# label = 2.2.13.1-4.1-a
# Base field F = Number Field in a with defining polynomial x^2 - x - 3
# Quaternion algebra given by i^2 = -1, j^2 = -1
# Order with basis over the integers given by [1, 2*i, 1/2*a + 1/2 + (-1/2*a)*i + 1/2*j, 1/2*a + (1/2*a - 1/2)*i + 1/2*k]

# Nmax = 500

[(1/3, [2*i, 1/2*a + 1/2 + (-1/2*a)*i + 1/2*j, 1/2*a + (1/2*a - 1/2)*i + 1/2*k]), (-1/3, [2*a*i, 1/2*a + 1/2 + (-1/2*a + 2)*i + 1/2*j, -1/2*a + 1/2 + (13/6*a - 13/6)*i + (-1/6*a + 1/6)*j + (-1/6*a + 1/6)*k])]
[((2,), -3/2*a - 7 + (7/2*a - 29/2)*i + (-3*a + 3/2)*k)]

# map: (a |-> -1.3) -> -1, (a |-> 2.3) -> -1, Fractional ideal (2) -> 1
[1, None, [(9, [(-3, -1, 1.262)]), (16, [(-4, -1, 1.893)]), (17, [(a - 5, 1, 0.9182), (-a - 4, 1, 0.9182)]), (48, [(4*a - 12, 1, 1.093), (-4*a - 8, 1, 1.093)]), (49, [(-7, 1, 0.5409)]), (64, [(-8, -1, 0.9465)]), (113, [(7*a - 20, -2, 1.425), (-7*a - 13, -2, 1.425)]), (121, [(-11, 0, 0)]), (129, [(-5*a - 12, -1, 0.3333), (5*a - 17, -1, 0.3333)]), (192, [(-8*a - 16, 1, 0.5465), (8*a - 24, 1, 0.5465)]), (225, [(-15, -1, 0.2524)]), (313, [(3*a - 20, -1, 0.2140), (-3*a - 17, -1, 0.2140)]), (321, [(-8*a - 19, 4, 3.381), (8*a - 27, 4, 3.381)]), (337, [(9*a - 29, -1, 0.2062), (-9*a - 20, -1, 0.2062)]), (361, [(-19, -2, 0.7971)]), (368, [(-8*a - 20, 2, 1.579), (8*a - 28, 2, 1.579)]), (393, [(16*a - 43, -1, 0.1910), (-16*a - 27, -1, 0.1910)]), (400, [(-20, -1, 0.3786)]), (417, [(a - 21, 3, 1.669), (-a - 20, 3, 1.669)]), (425, [(-5*a - 20, 1, 0.1836), (5*a - 25, 1, 0.1836)])]]

# map: (a |-> -1.3) -> -1, (a |-> 2.3) -> 1, Fractional ideal (2) -> -1
[-4*a + 5, -3/2*a - 1/2 + (1/2*a + 9/2)*i + (-1/2*a + 1/2)*j + (1/2*a + 1/2)*k, [(-3, [(a - 1, 1/3, 1.054)]), (-43, [(4*a + 1, -1/3, 0.2784)]), (-51, [(4*a - 3, -1/3, 0.2556), (5*a + 3, -1/3, 0.2556)]), (-75, [(5*a - 5, 1/3, 0.2108)]), (-107, [(9*a - 17, -4/3, 2.824)]), (-131, [(9*a + 7, 5/3, 3.988)]), (-139, [(7*a - 8, 1, 1.394)]), (-147, [(7*a, -7/3, 7.378)]), (-179, [(12*a - 23, 1/3, 0.1364)]), (-211, [(11*a + 8, 15, 254.5)]), (-251, [(9*a - 1, -4/3, 1.844)]), (-283, [(11*a - 16, 30, 879.0)]), (-299, [(12*a - 19, 2/3, 0.4223)]), (-339, [(17*a - 33, -2, 3.569), (13*a - 21, 0, 0)]), (-347, [(12*a + 5, 5/3, 2.450)]), (-363, [(11*a, -30, 776.1)]), (-387, [(12*a - 15, -1/3, 0.09280)]), (-419, [(12*a + 1, 1/3, 0.08918)]), (-443, [(12*a - 11, 5/3, 2.168)]), (-467, [(12*a - 7, -2/3, 0.3379)]), (-491, [(15*a + 8, -5/3, 2.060)])]]

