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.a.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 | \(-0.970753\pi\) |
0.418432 | − | 0.908248i | \(-0.362580\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | −2.00000 | −0.816497 | ||||||||
\(7\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.00000 | + | 1.73205i | −0.288675 | + | 0.500000i | ||||
\(13\) | 3.00000 | + | 5.19615i | 0.832050 | + | 1.44115i | 0.896410 | + | 0.443227i | \(0.146166\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 1.73205i | 0.258199 | − | 0.447214i | ||||
\(16\) | −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 | \(0.907015\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 1.00000 | + | 1.73205i | 0.204124 | + | 0.353553i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | −1.00000 | − | 1.73205i | −0.182574 | − | 0.316228i | ||||
\(31\) | 10.0000 | 1.79605 | 0.898027 | − | 0.439941i | \(-0.145001\pi\) | ||||
0.898027 | + | 0.439941i | \(0.145001\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −2.00000 | − | 3.46410i | −0.348155 | − | 0.603023i | ||||
\(34\) | 1.50000 | + | 2.59808i | 0.257248 | + | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.500000 | + | 6.06218i | −0.0821995 | + | 0.996616i | ||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 6.00000 | − | 10.3923i | 0.960769 | − | 1.66410i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 2.00000 | 0.291730 | 0.145865 | − | 0.989305i | \(-0.453403\pi\) | ||||
0.145865 | + | 0.989305i | \(0.453403\pi\) | |||||||
\(48\) | 2.00000 | 0.288675 | ||||||||
\(49\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 3.00000 | − | 5.19615i | 0.416025 | − | 0.720577i | ||||
\(53\) | 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 | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | + | 3.46410i | −0.264906 | + | 0.458831i | ||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | −4.00000 | + | 6.92820i | −0.520756 | + | 0.901975i | 0.478953 | + | 0.877841i | \(0.341016\pi\) |
−0.999709 | + | 0.0241347i | \(0.992317\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | 2.50000 | + | 4.33013i | 0.320092 | + | 0.554416i | 0.980507 | − | 0.196485i | \(-0.0629528\pi\) |
−0.660415 | + | 0.750901i | \(0.729619\pi\) | |||||||
\(62\) | 5.00000 | − | 8.66025i | 0.635001 | − | 1.09985i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 3.00000 | + | 5.19615i | 0.366508 | + | 0.634811i | 0.989017 | − | 0.147802i | \(-0.0472198\pi\) |
−0.622509 | + | 0.782613i | \(0.713886\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 6.00000 | + | 10.3923i | 0.722315 | + | 1.25109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 5.00000 | + | 3.46410i | 0.581238 | + | 0.402694i | ||||
\(75\) | −8.00000 | −0.923760 | ||||||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | − | 10.3923i | −0.679366 | − | 1.17670i | ||||
\(79\) | −3.00000 | − | 5.19615i | −0.337526 | − | 0.584613i | 0.646440 | − | 0.762964i | \(-0.276257\pi\) |
−0.983967 | + | 0.178352i | \(0.942924\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | −1.00000 | + | 1.73205i | −0.109764 | + | 0.190117i | −0.915675 | − | 0.401920i | \(-0.868343\pi\) |
0.805910 | + | 0.592037i | \(0.201676\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | 9.00000 | + | 15.5885i | 0.964901 | + | 1.67126i | ||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | 6.50000 | − | 11.2583i | 0.688999 | − | 1.19338i | −0.283164 | − | 0.959072i | \(-0.591384\pi\) |
0.972162 | − | 0.234309i | \(-0.0752827\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.00000 | + | 5.19615i | 0.312772 | + | 0.541736i | ||||
\(93\) | −10.0000 | − | 17.3205i | −1.03695 | − | 1.79605i | ||||
\(94\) | 1.00000 | − | 1.73205i | 0.103142 | − | 0.178647i | ||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 1.00000 | − | 1.73205i | 0.102062 | − | 0.176777i | ||||
\(97\) | 3.00000 | 0.304604 | 0.152302 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152302 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(98\) | −3.50000 | − | 6.06218i | −0.353553 | − | 0.612372i | ||||
\(99\) | −1.00000 | + | 1.73205i | −0.100504 | + | 0.174078i | ||||
\(100\) | −4.00000 | −0.400000 | ||||||||
\(101\) | 7.00000 | 0.696526 | 0.348263 | − | 0.937397i | \(-0.386772\pi\) | ||||
0.348263 | + | 0.937397i | \(0.386772\pi\) | |||||||
\(102\) | 3.00000 | − | 5.19615i | 0.297044 | − | 0.514496i | ||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −3.00000 | − | 5.19615i | −0.294174 | − | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | 2.00000 | + | 3.46410i | 0.192450 | + | 0.333333i | ||||
\(109\) | 6.50000 | − | 11.2583i | 0.622587 | − | 1.07835i | −0.366415 | − | 0.930451i | \(-0.619415\pi\) |
0.989002 | − | 0.147901i | \(-0.0472517\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 11.0000 | − | 5.19615i | 1.04407 | − | 0.493197i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | − | 8.66025i | 0.470360 | − | 0.814688i | −0.529065 | − | 0.848581i | \(-0.677457\pi\) |
0.999425 | + | 0.0338931i | \(0.0107906\pi\) | |||||||
\(114\) | 2.00000 | + | 3.46410i | 0.187317 | + | 0.324443i | ||||
\(115\) | −3.00000 | − | 5.19615i | −0.279751 | − | 0.484544i | ||||
\(116\) | 4.50000 | + | 7.79423i | 0.417815 | + | 0.723676i | ||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | 4.00000 | + | 6.92820i | 0.368230 | + | 0.637793i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 1.73205i | −0.0912871 | + | 0.158114i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 5.00000 | 0.452679 | ||||||||
\(123\) | −3.00000 | + | 5.19615i | −0.270501 | + | 0.468521i | ||||
\(124\) | −5.00000 | − | 8.66025i | −0.449013 | − | 0.777714i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000 | − | 12.1244i | 0.621150 | − | 1.07586i | −0.368122 | − | 0.929777i | \(-0.619999\pi\) |
0.989272 | − | 0.146085i | \(-0.0466674\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 8.00000 | + | 13.8564i | 0.704361 | + | 1.21999i | ||||
\(130\) | 3.00000 | + | 5.19615i | 0.263117 | + | 0.455733i | ||||
\(131\) | −7.00000 | + | 12.1244i | −0.611593 | + | 1.05931i | 0.379379 | + | 0.925241i | \(0.376138\pi\) |
−0.990972 | + | 0.134069i | \(0.957196\pi\) | |||||||
\(132\) | −2.00000 | + | 3.46410i | −0.174078 | + | 0.301511i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | −2.00000 | − | 3.46410i | −0.172133 | − | 0.298142i | ||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | −21.0000 | −1.79415 | −0.897076 | − | 0.441877i | \(-0.854313\pi\) | ||||
−0.897076 | + | 0.441877i | \(0.854313\pi\) | |||||||
\(138\) | 12.0000 | 1.02151 | ||||||||
\(139\) | −7.00000 | + | 12.1244i | −0.593732 | + | 1.02837i | 0.399992 | + | 0.916519i | \(0.369013\pi\) |
−0.993724 | + | 0.111856i | \(0.964321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | − | 3.46410i | −0.168430 | − | 0.291730i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 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 | ||||
\(146\) | −1.00000 | + | 1.73205i | −0.0827606 | + | 0.143346i | ||||
\(147\) | −14.0000 | −1.15470 | ||||||||
\(148\) | 5.50000 | − | 2.59808i | 0.452097 | − | 0.213561i | ||||
\(149\) | −9.00000 | −0.737309 | −0.368654 | − | 0.929567i | \(-0.620181\pi\) | ||||
−0.368654 | + | 0.929567i | \(0.620181\pi\) | |||||||
\(150\) | −4.00000 | + | 6.92820i | −0.326599 | + | 0.565685i | ||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −1.50000 | − | 2.59808i | −0.121268 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00000 | + | 8.66025i | 0.401610 | + | 0.695608i | ||||
\(156\) | −12.0000 | −0.960769 | ||||||||
