# label = 3.3.49.1-27.1-a
# Base field F = Number Field in a with defining polynomial x^3 - x^2 - 2*x + 1
# Quaternion algebra given by i^2 = -3, j^2 = -1
# Order with basis over the integers given by [1, 1/2 + 1/2*i, -j, 1/2*j + 1/2*k]

# Nmax = 1000

[(1, [1/2 + 1/2*i, -j, 1/2*j + 1/2*k]), (-1, [-1/2*a^2 - 1/2*a + 3/2 + (-1/2*a^2 - 1/2*a + 3/2)*i, i + j, (-45/13*a^2 - 30/13*a + 105/13)*i + (-3/26*a^2 - 1/13*a + 7/26)*j + (3/26*a^2 + 1/13*a - 7/26)*k])]
[((3,), 5/2*a^2 - 3/2*a + 3/2 + (-3/2*a^2 - 1/2*a + 1/2)*i + (-31/2*a^2 + 2*a + 3/2)*j + (-29/2*a^2 + a + 1/2)*k)]

# map: (a |-> -1.25) -> -1, (a |-> 0.45) -> -1, (a |-> 1.8) -> -1, Fractional ideal (3) -> -1
[1, None, [(-7, [(-a^2 + a - 1, -1, 1.011)]), (-27, [(-3, 1, 1.030)]), (-64, [(-4, 3, 3.011)]), (-379, [(-4*a^2 - a - 2, -7, 6.735), (-3*a^2 - 2*a - 3, -7, 6.735), (-5*a^2 - 3*a - 1, -7, 6.735)]), (-547, [(-3*a^2 - 4, 6, 4.119), (-4*a^2 - 4*a - 3, 6, 4.119)]), (-559, [(-4*a^2 - 3, -1, 0.1132), (-7*a^2 + 8*a - 4, -1, 0.1132), (-7*a^2 - 4*a, -1, 0.1132)]), (-832, [(-4*a^2 - 4, -1, 0.09277), (-4*a^2 - 4*a - 4, -1, 0.09277), (-8*a^2 - 4*a, -1, 0.09277)])]]

# map: (a |-> -1.25) -> -1, (a |-> 0.45) -> -1, (a |-> 1.8) -> 1, Fractional ideal (3) -> 1
[-a^2 - 3*a + 3, -15/2*a^2 + 3/2*a + 1/2 + (-9/2*a^2 + 1/2*a - 1/2)*i + (13/2*a^2 + 1/2*a + 1)*j + (1/2*a^2 + 1/2*a - 1)*k, [(13, [(2*a^2 + a - 3, -13, 2.182)]), (64, [(4*a^2 - 8, 13, 0.9834)]), (97, [(5*a^2 + a - 8, -26, 3.195)]), (169, [(a^2 + 4*a - 8, -13, 0.6052)]), (301, [(a^2 + 5*a - 8, -39, 4.081)]), (337, [(4*a^2 + 4*a - 7, 13, 0.4286)]), (349, [(5*a^2 + a - 12, 52, 6.738)]), (421, [(5*a^2 + 4*a - 8, -39, 3.451)]), (433, [(7*a^2 + a - 13, -13, 0.3781)]), (448, [(4*a^2 + 4*a - 8, 13, 0.3717)]), (601, [(4*a^2 + 3*a - 14, 39, 2.888)]), (673, [(9*a^2 + a - 16, -13, 0.3033)]), (757, [(4*a^2 + 4*a - 11, 0, 0)]), (769, [(9*a^2 + 2*a - 15, -39, 2.553)]), (832, [(4*a^2 + 4*a - 12, 65, 6.819), (8*a^2 - 20, 39, 2.455)]), (841, [(7*a^2 + a - 17, 26, 1.085)]), (853, [(3*a^2 + 5*a - 13, -65, 6.734)]), (889, [(4*a^2 + 4*a - 15, 13, 0.2639)]), (973, [(5*a^2 + 4*a - 12, 39, 2.270)])]]

# map: (a |-> -1.25) -> -1, (a |-> 0.45) -> 1, (a |-> 1.8) -> -1, Fractional ideal (3) -> 1
[4*a^2 - a - 6, -10*a^2 + 1/2*a + 1/2 + (-7*a^2 - 1/2*a - 1/2)*i + (17/2*a^2 + 1/2)*j + (5/2*a^2 + 3/2)*k, [(13, [(-4*a^2 + 7*a - 2, -13, 2.182)]), (64, [(-4*a^2 + 4*a, 13, 0.9834)]), (97, [(-4*a^2 + 4*a + 1, -26, 3.195)]), (169, [(-8*a^2 + 12*a - 3, -13, 0.6051)]), (301, [(-8*a^2 + 11*a - 2, 39, 4.081)]), (337, [(-7*a^2 + 4, -13, 0.4285)]), (349, [(-12*a^2 + 23*a - 6, 52, 6.738)]), (421, [(-7*a^2 + a + 4, -39, 3.451)]), (433, [(-7*a^2 + 6*a + 1, 13, 0.3781)]), (448, [(-8*a^2 + 4, 13, 0.3717)]), (601, [(-14*a^2 + 25*a - 7, 39, 2.888)]), (673, [(-8*a^2 + 8*a + 1, 13, 0.3032)]), (757, [(-11*a^2 + 18*a - 3, 0, 0)]), (769, [(-8*a^2 + 7*a + 2, -39, 2.553)]), (832, [(-12*a^2 + 20*a - 4, -65, 6.818), (-20*a^2 + 40*a - 12, 39, 2.455)]), (841, [(-17*a^2 + 33*a - 9, 26, 1.085)]), (853, [(-13*a^2 + 21*a - 5, 65, 6.734)]), (889, [(-15*a^2 + 26*a - 7, -13, 0.2638)]), (973, [(-12*a^2 + 20*a - 3, 39, 2.270)])]]

