"""
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the BMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data (if known).
"""

P = PolynomialRing(QQ, "x")
x = P.gen()
g = P([3, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((35, 7*a + 7))

primes_array = [
(-a,),(a-1,),(2,),(-a-1,),(a-2,),(-2*a+1,),(a+4,),(a-5,),(-3*a+4,),(3*a+1,),(-3*a-2,),(3*a-5,),(-2*a+7,),(2*a+5,),(7,),(-4*a+5,),(4*a+1,),(a+7,),(a-8,),(-3*a-5,),(3*a-8,),(-5*a+1,),(5*a-4,),(5*a+2,),(5*a-7,),(-3*a+10,),(3*a+7,),(-6*a+1,),(6*a-5,),(a+10,),(a-11,),(7*a-5,),(7*a-2,),(-3*a+13,),(3*a+10,),(-6*a-5,),(6*a-11,),(13,),(-5*a+13,),(-5*a-8,),(-3*a-11,),(3*a-14,),(-7*a+11,),(-7*a-4,),(-6*a+13,),(6*a+7,),(9*a-5,),(9*a-4,),(9*a-7,),(9*a-2,),(-5*a+16,),(5*a+11,),(-8*a-5,),(-8*a+13,),(-4*a+17,),(4*a+13,),(17,),(-10*a+11,),(10*a+1,),(-9*a+14,),(-9*a-5,),(7*a+10,),(7*a-17,),(-3*a+19,),(3*a+16,),(-11*a+1,),(11*a-10,),(19,),(-3*a-17,),(3*a-20,),(-9*a-8,),(9*a-17,),(a+19,),(a-20,),(11*a+2,),(11*a-13,),(-12*a+5,),(12*a-7,),(-8*a+19,),(-8*a-11,),(10*a-17,),(10*a+7,),(-12*a+1,),(12*a-11,),(-9*a+19,),(9*a+10,),(11*a+5,),(11*a-16,),(5*a+17,),(5*a-22,),(9*a+11,),(9*a-20,),(-13*a+8,),(13*a-5,),(-3*a-20,),(3*a-23,),(-6*a-17,),(6*a-23,),(a+22,),(a-23,),(-13*a+14,),(13*a+1,),(-3*a+25,),(3*a+22,),(-2*a+25,),(2*a+23,),(10*a+13,),(10*a-23,),(-8*a+25,),(8*a+17,),(15*a-8,),(15*a-7,),(-15*a+4,),(-15*a+11,),(7*a-26,),(7*a+19,),(9*a-25,),(9*a+16,),(-13*a+20,),(-13*a-7,),(a+25,),(a-26,),(-15*a+1,),(15*a-14,),(-14*a+19,),(-14*a-5,),(-15*a+16,),(15*a+1,),(15*a+2,),(15*a-17,),(-5*a+28,),(-5*a-23,),(-3*a+28,),(3*a+25,),(-15*a+19,),(-15*a-4,),(-12*a+25,),(12*a+13,),(-4*a+29,),(4*a+25,),(-17*a+7,),(17*a-10,),(9*a+20,),(9*a-29,),(15*a+7,),(15*a-22,),(-11*a+28,),(-11*a-17,),(29,),(-15*a+23,),(-15*a-8,),(-14*a-11,),(-14*a+25,),(-5*a+31,),(5*a+26,),(-6*a+31,),(6*a+25,),(-18*a+13,),(18*a-5,),(-2*a+31,),(2*a+29,),(-16*a+23,),(16*a+7,),(-7*a+32,),(-7*a-25,),(13*a+16,),(13*a-29,),(-17*a+22,),(17*a+5,),(11*a-31,),(11*a+20,),(-18*a+19,),(18*a+1,),(-19*a+5,),(-19*a+14,),(12*a+19,),(-12*a+31,),(15*a-28,),(15*a+13,),(19*a-17,),(19*a-2,),(-5*a-29,),(5*a-34,),(-18*a-5,),(18*a-23,),(9*a-34,),(9*a+25,),(-19*a+20,),(19*a+1,),(-20*a+7,),(-20*a+13,),(-6*a-29,),(6*a-35,),(-9*a-26,),(9*a-35,),(-15*a+31,),(15*a+16,),