Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(865,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.i (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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.2 | ||
Root | \(-0.651388 - 1.12824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.865 |
Dual form | 2592.2.i.bc.1729.2 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | 1.80278 | + | 3.12250i | 0.806226 | + | 1.39642i | 0.915460 | + | 0.402408i | \(0.131827\pi\) |
−0.109235 | + | 0.994016i | \(0.534840\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80278 | + | 3.12250i | −0.681385 | + | 1.18019i | 0.293173 | + | 0.956059i | \(0.405289\pi\) |
−0.974558 | + | 0.224134i | \(0.928045\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 3.46410i | −0.554700 | − | 0.960769i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.21110 | −1.65434 | −0.827170 | − | 0.561951i | \(-0.810051\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | + | 6.92820i | −0.800000 | + | 1.38564i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.60555 | + | 6.24500i | −0.669534 | + | 1.15967i | 0.308500 | + | 0.951224i | \(0.400173\pi\) |
−0.978035 | + | 0.208443i | \(0.933160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.80278 | + | 3.12250i | 0.323788 | + | 0.560817i | 0.981266 | − | 0.192656i | \(-0.0617102\pi\) |
−0.657478 | + | 0.753474i | \(0.728377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −13.0000 | −2.19740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60555 | − | 6.24500i | −0.563093 | − | 0.975305i | −0.997224 | − | 0.0744555i | \(-0.976278\pi\) |
0.434132 | − | 0.900849i | \(-0.357055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.60555 | + | 6.24500i | −0.549841 | + | 0.952353i | 0.448444 | + | 0.893811i | \(0.351979\pi\) |
−0.998285 | + | 0.0585421i | \(0.981355\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.00000 | + | 8.66025i | −0.729325 | + | 1.26323i | 0.227844 | + | 0.973698i | \(0.426832\pi\) |
−0.957169 | + | 0.289530i | \(0.906501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 5.19615i | −0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.60555 | 0.495261 | 0.247630 | − | 0.968855i | \(-0.420348\pi\) | ||||
0.247630 | + | 0.968855i | \(0.420348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.60555 | 0.486172 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.21110 | − | 12.4900i | 0.894427 | − | 1.54919i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.60555 | − | 6.24500i | −0.440488 | − | 0.762948i | 0.557237 | − | 0.830353i | \(-0.311861\pi\) |
−0.997726 | + | 0.0674052i | \(0.978528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | −0.351123 | −0.175562 | − | 0.984468i | \(-0.556174\pi\) | ||||
−0.175562 | + | 0.984468i | \(0.556174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.80278 | + | 3.12250i | 0.205445 | + | 0.355842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.21110 | − | 12.4900i | 0.811312 | − | 1.40523i | −0.100633 | − | 0.994924i | \(-0.532087\pi\) |
0.911946 | − | 0.410311i | \(-0.134580\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.21110 | −0.764375 | −0.382188 | − | 0.924085i | \(-0.624829\pi\) | ||||
−0.382188 | + | 0.924085i | \(0.624829\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4222 | 1.51186 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.0000 | − | 22.5167i | −1.33377 | − | 2.31016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50000 | + | 6.06218i | −0.355371 | + | 0.615521i | −0.987181 | − | 0.159602i | \(-0.948979\pi\) |
0.631810 | + | 0.775123i | \(0.282312\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.40833 | − | 9.36750i | 0.538149 | − | 0.932101i | −0.460855 | − | 0.887475i | \(-0.652457\pi\) |
0.999004 | − | 0.0446254i | \(-0.0142094\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.0000 | −1.64345 | −0.821726 | − | 0.569883i | \(-0.806989\pi\) | ||||
−0.821726 | + | 0.569883i | \(0.806989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.60555 | − | 6.24500i | −0.339182 | − | 0.587480i | 0.645097 | − | 0.764100i | \(-0.276817\pi\) |
−0.984279 | + | 0.176620i | \(0.943483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8167 | − | 18.7350i | 1.00866 | − | 1.74705i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.60555 | −0.319941 | −0.159970 | − | 0.987122i | \(-0.551140\pi\) | ||||
−0.159970 | + | 0.987122i | \(0.551140\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.500000 | + | 0.866025i | 0.0436852 | + | 0.0756650i | 0.887041 | − | 0.461690i | \(-0.152757\pi\) |
