Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.361 |
Dual form | 507.2.j.d.316.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | −0.161521 | − | 0.986869i | \(-0.551640\pi\) |
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | −0.974679 | − | 0.223607i | \(-0.928217\pi\) | ||
0.974679 | − | 0.223607i | \(-0.0717831\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 1.73205 | + | 1.00000i | 0.654654 | + | 0.377964i | 0.790237 | − | 0.612801i | \(-0.209957\pi\) |
−0.135583 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 1.73205 | − | 1.00000i | 0.522233 | − | 0.301511i | −0.215615 | − | 0.976478i | \(-0.569176\pi\) |
0.737848 | + | 0.674967i | \(0.235842\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0.866025 | − | 0.500000i | 0.223607 | − | 0.129099i | ||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | −3.50000 | + | 6.06218i | −0.848875 | + | 1.47029i | 0.0333386 | + | 0.999444i | \(0.489386\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 5.19615 | + | 3.00000i | 1.19208 | + | 0.688247i | 0.958778 | − | 0.284157i | \(-0.0917138\pi\) |
0.233301 | + | 0.972404i | \(0.425047\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | −2.59808 | + | 1.50000i | −0.530330 | + | 0.306186i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.73205 | + | 1.00000i | −0.327327 | + | 0.188982i | ||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | −4.33013 | − | 2.50000i | −0.765466 | − | 0.441942i | ||||
\(33\) | 1.73205 | + | 1.00000i | 0.301511 | + | 0.174078i | ||||
\(34\) | 7.00000i | 1.20049i | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −0.866025 | + | 0.500000i | −0.142374 | + | 0.0821995i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) |
0.427121 | + | 0.904194i | \(0.359528\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | 7.79423 | − | 4.50000i | 1.21725 | − | 0.702782i | 0.252924 | − | 0.967486i | \(-0.418608\pi\) |
0.964330 | + | 0.264704i | \(0.0852743\pi\) | |||||||
\(42\) | 1.00000 | + | 1.73205i | 0.154303 | + | 0.267261i | ||||
\(43\) | 3.00000 | − | 5.19615i | 0.457496 | − | 0.792406i | −0.541332 | − | 0.840809i | \(-0.682080\pi\) |
0.998828 | + | 0.0484030i | \(0.0154132\pi\) | |||||||
\(44\) | 2.00000i | 0.301511i | ||||||||
\(45\) | 0.866025 | + | 0.500000i | 0.129099 | + | 0.0745356i | ||||
\(46\) | −5.19615 | − | 3.00000i | −0.766131 | − | 0.442326i | ||||
\(47\) | − | 6.00000i | − | 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −1.50000 | − | 2.59808i | −0.214286 | − | 0.371154i | ||||
\(50\) | 3.46410 | − | 2.00000i | 0.489898 | − | 0.282843i | ||||
\(51\) | −7.00000 | −0.980196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | −1.00000 | − | 1.73205i | −0.134840 | − | 0.233550i | ||||
\(56\) | −3.00000 | + | 5.19615i | −0.400892 | + | 0.694365i | ||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0.866025 | + | 0.500000i | 0.113715 | + | 0.0656532i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −0.500000 | + | 0.866025i | −0.0640184 | + | 0.110883i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 2.00000 | + | 3.46410i | 0.254000 | + | 0.439941i | ||||
\(63\) | −1.73205 | + | 1.00000i | −0.218218 | + | 0.125988i | ||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | −1.73205 | + | 1.00000i | −0.211604 | + | 0.122169i | −0.602056 | − | 0.798454i | \(-0.705652\pi\) |
0.390453 | + | 0.920623i | \(0.372318\pi\) | |||||||
\(68\) | −3.50000 | − | 6.06218i | −0.424437 | − | 0.735147i | ||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | − | 2.00000i | − | 0.239046i | ||||||
\(71\) | −5.19615 | − | 3.00000i | −0.616670 | − | 0.356034i | 0.158901 | − | 0.987294i | \(-0.449205\pi\) |
−0.775571 | + | 0.631260i | \(0.782538\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | − | 11.0000i | − | 1.28745i | −0.765256 | − | 0.643726i | \(-0.777388\pi\) | ||
0.765256 | − | 0.643726i | \(-0.222612\pi\) | |||||||
\(74\) | −0.500000 | + | 0.866025i | −0.0581238 | + | 0.100673i | ||||
\(75\) | 2.00000 | + | 3.46410i | 0.230940 | + | 0.400000i | ||||
\(76\) | −5.19615 | + | 3.00000i | −0.596040 | + | 0.344124i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 4.50000 | − | 7.79423i | 0.496942 | − | 0.860729i | ||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | −1.73205 | − | 1.00000i | −0.188982 | − | 0.109109i | ||||
\(85\) | 6.06218 | + | 3.50000i | 0.657536 | + | 0.379628i | ||||
\(86\) | − | 6.00000i | − | 0.646997i | ||||||
\(87\) | −0.500000 | + | 0.866025i | −0.0536056 | + | 0.0928477i | ||||
\(88\) | 3.00000 | + | 5.19615i | 0.319801 | + | 0.553912i | ||||
\(89\) | 12.1244 | − | 7.00000i | 1.28518 | − | 0.741999i | 0.307389 | − | 0.951584i | \(-0.400545\pi\) |
0.977790 | + | 0.209585i | \(0.0672115\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | −3.46410 | + | 2.00000i | −0.359211 | + | 0.207390i | ||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 3.00000 | − | 5.19615i | 0.307794 | − | 0.533114i | ||||
\(96\) | − | 5.00000i | − | 0.510310i | ||||||
\(97\) | 1.73205 | + | 1.00000i | 0.175863 | + | 0.101535i | 0.585348 | − | 0.810782i | \(-0.300958\pi\) |
−0.409484 | + | 0.912317i | \(0.634291\pi\) | |||||||
\(98\) | −2.59808 | − | 1.50000i | −0.262445 | − | 0.151523i | ||||
\(99\) | 2.00000i | 0.201008i | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | −6.06218 | + | 3.50000i | −0.600245 | + | 0.346552i | ||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | −7.79423 | + | 4.50000i | −0.757042 | + | 0.437079i | ||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | −1.73205 | − | 1.00000i | −0.165145 | − | 0.0953463i | ||||
\(111\) | −0.866025 | − | 0.500000i | −0.0821995 | − | 0.0474579i | ||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 7.50000 | − | 12.9904i | 0.705541 | − | 1.22203i | −0.260955 | − | 0.965351i | \(-0.584038\pi\) |
0.966496 | − | 0.256681i | \(-0.0826291\pi\) | |||||||
\(114\) | 3.00000 | + | 5.19615i | 0.280976 | + | 0.486664i | ||||
\(115\) | −5.19615 | + | 3.00000i | −0.484544 | + | 0.279751i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.1244 | + | 7.00000i | −1.11144 | + | 0.641689i | ||||
\(120\) | 1.50000 | + | 2.59808i | 0.136931 | + | 0.237171i | ||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 1.00000i | 0.0905357i | ||||||||
\(123\) | 7.79423 | + | 4.50000i | 0.702782 | + | 0.405751i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | − | 9.00000i | − | 0.804984i | ||||||
\(126\) | −1.00000 | + | 1.73205i | −0.0890871 | + | 0.154303i | ||||
\(127\) | 10.0000 | + | 17.3205i | 0.887357 | + | 1.53695i | 0.842989 | + | 0.537931i | \(0.180794\pi\) |
0.0443678 | + | 0.999015i | \(0.485873\pi\) | |||||||
\(128\) | 2.59808 | − | 1.50000i | 0.229640 | − | 0.132583i | ||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | −1.73205 | + | 1.00000i | −0.150756 | + | 0.0870388i | ||||
\(133\) | 6.00000 | + | 10.3923i | 0.520266 | + | 0.901127i | ||||
\(134\) | −1.00000 | + | 1.73205i | −0.0863868 | + | 0.149626i | ||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | −18.1865 | − | 10.5000i | −1.55948 | − | 0.900368i | ||||
\(137\) | −2.59808 | − | 1.50000i | −0.221969 | − | 0.128154i | 0.384893 | − | 0.922961i | \(-0.374238\pi\) |
−0.606861 | + | 0.794808i | \(0.707572\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | −6.00000 | + | 10.3923i | −0.508913 | + | 0.881464i | 0.491033 | + | 0.871141i | \(0.336619\pi\) |
−0.999947 | + | 0.0103230i | \(0.996714\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | 5.19615 | − | 3.00000i | 0.437595 | − | 0.252646i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0.866025 | − | 0.500000i | 0.0719195 | − | 0.0415227i | ||||
\(146\) | −5.50000 | − | 9.52628i | −0.455183 | − | 0.788400i | ||||
\(147\) | 1.50000 | − | 2.59808i | 0.123718 | − | 0.214286i | ||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −2.59808 | − | 1.50000i | −0.212843 | − | 0.122885i | 0.389789 | − | 0.920904i | \(-0.372548\pi\) |
