Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,11,Mod(31,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.31");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.g (of order \(2\), degree \(1\), 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: | \(30.4971481283\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{2545})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 637x^{2} + 636x + 404496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(12.8620 - 22.2776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.31 |
Dual form | 48.11.g.c.31.4 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 140.296i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1960.75 | 0.627441 | 0.313720 | − | 0.949515i | \(-0.398425\pi\) | ||||
0.313720 | + | 0.949515i | \(0.398425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 28003.4i | − 1.66618i | −0.553141 | − | 0.833088i | \(-0.686571\pi\) | ||||
0.553141 | − | 0.833088i | \(-0.313429\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −19683.0 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43532.8i | 0.270304i | 0.990825 | + | 0.135152i | \(0.0431523\pi\) | ||||
−0.990825 | + | 0.135152i | \(0.956848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −139927. | −0.376864 | −0.188432 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188432 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 275086.i | − 0.362253i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12441e6 | 1.49621 | 0.748106 | − | 0.663580i | \(-0.230964\pi\) | ||||
0.748106 | + | 0.663580i | \(0.230964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.98220e6i | − 1.20439i | −0.798347 | − | 0.602197i | \(-0.794292\pi\) | ||||
0.798347 | − | 0.602197i | \(-0.205708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.92877e6 | −0.961967 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.60241e6i | 0.715066i | 0.933900 | + | 0.357533i | \(0.116382\pi\) | ||||
−0.933900 | + | 0.357533i | \(0.883618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.92108e6 | −0.606318 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.76145e6i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.90324e7 | −1.41545 | −0.707723 | − | 0.706490i | \(-0.750278\pi\) | ||||
−0.707723 | + | 0.706490i | \(0.750278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.52638e7i | − 0.533156i | −0.963813 | − | 0.266578i | \(-0.914107\pi\) | ||||
0.963813 | − | 0.266578i | \(-0.0858929\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.10748e6 | 0.156060 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 5.49077e7i | − 1.04543i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.18138e7 | −0.458783 | −0.229392 | − | 0.973334i | \(-0.573674\pi\) | ||||
−0.229392 | + | 0.973334i | \(0.573674\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.96312e7i | 0.217583i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.12718e8 | −1.83605 | −0.918024 | − | 0.396524i | \(-0.870216\pi\) | ||||
−0.918024 | + | 0.396524i | \(0.870216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.02316e8i | − 0.695989i | −0.937497 | − | 0.347995i | \(-0.886863\pi\) | ||||
0.937497 | − | 0.347995i | \(-0.113137\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.85935e7 | −0.209147 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.05477e8i | − 1.33195i | −0.745972 | − | 0.665977i | \(-0.768015\pi\) | ||||
0.745972 | − | 0.665977i | \(-0.231985\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.01715e8 | −1.77614 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2.98046e8i | − 0.863838i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21185e8 | 0.528903 | 0.264451 | − | 0.964399i | \(-0.414809\pi\) | ||||
0.264451 | + | 0.964399i | \(0.414809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.53569e7i | 0.169600i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.18391e8 | −0.695357 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.12527e8i | 0.856772i | 0.903596 | + | 0.428386i | \(0.140918\pi\) | ||||
−0.903596 | + | 0.428386i | \(0.859082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.10376e8 | −0.722684 | −0.361342 | − | 0.932433i | \(-0.617681\pi\) | ||||
−0.361342 | + | 0.932433i | \(0.617681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.51191e8i | 0.555392i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.74362e8 | −0.236460 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 5.40101e7i | − 0.0400038i | −0.999800 | − | 0.0200019i | \(-0.993633\pi\) | ||||
0.999800 | − | 0.0200019i | \(-0.00636722\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.45701e8 | 0.412844 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 2.86449e9i | − 1.58765i | −0.608144 | − | 0.793827i | \(-0.708086\pi\) | ||||
0.608144 | − | 0.793827i | \(-0.291914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.92732e9 | 1.41207 | 0.706033 | − | 0.708178i | \(-0.250483\pi\) | ||||
0.706033 | + | 0.708178i | \(0.250483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.30704e8i | 0.350058i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.21907e9 | 0.450374 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00200e9i | 0.650620i | 0.945607 | + | 0.325310i | \(0.105469\pi\) | ||||
−0.945607 | + | 0.325310i | \(0.894531\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.29668e9i | 0.836924i | 0.908234 | + | 0.418462i | \(0.137431\pi\) | ||||
−0.908234 | + | 0.418462i | \(0.862569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.16543e9 | 0.938784 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.07314e9i | 0.817208i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.15974e9 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239228\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.91843e9i | 0.627922i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.14145e9 | −0.307818 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 5.84735e9i | − 0.755686i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.41238e9 | −0.630274 | −0.315137 | − | 0.949046i | \(-0.602051\pi\) | ||||
−0.315137 | + | 0.949046i | \(0.602051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 8.56855e8i | − 0.0901014i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.69718e10 | 1.61481 | 0.807405 | − | 0.589997i | \(-0.200871\pi\) | ||||
0.807405 | + | 0.589997i | \(0.200871\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.12732e10i | 0.972432i | 0.873839 | + | 0.486216i | \(0.161623\pi\) | ||||
−0.873839 | + | 0.486216i | \(0.838377\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.70334e9 | −0.603577 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 8.02650e9i | − 0.572278i | −0.958188 | − | 0.286139i | \(-0.907628\pi\) | ||||
