Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2271,1,Mod(176,2271)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2271, base_ring=CyclotomicField(126))
chi = DirichletCharacter(H, H._module([63, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2271.176");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2271 = 3 \cdot 757 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2271.bm (of order \(126\), degree \(36\), 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: | \(1.13337664369\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Coefficient field: | \(\Q(\zeta_{63})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{36} - x^{33} + x^{27} - x^{24} + x^{18} - x^{12} + x^{9} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{63}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{63} - \cdots)\) |
Embedding invariants
Embedding label | 1700.1 | ||
Root | \(-0.797133 - 0.603804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2271.1700 |
Dual form | 2271.1.bm.a.2096.1 |
$q$-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 \(\left(\mathbb{Z}/2271\mathbb{Z}\right)^\times\).
\(n\) | \(758\) | \(1516\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{61}{63}\right)\) |
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 | 0.995031 | − | 0.0995678i | \(-0.0317460\pi\) | ||||
−0.995031 | + | 0.0995678i | \(0.968254\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(4\) | 0.980172 | − | 0.198146i | 0.980172 | − | 0.198146i | ||||
\(5\) | 0 | 0 | 0.270840 | − | 0.962624i | \(-0.412698\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587302\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.22226 | + | 0.247084i | 1.22226 | + | 0.247084i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.456211 | + | 0.889872i | \(0.349206\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.969077 | − | 0.246757i | \(-0.920635\pi\) | ||||
0.969077 | + | 0.246757i | \(0.0793651\pi\) | |||||||
\(12\) | −0.661686 | − | 0.749781i | −0.661686 | − | 0.749781i | ||||
\(13\) | −0.894347 | + | 1.24396i | −0.894347 | + | 1.24396i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.969077 | + | 0.246757i | \(0.920635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.921476 | − | 0.388435i | 0.921476 | − | 0.388435i | ||||
\(17\) | 0 | 0 | 0.456211 | − | 0.889872i | \(-0.349206\pi\) | ||||
−0.456211 | + | 0.889872i | \(0.650794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.61852 | − | 0.881399i | 1.61852 | − | 0.881399i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.995031 | − | 0.0995678i | \(-0.0317460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.397146 | − | 1.18205i | −0.397146 | − | 1.18205i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.853291 | − | 0.521435i | −0.853291 | − | 0.521435i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 1.00000 | ||||||||
\(28\) | 1.24698 | 1.24698 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.102282 | + | 0.816190i | 0.102282 | + | 0.816190i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.318487 | + | 0.947927i | −0.318487 | + | 0.947927i | ||||
\(37\) | 1.61852 | + | 0.682264i | 1.61852 | + | 0.682264i | 0.995031 | − | 0.0995678i | \(-0.0317460\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.52448 | + | 0.152547i | 1.52448 | + | 0.152547i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.797133 | − | 0.603804i | \(-0.793651\pi\) | ||||
0.797133 | + | 0.603804i | \(0.206349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.53018 | − | 0.0763683i | −1.53018 | − | 0.0763683i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.797133 | + | 0.603804i | \(0.793651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(48\) | −0.797133 | − | 0.603804i | −0.797133 | − | 0.603804i | ||||
\(49\) | 0.511381 | + | 0.215565i | 0.511381 | + | 0.215565i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.630128 | + | 1.39651i | −0.630128 | + | 1.39651i | ||||
\(53\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.57257 | − | 0.960980i | −1.57257 | − | 0.960980i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.63076 | + | 0.503024i | −1.63076 | + | 0.503024i | −0.969077 | − | 0.246757i | \(-0.920635\pi\) |
−0.661686 | + | 0.749781i | \(0.730159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.825109 | + | 0.934962i | −0.825109 | + | 0.934962i | ||||
\(64\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.346865 | − | 1.96717i | −0.346865 | − | 1.96717i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.124344 | − | 0.992239i | \(-0.539683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.878222 | − | 0.478254i | \(-0.841270\pi\) | ||||
0.878222 | + | 0.478254i | \(0.158730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.254586 | − | 1.44383i | −0.254586 | − | 1.44383i | −0.797133 | − | 0.603804i | \(-0.793651\pi\) |