−0.602632 | + | 0.798019i | \(0.705881\pi\) | |||||||
\(150\) | 3.46410 | + | 2.00000i | 0.282843 | + | 0.163299i | ||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | −9.00000 | + | 15.5885i | −0.729996 | + | 1.26439i | ||||
\(153\) | −3.50000 | − | 6.06218i | −0.282958 | − | 0.490098i | ||||
\(154\) | 3.46410 | − | 2.00000i | 0.279145 | − | 0.161165i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | −0.239426 | −0.119713 | − | 0.992809i | \(-0.538197\pi\) | ||||
−0.119713 | + | 0.992809i | \(0.538197\pi\) | |||||||
\(158\) | −3.46410 | + | 2.00000i | −0.275589 | + | 0.159111i | ||||
\(159\) | −4.50000 | − | 7.79423i | −0.356873 | − | 0.618123i | ||||
\(160\) | −2.50000 | + | 4.33013i | −0.197642 | + | 0.342327i | ||||
\(161\) | − | 12.0000i | − | 0.945732i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −3.46410 | − | 2.00000i | −0.271329 | − | 0.156652i | 0.358162 | − | 0.933659i | \(-0.383403\pi\) |
−0.629492 | + | 0.777007i | \(0.716737\pi\) | |||||||
\(164\) | 9.00000i | 0.702782i | ||||||||
\(165\) | 1.00000 | − | 1.73205i | 0.0778499 | − | 0.134840i | ||||
\(166\) | −7.00000 | − | 12.1244i | −0.543305 | − | 0.941033i | ||||
\(167\) | −13.8564 | + | 8.00000i | −1.07224 | + | 0.619059i | −0.928793 | − | 0.370599i | \(-0.879152\pi\) |
−0.143448 | + | 0.989658i | \(0.545819\pi\) | |||||||
\(168\) | −6.00000 | −0.462910 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.00000 | 0.536875 | ||||||||
\(171\) | −5.19615 | + | 3.00000i | −0.397360 | + | 0.229416i | ||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 1.00000i | 0.0758098i | ||||||||
\(175\) | 6.92820 | + | 4.00000i | 0.523723 | + | 0.302372i | ||||
\(176\) | 1.73205 | + | 1.00000i | 0.130558 | + | 0.0753778i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.00000 | − | 12.1244i | 0.524672 | − | 0.908759i | ||||
\(179\) | −1.00000 | − | 1.73205i | −0.0747435 | − | 0.129460i | 0.826231 | − | 0.563331i | \(-0.190480\pi\) |
−0.900975 | + | 0.433872i | \(0.857147\pi\) | |||||||
\(180\) | −0.866025 | + | 0.500000i | −0.0645497 | + | 0.0372678i | ||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 15.5885 | − | 9.00000i | 1.14920 | − | 0.663489i | ||||
\(185\) | 0.500000 | + | 0.866025i | 0.0367607 | + | 0.0636715i | ||||
\(186\) | −2.00000 | + | 3.46410i | −0.146647 | + | 0.254000i | ||||
\(187\) | 14.0000i | 1.02378i | ||||||||
\(188\) | 5.19615 | + | 3.00000i | 0.378968 | + | 0.218797i | ||||
\(189\) | −1.73205 | − | 1.00000i | −0.125988 | − | 0.0727393i | ||||
\(190\) | − | 6.00000i | − | 0.435286i | ||||||
\(191\) | 2.00000 | − | 3.46410i | 0.144715 | − | 0.250654i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) |
0.929267 | + | 0.369410i | \(0.120440\pi\) | |||||||
\(192\) | −3.50000 | − | 6.06218i | −0.252591 | − | 0.437500i | ||||
\(193\) | 7.79423 | − | 4.50000i | 0.561041 | − | 0.323917i | −0.192522 | − | 0.981293i | \(-0.561667\pi\) |
0.753563 | + | 0.657376i | \(0.228333\pi\) | |||||||
\(194\) | 2.00000 | 0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 5.19615 | − | 3.00000i | 0.370211 | − | 0.213741i | −0.303340 | − | 0.952882i | \(-0.598102\pi\) |
0.673550 | + | 0.739141i | \(0.264768\pi\) | |||||||
\(198\) | 1.00000 | + | 1.73205i | 0.0710669 | + | 0.123091i | ||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | 12.0000i | 0.848528i | ||||||||
\(201\) | −1.73205 | − | 1.00000i | −0.122169 | − | 0.0705346i | ||||
\(202\) | 2.59808 | + | 1.50000i | 0.182800 | + | 0.105540i | ||||
\(203\) | 2.00000i | 0.140372i | ||||||||
\(204\) | 3.50000 | − | 6.06218i | 0.245049 | − | 0.424437i | ||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | −5.19615 | + | 3.00000i | −0.362033 | + | 0.209020i | ||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 1.73205 | − | 1.00000i | 0.119523 | − | 0.0690066i | ||||
\(211\) | 4.00000 | + | 6.92820i | 0.275371 | + | 0.476957i | 0.970229 | − | 0.242190i | \(-0.0778659\pi\) |
−0.694857 | + | 0.719148i | \(0.744533\pi\) | |||||||
\(212\) | 4.50000 | − | 7.79423i | 0.309061 | − | 0.535310i | ||||
\(213\) | − | 6.00000i | − | 0.411113i | ||||||
\(214\) | 5.19615 | + | 3.00000i | 0.355202 | + | 0.205076i | ||||
\(215\) | −5.19615 | − | 3.00000i | −0.354375 | − | 0.204598i | ||||
\(216\) | − | 3.00000i | − | 0.204124i | ||||||
\(217\) | −4.00000 | + | 6.92820i | −0.271538 | + | 0.470317i | ||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | 9.52628 | − | 5.50000i | 0.643726 | − | 0.371656i | ||||
\(220\) | 2.00000 | 0.134840 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.00000 | −0.0671156 | ||||||||
\(223\) | 13.8564 | − | 8.00000i | 0.927894 | − | 0.535720i | 0.0417488 | − | 0.999128i | \(-0.486707\pi\) |
0.886145 | + | 0.463409i | \(0.153374\pi\) | |||||||
\(224\) | −5.00000 | − | 8.66025i | −0.334077 | − | 0.578638i | ||||
\(225\) | −2.00000 | + | 3.46410i | −0.133333 | + | 0.230940i | ||||
\(226\) | − | 15.0000i | − | 0.997785i | ||||||
\(227\) | 12.1244 | + | 7.00000i | 0.804722 | + | 0.464606i | 0.845120 | − | 0.534577i | \(-0.179529\pi\) |
−0.0403978 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(228\) | −5.19615 | − | 3.00000i | −0.344124 | − | 0.198680i | ||||
\(229\) | 22.0000i | 1.45380i | 0.686743 | + | 0.726900i | \(0.259040\pi\) | ||||
−0.686743 | + | 0.726900i | \(0.740960\pi\) | |||||||
\(230\) | −3.00000 | + | 5.19615i | −0.197814 | + | 0.342624i | ||||
\(231\) | 2.00000 | + | 3.46410i | 0.131590 | + | 0.227921i | ||||
\(232\) | −2.59808 | + | 1.50000i | −0.170572 | + | 0.0984798i | ||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.00000 | − | 3.46410i | −0.129914 | − | 0.225018i | ||||
\(238\) | −7.00000 | + | 12.1244i | −0.453743 | + | 0.785905i | ||||
\(239\) | 30.0000i | 1.94054i | 0.242028 | + | 0.970269i | \(0.422188\pi\) | ||||
−0.242028 | + | 0.970269i | \(0.577812\pi\) | |||||||
\(240\) | 0.866025 | + | 0.500000i | 0.0559017 | + | 0.0322749i | ||||
\(241\) | 6.06218 | + | 3.50000i | 0.390499 | + | 0.225455i | 0.682376 | − | 0.731001i | \(-0.260947\pi\) |
−0.291877 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −0.500000 | − | 0.866025i | −0.0320092 | − | 0.0554416i | ||||
\(245\) | −2.59808 | + | 1.50000i | −0.165985 | + | 0.0958315i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12.0000 | −0.762001 | ||||||||
\(249\) | 12.1244 | − | 7.00000i | 0.768350 | − | 0.443607i | ||||
\(250\) | −4.50000 | − | 7.79423i | −0.284605 | − | 0.492950i | ||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | −10.3923 | − | 6.00000i | −0.653359 | − | 0.377217i | ||||
\(254\) | 17.3205 | + | 10.0000i | 1.08679 | + | 0.627456i | ||||
\(255\) | 7.00000i | 0.438357i | ||||||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | −3.50000 | − | 6.06218i | −0.218324 | − | 0.378148i | 0.735972 | − | 0.677012i | \(-0.236726\pi\) |
−0.954296 | + | 0.298864i | \(0.903392\pi\) | |||||||
\(258\) | 5.19615 | − | 3.00000i | 0.323498 | − | 0.186772i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −6.92820 | + | 4.00000i | −0.428026 | + | 0.247121i | ||||
\(263\) | 15.0000 | + | 25.9808i | 0.924940 | + | 1.60204i | 0.791658 | + | 0.610964i | \(0.209218\pi\) |
0.133281 | + | 0.991078i | \(0.457449\pi\) | |||||||
\(264\) | −3.00000 | + | 5.19615i | −0.184637 | + | 0.319801i | ||||
\(265\) | 9.00000i | 0.552866i | ||||||||
\(266\) | 10.3923 | + | 6.00000i | 0.637193 | + | 0.367884i | ||||
\(267\) | 12.1244 | + | 7.00000i | 0.741999 | + | 0.428393i | ||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(272\) | −7.00000 | −0.424437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | −0.181237 | ||||||||
\(275\) | 6.92820 | − | 4.00000i | 0.417786 | − | 0.241209i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −15.5000 | + | 26.8468i | −0.931305 | + | 1.61307i | −0.150210 | + | 0.988654i | \(0.547995\pi\) |
