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lfunc_lfunctions • Show schema
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{'Lhash': '2474601394590514870117196337985', 'a10': -2, 'a2': 2, 'a3': 1, 'a4': 2, 'a5': -1, 'a6': 2, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 48.26956802186402, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [5, [1, 1]], [13, [1, 1]], [31, [1, -1]]], 'bad_primes': [3, 5, 13, 31], 'central_character': '6045.1', 'coefficient_field': '1.1.1.1', 'conductor': 6045, 'conductor_radical': 6045, 'degree': 2, 'euler_factors': [[1, -2, 2], [1, -1], [1, 1], [1, -2, 7], [1, 1, 11], [1, 1], [1, 4, 17], [1, 6, 19], [1, 6, 23], [1, 4, 29], [1, -1], [1, 11, 37], [1, 6, 41], [1, -10, 43], [1, -4, 47], [1, 4, 53], [1, -6, 59], [1, -2, 61], [1, -8, 67], [1, 0, 71], [1, 3, 73], [1, -12, 79], [1, 4, 83], [1, -11, 89], [1, 2, 97], [1, 3, 101], [1, -11, 103], [1, 5, 107], [1, 2, 109], [1, 11, 113]], 'euler_factors_factorization': [[[[1, -2, 2], 1]], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -2, 7], 1]], [[[1, 1, 11], 1]], [[[1, 1], 1]], [[[1, 4, 17], 1]], [[[1, 6, 19], 1]], [[[1, 6, 23], 1]], [[[1, 4, 29], 1]], [[[1, -1], 1]], [[[1, 11, 37], 1]], [[[1, 6, 41], 1]], [[[1, -10, 43], 1]], [[[1, -4, 47], 1]], [[[1, 4, 53], 1]], [[[1, -6, 59], 1]], [[[1, -2, 61], 1]], [[[1, -8, 67], 1]], [[[1, 0, 71], 1]], [[[1, 3, 73], 1]], [[[1, -12, 79], 1]], [[[1, 4, 83], 1]], [[[1, -11, 89], 1]], [[[1, 2, 97], 1]], [[[1, 3, 101], 1]], [[[1, -11, 103], 1]], [[[1, 5, 107], 1]], [[[1, 2, 109], 1]], [[[1, 11, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 239, 'label': '2-6045-1.1-c1-0-239', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/6045/2/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [9.096905829521819e-60, 0.4016811423733052, 0.8027054796302314, 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2.5115985564283037, 2.1689560093705866, 1.7822033432546425, 1.37304202841121, 0.9636105909805649, 0.5752385208536331, 0.22727740617429182, -0.0639275129301334], 'positive_zeros': ['1.95211629619785178674943996841101', '2.39536147801506979443252531729579', '3.53315244344984619909485359094128', '4.06962236451793862215646272970529', '4.68178518117835223397180910712026', '5.32244552148415198725030173279892', '6.21783146575167091851519070713141', '6.87794291995185622970121515143047', '7.63624796455271497038986254722311'], 'prelabel': '2-6045-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.947630388978966, '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': 457876545509127981, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95211629619785178674943996841', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39536147801506979443252531730', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53315244344984619909485359094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 48.26956802186402, 'bad_primes': [3, 5, 13, 31], 'central_character': '1.1', 'conductor': 6045, 'conductor_radical': 6045, 'degree': 2, 'dirichlet_coefficients': [1, 2, 1, 2, -1, 2, 2, 0, 1, -2, -1, 2, -1, 4, -1, -4, -4, 2, -6, -2, 2, -2, -6, 0, 1, -2, 1, 4, -4, -2, 1, -8, -1, -8, -2, 2, -11, -12, -1, 0, -6, 4, 10, -2, -1, -12, 4, -4, -3, 2, -4, -2, -4, 2, 1, 0, -6, -8, 6, -2, 2, 2, 2, -8, 1, -2, 8, -8, -6, -4, 0, 0, -3, -22, 1, -12, -2, -2, 12, 4, 1, -12, -4, 4, 4, 20, -4, 0, 11, -2, -2, -12, 1, 8, 6, -8, -2, -6, -1, 2], 'euler11': [1, 1, 11], 'euler13': [1, 1, 0], 'euler17': [1, 4, 17], 'euler19': [1, 6, 19], 'euler2': [1, -2, 2], 'euler23': [1, 6, 23], 'euler29': [1, 4, 29], 'euler3': [1, -1, 0], 'euler31': [1, -1, 0], 'euler37': [1, 11, 37], 'euler41': [1, 6, 41], 'euler43': [1, -10, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, 4, 53], 'euler59': [1, -6, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 3, 73], 'euler79': [1, -12, 79], 'euler83': [1, 4, 83], 'euler89': [1, -11, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -2, 2], [1, -1, 0], [1, 1, 0], [1, -2, 7], [1, 1, 11], [1, 1, 0], [1, 4, 17], [1, 6, 19], [1, 6, 23], [1, 4, 29], [1, -1, 0], [1, 11, 37], [1, 6, 41], [1, -10, 43], [1, -4, 47], [1, 4, 53], [1, -6, 59], [1, -2, 61], [1, -8, 67], [1, 0, 71], [1, 3, 73], [1, -12, 79], [1, 4, 83], [1, -11, 89], [1, 2, 97]], 'index': 239, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6045/k', 'ModularForm/GL2/Q/holomorphic/6045/2/a/k/1/1', 'ModularForm/GL2/Q/holomorphic/6045/2/a/k'], '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': '2-6045-1.1-c1-0-239', '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': '2-6045-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.947630388978966, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 457876545509127981, 'z1': {'__RealLiteral__': 0, 'data': '1.95211629619785178674943996841', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21861813
{'Lhash': '2474601394590514870117196337985', 'Lhash_array': ['2474601394590514870117196337985'], 'label': '2-6045-1.1-c1-0-239', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6045/2/a/k'}
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id: 24573172
{'Lhash': '2474601394590514870117196337985', 'Lhash_array': ['2474601394590514870117196337985'], 'label': '2-6045-1.1-c1-0-239', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6045/2/a/k/1/1'}
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id: 23432
{'Lhash': '457876545509127981', 'Lhash_array': ['457876545509127981'], 'label': '2-6045-1.1-c1-0-239', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6045/k'}