Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.590892974957\) |
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 | 47.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.2.c.b.63.1 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 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 | ||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 2.00000 | + | 3.46410i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −3.00000 | −0.948683 | ||||||||
\(11\) | −6.00000 | −1.80907 | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 1.00000 | − | 1.73205i | 0.288675 | − | 0.500000i | ||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | 4.00000 | 1.06904 | ||||||||
\(15\) | 3.00000 | − | 5.19615i | 0.774597 | − | 1.34164i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | −4.00000 | + | 6.92820i | −0.872872 | + | 1.51186i | ||||
\(22\) | −3.00000 | + | 5.19615i | −0.639602 | + | 1.10782i | ||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | −1.00000 | − | 1.73205i | −0.204124 | − | 0.353553i | ||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 2.00000 | − | 3.46410i | 0.377964 | − | 0.654654i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −3.00000 | − | 5.19615i | −0.547723 | − | 0.948683i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −6.00000 | − | 10.3923i | −1.04447 | − | 1.80907i | ||||
\(34\) | 1.50000 | + | 2.59808i | 0.257248 | + | 0.445566i | ||||
\(35\) | 6.00000 | − | 10.3923i | 1.01419 | − | 1.75662i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.50000 | + | 2.59808i | 0.904194 | + | 0.427121i | ||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 4.00000 | + | 6.92820i | 0.617213 | + | 1.06904i | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 3.00000 | + | 5.19615i | 0.452267 | + | 0.783349i | ||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | −2.00000 | −0.288675 | ||||||||
\(49\) | −4.50000 | + | 7.79423i | −0.642857 | + | 1.11346i | ||||
\(50\) | 2.00000 | + | 3.46410i | 0.282843 | + | 0.489898i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 2.00000 | − | 3.46410i | 0.272166 | − | 0.471405i | ||||
\(55\) | 9.00000 | + | 15.5885i | 1.21356 | + | 2.10195i | ||||
\(56\) | −2.00000 | − | 3.46410i | −0.267261 | − | 0.462910i | ||||
\(57\) | 2.00000 | − | 3.46410i | 0.264906 | − | 0.458831i | ||||
\(58\) | 1.50000 | − | 2.59808i | 0.196960 | − | 0.341144i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | −6.00000 | −0.774597 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 1.00000 | − | 1.73205i | 0.127000 | − | 0.219971i | ||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | −12.0000 | −1.47710 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 6.00000 | + | 10.3923i | 0.722315 | + | 1.25109i | ||||
\(70\) | −6.00000 | − | 10.3923i | −0.717137 | − | 1.24212i | ||||
\(71\) | 6.00000 | + | 10.3923i | 0.712069 | + | 1.23334i | 0.964079 | + | 0.265615i | \(0.0855750\pi\) |
−0.252010 | + | 0.967725i | \(0.581092\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | 5.00000 | − | 3.46410i | 0.581238 | − | 0.402694i | ||||
\(75\) | −8.00000 | −0.923760 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | −12.0000 | − | 20.7846i | −1.36753 | − | 2.36863i | ||||
\(78\) | −2.00000 | − | 3.46410i | −0.226455 | − | 0.392232i | ||||
\(79\) | −7.00000 | − | 12.1244i | −0.787562 | − | 1.36410i | −0.927457 | − | 0.373930i | \(-0.878010\pi\) |
0.139895 | − | 0.990166i | \(-0.455323\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | −3.00000 | + | 5.19615i | −0.329293 | + | 0.570352i | −0.982372 | − | 0.186938i | \(-0.940144\pi\) |
0.653079 | + | 0.757290i | \(0.273477\pi\) | |||||||
\(84\) | 8.00000 | 0.872872 | ||||||||
\(85\) | 9.00000 | 0.976187 | ||||||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | ||||
\(88\) | 6.00000 | 0.639602 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 1.50000 | − | 2.59808i | 0.158114 | − | 0.273861i | ||||
\(91\) | 4.00000 | − | 6.92820i | 0.419314 | − | 0.726273i | ||||
\(92\) | −3.00000 | − | 5.19615i | −0.312772 | − | 0.541736i | ||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | −1.00000 | + | 1.73205i | −0.102062 | + | 0.176777i | ||||
\(97\) | −13.0000 | −1.31995 | −0.659975 | − | 0.751288i | \(-0.729433\pi\) | ||||
−0.659975 | + | 0.751288i | \(0.729433\pi\) | |||||||
\(98\) | 4.50000 | + | 7.79423i | 0.454569 | + | 0.787336i | ||||
\(99\) | 3.00000 | − | 5.19615i | 0.301511 | − | 0.522233i | ||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 3.00000 | 0.298511 | 0.149256 | − | 0.988799i | \(-0.452312\pi\) | ||||
0.149256 | + | 0.988799i | \(0.452312\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 1.00000 | + | 1.73205i | 0.0980581 | + | 0.169842i | ||||
\(105\) | 24.0000 | 2.34216 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | 0.500000 | − | 0.866025i | 0.0478913 | − | 0.0829502i | −0.841086 | − | 0.540901i | \(-0.818083\pi\) |
0.888977 | + | 0.457951i | \(0.151417\pi\) | |||||||
\(110\) | 18.0000 | 1.71623 | ||||||||
\(111\) | 1.00000 | + | 12.1244i | 0.0949158 | + | 1.15079i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | 9.00000 | − | 15.5885i | 0.846649 | − | 1.46644i | −0.0375328 | − | 0.999295i | \(-0.511950\pi\) |
0.884182 | − | 0.467143i | \(-0.154717\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | −9.00000 | − | 15.5885i | −0.839254 | − | 1.45363i | ||||
\(116\) | −1.50000 | − | 2.59808i | −0.139272 | − | 0.241225i | ||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0000 | −1.10004 | ||||||||
\(120\) | −3.00000 | + | 5.19615i | −0.273861 | + | 0.474342i | ||||
\(121\) | 25.0000 | 2.27273 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 3.00000 | − | 5.19615i | 0.270501 | − | 0.468521i | ||||
\(124\) | −1.00000 | − | 1.73205i | −0.0898027 | − | 0.155543i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | −2.00000 | + | 3.46410i | −0.178174 | + | 0.308607i | ||||
\(127\) | 5.00000 | − | 8.66025i | 0.443678 | − | 0.768473i | −0.554281 | − | 0.832330i | \(-0.687007\pi\) |
0.997959 | + | 0.0638564i | \(0.0203400\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −4.00000 | − | 6.92820i | −0.352180 | − | 0.609994i | ||||
\(130\) | 3.00000 | + | 5.19615i | 0.263117 | + | 0.455733i | ||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | −6.00000 | + | 10.3923i | −0.522233 | + | 0.904534i | ||||
\(133\) | 4.00000 | − | 6.92820i | 0.346844 | − | 0.600751i | ||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | −6.00000 | − | 10.3923i | −0.516398 | − | 0.894427i | ||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | 3.00000 | 0.256307 | 0.128154 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | −1.00000 | + | 1.73205i | −0.0848189 | + | 0.146911i | −0.905314 | − | 0.424743i | \(-0.860365\pi\) |
0.820495 | + | 0.571654i | \(0.193698\pi\) | |||||||
\(140\) | −12.0000 | −1.01419 | ||||||||
\(141\) | −6.00000 | − | 10.3923i | −0.505291 | − | 0.875190i | ||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 6.00000 | + | 10.3923i | 0.501745 | + | 0.869048i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −4.50000 | − | 7.79423i | −0.373705 | − | 0.647275i | ||||
\(146\) | −5.00000 | + | 8.66025i | −0.413803 | + | 0.716728i | ||||
\(147\) | −18.0000 | −1.48461 | ||||||||
\(148\) | −0.500000 | − | 6.06218i | −0.0410997 | − | 0.498308i | ||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | −4.00000 | + | 6.92820i | −0.326599 | + | 0.565685i | ||||
\(151\) | 11.0000 | + | 19.0526i | 0.895167 | + | 1.55048i | 0.833597 | + | 0.552372i | \(0.186277\pi\) |
0.0615699 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | −24.0000 | −1.93398 | ||||||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −5.50000 | + | 9.52628i | −0.438948 | + | 0.760280i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −14.0000 | −1.11378 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | 1.50000 | − | 2.59808i | 0.118585 | − | 0.205396i | ||||
