Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1456,2,Mod(417,1456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1456.417");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1456 = 2^{4} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1456.r (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: | \(11.6262185343\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 417.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1456.417 |
Dual form | 1456.2.r.g.625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).
\(n\) | \(561\) | \(911\) | \(1093\) | \(1249\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.50000 | + | 6.06218i | −0.848875 | + | 1.47029i | 0.0333386 | + | 0.999444i | \(0.489386\pi\) |
−0.882213 | + | 0.470850i | \(0.843947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 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 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50000 | + | 6.06218i | 0.510527 | + | 0.884260i | 0.999926 | + | 0.0121990i | \(0.00388317\pi\) |
−0.489398 | + | 0.872060i | \(0.662783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.50000 | + | 2.59808i | −0.944911 | + | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00000 | 0.593391 | 0.296695 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296695 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 12.1244i | −0.819288 | + | 1.41905i | 0.0869195 | + | 0.996215i | \(0.472298\pi\) |
−0.906208 | + | 0.422833i | \(0.861036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | − | 5.19615i | −0.683763 | − | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | − | 5.19615i | −0.337526 | − | 0.584613i | 0.646440 | − | 0.762964i | \(-0.276257\pi\) |
−0.983967 | + | 0.178352i | \(0.942924\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.500000 | − | 2.59808i | 0.0524142 | − | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00000 | −0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.00000 | − | 12.1244i | 0.696526 | − | 1.20642i | −0.273138 | − | 0.961975i | \(-0.588061\pi\) |
0.969664 | − | 0.244443i | \(-0.0786053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | + | 6.92820i | 0.386695 | + | 0.669775i | 0.992003 | − | 0.126217i | \(-0.0402834\pi\) |
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50000 | − | 2.59808i | −0.138675 | − | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0000 | − | 12.1244i | −1.28338 | − | 1.11144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.00000 | + | 12.1244i | 0.611593 | + | 1.05931i | 0.990972 | + | 0.134069i | \(0.0428042\pi\) |
−0.379379 | + | 0.925241i | \(0.623862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.5000 | − | 6.06218i | 1.51744 | − | 0.525657i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | + | 3.46410i | −0.170872 | + | 0.295958i | −0.938725 | − | 0.344668i | \(-0.887992\pi\) |
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.50000 | − | 2.59808i | 0.125436 | − | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.50000 | + | 2.59808i | −0.122068 | + | 0.211428i | −0.920583 | − | 0.390547i | \(-0.872286\pi\) |
0.798515 | + | 0.601975i | \(0.205619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.0000 | −1.69775 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | + | 6.06218i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | − | 5.19615i | 1.18217 | − | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.50000 | − | 11.2583i | −0.509119 | − | 0.881820i | −0.999944 | − | 0.0105623i | \(-0.996638\pi\) |
0.490825 | − | 0.871258i | \(-0.336695\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.00000 | 0.541676 | 0.270838 | − | 0.962625i | \(-0.412699\pi\) | ||||
0.270838 | + | 0.962625i | \(0.412699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5000 | − | 18.1865i | 0.802955 | − | 1.39076i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.50000 | − | 6.06218i | −0.266100 | − | 0.460899i | 0.701751 | − | 0.712422i | \(-0.252402\pi\) |
−0.967851 | + | 0.251523i | \(0.919068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 8.66025i | 0.755929 | + | 0.654654i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.00000 | + | 8.66025i | −0.373718 | + | 0.647298i | −0.990134 | − | 0.140122i | \(-0.955250\pi\) |
