Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(49,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.q (of order \(3\), 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: | \(7.28235666434\) |
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 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.49 |
Dual form | 912.2.q.a.577.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | − | 4.33013i | −0.693375 | − | 1.20096i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.277350 | − | 0.960769i | \(-0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | − | 0.866025i | 0.109109 | − | 0.188982i | ||||
\(22\) | 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 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | + | 6.92820i | 0.742781 | + | 1.28654i | 0.951224 | + | 0.308500i | \(0.0998271\pi\) |
−0.208443 | + | 0.978035i | \(0.566840\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.00000 | 0.800641 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | − | 10.3923i | 0.937043 | − | 1.62301i | 0.166092 | − | 0.986110i | \(-0.446885\pi\) |
0.770950 | − | 0.636895i | \(-0.219782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | + | 3.46410i | 0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | − | 3.46410i | −0.274721 | − | 0.475831i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
−0.970065 | + | 0.242846i | \(0.921919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.500000 | + | 4.33013i | −0.0662266 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | − | 8.66025i | 0.650945 | − | 1.12747i | −0.331949 | − | 0.943297i | \(-0.607706\pi\) |
0.982894 | − | 0.184172i | \(-0.0589603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.50000 | + | 9.52628i | 0.671932 | + | 1.16382i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50000 | − | 9.52628i | 0.643726 | − | 1.11497i | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | −0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.00000 | −0.857690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | + | 4.33013i | 0.262071 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | + | 2.59808i | −0.155543 | + | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | − | 1.73205i | −0.100504 | − | 0.174078i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.00000 | − | 12.1244i | −0.696526 | − | 1.20642i | −0.969664 | − | 0.244443i | \(-0.921395\pi\) |
0.273138 | − | 0.961975i | \(-0.411939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0000 | −1.28093 | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||||
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.0000 | 1.74013 | 0.870063 | − | 0.492941i | \(-0.164078\pi\) | ||||
0.870063 | + | 0.492941i | \(0.164078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.50000 | + | 2.59808i | −0.142374 | + | 0.246598i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.50000 | + | 4.33013i | −0.231125 | + | 0.400320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | + | 3.46410i | −0.183340 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000 | + | 10.3923i | 0.541002 | + | 0.937043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | − | 6.92820i | −0.354943 | − | 0.614779i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.500000 | − | 0.866025i | −0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.00000 | + | 12.1244i | −0.611593 | + | 1.05931i | 0.379379 | + | 0.925241i | \(0.376138\pi\) |
−0.990972 | + | 0.134069i | \(0.957196\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 1.73205i | −0.346844 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | − | 15.5885i | −0.768922 | − | 1.33181i | −0.938148 | − | 0.346235i | \(-0.887460\pi\) |
0.169226 | − | 0.985577i | \(-0.445873\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.00000 | − | 8.66025i | −0.418121 | − | 0.724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | − | 5.19615i | 0.247436 | − | 0.428571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50000 | + | 2.59808i | −0.119713 | + | 0.207349i | −0.919654 | − | 0.392730i | \(-0.871531\pi\) |
0.799941 | + | 0.600079i | \(0.204864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | + | 3.46410i | 0.157622 | + | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.00000 | −0.234978 | −0.117489 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117489 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | − | 1.73205i | −0.0773823 | − | 0.134030i | 0.824737 | − | 0.565516i | \(-0.191323\pi\) |
−0.902120 | + | 0.431486i | \(0.857990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | + | 10.3923i | −0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50000 | − | 2.59808i | −0.267652 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 4.33013i | −0.188982 | − | 0.327327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00000 | + | 8.66025i | 0.375823 | + | 0.650945i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | + | 1.73205i | 0.0743294 | + | 0.128742i | 0.900794 | − | 0.434246i | \(-0.142985\pi\) |
−0.826465 | + | 0.562988i | \(0.809652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.0000 | −1.73658 | −0.868290 | − | 0.496058i | \(-0.834780\pi\) | ||||
−0.868290 | + | 0.496058i | \(0.834780\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | + | 16.4545i | −0.683825 | + | 1.18442i | 0.289980 | + | 0.957033i | \(0.406351\pi\) |
