""" 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([1, -1, 1]) F = NumberField(g, "a") a = F.gen() ZF = F.ring_of_integers() NN = ZF.ideal((19, 19*a)) primes_array = [ (a+1,),(2,),(-a-2,),(a-3,),(a+3,),(a-4,),(-2*a+5,),(2*a+3,),(5,),(a+5,),(a-6,),(-3*a+7,),(3*a+4,),(a+6,),(a-7,),(-4*a+9,),(4*a+5,),(-2*a+9,),(2*a+7,),(a+8,),(a-9,),(-3*a+10,),(3*a+7,),(-3*a-8,),(3*a-11,),(-2*a+11,),(2*a+9,),(5*a+7,),(5*a-12,),(11,),(-6*a+13,),(6*a+7,),(-3*a+13,),(3*a+10,),(-5*a-9,),(5*a-14,),(a+12,),(a-13,),(-3*a-11,),(3*a-14,),(-4*a-11,),(4*a-15,),(7*a+9,),(7*a-16,),(-2*a+15,),(2*a+13,),(a+14,),(a-15,),(-6*a-11,),(6*a-17,),(5*a+12,),(5*a-17,),(a+15,),(a-16,),(-9*a+19,),(9*a+10,),(7*a-19,),(7*a+12,),(-6*a+19,),(6*a+13,),(17,),(a+17,),(a-18,),(-3*a+19,),(3*a+16,),(-10*a+21,),(10*a+11,),(-8*a-13,),(-8*a+21,),(-3*a-17,),(3*a-20,),(9*a+13,),(9*a-22,),(-4*a+21,),(4*a+17,),(-7*a+22,),(7*a+15,),(-11*a+23,),(11*a+12,),(-8*a-15,),(8*a-23,),(a+20,),(a-21,),(11*a+13,),(11*a-24,),(-5*a+23,),(-5*a-18,),(7*a+17,),(7*a-24,),(a+21,),(a-22,),(-2*a+23,),(2*a+21,),(-7*a+25,),(-7*a-18,),(-9*a-17,),(9*a-26,),(23,),(-4*a+25,),(4*a+21,),(-13*a+27,),(13*a+14,),(-5*a+26,),(5*a+21,),(-8*a+27,),(-8*a-19,),(a+24,),(a-25,),(-3*a-23,),(3*a-26,),(-9*a+28,),(9*a+19,),(5*a+22,),(5*a-27,),(-14*a+29,),(14*a+15,),(-11*a-18,),(-11*a+29,),(9*a+20,),(9*a-29,),(-8*a-21,),(-8*a+29,),(-11*a-19,),(-11*a+30,),(-3*a+28,),(3*a+25,),(-13*a-18,),(13*a-31,),(12*a+19,),(-12*a+31,),(7*a+23,),(7*a-30,),(-10*a+31,),(10*a+21,),(a+27,),(a-28,),(15*a+17,),(15*a-32,),(-2*a+29,),(2*a+27,),(-6*a+31,),(6*a+25,),(-14*a+33,),(-14*a-19,),(-13*a+33,),(-13*a-20,),(29,),(-4*a-27,),(4*a-31,),(10*a+23,),(10*a-33,),(-3*a+31,),(3*a+28,),(13*a-34,),(-13*a-21,),(7*a-33,),(7*a+26,),(-17*a+35,),(17*a+18,),(-3*a-29,),(3*a-32,),(-7*a-27,),(7*a-34,),(-9*a-26,),(9*a-35,),(13*a-36,),(13*a+23,),(-8*a+35,),(-8*a-27,),(-11*a+36,),(-11*a-25,),(16*a+21,),(16*a-37,),(15*a+22,),(15*a-37,),(-6*a-29,),(6*a-35,),(-3*a+34,),(3*a+31,),(-12*a+37,),(12*a+25,),(17*a+21,),(17*a-38,),(-7*a+36,),(7*a+29,),(-9*a+37,),(9*a+28,),(a+33,),(a-34,),(-3*a-32,),(3*a-35,),(-16*a+39,),(16*a+23,),(-14*a-25,),(-14*a+39,),(19*a+21,),(19*a-40,),(-11*a+39,),(-11*a-28,),(-10*a-29,),(10*a-39,),(-4*a+37,),(4*a+33,),(-13*a+40,),(13*a+27,),(-5