(-20*a+1,),(20*a-19,),(a+34,),(a-35,),(21*a-11,),(21*a-10,),(-12*a-23,),(12*a-35,),(5*a+32,),(5*a-37,),(13*a-35,),(13*a+22,),(-9*a+37,),(9*a+28,),(18*a-29,),(-18*a-11,),(-17*a-14,),(-17*a+31,),(-21*a+1,),(21*a-20,),(-2*a+37,),(2*a+35,),(-15*a+34,),(-15*a-19,),(-22*a+5,),(22*a-17,),(-19*a+29,),(-19*a-10,),(a+37,),(a-38,),(21*a+4,),(21*a-25,),(16*a+19,),(16*a-35,),(-14*a-23,),(-14*a+37,),(21*a+5,),(21*a-26,),(9*a+31,),(9*a-40,),(15*a+22,),(15*a-37,),(19*a-32,),(19*a+13,),(-23*a+4,),(-23*a+19,),(-11*a-29,),(-11*a+40,),(-6*a-35,),(6*a-41,),(-15*a+38,),(-15*a-23,),(-18*a-17,),(18*a-35,),(-10*a+41,),(10*a+31,),(-17*a+37,),(-17*a-20,),(-24*a+7,),(24*a-17,),(-12*a+41,),(12*a+29,),(23*a+2,),(23*a-25,),(41,),(-8*a+43,),(-8*a-35,),(-6*a+43,),(6*a+37,),(-5*a+43,),(-5*a-38,),(-25*a+14,),(25*a-11,),(-15*a-26,),(-15*a+41,),(-3*a+43,),(3*a+40,),(-24*a+25,),(24*a+1,),(-9*a-35,),(9*a-44,),(-17*a+40,),(-17*a-23,),(-3*a-41,),(3*a-44,),(43,),(-13*a-31,),(13*a-44,),(-24*a+29,),(-24*a-5,),(15*a-43,),(15*a+28,),(-25*a+26,),(25*a+1,),(22*a+13,),(-22*a+35,),(-15*a-29,),(15*a-44,),(11*a+35,),(11*a-46,),(-26*a+1,),(26*a-25,),(-27*a+11,),(27*a-16,),(27*a-17,),(-27*a+10,),(7*a-47,),(7*a+40,),(9*a+38,),(9*a-47,),(10*a-47,),(10*a+37,),(-4*a-43,),(4*a-47,),(21*a-40,),(21*a+19,),(-25*a-7,),(25*a-32,),(-24*a+35,),(24*a+11,),(27*a-25,),(27*a-2,),(-21*a-20,),(21*a-41,),(-27*a+1,),(27*a-26,),(15*a+32,),(15*a-47,),(9*a+40,),(9*a-49,),(-28*a+23,),(28*a-5,),(-23*a-17,),(-23*a+40,),(-21*a+43,),(21*a+22,),(-3*a+49,),(3*a+46,),(-9*a+50,),(-9*a-41,),(-7*a+50,),(7*a+43,),(-27*a+31,),(-27*a-4,),(-29*a+10,),(-29*a+19,),(-15*a+49,),(-15*a-34,),(-27*a+32,),(27*a+5,),(13*a-50,),(13*a+37,),(-3*a-47,),(3*a-50,),(-28*a+29,),(28*a+1,),(19*a+28,),(19*a-47,),(29*a-25,),(29*a-4,),(-23*a-20,),(-23*a+43,),(-27*a-8,),(27*a-35,),(21*a+25,),(21*a-46,),(25*a-41,),(-25*a-16,),(-30*a+7,),(30*a-23,),(27*a+10,),(-27*a+37,),(10*a+43,),(10*a-53,),(-20*a+49,),(20*a+29,),(19*a-50,),(-19*a-31,),(31*a-20,),(-31*a+11,),(-30*a+1,),(30*a-29,),(-3*a-50,),(3*a-53,),(-17*a+52,),(17*a+35,),(-15*a+53,),(-15*a-38,),(-29*a+34,),(-29*a-5,),(-31*a+8,),(-31*a+23,),(27*a+13,),(27*a-40,),(25*a-44,),(25*a+19,),(16*a+37,),(16*a-53,),(-30*a+31,),(30*a+1,),(31*a-26,),(31*a-5,),(-8*a-47,),(8*a-55,),(12*a+43,),(-12*a+55,),(-6