Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2523,1,Mod(236,2523)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([7, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2523.236");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2523 = 3 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2523.h (of order \(14\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.25914102687\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{14})\) |
Coefficient field: | 24.0.326829122755018756096000000000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - 3 x^{22} + 8 x^{20} - 21 x^{18} + 55 x^{16} - 144 x^{14} + 377 x^{12} - 144 x^{10} + 55 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{5}\) |
Projective field: | Galois closure of 5.1.6365529.1 |
Embedding invariants
Embedding label | 1745.1 | ||
Root | \(1.57747 - 0.360046i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2523.1745 |
Dual form | 2523.1.h.c.1949.1 |
$q$-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 \(\left(\mathbb{Z}/2523\mathbb{Z}\right)^\times\).
\(n\) | \(842\) | \(1684\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{14}\right)\) |
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 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(3\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(4\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(5\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.137526 | − | 0.602539i | −0.137526 | − | 0.602539i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
0.858449 | − | 0.512899i | \(-0.171429\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(12\) | 1.00000i | 1.00000i | ||||||||
\(13\) | −1.45780 | − | 0.702039i | −1.45780 | − | 0.702039i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.57747 | − | 0.360046i | −1.57747 | − | 0.360046i | −0.657939 | − | 0.753071i | \(-0.728571\pi\) |
−0.919528 | + | 0.393025i | \(0.871429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.268155 | + | 0.556829i | 0.268155 | + | 0.556829i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | ||||
\(28\) | −0.618034 | −0.618034 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.483198 | − | 0.385338i | 0.483198 | − | 0.385338i | −0.351375 | − | 0.936235i | \(-0.614286\pi\) |
0.834573 | + | 0.550897i | \(0.185714\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(37\) | 0.702039 | + | 1.45780i | 0.702039 | + | 1.45780i | 0.880596 | + | 0.473869i | \(0.157143\pi\) |
−0.178557 | + | 0.983930i | \(0.557143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57747 | + | 0.360046i | 1.57747 | + | 0.360046i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.483198 | − | 0.385338i | −0.483198 | − | 0.385338i | 0.351375 | − | 0.936235i | \(-0.385714\pi\) |
−0.834573 | + | 0.550897i | \(0.814286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(48\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(49\) | 0.556829 | − | 0.268155i | 0.556829 | − | 0.268155i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.00883 | + | 1.26503i | −1.00883 | + | 1.26503i | ||||
\(53\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.61803 | 1.61803 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.602539 | + | 0.137526i | −0.602539 | + | 0.137526i | −0.512899 | − | 0.858449i | \(-0.671429\pi\) |
−0.0896393 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.385338 | − | 0.483198i | −0.385338 | − | 0.483198i | ||||
\(64\) | −0.623490 | + | 0.781831i | −0.623490 | + | 0.781831i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45780 | + | 0.702039i | −1.45780 | + | 0.702039i | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
−0.473869 | + | 0.880596i | \(0.657143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.26503 | − | 1.00883i | −1.26503 | − | 1.00883i | −0.998993 | − | 0.0448648i | \(-0.985714\pi\) |
−0.266037 | − | 0.963963i | \(-0.585714\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 1.00000i | ||||||
\(76\) | −0.702039 | + | 1.45780i | −0.702039 | + | 1.45780i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.702039 | − | 1.45780i | −0.702039 | − | 1.45780i | −0.880596 | − | 0.473869i | \(-0.842857\pi\) |
0.178557 | − | 0.983930i | \(-0.442857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(84\) | 0.602539 | − | 0.137526i | 0.602539 | − | 0.137526i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.385338 | + | 0.483198i | −0.385338 | + | 0.483198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.602539 | − | 0.137526i | −0.602539 | − | 0.137526i | −0.0896393 | − | 0.995974i | \(-0.528571\pi\) |
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(101\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.556829 | − | 0.268155i | −0.556829 | − | 0.268155i | 0.134233 | − | 0.990950i | \(-0.457143\pi\) |