*a+38,),(-5*a-33,),(-15*a-26,),(-15*a+41,),(-7*a+39,),(-7*a-32,),(-14*a-27,),(14*a-41,),(9*a+31,),(9*a-40,),(-19*a+42,),(-19*a-23,),(-4*a-35,),(4*a-39,),(-18*a-25,),(18*a-43,),(11*a-42,),(11*a+31,),(15*a-43,),(15*a+28,),(-2*a+39,),(2*a+37,),(21*a+23,),(21*a-44,),(13*a+30,),(13*a-43,),(-6*a-35,),(6*a-41,),(a+38,),(a-39,),(-3*a+40,),(3*a+37,),(19*a+26,),(-19*a+45,),(9*a-43,),(9*a+34,),(-17*a-28,),(-17*a+45,),(-3*a-38,),(3*a-41,),(5*a+37,),(5*a-42,),(-7*a+43,),(7*a+36,),(13*a+32,),(13*a-45,),(-9*a-35,),(9*a-44,),(-6*a+43,),(6*a+37,),(-23*a+47,),(23*a+24,),(21*a+26,),(21*a-47,),(-20*a+47,),(-20*a-27,),(41,),(-4*a-39,),(4*a-43,),(17*a-47,),(17*a+30,),(a+41,),(a-42,),(-5*a-39,),(5*a-44,),(-14*a+47,),(-14*a-33,),(-19*a+48,),(-19*a-29,),(7*a+38,),(7*a-45,),(-17*a-31,),(-17*a+48,),(-9*a+46,),(9*a+37,),(-12*a-35,),(12*a-47,),(-24*a+49,),(24*a+25,),(19*a-49,),(-19*a-30,),(-4*a+45,),(4*a+41,),(9*a+38,),(9*a-47,),(-16*a+49,),(16*a+33,),(-23*a+50,),(-23*a-27,),(13*a-49,),(13*a+36,),(-25*a+51,),(25*a+26,),(-3*a+46,),(3*a+43,),(19*a-51,),(19*a+32,),(5*a+42,),(5*a-47,),(-10*a-39,),(10*a-49,),(-7*a-41,),(7*a-48,),(25*a+27,),(25*a-52,),(21*a+31,),(21*a-52,),(-14*a-37,),(-14*a+51,),(-5*a+48,),(-5*a-43,),(-24*a+53,),(-24*a-29,),(-9*a+50,),(-9*a-41,),(-21*a+53,),(-21*a-32,),(-6*a+49,),(6*a+43,),(-11*a-40,),(-11*a+51,),(-18*a-35,),(18*a-53,),(-23*a+54,),(-23*a-31,),(47,),(-4*a+49,),(4*a+45,),(-15*a+53,),(-15*a-38,),(19*a-54,),(19*a+35,),(-27*a+55,),(27*a+28,),(-24*a+55,),(24*a+31,),(-17*a+54,),(-17*a-37,),(7*a+44,),(7*a-51,),(21*a+34,),(-21*a+55,),(19*a-55,),(19*a+36,),(11*a-53,),(11*a+42,),(-5*a+51,),(5*a+46,),(-23*a+56,),(23*a+33,),(13*a+41,),(13*a-54,),(7*a+45,),(7*a-52,),(-28*a+57,),(28*a+29,),(23*a+34,),(23*a-57,),(-17*a+56,),(17*a+39,),(-2*a+51,),(-2*a-49,),(-15*a-41,),(-15*a+56,),(25*a+33,),(25*a-58,),(a+50,),(a-51,),(-3*a+52,),(3*a+49,),(16*a+41,),(-16*a+57,),(-27*a+59,),(27*a+32,),(-14*a+57,),(14*a+43,),(-3*a-50,),(3*a-53,),(-5*a-49,),(5*a-54,),(-13*a-44,),(13*a-57,),(21*a-59,),(21*a+38,),(-7*a-48,),(7*a-55,),(-2*a+53,),(-2*a-51,),(9*a+47,),(9*a-56,),(15*a-58,),(15*a+43,),(-6*a+55,),(6*a+49,),(23*a-60,),(-23*a-37,),(17*a+42,),(17*a-59,),(-30*a+61,),(30*a+31,),(-28*a-33,),(28*a-61,),(-27*a+61,),(-27*a-34,),(53,),(24*a+37,),(-24*a+