−0.843356 | + | 0.537355i | \(0.819423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.0000 | − | 22.5167i | 1.12724 | − | 1.95244i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.8167 | + | 18.7350i | −0.924129 | + | 1.60064i | −0.131173 | + | 0.991359i | \(0.541874\pi\) |
−0.792956 | + | 0.609279i | \(0.791459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.21110 | + | 12.4900i | 0.611638 | + | 1.05939i | 0.990964 | + | 0.134125i | \(0.0428223\pi\) |
−0.379327 | + | 0.925263i | \(0.623844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.00000 | −0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.0000 | −2.15918 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.40833 | − | 9.36750i | −0.443067 | − | 0.767415i | 0.554848 | − | 0.831952i | \(-0.312776\pi\) |
−0.997915 | + | 0.0645365i | \(0.979443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.40833 | + | 9.36750i | −0.440123 | + | 0.762316i | −0.997698 | − | 0.0678106i | \(-0.978399\pi\) |
0.557575 | + | 0.830127i | \(0.311732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.50000 | + | 11.2583i | −0.522093 | + | 0.904291i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.6333 | 1.70494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4222 | 1.12963 | 0.564817 | − | 0.825216i | \(-0.308947\pi\) | ||||
0.564817 | + | 0.825216i | \(0.308947\pi\) | |||||||
\(164\) | 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 | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.40833 | + | 9.36750i | −0.411187 | + | 0.712198i | −0.995020 | − | 0.0996766i | \(-0.968219\pi\) |
0.583832 | + | 0.811874i | \(0.301553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.4222 | − | 24.9800i | −1.09022 | − | 1.88831i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | −1.12115 | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||||
−0.560576 | + | 0.828103i | \(0.689420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 18.0278 | + | 31.2250i | 1.32543 | + | 2.29571i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | + | 12.9904i | 0.539862 | + | 0.935068i | 0.998911 | + | 0.0466572i | \(0.0148568\pi\) |
−0.459049 | + | 0.888411i | \(0.651810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0278 | 1.28442 | 0.642212 | − | 0.766527i | \(-0.278017\pi\) | ||||
0.642212 | + | 0.766527i | \(0.278017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.60555 | −0.255591 | −0.127795 | − | 0.991801i | \(-0.540790\pi\) | ||||
−0.127795 | + | 0.991801i | \(0.540790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.0000 | − | 22.5167i | −0.912421 | − | 1.58036i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.0000 | − | 22.5167i | 0.907959 | − | 1.57263i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.60555 | + | 6.24500i | −0.249401 | + | 0.431976i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.60555 | + | 6.24500i | 0.248216 | + | 0.429923i | 0.963031 | − | 0.269391i | \(-0.0868223\pi\) |
−0.714815 | + | 0.699314i | \(0.753489\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.0000 | −1.77319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.0000 | −0.882498 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.21110 | + | 12.4900i | −0.482891 | + | 0.836392i | −0.999807 | − | 0.0196442i | \(-0.993747\pi\) |
0.516916 | + | 0.856036i | \(0.327080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.6333 | −1.41725 | −0.708623 | − | 0.705588i | \(-0.750683\pi\) | ||||
−0.708623 | + | 0.705588i | \(0.750683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.0555 | −2.35200 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | + | 5.19615i | 0.194054 | + | 0.336111i | 0.946590 | − | 0.322440i | \(-0.104503\pi\) |
−0.752536 | + | 0.658551i | \(0.771170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0000 | + | 19.0526i | −0.708572 | + | 1.22728i | 0.256814 | + | 0.966461i | \(0.417327\pi\) |
−0.965387 | + | 0.260822i | \(0.916006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.8167 | − | 18.7350i | 0.691051 | − | 1.19693i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.4222 | + | 24.9800i | 0.917663 | + | 1.58944i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.21110 | + | 12.4900i | 0.449816 | + | 0.779105i | 0.998374 | − | 0.0570083i | \(-0.0181561\pi\) |
−0.548557 | + | 0.836113i | \(0.684823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0278 | + | 31.2250i | −1.12019 | + | 1.94023i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.00000 | − | 15.5885i | 0.554964 | − | 0.961225i | −0.442943 | − | 0.896550i | \(-0.646065\pi\) |
0.997906 | − | 0.0646755i | \(-0.0206012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.50000 | + | 11.2583i | 0.399292 | + | 0.691594i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.6333 | −1.31901 | −0.659503 | − | 0.751702i | \(-0.729233\pi\) | ||||
