Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,2,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.6");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(0.343356728692\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.2.c.a.6.1 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | 0.353553 | − | 0.935414i | \(-0.384973\pi\) | ||||
0.353553 | + | 0.935414i | \(0.384973\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −1.50000 | + | 2.59808i | −0.566947 | + | 0.981981i | 0.429919 | + | 0.902867i | \(0.358542\pi\) |
−0.996866 | + | 0.0791130i | \(0.974791\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | −1.50000 | + | 2.59808i | −0.400892 | + | 0.694365i | ||||
\(15\) | 0.500000 | − | 0.866025i | 0.129099 | − | 0.223607i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 1.00000 | − | 1.73205i | 0.235702 | − | 0.408248i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 3.00000 | 0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.50000 | + | 6.06218i | 0.729800 | + | 1.26405i | 0.956967 | + | 0.290196i | \(0.0937204\pi\) |
−0.227167 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(24\) | 1.50000 | + | 2.59808i | 0.306186 | + | 0.530330i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 2.50000 | − | 4.33013i | 0.490290 | − | 0.849208i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | −2.50000 | − | 4.33013i | −0.449013 | − | 0.777714i | 0.549309 | − | 0.835619i | \(-0.314891\pi\) |
−0.998322 | + | 0.0579057i | \(0.981558\pi\) | |||||||
\(32\) | 5.00000 | 0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.50000 | + | 2.59808i | −0.257248 | + | 0.445566i | ||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 4.50000 | + | 7.79423i | 0.739795 | + | 1.28136i | 0.952587 | + | 0.304266i | \(0.0984111\pi\) |
−0.212792 | + | 0.977098i | \(0.568256\pi\) | |||||||
\(38\) | −0.500000 | − | 0.866025i | −0.0811107 | − | 0.140488i | ||||
\(39\) | −5.00000 | −0.800641 | ||||||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 3.00000 | 0.462910 | ||||||||
\(43\) | −4.00000 | − | 5.19615i | −0.609994 | − | 0.792406i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 3.50000 | + | 6.06218i | 0.516047 | + | 0.893819i | ||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 2.00000 | − | 3.46410i | 0.282843 | − | 0.489898i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | 2.50000 | + | 4.33013i | 0.343401 | + | 0.594789i | 0.985062 | − | 0.172200i | \(-0.0550875\pi\) |
−0.641661 | + | 0.766989i | \(0.721754\pi\) | |||||||
\(54\) | −5.00000 | −0.680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.50000 | − | 7.79423i | 0.601338 | − | 1.04155i | ||||
\(57\) | −0.500000 | + | 0.866025i | −0.0662266 | + | 0.114708i | ||||
\(58\) | −1.50000 | + | 2.59808i | −0.196960 | + | 0.341144i | ||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | −2.50000 | − | 4.33013i | −0.317500 | − | 0.549927i | ||||
\(63\) | 3.00000 | + | 5.19615i | 0.377964 | + | 0.654654i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 3.50000 | − | 6.06218i | 0.421350 | − | 0.729800i | ||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | 0.500000 | − | 0.866025i | 0.0593391 | − | 0.102778i | −0.834830 | − | 0.550508i | \(-0.814434\pi\) |
0.894169 | + | 0.447730i | \(0.147767\pi\) | |||||||
\(72\) | −3.00000 | + | 5.19615i | −0.353553 | + | 0.612372i | ||||
\(73\) | −5.50000 | + | 9.52628i | −0.643726 | + | 1.11497i | 0.340868 | + | 0.940111i | \(0.389279\pi\) |
−0.984594 | + | 0.174855i | \(0.944054\pi\) | |||||||
\(74\) | 4.50000 | + | 7.79423i | 0.523114 | + | 0.906061i | ||||
\(75\) | −4.00000 | −0.461880 | ||||||||
\(76\) | 0.500000 | + | 0.866025i | 0.0573539 | + | 0.0993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.00000 | −0.566139 | ||||||||
\(79\) | 2.50000 | − | 4.33013i | 0.281272 | − | 0.487177i | −0.690426 | − | 0.723403i | \(-0.742577\pi\) |
0.971698 | + | 0.236225i | \(0.0759104\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −10.0000 | −1.10432 | ||||||||
\(83\) | −4.50000 | − | 7.79423i | −0.493939 | − | 0.855528i | 0.506036 | − | 0.862512i | \(-0.331110\pi\) |
−0.999976 | + | 0.00698436i | \(0.997777\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | −4.00000 | − | 5.19615i | −0.431331 | − | 0.560316i | ||||
\(87\) | 3.00000 | 0.321634 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.500000 | + | 0.866025i | 0.0529999 | + | 0.0917985i | 0.891308 | − | 0.453398i | \(-0.149788\pi\) |
−0.838308 | + | 0.545197i | \(0.816455\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 7.50000 | + | 12.9904i | 0.786214 | + | 1.36176i | ||||
\(92\) | −3.50000 | − | 6.06218i | −0.364900 | − | 0.632026i | ||||
\(93\) | −2.50000 | + | 4.33013i | −0.259238 | + | 0.449013i | ||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 0.500000 | − | 0.866025i | 0.0512989 | − | 0.0888523i | ||||
\(96\) | −2.50000 | − | 4.33013i | −0.255155 | − | 0.441942i | ||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 4.50000 | − | 7.79423i | 0.447767 | − | 0.775555i | −0.550474 | − | 0.834853i | \(-0.685553\pi\) |
0.998240 | + | 0.0592978i | \(0.0188862\pi\) | |||||||
\(102\) | 3.00000 | 0.297044 | ||||||||
\(103\) | −3.50000 | + | 6.06218i | −0.344865 | + | 0.597324i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −7.50000 | + | 12.9904i | −0.735436 | + | 1.27381i | ||||
\(105\) | 1.50000 | + | 2.59808i | 0.146385 | + | 0.253546i | ||||
\(106\) | 2.50000 | + | 4.33013i | 0.242821 | + | 0.420579i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.50000 | − | 7.79423i | 0.427121 | − | 0.739795i | ||||
\(112\) | 1.50000 | − | 2.59808i | 0.141737 | − | 0.245495i | ||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | −3.50000 | + | 6.06218i | −0.326377 | + | 0.565301i | ||||
\(116\) | 1.50000 | − | 2.59808i | 0.139272 | − | 0.241225i | ||||
\(117\) | −5.00000 | − | 8.66025i | −0.462250 | − | 0.800641i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −4.50000 | − | 7.79423i | −0.412514 | − | 0.714496i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 6.50000 | − | 11.2583i | 0.588482 | − | 1.01928i | ||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 2.50000 | + | 4.33013i | 0.224507 | + | 0.388857i | ||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 3.00000 | + | 5.19615i | 0.267261 | + | 0.462910i | ||||
\(127\) | 16.0000 | 1.41977 | 0.709885 | − | 0.704317i | \(-0.248747\pi\) | ||||
0.709885 | + | 0.704317i | \(0.248747\pi\) | |||||||
\(128\) | −3.00000 | −0.265165 | ||||||||
\(129\) | −2.50000 | + | 6.06218i | −0.220113 | + | 0.533745i | ||||
\(130\) | 5.00000 | 0.438529 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | 1.50000 | + | 2.59808i | 0.129580 | + | 0.224440i | ||||
\(135\) | −2.50000 | − | 4.33013i | −0.215166 | − | 0.372678i | ||||
\(136\) | 4.50000 | − | 7.79423i | 0.385872 | − | 0.668350i | ||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 3.50000 | − | 6.06218i | 0.297940 | − | 0.516047i | ||||
\(139\) | −6.50000 | − | 11.2583i | −0.551323 | − | 0.954919i | −0.998179 | − | 0.0603135i | \(-0.980790\pi\) |
0.446857 | − | 0.894606i | \(-0.352543\pi\) | |||||||
\(140\) | 3.00000 | 0.253546 | ||||||||
\(141\) | 4.00000 | + | 6.92820i | 0.336861 | + | 0.583460i | ||||
\(142\) | 0.500000 | − | 0.866025i | 0.0419591 | − | 0.0726752i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | + | 1.73205i | −0.0833333 | + | 0.144338i | ||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | −5.50000 | + | 9.52628i | −0.455183 | + | 0.788400i | ||||
\(147\) | −1.00000 | + | 1.73205i | −0.0824786 | + | 0.142857i | ||||
\(148\) | −4.50000 | − | 7.79423i | −0.369898 | − | 0.640682i | ||||
\(149\) | 10.5000 | + | 18.1865i | 0.860194 | + | 1.48990i | 0.871742 | + | 0.489966i | \(0.162991\pi\) |
−0.0115483 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 1.50000 | + | 2.59808i | 0.121666 | + | 0.210732i | ||||
\(153\) | 3.00000 | + | 5.19615i | 0.242536 | + | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.50000 | − | 4.33013i | 0.200805 | − | 0.347804i | ||||
