Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(589,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.j (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: | \(14.0856109166\) |
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: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1177.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1177 |
Dual form | 1764.2.j.c.589.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 2.59808i | −0.416025 | − | 0.720577i | 0.579510 | − | 0.814965i | \(-0.303244\pi\) |
−0.995535 | + | 0.0943882i | \(0.969911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.46410i | − | 0.894427i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | − | 0.866025i | 0.0928477 | − | 0.160817i | −0.815861 | − | 0.578249i | \(-0.803736\pi\) |
0.908708 | + | 0.417432i | \(0.137070\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | + | 2.59808i | 0.269408 | + | 0.466628i | 0.968709 | − | 0.248199i | \(-0.0798387\pi\) |
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00000 | + | 3.46410i | −1.04447 | + | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0000 | 1.80839 | 0.904194 | − | 0.427121i | \(-0.140472\pi\) | ||||
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.19615i | − | 0.832050i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | + | 7.79423i | 0.702782 | + | 1.21725i | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50000 | + | 4.33013i | −0.381246 | + | 0.660338i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00000 | − | 5.19615i | 0.447214 | − | 0.774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | + | 2.59808i | −0.218797 | + | 0.378968i | −0.954441 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5000 | + | 6.06218i | 1.47029 | + | 0.848875i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50000 | + | 4.33013i | 0.993399 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50000 | + | 2.59808i | −0.192055 | + | 0.332650i | −0.945931 | − | 0.324367i | \(-0.894849\pi\) |
0.753876 | + | 0.657017i | \(0.228182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | + | 5.19615i | −0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.50000 | − | 11.2583i | −0.794101 | − | 1.37542i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) |
0.129307 | − | 0.991605i | \(-0.458725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.92820i | − | 0.834058i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | 0.819288 | 0.409644 | − | 0.912245i | \(-0.365653\pi\) | ||||
0.409644 | + | 0.912245i | \(0.365653\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.50000 | − | 0.866025i | 0.173205 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50000 | − | 7.79423i | 0.506290 | − | 0.876919i | −0.493684 | − | 0.869641i | \(-0.664350\pi\) |
0.999974 | − | 0.00727784i | \(-0.00231663\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.500000 | + | 0.866025i | −0.0548821 | + | 0.0950586i | −0.892161 | − | 0.451717i | \(-0.850812\pi\) |
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00000 | − | 12.1244i | −0.759257 | − | 1.31507i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50000 | − | 0.866025i | 0.160817 | − | 0.0928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19615i | 0.538816i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00000 | − | 8.66025i | −0.512989 | − | 0.888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50000 | − | 14.7224i | 0.863044 | − | 1.49484i | −0.00593185 | − | 0.999982i | \(-0.501888\pi\) |
0.868976 | − | 0.494854i | \(-0.164778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0000 | −1.20605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.5000 | + | 9.52628i | 1.56611 | + | 0.904194i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | + | 0.866025i | 0.0470360 | + | 0.0814688i | 0.888585 | − | 0.458712i | \(-0.151689\pi\) |
−0.841549 | + | 0.540181i | \(0.818356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | + | 6.92820i | −0.373002 | + | 0.646058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.50000 | − | 7.79423i | 0.416025 | − | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.5885i | 1.40556i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.50000 | + | 4.33013i | −0.660338 | + | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.00000 | − | 5.19615i | 0.774597 | − | 0.447214i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.00000 | + | 12.1244i | −0.598050 | + | 1.03585i | 0.395058 | + | 0.918656i | \(0.370724\pi\) |
−0.993109 | + | 0.117198i | \(0.962609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.50000 | + | 2.59808i | −0.378968 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.5000 | + | 18.1865i | 0.848875 | + | 1.47029i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | − | 5.19615i | 0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50000 | + | 11.2583i | 0.518756 | + | 0.898513i | 0.999762 | + | 0.0217953i | \(0.00693820\pi\) |
