Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (of order \(6\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 4.2 | ||
Root | \(-0.895644 + 1.09445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.4 |
Dual form | 273.2.t.b.205.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18890i | 1.54779i | 0.633316 | + | 0.773893i | \(0.281693\pi\) | ||||
−0.633316 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.79129 | −1.39564 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 1.89564 | − | 1.09445i | 0.773893 | − | 0.446808i | ||||
\(7\) | 2.29129 | + | 1.32288i | 0.866025 | + | 0.500000i | ||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.89564 | + | 3.28335i | 0.599455 | + | 1.03829i | ||||
\(11\) | 3.00000 | − | 1.73205i | 0.904534 | − | 0.522233i | 0.0258656 | − | 0.999665i | \(-0.491766\pi\) |
0.878668 | + | 0.477432i | \(0.158432\pi\) | |||||||
\(12\) | 1.39564 | + | 2.41733i | 0.402888 | + | 0.697822i | ||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | −2.89564 | + | 5.01540i | −0.773893 | + | 1.34042i | ||||
\(15\) | −1.50000 | − | 0.866025i | −0.387298 | − | 0.223607i | ||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | −1.89564 | − | 1.09445i | −0.446808 | − | 0.257964i | ||||
\(19\) | 4.58258 | + | 2.64575i | 1.05131 | + | 0.606977i | 0.923017 | − | 0.384759i | \(-0.125715\pi\) |
0.128298 | + | 0.991736i | \(0.459049\pi\) | |||||||
\(20\) | −4.18693 | + | 2.41733i | −0.936226 | + | 0.540531i | ||||
\(21\) | − | 2.64575i | − | 0.577350i | ||||||
\(22\) | 3.79129 | + | 6.56670i | 0.808305 | + | 1.40003i | ||||
\(23\) | −8.58258 | −1.78959 | −0.894795 | − | 0.446476i | \(-0.852679\pi\) | ||||
−0.894795 | + | 0.446476i | \(0.852679\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | −7.58258 | − | 2.18890i | −1.48707 | − | 0.429279i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.39564 | − | 3.69253i | −1.20866 | − | 0.697822i | ||||
\(29\) | 3.50000 | − | 6.06218i | 0.649934 | − | 1.12572i | −0.333205 | − | 0.942855i | \(-0.608130\pi\) |
0.983138 | − | 0.182864i | \(-0.0585367\pi\) | |||||||
\(30\) | 1.89564 | − | 3.28335i | 0.346096 | − | 0.599455i | ||||
\(31\) | 5.29129 | + | 3.05493i | 0.950343 | + | 0.548681i | 0.893188 | − | 0.449684i | \(-0.148463\pi\) |
0.0571558 | + | 0.998365i | \(0.481797\pi\) | |||||||
\(32\) | − | 7.38505i | − | 1.30551i | ||||||
\(33\) | −3.00000 | − | 1.73205i | −0.522233 | − | 0.301511i | ||||
\(34\) | 2.18890i | 0.375393i | ||||||||
\(35\) | 4.58258 | 0.774597 | ||||||||
\(36\) | 1.39564 | − | 2.41733i | 0.232607 | − | 0.402888i | ||||
\(37\) | − | 7.02355i | − | 1.15467i | −0.816509 | − | 0.577333i | \(-0.804094\pi\) | ||
0.816509 | − | 0.577333i | \(-0.195906\pi\) | |||||||
\(38\) | −5.79129 | + | 10.0308i | −0.939471 | + | 1.62721i | ||||
\(39\) | 3.50000 | − | 0.866025i | 0.560449 | − | 0.138675i | ||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | −3.08258 | − | 1.77973i | −0.481417 | − | 0.277946i | 0.239590 | − | 0.970874i | \(-0.422987\pi\) |
−0.721007 | + | 0.692928i | \(0.756320\pi\) | |||||||
\(42\) | 5.79129 | 0.893615 | ||||||||
\(43\) | −2.29129 | − | 3.96863i | −0.349418 | − | 0.605210i | 0.636728 | − | 0.771088i | \(-0.280287\pi\) |
−0.986146 | + | 0.165878i | \(0.946954\pi\) | |||||||
\(44\) | −8.37386 | + | 4.83465i | −1.26241 | + | 0.728851i | ||||
\(45\) | 1.73205i | 0.258199i | ||||||||
\(46\) | − | 18.7864i | − | 2.76990i | ||||||
\(47\) | −0.708712 | + | 0.409175i | −0.103376 | + | 0.0596843i | −0.550797 | − | 0.834639i | \(-0.685676\pi\) |
0.447421 | + | 0.894324i | \(0.352343\pi\) | |||||||
\(48\) | 0.895644 | + | 1.55130i | 0.129275 | + | 0.223911i | ||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | −3.79129 | − | 2.18890i | −0.536169 | − | 0.309557i | ||||
\(51\) | −0.500000 | − | 0.866025i | −0.0700140 | − | 0.121268i | ||||
\(52\) | 2.79129 | − | 9.66930i | 0.387082 | − | 1.34089i | ||||
\(53\) | 3.08258 | − | 5.33918i | 0.423424 | − | 0.733392i | −0.572848 | − | 0.819662i | \(-0.694161\pi\) |
0.996272 | + | 0.0862695i | \(0.0274946\pi\) | |||||||
\(54\) | 2.18890i | 0.297872i | ||||||||
\(55\) | 3.00000 | − | 5.19615i | 0.404520 | − | 0.700649i | ||||
\(56\) | 2.29129 | − | 3.96863i | 0.306186 | − | 0.530330i | ||||
\(57\) | − | 5.29150i | − | 0.700877i | ||||||
\(58\) | 13.2695 | + | 7.66115i | 1.74237 | + | 1.00596i | ||||
\(59\) | 4.28245i | 0.557528i | 0.960360 | + | 0.278764i | \(0.0899247\pi\) | ||||
−0.960360 | + | 0.278764i | \(0.910075\pi\) | |||||||
\(60\) | 4.18693 | + | 2.41733i | 0.540531 | + | 0.312075i | ||||
\(61\) | 2.58258 | − | 4.47315i | 0.330665 | − | 0.572728i | −0.651977 | − | 0.758238i | \(-0.726060\pi\) |
0.982642 | + | 0.185510i | \(0.0593937\pi\) | |||||||
\(62\) | −6.68693 | + | 11.5821i | −0.849241 | + | 1.47093i | ||||
\(63\) | −2.29129 | + | 1.32288i | −0.288675 | + | 0.166667i | ||||
\(64\) | 12.5826 | 1.57282 | ||||||||
\(65\) | 1.50000 | + | 6.06218i | 0.186052 | + | 0.751921i | ||||
\(66\) | 3.79129 | − | 6.56670i | 0.466675 | − | 0.808305i | ||||
\(67\) | −12.1652 | + | 7.02355i | −1.48621 | + | 0.858064i | −0.999877 | − | 0.0157098i | \(-0.994999\pi\) |
−0.486333 | + | 0.873773i | \(0.661666\pi\) | |||||||
\(68\) | −2.79129 | −0.338493 | ||||||||
\(69\) | 4.29129 | + | 7.43273i | 0.516610 | + | 0.894795i | ||||
\(70\) | 10.0308i | 1.19891i | ||||||||
\(71\) | −3.87386 | + | 2.23658i | −0.459743 | + | 0.265433i | −0.711936 | − | 0.702244i | \(-0.752181\pi\) |
0.252193 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(72\) | 1.50000 | + | 0.866025i | 0.176777 | + | 0.102062i | ||||
\(73\) | −7.50000 | − | 4.33013i | −0.877809 | − | 0.506803i | −0.00787336 | − | 0.999969i | \(-0.502506\pi\) |
−0.869935 | + | 0.493166i | \(0.835840\pi\) | |||||||
\(74\) | 15.3739 | 1.78718 | ||||||||
\(75\) | 2.00000 | 0.230940 | ||||||||
\(76\) | −12.7913 | − | 7.38505i | −1.46726 | − | 0.847124i | ||||
\(77\) | 9.16515 | 1.04447 | ||||||||
\(78\) | 1.89564 | + | 7.66115i | 0.214639 | + | 0.867455i | ||||
\(79\) | 0.708712 | + | 1.22753i | 0.0797363 | + | 0.138107i | 0.903136 | − | 0.429354i | \(-0.141259\pi\) |
−0.823400 | + | 0.567462i | \(0.807925\pi\) | |||||||
\(80\) | −2.68693 | + | 1.55130i | −0.300408 | + | 0.173441i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.89564 | − | 6.74745i | 0.430202 | − | 0.745132i | ||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 7.38505i | 0.805775i | ||||||||
\(85\) | 1.50000 | − | 0.866025i | 0.162698 | − | 0.0939336i | ||||
\(86\) | 8.68693 | − | 5.01540i | 0.936736 | − | 0.540825i | ||||
\(87\) | −7.00000 | −0.750479 | ||||||||
\(88\) | −3.00000 | − | 5.19615i | −0.319801 | − | 0.553912i | ||||
\(89\) | − | 15.5885i | − | 1.65237i | −0.563397 | − | 0.826187i | \(-0.690506\pi\) | ||
0.563397 | − | 0.826187i | \(-0.309494\pi\) | |||||||
\(90\) | −3.79129 | −0.399637 | ||||||||
\(91\) | −6.87386 | + | 6.61438i | −0.720577 | + | 0.693375i | ||||
\(92\) | 23.9564 | 2.49763 | ||||||||
\(93\) | − | 6.10985i | − | 0.633562i | ||||||
\(94\) | −0.895644 | − | 1.55130i | −0.0923786 | − | 0.160004i | ||||
\(95\) | 9.16515 | 0.940325 | ||||||||
\(96\) | −6.39564 | + | 3.69253i | −0.652753 | + | 0.376867i | ||||
\(97\) | 9.08258 | − | 5.24383i | 0.922196 | − | 0.532430i | 0.0378609 | − | 0.999283i | \(-0.487946\pi\) |
0.884335 | + | 0.466853i | \(0.154612\pi\) | |||||||
\(98\) | −13.2695 | + | 7.66115i | −1.34042 | + | 0.773893i | ||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 2.79129 | − | 4.83465i | 0.279129 | − | 0.483465i | ||||
\(101\) | −6.58258 | − | 11.4014i | −0.654991 | − | 1.13448i | −0.981896 | − | 0.189420i | \(-0.939339\pi\) |
0.326905 | − | 0.945057i | \(-0.393994\pi\) | |||||||
\(102\) | 1.89564 | − | 1.09445i | 0.187697 | − | 0.108367i | ||||
\(103\) | −1.70871 | − | 2.95958i | −0.168364 | − | 0.291616i | 0.769481 | − | 0.638670i | \(-0.220515\pi\) |
−0.937845 | + | 0.347055i | \(0.887182\pi\) | |||||||
\(104\) | 6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | ||||
\(105\) | −2.29129 | − | 3.96863i | −0.223607 | − | 0.387298i | ||||
\(106\) | 11.6869 | + | 6.74745i | 1.13514 | + | 0.655371i | ||||
\(107\) | −1.41742 | −0.137028 | −0.0685138 | − | 0.997650i | \(-0.521826\pi\) | ||||
−0.0685138 | + | 0.997650i | \(0.521826\pi\) | |||||||
\(108\) | −2.79129 | −0.268592 | ||||||||
\(109\) | −16.6652 | − | 9.62163i | −1.59623 | − | 0.921585i | −0.992204 | − | 0.124622i | \(-0.960228\pi\) |
−0.604028 | − | 0.796963i | \(-0.706438\pi\) | |||||||
\(110\) | 11.3739 | + | 6.56670i | 1.08446 | + | 0.626111i | ||||
\(111\) | −6.08258 | + | 3.51178i | −0.577333 | + | 0.333323i | ||||
\(112\) | −4.10436 | − | 2.36965i | −0.387825 | − | 0.223911i | ||||
\(113\) | −6.08258 | − | 10.5353i | −0.572201 | − | 0.991080i | −0.996340 | − | 0.0854834i | \(-0.972757\pi\) |
0.424139 | − | 0.905597i | \(-0.360577\pi\) | |||||||
\(114\) | 11.5826 | 1.08481 | ||||||||
\(115\) | −12.8739 | + | 7.43273i | −1.20049 | + | 0.693106i | ||||
\(116\) | −9.76951 | + | 16.9213i | −0.907076 | + | 1.57110i | ||||
\(117\) | −2.50000 | − | 2.59808i | −0.231125 | − | 0.240192i | ||||
\(118\) | −9.37386 | −0.862934 | ||||||||
\(119\) | 2.29129 | + | 1.32288i | 0.210042 | + | 0.121268i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | 9.79129 | + | 5.65300i | 0.886462 | + | 0.511799i | ||||
\(123\) | 3.55945i | 0.320945i | ||||||||
\(124\) | −14.7695 | − | 8.52718i | −1.32634 | − | 0.765763i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −2.89564 | − | 5.01540i | −0.257964 | − | 0.446808i | ||||