0.542546 | − | 0.840026i | \(-0.317460\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0249307 | + | 0.999689i | −0.0249307 | + | 0.999689i | ||||
\(76\) | 1.41178 | − | 1.18463i | 1.41178 | − | 1.18463i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(84\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.456211 | − | 0.889872i | \(-0.650794\pi\) | ||||
0.456211 | + | 0.889872i | \(0.349206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.40048 | + | 1.29946i | −1.40048 | + | 1.29946i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.655701 | − | 0.496674i | 0.655701 | − | 0.496674i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.93845 | + | 0.391866i | −1.93845 | + | 0.391866i | −0.939693 | + | 0.342020i | \(0.888889\pi\) |
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(101\) | 0 | 0 | −0.969077 | − | 0.246757i | \(-0.920635\pi\) | ||||
0.969077 | + | 0.246757i | \(0.0793651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.247452 | + | 1.97462i | −0.247452 | + | 1.97462i | −0.0249307 | + | 0.999689i | \(0.507937\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.878222 | − | 0.478254i | \(-0.158730\pi\) | ||||
−0.878222 | + | 0.478254i | \(0.841270\pi\) | |||||||
\(108\) | 0.980172 | − | 0.198146i | 0.980172 | − | 0.198146i | ||||
\(109\) | −0.795429 | − | 0.738050i | −0.795429 | − | 0.738050i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
−0.969077 | + | 0.246757i | \(0.920635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.218403 | − | 1.74281i | −0.218403 | − | 1.74281i | ||||
\(112\) | 1.22226 | − | 0.247084i | 1.22226 | − | 0.247084i | ||||
\(113\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.630128 | − | 1.39651i | −0.630128 | − | 1.39651i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.878222 | + | 0.478254i | 0.878222 | + | 0.478254i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.261979 | + | 0.779741i | 0.261979 | + | 0.779741i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.03030 | + | 1.29196i | 1.03030 | + | 1.29196i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.698955 | + | 1.36336i | 0.698955 | + | 1.36336i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.411287 | − | 0.911506i | \(-0.634921\pi\) | ||||
0.411287 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.19602 | − | 0.677384i | 2.19602 | − | 0.677384i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.998757 | − | 0.0498459i | \(-0.0158730\pi\) | ||||
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.131259 | − | 0.0714799i | 0.131259 | − | 0.0714799i | −0.411287 | − | 0.911506i | \(-0.634921\pi\) |
0.542546 | + | 0.840026i | \(0.317460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.124344 | + | 0.992239i | −0.124344 | + | 0.992239i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0690056 | − | 0.550651i | −0.0690056 | − | 0.550651i | ||||
\(148\) | 1.72162 | + | 0.348032i | 1.72162 | + | 0.348032i | ||||
\(149\) | 0 | 0 | 0.542546 | − | 0.840026i | \(-0.317460\pi\) | ||||
−0.542546 | + | 0.840026i | \(0.682540\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.729774 | − | 1.85943i | −0.729774 | − | 1.85943i | −0.411287 | − | 0.911506i | \(-0.634921\pi\) |
−0.318487 | − | 0.947927i | \(-0.603175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.52448 | − | 0.152547i | 1.52448 | − | 0.152547i | ||||
\(157\) | −0.120535 | − | 0.428408i | −0.120535 | − | 0.428408i | 0.878222 | − | 0.478254i | \(-0.158730\pi\) |
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.63402 | − | 0.246289i | −1.63402 | − | 0.246289i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.270840 | − | 0.962624i | \(-0.587302\pi\) | ||||
0.270840 | + | 0.962624i | \(0.412698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.429096 | − | 1.27714i | −0.429096 | − | 1.27714i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0459461 | + | 1.84238i | −0.0459461 | + | 1.84238i | ||||
\(172\) | −1.51498 | + | 0.228346i | −1.51498 | + | 0.228346i | ||||
\(173\) | 0 | 0 | −0.456211 | − | 0.889872i | \(-0.650794\pi\) | ||||
0.456211 | + | 0.889872i | \(0.349206\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.914101 | − | 0.848162i | −0.914101 | − | 0.848162i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.661686 | − | 0.749781i | \(-0.730159\pi\) | ||||
0.661686 | + | 0.749781i | \(0.269841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0476011 | − | 0.635192i | −0.0476011 | − | 0.635192i | −0.969077 | − | 0.246757i | \(-0.920635\pi\) |