−0.481006 | + | 0.876717i | \(0.659728\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.50000 | + | 2.59808i | 0.356873 | + | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0000 | −1.48819 | −0.744097 | − | 0.668071i | \(-0.767120\pi\) | ||||
−0.744097 | + | 0.668071i | \(0.767120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.0000 | + | 6.92820i | 0.934199 | + | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.5000 | − | 19.9186i | −0.889897 | − | 1.54135i | −0.839996 | − | 0.542592i | \(-0.817443\pi\) |
−0.0499004 | − | 0.998754i | \(-0.515890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | − | 3.46410i | 0.153846 | − | 0.266469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.50000 | + | 12.9904i | 0.573539 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.500000 | − | 0.866025i | 0.0380143 | − | 0.0658427i | −0.846392 | − | 0.532560i | \(-0.821230\pi\) |
0.884407 | + | 0.466717i | \(0.154563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.1244i | 0.911322i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.0000 | −1.56961 | −0.784807 | − | 0.619740i | \(-0.787238\pi\) | ||||
−0.784807 | + | 0.619740i | \(0.787238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.50000 | + | 2.59808i | −0.332650 | + | 0.192055i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.0000 | − | 19.0526i | −0.808736 | − | 1.40077i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.0000 | + | 24.2487i | −1.02378 | + | 1.77324i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | + | 12.9904i | −0.542681 | + | 0.939951i | 0.456068 | + | 0.889945i | \(0.349257\pi\) |
−0.998749 | + | 0.0500060i | \(0.984076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.500000 | + | 0.866025i | 0.0359908 | + | 0.0623379i | 0.883460 | − | 0.468507i | \(-0.155208\pi\) |
−0.847469 | + | 0.530845i | \(0.821875\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.00000 | + | 5.19615i | −0.644503 | + | 0.372104i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.0000 | −1.85242 | −0.926212 | − | 0.377004i | \(-0.876954\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0000 | −0.921546 | −0.460773 | − | 0.887518i | \(-0.652428\pi\) | ||||
−0.460773 | + | 0.887518i | \(0.652428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 22.5167i | − | 1.58820i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | − | 15.5885i | 0.628587 | − | 1.08875i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | − | 10.3923i | 0.417029 | − | 0.722315i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | + | 17.3205i | −0.691714 | + | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | + | 11.2583i | 0.447478 | + | 0.775055i | 0.998221 | − | 0.0596196i | \(-0.0189888\pi\) |
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.0000 | − | 6.92820i | −0.822226 | − | 0.474713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | 0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5000 | + | 6.06218i | 0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.5000 | − | 18.1865i | −0.706306 | − | 1.22336i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.50000 | − | 6.06218i | 0.234377 | − | 0.405953i | −0.724714 | − | 0.689050i | \(-0.758028\pi\) |
0.959092 | + | 0.283096i | \(0.0913615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 12.1244i | 0.462573 | + | 0.801200i | 0.999088 | − | 0.0426906i | \(-0.0135930\pi\) |
−0.536515 | + | 0.843891i | \(0.680260\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.0000 | −1.89985 | −0.949927 | − | 0.312473i | \(-0.898843\pi\) | ||||
−0.949927 | + | 0.312473i | \(0.898843\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5000 | − | 7.79423i | 0.876919 | − | 0.506290i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5000 | + | 18.1865i | 0.679189 | + | 1.17639i | 0.975226 | + | 0.221213i | \(0.0710015\pi\) |
−0.296037 | + | 0.955176i | \(0.595665\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | − | 8.66025i | 0.322078 | − | 0.557856i | −0.658838 | − | 0.752285i | \(-0.728952\pi\) |
0.980917 | + | 0.194429i | \(0.0622852\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.50000 | − | 12.9904i | −0.477214 | − | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.50000 | + | 0.866025i | −0.0950586 | + | 0.0548821i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 24.2487i | − | 1.51851i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | − | 15.5885i | −0.561405 | − | 0.972381i | −0.997374 | − | 0.0724199i | \(-0.976928\pi\) |
0.435970 | − | 0.899961i | \(-0.356405\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.5000 | + | 12.9904i | 1.37698 | + | 0.794998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | −0.0609711 | −0.0304855 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304855 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.00000 | −0.182237 | −0.0911185 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911185 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.50000 | + | 7.79423i | −0.269408 | + | 0.466628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.50000 | − | 14.7224i | 0.507067 | − | 0.878267i | −0.492899 | − | 0.870087i | \(-0.664063\pi\) |
