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lfunc_lfunctions • Show schema
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{'Lhash': '2349927182239213286111161317238', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.04108607387354, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '3136.1', 'coefficient_field': '1.1.1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 0, 5], [1], [1, 4, 11], [1, 4, 13], [1, -2, 17], [1, -6, 19], [1, 8, 23], [1, 2, 29], [1, 4, 31], [1, 10, 37], [1, -10, 41], [1, -4, 43], [1, -4, 47], [1, -2, 53], [1, 10, 59], [1, 8, 61], [1, 8, 67], [1, 0, 71], [1, -6, 73], [1, -16, 79], [1, 2, 83], [1, 18, 89], [1, -2, 97], [1, 0, 101], [1, 4, 103], [1, 16, 107], [1, 10, 109], [1, -6, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 0, 5], 1]], [1], [[[1, 4, 11], 1]], [[[1, 4, 13], 1]], [[[1, -2, 17], 1]], [[[1, -6, 19], 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-3.2318299802034236, -3.586553114679967, -3.84278838569058, -3.986472757471715, -4.009951857341533, -3.912283422655211, -3.699155603214302], 'positive_zeros': ['1.85376568418468736850245926472314', '2.60884071777472257455932823593664', '3.35969994906988033781424102779219', '4.23143308280647914859549127921372', '5.36926311260280225249673141611678', '5.80249737529463976328330224358462', '7.24762858405575842532755200215389', '7.74281557582837679435844331851624', '8.055916559826172153895328642713797'], 'prelabel': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, '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': 1539229072281170862, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85376568418468736850245926472', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60884071777472257455932823594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35969994906988033781424102779', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.04108607387354, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 3136, 'conductor_radical': 14, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 0, -4, 0, 0, 0, 2, 0, 6, 0, 0, 0, -8, 0, -5, 0, -4, 0, -2, 0, -4, 0, -8, 0, 0, 0, -10, 0, -8, 0, 10, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 12, 0, -10, 0, -8, 0, 0, 0, 0, 0, -8, 0, -16, 0, 0, 0, 6, 0, -10, 0, 0, 0, 16, 0, -11, 0, -2, 0, 0, 0, -4, 0, -18, 0, 0, 0, -8, 0, 0, 0, 2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, -6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 2, 29], 'euler3': [1, -2, 3], 'euler31': [1, 4, 31], 'euler37': [1, 10, 37], 'euler41': [1, -10, 41], 'euler43': [1, -4, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, 10, 59], 'euler61': [1, 8, 61], 'euler67': [1, 8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -6, 73], 'euler79': [1, -16, 79], 'euler83': [1, 2, 83], 'euler89': [1, 18, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 0, 5], [1, 0, 0], [1, 4, 11], [1, 4, 13], [1, -2, 17], [1, -6, 19], [1, 8, 23], [1, 2, 29], [1, 4, 31], [1, 10, 37], [1, -10, 41], [1, -4, 43], [1, -4, 47], [1, -2, 53], [1, 10, 59], [1, 8, 61], [1, 8, 67], [1, 0, 71], [1, -6, 73], [1, -16, 79], [1, 2, 83], [1, 18, 89], [1, -2, 97]], 'index': 70, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3136/y', 'ModularForm/GL2/Q/holomorphic/3136/2/a/y/1/1', 'ModularForm/GL2/Q/holomorphic/3136/2/a/y'], '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': '2-56e2-1.1-c1-0-70', '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': '2-56e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.004106920707584, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1539229072281170862, 'z1': {'__RealLiteral__': 0, 'data': '1.85376568418468736850245926472', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20321286
{'Lhash': '2349927182239213286111161317238', 'Lhash_array': ['2349927182239213286111161317238'], 'label': '2-56e2-1.1-c1-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/y'}
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id: 24560222
{'Lhash': '2349927182239213286111161317238', 'Lhash_array': ['2349927182239213286111161317238'], 'label': '2-56e2-1.1-c1-0-70', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3136/2/a/y/1/1'}
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id: 96697
{'Lhash': '1539229072281170862', 'Lhash_array': ['1539229072281170862'], 'label': '2-56e2-1.1-c1-0-70', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3136/y'}