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lfunc_lfunctions • Show schema
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{'Lhash': '2759596079366677511059750234385', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.593268090957619, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '450.1', 'coefficient_field': '1.1.1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1, 2, 7], [1, 2, 11], [1, 6, 13], [1, -2, 17], [1, 0, 19], [1, 4, 23], [1, 0, 29], [1, 8, 31], [1, 2, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, -6, 53], [1, 10, 59], [1, -2, 61], [1, -8, 67], [1, 12, 71], [1, -4, 73], [1, 0, 79], [1, 4, 83], [1, -10, 89], [1, -8, 97], [1, -8, 101], [1, -14, 103], [1, -12, 107], [1, -10, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [1], [[[1, 2, 7], 1]], [[[1, 2, 11], 1]], [[[1, 6, 13], 1]], [[[1, -2, 17], 1]], [[[1, 0, 19], 1]], [[[1, 4, 23], 1]], [[[1, 0, 29], 1]], [[[1, 8, 31], 1]], [[[1, 2, 37], 1]], [[[1, 2, 41], 1]], [[[1, -4, 43], 1]], [[[1, 8, 47], 1]], [[[1, -6, 53], 1]], [[[1, 10, 59], 1]], [[[1, -2, 61], 1]], [[[1, -8, 67], 1]], [[[1, 12, 71], 1]], [[[1, -4, 73], 1]], [[[1, 0, 79], 1]], [[[1, 4, 83], 1]], [[[1, -10, 89], 1]], [[[1, -8, 97], 1]], [[[1, -8, 101], 1]], [[[1, -14, 103], 1]], [[[1, -12, 107], 1]], [[[1, -10, 109], 1]], [[[1, -6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-450-1.1-c1-0-6', '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/450/2/a/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-2.1265213623323456e-121, 0.1770818878170425, 0.3580391317468681, 0.5454685606488223, 0.7396622192734765, 0.9379775823866718, 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3.3965758411394575, 2.308437435340031, 0.6829817846994566, -0.9751846537530131, -2.173984257952219, -2.584269034886628, -2.139248335797718], 'positive_zeros': ['2.17693746121355235992569926706078', '3.36984414779728341388392819786507', '4.95720185791601620138850804643098', '6.04674329942688851458805581355746', '7.19091277442794332068165955626912', '7.79436266718632723136861068704442', '8.977954234037566781689876272398665', '9.853706775295411456819711020421606', '10.29993155809996117013598530448133'], 'prelabel': '2-450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8955917521865353, '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': 2103906565792006133, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.17693746121355235992569926706', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36984414779728341388392819787', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95720185791601620138850804643', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.593268090957619, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 450, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -2, -1, 0, 0, -2, 0, -6, 2, 0, 1, 2, 0, 0, 0, 0, 2, -4, 0, 0, 6, 0, -2, 0, 0, -8, -1, 0, -2, 0, 0, -2, 0, 0, 0, -2, 0, 4, -2, 0, 4, -8, 0, -3, 0, 0, -6, 6, 0, 0, 2, 0, 0, -10, 0, 2, 8, 0, 1, 0, 0, 8, 2, 0, 0, -12, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 2, -4, 0, 0, -4, 0, 2, 10, 0, 12, -4, 0, 8, 0, 0, 8, 3, 0, 0], 'euler11': [1, 2, 11], 'euler13': [1, 6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -4, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 10, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, -10, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 2, 7], [1, 2, 11], [1, 6, 13], [1, -2, 17], [1, 0, 19], [1, 4, 23], [1, 0, 29], [1, 8, 31], [1, 2, 37], [1, 2, 41], [1, -4, 43], [1, 8, 47], [1, -6, 53], [1, 10, 59], [1, -2, 61], [1, -8, 67], [1, 12, 71], [1, -4, 73], [1, 0, 79], [1, 4, 83], [1, -10, 89], [1, -8, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/450/b', 'ModularForm/GL2/Q/holomorphic/450/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/450/2/a/b'], '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': '2-450-1.1-c1-0-6', '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': '2-450-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8955917521865353, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2103906565792006133, 'z1': {'__RealLiteral__': 0, 'data': '2.17693746121355235992569926706', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10840451
{'Lhash': '2759596079366677511059750234385', 'Lhash_array': ['2759596079366677511059750234385'], 'label': '2-450-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/a/b'}
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id: 24549388
{'Lhash': '2759596079366677511059750234385', 'Lhash_array': ['2759596079366677511059750234385'], 'label': '2-450-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/450/2/a/b/1/1'}
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id: 102828
{'Lhash': '2103906565792006133', 'Lhash_array': ['2103906565792006133'], 'label': '2-450-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/450/b'}