0.999967 | − | 0.00818015i | \(-0.00260385\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | − | 0.866025i | −0.0297219 | − | 0.0514799i | 0.850782 | − | 0.525519i | \(-0.176129\pi\) |
−0.880504 | + | 0.474039i | \(0.842796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 17.3205i | − | 1.02598i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.5000 | − | 14.7224i | 1.49484 | − | 0.863044i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5000 | − | 23.3827i | −0.788678 | − | 1.36603i | −0.926777 | − | 0.375613i | \(-0.877432\pi\) |
0.138098 | − | 0.990419i | \(-0.455901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | − | 12.1244i | 0.407556 | − | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0000 | − | 10.3923i | −1.04447 | − | 0.603023i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | + | 10.3923i | −0.346989 | + | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | + | 1.73205i | −0.172345 | + | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.00000 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 13.8564i | − | 0.788263i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5000 | + | 26.8468i | 0.878924 | + | 1.52234i | 0.852523 | + | 0.522690i | \(0.175072\pi\) |
0.0264017 | + | 0.999651i | \(0.491595\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | − | 14.7224i | 0.480448 | − | 0.832161i | −0.519300 | − | 0.854592i | \(-0.673807\pi\) |
0.999748 | + | 0.0224310i | \(0.00714060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | − | 7.79423i | 0.252745 | − | 0.437767i | −0.711535 | − | 0.702650i | \(-0.752000\pi\) |
0.964281 | + | 0.264883i | \(0.0853332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | + | 3.46410i | 0.111979 | + | 0.193952i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | − | 2.59808i | −0.251166 | − | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.0000 | 1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.00000 | −0.166410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5000 | + | 6.06218i | 0.580651 | + | 0.335239i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5000 | − | 21.6506i | 0.687062 | − | 1.19003i | −0.285722 | − | 0.958313i | \(-0.592233\pi\) |
0.972784 | − | 0.231714i | \(-0.0744333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.5000 | + | 28.5788i | 0.904194 | + | 1.56611i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.0000 | + | 22.5167i | −0.710266 | + | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.50000 | − | 2.59808i | −0.0817102 | − | 0.141526i | 0.822274 | − | 0.569091i | \(-0.192705\pi\) |
−0.903985 | + | 0.427565i | \(0.859372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.73205i | 0.0940721i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0000 | + | 6.92820i | −0.646058 | + | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.50000 | + | 12.9904i | 0.402621 | + | 0.697360i | 0.994041 | − | 0.109003i | \(-0.0347659\pi\) |
−0.591420 | + | 0.806363i | \(0.701433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50000 | − | 4.33013i | 0.133822 | − | 0.231786i | −0.791325 | − | 0.611396i | \(-0.790608\pi\) |
0.925147 | + | 0.379610i | \(0.123942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.5000 | − | 7.79423i | 0.720577 | − | 0.416025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | + | 5.19615i | −0.159674 | + | 0.276563i | −0.934751 | − | 0.355303i | \(-0.884378\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.0000 | −1.63612 | −0.818059 | − | 0.575135i | \(-0.804950\pi\) | ||||
−0.818059 | + | 0.575135i | \(0.804950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 8.66025i | − | 0.454545i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | − | 12.1244i | −0.366397 | − | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.5000 | + | 23.3827i | −0.702782 | + | 1.21725i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0000 | − | 10.3923i | −0.929516 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | −0.154508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.00000 | − | 13.8564i | −0.408781 | − | 0.708029i | 0.585973 | − | 0.810331i | \(-0.300713\pi\) |
−0.994753 | + | 0.102302i | \(0.967379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.0000 | −0.762493 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0000 | + | 22.5167i | −0.659126 | + | 1.14164i | 0.321716 | + | 0.946836i | \(0.395740\pi\) |
−0.980842 | + | 0.194804i | \(0.937593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0000 | − | 24.2487i | −0.708010 | − | 1.22631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.92820i | 0.349482i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.0000 | −0.905678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0000 | −1.05396 | −0.526980 | − | 0.849878i | \(-0.676676\pi\) | ||||
−0.526980 | + | 0.849878i | \(0.676676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | − | 25.9808i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199207 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50000 | − | 7.79423i | 0.224161 | − | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.0000 | + | 38.1051i | −1.09050 | + | 1.88880i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | − | 19.9186i | −0.568638 | − | 0.984911i | −0.996701 | − | 0.0811615i | \(-0.974137\pi\) |