\(157\) | 8.50000 | − | 14.7224i | 0.678374 | − | 1.17498i | −0.297097 | − | 0.954847i | \(-0.596018\pi\) |
0.975470 | − | 0.220131i | \(-0.0706483\pi\) | |||||||
\(158\) | −6.00000 | −0.477334 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 2.00000 | − | 3.46410i | 0.155700 | − | 0.269680i | ||||
\(166\) | 1.00000 | + | 1.73205i | 0.0776151 | + | 0.134433i | ||||
\(167\) | 10.0000 | + | 17.3205i | 0.773823 | + | 1.34030i | 0.935454 | + | 0.353450i | \(0.114991\pi\) |
−0.161630 | + | 0.986851i | \(0.551675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | −1.50000 | + | 2.59808i | −0.115045 | + | 0.199263i | ||||
\(171\) | 2.00000 | 0.152944 | ||||||||
\(172\) | 4.00000 | + | 6.92820i | 0.304997 | + | 0.528271i | ||||
\(173\) | −3.50000 | + | 6.06218i | −0.266100 | + | 0.460899i | −0.967851 | − | 0.251523i | \(-0.919068\pi\) |
0.701751 | + | 0.712422i | \(0.252402\pi\) | |||||||
\(174\) | 18.0000 | 1.36458 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 16.0000 | 1.20263 | ||||||||
\(178\) | −6.50000 | − | 11.2583i | −0.487196 | − | 0.843848i | ||||
\(179\) | 24.0000 | 1.79384 | 0.896922 | − | 0.442189i | \(-0.145798\pi\) | ||||
0.896922 | + | 0.442189i | \(0.145798\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −5.50000 | − | 9.52628i | −0.408812 | − | 0.708083i | 0.585945 | − | 0.810351i | \(-0.300723\pi\) |
−0.994757 | + | 0.102268i | \(0.967390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.00000 | − | 8.66025i | 0.369611 | − | 0.640184i | ||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | −5.50000 | + | 2.59808i | −0.404368 | + | 0.191014i | ||||
\(186\) | −20.0000 | −1.46647 | ||||||||
\(187\) | −3.00000 | + | 5.19615i | −0.219382 | + | 0.379980i | ||||
\(188\) | −1.00000 | − | 1.73205i | −0.0729325 | − | 0.126323i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000 | − | 1.73205i | −0.0725476 | − | 0.125656i | ||||
\(191\) | 22.0000 | 1.59186 | 0.795932 | − | 0.605386i | \(-0.206981\pi\) | ||||
0.795932 | + | 0.605386i | \(0.206981\pi\) | |||||||
\(192\) | −1.00000 | − | 1.73205i | −0.0721688 | − | 0.125000i | ||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | 1.50000 | − | 2.59808i | 0.107694 | − | 0.186531i | ||||
\(195\) | 12.0000 | 0.859338 | ||||||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 4.50000 | − | 7.79423i | 0.320612 | − | 0.555316i | −0.660003 | − | 0.751263i | \(-0.729445\pi\) |
0.980614 | + | 0.195947i | \(0.0627782\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 6.00000 | − | 10.3923i | 0.423207 | − | 0.733017i | ||||
\(202\) | 3.50000 | − | 6.06218i | 0.246259 | − | 0.426533i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | ||||
\(205\) | 1.50000 | − | 2.59808i | 0.104765 | − | 0.181458i | ||||
\(206\) | −4.00000 | + | 6.92820i | −0.278693 | + | 0.482711i | ||||
\(207\) | 3.00000 | − | 5.19615i | 0.208514 | − | 0.361158i | ||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | −2.00000 | − | 3.46410i | −0.138343 | − | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | −0.546869 | ||||||||
\(215\) | −4.00000 | − | 6.92820i | −0.272798 | − | 0.472500i | ||||
\(216\) | 4.00000 | 0.272166 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.50000 | − | 11.2583i | −0.440236 | − | 0.762510i | ||||
\(219\) | 2.00000 | + | 3.46410i | 0.135147 | + | 0.234082i | ||||
\(220\) | 1.00000 | − | 1.73205i | 0.0674200 | − | 0.116775i | ||||
\(221\) | −18.0000 | −1.21081 | ||||||||
\(222\) | 1.00000 | − | 12.1244i | 0.0671156 | − | 0.813733i | ||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | + | 3.46410i | 0.133333 | + | 0.230940i | ||||
\(226\) | −5.00000 | − | 8.66025i | −0.332595 | − | 0.576072i | ||||
\(227\) | −15.0000 | − | 25.9808i | −0.995585 | − | 1.72440i | −0.579082 | − | 0.815270i | \(-0.696589\pi\) |
−0.416503 | − | 0.909134i | \(-0.636745\pi\) | |||||||
\(228\) | 4.00000 | 0.264906 | ||||||||
\(229\) | 8.50000 | + | 14.7224i | 0.561696 | + | 0.972886i | 0.997349 | + | 0.0727709i | \(0.0231842\pi\) |
−0.435653 | + | 0.900115i | \(0.643482\pi\) | |||||||
\(230\) | −6.00000 | −0.395628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | −1.00000 | −0.0655122 | −0.0327561 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327561 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 1.00000 | + | 1.73205i | 0.0652328 | + | 0.112987i | ||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | −6.00000 | + | 10.3923i | −0.389742 | + | 0.675053i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.00000 | + | 3.46410i | −0.129369 | + | 0.224074i | −0.923432 | − | 0.383761i | \(-0.874629\pi\) |
0.794063 | + | 0.607835i | \(0.207962\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | 5.00000 | − | 8.66025i | 0.320750 | − | 0.555556i | ||||
\(244\) | 2.50000 | − | 4.33013i | 0.160046 | − | 0.277208i | ||||
\(245\) | 7.00000 | 0.447214 | ||||||||
\(246\) | 3.00000 | + | 5.19615i | 0.191273 | + | 0.331295i | ||||
\(247\) | 6.00000 | − | 10.3923i | 0.381771 | − | 0.661247i | ||||
\(248\) | −10.0000 | −0.635001 | ||||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 4.50000 | − | 7.79423i | 0.284605 | − | 0.492950i | ||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | −7.00000 | − | 12.1244i | −0.439219 | − | 0.760750i | ||||
\(255\) | 3.00000 | + | 5.19615i | 0.187867 | + | 0.325396i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.50000 | + | 16.4545i | −0.592594 | + | 1.02640i | 0.401288 | + | 0.915952i | \(0.368563\pi\) |
−0.993882 | + | 0.110450i | \(0.964771\pi\) | |||||||
\(258\) | 16.0000 | 0.996116 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | 7.00000 | + | 12.1244i | 0.432461 | + | 0.749045i | ||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 2.00000 | + | 3.46410i | 0.123091 | + | 0.213201i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.0000 | −1.59117 | ||||||||
\(268\) | 3.00000 | − | 5.19615i | 0.183254 | − | 0.317406i | ||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | −4.00000 | −0.243432 | ||||||||
\(271\) | −3.00000 | + | 5.19615i | −0.182237 | + | 0.315644i | −0.942642 | − | 0.333805i | \(-0.891667\pi\) |
0.760405 | + | 0.649449i | \(0.225000\pi\) | |||||||
\(272\) | −1.50000 | − | 2.59808i | −0.0909509 | − | 0.157532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.5000 | + | 18.1865i | −0.634328 | + | 1.09869i | ||||
\(275\) | 4.00000 | − | 6.92820i | 0.241209 | − | 0.417786i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 10.5000 | + | 18.1865i | 0.630884 | + | 1.09272i | 0.987371 | + | 0.158423i | \(0.0506409\pi\) |
−0.356488 | + | 0.934300i | \(0.616026\pi\) | |||||||
\(278\) | 7.00000 | + | 12.1244i | 0.419832 | + | 0.727171i | ||||
\(279\) | −5.00000 | + | 8.66025i | −0.299342 | + | 0.518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.50000 | − | 7.79423i | 0.268447 | − | 0.464965i | −0.700014 | − | 0.714130i | \(-0.746823\pi\) |
0.968461 | + | 0.249165i | \(0.0801561\pi\) | |||||||
\(282\) | −4.00000 | −0.238197 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −9.00000 | −0.528498 | ||||||||
\(291\) | −3.00000 | − | 5.19615i | −0.175863 | − | 0.304604i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | −3.50000 | − | 6.06218i | −0.204472 | − | 0.354156i | 0.745492 | − | 0.666514i | \(-0.232214\pi\) |
−0.949964 | + | 0.312358i | \(0.898881\pi\) | |||||||
\(294\) | −7.00000 | + | 12.1244i | −0.408248 | + | 0.707107i | ||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0.500000 | − | 6.06218i | 0.0290619 | − | 0.352357i | ||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | −4.50000 | + | 7.79423i | −0.260678 | + | 0.451508i | ||||