\(127\) | −3.29129 | + | 5.70068i | −0.292055 | + | 0.505853i | −0.974295 | − | 0.225274i | \(-0.927672\pi\) |
0.682241 | + | 0.731128i | \(0.261006\pi\) | |||||||
\(128\) | 12.7719i | 1.12889i | ||||||||
\(129\) | −2.29129 | + | 3.96863i | −0.201737 | + | 0.349418i | ||||
\(130\) | −13.2695 | + | 3.28335i | −1.16381 | + | 0.287969i | ||||
\(131\) | −0.708712 | − | 1.22753i | −0.0619205 | − | 0.107249i | 0.833403 | − | 0.552665i | \(-0.186389\pi\) |
−0.895324 | + | 0.445416i | \(0.853056\pi\) | |||||||
\(132\) | 8.37386 | + | 4.83465i | 0.728851 | + | 0.420802i | ||||
\(133\) | 7.00000 | + | 12.1244i | 0.606977 | + | 1.05131i | ||||
\(134\) | −15.3739 | − | 26.6283i | −1.32810 | − | 2.30034i | ||||
\(135\) | 1.50000 | − | 0.866025i | 0.129099 | − | 0.0745356i | ||||
\(136\) | − | 1.73205i | − | 0.148522i | ||||||
\(137\) | 8.66025i | 0.739895i | 0.929053 | + | 0.369948i | \(0.120624\pi\) | ||||
−0.929053 | + | 0.369948i | \(0.879376\pi\) | |||||||
\(138\) | −16.2695 | + | 9.39320i | −1.38495 | + | 0.799603i | ||||
\(139\) | 3.29129 | + | 5.70068i | 0.279163 | + | 0.483525i | 0.971177 | − | 0.238359i | \(-0.0766096\pi\) |
−0.692014 | + | 0.721884i | \(0.743276\pi\) | |||||||
\(140\) | −12.7913 | −1.08106 | ||||||||
\(141\) | 0.708712 | + | 0.409175i | 0.0596843 | + | 0.0344588i | ||||
\(142\) | −4.89564 | − | 8.47950i | −0.410833 | − | 0.711584i | ||||
\(143\) | 3.00000 | + | 12.1244i | 0.250873 | + | 1.01389i | ||||
\(144\) | 0.895644 | − | 1.55130i | 0.0746370 | − | 0.129275i | ||||
\(145\) | − | 12.1244i | − | 1.00687i | ||||||
\(146\) | 9.47822 | − | 16.4168i | 0.784423 | − | 1.35866i | ||||
\(147\) | 3.50000 | − | 6.06218i | 0.288675 | − | 0.500000i | ||||
\(148\) | 19.6048i | 1.61150i | ||||||||
\(149\) | 3.16515 | + | 1.82740i | 0.259299 | + | 0.149707i | 0.624015 | − | 0.781412i | \(-0.285500\pi\) |
−0.364716 | + | 0.931119i | \(0.618834\pi\) | |||||||
\(150\) | 4.37780i | 0.357446i | ||||||||
\(151\) | 14.4564 | + | 8.34643i | 1.17645 | + | 0.679223i | 0.955190 | − | 0.295993i | \(-0.0956503\pi\) |
0.221258 | + | 0.975215i | \(0.428984\pi\) | |||||||
\(152\) | 4.58258 | − | 7.93725i | 0.371696 | − | 0.643796i | ||||
\(153\) | −0.500000 | + | 0.866025i | −0.0404226 | + | 0.0700140i | ||||
\(154\) | 20.0616i | 1.61661i | ||||||||
\(155\) | 10.5826 | 0.850013 | ||||||||
\(156\) | −9.76951 | + | 2.41733i | −0.782187 | + | 0.193541i | ||||
\(157\) | −5.08258 | + | 8.80328i | −0.405634 | + | 0.702578i | −0.994395 | − | 0.105729i | \(-0.966282\pi\) |
0.588761 | + | 0.808307i | \(0.299616\pi\) | |||||||
\(158\) | −2.68693 | + | 1.55130i | −0.213761 | + | 0.123415i | ||||
\(159\) | −6.16515 | −0.488928 | ||||||||
\(160\) | −6.39564 | − | 11.0776i | −0.505620 | − | 0.875760i | ||||
\(161\) | −19.6652 | − | 11.3537i | −1.54983 | − | 0.894795i | ||||
\(162\) | 1.89564 | − | 1.09445i | 0.148936 | − | 0.0859882i | ||||
\(163\) | 3.00000 | + | 1.73205i | 0.234978 | + | 0.135665i | 0.612866 | − | 0.790186i | \(-0.290016\pi\) |
−0.377888 | + | 0.925851i | \(0.623350\pi\) | |||||||
\(164\) | 8.60436 | + | 4.96773i | 0.671887 | + | 0.387914i | ||||
\(165\) | −6.00000 | −0.467099 | ||||||||
\(166\) | 7.58258 | 0.588522 | ||||||||
\(167\) | 3.87386 | + | 2.23658i | 0.299769 | + | 0.173071i | 0.642339 | − | 0.766421i | \(-0.277964\pi\) |
−0.342570 | + | 0.939492i | \(0.611298\pi\) | |||||||
\(168\) | −4.58258 | −0.353553 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | 1.89564 | + | 3.28335i | 0.145389 | + | 0.251822i | ||||
\(171\) | −4.58258 | + | 2.64575i | −0.350438 | + | 0.202326i | ||||
\(172\) | 6.39564 | + | 11.0776i | 0.487663 | + | 0.844658i | ||||
\(173\) | −12.1652 | + | 21.0707i | −0.924899 | + | 1.60197i | −0.133176 | + | 0.991092i | \(0.542518\pi\) |
−0.791723 | + | 0.610880i | \(0.790816\pi\) | |||||||
\(174\) | − | 15.3223i | − | 1.16158i | ||||||
\(175\) | −4.58258 | + | 2.64575i | −0.346410 | + | 0.200000i | ||||
\(176\) | −5.37386 | + | 3.10260i | −0.405070 | + | 0.233867i | ||||
\(177\) | 3.70871 | − | 2.14123i | 0.278764 | − | 0.160944i | ||||
\(178\) | 34.1216 | 2.55752 | ||||||||
\(179\) | −0.417424 | − | 0.723000i | −0.0311998 | − | 0.0540396i | 0.850004 | − | 0.526776i | \(-0.176599\pi\) |
−0.881204 | + | 0.472737i | \(0.843266\pi\) | |||||||
\(180\) | − | 4.83465i | − | 0.360354i | ||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | −14.4782 | − | 15.0462i | −1.07320 | − | 1.11530i | ||||
\(183\) | −5.16515 | −0.381819 | ||||||||
\(184\) | 14.8655i | 1.09590i | ||||||||
\(185\) | −6.08258 | − | 10.5353i | −0.447200 | − | 0.774573i | ||||
\(186\) | 13.3739 | 0.980619 | ||||||||
\(187\) | 3.00000 | − | 1.73205i | 0.219382 | − | 0.126660i | ||||
\(188\) | 1.97822 | − | 1.14213i | 0.144276 | − | 0.0832981i | ||||
\(189\) | 2.29129 | + | 1.32288i | 0.166667 | + | 0.0962250i | ||||
\(190\) | 20.0616i | 1.45542i | ||||||||
\(191\) | 7.16515 | − | 12.4104i | 0.518452 | − | 0.897985i | −0.481318 | − | 0.876546i | \(-0.659842\pi\) |
0.999770 | − | 0.0214394i | \(-0.00682490\pi\) | |||||||
\(192\) | −6.29129 | − | 10.8968i | −0.454035 | − | 0.786411i | ||||
\(193\) | −3.16515 | + | 1.82740i | −0.227833 | + | 0.131539i | −0.609572 | − | 0.792731i | \(-0.708659\pi\) |
0.381739 | + | 0.924270i | \(0.375325\pi\) | |||||||
\(194\) | 11.4782 | + | 19.8809i | 0.824088 | + | 1.42736i | ||||
\(195\) | 4.50000 | − | 4.33013i | 0.322252 | − | 0.310087i | ||||
\(196\) | −9.76951 | − | 16.9213i | −0.697822 | − | 1.20866i | ||||
\(197\) | 15.2477 | + | 8.80328i | 1.08636 | + | 0.627208i | 0.932604 | − | 0.360902i | \(-0.117531\pi\) |
0.153752 | + | 0.988110i | \(0.450864\pi\) | |||||||
\(198\) | −7.58258 | −0.538870 | ||||||||
\(199\) | 2.58258 | 0.183074 | 0.0915370 | − | 0.995802i | \(-0.470822\pi\) | ||||
0.0915370 | + | 0.995802i | \(0.470822\pi\) | |||||||
\(200\) | 3.00000 | + | 1.73205i | 0.212132 | + | 0.122474i | ||||
\(201\) | 12.1652 | + | 7.02355i | 0.858064 | + | 0.495403i | ||||
\(202\) | 24.9564 | − | 14.4086i | 1.75593 | − | 1.01379i | ||||
\(203\) | 16.0390 | − | 9.26013i | 1.12572 | − | 0.649934i | ||||
\(204\) | 1.39564 | + | 2.41733i | 0.0977146 | + | 0.169247i | ||||
\(205\) | −6.16515 | −0.430593 | ||||||||
\(206\) | 6.47822 | − | 3.74020i | 0.451359 | − | 0.260592i | ||||
\(207\) | 4.29129 | − | 7.43273i | 0.298265 | − | 0.516610i | ||||
\(208\) | 1.79129 | − | 6.20520i | 0.124203 | − | 0.430253i | ||||
\(209\) | 18.3303 | 1.26793 | ||||||||
\(210\) | 8.68693 | − | 5.01540i | 0.599455 | − | 0.346096i | ||||
\(211\) | −3.29129 | + | 5.70068i | −0.226582 | + | 0.392451i | −0.956793 | − | 0.290771i | \(-0.906088\pi\) |
0.730211 | + | 0.683222i | \(0.239422\pi\) | |||||||
\(212\) | −8.60436 | + | 14.9032i | −0.590950 | + | 1.02355i | ||||
\(213\) | 3.87386 | + | 2.23658i | 0.265433 | + | 0.153248i | ||||
\(214\) | − | 3.10260i | − | 0.212089i | ||||||
\(215\) | −6.87386 | − | 3.96863i | −0.468794 | − | 0.270658i | ||||
\(216\) | − | 1.73205i | − | 0.117851i | ||||||
\(217\) | 8.08258 | + | 13.9994i | 0.548681 | + | 0.950343i | ||||
\(218\) | 21.0608 | − | 36.4784i | 1.42642 | − | 2.47063i | ||||
\(219\) | 8.66025i | 0.585206i | ||||||||
\(220\) | −8.37386 | + | 14.5040i | −0.564566 | + | 0.977857i | ||||
\(221\) | −1.00000 | + | 3.46410i | −0.0672673 | + | 0.233021i | ||||
\(222\) | −7.68693 | − | 13.3142i | −0.515913 | − | 0.893588i | ||||
\(223\) | −2.29129 | − | 1.32288i | −0.153436 | − | 0.0885863i | 0.421316 | − | 0.906914i | \(-0.361568\pi\) |
−0.574752 | + | 0.818327i | \(0.694902\pi\) | |||||||
\(224\) | 9.76951 | − | 16.9213i | 0.652753 | − | 1.13060i | ||||
\(225\) | −1.00000 | − | 1.73205i | −0.0666667 | − | 0.115470i | ||||
\(226\) | 23.0608 | − | 13.3142i | 1.53398 | − | 0.885645i | ||||
\(227\) | 27.2759i | 1.81036i | 0.425026 | + | 0.905181i | \(0.360265\pi\) | ||||
−0.425026 | + | 0.905181i | \(0.639735\pi\) | |||||||
\(228\) | 14.7701i | 0.978174i | ||||||||
\(229\) | −9.08258 | + | 5.24383i | −0.600193 | + | 0.346522i | −0.769118 | − | 0.639107i | \(-0.779304\pi\) |
0.168924 | + | 0.985629i | \(0.445971\pi\) | |||||||
\(230\) | −16.2695 | − | 28.1796i | −1.07278 | − | 1.85811i | ||||
\(231\) | −4.58258 | − | 7.93725i | −0.301511 | − | 0.522233i | ||||
\(232\) | −10.5000 | − | 6.06218i | −0.689359 | − | 0.398001i | ||||
\(233\) | −10.0826 | − | 17.4635i | −0.660531 | − | 1.14407i | −0.980476 | − | 0.196638i | \(-0.936998\pi\) |
0.319945 | − | 0.947436i | \(-0.396336\pi\) | |||||||
\(234\) | 5.68693 | − | 5.47225i | 0.371766 | − | 0.357732i | ||||
\(235\) | −0.708712 | + | 1.22753i | −0.0462313 | + | 0.0800749i | ||||
\(236\) | − | 11.9536i | − | 0.778110i | ||||||
\(237\) | 0.708712 | − | 1.22753i | 0.0460358 | − | 0.0797363i | ||||
\(238\) | −2.89564 | + | 5.01540i | −0.187697 | + | 0.325100i | ||||
\(239\) | 2.01810i | 0.130540i | 0.997868 | + | 0.0652701i | \(0.0207909\pi\) | ||||
−0.997868 | + | 0.0652701i | \(0.979209\pi\) | |||||||
\(240\) | 2.68693 | + | 1.55130i | 0.173441 | + | 0.100136i | ||||
\(241\) | − | 14.1425i | − | 0.910996i | −0.890237 | − | 0.455498i | \(-0.849461\pi\) | ||
0.890237 | − | 0.455498i | \(-0.150539\pi\) | |||||||
\(242\) | 1.89564 | + | 1.09445i | 0.121857 | + | 0.0703539i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −7.20871 | + | 12.4859i | −0.461491 | + | 0.799325i | ||||
\(245\) | 10.5000 | + | 6.06218i | 0.670820 | + | 0.387298i | ||||
\(246\) | −7.79129 | −0.496754 | ||||||||
\(247\) | −13.7477 | + | 13.2288i | −0.874747 | + | 0.841726i | ||||
\(248\) | 5.29129 | − | 9.16478i | 0.335997 | − | 0.581964i | ||||