0.616417 | + | 0.787420i | \(0.288584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5000 | − | 18.1865i | −0.767836 | − | 1.32993i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | − | 17.3205i | −0.723575 | − | 1.25327i | −0.959558 | − | 0.281511i | \(-0.909164\pi\) |
0.235983 | − | 0.971757i | \(-0.424169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | + | 12.1244i | −0.496217 | + | 0.859473i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.50000 | − | 12.9904i | 0.175466 | − | 0.911746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | − | 15.5885i | 0.625543 | − | 1.08347i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0000 | 1.45260 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.50000 | − | 6.06218i | 0.235435 | − | 0.407786i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0000 | −1.40626 | −0.703132 | − | 0.711059i | \(-0.748216\pi\) | ||||
−0.703132 | + | 0.711059i | \(0.748216\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0000 | + | 24.2487i | −0.929213 | + | 1.60944i | −0.144571 | + | 0.989494i | \(0.546180\pi\) |
−0.784642 | + | 0.619949i | \(0.787153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | − | 12.1244i | −0.462573 | − | 0.801200i | 0.536515 | − | 0.843891i | \(-0.319740\pi\) |
−0.999088 | + | 0.0426906i | \(0.986407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5000 | + | 23.3827i | 0.884414 | + | 1.53185i | 0.846383 | + | 0.532574i | \(0.178775\pi\) |
0.0380310 | + | 0.999277i | \(0.487891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0000 | 1.22901 | 0.614504 | − | 0.788914i | \(-0.289356\pi\) | ||||
0.614504 | + | 0.788914i | \(0.289356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | + | 24.2487i | −0.901819 | + | 1.56200i | −0.0766885 | + | 0.997055i | \(0.524435\pi\) |
−0.825131 | + | 0.564942i | \(0.808899\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.50000 | + | 6.06218i | 0.222700 | + | 0.385727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0000 | 0.883672 | 0.441836 | − | 0.897096i | \(-0.354327\pi\) | ||||
0.441836 | + | 0.897096i | \(0.354327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00000 | + | 12.1244i | 0.436648 | + | 0.756297i | 0.997429 | − | 0.0716680i | \(-0.0228322\pi\) |
−0.560781 | + | 0.827964i | \(0.689499\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | − | 6.92820i | 1.24274 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.50000 | − | 12.9904i | −0.464238 | − | 0.804084i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5000 | − | 18.1865i | 0.640196 | − | 1.10885i | −0.345192 | − | 0.938532i | \(-0.612186\pi\) |
0.985389 | − | 0.170321i | \(-0.0544803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50000 | − | 6.06218i | −0.212610 | − | 0.368251i | 0.739921 | − | 0.672694i | \(-0.234863\pi\) |
−0.952531 | + | 0.304443i | \(0.901530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.50000 | + | 12.9904i | 0.452267 | + | 0.783349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.50000 | − | 14.7224i | 0.510716 | − | 0.884585i | −0.489207 | − | 0.872167i | \(-0.662714\pi\) |
0.999923 | − | 0.0124177i | \(-0.00395278\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | + | 12.1244i | −0.416107 | + | 0.720718i | −0.995544 | − | 0.0942988i | \(-0.969939\pi\) |
0.579437 | + | 0.815017i | \(0.303272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | − | 27.7128i | −0.941176 | − | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.00000 | + | 5.19615i | 0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 5.19615i | 0.0576390 | − | 0.299501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.0000 | −1.19853 | −0.599267 | − | 0.800549i | \(-0.704541\pi\) | ||||
−0.599267 | + | 0.800549i | \(0.704541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.00000 | + | 12.1244i | 0.395663 | + | 0.685309i | 0.993186 | − | 0.116543i | \(-0.0371814\pi\) |
−0.597522 | + | 0.801852i | \(0.703848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.50000 | − | 12.9904i | 0.419919 | − | 0.727322i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.0000 | 2.72643 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.50000 | + | 4.33013i | −0.138675 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.5000 | + | 6.06218i | −0.964806 | + | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | − | 17.3205i | −0.549650 | − | 0.952021i | −0.998298 | − | 0.0583130i | \(-0.981428\pi\) |