0.958188 | − | 0.286139i | \(-0.0923719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.15037e10 | −1.39759 | −0.698797 | − | 0.715320i | \(-0.746281\pi\) | ||||
−0.698797 | + | 0.715320i | \(0.746281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.46336e9i | 0.264879i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.08540e9 | −0.276015 | −0.138008 | − | 0.990431i | \(-0.544070\pi\) | ||||
−0.138008 | + | 0.990431i | \(0.544070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.02419e9i | 0.448662i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.75418e9 | 0.125621 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 5.94906e10i | − 2.49295i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.40423e10 | 0.926936 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.98435e10i | 1.06004i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.07577e10 | −1.00787 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.17676e10i | − 0.961537i | −0.876847 | − | 0.480769i | \(-0.840358\pi\) | ||||
0.876847 | − | 0.480769i | \(-0.159642\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.43546e10 | −0.401830 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 6.33920e10i | − 1.64315i | −0.570098 | − | 0.821577i | \(-0.693095\pi\) | ||||
0.570098 | − | 0.821577i | \(-0.306905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.35117e10 | −2.00673 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.41452e9i | 0.120751i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.99756e9 | 0.103551 | 0.0517756 | − | 0.998659i | \(-0.483512\pi\) | ||||
0.0517756 | + | 0.998659i | \(0.483512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.93247e10i | 1.72146i | 0.509059 | + | 0.860732i | \(0.329993\pi\) | ||||
−0.509059 | + | 0.860732i | \(0.670007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.28572e10 | −0.769004 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 6.09141e9i | − 0.101868i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.69254e10 | −0.888109 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.03887e10i | 1.02545i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.01995e11 | 1.38882 | 0.694410 | − | 0.719579i | \(-0.255665\pi\) | ||||
0.694410 | + | 0.719579i | \(0.255665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1.05116e11i | − 1.33901i | −0.742809 | − | 0.669504i | \(-0.766507\pi\) | ||||
0.742809 | − | 0.669504i | \(-0.233493\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.18147e10 | −0.498737 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.99285e10i | − 0.334523i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.37587e11 | 1.44237 | 0.721187 | − | 0.692740i | \(-0.243597\pi\) | ||||
0.721187 | + | 0.692740i | \(0.243597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 3.10314e10i | − 0.305362i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.28883e11 | 1.19143 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.87748e11i | 1.63169i | 0.578271 | + | 0.815845i | \(0.303728\pi\) | ||||
−0.578271 | + | 0.815845i | \(0.696272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.19752e10 | 0.0979185 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.51202e11i | − 1.16406i | −0.813167 | − | 0.582030i | \(-0.802259\pi\) | ||||
0.813167 | − | 0.582030i | \(-0.197741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.18279e11 | −0.857973 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.86986e10i | 0.401465i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.32108e11 | 0.852510 | 0.426255 | − | 0.904603i | \(-0.359833\pi\) | ||||
0.426255 | + | 0.904603i | \(0.359833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.65810e11i | 1.01023i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.59352e10 | 0.494657 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.21702e10i | 0.229478i | 0.993396 | + | 0.114739i | \(0.0366031\pi\) | ||||
−0.993396 | + | 0.114739i | \(0.963397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.69890e11 | 0.874530 | 0.437265 | − | 0.899333i | \(-0.355947\pi\) | ||||
0.437265 | + | 0.899333i | \(0.355947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.56334e10i | 0.417242i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.23790e10 | −0.287859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.24812e10i | 0.404432i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.73300e10 | 0.320656 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 2.64701e11i | − 1.04133i | −0.853760 | − | 0.520666i | \(-0.825684\pi\) | ||||
0.853760 | − | 0.520666i | \(-0.174316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.57937e11 | 1.33666 | 0.668329 | − | 0.743866i | \(-0.267010\pi\) | ||||
0.668329 | + | 0.743866i | \(0.267010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.84920e10i | 0.136520i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.62491e10 | −0.324389 | −0.162194 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162194 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.65299e11i | − 0.529670i | −0.964294 | − | 0.264835i | \(-0.914683\pi\) | ||||
0.964294 | − | 0.264835i | \(-0.0853175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.57741e9 | −0.0230962 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.13007e11i | 2.35838i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.17086e11 | −1.15201 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 9.05893e10i | − 0.238355i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.29823e11 | 0.325553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.71076e10i | − 0.0887259i | −0.999015 | − | 0.0443630i | \(-0.985874\pi\) | ||||
0.999015 | − | 0.0443630i | \(-0.0141258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.01877e11 | −0.916632 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 2.00617e11i | − 0.436692i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.27438e11 | −0.888331 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4.10691e11i | − 0.815257i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.97262e11 | −0.563868 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.05438e12i | − 1.91193i | −0.293487 | − | 0.955963i | \(-0.594816\pi\) | ||||
0.293487 | − | 0.955963i | \(-0.405184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.16545e11 | 0.202106 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.28471e10i | 0.154042i | 0.997029 | + | 0.0770210i | \(0.0245408\pi\) | ||||
−0.997029 | + | 0.0770210i | \(0.975459\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.71477e11 | 0.431077 | 0.215538 | − | 0.976495i | \(-0.430849\pi\) | ||||
0.215538 | + | 0.976495i | \(0.430849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 1.71030e11i | − 0.260024i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.90552e11 | −1.29682 | −0.648410 | − | 0.761291i | \(-0.724566\pi\) | ||||