\(249\) | −3.00000 | + | 1.73205i | −0.190117 | + | 0.109764i | ||||
\(250\) | −26.5390 | −1.67847 | ||||||||
\(251\) | 10.2913 | + | 17.8250i | 0.649580 | + | 1.12511i | 0.983223 | + | 0.182407i | \(0.0583887\pi\) |
−0.333643 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(252\) | 6.39564 | − | 3.69253i | 0.402888 | − | 0.232607i | ||||
\(253\) | −25.7477 | + | 14.8655i | −1.61875 | + | 0.934583i | ||||
\(254\) | −12.4782 | − | 7.20430i | −0.782953 | − | 0.452038i | ||||
\(255\) | −1.50000 | − | 0.866025i | −0.0939336 | − | 0.0542326i | ||||
\(256\) | −2.79129 | −0.174455 | ||||||||
\(257\) | −9.33030 | −0.582008 | −0.291004 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291004 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(258\) | −8.68693 | − | 5.01540i | −0.540825 | − | 0.312245i | ||||
\(259\) | 9.29129 | − | 16.0930i | 0.577333 | − | 0.999969i | ||||
\(260\) | −4.18693 | − | 16.9213i | −0.259662 | − | 1.04941i | ||||
\(261\) | 3.50000 | + | 6.06218i | 0.216645 | + | 0.375239i | ||||
\(262\) | 2.68693 | − | 1.55130i | 0.165999 | − | 0.0958397i | ||||
\(263\) | 2.41742 | + | 4.18710i | 0.149065 | + | 0.258188i | 0.930882 | − | 0.365320i | \(-0.119040\pi\) |
−0.781817 | + | 0.623508i | \(0.785707\pi\) | |||||||
\(264\) | −3.00000 | + | 5.19615i | −0.184637 | + | 0.319801i | ||||
\(265\) | − | 10.6784i | − | 0.655966i | ||||||
\(266\) | −26.5390 | + | 15.3223i | −1.62721 | + | 0.939471i | ||||
\(267\) | −13.5000 | + | 7.79423i | −0.826187 | + | 0.476999i | ||||
\(268\) | 33.9564 | − | 19.6048i | 2.07422 | − | 1.19755i | ||||
\(269\) | 16.1652 | 0.985607 | 0.492803 | − | 0.870141i | \(-0.335972\pi\) | ||||
0.492803 | + | 0.870141i | \(0.335972\pi\) | |||||||
\(270\) | 1.89564 | + | 3.28335i | 0.115365 | + | 0.199818i | ||||
\(271\) | − | 11.5921i | − | 0.704167i | −0.935969 | − | 0.352084i | \(-0.885473\pi\) | ||
0.935969 | − | 0.352084i | \(-0.114527\pi\) | |||||||
\(272\) | −1.79129 | −0.108613 | ||||||||
\(273\) | 9.16515 | + | 2.64575i | 0.554700 | + | 0.160128i | ||||
\(274\) | −18.9564 | −1.14520 | ||||||||
\(275\) | 6.92820i | 0.417786i | ||||||||
\(276\) | −11.9782 | − | 20.7469i | −0.721004 | − | 1.24882i | ||||
\(277\) | 9.33030 | 0.560604 | 0.280302 | − | 0.959912i | \(-0.409565\pi\) | ||||
0.280302 | + | 0.959912i | \(0.409565\pi\) | |||||||
\(278\) | −12.4782 | + | 7.20430i | −0.748394 | + | 0.432085i | ||||
\(279\) | −5.29129 | + | 3.05493i | −0.316781 | + | 0.182894i | ||||
\(280\) | − | 7.93725i | − | 0.474342i | ||||||
\(281\) | 3.65480i | 0.218027i | 0.994040 | + | 0.109014i | \(0.0347692\pi\) | ||||
−0.994040 | + | 0.109014i | \(0.965231\pi\) | |||||||
\(282\) | −0.895644 | + | 1.55130i | −0.0533348 | + | 0.0923786i | ||||
\(283\) | 15.1652 | + | 26.2668i | 0.901475 | + | 1.56140i | 0.825581 | + | 0.564284i | \(0.190848\pi\) |
0.0758940 | + | 0.997116i | \(0.475819\pi\) | |||||||
\(284\) | 10.8131 | − | 6.24293i | 0.641638 | − | 0.370450i | ||||
\(285\) | −4.58258 | − | 7.93725i | −0.271448 | − | 0.470162i | ||||
\(286\) | −26.5390 | + | 6.56670i | −1.56928 | + | 0.388297i | ||||
\(287\) | −4.70871 | − | 8.15573i | −0.277946 | − | 0.481417i | ||||
\(288\) | 6.39564 | + | 3.69253i | 0.376867 | + | 0.217584i | ||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 26.5390 | 1.55842 | ||||||||
\(291\) | −9.08258 | − | 5.24383i | −0.532430 | − | 0.307399i | ||||
\(292\) | 20.9347 | + | 12.0866i | 1.22511 | + | 0.707317i | ||||
\(293\) | 16.8303 | − | 9.71698i | 0.983237 | − | 0.567672i | 0.0799910 | − | 0.996796i | \(-0.474511\pi\) |
0.903246 | + | 0.429124i | \(0.141178\pi\) | |||||||
\(294\) | 13.2695 | + | 7.66115i | 0.773893 | + | 0.446808i | ||||
\(295\) | 3.70871 | + | 6.42368i | 0.215930 | + | 0.374001i | ||||
\(296\) | −12.1652 | −0.707085 | ||||||||
\(297\) | 3.00000 | − | 1.73205i | 0.174078 | − | 0.100504i | ||||
\(298\) | −4.00000 | + | 6.92820i | −0.231714 | + | 0.401340i | ||||
\(299\) | 8.58258 | − | 29.7309i | 0.496343 | − | 1.71938i | ||||
\(300\) | −5.58258 | −0.322310 | ||||||||
\(301\) | − | 12.1244i | − | 0.698836i | ||||||
\(302\) | −18.2695 | + | 31.6437i | −1.05129 | + | 1.82089i | ||||
\(303\) | −6.58258 | + | 11.4014i | −0.378159 | + | 0.654991i | ||||
\(304\) | −8.20871 | − | 4.73930i | −0.470802 | − | 0.271818i | ||||
\(305\) | − | 8.94630i | − | 0.512264i | ||||||
\(306\) | −1.89564 | − | 1.09445i | −0.108367 | − | 0.0625656i | ||||
\(307\) | − | 20.9753i | − | 1.19712i | −0.801076 | − | 0.598562i | \(-0.795739\pi\) | ||
0.801076 | − | 0.598562i | \(-0.204261\pi\) | |||||||
\(308\) | −25.5826 | −1.45770 | ||||||||
\(309\) | −1.70871 | + | 2.95958i | −0.0972052 | + | 0.168364i | ||||
\(310\) | 23.1642i | 1.31564i | ||||||||
\(311\) | 4.29129 | − | 7.43273i | 0.243337 | − | 0.421471i | −0.718326 | − | 0.695707i | \(-0.755091\pi\) |
0.961663 | + | 0.274235i | \(0.0884247\pi\) | |||||||
\(312\) | −1.50000 | − | 6.06218i | −0.0849208 | − | 0.343203i | ||||
\(313\) | 6.91742 | + | 11.9813i | 0.390996 | + | 0.677225i | 0.992581 | − | 0.121584i | \(-0.0387973\pi\) |
−0.601585 | + | 0.798809i | \(0.705464\pi\) | |||||||
\(314\) | −19.2695 | − | 11.1253i | −1.08744 | − | 0.627834i | ||||
\(315\) | −2.29129 | + | 3.96863i | −0.129099 | + | 0.223607i | ||||
\(316\) | −1.97822 | − | 3.42638i | −0.111284 | − | 0.192749i | ||||
\(317\) | −1.66515 | + | 0.961376i | −0.0935242 | + | 0.0539962i | −0.546033 | − | 0.837764i | \(-0.683863\pi\) |
0.452508 | + | 0.891760i | \(0.350529\pi\) | |||||||
\(318\) | − | 13.4949i | − | 0.756757i | ||||||
\(319\) | − | 24.2487i | − | 1.35767i | ||||||
\(320\) | 18.8739 | − | 10.8968i | 1.05508 | − | 0.609151i | ||||
\(321\) | 0.708712 | + | 1.22753i | 0.0395565 | + | 0.0685138i | ||||
\(322\) | 24.8521 | − | 43.0451i | 1.38495 | − | 2.39881i | ||||
\(323\) | 4.58258 | + | 2.64575i | 0.254981 | + | 0.147214i | ||||
\(324\) | 1.39564 | + | 2.41733i | 0.0775358 | + | 0.134296i | ||||
\(325\) | −5.00000 | − | 5.19615i | −0.277350 | − | 0.288231i | ||||
\(326\) | −3.79129 | + | 6.56670i | −0.209980 | + | 0.363696i | ||||
\(327\) | 19.2433i | 1.06415i | ||||||||
\(328\) | −3.08258 | + | 5.33918i | −0.170207 | + | 0.294807i | ||||
\(329\) | −2.16515 | −0.119369 | ||||||||
\(330\) | − | 13.1334i | − | 0.722970i | ||||||
\(331\) | −22.5826 | − | 13.0381i | −1.24125 | − | 0.716636i | −0.271902 | − | 0.962325i | \(-0.587653\pi\) |
−0.969349 | + | 0.245689i | \(0.920986\pi\) | |||||||
\(332\) | 9.66930i | 0.530672i | ||||||||
\(333\) | 6.08258 | + | 3.51178i | 0.333323 | + | 0.192444i | ||||
\(334\) | −4.89564 | + | 8.47950i | −0.267878 | + | 0.463978i | ||||
\(335\) | −12.1652 | + | 21.0707i | −0.664653 | + | 1.15121i | ||||
\(336\) | 4.73930i | 0.258550i | ||||||||
\(337\) | 23.4955 | 1.27988 | 0.639939 | − | 0.768425i | \(-0.278959\pi\) | ||||
0.639939 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(338\) | 15.1652 | − | 24.0779i | 0.824875 | − | 1.30967i | ||||
\(339\) | −6.08258 | + | 10.5353i | −0.330360 | + | 0.572201i | ||||
\(340\) | −4.18693 | + | 2.41733i | −0.227068 | + | 0.131098i | ||||
\(341\) | 21.1652 | 1.14616 | ||||||||
\(342\) | −5.79129 | − | 10.0308i | −0.313157 | − | 0.542404i | ||||
\(343\) | 18.5203i | 1.00000i | ||||||||
\(344\) | −6.87386 | + | 3.96863i | −0.370614 | + | 0.213974i | ||||
\(345\) | 12.8739 | + | 7.43273i | 0.693106 | + | 0.400165i | ||||
\(346\) | −46.1216 | − | 26.6283i | −2.47951 | − | 1.43155i | ||||
\(347\) | −25.7477 | −1.38221 | −0.691105 | − | 0.722754i | \(-0.742876\pi\) | ||||
−0.691105 | + | 0.722754i | \(0.742876\pi\) | |||||||
\(348\) | 19.5390 | 1.04740 | ||||||||
\(349\) | 9.08258 | + | 5.24383i | 0.486179 | + | 0.280696i | 0.722988 | − | 0.690861i | \(-0.242768\pi\) |
−0.236809 | + | 0.971556i | \(0.576102\pi\) | |||||||
\(350\) | −5.79129 | − | 10.0308i | −0.309557 | − | 0.536169i | ||||
\(351\) | −1.00000 | + | 3.46410i | −0.0533761 | + | 0.184900i | ||||
\(352\) | −12.7913 | − | 22.1552i | −0.681778 | − | 1.18087i | ||||
\(353\) | −16.7477 | + | 9.66930i | −0.891392 | + | 0.514645i | −0.874397 | − | 0.485210i | \(-0.838743\pi\) |
−0.0169942 | + | 0.999856i | \(0.505410\pi\) | |||||||
\(354\) | 4.68693 | + | 8.11800i | 0.249108 | + | 0.431467i | ||||
\(355\) | −3.87386 | + | 6.70973i | −0.205603 | + | 0.356115i | ||||
\(356\) | 43.5119i | 2.30612i | ||||||||
\(357\) | − | 2.64575i | − | 0.140028i | ||||||
\(358\) | 1.58258 | − | 0.913701i | 0.0836417 | − | 0.0482906i | ||||
\(359\) | 16.0390 | − | 9.26013i | 0.846507 | − | 0.488731i | −0.0129639 | − | 0.999916i | \(-0.504127\pi\) |
0.859471 | + | 0.511185i | \(0.170793\pi\) | |||||||
\(360\) | 3.00000 | 0.158114 | ||||||||
\(361\) | 4.50000 | + | 7.79423i | 0.236842 | + | 0.410223i | ||||
\(362\) | 48.1558i | 2.53101i | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 19.1869 | − | 18.4626i | 1.00567 | − | 0.967705i | ||||
\(365\) | −15.0000 | −0.785136 | ||||||||
\(366\) | − | 11.3060i | − | 0.590974i | ||||||
\(367\) | −7.58258 | − | 13.1334i | −0.395807 | − | 0.685558i | 0.597397 | − | 0.801946i | \(-0.296202\pi\) |
−0.993204 | + | 0.116388i | \(0.962868\pi\) | |||||||
\(368\) | 15.3739 | 0.801418 | ||||||||
\(369\) | 3.08258 | − | 1.77973i | 0.160472 | − | 0.0926488i | ||||
\(370\) | 23.0608 | − | 13.3142i | 1.19887 | − | 0.692170i | ||||
\(371\) | 14.1261 | − | 8.15573i | 0.733392 | − | 0.423424i | ||||
\(372\) | 17.0544i | 0.884227i | ||||||||
\(373\) | 13.0000 | − | 22.5167i | 0.673114 | − | 1.16587i | −0.303902 | − | 0.952703i | \(-0.598289\pi\) |
0.977016 | − | 0.213165i | \(-0.0683772\pi\) | |||||||