0.921476 | − | 0.388435i | \(-0.126984\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.25101 | + | 1.16077i | 1.25101 | + | 1.16077i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.22226 | + | 0.247084i | 1.22226 | + | 0.247084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.921476 | − | 0.388435i | \(-0.873016\pi\) | ||||
0.921476 | + | 0.388435i | \(0.126984\pi\) | |||||||
\(192\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(193\) | 0.636181 | − | 0.0317505i | 0.636181 | − | 0.0317505i | 0.270840 | − | 0.962624i | \(-0.412698\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.543955 | + | 0.109963i | 0.543955 | + | 0.109963i | ||||
\(197\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.03688 | + | 0.319837i | 1.03688 | + | 0.319837i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.270840 | + | 0.962624i | \(0.412698\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.53018 | + | 1.28398i | −1.53018 | + | 1.28398i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.340922 | + | 1.49368i | −0.340922 | + | 1.49368i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.980172 | − | 0.198146i | −0.980172 | − | 0.198146i | −0.318487 | − | 0.947927i | \(-0.603175\pi\) |
−0.661686 | + | 0.749781i | \(0.730159\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0766531 | + | 1.02287i | −0.0766531 | + | 1.02287i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.12310 | + | 0.942393i | −1.12310 | + | 0.942393i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.857396 | + | 1.67241i | −0.857396 | + | 1.67241i | −0.124344 | + | 0.992239i | \(0.539683\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.878222 | − | 0.478254i | 0.878222 | − | 0.478254i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(228\) | −1.73181 | − | 0.630327i | −1.73181 | − | 0.630327i | ||||
\(229\) | −0.994008 | − | 1.24645i | −0.994008 | − | 1.24645i | −0.969077 | − | 0.246757i | \(-0.920635\pi\) |
−0.0249307 | − | 0.999689i | \(-0.507937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.583744 | − | 0.811938i | \(-0.698413\pi\) | ||||
0.583744 | + | 0.811938i | \(0.301587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.878222 | − | 0.478254i | \(-0.841270\pi\) | ||||
0.878222 | + | 0.478254i | \(0.158730\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.870687 | + | 1.09181i | 0.870687 | + | 1.09181i | 0.995031 | + | 0.0995678i | \(0.0317460\pi\) |
−0.124344 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(244\) | −1.49876 | + | 0.816180i | −1.49876 | + | 0.816180i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.351093 | + | 2.80165i | −0.351093 | + | 2.80165i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(252\) | −0.623490 | + | 1.07992i | −0.623490 | + | 1.07992i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.698237 | − | 0.715867i | 0.698237 | − | 0.715867i | ||||
\(257\) | 0 | 0 | 0.583744 | − | 0.811938i | \(-0.301587\pi\) | ||||
−0.583744 | + | 0.811938i | \(0.698413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.80967 | + | 1.23381i | 1.80967 | + | 1.23381i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.0249307 | − | 0.999689i | \(-0.492063\pi\) | ||||
−0.0249307 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.729774 | − | 1.85943i | −0.729774 | − | 1.85943i | ||||
\(269\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.818487 | + | 1.81395i | −0.818487 | + | 1.81395i | −0.318487 | + | 0.947927i | \(0.603175\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.82561 | + | 0.563125i | 1.82561 | + | 0.563125i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.535628 | + | 0.496990i | −0.535628 | + | 0.496990i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.757983 | − | 0.319516i | −0.757983 | − | 0.319516i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.456211 | − | 0.889872i | \(-0.349206\pi\) | ||||
−0.456211 | + | 0.889872i | \(0.650794\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.40012 | − | 0.762464i | −1.40012 | − | 0.762464i | −0.411287 | − | 0.911506i | \(-0.634921\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.583744 | − | 0.811938i | −0.583744 | − | 0.811938i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.30859 | + | 1.48281i | 1.30859 | + | 1.48281i | ||||
\(292\) | −0.535628 | − | 1.36476i | −0.535628 | − | 1.36476i | ||||
\(293\) | 0 | 0 | 0.124344 | − | 0.992239i | \(-0.460317\pi\) | ||||
−0.124344 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | ||||
\(301\) | −1.85141 | − | 0.471426i | −1.85141 | − | 0.471426i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.14906 | − | 1.44088i | 1.14906 | − | 1.44088i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.964623 | + | 0.657669i | −0.964623 | + | 0.657669i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.0249307 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.83379 | − | 0.773009i | 1.83379 | − | 0.773009i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.543524 | + | 1.61772i | 0.543524 | + | 1.61772i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.797133 | − | 0.603804i | 0.797133 | − | 0.603804i | ||||