−0.648410 | + | 0.761291i | \(0.724566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 5.98965e11i | − 0.835722i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.80872e11 | 0.375636 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.25803e10i | 0.0161326i | 0.999967 | + | 0.00806628i | \(0.00256760\pi\) | ||||
−0.999967 | + | 0.00806628i | \(0.997432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.96269e10 | −0.122544 | −0.0612719 | − | 0.998121i | \(-0.519516\pi\) | ||||
−0.0612719 | + | 0.998121i | \(0.519516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.43536e10i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.83740e11 | −1.11442 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.17290e11i | 0.453893i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.62511e11 | 0.483198 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.60779e12i | 1.61384i | 0.590659 | + | 0.806921i | \(0.298868\pi\) | ||||
−0.590659 | + | 0.806921i | \(0.701132\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00356e11 | −0.193285 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 5.84394e11i | − 0.542007i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.00716e12 | −0.898320 | −0.449160 | − | 0.893451i | \(-0.648277\pi\) | ||||
−0.449160 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.90896e11i | 0.764413i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.71445e11 | 0.471816 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.16466e11i | 0.0925594i | 0.998929 | + | 0.0462797i | \(0.0147365\pi\) | ||||
−0.998929 | + | 0.0462797i | \(0.985263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.33688e11 | 0.331855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.14478e12i | − 0.843656i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.19817e11 | −0.156063 | −0.0780313 | − | 0.996951i | \(-0.524863\pi\) | ||||
−0.0780313 | + | 0.996951i | \(0.524863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 4.67966e11i | − 0.320161i | −0.987104 | − | 0.160080i | \(-0.948825\pi\) | ||||
0.987104 | − | 0.160080i | \(-0.0511753\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.49741e11 | 0.362531 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.57761e11i | − 0.163890i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.67183e12 | 1.02516 | 0.512580 | − | 0.858639i | \(-0.328690\pi\) | ||||
0.512580 | + | 0.858639i | \(0.328690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.00437e11i | 0.177719i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.59078e12 | 0.907982 | 0.453991 | − | 0.891006i | \(-0.350000\pi\) | ||||
0.453991 | + | 0.891006i | \(0.350000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.30728e12i | − 1.27107i | −0.772074 | − | 0.635533i | \(-0.780781\pi\) | ||||
0.772074 | − | 0.635533i | \(-0.219219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.20361e11 | −0.436295 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.95682e12i | 3.05918i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.49711e12 | 1.23865 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.59336e11i | 0.363889i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.93730e12 | 1.82331 | 0.911655 | − | 0.410957i | \(-0.134805\pi\) | ||||
0.911655 | + | 0.410957i | \(0.134805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.20101e12i | 0.537573i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.20213e11 | −0.0520201 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 6.44002e11i | − 0.269483i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.86521e12 | −1.15964 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.38108e12i | − 0.932311i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.19680e12 | −0.453441 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.46935e10i | 0.00538808i | 0.999996 | + | 0.00269404i | \(0.000857541\pi\) | ||||
−0.999996 | + | 0.00269404i | \(0.999142\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.58158e12 | 0.561434 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.88632e12i | 0.648356i | 0.945996 | + | 0.324178i | \(0.105088\pi\) | ||||
−0.945996 | + | 0.324178i | \(0.894912\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.10199e12 | 1.36544 | 0.682721 | − | 0.730679i | \(-0.260797\pi\) | ||||
0.682721 | + | 0.730679i | \(0.260797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.08075e12i | 0.348475i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.75215e11 | 0.117215 | 0.0586077 | − | 0.998281i | \(-0.481334\pi\) | ||||
0.0586077 | + | 0.998281i | \(0.481334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.26386e12i | − 0.382601i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.12609e12 | −0.330405 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.33540e12i | − 1.80203i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.28519e11 | 0.228500 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.01689e12i | 0.806901i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.55440e12 | −2.21927 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.70388e12i | 0.428843i | 0.976741 | + | 0.214422i | \(0.0687867\pi\) | ||||
−0.976741 | + | 0.214422i | \(0.931213\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.26192e11 | 0.152928 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.05900e11i | − 0.0251000i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.60571e12 | −1.74981 | −0.874903 | − | 0.484298i | \(-0.839075\pi\) | ||||
−0.874903 | + | 0.484298i | \(0.839075\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.13463e11i | 0.159358i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.64475e11 | 0.144114 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.13947e12i | 1.29318i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.26606e12 | 0.259035 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 3.05813e12i | − 0.607867i | −0.952693 | − | 0.303933i | \(-0.901700\pi\) | ||||
0.952693 | − | 0.303933i | \(-0.0983000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.03496e12 | −0.199892 | −0.0999458 | − | 0.994993i | \(-0.531867\pi\) | ||||
−0.0999458 | + | 0.994993i | \(0.531867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 3.86401e11i | − 0.0725275i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.06228e12 | 0.558690 | 0.279345 | − | 0.960191i | \(-0.409883\pi\) | ||||
0.279345 | + | 0.960191i | \(0.409883\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.61655e12i | − 0.996158i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.34630e12 | −1.43931 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 1.08477e13i | − 1.81913i | −0.415562 | − | 0.909565i | \(-0.636415\pi\) | ||||