\(374\) | 3.79129 | + | 6.56670i | 0.196043 | + | 0.339556i | ||||
\(375\) | 10.5000 | − | 6.06218i | 0.542218 | − | 0.313050i | ||||
\(376\) | 0.708712 | + | 1.22753i | 0.0365490 | + | 0.0633048i | ||||
\(377\) | 17.5000 | + | 18.1865i | 0.901296 | + | 0.936654i | ||||
\(378\) | −2.89564 | + | 5.01540i | −0.148936 | + | 0.257964i | ||||
\(379\) | 16.0390 | + | 9.26013i | 0.823869 | + | 0.475661i | 0.851749 | − | 0.523950i | \(-0.175542\pi\) |
−0.0278799 | + | 0.999611i | \(0.508876\pi\) | |||||||
\(380\) | −25.5826 | −1.31236 | ||||||||
\(381\) | 6.58258 | 0.337236 | ||||||||
\(382\) | 27.1652 | + | 15.6838i | 1.38989 | + | 0.802453i | ||||
\(383\) | −15.3303 | − | 8.85095i | −0.783342 | − | 0.452263i | 0.0542715 | − | 0.998526i | \(-0.482716\pi\) |
−0.837613 | + | 0.546264i | \(0.816050\pi\) | |||||||
\(384\) | 11.0608 | − | 6.38595i | 0.564444 | − | 0.325882i | ||||
\(385\) | 13.7477 | − | 7.93725i | 0.700649 | − | 0.404520i | ||||
\(386\) | −4.00000 | − | 6.92820i | −0.203595 | − | 0.352636i | ||||
\(387\) | 4.58258 | 0.232945 | ||||||||
\(388\) | −25.3521 | + | 14.6370i | −1.28706 | + | 0.743083i | ||||
\(389\) | −13.6652 | + | 23.6687i | −0.692851 | + | 1.20005i | 0.278049 | + | 0.960567i | \(0.410312\pi\) |
−0.970900 | + | 0.239486i | \(0.923021\pi\) | |||||||
\(390\) | 9.47822 | + | 9.85005i | 0.479948 | + | 0.498777i | ||||
\(391\) | −8.58258 | −0.434040 | ||||||||
\(392\) | 10.5000 | − | 6.06218i | 0.530330 | − | 0.306186i | ||||
\(393\) | −0.708712 | + | 1.22753i | −0.0357498 | + | 0.0619205i | ||||
\(394\) | −19.2695 | + | 33.3758i | −0.970784 | + | 1.68145i | ||||
\(395\) | 2.12614 | + | 1.22753i | 0.106978 | + | 0.0617635i | ||||
\(396\) | − | 9.66930i | − | 0.485901i | ||||||
\(397\) | 31.9129 | + | 18.4249i | 1.60166 | + | 0.924720i | 0.991155 | + | 0.132708i | \(0.0423673\pi\) |
0.610506 | + | 0.792011i | \(0.290966\pi\) | |||||||
\(398\) | 5.65300i | 0.283359i | ||||||||
\(399\) | 7.00000 | − | 12.1244i | 0.350438 | − | 0.606977i | ||||
\(400\) | 1.79129 | − | 3.10260i | 0.0895644 | − | 0.155130i | ||||
\(401\) | 34.7364i | 1.73465i | 0.497741 | + | 0.867326i | \(0.334163\pi\) | ||||
−0.497741 | + | 0.867326i | \(0.665837\pi\) | |||||||
\(402\) | −15.3739 | + | 26.6283i | −0.766779 | + | 1.32810i | ||||
\(403\) | −15.8739 | + | 15.2746i | −0.790733 | + | 0.760884i | ||||
\(404\) | 18.3739 | + | 31.8245i | 0.914134 | + | 1.58333i | ||||
\(405\) | −1.50000 | − | 0.866025i | −0.0745356 | − | 0.0430331i | ||||
\(406\) | 20.2695 | + | 35.1078i | 1.00596 | + | 1.74237i | ||||
\(407\) | −12.1652 | − | 21.0707i | −0.603004 | − | 1.04443i | ||||
\(408\) | −1.50000 | + | 0.866025i | −0.0742611 | + | 0.0428746i | ||||
\(409\) | − | 31.2723i | − | 1.54631i | −0.634215 | − | 0.773157i | \(-0.718676\pi\) | ||
0.634215 | − | 0.773157i | \(-0.281324\pi\) | |||||||
\(410\) | − | 13.4949i | − | 0.666466i | ||||||
\(411\) | 7.50000 | − | 4.33013i | 0.369948 | − | 0.213589i | ||||
\(412\) | 4.76951 | + | 8.26103i | 0.234977 | + | 0.406992i | ||||
\(413\) | −5.66515 | + | 9.81233i | −0.278764 | + | 0.482833i | ||||
\(414\) | 16.2695 | + | 9.39320i | 0.799603 | + | 0.461651i | ||||
\(415\) | −3.00000 | − | 5.19615i | −0.147264 | − | 0.255069i | ||||
\(416\) | 25.5826 | + | 7.38505i | 1.25429 | + | 0.362082i | ||||
\(417\) | 3.29129 | − | 5.70068i | 0.161175 | − | 0.279163i | ||||
\(418\) | 40.1232i | 1.96249i | ||||||||
\(419\) | −5.87386 | + | 10.1738i | −0.286957 | + | 0.497024i | −0.973082 | − | 0.230460i | \(-0.925977\pi\) |
0.686125 | + | 0.727484i | \(0.259310\pi\) | |||||||
\(420\) | 6.39564 | + | 11.0776i | 0.312075 | + | 0.540531i | ||||
\(421\) | − | 40.5046i | − | 1.97407i | −0.160492 | − | 0.987037i | \(-0.551308\pi\) | ||
0.160492 | − | 0.987037i | \(-0.448692\pi\) | |||||||
\(422\) | −12.4782 | − | 7.20430i | −0.607430 | − | 0.350700i | ||||
\(423\) | − | 0.818350i | − | 0.0397896i | ||||||
\(424\) | −9.24773 | − | 5.33918i | −0.449109 | − | 0.259293i | ||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | −4.89564 | + | 8.47950i | −0.237195 | + | 0.410833i | ||||
\(427\) | 11.8348 | − | 6.83285i | 0.572728 | − | 0.330665i | ||||
\(428\) | 3.95644 | 0.191242 | ||||||||
\(429\) | 9.00000 | − | 8.66025i | 0.434524 | − | 0.418121i | ||||
\(430\) | 8.68693 | − | 15.0462i | 0.418921 | − | 0.725593i | ||||
\(431\) | −7.41742 | + | 4.28245i | −0.357285 | + | 0.206278i | −0.667889 | − | 0.744261i | \(-0.732802\pi\) |
0.310604 | + | 0.950539i | \(0.399469\pi\) | |||||||
\(432\) | −1.79129 | −0.0861834 | ||||||||
\(433\) | 7.66515 | + | 13.2764i | 0.368364 | + | 0.638025i | 0.989310 | − | 0.145829i | \(-0.0465848\pi\) |
−0.620946 | + | 0.783853i | \(0.713251\pi\) | |||||||
\(434\) | −30.6434 | + | 17.6920i | −1.47093 | + | 0.849241i | ||||
\(435\) | −10.5000 | + | 6.06218i | −0.503436 | + | 0.290659i | ||||
\(436\) | 46.5172 | + | 26.8567i | 2.22777 | + | 1.28620i | ||||
\(437\) | −39.3303 | − | 22.7074i | −1.88142 | − | 1.08624i | ||||
\(438\) | −18.9564 | −0.905774 | ||||||||
\(439\) | −10.5826 | −0.505079 | −0.252539 | − | 0.967587i | \(-0.581266\pi\) | ||||
−0.252539 | + | 0.967587i | \(0.581266\pi\) | |||||||
\(440\) | −9.00000 | − | 5.19615i | −0.429058 | − | 0.247717i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | −7.58258 | − | 2.18890i | −0.360666 | − | 0.104115i | ||||
\(443\) | 2.87386 | + | 4.97768i | 0.136541 | + | 0.236497i | 0.926185 | − | 0.377069i | \(-0.123068\pi\) |
−0.789644 | + | 0.613565i | \(0.789735\pi\) | |||||||
\(444\) | 16.9782 | − | 9.80238i | 0.805751 | − | 0.465200i | ||||
\(445\) | −13.5000 | − | 23.3827i | −0.639961 | − | 1.10845i | ||||
\(446\) | 2.89564 | − | 5.01540i | 0.137113 | − | 0.237486i | ||||
\(447\) | − | 3.65480i | − | 0.172866i | ||||||
\(448\) | 28.8303 | + | 16.6452i | 1.36210 | + | 0.786411i | ||||
\(449\) | −10.6652 | + | 6.15753i | −0.503320 | + | 0.290592i | −0.730083 | − | 0.683358i | \(-0.760519\pi\) |
0.226764 | + | 0.973950i | \(0.427185\pi\) | |||||||
\(450\) | 3.79129 | − | 2.18890i | 0.178723 | − | 0.103186i | ||||
\(451\) | −12.3303 | −0.580611 | ||||||||
\(452\) | 16.9782 | + | 29.4071i | 0.798588 | + | 1.38320i | ||||
\(453\) | − | 16.6929i | − | 0.784299i | ||||||
\(454\) | −59.7042 | −2.80206 | ||||||||
\(455\) | −4.58258 | + | 15.8745i | −0.214834 | + | 0.744208i | ||||
\(456\) | −9.16515 | −0.429198 | ||||||||
\(457\) | − | 3.75015i | − | 0.175425i | −0.996146 | − | 0.0877124i | \(-0.972044\pi\) | ||
0.996146 | − | 0.0877124i | \(-0.0279556\pi\) | |||||||
\(458\) | −11.4782 | − | 19.8809i | −0.536342 | − | 0.928972i | ||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 35.9347 | − | 20.7469i | 1.67546 | − | 0.967328i | ||||
\(461\) | −27.4129 | + | 15.8268i | −1.27675 | + | 0.737129i | −0.976248 | − | 0.216654i | \(-0.930486\pi\) |
−0.300497 | + | 0.953783i | \(0.597152\pi\) | |||||||
\(462\) | 17.3739 | − | 10.0308i | 0.808305 | − | 0.466675i | ||||
\(463\) | − | 38.4865i | − | 1.78862i | −0.447448 | − | 0.894310i | \(-0.647667\pi\) | ||
0.447448 | − | 0.894310i | \(-0.352333\pi\) | |||||||
\(464\) | −6.26951 | + | 10.8591i | −0.291055 | + | 0.504121i | ||||
\(465\) | −5.29129 | − | 9.16478i | −0.245378 | − | 0.425006i | ||||
\(466\) | 38.2259 | − | 22.0698i | 1.77078 | − | 1.02236i | ||||
\(467\) | 14.4564 | + | 25.0393i | 0.668964 | + | 1.15868i | 0.978194 | + | 0.207693i | \(0.0665954\pi\) |
−0.309230 | + | 0.950987i | \(0.600071\pi\) | |||||||
\(468\) | 6.97822 | + | 7.25198i | 0.322568 | + | 0.335223i | ||||
\(469\) | −37.1652 | −1.71613 | ||||||||
\(470\) | −2.68693 | − | 1.55130i | −0.123939 | − | 0.0715562i | ||||
\(471\) | 10.1652 | 0.468385 | ||||||||
\(472\) | 7.41742 | 0.341415 | ||||||||
\(473\) | −13.7477 | − | 7.93725i | −0.632121 | − | 0.364955i | ||||
\(474\) | 2.68693 | + | 1.55130i | 0.123415 | + | 0.0712536i | ||||
\(475\) | −9.16515 | + | 5.29150i | −0.420526 | + | 0.242791i | ||||
\(476\) | −6.39564 | − | 3.69253i | −0.293144 | − | 0.169247i | ||||
\(477\) | 3.08258 | + | 5.33918i | 0.141141 | + | 0.244464i | ||||
\(478\) | −4.41742 | −0.202048 | ||||||||
\(479\) | 24.4955 | − | 14.1425i | 1.11923 | − | 0.646185i | 0.178023 | − | 0.984026i | \(-0.443030\pi\) |
0.941203 | + | 0.337841i | \(0.109697\pi\) | |||||||
\(480\) | −6.39564 | + | 11.0776i | −0.291920 | + | 0.505620i | ||||
\(481\) | 24.3303 | + | 7.02355i | 1.10937 | + | 0.320246i | ||||
\(482\) | 30.9564 | 1.41003 | ||||||||
\(483\) | 22.7074i | 1.03322i | ||||||||
\(484\) | −1.39564 | + | 2.41733i | −0.0634384 | + | 0.109878i | ||||
\(485\) | 9.08258 | − | 15.7315i | 0.412419 | − | 0.714330i | ||||
\(486\) | −1.89564 | − | 1.09445i | −0.0859882 | − | 0.0496453i | ||||
\(487\) | 11.0200i | 0.499362i | 0.968328 | + | 0.249681i | \(0.0803257\pi\) | ||||
−0.968328 | + | 0.249681i | \(0.919674\pi\) | |||||||
\(488\) | −7.74773 | − | 4.47315i | −0.350723 | − | 0.202490i | ||||
\(489\) | − | 3.46410i | − | 0.156652i | ||||||
\(490\) | −13.2695 | + | 22.9835i | −0.599455 | + | 1.03829i | ||||
\(491\) | −1.87386 | + | 3.24563i | −0.0845663 | + | 0.146473i | −0.905206 | − | 0.424972i | \(-0.860284\pi\) |
0.820640 | + | 0.571445i | \(0.193617\pi\) | |||||||
\(492\) | − | 9.93545i | − | 0.447925i | ||||||
\(493\) | 3.50000 | − | 6.06218i | 0.157632 | − | 0.273027i | ||||
\(494\) | −28.9564 | − | 30.0924i | −1.30281 | − | 1.35392i | ||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | −9.47822 | − | 5.47225i | −0.425585 | − | 0.245711i | ||||
\(497\) | −11.8348 | −0.530866 | ||||||||
\(498\) | −3.79129 | − | 6.56670i | −0.169892 | − | 0.294261i | ||||