\(156\) | 5.00000 | 0.400320 | ||||||||
\(157\) | 0.500000 | − | 0.866025i | 0.0399043 | − | 0.0691164i | −0.845383 | − | 0.534160i | \(-0.820628\pi\) |
0.885288 | + | 0.465044i | \(0.153961\pi\) | |||||||
\(158\) | 2.50000 | − | 4.33013i | 0.198889 | − | 0.344486i | ||||
\(159\) | 2.50000 | − | 4.33013i | 0.198263 | − | 0.343401i | ||||
\(160\) | 2.50000 | + | 4.33013i | 0.197642 | + | 0.342327i | ||||
\(161\) | −21.0000 | −1.65503 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 0.500000 | − | 0.866025i | 0.0391630 | − | 0.0678323i | −0.845780 | − | 0.533533i | \(-0.820864\pi\) |
0.884943 | + | 0.465700i | \(0.154198\pi\) | |||||||
\(164\) | 10.0000 | 0.780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | − | 7.79423i | −0.349268 | − | 0.604949i | ||||
\(167\) | 1.50000 | + | 2.59808i | 0.116073 | + | 0.201045i | 0.918208 | − | 0.396098i | \(-0.129636\pi\) |
−0.802135 | + | 0.597143i | \(0.796303\pi\) | |||||||
\(168\) | −9.00000 | −0.694365 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | −3.00000 | −0.230089 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 4.00000 | + | 5.19615i | 0.304997 | + | 0.396203i | ||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 6.00000 | + | 10.3923i | 0.453557 | + | 0.785584i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | − | 10.3923i | −0.450988 | − | 0.781133i | ||||
\(178\) | 0.500000 | + | 0.866025i | 0.0374766 | + | 0.0649113i | ||||
\(179\) | 0.500000 | − | 0.866025i | 0.0373718 | − | 0.0647298i | −0.846735 | − | 0.532016i | \(-0.821435\pi\) |
0.884106 | + | 0.467286i | \(0.154768\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | −3.50000 | + | 6.06218i | −0.260153 | + | 0.450598i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) |
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(182\) | 7.50000 | + | 12.9904i | 0.555937 | + | 0.962911i | ||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | −10.5000 | − | 18.1865i | −0.774070 | − | 1.34073i | ||||
\(185\) | −4.50000 | + | 7.79423i | −0.330847 | + | 0.573043i | ||||
\(186\) | −2.50000 | + | 4.33013i | −0.183309 | + | 0.317500i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 7.50000 | − | 12.9904i | 0.545545 | − | 0.944911i | ||||
\(190\) | 0.500000 | − | 0.866025i | 0.0362738 | − | 0.0628281i | ||||
\(191\) | 9.50000 | + | 16.4545i | 0.687396 | + | 1.19060i | 0.972677 | + | 0.232161i | \(0.0745796\pi\) |
−0.285282 | + | 0.958444i | \(0.592087\pi\) | |||||||
\(192\) | −3.50000 | − | 6.06218i | −0.252591 | − | 0.437500i | ||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | −2.50000 | − | 4.33013i | −0.179029 | − | 0.310087i | ||||
\(196\) | 1.00000 | + | 1.73205i | 0.0714286 | + | 0.123718i | ||||
\(197\) | −5.50000 | + | 9.52628i | −0.391859 | + | 0.678719i | −0.992695 | − | 0.120653i | \(-0.961501\pi\) |
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | −6.00000 | + | 10.3923i | −0.424264 | + | 0.734847i | ||||
\(201\) | 1.50000 | − | 2.59808i | 0.105802 | − | 0.183254i | ||||
\(202\) | 4.50000 | − | 7.79423i | 0.316619 | − | 0.548400i | ||||
\(203\) | −4.50000 | − | 7.79423i | −0.315838 | − | 0.547048i | ||||
\(204\) | −3.00000 | −0.210042 | ||||||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | −3.50000 | + | 6.06218i | −0.243857 | + | 0.422372i | ||||
\(207\) | 14.0000 | 0.973067 | ||||||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.50000 | + | 2.59808i | 0.103510 | + | 0.179284i | ||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −2.50000 | − | 4.33013i | −0.171701 | − | 0.297394i | ||||
\(213\) | −1.00000 | −0.0685189 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 2.50000 | − | 6.06218i | 0.170499 | − | 0.413437i | ||||
\(216\) | 15.0000 | 1.02062 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | −3.50000 | − | 6.06218i | −0.237050 | − | 0.410582i | ||||
\(219\) | 11.0000 | 0.743311 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.50000 | + | 12.9904i | 0.504505 | + | 0.873828i | ||||
\(222\) | 4.50000 | − | 7.79423i | 0.302020 | − | 0.523114i | ||||
\(223\) | 20.0000 | 1.33930 | 0.669650 | − | 0.742677i | \(-0.266444\pi\) | ||||
0.669650 | + | 0.742677i | \(0.266444\pi\) | |||||||
\(224\) | −7.50000 | + | 12.9904i | −0.501115 | + | 0.867956i | ||||
\(225\) | −4.00000 | − | 6.92820i | −0.266667 | − | 0.461880i | ||||
\(226\) | −2.00000 | −0.133038 | ||||||||
\(227\) | 3.50000 | + | 6.06218i | 0.232303 | + | 0.402361i | 0.958485 | − | 0.285141i | \(-0.0920405\pi\) |
−0.726182 | + | 0.687502i | \(0.758707\pi\) | |||||||
\(228\) | 0.500000 | − | 0.866025i | 0.0331133 | − | 0.0573539i | ||||
\(229\) | 4.50000 | − | 7.79423i | 0.297368 | − | 0.515057i | −0.678165 | − | 0.734910i | \(-0.737224\pi\) |
0.975533 | + | 0.219853i | \(0.0705577\pi\) | |||||||
\(230\) | −3.50000 | + | 6.06218i | −0.230783 | + | 0.399728i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.50000 | − | 7.79423i | 0.295439 | − | 0.511716i | ||||
\(233\) | 4.50000 | − | 7.79423i | 0.294805 | − | 0.510617i | −0.680135 | − | 0.733087i | \(-0.738079\pi\) |
0.974939 | + | 0.222470i | \(0.0714120\pi\) | |||||||
\(234\) | −5.00000 | − | 8.66025i | −0.326860 | − | 0.566139i | ||||
\(235\) | −4.00000 | − | 6.92820i | −0.260931 | − | 0.451946i | ||||
\(236\) | −12.0000 | −0.781133 | ||||||||
\(237\) | −5.00000 | −0.324785 | ||||||||
\(238\) | −4.50000 | − | 7.79423i | −0.291692 | − | 0.505225i | ||||
\(239\) | −12.5000 | − | 21.6506i | −0.808558 | − | 1.40046i | −0.913863 | − | 0.406023i | \(-0.866915\pi\) |
0.105305 | − | 0.994440i | \(-0.466418\pi\) | |||||||
\(240\) | −0.500000 | + | 0.866025i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | −11.0000 | −0.707107 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −6.50000 | + | 11.2583i | −0.416120 | + | 0.720741i | ||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 5.00000 | + | 8.66025i | 0.318788 | + | 0.552158i | ||||
\(247\) | −5.00000 | −0.318142 | ||||||||
\(248\) | 7.50000 | + | 12.9904i | 0.476250 | + | 0.824890i | ||||
\(249\) | −4.50000 | + | 7.79423i | −0.285176 | + | 0.493939i | ||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −3.50000 | + | 6.06218i | −0.220918 | + | 0.382641i | −0.955087 | − | 0.296326i | \(-0.904239\pi\) |
0.734169 | + | 0.678967i | \(0.237572\pi\) | |||||||
\(252\) | −3.00000 | − | 5.19615i | −0.188982 | − | 0.327327i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | −2.50000 | + | 6.06218i | −0.155643 | + | 0.377415i | ||||
\(259\) | −27.0000 | −1.67770 | ||||||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −10.5000 | − | 18.1865i | −0.647458 | − | 1.12143i | −0.983728 | − | 0.179664i | \(-0.942499\pi\) |
0.336270 | − | 0.941766i | \(-0.390834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.50000 | + | 4.33013i | −0.153574 | + | 0.265998i | ||||
\(266\) | 3.00000 | 0.183942 | ||||||||
\(267\) | 0.500000 | − | 0.866025i | 0.0305995 | − | 0.0529999i | ||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | −2.50000 | − | 4.33013i | −0.152145 | − | 0.263523i | ||||
\(271\) | −11.5000 | + | 19.9186i | −0.698575 | + | 1.20997i | 0.270385 | + | 0.962752i | \(0.412849\pi\) |
−0.968960 | + | 0.247216i | \(0.920484\pi\) | |||||||
\(272\) | 1.50000 | − | 2.59808i | 0.0909509 | − | 0.157532i | ||||
\(273\) | 7.50000 | − | 12.9904i | 0.453921 | − | 0.786214i | ||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.50000 | + | 6.06218i | −0.210675 | + | 0.364900i | ||||
\(277\) | −3.50000 | − | 6.06218i | −0.210295 | − | 0.364241i | 0.741512 | − | 0.670940i | \(-0.234109\pi\) |
−0.951807 | + | 0.306699i | \(0.900776\pi\) | |||||||
\(278\) | −6.50000 | − | 11.2583i | −0.389844 | − | 0.675230i | ||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 9.00000 | 0.537853 | ||||||||
\(281\) | 8.50000 | + | 14.7224i | 0.507067 | + | 0.878267i | 0.999967 | + | 0.00818015i | \(0.00260385\pi\) |
−0.492899 | + | 0.870087i | \(0.664063\pi\) | |||||||
