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lfunc_lfunctions • Show schema
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{'Lhash': '1396443352810055621797771542350', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': -2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 42.41653355370416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [83, [1, 1]]], 'bad_primes': [2, 83], 'central_character': '5312.1', 'coefficient_field': '1.1.1.1', 'conductor': 5312, 'conductor_radical': 166, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, -2, 5], [1, -3, 7], [1, -3, 11], [1, -6, 13], [1, -5, 17], [1, -2, 19], [1, -4, 23], [1, -7, 29], [1, 5, 31], [1, -11, 37], [1, 2, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -5, 59], [1, 5, 61], [1, 2, 67], [1, 2, 71], [1, 0, 73], [1, 14, 79], [1, 1], [1, 0, 89], [1, 8, 97], [1, -6, 101], [1, -4, 103], [1, 18, 107], [1, -17, 109], [1, -15, 113]], 'euler_factors_factorization': [[1], [[[1, 1, 3], 1]], [[[1, -2, 5], 1]], [[[1, -3, 7], 1]], [[[1, -3, 11], 1]], [[[1, -6, 13], 1]], [[[1, -5, 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3.930315545052755, 3.984674092245395, 3.8881123953310643, 3.639086125931444, 3.2445049146523712, 2.7195234086414564, 2.086822735858599, 1.3754189990015988, 0.6190660048891694, -0.14565379986743557, -0.8814350549326051, -1.5524226395909713, -2.126316997968965, -2.576278957995827], 'positive_zeros': ['1.10159956738760523747148561915656', '1.51392803132280425667443874399880', '2.84692566072845257253775167245595', '3.69889287656033475652720645023585', '4.73425169524415203719187504640572', '5.39435567060411867274578529849869', '6.03908971095412582423394529075387', '6.43849364286368598220680598082504', '7.50704744345289358390695990949589', '8.329893308334208368803964563128034'], 'prelabel': '2-5312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.512797674863251, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1519240308058745739, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.10159956738760523747148561916', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.51392803132280425667443874400', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.84692566072845257253775167246', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 42.41653355370416, 'bad_primes': [2, 83], 'central_character': '1.1', 'conductor': 5312, 'conductor_radical': 166, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 2, 0, 3, 0, -2, 0, 3, 0, 6, 0, -2, 0, 5, 0, 2, 0, -3, 0, 4, 0, -1, 0, 5, 0, 7, 0, -5, 0, -3, 0, 6, 0, 11, 0, -6, 0, -2, 0, -8, 0, -4, 0, 0, 0, 2, 0, -5, 0, -6, 0, 6, 0, -2, 0, 5, 0, -5, 0, -6, 0, 12, 0, -2, 0, -4, 0, -2, 0, 0, 0, 1, 0, 9, 0, -14, 0, 1, 0, -1, 0, 10, 0, -7, 0, 0, 0, 18, 0, 5, 0, 4, 0, -8, 0, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, -6, 13], 'euler17': [1, -5, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -7, 29], 'euler3': [1, 1, 3], 'euler31': [1, 5, 31], 'euler37': [1, -11, 37], 'euler41': [1, 2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -5, 59], 'euler61': [1, 5, 61], 'euler67': [1, 2, 67], 'euler7': [1, -3, 7], 'euler71': [1, 2, 71], 'euler73': [1, 0, 73], 'euler79': [1, 14, 79], 'euler83': [1, 1, 0], 'euler89': [1, 0, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, -2, 5], [1, -3, 7], [1, -3, 11], [1, -6, 13], [1, -5, 17], [1, -2, 19], [1, -4, 23], [1, -7, 29], [1, 5, 31], [1, -11, 37], [1, 2, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -5, 59], [1, 5, 61], [1, 2, 67], [1, 2, 71], [1, 0, 73], [1, 14, 79], [1, 1, 0], [1, 0, 89], [1, 8, 97]], 'index': 88, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/5312/h', 'ModularForm/GL2/Q/holomorphic/5312/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/5312/2/a/h'], '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': '2-5312-1.1-c1-0-88', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.512797674863251, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1519240308058745739, 'z1': {'__RealLiteral__': 0, 'data': '1.10159956738760523747148561916', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21448066
{'Lhash': '1396443352810055621797771542350', 'Lhash_array': ['1396443352810055621797771542350'], 'label': '2-5312-1.1-c1-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5312/2/a/h'}
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id: 24569776
{'Lhash': '1396443352810055621797771542350', 'Lhash_array': ['1396443352810055621797771542350'], 'label': '2-5312-1.1-c1-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5312/2/a/h/1/1'}
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id: 98347
{'Lhash': '1519240308058745739', 'Lhash_array': ['1519240308058745739'], 'label': '2-5312-1.1-c1-0-88', 'type': 'ECQ', 'url': 'EllipticCurve/Q/5312/h'}