−0.973805 | + | 0.227387i | \(0.926982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.0000 | −1.85242 | −0.926212 | − | 0.377004i | \(-0.876954\pi\) | ||||
−0.926212 | + | 0.377004i | \(0.876954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | + | 18.1865i | 0.744325 | + | 1.28921i | 0.950509 | + | 0.310696i | \(0.100562\pi\) |
−0.206184 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.0000 | −0.775880 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.00000 | − | 6.92820i | −0.280745 | − | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | + | 3.46410i | −0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | − | 3.46410i | 0.553372 | − | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | + | 12.9904i | −0.516321 | + | 0.894295i | 0.483499 | + | 0.875345i | \(0.339366\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.00000 | + | 5.19615i | 0.205557 | + | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.50000 | + | 9.52628i | 0.371656 | + | 0.643726i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.0000 | −1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | − | 7.79423i | 0.301342 | − | 0.521940i | −0.675098 | − | 0.737728i | \(-0.735899\pi\) |
0.976440 | + | 0.215788i | \(0.0692320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.50000 | − | 4.33013i | 0.166667 | − | 0.288675i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0000 | 1.59294 | 0.796468 | − | 0.604681i | \(-0.206699\pi\) | ||||
0.796468 | + | 0.604681i | \(0.206699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.00000 | − | 1.73205i | 0.0657952 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.00000 | − | 5.19615i | 0.196537 | − | 0.340411i | −0.750867 | − | 0.660454i | \(-0.770364\pi\) |
0.947403 | + | 0.320043i | \(0.103697\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.500000 | + | 0.866025i | 0.0324785 | + | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.5000 | − | 12.9904i | −1.11350 | − | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | − | 1.73205i | −0.0631194 | − | 0.109326i | 0.832739 | − | 0.553666i | \(-0.186772\pi\) |
−0.895858 | + | 0.444340i | \(0.853438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | − | 6.92820i | −0.251478 | − | 0.435572i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.0000 | + | 17.3205i | 0.623783 | + | 1.08042i | 0.988775 | + | 0.149413i | \(0.0477384\pi\) |
−0.364992 | + | 0.931011i | \(0.618928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0000 | − | 22.5167i | 0.801614 | − | 1.38844i | −0.116939 | − | 0.993139i | \(-0.537308\pi\) |
0.918553 | − | 0.395298i | \(-0.129359\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00000 | + | 8.66025i | −0.304855 | + | 0.528025i | −0.977229 | − | 0.212187i | \(-0.931941\pi\) |
0.672374 | + | 0.740212i | \(0.265275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.00000 | −0.302614 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.00000 | + | 8.66025i | 0.301511 | + | 0.522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.50000 | − | 2.59808i | −0.0898027 | − | 0.155543i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.00000 | + | 6.92820i | 0.238620 | + | 0.413302i | 0.960319 | − | 0.278906i | \(-0.0899716\pi\) |
−0.721699 | + | 0.692207i | \(0.756638\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | + | 10.3923i | −0.354169 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.00000 | − | 1.73205i | −0.0586210 | − | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0000 | + | 17.3205i | −0.578315 | + | 1.00167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 0.866025i | 0.0288195 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.0000 | 0.804279 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.00000 | + | 10.3923i | −0.342438 | + | 0.593120i | −0.984885 | − | 0.173210i | \(-0.944586\pi\) |
0.642447 | + | 0.766330i | \(0.277919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.50000 | − | 11.2583i | 0.369772 | − | 0.640464i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0000 | − | 19.0526i | −0.621757 | − | 1.07691i | −0.989158 | − | 0.146852i | \(-0.953086\pi\) |
0.367402 | − | 0.930062i | \(-0.380247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00000 | + | 3.46410i | 0.112331 | + | 0.194563i | 0.916710 | − | 0.399554i | \(-0.130835\pi\) |
−0.804379 | + | 0.594117i | \(0.797502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | + | 13.8564i | 0.447914 | + | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | + | 15.5885i | −0.502331 | + | 0.870063i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | − | 17.3205i | 0.111283 | − | 0.963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5000 | − | 21.6506i | 0.693375 | − | 1.20096i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00000 | + | 1.73205i | 0.0553001 | + | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.00000 | + | 5.19615i | 0.165395 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0000 | 1.37412 | 0.687062 | − | 0.726599i | \(-0.258900\pi\) | ||||
0.687062 | + | 0.726599i | \(0.258900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.50000 | − | 2.59808i | −0.0821995 | − | 0.142374i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | + | 11.2583i | −0.354078 | + | 0.613280i | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.00000 | + | 1.73205i | −0.0543125 | + | 0.0940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.00000 | + | 13.8564i | −0.429463 | + | 0.743851i | −0.996826 | − | 0.0796169i | \(-0.974630\pi\) |