−0.659503 | + | 0.751702i | \(0.729233\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.8167 | −0.657065 | −0.328532 | − | 0.944493i | \(-0.606554\pi\) | ||||
−0.328532 | + | 0.944493i | \(0.606554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | + | 6.92820i | 0.241209 | + | 0.417786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.60555 | − | 6.24500i | −0.214328 | − | 0.371227i | 0.738737 | − | 0.673994i | \(-0.235423\pi\) |
−0.953064 | + | 0.302768i | \(0.902089\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.0000 | 1.53473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8167 | − | 18.7350i | −0.631916 | − | 1.09451i | −0.987160 | − | 0.159736i | \(-0.948936\pi\) |
0.355244 | − | 0.934774i | \(-0.384398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.21110 | − | 12.4900i | 0.419847 | − | 0.727196i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.0000 | − | 22.5167i | −0.749308 | − | 1.29784i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.00000 | + | 15.5885i | 0.510343 | + | 0.883940i | 0.999928 | + | 0.0119847i | \(0.00381495\pi\) |
−0.489585 | + | 0.871956i | \(0.662852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.40833 | − | 9.36750i | 0.303762 | − | 0.526131i | −0.673223 | − | 0.739440i | \(-0.735091\pi\) |
0.976985 | + | 0.213308i | \(0.0684239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.60555 | + | 6.24500i | 0.201872 | + | 0.349653i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.0000 | 1.77504 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.0278 | − | 31.2250i | −0.993902 | − | 1.72149i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.60555 | + | 6.24500i | −0.198179 | + | 0.343256i | −0.947938 | − | 0.318455i | \(-0.896836\pi\) |
0.749759 | + | 0.661711i | \(0.230169\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.0000 | − | 22.5167i | 0.710266 | − | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0000 | − | 22.5167i | −0.708155 | − | 1.22656i | −0.965541 | − | 0.260252i | \(-0.916194\pi\) |
0.257386 | − | 0.966309i | \(-0.417139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.60555 | 0.195252 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.60555 | −0.194681 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.500000 | − | 0.866025i | −0.0268414 | − | 0.0464907i | 0.852293 | − | 0.523065i | \(-0.175212\pi\) |
−0.879134 | + | 0.476575i | \(0.841878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | − | 1.73205i | 0.0535288 | − | 0.0927146i | −0.838019 | − | 0.545640i | \(-0.816286\pi\) |
0.891548 | + | 0.452926i | \(0.149620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.60555 | − | 6.24500i | 0.191904 | − | 0.332388i | −0.753977 | − | 0.656901i | \(-0.771867\pi\) |
0.945881 | + | 0.324513i | \(0.105200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4222 | − | 24.9800i | −0.765451 | − | 1.32580i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0000 | −0.527780 | −0.263890 | − | 0.964553i | \(-0.585006\pi\) | ||||
−0.263890 | + | 0.964553i | \(0.585006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.0000 | 1.73684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.40833 | − | 9.36750i | −0.283085 | − | 0.490317i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.40833 | + | 9.36750i | −0.282312 | + | 0.488979i | −0.971954 | − | 0.235172i | \(-0.924435\pi\) |
0.689642 | + | 0.724151i | \(0.257768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.50000 | + | 11.2583i | −0.337463 | + | 0.584503i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.00000 | + | 13.8564i | 0.414224 | + | 0.717458i | 0.995347 | − | 0.0963587i | \(-0.0307196\pi\) |
−0.581122 | + | 0.813816i | \(0.697386\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.8444 | 1.48556 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4222 | 0.740819 | 0.370409 | − | 0.928869i | \(-0.379217\pi\) | ||||
0.370409 | + | 0.928869i | \(0.379217\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.00000 | + | 6.92820i | 0.204390 | + | 0.354015i | 0.949938 | − | 0.312437i | \(-0.101145\pi\) |
−0.745548 | + | 0.666452i | \(0.767812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.50000 | + | 11.2583i | −0.331271 | + | 0.573778i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.40833 | + | 9.36750i | −0.274213 | + | 0.474951i | −0.969936 | − | 0.243359i | \(-0.921751\pi\) |
0.695723 | + | 0.718310i | \(0.255084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.0000 | 2.61640 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | 0.200754 | 0.100377 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100377 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.21110 | − | 12.4900i | −0.360105 | − | 0.623721i | 0.627873 | − | 0.778316i | \(-0.283926\pi\) |
