Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1873 |
Dual form | 2736.2.s.j.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | − | 4.33013i | −0.693375 | − | 1.20096i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.277350 | − | 0.960769i | \(-0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | − | 6.92820i | −0.742781 | − | 1.28654i | −0.951224 | − | 0.308500i | \(-0.900173\pi\) |
0.208443 | − | 0.978035i | \(-0.433160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | + | 10.3923i | −0.937043 | + | 1.62301i | −0.166092 | + | 0.986110i | \(0.553115\pi\) |
−0.770950 | + | 0.636895i | \(0.780218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | + | 0.866025i | −0.0762493 | + | 0.132068i | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | + | 3.46410i | 0.274721 | + | 0.475831i | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00000 | + | 8.66025i | −0.650945 | + | 1.12747i | 0.331949 | + | 0.943297i | \(0.392294\pi\) |
−0.982894 | + | 0.184172i | \(0.941040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.50000 | + | 9.52628i | 0.671932 | + | 1.16382i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) |
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | + | 5.19615i | −0.356034 | + | 0.616670i | −0.987294 | − | 0.158901i | \(-0.949205\pi\) |
0.631260 | + | 0.775571i | \(0.282538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.50000 | − | 9.52628i | 0.643726 | − | 1.11497i | −0.340868 | − | 0.940111i | \(-0.610721\pi\) |
0.984594 | − | 0.174855i | \(-0.0559458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | − | 0.866025i | 0.0562544 | − | 0.0974355i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
0.892781 | + | 0.450490i | \(0.148751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | + | 4.33013i | 0.262071 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | + | 1.73205i | −0.101535 | + | 0.175863i | −0.912317 | − | 0.409484i | \(-0.865709\pi\) |
0.810782 | + | 0.585348i | \(0.199042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00000 | + | 12.1244i | 0.696526 | + | 1.20642i | 0.969664 | + | 0.244443i | \(0.0786053\pi\) |
−0.273138 | + | 0.961975i | \(0.588061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.0000 | −1.28093 | −0.640464 | − | 0.767988i | \(-0.721258\pi\) | ||||
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | − | 3.46410i | 0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | − | 6.92820i | −0.354943 | − | 0.614779i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.987108 | + | 0.160055i | \(0.948833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 1.73205i | −0.346844 | + | 0.150188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 15.5885i | 0.768922 | + | 1.33181i | 0.938148 | + | 0.346235i | \(0.112540\pi\) |
−0.169226 | + | 0.985577i | \(0.554127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.00000 | + | 8.66025i | 0.418121 | + | 0.724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50000 | + | 2.59808i | −0.119713 | + | 0.207349i | −0.919654 | − | 0.392730i | \(-0.871531\pi\) |
0.799941 | + | 0.600079i | \(0.204864\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | − | 3.46410i | −0.157622 | − | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.00000 | −0.234978 | −0.117489 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117489 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | + | 1.73205i | 0.0773823 | + | 0.134030i | 0.902120 | − | 0.431486i | \(-0.142010\pi\) |
−0.824737 | + | 0.565516i | \(0.808677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | + | 10.3923i | −0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | − | 4.33013i | −0.188982 | − | 0.327327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | + | 1.73205i | 0.0743294 | + | 0.128742i | 0.900794 | − | 0.434246i | \(-0.142985\pi\) |
−0.826465 | + | 0.562988i | \(0.809652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | − | 6.92820i | 0.292509 | − | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | + | 16.4545i | −0.683825 | + | 1.18442i | 0.289980 | + | 0.957033i | \(0.406351\pi\) |
−0.973805 | + | 0.227387i | \(0.926982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000 | 1.85242 | 0.926212 | − | 0.377004i | \(-0.123046\pi\) | ||||