\(317\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.661686 | − | 0.749781i | −0.661686 | − | 0.749781i | ||||
\(325\) | 1.41178 | − | 0.595117i | 1.41178 | − | 0.595117i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.241456 | + | 1.05789i | −0.241456 | + | 1.05789i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.240997 | + | 1.92311i | 0.240997 | + | 1.92311i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.124344 | + | 0.992239i | \(0.539683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.40012 | + | 1.06055i | −1.40012 | + | 1.06055i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.825109 | − | 0.934962i | −0.825109 | − | 0.934962i | ||||
\(337\) | 0.240997 | − | 0.0613655i | 0.240997 | − | 0.0613655i | −0.124344 | − | 0.992239i | \(-0.539683\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.458528 | − | 0.312619i | −0.458528 | − | 0.312619i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.24356 | − | 0.452620i | 1.24356 | − | 0.452620i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.878222 | + | 0.478254i | \(0.158730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.894347 | + | 1.24396i | −0.894347 | + | 1.24396i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.998757 | − | 0.0498459i | \(-0.984127\pi\) | ||||
0.998757 | + | 0.0498459i | \(0.0158730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.980172 | − | 0.198146i | \(-0.936508\pi\) | ||||
0.980172 | + | 0.198146i | \(0.0634921\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.30020 | − | 2.01310i | 1.30020 | − | 2.01310i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0249307 | − | 0.999689i | −0.0249307 | − | 0.999689i | ||||
\(364\) | −1.11523 | + | 1.55119i | −1.11523 | + | 1.55119i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.222786 | + | 0.791830i | −0.222786 | + | 0.791830i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.544286 | − | 0.616751i | 0.544286 | − | 0.616751i | ||||
\(373\) | −0.509014 | − | 0.185266i | −0.509014 | − | 0.185266i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.583744 | + | 0.811938i | \(0.698413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.90165 | + | 0.190289i | 1.90165 | + | 0.190289i | 0.980172 | − | 0.198146i | \(-0.0634921\pi\) |
0.921476 | + | 0.388435i | \(0.126984\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.603718 | − | 1.53825i | 0.603718 | − | 1.53825i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.583744 | − | 0.811938i | \(-0.301587\pi\) | ||||
−0.583744 | + | 0.811938i | \(0.698413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.831229 | − | 1.28699i | 0.831229 | − | 1.28699i | ||||
\(388\) | −1.82237 | + | 0.768193i | −1.82237 | + | 0.768193i | ||||
\(389\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.722402 | − | 0.393399i | −0.722402 | − | 0.393399i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.797133 | + | 0.603804i | \(0.793651\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.68464 | − | 1.56312i | −1.68464 | − | 1.56312i | ||||
\(400\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(401\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.10678 | − | 0.602723i | −1.10678 | − | 0.602723i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.716194 | − | 0.144782i | 0.716194 | − | 0.144782i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.542546 | + | 0.840026i | \(0.317460\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.148717 | + | 1.98450i | 0.148717 | + | 1.98450i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.127533 | − | 0.0779338i | −0.127533 | − | 0.0779338i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.411287 | − | 0.911506i | \(-0.634921\pi\) | ||||
0.411287 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.19232 | + | 1.35106i | 1.19232 | + | 1.35106i | 0.921476 | + | 0.388435i | \(0.126984\pi\) |
0.270840 | + | 0.962624i | \(0.412698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.11750 | + | 0.211888i | −2.11750 | + | 0.211888i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.998757 | − | 0.0498459i | \(-0.984127\pi\) | ||||
0.998757 | + | 0.0498459i | \(0.0158730\pi\) | |||||||
\(432\) | 0.921476 | − | 0.388435i | 0.921476 | − | 0.388435i | ||||
\(433\) | 1.28245 | + | 1.45319i | 1.28245 | + | 1.45319i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.456211 | + | 0.889872i | \(0.349206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.925900 | − | 0.565805i | −0.925900 | − | 0.565805i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.205475 | − | 0.140091i | −0.205475 | − | 0.140091i | 0.456211 | − | 0.889872i | \(-0.349206\pi\) |