\(299\) | −18.0000 | − | 31.1769i | −1.04097 | − | 1.80301i | ||||
\(300\) | 4.00000 | + | 6.92820i | 0.230940 | + | 0.400000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.00000 | −0.345261 | ||||||||
\(303\) | −7.00000 | − | 12.1244i | −0.402139 | − | 0.696526i | ||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −2.50000 | + | 4.33013i | −0.143150 | + | 0.247942i | ||||
\(306\) | −3.00000 | −0.171499 | ||||||||
\(307\) | 32.0000 | 1.82634 | 0.913168 | − | 0.407583i | \(-0.133628\pi\) | ||||
0.913168 | + | 0.407583i | \(0.133628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | + | 13.8564i | 0.455104 | + | 0.788263i | ||||
\(310\) | 10.0000 | 0.567962 | ||||||||
\(311\) | 6.00000 | − | 10.3923i | 0.340229 | − | 0.589294i | −0.644246 | − | 0.764818i | \(-0.722829\pi\) |
0.984475 | + | 0.175525i | \(0.0561621\pi\) | |||||||
\(312\) | −6.00000 | + | 10.3923i | −0.339683 | + | 0.588348i | ||||
\(313\) | −9.50000 | + | 16.4545i | −0.536972 | + | 0.930062i | 0.462093 | + | 0.886831i | \(0.347098\pi\) |
−0.999065 | + | 0.0432311i | \(0.986235\pi\) | |||||||
\(314\) | −8.50000 | − | 14.7224i | −0.479683 | − | 0.830835i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | + | 5.19615i | −0.168763 | + | 0.292306i | ||||
\(317\) | −3.50000 | + | 6.06218i | −0.196580 | + | 0.340486i | −0.947417 | − | 0.320001i | \(-0.896317\pi\) |
0.750838 | + | 0.660487i | \(0.229650\pi\) | |||||||
\(318\) | −6.00000 | + | 10.3923i | −0.336463 | + | 0.582772i | ||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | −8.00000 | + | 13.8564i | −0.446516 | + | 0.773389i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 5.50000 | − | 9.52628i | 0.305556 | − | 0.529238i | ||||
\(325\) | 24.0000 | 1.33128 | ||||||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | −26.0000 | −1.43780 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.00000 | − | 3.46410i | −0.110096 | − | 0.190693i | ||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | −5.00000 | − | 3.46410i | −0.273998 | − | 0.189832i | ||||
\(334\) | 20.0000 | 1.09435 | ||||||||
\(335\) | −3.00000 | + | 5.19615i | −0.163908 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.50000 | − | 12.9904i | −0.408551 | − | 0.707631i | 0.586177 | − | 0.810183i | \(-0.300632\pi\) |
−0.994728 | + | 0.102552i | \(0.967299\pi\) | |||||||
\(338\) | 11.5000 | + | 19.9186i | 0.625518 | + | 1.08343i | ||||
\(339\) | −20.0000 | −1.08625 | ||||||||
\(340\) | 1.50000 | + | 2.59808i | 0.0813489 | + | 0.140900i | ||||
\(341\) | 20.0000 | 1.08306 | ||||||||
\(342\) | 1.00000 | − | 1.73205i | 0.0540738 | − | 0.0936586i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | −6.00000 | + | 10.3923i | −0.323029 | + | 0.559503i | ||||
\(346\) | 3.50000 | + | 6.06218i | 0.188161 | + | 0.325905i | ||||
\(347\) | −6.00000 | −0.322097 | −0.161048 | − | 0.986947i | \(-0.551488\pi\) | ||||
−0.161048 | + | 0.986947i | \(0.551488\pi\) | |||||||
\(348\) | 9.00000 | − | 15.5885i | 0.482451 | − | 0.835629i | ||||
\(349\) | −9.50000 | + | 16.4545i | −0.508523 | + | 0.880788i | 0.491428 | + | 0.870918i | \(0.336475\pi\) |
−0.999951 | + | 0.00987003i | \(0.996858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0000 | − | 20.7846i | −0.640513 | − | 1.10940i | ||||
\(352\) | 1.00000 | + | 1.73205i | 0.0533002 | + | 0.0923186i | ||||
\(353\) | 10.5000 | − | 18.1865i | 0.558859 | − | 0.967972i | −0.438733 | − | 0.898617i | \(-0.644573\pi\) |
0.997592 | − | 0.0693543i | \(-0.0220939\pi\) | |||||||
\(354\) | 8.00000 | − | 13.8564i | 0.425195 | − | 0.736460i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.0000 | −0.688999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | − | 20.7846i | 0.634220 | − | 1.09850i | ||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −11.0000 | −0.578147 | ||||||||
\(363\) | 7.00000 | + | 12.1244i | 0.367405 | + | 0.636364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | − | 1.73205i | −0.0523424 | − | 0.0906597i | ||||
\(366\) | −5.00000 | − | 8.66025i | −0.261354 | − | 0.452679i | ||||
\(367\) | 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 | ||||||||
\(370\) | −0.500000 | + | 6.06218i | −0.0259938 | + | 0.315158i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.0000 | + | 17.3205i | −0.518476 | + | 0.898027i | ||||
\(373\) | 18.5000 | + | 32.0429i | 0.957894 | + | 1.65912i | 0.727603 | + | 0.685999i | \(0.240634\pi\) |
0.230291 | + | 0.973122i | \(0.426032\pi\) | |||||||
\(374\) | 3.00000 | + | 5.19615i | 0.155126 | + | 0.268687i | ||||
\(375\) | −9.00000 | − | 15.5885i | −0.464758 | − | 0.804984i | ||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | −27.0000 | − | 46.7654i | −1.39057 | − | 2.40854i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | − | 17.3205i | 0.513665 | − | 0.889695i | −0.486209 | − | 0.873843i | \(-0.661621\pi\) |
0.999874 | − | 0.0158521i | \(-0.00504609\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | −28.0000 | −1.43448 | ||||||||
\(382\) | 11.0000 | − | 19.0526i | 0.562809 | − | 0.974814i | ||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.50000 | − | 9.52628i | 0.279943 | − | 0.484875i | ||||
\(387\) | 4.00000 | − | 6.92820i | 0.203331 | − | 0.352180i | ||||
\(388\) | −1.50000 | − | 2.59808i | −0.0761510 | − | 0.131897i | ||||
\(389\) | −5.50000 | − | 9.52628i | −0.278861 | − | 0.483002i | 0.692241 | − | 0.721666i | \(-0.256624\pi\) |
−0.971102 | + | 0.238665i | \(0.923290\pi\) | |||||||
\(390\) | 6.00000 | − | 10.3923i | 0.303822 | − | 0.526235i | ||||
\(391\) | 9.00000 | − | 15.5885i | 0.455150 | − | 0.788342i | ||||
\(392\) | −3.50000 | + | 6.06218i | −0.176777 | + | 0.306186i | ||||
\(393\) | 28.0000 | 1.41241 | ||||||||
\(394\) | −4.50000 | − | 7.79423i | −0.226707 | − | 0.392668i | ||||
\(395\) | 3.00000 | − | 5.19615i | 0.150946 | − | 0.261447i | ||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | −25.0000 | −1.25471 | −0.627357 | − | 0.778732i | \(-0.715863\pi\) | ||||
−0.627357 | + | 0.778732i | \(0.715863\pi\) | |||||||
\(398\) | −10.0000 | + | 17.3205i | −0.501255 | + | 0.868199i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | −6.00000 | − | 10.3923i | −0.299253 | − | 0.518321i | ||||
\(403\) | 30.0000 | + | 51.9615i | 1.49441 | + | 2.58839i | ||||
\(404\) | −3.50000 | − | 6.06218i | −0.174132 | − | 0.301605i | ||||
\(405\) | −5.50000 | + | 9.52628i | −0.273297 | + | 0.473365i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00000 | + | 12.1244i | −0.0495682 | + | 0.600982i | ||||
\(408\) | −6.00000 | −0.297044 | ||||||||
\(409\) | 10.5000 | − | 18.1865i | 0.519192 | − | 0.899266i | −0.480560 | − | 0.876962i | \(-0.659566\pi\) |
0.999751 | − | 0.0223042i | \(-0.00710022\pi\) | |||||||
\(410\) | −1.50000 | − | 2.59808i | −0.0740797 | − | 0.128310i | ||||
\(411\) | 21.0000 | + | 36.3731i | 1.03585 | + | 1.79415i | ||||
\(412\) | 4.00000 | + | 6.92820i | 0.197066 | + | 0.341328i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.00000 | − | 5.19615i | −0.147442 | − | 0.255377i | ||||
\(415\) | −2.00000 | −0.0981761 | ||||||||
\(416\) | −3.00000 | + | 5.19615i | −0.147087 | + | 0.254762i | ||||
\(417\) | 28.0000 | 1.37117 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 2.00000 | − | 3.46410i | 0.0977064 | − | 0.169232i | −0.813029 | − | 0.582224i | \(-0.802183\pi\) |
0.910735 | + | 0.412991i | \(0.135516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0000 | −1.21843 | −0.609213 | − | 0.793007i | \(-0.708514\pi\) | ||||
−0.609213 | + | 0.793007i | \(0.708514\pi\) | |||||||