0.926212 | + | 0.377004i | \(0.123046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | + | 18.1865i | 0.744325 | + | 1.28921i | 0.950509 | + | 0.310696i | \(0.100562\pi\) |
−0.206184 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00000 | + | 6.92820i | 0.280745 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | + | 3.46410i | −0.553372 | + | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | + | 12.9904i | −0.516321 | + | 0.894295i | 0.483499 | + | 0.875345i | \(0.339366\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.0000 | 1.34535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | − | 7.79423i | 0.301342 | − | 0.521940i | −0.675098 | − | 0.737728i | \(-0.735899\pi\) |
0.976440 | + | 0.215788i | \(0.0692320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.0000 | −1.59294 | −0.796468 | − | 0.604681i | \(-0.793301\pi\) | ||||
−0.796468 | + | 0.604681i | \(0.793301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | + | 6.06218i | 0.225455 | + | 0.390499i | 0.956456 | − | 0.291877i | \(-0.0942799\pi\) |
−0.731001 | + | 0.682376i | \(0.760947\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.5000 | − | 12.9904i | −1.11350 | − | 0.826558i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | + | 1.73205i | 0.0631194 | + | 0.109326i | 0.895858 | − | 0.444340i | \(-0.146562\pi\) |
−0.832739 | + | 0.553666i | \(0.813228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | − | 6.92820i | −0.251478 | − | 0.435572i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0000 | − | 17.3205i | −0.623783 | − | 1.08042i | −0.988775 | − | 0.149413i | \(-0.952262\pi\) |
0.364992 | − | 0.931011i | \(-0.381072\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0000 | + | 22.5167i | −0.801614 | + | 1.38844i | 0.116939 | + | 0.993139i | \(0.462692\pi\) |
−0.918553 | + | 0.395298i | \(0.870641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.00000 | − | 8.66025i | 0.304855 | − | 0.528025i | −0.672374 | − | 0.740212i | \(-0.734725\pi\) |
0.977229 | + | 0.212187i | \(0.0680585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.00000 | − | 8.66025i | −0.301511 | − | 0.522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | − | 6.92820i | −0.238620 | − | 0.413302i | 0.721699 | − | 0.692207i | \(-0.243362\pi\) |
−0.960319 | + | 0.278906i | \(0.910028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | − | 10.3923i | 0.354169 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0000 | − | 17.3205i | 0.578315 | − | 1.00167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.500000 | − | 0.866025i | 0.0288195 | − | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.00000 | + | 10.3923i | −0.342438 | + | 0.593120i | −0.984885 | − | 0.173210i | \(-0.944586\pi\) |
0.642447 | + | 0.766330i | \(0.277919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000 | 1.02069 | 0.510343 | − | 0.859971i | \(-0.329518\pi\) | ||||
0.510343 | + | 0.859971i | \(0.329518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0000 | − | 19.0526i | −0.621757 | − | 1.07691i | −0.989158 | − | 0.146852i | \(-0.953086\pi\) |
0.367402 | − | 0.930062i | \(-0.380247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00000 | − | 3.46410i | −0.112331 | − | 0.194563i | 0.804379 | − | 0.594117i | \(-0.202498\pi\) |
−0.916710 | + | 0.399554i | \(0.869165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | + | 13.8564i | 0.447914 | + | 0.775810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | + | 17.3205i | −0.111283 | + | 0.963739i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5000 | − | 21.6506i | 0.693375 | − | 1.20096i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.0000 | 1.37412 | 0.687062 | − | 0.726599i | \(-0.258900\pi\) | ||||
0.687062 | + | 0.726599i | \(0.258900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | + | 11.2583i | −0.354078 | + | 0.613280i | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.00000 | − | 13.8564i | 0.429463 | − | 0.743851i | −0.567363 | − | 0.823468i | \(-0.692036\pi\) |
0.996826 | + | 0.0796169i | \(0.0253697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0000 | −1.12410 | −0.562052 | − | 0.827102i | \(-0.689988\pi\) | ||||
