | ||||
\(472\) | −5.28078 | − | 9.14657i | −0.243067 | − | 0.421005i | ||||
\(473\) | −18.8078 | −0.864782 | ||||||||
\(474\) | −3.71922 | − | 6.44188i | −0.170830 | − | 0.295886i | ||||
\(475\) | 1.78078 | + | 3.08440i | 0.0817076 | + | 0.141522i | ||||
\(476\) | 18.2462 | 0.836314 | ||||||||
\(477\) | −2.21922 | − | 3.84381i | −0.101611 | − | 0.175996i | ||||
\(478\) | −6.68466 | + | 11.5782i | −0.305749 | + | 0.529573i | ||||
\(479\) | 10.8769 | − | 18.8393i | 0.496978 | − | 0.860791i | −0.503016 | − | 0.864277i | \(-0.667776\pi\) |
0.999994 | + | 0.00348601i | \(0.00110963\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 11.7192 | − | 9.14657i | 0.534351 | − | 0.417048i | ||||
\(482\) | −19.8769 | −0.905368 | ||||||||
\(483\) | 13.6847 | − | 23.7025i | 0.622674 | − | 1.07850i | ||||
\(484\) | −3.00000 | + | 5.19615i | −0.136364 | + | 0.236189i | ||||
\(485\) | −0.561553 | − | 0.972638i | −0.0254988 | − | 0.0441652i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 12.0270 | + | 20.8314i | 0.544995 | + | 0.943959i | 0.998607 | + | 0.0527597i | \(0.0168017\pi\) |
−0.453612 | + | 0.891199i | \(0.649865\pi\) | |||||||
\(488\) | −3.00000 | − | 5.19615i | −0.135804 | − | 0.235219i | ||||
\(489\) | −18.5616 | −0.839382 | ||||||||
\(490\) | −2.84233 | − | 4.92306i | −0.128403 | − | 0.222401i | ||||
\(491\) | 10.7808 | − | 18.6729i | 0.486530 | − | 0.842694i | −0.513350 | − | 0.858179i | \(-0.671596\pi\) |
0.999880 | + | 0.0154850i | \(0.00492923\pi\) | |||||||
\(492\) | 2.12311 | − | 3.67733i | 0.0957170 | − | 0.165787i | ||||
\(493\) | 33.6155 | 1.51397 | ||||||||
\(494\) | 11.9039 | + | 4.81645i | 0.535581 | + | 0.216702i | ||||
\(495\) | −4.12311 | −0.185320 | ||||||||
\(496\) | −2.84233 | + | 4.92306i | −0.127624 | + | 0.221052i | ||||
\(497\) | 8.68466 | − | 15.0423i | 0.389560 | − | 0.674738i | ||||
\(498\) | −0.561553 | − | 0.972638i | −0.0251638 | − | 0.0435850i | ||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 10.1847 | + | 17.6403i | 0.455017 | + | 0.788113i | ||||
\(502\) | 0.123106 | 0.00549447 | ||||||||
\(503\) | 2.97301 | + | 5.14941i | 0.132560 | + | 0.229601i | 0.924663 | − | 0.380787i | \(-0.124347\pi\) |
−0.792103 | + | 0.610388i | \(0.791014\pi\) | |||||||
\(504\) | −1.78078 | + | 3.08440i | −0.0793221 | + | 0.137390i | ||||
\(505\) | 8.56155 | − | 14.8290i | 0.380984 | − | 0.659884i | ||||
\(506\) | 31.6847 | 1.40855 | ||||||||
\(507\) | −12.5000 | + | 3.57071i | −0.555144 | + | 0.158581i | ||||
\(508\) | −4.43845 | −0.196924 | ||||||||
\(509\) | 14.7732 | − | 25.5879i | 0.654811 | − | 1.13417i | −0.327131 | − | 0.944979i | \(-0.606082\pi\) |
0.981941 | − | 0.189186i | \(-0.0605849\pi\) | |||||||
\(510\) | −2.56155 | + | 4.43674i | −0.113427 | + | 0.196462i | ||||
\(511\) | 27.3693 | + | 47.4050i | 1.21075 | + | 2.09708i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.78078 | + | 3.08440i | 0.0786232 | + | 0.136179i | ||||
\(514\) | 0.719224 | + | 1.24573i | 0.0317236 | + | 0.0549469i | ||||
\(515\) | 0.438447 | 0.0193203 | ||||||||
\(516\) | −2.28078 | − | 3.95042i | −0.100406 | − | 0.173908i | ||||
\(517\) | 14.4309 | − | 24.9950i | 0.634669 | − | 1.09928i | ||||
\(518\) | −7.34233 | + | 12.7173i | −0.322603 | + | 0.558766i | ||||
\(519\) | −25.1771 | −1.10515 | ||||||||
\(520\) | −3.34233 | − | 1.35234i | −0.146571 | − | 0.0593042i | ||||
\(521\) | −18.6847 | −0.818590 | −0.409295 | − | 0.912402i | \(-0.634225\pi\) | ||||
−0.409295 | + | 0.912402i | \(0.634225\pi\) | |||||||
\(522\) | −3.28078 | + | 5.68247i | −0.143596 | + | 0.248715i | ||||
\(523\) | 4.59612 | − | 7.96071i | 0.200974 | − | 0.348098i | −0.747868 | − | 0.663847i | \(-0.768923\pi\) |
0.948843 | + | 0.315749i | \(0.102256\pi\) | |||||||
\(524\) | −3.06155 | − | 5.30277i | −0.133745 | − | 0.231652i | ||||
\(525\) | 3.56155 | 0.155439 | ||||||||
\(526\) | 6.50000 | + | 11.2583i | 0.283413 | + | 0.490887i | ||||
\(527\) | −14.5616 | − | 25.2213i | −0.634311 | − | 1.09866i | ||||
\(528\) | −4.12311 | −0.179435 | ||||||||
\(529\) | −18.0270 | − | 31.2237i | −0.783782 | − | 1.35755i | ||||
\(530\) | −2.21922 | + | 3.84381i | −0.0963969 | + | 0.166964i | ||||
\(531\) | −5.28078 | + | 9.14657i | −0.229166 | + | 0.396927i | ||||
\(532\) | −12.6847 | −0.549950 | ||||||||
\(533\) | −12.0691 | + | 9.41967i | −0.522772 | + | 0.408011i | ||||
\(534\) | 1.80776 | 0.0782296 | ||||||||
\(535\) | −1.00000 | + | 1.73205i | −0.0432338 | + | 0.0748831i | ||||
\(536\) | −7.12311 | + | 12.3376i | −0.307671 | + | 0.532902i | ||||
\(537\) | 0.157671 | + | 0.273094i | 0.00680400 | + | 0.0117849i | ||||
\(538\) | −3.36932 | −0.145262 | ||||||||
\(539\) | 11.7192 | + | 20.2983i | 0.504783 | + | 0.874309i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −2.63068 | −0.113102 | −0.0565510 | − | 0.998400i | \(-0.518010\pi\) | ||||
−0.0565510 | + | 0.998400i | \(0.518010\pi\) | |||||||
\(542\) | −16.0885 | − | 27.8662i | −0.691062 | − | 1.19695i | ||||
\(543\) | −5.56155 | + | 9.63289i | −0.238669 | + | 0.413387i | ||||