0.415562 | − | 0.909565i | \(-0.363585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.76245e12 | −0.450566 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3.37304e12i | − 0.535167i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.73974e12 | 0.885988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.16676e12i | 0.325447i | 0.986672 | + | 0.162723i | \(0.0520278\pi\) | ||||
−0.986672 | + | 0.162723i | \(0.947972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.18692e12 | 0.612016 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.19393e12i | − 0.881245i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23356e13 | −1.70850 | −0.854252 | − | 0.519859i | \(-0.825984\pi\) | ||||
−0.854252 | + | 0.519859i | \(0.825984\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.31519e12i | 0.581894i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.06242e12 | 0.533431 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5.12686e12i | − 0.655624i | −0.944743 | − | 0.327812i | \(-0.893689\pi\) | ||||
0.944743 | − | 0.327812i | \(-0.106311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.45687e12 | −0.555144 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 8.94417e11i | − 0.108529i | −0.998527 | − | 0.0542645i | \(-0.982719\pi\) | ||||
0.998527 | − | 0.0542645i | \(-0.0172814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.39028e12 | 0.282583 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.01389e12i | 0.231996i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.57641e12 | −0.289246 | −0.144623 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144623 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.77739e12i | 1.06989i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.89365e12 | −0.948675 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.92542e12i | 0.408226i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.08854e12 | −0.211783 | −0.105891 | − | 0.994378i | \(-0.533770\pi\) | ||||
−0.105891 | + | 0.994378i | \(0.533770\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.17164e13i | 1.15859i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.73346e12 | 0.456517 | 0.228259 | − | 0.973601i | \(-0.426697\pi\) | ||||
0.228259 | + | 0.973601i | \(0.426697\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.13582e12i | 0.200927i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.59635e11 | 0.0697156 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.38494e12i | − 0.124011i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.02257e13 | 1.76721 | 0.883603 | − | 0.468237i | \(-0.155111\pi\) | ||||
0.883603 | + | 0.468237i | \(0.155111\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 7.01138e11i | − 0.0597853i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.71528e13 | 1.42753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.46397e12i | 0.525120i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.25319e13 | 0.993887 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1.51587e13i | − 1.17380i | −0.809661 | − | 0.586898i | \(-0.800349\pi\) | ||||
0.809661 | − | 0.586898i | \(-0.199651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.82326e12 | 0.440307 | 0.220154 | − | 0.975465i | \(-0.429344\pi\) | ||||
0.220154 | + | 0.975465i | \(0.429344\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.01270e12i | 0.443985i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.25788e13 | −0.907180 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.70926e13i | 1.20412i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.54601e11 | −0.0588135 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.05176e13i | − 0.707183i | −0.935400 | − | 0.353591i | \(-0.884960\pi\) | ||||
0.935400 | − | 0.353591i | \(-0.115040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.83926e12 | −0.186537 | −0.0932687 | − | 0.995641i | \(-0.529732\pi\) | ||||
−0.0932687 | + | 0.995641i | \(0.529732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.98641e12i | 0.512750i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.37253e13 | 0.861222 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 3.91291e12i | − 0.239981i | −0.992775 | − | 0.119990i | \(-0.961714\pi\) | ||||
0.992775 | − | 0.119990i | \(-0.0382864\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.87527e12 | 0.592047 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.18258e13i | 1.27924i | 0.768691 | + | 0.639621i | \(0.220909\pi\) | ||||
−0.768691 | + | 0.639621i | \(0.779091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.59992e13 | 0.916851 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.43095e13i | − 0.801836i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.19109e13 | −0.652699 | −0.326350 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326350 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 9.26018e12i | − 0.496292i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.47473e13 | −0.773076 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.68308e12i | 0.393984i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.98444e13 | −0.995534 | −0.497767 | − | 0.867311i | \(-0.665846\pi\) | ||||
−0.497767 | + | 0.867311i | \(0.665846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.86644e12i | 0.287946i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.59865e13 | 1.72836 | 0.864182 | − | 0.503179i | \(-0.167836\pi\) | ||||
0.864182 | + | 0.503179i | \(0.167836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.02191e13i | − 0.480295i | −0.970736 | − | 0.240148i | \(-0.922804\pi\) | ||||
0.970736 | − | 0.240148i | \(-0.0771958\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.19885e12 | −0.193137 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.51827e11i | 0.0383501i | 0.999816 | + | 0.0191751i | \(0.00610399\pi\) | ||||
−0.999816 | + | 0.0191751i | \(0.993896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.51247e12 | −0.0666533 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 1.93029e13i | − 0.832756i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.45411e12 | 0.188129 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.76578e13i | 0.730246i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.35358e12 | −0.176301 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 9.36597e12i | − 0.371428i | −0.982604 | − | 0.185714i | \(-0.940540\pi\) | ||||
0.982604 | − | 0.185714i | \(-0.0594599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.45162e12 | 0.172899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.80818e13i | − 0.687870i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.06123e13 | −0.395460 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.74139e13i | − 0.635700i | −0.948141 | − | 0.317850i | \(-0.897039\pi\) | ||||
