Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(361,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("490.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.471 |
Dual form | 490.2.e.e.361.1 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.00000 | + | 1.73205i | 0.577350 | + | 1.00000i | 0.995782 | + | 0.0917517i | \(0.0292466\pi\) |
−0.418432 | + | 0.908248i | \(0.637420\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 2.00000 | + | 3.46410i | 0.603023 | + | 1.04447i | 0.992361 | + | 0.123371i | \(0.0393705\pi\) |
−0.389338 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.00000 | + | 6.92820i | 0.970143 | + | 1.68034i | 0.695113 | + | 0.718900i | \(0.255354\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 1.00000 | + | 1.73205i | 0.204124 | + | 0.353553i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −4.00000 | + | 6.92820i | −0.696311 | + | 1.20605i | ||||
\(34\) | −8.00000 | −1.37199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.00000 | − | 8.66025i | 0.821995 | − | 1.42374i | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) |
0.904194 | − | 0.427121i | \(-0.140472\pi\) | |||||||
\(38\) | −3.00000 | − | 5.19615i | −0.486664 | − | 0.842927i | ||||
\(39\) | −2.00000 | − | 3.46410i | −0.320256 | − | 0.554700i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 2.00000 | − | 3.46410i | 0.291730 | − | 0.505291i | −0.682489 | − | 0.730896i | \(-0.739102\pi\) |
0.974219 | + | 0.225605i | \(0.0724358\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −8.00000 | + | 13.8564i | −1.12022 | + | 1.94029i | ||||
\(52\) | 1.00000 | + | 1.73205i | 0.138675 | + | 0.240192i | ||||
\(53\) | −5.00000 | − | 8.66025i | −0.686803 | − | 1.18958i | −0.972867 | − | 0.231367i | \(-0.925680\pi\) |
0.286064 | − | 0.958211i | \(-0.407653\pi\) | |||||||
\(54\) | −2.00000 | + | 3.46410i | −0.272166 | + | 0.471405i | ||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | −7.00000 | − | 12.1244i | −0.911322 | − | 1.57846i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
−0.0991242 | − | 0.995075i | \(-0.531604\pi\) | |||||||
\(60\) | −1.00000 | − | 1.73205i | −0.129099 | − | 0.223607i | ||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | −4.00000 | − | 6.92820i | −0.492366 | − | 0.852803i | ||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | 4.00000 | − | 6.92820i | 0.485071 | − | 0.840168i | ||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 2.00000 | + | 3.46410i | 0.234082 | + | 0.405442i | 0.959006 | − | 0.283387i | \(-0.0914581\pi\) |
−0.724923 | + | 0.688830i | \(0.758125\pi\) | |||||||
\(74\) | 5.00000 | + | 8.66025i | 0.581238 | + | 1.00673i | ||||
\(75\) | 1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 2.00000 | − | 3.46410i | 0.220863 | − | 0.382546i | ||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | −6.00000 | − | 10.3923i | −0.643268 | − | 1.11417i | ||||
\(88\) | 2.00000 | + | 3.46410i | 0.213201 | + | 0.369274i | ||||
\(89\) | 4.00000 | − | 6.92820i | 0.423999 | − | 0.734388i | −0.572327 | − | 0.820025i | \(-0.693959\pi\) |
0.996326 | + | 0.0856373i | \(0.0272926\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | −4.00000 | + | 6.92820i | −0.414781 | + | 0.718421i | ||||
\(94\) | 2.00000 | + | 3.46410i | 0.206284 | + | 0.357295i | ||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 1.00000 | − | 1.73205i | 0.102062 | − | 0.176777i | ||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | −8.00000 | − | 13.8564i | −0.792118 | − | 1.37199i | ||||
\(103\) | 2.00000 | − | 3.46410i | 0.197066 | − | 0.341328i | −0.750510 | − | 0.660859i | \(-0.770192\pi\) |
0.947576 | + | 0.319531i | \(0.103525\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 6.00000 | − | 10.3923i | 0.580042 | − | 1.00466i | −0.415432 | − | 0.909624i | \(-0.636370\pi\) |
0.995474 | − | 0.0950377i | \(-0.0302972\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | −5.00000 | − | 8.66025i | −0.478913 | − | 0.829502i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.999708 | + | 0.0241802i | \(0.992302\pi\) | |||||||
\(110\) | −2.00000 | + | 3.46410i | −0.190693 | + | 0.330289i | ||||
\(111\) | 20.0000 | 1.89832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 6.00000 | − | 10.3923i | 0.561951 | − | 0.973329i | ||||
\(115\) | −2.00000 | − | 3.46410i | −0.186501 | − | 0.323029i | ||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | 1.00000 | − | 1.73205i | 0.0924500 | − | 0.160128i | ||||
\(118\) | 14.0000 | 1.28880 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | 0.182574 | ||||||||
\(121\) | −2.50000 | + | 4.33013i | −0.227273 | + | 0.393648i | ||||
\(122\) | −5.00000 | − | 8.66025i | −0.452679 | − | 0.784063i | ||||
\(123\) | −4.00000 | − | 6.92820i | −0.360668 | − | 0.624695i | ||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | −1.00000 | − | 1.73205i | −0.0877058 | − | 0.151911i | ||||
\(131\) | 9.00000 | − | 15.5885i | 0.786334 | − | 1.36197i | −0.141865 | − | 0.989886i | \(-0.545310\pi\) |
0.928199 | − | 0.372084i | \(-0.121357\pi\) | |||||||
\(132\) | 8.00000 | 0.696311 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 2.00000 | − | 3.46410i | 0.172133 | − | 0.298142i | ||||
\(136\) | 4.00000 | + | 6.92820i | 0.342997 | + | 0.594089i | ||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | −4.00000 | + | 6.92820i | −0.340503 | + | 0.589768i | ||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | −6.00000 | + | 10.3923i | −0.503509 | + | 0.872103i | ||||
\(143\) | −4.00000 | − | 6.92820i | −0.334497 | − | 0.579365i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −3.00000 | + | 5.19615i | −0.249136 | + | 0.431517i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | 5.00000 | − | 8.66025i | 0.409616 | − | 0.709476i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.994847 | + | 0.101391i | \(0.0323294\pi\) | |||||||
\(150\) | 1.00000 | + | 1.73205i | 0.0816497 | + | 0.141421i | ||||
\(151\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(152\) | −3.00000 | + | 5.19615i | −0.243332 | + | 0.421464i | ||||
\(153\) | −8.00000 | −0.646762 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −2.00000 | + | 3.46410i | −0.160128 | + | 0.277350i | ||||
\(157\) | 1.00000 | + | 1.73205i | 0.0798087 | + | 0.138233i | 0.903167 | − | 0.429289i | \(-0.141236\pi\) |
−0.823359 | + | 0.567521i | \(0.807902\pi\) | |||||||
\(158\) | −2.00000 | − | 3.46410i | −0.159111 | − | 0.275589i | ||||
\(159\) | 10.0000 | − | 17.3205i | 0.793052 | − | 1.37361i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.0000 | −0.864242 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | 2.00000 | + | 3.46410i | 0.156174 | + | 0.270501i | ||||