\(422\) | −6.00000 | + | 10.3923i | −0.292075 | + | 0.505889i | ||||
\(423\) | −1.00000 | + | 1.73205i | −0.0486217 | + | 0.0842152i | ||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.00000 | + | 6.92820i | −0.193347 | + | 0.334887i | ||||
\(429\) | 12.0000 | − | 20.7846i | 0.579365 | − | 1.00349i | ||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 0.0481683 | + | 0.0834300i | 0.889104 | − | 0.457705i | \(-0.151328\pi\) |
−0.840936 | + | 0.541135i | \(0.817995\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | −9.00000 | −0.432512 | −0.216256 | − | 0.976337i | \(-0.569385\pi\) | ||||
−0.216256 | + | 0.976337i | \(0.569385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.00000 | + | 15.5885i | −0.431517 | + | 0.747409i | ||||
\(436\) | −13.0000 | −0.622587 | ||||||||
\(437\) | 6.00000 | + | 10.3923i | 0.287019 | + | 0.497131i | ||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | −1.00000 | − | 1.73205i | −0.0476731 | − | 0.0825723i | ||||
\(441\) | 3.50000 | + | 6.06218i | 0.166667 | + | 0.288675i | ||||
\(442\) | −9.00000 | + | 15.5885i | −0.428086 | + | 0.741467i | ||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | −10.0000 | − | 6.92820i | −0.474579 | − | 0.328798i | ||||
\(445\) | 13.0000 | 0.616259 | ||||||||
\(446\) | 1.00000 | − | 1.73205i | 0.0473514 | − | 0.0820150i | ||||
\(447\) | 9.00000 | + | 15.5885i | 0.425685 | + | 0.737309i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.0000 | + | 29.4449i | 0.802280 | + | 1.38959i | 0.918112 | + | 0.396320i | \(0.129713\pi\) |
−0.115833 | + | 0.993269i | \(0.536954\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | −3.00000 | − | 5.19615i | −0.141264 | − | 0.244677i | ||||
\(452\) | −10.0000 | −0.470360 | ||||||||
\(453\) | −6.00000 | + | 10.3923i | −0.281905 | + | 0.488273i | ||||
\(454\) | −30.0000 | −1.40797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.00000 | − | 3.46410i | 0.0936586 | − | 0.162221i | ||||
\(457\) | −13.5000 | − | 23.3827i | −0.631503 | − | 1.09380i | −0.987245 | − | 0.159211i | \(-0.949105\pi\) |
0.355741 | − | 0.934585i | \(-0.384228\pi\) | |||||||
\(458\) | 17.0000 | 0.794358 | ||||||||
\(459\) | 6.00000 | − | 10.3923i | 0.280056 | − | 0.485071i | ||||
\(460\) | −3.00000 | + | 5.19615i | −0.139876 | + | 0.242272i | ||||
\(461\) | −13.0000 | + | 22.5167i | −0.605470 | + | 1.04871i | 0.386507 | + | 0.922287i | \(0.373682\pi\) |
−0.991977 | + | 0.126419i | \(0.959652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0000 | + | 17.3205i | 0.464739 | + | 0.804952i | 0.999190 | − | 0.0402476i | \(-0.0128147\pi\) |
−0.534450 | + | 0.845200i | \(0.679481\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 10.0000 | − | 17.3205i | 0.463739 | − | 0.803219i | ||||
\(466\) | −0.500000 | + | 0.866025i | −0.0231621 | + | 0.0401179i | ||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 3.00000 | + | 5.19615i | 0.138675 | + | 0.240192i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.00000 | 0.0922531 | ||||||||
\(471\) | −34.0000 | −1.56664 | ||||||||
\(472\) | 4.00000 | − | 6.92820i | 0.184115 | − | 0.318896i | ||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | 6.00000 | + | 10.3923i | 0.275589 | + | 0.477334i | ||||
\(475\) | −8.00000 | −0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | + | 5.19615i | 0.137361 | + | 0.237915i | ||||
\(478\) | 2.00000 | + | 3.46410i | 0.0914779 | + | 0.158444i | ||||
\(479\) | −16.0000 | + | 27.7128i | −0.731059 | + | 1.26623i | 0.225372 | + | 0.974273i | \(0.427640\pi\) |
−0.956431 | + | 0.291958i | \(0.905693\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | −33.0000 | + | 15.5885i | −1.50467 | + | 0.710772i | ||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 1.50000 | + | 2.59808i | 0.0681115 | + | 0.117973i | ||||
\(486\) | −5.00000 | − | 8.66025i | −0.226805 | − | 0.392837i | ||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | −2.50000 | − | 4.33013i | −0.113170 | − | 0.196016i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 3.50000 | − | 6.06218i | 0.158114 | − | 0.273861i | ||||
\(491\) | −18.0000 | −0.812329 | −0.406164 | − | 0.913800i | \(-0.633134\pi\) | ||||
−0.406164 | + | 0.913800i | \(0.633134\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 13.5000 | − | 23.3827i | 0.608009 | − | 1.05310i | ||||
\(494\) | −6.00000 | − | 10.3923i | −0.269953 | − | 0.467572i | ||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −5.00000 | + | 8.66025i | −0.224507 | + | 0.388857i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.00000 | − | 3.46410i | 0.0896221 | − | 0.155230i | ||||
\(499\) | −15.0000 | − | 25.9808i | −0.671492 | − | 1.16306i | −0.977481 | − | 0.211024i | \(-0.932320\pi\) |
0.305989 | − | 0.952035i | \(-0.401013\pi\) | |||||||
\(500\) | −4.50000 | − | 7.79423i | −0.201246 | − | 0.348569i | ||||
\(501\) | 20.0000 | − | 34.6410i | 0.893534 | − | 1.54765i | ||||
\(502\) | 10.0000 | − | 17.3205i | 0.446322 | − | 0.773052i | ||||
\(503\) | −7.00000 | + | 12.1244i | −0.312115 | + | 0.540598i | −0.978820 | − | 0.204723i | \(-0.934371\pi\) |
0.666705 | + | 0.745321i | \(0.267704\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.50000 | + | 6.06218i | 0.155748 | + | 0.269763i | ||||
\(506\) | −6.00000 | + | 10.3923i | −0.266733 | + | 0.461994i | ||||
\(507\) | 46.0000 | 2.04293 | ||||||||
\(508\) | −14.0000 | −0.621150 | ||||||||
\(509\) | 4.50000 | − | 7.79423i | 0.199459 | − | 0.345473i | −0.748894 | − | 0.662690i | \(-0.769415\pi\) |
0.948353 | + | 0.317217i | \(0.102748\pi\) | |||||||
\(510\) | 6.00000 | 0.265684 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.00000 | + | 6.92820i | 0.176604 | + | 0.305888i | ||||
\(514\) | 9.50000 | + | 16.4545i | 0.419027 | + | 0.725776i | ||||
\(515\) | −4.00000 | − | 6.92820i | −0.176261 | − | 0.305293i | ||||
\(516\) | 8.00000 | − | 13.8564i | 0.352180 | − | 0.609994i | ||||
\(517\) | 4.00000 | 0.175920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | −15.0000 | − | 25.9808i | −0.657162 | − | 1.13824i | −0.981347 | − | 0.192244i | \(-0.938423\pi\) |
0.324185 | − | 0.945994i | \(-0.394910\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | −3.00000 | − | 5.19615i | −0.131181 | − | 0.227212i | 0.792951 | − | 0.609285i | \(-0.208544\pi\) |
−0.924132 | + | 0.382073i | \(0.875210\pi\) | |||||||
\(524\) | 14.0000 | 0.611593 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | −15.0000 | + | 25.9808i | −0.653410 | + | 1.13174i | ||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | −4.00000 | − | 6.92820i | −0.173585 | − | 0.300658i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00000 | − | 15.5885i | 0.389833 | − | 0.675211i | ||||
\(534\) | −13.0000 | + | 22.5167i | −0.562565 | + | 0.974391i | ||||
\(535\) | 4.00000 | − | 6.92820i | 0.172935 | − | 0.299532i | ||||
\(536\) | −3.00000 | − | 5.19615i | −0.129580 | − | 0.224440i | ||||
\(537\) | −24.0000 | − | 41.5692i | −1.03568 | − | 1.79384i | ||||
\(538\) | 1.00000 | − | 1.73205i | 0.0431131 | − | 0.0746740i | ||||
\(539\) | 7.00000 | − | 12.1244i | 0.301511 | − | 0.522233i | ||||
\(540\) | −2.00000 | + | 3.46410i | −0.0860663 | + | 0.149071i | ||||
\(541\) | −9.00000 | −0.386940 | −0.193470 | − | 0.981106i | \(-0.561974\pi\) | ||||
−0.193470 | + | 0.981106i | \(0.561974\pi\) | |||||||
\(542\) | 3.00000 | + | 5.19615i | 0.128861 | + | 0.223194i | ||||
\(543\) | −11.0000 | + | 19.0526i | −0.472055 | + | 0.817624i | ||||
\(544\) | −3.00000 | −0.128624 | ||||||||
