Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(38,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.38");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.ba (of order \(6\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 38.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.38 |
Dual form | 273.2.ba.b.194.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.866025 | − | 0.500000i | ||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.50000 | + | 4.33013i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −4.00000 | − | 3.46410i | −0.755929 | − | 0.654654i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | 10.5000 | − | 6.06218i | 1.72619 | − | 0.996616i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
0.904194 | − | 0.427121i | \(-0.140472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.50000 | − | 4.33013i | −0.720577 | − | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | −0.762493 | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | − | 6.92820i | − | 1.00000i | ||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.00000 | + | 5.19615i | −0.693375 | + | 0.720577i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.1244i | 1.60591i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | + | 3.46410i | −0.768221 | + | 0.443533i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.50000 | − | 2.59808i | 0.944911 | − | 0.327327i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5000 | − | 6.06218i | −1.28278 | − | 0.740613i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.50000 | + | 4.33013i | −0.866025 | + | 0.500000i | ||||
\(76\) | 14.0000 | 1.60591 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.50000 | − | 11.2583i | −0.731307 | − | 1.26666i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.225018 | − | 0.974355i | \(-0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −3.00000 | − | 8.66025i | −0.327327 | − | 0.944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | + | 8.66025i | −0.419314 | + | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.5000 | + | 6.06218i | −1.08880 | + | 0.628619i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0000 | 1.42148 | 0.710742 | − | 0.703452i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703452i | \(0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | + | 8.66025i | 0.500000 | + | 0.866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5000 | − | 9.52628i | 1.62579 | − | 0.938652i | 0.640464 | − | 0.767988i | \(-0.278742\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | −10.5000 | − | 6.06218i | −1.00572 | − | 0.580651i | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.0000 | 1.99323 | ||||||||
\(112\) | −10.0000 | + | 3.46410i | −0.944911 | + | 0.327327i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | − | 10.3923i | −0.277350 | − | 0.960769i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.00000 | + | 12.1244i | 0.628619 | + | 1.08880i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.0000 | 1.68598 | 0.842989 | − | 0.537931i | \(-0.180794\pi\) | ||||
0.842989 | + | 0.537931i | \(0.180794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.50000 | − | 4.33013i | −0.660338 | − | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5000 | − | 6.06218i | 1.51744 | − | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 22.5167i | − | 1.90984i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||
0.296866 | − | 0.954919i | \(-0.404058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 6.00000 | − | 10.3923i | 0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.50000 | − | 9.52628i | −0.618590 | − | 0.785714i | ||||
\(148\) | − | 24.2487i | − | 1.99323i | ||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.0000 | − | 12.1244i | −1.70896 | − | 0.986666i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
−0.773099 | − | 0.634285i | \(-0.781294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.0000 | + | 3.46410i | −0.960769 | + | 0.277350i | ||||
\(157\) | 18.0000 | + | 10.3923i | 1.43656 | + | 0.829396i | 0.997609 | − | 0.0691164i | \(-0.0220180\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0000 | − | 12.1244i | 1.64485 | − | 0.949653i | 0.665771 | − | 0.746156i | \(-0.268103\pi\) |
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.5000 | + | 18.1865i | −0.802955 | + | 1.39076i | ||||