*a+55,),(6*a+49,),(29*a-37,),(-29*a-8,),(-14*a-41,),(14*a-55,),(-23*a+49,),(-23*a-26,),(-3*a+55,),(3*a+52,),(-32*a+25,),(32*a-7,),(25*a-47,),(25*a+22,),(-2*a+55,),(-2*a-53,),(-24*a+49,),(24*a+25,),(17*a+38,),(17*a-55,),(29*a-40,),(-29*a-11,),(-15*a-41,),(-15*a+56,),(-33*a+19,),(33*a-14,),(-21*a+53,),(-21*a-32,),(-31*a+35,),(-31*a-4,),(-33*a+10,),(33*a-23,),(-32*a+1,),(32*a-31,),(-27*a+46,),(27*a+19,),(33*a-25,),(33*a-8,),(a+55,),(a-56,),(-11*a+58,),(-11*a-47,),(15*a-58,),(15*a+43,),(-10*a-49,),(10*a-59,),(-3*a+58,),(3*a+55,),(-13*a+59,),(-13*a-46,),(-32*a+37,),(32*a+5,),(-30*a+43,),(30*a+13,),(-15*a-44,),(15*a-59,),(-33*a+34,),(33*a+1,),(-34*a+5,),(-34*a+29,),(-3*a-56,),(3*a-59,),(-23*a-32,),(23*a-55,),(25*a+28,),(25*a-53,),(-35*a+16,),(35*a-19,),(35*a-22,),(-35*a+13,),(-18*a-41,),(18*a-59,),(-11*a+61,),(-11*a-50,),(-24*a+55,),(24*a+31,),(-33*a-5,),(33*a-38,),(-6*a+61,),(6*a+55,),(21*a-58,),(21*a+37,),(-5*a+61,),(5*a+56,),(30*a+17,),(-30*a+47,),(-9*a-53,),(9*a-62,),(33*a+7,),(-33*a+40,),(-7*a-55,),(7*a-62,),(-36*a+25,),(36*a-11,),(-23*a+58,),(-23*a-35,),(-26*a+55,),(-26*a-29,),(30*a+19,),(-30*a+49,),(28*a-53,),(28*a+25,),(-33*a+43,),(33*a+10,),(-20*a+61,),(20*a+41,),(-29*a-23,),(-29*a+52,),(61,),(-27*a+55,),(27*a+28,),(36*a-31,),(36*a-5,),(-37*a+20,),(37*a-17,),(-24*a+59,),(24*a+35,),(-37*a+26,),(37*a-11,),(-31*a-19,),(-31*a+50,),(-5*a-59,),(5*a-64,),(-36*a+1,),(36*a-35,),(-12*a+65,),(12*a+53,),(25*a+34,),(-25*a+59,),(7*a+58,),(7*a-65,),(-30*a-23,),(30*a-53,),(-3*a+64,),(3*a+61,),(-6*a-59,),(6*a-65,),(-37*a+5,),(37*a-32,),(-38*a+13,),(-38*a+25,),(-4*a+65,),(4*a+61,),(-35*a-8,),(35*a-43,),(18*a-65,),(-18*a-47,),(-31*a-22,),(31*a-53,),(33*a+16,),(33*a-49,),(-3*a-62,),(3*a-65,),(-19*a-46,),(19*a-65,),(-34*a-13,),(-34*a+47,),(36*a+5,),(36*a-41,),(9*a+58,),(9*a-67,),(-14*a-53,),(-14*a+67,),(15*a+52,),(15*a-67,),(-23*a+64,),(23*a+41,),(-17*a-50,),(17*a-67,),(5*a+62,),(5*a-67,),(-27*a+61,),(-27*a-34,),(37*a+4,),(37*a-41,),(-39*a+10,),(-39*a+29,),(31*a-56,),(31*a+25,),(33*a-53,),(-33*a-20,),(-32*a+55,),(32*a+23,),(-39*a+32,),(39*a-7,),(-20*a+67,),(-20*a-47,),(-27*a-35,),(27*a-62,),(-40*a+23,),(40*a-17,),(-39*a+4,),(-39*a+35,),(-3*a-65,),(3*a-68,),(40*a-11,),(-40*a+29,),(-11*a+70,),(-11*a-59,),(9*a-70,),(9*a+61,),(21*a+47,),(21*a-68,),(-38*a-