Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(68,273)]
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, 5, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.68");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.r (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 | 68.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.68 |
Dual form | 273.2.r.a.269.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.866025 | − | 0.500000i | ||||
\(13\) | −1.00000 | − | 3.46410i | −0.277350 | − | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.50000 | − | 4.33013i | 1.72062 | − | 0.993399i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | − | 4.33013i | −0.327327 | − | 0.944911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.50000 | + | 4.33013i | −1.34704 | + | 0.777714i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | −11.0000 | −1.80839 | −0.904194 | − | 0.427121i | \(-0.859528\pi\) | ||||
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.50000 | + | 6.06218i | −0.240192 | + | 0.970725i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | −6.00000 | − | 3.46410i | −0.866025 | − | 0.500000i | ||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | − | 6.92820i | −0.277350 | − | 0.960769i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.0000 | −1.98680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5000 | + | 7.79423i | −1.72850 | + | 0.997949i | −0.832240 | + | 0.554416i | \(0.812942\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50000 | + | 7.79423i | −0.188982 | + | 0.981981i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | + | 9.52628i | −0.671932 | + | 1.16382i | 0.305424 | + | 0.952217i | \(0.401202\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | + | 6.92820i | −1.40449 | + | 0.810885i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.66025i | − | 1.00000i | ||||||
\(76\) | 15.0000 | − | 8.66025i | 1.72062 | − | 0.993399i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −3.00000 | − | 8.66025i | −0.327327 | − | 0.944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 8.66025i | 0.419314 | − | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.0000 | 1.55543 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.50000 | − | 2.59808i | −0.456906 | − | 0.263795i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 3.00000 | + | 1.73205i | 0.295599 | + | 0.170664i | 0.640464 | − | 0.767988i | \(-0.278742\pi\) |
−0.344865 | + | 0.938652i | \(0.612075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | − | 10.3923i | − | 1.00000i | ||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.5000 | + | 9.52628i | 1.56611 | + | 0.904194i | ||||
\(112\) | 8.00000 | + | 6.92820i | 0.755929 | + | 0.654654i | ||||
\(113\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.50000 | − | 7.79423i | 0.693375 | − | 0.720577i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.50000 | − | 9.52628i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0000 | + | 8.66025i | −1.34704 | + | 0.777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | − | 17.3205i | −0.887357 | − | 1.53695i | −0.842989 | − | 0.537931i | \(-0.819206\pi\) |
−0.0443678 | − | 0.999015i | \(-0.514127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.0000 | + | 6.92820i | −1.05654 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.5000 | + | 4.33013i | 1.95100 | + | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.5000 | + | 11.2583i | 1.65397 | + | 0.954919i | 0.975417 | + | 0.220366i | \(0.0707252\pi\) |
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 4.50000 | − | 11.2583i | 0.371154 | − | 0.928571i | ||||
\(148\) | −22.0000 | −1.80839 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | − | 3.46410i | −0.162758 | − | 0.281905i | 0.773099 | − | 0.634285i | \(-0.218706\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.00000 | + | 12.1244i | −0.240192 | + | 0.970725i | ||||
\(157\) | −1.50000 | + | 0.866025i | −0.119713 | + | 0.0691164i | −0.558661 | − | 0.829396i | \(-0.688685\pi\) |
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.50000 | − | 14.7224i | −0.665771 | − | 1.15315i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.313304 | − | 0.949653i | \(-0.398564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | + | 6.92820i | −0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.5000 | + | 12.9904i | 1.72062 | + | 0.993399i | ||||
\(172\) | 8.00000 | − | 13.8564i | 0.609994 | − | 1.05654i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | + | 12.9904i | −0.188982 | + | 0.981981i | ||||