\(282\) | 4.00000 | + | 6.92820i | 0.238197 | + | 0.412568i | ||||
\(283\) | −1.50000 | + | 2.59808i | −0.0891657 | + | 0.154440i | −0.907159 | − | 0.420789i | \(-0.861753\pi\) |
0.817993 | + | 0.575228i | \(0.195087\pi\) | |||||||
\(284\) | −0.500000 | + | 0.866025i | −0.0296695 | + | 0.0513892i | ||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0000 | − | 25.9808i | 0.885422 | − | 1.53360i | ||||
\(288\) | 5.00000 | − | 8.66025i | 0.294628 | − | 0.510310i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | −3.00000 | −0.176166 | ||||||||
\(291\) | 1.00000 | + | 1.73205i | 0.0586210 | + | 0.101535i | ||||
\(292\) | 5.50000 | − | 9.52628i | 0.321863 | − | 0.557483i | ||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | −1.00000 | + | 1.73205i | −0.0583212 | + | 0.101015i | ||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | −13.5000 | − | 23.3827i | −0.784672 | − | 1.35909i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.5000 | + | 18.1865i | 0.608249 | + | 1.05352i | ||||
\(299\) | 35.0000 | 2.02410 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 19.5000 | − | 2.59808i | 1.12396 | − | 0.149751i | ||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | −9.00000 | −0.517036 | ||||||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 13.0000 | 0.744378 | ||||||||
\(306\) | 3.00000 | + | 5.19615i | 0.171499 | + | 0.297044i | ||||
\(307\) | −2.50000 | − | 4.33013i | −0.142683 | − | 0.247133i | 0.785823 | − | 0.618451i | \(-0.212239\pi\) |
−0.928506 | + | 0.371318i | \(0.878906\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.00000 | 0.398216 | ||||||||
\(310\) | 2.50000 | − | 4.33013i | 0.141990 | − | 0.245935i | ||||
\(311\) | 1.50000 | + | 2.59808i | 0.0850572 | + | 0.147323i | 0.905416 | − | 0.424526i | \(-0.139559\pi\) |
−0.820358 | + | 0.571850i | \(0.806226\pi\) | |||||||
\(312\) | 15.0000 | 0.849208 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 0.500000 | − | 0.866025i | 0.0282166 | − | 0.0488726i | ||||
\(315\) | −3.00000 | + | 5.19615i | −0.169031 | + | 0.292770i | ||||
\(316\) | −2.50000 | + | 4.33013i | −0.140636 | + | 0.243589i | ||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 2.50000 | − | 4.33013i | 0.140193 | − | 0.242821i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.50000 | + | 6.06218i | 0.195656 | + | 0.338886i | ||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | −21.0000 | −1.17028 | ||||||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | 0.500000 | + | 0.866025i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | −10.0000 | − | 17.3205i | −0.554700 | − | 0.960769i | ||||
\(326\) | 0.500000 | − | 0.866025i | 0.0276924 | − | 0.0479647i | ||||
\(327\) | −3.50000 | + | 6.06218i | −0.193550 | + | 0.335239i | ||||
\(328\) | 30.0000 | 1.65647 | ||||||||
\(329\) | 12.0000 | − | 20.7846i | 0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.50000 | + | 16.4545i | −0.522167 | + | 0.904420i | 0.477500 | + | 0.878632i | \(0.341543\pi\) |
−0.999667 | + | 0.0257885i | \(0.991790\pi\) | |||||||
\(332\) | 4.50000 | + | 7.79423i | 0.246970 | + | 0.427764i | ||||
\(333\) | 18.0000 | 0.986394 | ||||||||
\(334\) | 1.50000 | + | 2.59808i | 0.0820763 | + | 0.142160i | ||||
\(335\) | −1.50000 | + | 2.59808i | −0.0819538 | + | 0.141948i | ||||
\(336\) | −3.00000 | −0.163663 | ||||||||
\(337\) | −1.50000 | + | 2.59808i | −0.0817102 | + | 0.141526i | −0.903985 | − | 0.427565i | \(-0.859372\pi\) |
0.822274 | + | 0.569091i | \(0.192705\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 1.00000 | + | 1.73205i | 0.0543125 | + | 0.0940721i | ||||
\(340\) | 3.00000 | 0.162698 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 12.0000 | + | 15.5885i | 0.646997 | + | 0.840473i | ||||
\(345\) | 7.00000 | 0.376867 | ||||||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | −18.5000 | − | 32.0429i | −0.993132 | − | 1.72016i | −0.597890 | − | 0.801578i | \(-0.703994\pi\) |
−0.395242 | − | 0.918577i | \(-0.629339\pi\) | |||||||
\(348\) | −3.00000 | −0.160817 | ||||||||
\(349\) | 0.500000 | + | 0.866025i | 0.0267644 | + | 0.0463573i | 0.879097 | − | 0.476642i | \(-0.158146\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(350\) | 6.00000 | + | 10.3923i | 0.320713 | + | 0.555492i | ||||
\(351\) | −12.5000 | + | 21.6506i | −0.667201 | + | 1.15563i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5000 | − | 21.6506i | 0.665308 | − | 1.15235i | −0.313894 | − | 0.949458i | \(-0.601634\pi\) |
0.979202 | − | 0.202889i | \(-0.0650330\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | 1.00000 | 0.0530745 | ||||||||
\(356\) | −0.500000 | − | 0.866025i | −0.0264999 | − | 0.0458993i | ||||
\(357\) | −4.50000 | + | 7.79423i | −0.238165 | + | 0.412514i | ||||
\(358\) | 0.500000 | − | 0.866025i | 0.0264258 | − | 0.0457709i | ||||
\(359\) | −9.50000 | + | 16.4545i | −0.501391 | + | 0.868434i | 0.498608 | + | 0.866828i | \(0.333845\pi\) |
−0.999999 | + | 0.00160673i | \(0.999489\pi\) | |||||||
\(360\) | −6.00000 | −0.316228 | ||||||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | −3.50000 | + | 6.06218i | −0.183956 | + | 0.318621i | ||||
\(363\) | 5.50000 | + | 9.52628i | 0.288675 | + | 0.500000i | ||||
\(364\) | −7.50000 | − | 12.9904i | −0.393107 | − | 0.680881i | ||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | −13.0000 | −0.679521 | ||||||||
\(367\) | −6.50000 | − | 11.2583i | −0.339297 | − | 0.587680i | 0.645003 | − | 0.764180i | \(-0.276856\pi\) |
−0.984301 | + | 0.176500i | \(0.943523\pi\) | |||||||
\(368\) | −3.50000 | − | 6.06218i | −0.182450 | − | 0.316013i | ||||
\(369\) | −10.0000 | + | 17.3205i | −0.520579 | + | 0.901670i | ||||
\(370\) | −4.50000 | + | 7.79423i | −0.233944 | + | 0.405203i | ||||
\(371\) | −15.0000 | −0.778761 | ||||||||
\(372\) | 2.50000 | − | 4.33013i | 0.129619 | − | 0.224507i | ||||
\(373\) | −5.50000 | + | 9.52628i | −0.284779 | + | 0.493252i | −0.972556 | − | 0.232671i | \(-0.925254\pi\) |
0.687776 | + | 0.725923i | \(0.258587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.50000 | − | 7.79423i | −0.232379 | − | 0.402492i | ||||
\(376\) | 24.0000 | 1.23771 | ||||||||
\(377\) | 7.50000 | + | 12.9904i | 0.386270 | + | 0.669039i | ||||
\(378\) | 7.50000 | − | 12.9904i | 0.385758 | − | 0.668153i | ||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | −0.500000 | + | 0.866025i | −0.0256495 | + | 0.0444262i | ||||
\(381\) | −8.00000 | − | 13.8564i | −0.409852 | − | 0.709885i | ||||
\(382\) | 9.50000 | + | 16.4545i | 0.486062 | + | 0.841885i | ||||
\(383\) | 8.00000 | 0.408781 | 0.204390 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204390 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(384\) | 1.50000 | + | 2.59808i | 0.0765466 | + | 0.132583i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.00000 | 0.305392 | ||||||||
\(387\) | −13.0000 | + | 1.73205i | −0.660827 | + | 0.0880451i | ||||
\(388\) | 2.00000 | 0.101535 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | −2.50000 | − | 4.33013i | −0.126592 | − | 0.219265i | ||||
\(391\) | −21.0000 | −1.06202 | ||||||||
\(392\) | 3.00000 | + | 5.19615i | 0.151523 | + | 0.262445i | ||||
\(393\) | 2.00000 | + | 3.46410i | 0.100887 | + | 0.174741i | ||||
\(394\) | −5.50000 | + | 9.52628i | −0.277086 | + | 0.479927i | ||||
\(395\) | 5.00000 | 0.251577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5000 | + | 18.1865i | 0.526980 | + | 0.912756i | 0.999506 | + | 0.0314391i | \(0.0100090\pi\) |
−0.472526 | + | 0.881317i | \(0.656658\pi\) | |||||||
\(398\) | 8.00000 | 0.401004 | ||||||||
\(399\) | −1.50000 | − | 2.59808i | −0.0750939 | − | 0.130066i | ||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | 18.5000 | − | 32.0429i | 0.923846 | − | 1.60015i | 0.130439 | − | 0.991456i | \(-0.458361\pi\) |
0.793407 | − | 0.608692i | \(-0.208305\pi\) | |||||||
\(402\) | 1.50000 | − | 2.59808i | 0.0748132 | − | 0.129580i | ||||
\(403\) | −25.0000 | −1.24534 | ||||||||