\(165\) | 4.00000 | + | 6.92820i | 0.311400 | + | 0.539360i | ||||
\(166\) | −1.00000 | + | 1.73205i | −0.0776151 | + | 0.134433i | ||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −4.00000 | + | 6.92820i | −0.306786 | + | 0.531369i | ||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | 9.00000 | − | 15.5885i | 0.684257 | − | 1.18517i | −0.289412 | − | 0.957205i | \(-0.593460\pi\) |
0.973670 | − | 0.227964i | \(-0.0732068\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 14.0000 | − | 24.2487i | 1.05230 | − | 1.82264i | ||||
\(178\) | 4.00000 | + | 6.92820i | 0.299813 | + | 0.519291i | ||||
\(179\) | −2.00000 | − | 3.46410i | −0.149487 | − | 0.258919i | 0.781551 | − | 0.623841i | \(-0.214429\pi\) |
−0.931038 | + | 0.364922i | \(0.881096\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | −26.0000 | −1.93256 | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0000 | −1.47844 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | −5.00000 | − | 8.66025i | −0.367607 | − | 0.636715i | ||||
\(186\) | −4.00000 | − | 6.92820i | −0.293294 | − | 0.508001i | ||||
\(187\) | −16.0000 | + | 27.7128i | −1.17004 | + | 2.02656i | ||||
\(188\) | −4.00000 | −0.291730 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | 9.00000 | + | 15.5885i | 0.647834 | + | 1.12208i | 0.983639 | + | 0.180150i | \(0.0576584\pi\) |
−0.335805 | + | 0.941932i | \(0.609008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.00000 | −0.286446 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 2.00000 | − | 3.46410i | 0.142134 | − | 0.246183i | ||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −4.00000 | + | 6.92820i | −0.282138 | + | 0.488678i | ||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 16.0000 | 1.12022 | ||||||||
\(205\) | −2.00000 | + | 3.46410i | −0.139686 | + | 0.241943i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | 1.00000 | − | 1.73205i | 0.0693375 | − | 0.120096i | ||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | −5.00000 | + | 8.66025i | −0.343401 | + | 0.594789i | ||||
\(213\) | 12.0000 | + | 20.7846i | 0.822226 | + | 1.42414i | ||||
\(214\) | 6.00000 | + | 10.3923i | 0.410152 | + | 0.710403i | ||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −4.00000 | + | 6.92820i | −0.270295 | + | 0.468165i | ||||
\(220\) | −2.00000 | − | 3.46410i | −0.134840 | − | 0.233550i | ||||
\(221\) | −8.00000 | − | 13.8564i | −0.538138 | − | 0.932083i | ||||
\(222\) | −10.0000 | + | 17.3205i | −0.671156 | + | 1.16248i | ||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 1.00000 | − | 1.73205i | 0.0665190 | − | 0.115214i | ||||
\(227\) | −9.00000 | − | 15.5885i | −0.597351 | − | 1.03464i | −0.993210 | − | 0.116331i | \(-0.962887\pi\) |
0.395860 | − | 0.918311i | \(-0.370447\pi\) | |||||||
\(228\) | 6.00000 | + | 10.3923i | 0.397360 | + | 0.688247i | ||||
\(229\) | −7.00000 | + | 12.1244i | −0.462573 | + | 0.801200i | −0.999088 | − | 0.0426906i | \(-0.986407\pi\) |
0.536515 | + | 0.843891i | \(0.319740\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | −11.0000 | + | 19.0526i | −0.720634 | + | 1.24817i | 0.240112 | + | 0.970745i | \(0.422816\pi\) |
−0.960746 | + | 0.277429i | \(0.910518\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | −2.00000 | − | 3.46410i | −0.130466 | − | 0.225973i | ||||
\(236\) | −7.00000 | + | 12.1244i | −0.455661 | + | 0.789228i | ||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | −1.00000 | + | 1.73205i | −0.0645497 | + | 0.111803i | ||||
\(241\) | 2.00000 | + | 3.46410i | 0.128831 | + | 0.223142i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.794393 | + | 0.607404i | \(0.792211\pi\) | |||||||
\(242\) | −2.50000 | − | 4.33013i | −0.160706 | − | 0.278351i | ||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | 10.0000 | 0.640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.00000 | 0.510061 | ||||||||
\(247\) | 6.00000 | − | 10.3923i | 0.381771 | − | 0.661247i | ||||
\(248\) | 2.00000 | + | 3.46410i | 0.127000 | + | 0.219971i | ||||
\(249\) | 2.00000 | + | 3.46410i | 0.126745 | + | 0.219529i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −22.0000 | −1.38863 | −0.694314 | − | 0.719672i | \(-0.744292\pi\) | ||||
−0.694314 | + | 0.719672i | \(0.744292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 6.00000 | − | 10.3923i | 0.376473 | − | 0.652071i | ||||
\(255\) | 8.00000 | + | 13.8564i | 0.500979 | + | 0.867722i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 9.00000 | + | 15.5885i | 0.556022 | + | 0.963058i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | −4.00000 | + | 6.92820i | −0.246183 | + | 0.426401i | ||||
\(265\) | −10.0000 | −0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0000 | 0.979184 | ||||||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | 13.0000 | + | 22.5167i | 0.792624 | + | 1.37287i | 0.924337 | + | 0.381577i | \(0.124619\pi\) |
−0.131713 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(270\) | 2.00000 | + | 3.46410i | 0.121716 | + | 0.210819i | ||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | −4.00000 | − | 6.92820i | −0.240772 | − | 0.417029i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −5.00000 | + | 8.66025i | −0.299880 | + | 0.519408i | ||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | −4.00000 | + | 6.92820i | −0.238197 | + | 0.412568i | ||||
\(283\) | −13.0000 | − | 22.5167i | −0.772770 | − | 1.33848i | −0.936039 | − | 0.351895i | \(-0.885537\pi\) |
0.163270 | − | 0.986581i | \(-0.447796\pi\) | |||||||
\(284\) | −6.00000 | − | 10.3923i | −0.356034 | − | 0.616670i | ||||
\(285\) | −6.00000 | + | 10.3923i | −0.355409 | + | 0.615587i | ||||
\(286\) | 8.00000 | 0.473050 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −23.5000 | + | 40.7032i | −1.38235 | + | 2.39431i | ||||
\(290\) | −3.00000 | − | 5.19615i | −0.176166 | − | 0.305129i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0000 | −0.815112 | ||||||||
\(296\) | 5.00000 | − | 8.66025i | 0.290619 | − | 0.503367i | ||||
\(297\) | 8.00000 | + | 13.8564i | 0.464207 | + | 0.804030i | ||||
\(298\) | 5.00000 | + | 8.66025i | 0.289642 | + | 0.501675i | ||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | −2.00000 | −0.115470 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | − | 3.46410i | 0.114897 | − | 0.199007i | ||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 5.00000 | + | 8.66025i | 0.286299 | + | 0.495885i | ||||
\(306\) | 4.00000 | − | 6.92820i | 0.228665 | − | 0.396059i | ||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −2.00000 | + | 3.46410i | −0.113592 | + | 0.196748i | ||||