\(161\) | 12.0000 | + | 20.7846i | 0.945732 | + | 1.63806i | ||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | 8.00000 | − | 13.8564i | 0.626608 | − | 1.08532i | −0.361619 | − | 0.932326i | \(-0.617776\pi\) |
0.988227 | − | 0.152992i | \(-0.0488907\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | −18.0000 | + | 31.1769i | −1.40130 | + | 2.42712i | ||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −6.00000 | − | 10.3923i | −0.464294 | − | 0.804181i | 0.534875 | − | 0.844931i | \(-0.320359\pi\) |
−0.999169 | + | 0.0407502i | \(0.987025\pi\) | |||||||
\(168\) | 4.00000 | − | 6.92820i | 0.308607 | − | 0.534522i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 4.50000 | − | 7.79423i | 0.345134 | − | 0.597790i | ||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | −16.0000 | −1.20949 | ||||||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.50000 | + | 2.59808i | 0.112430 | + | 0.194734i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −1.50000 | − | 2.59808i | −0.111803 | − | 0.193649i | ||||
\(181\) | 0.500000 | + | 0.866025i | 0.0371647 | + | 0.0643712i | 0.884009 | − | 0.467469i | \(-0.154834\pi\) |
−0.846845 | + | 0.531840i | \(0.821501\pi\) | |||||||
\(182\) | −4.00000 | − | 6.92820i | −0.296500 | − | 0.513553i | ||||
\(183\) | −1.00000 | + | 1.73205i | −0.0739221 | + | 0.128037i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −1.50000 | − | 18.1865i | −0.110282 | − | 1.33710i | ||||
\(186\) | 4.00000 | 0.293294 | ||||||||
\(187\) | 9.00000 | − | 15.5885i | 0.658145 | − | 1.13994i | ||||
\(188\) | 3.00000 | + | 5.19615i | 0.218797 | + | 0.378968i | ||||
\(189\) | 8.00000 | + | 13.8564i | 0.581914 | + | 1.00791i | ||||
\(190\) | 3.00000 | + | 5.19615i | 0.217643 | + | 0.376969i | ||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | 1.00000 | + | 1.73205i | 0.0721688 | + | 0.125000i | ||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | −6.50000 | + | 11.2583i | −0.466673 | + | 0.808301i | ||||
\(195\) | −12.0000 | −0.859338 | ||||||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | −1.50000 | + | 2.59808i | −0.106871 | + | 0.185105i | −0.914501 | − | 0.404584i | \(-0.867416\pi\) |
0.807630 | + | 0.589689i | \(0.200750\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 2.00000 | − | 3.46410i | 0.141421 | − | 0.244949i | ||||
\(201\) | 2.00000 | − | 3.46410i | 0.141069 | − | 0.244339i | ||||
\(202\) | 1.50000 | − | 2.59808i | 0.105540 | − | 0.182800i | ||||
\(203\) | 6.00000 | + | 10.3923i | 0.421117 | + | 0.729397i | ||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | −2.00000 | + | 3.46410i | −0.139347 | + | 0.241355i | ||||
\(207\) | −3.00000 | + | 5.19615i | −0.208514 | + | 0.361158i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 6.00000 | + | 10.3923i | 0.415029 | + | 0.718851i | ||||
\(210\) | 12.0000 | − | 20.7846i | 0.828079 | − | 1.43427i | ||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | −12.0000 | + | 20.7846i | −0.822226 | + | 1.42414i | ||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 6.00000 | + | 10.3923i | 0.409197 | + | 0.708749i | ||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | 4.00000 | + | 6.92820i | 0.271538 | + | 0.470317i | ||||
\(218\) | −0.500000 | − | 0.866025i | −0.0338643 | − | 0.0586546i | ||||
\(219\) | −10.0000 | − | 17.3205i | −0.675737 | − | 1.17041i | ||||
\(220\) | 9.00000 | − | 15.5885i | 0.606780 | − | 1.05097i | ||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 11.0000 | + | 5.19615i | 0.738272 | + | 0.348743i | ||||
\(223\) | 14.0000 | 0.937509 | 0.468755 | − | 0.883328i | \(-0.344703\pi\) | ||||
0.468755 | + | 0.883328i | \(0.344703\pi\) | |||||||
\(224\) | −2.00000 | + | 3.46410i | −0.133631 | + | 0.231455i | ||||
\(225\) | −2.00000 | − | 3.46410i | −0.133333 | − | 0.230940i | ||||
\(226\) | −9.00000 | − | 15.5885i | −0.598671 | − | 1.03693i | ||||
\(227\) | 9.00000 | + | 15.5885i | 0.597351 | + | 1.03464i | 0.993210 | + | 0.116331i | \(0.0371134\pi\) |
−0.395860 | + | 0.918311i | \(0.629553\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −5.50000 | − | 9.52628i | −0.363450 | − | 0.629514i | 0.625076 | − | 0.780564i | \(-0.285068\pi\) |
−0.988526 | + | 0.151050i | \(0.951735\pi\) | |||||||
\(230\) | −18.0000 | −1.18688 | ||||||||
\(231\) | 24.0000 | − | 41.5692i | 1.57908 | − | 2.73505i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | −9.00000 | −0.589610 | −0.294805 | − | 0.955557i | \(-0.595255\pi\) | ||||
−0.294805 | + | 0.955557i | \(0.595255\pi\) | |||||||
\(234\) | 1.00000 | − | 1.73205i | 0.0653720 | − | 0.113228i | ||||
\(235\) | 9.00000 | + | 15.5885i | 0.587095 | + | 1.01688i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.0000 | − | 24.2487i | 0.909398 | − | 1.57512i | ||||
\(238\) | −6.00000 | + | 10.3923i | −0.388922 | + | 0.673633i | ||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | −7.00000 | − | 12.1244i | −0.450910 | − | 0.780998i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | 12.5000 | − | 21.6506i | 0.803530 | − | 1.39176i | ||||
\(243\) | −5.00000 | + | 8.66025i | −0.320750 | + | 0.555556i | ||||
\(244\) | 0.500000 | − | 0.866025i | 0.0320092 | − | 0.0554416i | ||||
\(245\) | 27.0000 | 1.72497 | ||||||||
\(246\) | −3.00000 | − | 5.19615i | −0.191273 | − | 0.331295i | ||||
\(247\) | −2.00000 | + | 3.46410i | −0.127257 | + | 0.220416i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | −1.50000 | + | 2.59808i | −0.0948683 | + | 0.164317i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.00000 | + | 3.46410i | 0.125988 | + | 0.218218i | ||||
\(253\) | −36.0000 | −2.26330 | ||||||||
\(254\) | −5.00000 | − | 8.66025i | −0.313728 | − | 0.543393i | ||||
\(255\) | 9.00000 | + | 15.5885i | 0.563602 | + | 0.976187i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.5000 | + | 23.3827i | −0.842107 | + | 1.45857i | 0.0460033 | + | 0.998941i | \(0.485352\pi\) |
−0.888110 | + | 0.459631i | \(0.847982\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 2.00000 | + | 24.2487i | 0.124274 | + | 1.50674i | ||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | −1.50000 | + | 2.59808i | −0.0928477 | + | 0.160817i | ||||
\(262\) | 9.00000 | + | 15.5885i | 0.556022 | + | 0.963058i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 6.00000 | + | 10.3923i | 0.369274 | + | 0.639602i | ||||
\(265\) | −18.0000 | −1.10573 | ||||||||
\(266\) | −4.00000 | − | 6.92820i | −0.245256 | − | 0.424795i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | −12.0000 | −0.730297 | ||||||||
\(271\) | 5.00000 | − | 8.66025i | 0.303728 | − | 0.526073i | −0.673249 | − | 0.739416i | \(-0.735102\pi\) |
0.976977 | + | 0.213343i | \(0.0684351\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | 1.50000 | − | 2.59808i | 0.0906183 | − | 0.156956i | ||||
\(275\) | 12.0000 | − | 20.7846i | 0.723627 | − | 1.25336i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 1.00000 | + | 1.73205i | 0.0599760 | + | 0.103882i | ||||
\(279\) | −1.00000 | + | 1.73205i | −0.0598684 | + | 0.103695i | ||||
\(280\) | −6.00000 | + | 10.3923i | −0.358569 | + | 0.621059i | ||||
\(281\) | −7.50000 | + | 12.9904i | −0.447412 | + | 0.774941i | −0.998217 | − | 0.0596933i | \(-0.980988\pi\) |
0.550804 | + | 0.834634i | \(0.314321\pi\) | |||||||
\(282\) | −12.0000 | −0.714590 | ||||||||
\(283\) | 8.00000 | + | 13.8564i | 0.475551 | + | 0.823678i | 0.999608 | − | 0.0280052i | \(-0.00891551\pi\) |
−0.524057 | + | 0.851683i | \(0.675582\pi\) | |||||||
\(284\) | 6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 6.00000 | − | 10.3923i | 0.354169 | − | 0.613438i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | −13.0000 | − | 22.5167i | −0.762073 | − | 1.31995i | ||||
