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 | 1729.2 | ||
Root | \(-0.651388 + 1.12824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1729 |
Dual form | 2592.2.i.bb.865.2 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | −0.109235 | − | 0.994016i | \(-0.534840\pi\) |
0.915460 | − | 0.402408i | \(-0.131827\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80278 | + | 3.12250i | 0.681385 | + | 1.18019i | 0.974558 | + | 0.224134i | \(0.0719554\pi\) |
−0.293173 | + | 0.956059i | \(0.594711\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | 0.780750 | − | 0.624844i | \(-0.214837\pi\) |
−0.931505 | + | 0.363727i | \(0.881504\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | 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 | \(-0.189949\pi\) | ||||
0.827170 | + | 0.561951i | \(0.189949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | \(-0.618211\pi\) |
0.988436 | − | 0.151642i | \(-0.0484560\pi\) | |||||||
\(24\) | 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 | −0.978035 | − | 0.208443i | \(-0.933160\pi\) |
0.308500 | − | 0.951224i | \(-0.400173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.80278 | + | 3.12250i | −0.323788 | + | 0.560817i | −0.981266 | − | 0.192656i | \(-0.938290\pi\) |
0.657478 | + | 0.753474i | \(0.271623\pi\) | |||||||
\(32\) | 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 | 0.434132 | + | 0.900849i | \(0.357055\pi\) |
−0.997224 | + | 0.0744555i | \(0.976278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.60555 | + | 6.24500i | 0.549841 | + | 0.952353i | 0.998285 | + | 0.0585421i | \(0.0186452\pi\) |
−0.448444 | + | 0.893811i | \(0.648021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.00000 | + | 8.66025i | 0.729325 | + | 1.26323i | 0.957169 | + | 0.289530i | \(0.0934991\pi\) |
−0.227844 | + | 0.973698i | \(0.573168\pi\) | |||||||
\(48\) | 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 | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 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 | \(-0.688139\pi\) |
0.997726 | + | 0.0674052i | \(0.0214720\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 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 | −0.911946 | − | 0.410311i | \(-0.865420\pi\) |
0.100633 | − | 0.994924i | \(-0.467913\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50000 | − | 7.79423i | −0.493939 | − | 0.855528i | 0.506036 | − | 0.862512i | \(-0.331110\pi\) |
−0.999976 | + | 0.00698436i | \(0.997777\pi\) | |||||||
\(84\) | 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 | 0.631810 | − | 0.775123i | \(-0.282312\pi\) |
−0.987181 | + | 0.159602i | \(0.948979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.40833 | + | 9.36750i | 0.538149 | + | 0.932101i | 0.999004 | + | 0.0446254i | \(0.0142094\pi\) |
−0.460855 | + | 0.887475i | \(0.652457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.0000 | 1.64345 | 0.821726 | − | 0.569883i | \(-0.193011\pi\) | ||||
0.821726 | + | 0.569883i | \(0.193011\pi\) | |||||||
\(108\) | 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 | −0.984279 | − | 0.176620i | \(-0.943483\pi\) |
0.645097 | + | 0.764100i | \(0.276817\pi\) | |||||||
\(114\) | 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 | \(-0.448860\pi\) | ||||
0.159970 | + | 0.987122i | \(0.448860\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | 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 | −0.792956 | − | 0.609279i | \(-0.791459\pi\) |
−0.131173 | − | 0.991359i | \(-0.541874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.21110 | + | 12.4900i | −0.611638 | + | 1.05939i | 0.379327 | + | 0.925263i | \(0.376156\pi\) |
−0.990964 | + | 0.134125i | \(0.957178\pi\) | |||||||
\(140\) | 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 | −0.997915 | − | 0.0645365i | \(-0.979443\pi\) |
0.554848 | + | 0.831952i | \(0.312776\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.40833 | + | 9.36750i | 0.440123 | + | 0.762316i | 0.997698 | − | 0.0678106i | \(-0.0216014\pi\) |
−0.557575 | + | 0.830127i | \(0.688268\pi\) | |||||||
\(152\) | 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 | −0.775113 | − | 0.631822i | \(-0.782307\pi\) |
0.934731 | + | 0.355357i | \(0.115641\pi\) | |||||||
\(158\) | 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 | \(-0.691053\pi\) | ||||