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | −3.46410 | − | 2.00000i | −0.207390 | − | 0.119737i | ||||
\(280\) | 5.19615 | + | 3.00000i | 0.310530 | + | 0.179284i | ||||
\(281\) | 19.0000i | 1.13344i | 0.823909 | + | 0.566722i | \(0.191789\pi\) | ||||
−0.823909 | + | 0.566722i | \(0.808211\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | −9.00000 | − | 15.5885i | −0.534994 | − | 0.926638i | −0.999164 | − | 0.0408910i | \(-0.986980\pi\) |
0.464169 | − | 0.885747i | \(-0.346353\pi\) | |||||||
\(284\) | 5.19615 | − | 3.00000i | 0.308335 | − | 0.178017i | ||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.0000 | 1.06251 | ||||||||
\(288\) | 4.33013 | − | 2.50000i | 0.255155 | − | 0.147314i | ||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | 0.500000 | − | 0.866025i | 0.0293610 | − | 0.0508548i | ||||
\(291\) | 2.00000i | 0.117242i | ||||||||
\(292\) | 9.52628 | + | 5.50000i | 0.557483 | + | 0.321863i | ||||
\(293\) | −7.79423 | − | 4.50000i | −0.455344 | − | 0.262893i | 0.254741 | − | 0.967009i | \(-0.418010\pi\) |
−0.710084 | + | 0.704117i | \(0.751343\pi\) | |||||||
\(294\) | − | 3.00000i | − | 0.174964i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | −1.73205 | + | 1.00000i | −0.100504 | + | 0.0580259i | ||||
\(298\) | −3.00000 | −0.173785 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 10.3923 | − | 6.00000i | 0.599002 | − | 0.345834i | ||||
\(302\) | 1.00000 | + | 1.73205i | 0.0575435 | + | 0.0996683i | ||||
\(303\) | −1.50000 | + | 2.59808i | −0.0861727 | + | 0.149256i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 0.866025 | + | 0.500000i | 0.0495885 | + | 0.0286299i | ||||
\(306\) | −6.06218 | − | 3.50000i | −0.346552 | − | 0.200082i | ||||
\(307\) | − | 14.0000i | − | 0.799022i | −0.916728 | − | 0.399511i | \(-0.869180\pi\) | ||
0.916728 | − | 0.399511i | \(-0.130820\pi\) | |||||||
\(308\) | −2.00000 | + | 3.46410i | −0.113961 | + | 0.197386i | ||||
\(309\) | −3.00000 | − | 5.19615i | −0.170664 | − | 0.295599i | ||||
\(310\) | 3.46410 | − | 2.00000i | 0.196748 | − | 0.113592i | ||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | −2.59808 | + | 1.50000i | −0.146618 | + | 0.0846499i | ||||
\(315\) | 1.00000 | + | 1.73205i | 0.0563436 | + | 0.0975900i | ||||
\(316\) | 2.00000 | − | 3.46410i | 0.112509 | − | 0.194871i | ||||
\(317\) | − | 25.0000i | − | 1.40414i | −0.712108 | − | 0.702070i | \(-0.752259\pi\) | ||
0.712108 | − | 0.702070i | \(-0.247741\pi\) | |||||||
\(318\) | −7.79423 | − | 4.50000i | −0.437079 | − | 0.252347i | ||||
\(319\) | 1.73205 | + | 1.00000i | 0.0969762 | + | 0.0559893i | ||||
\(320\) | 7.00000i | 0.391312i | ||||||||
\(321\) | −3.00000 | + | 5.19615i | −0.167444 | + | 0.290021i | ||||
\(322\) | −6.00000 | − | 10.3923i | −0.334367 | − | 0.579141i | ||||
\(323\) | −36.3731 | + | 21.0000i | −2.02385 | + | 1.16847i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 1.73205 | − | 1.00000i | 0.0957826 | − | 0.0553001i | ||||
\(328\) | 13.5000 | + | 23.3827i | 0.745413 | + | 1.29109i | ||||
\(329\) | 6.00000 | − | 10.3923i | 0.330791 | − | 0.572946i | ||||
\(330\) | − | 2.00000i | − | 0.110096i | ||||||
\(331\) | 3.46410 | + | 2.00000i | 0.190404 | + | 0.109930i | 0.592172 | − | 0.805812i | \(-0.298271\pi\) |
−0.401768 | + | 0.915742i | \(0.631604\pi\) | |||||||
\(332\) | 12.1244 | + | 7.00000i | 0.665410 | + | 0.384175i | ||||
\(333\) | − | 1.00000i | − | 0.0547997i | ||||||
\(334\) | −8.00000 | + | 13.8564i | −0.437741 | + | 0.758189i | ||||
\(335\) | 1.00000 | + | 1.73205i | 0.0546358 | + | 0.0946320i | ||||
\(336\) | −1.73205 | + | 1.00000i | −0.0944911 | + | 0.0545545i | ||||
\(337\) | 33.0000 | 1.79762 | 0.898812 | − | 0.438334i | \(-0.144431\pi\) | ||||
0.898812 | + | 0.438334i | \(0.144431\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | 0.814688 | ||||||||
\(340\) | −6.06218 | + | 3.50000i | −0.328768 | + | 0.189814i | ||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | −3.00000 | + | 5.19615i | −0.162221 | + | 0.280976i | ||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 15.5885 | + | 9.00000i | 0.840473 | + | 0.485247i | ||||
\(345\) | −5.19615 | − | 3.00000i | −0.279751 | − | 0.161515i | ||||
\(346\) | 6.00000i | 0.322562i | ||||||||
\(347\) | −9.00000 | + | 15.5885i | −0.483145 | + | 0.836832i | −0.999813 | − | 0.0193540i | \(-0.993839\pi\) |
0.516667 | + | 0.856186i | \(0.327172\pi\) | |||||||
\(348\) | −0.500000 | − | 0.866025i | −0.0268028 | − | 0.0464238i | ||||
\(349\) | 22.5167 | − | 13.0000i | 1.20529 | − | 0.695874i | 0.243563 | − | 0.969885i | \(-0.421684\pi\) |
0.961727 | + | 0.274011i | \(0.0883505\pi\) | |||||||
\(350\) | 8.00000 | 0.427618 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.0000 | −0.533002 | ||||||||
\(353\) | −9.52628 | + | 5.50000i | −0.507033 | + | 0.292735i | −0.731613 | − | 0.681720i | \(-0.761232\pi\) |
0.224580 | + | 0.974456i | \(0.427899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 14.0000i | 0.741999i | ||||||||
\(357\) | −12.1244 | − | 7.00000i | −0.641689 | − | 0.370479i | ||||
\(358\) | −1.73205 | − | 1.00000i | −0.0915417 | − | 0.0528516i | ||||
\(359\) | 18.0000i | 0.950004i | 0.879985 | + | 0.475002i | \(0.157553\pi\) | ||||
−0.879985 | + | 0.475002i | \(0.842447\pi\) | |||||||
\(360\) | −1.50000 | + | 2.59808i | −0.0790569 | + | 0.136931i | ||||
\(361\) | 8.50000 | + | 14.7224i | 0.447368 | + | 0.774865i | ||||
\(362\) | 6.06218 | − | 3.50000i | 0.318621 | − | 0.183956i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.0000 | −0.575766 | ||||||||
\(366\) | −0.866025 | + | 0.500000i | −0.0452679 | + | 0.0261354i | ||||
\(367\) | −5.00000 | − | 8.66025i | −0.260998 | − | 0.452062i | 0.705509 | − | 0.708700i | \(-0.250718\pi\) |
−0.966507 | + | 0.256639i | \(0.917385\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 9.00000i | 0.468521i | ||||||||
\(370\) | 0.866025 | + | 0.500000i | 0.0450225 | + | 0.0259938i | ||||
\(371\) | −15.5885 | − | 9.00000i | −0.809312 | − | 0.467257i | ||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 5.50000 | − | 9.52628i | 0.284779 | − | 0.493252i | −0.687776 | − | 0.725923i | \(-0.741413\pi\) |
0.972556 | + | 0.232671i | \(0.0747464\pi\) | |||||||
\(374\) | 7.00000 | + | 12.1244i | 0.361961 | + | 0.626936i | ||||
\(375\) | 7.79423 | − | 4.50000i | 0.402492 | − | 0.232379i | ||||
\(376\) | 18.0000 | 0.928279 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | −31.1769 | + | 18.0000i | −1.60145 | + | 0.924598i | −0.610253 | + | 0.792207i | \(0.708932\pi\) |
−0.991198 | + | 0.132391i | \(0.957734\pi\) | |||||||
\(380\) | 3.00000 | + | 5.19615i | 0.153897 | + | 0.266557i | ||||
\(381\) | −10.0000 | + | 17.3205i | −0.512316 | + | 0.887357i | ||||
\(382\) | − | 4.00000i | − | 0.204658i | ||||||
\(383\) | −6.92820 | − | 4.00000i | −0.354015 | − | 0.204390i | 0.312437 | − | 0.949938i | \(-0.398855\pi\) |
−0.666452 | + | 0.745548i | \(0.732188\pi\) | |||||||
\(384\) | 2.59808 | + | 1.50000i | 0.132583 | + | 0.0765466i | ||||
\(385\) | − | 4.00000i | − | 0.203859i | ||||||
\(386\) | 4.50000 | − | 7.79423i | 0.229044 | − | 0.396716i | ||||
\(387\) | 3.00000 | + | 5.19615i | 0.152499 | + | 0.264135i | ||||
\(388\) | −1.73205 | + | 1.00000i | −0.0879316 | + | 0.0507673i | ||||
\(389\) | −19.0000 | −0.963338 | −0.481669 | − | 0.876353i | \(-0.659969\pi\) | ||||
−0.481669 | + | 0.876353i | \(0.659969\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.0000 | 2.12403 | ||||||||
\(392\) | 7.79423 | − | 4.50000i | 0.393668 | − | 0.227284i | ||||
\(393\) | −4.00000 | − | 6.92820i | −0.201773 | − | 0.349482i | ||||
\(394\) | 3.00000 | − | 5.19615i | 0.151138 | − | 0.261778i | ||||
\(395\) | 4.00000i | 0.201262i | ||||||||
\(396\) | −1.73205 | − | 1.00000i | −0.0870388 | − | 0.0502519i | ||||
\(397\) | −29.4449 | − | 17.0000i | −1.47780 | − | 0.853206i | −0.478110 | − | 0.878300i | \(-0.658678\pi\) |
−0.999685 | + | 0.0250943i | \(0.992011\pi\) | |||||||
