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lfunc_lfunctions • Show schema
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{'Lhash': '1610245475158756685732872197957', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': -1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]]], 'bad_primes': [3, 5], 'central_character': '225.1', 'coefficient_field': '1.1.1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -10, 37], [1, 10, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, 10, 73], [1, 0, 79], [1, -12, 83], [1, -6, 89], [1, 2, 97], [1, 6, 101], [1, -16, 103], [1, 12, 107], [1, -14, 109], [1, -2, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [1], [1], [[[1, 0, 7], 1]], [[[1, -4, 11], 1]], [[[1, -2, 13], 1]], [[[1, -2, 17], 1]], [[[1, -4, 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-4.014533517122548, -3.380306393437591, -2.169498766019095, -0.6724179649805209, 0.7446539417661686, 1.7392896048650035, 2.086706708831334, 1.7414901917524936], 'positive_zeros': ['1.27025970316177507740293768623955', '3.55714635244582915245852508954412', '4.79492945983632365647604814265053', '6.20681526904542088835730053039281', '7.46261028773657489832215471573841', '8.455181921164028207665051683360638', '9.327820441539330420804608673051017', '10.04517050900761317536685250744864', '11.19897971912574422599178738873323', '12.10713864521281605598821868485510'], 'prelabel': '2-15e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 285895329455399408, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27025970316177507740293768624', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55714635244582915245852508954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.79492945983632365647604814265', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, 0, 0, 0, 3, 0, 0, 4, 0, 2, 0, 0, -1, 2, 0, 4, 0, 0, -4, 0, 0, 0, -2, 0, 0, 2, 0, 0, -5, 0, -2, 0, 0, 10, -4, 0, 0, -10, 0, -4, -4, 0, 0, 8, 0, -7, 0, 0, -2, -10, 0, 0, 0, 0, -2, 4, 0, -2, 0, 0, 7, 0, 0, -12, -2, 0, 0, 8, 0, -10, -10, 0, -4, 0, 0, 0, 0, 0, 10, 12, 0, 0, 4, 0, 12, 6, 0, 0, 0, 0, -8, 0, 0, -2, 7, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -10, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -4, 59], 'euler61': [1, 2, 61], 'euler67': [1, 12, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 0, 0], [1, 0, 7], [1, -4, 11], [1, -2, 13], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -10, 37], [1, 10, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, -4, 59], [1, 2, 61], [1, 12, 67], [1, -8, 71], [1, 10, 73], [1, 0, 79], [1, -12, 83], [1, -6, 89], [1, 2, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/225/b', 'ModularForm/GL2/Q/holomorphic/225/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/225/2/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': '2-15e2-1.1-c1-0-1', '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': '2-15e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 285895329455399408, 'z1': {'__RealLiteral__': 0, 'data': '1.27025970316177507740293768624', 'prec': 103}}
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lfunc_instances • Show schema
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id: 10064106
{'Lhash': '1610245475158756685732872197957', 'Lhash_array': ['1610245475158756685732872197957'], 'label': '2-15e2-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/a/b'}
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id: 24548400
{'Lhash': '1610245475158756685732872197957', 'Lhash_array': ['1610245475158756685732872197957'], 'label': '2-15e2-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/a/b/1/1'}
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id: 22008
{'Lhash': '285895329455399408', 'Lhash_array': ['285895329455399408'], 'label': '2-15e2-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/225/b'}