−0.987978 | + | 0.154596i | \(0.950593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.21110 | − | 12.4900i | 0.359211 | − | 0.622171i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.00000 | − | 8.66025i | 0.247841 | − | 0.429273i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.50000 | − | 6.06218i | −0.173064 | − | 0.299755i | 0.766426 | − | 0.642333i | \(-0.222033\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.4222 | 0.709670 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.4500 | 1.59291 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | + | 3.46410i | 0.0977064 | + | 0.169232i | 0.910735 | − | 0.412991i | \(-0.135516\pi\) |
−0.813029 | + | 0.582224i | \(0.802183\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | + | 27.7128i | −0.779792 | + | 1.35064i | 0.152269 | + | 0.988339i | \(0.451342\pi\) |
−0.932061 | + | 0.362301i | \(0.881991\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.0000 | −1.68199 | −0.840996 | − | 0.541041i | \(-0.818030\pi\) | ||||
−0.840996 | + | 0.541041i | \(0.818030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.6333 | + | 37.4700i | 1.03486 | + | 1.79243i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.01388 | − | 15.6125i | 0.430209 | − | 0.745144i | −0.566682 | − | 0.823937i | \(-0.691773\pi\) |
0.996891 | + | 0.0787928i | \(0.0251066\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.0000 | − | 22.5167i | −0.616259 | − | 1.06739i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.21110 | −0.340313 | −0.170156 | − | 0.985417i | \(-0.554427\pi\) | ||||
−0.170156 | + | 0.985417i | \(0.554427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.21110 | −0.339558 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.0000 | + | 45.0333i | 1.21890 | + | 2.11119i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5000 | + | 19.9186i | −0.537947 | + | 0.931752i | 0.461067 | + | 0.887365i | \(0.347467\pi\) |
−0.999014 | + | 0.0443868i | \(0.985867\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.40833 | + | 9.36750i | −0.251891 | + | 0.436288i | −0.964046 | − | 0.265734i | \(-0.914386\pi\) |
0.712156 | + | 0.702022i | \(0.247719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6194 | + | 21.8575i | 0.586475 | + | 1.01580i | 0.994690 | + | 0.102918i | \(0.0328180\pi\) |
−0.408215 | + | 0.912886i | \(0.633849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.0000 | 1.06431 | 0.532157 | − | 0.846646i | \(-0.321382\pi\) | ||||
0.532157 | + | 0.846646i | \(0.321382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0000 | 1.20057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.60555 | + | 6.24500i | 0.165783 | + | 0.287145i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8444 | − | 49.9600i | 1.32347 | − | 2.29232i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0000 | + | 36.3731i | −0.959514 | + | 1.66193i | −0.235833 | + | 0.971794i | \(0.575782\pi\) |
−0.723681 | + | 0.690134i | \(0.757551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | − | 34.6410i | −0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.2389 | −1.14604 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4222 | 0.653532 | 0.326766 | − | 0.945105i | \(-0.394041\pi\) | ||||
0.326766 | + | 0.945105i | \(0.394041\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.50000 | + | 6.06218i | 0.157953 | + | 0.273582i | 0.934130 | − | 0.356932i | \(-0.116177\pi\) |
−0.776178 | + | 0.630514i | \(0.782844\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.4222 | − | 24.9800i | 0.646924 | − | 1.12051i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8167 | + | 18.7350i | 0.484220 | + | 0.838694i | 0.999836 | − | 0.0181264i | \(-0.00577013\pi\) |
−0.515616 | + | 0.856820i | \(0.672437\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.0000 | 1.87269 | 0.936344 | − | 0.351085i | \(-0.114187\pi\) | ||||
0.936344 | + | 0.351085i | \(0.114187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.0000 | 1.73548 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.40833 | + | 9.36750i | 0.239720 | + | 0.415207i | 0.960634 | − | 0.277818i | \(-0.0896111\pi\) |
−0.720914 | + | 0.693025i | \(0.756278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.40833 | − | 9.36750i | 0.239250 | − | 0.414394i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.00000 | + | 8.66025i | 0.219900 | + | 0.380878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.2666 | −1.89554 | −0.947772 | − | 0.318947i | \(-0.896671\pi\) | ||||