\(292\) | 5.00000 | + | 8.66025i | 0.292603 | + | 0.506803i | ||||
\(293\) | −1.50000 | − | 2.59808i | −0.0876309 | − | 0.151781i | 0.818878 | − | 0.573967i | \(-0.194596\pi\) |
−0.906509 | + | 0.422186i | \(0.861263\pi\) | |||||||
\(294\) | −9.00000 | + | 15.5885i | −0.524891 | + | 0.909137i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.50000 | − | 2.59808i | −0.319681 | − | 0.151010i | ||||
\(297\) | −24.0000 | −1.39262 | ||||||||
\(298\) | −10.5000 | + | 18.1865i | −0.608249 | + | 1.05352i | ||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 4.00000 | + | 6.92820i | 0.230940 | + | 0.400000i | ||||
\(301\) | −8.00000 | − | 13.8564i | −0.461112 | − | 0.798670i | ||||
\(302\) | 22.0000 | 1.26596 | ||||||||
\(303\) | 3.00000 | + | 5.19615i | 0.172345 | + | 0.298511i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 1.50000 | − | 2.59808i | 0.0858898 | − | 0.148765i | ||||
\(306\) | −3.00000 | −0.171499 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | −12.0000 | + | 20.7846i | −0.683763 | + | 1.18431i | ||||
\(309\) | −4.00000 | − | 6.92820i | −0.227552 | − | 0.394132i | ||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | −2.00000 | + | 3.46410i | −0.113228 | + | 0.196116i | ||||
\(313\) | 6.50000 | − | 11.2583i | 0.367402 | − | 0.636358i | −0.621757 | − | 0.783210i | \(-0.713581\pi\) |
0.989158 | + | 0.146852i | \(0.0469141\pi\) | |||||||
\(314\) | 5.50000 | + | 9.52628i | 0.310383 | + | 0.537599i | ||||
\(315\) | 6.00000 | + | 10.3923i | 0.338062 | + | 0.585540i | ||||
\(316\) | −7.00000 | + | 12.1244i | −0.393781 | + | 0.682048i | ||||
\(317\) | 10.5000 | − | 18.1865i | 0.589739 | − | 1.02146i | −0.404528 | − | 0.914526i | \(-0.632564\pi\) |
0.994266 | − | 0.106932i | \(-0.0341026\pi\) | |||||||
\(318\) | 6.00000 | − | 10.3923i | 0.336463 | − | 0.582772i | ||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | −1.50000 | − | 2.59808i | −0.0838525 | − | 0.145237i | ||||
\(321\) | −12.0000 | + | 20.7846i | −0.669775 | + | 1.16008i | ||||
\(322\) | 24.0000 | 1.33747 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | −8.00000 | − | 13.8564i | −0.443079 | − | 0.767435i | ||||
\(327\) | 2.00000 | 0.110600 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | −12.0000 | − | 20.7846i | −0.661581 | − | 1.14589i | ||||
\(330\) | 18.0000 | + | 31.1769i | 0.990867 | + | 1.71623i | ||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | −5.00000 | + | 3.46410i | −0.273998 | + | 0.189832i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −3.00000 | + | 5.19615i | −0.163908 | + | 0.283896i | ||||
\(336\) | −4.00000 | − | 6.92820i | −0.218218 | − | 0.377964i | ||||
\(337\) | 12.5000 | + | 21.6506i | 0.680918 | + | 1.17939i | 0.974701 | + | 0.223513i | \(0.0717525\pi\) |
−0.293783 | + | 0.955872i | \(0.594914\pi\) | |||||||
\(338\) | −4.50000 | − | 7.79423i | −0.244768 | − | 0.423950i | ||||
\(339\) | 36.0000 | 1.95525 | ||||||||
\(340\) | −4.50000 | − | 7.79423i | −0.244047 | − | 0.422701i | ||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 1.00000 | − | 1.73205i | 0.0540738 | − | 0.0936586i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 18.0000 | − | 31.1769i | 0.969087 | − | 1.67851i | ||||
\(346\) | −10.5000 | − | 18.1865i | −0.564483 | − | 0.977714i | ||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | 0.500000 | − | 0.866025i | 0.0267644 | − | 0.0463573i | −0.852333 | − | 0.523000i | \(-0.824813\pi\) |
0.879097 | + | 0.476642i | \(0.158146\pi\) | |||||||
\(350\) | −8.00000 | + | 13.8564i | −0.427618 | + | 0.740656i | ||||
\(351\) | −4.00000 | − | 6.92820i | −0.213504 | − | 0.369800i | ||||
\(352\) | −3.00000 | − | 5.19615i | −0.159901 | − | 0.276956i | ||||
\(353\) | 10.5000 | − | 18.1865i | 0.558859 | − | 0.967972i | −0.438733 | − | 0.898617i | \(-0.644573\pi\) |
0.997592 | − | 0.0693543i | \(-0.0220939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.0000 | − | 31.1769i | 0.955341 | − | 1.65470i | ||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | −12.0000 | − | 20.7846i | −0.635107 | − | 1.10004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −3.00000 | −0.158114 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 1.00000 | 0.0525588 | ||||||||
\(363\) | 25.0000 | + | 43.3013i | 1.31216 | + | 2.27273i | ||||
\(364\) | −8.00000 | −0.419314 | ||||||||
\(365\) | 15.0000 | + | 25.9808i | 0.785136 | + | 1.35990i | ||||
\(366\) | 1.00000 | + | 1.73205i | 0.0522708 | + | 0.0905357i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −3.00000 | + | 5.19615i | −0.156386 | + | 0.270868i | ||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | −16.5000 | − | 7.79423i | −0.857794 | − | 0.405203i | ||||
\(371\) | 24.0000 | 1.24602 | ||||||||
\(372\) | 2.00000 | − | 3.46410i | 0.103695 | − | 0.179605i | ||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | −3.00000 | − | 5.19615i | −0.154919 | − | 0.268328i | ||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −3.00000 | − | 5.19615i | −0.154508 | − | 0.267615i | ||||
\(378\) | 16.0000 | 0.822951 | ||||||||
\(379\) | 8.00000 | − | 13.8564i | 0.410932 | − | 0.711756i | −0.584060 | − | 0.811711i | \(-0.698537\pi\) |
0.994992 | + | 0.0999550i | \(0.0318699\pi\) | |||||||
\(380\) | 6.00000 | 0.307794 | ||||||||
\(381\) | 20.0000 | 1.02463 | ||||||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | −6.00000 | − | 10.3923i | −0.306586 | − | 0.531022i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.977613 | + | 0.210411i | \(0.932520\pi\) | |||||||
\(384\) | 2.00000 | 0.102062 | ||||||||
\(385\) | −36.0000 | + | 62.3538i | −1.83473 | + | 3.17785i | ||||
\(386\) | 5.50000 | − | 9.52628i | 0.279943 | − | 0.484875i | ||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 6.50000 | + | 11.2583i | 0.329988 | + | 0.571555i | ||||
\(389\) | 4.50000 | + | 7.79423i | 0.228159 | + | 0.395183i | 0.957263 | − | 0.289220i | \(-0.0933960\pi\) |
−0.729103 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(390\) | −6.00000 | + | 10.3923i | −0.303822 | + | 0.526235i | ||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | 4.50000 | − | 7.79423i | 0.227284 | − | 0.393668i | ||||
\(393\) | −36.0000 | −1.81596 | ||||||||
\(394\) | 1.50000 | + | 2.59808i | 0.0755689 | + | 0.130889i | ||||
\(395\) | −21.0000 | + | 36.3731i | −1.05662 | + | 1.83013i | ||||
\(396\) | −6.00000 | −0.301511 | ||||||||
\(397\) | 35.0000 | 1.75660 | 0.878300 | − | 0.478110i | \(-0.158678\pi\) | ||||
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 4.00000 | − | 6.92820i | 0.200502 | − | 0.347279i | ||||
\(399\) | 16.0000 | 0.801002 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | −2.00000 | − | 3.46410i | −0.0997509 | − | 0.172774i | ||||
\(403\) | −2.00000 | − | 3.46410i | −0.0996271 | − | 0.172559i | ||||
\(404\) | −1.50000 | − | 2.59808i | −0.0746278 | − | 0.129259i | ||||
\(405\) | 16.5000 | − | 28.5788i | 0.819892 | − | 1.42009i | ||||
\(406\) | 12.0000 | 0.595550 | ||||||||
\(407\) | −33.0000 | − | 15.5885i | −1.63575 | − | 0.772691i | ||||
\(408\) | 6.00000 | 0.297044 | ||||||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | 4.50000 | + | 7.79423i | 0.222239 | + | 0.384930i | ||||
\(411\) | 3.00000 | + | 5.19615i | 0.147979 | + | 0.256307i | ||||
\(412\) | 2.00000 | + | 3.46410i | 0.0985329 | + | 0.170664i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.00000 | + | 5.19615i | 0.147442 | + | 0.255377i | ||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 12.0000 | 0.586939 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | −12.0000 | − | 20.7846i | −0.585540 | − | 1.01419i | ||||
\(421\) | −37.0000 | −1.80327 | −0.901635 | − | 0.432498i | \(-0.857632\pi\) | ||||