61,),(-14*a+59,),(-14*a-45,),(-8*a+57,),(8*a+49,),(29*a+33,),(29*a-62,),(-12*a-47,),(12*a-59,),(-11*a+59,),(-11*a-48,),(a+54,),(a-55,),(16*a-61,),(16*a+45,),(-25*a+63,),(-25*a-38,),(-4*a+57,),(4*a+53,),(-23*a-40,),(-23*a+63,),(11*a+49,),(11*a-60,),(22*a-63,),(22*a+41,),(-17*a-45,),(-17*a+62,),(-20*a+63,),(-20*a-43,),(25*a-64,),(-25*a-39,),(-6*a-53,),(6*a-59,),(-32*a+65,),(32*a+33,),(29*a+36,),(29*a-65,),(-17*a-46,),(17*a-63,),(-16*a-47,),(16*a-63,),(-7*a+60,),(-7*a-53,),(9*a-61,),(9*a+52,),(-23*a-42,),(-23*a+65,),(-31*a+66,),(-31*a-35,),(21*a+44,),(21*a-65,),(a+57,),(a-58,),(-3*a-56,),(3*a-59,),(13*a-63,),(13*a+50,),(25*a-66,),(-25*a-41,),(7*a-61,),(7*a+54,),(-15*a+64,),(-15*a-49,),(31*a+36,),(31*a-67,),(-6*a+61,),(6*a+55,),(-13*a-51,),(13*a-64,),(-24*a-43,),(-24*a+67,),(19*a+47,),(19*a-66,),(33*a+35,),(33*a-68,),(59,),(-22*a+67,),(22*a+45,),(-14*a-51,),(-14*a+65,),(-27*a+68,),(-27*a-41,),(-8*a-55,),(8*a-63,),(a+59,),(a-60,),(-3*a+61,),(3*a+58,),(5*a+57,),(5*a-62,),(-34*a+69,),(34*a+35,),(-31*a+69,),(31*a+38,),(-18*a+67,),(18*a+49,),(-28*a+69,),(28*a+41,),(-11*a-54,),(11*a-65,),(21*a+47,),(21*a-68,),(-26*a-43,),(-26*a+69,),(16*a+51,),(16*a-67,),(-31*a+70,),(-31*a-39,),(-7*a+64,),(7*a+57,),(15*a+52,),(15*a-67,),(22*a+47,),(22*a-69,),(-4*a-59,),(4*a-63,),(27*a+43,),(-27*a+70,),(-8*a+65,),(8*a+57,),(-32*a-39,),(32*a-71,),(-29*a+71,),(29*a+42,),(-2*a+63,),(-2*a-61,),(27*a-71,),(-27*a-44,),(-17*a+69,),(17*a+52,),(35*a+37,),(35*a-72,),(a+62,),(a-63,),(10*a-67,),(10*a+57,),(19*a-70,),(19*a+51,),(7*a+59,),(7*a-66,),(9*a+58,),(9*a-67,),(-34*a+73,),(-34*a-39,),(20*a+51,),(-20*a+71,),(31*a+42,),(-31*a+73,),(-5*a+66,),(5*a+61,),(-23*a+72,),(-23*a-49,),(-9*a+68,),(-9*a-59,),(-2*a+65,),(-2*a-63,),(-35*a+74,),(-35*a-39,),(25*a-73,),(25*a+48,),(-24*a+73,),(24*a+49,),(-13*a-57,),(13*a-70,),(-19*a-53,),(-19*a+72,),(-15*a-56,),(-15*a+71,),(-37*a+75,),(37*a+38,),(-34*a+75,),(-34*a-41,),(-14*a+71,),(14*a+57,),(-31*a+75,),(-31*a-44,),(-8*a-61,),(-8*a+69,),(-3*a+67,),(3*a+64,),(-7*a-62,),(7*a-69,),(-18*a+73,),(18*a+55,),(-33*a+76,),(33*a+43,),(-21*a+74,),(-21*a-53,),(a+66,),(a-67,),(-5*a-64,),(5*a-69,),(-38*a+77,),(38*a+39,),(-9*a-62,),(9*a-71,),(-17*a+74,),(-17*a-57,),(-11*a+72,),(-11*a-61,),(30*a+47,),(-30*a+77,),(13*a-73,),(-13*a-60,),