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lfunc_lfunctions • Show schema
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{'Lhash': '1903758853128377333879020104929', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.930660344511594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [13, [1, -1]]], 'bad_primes': [2, 3, 13], 'central_character': '2496.1', 'coefficient_field': '1.1.1.1', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 4, 5], [1, 0, 7], [1, -2, 11], [1, -1], [1, -2, 17], [1, 8, 19], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, 6, 37], [1, 12, 41], [1, 4, 43], [1, 6, 47], [1, -2, 53], [1, -14, 59], [1, 10, 61], [1, -4, 67], [1, -2, 71], [1, 2, 73], [1, 8, 79], [1, 14, 83], [1, 0, 89], [1, 10, 97], [1, -6, 101], [1, 8, 103], [1, 0, 107], [1, 10, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 4, 5], 1]], [[[1, 0, 7], 1]], [[[1, -2, 11], 1]], [[[1, -1], 1]], 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1.363086847815714, 1.0773433043517604, 0.7179209304918249, 0.3037791769285338, -0.14233888305839582, -0.5950793780546771, -1.0278138265554675, -1.4140677906460046, -1.7289650832553052, -1.9506087608795695], 'positive_zeros': ['1.50180093220136700598375543301213', '2.96468384245954072400571713269648', '3.68129802131091868207255830596255', '4.30246855345630396897009783279781', '5.14437425119067985622882248862025', '6.68867852483491298922981743768657', '6.90842466906101662199467048261080', '8.039381956247822929267892267786449', '8.423418847778347999015510445933622'], 'prelabel': '2-2496-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.464376814798634, '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': 1688034190512306212, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.50180093220136700598375543301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96468384245954072400571713270', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68129802131091868207255830596', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.930660344511594, 'bad_primes': [2, 3, 13], 'central_character': '1.1', 'conductor': 2496, 'conductor_radical': 78, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -4, 0, 0, 0, 1, 0, 2, 0, 1, 0, -4, 0, 2, 0, -8, 0, 0, 0, 4, 0, 11, 0, 1, 0, 6, 0, -4, 0, 2, 0, 0, 0, -6, 0, 1, 0, -12, 0, -4, 0, -4, 0, -6, 0, -7, 0, 2, 0, 2, 0, -8, 0, -8, 0, 14, 0, -10, 0, 0, 0, -4, 0, 4, 0, 4, 0, 2, 0, -2, 0, 11, 0, 0, 0, -8, 0, 1, 0, -14, 0, -8, 0, 6, 0, 0, 0, 0, 0, -4, 0, 32, 0, -10, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 6, 37], 'euler41': [1, 12, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 4, 5], 'euler53': [1, -2, 53], 'euler59': [1, -14, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -2, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 14, 83], 'euler89': [1, 0, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 4, 5], [1, 0, 7], [1, -2, 11], [1, -1, 0], [1, -2, 17], [1, 8, 19], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, 6, 37], [1, 12, 41], [1, 4, 43], [1, 6, 47], [1, -2, 53], [1, -14, 59], [1, 10, 61], [1, -4, 67], [1, -2, 71], [1, 2, 73], [1, 8, 79], [1, 14, 83], [1, 0, 89], [1, 10, 97]], 'index': 33, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2496/p', 'ModularForm/GL2/Q/holomorphic/2496/2/a/p/1/1', 'ModularForm/GL2/Q/holomorphic/2496/2/a/p'], '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': '2-2496-1.1-c1-0-33', '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': '2-2496-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.464376814798634, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1688034190512306212, 'z1': {'__RealLiteral__': 0, 'data': '1.50180093220136700598375543301', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20731512
{'Lhash': '1903758853128377333879020104929', 'Lhash_array': ['1903758853128377333879020104929'], 'label': '2-2496-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2496/2/a/p'}
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id: 24557487
{'Lhash': '1903758853128377333879020104929', 'Lhash_array': ['1903758853128377333879020104929'], 'label': '2-2496-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2496/2/a/p/1/1'}
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id: 103876
{'Lhash': '1688034190512306212', 'Lhash_array': ['1688034190512306212'], 'label': '2-2496-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2496/p'}