−0.901635 | + | 0.432498i | \(0.857632\pi\) | |||||||
\(422\) | −8.00000 | + | 13.8564i | −0.389434 | + | 0.674519i | ||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | −6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | ||||
\(426\) | 12.0000 | + | 20.7846i | 0.581402 | + | 1.00702i | ||||
\(427\) | −2.00000 | + | 3.46410i | −0.0967868 | + | 0.167640i | ||||
\(428\) | 6.00000 | − | 10.3923i | 0.290021 | − | 0.502331i | ||||
\(429\) | −12.0000 | + | 20.7846i | −0.579365 | + | 1.00349i | ||||
\(430\) | 12.0000 | 0.578691 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −2.00000 | + | 3.46410i | −0.0962250 | + | 0.166667i | ||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 8.00000 | 0.384012 | ||||||||
\(435\) | 9.00000 | − | 15.5885i | 0.431517 | − | 0.747409i | ||||
\(436\) | −1.00000 | −0.0478913 | ||||||||
\(437\) | −6.00000 | − | 10.3923i | −0.287019 | − | 0.497131i | ||||
\(438\) | −20.0000 | −0.955637 | ||||||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | −9.00000 | − | 15.5885i | −0.429058 | − | 0.743151i | ||||
\(441\) | −4.50000 | − | 7.79423i | −0.214286 | − | 0.371154i | ||||
\(442\) | 3.00000 | − | 5.19615i | 0.142695 | − | 0.247156i | ||||
\(443\) | −24.0000 | −1.14027 | −0.570137 | − | 0.821549i | \(-0.693110\pi\) | ||||
−0.570137 | + | 0.821549i | \(0.693110\pi\) | |||||||
\(444\) | 10.0000 | − | 6.92820i | 0.474579 | − | 0.328798i | ||||
\(445\) | 9.00000 | 0.426641 | ||||||||
\(446\) | 7.00000 | − | 12.1244i | 0.331460 | − | 0.574105i | ||||
\(447\) | −21.0000 | − | 36.3731i | −0.993266 | − | 1.72039i | ||||
\(448\) | 2.00000 | + | 3.46410i | 0.0944911 | + | 0.163663i | ||||
\(449\) | −3.00000 | − | 5.19615i | −0.141579 | − | 0.245222i | 0.786513 | − | 0.617574i | \(-0.211885\pi\) |
−0.928091 | + | 0.372353i | \(0.878551\pi\) | |||||||
\(450\) | −4.00000 | −0.188562 | ||||||||
\(451\) | 9.00000 | + | 15.5885i | 0.423793 | + | 0.734032i | ||||
\(452\) | −18.0000 | −0.846649 | ||||||||
\(453\) | −22.0000 | + | 38.1051i | −1.03365 | + | 1.79033i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | −24.0000 | −1.12514 | ||||||||
\(456\) | −2.00000 | + | 3.46410i | −0.0936586 | + | 0.162221i | ||||
\(457\) | 18.5000 | + | 32.0429i | 0.865393 | + | 1.49891i | 0.866656 | + | 0.498906i | \(0.166265\pi\) |
−0.00126243 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(458\) | −11.0000 | −0.513996 | ||||||||
\(459\) | −6.00000 | + | 10.3923i | −0.280056 | + | 0.485071i | ||||
\(460\) | −9.00000 | + | 15.5885i | −0.419627 | + | 0.726816i | ||||
\(461\) | 15.0000 | − | 25.9808i | 0.698620 | − | 1.21004i | −0.270326 | − | 0.962769i | \(-0.587131\pi\) |
0.968945 | − | 0.247276i | \(-0.0795353\pi\) | |||||||
\(462\) | −24.0000 | − | 41.5692i | −1.11658 | − | 1.93398i | ||||
\(463\) | 8.00000 | + | 13.8564i | 0.371792 | + | 0.643962i | 0.989841 | − | 0.142177i | \(-0.0454103\pi\) |
−0.618050 | + | 0.786139i | \(0.712077\pi\) | |||||||
\(464\) | −1.50000 | + | 2.59808i | −0.0696358 | + | 0.120613i | ||||
\(465\) | 6.00000 | − | 10.3923i | 0.278243 | − | 0.481932i | ||||
\(466\) | −4.50000 | + | 7.79423i | −0.208458 | + | 0.361061i | ||||
\(467\) | 36.0000 | 1.66588 | 0.832941 | − | 0.553362i | \(-0.186655\pi\) | ||||
0.832941 | + | 0.553362i | \(0.186655\pi\) | |||||||
\(468\) | −1.00000 | − | 1.73205i | −0.0462250 | − | 0.0800641i | ||||
\(469\) | 4.00000 | − | 6.92820i | 0.184703 | − | 0.319915i | ||||
\(470\) | 18.0000 | 0.830278 | ||||||||
\(471\) | −22.0000 | −1.01371 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.0000 | 1.10352 | ||||||||
\(474\) | −14.0000 | − | 24.2487i | −0.643041 | − | 1.11378i | ||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | 6.00000 | + | 10.3923i | 0.275010 | + | 0.476331i | ||||
\(477\) | 3.00000 | + | 5.19615i | 0.137361 | + | 0.237915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0000 | + | 20.7846i | −0.548294 | + | 0.949673i | 0.450098 | + | 0.892979i | \(0.351389\pi\) |
−0.998392 | + | 0.0566937i | \(0.981944\pi\) | |||||||
\(480\) | 6.00000 | 0.273861 | ||||||||
\(481\) | −1.00000 | − | 12.1244i | −0.0455961 | − | 0.552823i | ||||
\(482\) | −14.0000 | −0.637683 | ||||||||
\(483\) | −24.0000 | + | 41.5692i | −1.09204 | + | 1.89146i | ||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | 19.5000 | + | 33.7750i | 0.885449 | + | 1.53364i | ||||
\(486\) | 5.00000 | + | 8.66025i | 0.226805 | + | 0.392837i | ||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | −0.500000 | − | 0.866025i | −0.0226339 | − | 0.0392031i | ||||
\(489\) | 32.0000 | 1.44709 | ||||||||
\(490\) | 13.5000 | − | 23.3827i | 0.609868 | − | 1.05632i | ||||
\(491\) | 6.00000 | 0.270776 | 0.135388 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135388 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(492\) | −6.00000 | −0.270501 | ||||||||
\(493\) | −4.50000 | + | 7.79423i | −0.202670 | + | 0.351034i | ||||
\(494\) | 2.00000 | + | 3.46410i | 0.0899843 | + | 0.155857i | ||||
\(495\) | −18.0000 | −0.809040 | ||||||||
\(496\) | −1.00000 | + | 1.73205i | −0.0449013 | + | 0.0777714i | ||||
\(497\) | −24.0000 | + | 41.5692i | −1.07655 | + | 1.86463i | ||||
\(498\) | −6.00000 | + | 10.3923i | −0.268866 | + | 0.465690i | ||||
\(499\) | −7.00000 | − | 12.1244i | −0.313363 | − | 0.542761i | 0.665725 | − | 0.746197i | \(-0.268122\pi\) |
−0.979088 | + | 0.203436i | \(0.934789\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 12.0000 | − | 20.7846i | 0.536120 | − | 0.928588i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.0000 | + | 25.9808i | −0.668817 | + | 1.15842i | 0.309418 | + | 0.950926i | \(0.399866\pi\) |
−0.978235 | + | 0.207499i | \(0.933468\pi\) | |||||||
\(504\) | 4.00000 | 0.178174 | ||||||||
\(505\) | −4.50000 | − | 7.79423i | −0.200247 | − | 0.346839i | ||||
\(506\) | −18.0000 | + | 31.1769i | −0.800198 | + | 1.38598i | ||||
\(507\) | 18.0000 | 0.799408 | ||||||||
\(508\) | −10.0000 | −0.443678 | ||||||||
\(509\) | −13.5000 | + | 23.3827i | −0.598377 | + | 1.03642i | 0.394684 | + | 0.918817i | \(0.370854\pi\) |
−0.993061 | + | 0.117602i | \(0.962479\pi\) | |||||||
\(510\) | 18.0000 | 0.797053 | ||||||||
\(511\) | −20.0000 | − | 34.6410i | −0.884748 | − | 1.53243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.00000 | − | 6.92820i | −0.176604 | − | 0.305888i | ||||
\(514\) | 13.5000 | + | 23.3827i | 0.595459 | + | 1.03137i | ||||
\(515\) | 6.00000 | + | 10.3923i | 0.264392 | + | 0.457940i | ||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 36.0000 | 1.58328 | ||||||||
\(518\) | 22.0000 | + | 10.3923i | 0.966625 | + | 0.456612i | ||||
\(519\) | 42.0000 | 1.84360 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | −3.00000 | − | 5.19615i | −0.131432 | − | 0.227648i | 0.792797 | − | 0.609486i | \(-0.208624\pi\) |
−0.924229 | + | 0.381839i | \(0.875291\pi\) | |||||||
\(522\) | 1.50000 | + | 2.59808i | 0.0656532 | + | 0.113715i | ||||
\(523\) | −13.0000 | − | 22.5167i | −0.568450 | − | 0.984585i | −0.996719 | − | 0.0809336i | \(-0.974210\pi\) |
0.428269 | − | 0.903651i | \(-0.359124\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | −16.0000 | − | 27.7128i | −0.698297 | − | 1.20949i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.00000 | + | 5.19615i | −0.130682 | + | 0.226348i | ||||
\(528\) | 12.0000 | 0.522233 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | −9.00000 | + | 15.5885i | −0.390935 | + | 0.677119i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.00000 | −0.346844 | ||||||||
\(533\) | −3.00000 | + | 5.19615i | −0.129944 | + | 0.225070i | ||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | 18.0000 | − | 31.1769i | 0.778208 | − | 1.34790i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.00000 | − | 15.5885i | 0.388018 | − | 0.672066i | ||||