−0.564817 | + | 0.825216i | \(0.691053\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | + | 1.73205i | −0.0773823 | + | 0.134030i | −0.902120 | − | 0.431486i | \(-0.857990\pi\) |
0.824737 | + | 0.565516i | \(0.191323\pi\) | |||||||
\(168\) | 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 | 0.583832 | − | 0.811874i | \(-0.301553\pi\) |
−0.995020 | + | 0.0996766i | \(0.968219\pi\) | |||||||
\(174\) | 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 | \(-0.310580\pi\) | ||||
0.560576 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(180\) | 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 | \(-0.0237173\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | 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 | \(-0.459210\pi\) | ||||
0.127795 | + | 0.991801i | \(0.459210\pi\) | |||||||
\(200\) | 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 | \(-0.913178\pi\) |
0.714815 | + | 0.699314i | \(0.246511\pi\) | |||||||
\(212\) | 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 | \(-0.00625334\pi\) |
−0.516916 | + | 0.856036i | \(0.672920\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 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 | \(-0.895497\pi\) |
0.752536 | + | 0.658551i | \(0.228830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0000 | − | 19.0526i | −0.708572 | − | 1.22728i | −0.965387 | − | 0.260822i | \(-0.916006\pi\) |
0.256814 | − | 0.966461i | \(-0.417327\pi\) | |||||||
\(242\) | 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 | \(-0.773547\pi\) | ||||
−0.757433 | + | 0.652913i | \(0.773547\pi\) | |||||||
\(252\) | 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 | −0.548557 | − | 0.836113i | \(-0.684823\pi\) |
0.998374 | + | 0.0570083i | \(0.0181561\pi\) | |||||||
\(258\) | 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 | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | 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 | \(-0.393446\pi\) | ||||
0.328532 | + | 0.944493i | \(0.393446\pi\) | |||||||
\(272\) | 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 | 0.960810 | − | 0.277207i | \(-0.0894088\pi\) |
−0.720473 | + | 0.693482i | \(0.756075\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.60555 | − | 6.24500i | 0.214328 | − | 0.371227i | −0.738737 | − | 0.673994i | \(-0.764577\pi\) |
0.953064 | + | 0.302768i | \(0.0979106\pi\) | |||||||
\(284\) | 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 | 0.355244 | + | 0.934774i | \(0.384398\pi\) |
−0.987160 | + | 0.159736i | \(0.948936\pi\) | |||||||
\(294\) | 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 | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.500000 | − | 0.866025i | −0.0282617 | − | 0.0489506i | 0.851549 | − | 0.524276i | \(-0.175664\pi\) |
−0.879810 | + | 0.475325i | \(0.842331\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.40833 | + | 9.36750i | 0.303762 | + | 0.526131i | 0.976985 | − | 0.213308i | \(-0.0684239\pi\) |
−0.673223 | + | 0.739440i | \(0.735091\pi\) | |||||||
\(318\) | 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 | \(-0.103164\pi\) |
−0.749759 | + | 0.661711i | \(0.769831\pi\) | |||||||
\(332\) | 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 | 0.257386 | + | 0.966309i | \(0.417139\pi\) |
−0.965541 | + | 0.260252i | \(0.916194\pi\) | |||||||
\(338\) | 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 | \(-0.824788\pi\) |
0.879134 | + | 0.476575i | \(0.158122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.00000 | + | 1.73205i | 0.0535288 | + | 0.0927146i | 0.891548 | − | 0.452926i | \(-0.149620\pi\) |
−0.838019 | + | 0.545640i | \(0.816286\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.60555 | + | 6.24500i | 0.191904 | + | 0.332388i | 0.945881 | − | 0.324513i | \(-0.105200\pi\) |
−0.753977 | + | 0.656901i | \(0.771867\pi\) | |||||||
\(354\) | 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 | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 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 | \(-0.0755652\pi\) |
−0.689642 | + | 0.724151i | \(0.742232\pi\) | |||||||
\(368\) | 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 | −0.581122 | − | 0.813816i | \(-0.697386\pi\) |
0.995347 | + | 0.0963587i | \(0.0307196\pi\) | |||||||
\(374\) | 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 | \(-0.620783\pi\) | ||||
−0.370409 | + | 0.928869i | \(0.620783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.00000 | + | 6.92820i | −0.204390 | + | 0.354015i | −0.949938 | − | 0.312437i | \(-0.898855\pi\) |
