Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(44,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 4, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.44");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.cd (of order \(12\), degree \(4\), 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: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{12}]$ |
Embedding invariants
Embedding label | 86.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.86 |
Dual form | 273.2.cd.b.200.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0.866025 | + | 1.50000i | 0.500000 | + | 0.866025i | ||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(6\) | 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 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(12\) | 3.00000 | + | 1.73205i | 0.866025 | + | 0.500000i | ||||
\(13\) | −0.866025 | − | 3.50000i | −0.240192 | − | 0.970725i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23205 | + | 0.330127i | −0.282652 | + | 0.0757363i | −0.397360 | − | 0.917663i | \(-0.630073\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.46410 | + | 3.00000i | −0.755929 | + | 0.654654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.33013 | − | 2.50000i | 0.866025 | − | 0.500000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 3.46410 | + | 4.00000i | 0.654654 | + | 0.755929i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.86603 | + | 10.6962i | −0.514753 | + | 1.92109i | −0.155543 | + | 0.987829i | \(0.549713\pi\) |
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000i | 1.00000i | ||||||||
\(37\) | −2.40192 | − | 8.96410i | −0.394874 | − | 1.47369i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.427121 | − | 0.904194i | \(-0.359528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.50000 | − | 4.33013i | 0.720577 | − | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.1244i | − | 1.84895i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) | ||
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(48\) | 6.92820 | 1.00000 | ||||||||
\(49\) | −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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56218 | − | 1.56218i | −0.206916 | − | 0.206916i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410 | − | 6.00000i | 0.443533 | − | 0.768221i | −0.554416 | − | 0.832240i | \(-0.687058\pi\) |
0.997949 | + | 0.0640184i | \(0.0203916\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.50000 | − | 2.59808i | −0.944911 | − | 0.327327i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.205771 | − | 0.767949i | 0.0251390 | − | 0.0938199i | −0.952217 | − | 0.305424i | \(-0.901202\pi\) |
0.977356 | + | 0.211604i | \(0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.4282 | − | 4.13397i | −1.80573 | − | 0.483845i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.50000 | + | 4.33013i | 0.866025 | + | 0.500000i | ||||
\(76\) | −1.80385 | + | 1.80385i | −0.206916 | + | 0.206916i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.06218 | + | 10.5000i | −0.682048 | + | 1.18134i | 0.292306 | + | 0.956325i | \(0.405577\pi\) |
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | −3.00000 | + | 8.66025i | −0.327327 | + | 0.944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.66025 | − | 4.00000i | 0.907841 | − | 0.419314i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.5263 | + | 4.96410i | −1.92109 | + | 0.514753i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0717968 | + | 0.0717968i | 0.00728986 | + | 0.00728986i | 0.710742 | − | 0.703452i | \(-0.248359\pi\) |
−0.703452 | + | 0.710742i | \(0.748359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5000 | + | 9.52628i | 1.62579 | + | 0.938652i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.866025 | + | 0.500000i | ||||
\(109\) | −5.33013 | + | 19.8923i | −0.510534 | + | 1.90534i | −0.0957826 | + | 0.995402i | \(0.530535\pi\) |
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.3660 | − | 11.3660i | 1.07882 | − | 1.07882i | ||||
\(112\) | 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 | ||||||||
\(117\) | 10.3923 | + | 3.00000i | 0.960769 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.52628 | + | 5.50000i | 0.866025 | + | 0.500000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.73205 | + | 21.3923i | 0.514753 | + | 1.92109i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.0000i | − | 1.68598i | −0.537931 | − | 0.842989i | \(-0.680794\pi\) | ||