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0000 | −1.12410 | −0.562052 | − | 0.827102i | \(-0.689988\pi\) | ||||
−0.562052 | + | 0.827102i | \(0.689988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | − | 4.33013i | −0.133440 | − | 0.231125i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.00000 | 0.212899 | 0.106449 | − | 0.994318i | \(-0.466052\pi\) | ||||
0.106449 | + | 0.994318i | \(0.466052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.00000 | − | 3.46410i | −0.105851 | − | 0.183340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0000 | + | 17.3205i | −0.527780 | + | 0.914141i | 0.471696 | + | 0.881761i | \(0.343642\pi\) |
−0.999476 | + | 0.0323801i | \(0.989691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50000 | − | 6.06218i | 0.183702 | − | 0.318182i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.50000 | + | 6.06218i | 0.182699 | + | 0.316443i | 0.942799 | − | 0.333363i | \(-0.108183\pi\) |
−0.760100 | + | 0.649806i | \(0.774850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.0000 | −0.624695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | + | 3.46410i | 0.103835 | + | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.0000 | − | 34.6410i | 1.03005 | − | 1.78410i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | 0.409852 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.00000 | − | 12.1244i | 0.357683 | − | 0.619526i | −0.629890 | − | 0.776684i | \(-0.716900\pi\) |
0.987573 | + | 0.157159i | \(0.0502334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.00000 | 0.0508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.00000 | − | 12.1244i | −0.353103 | − | 0.611593i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.50000 | + | 6.06218i | −0.175660 | + | 0.304252i | −0.940389 | − | 0.340099i | \(-0.889539\pi\) |
0.764730 | + | 0.644351i | \(0.222873\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.500000 | − | 4.33013i | 0.0250313 | − | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.00000 | − | 5.19615i | 0.149813 | − | 0.259483i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.931158 | + | 0.364615i | \(0.118800\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.50000 | − | 12.9904i | −0.373602 | − | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | + | 12.1244i | 0.346128 | + | 0.599511i | 0.985558 | − | 0.169338i | \(-0.0541630\pi\) |
−0.639430 | + | 0.768849i | \(0.720830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.00000 | + | 8.66025i | −0.246034 | + | 0.426143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | −0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.0000 | 0.683945 | 0.341972 | − | 0.939710i | \(-0.388905\pi\) | ||||
0.341972 | + | 0.939710i | \(0.388905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.0000 | 0.970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50000 | − | 11.2583i | −0.314557 | − | 0.544829i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.0000 | 0.482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.00000 | − | 8.66025i | −0.240842 | − | 0.417150i | 0.720113 | − | 0.693857i | \(-0.244090\pi\) |
−0.960954 | + | 0.276707i | \(0.910757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.50000 | + | 7.79423i | 0.216256 | + | 0.374567i | 0.953660 | − | 0.300885i | \(-0.0972820\pi\) |
−0.737404 | + | 0.675452i | \(0.763949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.0000 | − | 10.3923i | −0.669711 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5000 | − | 30.3109i | 0.835229 | − | 1.44666i | −0.0586141 | − | 0.998281i | \(-0.518668\pi\) |
0.893843 | − | 0.448379i | \(-0.147999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.0000 | − | 27.7128i | −0.760183 | − | 1.31668i | −0.942756 | − | 0.333483i | \(-0.891776\pi\) |
0.182573 | − | 0.983192i | \(-0.441557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.00000 | + | 5.19615i | 0.141895 | + | 0.245770i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.00000 | − | 10.3923i | 0.281905 | − | 0.488273i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | − | 3.46410i | 0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0000 | + | 25.9808i | −0.698620 | + | 1.21004i | 0.270326 | + | 0.962769i | \(0.412869\pi\) |
−0.968945 | + | 0.247276i | \(0.920465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.0000 | −1.06890 | −0.534450 | − | 0.845200i | \(-0.679481\pi\) | ||||
−0.534450 | + | 0.845200i | \(0.679481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.50000 | − | 9.52628i | −0.253966 | − | 0.439883i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.50000 | − | 2.59808i | −0.0691164 | − | 0.119713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.5000 | + | 12.9904i | 0.802955 | + | 0.596040i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | + | 3.46410i | −0.0915737 | + | 0.158610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.00000 | + | 12.1244i | 0.319838 | + | 0.553976i | 0.980454 | − | 0.196748i | \(-0.0630381\pi\) |
