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lfunc_lfunctions • Show schema
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{'Lhash': '2226920295105676378307902811226', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.446453149448075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 23], 'central_character': '3312.1', 'coefficient_field': '1.1.1.1', 'conductor': 3312, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, -2, 7], [1, 6, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, 1], [1, 6, 29], [1, 8, 31], [1, 0, 37], [1, 10, 41], [1, -12, 43], [1, 8, 47], [1, 2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 10, 73], [1, -6, 79], [1, -14, 83], [1, 0, 89], [1, 6, 97], [1, -6, 101], [1, 14, 103], [1, -14, 107], [1, 16, 109], [1, -8, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -2, 5], 1]], [[[1, -2, 7], 1]], [[[1, 6, 11], 1]], [[[1, 2, 13], 1]], [[[1, 0, 17], 1]], 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0.41665992911946736, -0.02006372340502884, -0.3665465391178486, -0.6091654539094524, -0.7407177456323938, -0.7607444737921554, -0.6754607223607118, -0.49729611328896467, -0.24407193617780612], 'positive_zeros': ['1.75673035985210661335841948053446', '2.33137889789155181282145246785952', '3.38807414963777119141033594454317', '4.61781233004508478544485198077333', '5.34329120767643148260995938995975', '5.70446099983308366623422114204735', '6.81404055785242482314012546704418', '7.74940445665935159391608281760161', '8.009088544194373664704576673471975'], 'prelabel': '2-3312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.142611510647881, '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': 2082175344740535663, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.75673035985210661335841948053', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33137889789155181282145246786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38807414963777119141033594454', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.446453149448075, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 3312, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 2, 0, 0, 0, -6, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -6, 0, -8, 0, 0, 0, 4, 0, 0, 0, 0, 0, -10, 0, 12, 0, 0, 0, -8, 0, -3, 0, 0, 0, -2, 0, -12, 0, 0, 0, -12, 0, 4, 0, 0, 0, -4, 0, 12, 0, 0, 0, 0, 0, -10, 0, 0, 0, -12, 0, 6, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -6, 0, 0, 0], 'euler11': [1, 6, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, 0, 37], 'euler41': [1, 10, 41], 'euler43': [1, -12, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, -6, 79], 'euler83': [1, -14, 83], 'euler89': [1, 0, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, -2, 7], [1, 6, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, 1, 0], [1, 6, 29], [1, 8, 31], [1, 0, 37], [1, 10, 41], [1, -12, 43], [1, 8, 47], [1, 2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 10, 73], [1, -6, 79], [1, -14, 83], [1, 0, 89], [1, 6, 97]], 'index': 53, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3312/n', 'ModularForm/GL2/Q/holomorphic/3312/2/a/n/1/1', 'ModularForm/GL2/Q/holomorphic/3312/2/a/n'], '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': '2-3312-1.1-c1-0-53', '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': '2-3312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.142611510647881, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2082175344740535663, 'z1': {'__RealLiteral__': 0, 'data': '1.75673035985210661335841948053', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20546665
{'Lhash': '2226920295105676378307902811226', 'Lhash_array': ['2226920295105676378307902811226'], 'label': '2-3312-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3312/2/a/n'}
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id: 24561028
{'Lhash': '2226920295105676378307902811226', 'Lhash_array': ['2226920295105676378307902811226'], 'label': '2-3312-1.1-c1-0-53', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3312/2/a/n/1/1'}
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id: 97851
{'Lhash': '2082175344740535663', 'Lhash_array': ['2082175344740535663'], 'label': '2-3312-1.1-c1-0-53', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3312/n'}