(-19*a-56,),(19*a-75,),(37*a+41,),(37*a-78,),(-15*a-59,),(15*a-74,),(-12*a+73,),(12*a+61,),(-26*a-51,),(26*a-77,),(21*a+55,),(-21*a+76,),(-17*a+75,),(17*a+58,),(-6*a-65,),(6*a-71,),(-24*a+77,),(-24*a-53,),(-29*a-49,),(29*a-78,),(-33*a-46,),(33*a-79,),(7*a+65,),(7*a-72,),(25*a+53,),(25*a-78,),(-11*a-63,),(-11*a+74,),(-20*a-57,),(-20*a+77,),(39*a+41,),(39*a-80,),(-28*a+79,),(28*a+51,),(a+69,),(a-70,),(-15*a+76,),(15*a+61,),(-2*a+71,),(-2*a-69,),(-17*a+77,),(-17*a-60,),(-37*a+81,),(37*a+44,),(-35*a+81,),(35*a+46,),(13*a-76,),(13*a+63,),(-27*a-53,),(27*a-80,),(22*a+57,),(-22*a+79,),(32*a+49,),(-32*a+81,),(15*a+62,),(15*a-77,),(-31*a-50,),(-31*a+81,),(21*a-79,),(21*a+58,),(71,),(37*a-82,),(-37*a-45,),(28*a-81,),(28*a+53,),(19*a+60,),(19*a-79,),(33*a+49,),(33*a-82,),(a+71,),(a-72,),(-3*a+73,),(3*a+70,),(-41*a+83,),(41*a+42,),(-38*a+83,),(38*a+45,),(-36*a-47,),(36*a-83,),(35*a+48,),(-35*a+83,),(-23*a+81,),(-23*a-58,),(-16*a-63,),(16*a-79,),(-15*a+79,),(-15*a-64,),(29*a-83,),(29*a+54,),(-11*a+78,),(11*a+67,),(26*a+57,),(26*a-83,),(-31*a-53,),(31*a-84,),(-42*a+85,),(42*a+43,),(-39*a-46,),(39*a-85,),(12*a+67,),(-12*a+79,),(21*a-82,),(21*a+61,),(-37*a-48,),(37*a-85,),(-2*a+75,),(-2*a-73,),(-6*a-71,),(6*a-77,),(-16*a+81,),(16*a+65,),(19*a+63,),(19*a-82,),(-3*a+76,),(3*a+73,),(-39*a+86,),(-39*a-47,),(5*a+72,),(5*a-77,),(25*a+59,),(-25*a+84,),(-14*a-67,),(-14*a+81,),(-11*a+80,),(-11*a-69,),(33*a-86,),(-33*a-53,),(-23*a-61,),(-23*a+84,),(-27*a+85,),(-27*a-58,),(41*a+46,),(41*a-87,),(40*a+47,),(-40*a+87,),(a+75,),(a-76,),(7*a+72,),(7*a-79,),(-29*a-57,),(29*a-86,),(35*a+52,),(35*a-87,),(-2*a+77,),(-2*a-75,),(-11*a+81,),(-11*a-70,),(-19*a-65,),(19*a-84,),(13*a+69,),(13*a-82,),(22*a-85,),(22*a+63,),(-10*a+81,),(10*a+71,),(37*a-88,),(-37*a-51,),(-15*a+83,),(-15*a-68,),(-21*a+85,),(21*a+64,),(-14*a-69,),(14*a-83,),(-41*a+89,),(-41*a-48,),(a+77,),(a-78,),(-12*a-71,),(12*a-83,),(-7*a+81,),(-7*a-74,),(-9*a+82,),(9*a+73,),(-33*a-56,),(33*a-89,),(-43*a+90,),(-43*a-47,),(41*a+49,),(41*a-90,),(16*a+69,),(16*a-85,),(13*a+71,),(13*a-84,),(-30*a-59,),(30*a-89,),(a+78,),(a-79,),(7*a-82,),(7*a+75,),(-45*a+91,),(45*a+46,),(-43*a-48,),(43*a-91,),(-20*a+87,),(-20*a-67,),(-27*a-62,),(27*a-89,),(31*a-90,),(31*a+59,),(19*a-87,),(-19*a-68,),(36*a+55,),(-36