\(172\) | −5.00000 | + | 8.66025i | −0.381246 | + | 0.660338i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 8.66025i | 0.755929 | + | 0.654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.9808i | 1.93113i | 0.260153 | + | 0.965567i | \(0.416227\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0000 | −0.887066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.5000 | + | 2.59808i | 0.981981 | + | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −12.0000 | − | 6.92820i | −0.866025 | − | 0.500000i | ||||
\(193\) | 10.5000 | + | 6.06218i | 0.755807 | + | 0.436365i | 0.827788 | − | 0.561041i | \(-0.189599\pi\) |
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.0000 | + | 8.66025i | −0.785714 | + | 0.618590i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.00000 | + | 1.73205i | 0.212664 | + | 0.122782i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5000 | − | 18.1865i | −0.740613 | − | 1.28278i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | + | 13.8564i | 0.277350 | + | 0.960769i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.0000 | + | 12.1244i | 0.950382 | + | 0.823055i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.5000 | + | 6.06218i | −0.709524 | + | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.0000 | −1.87502 | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | −1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 21.0000 | + | 12.1244i | 1.39076 | + | 0.802955i | ||||
\(229\) | −3.50000 | − | 6.06218i | −0.231287 | − | 0.400600i | 0.726900 | − | 0.686743i | \(-0.240960\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 22.5167i | − | 1.46261i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | − | 12.1244i | 0.450910 | − | 0.780998i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.998443 | + | 0.0557856i | \(0.0177663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.00000 | − | 24.2487i | −0.445399 | − | 1.54291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 3.00000 | − | 15.5885i | 0.188982 | − | 0.981981i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.5000 | − | 30.3109i | −0.652438 | − | 1.88343i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.0000 | + | 12.1244i | −1.28278 | + | 0.740613i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | + | 24.2487i | 0.850439 | + | 1.47300i | 0.880812 | + | 0.473466i | \(0.156997\pi\) |
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.5000 | + | 9.52628i | −0.817057 | + | 0.576557i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5000 | − | 26.8468i | 0.931305 | − | 1.61307i | 0.150210 | − | 0.988654i | \(-0.452005\pi\) |
0.781094 | − | 0.624413i | \(-0.214662\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.0000 | −1.25724 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.5000 | − | 16.4545i | −1.69415 | − | 0.978117i | −0.951101 | − | 0.308879i | \(-0.900046\pi\) |
−0.743048 | − | 0.669238i | \(-0.766621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.0000 | + | 12.1244i | 1.23104 | + | 0.710742i | ||||
\(292\) | 7.00000 | + | 12.1244i | 0.409644 | + | 0.709524i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.3205i | 1.00000i | ||||||||
\(301\) | −2.50000 | + | 12.9904i | −0.144098 | + | 0.748753i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.0000 | − | 24.2487i | 0.802955 | − | 1.39076i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −35.0000 | −1.99756 | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) | ||||
−0.998778 | + | 0.0494267i | \(0.984261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.0000 | 1.87730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50000 | − | 2.59808i | 0.254355 | − | 0.146852i | −0.367402 | − | 0.930062i | \(-0.619753\pi\) |
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.0000 | −1.46261 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 9.00000 | + | 15.5885i | 0.500000 | + | 0.866025i | ||||
\(325\) | 12.5000 | − | 12.9904i | 0.693375 | − | 0.720577i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.5000 | − | 18.1865i | −0.580651 | − | 1.00572i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5000 | − | 18.1865i | 1.73140 | − | 0.999622i | 0.851957 | − | 0.523612i | \(-0.175416\pi\) |