\(311\) | 8.00000 | + | 13.8564i | 0.453638 | + | 0.785725i | 0.998609 | − | 0.0527306i | \(-0.0167924\pi\) |
−0.544970 | + | 0.838455i | \(0.683459\pi\) | |||||||
\(312\) | −2.00000 | − | 3.46410i | −0.113228 | − | 0.196116i | ||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | −2.00000 | −0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 10.0000 | + | 17.3205i | 0.560772 | + | 0.971286i | ||||
\(319\) | −12.0000 | − | 20.7846i | −0.671871 | − | 1.16371i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 24.0000 | 1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.0000 | −2.67079 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | 1.00000 | + | 1.73205i | 0.0554700 | + | 0.0960769i | ||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | 10.0000 | − | 17.3205i | 0.553001 | − | 0.957826i | ||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.00000 | −0.440386 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | −1.00000 | − | 1.73205i | −0.0548821 | − | 0.0950586i | ||||
\(333\) | 5.00000 | + | 8.66025i | 0.273998 | + | 0.474579i | ||||
\(334\) | 6.00000 | − | 10.3923i | 0.328305 | − | 0.568642i | ||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 4.50000 | − | 7.79423i | 0.244768 | − | 0.423950i | ||||
\(339\) | −2.00000 | − | 3.46410i | −0.108625 | − | 0.188144i | ||||
\(340\) | −4.00000 | − | 6.92820i | −0.216930 | − | 0.375735i | ||||
\(341\) | −8.00000 | + | 13.8564i | −0.433224 | + | 0.750366i | ||||
\(342\) | 6.00000 | 0.324443 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 4.00000 | − | 6.92820i | 0.215353 | − | 0.373002i | ||||
\(346\) | 9.00000 | + | 15.5885i | 0.483843 | + | 0.838041i | ||||
\(347\) | 2.00000 | + | 3.46410i | 0.107366 | + | 0.185963i | 0.914702 | − | 0.404128i | \(-0.132425\pi\) |
−0.807337 | + | 0.590091i | \(0.799092\pi\) | |||||||
\(348\) | −6.00000 | + | 10.3923i | −0.321634 | + | 0.557086i | ||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 2.00000 | − | 3.46410i | 0.106600 | − | 0.184637i | ||||
\(353\) | −6.00000 | − | 10.3923i | −0.319348 | − | 0.553127i | 0.661004 | − | 0.750382i | \(-0.270130\pi\) |
−0.980352 | + | 0.197256i | \(0.936797\pi\) | |||||||
\(354\) | 14.0000 | + | 24.2487i | 0.744092 | + | 1.28880i | ||||
\(355\) | 6.00000 | − | 10.3923i | 0.318447 | − | 0.551566i | ||||
\(356\) | −8.00000 | −0.423999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | 4.00000 | − | 6.92820i | 0.211112 | − | 0.365657i | −0.740951 | − | 0.671559i | \(-0.765625\pi\) |
0.952063 | + | 0.305903i | \(0.0989582\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 13.0000 | − | 22.5167i | 0.683265 | − | 1.18345i | ||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | 0.209370 | ||||||||
\(366\) | 10.0000 | − | 17.3205i | 0.522708 | − | 0.905357i | ||||
\(367\) | 4.00000 | + | 6.92820i | 0.208798 | + | 0.361649i | 0.951336 | − | 0.308155i | \(-0.0997115\pi\) |
−0.742538 | + | 0.669804i | \(0.766378\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | 2.00000 | − | 3.46410i | 0.104116 | − | 0.180334i | ||||
\(370\) | 10.0000 | 0.519875 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | 3.00000 | − | 5.19615i | 0.155334 | − | 0.269047i | −0.777847 | − | 0.628454i | \(-0.783688\pi\) |
0.933181 | + | 0.359408i | \(0.117021\pi\) | |||||||
\(374\) | −16.0000 | − | 27.7128i | −0.827340 | − | 1.43300i | ||||
\(375\) | −1.00000 | − | 1.73205i | −0.0516398 | − | 0.0894427i | ||||
\(376\) | 2.00000 | − | 3.46410i | 0.103142 | − | 0.178647i | ||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 3.00000 | − | 5.19615i | 0.153897 | − | 0.266557i | ||||
\(381\) | −12.0000 | − | 20.7846i | −0.614779 | − | 1.06483i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | 10.0000 | − | 17.3205i | 0.510976 | − | 0.885037i | −0.488943 | − | 0.872316i | \(-0.662617\pi\) |
0.999919 | − | 0.0127209i | \(-0.00404928\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.0000 | −0.916176 | ||||||||
\(387\) | −2.00000 | + | 3.46410i | −0.101666 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.00000 | − | 15.5885i | −0.456318 | − | 0.790366i | 0.542445 | − | 0.840091i | \(-0.317499\pi\) |
−0.998763 | + | 0.0497253i | \(0.984165\pi\) | |||||||
\(390\) | 2.00000 | − | 3.46410i | 0.101274 | − | 0.175412i | ||||
\(391\) | 32.0000 | 1.61831 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.0000 | 1.81596 | ||||||||
\(394\) | −9.00000 | + | 15.5885i | −0.453413 | + | 0.785335i | ||||
\(395\) | 2.00000 | + | 3.46410i | 0.100631 | + | 0.174298i | ||||
\(396\) | 2.00000 | + | 3.46410i | 0.100504 | + | 0.174078i | ||||
\(397\) | 13.0000 | − | 22.5167i | 0.652451 | − | 1.13008i | −0.330075 | − | 0.943955i | \(-0.607074\pi\) |
0.982526 | − | 0.186124i | \(-0.0595926\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.00000 | − | 12.1244i | 0.349563 | − | 0.605461i | −0.636609 | − | 0.771187i | \(-0.719663\pi\) |
0.986172 | + | 0.165726i | \(0.0529966\pi\) | |||||||
\(402\) | −4.00000 | − | 6.92820i | −0.199502 | − | 0.345547i | ||||
\(403\) | −4.00000 | − | 6.92820i | −0.199254 | − | 0.345118i | ||||
\(404\) | −1.00000 | + | 1.73205i | −0.0497519 | + | 0.0861727i | ||||
\(405\) | 11.0000 | 0.546594 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.0000 | 1.98273 | ||||||||
\(408\) | −8.00000 | + | 13.8564i | −0.396059 | + | 0.685994i | ||||
\(409\) | −10.0000 | − | 17.3205i | −0.494468 | − | 0.856444i | 0.505511 | − | 0.862820i | \(-0.331304\pi\) |
−0.999980 | + | 0.00637586i | \(0.997970\pi\) | |||||||
\(410\) | −2.00000 | − | 3.46410i | −0.0987730 | − | 0.171080i | ||||
\(411\) | −2.00000 | + | 3.46410i | −0.0986527 | + | 0.170872i | ||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.00000 | −0.196589 | ||||||||
\(415\) | 1.00000 | − | 1.73205i | 0.0490881 | − | 0.0850230i | ||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | 10.0000 | + | 17.3205i | 0.489702 | + | 0.848189i | ||||
\(418\) | 12.0000 | − | 20.7846i | 0.586939 | − | 1.01661i | ||||
\(419\) | −6.00000 | −0.293119 | −0.146560 | − | 0.989202i | \(-0.546820\pi\) | ||||
−0.146560 | + | 0.989202i | \(0.546820\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | −10.0000 | + | 17.3205i | −0.486792 | + | 0.843149i | ||||
\(423\) | 2.00000 | + | 3.46410i | 0.0972433 | + | 0.168430i | ||||
\(424\) | −5.00000 | − | 8.66025i | −0.242821 | − | 0.420579i | ||||
\(425\) | 4.00000 | − | 6.92820i | 0.194029 | − | 0.336067i | ||||
\(426\) | −24.0000 | −1.16280 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 8.00000 | − | 13.8564i | 0.386244 | − | 0.668994i | ||||
\(430\) | 2.00000 | + | 3.46410i | 0.0964486 | + | 0.167054i | ||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | 40.0000 | 1.92228 | 0.961139 | − | 0.276066i | \(-0.0890309\pi\) | ||||