\(404\) | −4.50000 | + | 7.79423i | −0.223883 | + | 0.387777i | ||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.00000 | −0.445566 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | −5.00000 | − | 8.66025i | −0.246932 | − | 0.427699i | ||||
\(411\) | 9.00000 | + | 15.5885i | 0.443937 | + | 0.768922i | ||||
\(412\) | 3.50000 | − | 6.06218i | 0.172433 | − | 0.298662i | ||||
\(413\) | −18.0000 | + | 31.1769i | −0.885722 | + | 1.53412i | ||||
\(414\) | 14.0000 | 0.688062 | ||||||||
\(415\) | 4.50000 | − | 7.79423i | 0.220896 | − | 0.382604i | ||||
\(416\) | 12.5000 | − | 21.6506i | 0.612863 | − | 1.06151i | ||||
\(417\) | −6.50000 | + | 11.2583i | −0.318306 | + | 0.551323i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | −1.50000 | − | 2.59808i | −0.0731925 | − | 0.126773i | ||||
\(421\) | 18.5000 | − | 32.0429i | 0.901635 | − | 1.56168i | 0.0762630 | − | 0.997088i | \(-0.475701\pi\) |
0.825372 | − | 0.564590i | \(-0.190966\pi\) | |||||||
\(422\) | 8.00000 | 0.389434 | ||||||||
\(423\) | −8.00000 | + | 13.8564i | −0.388973 | + | 0.673722i | ||||
\(424\) | −7.50000 | − | 12.9904i | −0.364232 | − | 0.630869i | ||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | −1.00000 | −0.0484502 | ||||||||
\(427\) | 19.5000 | + | 33.7750i | 0.943671 | + | 1.63449i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.50000 | − | 6.06218i | 0.120561 | − | 0.292344i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | −13.5000 | − | 23.3827i | −0.648769 | − | 1.12370i | −0.983417 | − | 0.181357i | \(-0.941951\pi\) |
0.334649 | − | 0.942343i | \(-0.391382\pi\) | |||||||
\(434\) | 15.0000 | 0.720023 | ||||||||
\(435\) | 1.50000 | + | 2.59808i | 0.0719195 | + | 0.124568i | ||||
\(436\) | 3.50000 | + | 6.06218i | 0.167620 | + | 0.290326i | ||||
\(437\) | 3.50000 | − | 6.06218i | 0.167428 | − | 0.289993i | ||||
\(438\) | 11.0000 | 0.525600 | ||||||||
\(439\) | 6.50000 | − | 11.2583i | 0.310228 | − | 0.537331i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.00000 | −0.190476 | ||||||||
\(442\) | 7.50000 | + | 12.9904i | 0.356739 | + | 0.617889i | ||||
\(443\) | 18.5000 | − | 32.0429i | 0.878962 | − | 1.52241i | 0.0264796 | − | 0.999649i | \(-0.491570\pi\) |
0.852482 | − | 0.522757i | \(-0.175096\pi\) | |||||||
\(444\) | −4.50000 | + | 7.79423i | −0.213561 | + | 0.369898i | ||||
\(445\) | −0.500000 | + | 0.866025i | −0.0237023 | + | 0.0410535i | ||||
\(446\) | 20.0000 | 0.947027 | ||||||||
\(447\) | 10.5000 | − | 18.1865i | 0.496633 | − | 0.860194i | ||||
\(448\) | −10.5000 | + | 18.1865i | −0.496078 | + | 0.859233i | ||||
\(449\) | 10.5000 | + | 18.1865i | 0.495526 | + | 0.858276i | 0.999987 | − | 0.00515887i | \(-0.00164213\pi\) |
−0.504461 | + | 0.863434i | \(0.668309\pi\) | |||||||
\(450\) | −4.00000 | − | 6.92820i | −0.188562 | − | 0.326599i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.00000 | 0.0940721 | ||||||||
\(453\) | 4.00000 | + | 6.92820i | 0.187936 | + | 0.325515i | ||||
\(454\) | 3.50000 | + | 6.06218i | 0.164263 | + | 0.284512i | ||||
\(455\) | −7.50000 | + | 12.9904i | −0.351605 | + | 0.608998i | ||||
\(456\) | 1.50000 | − | 2.59808i | 0.0702439 | − | 0.121666i | ||||
\(457\) | 6.00000 | 0.280668 | 0.140334 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140334 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(458\) | 4.50000 | − | 7.79423i | 0.210271 | − | 0.364200i | ||||
\(459\) | 7.50000 | − | 12.9904i | 0.350070 | − | 0.606339i | ||||
\(460\) | 3.50000 | − | 6.06218i | 0.163188 | − | 0.282650i | ||||
\(461\) | −1.50000 | − | 2.59808i | −0.0698620 | − | 0.121004i | 0.828978 | − | 0.559281i | \(-0.188923\pi\) |
−0.898840 | + | 0.438276i | \(0.855589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5000 | + | 19.9186i | 0.534450 | + | 0.925695i | 0.999190 | + | 0.0402476i | \(0.0128147\pi\) |
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | −5.00000 | −0.231869 | ||||||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | −10.5000 | − | 18.1865i | −0.485882 | − | 0.841572i | 0.513986 | − | 0.857798i | \(-0.328168\pi\) |
−0.999868 | + | 0.0162260i | \(0.994835\pi\) | |||||||
\(468\) | 5.00000 | + | 8.66025i | 0.231125 | + | 0.400320i | ||||
\(469\) | −9.00000 | −0.415581 | ||||||||
\(470\) | −4.00000 | − | 6.92820i | −0.184506 | − | 0.319574i | ||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | −36.0000 | −1.65703 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.00000 | −0.229658 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 4.50000 | + | 7.79423i | 0.206257 | + | 0.357248i | ||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | −12.5000 | − | 21.6506i | −0.571737 | − | 0.990277i | ||||
\(479\) | 7.50000 | + | 12.9904i | 0.342684 | + | 0.593546i | 0.984930 | − | 0.172953i | \(-0.0553307\pi\) |
−0.642246 | + | 0.766498i | \(0.721997\pi\) | |||||||
\(480\) | 2.50000 | − | 4.33013i | 0.114109 | − | 0.197642i | ||||
\(481\) | 45.0000 | 2.05182 | ||||||||
\(482\) | −7.50000 | + | 12.9904i | −0.341616 | + | 0.591696i | ||||
\(483\) | 10.5000 | + | 18.1865i | 0.477767 | + | 0.827516i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | −8.00000 | + | 13.8564i | −0.362887 | + | 0.628539i | ||||
\(487\) | 4.50000 | − | 7.79423i | 0.203914 | − | 0.353190i | −0.745872 | − | 0.666089i | \(-0.767967\pi\) |
0.949786 | + | 0.312899i | \(0.101300\pi\) | |||||||
\(488\) | −19.5000 | + | 33.7750i | −0.882724 | + | 1.52892i | ||||
\(489\) | −1.00000 | −0.0452216 | ||||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | 4.50000 | − | 7.79423i | 0.203082 | − | 0.351749i | −0.746438 | − | 0.665455i | \(-0.768237\pi\) |
0.949520 | + | 0.313707i | \(0.101571\pi\) | |||||||
\(492\) | −5.00000 | − | 8.66025i | −0.225417 | − | 0.390434i | ||||
\(493\) | −4.50000 | − | 7.79423i | −0.202670 | − | 0.351034i | ||||
\(494\) | −5.00000 | −0.224961 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.50000 | + | 4.33013i | 0.112253 | + | 0.194428i | ||||
\(497\) | 1.50000 | + | 2.59808i | 0.0672842 | + | 0.116540i | ||||
\(498\) | −4.50000 | + | 7.79423i | −0.201650 | + | 0.349268i | ||||
\(499\) | 8.50000 | − | 14.7224i | 0.380512 | − | 0.659067i | −0.610623 | − | 0.791921i | \(-0.709081\pi\) |
0.991136 | + | 0.132855i | \(0.0424144\pi\) | |||||||
\(500\) | −9.00000 | −0.402492 | ||||||||
\(501\) | 1.50000 | − | 2.59808i | 0.0670151 | − | 0.116073i | ||||
\(502\) | −3.50000 | + | 6.06218i | −0.156213 | + | 0.270568i | ||||
\(503\) | 4.50000 | − | 7.79423i | 0.200645 | − | 0.347527i | −0.748091 | − | 0.663596i | \(-0.769030\pi\) |
0.948736 | + | 0.316068i | \(0.102363\pi\) | |||||||
\(504\) | −9.00000 | − | 15.5885i | −0.400892 | − | 0.694365i | ||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | −16.0000 | −0.709885 | ||||||||
\(509\) | −13.5000 | + | 23.3827i | −0.598377 | + | 1.03642i | 0.394684 | + | 0.918817i | \(0.370854\pi\) |
−0.993061 | + | 0.117602i | \(0.962479\pi\) | |||||||
\(510\) | 1.50000 | + | 2.59808i | 0.0664211 | + | 0.115045i | ||||
\(511\) | −16.5000 | − | 28.5788i | −0.729917 | − | 1.26425i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 2.50000 | + | 4.33013i | 0.110378 | + | 0.191180i | ||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | −7.00000 | −0.308457 | ||||||||
\(516\) | 2.50000 | − | 6.06218i | 0.110056 | − | 0.266872i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −27.0000 | −1.18631 | ||||||||
\(519\) | 3.00000 | + | 5.19615i | 0.131685 | + | 0.228086i | ||||
\(520\) | −15.0000 | −0.657794 | ||||||||
\(521\) | −17.5000 | − | 30.3109i | −0.766689 | − | 1.32794i | −0.939349 | − | 0.342963i | \(-0.888570\pi\) |
0.172660 | − | 0.984981i | \(-0.444764\pi\) | |||||||
\(522\) | 3.00000 | + | 5.19615i | 0.131306 | + | 0.227429i | ||||
\(523\) | 10.5000 | − | 18.1865i | 0.459133 | − | 0.795242i | −0.539782 | − | 0.841805i | \(-0.681493\pi\) |
0.998915 | + | 0.0465630i | \(0.0148268\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 6.00000 | − | 10.3923i | 0.261861 | − | 0.453557i | ||||
\(526\) | −10.5000 | − | 18.1865i | −0.457822 | − | 0.792971i | ||||