\(398\) | − | 14.0000i | − | 0.701757i | ||||||
\(399\) | −6.00000 | + | 10.3923i | −0.300376 | + | 0.520266i | ||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | −0.866025 | + | 0.500000i | −0.0432472 | + | 0.0249688i | −0.521468 | − | 0.853271i | \(-0.674615\pi\) |
0.478220 | + | 0.878240i | \(0.341282\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3.00000 | −0.149256 | ||||||||
\(405\) | −0.866025 | + | 0.500000i | −0.0430331 | + | 0.0248452i | ||||
\(406\) | 1.00000 | + | 1.73205i | 0.0496292 | + | 0.0859602i | ||||
\(407\) | −1.00000 | + | 1.73205i | −0.0495682 | + | 0.0858546i | ||||
\(408\) | − | 21.0000i | − | 1.03965i | ||||||
\(409\) | −6.06218 | − | 3.50000i | −0.299755 | − | 0.173064i | 0.342578 | − | 0.939490i | \(-0.388700\pi\) |
−0.642333 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(410\) | −7.79423 | − | 4.50000i | −0.384930 | − | 0.222239i | ||||
\(411\) | − | 3.00000i | − | 0.147979i | ||||||
\(412\) | 3.00000 | − | 5.19615i | 0.147799 | − | 0.255996i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.19615 | − | 3.00000i | 0.255377 | − | 0.147442i | ||||
\(415\) | −14.0000 | −0.687233 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 10.3923 | − | 6.00000i | 0.508304 | − | 0.293470i | ||||
\(419\) | −8.00000 | − | 13.8564i | −0.390826 | − | 0.676930i | 0.601733 | − | 0.798697i | \(-0.294477\pi\) |
−0.992559 | + | 0.121768i | \(0.961144\pi\) | |||||||
\(420\) | −1.00000 | + | 1.73205i | −0.0487950 | + | 0.0845154i | ||||
\(421\) | − | 19.0000i | − | 0.926003i | −0.886357 | − | 0.463002i | \(-0.846772\pi\) | ||
0.886357 | − | 0.463002i | \(-0.153228\pi\) | |||||||
\(422\) | 6.92820 | + | 4.00000i | 0.337260 | + | 0.194717i | ||||
\(423\) | 5.19615 | + | 3.00000i | 0.252646 | + | 0.145865i | ||||
\(424\) | − | 27.0000i | − | 1.31124i | ||||||
\(425\) | −14.0000 | + | 24.2487i | −0.679100 | + | 1.17624i | ||||
\(426\) | −3.00000 | − | 5.19615i | −0.145350 | − | 0.251754i | ||||
\(427\) | −1.73205 | + | 1.00000i | −0.0838198 | + | 0.0483934i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | −0.289346 | ||||||||
\(431\) | −25.9808 | + | 15.0000i | −1.25145 | + | 0.722525i | −0.971397 | − | 0.237460i | \(-0.923685\pi\) |
−0.280052 | + | 0.959985i | \(0.590352\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 9.50000 | − | 16.4545i | 0.456541 | − | 0.790752i | −0.542234 | − | 0.840227i | \(-0.682422\pi\) |
0.998775 | + | 0.0494752i | \(0.0157549\pi\) | |||||||
\(434\) | 8.00000i | 0.384012i | ||||||||
\(435\) | 0.866025 | + | 0.500000i | 0.0415227 | + | 0.0239732i | ||||
\(436\) | 1.73205 | + | 1.00000i | 0.0829502 | + | 0.0478913i | ||||
\(437\) | − | 36.0000i | − | 1.72211i | ||||||
\(438\) | 5.50000 | − | 9.52628i | 0.262800 | − | 0.455183i | ||||
\(439\) | 7.00000 | + | 12.1244i | 0.334092 | + | 0.578664i | 0.983310 | − | 0.181938i | \(-0.0582371\pi\) |
−0.649218 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(440\) | 5.19615 | − | 3.00000i | 0.247717 | − | 0.143019i | ||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0.866025 | − | 0.500000i | 0.0410997 | − | 0.0237289i | ||||
\(445\) | −7.00000 | − | 12.1244i | −0.331832 | − | 0.574750i | ||||
\(446\) | 8.00000 | − | 13.8564i | 0.378811 | − | 0.656120i | ||||
\(447\) | − | 3.00000i | − | 0.141895i | ||||||
\(448\) | −12.1244 | − | 7.00000i | −0.572822 | − | 0.330719i | ||||
\(449\) | 29.4449 | + | 17.0000i | 1.38959 | + | 0.802280i | 0.993269 | − | 0.115833i | \(-0.0369536\pi\) |
0.396320 | + | 0.918112i | \(0.370287\pi\) | |||||||
\(450\) | 4.00000i | 0.188562i | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 7.50000 | + | 12.9904i | 0.352770 | + | 0.611016i | ||||
\(453\) | −1.73205 | + | 1.00000i | −0.0813788 | + | 0.0469841i | ||||
\(454\) | 14.0000 | 0.657053 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.0000 | −0.842927 | ||||||||
\(457\) | −11.2583 | + | 6.50000i | −0.526642 | + | 0.304057i | −0.739648 | − | 0.672994i | \(-0.765008\pi\) |
0.213006 | + | 0.977051i | \(0.431675\pi\) | |||||||
\(458\) | 11.0000 | + | 19.0526i | 0.513996 | + | 0.890268i | ||||
\(459\) | 3.50000 | − | 6.06218i | 0.163366 | − | 0.282958i | ||||
\(460\) | − | 6.00000i | − | 0.279751i | ||||||
\(461\) | −16.4545 | − | 9.50000i | −0.766362 | − | 0.442459i | 0.0652135 | − | 0.997871i | \(-0.479227\pi\) |
−0.831575 | + | 0.555412i | \(0.812560\pi\) | |||||||
\(462\) | 3.46410 | + | 2.00000i | 0.161165 | + | 0.0930484i | ||||
\(463\) | 26.0000i | 1.20832i | 0.796862 | + | 0.604161i | \(0.206492\pi\) | ||||
−0.796862 | + | 0.604161i | \(0.793508\pi\) | |||||||
\(464\) | −0.500000 | + | 0.866025i | −0.0232119 | + | 0.0402042i | ||||
\(465\) | 2.00000 | + | 3.46410i | 0.0927478 | + | 0.160644i | ||||
\(466\) | −8.66025 | + | 5.00000i | −0.401179 | + | 0.231621i | ||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | −5.19615 | + | 3.00000i | −0.239681 | + | 0.138380i | ||||
\(471\) | −1.50000 | − | 2.59808i | −0.0691164 | − | 0.119713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.0000i | − | 0.551761i | ||||||
\(474\) | −3.46410 | − | 2.00000i | −0.159111 | − | 0.0918630i | ||||
\(475\) | 20.7846 | + | 12.0000i | 0.953663 | + | 0.550598i | ||||
\(476\) | − | 14.0000i | − | 0.641689i | ||||||
\(477\) | 4.50000 | − | 7.79423i | 0.206041 | − | 0.356873i | ||||
\(478\) | 15.0000 | + | 25.9808i | 0.686084 | + | 1.18833i | ||||
\(479\) | −20.7846 | + | 12.0000i | −0.949673 | + | 0.548294i | −0.892979 | − | 0.450098i | \(-0.851389\pi\) |
−0.0566937 | + | 0.998392i | \(0.518056\pi\) | |||||||
\(480\) | −5.00000 | −0.228218 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.00000 | 0.318841 | ||||||||
\(483\) | 10.3923 | − | 6.00000i | 0.472866 | − | 0.273009i | ||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −15.5885 | − | 9.00000i | −0.706380 | − | 0.407829i | 0.103339 | − | 0.994646i | \(-0.467047\pi\) |
−0.809719 | + | 0.586817i | \(0.800381\pi\) | |||||||
\(488\) | −2.59808 | − | 1.50000i | −0.117609 | − | 0.0679018i | ||||
\(489\) | − | 4.00000i | − | 0.180886i | ||||||
\(490\) | −1.50000 | + | 2.59808i | −0.0677631 | + | 0.117369i | ||||
\(491\) | 3.00000 | + | 5.19615i | 0.135388 | + | 0.234499i | 0.925746 | − | 0.378147i | \(-0.123439\pi\) |
−0.790358 | + | 0.612646i | \(0.790105\pi\) | |||||||
\(492\) | −7.79423 | + | 4.50000i | −0.351391 | + | 0.202876i | ||||
\(493\) | −7.00000 | −0.315264 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | 0.0898933 | ||||||||
\(496\) | −3.46410 | + | 2.00000i | −0.155543 | + | 0.0898027i | ||||
\(497\) | −6.00000 | − | 10.3923i | −0.269137 | − | 0.466159i | ||||
\(498\) | 7.00000 | − | 12.1244i | 0.313678 | − | 0.543305i | ||||
\(499\) | 24.0000i | 1.07439i | 0.843459 | + | 0.537194i | \(0.180516\pi\) | ||||
−0.843459 | + | 0.537194i | \(0.819484\pi\) | |||||||
\(500\) | 7.79423 | + | 4.50000i | 0.348569 | + | 0.201246i | ||||
\(501\) | −13.8564 | − | 8.00000i | −0.619059 | − | 0.357414i | ||||
\(502\) | − | 12.0000i | − | 0.535586i | ||||||
\(503\) | 1.00000 | − | 1.73205i | 0.0445878 | − | 0.0772283i | −0.842870 | − | 0.538117i | \(-0.819136\pi\) |
0.887458 | + | 0.460889i | \(0.152469\pi\) | |||||||
\(504\) | −3.00000 | − | 5.19615i | −0.133631 | − | 0.231455i | ||||
\(505\) | 2.59808 | − | 1.50000i | 0.115613 | − | 0.0667491i | ||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.0000 | −0.887357 | ||||||||
\(509\) | 6.06218 | − | 3.50000i | 0.268701 | − | 0.155135i | −0.359596 | − | 0.933108i | \(-0.617085\pi\) |
0.628297 | + | 0.777973i | \(0.283752\pi\) | |||||||
\(510\) | 3.50000 | + | 6.06218i | 0.154983 | + | 0.268438i | ||||
\(511\) | 11.0000 | − | 19.0526i | 0.486611 | − | 0.842836i | ||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | −5.19615 | − | 3.00000i | −0.229416 | − | 0.132453i | ||||
\(514\) | −6.06218 | − | 3.50000i | −0.267391 | − | 0.154378i | ||||