*a+91,),(21*a+67,),(21*a-88,),(34*a-91,),(34*a+57,),(-24*a-65,),(24*a-89,),(33*a-91,),(33*a+58,),(41*a+51,),(41*a-92,),(17*a+70,),(17*a-87,),(39*a-92,),(-39*a-53,),(31*a-91,),(31*a+60,),(-6*a-77,),(6*a-83,),(-30*a+91,),(30*a+61,),(35*a-92,),(-35*a-57,),(a+80,),(a-81,),(40*a+53,),(40*a-93,),(-14*a+87,),(-14*a-73,),(27*a+64,),(-27*a+91,),(11*a-86,),(11*a+75,),(-37*a+93,),(-37*a-56,),(13*a-87,),(13*a+74,),(-35*a-58,),(-35*a+93,),(-29*a+92,),(-29*a-63,),(-5*a-79,),(5*a-84,),(-24*a-67,),(-24*a+91,),(-7*a+85,),(7*a+78,),(39*a+55,),(39*a-94,),(-9*a+86,),(-9*a-77,),(-27*a+92,),(27*a+65,),(-11*a-76,),(11*a-87,),(22*a+69,),(22*a-91,),(-44*a+95,),(44*a+51,),(-29*a+93,),(-29*a-64,),(-33*a+94,),(33*a+61,),(28*a+65,),(28*a-93,),(39*a+56,),(39*a-95,),(-14*a+89,),(-14*a-75,),(-31*a+94,),(31*a+63,),(83,),(26*a-93,),(-26*a-67,),(-25*a+93,),(25*a+68,),(-41*a+96,),(-41*a-55,),(-18*a+91,),(18*a+73,),(-5*a+86,),(5*a+81,),(-12*a+89,),(12*a+77,),(27*a+67,),(27*a-94,),(-23*a+93,),(23*a+70,),(-48*a+97,),(48*a+49,),(-45*a+97,),(45*a+52,),(-40*a-57,),(40*a-97,),(5*a+82,),(5*a-87,),(-7*a+88,),(-7*a-81,),(-47*a+98,),(-47*a-51,),(-36*a+97,),(36*a+61,),(45*a-98,),(-45*a-53,),(-4*a-83,),(4*a-87,),(19*a-93,),(19*a+74,),(33*a-97,),(33*a+64,),(15*a+77,),(15*a-92,),(-24*a-71,),(24*a-95,),(12*a+79,),(-12*a+91,),(-49*a+99,),(49*a+50,),(-23*a+95,),(-23*a-72,),(-43*a+99,),(43*a+56,),(-19*a-75,),(19*a-94,),(16*a-93,),(16*a+77,),(-33*a-65,),(33*a-98,),(-28*a+97,),(28*a+69,),(-3*a+88,),(3*a+85,),(37*a-99,),(37*a+62,),(-23*a+96,),(-23*a-73,),(43*a+57,),(43*a-100,),(-35*a-64,),(-35*a+99,),(-11*a+92,),(-11*a-81,),(34*a-99,),(34*a+65,),(29*a-98,),(-29*a-69,),(-39*a+100,),(-39*a-61,),(-18*a-77,),(18*a-95,),(-37*a+100,),(37*a+63,),(45*a+56,),(45*a-101,),(27*a-98,),(-27*a-71,),(17*a+78,),(-17*a+95,),(9*a+83,),(9*a-92,),(-42*a+101,),(42*a+59,),(-41*a+101,),(41*a+60,),(-19*a+96,),(19*a+77,),(-22*a+97,),(22*a+75,),(-33*a+100,),(33*a+67,),(43*a+59,),(-43*a+102,),(-17*a-79,),(-17*a+96,),(-23*a+98,),(-23*a-75,),(89,),(19*a+78,),(19*a-97,),(-4*a-87,),(4*a-91,),(-25*a-74,),(25*a-99,)] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -4, -1, -1, -4, -4, 1, 1, -1, -4, -4, 2, 2, -1, -1, -1, -1, -4, -4, -7, -7, 8, 8, 8, 8, 14, 14, -16, -16, -13, 2, 2, -13, -13, -10, -10, 