0.537931 | − | 0.842989i | \(-0.319206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.1865 | − | 10.5000i | 1.60123 | − | 0.924473i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.47372 | − | 3.03590i | −0.127788 | − | 0.263246i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.00000 | −0.593732 | −0.296866 | − | 0.954919i | \(-0.595942\pi\) | ||||
−0.296866 | + | 0.954919i | \(0.595942\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −9.52628 | − | 7.50000i | −0.785714 | − | 0.618590i | ||||
\(148\) | −13.1244 | − | 13.1244i | −1.07882 | − | 1.07882i | ||||
\(149\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2942 | + | 5.16987i | 1.57014 | + | 0.420718i | 0.935857 | − | 0.352381i | \(-0.114628\pi\) |
0.634285 | + | 0.773099i | \(0.281294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.46410 | − | 12.0000i | 0.277350 | − | 0.960769i | ||||
\(157\) | 7.00000 | + | 12.1244i | 0.558661 | + | 0.967629i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.90192 | + | 22.0263i | 0.462274 | + | 1.72523i | 0.665771 | + | 0.746156i | \(0.268103\pi\) |
−0.203497 | + | 0.979076i | \(0.565231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 6.06218i | −0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.990381 | − | 3.69615i | 0.0757363 | − | 0.282652i | ||||
\(172\) | −12.1244 | − | 21.0000i | −0.924473 | − | 1.60123i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.66025 | + | 10.0000i | 0.654654 | + | 0.755929i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | −2.59808 | − | 13.5000i | −0.188982 | − | 0.981981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.866025 | − | 0.500000i | ||||
\(193\) | −8.79423 | − | 2.35641i | −0.633022 | − | 0.169618i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
−0.561041 | + | 0.827788i | \(0.689599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.66025 | + | 11.0000i | −0.618590 | + | 0.785714i | ||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.2487 | + | 14.0000i | −1.71895 | + | 0.992434i | −0.798082 | + | 0.602549i | \(0.794152\pi\) |
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.33013 | − | 0.356406i | 0.0938199 | − | 0.0251390i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.8564 | − | 4.00000i | −0.960769 | − | 0.277350i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2487 | 1.66935 | 0.834675 | − | 0.550743i | \(-0.185655\pi\) | ||||
0.834675 | + | 0.550743i | \(0.185655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.2224 | − | 2.09808i | −1.98375 | − | 0.142427i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.16025 | − | 26.7224i | −0.483845 | − | 1.80573i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.80385 | + | 8.80385i | 0.589549 | + | 0.589549i | 0.937509 | − | 0.347960i | \(-0.113126\pi\) |
−0.347960 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000i | 1.00000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(228\) | −4.26795 | − | 1.14359i | −0.282652 | − | 0.0757363i | ||||
\(229\) | −4.10770 | − | 15.3301i | −0.271444 | − | 1.01304i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.686743 | − | 0.726900i | \(-0.259040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.0000 | −1.36410 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.36603 | + | 2.50962i | 0.603319 | + | 0.161659i | 0.547533 | − | 0.836784i | \(-0.315567\pi\) |
0.0557856 | + | 0.998443i | \(0.482234\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.79423 | − | 13.5000i | 0.500000 | − | 0.866025i | ||||
\(244\) | − | 13.8564i | − | 0.887066i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.22243 | + | 4.02628i | 0.141410 | + | 0.256186i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −15.5885 | + | 3.00000i | −0.981981 | + | 0.188982i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.0885 | − | 10.7224i | 1.37251 | − | 0.666259i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.411543 | − | 1.53590i | −0.0251390 | − | 0.0938199i | ||||
\(269\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.29423 | − | 30.9545i | −0.503839 | − | 1.88035i | −0.473466 | − | 0.880812i | \(-0.656997\pi\) |
−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 | ||||||||