\(527\) | 15.0000 | 0.653410 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | + | 22.5167i | −0.565217 | + | 0.978985i | ||||
\(530\) | −2.50000 | + | 4.33013i | −0.108593 | + | 0.188089i | ||||
\(531\) | 12.0000 | − | 20.7846i | 0.520756 | − | 0.901975i | ||||
\(532\) | −3.00000 | −0.130066 | ||||||||
\(533\) | −25.0000 | + | 43.3013i | −1.08287 | + | 1.87559i | ||||
\(534\) | 0.500000 | − | 0.866025i | 0.0216371 | − | 0.0374766i | ||||
\(535\) | 6.00000 | + | 10.3923i | 0.259403 | + | 0.449299i | ||||
\(536\) | −4.50000 | − | 7.79423i | −0.194370 | − | 0.336659i | ||||
\(537\) | −1.00000 | −0.0431532 | ||||||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.50000 | + | 4.33013i | 0.107583 | + | 0.186339i | ||||
\(541\) | −15.5000 | + | 26.8468i | −0.666397 | + | 1.15423i | 0.312507 | + | 0.949915i | \(0.398831\pi\) |
−0.978905 | + | 0.204318i | \(0.934502\pi\) | |||||||
\(542\) | −11.5000 | + | 19.9186i | −0.493967 | + | 0.855576i | ||||
\(543\) | 7.00000 | 0.300399 | ||||||||
\(544\) | −7.50000 | + | 12.9904i | −0.321560 | + | 0.556958i | ||||
\(545\) | 3.50000 | − | 6.06218i | 0.149924 | − | 0.259675i | ||||
\(546\) | 7.50000 | − | 12.9904i | 0.320970 | − | 0.555937i | ||||
\(547\) | −0.500000 | − | 0.866025i | −0.0213785 | − | 0.0370286i | 0.855138 | − | 0.518400i | \(-0.173472\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 18.0000 | 0.768922 | ||||||||
\(549\) | −13.0000 | − | 22.5167i | −0.554826 | − | 0.960988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | −10.5000 | + | 18.1865i | −0.446910 | + | 0.774070i | ||||
\(553\) | 7.50000 | + | 12.9904i | 0.318932 | + | 0.552407i | ||||
\(554\) | −3.50000 | − | 6.06218i | −0.148701 | − | 0.257557i | ||||
\(555\) | 9.00000 | 0.382029 | ||||||||
\(556\) | 6.50000 | + | 11.2583i | 0.275661 | + | 0.477460i | ||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | −10.0000 | −0.423334 | ||||||||
\(559\) | −32.5000 | + | 4.33013i | −1.37460 | + | 0.183145i | ||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.50000 | + | 14.7224i | 0.358551 | + | 0.621028i | ||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | −4.00000 | − | 6.92820i | −0.168430 | − | 0.291730i | ||||
\(565\) | −1.00000 | − | 1.73205i | −0.0420703 | − | 0.0728679i | ||||
\(566\) | −1.50000 | + | 2.59808i | −0.0630497 | + | 0.109205i | ||||
\(567\) | 3.00000 | 0.125988 | ||||||||
\(568\) | −1.50000 | + | 2.59808i | −0.0629386 | + | 0.109013i | ||||
\(569\) | 8.50000 | + | 14.7224i | 0.356339 | + | 0.617196i | 0.987346 | − | 0.158580i | \(-0.0506917\pi\) |
−0.631008 | + | 0.775777i | \(0.717358\pi\) | |||||||
\(570\) | −1.00000 | −0.0418854 | ||||||||
\(571\) | −6.50000 | − | 11.2583i | −0.272017 | − | 0.471146i | 0.697362 | − | 0.716720i | \(-0.254357\pi\) |
−0.969378 | + | 0.245573i | \(0.921024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.50000 | − | 16.4545i | 0.396868 | − | 0.687396i | ||||
\(574\) | 15.0000 | − | 25.9808i | 0.626088 | − | 1.08442i | ||||
\(575\) | 28.0000 | 1.16768 | ||||||||
\(576\) | 7.00000 | − | 12.1244i | 0.291667 | − | 0.505181i | ||||
\(577\) | 2.50000 | − | 4.33013i | 0.104076 | − | 0.180266i | −0.809284 | − | 0.587417i | \(-0.800145\pi\) |
0.913360 | + | 0.407152i | \(0.133478\pi\) | |||||||
\(578\) | 4.00000 | + | 6.92820i | 0.166378 | + | 0.288175i | ||||
\(579\) | −3.00000 | − | 5.19615i | −0.124676 | − | 0.215945i | ||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | 27.0000 | 1.12015 | ||||||||
\(582\) | 1.00000 | + | 1.73205i | 0.0414513 | + | 0.0717958i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 16.5000 | − | 28.5788i | 0.682775 | − | 1.18260i | ||||
\(585\) | 5.00000 | − | 8.66025i | 0.206725 | − | 0.358057i | ||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 6.50000 | − | 11.2583i | 0.268284 | − | 0.464681i | −0.700135 | − | 0.714010i | \(-0.746877\pi\) |
0.968419 | + | 0.249329i | \(0.0802102\pi\) | |||||||
\(588\) | 1.00000 | − | 1.73205i | 0.0412393 | − | 0.0714286i | ||||
\(589\) | −2.50000 | + | 4.33013i | −0.103011 | + | 0.178420i | ||||
\(590\) | 6.00000 | + | 10.3923i | 0.247016 | + | 0.427844i | ||||
\(591\) | 11.0000 | 0.452480 | ||||||||
\(592\) | −4.50000 | − | 7.79423i | −0.184949 | − | 0.320341i | ||||
\(593\) | 0.500000 | − | 0.866025i | 0.0205325 | − | 0.0355634i | −0.855577 | − | 0.517676i | \(-0.826797\pi\) |
0.876109 | + | 0.482113i | \(0.160130\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.50000 | − | 7.79423i | 0.184482 | − | 0.319532i | ||||
\(596\) | −10.5000 | − | 18.1865i | −0.430097 | − | 0.744949i | ||||
\(597\) | −4.00000 | − | 6.92820i | −0.163709 | − | 0.283552i | ||||
\(598\) | 35.0000 | 1.43126 | ||||||||
\(599\) | 15.5000 | + | 26.8468i | 0.633313 | + | 1.09693i | 0.986870 | + | 0.161517i | \(0.0516387\pi\) |
−0.353557 | + | 0.935413i | \(0.615028\pi\) | |||||||
\(600\) | 12.0000 | 0.489898 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 19.5000 | − | 2.59808i | 0.794761 | − | 0.105890i | ||||
\(603\) | 6.00000 | 0.244339 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −5.50000 | − | 9.52628i | −0.223607 | − | 0.387298i | ||||
\(606\) | −9.00000 | −0.365600 | ||||||||
\(607\) | 21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | \(0.170939\pi\) |
0.0134214 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(608\) | −2.50000 | − | 4.33013i | −0.101388 | − | 0.175610i | ||||
\(609\) | −4.50000 | + | 7.79423i | −0.182349 | + | 0.315838i | ||||
\(610\) | 13.0000 | 0.526355 | ||||||||
\(611\) | −20.0000 | + | 34.6410i | −0.809113 | + | 1.40143i | ||||
\(612\) | −3.00000 | − | 5.19615i | −0.121268 | − | 0.210042i | ||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | −2.50000 | − | 4.33013i | −0.100892 | − | 0.174750i | ||||
\(615\) | −5.00000 | + | 8.66025i | −0.201619 | + | 0.349215i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50000 | + | 2.59808i | −0.0603877 | + | 0.104595i | −0.894639 | − | 0.446790i | \(-0.852567\pi\) |
0.834251 | + | 0.551385i | \(0.185900\pi\) | |||||||
\(618\) | 7.00000 | 0.281581 | ||||||||
\(619\) | 10.5000 | − | 18.1865i | 0.422031 | − | 0.730978i | −0.574107 | − | 0.818780i | \(-0.694651\pi\) |
0.996138 | + | 0.0878015i | \(0.0279841\pi\) | |||||||
\(620\) | −2.50000 | + | 4.33013i | −0.100402 | + | 0.173902i | ||||
\(621\) | −17.5000 | − | 30.3109i | −0.702251 | − | 1.21633i | ||||
\(622\) | 1.50000 | + | 2.59808i | 0.0601445 | + | 0.104173i | ||||
\(623\) | −3.00000 | −0.120192 | ||||||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 8.50000 | + | 14.7224i | 0.339728 | + | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.500000 | + | 0.866025i | −0.0199522 | + | 0.0345582i | ||||
\(629\) | −27.0000 | −1.07656 | ||||||||
\(630\) | −3.00000 | + | 5.19615i | −0.119523 | + | 0.207020i | ||||
\(631\) | 4.50000 | − | 7.79423i | 0.179142 | − | 0.310283i | −0.762445 | − | 0.647053i | \(-0.776001\pi\) |
0.941587 | + | 0.336770i | \(0.109334\pi\) | |||||||
\(632\) | −7.50000 | + | 12.9904i | −0.298334 | + | 0.516730i | ||||
\(633\) | −4.00000 | − | 6.92820i | −0.158986 | − | 0.275371i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 8.00000 | + | 13.8564i | 0.317470 | + | 0.549875i | ||||
\(636\) | −2.50000 | + | 4.33013i | −0.0991314 | + | 0.171701i | ||||
\(637\) | −10.0000 | −0.396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | −6.00000 | − | 10.3923i | −0.236801 | − | 0.410152i | ||||
\(643\) | 12.0000 | 0.473234 | 0.236617 | − | 0.971603i | \(-0.423961\pi\) | ||||
0.236617 | + | 0.971603i | \(0.423961\pi\) | |||||||
\(644\) | 21.0000 | 0.827516 | ||||||||
\(645\) | −6.50000 | + | 0.866025i | −0.255937 | + | 0.0340997i | ||||
\(646\) | 3.00000 | 0.118033 | ||||||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 1.50000 | + | 2.59808i | 0.0589256 | + | 0.102062i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −10.0000 | − | 17.3205i | −0.392232 | − | 0.679366i | ||||
\(651\) | −7.50000 | − | 12.9904i | −0.293948 | − | 0.509133i | ||||