0.879440 | − | 0.476011i | \(-0.157918\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 31.5000 | + | 18.1865i | 1.72619 | + | 0.996616i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.0000 | − | 3.46410i | −0.981981 | − | 0.188982i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.50000 | − | 18.1865i | 0.240192 | − | 0.970725i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | 11.0000 | + | 15.5885i | 0.576557 | + | 0.817057i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5000 | − | 7.79423i | −0.704694 | − | 0.406855i | 0.104399 | − | 0.994535i | \(-0.466708\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 24.2487i | 1.25724i | ||||||||
\(373\) | −6.50000 | − | 11.2583i | −0.336557 | − | 0.582934i | 0.647225 | − | 0.762299i | \(-0.275929\pi\) |
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1244i | 0.622786i | 0.950281 | + | 0.311393i | \(0.100796\pi\) | ||||
−0.950281 | + | 0.311393i | \(0.899204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.5000 | + | 16.4545i | 1.46010 | + | 0.842989i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.50000 | − | 12.9904i | −0.381246 | − | 0.660338i | ||||
\(388\) | 14.0000 | − | 24.2487i | 0.710742 | − | 1.23104i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.5000 | − | 30.3109i | −0.878300 | − | 1.52126i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
−0.0250943 | − | 0.999685i | \(-0.507989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 31.5000 | + | 6.06218i | 1.57697 | + | 0.303488i | ||||
\(400\) | 20.0000 | 1.00000 | ||||||||
\(401\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5000 | − | 18.1865i | 0.871737 | − | 0.905936i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | − | 6.06218i | 0.173064 | − | 0.299755i | −0.766426 | − | 0.642333i | \(-0.777967\pi\) |
0.939490 | + | 0.342578i | \(0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 38.1051i | − | 1.87730i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.5000 | − | 33.7750i | 0.954919 | − | 1.65397i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.3731i | 1.77271i | 0.463002 | + | 0.886357i | \(0.346772\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | + | 17.3205i | 0.290360 | + | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | 22.5167i | 1.08208i | 0.840996 | + | 0.541041i | \(0.181970\pi\) | ||||
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.0000 | + | 12.1244i | −1.00572 | + | 0.580651i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.0000 | − | 15.5885i | 1.28864 | − | 0.743996i | 0.310228 | − | 0.950662i | \(-0.399595\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 21.0000 | − | 36.3731i | 0.996616 | − | 1.72619i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.00000 | + | 20.7846i | −0.188982 | + | 0.981981i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.0000 | − | 36.3731i | −0.986666 | − | 1.70896i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5000 | − | 6.06218i | 0.491169 | − | 0.283577i | −0.233890 | − | 0.972263i | \(-0.575146\pi\) |
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.3731i | − | 1.69040i | −0.534450 | − | 0.845200i | \(-0.679481\pi\) | ||
0.534450 | − | 0.845200i | \(-0.320519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(468\) | −21.0000 | − | 5.19615i | −0.970725 | − | 0.240192i | ||||
\(469\) | −21.0000 | + | 24.2487i | −0.969690 | + | 1.11970i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.0000 | + | 31.1769i | 0.829396 | + | 1.43656i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.0000 | −1.60591 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.0000 | + | 12.1244i | −1.91504 | + | 0.552823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5000 | + | 18.1865i | 1.42740 | + | 0.824110i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.0000 | 1.89931 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.0000 | 1.25724 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5000 | + | 6.06218i | −0.470045 | + | 0.271380i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.246214 | + | 0.969216i | \(0.420813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0000 | + | 19.0526i | 0.532939 | + | 0.846154i | ||||
\(508\) | 19.0000 | − | 32.9090i | 0.842989 | − | 1.46010i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.0000 | + | 12.1244i | 0.619324 | + | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −31.5000 | + | 18.1865i | −1.39076 | + | 0.802955i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.0000 | + | 8.66025i | −0.660338 | + | 0.381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.5000 | + | 14.7224i | −1.11504 | + | 0.643767i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) |