\(545\) | 13.0000 | 0.556859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.00000 | −0.256541 | −0.128271 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128271 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(548\) | 10.5000 | + | 18.1865i | 0.448538 | + | 0.776890i | ||||
\(549\) | −5.00000 | −0.213395 | ||||||||
\(550\) | −4.00000 | − | 6.92820i | −0.170561 | − | 0.295420i | ||||
\(551\) | 9.00000 | + | 15.5885i | 0.383413 | + | 0.664091i | ||||
\(552\) | −6.00000 | − | 10.3923i | −0.255377 | − | 0.442326i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.0000 | 0.892205 | ||||||||
\(555\) | 10.0000 | + | 6.92820i | 0.424476 | + | 0.294086i | ||||
\(556\) | 14.0000 | 0.593732 | ||||||||
\(557\) | −17.5000 | + | 30.3109i | −0.741499 | + | 1.28431i | 0.210314 | + | 0.977634i | \(0.432551\pi\) |
−0.951813 | + | 0.306680i | \(0.900782\pi\) | |||||||
\(558\) | 5.00000 | + | 8.66025i | 0.211667 | + | 0.366618i | ||||
\(559\) | −24.0000 | − | 41.5692i | −1.01509 | − | 1.75819i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | −4.50000 | − | 7.79423i | −0.189821 | − | 0.328780i | ||||
\(563\) | 10.0000 | 0.421450 | 0.210725 | − | 0.977545i | \(-0.432418\pi\) | ||||
0.210725 | + | 0.977545i | \(0.432418\pi\) | |||||||
\(564\) | −2.00000 | + | 3.46410i | −0.0842152 | + | 0.145865i | ||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0000 | 0.461144 | 0.230572 | − | 0.973055i | \(-0.425940\pi\) | ||||
0.230572 | + | 0.973055i | \(0.425940\pi\) | |||||||
\(570\) | −2.00000 | + | 3.46410i | −0.0837708 | + | 0.145095i | ||||
\(571\) | −9.00000 | + | 15.5885i | −0.376638 | + | 0.652357i | −0.990571 | − | 0.137002i | \(-0.956253\pi\) |
0.613933 | + | 0.789359i | \(0.289587\pi\) | |||||||
\(572\) | 6.00000 | − | 10.3923i | 0.250873 | − | 0.434524i | ||||
\(573\) | −22.0000 | − | 38.1051i | −0.919063 | − | 1.59186i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | + | 20.7846i | −0.500435 | + | 0.866778i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 1.00000 | − | 1.73205i | 0.0416305 | − | 0.0721062i | −0.844459 | − | 0.535620i | \(-0.820078\pi\) |
0.886090 | + | 0.463513i | \(0.153411\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | −11.0000 | − | 19.0526i | −0.457144 | − | 0.791797i | ||||
\(580\) | −4.50000 | + | 7.79423i | −0.186852 | + | 0.323638i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | 6.00000 | − | 10.3923i | 0.248495 | − | 0.430405i | ||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | −3.00000 | − | 5.19615i | −0.124035 | − | 0.214834i | ||||
\(586\) | −7.00000 | −0.289167 | ||||||||
\(587\) | −15.0000 | − | 25.9808i | −0.619116 | − | 1.07234i | −0.989647 | − | 0.143521i | \(-0.954158\pi\) |
0.370531 | − | 0.928820i | \(-0.379176\pi\) | |||||||
\(588\) | 7.00000 | + | 12.1244i | 0.288675 | + | 0.500000i | ||||
\(589\) | −10.0000 | − | 17.3205i | −0.412043 | − | 0.713679i | ||||
\(590\) | −4.00000 | + | 6.92820i | −0.164677 | + | 0.285230i | ||||
\(591\) | −18.0000 | −0.740421 | ||||||||
\(592\) | −5.00000 | − | 3.46410i | −0.205499 | − | 0.142374i | ||||
\(593\) | 19.0000 | 0.780236 | 0.390118 | − | 0.920765i | \(-0.372434\pi\) | ||||
0.390118 | + | 0.920765i | \(0.372434\pi\) | |||||||
\(594\) | −4.00000 | + | 6.92820i | −0.164122 | + | 0.284268i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.50000 | + | 7.79423i | 0.184327 | + | 0.319264i | ||||
\(597\) | 20.0000 | + | 34.6410i | 0.818546 | + | 1.41776i | ||||
\(598\) | −36.0000 | −1.47215 | ||||||||
\(599\) | −5.00000 | − | 8.66025i | −0.204294 | − | 0.353848i | 0.745613 | − | 0.666379i | \(-0.232157\pi\) |
−0.949908 | + | 0.312531i | \(0.898823\pi\) | |||||||
\(600\) | 8.00000 | 0.326599 | ||||||||
\(601\) | 2.50000 | − | 4.33013i | 0.101977 | − | 0.176630i | −0.810522 | − | 0.585708i | \(-0.800816\pi\) |
0.912499 | + | 0.409079i | \(0.134150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | −3.00000 | + | 5.19615i | −0.122068 | + | 0.211428i | ||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | −14.0000 | −0.568711 | ||||||||
\(607\) | −5.00000 | + | 8.66025i | −0.202944 | + | 0.351509i | −0.949476 | − | 0.313841i | \(-0.898384\pi\) |
0.746532 | + | 0.665350i | \(0.231718\pi\) | |||||||
\(608\) | 1.00000 | − | 1.73205i | 0.0405554 | − | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.50000 | + | 4.33013i | 0.101222 | + | 0.175322i | ||||
\(611\) | 6.00000 | + | 10.3923i | 0.242734 | + | 0.420428i | ||||
\(612\) | −1.50000 | + | 2.59808i | −0.0606339 | + | 0.105021i | ||||
\(613\) | −5.50000 | + | 9.52628i | −0.222143 | + | 0.384763i | −0.955458 | − | 0.295126i | \(-0.904638\pi\) |
0.733316 | + | 0.679888i | \(0.237972\pi\) | |||||||
\(614\) | 16.0000 | − | 27.7128i | 0.645707 | − | 1.11840i | ||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.00000 | + | 12.1244i | −0.281809 | + | 0.488108i | −0.971830 | − | 0.235681i | \(-0.924268\pi\) |
0.690021 | + | 0.723789i | \(0.257601\pi\) | |||||||
\(618\) | 16.0000 | 0.643614 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 5.00000 | − | 8.66025i | 0.200805 | − | 0.347804i | ||||
\(621\) | 24.0000 | 0.963087 | ||||||||
\(622\) | −6.00000 | − | 10.3923i | −0.240578 | − | 0.416693i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.00000 | + | 10.3923i | 0.240192 | + | 0.416025i | ||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 9.50000 | + | 16.4545i | 0.379696 | + | 0.657653i | ||||
\(627\) | −4.00000 | + | 6.92820i | −0.159745 | + | 0.276686i | ||||
\(628\) | −17.0000 | −0.678374 | ||||||||
\(629\) | −15.0000 | − | 10.3923i | −0.598089 | − | 0.414368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.00000 | + | 8.66025i | −0.199047 | + | 0.344759i | −0.948220 | − | 0.317615i | \(-0.897118\pi\) |
0.749173 | + | 0.662375i | \(0.230451\pi\) | |||||||
\(632\) | 3.00000 | + | 5.19615i | 0.119334 | + | 0.206692i | ||||
\(633\) | 12.0000 | + | 20.7846i | 0.476957 | + | 0.826114i | ||||
\(634\) | 3.50000 | + | 6.06218i | 0.139003 | + | 0.240760i | ||||
\(635\) | 14.0000 | 0.555573 | ||||||||
\(636\) | 6.00000 | + | 10.3923i | 0.237915 | + | 0.412082i | ||||
\(637\) | 42.0000 | 1.66410 | ||||||||
\(638\) | −9.00000 | + | 15.5885i | −0.356313 | + | 0.617153i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −9.50000 | + | 16.4545i | −0.375227 | + | 0.649913i | −0.990361 | − | 0.138510i | \(-0.955769\pi\) |
0.615134 | + | 0.788423i | \(0.289102\pi\) | |||||||
\(642\) | 8.00000 | + | 13.8564i | 0.315735 | + | 0.546869i | ||||
\(643\) | −34.0000 | −1.34083 | −0.670415 | − | 0.741987i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741987i | \(0.733884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | + | 13.8564i | −0.315000 | + | 0.545595i | ||||
\(646\) | 3.00000 | − | 5.19615i | 0.118033 | − | 0.204440i | ||||
\(647\) | −2.00000 | − | 3.46410i | −0.0786281 | − | 0.136188i | 0.824030 | − | 0.566546i | \(-0.191721\pi\) |
−0.902658 | + | 0.430358i | \(0.858387\pi\) | |||||||
\(648\) | −5.50000 | − | 9.52628i | −0.216060 | − | 0.374228i | ||||
\(649\) | −8.00000 | + | 13.8564i | −0.314027 | + | 0.543912i | ||||
\(650\) | 12.0000 | − | 20.7846i | 0.470679 | − | 0.815239i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.00000 | 0.156652 | ||||||||
\(653\) | −7.50000 | − | 12.9904i | −0.293498 | − | 0.508353i | 0.681137 | − | 0.732156i | \(-0.261486\pi\) |
−0.974634 | + | 0.223803i | \(0.928153\pi\) | |||||||
\(654\) | −13.0000 | + | 22.5167i | −0.508340 | + | 0.880471i | ||||
\(655\) | −14.0000 | −0.547025 | ||||||||
\(656\) | 3.00000 | 0.117130 | ||||||||
\(657\) | 1.00000 | − | 1.73205i | 0.0390137 | − | 0.0675737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0000 | + | 17.3205i | 0.389545 | + | 0.674711i | 0.992388 | − | 0.123148i | \(-0.0392990\pi\) |