−0.947772 | + | 0.318947i | \(0.896671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.4222 | + | 24.9800i | −0.624695 | + | 1.08200i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.6472 | − | 53.0825i | −1.32499 | − | 2.29496i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.00000 | −0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.60555 | + | 6.24500i | 0.154445 | + | 0.267506i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.0000 | − | 45.0333i | 1.10764 | − | 1.91848i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.0000 | + | 45.0333i | 1.10563 | + | 1.91501i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.6611 | 1.68049 | 0.840247 | − | 0.542204i | \(-0.182410\pi\) | ||||
0.840247 | + | 0.542204i | \(0.182410\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.8444 | 1.21999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.0000 | − | 22.5167i | 0.546914 | − | 0.947283i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.21110 | − | 12.4900i | 0.302305 | − | 0.523608i | −0.674353 | − | 0.738410i | \(-0.735577\pi\) |
0.976658 | + | 0.214802i | \(0.0689105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.21110 | − | 12.4900i | −0.301775 | − | 0.522690i | 0.674763 | − | 0.738035i | \(-0.264246\pi\) |
−0.976538 | + | 0.215345i | \(0.930913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.0000 | 2.00174 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.00000 | 0.249783 | 0.124892 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124892 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2250 | + | 28.1025i | 0.673126 | + | 1.16589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.80278 | − | 3.12250i | 0.0746633 | − | 0.129321i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.50000 | + | 2.59808i | −0.0619116 | + | 0.107234i | −0.895320 | − | 0.445424i | \(-0.853053\pi\) |
0.833408 | + | 0.552658i | \(0.186386\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.0000 | − | 22.5167i | −0.535656 | − | 0.927783i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.6333 | −0.888373 | −0.444187 | − | 0.895934i | \(-0.646507\pi\) | ||||
−0.444187 | + | 0.895934i | \(0.646507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.00000 | + | 12.1244i | 0.286012 | + | 0.495388i | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.50000 | − | 14.7224i | 0.346722 | − | 0.600541i | −0.638943 | − | 0.769254i | \(-0.720628\pi\) |
0.985665 | + | 0.168714i | \(0.0539613\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.0278 | + | 31.2250i | −0.732933 | + | 1.26948i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.21110 | + | 12.4900i | 0.292690 | + | 0.506953i | 0.974445 | − | 0.224627i | \(-0.0721164\pi\) |
−0.681755 | + | 0.731580i | \(0.738783\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.0000 | 1.61823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.0000 | −0.727013 | −0.363507 | − | 0.931592i | \(-0.618421\pi\) | ||||
−0.363507 | + | 0.931592i | \(0.618421\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8167 | − | 18.7350i | −0.435462 | − | 0.754242i | 0.561871 | − | 0.827225i | \(-0.310082\pi\) |
−0.997333 | + | 0.0729823i | \(0.976748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.6333 | + | 37.4700i | −0.869516 | + | 1.50605i | −0.00702402 | + | 0.999975i | \(0.502236\pi\) |
−0.862492 | + | 0.506071i | \(0.831098\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.0000 | − | 22.5167i | 0.520834 | − | 0.902111i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | + | 0.866025i | 0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.2389 | −1.00474 | −0.502372 | − | 0.864652i | \(-0.667539\pi\) | ||||
−0.502372 | + | 0.864652i | \(0.667539\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.50000 | − | 11.2583i | −0.257945 | − | 0.446773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | + | 20.7846i | −0.475457 | + | 0.823516i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0278 | + | 31.2250i | −0.712054 | + | 1.23331i | 0.252031 | + | 0.967719i | \(0.418901\pi\) |
−0.964085 | + | 0.265594i | \(0.914432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.6333 | + | 37.4700i | 0.853134 | + | 1.47767i | 0.878365 | + | 0.477990i | \(0.158635\pi\) |
−0.0252307 | + | 0.999682i | \(0.508032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.01388 | + | 15.6125i | 0.352740 | + | 0.610964i | 0.986729 | − | 0.162379i | \(-0.0519166\pi\) |
−0.633988 | + | 0.773343i | \(0.718583\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.80278 | + | 3.12250i | −0.0704403 | + | 0.122006i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5000 | − | 23.3827i | 0.525885 | − | 0.910860i | −0.473660 | − | 0.880708i | \(-0.657067\pi\) |