\(652\) | −0.500000 | + | 0.866025i | −0.0195815 | + | 0.0339162i | ||||
\(653\) | −50.0000 | −1.95665 | −0.978326 | − | 0.207072i | \(-0.933606\pi\) | ||||
−0.978326 | + | 0.207072i | \(0.933606\pi\) | |||||||
\(654\) | −3.50000 | + | 6.06218i | −0.136861 | + | 0.237050i | ||||
\(655\) | −2.00000 | − | 3.46410i | −0.0781465 | − | 0.135354i | ||||
\(656\) | 10.0000 | 0.390434 | ||||||||
\(657\) | 11.0000 | + | 19.0526i | 0.429151 | + | 0.743311i | ||||
\(658\) | 12.0000 | − | 20.7846i | 0.467809 | − | 0.810268i | ||||
\(659\) | −11.5000 | + | 19.9186i | −0.447976 | + | 0.775918i | −0.998254 | − | 0.0590638i | \(-0.981188\pi\) |
0.550278 | + | 0.834982i | \(0.314522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | −9.50000 | + | 16.4545i | −0.369228 | + | 0.639522i | ||||
\(663\) | 7.50000 | − | 12.9904i | 0.291276 | − | 0.504505i | ||||
\(664\) | 13.5000 | + | 23.3827i | 0.523902 | + | 0.907424i | ||||
\(665\) | 1.50000 | + | 2.59808i | 0.0581675 | + | 0.100749i | ||||
\(666\) | 18.0000 | 0.697486 | ||||||||
\(667\) | −21.0000 | −0.813123 | ||||||||
\(668\) | −1.50000 | − | 2.59808i | −0.0580367 | − | 0.100523i | ||||
\(669\) | −10.0000 | − | 17.3205i | −0.386622 | − | 0.669650i | ||||
\(670\) | −1.50000 | + | 2.59808i | −0.0579501 | + | 0.100372i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 15.0000 | 0.578638 | ||||||||
\(673\) | −23.5000 | + | 40.7032i | −0.905858 | + | 1.56899i | −0.0860977 | + | 0.996287i | \(0.527440\pi\) |
−0.819761 | + | 0.572706i | \(0.805894\pi\) | |||||||
\(674\) | −1.50000 | + | 2.59808i | −0.0577778 | + | 0.100074i | ||||
\(675\) | −10.0000 | + | 17.3205i | −0.384900 | + | 0.666667i | ||||
\(676\) | 6.00000 | + | 10.3923i | 0.230769 | + | 0.399704i | ||||
\(677\) | −14.0000 | −0.538064 | −0.269032 | − | 0.963131i | \(-0.586704\pi\) | ||||
−0.269032 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(678\) | 1.00000 | + | 1.73205i | 0.0384048 | + | 0.0665190i | ||||
\(679\) | 3.00000 | − | 5.19615i | 0.115129 | − | 0.199410i | ||||
\(680\) | 9.00000 | 0.345134 | ||||||||
\(681\) | 3.50000 | − | 6.06218i | 0.134120 | − | 0.232303i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.50000 | − | 7.79423i | −0.172188 | − | 0.298238i | 0.766997 | − | 0.641651i | \(-0.221750\pi\) |
−0.939184 | + | 0.343413i | \(0.888417\pi\) | |||||||
\(684\) | 2.00000 | 0.0764719 | ||||||||
\(685\) | −9.00000 | − | 15.5885i | −0.343872 | − | 0.595604i | ||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | −9.00000 | −0.343371 | ||||||||
\(688\) | 4.00000 | + | 5.19615i | 0.152499 | + | 0.198101i | ||||
\(689\) | 25.0000 | 0.952424 | ||||||||
\(690\) | 7.00000 | 0.266485 | ||||||||
\(691\) | −2.50000 | − | 4.33013i | −0.0951045 | − | 0.164726i | 0.814548 | − | 0.580097i | \(-0.196985\pi\) |
−0.909652 | + | 0.415371i | \(0.863652\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5000 | − | 32.0429i | −0.702250 | − | 1.21633i | ||||
\(695\) | 6.50000 | − | 11.2583i | 0.246559 | − | 0.427053i | ||||
\(696\) | −9.00000 | −0.341144 | ||||||||
\(697\) | 15.0000 | − | 25.9808i | 0.568166 | − | 0.984092i | ||||
\(698\) | 0.500000 | + | 0.866025i | 0.0189253 | + | 0.0327795i | ||||
\(699\) | −9.00000 | −0.340411 | ||||||||
\(700\) | −6.00000 | − | 10.3923i | −0.226779 | − | 0.392792i | ||||
\(701\) | −3.50000 | + | 6.06218i | −0.132193 | + | 0.228965i | −0.924522 | − | 0.381129i | \(-0.875535\pi\) |
0.792329 | + | 0.610095i | \(0.208869\pi\) | |||||||
\(702\) | −12.5000 | + | 21.6506i | −0.471782 | + | 0.817151i | ||||
\(703\) | 4.50000 | − | 7.79423i | 0.169721 | − | 0.293965i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | + | 6.92820i | −0.150649 | + | 0.260931i | ||||
\(706\) | 12.5000 | − | 21.6506i | 0.470444 | − | 0.814832i | ||||
\(707\) | 13.5000 | + | 23.3827i | 0.507720 | + | 0.879396i | ||||
\(708\) | 6.00000 | + | 10.3923i | 0.225494 | + | 0.390567i | ||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | 1.00000 | 0.0375293 | ||||||||
\(711\) | −5.00000 | − | 8.66025i | −0.187515 | − | 0.324785i | ||||
\(712\) | −1.50000 | − | 2.59808i | −0.0562149 | − | 0.0973670i | ||||
\(713\) | 17.5000 | − | 30.3109i | 0.655380 | − | 1.13515i | ||||
\(714\) | −4.50000 | + | 7.79423i | −0.168408 | + | 0.291692i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.500000 | + | 0.866025i | −0.0186859 | + | 0.0323649i | ||||
\(717\) | −12.5000 | + | 21.6506i | −0.466821 | + | 0.808558i | ||||
\(718\) | −9.50000 | + | 16.4545i | −0.354537 | + | 0.614076i | ||||
\(719\) | 15.5000 | + | 26.8468i | 0.578052 | + | 1.00122i | 0.995703 | + | 0.0926083i | \(0.0295204\pi\) |
−0.417650 | + | 0.908608i | \(0.637146\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | −10.5000 | − | 18.1865i | −0.391040 | − | 0.677302i | ||||
\(722\) | 9.00000 | − | 15.5885i | 0.334945 | − | 0.580142i | ||||
\(723\) | 15.0000 | 0.557856 | ||||||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | 6.00000 | + | 10.3923i | 0.222834 | + | 0.385961i | ||||
\(726\) | 5.50000 | + | 9.52628i | 0.204124 | + | 0.353553i | ||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | −22.5000 | − | 38.9711i | −0.833905 | − | 1.44437i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | 19.5000 | − | 2.59808i | 0.721234 | − | 0.0960933i | ||||
\(732\) | 13.0000 | 0.480494 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | −6.50000 | − | 11.2583i | −0.239919 | − | 0.415553i | ||||
\(735\) | −2.00000 | −0.0737711 | ||||||||
\(736\) | 17.5000 | + | 30.3109i | 0.645059 | + | 1.11727i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −10.0000 | + | 17.3205i | −0.368105 | + | 0.637577i | ||||
\(739\) | −4.00000 | −0.147142 | −0.0735712 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735712 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(740\) | 4.50000 | − | 7.79423i | 0.165423 | − | 0.286522i | ||||
\(741\) | 2.50000 | + | 4.33013i | 0.0918398 | + | 0.159071i | ||||
\(742\) | −15.0000 | −0.550667 | ||||||||
\(743\) | −10.5000 | − | 18.1865i | −0.385208 | − | 0.667199i | 0.606590 | − | 0.795015i | \(-0.292537\pi\) |
−0.991798 | + | 0.127815i | \(0.959204\pi\) | |||||||
\(744\) | 7.50000 | − | 12.9904i | 0.274963 | − | 0.476250i | ||||
\(745\) | −10.5000 | + | 18.1865i | −0.384690 | + | 0.666303i | ||||
\(746\) | −5.50000 | + | 9.52628i | −0.201369 | + | 0.348782i | ||||
\(747\) | −18.0000 | −0.658586 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 31.1769i | −0.657706 | + | 1.13918i | ||||
\(750\) | −4.50000 | − | 7.79423i | −0.164317 | − | 0.284605i | ||||
\(751\) | 13.5000 | + | 23.3827i | 0.492622 | + | 0.853246i | 0.999964 | − | 0.00849853i | \(-0.00270520\pi\) |
−0.507342 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 7.00000 | 0.255094 | ||||||||
\(754\) | 7.50000 | + | 12.9904i | 0.273134 | + | 0.473082i | ||||
\(755\) | −4.00000 | − | 6.92820i | −0.145575 | − | 0.252143i | ||||
\(756\) | −7.50000 | + | 12.9904i | −0.272772 | + | 0.472456i | ||||
\(757\) | 2.50000 | − | 4.33013i | 0.0908640 | − | 0.157381i | −0.817011 | − | 0.576622i | \(-0.804370\pi\) |
0.907875 | + | 0.419241i | \(0.137704\pi\) | |||||||
\(758\) | 20.0000 | 0.726433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.50000 | + | 2.59808i | −0.0544107 | + | 0.0942421i | ||||
\(761\) | 18.5000 | − | 32.0429i | 0.670624 | − | 1.16156i | −0.307103 | − | 0.951676i | \(-0.599360\pi\) |
0.977727 | − | 0.209879i | \(-0.0673071\pi\) | |||||||
\(762\) | −8.00000 | − | 13.8564i | −0.289809 | − | 0.501965i | ||||
\(763\) | 21.0000 | 0.760251 | ||||||||
\(764\) | −9.50000 | − | 16.4545i | −0.343698 | − | 0.595302i | ||||
\(765\) | −3.00000 | + | 5.19615i | −0.108465 | + | 0.187867i | ||||
\(766\) | 8.00000 | 0.289052 | ||||||||
\(767\) | 30.0000 | − | 51.9615i | 1.08324 | − | 1.87622i | ||||
\(768\) | 8.50000 | + | 14.7224i | 0.306717 | + | 0.531250i | ||||
\(769\) | 16.5000 | + | 28.5788i | 0.595005 | + | 1.03058i | 0.993546 | + | 0.113429i | \(0.0361834\pi\) |