0.448649 | − | 0.893708i | \(-0.351905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | − | 20.7846i | 0.657596 | − | 1.13899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.00000 | + | 12.1244i | −0.372572 | + | 0.645314i | −0.989960 | − | 0.141344i | \(-0.954858\pi\) |
0.617388 | + | 0.786659i | \(0.288191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | + | 6.92820i | 0.211112 | + | 0.365657i | 0.952063 | − | 0.305903i | \(-0.0989582\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | − | 12.1244i | 0.365397 | − | 0.632886i | −0.623443 | − | 0.781869i | \(-0.714267\pi\) |
0.988840 | + | 0.148983i | \(0.0475999\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 5.19615i | 0.311504 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.50000 | − | 12.9904i | −0.388335 | − | 0.672616i | 0.603890 | − | 0.797067i | \(-0.293616\pi\) |
−0.992226 | + | 0.124451i | \(0.960283\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.00000 | − | 5.19615i | −0.152499 | − | 0.264135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.50000 | − | 2.59808i | 0.0760530 | − | 0.131728i | −0.825491 | − | 0.564416i | \(-0.809102\pi\) |
0.901544 | + | 0.432688i | \(0.142435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.0000 | 2.12403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0000 | − | 19.0526i | −0.549314 | − | 0.951439i | −0.998322 | − | 0.0579116i | \(-0.981556\pi\) |
0.449008 | − | 0.893528i | \(-0.351777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | − | 24.2487i | 0.692255 | − | 1.19902i | −0.278842 | − | 0.960337i | \(-0.589950\pi\) |
0.971097 | − | 0.238685i | \(-0.0767162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.0000 | − | 12.1244i | −0.688895 | − | 0.596601i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.0000 | −0.683945 | −0.341972 | − | 0.939710i | \(-0.611095\pi\) | ||||
−0.341972 | + | 0.939710i | \(0.611095\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.5000 | + | 18.1865i | −0.510527 | + | 0.884260i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.5000 | + | 30.3109i | 0.848875 | + | 1.47029i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.5000 | + | 6.06218i | −0.846884 | + | 0.293369i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | + | 20.7846i | −0.578020 | + | 1.00116i | 0.417687 | + | 0.908591i | \(0.362841\pi\) |
−0.995706 | + | 0.0925683i | \(0.970492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0000 | 1.00920 | 0.504598 | − | 0.863355i | \(-0.331641\pi\) | ||||
0.504598 | + | 0.863355i | \(0.331641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.0000 | + | 36.3731i | −1.00457 | + | 1.73996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.00000 | + | 12.1244i | 0.334092 | + | 0.578664i | 0.983310 | − | 0.181938i | \(-0.0582371\pi\) |
−0.649218 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.0000 | − | 17.3205i | −0.475114 | − | 0.822922i | 0.524479 | − | 0.851423i | \(-0.324260\pi\) |
−0.999594 | + | 0.0285009i | \(0.990927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | + | 5.19615i | 0.140334 | + | 0.243066i | 0.927622 | − | 0.373519i | \(-0.121849\pi\) |
−0.787288 | + | 0.616585i | \(0.788516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.00000 | + | 12.1244i | 0.323921 | + | 0.561048i | 0.981293 | − | 0.192518i | \(-0.0616653\pi\) |
−0.657372 | + | 0.753566i | \(0.728332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | − | 5.19615i | −0.277054 | − | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.00000 | − | 5.19615i | 0.137940 | − | 0.238919i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.0000 | −1.60591 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | 0.412082 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.50000 | − | 6.06218i | 0.159919 | − | 0.276988i | −0.774920 | − | 0.632059i | \(-0.782210\pi\) |
0.934839 | + | 0.355071i | \(0.115543\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5000 | − | 21.6506i | 0.566429 | − | 0.981084i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