0.428063 | − | 0.903749i | \(-0.359196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.0000 | + | 12.1244i | −1.03585 | + | 0.598050i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000 | 0.0981761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.66025i | 0.424094i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.50000 | − | 12.9904i | −0.366399 | − | 0.634622i | 0.622601 | − | 0.782540i | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.50000 | − | 7.79423i | 0.219317 | − | 0.379867i | −0.735283 | − | 0.677761i | \(-0.762951\pi\) |
0.954599 | + | 0.297893i | \(0.0962839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.00000 | −0.437595 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.50000 | − | 6.06218i | 0.169775 | − | 0.294059i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.0000 | + | 10.3923i | 0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.0000 | 1.87856 | 0.939282 | − | 0.343146i | \(-0.111493\pi\) | ||||
0.939282 | + | 0.343146i | \(0.111493\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | − | 1.73205i | −0.143839 | − | 0.0830455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.0000 | − | 17.3205i | −0.478365 | − | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5000 | − | 18.1865i | 0.501138 | − | 0.867996i | −0.498861 | − | 0.866682i | \(-0.666248\pi\) |
0.999999 | − | 0.00131415i | \(-0.000418308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | − | 25.1147i | 0.688916 | − | 1.19324i | −0.283273 | − | 0.959039i | \(-0.591420\pi\) |
0.972189 | − | 0.234198i | \(-0.0752464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | − | 25.9808i | −0.711068 | − | 1.23161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3923i | 0.491539i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.0000 | −1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | − | 6.92820i | 0.563809 | − | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5000 | + | 26.8468i | −0.725059 | + | 1.25584i | 0.233890 | + | 0.972263i | \(0.424854\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.3731i | 1.69775i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5000 | + | 19.9186i | −0.535608 | + | 0.927701i | 0.463525 | + | 0.886084i | \(0.346584\pi\) |
−0.999134 | + | 0.0416172i | \(0.986749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50000 | + | 4.33013i | 0.116185 | + | 0.201238i | 0.918253 | − | 0.395995i | \(-0.129600\pi\) |
−0.802068 | + | 0.597233i | \(0.796267\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.00000 | − | 5.19615i | 0.417365 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000 | 0.786666 | 0.393333 | − | 0.919396i | \(-0.371322\pi\) | ||||
0.393333 | + | 0.919396i | \(0.371322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.5167i | 1.03751i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0000 | − | 17.3205i | −0.459800 | − | 0.796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.50000 | + | 7.79423i | 0.206041 | + | 0.356873i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00000 | − | 6.92820i | 0.182765 | − | 0.316558i | −0.760056 | − | 0.649857i | \(-0.774829\pi\) |
0.942821 | + | 0.333300i | \(0.108162\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.5000 | − | 28.5788i | −0.752335 | − | 1.30308i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.0000 | −1.54386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | −0.0453143 | −0.0226572 | − | 0.999743i | \(-0.507213\pi\) | ||||
−0.0226572 | + | 0.999743i | \(0.507213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −28.5000 | − | 16.4545i | −1.28881 | − | 0.744097i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.50000 | − | 6.06218i | 0.157632 | − | 0.273027i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.0000 | + | 20.7846i | 0.539360 | + | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | − | 3.46410i | −0.0895323 | − | 0.155074i | 0.817781 | − | 0.575529i | \(-0.195204\pi\) |
−0.907314 | + | 0.420455i | \(0.861871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 39.8372i | − | 1.77979i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.00000 | − | 3.46410i | 0.266469 | − | 0.153846i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 25.9808i | 1.14708i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | + | 13.8564i | −0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.50000 | − | 0.866025i | 0.0658427 | − | 0.0380143i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0000 | 1.26808 | 0.634041 | − | 0.773300i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773300i | \(0.281395\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.5000 | + | 18.1865i | 0.457387 | + | 0.792218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5000 | + | 18.1865i | −0.455661 | + | 0.789228i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5000 | − | 23.3827i | 0.584750 | − | 1.01282i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.00000 | + | 5.19615i | 0.129701 | + | 0.224649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.5000 | − | 18.1865i | −1.35933 | − | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.0000 | −1.41878 | −0.709390 | − | 0.704816i | \(-0.751030\pi\) | ||||