0.999545 | − | 0.0301523i | \(-0.00959924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 93.7443 | 3.63525 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.2666 | 1.67529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.50000 | − | 16.4545i | 0.366198 | − | 0.634274i | −0.622770 | − | 0.782405i | \(-0.713993\pi\) |
0.988968 | + | 0.148132i | \(0.0473259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.60555 | − | 6.24500i | 0.138573 | − | 0.240015i | −0.788384 | − | 0.615184i | \(-0.789082\pi\) |
0.926957 | + | 0.375169i | \(0.122415\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.6194 | − | 21.8575i | −0.484289 | − | 0.838814i | ||||
\(680\) | 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 | ||||||||
\(685\) | −78.0000 | −2.98023 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.21110 | − | 12.4900i | −0.274721 | − | 0.475831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.21110 | + | 12.4900i | −0.274323 | + | 0.475142i | −0.969964 | − | 0.243248i | \(-0.921787\pi\) |
0.695641 | + | 0.718390i | \(0.255120\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −26.0000 | + | 45.0333i | −0.986236 | + | 1.70821i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.8167 | −0.408539 | −0.204270 | − | 0.978915i | \(-0.565482\pi\) | ||||
−0.204270 | + | 0.978915i | \(0.565482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.1110 | −2.71972 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.5000 | + | 33.7750i | 0.733373 | + | 1.27024i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | + | 3.46410i | −0.0751116 | + | 0.130097i | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.8167 | − | 18.7350i | 0.405087 | − | 0.701631i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.21110 | − | 12.4900i | −0.269680 | − | 0.467099i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.00000 | 0.149175 | 0.0745874 | − | 0.997214i | \(-0.476236\pi\) | ||||
0.0745874 | + | 0.997214i | \(0.476236\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.8444 | − | 49.9600i | −1.07125 | − | 1.85547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.2250 | + | 28.1025i | −0.601751 | + | 1.04226i | 0.390805 | + | 0.920474i | \(0.372197\pi\) |
−0.992556 | + | 0.121790i | \(0.961137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | + | 39.8372i | 0.849524 | + | 1.47142i | 0.881633 | + | 0.471935i | \(0.156444\pi\) |
−0.0321090 | + | 0.999484i | \(0.510222\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.21110 | −0.265624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.8444 | −1.06106 | −0.530529 | − | 0.847667i | \(-0.678007\pi\) | ||||
−0.530529 | + | 0.847667i | \(0.678007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | − | 31.1769i | −0.660356 | − | 1.14377i | −0.980522 | − | 0.196409i | \(-0.937072\pi\) |
0.320166 | − | 0.947361i | \(-0.396261\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.5000 | − | 33.7750i | 0.714425 | − | 1.23742i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.6472 | − | 53.0825i | 1.11982 | − | 1.93959i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.4361 | + | 40.5925i | 0.855195 | + | 1.48124i | 0.876464 | + | 0.481467i | \(0.159896\pi\) |
−0.0212693 | + | 0.999774i | \(0.506771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.0000 | −1.41936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.60555 | + | 6.24500i | −0.130530 | + | 0.226084i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.00000 | + | 13.8564i | −0.288863 | + | 0.500326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50000 | + | 9.52628i | 0.198335 | + | 0.343526i | 0.947989 | − | 0.318304i | \(-0.103113\pi\) |
−0.749654 | + | 0.661830i | \(0.769780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.6333 | −0.778096 | −0.389048 | − | 0.921217i | \(-0.627196\pi\) | ||||
−0.389048 | + | 0.921217i | \(0.627196\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.8444 | −1.03612 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.0000 | + | 45.0333i | 0.931547 | + | 1.61349i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | + | 6.92820i | −0.143131 | + | 0.247911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.21110 | + | 12.4900i | −0.257375 | + | 0.445787i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.0000 | 0.924454 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.40833 | − | 9.36750i | −0.191573 | − | 0.331814i | 0.754199 | − | 0.656646i | \(-0.228025\pi\) |
−0.945772 | + | 0.324832i | \(0.894692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.50000 | + | 2.59808i | −0.0529339 | + | 0.0916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.0000 | + | 67.5500i | 1.37457 | + | 2.38082i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.4777 | −1.77470 | −0.887351 | − | 0.461095i | \(-0.847457\pi\) | ||||
