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lfunc_lfunctions • Show schema
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{'Lhash': '1869247708098852409513553519914', 'a10': -2, 'a2': 1, 'a3': 0, 'a4': -1, 'a5': -2, 'a6': 0, 'a7': -1, 'a8': -3, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.769089565735037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '2601.1', 'coefficient_field': '1.1.1.1', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'euler_factors': [[1, -1, 2], [1], [1, 2, 5], [1, 1, 7], [1, -6, 11], [1, -1, 13], [1], [1, -5, 19], [1, 2, 23], [1, 6, 29], [1, 7, 31], [1, 7, 37], [1, 6, 41], [1, -7, 43], [1, -12, 47], [1, 12, 53], [1, -6, 59], [1, 11, 61], [1, 11, 67], [1, -2, 71], [1, -6, 73], [1, 0, 79], [1, 2, 83], [1, 16, 89], [1, 17, 97], [1, -4, 101], [1, 7, 103], [1, 16, 107], [1, 6, 109], [1, -4, 113]], 'euler_factors_factorization': [[[[1, -1, 2], 1]], [1], [[[1, 2, 5], 1]], [[[1, 1, 7], 1]], [[[1, -6, 11], 1]], [[[1, -1, 13], 1]], [1], [[[1, -5, 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-0.3895432156816655, -0.7032078783189448, -1.0550196039245259, -1.4272410292502327, -1.8005144996295708, -2.15499613996426, -2.4715238363086556, -2.732750487705132, -2.9241755751208816], 'positive_zeros': ['1.47457643909316235195895560595416', '3.19141357944294142707644563983203', '3.79280785088461732586370661915614', '4.22527589632564621267877536062658', '5.35296107667423472592512536298224', '6.03235008616589723233178945896177', '6.91755284303484332905934769070174', '7.64398160342646731017446688378619', '8.617665338674477486335420041290097'], 'prelabel': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.5573116599301216, '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': 2107156278788362360, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47457643909316235195895560595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.19141357944294142707644563983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79280785088461732586370661916', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 20.769089565735037, 'bad_primes': [3, 17], 'central_character': '1.1', 'conductor': 2601, 'conductor_radical': 51, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, -2, 0, -1, -3, 0, -2, 6, 0, 1, -1, 0, -1, 0, 0, 5, 2, 0, 6, -2, 0, -1, 1, 0, 1, -6, 0, -7, 5, 0, 0, 2, 0, -7, 5, 0, 6, -6, 0, 7, -6, 0, -2, 12, 0, -6, -1, 0, -1, -12, 0, -12, 3, 0, -6, 6, 0, -11, -7, 0, 7, -2, 0, -11, 0, 0, 2, 2, 0, 6, -7, 0, -5, -6, 0, 0, 2, 0, -6, -2, 0, 0, 7, 0, -18, -16, 0, -1, 2, 0, 12, -10, 0, -17, -6, 0, 1], 'euler11': [1, -6, 11], 'euler13': [1, -1, 13], 'euler17': [1, 0, 0], 'euler19': [1, -5, 19], 'euler2': [1, -1, 2], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, 7, 37], 'euler41': [1, 6, 41], 'euler43': [1, -7, 43], 'euler47': [1, -12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 12, 53], 'euler59': [1, -6, 59], 'euler61': [1, 11, 61], 'euler67': [1, 11, 67], 'euler7': [1, 1, 7], 'euler71': [1, -2, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 2, 83], 'euler89': [1, 16, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, -1, 2], [1, 0, 0], [1, 2, 5], [1, 1, 7], [1, -6, 11], [1, -1, 13], [1, 0, 0], [1, -5, 19], [1, 2, 23], [1, 6, 29], [1, 7, 31], [1, 7, 37], [1, 6, 41], [1, -7, 43], [1, -12, 47], [1, 12, 53], [1, -6, 59], [1, 11, 61], [1, 11, 67], [1, -2, 71], [1, -6, 73], [1, 0, 79], [1, 2, 83], [1, 16, 89], [1, 17, 97]], 'index': 74, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2601/h', 'ModularForm/GL2/Q/holomorphic/2601/2/a/h/1/1', 'ModularForm/GL2/Q/holomorphic/2601/2/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': '2-51e2-1.1-c1-0-74', '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': '2-51e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.5573116599301216, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2107156278788362360, 'z1': {'__RealLiteral__': 0, 'data': '1.47457643909316235195895560595', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20411586
{'Lhash': '1869247708098852409513553519914', 'Lhash_array': ['1869247708098852409513553519914'], 'label': '2-51e2-1.1-c1-0-74', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2601/2/a/h'}
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id: 24557954
{'Lhash': '1869247708098852409513553519914', 'Lhash_array': ['1869247708098852409513553519914'], 'label': '2-51e2-1.1-c1-0-74', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2601/2/a/h/1/1'}
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id: 38572
{'Lhash': '2107156278788362360', 'Lhash_array': ['2107156278788362360'], 'label': '2-51e2-1.1-c1-0-74', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2601/h'}