# map: (a |-> -1.25) -> -1, (a |-> 0.45) -> 1, (a |-> 1.8) -> 1, Fractional ideal (3) -> -1
[a^2 - 2*a - 3, 2*a^2 + a - 13 + (-10*a^2 - 2*a - 79)*j + (-9*a^2 - 76)*k, [(-43, [(-a^2 + 5*a - 1, 13, 3.528)]), (-64, [(4*a, -13, 2.892)]), (-91, [(-3*a^2 + 10*a - 3, -13, 2.425)]), (-127, [(7*a - 2, 13, 2.053)]), (-139, [(-3*a^2 + 12*a - 4, -13, 1.962)]), (-211, [(-4*a^2 + 12*a - 3, 26, 6.371)]), (-223, [(-4*a^2 + 11*a - 2, 0, 0)]), (-307, [(-7*a^2 + 17*a - 4, -13, 1.320)]), (-351, [(-3*a^2 + 9*a, -13, 2.470)]), (-448, [(12*a - 4, -13, 1.093)]), (-463, [(-a^2 + 9*a - 1, -13, 1.075)]), (-559, [(-6*a^2 + 21*a - 7, -13, 0.9785), (-11*a^2 + 26*a - 7, -13, 0.9785)]), (-631, [(-7*a^2 + 22*a - 7, 26, 3.684)]), (-643, [(-10*a^2 + 25*a - 7, 13, 0.9124)]), (-679, [(-4*a^2 + 20*a - 7, 0, 0)]), (-727, [(-3*a^2 + 10*a + 1, -13, 0.8581)]), (-783, [(12*a - 3, 0, 0)]), (-811, [(11*a - 2, 0, 0)]), (-832, [(-4*a^2 + 12*a, 13, 0.8021), (-4*a^2 + 16*a - 4, -13, 0.8021), (-8*a^2 + 20*a - 4, 13, 0.8021)]), (-883, [(-7*a^2 + 18*a - 3, 39, 7.007)]), (-967, [(-17*a^2 + 41*a - 13, -13, 0.7440)])]]

# map: (a |-> -1.25) -> 1, (a |-> 0.45) -> -1, (a |-> 1.8) -> -1, Fractional ideal (3) -> 1
[-3*a^2 + 4*a + 4, -3*a^2 + 18*a + 1/2 + 1/2*i + (-60*a^2 + 1/2*a + 1)*j + (-61*a^2 + 1/2*a)*k, [(13, [(-2*a^2 - 3*a + 1, -13, 2.182)]), (64, [(-8*a^2 - 8*a + 4, 13, 0.9834)]), (97, [(-7*a^2 - 8*a + 4, -26, 3.195)]), (169, [(-3*a^2 - 6*a + 1, 13, 0.6052)]), (301, [(-2*a^2 - 7*a + 1, -39, 4.081)]), (337, [(-3*a^2 - 7*a, -13, 0.4286)]), (349, [(-6*a^2 - 11*a + 5, -52, 6.738)]), (421, [(-4*a^2 - 8*a + 1, -39, 3.451)]), (433, [(-12*a^2 - 13*a + 6, 13, 0.3781)]), (448, [(-12*a + 4, -13, 0.3717)]), (601, [(-7*a^2 - 11*a + 4, 39, 2.888)]), (673, [(-15*a^2 - 16*a + 8, 13, 0.3033)]), (757, [(-3*a^2 - 12*a + 4, 0, 0)]), (769, [(-13*a^2 - 15*a + 7, -39, 2.553)]), (832, [(-4*a^2 - 12*a + 4, 65, 6.819), (-12*a^2 - 16*a + 8, -39, 2.455)]), (841, [(-9*a^2 - 15*a + 7, -26, 1.085)]), (853, [(-5*a^2 - 11*a + 3, 65, 6.734)]), (889, [(-7*a^2 - 12*a + 4, 13, 0.2639)]), (973, [(-3*a^2 - 14*a + 5, -39, 2.270)])]]