0.745548 | + | 0.666452i | \(0.232188\pi\) | |||||||
\(384\) | 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 | 0.695723 | − | 0.718310i | \(-0.255084\pi\) |
−0.969936 | + | 0.243359i | \(0.921751\pi\) | |||||||
\(390\) | 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 | −0.987978 | − | 0.154596i | \(-0.950593\pi\) |
0.627873 | + | 0.778316i | \(0.283926\pi\) | |||||||
\(402\) | 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 | −0.939490 | − | 0.342578i | \(-0.888700\pi\) |
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 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 | \(-0.864484\pi\) |
0.813029 | + | 0.582224i | \(0.197817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | − | 27.7128i | −0.779792 | − | 1.35064i | −0.932061 | − | 0.362301i | \(-0.881991\pi\) |
0.152269 | − | 0.988339i | \(-0.451342\pi\) | |||||||
\(422\) | 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 | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 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 | \(-0.308227\pi\) |
−0.996891 | + | 0.0787928i | \(0.974893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | − | 10.3923i | −0.285069 | − | 0.493753i | 0.687557 | − | 0.726130i | \(-0.258683\pi\) |
−0.972626 | + | 0.232377i | \(0.925350\pi\) | |||||||
\(444\) | 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 | −0.999014 | − | 0.0443868i | \(-0.985867\pi\) |
0.461067 | − | 0.887365i | \(-0.347467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.40833 | − | 9.36750i | −0.251891 | − | 0.436288i | 0.712156 | − | 0.702022i | \(-0.247719\pi\) |
−0.964046 | + | 0.265734i | \(0.914386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6194 | + | 21.8575i | −0.586475 | + | 1.01580i | 0.408215 | + | 0.912886i | \(0.366151\pi\) |
−0.994690 | + | 0.102918i | \(0.967182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.0000 | −1.06431 | −0.532157 | − | 0.846646i | \(-0.678618\pi\) | ||||
−0.532157 | + | 0.846646i | \(0.678618\pi\) | |||||||
\(468\) | 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 | 0.723681 | + | 0.690134i | \(0.242449\pi\) |
0.235833 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(480\) | 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 | \(-0.605959\pi\) | ||||
−0.326766 | + | 0.945105i | \(0.605959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.50000 | + | 6.06218i | −0.157953 | + | 0.273582i | −0.934130 | − | 0.356932i | \(-0.883823\pi\) |
0.776178 | + | 0.630514i | \(0.217156\pi\) | |||||||
\(492\) | 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 | \(-0.994230\pi\) |
0.515616 | + | 0.856820i | \(0.327563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.0000 | −1.87269 | −0.936344 | − | 0.351085i | \(-0.885813\pi\) | ||||
−0.936344 | + | 0.351085i | \(0.885813\pi\) | |||||||
\(504\) | 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 | −0.720914 | − | 0.693025i | \(-0.756278\pi\) |
0.960634 | + | 0.277818i | \(0.0896111\pi\) | |||||||
\(510\) | 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 | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(548\) | 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 | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | 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 | 0.976658 | − | 0.214802i | \(-0.0689105\pi\) |
−0.674353 | + | 0.738410i | \(0.735577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.21110 | − | 12.4900i | 0.301775 | − | 0.522690i | −0.674763 | − | 0.738035i | \(-0.735754\pi\) |
0.976538 | + | 0.215345i | \(0.0690874\pi\) | |||||||
\(572\) | 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 | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | 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 | \(-0.925663\pi\) |
0.686842 | + | 0.726807i | \(0.258996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.50000 | + | 14.7224i | 0.346722 | + | 0.600541i | 0.985665 | − | 0.168714i | \(-0.0539613\pi\) |
−0.638943 | + | 0.769254i | \(0.720628\pi\) | |||||||
\(602\) | 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 | \(-0.927884\pi\) |
0.681755 | + | 0.731580i | \(0.261217\pi\) | |||||||
\(608\) | 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 | −0.997333 | − | 0.0729823i | \(-0.976748\pi\) |