0.948141 | − | 0.317850i | \(-0.102961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.63403e13 | 0.942056 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.83308e13i | 0.642354i | 0.947019 | + | 0.321177i | \(0.104078\pi\) | ||||
−0.947019 | + | 0.321177i | \(0.895922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.16767e13 | −2.11781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1.68008e12i | − 0.0565333i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.02155e13 | −2.64531 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.56274e13i | 0.505107i | 0.967583 | + | 0.252553i | \(0.0812704\pi\) | ||||
−0.967583 | + | 0.252553i | \(0.918730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.12131e13 | −0.672070 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.43952e13i | 1.06821i | 0.845417 | + | 0.534107i | \(0.179352\pi\) | ||||
−0.845417 | + | 0.534107i | \(0.820648\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.32775e13 | 1.01320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.65941e13i | 0.495351i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.78947e13 | −1.40184 | −0.700921 | − | 0.713239i | \(-0.747227\pi\) | ||||
−0.700921 | + | 0.713239i | \(0.747227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 8.19748e13i | − 2.35275i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.23519e12 | 0.231786 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.21039e13i | 0.610143i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.32983e13 | 0.360033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 1.85343e13i | − 0.492197i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.18118e13 | −1.08921 | −0.544603 | − | 0.838694i | \(-0.683320\pi\) | ||||
−0.544603 | + | 0.838694i | \(0.683320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.21493e13i | − 0.566047i | −0.959113 | − | 0.283023i | \(-0.908663\pi\) | ||||
0.959113 | − | 0.283023i | \(-0.0913374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.32625e13 | 0.583258 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.24265e13i | − 0.797713i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.02443e13 | 0.488680 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1.20564e13i | − 0.285591i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.97649e13 | 0.691941 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 1.57380e13i | − 0.359071i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.91631e12 | 0.132489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.18411e13i | − 0.480098i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.49671e13 | −0.322962 | −0.161481 | − | 0.986876i | \(-0.551627\pi\) | ||||
−0.161481 | + | 0.986876i | \(0.551627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 2.38349e13i | − 0.504910i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.21634e13 | −0.876907 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.38678e12i | − 0.191681i | −0.995397 | − | 0.0958407i | \(-0.969446\pi\) | ||||
0.995397 | − | 0.0958407i | \(-0.0305539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20140e13 | 0.240895 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.65805e13i | 1.70476i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.60627e13 | 1.08405 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.75154e12i | 0.166196i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.82168e13 | 1.27238 | 0.636188 | − | 0.771534i | \(-0.280510\pi\) | ||||
0.636188 | + | 0.771534i | \(0.280510\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.43168e13i | 0.262293i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29748e13 | 0.233499 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03609e14i | 1.83170i | 0.401516 | + | 0.915852i | \(0.368483\pi\) | ||||
−0.401516 | + | 0.915852i | \(0.631517\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.97122e12 | −0.173183 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.08491e13i | − 0.185131i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.65090e13 | −0.444460 | −0.222230 | − | 0.974994i | \(-0.571334\pi\) | ||||
−0.222230 | + | 0.974994i | \(0.571334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.96650e13i | 1.31246i | 0.754560 | + | 0.656231i | \(0.227850\pi\) | ||||
−0.754560 | + | 0.656231i | \(0.772150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.71366e13 | −0.601214 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.72512e13i | − 0.433558i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.76404e13 | 0.275822 | 0.137911 | − | 0.990445i | \(-0.455961\pi\) | ||||
0.137911 | + | 0.990445i | \(0.455961\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 5.02172e13i | − 0.771720i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.23182e13 | 1.39446 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.62878e12i | 0.142965i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.40027e12 | 0.0788200 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.21258e13i | 0.891418i | 0.895178 | + | 0.445709i | \(0.147048\pi\) | ||||
−0.895178 | + | 0.445709i | \(0.852952\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.55197e13 | −0.642130 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.35034e13i | 0.187286i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.41591e13 | 0.738581 | 0.369291 | − | 0.929314i | \(-0.379601\pi\) | ||||
0.369291 | + | 0.929314i | \(0.379601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.16646e14i | − 1.56418i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.31908e13 | −0.305805 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17345e13i | 0.152170i | 0.997101 | + | 0.0760850i | \(0.0242420\pi\) | ||||
−0.997101 | + | 0.0760850i | \(0.975758\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.93118e13 | 1.13903 | 0.569517 | − | 0.821980i | \(-0.307130\pi\) | ||||
0.569517 | + | 0.821980i | \(0.307130\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.06308e12i | 0.0133346i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.71410e13 | 0.581597 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.48549e13i | 0.544335i | 0.962250 | + | 0.272167i | \(0.0877405\pi\) | ||||
−0.962250 | + | 0.272167i | \(0.912260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.14062e14 | 1.36161 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.27445e13i | 0.501966i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.54738e12 | 0.0525362 | 0.0262681 | − | 0.999655i | \(-0.491638\pi\) | ||||
0.0262681 | + | 0.999655i | \(0.491638\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.85156e13i | 0.665114i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.06819e13 | −0.902299 | −0.451149 | − | 0.892448i | \(-0.648986\pi\) | ||||