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.50000 | + | 21.6506i | 0.327327 | + | 0.944911i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.00000 | − | 36.3731i | 0.303488 | − | 1.57697i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.5000 | − | 18.1865i | 1.35429 | − | 0.781900i | 0.365444 | − | 0.930834i | \(-0.380917\pi\) |
0.988847 | + | 0.148933i | \(0.0475840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.5000 | + | 38.9711i | −0.965567 | + | 1.67241i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.0000 | −1.71028 | −0.855138 | − | 0.518400i | \(-0.826528\pi\) | ||||
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.0000 | − | 10.3923i | −0.768221 | − | 0.443533i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.5000 | + | 11.2583i | −1.38204 | + | 0.478753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −39.0000 | − | 22.5167i | −1.65397 | − | 0.954919i | ||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.5000 | + | 4.33013i | 0.740171 | + | 0.183145i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.5000 | + | 26.8468i | −0.648655 | + | 1.12350i | 0.334790 | + | 0.942293i | \(0.391335\pi\) |
−0.983444 | + | 0.181210i | \(0.941999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0000 | − | 20.7846i | −0.500000 | − | 0.866025i | ||||
\(577\) | −17.5000 | + | 30.3109i | −0.728535 | + | 1.26186i | 0.228968 | + | 0.973434i | \(0.426465\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.5000 | + | 18.1865i | 0.436365 | + | 0.755807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −24.0000 | + | 3.46410i | −0.989743 | + | 0.142857i | ||||
\(589\) | −49.0000 | −2.01901 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −42.0000 | − | 24.2487i | −1.72619 | − | 0.996616i | ||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.00000 | + | 5.19615i | 0.122782 | + | 0.212664i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.73205i | − | 0.0706518i | −0.999376 | − | 0.0353259i | \(-0.988753\pi\) | ||
0.999376 | − | 0.0353259i | \(-0.0112469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 36.3731i | − | 1.48123i | ||||||
\(604\) | −42.0000 | + | 24.2487i | −1.70896 | + | 0.986666i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.50000 | + | 2.59808i | −0.182649 | + | 0.105453i | −0.588537 | − | 0.808470i | \(-0.700296\pi\) |
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0000 | + | 24.2487i | 1.69636 | + | 0.979396i | 0.949156 | + | 0.314806i | \(0.101939\pi\) |
0.747208 | + | 0.664590i | \(0.231394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5000 | − | 42.4352i | 0.984738 | − | 1.70562i | 0.341644 | − | 0.939829i | \(-0.389016\pi\) |
0.643094 | − | 0.765787i | \(-0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | + | 24.2487i | −0.240192 | + | 0.970725i | ||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.0000 | − | 20.7846i | 1.43656 | − | 0.829396i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.2487i | − | 0.965326i | −0.875806 | − | 0.482663i | \(-0.839670\pi\) | ||
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.0000 | − | 13.8564i | −0.953914 | − | 0.550743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.5000 | + | 14.7224i | 0.812240 | + | 0.583324i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.00000 | 0.276053 | 0.138027 | − | 0.990429i | \(-0.455924\pi\) | ||||
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5000 | + | 30.3109i | 0.411527 | + | 1.18798i | ||||
\(652\) | − | 48.4974i | − | 1.89931i | ||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.0000 | −0.819288 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5000 | + | 42.4352i | −0.952940 | + | 1.65054i | −0.213925 | + | 0.976850i | \(0.568625\pi\) |
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −42.0000 | − | 24.2487i | −1.62381 | − | 0.937509i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.0000 | 1.42625 | 0.713123 | − | 0.701039i | \(-0.247280\pi\) | ||||
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.5000 | − | 12.9904i | −0.866025 | − | 0.500000i | ||||
\(676\) | 22.0000 | − | 13.8564i | 0.846154 | − | 0.532939i | ||||
\(677\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | − | 36.3731i | 0.268635 | − | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(684\) | 21.0000 | + | 36.3731i | 0.802955 | + | 1.39076i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12.1244i | − | 0.462573i | ||||||
\(688\) | 10.0000 | + | 17.3205i | 0.381246 | + | 0.660338i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.5000 | + | 42.4352i | 0.932024 | + | 1.61431i | 0.779857 | + | 0.625958i | \(0.215292\pi\) |