0.996915 | − | 0.0784867i | \(-0.0250088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0000 | −1.35388 | −0.676941 | − | 0.736038i | \(-0.736695\pi\) | ||||
−0.676941 | + | 0.736038i | \(0.736695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.5000 | − | 30.3109i | 0.788160 | − | 1.36513i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.50000 | + | 12.9904i | −0.112140 | + | 0.582698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | + | 6.92820i | 0.179065 | + | 0.310149i | 0.941560 | − | 0.336844i | \(-0.109360\pi\) |
−0.762496 | + | 0.646993i | \(0.776026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.0000 | 1.24846 | 0.624229 | − | 0.781241i | \(-0.285413\pi\) | ||||
0.624229 | + | 0.781241i | \(0.285413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | + | 24.2487i | 0.620539 | + | 1.07481i | 0.989385 | + | 0.145315i | \(0.0464195\pi\) |
−0.368846 | + | 0.929490i | \(0.620247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.0000 | − | 24.2487i | −1.23865 | − | 1.07270i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.0000 | −0.923579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.00000 | − | 12.1244i | 0.306676 | − | 0.531178i | −0.670957 | − | 0.741496i | \(-0.734117\pi\) |
0.977633 | + | 0.210318i | \(0.0674500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | − | 12.1244i | −0.306089 | − | 0.530161i | 0.671414 | − | 0.741082i | \(-0.265687\pi\) |
−0.977503 | + | 0.210921i | \(0.932354\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | −21.0000 | −0.911322 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | \(-0.221681\pi\) |
−0.939110 | + | 0.343617i | \(0.888348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00000 | −0.0855138 | −0.0427569 | − | 0.999086i | \(-0.513614\pi\) | ||||
−0.0427569 | + | 0.999086i | \(0.513614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5000 | + | 18.1865i | −0.448129 | + | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.5000 | + | 30.3109i | 0.745525 | + | 1.29129i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.0000 | − | 5.19615i | 0.637865 | − | 0.220963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | + | 15.5885i | −0.381342 | + | 0.660504i | −0.991254 | − | 0.131965i | \(-0.957871\pi\) |
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | − | 15.5885i | −0.755929 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.500000 | − | 0.866025i | −0.0209611 | − | 0.0363057i | 0.855355 | − | 0.518043i | \(-0.173339\pi\) |
−0.876316 | + | 0.481737i | \(0.840006\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.0000 | −1.25109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | + | 12.1244i | −0.291414 | + | 0.504744i | −0.974144 | − | 0.225927i | \(-0.927459\pi\) |
0.682730 | + | 0.730670i | \(0.260792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.50000 | + | 7.79423i | 0.186371 | + | 0.322804i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.0000 | −0.866763 | −0.433381 | − | 0.901211i | \(-0.642680\pi\) | ||||
−0.433381 | + | 0.901211i | \(0.642680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0000 | − | 27.7128i | 0.653742 | − | 1.13231i | −0.328465 | − | 0.944516i | \(-0.606531\pi\) |
0.982208 | − | 0.187799i | \(-0.0601353\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | −0.285536 | −0.142768 | − | 0.989756i | \(-0.545600\pi\) | ||||
−0.142768 | + | 0.989756i | \(0.545600\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00000 | + | 12.1244i | 0.284121 | + | 0.492112i | 0.972396 | − | 0.233338i | \(-0.0749648\pi\) |
−0.688274 | + | 0.725450i | \(0.741632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.50000 | − | 6.06218i | −0.141595 | − | 0.245249i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.0000 | + | 27.7128i | −0.646234 | + | 1.11931i | 0.337781 | + | 0.941225i | \(0.390324\pi\) |
−0.984015 | + | 0.178085i | \(0.943010\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.0000 | 1.20775 | 0.603877 | − | 0.797077i | \(-0.293622\pi\) | ||||
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.0000 | + | 24.2487i | −0.562708 | + | 0.974638i | 0.434551 | + | 0.900647i | \(0.356907\pi\) |