\(544\) | −2.56155 | + | 4.43674i | −0.109826 | + | 0.190224i | ||||
\(545\) | −20.2462 | −0.867252 | ||||||||
\(546\) | 10.1231 | − | 7.90084i | 0.433229 | − | 0.338125i | ||||
\(547\) | 35.6155 | 1.52281 | 0.761405 | − | 0.648276i | \(-0.224510\pi\) | ||||
0.761405 | + | 0.648276i | \(0.224510\pi\) | |||||||
\(548\) | 4.40388 | − | 7.62775i | 0.188125 | − | 0.325841i | ||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | 2.06155 | + | 3.57071i | 0.0879049 | + | 0.152256i | ||||
\(551\) | −23.3693 | −0.995566 | ||||||||
\(552\) | 3.84233 | + | 6.65511i | 0.163540 | + | 0.283260i | ||||
\(553\) | −13.2462 | − | 22.9431i | −0.563286 | − | 0.975640i | ||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | −2.06155 | − | 3.57071i | −0.0875080 | − | 0.151568i | ||||
\(556\) | −4.21922 | + | 7.30791i | −0.178935 | + | 0.309924i | ||||
\(557\) | 2.21922 | − | 3.84381i | 0.0940315 | − | 0.162867i | −0.815172 | − | 0.579218i | \(-0.803358\pi\) |
0.909204 | + | 0.416351i | \(0.136691\pi\) | |||||||
\(558\) | 5.68466 | 0.240651 | ||||||||
\(559\) | 2.28078 | + | 16.2880i | 0.0964666 | + | 0.688909i | ||||
\(560\) | 3.56155 | 0.150503 | ||||||||
\(561\) | 10.5616 | − | 18.2931i | 0.445909 | − | 0.772337i | ||||
\(562\) | 0.123106 | − | 0.213225i | 0.00519290 | − | 0.00899436i | ||||
\(563\) | −16.4924 | − | 28.5657i | −0.695073 | − | 1.20390i | −0.970156 | − | 0.242481i | \(-0.922039\pi\) |
0.275083 | − | 0.961420i | \(-0.411295\pi\) | |||||||
\(564\) | 7.00000 | 0.294753 | ||||||||
\(565\) | 1.84233 | + | 3.19101i | 0.0775074 | + | 0.134247i | ||||
\(566\) | −5.71922 | − | 9.90599i | −0.240397 | − | 0.416380i | ||||
\(567\) | 3.56155 | 0.149571 | ||||||||
\(568\) | 2.43845 | + | 4.22351i | 0.102315 | + | 0.177215i | ||||
\(569\) | 9.58854 | − | 16.6078i | 0.401973 | − | 0.696237i | −0.591991 | − | 0.805944i | \(-0.701658\pi\) |
0.993964 | + | 0.109707i | \(0.0349914\pi\) | |||||||
\(570\) | 1.78078 | − | 3.08440i | 0.0745885 | − | 0.129191i | ||||
\(571\) | 11.3153 | 0.473532 | 0.236766 | − | 0.971567i | \(-0.423912\pi\) | ||||
0.236766 | + | 0.971567i | \(0.423912\pi\) | |||||||
\(572\) | 13.7808 | + | 5.57586i | 0.576203 | + | 0.233138i | ||||
\(573\) | 19.1231 | 0.798879 | ||||||||
\(574\) | 7.56155 | − | 13.0970i | 0.315613 | − | 0.546658i | ||||
\(575\) | 3.84233 | − | 6.65511i | 0.160236 | − | 0.277537i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 8.73863 | 0.363794 | 0.181897 | − | 0.983318i | \(-0.441776\pi\) | ||||
0.181897 | + | 0.983318i | \(0.441776\pi\) | |||||||
\(578\) | −4.62311 | − | 8.00745i | −0.192296 | − | 0.333066i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.56155 | 0.272454 | ||||||||
\(581\) | −2.00000 | − | 3.46410i | −0.0829740 | − | 0.143715i | ||||
\(582\) | −0.561553 | + | 0.972638i | −0.0232771 | + | 0.0403171i | ||||
\(583\) | 9.15009 | − | 15.8484i | 0.378958 | − | 0.656375i | ||||
\(584\) | −15.3693 | −0.635987 | ||||||||
\(585\) | 0.500000 | + | 3.57071i | 0.0206725 | + | 0.147631i | ||||
\(586\) | −24.9309 | −1.02988 | ||||||||
\(587\) | 11.8769 | − | 20.5714i | 0.490212 | − | 0.849072i | −0.509725 | − | 0.860338i | \(-0.670253\pi\) |
0.999937 | + | 0.0112657i | \(0.00358606\pi\) | |||||||
\(588\) | −2.84233 | + | 4.92306i | −0.117216 | + | 0.203024i | ||||
\(589\) | 10.1231 | + | 17.5337i | 0.417115 | + | 0.722465i | ||||
\(590\) | 10.5616 | 0.434812 | ||||||||
\(591\) | 3.90388 | + | 6.76172i | 0.160584 | + | 0.278140i | ||||
\(592\) | −2.06155 | − | 3.57071i | −0.0847293 | − | 0.146755i | ||||
\(593\) | −12.1771 | −0.500053 | −0.250026 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250026 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(594\) | 2.06155 | + | 3.57071i | 0.0845865 | + | 0.146508i | ||||
\(595\) | −9.12311 | + | 15.8017i | −0.374011 | + | 0.647806i | ||||
\(596\) | 11.4039 | − | 19.7521i | 0.467121 | − | 0.809078i | ||||
\(597\) | 11.1231 | 0.455238 | ||||||||
\(598\) | −3.84233 | − | 27.4397i | −0.157125 | − | 1.12209i | ||||
\(599\) | −14.0000 | −0.572024 | −0.286012 | − | 0.958226i | \(-0.592330\pi\) | ||||
−0.286012 | + | 0.958226i | \(0.592330\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 17.9924 | − | 31.1638i | 0.733926 | − | 1.27120i | −0.221267 | − | 0.975213i | \(-0.571019\pi\) |
0.955193 | − | 0.295984i | \(-0.0956476\pi\) | |||||||
\(602\) | −8.12311 | − | 14.0696i | −0.331073 | − | 0.573435i | ||||
\(603\) | 14.2462 | 0.580151 | ||||||||
\(604\) | −4.68466 | − | 8.11407i | −0.190616 | − | 0.330157i | ||||
\(605\) | −3.00000 | − | 5.19615i | −0.121967 | − | 0.211254i | ||||
\(606\) | −17.1231 | −0.695579 | ||||||||
\(607\) | 14.7116 | + | 25.4813i | 0.597127 | + | 1.03425i | 0.993243 | + | 0.116054i | \(0.0370246\pi\) |
−0.396116 | + | 0.918201i | \(0.629642\pi\) | |||||||
\(608\) | 1.78078 | − | 3.08440i | 0.0722200 | − | 0.125089i | ||||
\(609\) | −11.6847 | + | 20.2384i | −0.473486 | + | 0.820102i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −23.3963 | − | 9.46641i | −0.946513 | − | 0.382970i | ||||