−0.451149 | + | 0.892448i | \(0.648986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.71647e14i | 1.88879i | 0.328815 | + | 0.944394i | \(0.393351\pi\) | ||||
−0.328815 | + | 0.944394i | \(0.606649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.27093e13 | −0.137615 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.28500e14i | − 2.43471i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.48526e12 | −0.0260598 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.82137e13i | − 0.187958i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.75855e13 | −0.686436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.26821e14i | 1.26778i | 0.773422 | + | 0.633892i | \(0.218544\pi\) | ||||
−0.773422 | + | 0.633892i | \(0.781456\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.20605e12 | −0.0512259 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 6.22884e13i | − 0.603308i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.02036e13 | 0.669363 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.63818e13i | 0.529218i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.07570e13 | 0.0994032 | 0.0497016 | − | 0.998764i | \(-0.484173\pi\) | ||||
0.0497016 | + | 0.998764i | \(0.484173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.97002e14i | − 1.79232i | −0.443730 | − | 0.896161i | \(-0.646345\pi\) | ||||
0.443730 | − | 0.896161i | \(-0.353655\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.81458e13 | −0.252124 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.12762e13i | 0.452267i | 0.974096 | + | 0.226133i | \(0.0726085\pi\) | ||||
−0.974096 | + | 0.226133i | \(0.927391\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.66650e13 | −0.231589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.99679e13i | 0.512878i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.25652e13 | 0.611171 | 0.305585 | − | 0.952165i | \(-0.401148\pi\) | ||||
0.305585 | + | 0.952165i | \(0.401148\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 1.24296e14i | − 1.03098i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.76184e13 | −0.470689 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 2.28320e14i | − 1.83703i | −0.395384 | − | 0.918516i | \(-0.629388\pi\) | ||||
0.395384 | − | 0.918516i | \(-0.370612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.92435e14 | −1.52503 | −0.762514 | − | 0.646972i | \(-0.776035\pi\) | ||||
−0.762514 | + | 0.646972i | \(0.776035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.17047e13i | 0.325550i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.63746e14 | −1.25910 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.33619e14i | − 1.01214i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.47925e14 | −1.10385 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 2.65714e13i | − 0.195344i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.05450e13 | −0.438534 | −0.219267 | − | 0.975665i | \(-0.570367\pi\) | ||||
−0.219267 | + | 0.975665i | \(0.570367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1.63507e13i | − 0.116686i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.35241e14 | 0.950965 | 0.475483 | − | 0.879725i | \(-0.342273\pi\) | ||||
0.475483 | + | 0.879725i | \(0.342273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51565e14i | 1.05015i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.30261e13 | 0.0889362 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.81334e13i | − 0.122005i | −0.998138 | − | 0.0610023i | \(-0.980570\pi\) | ||||
0.998138 | − | 0.0610023i | \(-0.0194297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.79897e12 | 0.0649722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.80871e13i | − 0.248882i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.09497e13 | −0.199325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.86141e14i | 1.18155i | 0.806836 | + | 0.590775i | \(0.201178\pi\) | ||||
−0.806836 | + | 0.590775i | \(0.798822\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.39949e13 | −0.150125 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.75144e14i | 1.08012i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.51898e14 | −2.74712 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.24941e14i | 0.748719i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.30460e14 | 0.770705 | 0.385353 | − | 0.922769i | \(-0.374080\pi\) | ||||
0.385353 | + | 0.922769i | \(0.374080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.48752e13i | 0.552556i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.40324e13 | −0.482504 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.75269e14i | − 2.69056i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.34678e13 | −0.0751734 | −0.0375867 | − | 0.999293i | \(-0.511967\pi\) | ||||
−0.0375867 | + | 0.999293i | \(0.511967\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 3.94053e13i | − 0.216873i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.02503e13 | 0.381242 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.19437e13i | − 0.0639161i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.76497e12 | 0.00931413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.37711e13i | 0.123710i | 0.998085 | + | 0.0618551i | \(0.0197017\pi\) | ||||
−0.998085 | + | 0.0618551i | \(0.980298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.15687e14 | 1.62024 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.39773e13i | 0.0707507i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.71903e14 | 0.858211 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.82784e13i | 0.139246i | 0.997573 | + | 0.0696229i | \(0.0221796\pi\) | ||||
−0.997573 | + | 0.0696229i | \(0.977820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.62560e12 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.17361e14i | − 1.04135i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.57811e13 | −0.452647 | −0.226324 | − | 0.974052i | \(-0.572671\pi\) | ||||
−0.226324 | + | 0.974052i | \(0.572671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.38015e14i | 0.643412i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.35121e12 | 0.0108132 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.94507e14i | − 1.33621i | −0.744069 | − | 0.668103i | \(-0.767107\pi\) | ||||
0.744069 | − | 0.668103i | \(-0.232893\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.85442e13 | 0.262055 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.05112e14i | 0.464201i | 0.972692 | + | 0.232101i | \(0.0745599\pi\) | ||||