5,),(38*a-43,),(-30*a+61,),(30*a+31,),(-39*a+40,),(39*a+1,),(-12*a-59,),(12*a-71,),(41*a-16,),(41*a-25,),(-15*a-56,),(-15*a+71,),(-27*a+65,),(27*a+38,),(-16*a+71,),(16*a+55,),(-41*a+13,),(41*a-28,),(-7*a+71,),(7*a+64,),(-6*a-65,),(6*a-71,),(41*a-31,),(41*a-10,),(-39*a+44,),(-39*a-5,),(-36*a+53,),(36*a+17,),(-25*a+68,),(25*a+43,),(33*a-59,),(-33*a-26,),(-38*a+49,),(38*a+11,),(-23*a+70,),(23*a+47,),(-11*a-62,),(-11*a+73,),(15*a-73,),(15*a+58,),(-22*a+71,),(22*a+49,),(36*a+19,),(-36*a+55,),(-8*a+73,),(8*a+65,),(34*a-59,),(-34*a-25,),(42*a-31,),(-42*a+11,),(a+70,),(a-71,),(-18*a+73,),(18*a+55,),(-6*a+73,),(6*a+67,),(-41*a+1,),(41*a-40,),(-35*a-23,),(-35*a+58,),(13*a-74,),(13*a+61,),(-5*a+73,),(-5*a-68,),(-43*a+23,),(43*a-20,),(-42*a+5,),(42*a-37,),(-39*a-11,),(39*a-50,),(21*a+52,),(21*a-73,),(19*a-74,),(19*a+55,),(-37*a+56,),(-37*a-19,),(-30*a+67,),(30*a+37,),(27*a+43,),(-27*a+70,),(-23*a+73,),(-23*a-50,),(-35*a-26,),(-35*a+61,),(41*a+5,),(41*a-46,),(-3*a-71,),(3*a-74,),(-11*a-65,),(11*a-76,),(73,),(-44*a+19,),(44*a-25,),(-33*a-32,),(33*a-65,),(17*a+59,),(17*a-76,),(29*a+41,),(29*a-70,),(31*a+37,),(31*a-68,),(-36*a+61,),(36*a+25,),(-32*a+67,),(-32*a-35,),(-12*a+77,),(12*a+65,),(39*a+16,),(39*a-55,),(15*a+62,),(15*a-77,),(-5*a+76,),(5*a+71,),(-9*a+77,),(-9*a-68,),(34*a-65,),(34*a+31,),(-25*a-49,),(25*a-74,),(21*a+55,),(-21*a+76,),(-42*a+47,),(42*a+5,),(-35*a-29,),(-35*a+64,),(45*a-23,),(45*a-22,),(45*a-19,),(45*a-26,),(-43*a+44,),(43*a+1,),(-45*a+31,),(45*a-14,),(33*a+35,),(33*a-68,),(37*a-62,),(37*a+25,),(-45*a+13,),(45*a-32,),(-4*a+77,),(4*a+73,),(45*a-34,),(45*a-11,),(-39*a+59,),(-39*a-20,),(45*a-8,),(-45*a+37,),(-18*a-61,),(18*a-79,),(-8*a-71,),(8*a-79,),(-41*a+55,),(-41*a-14,),(-30*a+73,),(30*a+43,),(33*a+37,),(33*a-70,),(-20*a-59,),(20*a-79,),(13*a+67,),(13*a-80,),(25*a+52,),(25*a-77,),(43*a+7,),(43*a-50,),(-9*a-71,),(9*a-80,),(37*a-65,),(37*a+28,),(7*a+73,),(7*a-80,),(-42*a+55,),(42*a+13,),(-23*a+79,),(23*a+56,),(41*a+17,),(41*a-58,),(-27*a-50,),(-27*a+77,),(21*a-80,),(21*a+59,),(-44*a+49,),(-44*a-5,),(-24*a+79,),(24*a+55,),(-45*a+46,),(45*a+1,),(-47*a+16,),(-47*a+31,),(46*a-41,),(46*a-5,),(39*a+25,),(-39*a+64,),(-17*a-65,),(-17*a+82,),(-9*a+82,),(9*a+73,),(79,),(47*a-37,),(-47*a+10,),(41*a+20,),(41*a-61,),(45*a+4,),(45*a-49,),(33*