−0.997259 | + | 0.0739910i | \(0.976426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.0000 | 2.23287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.50000 | + | 2.59808i | 0.257539 | + | 0.102940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.50000 | + | 12.9904i | 0.296695 | + | 0.513892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.00000 | 0.276053 | 0.138027 | − | 0.990429i | \(-0.455924\pi\) | ||||
0.138027 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.0000 | + | 36.3731i | −0.825595 | + | 1.42997i | 0.0758684 | + | 0.997118i | \(0.475827\pi\) |
−0.901464 | + | 0.432855i | \(0.857506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5000 | − | 18.1865i | −0.412161 | − | 0.713884i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −42.0000 | −1.63858 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.0000 | 1.55818 | 0.779089 | − | 0.626913i | \(-0.215682\pi\) | ||||
0.779089 | + | 0.626913i | \(0.215682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000 | + | 25.9808i | 0.580802 | + | 1.00598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0000 | −0.810696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.5000 | + | 30.3109i | 0.672580 | + | 1.16494i | 0.977170 | + | 0.212459i | \(0.0681471\pi\) |
−0.304590 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | − | 36.3731i | 0.268635 | − | 1.39587i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | + | 20.7846i | −0.459167 | + | 0.795301i | −0.998917 | − | 0.0465244i | \(-0.985185\pi\) |
0.539750 | + | 0.841825i | \(0.318519\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.50000 | + | 2.59808i | −0.0571454 | + | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5000 | + | 30.3109i | 0.665731 | + | 1.15308i | 0.979086 | + | 0.203445i | \(0.0652137\pi\) |
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.50000 | − | 23.3827i | 0.170941 | − | 0.888235i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.0000 | + | 48.4974i | −1.05604 | + | 1.82911i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0000 | + | 24.2487i | 1.05305 | + | 0.911967i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0000 | − | 43.3013i | −0.938895 | − | 1.62621i | −0.767537 | − | 0.641004i | \(-0.778518\pi\) |
−0.171358 | − | 0.985209i | \(-0.554815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00000 | − | 15.5885i | 0.337526 | − | 0.584613i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0000 | − | 36.3731i | −0.783168 | − | 1.35649i | −0.930087 | − | 0.367338i | \(-0.880269\pi\) |
0.146920 | − | 0.989148i | \(-0.453064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.0000 | + | 12.1244i | −1.30347 | + | 0.451535i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.5000 | + | 21.6506i | −0.464238 | + | 0.804084i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.00000 | − | 12.1244i | 0.258904 | − | 0.448435i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0000 | − | 36.3731i | −0.775653 | − | 1.34347i | −0.934427 | − | 0.356155i | \(-0.884088\pi\) |
0.158774 | − | 0.987315i | \(-0.449246\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000 | − | 3.46410i | 0.0735712 | − | 0.127429i | −0.826893 | − | 0.562360i | \(-0.809894\pi\) |
0.900464 | + | 0.434930i | \(0.143227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.00000 | −0.330178 | −0.165089 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165089 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.0000 | + | 6.92820i | −0.730784 | + | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0000 | − | 17.3205i | −0.364905 | − | 0.632034i | 0.623856 | − | 0.781540i | \(-0.285565\pi\) |
−0.988761 | + | 0.149505i | \(0.952232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.00000 | 0.327111 | 0.163555 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163555 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −8.00000 | − | 6.92820i | −0.289619 | − | 0.250818i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.50000 | − | 6.06218i | 0.126378 | − | 0.218893i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.0000 | + | 36.3731i | −0.755318 | + | 1.30825i | 0.189899 | + | 0.981804i | \(0.439184\pi\) |
−0.945216 | + | 0.326445i | \(0.894149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.50000 | + | 12.9904i | −0.268371 | + | 0.464832i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.50000 | − | 6.06218i | 0.124762 | − | 0.216093i | −0.796878 | − | 0.604140i | \(-0.793517\pi\) |