−0.972692 | + | 0.232101i | \(0.925440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99986e14 | 0.871402 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 6.48885e13i | − 0.278975i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.24769e14 | −0.953516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.11066e14i | 0.883524i | 0.897132 | + | 0.441762i | \(0.145646\pi\) | ||||
−0.897132 | + | 0.441762i | \(0.854354\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.25567e14 | 0.931752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2.06106e14i | − 0.840148i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46472e14 | 0.589217 | 0.294609 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294609 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.81091e13i | 0.111593i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.59301e14 | 0.624160 | 0.312080 | − | 0.950056i | \(-0.398974\pi\) | ||||
0.312080 | + | 0.950056i | \(0.398974\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.02177e14i | 2.32864i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.19882e13 | −0.312928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.57091e13i | − 0.322887i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.73317e13 | 0.287558 | 0.143779 | − | 0.989610i | \(-0.454075\pi\) | ||||
0.143779 | + | 0.989610i | \(0.454075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.41300e14i | 0.518645i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.30206e14 | −0.471775 | −0.235888 | − | 0.971780i | \(-0.575800\pi\) | ||||
−0.235888 | + | 0.971780i | \(0.575800\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.03781e13i | 0.323262i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.24989e14 | 0.441334 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.34366e14i | 2.21133i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.24699e14 | 0.429149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 8.01716e13i | − 0.272403i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.69773e14 | 0.905005 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.11665e13i | − 0.103232i | −0.998667 | − | 0.0516161i | \(-0.983563\pi\) | ||||
0.998667 | − | 0.0516161i | \(-0.0164372\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.63397e13 | 0.0534392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.42409e14i | 0.459890i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.54081e13 | 0.272354 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6.08448e13i | − 0.191597i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.30484e13 | 0.133864 | 0.0669322 | − | 0.997758i | \(-0.478679\pi\) | ||||
0.0669322 | + | 0.997758i | \(0.478679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 6.48957e14i | − 1.99288i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.60608e14 | −0.487085 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.27434e14i | 0.381688i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.52708e14 | 0.747549 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.08394e13i | 0.0901028i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.13586e14 | 1.48208 | 0.741038 | − | 0.671464i | \(-0.234334\pi\) | ||||
0.741038 | + | 0.671464i | \(0.234334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 4.73516e14i | − 1.34968i | −0.737964 | − | 0.674840i | \(-0.764213\pi\) | ||||
0.737964 | − | 0.674840i | \(-0.235787\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.56538e13 | −0.184845 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.68127e14i | 1.02379i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.05128e14 | −0.838246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 7.71265e13i | − 0.209307i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.80616e14 | 0.484218 | 0.242109 | − | 0.970249i | \(-0.422161\pi\) | ||||
0.242109 | + | 0.970249i | \(0.422161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.69478e14i | 1.50826i | 0.656723 | + | 0.754132i | \(0.271942\pi\) | ||||
−0.656723 | + | 0.754132i | \(0.728058\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.61628e13 | −0.0946222 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.66425e14i | 0.947235i | 0.880731 | + | 0.473617i | \(0.157052\pi\) | ||||
−0.880731 | + | 0.473617i | \(0.842948\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.56256e14 | −0.909891 | −0.454945 | − | 0.890519i | \(-0.650341\pi\) | ||||
−0.454945 | + | 0.890519i | \(0.650341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2.34551e14i | − 0.591877i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.06585e15 | −2.65748 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.96470e14i | − 0.730378i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.21502e13 | 0.102606 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.22645e13i | 0.0295012i | 0.999891 | + | 0.0147506i | \(0.00469543\pi\) | ||||
−0.999891 | + | 0.0147506i | \(0.995305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.22175e14 | 1.00349 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.23180e14i | − 0.524224i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.31916e14 | −0.538327 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.73267e14i | − 1.54444i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.23702e14 | −0.733850 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.46420e14i | − 0.328060i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.11937e14 | −0.912190 | −0.456095 | − | 0.889931i | \(-0.650752\pi\) | ||||
−0.456095 | + | 0.889931i | \(0.650752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.15093e14i | 0.251895i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.28656e14 | −1.35991 | −0.679953 | − | 0.733255i | \(-0.738000\pi\) | ||||
−0.679953 | + | 0.733255i | \(0.738000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.82662e14i | 0.818180i | 0.912494 | + | 0.409090i | \(0.134154\pi\) | ||||
−0.912494 | + | 0.409090i | \(0.865846\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.35718e14 | 1.76622 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 5.82551e14i | − 1.21697i | −0.793565 | − | 0.608485i | \(-0.791778\pi\) | ||||
0.793565 | − | 0.608485i | \(-0.208222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.59032e14 | 0.534900 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 3.50334e14i | − 0.715133i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.71524e13 | −0.175865 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.55747e12i | 0.0150760i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.06532e14 | 0.210091 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.61321e14i | 1.67929i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.76512e14 | 0.340233 | 0.170116 | − | 0.985424i | \(-0.445586\pi\) | ||||
0.170116 | + | 0.985424i | \(0.445586\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 5.52388e14i | − 1.05269i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.11184e12 | 0.00586324 | 0.00293162 | − | 0.999996i | \(-0.499067\pi\) | ||||