−0.709390 | + | 0.704816i | \(0.751030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.00000 | − | 5.19615i | −0.386227 | − | 0.222988i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.00000 | − | 12.1244i | −0.299847 | − | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.5000 | + | 28.5788i | −0.705489 | + | 1.22194i | 0.261026 | + | 0.965332i | \(0.415939\pi\) |
−0.966515 | + | 0.256611i | \(0.917394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.00000 | −0.384111 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.50000 | − | 4.33013i | 0.106504 | − | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 38.1051i | − | 1.61747i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0000 | 0.466085 | 0.233042 | − | 0.972467i | \(-0.425132\pi\) | ||||
0.233042 | + | 0.972467i | \(0.425132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.0000 | 0.634432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.0000 | + | 24.2487i | −1.77324 | + | 1.02378i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.50000 | − | 11.2583i | −0.273942 | − | 0.474482i | 0.695925 | − | 0.718114i | \(-0.254994\pi\) |
−0.969868 | + | 0.243632i | \(0.921661\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | − | 1.73205i | 0.0420703 | − | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5000 | + | 23.3827i | −0.565949 | + | 0.980253i | 0.431011 | + | 0.902347i | \(0.358157\pi\) |
−0.996961 | + | 0.0779066i | \(0.975176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50000 | + | 2.59808i | 0.0627730 | + | 0.108726i | 0.895704 | − | 0.444651i | \(-0.146672\pi\) |
−0.832931 | + | 0.553377i | \(0.813339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.5000 | + | 12.9904i | −0.939951 | + | 0.542681i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00000 | 0.291414 | 0.145707 | − | 0.989328i | \(-0.453454\pi\) | ||||
0.145707 | + | 0.989328i | \(0.453454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.73205i | 0.0719816i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.0000 | −0.744208 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.5000 | + | 32.0429i | −0.763577 | + | 1.32255i | 0.177419 | + | 0.984135i | \(0.443225\pi\) |
−0.940996 | + | 0.338418i | \(0.890108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.50000 | + | 12.9904i | 0.309032 | + | 0.535259i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −39.0000 | − | 22.5167i | −1.60425 | − | 0.926212i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.0000 | 1.10876 | 0.554379 | − | 0.832265i | \(-0.312956\pi\) | ||||
0.554379 | + | 0.832265i | \(0.312956\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5000 | − | 11.2583i | −0.798082 | − | 0.460773i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50000 | + | 2.59808i | 0.0612883 | + | 0.106155i | 0.895042 | − | 0.445983i | \(-0.147146\pi\) |
−0.833753 | + | 0.552137i | \(0.813812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5000 | − | 33.7750i | 0.794101 | − | 1.37542i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0000 | + | 41.5692i | 0.974130 | + | 1.68724i | 0.682777 | + | 0.730627i | \(0.260772\pi\) |
0.291353 | + | 0.956616i | \(0.405895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | 0.364101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.00000 | −0.363507 | −0.181753 | − | 0.983344i | \(-0.558177\pi\) | ||||
−0.181753 | + | 0.983344i | \(0.558177\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.0000 | − | 15.5885i | 1.08875 | − | 0.628587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.5000 | − | 37.2391i | −0.865557 | − | 1.49919i | −0.866493 | − | 0.499190i | \(-0.833631\pi\) |
0.000935233 | − | 1.00000i | \(-0.499702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | − | 17.3205i | 0.401934 | − | 0.696170i | −0.592025 | − | 0.805919i | \(-0.701671\pi\) |
0.993959 | + | 0.109749i | \(0.0350048\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | − | 10.3923i | 0.722315 | − | 0.417029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.0000 | + | 17.3205i | −1.19808 | + | 0.691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 77.0000 | 3.07019 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.5167i | 0.894957i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | − | 20.7846i | −0.474713 | − | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50000 | + | 11.2583i | 0.256335 | + | 0.443985i | 0.965257 | − | 0.261301i | \(-0.0841516\pi\) |
−0.708922 | + | 0.705287i | \(0.750818\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | + | 8.66025i | 0.590624 | + | 0.340997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.00000 | 0.117942 | 0.0589711 | − | 0.998260i | \(-0.481218\pi\) | ||||
