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  • lfunc_lfunctions • Show schema
    {'Lhash': '1019899135079327448096035381793,1064350017051845180809331451695,1287507223281460707535267972580', 'a10': -18, 'a2': 3, 'a3': -3, 'a4': 6, 'a5': -6, 'a6': -9, 'a7': 3, 'a8': 10, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5173.764754286384, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, -3, 3, -1]], [3, [1, 3, 3, 1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '2166.1', 'coefficient_field': '1.1.1.1', 'conductor': 10161910296, 'conductor_radical': 114, 'degree': 6, 'euler_factors': [[1, -3, 3, -1], [1, 3, 3, 1], [1, 6, 24, 61, 120, 150, 125], [1, -3, 3, 15, 21, -147, 343], [1, 0, 12, 37, 132, 0, 1331], [1, -6, 42, -155, 546, -1014, 2197], [1, 6, 60, 207, 1020, 1734, 4913], [1], [1, -6, 0, 121, 0, -3174, 12167], [1, -6, 96, -349, 2784, -5046, 24389], [1, -15, 165, -1039, 5115, -14415, 29791], [1, 3, 66, 239, 2442, 4107, 50653], [1, -9, 129, -685, 5289, -15129, 68921], [1, -9, 99, 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'5.18542897435060327636616578343653', '5.61710732190131596883591199080367', '5.95223525895668392270859585770405', '5.97004086615526249419146877733256', '6.51141979290713474130333236007094', '6.72055175034900457034171013074976', '6.86242043576251519762161699678162', '6.97860466397803875160037265231891', '7.51344458179378749337477746297432', '7.56590854427988486384970129249821', '8.007163940479088417142477848001214', '8.234802166586672048974903847152508', '8.272652510254526832897274600048461', '8.740794666247843875898366627111169', '8.754799930959233686664831858591341', '9.277314184523635179495568983899884'], 'prelabel': '6-2166e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.158797551914415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1468944487136685584, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.804558554932805246678121583302', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '0.839624117923517940111770228900', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.01566411363640445936628896811', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 5173.764754286384, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 10161910296, 'conductor_radical': 114, 'degree': 6, 'dirichlet_coefficients': [1, 3, -3, 6, -6, -9, 3, 10, 6, -18, 0, -18, 6, 9, 18, 15, -6, 18, 0, -36, -9, 0, 6, -30, 12, 18, -10, 18, 6, 54, 15, 21, 0, -18, -18, 36, -3, 0, -18, -60, 9, -27, 9, 0, -36, 18, -9, -45, 6, 36, 18, 36, 27, -30, 0, 30, 0, 18, 18, 108, 3, 45, 18, 28, -36, 0, 12, -36, -18, -54, 21, 60, 15, -9, -36, 0, 0, -54, 15, -90, 15, 27, -3, -54, 36, 27, -18, 0, 3, -108, 18, 36, -45, -27, 0, -63, 12, 18, 0, 72], 'euler11': [1, 0, 12, 37, 132, 0, 1331], 'euler13': [1, -6, 42, -155, 546, -1014, 2197], 'euler17': [1, 6, 60, 207, 1020, 1734, 4913], 'euler19': [1, 0, 0, 0, 0, 0, 0], 'euler2': [1, -3, 3, -1, 0, 0, 0], 'euler23': [1, -6, 0, 121, 0, -3174, 12167], 'euler29': [1, -6, 96, -349, 2784, -5046, 24389], 'euler3': [1, 3, 3, 1, 0, 0, 0], 'euler31': [1, -15, 165, -1039, 5115, -14415, 29791], 'euler37': [1, 3, 66, 239, 2442, 4107, 50653], 'euler41': [1, -9, 129, -685, 5289, -15129, 68921], 'euler43': [1, -9, 99, -523, 4257, -16641, 79507], 'euler47': [1, 9, 129, 775, 6063, 19881, 103823], 'euler5': [1, 6, 24, 61, 120, 150, 125], 'euler53': [1, -27, 390, -3491, 20670, -75843, 148877], 'euler59': [1, -18, 222, -2133, 13098, -62658, 205379], 'euler61': [1, -3, 165, -383, 10065, -11163, 226981], 'euler67': [1, -12, -24, 1041, -1608, -53868, 300763], 'euler7': [1, -3, 3, 15, 21, -147, 343], 'euler71': [1, -21, 303, -2819, 21513, -105861, 357911], 'euler73': [1, -15, 273, -2247, 19929, -79935, 389017], 'euler79': [1, -15, 249, -2189, 19671, -93615, 493039], 'euler83': [1, 3, 213, 549, 17679, 20667, 571787], 'euler89': [1, -3, 123, -45, 10947, -23763, 704969], 'euler97': [1, -12, 168, -1861, 16296, -112908, 912673], 'euler_factors': [[1, -3, 3, -1, 0, 0, 0], [1, 3, 3, 1, 0, 0, 0], [1, 6, 24, 61, 120, 150, 125], [1, -3, 3, 15, 21, -147, 343], [1, 0, 12, 37, 132, 0, 1331], [1, -6, 42, -155, 546, -1014, 2197], [1, 6, 60, 207, 1020, 1734, 4913], [1, 0, 0, 0, 0, 0, 0], [1, -6, 0, 121, 0, -3174, 12167], [1, -6, 96, -349, 2784, -5046, 24389], [1, -15, 165, -1039, 5115, -14415, 29791], [1, 3, 66, 239, 2442, 4107, 50653], [1, -9, 129, -685, 5289, -15129, 68921], [1, -9, 99, -523, 4257, -16641, 79507], [1, 9, 129, 775, 6063, 19881, 103823], [1, -27, 390, -3491, 20670, -75843, 148877], [1, -18, 222, -2133, 13098, -62658, 205379], [1, -3, 165, -383, 10065, -11163, 226981], [1, -12, -24, 1041, -1608, -53868, 300763], [1, -21, 303, -2819, 21513, -105861, 357911], [1, -15, 273, -2247, 19929, -79935, 389017], [1, -15, 249, -2189, 19671, -93615, 493039], [1, 3, 213, 549, 17679, 20667, 571787], [1, -3, 123, -45, 10947, -23763, 704969], [1, -12, 168, -1861, 16296, -112908, 912673]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2166/2/a/r'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-2166e3-1.1-c1e3-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-2166e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.158797551914415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1468944487136685584, 'z1': {'__RealLiteral__': 0, 'data': '0.804558554932805246678121583302', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1019899135079327448096035381793,1064350017051845180809331451695,1287507223281460707535267972580', 'Lhash_array': ['1019899135079327448096035381793', '1064350017051845180809331451695', '1287507223281460707535267972580'], 'factors': ['2-2166-1.1-c1-0-7', '2-2166-1.1-c1-0-9', '2-2166-1.1-c1-0-16'], 'label': '6-2166e3-1.1-c1e3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2166/2/a/r'}