\(612\) | 5.12311 | 0.207089 | ||||||||
\(613\) | −14.0616 | + | 24.3553i | −0.567941 | + | 0.983702i | 0.428829 | + | 0.903386i | \(0.358926\pi\) |
−0.996769 | + | 0.0803164i | \(0.974407\pi\) | |||||||
\(614\) | 7.80776 | − | 13.5234i | 0.315096 | − | 0.545762i | ||||
\(615\) | 2.12311 | + | 3.67733i | 0.0856119 | + | 0.148284i | ||||
\(616\) | −14.6847 | −0.591662 | ||||||||
\(617\) | 20.8423 | + | 36.1000i | 0.839081 | + | 1.45333i | 0.890664 | + | 0.454662i | \(0.150240\pi\) |
−0.0515837 | + | 0.998669i | \(0.516427\pi\) | |||||||
\(618\) | −0.219224 | − | 0.379706i | −0.00881847 | − | 0.0152740i | ||||
\(619\) | −16.4384 | −0.660717 | −0.330358 | − | 0.943856i | \(-0.607170\pi\) | ||||
−0.330358 | + | 0.943856i | \(0.607170\pi\) | |||||||
\(620\) | −2.84233 | − | 4.92306i | −0.114151 | − | 0.197715i | ||||
\(621\) | 3.84233 | − | 6.65511i | 0.154187 | − | 0.267060i | ||||
\(622\) | 9.36932 | − | 16.2281i | 0.375675 | − | 0.650689i | ||||
\(623\) | 6.43845 | 0.257951 | ||||||||
\(624\) | 0.500000 | + | 3.57071i | 0.0200160 | + | 0.142943i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.31534 | + | 5.74234i | −0.132508 | + | 0.229510i | ||||
\(627\) | −7.34233 | + | 12.7173i | −0.293224 | + | 0.507880i | ||||
\(628\) | −11.0616 | − | 19.1592i | −0.441404 | − | 0.764534i | ||||
\(629\) | 21.1231 | 0.842233 | ||||||||
\(630\) | −1.78078 | − | 3.08440i | −0.0709478 | − | 0.122885i | ||||
\(631\) | 15.1231 | + | 26.1940i | 0.602041 | + | 1.04277i | 0.992512 | + | 0.122151i | \(0.0389791\pi\) |
−0.390470 | + | 0.920616i | \(0.627688\pi\) | |||||||
\(632\) | 7.43845 | 0.295886 | ||||||||
\(633\) | −3.46543 | − | 6.00231i | −0.137739 | − | 0.238570i | ||||
\(634\) | 2.09612 | − | 3.63058i | 0.0832475 | − | 0.144189i | ||||
\(635\) | 2.21922 | − | 3.84381i | 0.0880672 | − | 0.152537i | ||||
\(636\) | 4.43845 | 0.175996 | ||||||||
\(637\) | 16.1577 | − | 12.6107i | 0.640190 | − | 0.499653i | ||||
\(638\) | −27.0540 | −1.07108 | ||||||||
\(639\) | 2.43845 | − | 4.22351i | 0.0964635 | − | 0.167080i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 7.78078 | + | 13.4767i | 0.307322 | + | 0.532298i | 0.977776 | − | 0.209654i | \(-0.0672337\pi\) |
−0.670453 | + | 0.741952i | \(0.733900\pi\) | |||||||
\(642\) | 2.00000 | 0.0789337 | ||||||||
\(643\) | −19.1231 | − | 33.1222i | −0.754142 | − | 1.30621i | −0.945800 | − | 0.324750i | \(-0.894720\pi\) |
0.191658 | − | 0.981462i | \(-0.438613\pi\) | |||||||
\(644\) | 13.6847 | + | 23.7025i | 0.539251 | + | 0.934010i | ||||
\(645\) | 4.56155 | 0.179611 | ||||||||
\(646\) | 9.12311 | + | 15.8017i | 0.358944 | + | 0.621709i | ||||
\(647\) | 1.02699 | − | 1.77879i | 0.0403751 | − | 0.0699316i | −0.845132 | − | 0.534558i | \(-0.820478\pi\) |
0.885507 | + | 0.464626i | \(0.153811\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −43.5464 | −1.70935 | ||||||||
\(650\) | 2.84233 | − | 2.21837i | 0.111485 | − | 0.0870116i | ||||
\(651\) | 20.2462 | 0.793512 | ||||||||
\(652\) | 9.28078 | − | 16.0748i | 0.363463 | − | 0.629537i | ||||
\(653\) | 20.2192 | − | 35.0207i | 0.791239 | − | 1.37047i | −0.133961 | − | 0.990987i | \(-0.542770\pi\) |
0.925200 | − | 0.379480i | \(-0.123897\pi\) | |||||||
\(654\) | 10.1231 | + | 17.5337i | 0.395845 | + | 0.685623i | ||||
\(655\) | 6.12311 | 0.239250 | ||||||||
\(656\) | 2.12311 | + | 3.67733i | 0.0828933 | + | 0.143575i | ||||
\(657\) | 7.68466 | + | 13.3102i | 0.299807 | + | 0.519281i | ||||
\(658\) | 24.9309 | 0.971906 | ||||||||
\(659\) | −15.5270 | − | 26.8935i | −0.604846 | − | 1.04762i | −0.992076 | − | 0.125640i | \(-0.959902\pi\) |
0.387230 | − | 0.921983i | \(-0.373432\pi\) | |||||||
\(660\) | 2.06155 | − | 3.57071i | 0.0802458 | − | 0.138990i | ||||
\(661\) | 5.80776 | − | 10.0593i | 0.225896 | − | 0.391263i | −0.730692 | − | 0.682707i | \(-0.760802\pi\) |
0.956588 | + | 0.291444i | \(0.0941358\pi\) | |||||||
\(662\) | −18.7386 | −0.728298 | ||||||||
\(663\) | −17.1231 | − | 6.92820i | −0.665006 | − | 0.269069i | ||||
\(664\) | 1.12311 | 0.0435850 | ||||||||
\(665\) | 6.34233 | − | 10.9852i | 0.245945 | − | 0.425989i | ||||
\(666\) | −2.06155 | + | 3.57071i | −0.0798835 | + | 0.138362i | ||||
\(667\) | 25.2116 | + | 43.6679i | 0.976199 | + | 1.69083i | ||||
\(668\) | −20.3693 | −0.788113 | ||||||||
\(669\) | 13.1501 | + | 22.7766i | 0.508412 | + | 0.880595i | ||||
\(670\) | −7.12311 | − | 12.3376i | −0.275190 | − | 0.476642i | ||||
\(671\) | −24.7386 | −0.955024 | ||||||||
\(672\) | −1.78078 | − | 3.08440i | −0.0686949 | − | 0.118983i | ||||
\(673\) | −21.1231 | + | 36.5863i | −0.814236 | + | 1.41030i | 0.0956394 | + | 0.995416i | \(0.469510\pi\) |
−0.909875 | + | 0.414882i | \(0.863823\pi\) | |||||||
\(674\) | 3.00000 | − | 5.19615i | 0.115556 | − | 0.200148i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 3.15767 | − | 12.6107i | 0.121449 | − | 0.485026i | ||||
\(677\) | −28.8769 | −1.10983 | −0.554915 | − | 0.831907i | \(-0.687249\pi\) | ||||