# map: (a |-> -1.25) -> 1, (a |-> 0.45) -> -1, (a |-> 1.8) -> 1, Fractional ideal (3) -> -1
[-5*a^2 + a + 7, 9*a^2 + 7/2 + (2*a - 5/2)*i + (-a - 1/2)*j + 1/2*k, [(-43, [(3*a^2 - 3*a - 1, 26, 3.528)]), (-64, [(4*a^2 - 4*a, -26, 2.892)]), (-91, [(5*a^2 - 4*a, 26, 2.425)]), (-127, [(5*a^2 - 7*a, 26, 2.053)]), (-139, [(6*a^2 - 7*a + 1, 26, 1.962)]), (-211, [(10*a^2 - 19*a + 5, -52, 6.371)]), (-223, [(9*a^2 - 16*a + 4, 0, 0)]), (-307, [(8*a^2 - 13*a + 2, 26, 1.320)]), (-351, [(6*a^2 - 3*a - 3, -26, 2.470)]), (-448, [(8*a^2 - 12*a, -26, 1.093)]), (-463, [(7*a^2 - 7*a - 1, -26, 1.075)]), (-559, [(9*a^2 - 10*a + 1, 26, 0.9785), (9*a^2 - 14*a + 1, 26, 0.9785)]), (-631, [(9*a^2 - 8*a, -52, 3.684)]), (-643, [(11*a^2 - 19*a + 3, -26, 0.9124)]), (-679, [(11*a^2 - 15*a + 3, 0, 0)]), (-727, [(8*a^2 - 4*a - 3, -26, 0.8580)]), (-783, [(9*a^2 - 12*a, 0, 0)]), (-811, [(9*a^2 - 11*a, 0, 0)]), (-832, [(8*a^2 - 4*a - 4, 26, 0.8020), (8*a^2 - 8*a - 4, -26, 0.8020), (12*a^2 - 20*a + 4, -26, 0.8020)]), (-883, [(13*a^2 - 22*a + 5, -78, 7.007)]), (-967, [(9*a^2 - 3*a - 4, 26, 0.7440)])]]

# map: (a |-> -1.25) -> 1, (a |-> 0.45) -> 1, (a |-> 1.8) -> -1, Fractional ideal (3) -> -1
[a^2 + a - 4, 5/2*a^2 + 14 + (1/2*a^2 - a)*i + (-2*a^2 - 3/2*a + 5)*j + (-a^2 - 5/2*a + 5)*k, [(-43, [(-7*a^2 - 6*a + 5, 13, 3.528)]), (-64, [(-4*a^2 - 4*a + 4, -13, 2.892)]), (-91, [(-3*a^2 - 4*a + 4, 13, 2.425)]), (-127, [(-9*a^2 - 7*a + 7, 13, 2.053)]), (-139, [(-4*a^2 - 4*a + 5, 13, 1.962)]), (-211, [(-3*a^2 - 6*a + 5, -26, 6.370)]), (-223, [(-2*a^2 - 7*a + 5, 0, 0)]), (-307, [(-4*a^2 - 9*a + 6, 13, 1.320)]), (-351, [(-9*a + 6, 13, 2.470)]), (-448, [(-8*a^2 - 12*a + 8, -13, 1.093)]), (-463, [(-11*a^2 - 10*a + 9, -13, 1.075)]), (-559, [(-7*a^2 - 7*a + 8, 13, 0.9784), (-7*a^2 - 12*a + 8, 13, 0.9784)]), (-631, [(-7*a^2 - 8*a + 8, -26, 3.684)]), (-643, [(-7*a^2 - 11*a + 8, -13, 0.9123)]), (-679, [(-7*a^2 - 6*a + 9, 0, 0)]), (-727, [(-12*a^2 - 13*a + 10, -13, 0.8580)]), (-783, [(-15*a^2 - 12*a + 12, 0, 0)]), (-811, [(-13*a^2 - 11*a + 11, 0, 0)]), (-832, [(-4*a^2 - 8*a + 8, 13, 0.8020), (-12*a + 8, -13, 0.8020), (-4*a^2 - 12*a + 8, -13, 0.8020)]), (-883, [(-3*a^2 - 12*a + 8, -39, 7.006)]), (-967, [(-13*a^2 - 15*a + 11, 13, 0.7439)])]]

# map: (a |-> -1.25) -> 1, (a |-> 0.45) -> 1, (a |-> 1.8) -> 1, Fractional ideal (3) -> 1
[a^2 - 4, 4*a^2 - 1/2*a + 3/2 + (-1/2*a + 1/2)*i + (1/2*a^2 + 7/2*a - 1/2)*j + (-1/2*a^2 + 5/2*a - 3/2)*k, [(1, [(a^2, -1, 0.4026)]), (181, [(4*a^2 + 1, -13, 5.057), (6*a^2 - 3*a + 1, -13, 5.057), (8*a^2 + 3*a - 2, -13, 5.057)]), (448, [(12*a^2 + 8*a - 4, -13, 3.215)]), (832, [(8*a^2 + 4*a, -13, 2.359), (16*a^2 + 4*a - 4, 13, 2.359), (20*a^2 + 12*a - 8, -13, 2.359)]), (937, [(8*a^2 + 1, 13, 2.223), (10*a^2 - 3*a + 1, 13, 2.223), (12*a^2 + 3*a - 2, 13, 2.223)])]]