\(499\) | −21.7087 | + | 12.5335i | −0.971815 | + | 0.561078i | −0.899789 | − | 0.436325i | \(-0.856280\pi\) |
−0.0720262 | + | 0.997403i | \(0.522947\pi\) | |||||||
\(500\) | − | 33.8426i | − | 1.51349i | ||||||
\(501\) | − | 4.47315i | − | 0.199846i | ||||||
\(502\) | −39.0172 | + | 22.5266i | −1.74142 | + | 1.00541i | ||||
\(503\) | −0.873864 | − | 1.51358i | −0.0389636 | − | 0.0674870i | 0.845886 | − | 0.533364i | \(-0.179072\pi\) |
−0.884850 | + | 0.465877i | \(0.845739\pi\) | |||||||
\(504\) | 2.29129 | + | 3.96863i | 0.102062 | + | 0.176777i | ||||
\(505\) | −19.7477 | − | 11.4014i | −0.878762 | − | 0.507354i | ||||
\(506\) | −32.5390 | − | 56.3592i | −1.44654 | − | 2.50547i | ||||
\(507\) | −0.500000 | + | 12.9904i | −0.0222058 | + | 0.576923i | ||||
\(508\) | 9.18693 | − | 15.9122i | 0.407604 | − | 0.705991i | ||||
\(509\) | − | 27.9989i | − | 1.24103i | −0.784195 | − | 0.620514i | \(-0.786924\pi\) | ||
0.784195 | − | 0.620514i | \(-0.213076\pi\) | |||||||
\(510\) | 1.89564 | − | 3.28335i | 0.0839405 | − | 0.145389i | ||||
\(511\) | −11.4564 | − | 19.8431i | −0.506803 | − | 0.877809i | ||||
\(512\) | 19.4340i | 0.858868i | ||||||||
\(513\) | 4.58258 | + | 2.64575i | 0.202326 | + | 0.116813i | ||||
\(514\) | − | 20.4231i | − | 0.900825i | ||||||
\(515\) | −5.12614 | − | 2.95958i | −0.225885 | − | 0.130415i | ||||
\(516\) | 6.39564 | − | 11.0776i | 0.281553 | − | 0.487663i | ||||
\(517\) | −1.41742 | + | 2.45505i | −0.0623382 | + | 0.107973i | ||||
\(518\) | 35.2259 | + | 20.3377i | 1.54774 | + | 0.893588i | ||||
\(519\) | 24.3303 | 1.06798 | ||||||||
\(520\) | 10.5000 | − | 2.59808i | 0.460455 | − | 0.113933i | ||||
\(521\) | −1.66515 | + | 2.88413i | −0.0729516 | + | 0.126356i | −0.900194 | − | 0.435490i | \(-0.856575\pi\) |
0.827242 | + | 0.561846i | \(0.189909\pi\) | |||||||
\(522\) | −13.2695 | + | 7.66115i | −0.580791 | + | 0.335320i | ||||
\(523\) | −9.74773 | −0.426238 | −0.213119 | − | 0.977026i | \(-0.568362\pi\) | ||||
−0.213119 | + | 0.977026i | \(0.568362\pi\) | |||||||
\(524\) | 1.97822 | + | 3.42638i | 0.0864189 | + | 0.149682i | ||||
\(525\) | 4.58258 | + | 2.64575i | 0.200000 | + | 0.115470i | ||||
\(526\) | −9.16515 | + | 5.29150i | −0.399620 | + | 0.230720i | ||||
\(527\) | 5.29129 | + | 3.05493i | 0.230492 | + | 0.133075i | ||||
\(528\) | 5.37386 | + | 3.10260i | 0.233867 | + | 0.135023i | ||||
\(529\) | 50.6606 | 2.20264 | ||||||||
\(530\) | 23.3739 | 1.01530 | ||||||||
\(531\) | −3.70871 | − | 2.14123i | −0.160944 | − | 0.0929213i | ||||
\(532\) | −19.5390 | − | 33.8426i | −0.847124 | − | 1.46726i | ||||
\(533\) | 9.24773 | − | 8.89863i | 0.400564 | − | 0.385442i | ||||
\(534\) | −17.0608 | − | 29.5502i | −0.738293 | − | 1.27876i | ||||
\(535\) | −2.12614 | + | 1.22753i | −0.0919209 | + | 0.0530706i | ||||
\(536\) | 12.1652 | + | 21.0707i | 0.525455 | + | 0.910114i | ||||
\(537\) | −0.417424 | + | 0.723000i | −0.0180132 | + | 0.0311998i | ||||
\(538\) | 35.3839i | 1.52551i | ||||||||
\(539\) | 21.0000 | + | 12.1244i | 0.904534 | + | 0.522233i | ||||
\(540\) | −4.18693 | + | 2.41733i | −0.180177 | + | 0.104025i | ||||
\(541\) | 7.33485 | − | 4.23478i | 0.315350 | − | 0.182067i | −0.333968 | − | 0.942584i | \(-0.608388\pi\) |
0.649318 | + | 0.760517i | \(0.275054\pi\) | |||||||
\(542\) | 25.3739 | 1.08990 | ||||||||
\(543\) | −11.0000 | − | 19.0526i | −0.472055 | − | 0.817624i | ||||
\(544\) | − | 7.38505i | − | 0.316632i | ||||||
\(545\) | −33.3303 | −1.42771 | ||||||||
\(546\) | −5.79129 | + | 20.0616i | −0.247844 | + | 0.858558i | ||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | − | 24.1733i | − | 1.03263i | ||||||
\(549\) | 2.58258 | + | 4.47315i | 0.110222 | + | 0.190909i | ||||
\(550\) | −15.1652 | −0.646644 | ||||||||
\(551\) | 32.0780 | − | 18.5203i | 1.36657 | − | 0.788990i | ||||
\(552\) | 12.8739 | − | 7.43273i | 0.547948 | − | 0.316358i | ||||
\(553\) | 3.75015i | 0.159473i | ||||||||
\(554\) | 20.4231i | 0.867695i | ||||||||
\(555\) | −6.08258 | + | 10.5353i | −0.258191 | + | 0.447200i | ||||
\(556\) | −9.18693 | − | 15.9122i | −0.389613 | − | 0.674829i | ||||
\(557\) | −21.1652 | + | 12.2197i | −0.896796 | + | 0.517766i | −0.876159 | − | 0.482021i | \(-0.839903\pi\) |
−0.0206368 | + | 0.999787i | \(0.506569\pi\) | |||||||
\(558\) | −6.68693 | − | 11.5821i | −0.283080 | − | 0.490310i | ||||
\(559\) | 16.0390 | − | 3.96863i | 0.678378 | − | 0.167855i | ||||
\(560\) | −8.20871 | −0.346881 | ||||||||
\(561\) | −3.00000 | − | 1.73205i | −0.126660 | − | 0.0731272i | ||||
\(562\) | −8.00000 | −0.337460 | ||||||||
\(563\) | 5.41742 | 0.228317 | 0.114159 | − | 0.993463i | \(-0.463583\pi\) | ||||
0.114159 | + | 0.993463i | \(0.463583\pi\) | |||||||
\(564\) | −1.97822 | − | 1.14213i | −0.0832981 | − | 0.0480922i | ||||
\(565\) | −18.2477 | − | 10.5353i | −0.767688 | − | 0.443225i | ||||
\(566\) | −57.4955 | + | 33.1950i | −2.41671 | + | 1.39529i | ||||
\(567\) | − | 2.64575i | − | 0.111111i | ||||||
\(568\) | 3.87386 | + | 6.70973i | 0.162544 | + | 0.281534i | ||||
\(569\) | −5.33030 | −0.223458 | −0.111729 | − | 0.993739i | \(-0.535639\pi\) | ||||
−0.111729 | + | 0.993739i | \(0.535639\pi\) | |||||||
\(570\) | 17.3739 | − | 10.0308i | 0.727711 | − | 0.420144i | ||||
\(571\) | −23.8739 | + | 41.3507i | −0.999090 | + | 1.73047i | −0.462609 | + | 0.886562i | \(0.653087\pi\) |
−0.536481 | + | 0.843913i | \(0.680247\pi\) | |||||||
\(572\) | −8.37386 | − | 33.8426i | −0.350129 | − | 1.41503i | ||||
\(573\) | −14.3303 | −0.598657 | ||||||||
\(574\) | 17.8521 | − | 10.3069i | 0.745132 | − | 0.430202i | ||||
\(575\) | 8.58258 | − | 14.8655i | 0.357918 | − | 0.619932i | ||||
\(576\) | −6.29129 | + | 10.8968i | −0.262137 | + | 0.454035i | ||||
\(577\) | 12.0826 | + | 6.97588i | 0.503004 | + | 0.290410i | 0.729953 | − | 0.683497i | \(-0.239542\pi\) |
−0.226949 | + | 0.973907i | \(0.572875\pi\) | |||||||
\(578\) | − | 35.0224i | − | 1.45674i | ||||||
\(579\) | 3.16515 | + | 1.82740i | 0.131539 | + | 0.0759442i | ||||
\(580\) | 33.8426i | 1.40524i | ||||||||
\(581\) | 4.58258 | − | 7.93725i | 0.190117 | − | 0.329293i | ||||
\(582\) | 11.4782 | − | 19.8809i | 0.475788 | − | 0.824088i | ||||
\(583\) | − | 21.3567i | − | 0.884505i | ||||||
\(584\) | −7.50000 | + | 12.9904i | −0.310352 | + | 0.537546i | ||||
\(585\) | −6.00000 | − | 1.73205i | −0.248069 | − | 0.0716115i | ||||
\(586\) | 21.2695 | + | 36.8399i | 0.878635 | + | 1.52184i | ||||
\(587\) | −18.8739 | − | 10.8968i | −0.779008 | − | 0.449760i | 0.0570708 | − | 0.998370i | \(-0.481824\pi\) |
−0.836079 | + | 0.548610i | \(0.815157\pi\) | |||||||
\(588\) | −9.76951 | + | 16.9213i | −0.402888 | + | 0.697822i | ||||
\(589\) | 16.1652 | + | 27.9989i | 0.666073 | + | 1.15367i | ||||
\(590\) | −14.0608 | + | 8.11800i | −0.578874 | + | 0.334213i | ||||
\(591\) | − | 17.6066i | − | 0.724237i | ||||||
\(592\) | 12.5812i | 0.517084i | ||||||||
\(593\) | −15.2477 | + | 8.80328i | −0.626149 | + | 0.361507i | −0.779259 | − | 0.626702i | \(-0.784404\pi\) |
0.153110 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(594\) | 3.79129 | + | 6.56670i | 0.155558 | + | 0.269435i | ||||
\(595\) | 4.58258 | 0.187867 | ||||||||
\(596\) | −8.83485 | − | 5.10080i | −0.361889 | − | 0.208937i | ||||
\(597\) | −1.29129 | − | 2.23658i | −0.0528489 | − | 0.0915370i | ||||
\(598\) | 65.0780 | + | 18.7864i | 2.66124 | + | 0.768233i | ||||
\(599\) | −4.12614 | + | 7.14668i | −0.168589 | + | 0.292005i | −0.937924 | − | 0.346841i | \(-0.887255\pi\) |
0.769335 | + | 0.638846i | \(0.220588\pi\) | |||||||
\(600\) | − | 3.46410i | − | 0.141421i | ||||||
\(601\) | −13.0826 | + | 22.6597i | −0.533649 | + | 0.924308i | 0.465578 | + | 0.885007i | \(0.345846\pi\) |
−0.999227 | + | 0.0393010i | \(0.987487\pi\) | |||||||
\(602\) | 26.5390 | 1.08165 | ||||||||
\(603\) | − | 14.0471i | − | 0.572042i | ||||||
\(604\) | −40.3521 | − | 23.2973i | −1.64190 | − | 0.947953i | ||||
\(605\) | − | 1.73205i | − | 0.0704179i | ||||||
\(606\) | −24.9564 | − | 14.4086i | −1.01379 | − | 0.585310i | ||||
\(607\) | 4.00000 | − | 6.92820i | 0.162355 | − | 0.281207i | −0.773358 | − | 0.633970i | \(-0.781424\pi\) |
0.935713 | + | 0.352763i | \(0.114758\pi\) | |||||||
\(608\) | 19.5390 | − | 33.8426i | 0.792412 | − | 1.37250i | ||||
\(609\) | −16.0390 | − | 9.26013i | −0.649934 | − | 0.375239i | ||||
\(610\) | 19.5826 | 0.792875 | ||||||||
\(611\) | −0.708712 | − | 2.86423i | −0.0286714 | − | 0.115874i | ||||
\(612\) | 1.39564 | − | 2.41733i | 0.0564156 | − | 0.0977146i | ||||
\(613\) | 21.1652 | − | 12.2197i | 0.854852 | − | 0.493549i | −0.00743271 | − | 0.999972i | \(-0.502366\pi\) |
0.862285 | + | 0.506423i | \(0.169033\pi\) | |||||||
\(614\) | 45.9129 | 1.85289 | ||||||||
\(615\) | 3.08258 | + | 5.33918i | 0.124301 | + | 0.215296i | ||||
\(616\) | − | 15.8745i | − | 0.639602i | ||||||
\(617\) | −18.2477 | + | 10.5353i | −0.734626 | + | 0.424136i | −0.820112 | − | 0.572203i | \(-0.806089\pi\) |
0.0854862 | + | 0.996339i | \(0.472756\pi\) | |||||||
\(618\) | −6.47822 | − | 3.74020i | −0.260592 | − | 0.150453i | ||||
\(619\) | −1.03901 | − | 0.599876i | −0.0417615 | − | 0.0241110i | 0.478974 | − | 0.877829i | \(-0.341009\pi\) |
−0.520735 | + | 0.853718i | \(0.674342\pi\) | |||||||
\(620\) | −29.5390 | −1.18632 | ||||||||
\(621\) | −8.58258 | −0.344407 | ||||||||
\(622\) | 16.2695 | + | 9.39320i | 0.652348 | + | 0.376633i | ||||
\(623\) | 20.6216 | − | 35.7176i | 0.826187 | − | 1.43100i | ||||