\(277\) | −10.5000 | + | 6.06218i | −0.630884 | + | 0.364241i | −0.781094 | − | 0.624413i | \(-0.785338\pi\) |
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.4904 | − | 23.4904i | −1.40633 | − | 1.40633i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.06218 | − | 3.50000i | 0.360359 | − | 0.208053i | −0.308879 | − | 0.951101i | \(-0.599954\pi\) |
0.669238 | + | 0.743048i | \(0.266621\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −0.0455173 | + | 0.169873i | −0.00266827 | + | 0.00995813i | ||||
\(292\) | −30.8564 | + | 8.26795i | −1.80573 | + | 0.483845i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 17.3205 | 1.00000 | ||||||||
\(301\) | 31.5000 | − | 6.06218i | 1.81563 | − | 0.349418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.32051 | + | 4.92820i | −0.0757363 | + | 0.282652i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.6340 | − | 16.6340i | 0.949351 | − | 0.949351i | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) |
0.998778 | + | 0.0494267i | \(0.0157394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 33.0000i | 1.87730i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.59808 | + | 4.50000i | −0.146852 | + | 0.254355i | −0.930062 | − | 0.367402i | \(-0.880247\pi\) |
0.783210 | + | 0.621757i | \(0.213581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.2487i | 1.36410i | ||||||||
\(317\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −15.5885 | − | 9.00000i | −0.866025 | − | 0.500000i | ||||
\(325\) | −12.5000 | − | 12.9904i | −0.693375 | − | 0.720577i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −34.4545 | + | 9.23205i | −1.90534 | + | 0.510534i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1603 | − | 6.47372i | 1.32797 | − | 0.355828i | 0.476011 | − | 0.879440i | \(-0.342082\pi\) |
0.851957 | + | 0.523612i | \(0.175416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.8923 | + | 7.20577i | 1.47369 | + | 0.394874i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.46410 | + | 18.0000i | 0.188982 | + | 0.981981i | ||||
\(337\) | − | 5.00000i | − | 0.272367i | −0.990684 | − | 0.136184i | \(-0.956516\pi\) | ||
0.990684 | − | 0.136184i | \(-0.0434837\pi\) | |||||||
\(338\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.3205 | + | 24.3205i | −1.30185 | + | 1.30185i | −0.374701 | + | 0.927146i | \(0.622255\pi\) |
−0.927146 | + | 0.374701i | \(0.877745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.50000 | + | 18.1865i | 0.240192 | + | 0.970725i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0455 | + | 8.68653i | −0.791869 | + | 0.457186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | 11.0000 | − | 15.5885i | 0.576557 | − | 0.817057i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5000 | + | 30.3109i | 0.913493 | + | 1.58222i | 0.809093 | + | 0.587680i | \(0.199959\pi\) |
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −27.1244 | + | 27.1244i | −1.40633 | + | 1.40633i | ||||
\(373\) | −18.1865 | + | 31.5000i | −0.941663 | + | 1.63101i | −0.179364 | + | 0.983783i | \(0.557404\pi\) |
−0.762299 | + | 0.647225i | \(0.775929\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4378 | − | 12.4378i | −0.638888 | − | 0.638888i | 0.311393 | − | 0.950281i | \(-0.399204\pi\) |
−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 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.5000 | + | 18.1865i | 1.60123 | + | 0.924473i | ||||
\(388\) | 0.196152 | + | 0.0525589i | 0.00995813 | + | 0.00266827i | ||||
\(389\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.89230 | − | 36.9186i | −0.496481 | − | 1.85289i | −0.521575 | − | 0.853206i | \(-0.674655\pi\) |
0.0250943 | − | 0.999685i | \(-0.492011\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.27757 | − | 4.83975i | 0.164084 | − | 0.242290i | ||||
\(400\) | − | 20.0000i | − | 1.00000i | ||||||
\(401\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.9186 | + | 0.767949i | 1.98849 | + | 0.0382543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.57180 | − | 31.9904i | 0.423848 | − | 1.58182i | −0.342578 | − | 0.939490i | \(-0.611300\pi\) |
0.766426 | − | 0.642333i | \(-0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.1051 | 1.87730 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.06218 | − | 10.5000i | −0.296866 | − | 0.514187i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6865 | + | 27.6865i | 1.34936 | + | 1.34936i | 0.886357 | + | 0.463002i | \(0.153228\pi\) |