−0.691063 | + | 0.722795i | \(0.742857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(108\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(109\) | 0.137526 | + | 0.602539i | 0.137526 | + | 0.602539i | 0.995974 | + | 0.0896393i | \(0.0285714\pi\) |
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.00883 | − | 1.26503i | −1.00883 | − | 1.26503i | ||||
\(112\) | −0.137526 | + | 0.602539i | −0.137526 | + | 0.602539i | ||||
\(113\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.61803 | −1.61803 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.268155 | − | 0.556829i | −0.268155 | − | 0.556829i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.268155 | + | 0.556829i | −0.268155 | + | 0.556829i | −0.990950 | − | 0.134233i | \(-0.957143\pi\) |
0.722795 | + | 0.691063i | \(0.242857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.556829 | + | 0.268155i | 0.556829 | + | 0.268155i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000i | 1.00000i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.385338 | − | 0.483198i | 0.385338 | − | 0.483198i | −0.550897 | − | 0.834573i | \(-0.685714\pi\) |
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.483198 | + | 0.385338i | −0.483198 | + | 0.385338i | ||||
\(148\) | 1.57747 | − | 0.360046i | 1.57747 | − | 0.360046i | ||||
\(149\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00883 | − | 1.26503i | 1.00883 | − | 1.26503i | 0.0448648 | − | 0.998993i | \(-0.485714\pi\) |
0.963963 | − | 0.266037i | \(-0.0857143\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.702039 | − | 1.45780i | 0.702039 | − | 1.45780i | ||||
\(157\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.268155 | − | 0.556829i | 0.268155 | − | 0.556829i | −0.722795 | − | 0.691063i | \(-0.757143\pi\) |
0.990950 | + | 0.134233i | \(0.0428571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00883 | + | 1.26503i | 1.00883 | + | 1.26503i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.57747 | + | 0.360046i | −1.57747 | + | 0.360046i | ||||
\(172\) | −0.483198 | + | 0.385338i | −0.483198 | + | 0.385338i | ||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.618034 | 0.618034 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.360046 | + | 1.57747i | 0.360046 | + | 1.57747i | 0.753071 | + | 0.657939i | \(0.228571\pi\) |
−0.393025 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.556829 | − | 0.268155i | 0.556829 | − | 0.268155i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.483198 | + | 0.385338i | 0.483198 | + | 0.385338i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(193\) | 0.602539 | + | 0.137526i | 0.602539 | + | 0.137526i | 0.512899 | − | 0.858449i | \(-0.328571\pi\) |
0.0896393 | + | 0.995974i | \(0.471429\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.137526 | − | 0.602539i | −0.137526 | − | 0.602539i | ||||
\(197\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.360046 | − | 1.57747i | 0.360046 | − | 1.57747i | −0.393025 | − | 0.919528i | \(-0.628571\pi\) |
0.753071 | − | 0.657939i | \(-0.228571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.26503 | − | 1.00883i | 1.26503 | − | 1.00883i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00883 | + | 1.26503i | 1.00883 | + | 1.26503i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.867767 | − | 1.80194i | −0.867767 | − | 1.80194i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
−0.433884 | − | 0.900969i | \(-0.642857\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.298633 | − | 0.238152i | −0.298633 | − | 0.238152i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.45780 | + | 0.702039i | 1.45780 | + | 0.702039i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.556829 | + | 0.268155i | −0.556829 | + | 0.268155i | −0.691063 | − | 0.722795i | \(-0.742857\pi\) |
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(228\) | 0.360046 | − | 1.57747i | 0.360046 | − | 1.57747i | ||||
\(229\) | 1.94986 | − | 0.445042i | 1.94986 | − | 0.445042i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00883 | + | 1.26503i | 1.00883 | + | 1.26503i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.556829 | − | 0.268155i | 0.556829 | − | 0.268155i | −0.134233 | − | 0.990950i | \(-0.542857\pi\) |
0.691063 | + | 0.722795i | \(0.257143\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(244\) | 0.618034i | 0.618034i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.04686 | + | 1.63232i | 2.04686 | + | 1.63232i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(252\) | −0.556829 | + | 0.268155i | −0.556829 | + | 0.268155i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(257\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.360046 | + | 1.57747i | 0.360046 | + | 1.57747i | ||||