\(515\) | 6.00000i | 0.264392i | ||||||||
\(516\) | −3.00000 | + | 5.19615i | −0.132068 | + | 0.228748i | ||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | −1.73205 | + | 1.00000i | −0.0761019 | + | 0.0439375i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | −0.131432 | −0.0657162 | − | 0.997838i | \(-0.520933\pi\) | ||||
−0.0657162 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(522\) | −0.866025 | + | 0.500000i | −0.0379049 | + | 0.0218844i | ||||
\(523\) | −7.00000 | − | 12.1244i | −0.306089 | − | 0.530161i | 0.671414 | − | 0.741082i | \(-0.265687\pi\) |
−0.977503 | + | 0.210921i | \(0.932354\pi\) | |||||||
\(524\) | 4.00000 | − | 6.92820i | 0.174741 | − | 0.302660i | ||||
\(525\) | 8.00000i | 0.349149i | ||||||||
\(526\) | 25.9808 | + | 15.0000i | 1.13282 | + | 0.654031i | ||||
\(527\) | −24.2487 | − | 14.0000i | −1.05629 | − | 0.609850i | ||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | −0.520266 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.0000 | 0.605839 | ||||||||
\(535\) | 5.19615 | − | 3.00000i | 0.224649 | − | 0.129701i | ||||
\(536\) | −3.00000 | − | 5.19615i | −0.129580 | − | 0.224440i | ||||
\(537\) | 1.00000 | − | 1.73205i | 0.0431532 | − | 0.0747435i | ||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | −5.19615 | − | 3.00000i | −0.223814 | − | 0.129219i | ||||
\(540\) | −0.866025 | − | 0.500000i | −0.0372678 | − | 0.0215166i | ||||
\(541\) | − | 45.0000i | − | 1.93470i | −0.253442 | − | 0.967351i | \(-0.581563\pi\) | ||
0.253442 | − | 0.967351i | \(-0.418437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.50000 | + | 6.06218i | 0.150199 | + | 0.260153i | ||||
\(544\) | 30.3109 | − | 17.5000i | 1.29957 | − | 0.750306i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.0000 | −1.11168 | −0.555840 | − | 0.831289i | \(-0.687603\pi\) | ||||
−0.555840 | + | 0.831289i | \(0.687603\pi\) | |||||||
\(548\) | 2.59808 | − | 1.50000i | 0.110984 | − | 0.0640768i | ||||
\(549\) | −0.500000 | − | 0.866025i | −0.0213395 | − | 0.0369611i | ||||
\(550\) | 4.00000 | − | 6.92820i | 0.170561 | − | 0.295420i | ||||
\(551\) | 6.00000i | 0.255609i | ||||||||
\(552\) | 15.5885 | + | 9.00000i | 0.663489 | + | 0.383065i | ||||
\(553\) | −6.92820 | − | 4.00000i | −0.294617 | − | 0.170097i | ||||
\(554\) | 31.0000i | 1.31706i | ||||||||
\(555\) | −0.500000 | + | 0.866025i | −0.0212238 | + | 0.0367607i | ||||
\(556\) | −6.00000 | − | 10.3923i | −0.254457 | − | 0.440732i | ||||
\(557\) | 7.79423 | − | 4.50000i | 0.330252 | − | 0.190671i | −0.325701 | − | 0.945473i | \(-0.605600\pi\) |
0.655953 | + | 0.754802i | \(0.272267\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | −12.1244 | + | 7.00000i | −0.511891 | + | 0.295540i | ||||
\(562\) | 9.50000 | + | 16.4545i | 0.400733 | + | 0.694090i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 6.00000i | 0.252646i | ||||||||
\(565\) | −12.9904 | − | 7.50000i | −0.546509 | − | 0.315527i | ||||
\(566\) | −15.5885 | − | 9.00000i | −0.655232 | − | 0.378298i | ||||
\(567\) | − | 2.00000i | − | 0.0839921i | ||||||
\(568\) | 9.00000 | − | 15.5885i | 0.377632 | − | 0.654077i | ||||
\(569\) | 11.0000 | + | 19.0526i | 0.461144 | + | 0.798725i | 0.999018 | − | 0.0443003i | \(-0.0141058\pi\) |
−0.537874 | + | 0.843025i | \(0.680772\pi\) | |||||||
\(570\) | 5.19615 | − | 3.00000i | 0.217643 | − | 0.125656i | ||||
\(571\) | −26.0000 | −1.08807 | −0.544033 | − | 0.839064i | \(-0.683103\pi\) | ||||
−0.544033 | + | 0.839064i | \(0.683103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.00000 | 0.167102 | ||||||||
\(574\) | 15.5885 | − | 9.00000i | 0.650650 | − | 0.375653i | ||||
\(575\) | −12.0000 | − | 20.7846i | −0.500435 | − | 0.866778i | ||||
\(576\) | 3.50000 | − | 6.06218i | 0.145833 | − | 0.252591i | ||||
\(577\) | 11.0000i | 0.457936i | 0.973434 | + | 0.228968i | \(0.0735351\pi\) | ||||
−0.973434 | + | 0.228968i | \(0.926465\pi\) | |||||||
\(578\) | −27.7128 | − | 16.0000i | −1.15270 | − | 0.665512i | ||||
\(579\) | 7.79423 | + | 4.50000i | 0.323917 | + | 0.187014i | ||||
\(580\) | 1.00000i | 0.0415227i | ||||||||
\(581\) | 14.0000 | − | 24.2487i | 0.580818 | − | 1.00601i | ||||
\(582\) | 1.00000 | + | 1.73205i | 0.0414513 | + | 0.0717958i | ||||
\(583\) | −15.5885 | + | 9.00000i | −0.645608 | + | 0.372742i | ||||
\(584\) | 33.0000 | 1.36555 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.00000 | −0.371787 | ||||||||
\(587\) | 13.8564 | − | 8.00000i | 0.571915 | − | 0.330195i | −0.185999 | − | 0.982550i | \(-0.559552\pi\) |
0.757914 | + | 0.652355i | \(0.226219\pi\) | |||||||
\(588\) | 1.50000 | + | 2.59808i | 0.0618590 | + | 0.107143i | ||||
\(589\) | −12.0000 | + | 20.7846i | −0.494451 | + | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.19615 | + | 3.00000i | 0.213741 | + | 0.123404i | ||||
\(592\) | −0.866025 | − | 0.500000i | −0.0355934 | − | 0.0205499i | ||||
\(593\) | − | 13.0000i | − | 0.533846i | −0.963718 | − | 0.266923i | \(-0.913993\pi\) | ||
0.963718 | − | 0.266923i | \(-0.0860069\pi\) | |||||||
\(594\) | −1.00000 | + | 1.73205i | −0.0410305 | + | 0.0710669i | ||||
\(595\) | 7.00000 | + | 12.1244i | 0.286972 | + | 0.497050i | ||||
\(596\) | 2.59808 | − | 1.50000i | 0.106421 | − | 0.0614424i | ||||
\(597\) | 14.0000 | 0.572982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0000 | −0.653742 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(600\) | −10.3923 | + | 6.00000i | −0.424264 | + | 0.244949i | ||||
\(601\) | 2.50000 | + | 4.33013i | 0.101977 | + | 0.176630i | 0.912499 | − | 0.409079i | \(-0.134150\pi\) |
−0.810522 | + | 0.585708i | \(0.800816\pi\) | |||||||
\(602\) | 6.00000 | − | 10.3923i | 0.244542 | − | 0.423559i | ||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | −1.73205 | − | 1.00000i | −0.0704761 | − | 0.0406894i | ||||
\(605\) | 6.06218 | + | 3.50000i | 0.246463 | + | 0.142295i | ||||
\(606\) | 3.00000i | 0.121867i | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | −15.0000 | − | 25.9808i | −0.608330 | − | 1.05366i | ||||
\(609\) | −1.73205 | + | 1.00000i | −0.0701862 | + | 0.0405220i | ||||
\(610\) | 1.00000 | 0.0404888 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.00000 | 0.282958 | ||||||||
\(613\) | −19.9186 | + | 11.5000i | −0.804504 | + | 0.464481i | −0.845044 | − | 0.534697i | \(-0.820426\pi\) |
0.0405396 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(614\) | −7.00000 | − | 12.1244i | −0.282497 | − | 0.489299i | ||||
\(615\) | 4.50000 | − | 7.79423i | 0.181458 | − | 0.314294i | ||||
\(616\) | 12.0000i | 0.483494i | ||||||||
\(617\) | −11.2583 | − | 6.50000i | −0.453243 | − | 0.261680i | 0.255956 | − | 0.966689i | \(-0.417610\pi\) |
−0.709199 | + | 0.705008i | \(0.750943\pi\) | |||||||
\(618\) | −5.19615 | − | 3.00000i | −0.209020 | − | 0.120678i | ||||
\(619\) | 24.0000i | 0.964641i | 0.875995 | + | 0.482321i | \(0.160206\pi\) | ||||
−0.875995 | + | 0.482321i | \(0.839794\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | −15.5885 | + | 9.00000i | −0.625040 | + | 0.360867i | ||||
\(623\) | 28.0000 | 1.12180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 5.19615 | − | 3.00000i | 0.207680 | − | 0.119904i | ||||
\(627\) | 6.00000 | + | 10.3923i | 0.239617 | + | 0.415029i | ||||
\(628\) | 1.50000 | − | 2.59808i | 0.0598565 | − | 0.103675i | ||||
\(629\) | − | 7.00000i | − | 0.279108i | ||||||
\(630\) | 1.73205 | + | 1.00000i | 0.0690066 | + | 0.0398410i | ||||
\(631\) | 17.3205 | + | 10.0000i | 0.689519 | + | 0.398094i | 0.803432 | − | 0.595397i | \(-0.203005\pi\) |
−0.113913 | + | 0.993491i | \(0.536339\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | −4.00000 | + | 6.92820i | −0.158986 | + | 0.275371i | ||||
\(634\) | −12.5000 | − | 21.6506i | −0.496438 | − | 0.859857i | ||||
\(635\) | 17.3205 | − | 10.0000i | 0.687343 | − | 0.396838i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.00000 | 0.0791808 | ||||||||