0.921640 | + | 0.388047i | \(0.126850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.50000 | + | 23.3827i | −0.160002 | + | 0.831393i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.50000 | − | 6.06218i | −0.124289 | − | 0.215274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0000 | −1.48772 | −0.743858 | − | 0.668338i | \(-0.767006\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.0000 | −1.73350 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | − | 36.3731i | −0.741074 | − | 1.28358i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5000 | − | 26.8468i | 0.544951 | − | 0.943883i | −0.453659 | − | 0.891175i | \(-0.649882\pi\) |
0.998610 | − | 0.0527074i | \(-0.0167851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | + | 12.1244i | 0.244899 | + | 0.424178i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.50000 | − | 2.59808i | 0.262071 | − | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | − | 31.1769i | −0.628204 | − | 1.08808i | −0.987912 | − | 0.155017i | \(-0.950457\pi\) |
0.359708 | − | 0.933065i | \(-0.382876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.00000 | 0.173867 | 0.0869335 | − | 0.996214i | \(-0.472293\pi\) | ||||
0.0869335 | + | 0.996214i | \(0.472293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5000 | + | 30.3109i | −0.607800 | + | 1.05274i | 0.383802 | + | 0.923415i | \(0.374614\pi\) |
−0.991602 | + | 0.129325i | \(0.958719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.5000 | − | 30.3109i | 1.33395 | − | 1.05021i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.00000 | −0.241667 | −0.120833 | − | 0.992673i | \(-0.538557\pi\) | ||||
−0.120833 | + | 0.992673i | \(0.538557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | + | 1.73205i | −0.171802 | + | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | + | 41.5692i | −0.822709 | + | 1.42497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.0000 | −1.43805 | −0.719026 | − | 0.694983i | \(-0.755412\pi\) | ||||
−0.719026 | + | 0.694983i | \(0.755412\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5000 | + | 18.1865i | −0.358673 | + | 0.621240i | −0.987739 | − | 0.156112i | \(-0.950104\pi\) |
0.629066 | + | 0.777352i | \(0.283437\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0000 | − | 48.4974i | −0.955348 | − | 1.65471i | −0.733571 | − | 0.679613i | \(-0.762148\pi\) |
−0.221777 | − | 0.975097i | \(-0.571186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.0000 | − | 17.3205i | −0.340404 | − | 0.589597i | 0.644104 | − | 0.764938i | \(-0.277230\pi\) |
−0.984508 | + | 0.175341i | \(0.943897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50000 | − | 2.59808i | 0.0508256 | − | 0.0880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.0000 | − | 36.3731i | −0.710742 | − | 1.23104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0000 | + | 41.5692i | 0.810422 | + | 1.40369i | 0.912569 | + | 0.408923i | \(0.134096\pi\) |
−0.102146 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0000 | 1.34611 | 0.673054 | − | 0.739594i | \(-0.264982\pi\) | ||||
0.673054 | + | 0.739594i | \(0.264982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0000 | + | 36.3731i | 0.705111 | + | 1.22129i | 0.966651 | + | 0.256096i | \(0.0824362\pi\) |
−0.261540 | + | 0.965193i | \(0.584230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | − | 5.19615i | 0.0335389 | − | 0.174273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.5000 | − | 42.4352i | 0.819861 | − | 1.42004i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.5000 | + | 18.1865i | 0.349806 | + | 0.605881i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0000 | + | 32.9090i | −0.630885 | + | 1.09272i | 0.356487 | + | 0.934300i | \(0.383975\pi\) |
−0.987371 | + | 0.158424i | \(0.949359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42.0000 | 1.39305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35.0000 | + | 12.1244i | −1.15580 | + | 0.400381i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0000 | + | 43.3013i | 0.824674 | + | 1.42838i | 0.902168 | + | 0.431384i | \(0.141975\pi\) |