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.3205 | + | 6.00000i | 0.838198 | + | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.500000 | + | 0.866025i | ||||
\(433\) | − | 35.0000i | − | 1.68199i | −0.541041 | − | 0.840996i | \(-0.681970\pi\) | ||
0.541041 | − | 0.840996i | \(-0.318030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.6603 | + | 39.7846i | 0.510534 | + | 1.90534i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0000 | − | 15.5885i | −1.28864 | − | 0.743996i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | − | 20.7846i | 0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 8.32051 | − | 31.0526i | 0.394874 | − | 1.47369i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7846 | − | 4.00000i | 0.981981 | − | 0.188982i | ||||
\(449\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.95448 | + | 33.4186i | 0.420718 | + | 1.57014i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.2846 | + | 9.72243i | −1.69732 | + | 0.454796i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.68653 | + | 6.68653i | −0.310750 | + | 0.310750i | −0.845200 | − | 0.534450i | \(-0.820519\pi\) |
0.534450 | + | 0.845200i | \(0.320519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 21.0000 | − | 5.19615i | 0.970725 | − | 0.240192i | ||||
\(469\) | 2.09808 | + | 0.150635i | 0.0968802 | + | 0.00695568i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1244 | + | 21.0000i | −0.558661 | + | 0.967629i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.50962 | + | 4.50962i | −0.206916 | + | 0.206916i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.2942 | + | 16.1699i | −1.33570 | + | 0.737283i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2321 | + | 41.9186i | −0.508973 | + | 1.89951i | −0.0784867 | + | 0.996915i | \(0.525009\pi\) |
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.9282 | + | 27.9282i | −1.26296 | + | 1.26296i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 31.3205 | + | 31.3205i | 1.40633 | + | 1.40633i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.6506 | − | 10.0885i | 1.68547 | − | 0.451621i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
0.969216 | + | 0.246214i | \(0.0791865\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.0526 | − | 12.0000i | −0.846154 | − | 0.532939i | ||||
\(508\) | −19.0000 | − | 32.9090i | −0.842989 | − | 1.46010i | ||||
\(509\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.02628 | − | 42.1506i | 0.133875 | − | 1.86463i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.40192 | − | 1.71539i | 0.282652 | − | 0.0757363i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 21.0000 | − | 36.3731i | 0.924473 | − | 1.60123i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5000 | − | 30.3109i | 0.765222 | − | 1.32540i | −0.174908 | − | 0.984585i | \(-0.555963\pi\) |
0.940129 | − | 0.340818i | \(-0.110704\pi\) | |||||||
\(524\) | 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 | ||||||||
\(532\) | −5.58846 | − | 3.78461i | −0.242290 | − | 0.164084i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9641 | − | 44.6506i | −0.514377 | − | 1.91968i | −0.365444 | − | 0.930834i | \(-0.619083\pi\) |
−0.148933 | − | 0.988847i | \(-0.547584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.9711 | + | 22.5000i | −1.67241 | + | 0.965567i | ||||
\(544\) | 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 | ||||||||
\(549\) | 10.3923 | + | 18.0000i | 0.443533 | + | 0.768221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.3109 | − | 10.5000i | −1.28895 | − | 0.446505i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.1244 | + | 7.00000i | −0.514187 | + | 0.296866i | ||||
\(557\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.4352 | + | 10.5000i | −1.79482 | + | 0.444103i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8468 | + | 15.5000i | −1.12350 | + | 0.648655i | −0.942293 | − | 0.334790i | \(-0.891335\pi\) |
−0.181210 | + | 0.983444i | \(0.558001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.7846 | + | 12.0000i | 0.866025 | + | 0.500000i | ||||
\(577\) | 12.4282 | − | 46.3827i | 0.517393 | − | 1.93094i | 0.228968 | − | 0.973434i | \(-0.426465\pi\) |