\(176\) | 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 | ||||||||
\(181\) | − | 19.0526i | − | 1.41617i | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||
0.706129 | − | 0.708083i | \(-0.250440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.0000 | 1.99590 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 10.3923i | 0.654654 | − | 0.755929i | ||||
\(190\) | 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 | ||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | + | 13.8564i | 0.142857 | + | 0.989743i | ||||
\(197\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25.9808i | − | 1.84173i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) | ||
0.389885 | − | 0.920864i | \(-0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.5000 | − | 9.52628i | 1.16382 | − | 0.671932i | ||||
\(202\) | 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 | ||||||||
\(211\) | 14.5000 | + | 25.1147i | 0.998221 | + | 1.72897i | 0.550743 | + | 0.834675i | \(0.314345\pi\) |
0.447478 | + | 0.894295i | \(0.352322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.5000 | − | 4.33013i | −1.52740 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.0000 | 1.62177 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.00000 | + | 5.19615i | −0.602685 | + | 0.347960i | −0.770097 | − | 0.637927i | \(-0.779792\pi\) |
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.50000 | + | 12.9904i | −0.500000 | + | 0.866025i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | −30.0000 | −1.98680 | ||||||||
\(229\) | −7.50000 | − | 4.33013i | −0.495614 | − | 0.286143i | 0.231287 | − | 0.972886i | \(-0.425707\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.5000 | + | 11.2583i | −1.26666 | + | 0.731307i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.7128i | 1.78514i | 0.450910 | + | 0.892570i | \(0.351100\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | −27.0000 | + | 15.5885i | −1.72850 | + | 0.997949i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.5000 | − | 21.6506i | −1.43164 | − | 1.37760i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | −3.00000 | + | 15.5885i | −0.188982 | + | 0.981981i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.0000 | − | 19.0526i | −1.36701 | − | 1.18387i | ||||
\(260\) | 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 | ||||||||
\(268\) | −11.0000 | + | 19.0526i | −0.671932 | + | 1.16382i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.9090i | 1.99908i | 0.0303728 | + | 0.999539i | \(0.490331\pi\) | ||||
−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 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.5000 | − | 12.9904i | −1.34704 | − | 0.777714i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.00000 | − | 5.19615i | −0.534994 | − | 0.308879i | 0.208053 | − | 0.978117i | \(-0.433287\pi\) |
−0.743048 | + | 0.669238i | \(0.766621\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.50000 | + | 7.79423i | 0.263795 | + | 0.456906i | ||||
\(292\) | −24.0000 | + | 13.8564i | −1.40449 | + | 0.810885i | ||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | − | 17.3205i | − | 1.00000i | ||||||
\(301\) | 20.0000 | − | 6.92820i | 1.15278 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 30.0000 | − | 17.3205i | 1.72062 | − | 0.993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.73205i | 0.0988534i | 0.998778 | + | 0.0494267i | \(0.0157394\pi\) | ||||
−0.998778 | + | 0.0494267i | \(0.984261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.00000 | − | 5.19615i | −0.170664 | − | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0000 | + | 13.8564i | 1.35656 | + | 0.783210i | 0.989158 | − | 0.146852i | \(-0.0469141\pi\) |
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | − | 22.5167i | 0.731307 | − | 1.26666i | ||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | − | 3.46410i | − | 0.191565i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0000 | + | 27.7128i | 0.879440 | + | 1.52323i | 0.851957 | + | 0.523612i | \(0.175416\pi\) |
0.0274825 | + | 0.999622i | \(0.491251\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.5000 | − | 28.5788i | −0.904194 | − | 1.56611i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | − | 17.3205i | −0.327327 | − | 0.944911i | ||||