\(624\) | −6.26951 | + | 1.55130i | −0.250981 | + | 0.0621017i | ||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −26.2259 | + | 15.1416i | −1.04820 | + | 0.605178i | ||||
\(627\) | −9.16515 | − | 15.8745i | −0.366021 | − | 0.633967i | ||||
\(628\) | 14.1869 | − | 24.5725i | 0.566120 | − | 0.980549i | ||||
\(629\) | − | 7.02355i | − | 0.280047i | ||||||
\(630\) | −8.68693 | − | 5.01540i | −0.346096 | − | 0.199818i | ||||
\(631\) | −30.8739 | + | 17.8250i | −1.22907 | + | 0.709603i | −0.966835 | − | 0.255401i | \(-0.917793\pi\) |
−0.262234 | + | 0.965004i | \(0.584459\pi\) | |||||||
\(632\) | 2.12614 | − | 1.22753i | 0.0845732 | − | 0.0488283i | ||||
\(633\) | 6.58258 | 0.261634 | ||||||||
\(634\) | −2.10436 | − | 3.64485i | −0.0835747 | − | 0.144756i | ||||
\(635\) | 11.4014i | 0.452449i | ||||||||
\(636\) | 17.2087 | 0.682370 | ||||||||
\(637\) | −24.5000 | + | 6.06218i | −0.970725 | + | 0.240192i | ||||
\(638\) | 53.0780 | 2.10138 | ||||||||
\(639\) | − | 4.47315i | − | 0.176955i | ||||||
\(640\) | 11.0608 | + | 19.1579i | 0.437216 | + | 0.757281i | ||||
\(641\) | −16.4955 | −0.651531 | −0.325766 | − | 0.945451i | \(-0.605622\pi\) | ||||
−0.325766 | + | 0.945451i | \(0.605622\pi\) | |||||||
\(642\) | −2.68693 | + | 1.55130i | −0.106045 | + | 0.0612250i | ||||
\(643\) | 29.4564 | − | 17.0067i | 1.16165 | − | 0.670678i | 0.209950 | − | 0.977712i | \(-0.432670\pi\) |
0.951699 | + | 0.307034i | \(0.0993365\pi\) | |||||||
\(644\) | 54.8911 | + | 31.6914i | 2.16301 | + | 1.24882i | ||||
\(645\) | 7.93725i | 0.312529i | ||||||||
\(646\) | −5.79129 | + | 10.0308i | −0.227855 | + | 0.394657i | ||||
\(647\) | 19.1652 | + | 33.1950i | 0.753460 | + | 1.30503i | 0.946136 | + | 0.323768i | \(0.104950\pi\) |
−0.192677 | + | 0.981262i | \(0.561717\pi\) | |||||||
\(648\) | −1.50000 | + | 0.866025i | −0.0589256 | + | 0.0340207i | ||||
\(649\) | 7.41742 | + | 12.8474i | 0.291159 | + | 0.504303i | ||||
\(650\) | 11.3739 | − | 10.9445i | 0.446120 | − | 0.429279i | ||||
\(651\) | 8.08258 | − | 13.9994i | 0.316781 | − | 0.548681i | ||||
\(652\) | −8.37386 | − | 4.83465i | −0.327946 | − | 0.189340i | ||||
\(653\) | 26.4955 | 1.03685 | 0.518424 | − | 0.855124i | \(-0.326519\pi\) | ||||
0.518424 | + | 0.855124i | \(0.326519\pi\) | |||||||
\(654\) | −42.1216 | −1.64708 | ||||||||
\(655\) | −2.12614 | − | 1.22753i | −0.0830750 | − | 0.0479634i | ||||
\(656\) | 5.52178 | + | 3.18800i | 0.215589 | + | 0.124471i | ||||
\(657\) | 7.50000 | − | 4.33013i | 0.292603 | − | 0.168934i | ||||
\(658\) | − | 4.73930i | − | 0.184757i | ||||||
\(659\) | −10.0390 | − | 17.3881i | −0.391064 | − | 0.677344i | 0.601526 | − | 0.798853i | \(-0.294560\pi\) |
−0.992590 | + | 0.121510i | \(0.961226\pi\) | |||||||
\(660\) | 16.7477 | 0.651904 | ||||||||
\(661\) | 4.74773 | − | 2.74110i | 0.184665 | − | 0.106616i | −0.404818 | − | 0.914397i | \(-0.632665\pi\) |
0.589483 | + | 0.807781i | \(0.299332\pi\) | |||||||
\(662\) | 28.5390 | − | 49.4310i | 1.10920 | − | 1.92119i | ||||
\(663\) | 3.50000 | − | 0.866025i | 0.135929 | − | 0.0336336i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 21.0000 | + | 12.1244i | 0.814345 | + | 0.470162i | ||||
\(666\) | −7.68693 | + | 13.3142i | −0.297863 | + | 0.515913i | ||||
\(667\) | −30.0390 | + | 52.0291i | −1.16312 | + | 2.01457i | ||||
\(668\) | −10.8131 | − | 6.24293i | −0.418370 | − | 0.241546i | ||||
\(669\) | 2.64575i | 0.102291i | ||||||||
\(670\) | −46.1216 | − | 26.6283i | −1.78183 | − | 1.02874i | ||||
\(671\) | − | 17.8926i | − | 0.690737i | ||||||
\(672\) | −19.5390 | −0.753734 | ||||||||
\(673\) | 17.6652 | − | 30.5969i | 0.680942 | − | 1.17943i | −0.293752 | − | 0.955882i | \(-0.594904\pi\) |
0.974694 | − | 0.223544i | \(-0.0717626\pi\) | |||||||
\(674\) | 51.4292i | 1.98098i | ||||||||
\(675\) | −1.00000 | + | 1.73205i | −0.0384900 | + | 0.0666667i | ||||
\(676\) | 30.7042 | + | 19.3386i | 1.18093 | + | 0.743793i | ||||
\(677\) | −14.9174 | − | 25.8377i | −0.573323 | − | 0.993025i | −0.996222 | − | 0.0868478i | \(-0.972321\pi\) |
0.422898 | − | 0.906177i | \(-0.361013\pi\) | |||||||
\(678\) | −23.0608 | − | 13.3142i | −0.885645 | − | 0.511327i | ||||
\(679\) | 27.7477 | 1.06486 | ||||||||
\(680\) | −1.50000 | − | 2.59808i | −0.0575224 | − | 0.0996317i | ||||
\(681\) | 23.6216 | − | 13.6379i | 0.905181 | − | 0.522607i | ||||
\(682\) | 46.3284i | 1.77401i | ||||||||
\(683\) | − | 39.1142i | − | 1.49666i | −0.663325 | − | 0.748331i | \(-0.730855\pi\) | ||
0.663325 | − | 0.748331i | \(-0.269145\pi\) | |||||||
\(684\) | 12.7913 | − | 7.38505i | 0.489087 | − | 0.282375i | ||||
\(685\) | 7.50000 | + | 12.9904i | 0.286560 | + | 0.496337i | ||||
\(686\) | −40.5390 | −1.54779 | ||||||||
\(687\) | 9.08258 | + | 5.24383i | 0.346522 | + | 0.200064i | ||||
\(688\) | 4.10436 | + | 7.10895i | 0.156477 | + | 0.271026i | ||||
\(689\) | 15.4129 | + | 16.0175i | 0.587184 | + | 0.610219i | ||||
\(690\) | −16.2695 | + | 28.1796i | −0.619370 | + | 1.07278i | ||||
\(691\) | − | 7.55585i | − | 0.287438i | −0.989619 | − | 0.143719i | \(-0.954094\pi\) | ||
0.989619 | − | 0.143719i | \(-0.0459062\pi\) | |||||||
\(692\) | 33.9564 | − | 58.8143i | 1.29083 | − | 2.23578i | ||||
\(693\) | −4.58258 | + | 7.93725i | −0.174078 | + | 0.301511i | ||||
\(694\) | − | 56.3592i | − | 2.13937i | ||||||
\(695\) | 9.87386 | + | 5.70068i | 0.374537 | + | 0.216239i | ||||
\(696\) | 12.1244i | 0.459573i | ||||||||
\(697\) | −3.08258 | − | 1.77973i | −0.116761 | − | 0.0674119i | ||||
\(698\) | −11.4782 | + | 19.8809i | −0.434457 | + | 0.752502i | ||||
\(699\) | −10.0826 | + | 17.4635i | −0.381358 | + | 0.660531i | ||||
\(700\) | 12.7913 | − | 7.38505i | 0.483465 | − | 0.279129i | ||||
\(701\) | 34.0000 | 1.28416 | 0.642081 | − | 0.766637i | \(-0.278071\pi\) | ||||
0.642081 | + | 0.766637i | \(0.278071\pi\) | |||||||
\(702\) | −7.58258 | − | 2.18890i | −0.286186 | − | 0.0826147i | ||||
\(703\) | 18.5826 | − | 32.1860i | 0.700855 | − | 1.21392i | ||||
\(704\) | 37.7477 | − | 21.7937i | 1.42267 | − | 0.821379i | ||||
\(705\) | 1.41742 | 0.0533833 | ||||||||
\(706\) | −21.1652 | − | 36.6591i | −0.796561 | − | 1.37968i | ||||
\(707\) | − | 34.8317i | − | 1.30998i | ||||||
\(708\) | −10.3521 | + | 5.97678i | −0.389055 | + | 0.224621i | ||||
\(709\) | 25.5826 | + | 14.7701i | 0.960774 | + | 0.554703i | 0.896411 | − | 0.443224i | \(-0.146165\pi\) |
0.0643627 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(710\) | −14.6869 | − | 8.47950i | −0.551191 | − | 0.318230i | ||||
\(711\) | −1.41742 | −0.0531576 | ||||||||
\(712\) | −27.0000 | −1.01187 | ||||||||
\(713\) | −45.4129 | − | 26.2191i | −1.70073 | − | 0.981914i | ||||
\(714\) | 5.79129 | 0.216734 | ||||||||
\(715\) | 15.0000 | + | 15.5885i | 0.560968 | + | 0.582975i | ||||
\(716\) | 1.16515 | + | 2.01810i | 0.0435438 | + | 0.0754200i | ||||
\(717\) | 1.74773 | − | 1.00905i | 0.0652701 | − | 0.0376837i | ||||
\(718\) | 20.2695 | + | 35.1078i | 0.756451 | + | 1.31021i | ||||
\(719\) | 17.1652 | − | 29.7309i | 0.640152 | − | 1.10878i | −0.345246 | − | 0.938512i | \(-0.612205\pi\) |
0.985398 | − | 0.170264i | \(-0.0544620\pi\) | |||||||
\(720\) | − | 3.10260i | − | 0.115627i | ||||||
\(721\) | − | 9.04165i | − | 0.336729i | ||||||
\(722\) | −17.0608 | + | 9.85005i | −0.634937 | + | 0.366581i | ||||
\(723\) | −12.2477 | + | 7.07123i | −0.455498 | + | 0.262982i | ||||
\(724\) | −61.4083 | −2.28222 | ||||||||
\(725\) | 7.00000 | + | 12.1244i | 0.259973 | + | 0.450287i | ||||
\(726\) | − | 2.18890i | − | 0.0812377i | ||||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | 11.4564 | + | 11.9059i | 0.424604 | + | 0.441261i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 32.8335i | − | 1.21522i | ||||||
\(731\) | −2.29129 | − | 3.96863i | −0.0847463 | − | 0.146785i | ||||
\(732\) | 14.4174 | 0.532883 | ||||||||
\(733\) | −25.8303 | + | 14.9131i | −0.954064 | + | 0.550829i | −0.894341 | − | 0.447386i | \(-0.852355\pi\) |
−0.0597230 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(734\) | 28.7477 | − | 16.5975i | 1.06110 | − | 0.612625i | ||||
\(735\) | − | 12.1244i | − | 0.447214i | ||||||
\(736\) | 63.3828i | 2.33632i | ||||||||
\(737\) | −24.3303 | + | 42.1413i | −0.896218 | + | 1.55230i | ||||
\(738\) | 3.89564 | + | 6.74745i | 0.143401 | + | 0.248377i | ||||
\(739\) | 16.5826 | − | 9.57395i | 0.610000 | − | 0.352184i | −0.162966 | − | 0.986632i | \(-0.552106\pi\) |
0.772965 | + | 0.634448i | \(0.218773\pi\) | |||||||
\(740\) | 16.9782 | + | 29.4071i | 0.624132 | + | 1.08103i | ||||
\(741\) | 18.3303 | + | 5.29150i | 0.673380 | + | 0.194388i | ||||
\(742\) | 17.8521 | + | 30.9207i | 0.655371 | + | 1.13514i | ||||
\(743\) | 6.70871 | + | 3.87328i | 0.246119 | + | 0.142097i | 0.617986 | − | 0.786189i | \(-0.287949\pi\) |
−0.371867 | + | 0.928286i | \(0.621282\pi\) | |||||||
\(744\) | −10.5826 | −0.387976 | ||||||||
\(745\) | 6.33030 | 0.231924 | ||||||||
\(746\) | 49.2867 | + | 28.4557i | 1.80452 | + | 1.04184i | ||||
\(747\) | 3.00000 | + | 1.73205i | 0.109764 | + | 0.0633724i | ||||
\(748\) | −8.37386 | + | 4.83465i | −0.306179 | + | 0.176772i | ||||
\(749\) | −3.24773 | − | 1.87508i | −0.118669 | − | 0.0685138i | ||||
\(750\) | 13.2695 | + | 22.9835i | 0.484534 | + | 0.839237i | ||||
\(751\) | −12.9129 | −0.471198 | −0.235599 | − | 0.971850i | \(-0.575705\pi\) | ||||
−0.235599 | + | 0.971850i | \(0.575705\pi\) | |||||||
\(752\) | 1.26951 | − | 0.732950i | 0.0462942 | − | 0.0267280i | ||||
\(753\) | 10.2913 | − | 17.8250i | 0.375035 | − | 0.649580i | ||||
\(754\) | −39.8085 | + | 38.3058i | −1.44974 | + | 1.39501i | ||||