−0.562052 | + | 0.827102i | \(0.689988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.00000 | −0.212899 | −0.106449 | − | 0.994318i | \(-0.533948\pi\) | ||||
−0.106449 | + | 0.994318i | \(0.533948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0000 | − | 17.3205i | 0.527780 | − | 0.914141i | −0.471696 | − | 0.881761i | \(-0.656358\pi\) |
0.999476 | − | 0.0323801i | \(-0.0103087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.50000 | + | 6.06218i | 0.182699 | + | 0.316443i | 0.942799 | − | 0.333363i | \(-0.108183\pi\) |
−0.760100 | + | 0.649806i | \(0.774850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | − | 3.46410i | −0.103835 | − | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.0000 | + | 34.6410i | −1.03005 | + | 1.78410i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.00000 | + | 12.1244i | −0.357683 | + | 0.619526i | −0.987573 | − | 0.157159i | \(-0.949767\pi\) |
0.629890 | + | 0.776684i | \(0.283100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0000 | − | 20.7846i | −0.608424 | − | 1.05382i | −0.991500 | − | 0.130105i | \(-0.958469\pi\) |
0.383076 | − | 0.923717i | \(-0.374865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0000 | −0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.50000 | + | 6.06218i | −0.175660 | + | 0.304252i | −0.940389 | − | 0.340099i | \(-0.889539\pi\) |
0.764730 | + | 0.644351i | \(0.222873\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.50000 | − | 12.9904i | −0.373602 | − | 0.647097i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00000 | + | 12.1244i | 0.346128 | + | 0.599511i | 0.985558 | − | 0.169338i | \(-0.0541630\pi\) |
−0.639430 | + | 0.768849i | \(0.720830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.00000 | − | 8.66025i | 0.246034 | − | 0.426143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0000 | − | 19.0526i | 0.536107 | − | 0.928565i | −0.463002 | − | 0.886357i | \(-0.653228\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50000 | − | 11.2583i | −0.314557 | − | 0.544829i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.00000 | + | 8.66025i | 0.240842 | + | 0.417150i | 0.960954 | − | 0.276707i | \(-0.0892433\pi\) |
−0.720113 | + | 0.693857i | \(0.755910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.50000 | + | 7.79423i | 0.216256 | + | 0.374567i | 0.953660 | − | 0.300885i | \(-0.0972820\pi\) |
−0.737404 | + | 0.675452i | \(0.763949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.0000 | + | 10.3923i | 0.669711 | + | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.5000 | − | 30.3109i | 0.835229 | − | 1.44666i | −0.0586141 | − | 0.998281i | \(-0.518668\pi\) |
0.893843 | − | 0.448379i | \(-0.147999\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0000 | + | 27.7128i | 0.760183 | + | 1.31668i | 0.942756 | + | 0.333483i | \(0.108224\pi\) |
−0.182573 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0000 | − | 25.9808i | 0.698620 | − | 1.21004i | −0.270326 | − | 0.962769i | \(-0.587131\pi\) |
0.968945 | − | 0.247276i | \(-0.0795353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.0000 | −1.06890 | −0.534450 | − | 0.845200i | \(-0.679481\pi\) | ||||
−0.534450 | + | 0.845200i | \(0.679481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.50000 | − | 9.52628i | −0.253966 | − | 0.439883i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00000 | − | 1.73205i | 0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.5000 | + | 12.9904i | 0.802955 | + | 0.596040i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.00000 | − | 12.1244i | −0.319838 | − | 0.553976i | 0.660616 | − | 0.750724i | \(-0.270295\pi\) |
−0.980454 | + | 0.196748i | \(0.936962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.50000 | − | 12.9904i | −0.341971 | − | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | + | 5.19615i | −0.135388 | + | 0.234499i | −0.925746 | − | 0.378147i | \(-0.876561\pi\) |
0.790358 | + | 0.612646i | \(0.209895\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.0000 | 1.44121 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | − | 5.19615i | 0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5000 | − | 25.1147i | 0.649109 | − | 1.12429i | −0.334227 | − | 0.942493i | \(-0.608475\pi\) |