−0.554915 | + | 0.831907i | \(0.687249\pi\) | |||||||
\(678\) | 1.84233 | − | 3.19101i | 0.0707542 | − | 0.122550i | ||||
\(679\) | −2.00000 | + | 3.46410i | −0.0767530 | + | 0.132940i | ||||
\(680\) | −2.56155 | − | 4.43674i | −0.0982311 | − | 0.170141i | ||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 11.7192 | + | 20.2983i | 0.448752 | + | 0.777262i | ||||
\(683\) | −4.43845 | − | 7.68762i | −0.169832 | − | 0.294158i | 0.768528 | − | 0.639816i | \(-0.220989\pi\) |
−0.938361 | + | 0.345657i | \(0.887656\pi\) | |||||||
\(684\) | −3.56155 | −0.136179 | ||||||||
\(685\) | 4.40388 | + | 7.62775i | 0.168264 | + | 0.291441i | ||||
\(686\) | 2.34233 | − | 4.05703i | 0.0894305 | − | 0.154898i | ||||
\(687\) | 3.87689 | − | 6.71498i | 0.147913 | − | 0.256192i | ||||
\(688\) | 4.56155 | 0.173908 | ||||||||
\(689\) | −14.8348 | − | 6.00231i | −0.565159 | − | 0.228670i | ||||
\(690\) | −7.68466 | −0.292550 | ||||||||
\(691\) | 8.21922 | − | 14.2361i | 0.312674 | − | 0.541567i | −0.666266 | − | 0.745714i | \(-0.732109\pi\) |
0.978940 | + | 0.204147i | \(0.0654419\pi\) | |||||||
\(692\) | 12.5885 | − | 21.8040i | 0.478545 | − | 0.828863i | ||||
\(693\) | 7.34233 | + | 12.7173i | 0.278912 | + | 0.483090i | ||||
\(694\) | 9.12311 | 0.346308 | ||||||||
\(695\) | −4.21922 | − | 7.30791i | −0.160044 | − | 0.277205i | ||||
\(696\) | −3.28078 | − | 5.68247i | −0.124358 | − | 0.215394i | ||||
\(697\) | −21.7538 | −0.823984 | ||||||||
\(698\) | 12.2462 | + | 21.2111i | 0.463526 | + | 0.802850i | ||||
\(699\) | 8.84233 | − | 15.3154i | 0.334448 | − | 0.579280i | ||||
\(700\) | −1.78078 | + | 3.08440i | −0.0673070 | + | 0.116579i | ||||
\(701\) | 17.3002 | 0.653419 | 0.326710 | − | 0.945125i | \(-0.394060\pi\) | ||||
0.326710 | + | 0.945125i | \(0.394060\pi\) | |||||||
\(702\) | 2.84233 | − | 2.21837i | 0.107277 | − | 0.0837270i | ||||
\(703\) | −14.6847 | −0.553842 | ||||||||
\(704\) | 2.06155 | − | 3.57071i | 0.0776977 | − | 0.134576i | ||||
\(705\) | −3.50000 | + | 6.06218i | −0.131818 | + | 0.228315i | ||||
\(706\) | −15.9309 | − | 27.5931i | −0.599566 | − | 1.03848i | ||||
\(707\) | −60.9848 | −2.29357 | ||||||||
\(708\) | −5.28078 | − | 9.14657i | −0.198464 | − | 0.343749i | ||||
\(709\) | −8.87689 | − | 15.3752i | −0.333379 | − | 0.577429i | 0.649793 | − | 0.760111i | \(-0.274855\pi\) |
−0.983172 | + | 0.182682i | \(0.941522\pi\) | |||||||
\(710\) | −4.87689 | −0.183027 | ||||||||
\(711\) | −3.71922 | − | 6.44188i | −0.139482 | − | 0.241590i | ||||
\(712\) | −0.903882 | + | 1.56557i | −0.0338744 | + | 0.0586722i | ||||
\(713\) | 21.8423 | − | 37.8320i | 0.818002 | − | 1.41682i | ||||
\(714\) | 18.2462 | 0.682847 | ||||||||
\(715\) | −11.7192 | + | 9.14657i | −0.438274 | + | 0.342062i | ||||
\(716\) | −0.315342 | −0.0117849 | ||||||||
\(717\) | −6.68466 | + | 11.5782i | −0.249643 | + | 0.432395i | ||||
\(718\) | −2.43845 | + | 4.22351i | −0.0910020 | + | 0.157620i | ||||
\(719\) | 10.4924 | + | 18.1734i | 0.391301 | + | 0.677754i | 0.992621 | − | 0.121254i | \(-0.0386917\pi\) |
−0.601320 | + | 0.799008i | \(0.705358\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −0.780776 | − | 1.35234i | −0.0290776 | − | 0.0503639i | ||||
\(722\) | 3.15767 | + | 5.46925i | 0.117516 | + | 0.203544i | ||||
\(723\) | −19.8769 | −0.739230 | ||||||||
\(724\) | −5.56155 | − | 9.63289i | −0.206693 | − | 0.358004i | ||||
\(725\) | −3.28078 | + | 5.68247i | −0.121845 | + | 0.211042i | ||||
\(726\) | −3.00000 | + | 5.19615i | −0.111340 | + | 0.192847i | ||||
\(727\) | −23.4233 | −0.868722 | −0.434361 | − | 0.900739i | \(-0.643026\pi\) | ||||
−0.434361 | + | 0.900739i | \(0.643026\pi\) | |||||||
\(728\) | 1.78078 | + | 12.7173i | 0.0660000 | + | 0.471334i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.68466 | − | 13.3102i | 0.284422 | − | 0.492633i | ||||
\(731\) | −11.6847 | + | 20.2384i | −0.432173 | + | 0.748545i | ||||
\(732\) | −3.00000 | − | 5.19615i | −0.110883 | − | 0.192055i | ||||
\(733\) | 48.9309 | 1.80730 | 0.903651 | − | 0.428269i | \(-0.140876\pi\) | ||||
0.903651 | + | 0.428269i | \(0.140876\pi\) | |||||||
\(734\) | 10.2462 | + | 17.7470i | 0.378195 | + | 0.655052i | ||||
\(735\) | −2.84233 | − | 4.92306i | −0.104841 | − | 0.181590i | ||||
\(736\) | −7.68466 | −0.283260 | ||||||||
\(737\) | 29.3693 | + | 50.8691i | 1.08183 | + | 1.87379i | ||||
\(738\) | 2.12311 | − | 3.67733i | 0.0781526 | − | 0.135364i | ||||
\(739\) | −21.2732 | + | 36.8463i | −0.782547 | + | 1.35541i | 0.147906 | + | 0.989001i | \(0.452747\pi\) |
−0.930453 | + | 0.366410i | \(0.880587\pi\) | |||||||
\(740\) | 4.12311 | 0.151568 | ||||||||
\(741\) | 11.9039 | + | 4.81645i | 0.437300 | + | 0.176937i | ||||
\(742\) | 15.8078 | 0.580321 | ||||||||
\(743\) | 16.0885 | − | 27.8662i | 0.590231 | − | 1.02231i | −0.403970 | − | 0.914772i | \(-0.632370\pi\) |
0.994201 | − | 0.107538i | \(-0.0342968\pi\) | |||||||
\(744\) | −2.84233 | + | 4.92306i | −0.104205 | + | 0.180488i | ||||