\(337\) | 34.0000 | 1.85210 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.50000 | − | 2.59808i | 0.240879 | − | 0.139072i | −0.374701 | − | 0.927146i | \(-0.622255\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | + | 5.19615i | −0.960769 | + | 0.277350i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.0000 | − | 48.4974i | 1.47368 | − | 2.55250i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | 8.00000 | − | 17.3205i | 0.419314 | − | 0.907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.0000 | + | 19.0526i | 1.72259 | + | 0.994535i | 0.913493 | + | 0.406855i | \(0.133375\pi\) |
0.809093 | + | 0.587680i | \(0.199959\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 30.0000 | 1.55543 | ||||||||
\(373\) | 6.50000 | + | 11.2583i | 0.336557 | + | 0.582934i | 0.983783 | − | 0.179364i | \(-0.0574041\pi\) |
−0.647225 | + | 0.762299i | \(0.724071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5000 | − | 32.0429i | −0.950281 | − | 1.64594i | −0.744815 | − | 0.667271i | \(-0.767462\pi\) |
−0.205466 | − | 0.978664i | \(-0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.6410i | 1.77471i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.0000 | 1.21999 | ||||||||
\(388\) | −9.00000 | − | 5.19615i | −0.456906 | − | 0.263795i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | − | 10.3923i | 0.903394 | − | 0.521575i | 0.0250943 | − | 0.999685i | \(-0.492011\pi\) |
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.0000 | − | 25.9808i | −1.50188 | − | 1.30066i | ||||
\(400\) | 10.0000 | + | 17.3205i | 0.500000 | + | 0.866025i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.5000 | + | 21.6506i | 1.12080 | + | 1.07849i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.8564i | − | 0.685155i | −0.939490 | − | 0.342578i | \(-0.888700\pi\) | ||
0.939490 | − | 0.342578i | \(-0.111300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.00000 | + | 3.46410i | 0.295599 | + | 0.170664i | ||||
\(413\) | 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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.5000 | − | 7.79423i | −1.95993 | − | 0.377189i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | − | 20.7846i | − | 1.00000i | ||||||
\(433\) | 19.5000 | + | 11.2583i | 0.937110 | + | 0.541041i | 0.889053 | − | 0.457804i | \(-0.151364\pi\) |
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.66025i | 0.413331i | 0.978412 | + | 0.206666i | \(0.0662612\pi\) | ||||
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.5000 | + | 12.9904i | −0.785714 | + | 0.618590i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 33.0000 | + | 19.0526i | 1.56611 | + | 0.904194i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000 | + | 13.8564i | 0.755929 | + | 0.654654i | ||||
\(449\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820i | 0.325515i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.0000 | −1.91790 | −0.958950 | − | 0.283577i | \(-0.908479\pi\) | ||||
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 15.0000 | − | 15.5885i | 0.693375 | − | 0.720577i | ||||
\(469\) | −27.5000 | + | 9.52628i | −1.26983 | + | 0.439883i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.00000 | 0.138233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.5000 | + | 21.6506i | 1.72062 | + | 0.993399i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.0000 | + | 38.1051i | 0.501557 | + | 1.73744i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | − | 19.0526i | −0.500000 | − | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.0000 | 0.860972 | 0.430486 | − | 0.902597i | \(-0.358342\pi\) | ||||
0.430486 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.4449i | 1.33154i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.0000 | + | 17.3205i | −1.34704 | + | 0.777714i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.50000 | − | 9.52628i | 0.246214 | − | 0.426455i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.962472 | + | 0.271380i | \(0.0874801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.5000 | − | 0.866025i | 0.999260 | − | 0.0384615i | ||||
\(508\) | −20.0000 | − | 34.6410i | −0.887357 | − | 1.53695i | ||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.0000 | − | 6.92820i | −1.59255 | − | 0.306486i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.5000 | − | 38.9711i | −0.993399 | − | 1.72062i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −24.0000 | + | 13.8564i | −1.05654 | + | 0.609994i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.5885i | − | 0.681636i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) | ||