−0.0774944 | + | 0.996993i | \(0.524692\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.00000 | −0.164577 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | −1.31519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.0000 | + | 36.3731i | −0.689730 | + | 1.19465i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.00000 | − | 12.1244i | −0.229663 | − | 0.397787i | 0.728046 | − | 0.685529i | \(-0.240429\pi\) |
−0.957708 | + | 0.287742i | \(0.907096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | + | 48.4974i | 0.229416 | + | 1.58944i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | 0.228680 | 0.114340 | − | 0.993442i | \(-0.463525\pi\) | ||||
0.114340 | + | 0.993442i | \(0.463525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0000 | + | 24.2487i | −0.456387 | + | 0.790485i | −0.998767 | − | 0.0496480i | \(-0.984190\pi\) |
0.542380 | + | 0.840133i | \(0.317523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 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 | ||||||||
\(949\) | 7.00000 | − | 12.1244i | 0.227230 | − | 0.393573i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.00000 | 0.291539 | 0.145769 | − | 0.989319i | \(-0.453434\pi\) | ||||
0.145769 | + | 0.989319i | \(0.453434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.00000 | − | 6.92820i | −0.258333 | − | 0.223723i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | + | 20.7846i | −0.386695 | + | 0.669775i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.00000 | 0.160789 | 0.0803946 | − | 0.996763i | \(-0.474382\pi\) | ||||
0.0803946 | + | 0.996763i | \(0.474382\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0000 | − | 24.2487i | −0.449281 | − | 0.778178i | 0.549058 | − | 0.835784i | \(-0.314987\pi\) |
−0.998339 | + | 0.0576061i | \(0.981653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.0000 | − | 32.9090i | 0.607864 | − | 1.05285i | −0.383728 | − | 0.923446i | \(-0.625360\pi\) |
0.991592 | − | 0.129405i | \(-0.0413067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.0000 | −0.383131 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.50000 | + | 6.06218i | −0.111633 | + | 0.193353i | −0.916429 | − | 0.400198i | \(-0.868941\pi\) |
0.804796 | + | 0.593551i | \(0.202275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | + | 10.3923i | 0.190789 | + | 0.330456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | − | 3.46410i | 0.0635321 | − | 0.110041i | −0.832510 | − | 0.554010i | \(-0.813097\pi\) |
0.896042 | + | 0.443969i | \(0.146430\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.50000 | − | 6.06218i | 0.110846 | − | 0.191991i | −0.805266 | − | 0.592914i | \(-0.797977\pi\) |
0.916112 | + | 0.400923i | \(0.131311\pi\) | |||||||
\(998\) | 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 | 1456.2.r.g.417.1 | 2 | ||
4.3 | odd | 2 | 91.2.e.a.53.1 | ✓ | 2 | ||
7.2 | even | 3 | inner | 1456.2.r.g.625.1 | 2 | ||
12.11 | even | 2 | 819.2.j.b.235.1 | 2 | |||
28.3 | even | 6 | 637.2.a.d.1.1 | 1 | |||
28.11 | odd | 6 | 637.2.a.c.1.1 | 1 | |||
28.19 | even | 6 | 637.2.e.a.79.1 | 2 | |||
28.23 | odd | 6 | 91.2.e.a.79.1 | yes | 2 | ||
28.27 | even | 2 | 637.2.e.a.508.1 | 2 | |||
52.51 | odd | 2 | 1183.2.e.b.508.1 | 2 | |||
84.11 | even | 6 | 5733.2.a.c.1.1 | 1 | |||
84.23 | even | 6 | 819.2.j.b.352.1 | 2 | |||
84.59 | odd | 6 | 5733.2.a.d.1.1 | 1 | |||
364.51 | odd | 6 | 1183.2.e.b.170.1 | 2 | |||
364.207 | odd | 6 | 8281.2.a.f.1.1 | 1 | |||
364.311 | even | 6 | 8281.2.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.a.53.1 | ✓ | 2 | 4.3 | odd | 2 | ||
91.2.e.a.79.1 | yes | 2 | 28.23 | odd | 6 | ||
637.2.a.c.1.1 | 1 | 28.11 | odd | 6 | |||
637.2.a.d.1.1 | 1 | 28.3 | even | 6 | |||
637.2.e.a.79.1 | 2 | 28.19 | even | 6 | |||
637.2.e.a.508.1 | 2 | 28.27 | even | 2 | |||
819.2.j.b.235.1 | 2 | 12.11 | even | 2 | |||
819.2.j.b.352.1 | 2 | 84.23 | even | 6 | |||
1183.2.e.b.170.1 | 2 | 364.51 | odd | 6 | |||
1183.2.e.b.508.1 | 2 | 52.51 | odd | 2 | |||
1456.2.r.g.417.1 | 2 | 1.1 | even | 1 | trivial | ||
1456.2.r.g.625.1 | 2 | 7.2 | even | 3 | inner | ||
5733.2.a.c.1.1 | 1 | 84.11 | even | 6 | |||
5733.2.a.d.1.1 | 1 | 84.59 | odd | 6 | |||
8281.2.a.e.1.1 | 1 | 364.311 | even | 6 | |||
8281.2.a.f.1.1 | 1 | 364.207 | odd | 6 |