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lfunc_lfunctions • Show schema
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{'Lhash': '1833345869578243652591973700233', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -2, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.762974500266903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [3, 5, 11], 'central_character': '2475.1', 'coefficient_field': '1.1.1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[1, 0, 2], [1], [1], [1, -1, 7], [1, -1], [1, -1, 13], [1, 6, 17], [1, 7, 19], [1, -6, 23], [1, -6, 29], [1, 7, 31], [1, 2, 37], [1, -6, 41], [1, -1, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -5, 61], [1, 5, 67], [1, -12, 71], [1, 14, 73], [1, 4, 79], [1, 6, 83], [1, 6, 89], [1, 17, 97], [1, 0, 101], [1, 8, 103], [1, 6, 107], [1, -11, 109], [1, 18, 113]], 'euler_factors_factorization': [[[[1, 0, 2], 1]], [1], [1], [[[1, -1, 7], 1]], [[[1, -1], 1]], [[[1, -1, 13], 1]], [[[1, 6, 17], 1]], 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1.2854338410297301, 1.1526262368775777, 0.947097450609511, 0.6891459295346596, 0.4013753206859155, 0.10738347103094331, -0.16959596927344137, -0.40802350965600087], 'positive_zeros': ['1.44625488225869633667383305183972', '2.69203750343984022101198568162611', '3.93260401970958534385260320255270', '4.48881609881667067649164980342881', '5.23058676244714842631111750230004', '6.25997416322047035967534085705753', '6.94177064779494456719577763042902', '8.001893150916943033064179219919853', '8.768041607540139167824161107173799'], 'prelabel': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, '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': 917706322866072983, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44625488225869633667383305184', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.69203750343984022101198568163', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93260401970958534385260320255', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.762974500266903, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 2475, 'conductor_radical': 165, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, -2, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 4, -6, 0, -7, 0, 0, 0, 6, 0, 0, 0, 0, -2, 6, 0, -7, 0, 0, 0, 0, 0, -2, 0, 0, 0, 6, 0, 1, -2, 0, 0, 0, 0, -6, 0, 0, -2, -6, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -8, 0, 0, -5, 12, 0, 0, 12, 0, -14, 0, 0, 14, 1, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, -6, 0, 1, -12, 0, 0, 0, 0, -17, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -1, 13], 'euler17': [1, 6, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 2], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -1, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -5, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 7], 'euler71': [1, -12, 71], 'euler73': [1, 14, 73], 'euler79': [1, 4, 79], 'euler83': [1, 6, 83], 'euler89': [1, 6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 0, 2], [1, 0, 0], [1, 0, 0], [1, -1, 7], [1, -1, 0], [1, -1, 13], [1, 6, 17], [1, 7, 19], [1, -6, 23], [1, -6, 29], [1, 7, 31], [1, 2, 37], [1, -6, 41], [1, -1, 43], [1, 0, 47], [1, 6, 53], [1, 0, 59], [1, -5, 61], [1, 5, 67], [1, -12, 71], [1, 14, 73], [1, 4, 79], [1, 6, 83], [1, 6, 89], [1, 17, 97]], 'index': 57, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2475/f', 'ModularForm/GL2/Q/holomorphic/2475/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/2475/2/a/f'], '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': '2-2475-1.1-c1-0-57', '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': '2-2475-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.445556714323517, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 917706322866072983, 'z1': {'__RealLiteral__': 0, 'data': '1.44625488225869633667383305184', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20667338
{'Lhash': '1833345869578243652591973700233', 'Lhash_array': ['1833345869578243652591973700233'], 'label': '2-2475-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/f'}
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id: 24557385
{'Lhash': '1833345869578243652591973700233', 'Lhash_array': ['1833345869578243652591973700233'], 'label': '2-2475-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2475/2/a/f/1/1'}
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id: 24307
{'Lhash': '917706322866072983', 'Lhash_array': ['917706322866072983'], 'label': '2-2475-1.1-c1-0-57', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2475/f'}