0.561871 | + | 0.827225i | \(0.310082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6333 | + | 37.4700i | 0.869516 | + | 1.50605i | 0.862492 | + | 0.506071i | \(0.168902\pi\) |
0.00702402 | + | 0.999975i | \(0.497764\pi\) | |||||||
\(620\) | 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 | \(-0.332461\pi\) | ||||
0.502372 | + | 0.864652i | \(0.332461\pi\) | |||||||
\(632\) | 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 | −0.964085 | − | 0.265594i | \(-0.914432\pi\) |
0.252031 | − | 0.967719i | \(-0.418901\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6333 | + | 37.4700i | −0.853134 | + | 1.47767i | 0.0252307 | + | 0.999682i | \(0.491968\pi\) |
−0.878365 | + | 0.477990i | \(0.841365\pi\) | |||||||
\(644\) | 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 | −0.633988 | − | 0.773343i | \(-0.718583\pi\) |
0.986729 | + | 0.162379i | \(0.0519166\pi\) | |||||||
\(654\) | 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 | −0.999545 | − | 0.0301523i | \(-0.990401\pi\) |
0.473660 | − | 0.880708i | \(-0.342933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | + | 12.1244i | −0.272268 | + | 0.471583i | −0.969442 | − | 0.245319i | \(-0.921107\pi\) |
0.697174 | + | 0.716902i | \(0.254441\pi\) | |||||||
\(662\) | 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 | 0.988968 | − | 0.148132i | \(-0.0473259\pi\) |
−0.622770 | + | 0.782405i | \(0.713993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.60555 | + | 6.24500i | 0.138573 | + | 0.240015i | 0.926957 | − | 0.375169i | \(-0.122415\pi\) |
−0.788384 | + | 0.615184i | \(0.789082\pi\) | |||||||
\(678\) | 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 | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 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 | \(-0.0782128\pi\) |
−0.695641 | + | 0.718390i | \(0.744880\pi\) | |||||||
\(692\) | 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 | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 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 | \(-0.523764\pi\) | ||||
−0.0745874 | + | 0.997214i | \(0.523764\pi\) | |||||||
\(720\) | 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 | 0.992556 | + | 0.121790i | \(0.0388635\pi\) |
−0.390805 | + | 0.920474i | \(0.627803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0000 | − | 39.8372i | 0.849524 | − | 1.47142i | −0.0321090 | − | 0.999484i | \(-0.510222\pi\) |
0.881633 | − | 0.471935i | \(-0.156444\pi\) | |||||||
\(734\) | 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 | \(-0.321993\pi\) | ||||
0.530529 | + | 0.847667i | \(0.321993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | − | 31.1769i | 0.660356 | − | 1.14377i | −0.320166 | − | 0.947361i | \(-0.603739\pi\) |
0.980522 | − | 0.196409i | \(-0.0629279\pi\) | |||||||
\(744\) | 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 | 0.0212693 | + | 0.999774i | \(0.493229\pi\) |
−0.876464 | + | 0.481467i | \(0.840104\pi\) | |||||||
\(752\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 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 | −0.749654 | − | 0.661830i | \(-0.769780\pi\) |
0.947989 | + | 0.318304i | \(0.103113\pi\) | |||||||
\(770\) | 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 | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(788\) | 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 | −0.945772 | − | 0.324832i | \(-0.894692\pi\) |
0.754199 | + | 0.656646i | \(0.228025\pi\) | |||||||
\(798\) | 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 | \(-0.459591\pi\) | ||||
0.126608 | + | 0.991953i | \(0.459591\pi\) | |||||||
\(812\) | 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 | 0.796224 | − | 0.605002i | \(-0.206828\pi\) |
−0.922059 | + | 0.387050i | \(0.873494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.01388 | + | 15.6125i | −0.314204 | + | 0.544217i | −0.979268 | − | 0.202569i | \(-0.935071\pi\) |
0.665064 | + | 0.746786i | \(0.268404\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0000 | 0.556375 | 0.278187 | − | 0.960527i | \(-0.410266\pi\) | ||||
0.278187 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(828\) | 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 | 0.971682 | + | 0.236293i | \(0.0759325\pi\) |
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(840\) | 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 | 0.961386 | + | 0.275204i | \(0.0887453\pi\) |