\(539\) | 27.0000 | − | 46.7654i | 1.16297 | − | 2.01433i | ||||
\(540\) | −6.00000 | + | 10.3923i | −0.258199 | + | 0.447214i | ||||
\(541\) | 35.0000 | 1.50477 | 0.752384 | − | 0.658725i | \(-0.228904\pi\) | ||||
0.752384 | + | 0.658725i | \(0.228904\pi\) | |||||||
\(542\) | −5.00000 | − | 8.66025i | −0.214768 | − | 0.371990i | ||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | −3.00000 | −0.128624 | ||||||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 8.00000 | − | 13.8564i | 0.342368 | − | 0.592999i | ||||
\(547\) | −22.0000 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(548\) | −1.50000 | − | 2.59808i | −0.0640768 | − | 0.110984i | ||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −12.0000 | − | 20.7846i | −0.511682 | − | 0.886259i | ||||
\(551\) | −3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | ||||
\(552\) | −6.00000 | − | 10.3923i | −0.255377 | − | 0.442326i | ||||
\(553\) | 28.0000 | − | 48.4974i | 1.19068 | − | 2.06232i | ||||
\(554\) | 1.00000 | 0.0424859 | ||||||||
\(555\) | 30.0000 | − | 20.7846i | 1.27343 | − | 0.882258i | ||||
\(556\) | 2.00000 | 0.0848189 | ||||||||
\(557\) | 16.5000 | − | 28.5788i | 0.699127 | − | 1.21092i | −0.269642 | − | 0.962961i | \(-0.586905\pi\) |
0.968769 | − | 0.247964i | \(-0.0797613\pi\) | |||||||
\(558\) | 1.00000 | + | 1.73205i | 0.0423334 | + | 0.0733236i | ||||
\(559\) | 4.00000 | + | 6.92820i | 0.169182 | + | 0.293032i | ||||
\(560\) | 6.00000 | + | 10.3923i | 0.253546 | + | 0.439155i | ||||
\(561\) | 36.0000 | 1.51992 | ||||||||
\(562\) | 7.50000 | + | 12.9904i | 0.316368 | + | 0.547966i | ||||
\(563\) | 6.00000 | 0.252870 | 0.126435 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126435 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(564\) | −6.00000 | + | 10.3923i | −0.252646 | + | 0.437595i | ||||
\(565\) | −54.0000 | −2.27180 | ||||||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | −22.0000 | + | 38.1051i | −0.923913 | + | 1.60026i | ||||
\(568\) | −6.00000 | − | 10.3923i | −0.251754 | − | 0.436051i | ||||
\(569\) | 3.00000 | 0.125767 | 0.0628833 | − | 0.998021i | \(-0.479970\pi\) | ||||
0.0628833 | + | 0.998021i | \(0.479970\pi\) | |||||||
\(570\) | −6.00000 | + | 10.3923i | −0.251312 | + | 0.435286i | ||||
\(571\) | −19.0000 | + | 32.9090i | −0.795125 | + | 1.37720i | 0.127634 | + | 0.991821i | \(0.459262\pi\) |
−0.922760 | + | 0.385376i | \(0.874072\pi\) | |||||||
\(572\) | 6.00000 | − | 10.3923i | 0.250873 | − | 0.434524i | ||||
\(573\) | −6.00000 | − | 10.3923i | −0.250654 | − | 0.434145i | ||||
\(574\) | −6.00000 | − | 10.3923i | −0.250435 | − | 0.433766i | ||||
\(575\) | −12.0000 | + | 20.7846i | −0.500435 | + | 0.866778i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 17.0000 | − | 29.4449i | 0.707719 | − | 1.22581i | −0.257982 | − | 0.966150i | \(-0.583058\pi\) |
0.965701 | − | 0.259656i | \(-0.0836092\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 11.0000 | + | 19.0526i | 0.457144 | + | 0.791797i | ||||
\(580\) | −4.50000 | + | 7.79423i | −0.186852 | + | 0.323638i | ||||
\(581\) | −24.0000 | −0.995688 | ||||||||
\(582\) | −26.0000 | −1.07773 | ||||||||
\(583\) | −18.0000 | + | 31.1769i | −0.745484 | + | 1.29122i | ||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | −3.00000 | − | 5.19615i | −0.124035 | − | 0.214834i | ||||
\(586\) | −3.00000 | −0.123929 | ||||||||
\(587\) | −9.00000 | − | 15.5885i | −0.371470 | − | 0.643404i | 0.618322 | − | 0.785925i | \(-0.287813\pi\) |
−0.989792 | + | 0.142520i | \(0.954479\pi\) | |||||||
\(588\) | 9.00000 | + | 15.5885i | 0.371154 | + | 0.642857i | ||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | −5.00000 | + | 3.46410i | −0.205499 | + | 0.142374i | ||||
\(593\) | 27.0000 | 1.10876 | 0.554379 | − | 0.832265i | \(-0.312956\pi\) | ||||
0.554379 | + | 0.832265i | \(0.312956\pi\) | |||||||
\(594\) | −12.0000 | + | 20.7846i | −0.492366 | + | 0.852803i | ||||
\(595\) | 18.0000 | + | 31.1769i | 0.737928 | + | 1.27813i | ||||
\(596\) | 10.5000 | + | 18.1865i | 0.430097 | + | 0.744949i | ||||
\(597\) | 8.00000 | + | 13.8564i | 0.327418 | + | 0.567105i | ||||
\(598\) | −12.0000 | −0.490716 | ||||||||
\(599\) | 3.00000 | + | 5.19615i | 0.122577 | + | 0.212309i | 0.920783 | − | 0.390075i | \(-0.127551\pi\) |
−0.798206 | + | 0.602384i | \(0.794218\pi\) | |||||||
\(600\) | 8.00000 | 0.326599 | ||||||||
\(601\) | 6.50000 | − | 11.2583i | 0.265141 | − | 0.459237i | −0.702460 | − | 0.711723i | \(-0.747915\pi\) |
0.967600 | + | 0.252486i | \(0.0812483\pi\) | |||||||
\(602\) | −16.0000 | −0.652111 | ||||||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 11.0000 | − | 19.0526i | 0.447584 | − | 0.775238i | ||||
\(605\) | −37.5000 | − | 64.9519i | −1.52459 | − | 2.64067i | ||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | 1.00000 | − | 1.73205i | 0.0405554 | − | 0.0702439i | ||||
\(609\) | −12.0000 | + | 20.7846i | −0.486265 | + | 0.842235i | ||||
\(610\) | −1.50000 | − | 2.59808i | −0.0607332 | − | 0.105193i | ||||
\(611\) | 6.00000 | + | 10.3923i | 0.242734 | + | 0.420428i | ||||
\(612\) | −1.50000 | + | 2.59808i | −0.0606339 | + | 0.105021i | ||||
\(613\) | 12.5000 | − | 21.6506i | 0.504870 | − | 0.874461i | −0.495114 | − | 0.868828i | \(-0.664874\pi\) |
0.999984 | − | 0.00563283i | \(-0.00179300\pi\) | |||||||
\(614\) | −14.0000 | + | 24.2487i | −0.564994 | + | 0.978598i | ||||
\(615\) | −18.0000 | −0.725830 | ||||||||
\(616\) | 12.0000 | + | 20.7846i | 0.483494 | + | 0.837436i | ||||
\(617\) | 9.00000 | − | 15.5885i | 0.362326 | − | 0.627568i | −0.626017 | − | 0.779809i | \(-0.715316\pi\) |
0.988343 | + | 0.152242i | \(0.0486493\pi\) | |||||||
\(618\) | −8.00000 | −0.321807 | ||||||||
\(619\) | −40.0000 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(620\) | −3.00000 | + | 5.19615i | −0.120483 | + | 0.208683i | ||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | −0.480770 | ||||||||
\(624\) | 2.00000 | + | 3.46410i | 0.0800641 | + | 0.138675i | ||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | −6.50000 | − | 11.2583i | −0.259792 | − | 0.449973i | ||||
\(627\) | −12.0000 | + | 20.7846i | −0.479234 | + | 0.830057i | ||||
\(628\) | 11.0000 | 0.438948 | ||||||||
\(629\) | −15.0000 | + | 10.3923i | −0.598089 | + | 0.414368i | ||||
\(630\) | 12.0000 | 0.478091 | ||||||||
\(631\) | 5.00000 | − | 8.66025i | 0.199047 | − | 0.344759i | −0.749173 | − | 0.662375i | \(-0.769549\pi\) |
0.948220 | + | 0.317615i | \(0.102882\pi\) | |||||||
\(632\) | 7.00000 | + | 12.1244i | 0.278445 | + | 0.482281i | ||||
\(633\) | −16.0000 | − | 27.7128i | −0.635943 | − | 1.10149i | ||||
\(634\) | −10.5000 | − | 18.1865i | −0.417008 | − | 0.722280i | ||||
\(635\) | −30.0000 | −1.19051 | ||||||||
\(636\) | −6.00000 | − | 10.3923i | −0.237915 | − | 0.412082i | ||||
\(637\) | 18.0000 | 0.713186 | ||||||||
\(638\) | −9.00000 | + | 15.5885i | −0.356313 | + | 0.617153i | ||||
\(639\) | −12.0000 | −0.474713 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | 10.5000 | − | 18.1865i | 0.414725 | − | 0.718325i | −0.580674 | − | 0.814136i | \(-0.697211\pi\) |
0.995400 | + | 0.0958109i | \(0.0305444\pi\) | |||||||
\(642\) | 12.0000 | + | 20.7846i | 0.473602 | + | 0.820303i | ||||
\(643\) | −34.0000 | −1.34083 | −0.670415 | − | 0.741987i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741987i | \(0.733884\pi\) | |||||||
\(644\) | 12.0000 | − | 20.7846i | 0.472866 | − | 0.819028i | ||||
\(645\) | −12.0000 | + | 20.7846i | −0.472500 | + | 0.818393i | ||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | −12.0000 | − | 20.7846i | −0.471769 | − | 0.817127i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(648\) | −5.50000 | − | 9.52628i | −0.216060 | − | 0.374228i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 4.00000 | − | 6.92820i | 0.156893 | − | 0.271746i | ||||