−0.398541 | + | 0.917151i | \(0.630483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00000 | − | 5.19615i | −0.108042 | − | 0.187135i | ||||
\(772\) | −6.00000 | −0.215945 | ||||||||
\(773\) | 26.0000 | 0.935155 | 0.467578 | − | 0.883952i | \(-0.345127\pi\) | ||||
0.467578 | + | 0.883952i | \(0.345127\pi\) | |||||||
\(774\) | −13.0000 | + | 1.73205i | −0.467275 | + | 0.0622573i | ||||
\(775\) | −20.0000 | −0.718421 | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 13.5000 | + | 23.3827i | 0.484310 | + | 0.838849i | ||||
\(778\) | −6.00000 | −0.215110 | ||||||||
\(779\) | 5.00000 | + | 8.66025i | 0.179144 | + | 0.310286i | ||||
\(780\) | 2.50000 | + | 4.33013i | 0.0895144 | + | 0.155043i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −21.0000 | −0.750958 | ||||||||
\(783\) | 7.50000 | − | 12.9904i | 0.268028 | − | 0.464238i | ||||
\(784\) | 1.00000 | + | 1.73205i | 0.0357143 | + | 0.0618590i | ||||
\(785\) | 1.00000 | 0.0356915 | ||||||||
\(786\) | 2.00000 | + | 3.46410i | 0.0713376 | + | 0.123560i | ||||
\(787\) | 2.50000 | − | 4.33013i | 0.0891154 | − | 0.154352i | −0.818022 | − | 0.575187i | \(-0.804929\pi\) |
0.907137 | + | 0.420834i | \(0.138263\pi\) | |||||||
\(788\) | 5.50000 | − | 9.52628i | 0.195929 | − | 0.339360i | ||||
\(789\) | −10.5000 | + | 18.1865i | −0.373810 | + | 0.647458i | ||||
\(790\) | 5.00000 | 0.177892 | ||||||||
\(791\) | 3.00000 | − | 5.19615i | 0.106668 | − | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.5000 | − | 56.2917i | −1.15411 | − | 1.99898i | ||||
\(794\) | 10.5000 | + | 18.1865i | 0.372631 | + | 0.645416i | ||||
\(795\) | 5.00000 | 0.177332 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 10.5000 | + | 18.1865i | 0.371929 | + | 0.644200i | 0.989862 | − | 0.142031i | \(-0.0453631\pi\) |
−0.617933 | + | 0.786231i | \(0.712030\pi\) | |||||||
\(798\) | −1.50000 | − | 2.59808i | −0.0530994 | − | 0.0919709i | ||||
\(799\) | 12.0000 | − | 20.7846i | 0.424529 | − | 0.735307i | ||||
\(800\) | 10.0000 | − | 17.3205i | 0.353553 | − | 0.612372i | ||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | 18.5000 | − | 32.0429i | 0.653258 | − | 1.13148i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.50000 | + | 2.59808i | −0.0529009 | + | 0.0916271i | ||||
\(805\) | −10.5000 | − | 18.1865i | −0.370076 | − | 0.640991i | ||||
\(806\) | −25.0000 | −0.880587 | ||||||||
\(807\) | −7.00000 | − | 12.1244i | −0.246412 | − | 0.426798i | ||||
\(808\) | −13.5000 | + | 23.3827i | −0.474928 | + | 0.822600i | ||||
\(809\) | −34.0000 | −1.19538 | −0.597688 | − | 0.801729i | \(-0.703914\pi\) | ||||
−0.597688 | + | 0.801729i | \(0.703914\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | 23.5000 | + | 40.7032i | 0.825197 | + | 1.42928i | 0.901769 | + | 0.432218i | \(0.142269\pi\) |
−0.0765723 | + | 0.997064i | \(0.524398\pi\) | |||||||
\(812\) | 4.50000 | + | 7.79423i | 0.157919 | + | 0.273524i | ||||
\(813\) | 23.0000 | 0.806645 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000 | 0.0350285 | ||||||||
\(816\) | −3.00000 | −0.105021 | ||||||||
\(817\) | −2.50000 | + | 6.06218i | −0.0874639 | + | 0.212089i | ||||
\(818\) | −18.0000 | −0.629355 | ||||||||
\(819\) | 30.0000 | 1.04828 | ||||||||
\(820\) | 5.00000 | + | 8.66025i | 0.174608 | + | 0.302429i | ||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 9.00000 | + | 15.5885i | 0.313911 | + | 0.543710i | ||||
\(823\) | 15.5000 | + | 26.8468i | 0.540296 | + | 0.935820i | 0.998887 | + | 0.0471726i | \(0.0150211\pi\) |
−0.458591 | + | 0.888648i | \(0.651646\pi\) | |||||||
\(824\) | 10.5000 | − | 18.1865i | 0.365785 | − | 0.633558i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | + | 31.1769i | −0.626300 | + | 1.08478i | ||||
\(827\) | −16.5000 | − | 28.5788i | −0.573761 | − | 0.993784i | −0.996175 | − | 0.0873805i | \(-0.972150\pi\) |
0.422414 | − | 0.906403i | \(-0.361183\pi\) | |||||||
\(828\) | −14.0000 | −0.486534 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 4.50000 | − | 7.79423i | 0.156197 | − | 0.270542i | ||||
\(831\) | −3.50000 | + | 6.06218i | −0.121414 | + | 0.210295i | ||||
\(832\) | 17.5000 | − | 30.3109i | 0.606703 | − | 1.05084i | ||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | −6.50000 | + | 11.2583i | −0.225077 | + | 0.389844i | ||||
\(835\) | −1.50000 | + | 2.59808i | −0.0519096 | + | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.5000 | + | 21.6506i | 0.432063 | + | 0.748355i | ||||
\(838\) | −28.0000 | −0.967244 | ||||||||
\(839\) | −52.0000 | −1.79524 | −0.897620 | − | 0.440771i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440771i | \(0.854705\pi\) | |||||||
\(840\) | −4.50000 | − | 7.79423i | −0.155265 | − | 0.268926i | ||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 18.5000 | − | 32.0429i | 0.637552 | − | 1.10427i | ||||
\(843\) | 8.50000 | − | 14.7224i | 0.292756 | − | 0.507067i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | −8.00000 | + | 13.8564i | −0.275046 | + | 0.476393i | ||||
\(847\) | 16.5000 | − | 28.5788i | 0.566947 | − | 0.981981i | ||||
\(848\) | −2.50000 | − | 4.33013i | −0.0858504 | − | 0.148697i | ||||
\(849\) | 3.00000 | 0.102960 | ||||||||
\(850\) | 6.00000 | + | 10.3923i | 0.205798 | + | 0.356453i | ||||
\(851\) | −31.5000 | + | 54.5596i | −1.07981 | + | 1.87028i | ||||
\(852\) | 1.00000 | 0.0342594 | ||||||||
\(853\) | 2.50000 | − | 4.33013i | 0.0855984 | − | 0.148261i | −0.820048 | − | 0.572295i | \(-0.806053\pi\) |
0.905646 | + | 0.424034i | \(0.139386\pi\) | |||||||
\(854\) | 19.5000 | + | 33.7750i | 0.667276 | + | 1.15576i | ||||
\(855\) | −1.00000 | − | 1.73205i | −0.0341993 | − | 0.0592349i | ||||
\(856\) | −36.0000 | −1.23045 | ||||||||
\(857\) | −17.5000 | − | 30.3109i | −0.597789 | − | 1.03540i | −0.993147 | − | 0.116873i | \(-0.962713\pi\) |
0.395358 | − | 0.918527i | \(-0.370620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.00000 | 0.136478 | 0.0682391 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682391 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(860\) | −2.50000 | + | 6.06218i | −0.0852493 | + | 0.206719i | ||||
\(861\) | −30.0000 | −1.02240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.5000 | + | 23.3827i | 0.459545 | + | 0.795956i | 0.998937 | − | 0.0460992i | \(-0.0146790\pi\) |
−0.539392 | + | 0.842055i | \(0.681346\pi\) | |||||||
\(864\) | −25.0000 | −0.850517 | ||||||||
\(865\) | −3.00000 | − | 5.19615i | −0.102003 | − | 0.176674i | ||||
\(866\) | −13.5000 | − | 23.3827i | −0.458749 | − | 0.794576i | ||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | −15.0000 | −0.509133 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.50000 | + | 2.59808i | 0.0508548 | + | 0.0880830i | ||||
\(871\) | 15.0000 | 0.508256 | ||||||||
\(872\) | 10.5000 | + | 18.1865i | 0.355575 | + | 0.615874i | ||||
\(873\) | −2.00000 | + | 3.46410i | −0.0676897 | + | 0.117242i | ||||
\(874\) | 3.50000 | − | 6.06218i | 0.118389 | − | 0.205056i | ||||
\(875\) | −13.5000 | + | 23.3827i | −0.456383 | + | 0.790479i | ||||
\(876\) | −11.0000 | −0.371656 | ||||||||
\(877\) | −11.5000 | + | 19.9186i | −0.388327 | + | 0.672603i | −0.992225 | − | 0.124459i | \(-0.960280\pi\) |
0.603897 | + | 0.797062i | \(0.293614\pi\) | |||||||
\(878\) | 6.50000 | − | 11.2583i | 0.219364 | − | 0.379950i | ||||
\(879\) | 7.00000 | + | 12.1244i | 0.236104 | + | 0.408944i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0000 | 1.54978 | 0.774890 | − | 0.632096i | \(-0.217805\pi\) | ||||
0.774890 | + | 0.632096i | \(0.217805\pi\) | |||||||
\(882\) | −4.00000 | −0.134687 | ||||||||
\(883\) | −6.50000 | − | 11.2583i | −0.218742 | − | 0.378873i | 0.735681 | − | 0.677328i | \(-0.236862\pi\) |
−0.954424 | + | 0.298455i | \(0.903529\pi\) | |||||||
\(884\) | −7.50000 | − | 12.9904i | −0.252252 | − | 0.436914i | ||||
\(885\) | 6.00000 | − | 10.3923i | 0.201688 | − | 0.349334i | ||||
\(886\) | 18.5000 | − | 32.0429i | 0.621520 | − | 1.07650i | ||||