0.288425 | − | 0.957503i | \(-0.406868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.08142 | − | 15.2321i | −0.169618 | − | 0.633022i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(588\) | −24.0000 | − | 3.46410i | −0.989743 | − | 0.142857i | ||||
\(589\) | − | 14.1244i | − | 0.581984i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −35.8564 | − | 9.60770i | −1.47369 | − | 0.394874i | ||||
\(593\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −42.0000 | − | 24.2487i | −1.71895 | − | 0.992434i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73205 | 0.0706518 | 0.0353259 | − | 0.999376i | \(-0.488753\pi\) | ||||
0.0353259 | + | 0.999376i | \(0.488753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.68653 | + | 1.68653i | 0.0686810 | + | 0.0686810i | ||||
\(604\) | 38.5885 | − | 10.3397i | 1.57014 | − | 0.420718i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5000 | + | 42.4352i | −0.994424 | + | 1.72239i | −0.405887 | + | 0.913923i | \(0.633038\pi\) |
−0.588537 | + | 0.808470i | \(0.700296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.04552 | − | 26.2942i | 0.284566 | − | 1.06201i | −0.664590 | − | 0.747208i | \(-0.731394\pi\) |
0.949156 | − | 0.314806i | \(-0.101939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.3827 | − | 10.5526i | −1.58292 | − | 0.424143i | −0.643094 | − | 0.765787i | \(-0.722350\pi\) |
−0.939829 | + | 0.341644i | \(0.889016\pi\) | |||||||
\(620\) | 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 | ||||||||
\(628\) | 24.2487 | + | 14.0000i | 0.967629 | + | 0.558661i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.87564 | + | 9.87564i | −0.393143 | + | 0.393143i | −0.875806 | − | 0.482663i | \(-0.839670\pi\) |
0.482663 | + | 0.875806i | \(0.339670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.0000 | + | 36.3731i | 0.834675 | + | 1.44570i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7224 | + | 20.5000i | 0.583324 | + | 0.812240i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6147 | − | 21.6147i | −0.852402 | − | 0.852402i | 0.138027 | − | 0.990429i | \(-0.455924\pi\) |
−0.990429 | + | 0.138027i | \(0.955924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −22.1603 | − | 45.6506i | −0.868529 | − | 1.78919i | ||||
\(652\) | 32.2487 | + | 32.2487i | 1.26296 | + | 1.26296i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.8827 | − | 33.8827i | 1.32189 | − | 1.32189i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.1147 | + | 11.8205i | 1.71586 | + | 0.459764i | 0.976850 | − | 0.213925i | \(-0.0686249\pi\) |
0.739014 | + | 0.673690i | \(0.235292\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.58142 | + | 20.8301i | −0.215790 | + | 0.805339i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 36.3731i | − | 1.40208i | −0.713123 | − | 0.701039i | \(-0.752720\pi\) | ||
0.713123 | − | 0.701039i | \(-0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.5000 | + | 12.9904i | −0.866025 | + | 0.500000i | ||||
\(676\) | −13.8564 | + | 22.0000i | −0.532939 | + | 0.846154i | ||||
\(677\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.150635 | + | 0.222432i | −0.00578084 | + | 0.00853615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(684\) | −1.98076 | − | 7.39230i | −0.0757363 | − | 0.282652i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.4378 | − | 19.4378i | 0.741599 | − | 0.741599i | ||||
\(688\) | −42.0000 | − | 24.2487i | −1.60123 | − | 0.924473i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.4808 | − | 12.4545i | 1.76821 | − | 0.473791i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
0.988355 | + | 0.152167i | \(0.0486252\pi\) | |||||||
\(692\) | 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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.91858 | + | 10.2513i | 0.223224 | + | 0.386635i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.84936 | + | 18.0981i | 0.182122 | + | 0.679688i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.813107 | + | 0.582115i | \(0.802225\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.1865 | − | 31.5000i | −0.682048 | − | 1.18134i | ||||
\(712\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5000 | + | 47.6314i | −0.614492 | + | 1.77389i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.34679 | + | 16.2224i | 0.161659 | + | 0.603319i | ||||
\(724\) | 25.9808 | + | 45.0000i | 0.965567 | + | 1.67241i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.0000i | 1.81731i | 0.417548 | + | 0.908655i | \(0.362889\pi\) | ||||