0.961139 | + | 0.276066i | \(0.0890309\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0000 | −0.575356 | ||||||||
\(436\) | −5.00000 | + | 8.66025i | −0.239457 | + | 0.414751i | ||||
\(437\) | 12.0000 | + | 20.7846i | 0.574038 | + | 0.994263i | ||||
\(438\) | −4.00000 | − | 6.92820i | −0.191127 | − | 0.331042i | ||||
\(439\) | −16.0000 | + | 27.7128i | −0.763638 | + | 1.32266i | 0.177325 | + | 0.984152i | \(0.443256\pi\) |
−0.940963 | + | 0.338508i | \(0.890078\pi\) | |||||||
\(440\) | 4.00000 | 0.190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | −10.0000 | − | 17.3205i | −0.474579 | − | 0.821995i | ||||
\(445\) | −4.00000 | − | 6.92820i | −0.189618 | − | 0.328428i | ||||
\(446\) | −4.00000 | + | 6.92820i | −0.189405 | + | 0.328060i | ||||
\(447\) | 20.0000 | 0.945968 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −8.00000 | − | 13.8564i | −0.376705 | − | 0.652473i | ||||
\(452\) | 1.00000 | + | 1.73205i | 0.0470360 | + | 0.0814688i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | −3.00000 | + | 5.19615i | −0.140334 | + | 0.243066i | −0.927622 | − | 0.373519i | \(-0.878151\pi\) |
0.787288 | + | 0.616585i | \(0.211484\pi\) | |||||||
\(458\) | −7.00000 | − | 12.1244i | −0.327089 | − | 0.566534i | ||||
\(459\) | 16.0000 | + | 27.7128i | 0.746816 | + | 1.29352i | ||||
\(460\) | −2.00000 | + | 3.46410i | −0.0932505 | + | 0.161515i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 3.00000 | − | 5.19615i | 0.139272 | − | 0.241225i | ||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | −11.0000 | − | 19.0526i | −0.509565 | − | 0.882593i | ||||
\(467\) | −5.00000 | + | 8.66025i | −0.231372 | + | 0.400749i | −0.958212 | − | 0.286058i | \(-0.907655\pi\) |
0.726840 | + | 0.686807i | \(0.240988\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | 0.184506 | ||||||||
\(471\) | −2.00000 | + | 3.46410i | −0.0921551 | + | 0.159617i | ||||
\(472\) | −7.00000 | − | 12.1244i | −0.322201 | − | 0.558069i | ||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 4.00000 | − | 6.92820i | 0.183726 | − | 0.318223i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | 4.00000 | − | 6.92820i | 0.182956 | − | 0.316889i | ||||
\(479\) | 2.00000 | + | 3.46410i | 0.0913823 | + | 0.158279i | 0.908093 | − | 0.418769i | \(-0.137538\pi\) |
−0.816711 | + | 0.577047i | \(0.804205\pi\) | |||||||
\(480\) | −1.00000 | − | 1.73205i | −0.0456435 | − | 0.0790569i | ||||
\(481\) | −10.0000 | + | 17.3205i | −0.455961 | + | 0.789747i | ||||
\(482\) | −4.00000 | −0.182195 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.00000 | − | 8.66025i | −0.226805 | − | 0.392837i | ||||
\(487\) | 22.0000 | + | 38.1051i | 0.996915 | + | 1.72671i | 0.566429 | + | 0.824110i | \(0.308325\pi\) |
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | −5.00000 | + | 8.66025i | −0.226339 | + | 0.392031i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −4.00000 | + | 6.92820i | −0.180334 | + | 0.312348i | ||||
\(493\) | −24.0000 | − | 41.5692i | −1.08091 | − | 1.87218i | ||||
\(494\) | 6.00000 | + | 10.3923i | 0.269953 | + | 0.467572i | ||||
\(495\) | −2.00000 | + | 3.46410i | −0.0898933 | + | 0.155700i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.00000 | −0.179244 | ||||||||
\(499\) | −14.0000 | + | 24.2487i | −0.626726 | + | 1.08552i | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −12.0000 | − | 20.7846i | −0.536120 | − | 0.928588i | ||||
\(502\) | 11.0000 | − | 19.0526i | 0.490954 | − | 0.850357i | ||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | −0.0889988 | ||||||||
\(506\) | −8.00000 | + | 13.8564i | −0.355643 | + | 0.615992i | ||||
\(507\) | −9.00000 | − | 15.5885i | −0.399704 | − | 0.692308i | ||||
\(508\) | 6.00000 | + | 10.3923i | 0.266207 | + | 0.461084i | ||||
\(509\) | −3.00000 | + | 5.19615i | −0.132973 | + | 0.230315i | −0.924821 | − | 0.380402i | \(-0.875786\pi\) |
0.791849 | + | 0.610718i | \(0.209119\pi\) | |||||||
\(510\) | −16.0000 | −0.708492 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −12.0000 | + | 20.7846i | −0.529813 | + | 0.917663i | ||||
\(514\) | 6.00000 | + | 10.3923i | 0.264649 | + | 0.458385i | ||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | 4.00000 | − | 6.92820i | 0.176090 | − | 0.304997i | ||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.0000 | 1.58022 | ||||||||
\(520\) | −1.00000 | + | 1.73205i | −0.0438529 | + | 0.0759555i | ||||
\(521\) | −6.00000 | − | 10.3923i | −0.262865 | − | 0.455295i | 0.704137 | − | 0.710064i | \(-0.251334\pi\) |
−0.967002 | + | 0.254769i | \(0.918001\pi\) | |||||||
\(522\) | 3.00000 | + | 5.19615i | 0.131306 | + | 0.227429i | ||||
\(523\) | −17.0000 | + | 29.4449i | −0.743358 | + | 1.28753i | 0.207600 | + | 0.978214i | \(0.433435\pi\) |
−0.950958 | + | 0.309320i | \(0.899899\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0000 | + | 27.7128i | −0.696971 | + | 1.20719i | ||||
\(528\) | −4.00000 | − | 6.92820i | −0.174078 | − | 0.301511i | ||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 5.00000 | − | 8.66025i | 0.217186 | − | 0.376177i | ||||
\(531\) | 14.0000 | 0.607548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.00000 | 0.346518 | ||||||||
\(534\) | −8.00000 | + | 13.8564i | −0.346194 | + | 0.599625i | ||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 2.00000 | + | 3.46410i | 0.0863868 | + | 0.149626i | ||||
\(537\) | 4.00000 | − | 6.92820i | 0.172613 | − | 0.298974i | ||||
\(538\) | −26.0000 | −1.12094 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.00000 | −0.172133 | ||||||||
\(541\) | 17.0000 | − | 29.4449i | 0.730887 | − | 1.26593i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.956504 | − | 0.291718i | \(-0.0942267\pi\) | |||||||
\(542\) | 8.00000 | + | 13.8564i | 0.343629 | + | 0.595184i | ||||
\(543\) | −26.0000 | − | 45.0333i | −1.11577 | − | 1.93256i | ||||
\(544\) | 4.00000 | − | 6.92820i | 0.171499 | − | 0.297044i | ||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 1.00000 | − | 1.73205i | 0.0427179 | − | 0.0739895i | ||||
\(549\) | −5.00000 | − | 8.66025i | −0.213395 | − | 0.369611i | ||||
\(550\) | 2.00000 | + | 3.46410i | 0.0852803 | + | 0.147710i | ||||
\(551\) | 18.0000 | − | 31.1769i | 0.766826 | − | 1.32818i | ||||
\(552\) | 8.00000 | 0.340503 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 10.0000 | − | 17.3205i | 0.424476 | − | 0.735215i | ||||
\(556\) | −5.00000 | − | 8.66025i | −0.212047 | − | 0.367277i | ||||
\(557\) | 3.00000 | + | 5.19615i | 0.127114 | + | 0.220168i | 0.922557 | − | 0.385860i | \(-0.126095\pi\) |