\(651\) | −8.00000 | + | 13.8564i | −0.313545 | + | 0.543075i | ||||
\(652\) | −16.0000 | −0.626608 | ||||||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 54.0000 | 2.10995 | ||||||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 5.00000 | − | 8.66025i | 0.195069 | − | 0.337869i | ||||
\(658\) | −24.0000 | −0.935617 | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | 36.0000 | 1.40130 | ||||||||
\(661\) | 12.5000 | + | 21.6506i | 0.486194 | + | 0.842112i | 0.999874 | − | 0.0158695i | \(-0.00505163\pi\) |
−0.513680 | + | 0.857982i | \(0.671718\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | 6.00000 | + | 10.3923i | 0.233021 | + | 0.403604i | ||||
\(664\) | 3.00000 | − | 5.19615i | 0.116423 | − | 0.201650i | ||||
\(665\) | −24.0000 | −0.930680 | ||||||||
\(666\) | 0.500000 | + | 6.06218i | 0.0193746 | + | 0.234905i | ||||
\(667\) | 18.0000 | 0.696963 | ||||||||
\(668\) | −6.00000 | + | 10.3923i | −0.232147 | + | 0.402090i | ||||
\(669\) | 14.0000 | + | 24.2487i | 0.541271 | + | 0.937509i | ||||
\(670\) | 3.00000 | + | 5.19615i | 0.115900 | + | 0.200745i | ||||
\(671\) | −3.00000 | − | 5.19615i | −0.115814 | − | 0.200595i | ||||
\(672\) | −8.00000 | −0.308607 | ||||||||
\(673\) | 5.00000 | + | 8.66025i | 0.192736 | + | 0.333828i | 0.946156 | − | 0.323711i | \(-0.104931\pi\) |
−0.753420 | + | 0.657539i | \(0.771597\pi\) | |||||||
\(674\) | 25.0000 | 0.962964 | ||||||||
\(675\) | −8.00000 | + | 13.8564i | −0.307920 | + | 0.533333i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 3.00000 | 0.115299 | 0.0576497 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576497 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(678\) | 18.0000 | − | 31.1769i | 0.691286 | − | 1.19734i | ||||
\(679\) | −26.0000 | − | 45.0333i | −0.997788 | − | 1.72822i | ||||
\(680\) | −9.00000 | −0.345134 | ||||||||
\(681\) | −18.0000 | + | 31.1769i | −0.689761 | + | 1.19470i | ||||
\(682\) | −6.00000 | + | 10.3923i | −0.229752 | + | 0.397942i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | −1.00000 | − | 1.73205i | −0.0382360 | − | 0.0662266i | ||||
\(685\) | −4.50000 | − | 7.79423i | −0.171936 | − | 0.297802i | ||||
\(686\) | −4.00000 | + | 6.92820i | −0.152721 | + | 0.264520i | ||||
\(687\) | 11.0000 | − | 19.0526i | 0.419676 | − | 0.726900i | ||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | −18.0000 | − | 31.1769i | −0.685248 | − | 1.18688i | ||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | −21.0000 | −0.798300 | ||||||||
\(693\) | 24.0000 | 0.911685 | ||||||||
\(694\) | 3.00000 | − | 5.19615i | 0.113878 | − | 0.197243i | ||||
\(695\) | 6.00000 | 0.227593 | ||||||||
\(696\) | −3.00000 | − | 5.19615i | −0.113715 | − | 0.196960i | ||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | −0.500000 | − | 0.866025i | −0.0189253 | − | 0.0327795i | ||||
\(699\) | −9.00000 | − | 15.5885i | −0.340411 | − | 0.589610i | ||||
\(700\) | 8.00000 | + | 13.8564i | 0.302372 | + | 0.523723i | ||||
\(701\) | −15.0000 | + | 25.9808i | −0.566542 | + | 0.981280i | 0.430362 | + | 0.902656i | \(0.358386\pi\) |
−0.996904 | + | 0.0786236i | \(0.974947\pi\) | |||||||
\(702\) | −8.00000 | −0.301941 | ||||||||
\(703\) | −1.00000 | − | 12.1244i | −0.0377157 | − | 0.457279i | ||||
\(704\) | −6.00000 | −0.226134 | ||||||||
\(705\) | −18.0000 | + | 31.1769i | −0.677919 | + | 1.17419i | ||||
\(706\) | −10.5000 | − | 18.1865i | −0.395173 | − | 0.684459i | ||||
\(707\) | 6.00000 | + | 10.3923i | 0.225653 | + | 0.390843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | −18.0000 | − | 31.1769i | −0.675528 | − | 1.17005i | ||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 1.50000 | − | 2.59808i | 0.0562149 | − | 0.0973670i | ||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | −24.0000 | −0.898177 | ||||||||
\(715\) | 18.0000 | − | 31.1769i | 0.673162 | − | 1.16595i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0000 | − | 36.3731i | 0.783168 | − | 1.35649i | −0.146920 | − | 0.989148i | \(-0.546936\pi\) |
0.930087 | − | 0.367338i | \(-0.119731\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | −8.00000 | − | 13.8564i | −0.297936 | − | 0.516040i | ||||
\(722\) | −7.50000 | − | 12.9904i | −0.279121 | − | 0.483452i | ||||
\(723\) | 14.0000 | − | 24.2487i | 0.520666 | − | 0.901819i | ||||
\(724\) | 0.500000 | − | 0.866025i | 0.0185824 | − | 0.0321856i | ||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 50.0000 | 1.85567 | ||||||||
\(727\) | 2.00000 | + | 3.46410i | 0.0741759 | + | 0.128476i | 0.900728 | − | 0.434384i | \(-0.143034\pi\) |
−0.826552 | + | 0.562861i | \(0.809701\pi\) | |||||||
\(728\) | −4.00000 | + | 6.92820i | −0.148250 | + | 0.256776i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 30.0000 | 1.11035 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 2.00000 | 0.0739221 | ||||||||
\(733\) | −1.00000 | − | 1.73205i | −0.0369358 | − | 0.0639748i | 0.846967 | − | 0.531646i | \(-0.178426\pi\) |
−0.883902 | + | 0.467671i | \(0.845093\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | 27.0000 | + | 46.7654i | 0.995910 | + | 1.72497i | ||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | 6.00000 | + | 10.3923i | 0.221013 | + | 0.382805i | ||||
\(738\) | 1.50000 | − | 2.59808i | 0.0552158 | − | 0.0956365i | ||||
\(739\) | 38.0000 | 1.39785 | 0.698926 | − | 0.715194i | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(740\) | −15.0000 | + | 10.3923i | −0.551411 | + | 0.382029i | ||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 12.0000 | − | 20.7846i | 0.440534 | − | 0.763027i | ||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | −2.00000 | − | 3.46410i | −0.0733236 | − | 0.127000i | ||||
\(745\) | 31.5000 | + | 54.5596i | 1.15407 | + | 1.99891i | ||||
\(746\) | 25.0000 | 0.915315 | ||||||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | −18.0000 | −0.658145 | ||||||||
\(749\) | −24.0000 | + | 41.5692i | −0.876941 | + | 1.51891i | ||||
\(750\) | −6.00000 | −0.219089 | ||||||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | 3.00000 | − | 5.19615i | 0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.00000 | −0.218507 | ||||||||
\(755\) | 33.0000 | − | 57.1577i | 1.20099 | − | 2.08018i | ||||
\(756\) | 8.00000 | − | 13.8564i | 0.290957 | − | 0.503953i | ||||
\(757\) | −17.5000 | + | 30.3109i | −0.636048 | + | 1.10167i | 0.350244 | + | 0.936659i | \(0.386099\pi\) |
−0.986292 | + | 0.165009i | \(0.947235\pi\) | |||||||
\(758\) | −8.00000 | − | 13.8564i | −0.290573 | − | 0.503287i | ||||
\(759\) | −36.0000 | − | 62.3538i | −1.30672 | − | 2.26330i | ||||
\(760\) | 3.00000 | − | 5.19615i | 0.108821 | − | 0.188484i | ||||
\(761\) | −13.5000 | + | 23.3827i | −0.489375 | + | 0.847622i | −0.999925 | − | 0.0122260i | \(-0.996108\pi\) |
0.510551 | + | 0.859848i | \(0.329442\pi\) | |||||||
\(762\) | 10.0000 | − | 17.3205i | 0.362262 | − | 0.627456i | ||||
\(763\) | 4.00000 | 0.144810 | ||||||||
\(764\) | 3.00000 | + | 5.19615i | 0.108536 | + | 0.187990i | ||||
\(765\) | −4.50000 | + | 7.79423i | −0.162698 | + | 0.281801i | ||||
\(766\) | −12.0000 | −0.433578 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | − | 1.73205i | 0.0360844 | − | 0.0625000i | ||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 36.0000 | + | 62.3538i | 1.29735 | + | 2.24708i | ||||
\(771\) | −54.0000 | −1.94476 | ||||||||
\(772\) | −5.50000 | − | 9.52628i | −0.197949 | − | 0.342858i | ||||
\(773\) | 10.5000 | + | 18.1865i | 0.377659 | + | 0.654124i | 0.990721 | − | 0.135910i | \(-0.0433959\pi\) |
−0.613062 | + | 0.790034i | \(0.710063\pi\) | |||||||
\(774\) | −2.00000 | − | 3.46410i | −0.0718885 | − | 0.124515i | ||||