\(745\) | 11.4039 | + | 19.7521i | 0.417806 | + | 0.723661i | ||||
\(746\) | −5.19224 | −0.190101 | ||||||||
\(747\) | −0.561553 | − | 0.972638i | −0.0205461 | − | 0.0355870i | ||||
\(748\) | 10.5616 | + | 18.2931i | 0.386169 | + | 0.668864i | ||||
\(749\) | 7.12311 | 0.260273 | ||||||||
\(750\) | −0.500000 | − | 0.866025i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | 1.59612 | − | 2.76456i | 0.0582432 | − | 0.100880i | −0.835434 | − | 0.549591i | \(-0.814783\pi\) |
0.893677 | + | 0.448711i | \(0.148117\pi\) | |||||||
\(752\) | −3.50000 | + | 6.06218i | −0.127632 | + | 0.221065i | ||||
\(753\) | 0.123106 | 0.00448622 | ||||||||
\(754\) | 3.28078 | + | 23.4294i | 0.119479 | + | 0.853250i | ||||
\(755\) | 9.36932 | 0.340984 | ||||||||
\(756\) | −1.78078 | + | 3.08440i | −0.0647662 | + | 0.112178i | ||||
\(757\) | −16.7116 | + | 28.9454i | −0.607395 | + | 1.05204i | 0.384273 | + | 0.923220i | \(0.374452\pi\) |
−0.991668 | + | 0.128820i | \(0.958881\pi\) | |||||||
\(758\) | 2.65767 | + | 4.60322i | 0.0965309 | + | 0.167197i | ||||
\(759\) | 31.6847 | 1.15008 | ||||||||
\(760\) | 1.78078 | + | 3.08440i | 0.0645955 | + | 0.111883i | ||||
\(761\) | −5.46543 | − | 9.46641i | −0.198122 | − | 0.343157i | 0.749798 | − | 0.661667i | \(-0.230151\pi\) |
−0.947919 | + | 0.318510i | \(0.896818\pi\) | |||||||
\(762\) | −4.43845 | −0.160788 | ||||||||
\(763\) | 36.0540 | + | 62.4473i | 1.30524 | + | 2.26074i | ||||
\(764\) | −9.56155 | + | 16.5611i | −0.345925 | + | 0.599159i | ||||
\(765\) | −2.56155 | + | 4.43674i | −0.0926131 | + | 0.160411i | ||||
\(766\) | 20.8078 | 0.751815 | ||||||||
\(767\) | 5.28078 | + | 37.7123i | 0.190678 | + | 1.36171i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 22.8423 | − | 39.5641i | 0.823715 | − | 1.42672i | −0.0791816 | − | 0.996860i | \(-0.525231\pi\) |
0.902897 | − | 0.429857i | \(-0.141436\pi\) | |||||||
\(770\) | 7.34233 | − | 12.7173i | 0.264599 | − | 0.458299i | ||||
\(771\) | 0.719224 | + | 1.24573i | 0.0259022 | + | 0.0448639i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5885 | + | 18.3399i | 0.380843 | + | 0.659640i | 0.991183 | − | 0.132500i | \(-0.0423004\pi\) |
−0.610340 | + | 0.792140i | \(0.708967\pi\) | |||||||
\(774\) | −2.28078 | − | 3.95042i | −0.0819808 | − | 0.141995i | ||||
\(775\) | 5.68466 | 0.204199 | ||||||||
\(776\) | −0.561553 | − | 0.972638i | −0.0201586 | − | 0.0349157i | ||||
\(777\) | −7.34233 | + | 12.7173i | −0.263405 | + | 0.456230i | ||||
\(778\) | −9.52699 | + | 16.5012i | −0.341559 | + | 0.591598i | ||||
\(779\) | 15.1231 | 0.541841 | ||||||||
\(780\) | −3.34233 | − | 1.35234i | −0.119675 | − | 0.0484217i | ||||
\(781\) | 20.1080 | 0.719519 | ||||||||
\(782\) | 19.6847 | − | 34.0948i | 0.703922 | − | 1.21923i | ||||
\(783\) | −3.28078 | + | 5.68247i | −0.117245 | + | 0.203075i | ||||
\(784\) | −2.84233 | − | 4.92306i | −0.101512 | − | 0.175824i | ||||
\(785\) | 22.1231 | 0.789607 | ||||||||
\(786\) | −3.06155 | − | 5.30277i | −0.109202 | − | 0.189143i | ||||
\(787\) | −21.8423 | − | 37.8320i | −0.778595 | − | 1.34857i | −0.932752 | − | 0.360520i | \(-0.882599\pi\) |
0.154157 | − | 0.988046i | \(-0.450734\pi\) | |||||||
\(788\) | −7.80776 | −0.278140 | ||||||||
\(789\) | 6.50000 | + | 11.2583i | 0.231406 | + | 0.400807i | ||||
\(790\) | −3.71922 | + | 6.44188i | −0.132324 | + | 0.229192i | ||||
\(791\) | 6.56155 | − | 11.3649i | 0.233302 | − | 0.404091i | ||||
\(792\) | −4.12311 | −0.146508 | ||||||||
\(793\) | 3.00000 | + | 21.4243i | 0.106533 | + | 0.760799i | ||||
\(794\) | −11.8769 | −0.421495 | ||||||||
\(795\) | −2.21922 | + | 3.84381i | −0.0787077 | + | 0.136326i | ||||
\(796\) | −5.56155 | + | 9.63289i | −0.197124 | + | 0.341429i | ||||
\(797\) | −2.43845 | − | 4.22351i | −0.0863742 | − | 0.149605i | 0.819602 | − | 0.572934i | \(-0.194195\pi\) |
−0.905976 | + | 0.423329i | \(0.860861\pi\) | |||||||
\(798\) | −12.6847 | −0.449032 | ||||||||
\(799\) | −17.9309 | − | 31.0572i | −0.634349 | − | 1.09872i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 1.80776 | 0.0638742 | ||||||||
\(802\) | −6.34233 | − | 10.9852i | −0.223955 | − | 0.387902i | ||||
\(803\) | −31.6847 | + | 54.8794i | −1.11813 | + | 1.93665i | ||||
\(804\) | −7.12311 | + | 12.3376i | −0.251213 | + | 0.435113i | ||||
\(805\) | −27.3693 | −0.964642 | ||||||||
\(806\) | 16.1577 | − | 12.6107i | 0.569130 | − | 0.444192i | ||||
\(807\) | −3.36932 | −0.118606 | ||||||||
\(808\) | 8.56155 | − | 14.8290i | 0.301194 | − | 0.521684i | ||||
\(809\) | −9.24621 | + | 16.0149i | −0.325079 | + | 0.563054i | −0.981528 | − | 0.191316i | \(-0.938724\pi\) |
0.656449 | + | 0.754370i | \(0.272058\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | −22.5464 | −0.791711 | −0.395856 | − | 0.918313i | \(-0.629552\pi\) | ||||
−0.395856 | + | 0.918313i | \(0.629552\pi\) | |||||||
\(812\) | −11.6847 | − | 20.2384i | −0.410051 | − | 0.710229i | ||||
\(813\) | −16.0885 | − | 27.8662i | −0.564250 | − | 0.977309i | ||||
\(814\) | −17.0000 | −0.595850 | ||||||||