−0.795443 | + | 0.606028i | \(0.792762\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64.0000 | −2.70208 | ||||||||
\(562\) | 5.00000 | − | 8.66025i | 0.210912 | − | 0.365311i | ||||
\(563\) | 9.00000 | + | 15.5885i | 0.379305 | + | 0.656975i | 0.990961 | − | 0.134148i | \(-0.0428299\pi\) |
−0.611656 | + | 0.791123i | \(0.709497\pi\) | |||||||
\(564\) | −4.00000 | − | 6.92820i | −0.168430 | − | 0.291730i | ||||
\(565\) | −1.00000 | + | 1.73205i | −0.0420703 | + | 0.0728679i | ||||
\(566\) | 26.0000 | 1.09286 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | 19.0000 | − | 32.9090i | 0.796521 | − | 1.37962i | −0.125347 | − | 0.992113i | \(-0.540004\pi\) |
0.921869 | − | 0.387503i | \(-0.126662\pi\) | |||||||
\(570\) | −6.00000 | − | 10.3923i | −0.251312 | − | 0.435286i | ||||
\(571\) | 18.0000 | + | 31.1769i | 0.753277 | + | 1.30471i | 0.946227 | + | 0.323505i | \(0.104861\pi\) |
−0.192950 | + | 0.981209i | \(0.561806\pi\) | |||||||
\(572\) | −4.00000 | + | 6.92820i | −0.167248 | + | 0.289683i | ||||
\(573\) | −24.0000 | −1.00261 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.0000 | − | 17.3205i | −0.416305 | − | 0.721062i | 0.579259 | − | 0.815144i | \(-0.303342\pi\) |
−0.995565 | + | 0.0940813i | \(0.970009\pi\) | |||||||
\(578\) | −23.5000 | − | 40.7032i | −0.977471 | − | 1.69303i | ||||
\(579\) | −18.0000 | + | 31.1769i | −0.748054 | + | 1.29567i | ||||
\(580\) | 6.00000 | 0.249136 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.0000 | − | 34.6410i | 0.828315 | − | 1.43468i | ||||
\(584\) | 2.00000 | + | 3.46410i | 0.0827606 | + | 0.143346i | ||||
\(585\) | −1.00000 | − | 1.73205i | −0.0413449 | − | 0.0716115i | ||||
\(586\) | 3.00000 | − | 5.19615i | 0.123929 | − | 0.214651i | ||||
\(587\) | −2.00000 | −0.0825488 | −0.0412744 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412744 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 7.00000 | − | 12.1244i | 0.288185 | − | 0.499152i | ||||
\(591\) | 18.0000 | + | 31.1769i | 0.740421 | + | 1.28245i | ||||
\(592\) | 5.00000 | + | 8.66025i | 0.205499 | + | 0.355934i | ||||
\(593\) | −10.0000 | + | 17.3205i | −0.410651 | + | 0.711268i | −0.994961 | − | 0.100262i | \(-0.968032\pi\) |
0.584310 | + | 0.811530i | \(0.301365\pi\) | |||||||
\(594\) | −16.0000 | −0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | −4.00000 | + | 6.92820i | −0.163709 | + | 0.283552i | ||||
\(598\) | −4.00000 | − | 6.92820i | −0.163572 | − | 0.283315i | ||||
\(599\) | 14.0000 | + | 24.2487i | 0.572024 | + | 0.990775i | 0.996358 | + | 0.0852695i | \(0.0271751\pi\) |
−0.424333 | + | 0.905506i | \(0.639492\pi\) | |||||||
\(600\) | 1.00000 | − | 1.73205i | 0.0408248 | − | 0.0707107i | ||||
\(601\) | −40.0000 | −1.63163 | −0.815817 | − | 0.578310i | \(-0.803712\pi\) | ||||
−0.815817 | + | 0.578310i | \(0.803712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | + | 4.33013i | 0.101639 | + | 0.176045i | ||||
\(606\) | 2.00000 | + | 3.46410i | 0.0812444 | + | 0.140720i | ||||
\(607\) | −8.00000 | + | 13.8564i | −0.324710 | + | 0.562414i | −0.981454 | − | 0.191700i | \(-0.938600\pi\) |
0.656744 | + | 0.754114i | \(0.271933\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | −4.00000 | + | 6.92820i | −0.161823 | + | 0.280285i | ||||
\(612\) | 4.00000 | + | 6.92820i | 0.161690 | + | 0.280056i | ||||
\(613\) | 1.00000 | + | 1.73205i | 0.0403896 | + | 0.0699569i | 0.885514 | − | 0.464614i | \(-0.153807\pi\) |
−0.845124 | + | 0.534570i | \(0.820473\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | −8.00000 | −0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −4.00000 | + | 6.92820i | −0.160904 | + | 0.278693i | ||||
\(619\) | −3.00000 | − | 5.19615i | −0.120580 | − | 0.208851i | 0.799416 | − | 0.600777i | \(-0.205142\pi\) |
−0.919997 | + | 0.391926i | \(0.871809\pi\) | |||||||
\(620\) | −2.00000 | − | 3.46410i | −0.0803219 | − | 0.139122i | ||||
\(621\) | 8.00000 | − | 13.8564i | 0.321029 | − | 0.556038i | ||||
\(622\) | −16.0000 | −0.641542 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.00000 | − | 6.92820i | −0.159872 | − | 0.276907i | ||||
\(627\) | −24.0000 | − | 41.5692i | −0.958468 | − | 1.66011i | ||||
\(628\) | 1.00000 | − | 1.73205i | 0.0399043 | − | 0.0691164i | ||||
\(629\) | 80.0000 | 3.18981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.00000 | 0.159237 | 0.0796187 | − | 0.996825i | \(-0.474630\pi\) | ||||
0.0796187 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(632\) | −2.00000 | + | 3.46410i | −0.0795557 | + | 0.137795i | ||||
\(633\) | 20.0000 | + | 34.6410i | 0.794929 | + | 1.37686i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | −20.0000 | −0.793052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 24.0000 | 0.950169 | ||||||||
\(639\) | −6.00000 | + | 10.3923i | −0.237356 | + | 0.411113i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | −12.0000 | + | 20.7846i | −0.473602 | + | 0.820303i | ||||
\(643\) | −18.0000 | −0.709851 | −0.354925 | − | 0.934895i | \(-0.615494\pi\) | ||||
−0.354925 | + | 0.934895i | \(0.615494\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 24.0000 | − | 41.5692i | 0.944267 | − | 1.63552i | ||||
\(647\) | 14.0000 | + | 24.2487i | 0.550397 | + | 0.953315i | 0.998246 | + | 0.0592060i | \(0.0188569\pi\) |
−0.447849 | + | 0.894109i | \(0.647810\pi\) | |||||||
\(648\) | 5.50000 | + | 9.52628i | 0.216060 | + | 0.374228i | ||||
\(649\) | 28.0000 | − | 48.4974i | 1.09910 | − | 1.90369i | ||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 10.0000 | + | 17.3205i | 0.391031 | + | 0.677285i | ||||
\(655\) | −9.00000 | − | 15.5885i | −0.351659 | − | 0.609091i | ||||
\(656\) | 2.00000 | − | 3.46410i | 0.0780869 | − | 0.135250i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 4.00000 | − | 6.92820i | 0.155700 | − | 0.269680i | ||||
\(661\) | −1.00000 | − | 1.73205i | −0.0388955 | − | 0.0673690i | 0.845922 | − | 0.533306i | \(-0.179051\pi\) |
−0.884818 | + | 0.465937i | \(0.845717\pi\) | |||||||
\(662\) | 14.0000 | + | 24.2487i | 0.544125 | + | 0.942453i | ||||
\(663\) | 16.0000 | − | 27.7128i | 0.621389 | − | 1.07628i | ||||
\(664\) | 2.00000 | 0.0776151 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0000 | −0.387492 | ||||||||
\(667\) | −12.0000 | + | 20.7846i | −0.464642 | + | 0.804783i | ||||
\(668\) | 6.00000 | + | 10.3923i | 0.232147 | + | 0.402090i | ||||
\(669\) | 8.00000 | + | 13.8564i | 0.309298 | + | 0.535720i | ||||
\(670\) | −2.00000 | + | 3.46410i | −0.0772667 | + | 0.133830i | ||||
\(671\) | −40.0000 | −1.54418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 7.00000 | − | 12.1244i | 0.269630 | − | 0.467013i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −23.0000 | + | 39.8372i | −0.883962 | + | 1.53107i | −0.0370628 | + | 0.999313i | \(0.511800\pi\) |