0.00293162 | + | 0.999996i | \(0.499067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.42282e14i | − 1.19653i | −0.801300 | − | 0.598263i | \(-0.795858\pi\) | ||||
0.801300 | − | 0.598263i | \(-0.204142\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.68498e14 | 0.310368 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 7.46478e14i | − 1.35956i | −0.733416 | − | 0.679781i | \(-0.762075\pi\) | ||||
0.733416 | − | 0.679781i | \(-0.237925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.89602e14 | −1.60209 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.68655e13i | 0.0300338i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.10993e14 | −1.60420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.26852e13i | 0.143984i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.03510e13 | −0.155586 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.43145e14i | 0.754653i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.69886e14 | 0.791350 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.01977e14i | 0.669519i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.33112e14 | 0.548716 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.63392e12i | − 0.0156952i | −0.999969 | − | 0.00784760i | \(-0.997502\pi\) | ||||
0.999969 | − | 0.00784760i | \(-0.00249799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.34056e14 | −0.538270 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.46133e14i | 0.870375i | 0.900340 | + | 0.435188i | \(0.143318\pi\) | ||||
−0.900340 | + | 0.435188i | \(0.856682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.43513e14 | −0.226224 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.67906e14i | 0.261794i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.77519e15 | −2.73778 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 4.59623e14i | − 0.701171i | −0.936531 | − | 0.350586i | \(-0.885983\pi\) | ||||
0.936531 | − | 0.350586i | \(-0.114017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.06144e12 | 0.00311081 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.00820e14i | 0.598330i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.88372e14 | 0.278169 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.21889e14i | − 0.324144i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.06601e14 | 1.02116 | 0.510582 | − | 0.859829i | \(-0.329430\pi\) | ||||
0.510582 | + | 0.859829i | \(0.329430\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.49622e15i | 2.13917i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.64643e14 | 0.374328 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.81333e14i | 0.253757i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.51470e14 | −0.486621 | −0.243311 | − | 0.969948i | \(-0.578233\pi\) | ||||
−0.243311 | + | 0.969948i | \(0.578233\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.75494e14i | − 0.788338i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.00424e15 | 1.36110 | 0.680548 | − | 0.732704i | \(-0.261742\pi\) | ||||
0.680548 | + | 0.732704i | \(0.261742\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.79014e14i | − 1.31290i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.51625e14 | 0.201192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.10610e14i | 0.145226i | 0.997360 | + | 0.0726128i | \(0.0231337\pi\) | ||||
−0.997360 | + | 0.0726128i | \(0.976866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.09611e14 | −0.532157 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 5.26413e13i | − 0.0676743i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.36100e15 | 1.73138 | 0.865690 | − | 0.500580i | \(-0.166880\pi\) | ||||
0.865690 | + | 0.500580i | \(0.166880\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 5.19014e14i | − 0.653374i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.77315e14 | −0.220895 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1.39949e14i | − 0.172534i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.86645e14 | 0.715745 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.57986e14i | 0.190759i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.01826e14 | 0.838674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.16847e13i | − 0.0492998i | −0.999696 | − | 0.0246499i | \(-0.992153\pi\) | ||||
0.999696 | − | 0.0246499i | \(-0.00784709\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.88832e14 | −1.04040 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.32216e14i | 0.848288i | 0.905595 | + | 0.424144i | \(0.139425\pi\) | ||||
−0.905595 | + | 0.424144i | \(0.860575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50140e15 | 2.86826 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.16238e14i | − 0.131924i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.03714e14 | 0.228849 | 0.114424 | − | 0.993432i | \(-0.463498\pi\) | ||||
0.114424 | + | 0.993432i | \(0.463498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.55216e14i | 0.394983i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.23258e14 | 0.465865 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.48032e14i | 0.270234i | 0.990830 | + | 0.135117i | \(0.0431410\pi\) | ||||
−0.990830 | + | 0.135117i | \(0.956859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.88721e14 | −0.203535 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.20015e15i | 1.28130i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.70902e14 | 0.497679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 5.10805e14i | − 0.534425i | −0.963638 | − | 0.267213i | \(-0.913897\pi\) | ||||
0.963638 | − | 0.267213i | \(-0.0861026\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.39048e14 | 0.247593 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.24111e14i | − 0.332336i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.44756e14 | −0.451488 | −0.225744 | − | 0.974187i | \(-0.572481\pi\) | ||||
−0.225744 | + | 0.974187i | \(0.572481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 8.78523e13i | − 0.0882928i |
(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 | 48.11.g.c.31.2 | ✓ | 4 | |
3.2 | odd | 2 | 144.11.g.e.127.1 | 4 | |||
4.3 | odd | 2 | inner | 48.11.g.c.31.4 | yes | 4 | |
8.3 | odd | 2 | 192.11.g.b.127.1 | 4 | |||
8.5 | even | 2 | 192.11.g.b.127.3 | 4 | |||
12.11 | even | 2 | 144.11.g.e.127.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.11.g.c.31.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
48.11.g.c.31.4 | yes | 4 | 4.3 | odd | 2 | inner | |
144.11.g.e.127.1 | 4 | 3.2 | odd | 2 | |||
144.11.g.e.127.2 | 4 | 12.11 | even | 2 | |||
192.11.g.b.127.1 | 4 | 8.3 | odd | 2 | |||
192.11.g.b.127.3 | 4 | 8.5 | even | 2 |