\(269\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.94986 | − | 0.445042i | −1.94986 | − | 0.445042i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.974928 | − | 0.222521i | \(-0.928571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.00000i | − | 1.00000i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.45780 | + | 0.702039i | 1.45780 | + | 0.702039i | 0.983930 | − | 0.178557i | \(-0.0571429\pi\) |
0.473869 | + | 0.880596i | \(0.342857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.268155 | − | 0.556829i | 0.268155 | − | 0.556829i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.360046 | − | 1.57747i | −0.360046 | − | 1.57747i | −0.753071 | − | 0.657939i | \(-0.771429\pi\) |
0.393025 | − | 0.919528i | \(-0.371429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.618034 | 0.618034 | ||||||||
\(292\) | −1.26503 | + | 1.00883i | −1.26503 | + | 1.00883i | ||||
\(293\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | ||||
\(301\) | −0.165729 | + | 0.344139i | −0.165729 | + | 0.344139i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.26503 | + | 1.00883i | 1.26503 | + | 1.00883i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.602539 | + | 0.137526i | 0.602539 | + | 0.137526i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.385338 | − | 0.483198i | 0.385338 | − | 0.483198i | −0.550897 | − | 0.834573i | \(-0.685714\pi\) |
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.57747 | + | 0.360046i | −1.57747 | + | 0.360046i | ||||
\(317\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(325\) | 1.00883 | − | 1.26503i | 1.00883 | − | 1.26503i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.268155 | − | 0.556829i | −0.268155 | − | 0.556829i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.618034i | 0.618034i | 0.951057 | + | 0.309017i | \(0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.26503 | + | 1.00883i | 1.26503 | + | 1.00883i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 0.618034i | − | 0.618034i | ||||||
\(337\) | 0.867767 | − | 1.80194i | 0.867767 | − | 1.80194i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57747 | − | 0.360046i | 1.57747 | − | 0.360046i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.45780 | + | 0.702039i | 1.45780 | + | 0.702039i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(364\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.602539 | + | 0.137526i | 0.602539 | + | 0.137526i | 0.512899 | − | 0.858449i | \(-0.328571\pi\) |
0.0896393 | + | 0.995974i | \(0.471429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.385338 | + | 0.483198i | 0.385338 | + | 0.483198i | ||||
\(373\) | −0.137526 | + | 0.602539i | −0.137526 | + | 0.602539i | 0.858449 | + | 0.512899i | \(0.171429\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.56366 | − | 1.24698i | 1.56366 | − | 1.24698i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.137526 | − | 0.602539i | 0.137526 | − | 0.602539i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.602539 | − | 0.137526i | −0.602539 | − | 0.137526i | ||||
\(388\) | −0.268155 | + | 0.556829i | −0.268155 | + | 0.556829i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.556829 | + | 0.268155i | −0.556829 | + | 0.268155i | −0.691063 | − | 0.722795i | \(-0.742857\pi\) |
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(400\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(401\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.57747 | − | 0.360046i | 1.57747 | − | 0.360046i | 0.657939 | − | 0.753071i | \(-0.271429\pi\) |
0.919528 | + | 0.393025i | \(0.128571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.385338 | + | 0.483198i | −0.385338 | + | 0.483198i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.268155 | + | 0.556829i | −0.268155 | + | 0.556829i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.26503 | − | 1.00883i | −1.26503 | − | 1.00883i | −0.998993 | − | 0.0448648i | \(-0.985714\pi\) |
−0.266037 | − | 0.963963i | \(-0.585714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.165729 | + | 0.344139i | 0.165729 | + | 0.344139i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(432\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(433\) | 1.26503 | − | 1.00883i | 1.26503 | − | 1.00883i | 0.266037 | − | 0.963963i | \(-0.414286\pi\) |
0.998993 | − | 0.0448648i | \(-0.0142857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.618034 | 0.618034 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.360046 | + | 1.57747i | −0.360046 | + | 1.57747i | 0.393025 | + | 0.919528i | \(0.371429\pi\) |