−0.846899 | + | 0.531754i | \(0.821533\pi\) | |||||||
\(678\) | 4.00000 | 0.153619 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.00000 | 0.306786 | ||||||||
\(681\) | 18.0000 | − | 31.1769i | 0.689761 | − | 1.19470i | ||||
\(682\) | −8.00000 | − | 13.8564i | −0.306336 | − | 0.530589i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | −3.00000 | + | 5.19615i | −0.114708 | + | 0.198680i | ||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.0000 | −1.06827 | ||||||||
\(688\) | −2.00000 | + | 3.46410i | −0.0762493 | + | 0.132068i | ||||
\(689\) | 10.0000 | + | 17.3205i | 0.380970 | + | 0.659859i | ||||
\(690\) | 4.00000 | + | 6.92820i | 0.152277 | + | 0.263752i | ||||
\(691\) | −23.0000 | + | 39.8372i | −0.874961 | + | 1.51548i | −0.0181572 | + | 0.999835i | \(0.505780\pi\) |
−0.856804 | + | 0.515642i | \(0.827553\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 5.00000 | − | 8.66025i | 0.189661 | − | 0.328502i | ||||
\(696\) | −6.00000 | − | 10.3923i | −0.227429 | − | 0.393919i | ||||
\(697\) | −16.0000 | − | 27.7128i | −0.606043 | − | 1.04970i | ||||
\(698\) | 5.00000 | − | 8.66025i | 0.189253 | − | 0.327795i | ||||
\(699\) | −44.0000 | −1.66423 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.0000 | −1.43524 | −0.717620 | − | 0.696435i | \(-0.754769\pi\) | ||||
−0.717620 | + | 0.696435i | \(0.754769\pi\) | |||||||
\(702\) | 4.00000 | − | 6.92820i | 0.150970 | − | 0.261488i | ||||
\(703\) | 30.0000 | + | 51.9615i | 1.13147 | + | 1.95977i | ||||
\(704\) | 2.00000 | + | 3.46410i | 0.0753778 | + | 0.130558i | ||||
\(705\) | 4.00000 | − | 6.92820i | 0.150649 | − | 0.260931i | ||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −28.0000 | −1.05230 | ||||||||
\(709\) | −21.0000 | + | 36.3731i | −0.788672 | + | 1.36602i | 0.138109 | + | 0.990417i | \(0.455897\pi\) |
−0.926781 | + | 0.375602i | \(0.877436\pi\) | |||||||
\(710\) | 6.00000 | + | 10.3923i | 0.225176 | + | 0.390016i | ||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | 4.00000 | − | 6.92820i | 0.149906 | − | 0.259645i | ||||
\(713\) | 16.0000 | 0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | −0.299183 | ||||||||
\(716\) | −2.00000 | + | 3.46410i | −0.0747435 | + | 0.129460i | ||||
\(717\) | −8.00000 | − | 13.8564i | −0.298765 | − | 0.517477i | ||||
\(718\) | 4.00000 | + | 6.92820i | 0.149279 | + | 0.258558i | ||||
\(719\) | 18.0000 | − | 31.1769i | 0.671287 | − | 1.16270i | −0.306253 | − | 0.951950i | \(-0.599075\pi\) |
0.977539 | − | 0.210752i | \(-0.0675914\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | −4.00000 | + | 6.92820i | −0.148762 | + | 0.257663i | ||||
\(724\) | 13.0000 | + | 22.5167i | 0.483141 | + | 0.836825i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | −20.0000 | −0.741759 | −0.370879 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370879 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.00000 | + | 3.46410i | −0.0740233 | + | 0.128212i | ||||
\(731\) | 16.0000 | + | 27.7128i | 0.591781 | + | 1.02500i | ||||
\(732\) | 10.0000 | + | 17.3205i | 0.369611 | + | 0.640184i | ||||
\(733\) | 15.0000 | − | 25.9808i | 0.554038 | − | 0.959621i | −0.443940 | − | 0.896056i | \(-0.646420\pi\) |
0.997978 | − | 0.0635649i | \(-0.0202470\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −8.00000 | + | 13.8564i | −0.294684 | + | 0.510407i | ||||
\(738\) | 2.00000 | + | 3.46410i | 0.0736210 | + | 0.127515i | ||||
\(739\) | −6.00000 | − | 10.3923i | −0.220714 | − | 0.382287i | 0.734311 | − | 0.678813i | \(-0.237505\pi\) |
−0.955025 | + | 0.296526i | \(0.904172\pi\) | |||||||
\(740\) | −5.00000 | + | 8.66025i | −0.183804 | + | 0.318357i | ||||
\(741\) | 24.0000 | 0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.0000 | −0.440237 | −0.220119 | − | 0.975473i | \(-0.570644\pi\) | ||||
−0.220119 | + | 0.975473i | \(0.570644\pi\) | |||||||
\(744\) | −4.00000 | + | 6.92820i | −0.146647 | + | 0.254000i | ||||
\(745\) | −5.00000 | − | 8.66025i | −0.183186 | − | 0.317287i | ||||
\(746\) | 3.00000 | + | 5.19615i | 0.109838 | + | 0.190245i | ||||
\(747\) | −1.00000 | + | 1.73205i | −0.0365881 | + | 0.0633724i | ||||
\(748\) | 32.0000 | 1.17004 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.00000 | 0.0730297 | ||||||||
\(751\) | −20.0000 | + | 34.6410i | −0.729810 | + | 1.26407i | 0.227153 | + | 0.973859i | \(0.427058\pi\) |
−0.956963 | + | 0.290209i | \(0.906275\pi\) | |||||||
\(752\) | 2.00000 | + | 3.46410i | 0.0729325 | + | 0.126323i | ||||
\(753\) | −22.0000 | − | 38.1051i | −0.801725 | − | 1.38863i | ||||
\(754\) | −6.00000 | + | 10.3923i | −0.218507 | + | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 2.00000 | − | 3.46410i | 0.0726433 | − | 0.125822i | ||||
\(759\) | 16.0000 | + | 27.7128i | 0.580763 | + | 1.00591i | ||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | −6.00000 | + | 10.3923i | −0.217500 | + | 0.376721i | −0.954043 | − | 0.299670i | \(-0.903123\pi\) |
0.736543 | + | 0.676391i | \(0.236457\pi\) | |||||||
\(762\) | 24.0000 | 0.869428 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | −4.00000 | + | 6.92820i | −0.144620 | + | 0.250490i | ||||
\(766\) | 10.0000 | + | 17.3205i | 0.361315 | + | 0.625815i | ||||
\(767\) | 14.0000 | + | 24.2487i | 0.505511 | + | 0.875570i | ||||
\(768\) | 1.00000 | − | 1.73205i | 0.0360844 | − | 0.0625000i | ||||
\(769\) | −28.0000 | −1.00971 | −0.504853 | − | 0.863205i | \(-0.668453\pi\) | ||||
−0.504853 | + | 0.863205i | \(0.668453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0000 | 0.864339 | ||||||||
\(772\) | 9.00000 | − | 15.5885i | 0.323917 | − | 0.561041i | ||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | −2.00000 | − | 3.46410i | −0.0718885 | − | 0.124515i | ||||
\(775\) | 2.00000 | − | 3.46410i | 0.0718421 | − | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 2.00000 | + | 3.46410i | 0.0716115 | + | 0.124035i | ||||
\(781\) | 24.0000 | + | 41.5692i | 0.858788 | + | 1.48746i | ||||
\(782\) | −16.0000 | + | 27.7128i | −0.572159 | + | 0.991008i | ||||
\(783\) | −24.0000 | −0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00000 | 0.0713831 | ||||||||
\(786\) | −18.0000 | + | 31.1769i | −0.642039 | + | 1.11204i | ||||
\(787\) | 3.00000 | + | 5.19615i | 0.106938 | + | 0.185223i | 0.914529 | − | 0.404521i | \(-0.132562\pi\) |
−0.807590 | + | 0.589744i | \(0.799229\pi\) | |||||||
\(788\) | −9.00000 | − | 15.5885i | −0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.00000 | −0.142314 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.00000 | −0.142134 | ||||||||