−0.660616 | + | 0.750724i | \(0.729705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | − | 12.9904i | −0.341971 | − | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.00000 | −0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.50000 | − | 2.59808i | 0.0678323 | − | 0.117489i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | − | 5.19615i | 0.135388 | − | 0.234499i | −0.790358 | − | 0.612646i | \(-0.790105\pi\) |
0.925746 | + | 0.378147i | \(0.123439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0000 | 1.44121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00000 | 0.0893534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000 | + | 34.6410i | 0.891756 | + | 1.54457i | 0.837769 | + | 0.546025i | \(0.183860\pi\) |
0.0539870 | + | 0.998542i | \(0.482807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.50000 | + | 9.52628i | −0.243306 | + | 0.421418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | − | 1.73205i | 0.176604 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | + | 25.1147i | 0.634041 | + | 1.09819i | 0.986718 | + | 0.162446i | \(0.0519382\pi\) |
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.00000 | 0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −60.0000 | −2.59889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | − | 10.3923i | 0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0000 | −0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5000 | + | 33.7750i | 0.838370 | + | 1.45210i | 0.891256 | + | 0.453500i | \(0.149825\pi\) |
−0.0528859 | + | 0.998601i | \(0.516842\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5000 | − | 25.1147i | −0.619975 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.50000 | − | 11.2583i | 0.277413 | − | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.0000 | + | 20.7846i | 1.19284 | + | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 0.866025i | −0.0212622 | + | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.0000 | + | 32.9090i | 0.805056 | + | 1.39440i | 0.916253 | + | 0.400599i | \(0.131198\pi\) |
−0.111198 | + | 0.993798i | \(0.535469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | + | 6.92820i | 0.168880 | + | 0.292509i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.500000 | − | 0.866025i | 0.0209980 | − | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | − | 20.7846i | 0.501307 | − | 0.868290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.0000 | − | 17.3205i | 0.417029 | − | 0.722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.50000 | − | 16.4545i | −0.394807 | − | 0.683825i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00000 | − | 6.92820i | −0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.0000 | + | 22.5167i | −0.536567 | + | 0.929362i | 0.462518 | + | 0.886610i | \(0.346946\pi\) |
−0.999086 | + | 0.0427523i | \(0.986387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | − | 5.19615i | 0.494451 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0000 | − | 22.5167i | 0.534749 | − | 0.926212i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0000 | −0.859473 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.00000 | + | 15.5885i | 0.367730 | + | 0.636927i | 0.989210 | − | 0.146503i | \(-0.0468017\pi\) |
−0.621480 | + | 0.783430i | \(0.713468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0000 | −0.856608 | −0.428304 | − | 0.903635i | \(-0.640889\pi\) | ||||
−0.428304 | + | 0.903635i | \(0.640889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.50000 | − | 9.52628i | 0.223977 | − | 0.387940i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.0000 | 1.74532 | 0.872658 | − | 0.488332i | \(-0.162394\pi\) | ||||
0.872658 | + | 0.488332i | \(0.162394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00000 | 0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | + | 25.9808i | −0.606835 | + | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | − | 25.9808i | 0.605844 | − | 1.04935i | −0.386073 | − | 0.922468i | \(-0.626169\pi\) |
0.991917 | − | 0.126885i | \(-0.0404979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00000 | − | 5.19615i | −0.120775 | − | 0.209189i | 0.799298 | − | 0.600935i | \(-0.205205\pi\) |
−0.920074 | + | 0.391745i | \(0.871871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.0000 | −1.00483 | −0.502417 | − | 0.864625i | \(-0.667556\pi\) | ||||
−0.502417 | + | 0.864625i | \(0.667556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.00000 | − | 5.19615i | −0.120192 | − | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.00000 | + | 8.66025i | −0.0399362 | + | 0.345857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | − | 10.3923i | 0.239236 | − | 0.414368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.50000 | − | 12.9904i | −0.298570 | − | 0.517139i | 0.677239 | − | 0.735763i | \(-0.263176\pi\) |
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.50000 | − | 12.9904i | −0.298098 | − | 0.516321i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 25.9808i | 0.594322 | + | 1.02940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.00000 | −0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.0000 | − | 25.9808i | 0.592464 | − | 1.02618i | −0.401435 | − | 0.915888i | \(-0.631488\pi\) |
0.993899 | − | 0.110291i | \(-0.0351782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.50000 | + | 16.4545i | −0.374643 | + | 0.648901i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) |