a+41,),(33*a-74,),(-13*a-70,),(13*a-83,),(a+79,),(a-80,),(16*a+67,),(16*a-83,),(-48*a+23,),(48*a-25,),(10*a+73,),(10*a-83,),(-48*a+29,),(48*a-19,),(18*a-83,),(-18*a-65,),(-36*a-35,),(36*a-71,),(5*a+77,),(5*a-82,),(-27*a-53,),(27*a-80,),(-35*a+73,),(-35*a-38,),(-42*a-19,),(42*a-61,),(-21*a-62,),(21*a-83,),(29*a+50,),(-29*a+79,),(43*a+16,),(-43*a+59,),(37*a-71,),(37*a+34,),(30*a+49,),(-30*a+79,),(-47*a+1,),(47*a-46,),(-12*a+85,),(12*a+73,),(-11*a-74,),(-11*a+85,),(49*a-32,),(-49*a+17,),(25*a+58,),(25*a-83,),(45*a+11,),(45*a-56,),(9*a+76,),(9*a-85,),(-46*a-7,),(46*a-53,),(-39*a-31,),(-39*a+70,),(-8*a-77,),(-8*a+85,),(-21*a+85,),(21*a+64,),(34*a+43,),(-34*a+77,),(-15*a-71,),(-15*a+86,),(-35*a+76,),(-35*a-41,),(31*a+49,),(31*a-80,),(-6*a+85,),(6*a+79,),(-45*a+58,),(45*a+13,),(-23*a-62,),(23*a-85,),(-29*a-53,),(-29*a+82,),(83,),(-50*a+31,),(-50*a+19,),(-28*a-55,),(28*a-83,),(-48*a+49,),(48*a+1,),(42*a+25,),(-42*a+67,),(-43*a+65,),(-43*a-22,),(-49*a+5,),(-49*a+44,),(-3*a+85,),(3*a+82,),(-40*a-31,),(40*a-71,),(50*a-37,),(-50*a+13,),(-33*a-47,),(33*a-80,),(26*a+59,),(-26*a+85,),(49*a-47,),(49*a-2,),(-25*a-61,),(25*a-86,),(45*a-62,),(-45*a-17,),(-35*a+79,),(-35*a-44,),(-51*a+23,),(-51*a+28,),(-48*a-5,),(48*a-53,),(37*a+40,),(37*a-77,),(21*a+67,),(21*a-88,),(-51*a+16,),(51*a-35,),(43*a+25,),(43*a-68,),(-49*a+50,),(49*a+1,),(29*a-85,),(29*a+56,),(-48*a+55,),(-48*a-7,),(-23*a-65,),(-23*a+88,),(-51*a+13,),(-51*a+38,),(-10*a-79,),(10*a-89,),(44*a+23,),(-44*a+67,),(-42*a-29,),(42*a-71,),(51*a-41,),(51*a-10,),(-33*a+83,),(-33*a-50,),(-50*a+1,),(50*a-49,),(-51*a+43,),(51*a-8,),(-47*a-14,),(47*a-61,),(-39*a-38,),(39*a-77,),(-3*a+88,),(3*a+85,),(52*a-35,),(52*a-17,),(-35*a+82,),(-35*a-47,),(37*a+43,),(37*a-80,),(45*a+22,),(45*a-67,),(-48*a-11,),(48*a-59,),(51*a-46,),(51*a-5,),(-32*a-53,),(-32*a+85,),(-46*a+65,),(-46*a-19,),(-15*a+91,),(15*a+76,),(12*a+79,),(-12*a+91,),(-45*a+68,),(-45*a-23,),(-11*a+91,),(-11*a-80,),(40*a-77,),(40*a+37,),(-3*a-86,),(3*a-89,),(33*a-85,),(-33*a-52,),(-41*a-35,),(-41*a+76,),(-39*a+79,),(39*a+40,),(-53*a+25,),(53*a-28,),(-51*a+1,),(51*a-50,),(15*a+77,),(15*a-92,),(-36*a-47,),(36*a-83,),(-49*a+59,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [2, -2, 1, -1, 2, 4, 4, 4, 10, 6, -6, -6, -6, -2, 1, 10, -6, -6, -2, 0, 16, -12, 