\(793\) | 10.0000 | − | 17.3205i | 0.355110 | − | 0.615069i | ||||
\(794\) | 13.0000 | + | 22.5167i | 0.461353 | + | 0.799086i | ||||
\(795\) | −10.0000 | − | 17.3205i | −0.354663 | − | 0.614295i | ||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | −2.00000 | −0.0708436 | −0.0354218 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354218 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0000 | 1.13208 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 4.00000 | + | 6.92820i | 0.141333 | + | 0.244796i | ||||
\(802\) | 7.00000 | + | 12.1244i | 0.247179 | + | 0.428126i | ||||
\(803\) | −8.00000 | + | 13.8564i | −0.282314 | + | 0.488982i | ||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | −26.0000 | + | 45.0333i | −0.915243 | + | 1.58525i | ||||
\(808\) | −1.00000 | − | 1.73205i | −0.0351799 | − | 0.0609333i | ||||
\(809\) | 5.00000 | + | 8.66025i | 0.175791 | + | 0.304478i | 0.940435 | − | 0.339975i | \(-0.110418\pi\) |
−0.764644 | + | 0.644453i | \(0.777085\pi\) | |||||||
\(810\) | −5.50000 | + | 9.52628i | −0.193250 | + | 0.334719i | ||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.0000 | 1.12229 | ||||||||
\(814\) | −20.0000 | + | 34.6410i | −0.701000 | + | 1.21417i | ||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | −8.00000 | − | 13.8564i | −0.280056 | − | 0.485071i | ||||
\(817\) | −12.0000 | + | 20.7846i | −0.419827 | + | 0.727161i | ||||
\(818\) | 20.0000 | 0.699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | −2.00000 | − | 3.46410i | −0.0697580 | − | 0.120824i | ||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | 8.00000 | 0.278524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44.0000 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | 7.00000 | + | 12.1244i | 0.243120 | + | 0.421096i | 0.961601 | − | 0.274450i | \(-0.0884958\pi\) |
−0.718481 | + | 0.695546i | \(0.755162\pi\) | |||||||
\(830\) | 1.00000 | + | 1.73205i | 0.0347105 | + | 0.0601204i | ||||
\(831\) | 2.00000 | − | 3.46410i | 0.0693792 | − | 0.120168i | ||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.0000 | −0.692543 | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | 12.0000 | + | 20.7846i | 0.415029 | + | 0.718851i | ||||
\(837\) | 8.00000 | + | 13.8564i | 0.276520 | + | 0.478947i | ||||
\(838\) | 3.00000 | − | 5.19615i | 0.103633 | − | 0.179498i | ||||
\(839\) | 36.0000 | 1.24286 | 0.621429 | − | 0.783470i | \(-0.286552\pi\) | ||||
0.621429 | + | 0.783470i | \(0.286552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 17.0000 | − | 29.4449i | 0.585859 | − | 1.01474i | ||||
\(843\) | −10.0000 | − | 17.3205i | −0.344418 | − | 0.596550i | ||||
\(844\) | −10.0000 | − | 17.3205i | −0.344214 | − | 0.596196i | ||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | −4.00000 | −0.137523 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.0000 | 0.343401 | ||||||||
\(849\) | 26.0000 | − | 45.0333i | 0.892318 | − | 1.54554i | ||||
\(850\) | 4.00000 | + | 6.92820i | 0.137199 | + | 0.237635i | ||||
\(851\) | −20.0000 | − | 34.6410i | −0.685591 | − | 1.18748i | ||||
\(852\) | 12.0000 | − | 20.7846i | 0.411113 | − | 0.712069i | ||||
\(853\) | −50.0000 | −1.71197 | −0.855984 | − | 0.517003i | \(-0.827048\pi\) | ||||
−0.855984 | + | 0.517003i | \(0.827048\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | −12.0000 | − | 20.7846i | −0.409912 | − | 0.709989i | 0.584967 | − | 0.811057i | \(-0.301107\pi\) |
−0.994880 | + | 0.101068i | \(0.967774\pi\) | |||||||
\(858\) | 8.00000 | + | 13.8564i | 0.273115 | + | 0.473050i | ||||
\(859\) | 19.0000 | − | 32.9090i | 0.648272 | − | 1.12284i | −0.335264 | − | 0.942124i | \(-0.608825\pi\) |
0.983535 | − | 0.180715i | \(-0.0578412\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0000 | − | 20.7846i | 0.408485 | − | 0.707516i | −0.586235 | − | 0.810141i | \(-0.699391\pi\) |
0.994720 | + | 0.102624i | \(0.0327240\pi\) | |||||||
\(864\) | −2.00000 | − | 3.46410i | −0.0680414 | − | 0.117851i | ||||
\(865\) | −9.00000 | − | 15.5885i | −0.306009 | − | 0.530023i | ||||
\(866\) | −20.0000 | + | 34.6410i | −0.679628 | + | 1.17715i | ||||
\(867\) | −94.0000 | −3.19241 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.0000 | −0.542763 | ||||||||
\(870\) | 6.00000 | − | 10.3923i | 0.203419 | − | 0.352332i | ||||
\(871\) | −4.00000 | − | 6.92820i | −0.135535 | − | 0.234753i | ||||
\(872\) | −5.00000 | − | 8.66025i | −0.169321 | − | 0.293273i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.00000 | 0.270295 | ||||||||
\(877\) | 21.0000 | − | 36.3731i | 0.709120 | − | 1.22823i | −0.256064 | − | 0.966660i | \(-0.582426\pi\) |
0.965184 | − | 0.261571i | \(-0.0842407\pi\) | |||||||
\(878\) | −16.0000 | − | 27.7128i | −0.539974 | − | 0.935262i | ||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | −2.00000 | + | 3.46410i | −0.0674200 | + | 0.116775i | ||||
\(881\) | 40.0000 | 1.34763 | 0.673817 | − | 0.738898i | \(-0.264654\pi\) | ||||
0.673817 | + | 0.738898i | \(0.264654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | −8.00000 | + | 13.8564i | −0.269069 | + | 0.466041i | ||||
\(885\) | −14.0000 | − | 24.2487i | −0.470605 | − | 0.815112i | ||||
\(886\) | −2.00000 | − | 3.46410i | −0.0671913 | − | 0.116379i | ||||
\(887\) | 2.00000 | − | 3.46410i | 0.0671534 | − | 0.116313i | −0.830494 | − | 0.557028i | \(-0.811942\pi\) |
0.897647 | + | 0.440715i | \(0.145275\pi\) | |||||||
\(888\) | 20.0000 | 0.671156 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.00000 | 0.268161 | ||||||||
\(891\) | −22.0000 | + | 38.1051i | −0.737028 | + | 1.27657i | ||||
\(892\) | −4.00000 | − | 6.92820i | −0.133930 | − | 0.231973i | ||||
\(893\) | 12.0000 | + | 20.7846i | 0.401565 | + | 0.695530i | ||||
\(894\) | −10.0000 | + | 17.3205i | −0.334450 | + | 0.579284i | ||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | −9.00000 | + | 15.5885i | −0.300334 | + | 0.520194i | ||||
\(899\) | −12.0000 | − | 20.7846i | −0.400222 | − | 0.693206i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | 40.0000 | − | 69.2820i | 1.33259 | − | 2.30812i | ||||
\(902\) | 16.0000 | 0.532742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | −13.0000 | + | 22.5167i | −0.432135 | + | 0.748479i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | − | 3.46410i | −0.0664089 | − | 0.115024i | 0.830909 | − | 0.556408i | \(-0.187821\pi\) |
−0.897318 | + | 0.441384i | \(0.854488\pi\) | |||||||
\(908\) | −9.00000 | + | 15.5885i | −0.298675 | + | 0.517321i | ||||
\(909\) | 2.00000 | 0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 6.00000 | − | 10.3923i | 0.198680 | − | 0.344124i | ||||
\(913\) | 4.00000 | + | 6.92820i | 0.132381 | + | 0.229290i | ||||