\(815\) | 9.28078 | + | 16.0748i | 0.325091 | + | 0.563075i | ||||
\(816\) | −2.56155 | + | 4.43674i | −0.0896723 | + | 0.155317i | ||||
\(817\) | 8.12311 | − | 14.0696i | 0.284191 | − | 0.492234i | ||||
\(818\) | 1.80776 | 0.0632070 | ||||||||
\(819\) | 10.1231 | − | 7.90084i | 0.353730 | − | 0.276078i | ||||
\(820\) | −4.24621 | −0.148284 | ||||||||
\(821\) | 6.28078 | − | 10.8786i | 0.219201 | − | 0.379667i | −0.735363 | − | 0.677673i | \(-0.762988\pi\) |
0.954564 | + | 0.298007i | \(0.0963217\pi\) | |||||||
\(822\) | 4.40388 | − | 7.62775i | 0.153603 | − | 0.266048i | ||||
\(823\) | 16.0270 | + | 27.7596i | 0.558666 | + | 0.967637i | 0.997608 | + | 0.0691222i | \(0.0220198\pi\) |
−0.438943 | + | 0.898515i | \(0.644647\pi\) | |||||||
\(824\) | 0.438447 | 0.0152740 | ||||||||
\(825\) | 2.06155 | + | 3.57071i | 0.0717741 | + | 0.124316i | ||||
\(826\) | −18.8078 | − | 32.5760i | −0.654406 | − | 1.13346i | ||||
\(827\) | −11.7538 | −0.408719 | −0.204360 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204360 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(828\) | 3.84233 | + | 6.65511i | 0.133530 | + | 0.231281i | ||||
\(829\) | −26.8078 | + | 46.4324i | −0.931072 | + | 1.61266i | −0.149580 | + | 0.988750i | \(0.547792\pi\) |
−0.781493 | + | 0.623915i | \(0.785541\pi\) | |||||||
\(830\) | −0.561553 | + | 0.972638i | −0.0194918 | + | 0.0337608i | ||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | −3.34233 | − | 1.35234i | −0.115874 | − | 0.0468841i | ||||
\(833\) | 29.1231 | 1.00906 | ||||||||
\(834\) | −4.21922 | + | 7.30791i | −0.146100 | + | 0.253052i | ||||
\(835\) | 10.1847 | − | 17.6403i | 0.352455 | − | 0.610469i | ||||
\(836\) | −7.34233 | − | 12.7173i | −0.253940 | − | 0.439837i | ||||
\(837\) | 5.68466 | 0.196491 | ||||||||
\(838\) | 0.246211 | + | 0.426450i | 0.00850523 | + | 0.0147315i | ||||
\(839\) | 6.36932 | + | 11.0320i | 0.219893 | + | 0.380866i | 0.954775 | − | 0.297329i | \(-0.0960958\pi\) |
−0.734882 | + | 0.678195i | \(0.762762\pi\) | |||||||
\(840\) | 3.56155 | 0.122885 | ||||||||
\(841\) | −7.02699 | − | 12.1711i | −0.242310 | − | 0.419693i | ||||
\(842\) | −0.246211 | + | 0.426450i | −0.00848500 | + | 0.0146965i | ||||
\(843\) | 0.123106 | − | 0.213225i | 0.00423998 | − | 0.00734387i | ||||
\(844\) | 6.93087 | 0.238570 | ||||||||
\(845\) | 9.34233 | + | 9.03996i | 0.321386 | + | 0.310984i | ||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | −10.6847 | + | 18.5064i | −0.367129 | + | 0.635886i | ||||
\(848\) | −2.21922 | + | 3.84381i | −0.0762085 | + | 0.131997i | ||||
\(849\) | −5.71922 | − | 9.90599i | −0.196283 | − | 0.339973i | ||||
\(850\) | 5.12311 | 0.175721 | ||||||||
\(851\) | 15.8423 | + | 27.4397i | 0.543068 | + | 0.940621i | ||||
\(852\) | 2.43845 | + | 4.22351i | 0.0835398 | + | 0.144695i | ||||
\(853\) | −51.3002 | −1.75648 | −0.878242 | − | 0.478216i | \(-0.841284\pi\) | ||||
−0.878242 | + | 0.478216i | \(0.841284\pi\) | |||||||
\(854\) | −10.6847 | − | 18.5064i | −0.365621 | − | 0.633275i | ||||
\(855\) | 1.78078 | − | 3.08440i | 0.0609013 | − | 0.105484i | ||||
\(856\) | −1.00000 | + | 1.73205i | −0.0341793 | + | 0.0592003i | ||||
\(857\) | −26.8078 | −0.915736 | −0.457868 | − | 0.889020i | \(-0.651387\pi\) | ||||
−0.457868 | + | 0.889020i | \(0.651387\pi\) | |||||||
\(858\) | 13.7808 | + | 5.57586i | 0.470468 | + | 0.190357i | ||||
\(859\) | −46.7926 | −1.59654 | −0.798272 | − | 0.602298i | \(-0.794252\pi\) | ||||
−0.798272 | + | 0.602298i | \(0.794252\pi\) | |||||||
\(860\) | −2.28078 | + | 3.95042i | −0.0777738 | + | 0.134708i | ||||
\(861\) | 7.56155 | − | 13.0970i | 0.257697 | − | 0.446344i | ||||
\(862\) | −13.3693 | − | 23.1563i | −0.455361 | − | 0.788708i | ||||
\(863\) | 6.56155 | 0.223358 | 0.111679 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111679 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 12.5885 | + | 21.8040i | 0.428023 | + | 0.741358i | ||||
\(866\) | 30.7386 | 1.04454 | ||||||||
\(867\) | −4.62311 | − | 8.00745i | −0.157009 | − | 0.271947i | ||||
\(868\) | −10.1231 | + | 17.5337i | −0.343601 | + | 0.595134i | ||||
\(869\) | 15.3348 | − | 26.5606i | 0.520196 | − | 0.901006i | ||||
\(870\) | 6.56155 | 0.222457 | ||||||||
\(871\) | 40.4924 | − | 31.6034i | 1.37203 | − | 1.07084i | ||||
\(872\) | −20.2462 | −0.685623 | ||||||||
\(873\) | −0.561553 | + | 0.972638i | −0.0190057 | + | 0.0329188i | ||||
\(874\) | −13.6847 | + | 23.7025i | −0.462890 | + | 0.801750i | ||||
\(875\) | −1.78078 | − | 3.08440i | −0.0602012 | − | 0.104272i | ||||
\(876\) | −15.3693 | −0.519281 | ||||||||
\(877\) | −6.28078 | − | 10.8786i | −0.212087 | − | 0.367345i | 0.740281 | − | 0.672298i | \(-0.234693\pi\) |
−0.952367 | + | 0.304953i | \(0.901359\pi\) | |||||||
\(878\) | −8.43845 | − | 14.6158i | −0.284784 | − | 0.493260i | ||||
\(879\) | −24.9309 | −0.840897 | ||||||||
\(880\) | 2.06155 | + | 3.57071i | 0.0694949 | + | 0.120369i | ||||