\(775\) | −4.00000 | + | 6.92820i | −0.143684 | + | 0.248868i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | −40.0000 | + | 27.7128i | −1.43499 | + | 0.994192i | ||||
\(778\) | 9.00000 | 0.322666 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | 6.00000 | + | 10.3923i | 0.214834 | + | 0.372104i | ||||
\(781\) | −36.0000 | − | 62.3538i | −1.28818 | − | 2.23120i | ||||
\(782\) | 9.00000 | + | 15.5885i | 0.321839 | + | 0.557442i | ||||
\(783\) | 12.0000 | 0.428845 | ||||||||
\(784\) | −4.50000 | − | 7.79423i | −0.160714 | − | 0.278365i | ||||
\(785\) | 33.0000 | 1.17782 | ||||||||
\(786\) | −18.0000 | + | 31.1769i | −0.642039 | + | 1.11204i | ||||
\(787\) | 20.0000 | 0.712923 | 0.356462 | − | 0.934310i | \(-0.383983\pi\) | ||||
0.356462 | + | 0.934310i | \(0.383983\pi\) | |||||||
\(788\) | 3.00000 | 0.106871 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.0000 | + | 36.3731i | 0.747146 | + | 1.29410i | ||||
\(791\) | 72.0000 | 2.56003 | ||||||||
\(792\) | −3.00000 | + | 5.19615i | −0.106600 | + | 0.184637i | ||||
\(793\) | 1.00000 | − | 1.73205i | 0.0355110 | − | 0.0615069i | ||||
\(794\) | 17.5000 | − | 30.3109i | 0.621052 | − | 1.07569i | ||||
\(795\) | −18.0000 | − | 31.1769i | −0.638394 | − | 1.10573i | ||||
\(796\) | −4.00000 | − | 6.92820i | −0.141776 | − | 0.245564i | ||||
\(797\) | 9.00000 | − | 15.5885i | 0.318796 | − | 0.552171i | −0.661441 | − | 0.749997i | \(-0.730055\pi\) |
0.980237 | + | 0.197826i | \(0.0633881\pi\) | |||||||
\(798\) | 8.00000 | − | 13.8564i | 0.283197 | − | 0.490511i | ||||
\(799\) | 9.00000 | − | 15.5885i | 0.318397 | − | 0.551480i | ||||
\(800\) | −4.00000 | −0.141421 | ||||||||
\(801\) | −1.50000 | − | 2.59808i | −0.0529999 | − | 0.0917985i | ||||
\(802\) | 3.00000 | − | 5.19615i | 0.105934 | − | 0.183483i | ||||
\(803\) | 60.0000 | 2.11735 | ||||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | 36.0000 | − | 62.3538i | 1.26883 | − | 2.19768i | ||||
\(806\) | −4.00000 | −0.140894 | ||||||||
\(807\) | 18.0000 | + | 31.1769i | 0.633630 | + | 1.09748i | ||||
\(808\) | −3.00000 | −0.105540 | ||||||||
\(809\) | −21.0000 | − | 36.3731i | −0.738321 | − | 1.27881i | −0.953251 | − | 0.302180i | \(-0.902286\pi\) |
0.214930 | − | 0.976629i | \(-0.431048\pi\) | |||||||
\(810\) | −16.5000 | − | 28.5788i | −0.579751 | − | 1.00416i | ||||
\(811\) | 8.00000 | + | 13.8564i | 0.280918 | + | 0.486564i | 0.971611 | − | 0.236584i | \(-0.0760278\pi\) |
−0.690693 | + | 0.723148i | \(0.742694\pi\) | |||||||
\(812\) | 6.00000 | − | 10.3923i | 0.210559 | − | 0.364698i | ||||
\(813\) | 20.0000 | 0.701431 | ||||||||
\(814\) | −30.0000 | + | 20.7846i | −1.05150 | + | 0.728500i | ||||
\(815\) | −48.0000 | −1.68137 | ||||||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 4.00000 | + | 6.92820i | 0.139942 | + | 0.242387i | ||||
\(818\) | 5.50000 | + | 9.52628i | 0.192303 | + | 0.333079i | ||||
\(819\) | 4.00000 | + | 6.92820i | 0.139771 | + | 0.242091i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | −9.00000 | − | 15.5885i | −0.314102 | − | 0.544041i | 0.665144 | − | 0.746715i | \(-0.268370\pi\) |
−0.979246 | + | 0.202674i | \(0.935037\pi\) | |||||||
\(822\) | 6.00000 | 0.209274 | ||||||||
\(823\) | 17.0000 | − | 29.4449i | 0.592583 | − | 1.02638i | −0.401300 | − | 0.915947i | \(-0.631442\pi\) |
0.993883 | − | 0.110437i | \(-0.0352250\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 48.0000 | 1.67115 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | − | 20.7846i | −0.417281 | − | 0.722752i | 0.578384 | − | 0.815765i | \(-0.303684\pi\) |
−0.995665 | + | 0.0930129i | \(0.970350\pi\) | |||||||
\(828\) | 6.00000 | 0.208514 | ||||||||
\(829\) | −13.0000 | + | 22.5167i | −0.451509 | + | 0.782036i | −0.998480 | − | 0.0551154i | \(-0.982447\pi\) |
0.546971 | + | 0.837151i | \(0.315781\pi\) | |||||||
\(830\) | 9.00000 | − | 15.5885i | 0.312395 | − | 0.541083i | ||||
\(831\) | −1.00000 | + | 1.73205i | −0.0346896 | + | 0.0600842i | ||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | −13.5000 | − | 23.3827i | −0.467747 | − | 0.810162i | ||||
\(834\) | −2.00000 | + | 3.46410i | −0.0692543 | + | 0.119952i | ||||
\(835\) | −18.0000 | + | 31.1769i | −0.622916 | + | 1.07892i | ||||
\(836\) | 6.00000 | − | 10.3923i | 0.207514 | − | 0.359425i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.00000 | + | 5.19615i | −0.103572 | + | 0.179391i | −0.913154 | − | 0.407615i | \(-0.866360\pi\) |
0.809582 | + | 0.587007i | \(0.199694\pi\) | |||||||
\(840\) | −24.0000 | −0.828079 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −18.5000 | + | 32.0429i | −0.637552 | + | 1.10427i | ||||
\(843\) | −30.0000 | −1.03325 | ||||||||
\(844\) | 8.00000 | + | 13.8564i | 0.275371 | + | 0.476957i | ||||
\(845\) | −27.0000 | −0.928828 | ||||||||
\(846\) | −3.00000 | − | 5.19615i | −0.103142 | − | 0.178647i | ||||
\(847\) | 50.0000 | + | 86.6025i | 1.71802 | + | 2.97570i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | −16.0000 | + | 27.7128i | −0.549119 | + | 0.951101i | ||||
\(850\) | −12.0000 | −0.411597 | ||||||||
\(851\) | 33.0000 | + | 15.5885i | 1.13123 | + | 0.534365i | ||||
\(852\) | 24.0000 | 0.822226 | ||||||||
\(853\) | 18.5000 | − | 32.0429i | 0.633428 | − | 1.09713i | −0.353418 | − | 0.935466i | \(-0.614981\pi\) |
0.986846 | − | 0.161664i | \(-0.0516860\pi\) | |||||||
\(854\) | 2.00000 | + | 3.46410i | 0.0684386 | + | 0.118539i | ||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 12.0000 | + | 20.7846i | 0.409673 | + | 0.709575i | ||||
\(859\) | −52.0000 | −1.77422 | −0.887109 | − | 0.461561i | \(-0.847290\pi\) | ||||
−0.887109 | + | 0.461561i | \(0.847290\pi\) | |||||||
\(860\) | 6.00000 | − | 10.3923i | 0.204598 | − | 0.354375i | ||||
\(861\) | 24.0000 | 0.817918 | ||||||||
\(862\) | −6.00000 | −0.204361 | ||||||||
\(863\) | −24.0000 | + | 41.5692i | −0.816970 | + | 1.41503i | 0.0909355 | + | 0.995857i | \(0.471014\pi\) |
−0.907905 | + | 0.419176i | \(0.862319\pi\) | |||||||
\(864\) | 2.00000 | + | 3.46410i | 0.0680414 | + | 0.117851i | ||||
\(865\) | −63.0000 | −2.14206 | ||||||||
\(866\) | −12.5000 | + | 21.6506i | −0.424767 | + | 0.735719i | ||||
\(867\) | −8.00000 | + | 13.8564i | −0.271694 | + | 0.470588i | ||||
\(868\) | 4.00000 | − | 6.92820i | 0.135769 | − | 0.235159i | ||||
\(869\) | 42.0000 | + | 72.7461i | 1.42475 | + | 2.46774i | ||||
\(870\) | −9.00000 | − | 15.5885i | −0.305129 | − | 0.528498i | ||||
\(871\) | −2.00000 | + | 3.46410i | −0.0677674 | + | 0.117377i | ||||
\(872\) | −0.500000 | + | 0.866025i | −0.0169321 | + | 0.0293273i | ||||
\(873\) | 6.50000 | − | 11.2583i | 0.219992 | − | 0.381037i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | −6.00000 | − | 10.3923i | −0.202837 | − | 0.351324i | ||||
\(876\) | −10.0000 | + | 17.3205i | −0.337869 | + | 0.585206i | ||||
\(877\) | −25.0000 | −0.844190 | −0.422095 | − | 0.906552i | \(-0.638705\pi\) | ||||
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | −32.0000 | −1.07995 | ||||||||
\(879\) | 3.00000 | − | 5.19615i | 0.101187 | − | 0.175262i | ||||
\(880\) | −18.0000 | −0.606780 | ||||||||
\(881\) | −25.5000 | − | 44.1673i | −0.859117 | − | 1.48803i | −0.872772 | − | 0.488127i | \(-0.837680\pi\) |
0.0136556 | − | 0.999907i | \(-0.495653\pi\) | |||||||
\(882\) | −9.00000 | −0.303046 | ||||||||
\(883\) | −1.00000 | − | 1.73205i | −0.0336527 | − | 0.0582882i | 0.848709 | − | 0.528861i | \(-0.177381\pi\) |
−0.882361 | + | 0.470573i | \(0.844047\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | + | 20.7846i | −0.403148 | + | 0.698273i | ||||
\(887\) | 6.00000 | 0.201460 | 0.100730 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100730 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(888\) | −1.00000 | − | 12.1244i | −0.0335578 | − | 0.406867i | ||||
\(889\) | 40.0000 | 1.34156 | ||||||||