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | − | 17.3205i | 0.392534 | − | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.50000 | − | 2.59808i | 0.0587896 | − | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.0000 | −0.429151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0000 | + | 29.4449i | 0.662226 | + | 1.14701i | 0.980029 | + | 0.198852i | \(0.0637214\pi\) |
−0.317803 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0000 | − | 36.3731i | −0.816805 | − | 1.41475i | −0.908024 | − | 0.418917i | \(-0.862410\pi\) |
0.0912190 | − | 0.995831i | \(-0.470924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.0000 | − | 17.3205i | 0.388368 | − | 0.672673i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | − | 27.7128i | 0.619522 | − | 1.07304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.50000 | + | 7.79423i | 0.173980 | + | 0.301342i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.0000 | + | 22.5167i | 0.501859 | + | 0.869246i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.0000 | −1.27206 | −0.636028 | − | 0.771666i | \(-0.719424\pi\) | ||||
−0.636028 | + | 0.771666i | \(0.719424\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.0000 | 1.30673 | 0.653363 | − | 0.757045i | \(-0.273358\pi\) | ||||
0.653363 | + | 0.757045i | \(0.273358\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00000 | − | 1.73205i | 0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | + | 20.7846i | −0.459841 | + | 0.796468i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.50000 | + | 11.2583i | −0.247990 | + | 0.429532i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | + | 17.3205i | −0.380970 | + | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | + | 1.73205i | 0.0379869 | + | 0.0657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | − | 41.5692i | −0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | + | 17.3205i | −0.377695 | + | 0.654187i | −0.990726 | − | 0.135872i | \(-0.956616\pi\) |
0.613032 | + | 0.790058i | \(0.289950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 5.19615i | 0.452589 | − | 0.195977i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.00000 | + | 12.1244i | 0.263262 | + | 0.455983i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.5000 | + | 33.7750i | 0.732338 | + | 1.26845i | 0.955882 | + | 0.293752i | \(0.0949041\pi\) |
−0.223544 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.00000 | + | 10.3923i | −0.224074 | + | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0000 | 0.484145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.00000 | −0.260333 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0000 | + | 34.6410i | −0.742781 | + | 1.28654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5000 | + | 40.7032i | −0.871567 | + | 1.50960i | −0.0111912 | + | 0.999937i | \(0.503562\pi\) |
−0.860376 | + | 0.509661i | \(0.829771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.00000 | + | 3.46410i | 0.0739727 | + | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.0000 | −1.84679 | −0.923396 | − | 0.383849i | \(-0.874598\pi\) | ||||
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0000 | + | 19.0526i | 0.405190 | + | 0.701810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | − | 16.4545i | 0.349463 | − | 0.605288i | −0.636691 | − | 0.771119i | \(-0.719697\pi\) |
0.986154 | + | 0.165831i | \(0.0530307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0000 | − | 8.66025i | 0.734718 | − | 0.318142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.0000 | + | 43.3013i | −0.917161 | + | 1.58857i | −0.113455 | + | 0.993543i | \(0.536192\pi\) |
−0.803706 | + | 0.595026i | \(0.797142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | −0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5000 | + | 38.9711i | 0.821037 | + | 1.42208i | 0.904911 | + | 0.425601i | \(0.139937\pi\) |
−0.0838743 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.00000 | 0.0728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.50000 | + | 11.2583i | −0.236247 | + | 0.409191i | −0.959634 | − | 0.281251i | \(-0.909251\pi\) |
0.723388 | + | 0.690442i | \(0.242584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | + | 1.73205i | −0.0362024 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.0000 | −1.80540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5000 | + | 32.0429i | 0.667127 | + | 1.15550i | 0.978704 | + | 0.205277i | \(0.0658095\pi\) |
−0.311577 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0000 | −0.720282 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.00000 | − | 12.1244i | −0.251773 | − | 0.436083i | 0.712241 | − | 0.701935i | \(-0.247680\pi\) |
−0.964014 | + | 0.265852i | \(0.914347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.50000 | + | 12.9904i | 0.269408 | + | 0.466628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.50000 | − | 2.59808i | 0.0538122 | − | 0.0932055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | − | 51.9615i | 0.214972 | − | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.00000 | + | 6.92820i | 0.142948 | + | 0.247594i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.0000 | −0.891154 | −0.445577 | − | 0.895244i | \(-0.647001\pi\) | ||||
−0.445577 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.0000 | + | 22.5167i | 0.462812 | + | 0.801614i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.5000 | − | 56.2917i | 1.15411 | − | 1.99898i |