\(881\) | 10.2192 | − | 17.7002i | 0.344294 | − | 0.596335i | −0.640931 | − | 0.767599i | \(-0.721452\pi\) |
0.985225 | + | 0.171263i | \(0.0547848\pi\) | |||||||
\(882\) | −2.84233 | + | 4.92306i | −0.0957062 | + | 0.165768i | ||||
\(883\) | 26.1771 | 0.880929 | 0.440464 | − | 0.897770i | \(-0.354814\pi\) | ||||
0.440464 | + | 0.897770i | \(0.354814\pi\) | |||||||
\(884\) | 14.5616 | − | 11.3649i | 0.489758 | − | 0.382244i | ||||
\(885\) | 10.5616 | 0.355023 | ||||||||
\(886\) | 2.43845 | − | 4.22351i | 0.0819212 | − | 0.141892i | ||||
\(887\) | −20.5540 | + | 35.6005i | −0.690135 | + | 1.19535i | 0.281658 | + | 0.959515i | \(0.409116\pi\) |
−0.971793 | + | 0.235834i | \(0.924218\pi\) | |||||||
\(888\) | −2.06155 | − | 3.57071i | −0.0691812 | − | 0.119825i | ||||
\(889\) | −15.8078 | −0.530175 | ||||||||
\(890\) | −0.903882 | − | 1.56557i | −0.0302982 | − | 0.0524780i | ||||
\(891\) | 2.06155 | + | 3.57071i | 0.0690646 | + | 0.119623i | ||||
\(892\) | −26.3002 | −0.880595 | ||||||||
\(893\) | 12.4654 | + | 21.5908i | 0.417140 | + | 0.722507i | ||||
\(894\) | 11.4039 | − | 19.7521i | 0.381403 | − | 0.660609i | ||||
\(895\) | 0.157671 | − | 0.273094i | 0.00527035 | − | 0.00912852i | ||||
\(896\) | 3.56155 | 0.118983 | ||||||||
\(897\) | −3.84233 | − | 27.4397i | −0.128292 | − | 0.916186i | ||||
\(898\) | 25.1771 | 0.840170 | ||||||||
\(899\) | −18.6501 | + | 32.3029i | −0.622015 | + | 1.07736i | ||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −11.3693 | − | 19.6922i | −0.378767 | − | 0.656043i | ||||
\(902\) | 17.5076 | 0.582939 | ||||||||
\(903\) | −8.12311 | − | 14.0696i | −0.270320 | − | 0.468208i | ||||
\(904\) | 1.84233 | + | 3.19101i | 0.0612750 | + | 0.106131i | ||||
\(905\) | 11.1231 | 0.369745 | ||||||||
\(906\) | −4.68466 | − | 8.11407i | −0.155637 | − | 0.269572i | ||||
\(907\) | −20.4579 | + | 35.4340i | −0.679292 | + | 1.17657i | 0.295902 | + | 0.955218i | \(0.404380\pi\) |
−0.975194 | + | 0.221350i | \(0.928954\pi\) | |||||||
\(908\) | 10.0000 | − | 17.3205i | 0.331862 | − | 0.574801i | ||||
\(909\) | −17.1231 | −0.567938 | ||||||||
\(910\) | −11.9039 | − | 4.81645i | −0.394610 | − | 0.159664i | ||||
\(911\) | −43.3693 | −1.43689 | −0.718445 | − | 0.695584i | \(-0.755146\pi\) | ||||
−0.718445 | + | 0.695584i | \(0.755146\pi\) | |||||||
\(912\) | 1.78078 | − | 3.08440i | 0.0589674 | − | 0.102135i | ||||
\(913\) | 2.31534 | − | 4.01029i | 0.0766266 | − | 0.132721i | ||||
\(914\) | −1.87689 | − | 3.25088i | −0.0620821 | − | 0.107529i | ||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | 3.87689 | + | 6.71498i | 0.128096 | + | 0.221869i | ||||
\(917\) | −10.9039 | − | 18.8861i | −0.360078 | − | 0.623673i | ||||
\(918\) | 5.12311 | 0.169088 | ||||||||
\(919\) | −20.6847 | − | 35.8269i | −0.682324 | − | 1.18182i | −0.974270 | − | 0.225385i | \(-0.927636\pi\) |
0.291946 | − | 0.956435i | \(-0.405697\pi\) | |||||||
\(920\) | 3.84233 | − | 6.65511i | 0.126678 | − | 0.219412i | ||||
\(921\) | 7.80776 | − | 13.5234i | 0.257275 | − | 0.445613i | ||||
\(922\) | 7.05398 | 0.232310 | ||||||||
\(923\) | −2.43845 | − | 17.4140i | −0.0802625 | − | 0.573189i | ||||
\(924\) | −14.6847 | −0.483090 | ||||||||
\(925\) | −2.06155 | + | 3.57071i | −0.0677834 | + | 0.117404i | ||||
\(926\) | −16.8078 | + | 29.1119i | −0.552337 | + | 0.956676i | ||||
\(927\) | −0.219224 | − | 0.379706i | −0.00720025 | − | 0.0124712i | ||||
\(928\) | 6.56155 | 0.215394 | ||||||||
\(929\) | 8.43845 | + | 14.6158i | 0.276856 | + | 0.479529i | 0.970602 | − | 0.240691i | \(-0.0773740\pi\) |
−0.693745 | + | 0.720220i | \(0.744041\pi\) | |||||||
\(930\) | −2.84233 | − | 4.92306i | −0.0932036 | − | 0.161433i | ||||
\(931\) | −20.2462 | −0.663543 | ||||||||
\(932\) | 8.84233 | + | 15.3154i | 0.289640 | + | 0.501671i | ||||
\(933\) | 9.36932 | − | 16.2281i | 0.306738 | − | 0.531285i | ||||
\(934\) | −19.9309 | + | 34.5213i | −0.652158 | + | 1.12957i | ||||
\(935\) | −21.1231 | −0.690799 | ||||||||
\(936\) | 0.500000 | + | 3.57071i | 0.0163430 | + | 0.116712i | ||||
\(937\) | −29.2311 | −0.954937 | −0.477468 | − | 0.878649i | \(-0.658446\pi\) | ||||
−0.477468 | + | 0.878649i | \(0.658446\pi\) | |||||||
\(938\) | −25.3693 | + | 43.9409i | −0.828338 | + | 1.43472i | ||||
\(939\) | −3.31534 | + | 5.74234i | −0.108192 | + | 0.187394i | ||||
\(940\) | −3.50000 | − | 6.06218i | −0.114157 | − | 0.197726i | ||||
\(941\) | −0.630683 | −0.0205597 | −0.0102798 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102798 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(942\) | −11.0616 | − | 19.1592i | −0.360405 | − | 0.624240i | ||||
\(943\) | −16.3153 | − | 28.2590i | −0.531301 | − | 0.920240i | ||||
\(944\) | 10.5616 | 0.343749 | ||||||||
\(945\) | −1.78078 | − | 3.08440i | −0.0579287 | − | 0.100335i | ||||
\(946\) | 9.40388 | − | 16.2880i | 0.305747 | − | 0.529569i | ||||
\(947\) | −6.93087 | + | 12.0046i | −0.225223 | + | 0.390098i | −0.956386 | − | 0.292105i | \(-0.905644\pi\) |
0.731163 | + | 0.682202i | \(0.238978\pi\) | |||||||
