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lfunc_lfunctions • Show schema
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{'Lhash': '3357242631570005225596235754029', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '441.1', 'coefficient_field': '1.1.1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, 2, 5], [1], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, -4, 67], [1, 0, 71], [1, -6, 73], [1, 16, 79], [1, 12, 83], [1, 14, 89], [1, 18, 97], [1, -14, 101], [1, 8, 103], [1, 4, 107], [1, 18, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, 2, 5], 1]], [1], [[[1, 4, 11], 1]], [[[1, -2, 13], 1]], [[[1, 6, 17], 1]], [[[1, 4, 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0.691557322967918, 0.618079482577448, 0.32230434398938196, -0.02326635559806271, -0.20686587324653724, -0.06552081810381155, 0.443026012343239], 'positive_zeros': ['2.64839746138688614832708523228765', '3.94328917656394473634657471262801', '4.61914309368534933978095799917274', '5.73267711633132091527857634664141', '6.81422856027217448872168795498830', '8.123916451859490481483222873179291', '8.609463409035164758983775505912018', '9.800766905340478341584155035884604', '10.92437047522813718231601421137136'], 'prelabel': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1300721734907509229, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.64839746138688614832708523229', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94328917656394473634657471263', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61914309368534933978095799917', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, -2, 0, 0, -3, 0, -2, -4, 0, 2, 0, 0, -1, -6, 0, -4, 2, 0, -4, 0, 0, -1, 2, 0, 0, 2, 0, 0, 5, 0, -6, 0, 0, 6, -4, 0, 6, 2, 0, -4, 4, 0, 0, 0, 0, 0, -1, 0, -2, -6, 0, 8, 0, 0, 2, 12, 0, 2, 0, 0, 7, -4, 0, 4, 6, 0, 0, 0, 0, 6, 6, 0, 4, 0, 0, -16, 2, 0, 2, -12, 0, 12, -4, 0, 12, -14, 0, 0, 0, 0, 0, 8, 0, -18, 0, 0, 1], 'euler11': [1, 4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -6, 73], 'euler79': [1, 16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 2, 5], [1, 0, 0], [1, 4, 11], [1, -2, 13], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -6, 37], [1, -2, 41], [1, 4, 43], [1, 0, 47], [1, 6, 53], [1, -12, 59], [1, -2, 61], [1, -4, 67], [1, 0, 71], [1, -6, 73], [1, 16, 79], [1, 12, 83], [1, 14, 89], [1, 18, 97]], 'index': 13, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/441/f', 'ModularForm/GL2/Q/holomorphic/441/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/441/2/a/f'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-21e2-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-21e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1300721734907509229, 'z1': {'__RealLiteral__': 0, 'data': '2.64839746138688614832708523229', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10786784
{'Lhash': '3357242631570005225596235754029', 'Lhash_array': ['3357242631570005225596235754029'], 'label': '2-21e2-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/a/f'}
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id: 24549359
{'Lhash': '3357242631570005225596235754029', 'Lhash_array': ['3357242631570005225596235754029'], 'label': '2-21e2-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/a/f/1/1'}
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id: 93400
{'Lhash': '1300721734907509229', 'Lhash_array': ['1300721734907509229'], 'label': '2-21e2-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/441/f'}