0.940129 | − | 0.340818i | \(-0.110704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.0000 | − | 17.3205i | 0.654654 | − | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 45.0000 | + | 8.66025i | 1.95100 | + | 0.375470i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0000 | − | 39.8372i | 0.988847 | − | 1.71273i | 0.365444 | − | 0.930834i | \(-0.380917\pi\) |
0.623404 | − | 0.781900i | \(-0.285749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.5000 | + | 28.5788i | −0.708083 | + | 1.22644i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | −0.0213785 | − | 0.999771i | \(-0.506805\pi\) | ||||
−0.0213785 | + | 0.999771i | \(0.506805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.5000 | − | 23.3827i | −1.72850 | − | 0.997949i | ||||
\(550\) | 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 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0000 | − | 6.92820i | −1.18427 | − | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.5000 | + | 7.79423i | −0.944911 | + | 0.327327i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.5000 | − | 40.7032i | −0.983444 | − | 1.70338i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
−0.334790 | − | 0.942293i | \(-0.608665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.500000 | + | 0.866025i | ||||
\(577\) | 40.5000 | − | 23.3827i | 1.68604 | − | 0.973434i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
0.957503 | − | 0.288425i | \(-0.0931316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.00000 | + | 1.73205i | −0.124676 | + | 0.0719816i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(588\) | 9.00000 | − | 22.5167i | 0.371154 | − | 0.928571i | ||||
\(589\) | −37.5000 | + | 64.9519i | −1.54516 | + | 2.67630i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −44.0000 | −1.80839 | ||||||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.5000 | + | 38.9711i | −0.920864 | + | 1.59498i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.5000 | + | 21.6506i | −1.52966 | + | 0.883148i | −0.530281 | + | 0.847822i | \(0.677914\pi\) |
−0.999376 | + | 0.0353259i | \(0.988753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.0000 | −1.34386 | ||||||||
\(604\) | −4.00000 | − | 6.92820i | −0.162758 | − | 0.281905i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.5000 | + | 19.9186i | −1.40031 | + | 0.808470i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) |
−0.405887 | + | 0.913923i | \(0.633038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5000 | + | 40.7032i | −0.949156 | + | 1.64399i | −0.201948 | + | 0.979396i | \(0.564727\pi\) |
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.0000 | + | 19.0526i | −1.32638 | + | 0.765787i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
−0.341644 | + | 0.939829i | \(0.610984\pi\) | |||||||
\(620\) | 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 | ||||||||
\(628\) | −3.00000 | + | 1.73205i | −0.119713 | + | 0.0691164i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5000 | − | 37.2391i | 0.855901 | − | 1.48246i | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) |
0.875806 | − | 0.482663i | \(-0.160330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 50.2295i | − | 1.99644i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.0000 | − | 10.3923i | 0.911293 | − | 0.411758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0000 | + | 15.5885i | 1.06478 | + | 0.614749i | 0.926750 | − | 0.375680i | \(-0.122591\pi\) |
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 | ||||||||
\(651\) | 30.0000 | + | 25.9808i | 1.17579 | + | 1.01827i | ||||
\(652\) | −17.0000 | − | 29.4449i | −0.665771 | − | 1.15315i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.0000 | − | 20.7846i | −1.40449 | − | 0.810885i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.5000 | − | 7.79423i | −0.525089 | − | 0.303160i | 0.213925 | − | 0.976850i | \(-0.431375\pi\) |
−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 | ||||||||
\(669\) | 18.0000 | 0.695920 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | + | 43.3013i | 0.963679 | + | 1.66914i | 0.713123 | + | 0.701039i | \(0.247280\pi\) |
0.250557 | + | 0.968102i | \(0.419386\pi\) | |||||||
\(674\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | − | 12.9904i | −0.172694 | − | 0.498525i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 45.0000 | + | 25.9808i | 1.72062 | + | 0.993399i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.50000 | + | 12.9904i | 0.286143 | + | 0.495614i | ||||
\(688\) | 16.0000 | − | 27.7128i | 0.609994 | − | 1.05654i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 51.9615i | − | 1.97671i | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||