−0.753071 | + | 0.657939i | \(0.771429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.385338 | − | 0.483198i | 0.385338 | − | 0.483198i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(444\) | −1.45780 | + | 0.702039i | −1.45780 | + | 0.702039i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.556829 | + | 0.268155i | 0.556829 | + | 0.268155i | ||||
\(449\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.702039 | + | 1.45780i | −0.702039 | + | 1.45780i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.137526 | + | 0.602539i | 0.137526 | + | 0.602539i | 0.995974 | + | 0.0896393i | \(0.0285714\pi\) |
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(468\) | −0.360046 | + | 1.57747i | −0.360046 | + | 1.57747i | ||||
\(469\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.360046 | + | 1.57747i | 0.360046 | + | 1.57747i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.702039 | − | 1.45780i | 0.702039 | − | 1.45780i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.61803i | − | 2.61803i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00883 | + | 1.26503i | −1.00883 | + | 1.26503i | −0.0448648 | + | 0.998993i | \(0.514286\pi\) |
−0.963963 | + | 0.266037i | \(0.914286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.137526 | + | 0.602539i | −0.137526 | + | 0.602539i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.602539 | + | 0.137526i | −0.602539 | + | 0.137526i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.385338 | + | 0.483198i | −0.385338 | + | 0.483198i | −0.936235 | − | 0.351375i | \(-0.885714\pi\) |
0.550897 | + | 0.834573i | \(0.314286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.26503 | − | 1.00883i | −1.26503 | − | 1.00883i | ||||
\(508\) | 0.483198 | + | 0.385338i | 0.483198 | + | 0.385338i | ||||
\(509\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.45780 | − | 0.702039i | 1.45780 | − | 0.702039i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.385338 | − | 0.483198i | 0.385338 | − | 0.483198i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.602539 | + | 0.137526i | −0.602539 | + | 0.137526i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.94986 | + | 0.445042i | 1.94986 | + | 0.445042i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.702039 | − | 1.45780i | −0.702039 | − | 1.45780i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.360046 | − | 1.57747i | 0.360046 | − | 1.57747i | −0.393025 | − | 0.919528i | \(-0.628571\pi\) |
0.753071 | − | 0.657939i | \(-0.228571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.483198 | + | 0.385338i | −0.483198 | + | 0.385338i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.385338 | − | 0.483198i | −0.385338 | − | 0.483198i | ||||
\(557\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.556829 | − | 0.268155i | −0.556829 | − | 0.268155i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.45780 | − | 0.702039i | 1.45780 | − | 0.702039i | 0.473869 | − | 0.880596i | \(-0.342857\pi\) |
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(577\) | 0.602539 | − | 0.137526i | 0.602539 | − | 0.137526i | 0.0896393 | − | 0.995974i | \(-0.471429\pi\) |
0.512899 | + | 0.858449i | \(0.328571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.618034 | −0.618034 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(588\) | 0.268155 | + | 0.556829i | 0.268155 | + | 0.556829i | ||||
\(589\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.61803i | − | 1.61803i | ||||||
\(593\) | 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 | ||||||||
\(597\) | 1.61803i | 1.61803i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.268155 | + | 0.556829i | 0.268155 | + | 0.556829i | 0.990950 | − | 0.134233i | \(-0.0428571\pi\) |
−0.722795 | + | 0.691063i | \(0.757143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00883 | + | 1.26503i | −1.00883 | + | 1.26503i | ||||
\(604\) | −1.00883 | − | 1.26503i | −1.00883 | − | 1.26503i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.56366 | + | 1.24698i | −1.56366 | + | 1.24698i | −0.781831 | + | 0.623490i | \(0.785714\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.137526 | − | 0.602539i | 0.137526 | − | 0.602539i | −0.858449 | − | 0.512899i | \(-0.828571\pi\) |
0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.57747 | + | 0.360046i | 1.57747 | + | 0.360046i | 0.919528 | − | 0.393025i | \(-0.128571\pi\) |
0.657939 | + | 0.753071i | \(0.271429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.26503 | − | 1.00883i | −1.26503 | − | 1.00883i | ||||