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.0000 | − | 8.66025i | 0.944911 | − | 0.327327i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 73.5000 | + | 42.4352i | 2.77211 | + | 1.60048i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.0000 | + | 24.2487i | −1.57734 | + | 0.910679i | −0.582115 | + | 0.813107i | \(0.697775\pi\) |
−0.995228 | + | 0.0975728i | \(0.968892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.5000 | − | 33.7750i | 0.731307 | − | 1.26666i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5000 | − | 47.6314i | −0.614492 | − | 1.77389i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.0000 | − | 12.1244i | 0.780998 | − | 0.450910i | ||||
\(724\) | 45.0000 | + | 25.9808i | 1.67241 | + | 0.965567i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.5167i | 0.835097i | 0.908655 | + | 0.417548i | \(0.137111\pi\) | ||||
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −12.0000 | + | 20.7846i | −0.443533 | + | 0.768221i | ||||
\(733\) | −3.50000 | − | 6.06218i | −0.129275 | − | 0.223912i | 0.794121 | − | 0.607760i | \(-0.207932\pi\) |
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5000 | − | 6.06218i | −0.386249 | − | 0.223001i | 0.294285 | − | 0.955718i | \(-0.404919\pi\) |
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.5000 | − | 42.4352i | 0.385727 | − | 1.55890i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.5000 | + | 35.5070i | 0.748056 | + | 1.29567i | 0.948753 | + | 0.316017i | \(0.102346\pi\) |
−0.200698 | + | 0.979653i | \(0.564321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.0000 | − | 20.7846i | 0.654654 | − | 0.755929i | ||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.0000 | + | 24.2487i | −0.760251 | + | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.0000 | + | 13.8564i | −0.866025 | + | 0.500000i | ||||
\(769\) | 49.0000 | 1.76699 | 0.883493 | − | 0.468445i | \(-0.155186\pi\) | ||||
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.0000 | − | 12.1244i | 0.755807 | − | 0.436365i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5000 | − | 30.3109i | −0.628619 | − | 1.08880i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5000 | − | 54.5596i | 0.376685 | − | 1.95731i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.00000 | + | 27.7128i | 0.142857 | + | 0.989743i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0000 | + | 48.4974i | −0.998092 | + | 1.72875i | −0.445577 | + | 0.895244i | \(0.647001\pi\) |
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | − | 6.92820i | 0.852265 | − | 0.246028i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.00000 | − | 3.46410i | 0.212664 | − | 0.122782i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −1.48123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −56.0000 | −1.96643 | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 48.4974i | 1.70088i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.5000 | − | 30.3109i | −0.612247 | − | 1.06044i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.5000 | + | 2.59808i | −0.995871 | + | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.0000 | − | 45.0333i | 0.906303 | − | 1.56976i | 0.0871445 | − | 0.996196i | \(-0.472226\pi\) |
0.819159 | − | 0.573567i | \(-0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.5000 | − | 28.5788i | −1.71921 | − | 0.992584i | −0.920383 | − | 0.391018i | \(-0.872123\pi\) |
−0.798823 | − | 0.601566i | \(-0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 46.5000 | − | 26.8468i | 1.61307 | − | 0.931305i | ||||
\(832\) | 28.0000 | + | 6.92820i | 0.970725 | + | 0.240192i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.5000 | − | 18.1865i | −1.08880 | − | 0.628619i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | + | 27.7128i | −0.550743 | + | 0.953914i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5000 | − | 9.52628i | 0.944911 | − | 0.327327i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.5000 | − | 49.3634i | −0.978117 | − | 1.69415i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0000 | 1.19838 | 0.599189 | − | 0.800608i | \(-0.295490\pi\) | ||||
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0000 | − | 8.66025i | 0.511793 | − | 0.295484i | −0.221777 | − | 0.975097i | \(-0.571186\pi\) |
0.733571 | + | 0.679613i | \(0.237852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.4449i | 1.00000i | ||||||||