# map: (a |-> -1.3) -> 1, (a |-> 2.3) -> -1, Fractional ideal (2) -> -1
[a - 1, -6*a - 5 + (-7/2*a + 35/2)*i + (-1/2)*j + (-3/2*a - 2)*k, [(-3, [(-a, -1/3, 1.054)]), (-43, [(-4*a + 5, -1/3, 0.2784)]), (-51, [(-4*a + 1, 1/3, 0.2556), (-5*a + 8, 1/3, 0.2556)]), (-75, [(-5*a, 1/3, 0.2108)]), (-107, [(-9*a - 8, -2/3, 0.7059)]), (-131, [(-9*a + 16, 1/3, 0.1595)]), (-139, [(-7*a - 1, 1, 1.394)]), (-147, [(-7*a + 7, -1/3, 0.1506)]), (-179, [(-12*a - 11, 1/3, 0.1364)]), (-211, [(-11*a + 19, 5, 28.28)]), (-251, [(-9*a + 8, 0, 0)]), (-283, [(-11*a - 5, 10, 97.67)]), (-299, [(-12*a - 7, 0, 0)]), (-339, [(-13*a - 8, -2/3, 0.3966), (-17*a - 16, 4/3, 1.586)]), (-347, [(-12*a + 17, -1/3, 0.09800)]), (-363, [(-11*a + 11, -10, 86.24)]), (-387, [(-12*a - 3, -1/3, 0.09280)]), (-419, [(-12*a + 13, 1/3, 0.08918)]), (-443, [(-12*a + 1, 1/3, 0.08674)]), (-467, [(-12*a + 5, 4/3, 1.352)]), (-491, [(-15*a + 23, -5/3, 2.060)])]]

# map: (a |-> -1.3) -> 1, (a |-> 2.3) -> 1, Fractional ideal (2) -> 1
[-a - 4, 5*a + 17/2 + (-7/2*a - 1)*i + (a + 1)*j + (3/2*a + 1/2)*k, [(1, [(1, 1, 0.3168)]), (25, [(5, -5, 1.584)]), (48, [(4*a + 8, -5, 2.286), (-4*a + 12, -5, 2.286)]), (64, [(8, 5, 1.980)]), (129, [(a + 11, -5, 0.6973), (-a + 12, -5, 0.6973)]), (144, [(12, 5, 1.320)]), (153, [(3*a + 12, 5, 0.6403), (-3*a + 15, 5, 0.6403)]), (192, [(-8*a + 24, 5, 1.143), (8*a + 16, 5, 1.143)]), (208, [(-12*a + 32, 0, 0)]), (233, [(-8*a + 25, 5, 0.5189), (8*a + 17, 5, 0.5189)]), (257, [(-11*a + 31, -5, 0.4940), (11*a + 20, -5, 0.4940)]), (272, [(4*a + 16, -5, 0.9604), (-4*a + 20, -5, 0.9604)]), (289, [(17, 15, 4.193)]), (321, [(-13*a + 36, 10, 1.768), (13*a + 23, 10, 1.768)]), (368, [(-8*a + 28, 0, 0), (8*a + 20, 0, 0)]), (377, [(a + 19, 10, 1.632), (-a + 20, 10, 1.632)]), (393, [(7*a + 20, -15, 3.596), (-7*a + 27, -15, 3.596)]), (417, [(-8*a + 29, -5, 0.3878), (8*a + 21, -5, 0.3878)]), (433, [(3*a + 20, 5, 0.3806), (-3*a + 23, 5, 0.3806)]), (441, [(21, -15, 3.394)]), (464, [(16*a + 28, -10, 2.941), (-16*a + 44, -10, 2.941)])]]