−0.661686 | + | 0.749781i | \(0.730159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.442375 | + | 0.335086i | −0.442375 | + | 0.335086i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(444\) | −0.559404 | − | 1.66498i | −0.559404 | − | 1.66498i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.14906 | − | 0.484370i | 1.14906 | − | 0.484370i | ||||
\(449\) | 0 | 0 | −0.969077 | − | 0.246757i | \(-0.920635\pi\) | ||||
0.969077 | + | 0.246757i | \(0.0793651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.24543 | + | 1.56172i | −1.24543 | + | 1.56172i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0431841 | − | 0.244909i | −0.0431841 | − | 0.244909i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.995031 | − | 0.0995678i | \(-0.968254\pi\) | ||||
0.995031 | + | 0.0995678i | \(0.0317460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.379750 | + | 1.66379i | 0.379750 | + | 1.66379i | 0.698237 | + | 0.715867i | \(0.253968\pi\) |
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(468\) | −0.894347 | − | 1.24396i | −0.894347 | − | 1.24396i | ||||
\(469\) | 0.0620988 | − | 2.49008i | 0.0620988 | − | 2.49008i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.310745 | + | 0.318591i | −0.310745 | + | 0.318591i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.84066 | − | 0.0918636i | −1.84066 | − | 0.0918636i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.29623 | + | 1.40320i | −2.29623 | + | 1.40320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.229801 | + | 1.30327i | −0.229801 | + | 1.30327i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.603718 | + | 1.53825i | 0.603718 | + | 1.53825i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.921476 | − | 0.388435i | \(-0.126984\pi\) | ||||
−0.921476 | + | 0.388435i | \(0.873016\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.411287 | + | 0.712370i | 0.411287 | + | 0.712370i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.633416 | − | 0.980720i | −0.633416 | − | 0.980720i | −0.998757 | − | 0.0498459i | \(-0.984127\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.698237 | − | 0.715867i | \(-0.746032\pi\) | ||||
0.698237 | + | 0.715867i | \(0.253968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.891487 | + | 1.01018i | −0.891487 | + | 1.01018i | ||||
\(508\) | 1.26587 | + | 1.06219i | 1.26587 | + | 1.06219i | ||||
\(509\) | 0 | 0 | −0.411287 | − | 0.911506i | \(-0.634921\pi\) | ||||
0.411287 | + | 0.911506i | \(0.365079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0455783 | − | 1.82763i | 0.0455783 | − | 1.82763i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.61852 | − | 0.881399i | 1.61852 | − | 0.881399i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.955242 | + | 1.19784i | 0.955242 | + | 1.19784i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.797133 | − | 0.603804i | \(-0.206349\pi\) | ||||
−0.797133 | + | 0.603804i | \(0.793651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.277479 | + | 1.21572i | −0.277479 | + | 1.21572i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.01826 | − | 1.09909i | 2.01826 | − | 1.09909i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.82624 | − | 0.563320i | 1.82624 | − | 0.563320i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
1.00000 | \(0\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.526292 | + | 0.358820i | −0.526292 | + | 0.358820i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.85839 | − | 0.280108i | 1.85839 | − | 0.280108i | 0.878222 | − | 0.478254i | \(-0.158730\pi\) |
0.980172 | + | 0.198146i | \(0.0634921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.379750 | − | 1.66379i | 0.379750 | − | 1.66379i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20842 | − | 0.307701i | 1.20842 | − | 0.307701i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.114493 | − | 0.0960712i | 0.114493 | − | 0.0960712i | ||||
\(557\) | 0 | 0 | −0.969077 | − | 0.246757i | \(-0.920635\pi\) | ||||
0.969077 | + | 0.246757i | \(0.0793651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.46352 | − | 1.83519i | 1.46352 | − | 1.83519i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.397146 | − | 1.18205i | −0.397146 | − | 1.18205i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.456211 | − | 0.889872i | \(-0.349206\pi\) | ||||
−0.456211 | + | 0.889872i | \(0.650794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.109562 | + | 0.101659i | −0.109562 | + | 0.101659i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(577\) | −1.48883 | − | 1.01507i | −1.48883 | − | 1.01507i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.345587 | − | 0.535074i | −0.345587 | − | 0.535074i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.797133 | − | 0.603804i | \(-0.793651\pi\) | ||||