14, 14, 20, 20, 2, 2, -4, -4, 11, 11, 14, 14, -10, -10, 5, 5, -10, -10, -16, -16, -19, -19, -13, -13, -25, 20, 20, -10, -10, -28, -28, 32, 32, 17, 17, 8, 8, -4, -4, -34, -34, -7, -7, -4, -4, 8, 8, 2, 2, -10, -10, -37, -37, -31, -31, 2, 2, 5, 5, 38, 38, -46, -25, -25, -28, -28, -4, -4, 11, 11, 26, 26, 32, 32, 29, 29, 44, 44, 11, 11, -13, -13, 32, 32, -10, -10, 17, 17, 26, 26, -19, -19, -22, -22, 11, 11, 32, 32, -25, -25, 23, 23, -4, -4, -16, -16, -49, -49, -16, -16, -22, 26, 26, -49, -49, -22, -22, 47, 47, 8, 8, 20, 20, -7, -7, -40, -40, -34, -34, 17, 17, 20, 20, -40, -40, 26, 26, -4, -4, 44, 44, 56, 56, -1, -1, -19, -19, -58, -58, -34, -34, 26, 26, 50, 50, -34, -34, 56, 56, 5, 5, -46, -46, -10, -10, -40, -40, -10, -10, -7, -7, 14, 14, 2, 2, -1, -1, -10, -10, 32, 32, 14, 14, 14, 14, -7, -7, 71, 71, 62, 62, 59, 59, -52, -52, 68, 68, -55, -55, -31, -31, -7, -7, -40, -40, 38, 38, -43, -43, 32, 32, 50, 50, -64, -64, 29, 29, 26, 26, -70, -70, -46, -46, -13, -13, -46, 74, 74, -64, -64, -22, -22, 32, 32, -34, -34, 17, 17, -49, -49, 32, 32, 56, 56, 44, 44, -34, -34, -4, -4, -10, -10, -49, -49, -25, -25, -1, -1, 26, 26, 8, 8, -19, -19, -31, -31, -25, -25, 5, 5, 20, 20, 14, 14, 74, 74, -58, -58, -16, -16, -1, -1, 62, 62, 41, 41, -16, -16, -52, -52, 20, 20, -46, -46, -85, 71, 71, -64, -64, -61, -61, 20, 20, 59, 59, -16, -16, 80, 80, -64, -64, 2, 2, 26, 26, -22, -22, -52, -52, 62, 62, -40, -40, -55, -55, -7, -7, -46, -46, 74, 74, -16, -16, 74, 74, 59, 59, 65, 65, 11, 11, 8, 8, -43, -43, -22, -22, -64, -64, -22, -22, -7, -7, -46, -46, -55, -55, -22, -22, 20, 20, 50, 50, -76, -76, -40, -40, -43, -43, -19, -19, 14, 14, 38, 8, 8, -19, -19, 50, 50, -28, -28, 2, 2, -52, -52, -61, -61, 50, 50, 23, 23, 95, 95, 17, 17, -34, -34, -64, -64, -7, -7, -4, -4, -109, -109, -13, -13, 92, 92, -94, -94, 2, 2, 95, 95, 8, 8, 77, 77, 2, 2, -4, -4, 44, 44, 68, 68, -43, -43, -28, -28, 65, 65, 14, 14, 86, 86, -10, -10, 8, 8, -58, -58, 56, 56, -1, -1, -49, -49, -82, 26, 26, -52, -52, -28, -28, -34, -34, 77, 77, -70, -70, 41, 41, 80, 80, 101, 101, -55, -55, 68, 68, 14, 14, 38, 38, -118, -118, 29, 29, -7, -7, -82, -82, -70, -70, -52, -52, -82, -82, -112, -112, 17, 17, -22, -22, 89, 89, -112, -112, -34, -34, 35, 35, 110, 110, 92, 92, 59, 59, 35, 35, -52, -52, 