\(755\) | 28.9129 | 1.05225 | ||||||||
\(756\) | −6.39564 | − | 3.69253i | −0.232607 | − | 0.134296i | ||||
\(757\) | −2.24773 | + | 3.89318i | −0.0816950 | + | 0.141500i | −0.903978 | − | 0.427579i | \(-0.859367\pi\) |
0.822283 | + | 0.569079i | \(0.192700\pi\) | |||||||
\(758\) | −20.2695 | + | 35.1078i | −0.736222 | + | 1.27517i | ||||
\(759\) | 25.7477 | + | 14.8655i | 0.934583 | + | 0.539582i | ||||
\(760\) | − | 15.8745i | − | 0.575829i | ||||||
\(761\) | −1.25227 | − | 0.723000i | −0.0453949 | − | 0.0262087i | 0.477131 | − | 0.878832i | \(-0.341677\pi\) |
−0.522526 | + | 0.852624i | \(0.675010\pi\) | |||||||
\(762\) | 14.4086i | 0.521969i | ||||||||
\(763\) | −25.4564 | − | 44.0918i | −0.921585 | − | 1.59623i | ||||
\(764\) | −20.0000 | + | 34.6410i | −0.723575 | + | 1.25327i | ||||
\(765\) | 1.73205i | 0.0626224i | ||||||||
\(766\) | 19.3739 | − | 33.5565i | 0.700006 | − | 1.21245i | ||||
\(767\) | −14.8348 | − | 4.28245i | −0.535655 | − | 0.154630i | ||||
\(768\) | 1.39564 | + | 2.41733i | 0.0503610 | + | 0.0872277i | ||||
\(769\) | −2.91742 | − | 1.68438i | −0.105205 | − | 0.0607401i | 0.446474 | − | 0.894796i | \(-0.352679\pi\) |
−0.551679 | + | 0.834056i | \(0.686013\pi\) | |||||||
\(770\) | 17.3739 | + | 30.0924i | 0.626111 | + | 1.08446i | ||||
\(771\) | 4.66515 | + | 8.08028i | 0.168011 | + | 0.291004i | ||||
\(772\) | 8.83485 | − | 5.10080i | 0.317973 | − | 0.183582i | ||||
\(773\) | − | 24.5348i | − | 0.882454i | −0.897396 | − | 0.441227i | \(-0.854543\pi\) | ||
0.897396 | − | 0.441227i | \(-0.145457\pi\) | |||||||
\(774\) | 10.0308i | 0.360550i | ||||||||
\(775\) | −10.5826 | + | 6.10985i | −0.380137 | + | 0.219472i | ||||
\(776\) | −9.08258 | − | 15.7315i | −0.326045 | − | 0.564727i | ||||
\(777\) | −18.5826 | −0.666646 | ||||||||
\(778\) | −51.8085 | − | 29.9117i | −1.85743 | − | 1.07239i | ||||
\(779\) | −9.41742 | − | 16.3115i | −0.337414 | − | 0.584419i | ||||
\(780\) | −12.5608 | + | 12.0866i | −0.449749 | + | 0.432771i | ||||
\(781\) | −7.74773 | + | 13.4195i | −0.277235 | + | 0.480186i | ||||
\(782\) | − | 18.7864i | − | 0.671801i | ||||||
\(783\) | 3.50000 | − | 6.06218i | 0.125080 | − | 0.216645i | ||||
\(784\) | −6.26951 | − | 10.8591i | −0.223911 | − | 0.387825i | ||||
\(785\) | 17.6066i | 0.628405i | ||||||||
\(786\) | −2.68693 | − | 1.55130i | −0.0958397 | − | 0.0553331i | ||||
\(787\) | 30.3586i | 1.08217i | 0.840969 | + | 0.541083i | \(0.181986\pi\) | ||||
−0.840969 | + | 0.541083i | \(0.818014\pi\) | |||||||
\(788\) | −42.5608 | − | 24.5725i | −1.51617 | − | 0.875359i | ||||
\(789\) | 2.41742 | − | 4.18710i | 0.0860626 | − | 0.149065i | ||||
\(790\) | −2.68693 | + | 4.65390i | −0.0955967 | + | 0.165578i | ||||
\(791\) | − | 32.1860i | − | 1.14440i | ||||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 12.9129 | + | 13.4195i | 0.458550 | + | 0.476539i | ||||
\(794\) | −40.3303 | + | 69.8541i | −1.43127 | + | 2.47903i | ||||
\(795\) | −9.24773 | + | 5.33918i | −0.327983 | + | 0.189361i | ||||
\(796\) | −7.20871 | −0.255506 | ||||||||
\(797\) | −12.0826 | − | 20.9276i | −0.427987 | − | 0.741295i | 0.568707 | − | 0.822540i | \(-0.307444\pi\) |
−0.996694 | + | 0.0812451i | \(0.974110\pi\) | |||||||
\(798\) | 26.5390 | + | 15.3223i | 0.939471 | + | 0.542404i | ||||
\(799\) | −0.708712 | + | 0.409175i | −0.0250724 | + | 0.0144756i | ||||
\(800\) | 12.7913 | + | 7.38505i | 0.452240 | + | 0.261101i | ||||
\(801\) | 13.5000 | + | 7.79423i | 0.476999 | + | 0.275396i | ||||
\(802\) | −76.0345 | −2.68487 | ||||||||
\(803\) | −30.0000 | −1.05868 | ||||||||
\(804\) | −33.9564 | − | 19.6048i | −1.19755 | − | 0.691407i | ||||
\(805\) | −39.3303 | −1.38621 | ||||||||
\(806\) | −33.4347 | − | 34.7463i | −1.17769 | − | 1.22389i | ||||
\(807\) | −8.08258 | − | 13.9994i | −0.284520 | − | 0.492803i | ||||
\(808\) | −19.7477 | + | 11.4014i | −0.694723 | + | 0.401098i | ||||
\(809\) | 16.5826 | + | 28.7219i | 0.583012 | + | 1.00981i | 0.995120 | + | 0.0986718i | \(0.0314594\pi\) |
−0.412108 | + | 0.911135i | \(0.635207\pi\) | |||||||
\(810\) | 1.89564 | − | 3.28335i | 0.0666061 | − | 0.115365i | ||||
\(811\) | 0.190700i | 0.00669640i | 0.999994 | + | 0.00334820i | \(0.00106577\pi\) | ||||
−0.999994 | + | 0.00334820i | \(0.998934\pi\) | |||||||
\(812\) | −44.7695 | + | 25.8477i | −1.57110 | + | 0.907076i | ||||
\(813\) | −10.0390 | + | 5.79603i | −0.352084 | + | 0.203276i | ||||
\(814\) | 46.1216 | − | 26.6283i | 1.61656 | − | 0.933322i | ||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 0.895644 | + | 1.55130i | 0.0313538 | + | 0.0543064i | ||||
\(817\) | − | 24.2487i | − | 0.848355i | ||||||
\(818\) | 68.4519 | 2.39336 | ||||||||
\(819\) | −2.29129 | − | 9.26013i | −0.0800641 | − | 0.323575i | ||||
\(820\) | 17.2087 | 0.600954 | ||||||||
\(821\) | 38.3912i | 1.33986i | 0.742424 | + | 0.669931i | \(0.233676\pi\) | ||||
−0.742424 | + | 0.669931i | \(0.766324\pi\) | |||||||
\(822\) | 9.47822 | + | 16.4168i | 0.330591 | + | 0.572600i | ||||
\(823\) | 30.5826 | 1.06604 | 0.533021 | − | 0.846102i | \(-0.321057\pi\) | ||||
0.533021 | + | 0.846102i | \(0.321057\pi\) | |||||||
\(824\) | −5.12614 | + | 2.95958i | −0.178577 | + | 0.103102i | ||||
\(825\) | 6.00000 | − | 3.46410i | 0.208893 | − | 0.120605i | ||||
\(826\) | −21.4782 | − | 12.4005i | −0.747323 | − | 0.431467i | ||||
\(827\) | 36.6591i | 1.27476i | 0.770549 | + | 0.637381i | \(0.219982\pi\) | ||||
−0.770549 | + | 0.637381i | \(0.780018\pi\) | |||||||
\(828\) | −11.9782 | + | 20.7469i | −0.416272 | + | 0.721004i | ||||
\(829\) | 23.3303 | + | 40.4093i | 0.810295 | + | 1.40347i | 0.912658 | + | 0.408725i | \(0.134026\pi\) |
−0.102363 | + | 0.994747i | \(0.532640\pi\) | |||||||
\(830\) | 11.3739 | − | 6.56670i | 0.394793 | − | 0.227934i | ||||
\(831\) | −4.66515 | − | 8.08028i | −0.161832 | − | 0.280302i | ||||
\(832\) | −12.5826 | + | 43.5873i | −0.436222 | + | 1.51112i | ||||
\(833\) | 3.50000 | + | 6.06218i | 0.121268 | + | 0.210042i | ||||
\(834\) | 12.4782 | + | 7.20430i | 0.432085 | + | 0.249465i | ||||
\(835\) | 7.74773 | 0.268121 | ||||||||
\(836\) | −51.1652 | −1.76958 | ||||||||
\(837\) | 5.29129 | + | 3.05493i | 0.182894 | + | 0.105594i | ||||
\(838\) | −22.2695 | − | 12.8573i | −0.769287 | − | 0.444148i | ||||
\(839\) | −23.1261 | + | 13.3519i | −0.798403 | + | 0.460958i | −0.842912 | − | 0.538051i | \(-0.819161\pi\) |
0.0445095 | + | 0.999009i | \(0.485828\pi\) | |||||||
\(840\) | −6.87386 | + | 3.96863i | −0.237171 | + | 0.136931i | ||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | 88.6606 | 3.05545 | ||||||||
\(843\) | 3.16515 | − | 1.82740i | 0.109014 | − | 0.0629390i | ||||
\(844\) | 9.18693 | − | 15.9122i | 0.316227 | − | 0.547722i | ||||
\(845\) | −22.5000 | − | 0.866025i | −0.774024 | − | 0.0297922i | ||||
\(846\) | 1.79129 | 0.0615857 | ||||||||
\(847\) | 2.29129 | − | 1.32288i | 0.0787296 | − | 0.0454545i | ||||
\(848\) | −5.52178 | + | 9.56400i | −0.189619 | + | 0.328429i | ||||
\(849\) | 15.1652 | − | 26.2668i | 0.520467 | − | 0.901475i | ||||
\(850\) | −3.79129 | − | 2.18890i | −0.130040 | − | 0.0750787i | ||||
\(851\) | 60.2802i | 2.06638i | ||||||||
\(852\) | −10.8131 | − | 6.24293i | −0.370450 | − | 0.213879i | ||||
\(853\) | 30.9862i | 1.06095i | 0.847701 | + | 0.530474i | \(0.177986\pi\) | ||||
−0.847701 | + | 0.530474i | \(0.822014\pi\) | |||||||
\(854\) | 14.9564 | + | 25.9053i | 0.511799 | + | 0.886462i | ||||
\(855\) | −4.58258 | + | 7.93725i | −0.156721 | + | 0.271448i | ||||
\(856\) | 2.45505i | 0.0839119i | ||||||||
\(857\) | −5.66515 | + | 9.81233i | −0.193518 | + | 0.335183i | −0.946414 | − | 0.322957i | \(-0.895323\pi\) |
0.752896 | + | 0.658140i | \(0.228656\pi\) | |||||||
\(858\) | 18.9564 | + | 19.7001i | 0.647162 | + | 0.672551i | ||||
\(859\) | 23.4564 | + | 40.6277i | 0.800323 | + | 1.38620i | 0.919403 | + | 0.393316i | \(0.128672\pi\) |
−0.119080 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(860\) | 19.1869 | + | 11.0776i | 0.654269 | + | 0.377742i | ||||
\(861\) | −4.70871 | + | 8.15573i | −0.160472 | + | 0.277946i | ||||
\(862\) | −9.37386 | − | 16.2360i | −0.319275 | − | 0.553001i | ||||
\(863\) | −17.4564 | + | 10.0785i | −0.594224 | + | 0.343075i | −0.766766 | − | 0.641927i | \(-0.778135\pi\) |
0.172542 | + | 0.985002i | \(0.444802\pi\) | |||||||
\(864\) | − | 7.38505i | − | 0.251245i | ||||||
\(865\) | 42.1413i | 1.43285i | ||||||||
\(866\) | −29.0608 | + | 16.7783i | −0.987526 | + | 0.570148i | ||||
\(867\) | 8.00000 | + | 13.8564i | 0.271694 | + | 0.470588i | ||||
\(868\) | −22.5608 | − | 39.0764i | −0.765763 | − | 1.32634i | ||||
\(869\) | 4.25227 | + | 2.45505i | 0.144248 | + | 0.0832819i | ||||
\(870\) | −13.2695 | − | 22.9835i | −0.449878 | − | 0.779212i | ||||
\(871\) | −12.1652 | − | 49.1649i | −0.412200 | − | 1.66589i | ||||
\(872\) | −16.6652 | + | 28.8649i | −0.564353 | + | 0.977488i | ||||
\(873\) | 10.4877i | 0.354953i | ||||||||
\(874\) | 49.7042 | − | 86.0901i | 1.68127 | − | 2.91204i | ||||
\(875\) | −16.0390 | + | 27.7804i | −0.542218 | + | 0.939149i | ||||
\(876\) | − | 24.1733i | − | 0.816739i | ||||||
\(877\) | −13.9129 | − | 8.03260i | −0.469805 | − | 0.271242i | 0.246353 | − | 0.969180i | \(-0.420768\pi\) |
−0.716158 | + | 0.697938i | \(0.754101\pi\) | |||||||
\(878\) | − | 23.1642i | − | 0.781754i | ||||||
\(879\) | −16.8303 | − | 9.71698i | −0.567672 | − | 0.327746i | ||||
\(880\) | −5.37386 | + | 9.30780i | −0.181153 | + | 0.313766i | ||||
\(881\) | −9.24773 | + | 16.0175i | −0.311564 | + | 0.539644i | −0.978701 | − | 0.205290i | \(-0.934186\pi\) |