\(890\) | 4.50000 | − | 7.79423i | 0.150840 | − | 0.261263i | ||||
\(891\) | −33.0000 | − | 57.1577i | −1.10554 | − | 1.91485i | ||||
\(892\) | −7.00000 | − | 12.1244i | −0.234377 | − | 0.405953i | ||||
\(893\) | 6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | ||||
\(894\) | −42.0000 | −1.40469 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.00000 | 0.133631 | ||||||||
\(897\) | 12.0000 | − | 20.7846i | 0.400668 | − | 0.693978i | ||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | 6.00000 | 0.200111 | ||||||||
\(900\) | −2.00000 | + | 3.46410i | −0.0666667 | + | 0.115470i | ||||
\(901\) | 9.00000 | + | 15.5885i | 0.299833 | + | 0.519327i | ||||
\(902\) | 18.0000 | 0.599334 | ||||||||
\(903\) | 16.0000 | − | 27.7128i | 0.532447 | − | 0.922225i | ||||
\(904\) | −9.00000 | + | 15.5885i | −0.299336 | + | 0.518464i | ||||
\(905\) | 1.50000 | − | 2.59808i | 0.0498617 | − | 0.0863630i | ||||
\(906\) | 22.0000 | + | 38.1051i | 0.730901 | + | 1.26596i | ||||
\(907\) | 29.0000 | + | 50.2295i | 0.962929 | + | 1.66784i | 0.715079 | + | 0.699044i | \(0.246391\pi\) |
0.247851 | + | 0.968798i | \(0.420276\pi\) | |||||||
\(908\) | 9.00000 | − | 15.5885i | 0.298675 | − | 0.517321i | ||||
\(909\) | −1.50000 | + | 2.59808i | −0.0497519 | + | 0.0861727i | ||||
\(910\) | −12.0000 | + | 20.7846i | −0.397796 | + | 0.689003i | ||||
\(911\) | −42.0000 | −1.39152 | −0.695761 | − | 0.718273i | \(-0.744933\pi\) | ||||
−0.695761 | + | 0.718273i | \(0.744933\pi\) | |||||||
\(912\) | 2.00000 | + | 3.46410i | 0.0662266 | + | 0.114708i | ||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 37.0000 | 1.22385 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | −5.50000 | + | 9.52628i | −0.181725 | + | 0.314757i | ||||
\(917\) | −72.0000 | −2.37765 | ||||||||
\(918\) | 6.00000 | + | 10.3923i | 0.198030 | + | 0.342997i | ||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | 9.00000 | + | 15.5885i | 0.296721 | + | 0.513936i | ||||
\(921\) | −28.0000 | − | 48.4974i | −0.922631 | − | 1.59804i | ||||
\(922\) | −15.0000 | − | 25.9808i | −0.493999 | − | 0.855631i | ||||
\(923\) | 12.0000 | − | 20.7846i | 0.394985 | − | 0.684134i | ||||
\(924\) | −48.0000 | −1.57908 | ||||||||
\(925\) | −20.0000 | + | 13.8564i | −0.657596 | + | 0.455596i | ||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 1.50000 | + | 2.59808i | 0.0492399 | + | 0.0852860i | ||||
\(929\) | 4.50000 | + | 7.79423i | 0.147640 | + | 0.255720i | 0.930355 | − | 0.366660i | \(-0.119499\pi\) |
−0.782715 | + | 0.622381i | \(0.786166\pi\) | |||||||
\(930\) | −6.00000 | − | 10.3923i | −0.196748 | − | 0.340777i | ||||
\(931\) | 18.0000 | 0.589926 | ||||||||
\(932\) | 4.50000 | + | 7.79423i | 0.147402 | + | 0.255308i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.0000 | − | 31.1769i | 0.588978 | − | 1.02014i | ||||
\(935\) | −54.0000 | −1.76599 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 0.500000 | − | 0.866025i | 0.0163343 | − | 0.0282918i | −0.857743 | − | 0.514079i | \(-0.828134\pi\) |
0.874077 | + | 0.485787i | \(0.161467\pi\) | |||||||
\(938\) | −4.00000 | − | 6.92820i | −0.130605 | − | 0.226214i | ||||
\(939\) | 26.0000 | 0.848478 | ||||||||
\(940\) | 9.00000 | − | 15.5885i | 0.293548 | − | 0.508439i | ||||
\(941\) | −13.5000 | + | 23.3827i | −0.440087 | + | 0.762254i | −0.997695 | − | 0.0678506i | \(-0.978386\pi\) |
0.557608 | + | 0.830104i | \(0.311719\pi\) | |||||||
\(942\) | −11.0000 | + | 19.0526i | −0.358399 | + | 0.620766i | ||||
\(943\) | −9.00000 | − | 15.5885i | −0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 24.0000 | − | 41.5692i | 0.780720 | − | 1.35225i | ||||
\(946\) | 12.0000 | − | 20.7846i | 0.390154 | − | 0.675766i | ||||
\(947\) | 24.0000 | − | 41.5692i | 0.779895 | − | 1.35082i | −0.152106 | − | 0.988364i | \(-0.548606\pi\) |
0.932002 | − | 0.362454i | \(-0.118061\pi\) | |||||||
\(948\) | −28.0000 | −0.909398 | ||||||||
\(949\) | 10.0000 | + | 17.3205i | 0.324614 | + | 0.562247i | ||||
\(950\) | 4.00000 | − | 6.92820i | 0.129777 | − | 0.224781i | ||||
\(951\) | 42.0000 | 1.36194 | ||||||||
\(952\) | 12.0000 | 0.388922 | ||||||||
\(953\) | 3.00000 | − | 5.19615i | 0.0971795 | − | 0.168320i | −0.813337 | − | 0.581793i | \(-0.802351\pi\) |
0.910516 | + | 0.413473i | \(0.135685\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18.0000 | − | 31.1769i | −0.581857 | − | 1.00781i | ||||
\(958\) | 12.0000 | + | 20.7846i | 0.387702 | + | 0.671520i | ||||
\(959\) | 6.00000 | + | 10.3923i | 0.193750 | + | 0.335585i | ||||
\(960\) | 3.00000 | − | 5.19615i | 0.0968246 | − | 0.167705i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −11.0000 | − | 5.19615i | −0.354654 | − | 0.167531i | ||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | −7.00000 | + | 12.1244i | −0.225455 | + | 0.390499i | ||||
\(965\) | −16.5000 | − | 28.5788i | −0.531154 | − | 0.919985i | ||||
\(966\) | 24.0000 | + | 41.5692i | 0.772187 | + | 1.33747i | ||||
\(967\) | 26.0000 | + | 45.0333i | 0.836104 | + | 1.44817i | 0.893129 | + | 0.449801i | \(0.148505\pi\) |
−0.0570251 | + | 0.998373i | \(0.518161\pi\) | |||||||
\(968\) | −25.0000 | −0.803530 | ||||||||
\(969\) | 6.00000 | + | 10.3923i | 0.192748 | + | 0.333849i | ||||
\(970\) | 39.0000 | 1.25221 | ||||||||
\(971\) | −15.0000 | + | 25.9808i | −0.481373 | + | 0.833762i | −0.999771 | − | 0.0213768i | \(-0.993195\pi\) |
0.518399 | + | 0.855139i | \(0.326528\pi\) | |||||||
\(972\) | 10.0000 | 0.320750 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 1.00000 | − | 1.73205i | 0.0320421 | − | 0.0554985i | ||||
\(975\) | 8.00000 | + | 13.8564i | 0.256205 | + | 0.443760i | ||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 16.0000 | − | 27.7128i | 0.511624 | − | 0.886158i | ||||
\(979\) | 9.00000 | − | 15.5885i | 0.287641 | − | 0.498209i | ||||
\(980\) | −13.5000 | − | 23.3827i | −0.431242 | − | 0.746933i | ||||
\(981\) | 0.500000 | + | 0.866025i | 0.0159638 | + | 0.0276501i | ||||
\(982\) | 3.00000 | − | 5.19615i | 0.0957338 | − | 0.165816i | ||||
\(983\) | 15.0000 | − | 25.9808i | 0.478426 | − | 0.828658i | −0.521268 | − | 0.853393i | \(-0.674541\pi\) |
0.999694 | + | 0.0247352i | \(0.00787426\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | 9.00000 | 0.286764 | ||||||||
\(986\) | 4.50000 | + | 7.79423i | 0.143309 | + | 0.248219i | ||||
\(987\) | 24.0000 | − | 41.5692i | 0.763928 | − | 1.32316i | ||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | −24.0000 | −0.763156 | ||||||||
\(990\) | −9.00000 | + | 15.5885i | −0.286039 | + | 0.495434i | ||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 8.00000 | 0.253872 | ||||||||
\(994\) | 24.0000 | + | 41.5692i | 0.761234 | + | 1.31850i | ||||
\(995\) | −12.0000 | − | 20.7846i | −0.380426 | − | 0.658916i | ||||
\(996\) | 6.00000 | + | 10.3923i | 0.190117 | + | 0.329293i | ||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | −14.0000 | −0.443162 | ||||||||
\(999\) | 22.0000 | + | 10.3923i | 0.696049 | + | 0.328798i |
(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 | 74.2.c.b.47.1 | ✓ | 2 | |
3.2 | odd | 2 | 666.2.f.d.343.1 | 2 | |||
4.3 | odd | 2 | 592.2.i.a.417.1 | 2 | |||
37.10 | even | 3 | 2738.2.a.a.1.1 | 1 | |||
37.26 | even | 3 | inner | 74.2.c.b.63.1 | yes | 2 | |
37.27 | even | 6 | 2738.2.a.c.1.1 | 1 | |||
111.26 | odd | 6 | 666.2.f.d.433.1 | 2 | |||
148.63 | odd | 6 | 592.2.i.a.433.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.c.b.47.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
74.2.c.b.63.1 | yes | 2 | 37.26 | even | 3 | inner | |
592.2.i.a.417.1 | 2 | 4.3 | odd | 2 | |||
592.2.i.a.433.1 | 2 | 148.63 | odd | 6 | |||
666.2.f.d.343.1 | 2 | 3.2 | odd | 2 | |||
666.2.f.d.433.1 | 2 | 111.26 | odd | 6 | |||
2738.2.a.a.1.1 | 1 | 37.10 | even | 3 | |||
2738.2.a.c.1.1 | 1 | 37.27 | even | 6 |