0.797133 | + | 0.603804i | \(0.206349\pi\) | |||||||
\(588\) | −0.176747 | − | 0.526060i | −0.176747 | − | 0.526060i | ||||
\(589\) | 0.884935 | + | 1.23087i | 0.884935 | + | 1.23087i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.75644 | 1.75644 | ||||||||
\(593\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.241456 | − | 1.05789i | −0.241456 | − | 1.05789i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.853291 | − | 0.521435i | \(-0.174603\pi\) | ||||
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.16169 | + | 0.116244i | −1.16169 | + | 0.116244i | −0.661686 | − | 0.749781i | \(-0.730159\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.87705 | + | 0.683190i | 1.87705 | + | 0.683190i | ||||
\(604\) | −1.08374 | − | 1.67796i | −1.08374 | − | 1.67796i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.119140 | − | 1.58981i | −0.119140 | − | 1.58981i | −0.661686 | − | 0.749781i | \(-0.730159\pi\) |
0.542546 | − | 0.840026i | \(-0.317460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.164553 | − | 1.31310i | 0.164553 | − | 1.31310i | −0.661686 | − | 0.749781i | \(-0.730159\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.270840 | − | 0.962624i | \(-0.412698\pi\) | ||||
−0.270840 | + | 0.962624i | \(0.587302\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.25818 | + | 0.605907i | −1.25818 | + | 0.605907i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.46402 | − | 0.451591i | 1.46402 | − | 0.451591i | ||||
\(625\) | 0.456211 | + | 0.889872i | 0.456211 | + | 0.889872i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.203033 | − | 0.396030i | −0.203033 | − | 0.396030i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.727916 | + | 1.01247i | −0.727916 | + | 1.01247i | 0.270840 | + | 0.962624i | \(0.412698\pi\) |
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.318487 | + | 0.947927i | 0.318487 | + | 0.947927i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.725506 | + | 0.443348i | −0.725506 | + | 0.443348i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.69327 | + | 0.815435i | 1.69327 | + | 0.815435i | 0.995031 | + | 0.0995678i | \(0.0317460\pi\) |
0.698237 | + | 0.715867i | \(0.253968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.411287 | − | 0.911506i | \(-0.365079\pi\) | ||||
−0.411287 | + | 0.911506i | \(0.634921\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.924154 | − | 0.445049i | 0.924154 | − | 0.445049i | ||||
\(652\) | −1.65042 | + | 0.0823692i | −1.65042 | + | 0.0823692i | ||||
\(653\) | 0 | 0 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.37769 | + | 0.501437i | 1.37769 | + | 0.501437i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.57257 | − | 0.960980i | −1.57257 | − | 0.960980i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.583744 | − | 0.811938i | \(-0.698413\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.87705 | − | 0.0936796i | 1.87705 | − | 0.0936796i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.853291 | − | 0.521435i | −0.853291 | − | 0.521435i | ||||
\(676\) | −0.673648 | − | 1.16679i | −0.673648 | − | 1.16679i | ||||
\(677\) | 0 | 0 | −0.124344 | − | 0.992239i | \(-0.539683\pi\) | ||||
0.124344 | + | 0.992239i | \(0.460317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.46610 | −2.46610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(684\) | 0.320025 | + | 1.81495i | 0.320025 | + | 1.81495i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.582450 | + | 1.48406i | −0.582450 | + | 1.48406i | ||||
\(688\) | −1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.535628 | − | 1.36476i | −0.535628 | − | 1.36476i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.06404 | − | 0.650219i | −1.06404 | − | 0.650219i | ||||
\(701\) | 0 | 0 | 0.995031 | − | 0.0995678i | \(-0.0317460\pi\) | ||||
−0.995031 | + | 0.0995678i | \(0.968254\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.22096 | − | 0.322305i | 3.22096 | − | 0.322305i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.05490 | + | 0.799058i | 1.05490 | + | 0.799058i | 0.980172 | − | 0.198146i | \(-0.0634921\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0747301 | + | 0.997204i | −0.0747301 | + | 0.997204i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.790346 | + | 2.35234i | −0.790346 | + | 2.35234i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.510189 | − | 1.29994i | 0.510189 | − | 1.29994i | ||||
\(724\) | −0.172518 | − | 0.613166i | −0.172518 | − | 0.613166i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.09708 | − | 0.399304i | 1.09708 | − | 0.399304i | 0.270840 | − | 0.962624i | \(-0.412698\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.45621 | + | 0.889872i | 1.45621 | + | 0.889872i | ||||