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 | ||||||||
\(700\) | −5.00000 | + | 25.9808i | −0.188982 | + | 0.981981i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −82.5000 | + | 47.6314i | −3.11155 | + | 1.79645i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.5000 | − | 26.8468i | −0.582115 | − | 1.00825i | −0.995228 | − | 0.0975728i | \(-0.968892\pi\) |
0.413114 | − | 0.910679i | \(-0.364441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.0000 | 1.46261 | ||||||||
\(712\) | 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 | ||||||||
\(721\) | 3.00000 | + | 8.66025i | 0.111726 | + | 0.322525i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.0000 | − | 41.5692i | 0.892570 | − | 1.54598i | ||||
\(724\) | − | 38.1051i | − | 1.41617i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 22.5167i | − | 0.835097i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) | ||
0.908655 | − | 0.417548i | \(-0.137111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 54.0000 | 1.99590 | ||||||||
\(733\) | 46.5000 | + | 26.8468i | 1.71752 | + | 0.991609i | 0.923396 | + | 0.383849i | \(0.125402\pi\) |
0.794121 | + | 0.607760i | \(0.207932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.5000 | − | 32.0429i | 0.680534 | − | 1.17872i | −0.294285 | − | 0.955718i | \(-0.595081\pi\) |
0.974818 | − | 0.223001i | \(-0.0715853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.0000 | + | 51.9615i | 0.551039 | + | 1.90885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0000 | −0.401396 | −0.200698 | − | 0.979653i | \(-0.564321\pi\) | ||||
−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 | ||||
\(757\) | 13.0000 | + | 22.5167i | 0.472493 | + | 0.818382i | 0.999505 | − | 0.0314762i | \(-0.0100208\pi\) |
−0.527011 | + | 0.849858i | \(0.676688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | + | 5.19615i | −0.0362024 | + | 0.188113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.0000 | − | 13.8564i | −0.866025 | − | 0.500000i | ||||
\(769\) | 25.5000 | − | 14.7224i | 0.919554 | − | 0.530904i | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) |
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | − | 3.46410i | 0.0719816 | − | 0.124676i | ||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.5000 | − | 21.6506i | −1.34704 | − | 0.777714i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.5000 | + | 47.6314i | 0.591934 | + | 1.70877i | ||||
\(778\) | 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 | ||||||||
\(787\) | 46.7654i | 1.66701i | 0.552515 | + | 0.833503i | \(0.313668\pi\) | ||||
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.5000 | + | 38.9711i | 1.43820 | + | 1.38391i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 51.9615i | − | 1.84173i | ||||||
\(797\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 33.0000 | − | 19.0526i | 1.16382 | − | 0.671932i | ||||
\(805\) | 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 | ||||||||
\(811\) | − | 43.3013i | − | 1.52051i | −0.649623 | − | 0.760257i | \(-0.725073\pi\) | ||
0.649623 | − | 0.760257i | \(-0.274927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5000 | − | 49.3634i | 0.999539 | − | 1.73125i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 69.2820i | − | 2.42387i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.5000 | − | 2.59808i | 0.995871 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.0000 | −1.81261 | −0.906303 | − | 0.422628i | \(-0.861108\pi\) | ||||
−0.906303 | + | 0.422628i | \(0.861108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0000 | − | 17.3205i | −1.04194 | − | 0.601566i | −0.121560 | − | 0.992584i | \(-0.538790\pi\) |
−0.920383 | + | 0.391018i | \(0.872123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.50000 | − | 4.33013i | −0.260172 | − | 0.150210i | ||||
\(832\) | −8.00000 | − | 27.7128i | −0.277350 | − | 0.960769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.5000 | + | 38.9711i | 0.777714 | + | 1.34704i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.5000 | + | 25.1147i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29.0000 | + | 50.2295i | 0.998221 | + | 1.72897i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.50000 | − | 28.5788i | 0.188982 | − | 0.981981i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.00000 | + | 15.5885i | 0.308879 | + | 0.534994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46.7654i | − | 1.60122i | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||