\(914\) | −3.00000 | − | 5.19615i | −0.0992312 | − | 0.171873i | ||||
\(915\) | −10.0000 | + | 17.3205i | −0.330590 | + | 0.572598i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −32.0000 | −1.05616 | ||||||||
\(919\) | 2.00000 | − | 3.46410i | 0.0659739 | − | 0.114270i | −0.831152 | − | 0.556046i | \(-0.812318\pi\) |
0.897126 | + | 0.441776i | \(0.145651\pi\) | |||||||
\(920\) | −2.00000 | − | 3.46410i | −0.0659380 | − | 0.114208i | ||||
\(921\) | 2.00000 | + | 3.46410i | 0.0659022 | + | 0.114146i | ||||
\(922\) | −3.00000 | + | 5.19615i | −0.0987997 | + | 0.171126i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | 2.00000 | + | 3.46410i | 0.0656886 | + | 0.113776i | ||||
\(928\) | 3.00000 | + | 5.19615i | 0.0984798 | + | 0.170572i | ||||
\(929\) | −6.00000 | + | 10.3923i | −0.196854 | + | 0.340960i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.750653 | + | 0.660697i | \(0.229739\pi\) | |||||||
\(930\) | −8.00000 | −0.262330 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.0000 | 0.720634 | ||||||||
\(933\) | −16.0000 | + | 27.7128i | −0.523816 | + | 0.907277i | ||||
\(934\) | −5.00000 | − | 8.66025i | −0.163605 | − | 0.283372i | ||||
\(935\) | 16.0000 | + | 27.7128i | 0.523256 | + | 0.906306i | ||||
\(936\) | 1.00000 | − | 1.73205i | 0.0326860 | − | 0.0566139i | ||||
\(937\) | −12.0000 | −0.392023 | −0.196011 | − | 0.980602i | \(-0.562799\pi\) | ||||
−0.196011 | + | 0.980602i | \(0.562799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | −2.00000 | + | 3.46410i | −0.0652328 | + | 0.112987i | ||||
\(941\) | −5.00000 | − | 8.66025i | −0.162995 | − | 0.282316i | 0.772946 | − | 0.634472i | \(-0.218782\pi\) |
−0.935942 | + | 0.352155i | \(0.885449\pi\) | |||||||
\(942\) | −2.00000 | − | 3.46410i | −0.0651635 | − | 0.112867i | ||||
\(943\) | −8.00000 | + | 13.8564i | −0.260516 | + | 0.451227i | ||||
\(944\) | 14.0000 | 0.455661 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0000 | −0.520205 | ||||||||
\(947\) | 6.00000 | − | 10.3923i | 0.194974 | − | 0.337705i | −0.751918 | − | 0.659256i | \(-0.770871\pi\) |
0.946892 | + | 0.321552i | \(0.104204\pi\) | |||||||
\(948\) | 4.00000 | + | 6.92820i | 0.129914 | + | 0.225018i | ||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | −3.00000 | + | 5.19615i | −0.0973329 | + | 0.168585i | ||||
\(951\) | −36.0000 | −1.16738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | −5.00000 | + | 8.66025i | −0.161881 | + | 0.280386i | ||||
\(955\) | 6.00000 | + | 10.3923i | 0.194155 | + | 0.336287i | ||||
\(956\) | 4.00000 | + | 6.92820i | 0.129369 | + | 0.224074i | ||||
\(957\) | 24.0000 | − | 41.5692i | 0.775810 | − | 1.34374i | ||||
\(958\) | −4.00000 | −0.129234 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | −10.0000 | − | 17.3205i | −0.322413 | − | 0.558436i | ||||
\(963\) | 6.00000 | + | 10.3923i | 0.193347 | + | 0.334887i | ||||
\(964\) | 2.00000 | − | 3.46410i | 0.0644157 | − | 0.111571i | ||||
\(965\) | 18.0000 | 0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.0000 | −1.67221 | −0.836104 | − | 0.548572i | \(-0.815172\pi\) | ||||
−0.836104 | + | 0.548572i | \(0.815172\pi\) | |||||||
\(968\) | −2.50000 | + | 4.33013i | −0.0803530 | + | 0.139176i | ||||
\(969\) | −48.0000 | − | 83.1384i | −1.54198 | − | 2.67079i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.0000 | + | 53.6936i | −0.994837 | + | 1.72311i | −0.409532 | + | 0.912296i | \(0.634308\pi\) |
−0.585305 | + | 0.810813i | \(0.699025\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −44.0000 | −1.40985 | ||||||||
\(975\) | −2.00000 | + | 3.46410i | −0.0640513 | + | 0.110940i | ||||
\(976\) | −5.00000 | − | 8.66025i | −0.160046 | − | 0.277208i | ||||
\(977\) | −27.0000 | − | 46.7654i | −0.863807 | − | 1.49616i | −0.868227 | − | 0.496167i | \(-0.834741\pi\) |
0.00442082 | − | 0.999990i | \(-0.498593\pi\) | |||||||
\(978\) | −4.00000 | + | 6.92820i | −0.127906 | + | 0.221540i | ||||
\(979\) | 32.0000 | 1.02272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | 10.0000 | + | 17.3205i | 0.318950 | + | 0.552438i | 0.980269 | − | 0.197666i | \(-0.0633363\pi\) |
−0.661319 | + | 0.750105i | \(0.730003\pi\) | |||||||
\(984\) | −4.00000 | − | 6.92820i | −0.127515 | − | 0.220863i | ||||
\(985\) | 9.00000 | − | 15.5885i | 0.286764 | − | 0.496690i | ||||
\(986\) | 48.0000 | 1.52863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | 8.00000 | − | 13.8564i | 0.254385 | − | 0.440608i | ||||
\(990\) | −2.00000 | − | 3.46410i | −0.0635642 | − | 0.110096i | ||||
\(991\) | 18.0000 | + | 31.1769i | 0.571789 | + | 0.990367i | 0.996382 | + | 0.0849833i | \(0.0270837\pi\) |
−0.424594 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | 56.0000 | 1.77711 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 2.00000 | − | 3.46410i | 0.0633724 | − | 0.109764i | ||||
\(997\) | −21.0000 | − | 36.3731i | −0.665077 | − | 1.15195i | −0.979265 | − | 0.202586i | \(-0.935066\pi\) |
0.314188 | − | 0.949361i | \(-0.398268\pi\) | |||||||
\(998\) | −14.0000 | − | 24.2487i | −0.443162 | − | 0.767580i | ||||
\(999\) | 20.0000 | − | 34.6410i | 0.632772 | − | 1.09599i |
(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 | 490.2.e.e.471.1 | 2 | ||
7.2 | even | 3 | 490.2.a.f.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 490.2.e.b.361.1 | 2 | |||
7.4 | even | 3 | inner | 490.2.e.e.361.1 | 2 | ||
7.5 | odd | 6 | 490.2.a.i.1.1 | yes | 1 | ||
7.6 | odd | 2 | 490.2.e.b.471.1 | 2 | |||
21.2 | odd | 6 | 4410.2.a.s.1.1 | 1 | |||
21.5 | even | 6 | 4410.2.a.i.1.1 | 1 | |||
28.19 | even | 6 | 3920.2.a.j.1.1 | 1 | |||
28.23 | odd | 6 | 3920.2.a.bg.1.1 | 1 | |||
35.2 | odd | 12 | 2450.2.c.b.99.2 | 2 | |||
35.9 | even | 6 | 2450.2.a.n.1.1 | 1 | |||
35.12 | even | 12 | 2450.2.c.n.99.2 | 2 | |||
35.19 | odd | 6 | 2450.2.a.d.1.1 | 1 | |||
35.23 | odd | 12 | 2450.2.c.b.99.1 | 2 | |||
35.33 | even | 12 | 2450.2.c.n.99.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.2.a.f.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
490.2.a.i.1.1 | yes | 1 | 7.5 | odd | 6 | ||
490.2.e.b.361.1 | 2 | 7.3 | odd | 6 | |||
490.2.e.b.471.1 | 2 | 7.6 | odd | 2 | |||
490.2.e.e.361.1 | 2 | 7.4 | even | 3 | inner | ||
490.2.e.e.471.1 | 2 | 1.1 | even | 1 | trivial | ||
2450.2.a.d.1.1 | 1 | 35.19 | odd | 6 | |||
2450.2.a.n.1.1 | 1 | 35.9 | even | 6 | |||
2450.2.c.b.99.1 | 2 | 35.23 | odd | 12 | |||
2450.2.c.b.99.2 | 2 | 35.2 | odd | 12 | |||
2450.2.c.n.99.1 | 2 | 35.33 | even | 12 | |||
2450.2.c.n.99.2 | 2 | 35.12 | even | 12 | |||
3920.2.a.j.1.1 | 1 | 28.19 | even | 6 | |||
3920.2.a.bg.1.1 | 1 | 28.23 | odd | 6 | |||
4410.2.a.i.1.1 | 1 | 21.5 | even | 6 | |||
4410.2.a.s.1.1 | 1 | 21.2 | odd | 6 |