\(733\) | −1.02369 | − | 0.949843i | −1.02369 | − | 0.949843i | −0.0249307 | − | 0.999689i | \(-0.507937\pi\) |
−0.998757 | + | 0.0498459i | \(0.984127\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.797138 | − | 1.76664i | 0.797138 | − | 1.76664i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.60185 | − | 1.09677i | 2.60185 | − | 1.09677i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.995031 | − | 0.0995678i | \(-0.968254\pi\) | ||||
0.995031 | + | 0.0995678i | \(0.0317460\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.05187 | + | 1.46306i | 1.05187 | + | 1.46306i | 0.878222 | + | 0.478254i | \(0.158730\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.24698 | 1.24698 | ||||||||
\(757\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.980172 | − | 0.198146i | \(-0.0634921\pi\) | ||||
−0.980172 | + | 0.198146i | \(0.936508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.789857 | − | 1.09862i | −0.789857 | − | 1.09862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.969077 | − | 0.246757i | −0.969077 | − | 0.246757i | ||||
\(769\) | −0.0988957 | − | 0.112062i | −0.0988957 | − | 0.112062i | 0.698237 | − | 0.715867i | \(-0.253968\pi\) |
−0.797133 | + | 0.603804i | \(0.793651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.617276 | − | 0.157178i | 0.617276 | − | 0.157178i | ||||
\(773\) | 0 | 0 | 0.921476 | − | 0.388435i | \(-0.126984\pi\) | ||||
−0.921476 | + | 0.388435i | \(0.873016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.338314 | − | 0.749781i | 0.338314 | − | 0.749781i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.163677 | − | 2.18412i | 0.163677 | − | 2.18412i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.554958 | 0.554958 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
1.00000 | \(0\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.832726 | − | 2.47848i | 0.832726 | − | 2.47848i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.07970 | + | 0.108040i | 1.07970 | + | 0.108040i | ||||
\(797\) | 0 | 0 | −0.0249307 | − | 0.999689i | \(-0.507937\pi\) | ||||
0.0249307 | + | 0.999689i | \(0.492063\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.24543 | + | 1.56172i | −1.24543 | + | 1.56172i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.411287 | − | 0.911506i | \(-0.365079\pi\) | ||||
−0.411287 | + | 0.911506i | \(0.634921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.99006 | − | 0.199136i | 1.99006 | − | 0.199136i | 0.995031 | − | 0.0995678i | \(-0.0317460\pi\) |
0.995031 | − | 0.0995678i | \(-0.0317460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.98017 | − | 0.198146i | 1.98017 | − | 0.198146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.54395 | + | 1.22510i | −2.54395 | + | 1.22510i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.425123 | − | 1.86258i | −0.425123 | − | 1.86258i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.510189 | + | 1.29994i | 0.510189 | + | 1.29994i | 0.921476 | + | 0.388435i | \(0.126984\pi\) |
−0.411287 | + | 0.911506i | \(0.634921\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.203033 | + | 0.889545i | −0.203033 | + | 0.889545i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
−0.969077 | + | 0.246757i | \(0.920635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.698220 | + | 0.215372i | 0.698220 | + | 0.215372i | ||||
\(832\) | −0.0381960 | + | 1.53161i | −0.0381960 | + | 1.53161i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.102282 | + | 0.816190i | 0.102282 | + | 0.816190i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.853291 | − | 0.521435i | \(-0.825397\pi\) | ||||
0.853291 | + | 0.521435i | \(0.174603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.00000 | −1.00000 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.955242 | + | 0.801543i | 0.955242 | + | 0.801543i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0397461 | + | 1.59377i | 0.0397461 | + | 1.59377i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.0425463 | + | 0.0259995i | 0.0425463 | + | 0.0259995i | 0.542546 | − | 0.840026i | \(-0.317460\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.82237 | + | 0.274678i | −1.82237 | + | 0.274678i | −0.969077 | − | 0.246757i | \(-0.920635\pi\) |
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.411287 | + | 0.911506i | −0.411287 | + | 0.911506i | ||||
\(868\) | 0.127543 | + | 1.01777i | 0.127543 | + | 1.01777i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.75730 | + | 1.32784i | 2.75730 | + | 1.32784i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.629859 | − | 1.87468i | 0.629859 | − | 1.87468i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.914101 | + | 1.14625i | −0.914101 | + | 1.14625i | ||||