−0.887351 | + | 0.461095i | \(0.847457\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.21110 | −0.253216 | −0.126608 | − | 0.991953i | \(-0.540409\pi\) | ||||
−0.126608 | + | 0.991953i | \(0.540409\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.0000 | + | 45.0333i | 0.910740 | + | 1.57745i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0000 | − | 45.0333i | 0.909625 | − | 1.57552i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.60555 | + | 6.24500i | −0.125835 | + | 0.217952i | −0.922059 | − | 0.387050i | \(-0.873494\pi\) |
0.796224 | + | 0.605002i | \(0.206828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.01388 | + | 15.6125i | 0.314204 | + | 0.544217i | 0.979268 | − | 0.202569i | \(-0.0649291\pi\) |
−0.665064 | + | 0.746786i | \(0.731596\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.0000 | −0.556375 | −0.278187 | − | 0.960527i | \(-0.589734\pi\) | ||||
−0.278187 | + | 0.960527i | \(0.589734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0000 | −1.59765 | −0.798823 | − | 0.601566i | \(-0.794544\pi\) | ||||
−0.798823 | + | 0.601566i | \(0.794544\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.60555 | + | 6.24500i | −0.124775 | + | 0.216117i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0000 | + | 34.6410i | −0.690477 | + | 1.19594i | 0.281205 | + | 0.959648i | \(0.409266\pi\) |
−0.971682 | + | 0.236293i | \(0.924067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5000 | − | 19.9186i | −0.396552 | − | 0.686848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.8167 | −0.372104 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.0555 | −1.23888 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.0000 | − | 51.9615i | −1.02839 | − | 1.78122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.0000 | − | 36.3731i | 0.719026 | − | 1.24539i | −0.242360 | − | 0.970186i | \(-0.577921\pi\) |
0.961386 | − | 0.275204i | \(-0.0887453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.4222 | − | 24.9800i | 0.492653 | − | 0.853300i | −0.507311 | − | 0.861763i | \(-0.669360\pi\) |
0.999964 | + | 0.00846275i | \(0.00269381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4222 | − | 24.9800i | −0.492079 | − | 0.852306i | 0.507879 | − | 0.861428i | \(-0.330430\pi\) |
−0.999958 | + | 0.00912203i | \(0.997096\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.0000 | 0.953131 | 0.476566 | − | 0.879139i | \(-0.341881\pi\) | ||||
0.476566 | + | 0.879139i | \(0.341881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.0000 | −1.32604 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.21110 | − | 12.4900i | −0.244620 | − | 0.423694i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4222 | + | 24.9800i | −0.488678 | + | 0.846415i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.5000 | − | 33.7750i | 0.659220 | − | 1.14180i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0000 | − | 29.4449i | −0.574049 | − | 0.994282i | −0.996144 | − | 0.0877308i | \(-0.972038\pi\) |
0.422095 | − | 0.906552i | \(-0.361295\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.2666 | −1.45769 | −0.728845 | − | 0.684679i | \(-0.759942\pi\) | ||||
−0.728845 | + | 0.684679i | \(0.759942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.4777 | 1.69871 | 0.849355 | − | 0.527822i | \(-0.176991\pi\) | ||||
0.849355 | + | 0.527822i | \(0.176991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0000 | − | 31.1769i | −0.604381 | − | 1.04682i | −0.992149 | − | 0.125061i | \(-0.960087\pi\) |
0.387768 | − | 0.921757i | \(-0.373246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.50000 | − | 11.2583i | 0.218003 | − | 0.377592i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0555 | − | 62.4500i | 1.20655 | − | 2.08981i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.0416 | − | 46.8375i | −0.903902 | − | 1.56560i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.0000 | −0.867149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.4222 | + | 24.9800i | 0.479410 | + | 0.830363i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.60555 | − | 6.24500i | 0.119720 | − | 0.207362i | −0.799936 | − | 0.600085i | \(-0.795134\pi\) |
0.919657 | + | 0.392723i | \(0.128467\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.0000 | − | 25.9808i | 0.496972 | − | 0.860781i | −0.503022 | − | 0.864274i | \(-0.667778\pi\) |
0.999994 | + | 0.00349271i | \(0.00111177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | − | 7.79423i | −0.148928 | − | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.60555 | −0.119066 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.0833 | 1.78404 | 0.892021 | − | 0.451994i | \(-0.149287\pi\) | ||||
