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lfunc_lfunctions • Show schema
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{'Lhash': '705278851353699197679160955380', 'a10': [0.5539461317991067, -4.971263619592647], 'a2': [-0.5789721098992482, -2.160753330309346], 'a3': [-0.23146653422330155, -1.7165148538636807], 'a4': [-2.6015954428328647, 1.502031829242058], 'a5': [2.0824984996971594, 0.8143709220982052], 'a6': [-3.574952519321077, 1.4939563112930159], 'a7': [-1.3338385371725607, 4.977953189821346], 'a8': [1.5882090390864325, 1.5882090390864325], 'a9': [-2.8928464870693062, 0.7946314883332862], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.431697312181064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.23146653422330155, 1.7165148538636807]]], [5, [[1.0, 0], [-2.0824984996971594, -0.8143709220982052]]], [37, [[1.0, 0], [1.199736966029293, 5.963273531571634]]]], 'bad_primes': [3, 5, 37], 'central_character': '555.47', 'coefficient_field': 'CDF', 'conductor': 555, 'conductor_radical': 555, 'conjugate': 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'3.40032943944638312661515432258757', '4.48595392736317046261505874819460', '5.55069068842573753580254684073497', '6.27302867259895601781229959436764', '7.04626758140528142623851914685731', '8.338601351407443017591963441734364', '8.888888796260419793252027091406087', '9.793283675050428932161286481622585', '10.55796449465070300497263444372542'], 'prelabel': '2-555-555.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.105159688047694, 'root_angle': 0.12309576822829382, 'root_number': '0.9261523218911486 + 0.3771496740760016*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0615478841141', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.55636691311211457643534801360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.40032943944638312661515432259', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.48595392736317046261505874819', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.431697312181064, 'bad_primes': [3, 5, 37], 'central_character': '555.47', 'conductor': 555, 'conductor_radical': 555, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/555/2/bi/a/47/10'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-555-555.47-c1-0-8', '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': '2-555-555.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.105159688047694, 'root_angle': 0.06154788411414691, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55636691311211457643534801360', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '705278851353699197679160955380', 'Lhash_array': ['705278851353699197679160955380'], 'label': '2-555-555.47-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/555/2/bi/a/47/10'}