\(639\) | 5.19615 | − | 3.00000i | 0.205557 | − | 0.118678i | ||||
\(640\) | −1.50000 | − | 2.59808i | −0.0592927 | − | 0.102698i | ||||
\(641\) | −15.5000 | + | 26.8468i | −0.612213 | + | 1.06038i | 0.378653 | + | 0.925539i | \(0.376387\pi\) |
−0.990867 | + | 0.134846i | \(0.956946\pi\) | |||||||
\(642\) | 6.00000i | 0.236801i | ||||||||
\(643\) | 13.8564 | + | 8.00000i | 0.546443 | + | 0.315489i | 0.747686 | − | 0.664052i | \(-0.231165\pi\) |
−0.201243 | + | 0.979541i | \(0.564498\pi\) | |||||||
\(644\) | 10.3923 | + | 6.00000i | 0.409514 | + | 0.236433i | ||||
\(645\) | − | 6.00000i | − | 0.236250i | ||||||
\(646\) | −21.0000 | + | 36.3731i | −0.826234 | + | 1.43108i | ||||
\(647\) | −16.0000 | − | 27.7128i | −0.629025 | − | 1.08950i | −0.987748 | − | 0.156059i | \(-0.950121\pi\) |
0.358723 | − | 0.933444i | \(-0.383212\pi\) | |||||||
\(648\) | 2.59808 | − | 1.50000i | 0.102062 | − | 0.0589256i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 3.46410 | − | 2.00000i | 0.135665 | − | 0.0783260i | ||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | 7.79423 | + | 4.50000i | 0.304314 | + | 0.175695i | ||||
\(657\) | 9.52628 | + | 5.50000i | 0.371656 | + | 0.214575i | ||||
\(658\) | − | 12.0000i | − | 0.467809i | ||||||
\(659\) | 4.00000 | − | 6.92820i | 0.155818 | − | 0.269884i | −0.777539 | − | 0.628835i | \(-0.783532\pi\) |
0.933357 | + | 0.358951i | \(0.116865\pi\) | |||||||
\(660\) | 1.00000 | + | 1.73205i | 0.0389249 | + | 0.0674200i | ||||
\(661\) | −38.9711 | + | 22.5000i | −1.51580 | + | 0.875149i | −0.515974 | + | 0.856604i | \(0.672570\pi\) |
−0.999828 | + | 0.0185442i | \(0.994097\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.0000 | 1.62992 | ||||||||
\(665\) | 10.3923 | − | 6.00000i | 0.402996 | − | 0.232670i | ||||
\(666\) | −0.500000 | − | 0.866025i | −0.0193746 | − | 0.0335578i | ||||
\(667\) | 3.00000 | − | 5.19615i | 0.116160 | − | 0.201196i | ||||
\(668\) | − | 16.0000i | − | 0.619059i | ||||||
\(669\) | 13.8564 | + | 8.00000i | 0.535720 | + | 0.309298i | ||||
\(670\) | 1.73205 | + | 1.00000i | 0.0669150 | + | 0.0386334i | ||||
\(671\) | 2.00000i | 0.0772091i | ||||||||
\(672\) | 5.00000 | − | 8.66025i | 0.192879 | − | 0.334077i | ||||
\(673\) | −14.5000 | − | 25.1147i | −0.558934 | − | 0.968102i | −0.997586 | − | 0.0694449i | \(-0.977877\pi\) |
0.438652 | − | 0.898657i | \(-0.355456\pi\) | |||||||
\(674\) | 28.5788 | − | 16.5000i | 1.10082 | − | 0.635556i | ||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.0000 | 1.30673 | 0.653363 | − | 0.757045i | \(-0.273358\pi\) | ||||
0.653363 | + | 0.757045i | \(0.273358\pi\) | |||||||
\(678\) | 12.9904 | − | 7.50000i | 0.498893 | − | 0.288036i | ||||
\(679\) | 2.00000 | + | 3.46410i | 0.0767530 | + | 0.132940i | ||||
\(680\) | −10.5000 | + | 18.1865i | −0.402657 | + | 0.697422i | ||||
\(681\) | 14.0000i | 0.536481i | ||||||||
\(682\) | 6.92820 | + | 4.00000i | 0.265295 | + | 0.153168i | ||||
\(683\) | −20.7846 | − | 12.0000i | −0.795301 | − | 0.459167i | 0.0465244 | − | 0.998917i | \(-0.485185\pi\) |
−0.841825 | + | 0.539750i | \(0.818519\pi\) | |||||||
\(684\) | − | 6.00000i | − | 0.229416i | ||||||
\(685\) | −1.50000 | + | 2.59808i | −0.0573121 | + | 0.0992674i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −19.0526 | + | 11.0000i | −0.726900 | + | 0.419676i | ||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.00000 | −0.228416 | ||||||||
\(691\) | 36.3731 | − | 21.0000i | 1.38370 | − | 0.798878i | 0.391102 | − | 0.920348i | \(-0.372094\pi\) |
0.992595 | + | 0.121470i | \(0.0387608\pi\) | |||||||
\(692\) | −3.00000 | − | 5.19615i | −0.114043 | − | 0.197528i | ||||
\(693\) | −2.00000 | + | 3.46410i | −0.0759737 | + | 0.131590i | ||||
\(694\) | 18.0000i | 0.683271i | ||||||||
\(695\) | 10.3923 | + | 6.00000i | 0.394203 | + | 0.227593i | ||||
\(696\) | −2.59808 | − | 1.50000i | −0.0984798 | − | 0.0568574i | ||||
\(697\) | 63.0000i | 2.38630i | ||||||||
\(698\) | 13.0000 | − | 22.5167i | 0.492057 | − | 0.852268i | ||||
\(699\) | −5.00000 | − | 8.66025i | −0.189117 | − | 0.327561i | ||||
\(700\) | −6.92820 | + | 4.00000i | −0.261861 | + | 0.151186i | ||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | −12.1244 | + | 7.00000i | −0.456954 | + | 0.263822i | ||||
\(705\) | −3.00000 | − | 5.19615i | −0.112987 | − | 0.195698i | ||||
\(706\) | −5.50000 | + | 9.52628i | −0.206995 | + | 0.358526i | ||||
\(707\) | 6.00000i | 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.52628 | − | 5.50000i | −0.357767 | − | 0.206557i | 0.310334 | − | 0.950628i | \(-0.399559\pi\) |
−0.668101 | + | 0.744071i | \(0.732892\pi\) | |||||||
\(710\) | 6.00000i | 0.225176i | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | 21.0000 | + | 36.3731i | 0.787008 | + | 1.36314i | ||||
\(713\) | 20.7846 | − | 12.0000i | 0.778390 | − | 0.449404i | ||||
\(714\) | −14.0000 | −0.523937 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.00000 | 0.0747435 | ||||||||
\(717\) | −25.9808 | + | 15.0000i | −0.970269 | + | 0.560185i | ||||
\(718\) | 9.00000 | + | 15.5885i | 0.335877 | + | 0.581756i | ||||
\(719\) | −24.0000 | + | 41.5692i | −0.895049 | + | 1.55027i | −0.0613050 | + | 0.998119i | \(0.519526\pi\) |
−0.833744 | + | 0.552151i | \(0.813807\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | −10.3923 | − | 6.00000i | −0.387030 | − | 0.223452i | ||||
\(722\) | 14.7224 | + | 8.50000i | 0.547912 | + | 0.316337i | ||||
\(723\) | 7.00000i | 0.260333i | ||||||||
\(724\) | −3.50000 | + | 6.06218i | −0.130076 | + | 0.225299i | ||||
\(725\) | 2.00000 | + | 3.46410i | 0.0742781 | + | 0.128654i | ||||
\(726\) | −6.06218 | + | 3.50000i | −0.224989 | + | 0.129897i | ||||
\(727\) | −14.0000 | −0.519231 | −0.259616 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259616 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.52628 | + | 5.50000i | −0.352583 | + | 0.203564i | ||||
\(731\) | 21.0000 | + | 36.3731i | 0.776713 | + | 1.34531i | ||||
\(732\) | 0.500000 | − | 0.866025i | 0.0184805 | − | 0.0320092i | ||||
\(733\) | − | 15.0000i | − | 0.554038i | −0.960864 | − | 0.277019i | \(-0.910654\pi\) | ||
0.960864 | − | 0.277019i | \(-0.0893464\pi\) | |||||||
\(734\) | −8.66025 | − | 5.00000i | −0.319656 | − | 0.184553i | ||||
\(735\) | −2.59808 | − | 1.50000i | −0.0958315 | − | 0.0553283i | ||||
\(736\) | 30.0000i | 1.10581i | ||||||||
\(737\) | −2.00000 | + | 3.46410i | −0.0736709 | + | 0.127602i | ||||
\(738\) | 4.50000 | + | 7.79423i | 0.165647 | + | 0.286910i | ||||
\(739\) | 13.8564 | − | 8.00000i | 0.509716 | − | 0.294285i | −0.223001 | − | 0.974818i | \(-0.571585\pi\) |
0.732717 | + | 0.680534i | \(0.238252\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.0000 | −0.660801 | ||||||||
\(743\) | −31.1769 | + | 18.0000i | −1.14377 | + | 0.660356i | −0.947361 | − | 0.320166i | \(-0.896261\pi\) |
−0.196409 | + | 0.980522i | \(0.562928\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | −1.50000 | + | 2.59808i | −0.0549557 | + | 0.0951861i | ||||
\(746\) | − | 11.0000i | − | 0.402739i | ||||||
\(747\) | 12.1244 | + | 7.00000i | 0.443607 | + | 0.256117i | ||||
\(748\) | −12.1244 | − | 7.00000i | −0.443310 | − | 0.255945i | ||||
\(749\) | 12.0000i | 0.438470i | ||||||||
\(750\) | 4.50000 | − | 7.79423i | 0.164317 | − | 0.284605i | ||||
\(751\) | −17.0000 | − | 29.4449i | −0.620339 | − | 1.07446i | −0.989423 | − | 0.145062i | \(-0.953662\pi\) |
0.369084 | − | 0.929396i | \(-0.379672\pi\) | |||||||
\(752\) | 5.19615 | − | 3.00000i | 0.189484 | − | 0.109399i | ||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.00000 | 0.0727875 | ||||||||
\(756\) | 1.73205 | − | 1.00000i | 0.0629941 | − | 0.0363696i | ||||
\(757\) | 25.0000 | + | 43.3013i | 0.908640 | + | 1.57381i | 0.815955 | + | 0.578116i | \(0.196212\pi\) |
0.0926859 | + | 0.995695i | \(0.470455\pi\) | |||||||
\(758\) | −18.0000 | + | 31.1769i | −0.653789 | + | 1.13240i | ||||