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(660\) | −4.00000 | −0.155700 | ||||||||
\(661\) | −13.5000 | − | 23.3827i | −0.525089 | − | 0.909481i | −0.999573 | − | 0.0292169i | \(-0.990699\pi\) |
0.474484 | − | 0.880264i | \(-0.342635\pi\) | |||||||
\(662\) | −10.0000 | − | 17.3205i | −0.388661 | − | 0.673181i | ||||
\(663\) | 18.0000 | + | 31.1769i | 0.699062 | + | 1.21081i | ||||
\(664\) | 1.00000 | − | 1.73205i | 0.0388075 | − | 0.0672166i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.50000 | + | 2.59808i | −0.213121 | + | 0.100673i | ||||
\(667\) | 54.0000 | 2.09089 | ||||||||
\(668\) | 10.0000 | − | 17.3205i | 0.386912 | − | 0.670151i | ||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 3.00000 | + | 5.19615i | 0.115900 | + | 0.200745i | ||||
\(671\) | 5.00000 | + | 8.66025i | 0.193023 | + | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00000 | + | 1.73205i | 0.0385472 | + | 0.0667657i | 0.884655 | − | 0.466246i | \(-0.154394\pi\) |
−0.846108 | + | 0.533011i | \(0.821060\pi\) | |||||||
\(674\) | −15.0000 | −0.577778 | ||||||||
\(675\) | −8.00000 | + | 13.8564i | −0.307920 | + | 0.533333i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 47.0000 | 1.80636 | 0.903178 | − | 0.429265i | \(-0.141228\pi\) | ||||
0.903178 | + | 0.429265i | \(0.141228\pi\) | |||||||
\(678\) | −10.0000 | + | 17.3205i | −0.384048 | + | 0.665190i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.00000 | 0.115045 | ||||||||
\(681\) | −30.0000 | + | 51.9615i | −1.14960 | + | 1.99117i | ||||
\(682\) | 10.0000 | − | 17.3205i | 0.382920 | − | 0.663237i | ||||
\(683\) | 12.0000 | − | 20.7846i | 0.459167 | − | 0.795301i | −0.539750 | − | 0.841825i | \(-0.681481\pi\) |
0.998917 | + | 0.0465244i | \(0.0148145\pi\) | |||||||
\(684\) | −1.00000 | − | 1.73205i | −0.0382360 | − | 0.0662266i | ||||
\(685\) | −10.5000 | − | 18.1865i | −0.401184 | − | 0.694872i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.0000 | − | 29.4449i | 0.648590 | − | 1.12339i | ||||
\(688\) | 4.00000 | − | 6.92820i | 0.152499 | − | 0.264135i | ||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 6.00000 | + | 10.3923i | 0.228416 | + | 0.395628i | ||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | 7.00000 | 0.266100 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.00000 | + | 5.19615i | −0.113878 | + | 0.197243i | ||||
\(695\) | −14.0000 | −0.531050 | ||||||||
\(696\) | −9.00000 | − | 15.5885i | −0.341144 | − | 0.590879i | ||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 9.50000 | + | 16.4545i | 0.359580 | + | 0.622811i | ||||
\(699\) | 1.00000 | + | 1.73205i | 0.0378235 | + | 0.0655122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.00000 | − | 1.73205i | 0.0377695 | − | 0.0654187i | −0.846523 | − | 0.532353i | \(-0.821308\pi\) |
0.884292 | + | 0.466934i | \(0.154641\pi\) | |||||||
\(702\) | −24.0000 | −0.905822 | ||||||||
\(703\) | 11.0000 | − | 5.19615i | 0.414873 | − | 0.195977i | ||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 2.00000 | − | 3.46410i | 0.0753244 | − | 0.130466i | ||||
\(706\) | −10.5000 | − | 18.1865i | −0.395173 | − | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.00000 | − | 13.8564i | −0.300658 | − | 0.520756i | ||||
\(709\) | −6.00000 | −0.225335 | −0.112667 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112667 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.00000 | 0.225018 | ||||||||
\(712\) | −6.50000 | + | 11.2583i | −0.243598 | + | 0.421924i | ||||
\(713\) | −60.0000 | −2.24702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | + | 10.3923i | −0.224387 | + | 0.388650i | ||||
\(716\) | −12.0000 | − | 20.7846i | −0.448461 | − | 0.776757i | ||||
\(717\) | 8.00000 | 0.298765 | ||||||||
\(718\) | 8.00000 | − | 13.8564i | 0.298557 | − | 0.517116i | ||||
\(719\) | −9.00000 | + | 15.5885i | −0.335643 | + | 0.581351i | −0.983608 | − | 0.180319i | \(-0.942287\pi\) |
0.647965 | + | 0.761670i | \(0.275620\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.50000 | − | 12.9904i | −0.279121 | − | 0.483452i | ||||
\(723\) | 10.0000 | − | 17.3205i | 0.371904 | − | 0.644157i | ||||
\(724\) | −5.50000 | + | 9.52628i | −0.204406 | + | 0.354041i | ||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 14.0000 | 0.519589 | ||||||||
\(727\) | 14.0000 | + | 24.2487i | 0.519231 | + | 0.899335i | 0.999750 | + | 0.0223506i | \(0.00711500\pi\) |
−0.480519 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −2.00000 | −0.0740233 | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | −10.0000 | −0.369611 | ||||||||
\(733\) | −13.0000 | − | 22.5167i | −0.480166 | − | 0.831672i | 0.519575 | − | 0.854425i | \(-0.326090\pi\) |
−0.999741 | + | 0.0227529i | \(0.992757\pi\) | |||||||
\(734\) | 4.00000 | 0.147643 | ||||||||
\(735\) | −7.00000 | − | 12.1244i | −0.258199 | − | 0.447214i | ||||
\(736\) | −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 | ||||
\(739\) | 34.0000 | 1.25071 | 0.625355 | − | 0.780340i | \(-0.284954\pi\) | ||||
0.625355 | + | 0.780340i | \(0.284954\pi\) | |||||||
\(740\) | 5.00000 | + | 3.46410i | 0.183804 | + | 0.127343i | ||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | − | 15.5885i | −0.330178 | − | 0.571885i | 0.652369 | − | 0.757902i | \(-0.273775\pi\) |
−0.982547 | + | 0.186017i | \(0.940442\pi\) | |||||||
\(744\) | 10.0000 | + | 17.3205i | 0.366618 | + | 0.635001i | ||||
\(745\) | −4.50000 | − | 7.79423i | −0.164867 | − | 0.285558i | ||||
\(746\) | 37.0000 | 1.35467 | ||||||||
\(747\) | −1.00000 | − | 1.73205i | −0.0365881 | − | 0.0633724i | ||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −18.0000 | −0.657267 | ||||||||
\(751\) | −4.00000 | −0.145962 | −0.0729810 | − | 0.997333i | \(-0.523251\pi\) | ||||
−0.0729810 | + | 0.997333i | \(0.523251\pi\) | |||||||
\(752\) | −1.00000 | + | 1.73205i | −0.0364662 | + | 0.0631614i | ||||
\(753\) | −20.0000 | − | 34.6410i | −0.728841 | − | 1.26239i | ||||
\(754\) | −54.0000 | −1.96656 | ||||||||
\(755\) | 3.00000 | − | 5.19615i | 0.109181 | − | 0.189107i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50000 | − | 14.7224i | 0.308938 | − | 0.535096i | −0.669193 | − | 0.743089i | \(-0.733360\pi\) |
0.978130 | + | 0.207993i | \(0.0666932\pi\) | |||||||
\(758\) | −10.0000 | − | 17.3205i | −0.363216 | − | 0.629109i | ||||
\(759\) | 12.0000 | + | 20.7846i | 0.435572 | + | 0.754434i | ||||
\(760\) | −1.00000 | + | 1.73205i | −0.0362738 | + | 0.0628281i | ||||
\(761\) | 6.50000 | − | 11.2583i | 0.235625 | − | 0.408114i | −0.723829 | − | 0.689979i | \(-0.757620\pi\) |
0.959454 | + | 0.281865i | \(0.0909530\pi\) | |||||||
\(762\) | −14.0000 | + | 24.2487i | −0.507166 | + | 0.878438i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.0000 | − | 19.0526i | −0.397966 | − | 0.689297i | ||||
\(765\) | 1.50000 | − | 2.59808i | 0.0542326 | − | 0.0939336i | ||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | −48.0000 | −1.73318 | ||||||||
\(768\) | −1.00000 | + | 1.73205i | −0.0360844 | + | 0.0625000i | ||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0000 | 1.36854 | ||||||||
\(772\) | −5.50000 | − | 9.52628i | −0.197949 | − | 0.342858i | ||||
\(773\) | −11.5000 | − | 19.9186i | −0.413626 | − | 0.716422i | 0.581657 | − | 0.813434i | \(-0.302405\pi\) |
−0.995283 | + | 0.0970125i | \(0.969071\pi\) | |||||||
\(774\) | −4.00000 | − | 6.92820i | −0.143777 | − | 0.249029i | ||||
\(775\) | 20.0000 | − | 34.6410i | 0.718421 | − | 1.24434i | ||||