\(887\) | −16.0000 | −0.537227 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(888\) | −13.5000 | + | 23.3827i | −0.453030 | + | 0.784672i | ||||
\(889\) | −24.0000 | + | 41.5692i | −0.804934 | + | 1.39419i | ||||
\(890\) | −0.500000 | + | 0.866025i | −0.0167600 | + | 0.0290292i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.0000 | −0.669650 | ||||||||
\(893\) | 4.00000 | + | 6.92820i | 0.133855 | + | 0.231843i | ||||
\(894\) | 10.5000 | − | 18.1865i | 0.351173 | − | 0.608249i | ||||
\(895\) | 1.00000 | 0.0334263 | ||||||||
\(896\) | 4.50000 | − | 7.79423i | 0.150334 | − | 0.260387i | ||||
\(897\) | −17.5000 | − | 30.3109i | −0.584308 | − | 1.01205i | ||||
\(898\) | 10.5000 | + | 18.1865i | 0.350390 | + | 0.606892i | ||||
\(899\) | 15.0000 | 0.500278 | ||||||||
\(900\) | 4.00000 | + | 6.92820i | 0.133333 | + | 0.230940i | ||||
\(901\) | −15.0000 | −0.499722 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0000 | − | 15.5885i | −0.399335 | − | 0.518751i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | −7.00000 | −0.232688 | ||||||||
\(906\) | 4.00000 | + | 6.92820i | 0.132891 | + | 0.230174i | ||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | −3.50000 | − | 6.06218i | −0.116152 | − | 0.201180i | ||||
\(909\) | −9.00000 | − | 15.5885i | −0.298511 | − | 0.517036i | ||||
\(910\) | −7.50000 | + | 12.9904i | −0.248623 | + | 0.430627i | ||||
\(911\) | −52.0000 | −1.72284 | −0.861418 | − | 0.507896i | \(-0.830423\pi\) | ||||
−0.861418 | + | 0.507896i | \(0.830423\pi\) | |||||||
\(912\) | 0.500000 | − | 0.866025i | 0.0165567 | − | 0.0286770i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.00000 | 0.198462 | ||||||||
\(915\) | −6.50000 | − | 11.2583i | −0.214883 | − | 0.372189i | ||||
\(916\) | −4.50000 | + | 7.79423i | −0.148684 | + | 0.257529i | ||||
\(917\) | 6.00000 | − | 10.3923i | 0.198137 | − | 0.343184i | ||||
\(918\) | 7.50000 | − | 12.9904i | 0.247537 | − | 0.428746i | ||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | 10.5000 | − | 18.1865i | 0.346175 | − | 0.599592i | ||||
\(921\) | −2.50000 | + | 4.33013i | −0.0823778 | + | 0.142683i | ||||
\(922\) | −1.50000 | − | 2.59808i | −0.0493999 | − | 0.0855631i | ||||
\(923\) | −2.50000 | − | 4.33013i | −0.0822885 | − | 0.142528i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.0000 | 1.18367 | ||||||||
\(926\) | 11.5000 | + | 19.9186i | 0.377913 | + | 0.654565i | ||||
\(927\) | 7.00000 | + | 12.1244i | 0.229910 | + | 0.398216i | ||||
\(928\) | −7.50000 | + | 12.9904i | −0.246200 | + | 0.426430i | ||||
\(929\) | 28.5000 | − | 49.3634i | 0.935055 | − | 1.61956i | 0.160518 | − | 0.987033i | \(-0.448683\pi\) |
0.774536 | − | 0.632529i | \(-0.217983\pi\) | |||||||
\(930\) | −5.00000 | −0.163956 | ||||||||
\(931\) | −1.00000 | + | 1.73205i | −0.0327737 | + | 0.0567657i | ||||
\(932\) | −4.50000 | + | 7.79423i | −0.147402 | + | 0.255308i | ||||
\(933\) | 1.50000 | − | 2.59808i | 0.0491078 | − | 0.0850572i | ||||
\(934\) | −10.5000 | − | 18.1865i | −0.343570 | − | 0.595082i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15.0000 | + | 25.9808i | 0.490290 | + | 0.849208i | ||||
\(937\) | −17.5000 | + | 30.3109i | −0.571700 | + | 0.990214i | 0.424691 | + | 0.905338i | \(0.360383\pi\) |
−0.996392 | + | 0.0848755i | \(0.972951\pi\) | |||||||
\(938\) | −9.00000 | −0.293860 | ||||||||
\(939\) | 8.50000 | − | 14.7224i | 0.277387 | − | 0.480448i | ||||
\(940\) | 4.00000 | + | 6.92820i | 0.130466 | + | 0.225973i | ||||
\(941\) | 4.50000 | + | 7.79423i | 0.146696 | + | 0.254085i | 0.930004 | − | 0.367549i | \(-0.119803\pi\) |
−0.783309 | + | 0.621633i | \(0.786469\pi\) | |||||||
\(942\) | −1.00000 | −0.0325818 | ||||||||
\(943\) | −35.0000 | − | 60.6218i | −1.13976 | − | 1.97412i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 15.0000 | 0.487950 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | 5.00000 | 0.162392 | ||||||||
\(949\) | 27.5000 | + | 47.6314i | 0.892688 | + | 1.54618i | ||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | 9.00000 | + | 15.5885i | 0.291845 | + | 0.505490i | ||||
\(952\) | 13.5000 | + | 23.3827i | 0.437538 | + | 0.757837i | ||||
\(953\) | 20.5000 | − | 35.5070i | 0.664060 | − | 1.15019i | −0.315479 | − | 0.948933i | \(-0.602165\pi\) |
0.979539 | − | 0.201253i | \(-0.0645015\pi\) | |||||||
\(954\) | 10.0000 | 0.323762 | ||||||||
\(955\) | −9.50000 | + | 16.4545i | −0.307413 | + | 0.532455i | ||||
\(956\) | 12.5000 | + | 21.6506i | 0.404279 | + | 0.700232i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.50000 | + | 12.9904i | 0.242314 | + | 0.419700i | ||||
\(959\) | 27.0000 | − | 46.7654i | 0.871875 | − | 1.51013i | ||||
\(960\) | 3.50000 | − | 6.06218i | 0.112962 | − | 0.195656i | ||||
\(961\) | 3.00000 | − | 5.19615i | 0.0967742 | − | 0.167618i | ||||
\(962\) | 45.0000 | 1.45086 | ||||||||
\(963\) | 12.0000 | − | 20.7846i | 0.386695 | − | 0.669775i | ||||
\(964\) | 7.50000 | − | 12.9904i | 0.241559 | − | 0.418392i | ||||
\(965\) | 3.00000 | + | 5.19615i | 0.0965734 | + | 0.167270i | ||||
\(966\) | 10.5000 | + | 18.1865i | 0.337832 | + | 0.585142i | ||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 33.0000 | 1.06066 | ||||||||
\(969\) | −1.50000 | − | 2.59808i | −0.0481869 | − | 0.0834622i | ||||
\(970\) | −1.00000 | − | 1.73205i | −0.0321081 | − | 0.0556128i | ||||
\(971\) | −17.5000 | + | 30.3109i | −0.561602 | + | 0.972723i | 0.435755 | + | 0.900065i | \(0.356481\pi\) |
−0.997357 | + | 0.0726575i | \(0.976852\pi\) | |||||||
\(972\) | 8.00000 | − | 13.8564i | 0.256600 | − | 0.444444i | ||||
\(973\) | 39.0000 | 1.25028 | ||||||||
\(974\) | 4.50000 | − | 7.79423i | 0.144189 | − | 0.249743i | ||||
\(975\) | −10.0000 | + | 17.3205i | −0.320256 | + | 0.554700i | ||||
\(976\) | −6.50000 | + | 11.2583i | −0.208060 | + | 0.360370i | ||||
\(977\) | 20.5000 | + | 35.5070i | 0.655853 | + | 1.13597i | 0.981679 | + | 0.190541i | \(0.0610243\pi\) |
−0.325826 | + | 0.945430i | \(0.605642\pi\) | |||||||
\(978\) | −1.00000 | −0.0319765 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | + | 1.73205i | −0.0319438 | + | 0.0553283i | ||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 4.50000 | − | 7.79423i | 0.143601 | − | 0.248724i | ||||
\(983\) | 25.5000 | + | 44.1673i | 0.813324 | + | 1.40872i | 0.910525 | + | 0.413453i | \(0.135677\pi\) |
−0.0972017 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(984\) | −15.0000 | − | 25.9808i | −0.478183 | − | 0.828236i | ||||
\(985\) | −11.0000 | −0.350489 | ||||||||
\(986\) | −4.50000 | − | 7.79423i | −0.143309 | − | 0.248219i | ||||
\(987\) | −24.0000 | −0.763928 | ||||||||
\(988\) | 5.00000 | 0.159071 | ||||||||
\(989\) | 17.5000 | − | 42.4352i | 0.556468 | − | 1.34936i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | −12.5000 | − | 21.6506i | −0.396875 | − | 0.687408i | ||||
\(993\) | 19.0000 | 0.602947 | ||||||||
\(994\) | 1.50000 | + | 2.59808i | 0.0475771 | + | 0.0824060i | ||||
\(995\) | 4.00000 | + | 6.92820i | 0.126809 | + | 0.219639i | ||||
\(996\) | 4.50000 | − | 7.79423i | 0.142588 | − | 0.246970i | ||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 8.50000 | − | 14.7224i | 0.269063 | − | 0.466030i | ||||
\(999\) | −22.5000 | − | 38.9711i | −0.711868 | − | 1.23299i |
(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 | 43.2.c.a.36.1 | yes | 2 | |
3.2 | odd | 2 | 387.2.h.a.208.1 | 2 | |||
4.3 | odd | 2 | 688.2.i.d.337.1 | 2 | |||
43.6 | even | 3 | inner | 43.2.c.a.6.1 | ✓ | 2 | |
43.7 | odd | 6 | 1849.2.a.a.1.1 | 1 | |||
43.36 | even | 3 | 1849.2.a.c.1.1 | 1 | |||
129.92 | odd | 6 | 387.2.h.a.307.1 | 2 | |||
172.135 | odd | 6 | 688.2.i.d.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.c.a.6.1 | ✓ | 2 | 43.6 | even | 3 | inner | |
43.2.c.a.36.1 | yes | 2 | 1.1 | even | 1 | trivial | |
387.2.h.a.208.1 | 2 | 3.2 | odd | 2 | |||
387.2.h.a.307.1 | 2 | 129.92 | odd | 6 | |||
688.2.i.d.49.1 | 2 | 172.135 | odd | 6 | |||
688.2.i.d.337.1 | 2 | 4.3 | odd | 2 | |||
1849.2.a.a.1.1 | 1 | 43.7 | odd | 6 | |||
1849.2.a.c.1.1 | 1 | 43.36 | even | 3 |