\(759\) | − | 12.0000i | − | 0.435572i | ||||||
\(760\) | 15.5885 | + | 9.00000i | 0.565453 | + | 0.326464i | ||||
\(761\) | 43.3013 | + | 25.0000i | 1.56967 | + | 0.906249i | 0.996207 | + | 0.0870179i | \(0.0277337\pi\) |
0.573463 | + | 0.819231i | \(0.305600\pi\) | |||||||
\(762\) | 20.0000i | 0.724524i | ||||||||
\(763\) | 2.00000 | − | 3.46410i | 0.0724049 | − | 0.125409i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | −6.06218 | + | 3.50000i | −0.219179 | + | 0.126543i | ||||
\(766\) | −8.00000 | −0.289052 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.0000 | 0.613435 | ||||||||
\(769\) | 25.9808 | − | 15.0000i | 0.936890 | − | 0.540914i | 0.0479061 | − | 0.998852i | \(-0.484745\pi\) |
0.888984 | + | 0.457938i | \(0.151412\pi\) | |||||||
\(770\) | −2.00000 | − | 3.46410i | −0.0720750 | − | 0.124838i | ||||
\(771\) | 3.50000 | − | 6.06218i | 0.126049 | − | 0.218324i | ||||
\(772\) | 9.00000i | 0.323917i | ||||||||
\(773\) | 12.1244 | + | 7.00000i | 0.436083 | + | 0.251773i | 0.701935 | − | 0.712241i | \(-0.252320\pi\) |
−0.265852 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(774\) | 5.19615 | + | 3.00000i | 0.186772 | + | 0.107833i | ||||
\(775\) | 16.0000i | 0.574737i | ||||||||
\(776\) | −3.00000 | + | 5.19615i | −0.107694 | + | 0.186531i | ||||
\(777\) | −1.00000 | − | 1.73205i | −0.0358748 | − | 0.0621370i | ||||
\(778\) | −16.4545 | + | 9.50000i | −0.589922 | + | 0.340592i | ||||
\(779\) | 54.0000 | 1.93475 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 36.3731 | − | 21.0000i | 1.30070 | − | 0.750958i | ||||
\(783\) | −0.500000 | − | 0.866025i | −0.0178685 | − | 0.0309492i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 3.00000i | 0.107075i | ||||||||
\(786\) | −6.92820 | − | 4.00000i | −0.247121 | − | 0.142675i | ||||
\(787\) | 24.2487 | + | 14.0000i | 0.864373 | + | 0.499046i | 0.865474 | − | 0.500953i | \(-0.167017\pi\) |
−0.00110111 | + | 0.999999i | \(0.500350\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | −15.0000 | + | 25.9808i | −0.534014 | + | 0.924940i | ||||
\(790\) | 2.00000 | + | 3.46410i | 0.0711568 | + | 0.123247i | ||||
\(791\) | 25.9808 | − | 15.0000i | 0.923770 | − | 0.533339i | ||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −34.0000 | −1.20661 | ||||||||
\(795\) | −7.79423 | + | 4.50000i | −0.276433 | + | 0.159599i | ||||
\(796\) | 7.00000 | + | 12.1244i | 0.248108 | + | 0.429736i | ||||
\(797\) | −1.00000 | + | 1.73205i | −0.0354218 | + | 0.0613524i | −0.883193 | − | 0.469010i | \(-0.844611\pi\) |
0.847771 | + | 0.530362i | \(0.177944\pi\) | |||||||
\(798\) | 12.0000i | 0.424795i | ||||||||
\(799\) | 36.3731 | + | 21.0000i | 1.28679 | + | 0.742927i | ||||
\(800\) | −17.3205 | − | 10.0000i | −0.612372 | − | 0.353553i | ||||
\(801\) | 14.0000i | 0.494666i | ||||||||
\(802\) | −0.500000 | + | 0.866025i | −0.0176556 | + | 0.0305804i | ||||
\(803\) | −11.0000 | − | 19.0526i | −0.388182 | − | 0.672350i | ||||
\(804\) | 1.73205 | − | 1.00000i | 0.0610847 | − | 0.0352673i | ||||
\(805\) | −12.0000 | −0.422944 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | −7.79423 | + | 4.50000i | −0.274200 | + | 0.158309i | ||||
\(809\) | −16.5000 | − | 28.5788i | −0.580109 | − | 1.00478i | −0.995466 | − | 0.0951198i | \(-0.969677\pi\) |
0.415357 | − | 0.909659i | \(-0.363657\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | − | 28.0000i | − | 0.983213i | −0.870817 | − | 0.491606i | \(-0.836410\pi\) | ||
0.870817 | − | 0.491606i | \(-0.163590\pi\) | |||||||
\(812\) | −1.73205 | − | 1.00000i | −0.0607831 | − | 0.0350931i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.00000i | 0.0701000i | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | −3.50000 | − | 6.06218i | −0.122525 | − | 0.212219i | ||||
\(817\) | 31.1769 | − | 18.0000i | 1.09074 | − | 0.629740i | ||||
\(818\) | −7.00000 | −0.244749 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | 43.3013 | − | 25.0000i | 1.51122 | − | 0.872506i | 0.511311 | − | 0.859396i | \(-0.329160\pi\) |
0.999914 | − | 0.0131101i | \(-0.00417319\pi\) | |||||||
\(822\) | −1.50000 | − | 2.59808i | −0.0523185 | − | 0.0906183i | ||||
\(823\) | −12.0000 | + | 20.7846i | −0.418294 | + | 0.724506i | −0.995768 | − | 0.0919029i | \(-0.970705\pi\) |
0.577474 | + | 0.816409i | \(0.304038\pi\) | |||||||
\(824\) | − | 18.0000i | − | 0.627060i | ||||||
\(825\) | 6.92820 | + | 4.00000i | 0.241209 | + | 0.139262i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.0000i | − | 0.556375i | −0.960527 | − | 0.278187i | \(-0.910266\pi\) | ||
0.960527 | − | 0.278187i | \(-0.0897336\pi\) | |||||||
\(828\) | −3.00000 | + | 5.19615i | −0.104257 | + | 0.180579i | ||||
\(829\) | 8.50000 | + | 14.7224i | 0.295217 | + | 0.511331i | 0.975035 | − | 0.222049i | \(-0.0712747\pi\) |
−0.679818 | + | 0.733381i | \(0.737941\pi\) | |||||||
\(830\) | −12.1244 | + | 7.00000i | −0.420843 | + | 0.242974i | ||||
\(831\) | −31.0000 | −1.07538 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.0000 | 0.727607 | ||||||||
\(834\) | −10.3923 | + | 6.00000i | −0.359856 | + | 0.207763i | ||||
\(835\) | 8.00000 | + | 13.8564i | 0.276851 | + | 0.479521i | ||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | − | 4.00000i | − | 0.138260i | ||||||
\(838\) | −13.8564 | − | 8.00000i | −0.478662 | − | 0.276355i | ||||
\(839\) | 10.3923 | + | 6.00000i | 0.358782 | + | 0.207143i | 0.668546 | − | 0.743670i | \(-0.266917\pi\) |
−0.309764 | + | 0.950813i | \(0.600250\pi\) | |||||||
\(840\) | 6.00000i | 0.207020i | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | −9.50000 | − | 16.4545i | −0.327392 | − | 0.567059i | ||||
\(843\) | −16.4545 | + | 9.50000i | −0.566722 | + | 0.327197i | ||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | −12.1244 | + | 7.00000i | −0.416598 | + | 0.240523i | ||||
\(848\) | −4.50000 | − | 7.79423i | −0.154531 | − | 0.267655i | ||||
\(849\) | 9.00000 | − | 15.5885i | 0.308879 | − | 0.534994i | ||||
\(850\) | 28.0000i | 0.960392i | ||||||||
\(851\) | 5.19615 | + | 3.00000i | 0.178122 | + | 0.102839i | ||||
\(852\) | 5.19615 | + | 3.00000i | 0.178017 | + | 0.102778i | ||||
\(853\) | − | 21.0000i | − | 0.719026i | −0.933140 | − | 0.359513i | \(-0.882943\pi\) | ||
0.933140 | − | 0.359513i | \(-0.117057\pi\) | |||||||
\(854\) | −1.00000 | + | 1.73205i | −0.0342193 | + | 0.0592696i | ||||
\(855\) | 3.00000 | + | 5.19615i | 0.102598 | + | 0.177705i | ||||
\(856\) | −15.5885 | + | 9.00000i | −0.532803 | + | 0.307614i | ||||
\(857\) | 31.0000 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.0000 | 1.16007 | 0.580033 | − | 0.814593i | \(-0.303040\pi\) | ||||
0.580033 | + | 0.814593i | \(0.303040\pi\) | |||||||
\(860\) | 5.19615 | − | 3.00000i | 0.177187 | − | 0.102299i | ||||
\(861\) | 9.00000 | + | 15.5885i | 0.306719 | + | 0.531253i | ||||
\(862\) | −15.0000 | + | 25.9808i | −0.510902 | + | 0.884908i | ||||
\(863\) | 10.0000i | 0.340404i | 0.985409 | + | 0.170202i | \(0.0544420\pi\) | ||||
−0.985409 | + | 0.170202i | \(0.945558\pi\) | |||||||
\(864\) | 4.33013 | + | 2.50000i | 0.147314 | + | 0.0850517i | ||||
\(865\) | 5.19615 | + | 3.00000i | 0.176674 | + | 0.102003i | ||||
\(866\) | − | 19.0000i | − | 0.645646i | ||||||
\(867\) | 16.0000 | − | 27.7128i | 0.543388 | − | 0.941176i | ||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | −6.92820 | + | 4.00000i | −0.235023 | + | 0.135691i | ||||
\(870\) | 1.00000 | 0.0339032 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | 0.203186 | ||||||||
\(873\) | −1.73205 | + | 1.00000i | −0.0586210 | + | 0.0338449i | ||||
\(874\) | −18.0000 | − | 31.1769i | −0.608859 | − | 1.05457i | ||||
\(875\) | 9.00000 | − | 15.5885i | 0.304256 | − | 0.526986i | ||||
\(876\) | 11.0000i | 0.371656i | ||||||||
\(877\) | −14.7224 | − | 8.50000i | −0.497141 | − | 0.287025i | 0.230391 | − | 0.973098i | \(-0.425999\pi\) |