\(877\) | 1.68752 | − | 1.03122i | 1.68752 | − | 1.03122i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
0.921476 | − | 0.388435i | \(-0.126984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.318487 | − | 0.947927i | \(-0.603175\pi\) | ||||
0.318487 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.855829 | − | 1.19039i | 0.855829 | − | 1.19039i | −0.124344 | − | 0.992239i | \(-0.539683\pi\) |
0.980172 | − | 0.198146i | \(-0.0634921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.698237 | − | 0.715867i | \(-0.746032\pi\) | ||||
0.698237 | + | 0.715867i | \(0.253968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.940070 | + | 1.83368i | 0.940070 | + | 1.83368i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.509014 | + | 1.80914i | −0.509014 | + | 1.80914i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.517436 | + | 1.83908i | 0.517436 | + | 1.83908i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0546039 | + | 0.728639i | 0.0546039 | + | 0.728639i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(912\) | −1.82237 | − | 0.274678i | −1.82237 | − | 0.274678i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.22128 | − | 1.02477i | −1.22128 | − | 1.02477i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.727916 | − | 1.01247i | −0.727916 | − | 1.01247i | −0.998757 | − | 0.0498459i | \(-0.984127\pi\) |
0.270840 | − | 0.962624i | \(-0.412698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.05187 | + | 0.506554i | 1.05187 | + | 0.506554i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.02531 | − | 1.42612i | −1.02531 | − | 1.42612i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.58634 | − | 1.20161i | −1.58634 | − | 1.20161i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.01768 | − | 0.101834i | 1.01768 | − | 0.101834i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.60138 | − | 1.09180i | −1.60138 | − | 1.09180i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
−0.661686 | − | 0.749781i | \(-0.730159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12922 | − | 1.27956i | 1.12922 | − | 1.27956i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.124344 | − | 0.992239i | \(-0.539683\pi\) | ||||
0.124344 | + | 0.992239i | \(0.460317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.318487 | − | 0.947927i | \(-0.603175\pi\) | ||||
0.318487 | + | 0.947927i | \(0.396825\pi\) | |||||||
\(948\) | −0.921476 | − | 0.388435i | −0.921476 | − | 0.388435i | ||||
\(949\) | 2.02376 | + | 0.974590i | 2.02376 | + | 0.974590i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.980172 | − | 0.198146i | \(-0.936508\pi\) | ||||
0.980172 | + | 0.198146i | \(0.0634921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.313372 | − | 0.0797944i | 0.313372 | − | 0.0797944i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.06976 | + | 0.897636i | 1.06976 | + | 0.897636i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.902230 | + | 0.135989i | −0.902230 | + | 0.135989i | −0.583744 | − | 0.811938i | \(-0.698413\pi\) |
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(972\) | −0.318487 | + | 0.947927i | −0.318487 | + | 0.947927i | ||||
\(973\) | 0.178094 | − | 0.0549346i | 0.178094 | − | 0.0549346i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.22128 | − | 0.925082i | −1.22128 | − | 0.925082i | ||||
\(976\) | −1.30732 | + | 1.09697i | −1.30732 | + | 1.09697i | ||||
\(977\) | 0 | 0 | 0.318487 | − | 0.947927i | \(-0.396825\pi\) | ||||
−0.318487 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.03688 | − | 0.319837i | 1.03688 | − | 0.319837i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.211005 | + | 2.81567i | 0.211005 | + | 2.81567i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.623490 | − | 1.07992i | −0.623490 | − | 1.07992i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.54497 | − | 1.17027i | 1.54497 | − | 1.17027i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.354757 | − | 0.268718i | 0.354757 | − | 0.268718i | −0.411287 | − | 0.911506i | \(-0.634921\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.61852 | + | 0.682264i | 1.61852 | + | 0.682264i |
(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 | 2271.1.bm.a.1700.1 | ✓ | 36 | |
3.2 | odd | 2 | CM | 2271.1.bm.a.1700.1 | ✓ | 36 | |
757.582 | even | 63 | inner | 2271.1.bm.a.2096.1 | yes | 36 | |
2271.2096 | odd | 126 | inner | 2271.1.bm.a.2096.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2271.1.bm.a.1700.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
2271.1.bm.a.1700.1 | ✓ | 36 | 3.2 | odd | 2 | CM | |
2271.1.bm.a.2096.1 | yes | 36 | 757.582 | even | 63 | inner | |
2271.1.bm.a.2096.1 | yes | 36 | 2271.2096 | odd | 126 | inner |