0.983336 | − | 0.181797i | \(-0.0581915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.0000 | − | 34.6410i | −0.891756 | − | 1.54457i | −0.837769 | − | 0.546025i | \(-0.816140\pi\) |
−0.0539870 | − | 0.998542i | \(-0.517193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | − | 5.19615i | −0.132973 | − | 0.230315i | 0.791849 | − | 0.610718i | \(-0.209119\pi\) |
−0.924821 | + | 0.380402i | \(0.875786\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.50000 | + | 9.52628i | −0.243306 | + | 0.421418i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.00000 | − | 10.3923i | −0.263880 | − | 0.457053i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | + | 25.1147i | 0.634041 | + | 1.09819i | 0.986718 | + | 0.162446i | \(0.0519382\pi\) |
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 60.0000 | 2.59889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5000 | + | 33.7750i | 0.838370 | + | 1.45210i | 0.891256 | + | 0.453500i | \(0.149825\pi\) |
−0.0528859 | + | 0.998601i | \(0.516842\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5000 | − | 25.1147i | −0.619975 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0000 | − | 20.7846i | −1.19284 | − | 0.885454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | + | 0.866025i | −0.0212622 | + | 0.0368271i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0000 | − | 32.9090i | −0.805056 | − | 1.39440i | −0.916253 | − | 0.400599i | \(-0.868802\pi\) |
0.111198 | − | 0.993798i | \(-0.464531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0000 | 0.758610 | 0.379305 | − | 0.925272i | \(-0.376163\pi\) | ||||
0.379305 | + | 0.925272i | \(0.376163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0000 | −1.00613 | −0.503066 | − | 0.864248i | \(-0.667795\pi\) | ||||
−0.503066 | + | 0.864248i | \(0.667795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0000 | −1.38101 | −0.690504 | − | 0.723329i | \(-0.742611\pi\) | ||||
−0.690504 | + | 0.723329i | \(0.742611\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.0000 | + | 17.3205i | −0.417029 | + | 0.722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00000 | − | 6.92820i | −0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0000 | − | 22.5167i | 0.536567 | − | 0.929362i | −0.462518 | − | 0.886610i | \(-0.653054\pi\) |
0.999086 | − | 0.0427523i | \(-0.0136126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | − | 5.19615i | 0.494451 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.00000 | − | 5.19615i | −0.123195 | − | 0.213380i | 0.797831 | − | 0.602881i | \(-0.205981\pi\) |
−0.921026 | + | 0.389501i | \(0.872647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.00000 | − | 15.5885i | −0.367730 | − | 0.636927i | 0.621480 | − | 0.783430i | \(-0.286532\pi\) |
−0.989210 | + | 0.146503i | \(0.953198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0000 | −0.856608 | −0.428304 | − | 0.903635i | \(-0.640889\pi\) | ||||
−0.428304 | + | 0.903635i | \(0.640889\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.0000 | 1.74532 | 0.872658 | − | 0.488332i | \(-0.162394\pi\) | ||||
0.872658 | + | 0.488332i | \(0.162394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | − | 25.9808i | 0.606835 | − | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | − | 25.9808i | 0.605844 | − | 1.04935i | −0.386073 | − | 0.922468i | \(-0.626169\pi\) |
0.991917 | − | 0.126885i | \(-0.0404979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.00000 | + | 5.19615i | 0.120775 | + | 0.209189i | 0.920074 | − | 0.391745i | \(-0.128129\pi\) |
−0.799298 | + | 0.600935i | \(0.794795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.0000 | −1.00483 | −0.502417 | − | 0.864625i | \(-0.667556\pi\) | ||||
−0.502417 | + | 0.864625i | \(0.667556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.00000 | + | 5.19615i | 0.120192 | + | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.00000 | + | 10.3923i | −0.239236 | + | 0.414368i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.50000 | − | 12.9904i | −0.298570 | − | 0.517139i | 0.677239 | − | 0.735763i | \(-0.263176\pi\) |