\(948\) | 7.43845 | 0.241590 | ||||||||
\(949\) | 51.3693 | + | 20.7846i | 1.66752 | + | 0.674697i | ||||
\(950\) | −3.56155 | −0.115552 | ||||||||
\(951\) | 2.09612 | − | 3.63058i | 0.0679713 | − | 0.117730i | ||||
\(952\) | −9.12311 | + | 15.8017i | −0.295682 | + | 0.512135i | ||||
\(953\) | −2.91146 | − | 5.04280i | −0.0943114 | − | 0.163352i | 0.815010 | − | 0.579447i | \(-0.196732\pi\) |
−0.909321 | + | 0.416095i | \(0.863398\pi\) | |||||||
\(954\) | 4.43845 | 0.143700 | ||||||||
\(955\) | −9.56155 | − | 16.5611i | −0.309405 | − | 0.535904i | ||||
\(956\) | −6.68466 | − | 11.5782i | −0.216197 | − | 0.374465i | ||||
\(957\) | −27.0540 | −0.874531 | ||||||||
\(958\) | 10.8769 | + | 18.8393i | 0.351417 | + | 0.608671i | ||||
\(959\) | 15.6847 | − | 27.1666i | 0.506484 | − | 0.877256i | ||||
\(960\) | −0.500000 | + | 0.866025i | −0.0161374 | + | 0.0279508i | ||||
\(961\) | 1.31534 | 0.0424304 | ||||||||
\(962\) | 2.06155 | + | 14.7224i | 0.0664671 | + | 0.474670i | ||||
\(963\) | 2.00000 | 0.0644491 | ||||||||
\(964\) | 9.93845 | − | 17.2139i | 0.320096 | − | 0.554422i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 13.6847 | + | 23.7025i | 0.440297 | + | 0.762616i | ||||
\(967\) | 3.31534 | 0.106614 | 0.0533071 | − | 0.998578i | \(-0.483024\pi\) | ||||
0.0533071 | + | 0.998578i | \(0.483024\pi\) | |||||||
\(968\) | −3.00000 | − | 5.19615i | −0.0964237 | − | 0.167011i | ||||
\(969\) | 9.12311 | + | 15.8017i | 0.293076 | + | 0.507623i | ||||
\(970\) | 1.12311 | 0.0360607 | ||||||||
\(971\) | 8.34233 | + | 14.4493i | 0.267718 | + | 0.463701i | 0.968272 | − | 0.249898i | \(-0.0803971\pi\) |
−0.700554 | + | 0.713599i | \(0.747064\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | −15.0270 | + | 26.0275i | −0.481743 | + | 0.834404i | ||||
\(974\) | −24.0540 | −0.770739 | ||||||||
\(975\) | 2.84233 | − | 2.21837i | 0.0910274 | − | 0.0710447i | ||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −2.65009 | + | 4.59010i | −0.0847840 | + | 0.146850i | −0.905299 | − | 0.424775i | \(-0.860353\pi\) |
0.820515 | + | 0.571625i | \(0.193687\pi\) | |||||||
\(978\) | 9.28078 | − | 16.0748i | 0.296767 | − | 0.514015i | ||||
\(979\) | 3.72680 | + | 6.45501i | 0.119109 | + | 0.206303i | ||||
\(980\) | 5.68466 | 0.181590 | ||||||||
\(981\) | 10.1231 | + | 17.5337i | 0.323206 | + | 0.559809i | ||||
\(982\) | 10.7808 | + | 18.6729i | 0.344028 | + | 0.595875i | ||||
\(983\) | 23.8769 | 0.761555 | 0.380777 | − | 0.924667i | \(-0.375656\pi\) | ||||
0.380777 | + | 0.924667i | \(0.375656\pi\) | |||||||
\(984\) | 2.12311 | + | 3.67733i | 0.0676821 | + | 0.117229i | ||||
\(985\) | 3.90388 | − | 6.76172i | 0.124388 | − | 0.215446i | ||||
\(986\) | −16.8078 | + | 29.1119i | −0.535268 | + | 0.927112i | ||||
\(987\) | 24.9309 | 0.793558 | ||||||||
\(988\) | −10.1231 | + | 7.90084i | −0.322059 | + | 0.251359i | ||||
\(989\) | −35.0540 | −1.11465 | ||||||||
\(990\) | 2.06155 | − | 3.57071i | 0.0655204 | − | 0.113485i | ||||
\(991\) | 6.21165 | − | 10.7589i | 0.197319 | − | 0.341767i | −0.750339 | − | 0.661053i | \(-0.770110\pi\) |
0.947658 | + | 0.319286i | \(0.103443\pi\) | |||||||
\(992\) | −2.84233 | − | 4.92306i | −0.0902440 | − | 0.156307i | ||||
\(993\) | −18.7386 | −0.594653 | ||||||||
\(994\) | 8.68466 | + | 15.0423i | 0.275461 | + | 0.477112i | ||||
\(995\) | −5.56155 | − | 9.63289i | −0.176313 | − | 0.305383i | ||||
\(996\) | 1.12311 | 0.0355870 | ||||||||
\(997\) | −16.2732 | − | 28.1860i | −0.515377 | − | 0.892660i | −0.999841 | − | 0.0178482i | \(-0.994318\pi\) |
0.484463 | − | 0.874812i | \(-0.339015\pi\) | |||||||
\(998\) | −2.00000 | + | 3.46410i | −0.0633089 | + | 0.109654i | ||||
\(999\) | −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 | 390.2.i.g.61.1 | ✓ | 4 | |
3.2 | odd | 2 | 1170.2.i.o.451.1 | 4 | |||
5.2 | odd | 4 | 1950.2.z.n.1699.2 | 8 | |||
5.3 | odd | 4 | 1950.2.z.n.1699.3 | 8 | |||
5.4 | even | 2 | 1950.2.i.bi.451.2 | 4 | |||
13.3 | even | 3 | inner | 390.2.i.g.211.1 | yes | 4 | |
13.4 | even | 6 | 5070.2.a.bb.1.1 | 2 | |||
13.6 | odd | 12 | 5070.2.b.r.1351.2 | 4 | |||
13.7 | odd | 12 | 5070.2.b.r.1351.3 | 4 | |||
13.9 | even | 3 | 5070.2.a.bi.1.2 | 2 | |||
39.29 | odd | 6 | 1170.2.i.o.991.1 | 4 | |||
65.3 | odd | 12 | 1950.2.z.n.1849.2 | 8 | |||
65.29 | even | 6 | 1950.2.i.bi.601.2 | 4 | |||
65.42 | odd | 12 | 1950.2.z.n.1849.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
390.2.i.g.211.1 | yes | 4 | 13.3 | even | 3 | inner | |
1170.2.i.o.451.1 | 4 | 3.2 | odd | 2 | |||
1170.2.i.o.991.1 | 4 | 39.29 | odd | 6 | |||
1950.2.i.bi.451.2 | 4 | 5.4 | even | 2 | |||
1950.2.i.bi.601.2 | 4 | 65.29 | even | 6 | |||
1950.2.z.n.1699.2 | 8 | 5.2 | odd | 4 | |||
1950.2.z.n.1699.3 | 8 | 5.3 | odd | 4 | |||
1950.2.z.n.1849.2 | 8 | 65.3 | odd | 12 | |||
1950.2.z.n.1849.3 | 8 | 65.42 | odd | 12 | |||
5070.2.a.bb.1.1 | 2 | 13.4 | even | 6 | |||
5070.2.a.bi.1.2 | 2 | 13.9 | even | 3 | |||
5070.2.b.r.1351.2 | 4 | 13.6 | odd | 12 | |||
5070.2.b.r.1351.3 | 4 | 13.7 | odd | 12 |