\(776\) | −3.00000 | −0.107694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.0000 | −0.394369 | ||||||||
\(779\) | −3.00000 | + | 5.19615i | −0.107486 | + | 0.186171i | ||||
\(780\) | −6.00000 | − | 10.3923i | −0.214834 | − | 0.372104i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.00000 | − | 15.5885i | −0.321839 | − | 0.557442i | ||||
\(783\) | 36.0000 | 1.28654 | ||||||||
\(784\) | 3.50000 | + | 6.06218i | 0.125000 | + | 0.216506i | ||||
\(785\) | 17.0000 | 0.606756 | ||||||||
\(786\) | 14.0000 | − | 24.2487i | 0.499363 | − | 0.864923i | ||||
\(787\) | 4.00000 | 0.142585 | 0.0712923 | − | 0.997455i | \(-0.477288\pi\) | ||||
0.0712923 | + | 0.997455i | \(0.477288\pi\) | |||||||
\(788\) | −9.00000 | −0.320612 | ||||||||
\(789\) | 24.0000 | − | 41.5692i | 0.854423 | − | 1.47990i | ||||
\(790\) | −3.00000 | − | 5.19615i | −0.106735 | − | 0.184871i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00000 | − | 1.73205i | 0.0355335 | − | 0.0615457i | ||||
\(793\) | −15.0000 | + | 25.9808i | −0.532666 | + | 0.922604i | ||||
\(794\) | −12.5000 | + | 21.6506i | −0.443608 | + | 0.768352i | ||||
\(795\) | −6.00000 | − | 10.3923i | −0.212798 | − | 0.368577i | ||||
\(796\) | 10.0000 | + | 17.3205i | 0.354441 | + | 0.613909i | ||||
\(797\) | 17.0000 | − | 29.4449i | 0.602171 | − | 1.04299i | −0.390321 | − | 0.920679i | \(-0.627636\pi\) |
0.992492 | − | 0.122312i | \(-0.0390308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00000 | + | 5.19615i | −0.106132 | + | 0.183827i | ||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | 6.50000 | + | 11.2583i | 0.229666 | + | 0.397794i | ||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | −4.00000 | −0.141157 | ||||||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60.0000 | 2.11341 | ||||||||
\(807\) | −2.00000 | − | 3.46410i | −0.0704033 | − | 0.121942i | ||||
\(808\) | −7.00000 | −0.246259 | ||||||||
\(809\) | 27.0000 | + | 46.7654i | 0.949269 | + | 1.64418i | 0.746968 | + | 0.664860i | \(0.231509\pi\) |
0.202301 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(810\) | 5.50000 | + | 9.52628i | 0.193250 | + | 0.334719i | ||||
\(811\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000 | 0.420858 | ||||||||
\(814\) | 10.0000 | + | 6.92820i | 0.350500 | + | 0.242833i | ||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | −10.5000 | − | 18.1865i | −0.367124 | − | 0.635877i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.00000 | −0.104765 | ||||||||
\(821\) | 23.0000 | + | 39.8372i | 0.802706 | + | 1.39033i | 0.917829 | + | 0.396976i | \(0.129940\pi\) |
−0.115124 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(822\) | 42.0000 | 1.46492 | ||||||||
\(823\) | 27.0000 | − | 46.7654i | 0.941161 | − | 1.63014i | 0.177899 | − | 0.984049i | \(-0.443070\pi\) |
0.763261 | − | 0.646090i | \(-0.223597\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | −16.0000 | −0.557048 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.00000 | − | 6.92820i | −0.139094 | − | 0.240917i | 0.788060 | − | 0.615598i | \(-0.211086\pi\) |
−0.927154 | + | 0.374681i | \(0.877752\pi\) | |||||||
\(828\) | −6.00000 | −0.208514 | ||||||||
\(829\) | −25.0000 | + | 43.3013i | −0.868286 | + | 1.50392i | −0.00453881 | + | 0.999990i | \(0.501445\pi\) |
−0.863747 | + | 0.503926i | \(0.831889\pi\) | |||||||
\(830\) | −1.00000 | + | 1.73205i | −0.0347105 | + | 0.0601204i | ||||
\(831\) | 21.0000 | − | 36.3731i | 0.728482 | − | 1.26177i | ||||
\(832\) | 3.00000 | + | 5.19615i | 0.104006 | + | 0.180144i | ||||
\(833\) | 10.5000 | + | 18.1865i | 0.363803 | + | 0.630126i | ||||
\(834\) | 14.0000 | − | 24.2487i | 0.484780 | − | 0.839664i | ||||
\(835\) | −10.0000 | + | 17.3205i | −0.346064 | + | 0.599401i | ||||
\(836\) | −2.00000 | + | 3.46410i | −0.0691714 | + | 0.119808i | ||||
\(837\) | −40.0000 | −1.38260 | ||||||||
\(838\) | −2.00000 | − | 3.46410i | −0.0690889 | − | 0.119665i | ||||
\(839\) | 7.00000 | − | 12.1244i | 0.241667 | − | 0.418579i | −0.719522 | − | 0.694469i | \(-0.755639\pi\) |
0.961189 | + | 0.275890i | \(0.0889726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | −12.5000 | + | 21.6506i | −0.430778 | + | 0.746130i | ||||
\(843\) | −18.0000 | −0.619953 | ||||||||
\(844\) | 6.00000 | + | 10.3923i | 0.206529 | + | 0.357718i | ||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | 1.00000 | + | 1.73205i | 0.0343807 | + | 0.0595491i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | −4.00000 | + | 6.92820i | −0.137280 | + | 0.237775i | ||||
\(850\) | 12.0000 | 0.411597 | ||||||||
\(851\) | 3.00000 | − | 36.3731i | 0.102839 | − | 1.24685i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5000 | + | 19.9186i | −0.393753 | + | 0.681999i | −0.992941 | − | 0.118609i | \(-0.962157\pi\) |
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | + | 1.73205i | 0.0341993 | + | 0.0592349i | ||||
\(856\) | 4.00000 | + | 6.92820i | 0.136717 | + | 0.236801i | ||||
\(857\) | −5.00000 | −0.170797 | −0.0853984 | − | 0.996347i | \(-0.527216\pi\) | ||||
−0.0853984 | + | 0.996347i | \(0.527216\pi\) | |||||||
\(858\) | −12.0000 | − | 20.7846i | −0.409673 | − | 0.709575i | ||||
\(859\) | −32.0000 | −1.09183 | −0.545913 | − | 0.837842i | \(-0.683817\pi\) | ||||
−0.545913 | + | 0.837842i | \(0.683817\pi\) | |||||||
\(860\) | −4.00000 | + | 6.92820i | −0.136399 | + | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00000 | 0.0681203 | ||||||||
\(863\) | −12.0000 | + | 20.7846i | −0.408485 | + | 0.707516i | −0.994720 | − | 0.102624i | \(-0.967276\pi\) |
0.586235 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(864\) | −2.00000 | − | 3.46410i | −0.0680414 | − | 0.117851i | ||||
\(865\) | −7.00000 | −0.238007 | ||||||||
\(866\) | −4.50000 | + | 7.79423i | −0.152916 | + | 0.264859i | ||||
\(867\) | 8.00000 | − | 13.8564i | 0.271694 | − | 0.470588i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | − | 10.3923i | −0.203536 | − | 0.352535i | ||||
\(870\) | 9.00000 | + | 15.5885i | 0.305129 | + | 0.528498i | ||||
\(871\) | −18.0000 | + | 31.1769i | −0.609907 | + | 1.05639i | ||||
\(872\) | −6.50000 | + | 11.2583i | −0.220118 | + | 0.381255i | ||||
\(873\) | −1.50000 | + | 2.59808i | −0.0507673 | + | 0.0879316i | ||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | − | 3.46410i | 0.0675737 | − | 0.117041i | ||||
\(877\) | −5.00000 | −0.168838 | −0.0844190 | − | 0.996430i | \(-0.526903\pi\) | ||||
−0.0844190 | + | 0.996430i | \(0.526903\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | −7.00000 | + | 12.1244i | −0.236104 | + | 0.408944i | ||||
\(880\) | −2.00000 | −0.0674200 | ||||||||
\(881\) | −25.5000 | − | 44.1673i | −0.859117 | − | 1.48803i | −0.872772 | − | 0.488127i | \(-0.837680\pi\) |
0.0136556 | − | 0.999907i | \(-0.495653\pi\) | |||||||
\(882\) | 7.00000 | 0.235702 | ||||||||
\(883\) | −23.0000 | − | 39.8372i | −0.774012 | − | 1.34063i | −0.935348 | − | 0.353728i | \(-0.884914\pi\) |
0.161337 | − | 0.986899i | \(-0.448419\pi\) | |||||||
\(884\) | 9.00000 | + | 15.5885i | 0.302703 | + | 0.524297i | ||||
\(885\) | 8.00000 | + | 13.8564i | 0.268917 | + | 0.465778i | ||||
\(886\) | 12.0000 | − | 20.7846i | 0.403148 | − | 0.698273i | ||||
\(887\) | −14.0000 | −0.470074 | −0.235037 | − | 0.971986i | \(-0.575521\pi\) | ||||
−0.235037 | + | 0.971986i | \(0.575521\pi\) | |||||||
\(888\) | −11.0000 | + | 5.19615i | −0.369136 | + | 0.174371i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.50000 | − | 11.2583i | 0.217880 | − | 0.377380i | ||||
\(891\) | 11.0000 | + | 19.0526i | 0.368514 | + | 0.638285i | ||||
\(892\) | −1.00000 | − | 1.73205i | −0.0334825 | − | 0.0579934i | ||||