0.667137 | + | 0.744935i | \(0.267519\pi\) | |||||||
\(882\) | − | 15.3223i | − | 0.515929i | ||||||
\(883\) | 50.3303 | 1.69375 | 0.846875 | − | 0.531792i | \(-0.178481\pi\) | ||||
0.846875 | + | 0.531792i | \(0.178481\pi\) | |||||||
\(884\) | 2.79129 | − | 9.66930i | 0.0938812 | − | 0.325214i | ||||
\(885\) | 3.70871 | − | 6.42368i | 0.124667 | − | 0.215930i | ||||
\(886\) | −10.8956 | + | 6.29060i | −0.366046 | + | 0.211337i | ||||
\(887\) | −37.4174 | −1.25635 | −0.628177 | − | 0.778070i | \(-0.716199\pi\) | ||||
−0.628177 | + | 0.778070i | \(0.716199\pi\) | |||||||
\(888\) | 6.08258 | + | 10.5353i | 0.204118 | + | 0.353543i | ||||
\(889\) | −15.0826 | + | 8.70793i | −0.505853 | + | 0.292055i | ||||
\(890\) | 51.1824 | − | 29.5502i | 1.71564 | − | 0.990524i | ||||
\(891\) | −3.00000 | − | 1.73205i | −0.100504 | − | 0.0580259i | ||||
\(892\) | 6.39564 | + | 3.69253i | 0.214142 | + | 0.123635i | ||||
\(893\) | −4.33030 | −0.144908 | ||||||||
\(894\) | 8.00000 | 0.267560 | ||||||||
\(895\) | −1.25227 | − | 0.723000i | −0.0418589 | − | 0.0241672i | ||||
\(896\) | −16.8956 | + | 29.2641i | −0.564444 | + | 0.977645i | ||||
\(897\) | −30.0390 | + | 7.43273i | −1.00297 | + | 0.248172i | ||||
\(898\) | −13.4782 | − | 23.3450i | −0.449774 | − | 0.779031i | ||||
\(899\) | 37.0390 | − | 21.3845i | 1.23532 | − | 0.713213i | ||||
\(900\) | 2.79129 | + | 4.83465i | 0.0930429 | + | 0.161155i | ||||
\(901\) | 3.08258 | − | 5.33918i | 0.102695 | − | 0.177874i | ||||
\(902\) | − | 26.9898i | − | 0.898662i | ||||||
\(903\) | −10.5000 | + | 6.06218i | −0.349418 | + | 0.201737i | ||||
\(904\) | −18.2477 | + | 10.5353i | −0.606910 | + | 0.350400i | ||||
\(905\) | 33.0000 | − | 19.0526i | 1.09696 | − | 0.633328i | ||||
\(906\) | 36.5390 | 1.21393 | ||||||||
\(907\) | −4.41742 | − | 7.65120i | −0.146678 | − | 0.254054i | 0.783320 | − | 0.621619i | \(-0.213525\pi\) |
−0.929998 | + | 0.367565i | \(0.880192\pi\) | |||||||
\(908\) | − | 76.1348i | − | 2.52662i | ||||||
\(909\) | 13.1652 | 0.436661 | ||||||||
\(910\) | −34.7477 | − | 10.0308i | −1.15188 | − | 0.332518i | ||||
\(911\) | 48.6606 | 1.61220 | 0.806099 | − | 0.591781i | \(-0.201575\pi\) | ||||
0.806099 | + | 0.591781i | \(0.201575\pi\) | |||||||
\(912\) | 9.47860i | 0.313868i | ||||||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | 8.20871 | 0.271520 | ||||||||
\(915\) | −7.74773 | + | 4.47315i | −0.256132 | + | 0.147878i | ||||
\(916\) | 25.3521 | − | 14.6370i | 0.837656 | − | 0.483621i | ||||
\(917\) | − | 3.75015i | − | 0.123841i | ||||||
\(918\) | 2.18890i | 0.0722445i | ||||||||
\(919\) | 2.41742 | − | 4.18710i | 0.0797435 | − | 0.138120i | −0.823396 | − | 0.567468i | \(-0.807923\pi\) |
0.903139 | + | 0.429348i | \(0.141257\pi\) | |||||||
\(920\) | 12.8739 | + | 22.2982i | 0.424439 | + | 0.735149i | ||||
\(921\) | −18.1652 | + | 10.4877i | −0.598562 | + | 0.345580i | ||||
\(922\) | −34.6434 | − | 60.0041i | −1.14092 | − | 1.97613i | ||||
\(923\) | −3.87386 | − | 15.6560i | −0.127510 | − | 0.515325i | ||||
\(924\) | 12.7913 | + | 22.1552i | 0.420802 | + | 0.728851i | ||||
\(925\) | 12.1652 | + | 7.02355i | 0.399988 | + | 0.230933i | ||||
\(926\) | 84.2432 | 2.76840 | ||||||||
\(927\) | 3.41742 | 0.112243 | ||||||||
\(928\) | −44.7695 | − | 25.8477i | −1.46963 | − | 0.848492i | ||||
\(929\) | −36.6606 | − | 21.1660i | −1.20280 | − | 0.694434i | −0.241620 | − | 0.970371i | \(-0.577679\pi\) |
−0.961176 | + | 0.275937i | \(0.911012\pi\) | |||||||
\(930\) | 20.0608 | − | 11.5821i | 0.657819 | − | 0.379792i | ||||
\(931\) | 37.0405i | 1.21395i | ||||||||
\(932\) | 28.1434 | + | 48.7457i | 0.921867 | + | 1.59672i | ||||
\(933\) | −8.58258 | −0.280981 | ||||||||
\(934\) | −54.8085 | + | 31.6437i | −1.79339 | + | 1.03541i | ||||
\(935\) | 3.00000 | − | 5.19615i | 0.0981105 | − | 0.169932i | ||||
\(936\) | −4.50000 | + | 4.33013i | −0.147087 | + | 0.141535i | ||||
\(937\) | 0.504546 | 0.0164828 | 0.00824140 | − | 0.999966i | \(-0.497377\pi\) | ||||
0.00824140 | + | 0.999966i | \(0.497377\pi\) | |||||||
\(938\) | − | 81.3508i | − | 2.65620i | ||||||
\(939\) | 6.91742 | − | 11.9813i | 0.225742 | − | 0.390996i | ||||
\(940\) | 1.97822 | − | 3.42638i | 0.0645224 | − | 0.111756i | ||||
\(941\) | −28.8303 | − | 16.6452i | −0.939841 | − | 0.542617i | −0.0499305 | − | 0.998753i | \(-0.515900\pi\) |
−0.889910 | + | 0.456135i | \(0.849233\pi\) | |||||||
\(942\) | 22.2505i | 0.724961i | ||||||||
\(943\) | 26.4564 | + | 15.2746i | 0.861540 | + | 0.497410i | ||||
\(944\) | − | 7.67110i | − | 0.249673i | ||||||
\(945\) | 4.58258 | 0.149071 | ||||||||
\(946\) | 17.3739 | − | 30.0924i | 0.564873 | − | 0.978389i | ||||
\(947\) | − | 15.0562i | − | 0.489259i | −0.969617 | − | 0.244630i | \(-0.921334\pi\) | ||
0.969617 | − | 0.244630i | \(-0.0786664\pi\) | |||||||
\(948\) | −1.97822 | + | 3.42638i | −0.0642496 | + | 0.111284i | ||||
\(949\) | 22.5000 | − | 21.6506i | 0.730381 | − | 0.702809i | ||||
\(950\) | −11.5826 | − | 20.0616i | −0.375788 | − | 0.650885i | ||||
\(951\) | 1.66515 | + | 0.961376i | 0.0539962 | + | 0.0311747i | ||||
\(952\) | 2.29129 | − | 3.96863i | 0.0742611 | − | 0.128624i | ||||
\(953\) | −23.6652 | − | 40.9892i | −0.766589 | − | 1.32777i | −0.939402 | − | 0.342817i | \(-0.888619\pi\) |
0.172813 | − | 0.984955i | \(-0.444714\pi\) | |||||||
\(954\) | −11.6869 | + | 6.74745i | −0.378378 | + | 0.218457i | ||||
\(955\) | − | 24.8208i | − | 0.803183i | ||||||
\(956\) | − | 5.63310i | − | 0.182188i | ||||||
\(957\) | −21.0000 | + | 12.1244i | −0.678834 | + | 0.391925i | ||||
\(958\) | 30.9564 | + | 53.6181i | 1.00016 | + | 1.73232i | ||||
\(959\) | −11.4564 | + | 19.8431i | −0.369948 | + | 0.640768i | ||||
\(960\) | −18.8739 | − | 10.8968i | −0.609151 | − | 0.351694i | ||||
\(961\) | 3.16515 | + | 5.48220i | 0.102102 | + | 0.176845i | ||||
\(962\) | −15.3739 | + | 53.2566i | −0.495673 | + | 1.71706i | ||||
\(963\) | 0.708712 | − | 1.22753i | 0.0228379 | − | 0.0395565i | ||||
\(964\) | 39.4757i | 1.27143i | ||||||||
\(965\) | −3.16515 | + | 5.48220i | −0.101890 | + | 0.176478i | ||||
\(966\) | −49.7042 | −1.59921 | ||||||||
\(967\) | − | 5.29150i | − | 0.170163i | −0.996374 | − | 0.0850816i | \(-0.972885\pi\) | ||
0.996374 | − | 0.0850816i | \(-0.0271151\pi\) | |||||||
\(968\) | −1.50000 | − | 0.866025i | −0.0482118 | − | 0.0278351i | ||||
\(969\) | − | 5.29150i | − | 0.169988i | ||||||
\(970\) | 34.4347 | + | 19.8809i | 1.10563 | + | 0.638336i | ||||
\(971\) | −25.1652 | + | 43.5873i | −0.807588 | + | 1.39878i | 0.106942 | + | 0.994265i | \(0.465894\pi\) |
−0.914530 | + | 0.404518i | \(0.867439\pi\) | |||||||
\(972\) | 1.39564 | − | 2.41733i | 0.0447653 | − | 0.0775358i | ||||
\(973\) | 17.4159i | 0.558327i | ||||||||
\(974\) | −24.1216 | −0.772906 | ||||||||
\(975\) | −2.00000 | + | 6.92820i | −0.0640513 | + | 0.221880i | ||||
\(976\) | −4.62614 | + | 8.01270i | −0.148079 | + | 0.256480i | ||||
\(977\) | 3.16515 | − | 1.82740i | 0.101262 | − | 0.0584637i | −0.448514 | − | 0.893776i | \(-0.648046\pi\) |
0.549776 | + | 0.835312i | \(0.314713\pi\) | |||||||
\(978\) | 7.58258 | 0.242464 | ||||||||
\(979\) | −27.0000 | − | 46.7654i | −0.862924 | − | 1.49463i | ||||
\(980\) | −29.3085 | − | 16.9213i | −0.936226 | − | 0.540531i | ||||
\(981\) | 16.6652 | − | 9.62163i | 0.532077 | − | 0.307195i | ||||
\(982\) | −7.10436 | − | 4.10170i | −0.226709 | − | 0.130891i | ||||
\(983\) | 20.2913 | + | 11.7152i | 0.647192 | + | 0.373656i | 0.787379 | − | 0.616469i | \(-0.211437\pi\) |
−0.140188 | + | 0.990125i | \(0.544771\pi\) | |||||||
\(984\) | 6.16515 | 0.196538 | ||||||||
\(985\) | 30.4955 | 0.971666 | ||||||||
\(986\) | 13.2695 | + | 7.66115i | 0.422587 | + | 0.243981i | ||||
\(987\) | 1.08258 | + | 1.87508i | 0.0344588 | + | 0.0596843i | ||||
\(988\) | 38.3739 | − | 36.9253i | 1.22084 | − | 1.17475i | ||||
\(989\) | 19.6652 | + | 34.0610i | 0.625315 | + | 1.08308i | ||||
\(990\) | −11.3739 | + | 6.56670i | −0.361485 | + | 0.208704i | ||||
\(991\) | −16.3303 | − | 28.2849i | −0.518749 | − | 0.898500i | −0.999763 | − | 0.0217867i | \(-0.993065\pi\) |
0.481013 | − | 0.876713i | \(-0.340269\pi\) | |||||||
\(992\) | 22.5608 | − | 39.0764i | 0.716306 | − | 1.24068i | ||||
\(993\) | 26.0761i | 0.827500i | ||||||||
\(994\) | − | 25.9053i | − | 0.821667i | ||||||
\(995\) | 3.87386 | − | 2.23658i | 0.122810 | − | 0.0709042i | ||||
\(996\) | 8.37386 | − | 4.83465i | 0.265336 | − | 0.153192i | ||||
\(997\) | −47.3303 | −1.49897 | −0.749483 | − | 0.662024i | \(-0.769698\pi\) | ||||
−0.749483 | + | 0.662024i | \(0.769698\pi\) | |||||||
\(998\) | −27.4347 | − | 47.5182i | −0.868429 | − | 1.50416i | ||||
\(999\) | − | 7.02355i | − | 0.222215i |
(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 | 273.2.t.b.4.2 | ✓ | 4 | |
3.2 | odd | 2 | 819.2.bm.d.550.1 | 4 | |||
7.2 | even | 3 | 273.2.bl.b.121.2 | yes | 4 | ||
13.10 | even | 6 | 273.2.bl.b.88.2 | yes | 4 | ||
21.2 | odd | 6 | 819.2.do.d.667.1 | 4 | |||
39.23 | odd | 6 | 819.2.do.d.361.1 | 4 | |||
91.23 | even | 6 | inner | 273.2.t.b.205.1 | yes | 4 | |
273.23 | odd | 6 | 819.2.bm.d.478.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.b.4.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
273.2.t.b.205.1 | yes | 4 | 91.23 | even | 6 | inner | |
273.2.bl.b.88.2 | yes | 4 | 13.10 | even | 6 | ||
273.2.bl.b.121.2 | yes | 4 | 7.2 | even | 3 | ||
819.2.bm.d.478.2 | 4 | 273.23 | odd | 6 | |||
819.2.bm.d.550.1 | 4 | 3.2 | odd | 2 | |||
819.2.do.d.361.1 | 4 | 39.23 | odd | 6 | |||
819.2.do.d.667.1 | 4 | 21.2 | odd | 6 |