12, -6, -6, 2, 2, -14, 6, -14, -14, 6, -10, -14, -22, 8, 8, -10, 4, 20, 26, 2, 16, 0, -18, 2, 10, -2, -14, -6, -30, 6, -6, 26, -30, 10, 14, 10, -10, -14, -14, 14, -2, 20, -12, -6, -22, 26, 2, -10, 8, 0, 14, 26, 30, -18, -30, -38, 18, -14, 14, -6, 10, -6, -14, 2, -28, -4, 38, 6, -20, -36, 26, 22, 28, -4, -24, 0, -14, 10, 18, 18, 18, -46, -42, 42, 36, 44, -26, 22, -34, -6, 8, -8, 30, -34, 6, 26, -18, 26, 6, 6, 10, 18, 4, -4, 14, 10, 46, -2, 42, -10, -22, -2, -4, -28, -2, -2, 18, -6, 10, -46, 8, 48, -54, 34, 34, -18, -6, 14, -22, 16, 56, -30, -14, 52, -36, 40, -8, -12, -20, -6, 10, 28, -12, 6, -30, 2, -30, 42, -18, 4, 44, 50, -6, 50, -38, 10, -10, 58, 42, -6, 26, -48, 24, 30, -34, 24, -32, 34, -6, 22, -22, 26, 10, -40, 32, 18, -6, 26, -54, -62, 66, -14, 42, -34, 26, 18, 10, 22, -22, -34, 42, 10, 18, -32, 8, 30, -30, -62, 34, 20, 52, 38, -26, 38, 6, 56, 32, -6, 26, -64, 16, -46, -14, -2, -46, -14, -46, 56, 0, -66, -30, -64, 16, 26, -2, 2, -46, -10, -30, 46, 42, -12, 52, -22, 74, 42, 10, -62, -22, 46, 42, 42, 26, -18, 34, -14, 42, -70, 2, -54, 40, 24, -14, 18, -46, -26, 84, 12, -12, 44, -22, 12, 20, 70, -74, -74, 26, 2, -78, 22, 26, -78, -2, 2, -38, -56, 72, 16, 8, -18, -34, 36, -36, 74, 50, -24, -40, 78, 30, -36, 4, -6, 78, -14, -62, -38, -38, 40, -32, 90, -38, 40, 16, 54, -6, -30, -30, -42, -22, 66, -30, 10, 58, -90, -10, -58, -74, -80, -16, -90, 6, 42, -30, -88, 40, -22, 18, 94, 46, -2, -34, 50, 46, 64, -24, -16, -72, -98, -46, 6, 54, 32, -40, -30, -10, 18, -94, -10, -78, -30, 90, -66, 78, -90, -14, -32, -80, -14, -54, -34, -6, -18, 78, 66, -102, 40, -16, 10, -26, 80, 32, -86, -70, 72, 96, -62, 66, -38, -38, -50, -98, 6, -38, -18, 26, -20, 36, 42, -78, -50, 58, -22, -70, -74, -26, 52, 36, -22, 106, 66, 74, 8, -88, 30, -86, -54, 42, -60, 20, 66, -26, 58, -62, 18, 50, 62, 46, -8, -8, -98, 18, -50, -18, 58, 74, 58, -90, -58, -10, 54, 54, -70, -6, 100, 20, -60, -52, 38, 102, -66, -14, -78, 70, 0, 48, -94, -98, 68, 100, -30, -30, 102, -54, 10, -102, 18, 82, 82, -14, 22, 34, 50, -14, -34, -6, -18, -86, -2, -66, -14, 78, -90, -42, -98, -50, -62, -46, 24, 0, -58, 106, -50, -34, -58, -106, -30, 42, -12, 76, 6, -10, 2, -98, -34, -100, 76, 50, -46, -22, 50, -54, -22, 0, -40, -70, -46, 98, 10, 10, -6, -66, 78, -62, 62, 40, 16, -76, 20, -78, 