0.0589711 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.0000 | −1.09910 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | + | 15.5885i | 0.352197 | + | 0.610023i | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) |
−0.634437 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000 | − | 6.92820i | 0.156293 | − | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5000 | + | 18.1865i | 0.409644 | + | 0.709524i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5000 | + | 21.6506i | −0.486931 | + | 0.843389i | −0.999887 | − | 0.0150258i | \(-0.995217\pi\) |
0.512956 | + | 0.858415i | \(0.328550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.50000 | + | 14.7224i | 0.330612 | + | 0.572636i | 0.982632 | − | 0.185565i | \(-0.0594116\pi\) |
−0.652020 | + | 0.758202i | \(0.726078\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 36.3731i | − | 1.41261i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | −0.154881 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.5000 | − | 6.06218i | 0.405953 | − | 0.234377i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | − | 10.3923i | −0.231627 | − | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.5000 | − | 21.6506i | 0.481840 | − | 0.834571i | −0.517943 | − | 0.855415i | \(-0.673302\pi\) |
0.999783 | + | 0.0208444i | \(0.00663546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.5000 | + | 23.3827i | −0.518847 | + | 0.898670i | 0.480913 | + | 0.876768i | \(0.340305\pi\) |
−0.999760 | + | 0.0219013i | \(0.993028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | − | 10.3923i | 0.689761 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0000 | −0.803543 | −0.401771 | − | 0.915740i | \(-0.631605\pi\) | ||||
−0.401771 | + | 0.915740i | \(0.631605\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | 1.06983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.2487i | 0.925146i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.50000 | − | 7.79423i | −0.171436 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.50000 | + | 9.52628i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.00000 | − | 8.66025i | 0.189661 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5000 | + | 54.5596i | 1.19315 | + | 2.06659i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.5000 | − | 25.1147i | −1.64532 | − | 0.949927i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0000 | −0.830929 | −0.415464 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415464 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.0000 | 2.07436 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.00000 | + | 5.19615i | 0.338960 | + | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5000 | − | 21.6506i | 0.469447 | − | 0.813107i | −0.529943 | − | 0.848034i | \(-0.677787\pi\) |
0.999390 | + | 0.0349269i | \(0.0111198\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.0000 | 1.01258 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | − | 10.3923i | 0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 20.7846i | −0.448775 | − | 0.777300i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 36.3731i | 1.35838i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.0000 | −0.559406 | −0.279703 | − | 0.960087i | \(-0.590236\pi\) | ||||
−0.279703 | + | 0.960087i | \(0.590236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.0000 | − | 8.66025i | 0.557856 | − | 0.322078i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.500000 | − | 0.866025i | −0.0185695 | − | 0.0321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5000 | − | 40.7032i | 0.871567 | − | 1.50960i | 0.0111912 | − | 0.999937i | \(-0.496438\pi\) |
0.860376 | − | 0.509661i | \(-0.170229\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5000 | + | 30.3109i | −0.647261 | + | 1.12109i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.0000 | − | 25.9808i | −0.554038 | − | 0.959621i | −0.997978 | − | 0.0635649i | \(-0.979753\pi\) |
0.443940 | − | 0.896056i | \(-0.353580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.0000 | 1.91544 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0000 | −0.772497 | −0.386249 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386249 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 25.9808i | − | 0.954427i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50000 | + | 7.79423i | 0.165089 | + | 0.285943i | 0.936687 | − | 0.350168i | \(-0.113876\pi\) |
−0.771598 | + | 0.636111i | \(0.780542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | − | 10.3923i | 0.219823 | − | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | −0.109764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | + | 20.7846i | 0.437886 | + | 0.758441i | 0.997526 | − | 0.0702946i | \(-0.0223939\pi\) |
−0.559640 | + | 0.828736i | \(0.689061\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.0000 | + | 13.8564i | 0.871145 | + | 0.502956i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.00000 | + | 1.73205i | 0.0362500 | + | 0.0627868i | 0.883581 | − | 0.468278i | \(-0.155125\pi\) |