0.892021 | + | 0.451994i | \(0.149287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | + | 27.7128i | 0.526646 | + | 0.912178i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | + | 69.2820i | −1.31519 | + | 2.27798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6333 | + | 37.4700i | −0.709766 | + | 1.22935i | 0.255178 | + | 0.966894i | \(0.417866\pi\) |
−0.964944 | + | 0.262456i | \(0.915467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6333 | + | 37.4700i | 0.709003 | + | 1.22803i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.6194 | − | 21.8575i | −0.411382 | − | 0.712534i | 0.583659 | − | 0.811999i | \(-0.301620\pi\) |
−0.995041 | + | 0.0994646i | \(0.968287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.6333 | + | 37.4700i | −0.704477 | + | 1.22019i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5000 | − | 23.3827i | 0.438691 | − | 0.759835i | −0.558898 | − | 0.829237i | \(-0.688776\pi\) |
0.997589 | + | 0.0694014i | \(0.0221089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | + | 10.3923i | 0.194768 | + | 0.337348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.2666 | 1.40154 | 0.700772 | − | 0.713386i | \(-0.252839\pi\) | ||||
0.700772 | + | 0.713386i | \(0.252839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.2666 | −1.40007 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.0000 | − | 67.5500i | −1.25938 | − | 2.18130i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.00000 | − | 15.5885i | 0.290323 | − | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.0416 | + | 46.8375i | −0.870501 | + | 1.50775i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.40833 | + | 9.36750i | 0.173920 | + | 0.301238i | 0.939787 | − | 0.341761i | \(-0.111023\pi\) |
−0.765867 | + | 0.642999i | \(0.777690\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.0000 | −0.802288 | −0.401144 | − | 0.916015i | \(-0.631387\pi\) | ||||
−0.401144 | + | 0.916015i | \(0.631387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.0000 | −1.66704 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0278 | + | 31.2250i | 0.576759 | + | 0.998976i | 0.995848 | + | 0.0910308i | \(0.0290162\pi\) |
−0.419089 | + | 0.907945i | \(0.637650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.60555 | + | 6.24500i | −0.115234 | + | 0.199591i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.5000 | + | 56.2917i | 1.03554 | + | 1.79360i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.2666 | 1.37580 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.2944 | 1.94708 | 0.973540 | − | 0.228517i | \(-0.0733876\pi\) | ||||
0.973540 | + | 0.228517i | \(0.0733876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.50000 | − | 11.2583i | −0.206064 | − | 0.356913i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0000 | + | 31.1769i | −0.570066 | + | 0.987383i | 0.426493 | + | 0.904491i | \(0.359749\pi\) |
−0.996559 | + | 0.0828918i | \(0.973584\pi\) | |||||||
\(998\) | 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 | 2592.2.i.bc.865.2 | 4 | ||
3.2 | odd | 2 | 2592.2.i.bb.865.1 | 4 | |||
4.3 | odd | 2 | 2592.2.i.bb.865.2 | 4 | |||
9.2 | odd | 6 | 864.2.a.n.1.2 | yes | 2 | ||
9.4 | even | 3 | inner | 2592.2.i.bc.1729.2 | 4 | ||
9.5 | odd | 6 | 2592.2.i.bb.1729.1 | 4 | |||
9.7 | even | 3 | 864.2.a.m.1.1 | ✓ | 2 | ||
12.11 | even | 2 | inner | 2592.2.i.bc.865.1 | 4 | ||
36.7 | odd | 6 | 864.2.a.n.1.1 | yes | 2 | ||
36.11 | even | 6 | 864.2.a.m.1.2 | yes | 2 | ||
36.23 | even | 6 | inner | 2592.2.i.bc.1729.1 | 4 | ||
36.31 | odd | 6 | 2592.2.i.bb.1729.2 | 4 | |||
72.11 | even | 6 | 1728.2.a.bd.1.1 | 2 | |||
72.29 | odd | 6 | 1728.2.a.bc.1.1 | 2 | |||
72.43 | odd | 6 | 1728.2.a.bc.1.2 | 2 | |||
72.61 | even | 6 | 1728.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.a.m.1.1 | ✓ | 2 | 9.7 | even | 3 | ||
864.2.a.m.1.2 | yes | 2 | 36.11 | even | 6 | ||
864.2.a.n.1.1 | yes | 2 | 36.7 | odd | 6 | ||
864.2.a.n.1.2 | yes | 2 | 9.2 | odd | 6 | ||
1728.2.a.bc.1.1 | 2 | 72.29 | odd | 6 | |||
1728.2.a.bc.1.2 | 2 | 72.43 | odd | 6 | |||
1728.2.a.bd.1.1 | 2 | 72.11 | even | 6 | |||
1728.2.a.bd.1.2 | 2 | 72.61 | even | 6 | |||
2592.2.i.bb.865.1 | 4 | 3.2 | odd | 2 | |||
2592.2.i.bb.865.2 | 4 | 4.3 | odd | 2 | |||
2592.2.i.bb.1729.1 | 4 | 9.5 | odd | 6 | |||
2592.2.i.bb.1729.2 | 4 | 36.31 | odd | 6 | |||
2592.2.i.bc.865.1 | 4 | 12.11 | even | 2 | inner | ||
2592.2.i.bc.865.2 | 4 | 1.1 | even | 1 | trivial | ||
2592.2.i.bc.1729.1 | 4 | 36.23 | even | 6 | inner | ||
2592.2.i.bc.1729.2 | 4 | 9.4 | even | 3 | inner |