−0.242360 | + | 0.970186i | \(0.577921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.4222 | + | 24.9800i | 0.492653 | + | 0.853300i | 0.999964 | − | 0.00846275i | \(-0.00269381\pi\) |
−0.507311 | + | 0.861763i | \(0.669360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4222 | − | 24.9800i | 0.492079 | − | 0.852306i | −0.507879 | − | 0.861428i | \(-0.669570\pi\) |
0.999958 | + | 0.00912203i | \(0.00290367\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.0000 | −0.953131 | −0.476566 | − | 0.879139i | \(-0.658119\pi\) | ||||
−0.476566 | + | 0.879139i | \(0.658119\pi\) | |||||||
\(864\) | 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 | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | 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 | \(-0.823009\pi\) | ||||
−0.849355 | + | 0.527822i | \(0.823009\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0000 | − | 31.1769i | 0.604381 | − | 1.04682i | −0.387768 | − | 0.921757i | \(-0.626754\pi\) |
0.992149 | − | 0.125061i | \(-0.0399128\pi\) | |||||||
\(888\) | 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 | \(-0.204866\pi\) |
−0.919657 | + | 0.392723i | \(0.871533\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | − | 25.9808i | −0.496972 | − | 0.860781i | 0.503022 | − | 0.864274i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349271i | \(0.998888\pi\) | |||||||
\(912\) | 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 | \(-0.850713\pi\) | ||||
−0.892021 | + | 0.451994i | \(0.850713\pi\) | |||||||
\(920\) | 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 | −0.964944 | − | 0.262456i | \(-0.915467\pi\) |
0.255178 | − | 0.966894i | \(-0.417866\pi\) | |||||||
\(930\) | 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 | −0.995041 | − | 0.0994646i | \(-0.968287\pi\) |
0.583659 | + | 0.811999i | \(0.301620\pi\) | |||||||
\(942\) | 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 | \(-0.311224\pi\) |
−0.997589 | + | 0.0694014i | \(0.977891\pi\) | |||||||
\(948\) | 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 | \(-0.888977\pi\) |
0.765867 | + | 0.642999i | \(0.222310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.0000 | 0.802288 | 0.401144 | − | 0.916015i | \(-0.368613\pi\) | ||||
0.401144 | + | 0.916015i | \(0.368613\pi\) | |||||||
\(972\) | 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 | −0.419089 | − | 0.907945i | \(-0.637650\pi\) |
0.995848 | − | 0.0910308i | \(-0.0290162\pi\) | |||||||
\(978\) | 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 | \(-0.197171\pi\) |
−0.909894 | + | 0.414840i | \(0.863838\pi\) | |||||||
\(984\) | 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 | \(-0.926612\pi\) | ||||
−0.973540 | + | 0.228517i | \(0.926612\pi\) | |||||||
\(992\) | 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 | −0.996559 | − | 0.0828918i | \(-0.973584\pi\) |
0.426493 | − | 0.904491i | \(-0.359749\pi\) | |||||||
\(998\) | 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.bb.1729.2 | 4 | ||
3.2 | odd | 2 | 2592.2.i.bc.1729.1 | 4 | |||
4.3 | odd | 2 | 2592.2.i.bc.1729.2 | 4 | |||
9.2 | odd | 6 | 2592.2.i.bc.865.1 | 4 | |||
9.4 | even | 3 | 864.2.a.n.1.1 | yes | 2 | ||
9.5 | odd | 6 | 864.2.a.m.1.2 | yes | 2 | ||
9.7 | even | 3 | inner | 2592.2.i.bb.865.2 | 4 | ||
12.11 | even | 2 | inner | 2592.2.i.bb.1729.1 | 4 | ||
36.7 | odd | 6 | 2592.2.i.bc.865.2 | 4 | |||
36.11 | even | 6 | inner | 2592.2.i.bb.865.1 | 4 | ||
36.23 | even | 6 | 864.2.a.n.1.2 | yes | 2 | ||
36.31 | odd | 6 | 864.2.a.m.1.1 | ✓ | 2 | ||
72.5 | odd | 6 | 1728.2.a.bd.1.1 | 2 | |||
72.13 | even | 6 | 1728.2.a.bc.1.2 | 2 | |||
72.59 | even | 6 | 1728.2.a.bc.1.1 | 2 | |||
72.67 | odd | 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 | 36.31 | odd | 6 | ||
864.2.a.m.1.2 | yes | 2 | 9.5 | odd | 6 | ||
864.2.a.n.1.1 | yes | 2 | 9.4 | even | 3 | ||
864.2.a.n.1.2 | yes | 2 | 36.23 | even | 6 | ||
1728.2.a.bc.1.1 | 2 | 72.59 | even | 6 | |||
1728.2.a.bc.1.2 | 2 | 72.13 | even | 6 | |||
1728.2.a.bd.1.1 | 2 | 72.5 | odd | 6 | |||
1728.2.a.bd.1.2 | 2 | 72.67 | odd | 6 | |||
2592.2.i.bb.865.1 | 4 | 36.11 | even | 6 | inner | ||
2592.2.i.bb.865.2 | 4 | 9.7 | even | 3 | inner | ||
2592.2.i.bb.1729.1 | 4 | 12.11 | even | 2 | inner | ||
2592.2.i.bb.1729.2 | 4 | 1.1 | even | 1 | trivial | ||
2592.2.i.bc.865.1 | 4 | 9.2 | odd | 6 | |||
2592.2.i.bc.865.2 | 4 | 36.7 | odd | 6 | |||
2592.2.i.bc.1729.1 | 4 | 3.2 | odd | 2 | |||
2592.2.i.bc.1729.2 | 4 | 4.3 | odd | 2 |