−0.847331 | + | 0.531065i | \(0.821792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.0000 | − | 36.3731i | 0.759257 | − | 1.31507i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.5000 | − | 18.1865i | 0.379133 | − | 0.656678i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | + | 4.33013i | 0.0901523 | + | 0.156148i | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 31.1769i | − | 1.12281i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.0000 | 0.827253 | 0.413626 | − | 0.910447i | \(-0.364262\pi\) | ||||
0.413626 | + | 0.910447i | \(0.364262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.00000 | 0.107763 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.5000 | + | 38.9711i | 0.806146 | + | 1.39629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50000 | + | 2.59808i | 0.160817 | + | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.0000 | − | 22.5167i | 0.463990 | − | 0.803654i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.5000 | − | 18.1865i | −0.374285 | − | 0.648280i | 0.615935 | − | 0.787797i | \(-0.288778\pi\) |
−0.990220 | + | 0.139517i | \(0.955445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | 0.319599 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 10.3923i | − | 0.368577i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.50000 | − | 12.9904i | −0.265664 | − | 0.460143i | 0.702074 | − | 0.712104i | \(-0.252258\pi\) |
−0.967737 | + | 0.251961i | \(0.918924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5000 | + | 18.1865i | −0.371463 | + | 0.643393i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.5000 | + | 38.9711i | 0.794998 | + | 1.37698i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0000 | + | 24.2487i | −0.494049 | + | 0.855718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.50000 | − | 0.866025i | −0.0528025 | − | 0.0304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.00000 | −0.0351581 | −0.0175791 | − | 0.999845i | \(-0.505596\pi\) | ||||
−0.0175791 | + | 0.999845i | \(0.505596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.50000 | − | 2.59808i | −0.157822 | − | 0.0911185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0000 | + | 32.9090i | 0.665541 | + | 1.15275i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.5000 | + | 21.6506i | −0.437320 | + | 0.757460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.5000 | − | 45.8993i | 0.924856 | − | 1.60190i | 0.133064 | − | 0.991107i | \(-0.457518\pi\) |
0.791792 | − | 0.610791i | \(-0.209148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5000 | + | 19.9186i | 0.400865 | + | 0.694318i | 0.993831 | − | 0.110910i | \(-0.0353764\pi\) |
−0.592966 | + | 0.805228i | \(0.702043\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.92820i | 0.241209i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000 | 0.659897 | 0.329949 | − | 0.943999i | \(-0.392969\pi\) | ||||
0.329949 | + | 0.943999i | \(0.392969\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.00000 | + | 1.73205i | −0.104069 | + | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.0000 | + | 39.8372i | −0.795948 | + | 1.37862i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5000 | + | 7.79423i | −0.466628 | + | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.5000 | − | 19.9186i | 0.397024 | − | 0.687666i | −0.596333 | − | 0.802737i | \(-0.703376\pi\) |
0.993357 | + | 0.115071i | \(0.0367096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.5000 | − | 14.7224i | 0.878267 | − | 0.507067i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.00000 | −0.275208 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.73205i | − | 0.0594438i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.0000 | − | 38.1051i | −0.754150 | − | 1.30623i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5000 | + | 30.3109i | −0.599189 | + | 1.03783i | 0.393753 | + | 0.919216i | \(0.371177\pi\) |
−0.992941 | + | 0.118609i | \(0.962157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.0000 | − | 25.9808i | 0.512989 | − | 0.888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.00000 | − | 15.5885i | 0.307434 | − | 0.532492i | −0.670366 | − | 0.742030i | \(-0.733863\pi\) |
0.977800 | + | 0.209539i | \(0.0671963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0000 | − | 38.1051i | −0.750630 | − | 1.30013i | −0.947518 | − | 0.319704i | \(-0.896417\pi\) |
0.196887 | − | 0.980426i | \(-0.436917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0000 | 1.39566 | 0.697828 | − | 0.716265i | \(-0.254150\pi\) | ||||
0.697828 | + | 0.716265i | \(0.254150\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | −0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.0000 | + | 27.7128i | 1.63017 | + | 0.941176i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000 | + | 31.1769i | 0.610608 | + | 1.05760i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.5000 | + | 33.7750i | −0.660732 | + | 1.14442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 51.0000 | 1.72609 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0000 | + | 32.9090i | 0.641584 | + | 1.11126i | 0.985079 | + | 0.172102i | \(0.0550559\pi\) |
