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lfunc_lfunctions • Show schema
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{'Lhash': '2421172475632142425042223699726', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.04108607387354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '3136.1', 'coefficient_field': '1.1.1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 0, 5], [1], [1, 0, 11], [1, 4, 13], [1, 6, 17], [1, 2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, -8, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -6, 83], [1, -6, 89], [1, -10, 97], [1, 0, 101], [1, 4, 103], [1, -12, 107], [1, 2, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 0, 5], 1]], [1], [[[1, 0, 11], 1]], [[[1, 4, 13], 1]], [[[1, 6, 17], 1]], [[[1, 2, 19], 1]], [[[1, 0, 23], 1]], [[[1, -6, 29], 1]], [[[1, 4, 31], 1]], [[[1, 2, 37], 1]], [[[1, 6, 41], 1]], [[[1, -8, 43], 1]], [[[1, 12, 47], 1]], [[[1, 6, 53], 1]], [[[1, -6, 59], 1]], [[[1, -8, 61], 1]], [[[1, 4, 67], 1]], [[[1, 0, 71], 1]], [[[1, 2, 73], 1]], [[[1, 8, 79], 1]], [[[1, -6, 83], 1]], [[[1, -6, 89], 1]], [[[1, -10, 97], 1]], [[[1, 0, 101], 1]], [[[1, 4, 103], 1]], [[[1, -12, 107], 1]], [[[1, 2, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 73, 'label': '2-56e2-1.1-c1-0-73', '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/3136/2/a/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.8766280447300005e-60, 0.2263889613846435, 0.452537233694687, 0.6781464074437115, 0.9028060732057087, 1.125946142375331, 1.3467984100910964, 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-1.1020615989272649, -1.3663888779539617, -1.5146235074685144, -1.5455464752614734, -1.4645828315234923], 'positive_zeros': ['1.90996831082337002056034743404815', '2.49739457868022289115900838846775', '3.42443184461883656887541100920699', '4.31547623044891473234039816601196', '5.06701824847582369879735343431404', '6.17368924384109906924363362759475', '6.96175265373852036821224883682524', '7.68957389720506083723150978195389', '8.408228795468761224431793416064165'], 'prelabel': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, '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': 1452702164727856560, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90996831082337002056034743405', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49739457868022289115900838847', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42443184461883656887541100921', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.04108607387354, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -4, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, -5, 0, -4, 0, 6, 0, -4, 0, 0, 0, 0, 0, -2, 0, -8, 0, -6, 0, 8, 0, 0, 0, -12, 0, 0, 0, -12, 0, -6, 0, 0, 0, -4, 0, 6, 0, 8, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, -8, 0, -11, 0, 6, 0, 0, 0, 12, 0, 6, 0, 0, 0, -8, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 0, 5], [1, 0, 0], [1, 0, 11], [1, 4, 13], [1, 6, 17], [1, 2, 19], [1, 0, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -8, 43], [1, 12, 47], [1, 6, 53], [1, -6, 59], [1, -8, 61], [1, 4, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -6, 83], [1, -6, 89], [1, -10, 97]], 'index': 73, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3136/z', 'ModularForm/GL2/Q/holomorphic/3136/2/a/z/1/1', 'ModularForm/GL2/Q/holomorphic/3136/2/a/z'], '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': '2-56e2-1.1-c1-0-73', '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': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1452702164727856560, 'z1': {'__RealLiteral__': 0, 'data': '1.90996831082337002056034743405', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20321287
{'Lhash': '2421172475632142425042223699726', 'Lhash_array': ['2421172475632142425042223699726'], 'label': '2-56e2-1.1-c1-0-73', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/z'}
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id: 24560223
{'Lhash': '2421172475632142425042223699726', 'Lhash_array': ['2421172475632142425042223699726'], 'label': '2-56e2-1.1-c1-0-73', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/z/1/1'}
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id: 33903
{'Lhash': '1452702164727856560', 'Lhash_array': ['1452702164727856560'], 'label': '2-56e2-1.1-c1-0-73', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3136/z'}