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 20.7846 | − | 12.0000i | 0.768221 | − | 0.443533i | ||||
\(733\) | 41.4545 | − | 11.1077i | 1.53116 | − | 0.410272i | 0.607760 | − | 0.794121i | \(-0.292068\pi\) |
0.923396 | + | 0.383849i | \(0.125402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.4808 | + | 11.9186i | 1.63625 | + | 0.438432i | 0.955718 | − | 0.294285i | \(-0.0950814\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.11474 | + | 6.82051i | −0.151159 | + | 0.250558i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5000 | + | 18.1865i | 1.14945 | + | 0.663636i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
0.200698 | + | 0.979653i | \(0.435679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.0000 | − | 20.7846i | −0.654654 | − | 0.755929i | ||||
\(757\) | −48.4974 | −1.76267 | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||||
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.3468 | − | 3.90192i | −1.96749 | − | 0.141259i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 13.8564 | − | 24.0000i | 0.500000 | − | 0.866025i | ||||
\(769\) | −11.5096 | − | 11.5096i | −0.415047 | − | 0.415047i | 0.468445 | − | 0.883493i | \(-0.344814\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.5885 | + | 4.71281i | −0.633022 | + | 0.169618i | ||||
\(773\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.3301 | + | 53.4808i | 0.514753 | + | 1.92109i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.2128 | + | 23.8468i | 1.26325 | + | 0.855499i | ||||
\(778\) | 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 | ||||||||
\(787\) | −40.6147 | − | 10.8827i | −1.44776 | − | 0.387926i | −0.552515 | − | 0.833503i | \(-0.686332\pi\) |
−0.895244 | + | 0.445577i | \(0.852999\pi\) | |||||||
\(788\) | 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 | ||||||||
\(796\) | −28.0000 | + | 48.4974i | −0.992434 | + | 1.71895i | ||||
\(797\) | 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 | ||||||||
\(804\) | 1.94744 | − | 1.94744i | 0.0686810 | − | 0.0686810i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.8038 | − | 22.8038i | −0.800751 | − | 0.800751i | 0.182462 | − | 0.983213i | \(-0.441593\pi\) |
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.2487 | − | 39.2487i | 1.37651 | − | 1.37651i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00258 | + | 14.9378i | 0.140032 | + | 0.522608i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.59808 | + | 28.5000i | −0.0907841 | + | 0.995871i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0000 | − | 12.1244i | 0.732014 | − | 0.422628i | −0.0871445 | − | 0.996196i | \(-0.527774\pi\) |
0.819159 | + | 0.573567i | \(0.194441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.06218 | − | 3.50000i | 0.210548 | − | 0.121560i | −0.391018 | − | 0.920383i | \(-0.627877\pi\) |
0.601566 | + | 0.798823i | \(0.294544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.1865 | − | 10.5000i | −0.630884 | − | 0.364241i | ||||
\(832\) | −28.0000 | + | 6.92820i | −0.970725 | + | 0.240192i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.8923 | − | 55.5788i | 0.514753 | − | 1.92109i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42.0000 | − | 24.2487i | 1.44570 | − | 0.834675i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.52628 | + | 27.5000i | −0.327327 | + | 0.944911i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.5000 | + | 6.06218i | 0.360359 | + | 0.208053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.88269 | + | 5.88269i | −0.201419 | + | 0.201419i | −0.800608 | − | 0.599189i | \(-0.795490\pi\) |
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 | ||||||||
\(859\) | 8.66025 | − | 15.0000i | 0.295484 | − | 0.511793i | −0.679613 | − | 0.733571i | \(-0.737852\pi\) |
0.975097 | + | 0.221777i | \(0.0711857\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.4449 | 1.00000 | ||||||||
\(868\) | −52.7128 | + | 25.5885i | −1.78919 | + | 0.868529i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.86603 | − | 0.0551363i | −0.0971116 | − | 0.00186822i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.294229 | + | 0.0788383i | −0.00995813 | + | 0.00266827i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −39.1244 | − | 39.1244i | −1.32189 | − | 1.32189i | ||||