−0.975809 | + | 0.218624i | \(0.929843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0000 | + | 25.9808i | 0.594322 | + | 1.02940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.50000 | + | 16.4545i | −0.374643 | + | 0.648901i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) |
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | − | 17.3205i | 0.392534 | − | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0000 | 0.704394 | 0.352197 | − | 0.935926i | \(-0.385435\pi\) | ||||
0.352197 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0000 | − | 29.4449i | −0.662226 | − | 1.14701i | −0.980029 | − | 0.198852i | \(-0.936279\pi\) |
0.317803 | − | 0.948157i | \(-0.397055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0000 | − | 36.3731i | −0.816805 | − | 1.41475i | −0.908024 | − | 0.418917i | \(-0.862410\pi\) |
0.0912190 | − | 0.995831i | \(-0.470924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | − | 27.7128i | 0.619522 | − | 1.07304i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.0000 | − | 22.5167i | −0.501859 | − | 0.869246i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.0000 | −1.27206 | −0.636028 | − | 0.771666i | \(-0.719424\pi\) | ||||
−0.636028 | + | 0.771666i | \(0.719424\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.0000 | −1.30673 | −0.653363 | − | 0.757045i | \(-0.726642\pi\) | ||||
−0.653363 | + | 0.757045i | \(0.726642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.00000 | − | 1.73205i | 0.0383765 | − | 0.0664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0000 | − | 17.3205i | 0.380970 | − | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0000 | −0.760836 | −0.380418 | − | 0.924815i | \(-0.624220\pi\) | ||||
−0.380418 | + | 0.924815i | \(0.624220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | − | 41.5692i | −0.909065 | − | 1.57455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | − | 17.3205i | 0.377695 | − | 0.654187i | −0.613032 | − | 0.790058i | \(-0.710050\pi\) |
0.990726 | + | 0.135872i | \(0.0433835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 5.19615i | 0.452589 | − | 0.195977i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.00000 | − | 12.1244i | −0.263262 | − | 0.455983i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.5000 | + | 33.7750i | 0.732338 | + | 1.26845i | 0.955882 | + | 0.293752i | \(0.0949041\pi\) |
−0.223544 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | 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 | ||||||||
\(721\) | 13.0000 | 0.484145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.0000 | − | 34.6410i | 0.742781 | − | 1.28654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.5000 | + | 40.7032i | −0.871567 | + | 1.50960i | −0.0111912 | + | 0.999937i | \(0.503562\pi\) |
−0.860376 | + | 0.509661i | \(0.829771\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.00000 | − | 3.46410i | −0.0739727 | − | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.0000 | −1.84679 | −0.923396 | − | 0.383849i | \(-0.874598\pi\) | ||||
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0000 | − | 19.0526i | −0.405190 | − | 0.701810i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | − | 16.4545i | 0.349463 | − | 0.605288i | −0.636691 | − | 0.771119i | \(-0.719697\pi\) |
0.986154 | + | 0.165831i | \(0.0530307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.0000 | − | 43.3013i | 0.917161 | − | 1.58857i | 0.113455 | − | 0.993543i | \(-0.463808\pi\) |
0.803706 | − | 0.595026i | \(-0.202858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | 0.657706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.5000 | + | 38.9711i | 0.821037 | + | 1.42208i | 0.904911 | + | 0.425601i | \(0.139937\pi\) |
−0.0838743 | + | 0.996476i | \(0.526729\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.50000 | + | 11.2583i | −0.236247 | + | 0.409191i | −0.959634 | − | 0.281251i | \(-0.909251\pi\) |
0.723388 | + | 0.690442i | \(0.242584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00000 | + | 1.73205i | −0.0362024 | + | 0.0627044i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 50.0000 | 1.80540 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.5000 | + | 32.0429i | 0.667127 | + | 1.15550i | 0.978704 | + | 0.205277i | \(0.0658095\pi\) |