80, 80, 80, 80, -10, -10, -4, -4, -25, -25, -100, -100, 116, 116, -94, -94, 80, 80, -91, -91, -13, -13, -43, -43, -25, -25, -28, -28, 89, 89, -34, -34, 104, 104, -67, -67, 98, 98, -58, -58, -28, -28, -124, -124, -7, -7, 44, 44, 14, 14, 68, 68, -7, -7, -52, -52, -28, -28, -112, -112, 65, 65, -94, -94, 107, 107, 23, 23, 56, 56, 134, 134, -76, -76, -85, -85, 50, 50, 80, 80, 86, 86, -70, -70, 71, 71, 23, 23, 80, 80, -4, -4, 11, 11, -76, -76, 26, 26, 8, 8, 65, 65, 8, 8, -94, -94, -124, -124, 56, 56, -73, -73, 38, 38, 29, 29, 44, 44, -4, -4, 62, 62, -61, -61, -106, -16, -16, 83, 83, 107, 107, -40, -40, 92, 92, 44, 44, 56, 56, 131, 131, -4, -4, 62, 62, -82, -82, -58, -58, 62, 62, -4, -4, 128, 128, -73, -73, 59, 59, -115, -115, -112, -112, -70, -70, -19, -19, 68, 68, -91, -91, 122, 122, 59, 59, 56, 56, -67, -67, -70, -70, -10, -10, 20, 20, -46, -46, -127, -127, 68, 68, 20, 20, 80, 80, -40, -40, 38, 38, -130, -130, -76, -76, -25, -25, -10, -10, -70, -70, -58, -58, -37, -37, 122, 122, -1, -1, 20, 20, 35, 35, -70, -70, 140, 140, 20, 20, 50, 50, 68, 68, -46, -46, 95, 95, -88, -88, -10, -10, -76, -76, -19, -19, -142, -142, -94, -94, -40, -40, -28, -28, 53, 53, -52, -52, -82, -82, -115, -115, -16, -16, 107, 107, -94, -94, 146, 146, 20, 20, -91, -91, 8, 8, 68, 68, -106, -106, -64, -64, -64, -64, -148, -148, -25, -25, 80, 80, 71, 71, 2, 2, -4, -4, 59, 59, -115, -115, -16, -16, 8, 8, -88, -88, 131, 131, 86, 86, -70, -70, 41, 41, 92, 92, -4, -4, 8, 8, -148, -148, 11, 11, -76, -76, -130, -130, 62, 62, 128, 128, -10, -10, 38, 38, -22, -22, 89, 89, -22, 32, 32, 146, 146, 122, 122, 56, 56, 26, 26, -58, -58, 17, 17, -115, -115, 2, 2, -121, -121, -43, -43, -40, -40, -58, -58, -37, -37, 32, 32, 110, 110, 137, 137, 143, 143, -1, -1, 20, 20, -139, -139, 116, 116, 125, 125, -37, -37, 68, 68, -40, -40, 65, 65, -109, -109, 98, 98, -16, -16, -160, -160, 14, 14, -37, -37, 20, 20, 86, 86, 50, 50, -82, -82, -118, -118, -136, -136, -34, -34, -130, -130, 65, 65, 77, 77, 14, 14, -25, -25, 128, 128, -103, -103, 56, 56, 14, 14, -79, -79, -46, -46, -76, -76, -34, 125, 125, 122, 122, -85, -85] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal((-2*a + 5,))] = -1 AL_eigenvalues[ZF.ideal((2*a + 3,))] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]