\(893\) | −2.00000 | − | 3.46410i | −0.0669274 | − | 0.115922i | ||||
\(894\) | 18.0000 | 0.602010 | ||||||||
\(895\) | 12.0000 | + | 20.7846i | 0.401116 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | + | 62.3538i | −1.20201 | + | 2.08193i | ||||
\(898\) | 34.0000 | 1.13459 | ||||||||
\(899\) | −90.0000 | −3.00167 | ||||||||
\(900\) | 2.00000 | − | 3.46410i | 0.0666667 | − | 0.115470i | ||||
\(901\) | 9.00000 | + | 15.5885i | 0.299833 | + | 0.519327i | ||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.00000 | + | 8.66025i | −0.166298 | + | 0.288036i | ||||
\(905\) | 5.50000 | − | 9.52628i | 0.182826 | − | 0.316664i | ||||
\(906\) | 6.00000 | + | 10.3923i | 0.199337 | + | 0.345261i | ||||
\(907\) | −7.00000 | − | 12.1244i | −0.232431 | − | 0.402583i | 0.726092 | − | 0.687598i | \(-0.241335\pi\) |
−0.958523 | + | 0.285015i | \(0.908001\pi\) | |||||||
\(908\) | −15.0000 | + | 25.9808i | −0.497792 | + | 0.862202i | ||||
\(909\) | −3.50000 | + | 6.06218i | −0.116088 | + | 0.201070i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.00000 | 0.0662630 | 0.0331315 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331315 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | −2.00000 | + | 3.46410i | −0.0661903 | + | 0.114645i | ||||
\(914\) | −27.0000 | −0.893081 | ||||||||
\(915\) | 10.0000 | 0.330590 | ||||||||
\(916\) | 8.50000 | − | 14.7224i | 0.280848 | − | 0.486443i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.00000 | − | 10.3923i | −0.198030 | − | 0.342997i | ||||
\(919\) | 10.0000 | 0.329870 | 0.164935 | − | 0.986304i | \(-0.447259\pi\) | ||||
0.164935 | + | 0.986304i | \(0.447259\pi\) | |||||||
\(920\) | 3.00000 | + | 5.19615i | 0.0989071 | + | 0.171312i | ||||
\(921\) | −32.0000 | − | 55.4256i | −1.05444 | − | 1.82634i | ||||
\(922\) | 13.0000 | + | 22.5167i | 0.428132 | + | 0.741547i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | + | 13.8564i | 0.657596 | + | 0.455596i | ||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 4.00000 | − | 6.92820i | 0.131377 | − | 0.227552i | ||||
\(928\) | −4.50000 | − | 7.79423i | −0.147720 | − | 0.255858i | ||||
\(929\) | 24.5000 | + | 42.4352i | 0.803819 | + | 1.39226i | 0.917086 | + | 0.398691i | \(0.130535\pi\) |
−0.113267 | + | 0.993565i | \(0.536131\pi\) | |||||||
\(930\) | −10.0000 | − | 17.3205i | −0.327913 | − | 0.567962i | ||||
\(931\) | −14.0000 | −0.458831 | ||||||||
\(932\) | 0.500000 | + | 0.866025i | 0.0163780 | + | 0.0283676i | ||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | −6.00000 | −0.196221 | ||||||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | 0.500000 | − | 0.866025i | 0.0163343 | − | 0.0282918i | −0.857743 | − | 0.514079i | \(-0.828134\pi\) |
0.874077 | + | 0.485787i | \(0.161467\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.0000 | 1.24008 | ||||||||
\(940\) | 1.00000 | − | 1.73205i | 0.0326164 | − | 0.0564933i | ||||
\(941\) | −7.50000 | + | 12.9904i | −0.244493 | + | 0.423474i | −0.961989 | − | 0.273088i | \(-0.911955\pi\) |
0.717496 | + | 0.696563i | \(0.245288\pi\) | |||||||
\(942\) | −17.0000 | + | 29.4449i | −0.553890 | + | 0.959366i | ||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | −4.00000 | − | 6.92820i | −0.130189 | − | 0.225494i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | + | 13.8564i | −0.260102 | + | 0.450511i | ||||
\(947\) | −12.0000 | + | 20.7846i | −0.389948 | + | 0.675409i | −0.992442 | − | 0.122714i | \(-0.960840\pi\) |
0.602494 | + | 0.798123i | \(0.294174\pi\) | |||||||
\(948\) | 12.0000 | 0.389742 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | −4.00000 | + | 6.92820i | −0.129777 | + | 0.224781i | ||||
\(951\) | 14.0000 | 0.453981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.00000 | + | 8.66025i | −0.161966 | + | 0.280533i | −0.935574 | − | 0.353132i | \(-0.885117\pi\) |
0.773608 | + | 0.633665i | \(0.218450\pi\) | |||||||
\(954\) | 6.00000 | 0.194257 | ||||||||
\(955\) | 11.0000 | + | 19.0526i | 0.355952 | + | 0.616526i | ||||
\(956\) | 4.00000 | 0.129369 | ||||||||
\(957\) | 18.0000 | + | 31.1769i | 0.581857 | + | 1.00781i | ||||
\(958\) | 16.0000 | + | 27.7128i | 0.516937 | + | 0.895360i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | − | 1.73205i | 0.0322749 | − | 0.0559017i | ||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | −3.00000 | + | 36.3731i | −0.0967239 | + | 1.17271i | ||||
\(963\) | 8.00000 | 0.257796 | ||||||||
\(964\) | 5.00000 | − | 8.66025i | 0.161039 | − | 0.278928i | ||||
\(965\) | 5.50000 | + | 9.52628i | 0.177051 | + | 0.306662i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.0000 | − | 17.3205i | −0.321578 | − | 0.556990i | 0.659236 | − | 0.751936i | \(-0.270880\pi\) |
−0.980814 | + | 0.194946i | \(0.937547\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | −6.00000 | − | 10.3923i | −0.192748 | − | 0.333849i | ||||
\(970\) | 3.00000 | 0.0963242 | ||||||||
\(971\) | 3.00000 | − | 5.19615i | 0.0962746 | − | 0.166752i | −0.813865 | − | 0.581054i | \(-0.802641\pi\) |
0.910140 | + | 0.414301i | \(0.135974\pi\) | |||||||
\(972\) | −10.0000 | −0.320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.00000 | + | 1.73205i | −0.0320421 | + | 0.0554985i | ||||
\(975\) | −24.0000 | − | 41.5692i | −0.768615 | − | 1.33128i | ||||
\(976\) | −5.00000 | −0.160046 | ||||||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 4.00000 | − | 6.92820i | 0.127906 | − | 0.221540i | ||||
\(979\) | 13.0000 | − | 22.5167i | 0.415482 | − | 0.719636i | ||||
\(980\) | −3.50000 | − | 6.06218i | −0.111803 | − | 0.193649i | ||||
\(981\) | 6.50000 | + | 11.2583i | 0.207529 | + | 0.359451i | ||||
\(982\) | −9.00000 | + | 15.5885i | −0.287202 | + | 0.497448i | ||||
\(983\) | 27.0000 | − | 46.7654i | 0.861166 | − | 1.49158i | −0.00963785 | − | 0.999954i | \(-0.503068\pi\) |
0.870804 | − | 0.491630i | \(-0.163599\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 9.00000 | 0.286764 | ||||||||
\(986\) | −13.5000 | − | 23.3827i | −0.429928 | − | 0.744656i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | 48.0000 | 1.52631 | ||||||||
\(990\) | −1.00000 | + | 1.73205i | −0.0317821 | + | 0.0550482i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 5.00000 | + | 8.66025i | 0.158750 | + | 0.274963i | ||||
\(993\) | −40.0000 | −1.26936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.0000 | − | 17.3205i | −0.317021 | − | 0.549097i | ||||
\(996\) | −2.00000 | − | 3.46410i | −0.0633724 | − | 0.109764i | ||||
\(997\) | 15.0000 | − | 25.9808i | 0.475055 | − | 0.822819i | −0.524537 | − | 0.851388i | \(-0.675762\pi\) |
0.999592 | + | 0.0285686i | \(0.00909491\pi\) | |||||||
\(998\) | −30.0000 | −0.949633 | ||||||||
\(999\) | 2.00000 | − | 24.2487i | 0.0632772 | − | 0.767195i |
(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.a.47.1 | ✓ | 2 | |
3.2 | odd | 2 | 666.2.f.b.343.1 | 2 | |||
4.3 | odd | 2 | 592.2.i.d.417.1 | 2 | |||
37.10 | even | 3 | 2738.2.a.b.1.1 | 1 | |||
37.26 | even | 3 | inner | 74.2.c.a.63.1 | yes | 2 | |
37.27 | even | 6 | 2738.2.a.d.1.1 | 1 | |||
111.26 | odd | 6 | 666.2.f.b.433.1 | 2 | |||
148.63 | odd | 6 | 592.2.i.d.433.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.c.a.47.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
74.2.c.a.63.1 | yes | 2 | 37.26 | even | 3 | inner | |
592.2.i.d.417.1 | 2 | 4.3 | odd | 2 | |||
592.2.i.d.433.1 | 2 | 148.63 | odd | 6 | |||
666.2.f.b.343.1 | 2 | 3.2 | odd | 2 | |||
666.2.f.b.433.1 | 2 | 111.26 | odd | 6 | |||
2738.2.a.b.1.1 | 1 | 37.10 | even | 3 | |||
2738.2.a.d.1.1 | 1 | 37.27 | even | 6 |