46, -2, 42, 114, -14, 12, 76, 84, -52, 114, 18, 110, -54, 74, 42, -6, -22, -78, 14, 50, 106, 74, -102, -100, 76, -64, 112, 20, 84, 90, 58, 30, 14, -102, 50, -92, -68, 82, -78, 58, 86, -100, 44, 102, 22, 78, -70, 70, 54, -38, 2, 34, -78, -2, 26, -88, 80, -46, 114, -6, -126, -86, 26, 72, 88, 96, -16, 50, -34, 32, 112, 118, 6, 64, 48, -126, -26, 6, -106, 18, 18, -42, -38, -36, 76, -10, 10, -30, 34, -104, 16, 38, -26, -28, -4, -86, 106, -46, 46, 42, -62, 10, -54, -46, 34, 54, 2, -70, 50, 74, 74, 64, 56, 40, -72, -78, 138, -78, -82, 32, -32, 90, 54, -30, -94, 66, 18, -18, -46, 102, -78, 92, -28, -38, 58, 40, -40, -78, 114, 66, 22, 22, -30, 98, 26, 42, 122, -66, 126, 110, 30, -94, 114, 132, -12, 94, 18, -38, -26, -86, 18, -82, 18, -46, 24, -40, -54, -38, 90, 122, 2, 58, 64, 64, 10, 58, 144, -32, -62, -114, 64, -32, -78, -38, -24, 64, -32, -24, -100, 60, -10, 86, -98, -66, 110, 18, -126, -94, -38, -98, 42, 42, 14, 74, 66, 42, 10, 50, -70, -146, 0, 88, -40, -40, -30, 18, -6, -126, 140, -76, 138, -22, -22, -6, 92, 4, 30, -78, 98, -126, 48, -48, 126, 138, 12, -92, -88, 128, -90, -126, -62, 50, -62, -38, -28, -148, -54, 114, 46, 30, 74, -22, 18, 134, -124, -12, -30, 94, -54, -22, 146, -86, -78, 90, -6, 114, -26, -50, 98, 70, 86, 74, 18, -24, -8, 14, -114, 2, -94, -14, 126, -86, 74, -132, -52, 50, -70, -78, 106, 68, -52, -14, -14, 12, 124, 38, 6, -134, 42, -64, 8, 70, -90, -78, 118, -102, -54, -74, 22, -54, -46, -108, 36, 50, -14, -10, -30, -80, 104, 90, -26, 2, 138, -30, 162, 52, 92, 54, 66, -110, 122, -160, 128, -14, 46, -54, -146, -126, 18, -6, 58, 110, -98, 122, -76, -20, -38, 58, 2, -78, 56, 16, -86, -102, 32, -8, 142, -50, 78, -18, -138, 34, 58, -42, -96, 16, -42, -138, -66, -162, -30, 50, 136, 40, 38, 74, -114, 94, 158, -78, -20, -36, -138, 26, -36, -116, -86, 42, 30, 66, 50, -110, 82, -18, -30, 82, -68, 108, -110, 90, -80, 64, -46, -14, 106, -22, -50, -6, -108, -12, 98, 82, 2, -110, -38, -74, -54, 114, 106, -150, 72, -152, -86, 98, 22, -42, -54, 98, 90, -102, 24, 96, 58, 38, -38, -46, -40, 136, -78, 30, 18, -126, -110, 18, -164, -20, 82, 6, 76, 52, 62, 90, -58, -42, 34, -98, -94, 154, 66]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((-a - 1,))] = 1
AL_eigenvalues[ZF.ideal((7,))] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]