−0.727532 | + | 0.686074i | \(0.759333\pi\) | |||||||
\(878\) | 12.1244 | + | 7.00000i | 0.409177 | + | 0.236239i | ||||
\(879\) | − | 9.00000i | − | 0.303562i | ||||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | 18.5000 | + | 32.0429i | 0.623281 | + | 1.07955i | 0.988871 | + | 0.148778i | \(0.0475340\pi\) |
−0.365590 | + | 0.930776i | \(0.619133\pi\) | |||||||
\(882\) | 2.59808 | − | 1.50000i | 0.0874818 | − | 0.0505076i | ||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.46410 | + | 2.00000i | −0.116379 | + | 0.0671913i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 1.50000 | − | 2.59808i | 0.0503367 | − | 0.0871857i | ||||
\(889\) | 40.0000i | 1.34156i | ||||||||
\(890\) | −12.1244 | − | 7.00000i | −0.406409 | − | 0.234641i | ||||
\(891\) | −1.73205 | − | 1.00000i | −0.0580259 | − | 0.0335013i | ||||
\(892\) | 16.0000i | 0.535720i | ||||||||
\(893\) | 18.0000 | − | 31.1769i | 0.602347 | − | 1.04330i | ||||
\(894\) | −1.50000 | − | 2.59808i | −0.0501675 | − | 0.0868927i | ||||
\(895\) | −1.73205 | + | 1.00000i | −0.0578961 | + | 0.0334263i | ||||
\(896\) | 6.00000 | 0.200446 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.0000 | 1.13459 | ||||||||
\(899\) | −3.46410 | + | 2.00000i | −0.115534 | + | 0.0667037i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 31.5000 | − | 54.5596i | 1.04942 | − | 1.81764i | ||||
\(902\) | − | 18.0000i | − | 0.599334i | ||||||
\(903\) | 10.3923 | + | 6.00000i | 0.345834 | + | 0.199667i | ||||
\(904\) | 38.9711 | + | 22.5000i | 1.29616 | + | 0.748339i | ||||
\(905\) | − | 7.00000i | − | 0.232688i | ||||||
\(906\) | −1.00000 | + | 1.73205i | −0.0332228 | + | 0.0575435i | ||||
\(907\) | 6.00000 | + | 10.3923i | 0.199227 | + | 0.345071i | 0.948278 | − | 0.317441i | \(-0.102824\pi\) |
−0.749051 | + | 0.662512i | \(0.769490\pi\) | |||||||
\(908\) | −12.1244 | + | 7.00000i | −0.402361 | + | 0.232303i | ||||
\(909\) | −3.00000 | −0.0995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | −5.19615 | + | 3.00000i | −0.172062 | + | 0.0993399i | ||||
\(913\) | −14.0000 | − | 24.2487i | −0.463332 | − | 0.802515i | ||||
\(914\) | −6.50000 | + | 11.2583i | −0.215001 | + | 0.372392i | ||||
\(915\) | 1.00000i | 0.0330590i | ||||||||
\(916\) | −19.0526 | − | 11.0000i | −0.629514 | − | 0.363450i | ||||
\(917\) | −13.8564 | − | 8.00000i | −0.457579 | − | 0.264183i | ||||
\(918\) | − | 7.00000i | − | 0.231034i | ||||||
\(919\) | −12.0000 | + | 20.7846i | −0.395843 | + | 0.685621i | −0.993208 | − | 0.116348i | \(-0.962881\pi\) |
0.597365 | + | 0.801970i | \(0.296214\pi\) | |||||||
\(920\) | −9.00000 | − | 15.5885i | −0.296721 | − | 0.513936i | ||||
\(921\) | 12.1244 | − | 7.00000i | 0.399511 | − | 0.230658i | ||||
\(922\) | −19.0000 | −0.625732 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.00000 | −0.131590 | ||||||||
\(925\) | −3.46410 | + | 2.00000i | −0.113899 | + | 0.0657596i | ||||
\(926\) | 13.0000 | + | 22.5167i | 0.427207 | + | 0.739943i | ||||
\(927\) | 3.00000 | − | 5.19615i | 0.0985329 | − | 0.170664i | ||||
\(928\) | − | 5.00000i | − | 0.164133i | ||||||
\(929\) | 23.3827 | + | 13.5000i | 0.767161 | + | 0.442921i | 0.831861 | − | 0.554984i | \(-0.187276\pi\) |
−0.0646999 | + | 0.997905i | \(0.520609\pi\) | |||||||
\(930\) | 3.46410 | + | 2.00000i | 0.113592 | + | 0.0655826i | ||||
\(931\) | − | 18.0000i | − | 0.589926i | ||||||
\(932\) | 5.00000 | − | 8.66025i | 0.163780 | − | 0.283676i | ||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −5.19615 | + | 3.00000i | −0.170023 | + | 0.0981630i | ||||
\(935\) | 14.0000 | 0.457849 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.0000 | −1.60076 | −0.800380 | − | 0.599493i | \(-0.795369\pi\) | ||||
−0.800380 | + | 0.599493i | \(0.795369\pi\) | |||||||
\(938\) | −3.46410 | + | 2.00000i | −0.113107 | + | 0.0653023i | ||||
\(939\) | 3.00000 | + | 5.19615i | 0.0979013 | + | 0.169570i | ||||
\(940\) | 3.00000 | − | 5.19615i | 0.0978492 | − | 0.169480i | ||||
\(941\) | − | 38.0000i | − | 1.23876i | −0.785090 | − | 0.619382i | \(-0.787383\pi\) | ||
0.785090 | − | 0.619382i | \(-0.212617\pi\) | |||||||
\(942\) | −2.59808 | − | 1.50000i | −0.0846499 | − | 0.0488726i | ||||
\(943\) | −46.7654 | − | 27.0000i | −1.52289 | − | 0.879241i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | + | 1.73205i | −0.0325300 | + | 0.0563436i | ||||
\(946\) | −6.00000 | − | 10.3923i | −0.195077 | − | 0.337883i | ||||
\(947\) | 41.5692 | − | 24.0000i | 1.35082 | − | 0.779895i | 0.362454 | − | 0.932002i | \(-0.381939\pi\) |
0.988364 | + | 0.152106i | \(0.0486057\pi\) | |||||||
\(948\) | 4.00000 | 0.129914 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.0000 | 0.778663 | ||||||||
\(951\) | 21.6506 | − | 12.5000i | 0.702070 | − | 0.405340i | ||||
\(952\) | −21.0000 | − | 36.3731i | −0.680614 | − | 1.17886i | ||||
\(953\) | 3.00000 | − | 5.19615i | 0.0971795 | − | 0.168320i | −0.813337 | − | 0.581793i | \(-0.802351\pi\) |
0.910516 | + | 0.413473i | \(0.135685\pi\) | |||||||
\(954\) | − | 9.00000i | − | 0.291386i | ||||||
\(955\) | −3.46410 | − | 2.00000i | −0.112096 | − | 0.0647185i | ||||
\(956\) | −25.9808 | − | 15.0000i | −0.840278 | − | 0.485135i | ||||
\(957\) | 2.00000i | 0.0646508i | ||||||||
\(958\) | −12.0000 | + | 20.7846i | −0.387702 | + | 0.671520i | ||||
\(959\) | −3.00000 | − | 5.19615i | −0.0968751 | − | 0.167793i | ||||
\(960\) | −6.06218 | + | 3.50000i | −0.195656 | + | 0.112962i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −6.06218 | + | 3.50000i | −0.195250 | + | 0.112727i | ||||
\(965\) | −4.50000 | − | 7.79423i | −0.144860 | − | 0.250905i | ||||
\(966\) | 6.00000 | − | 10.3923i | 0.193047 | − | 0.334367i | ||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | −18.1865 | − | 10.5000i | −0.584537 | − | 0.337483i | ||||
\(969\) | −36.3731 | − | 21.0000i | −1.16847 | − | 0.674617i | ||||
\(970\) | − | 2.00000i | − | 0.0642161i | ||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −20.7846 | + | 12.0000i | −0.666324 | + | 0.384702i | ||||
\(974\) | −18.0000 | −0.576757 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 28.5788 | − | 16.5000i | 0.914318 | − | 0.527882i | 0.0325001 | − | 0.999472i | \(-0.489653\pi\) |
0.881818 | + | 0.471590i | \(0.156320\pi\) | |||||||
\(978\) | −2.00000 | − | 3.46410i | −0.0639529 | − | 0.110770i | ||||
\(979\) | 14.0000 | − | 24.2487i | 0.447442 | − | 0.774992i | ||||
\(980\) | − | 3.00000i | − | 0.0958315i | ||||||
\(981\) | 1.73205 | + | 1.00000i | 0.0553001 | + | 0.0319275i | ||||
\(982\) | 5.19615 | + | 3.00000i | 0.165816 | + | 0.0957338i | ||||
\(983\) | − | 4.00000i | − | 0.127580i | −0.997963 | − | 0.0637901i | \(-0.979681\pi\) | ||
0.997963 | − | 0.0637901i | \(-0.0203188\pi\) | |||||||
\(984\) | −13.5000 | + | 23.3827i | −0.430364 | + | 0.745413i | ||||
\(985\) | −3.00000 | − | 5.19615i | −0.0955879 | − | 0.165563i | ||||
\(986\) | −6.06218 | + | 3.50000i | −0.193059 | + | 0.111463i | ||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0000 | −1.14473 | ||||||||
\(990\) | 1.73205 | − | 1.00000i | 0.0550482 | − | 0.0317821i | ||||
\(991\) | 1.00000 | + | 1.73205i | 0.0317660 | + | 0.0550204i | 0.881471 | − | 0.472237i | \(-0.156554\pi\) |
−0.849705 | + | 0.527258i | \(0.823220\pi\) | |||||||
\(992\) | 10.0000 | − | 17.3205i | 0.317500 | − | 0.549927i | ||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | −10.3923 | − | 6.00000i | −0.329624 | − | 0.190308i | ||||
\(995\) | −12.1244 | − | 7.00000i | −0.384368 | − | 0.221915i | ||||
\(996\) | 14.0000i | 0.443607i | ||||||||
\(997\) | 17.5000 | − | 30.3109i | 0.554231 | − | 0.959955i | −0.443732 | − | 0.896159i | \(-0.646346\pi\) |
0.997963 | − | 0.0637961i | \(-0.0203207\pi\) | |||||||
\(998\) | 12.0000 | + | 20.7846i | 0.379853 | + | 0.657925i | ||||
\(999\) | 0.866025 | − | 0.500000i | 0.0273998 | − | 0.0158193i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))