−0.311577 | + | 0.950221i | \(0.600857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.00000 | + | 12.1244i | 0.251773 | + | 0.436083i | 0.964014 | − | 0.265852i | \(-0.0856532\pi\) |
−0.712241 | + | 0.701935i | \(0.752320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.50000 | + | 12.9904i | 0.269408 | + | 0.466628i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | + | 51.9615i | −0.214972 | + | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | − | 10.3923i | 0.214697 | − | 0.371866i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.0000 | −0.891154 | −0.445577 | − | 0.895244i | \(-0.647001\pi\) | ||||
−0.445577 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.5000 | − | 56.2917i | 1.15411 | − | 1.99898i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.0000 | 0.495905 | 0.247953 | − | 0.968772i | \(-0.420242\pi\) | ||||
0.247953 | + | 0.968772i | \(0.420242\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0000 | + | 19.0526i | −0.388182 | + | 0.672350i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0000 | 0.562530 | 0.281265 | − | 0.959630i | \(-0.409246\pi\) | ||||
0.281265 | + | 0.959630i | \(0.409246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | − | 38.1051i | −0.772524 | − | 1.33805i | −0.936175 | − | 0.351533i | \(-0.885660\pi\) |
0.163651 | − | 0.986518i | \(-0.447673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.500000 | + | 4.33013i | −0.0174928 | + | 0.151492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | + | 20.7846i | 0.418803 | + | 0.725388i | 0.995819 | − | 0.0913446i | \(-0.0291165\pi\) |
−0.577016 | + | 0.816733i | \(0.695783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | + | 3.46410i | 0.0697156 | + | 0.120751i | 0.898776 | − | 0.438408i | \(-0.144457\pi\) |
−0.829060 | + | 0.559159i | \(0.811124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000 | + | 31.1769i | 0.625921 | + | 1.08413i | 0.988362 | + | 0.152121i | \(0.0486102\pi\) |
−0.362441 | + | 0.932007i | \(0.618056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.0000 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0000 | − | 20.7846i | 0.415775 | − | 0.720144i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.00000 | − | 10.3923i | 0.207143 | − | 0.358782i | −0.743670 | − | 0.668546i | \(-0.766917\pi\) |
0.950813 | + | 0.309764i | \(0.100250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | + | 30.3109i | −0.603448 | + | 1.04520i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | 0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.50000 | − | 4.33013i | 0.0855984 | − | 0.148261i | −0.820048 | − | 0.572295i | \(-0.806053\pi\) |
0.905646 | + | 0.424034i | \(0.139386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.00000 | − | 8.66025i | 0.170797 | − | 0.295829i | −0.767902 | − | 0.640567i | \(-0.778699\pi\) |
0.938699 | + | 0.344739i | \(0.112033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.50000 | + | 12.9904i | 0.255897 | + | 0.443226i | 0.965139 | − | 0.261739i | \(-0.0842960\pi\) |
−0.709242 | + | 0.704965i | \(0.750963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.0000 | 0.340404 | 0.170202 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170202 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.00000 | + | 1.73205i | −0.0339227 | + | 0.0587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5000 | − | 47.6314i | 0.931802 | − | 1.61393i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.50000 | + | 12.9904i | −0.253257 | + | 0.438654i | −0.964421 | − | 0.264373i | \(-0.914835\pi\) |
0.711164 | + | 0.703027i | \(0.248168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.0000 | 0.943344 | 0.471672 | − | 0.881774i | \(-0.343651\pi\) | ||||
0.471672 | + | 0.881774i | \(0.343651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.500000 | − | 0.866025i | −0.0168263 | − | 0.0291441i | 0.857490 | − | 0.514501i | \(-0.172023\pi\) |
−0.874316 | + | 0.485357i | \(0.838690\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.00000 | + | 5.19615i | 0.100730 | + | 0.174470i | 0.911986 | − | 0.410222i | \(-0.134549\pi\) |