0.599189 | − | 0.800608i | \(-0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.5000 | + | 19.9186i | 1.17712 | + | 0.679613i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.5000 | + | 14.7224i | 0.866025 | + | 0.500000i | ||||
\(868\) | −45.0000 | − | 8.66025i | −1.52740 | − | 0.293948i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.5000 | + | 9.52628i | 1.30452 | + | 0.322786i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 15.5885i | − | 0.527589i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 48.0000 | 1.62177 | ||||||||
\(877\) | 17.0000 | + | 29.4449i | 0.574049 | + | 0.994282i | 0.996144 | + | 0.0877308i | \(0.0279615\pi\) |
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | − | 51.9615i | 0.335389 | − | 1.74273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.0000 | + | 10.3923i | −0.602685 | + | 0.347960i | ||||
\(893\) | 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 | ||||||||
\(903\) | −36.0000 | − | 6.92820i | −1.19800 | − | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.50000 | + | 16.4545i | −0.315442 | + | 0.546362i | −0.979531 | − | 0.201291i | \(-0.935486\pi\) |
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −60.0000 | −1.98680 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.0000 | − | 8.66025i | −0.495614 | − | 0.286143i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.5000 | + | 45.8993i | 0.874154 | + | 1.51408i | 0.857661 | + | 0.514216i | \(0.171917\pi\) |
0.0164935 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50000 | − | 2.59808i | 0.0494267 | − | 0.0856095i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.5000 | − | 47.6314i | −0.904194 | − | 1.56611i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.3923i | 0.341328i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.5000 | + | 47.6314i | 1.22901 | + | 1.56106i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.19615i | 0.169751i | 0.996392 | + | 0.0848755i | \(0.0270492\pi\) | ||||
−0.996392 | + | 0.0848755i | \(0.972951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.0000 | − | 41.5692i | −0.783210 | − | 1.35656i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | −39.0000 | + | 22.5167i | −1.26666 | + | 0.731307i | ||||
\(949\) | 36.0000 | + | 34.6410i | 1.16861 | + | 1.12449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0000 | − | 38.1051i | 0.709677 | − | 1.22920i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 55.4256i | 1.78514i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0000 | 1.31847 | 0.659236 | − | 0.751936i | \(-0.270880\pi\) | ||||
0.659236 | + | 0.751936i | \(0.270880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | 27.0000 | − | 15.5885i | 0.866025 | − | 0.500000i | ||||
\(973\) | 19.5000 | + | 56.2917i | 0.625141 | + | 1.80463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.0000 | + | 8.66025i | −0.960769 | + | 0.277350i | ||||
\(976\) | −54.0000 | + | 31.1769i | −1.72850 | + | 0.997949i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.00000 | + | 5.19615i | −0.0957826 | + | 0.165900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −45.0000 | − | 43.3013i | −1.43164 | − | 1.37760i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.5000 | + | 52.8275i | −0.968864 | + | 1.67812i | −0.270011 | + | 0.962857i | \(0.587027\pi\) |
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 55.4256i | − | 1.75888i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 62.3538i | − | 1.97477i | −0.158352 | − | 0.987383i | \(-0.550618\pi\) | ||
0.158352 | − | 0.987383i | \(-0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 57.1577i | 1.80839i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 273.2.r.a.68.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 273.2.r.a.68.1 | ✓ | 2 | |
7.3 | odd | 6 | 273.2.bf.a.185.1 | yes | 2 | ||
13.9 | even | 3 | 273.2.bf.a.152.1 | yes | 2 | ||
21.17 | even | 6 | 273.2.bf.a.185.1 | yes | 2 | ||
39.35 | odd | 6 | 273.2.bf.a.152.1 | yes | 2 | ||
91.87 | odd | 6 | inner | 273.2.r.a.269.1 | yes | 2 | |
273.269 | even | 6 | inner | 273.2.r.a.269.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.r.a.68.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
273.2.r.a.68.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
273.2.r.a.269.1 | yes | 2 | 91.87 | odd | 6 | inner | |
273.2.r.a.269.1 | yes | 2 | 273.269 | even | 6 | inner | |
273.2.bf.a.152.1 | yes | 2 | 13.9 | even | 3 | ||
273.2.bf.a.152.1 | yes | 2 | 39.35 | odd | 6 | ||
273.2.bf.a.185.1 | yes | 2 | 7.3 | odd | 6 | ||
273.2.bf.a.185.1 | yes | 2 | 21.17 | even | 6 |