\(877\) | 56.3468 | − | 15.0981i | 1.90270 | − | 0.509826i | 0.906552 | − | 0.422095i | \(-0.138705\pi\) |
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 | ||||||||
\(883\) | 47.0000i | 1.58168i | 0.612026 | + | 0.790838i | \(0.290355\pi\) | ||||
−0.612026 | + | 0.790838i | \(0.709645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.3634 | − | 9.50000i | 1.65560 | − | 0.318620i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 24.0526 | + | 6.44486i | 0.805339 | + | 0.215790i | ||||
\(893\) | 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 | ||||||||
\(903\) | 36.3731 | + | 42.0000i | 1.21042 | + | 1.39767i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.0955 | − | 29.5000i | 1.69660 | − | 0.979531i | 0.747653 | − | 0.664089i | \(-0.231180\pi\) |
0.948945 | − | 0.315442i | \(-0.102153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −8.53590 | + | 2.28719i | −0.282652 | + | 0.0757363i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.4449 | − | 22.4449i | −0.741599 | − | 0.741599i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.3109 | + | 52.5000i | −0.999864 | + | 1.73182i | −0.485648 | + | 0.874154i | \(0.661416\pi\) |
−0.514216 | + | 0.857661i | \(0.671917\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.3564 | + | 10.5455i | 1.29684 | + | 0.347487i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.8109 | − | 32.8109i | −1.07882 | − | 1.07882i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.5000 | + | 28.5788i | −1.62579 | + | 0.938652i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.15064 | − | 5.34679i | 0.234353 | − | 0.175234i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.2295 | 1.64093 | 0.820463 | − | 0.571700i | \(-0.193716\pi\) | ||||
0.820463 | + | 0.571700i | \(0.193716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.00000 | −0.293704 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(948\) | −36.3731 | + | 21.0000i | −1.18134 | + | 0.682048i | ||||
\(949\) | −1.10770 | + | 57.5788i | −0.0359573 | + | 1.86909i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −79.3468 | − | 45.8109i | −2.55957 | − | 1.47777i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.7321 | − | 5.01924i | 0.603319 | − | 0.161659i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4378 | + | 24.4378i | 0.785867 | + | 0.785867i | 0.980814 | − | 0.194946i | \(-0.0624533\pi\) |
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(972\) | − | 31.1769i | − | 1.00000i | ||||||
\(973\) | −3.50000 | − | 18.1865i | −0.112205 | − | 0.583033i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.66025 | − | 30.0000i | 0.277350 | − | 0.960769i | ||||
\(976\) | −13.8564 | − | 24.0000i | −0.443533 | − | 0.768221i | ||||
\(977\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.6865 | − | 43.6865i | −1.39480 | − | 1.39480i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.87564 | + | 4.75129i | 0.250558 | + | 0.151159i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.50000 | − | 14.7224i | −0.270011 | − | 0.467673i | 0.698853 | − | 0.715265i | \(-0.253694\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.6340 | + | 30.6340i | 0.972140 | + | 0.972140i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.5000 | − | 42.4352i | −0.775923 | − | 1.34394i | −0.934274 | − | 0.356555i | \(-0.883951\pi\) |
0.158352 | − | 0.987383i | \(-0.449382\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.4808 | + | 46.5788i | 0.394874 | + | 1.47369i |
(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.cd.b.86.1 | yes | 4 | |
3.2 | odd | 2 | CM | 273.2.cd.b.86.1 | yes | 4 | |
7.4 | even | 3 | 273.2.cd.a.242.1 | yes | 4 | ||
13.5 | odd | 4 | 273.2.cd.a.44.1 | ✓ | 4 | ||
21.11 | odd | 6 | 273.2.cd.a.242.1 | yes | 4 | ||
39.5 | even | 4 | 273.2.cd.a.44.1 | ✓ | 4 | ||
91.18 | odd | 12 | inner | 273.2.cd.b.200.1 | yes | 4 | |
273.200 | even | 12 | inner | 273.2.cd.b.200.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.cd.a.44.1 | ✓ | 4 | 13.5 | odd | 4 | ||
273.2.cd.a.44.1 | ✓ | 4 | 39.5 | even | 4 | ||
273.2.cd.a.242.1 | yes | 4 | 7.4 | even | 3 | ||
273.2.cd.a.242.1 | yes | 4 | 21.11 | odd | 6 | ||
273.2.cd.b.86.1 | yes | 4 | 1.1 | even | 1 | trivial | |
273.2.cd.b.86.1 | yes | 4 | 3.2 | odd | 2 | CM | |
273.2.cd.b.200.1 | yes | 4 | 91.18 | odd | 12 | inner | |
273.2.cd.b.200.1 | yes | 4 | 273.200 | even | 12 | inner |