−0.811256 | + | 0.584692i | \(0.801215\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | + | 6.92820i | 0.134156 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0000 | + | 15.5885i | 0.702738 | + | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | − | 20.7846i | −0.400222 | − | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0000 | + | 38.1051i | −0.730498 | + | 1.26526i | 0.226173 | + | 0.974087i | \(0.427379\pi\) |
−0.956671 | + | 0.291172i | \(0.905955\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.00000 | + | 12.1244i | −0.231160 | + | 0.400381i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0000 | 0.824674 | 0.412337 | − | 0.911031i | \(-0.364713\pi\) | ||||
0.412337 | + | 0.911031i | \(0.364713\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.0000 | 0.987462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.50000 | + | 12.9904i | 0.246598 | + | 0.427121i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | − | 24.2487i | 0.459325 | − | 0.795574i | −0.539600 | − | 0.841921i | \(-0.681425\pi\) |
0.998925 | + | 0.0463469i | \(0.0147580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | + | 10.3923i | −0.786568 | + | 0.340594i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.50000 | + | 7.79423i | 0.147009 | + | 0.254626i | 0.930121 | − | 0.367254i | \(-0.119702\pi\) |
−0.783112 | + | 0.621881i | \(0.786369\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −48.0000 | −1.56310 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.0000 | + | 43.3013i | −0.812391 | + | 1.40710i | 0.0987955 | + | 0.995108i | \(0.468501\pi\) |
−0.911186 | + | 0.411994i | \(0.864832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.0000 | −1.78538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.0000 | − | 29.4449i | 0.550684 | − | 0.953813i | −0.447541 | − | 0.894263i | \(-0.647700\pi\) |
0.998225 | − | 0.0595495i | \(-0.0189664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | − | 15.5885i | −0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.5000 | + | 25.1147i | −0.466289 | + | 0.807635i | −0.999259 | − | 0.0384986i | \(-0.987742\pi\) |
0.532970 | + | 0.846134i | \(0.321076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0000 | − | 36.3731i | 0.673922 | − | 1.16727i | −0.302861 | − | 0.953035i | \(-0.597942\pi\) |
0.976783 | − | 0.214232i | \(-0.0687250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.50000 | − | 4.33013i | −0.0801463 | − | 0.138817i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.0000 | −1.72761 | −0.863807 | − | 0.503824i | \(-0.831926\pi\) | ||||
−0.863807 | + | 0.503824i | \(0.831926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | + | 10.3923i | 0.191761 | + | 0.332140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.00000 | + | 8.66025i | −0.159475 | + | 0.276219i | −0.934680 | − | 0.355491i | \(-0.884314\pi\) |
0.775204 | + | 0.631711i | \(0.217647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5000 | − | 40.7032i | 0.746502 | − | 1.29298i | −0.202988 | − | 0.979181i | \(-0.565065\pi\) |
0.949490 | − | 0.313798i | \(-0.101602\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.50000 | − | 6.06218i | −0.110846 | − | 0.191991i | 0.805266 | − | 0.592914i | \(-0.202023\pi\) |
−0.916112 | + | 0.400923i | \(0.868689\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.2.s.j.1873.1 | 2 | ||
3.2 | odd | 2 | 912.2.q.a.49.1 | 2 | |||
4.3 | odd | 2 | 171.2.f.a.163.1 | 2 | |||
12.11 | even | 2 | 57.2.e.a.49.1 | yes | 2 | ||
19.7 | even | 3 | inner | 2736.2.s.j.577.1 | 2 | ||
57.26 | odd | 6 | 912.2.q.a.577.1 | 2 | |||
76.7 | odd | 6 | 171.2.f.a.64.1 | 2 | |||
76.11 | odd | 6 | 3249.2.a.c.1.1 | 1 | |||
76.27 | even | 6 | 3249.2.a.f.1.1 | 1 | |||
228.11 | even | 6 | 1083.2.a.c.1.1 | 1 | |||
228.83 | even | 6 | 57.2.e.a.7.1 | ✓ | 2 | ||
228.179 | odd | 6 | 1083.2.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.e.a.7.1 | ✓ | 2 | 228.83 | even | 6 | ||
57.2.e.a.49.1 | yes | 2 | 12.11 | even | 2 | ||
171.2.f.a.64.1 | 2 | 76.7 | odd | 6 | |||
171.2.f.a.163.1 | 2 | 4.3 | odd | 2 | |||
912.2.q.a.49.1 | 2 | 3.2 | odd | 2 | |||
912.2.q.a.577.1 | 2 | 57.26 | odd | 6 | |||
1083.2.a.b.1.1 | 1 | 228.179 | odd | 6 | |||
1083.2.a.c.1.1 | 1 | 228.11 | even | 6 | |||
2736.2.s.j.577.1 | 2 | 19.7 | even | 3 | inner | ||
2736.2.s.j.1873.1 | 2 | 1.1 | even | 1 | trivial | ||
3249.2.a.c.1.1 | 1 | 76.11 | odd | 6 | |||
3249.2.a.f.1.1 | 1 | 76.27 | even | 6 |