\(868\) | 35.0000 | − | 12.1244i | 1.18798 | − | 0.411527i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5000 | + | 30.3109i | 1.06734 | + | 1.02705i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.0000 | + | 36.3731i | 0.710742 | + | 1.23104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 24.2487i | 0.819288i | ||||||||
\(877\) | 42.0000 | − | 24.2487i | 1.41824 | − | 0.818821i | 0.422095 | − | 0.906552i | \(-0.361295\pi\) |
0.996144 | + | 0.0877308i | \(0.0279615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.0000 | 1.58168 | 0.790838 | − | 0.612026i | \(-0.209645\pi\) | ||||
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.50000 | − | 49.3634i | 0.318620 | − | 1.65560i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.0000 | + | 48.4974i | −0.937509 | + | 1.62381i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −15.0000 | + | 25.9808i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.0000 | + | 17.3205i | −0.499169 | + | 0.576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.5000 | + | 51.0955i | −0.979531 | + | 1.69660i | −0.315442 | + | 0.948945i | \(0.602153\pi\) |
−0.664089 | + | 0.747653i | \(0.731180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 42.0000 | − | 24.2487i | 1.39076 | − | 0.802955i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | −0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.500000 | + | 0.866025i | 0.0164935 | + | 0.0285675i | 0.874154 | − | 0.485648i | \(-0.161416\pi\) |
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −52.5000 | − | 30.3109i | −1.72993 | − | 0.998778i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60.6218i | 1.99323i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 49.5000 | + | 28.5788i | 1.62579 | + | 0.938652i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | − | 48.4974i | −0.229416 | − | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 50.2295i | − | 1.64093i | −0.571700 | − | 0.820463i | \(-0.693716\pi\) | ||
0.571700 | − | 0.820463i | \(-0.306284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.00000 | 0.293704 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(948\) | −39.0000 | − | 22.5167i | −1.26666 | − | 0.731307i | ||||
\(949\) | 17.5000 | − | 18.1865i | 0.568074 | − | 0.590360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.0000 | − | 24.2487i | −0.450910 | − | 0.780998i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.1244i | − | 0.389893i | −0.980814 | − | 0.194946i | \(-0.937547\pi\) | ||
0.980814 | − | 0.194946i | \(-0.0624533\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 31.1769i | 1.00000i | ||||||||
\(973\) | −58.5000 | − | 11.2583i | −1.87542 | − | 0.360925i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.0000 | − | 8.66025i | 0.960769 | − | 0.277350i | ||||
\(976\) | 24.0000 | + | 13.8564i | 0.768221 | + | 0.443533i | ||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 36.3731i | − | 1.16130i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −49.0000 | − | 12.1244i | −1.55890 | − | 0.385727i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.50000 | − | 14.7224i | 0.270011 | − | 0.467673i | −0.698853 | − | 0.715265i | \(-0.746306\pi\) |
0.968864 | + | 0.247592i | \(0.0796392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 63.0000 | 1.99924 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.5000 | − | 19.9186i | −1.09263 | − | 0.630828i | −0.158352 | − | 0.987383i | \(-0.550618\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.5000 | + | 54.5596i | 0.996616 | + | 1.72619i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 273.2.ba.b.38.1 | yes | 2 | |
3.2 | odd | 2 | CM | 273.2.ba.b.38.1 | yes | 2 | |
7.5 | odd | 6 | 273.2.ba.a.194.1 | yes | 2 | ||
13.12 | even | 2 | 273.2.ba.a.38.1 | ✓ | 2 | ||
21.5 | even | 6 | 273.2.ba.a.194.1 | yes | 2 | ||
39.38 | odd | 2 | 273.2.ba.a.38.1 | ✓ | 2 | ||
91.12 | odd | 6 | inner | 273.2.ba.b.194.1 | yes | 2 | |
273.194 | even | 6 | inner | 273.2.ba.b.194.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.ba.a.38.1 | ✓ | 2 | 13.12 | even | 2 | ||
273.2.ba.a.38.1 | ✓ | 2 | 39.38 | odd | 2 | ||
273.2.ba.a.194.1 | yes | 2 | 7.5 | odd | 6 | ||
273.2.ba.a.194.1 | yes | 2 | 21.5 | even | 6 | ||
273.2.ba.b.38.1 | yes | 2 | 1.1 | even | 1 | trivial | |
273.2.ba.b.38.1 | yes | 2 | 3.2 | odd | 2 | CM | |
273.2.ba.b.194.1 | yes | 2 | 91.12 | odd | 6 | inner | |
273.2.ba.b.194.1 | yes | 2 | 273.194 | even | 6 | inner |