−0.343495 | + | 0.939155i | \(0.611611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 46.7654i | − | 1.57736i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.0000 | − | 12.1244i | 0.705907 | − | 0.407556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0000 | − | 31.1769i | −0.603023 | − | 1.04447i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.50000 | + | 12.9904i | −0.250978 | + | 0.434707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.0000 | + | 36.3731i | 0.701953 | + | 1.21582i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0000 | + | 10.3923i | −0.601003 | + | 0.346989i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.00000 | 0.100056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0000 | 0.699611 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | + | 10.3923i | 0.199447 | + | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.0000 | + | 31.1769i | −0.597680 | + | 1.03521i | 0.395482 | + | 0.918474i | \(0.370577\pi\) |
−0.993163 | + | 0.116739i | \(0.962756\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.5000 | − | 33.7750i | 0.646064 | − | 1.11902i | −0.337991 | − | 0.941149i | \(-0.609747\pi\) |
0.984055 | − | 0.177866i | \(-0.0569194\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | − | 3.46410i | −0.0661903 | − | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.00000 | + | 5.19615i | 0.297531 | + | 0.171780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.0000 | −1.15454 | −0.577272 | − | 0.816552i | \(-0.695883\pi\) | ||||
−0.577272 | + | 0.816552i | \(0.695883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.0000 | − | 6.92820i | −0.395413 | − | 0.228292i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | + | 20.7846i | 0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.50000 | − | 9.52628i | 0.180839 | − | 0.313222i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.0000 | − | 20.7846i | 0.394132 | − | 0.682656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.50000 | + | 2.59808i | −0.0492134 | + | 0.0852401i | −0.889583 | − | 0.456774i | \(-0.849005\pi\) |
0.840369 | + | 0.542014i | \(0.182338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.6936i | 1.75785i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 56.0000 | 1.83140 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5000 | − | 14.7224i | 0.832161 | − | 0.480448i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.5000 | − | 51.0955i | −0.961673 | − | 1.66567i | −0.718301 | − | 0.695733i | \(-0.755080\pi\) |
−0.243372 | − | 0.969933i | \(-0.578253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | − | 31.1769i | 0.586161 | − | 1.01526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5000 | − | 21.6506i | 0.406195 | − | 0.703551i | −0.588264 | − | 0.808669i | \(-0.700189\pi\) |
0.994460 | + | 0.105118i | \(0.0335219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.5000 | − | 18.1865i | −0.340844 | − | 0.590360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.5000 | − | 7.79423i | 0.437767 | − | 0.252745i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.0000 | 0.970777 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.92820i | 0.223957i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.50000 | − | 7.79423i | −0.145010 | − | 0.251166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00000 | − | 1.73205i | 0.0321911 | − | 0.0557567i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.5000 | − | 40.7032i | −0.755709 | − | 1.30893i | −0.945021 | − | 0.327009i | \(-0.893959\pi\) |
0.189312 | − | 0.981917i | \(-0.439374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 52.5000 | + | 30.3109i | 1.68654 | + | 0.973726i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | −0.481373 | −0.240686 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.50000 | − | 2.59808i | −0.144115 | − | 0.0832050i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.0000 | + | 51.9615i | −0.958804 | + | 1.66070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5000 | + | 18.1865i | 0.335239 | + | 0.580651i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | − | 31.1769i | 0.574111 | − | 0.994389i | −0.422027 | − | 0.906583i | \(-0.638681\pi\) |
0.996138 | − | 0.0878058i | \(-0.0279855\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.0000 | + | 45.0333i | 0.828429 | + | 1.43488i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.0000 | 0.635963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.0000 | −1.17534 | −0.587672 | − | 0.809099i | \(-0.699955\pi\) | ||||
−0.587672 | + | 0.809099i | \(0.699955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.5000 | − | 21.6506i | 1.19003 | − | 0.687062i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0000 | + | 22.5167i | 0.412128 | + | 0.713826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57.1577i | 1.80839i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))