\(625\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.57747 | − | 0.360046i | −1.57747 | − | 0.360046i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.445042 | + | 1.94986i | 0.445042 | + | 1.94986i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.24698 | + | 1.56366i | 1.24698 | + | 1.56366i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −1.00000 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24698 | − | 1.56366i | −1.24698 | − | 1.56366i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
−0.623490 | − | 0.781831i | \(-0.714286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.344139 | + | 0.165729i | 0.344139 | + | 0.165729i | ||||
\(652\) | −0.483198 | − | 0.385338i | −0.483198 | − | 0.385338i | ||||
\(653\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.57747 | − | 0.360046i | −1.57747 | − | 0.360046i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.24698 | − | 1.56366i | 1.24698 | − | 1.56366i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.483198 | − | 0.385338i | 0.483198 | − | 0.385338i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.24698 | + | 1.56366i | −1.24698 | + | 1.56366i | −0.623490 | + | 0.781831i | \(0.714286\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.433884 | − | 0.900969i | −0.433884 | − | 0.900969i | ||||
\(676\) | 1.45780 | − | 0.702039i | 1.45780 | − | 0.702039i | ||||
\(677\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.381966i | 0.381966i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(684\) | 1.61803i | 1.61803i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.80194 | + | 0.867767i | −1.80194 | + | 0.867767i | ||||
\(688\) | 0.268155 | + | 0.556829i | 0.268155 | + | 0.556829i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.00883 | − | 1.26503i | −1.00883 | − | 1.26503i | −0.963963 | − | 0.266037i | \(-0.914286\pi\) |
−0.0448648 | − | 0.998993i | \(-0.514286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.137526 | − | 0.602539i | 0.137526 | − | 0.602539i | ||||
\(701\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.582567 | − | 2.55239i | −0.582567 | − | 2.55239i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.45780 | − | 0.702039i | −1.45780 | − | 0.702039i | −0.473869 | − | 0.880596i | \(-0.657143\pi\) |
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.26503 | − | 1.00883i | −1.26503 | − | 1.00883i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0849954 | + | 0.372389i | −0.0849954 | + | 0.372389i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.483198 | + | 0.385338i | −0.483198 | + | 0.385338i | ||||
\(724\) | 1.61803 | 1.61803 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.26503 | + | 1.00883i | −1.26503 | + | 1.00883i | −0.266037 | + | 0.963963i | \(0.585714\pi\) |
−0.998993 | + | 0.0448648i | \(0.985714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.137526 | − | 0.602539i | −0.137526 | − | 0.602539i | ||||
\(733\) | −0.268155 | − | 0.556829i | −0.268155 | − | 0.556829i | 0.722795 | − | 0.691063i | \(-0.242857\pi\) |
−0.990950 | + | 0.134233i | \(0.957143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.483198 | − | 0.385338i | −0.483198 | − | 0.385338i | 0.351375 | − | 0.936235i | \(-0.385714\pi\) |
−0.834573 | + | 0.550897i | \(0.814286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.35877 | − | 1.13592i | −2.35877 | − | 1.13592i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.602539 | − | 0.137526i | 0.602539 | − | 0.137526i | 0.0896393 | − | 0.995974i | \(-0.471429\pi\) |
0.512899 | + | 0.858449i | \(0.328571\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.483198 | − | 0.385338i | 0.483198 | − | 0.385338i | ||||
\(757\) | −1.94986 | + | 0.445042i | −1.94986 | + | 0.445042i | −0.974928 | + | 0.222521i | \(0.928571\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.344139 | − | 0.165729i | 0.344139 | − | 0.165729i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(769\) | 0.483198 | + | 0.385338i | 0.483198 | + | 0.385338i | 0.834573 | − | 0.550897i | \(-0.185714\pi\) |
−0.351375 | + | 0.936235i | \(0.614286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.268155 | − | 0.556829i | 0.268155 | − | 0.556829i | ||||
\(773\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.268155 | + | 0.556829i | 0.268155 | + | 0.556829i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.623490 | + | 0.781831i | −0.623490 | + | 0.781831i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.618034 | −0.618034 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.445042 | − | 1.94986i | 0.445042 | − | 1.94986i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.222521 | − | 0.974928i | \(-0.428571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.45780 | − | 0.702039i | −1.45780 | − | 0.702039i | ||||
\(797\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(798\) | 0 | 0 |