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lfunc_lfunctions • Show schema
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{'Lhash': '1002864043427312066690529789136', 'a10': [-1.0, 0.0], 'a2': [0.5176380902050415, 0.0], 'a3': [-1.0, 0.0], 'a4': [-0.7320508075688773, 0.0], 'a5': [-1.9318516525781366, 0.0], 'a6': [-0.5176380902050415, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.8965754721680536, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5943864300459059, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [397, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 397], 'central_character': '1191.1190', 'coefficient_field': 'CDF', 'conductor': 1191, 'conductor_radical': 1191, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 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[[1.0, 0], [1.7320508075688772, 0], [1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.9318516525781366, 0], [1.0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5176380902050415, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-1191-1191.1190-c0-0-1', 'leading_term': '0.52282189309808477992722511783328', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1191/1/d/f/1190/3', 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'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.791120237111673491467288084319', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '3.43569077845467126756922201425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80828078042584629179448749609', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5943864300459059, 'bad_primes': [3, 397], 'central_character': '1191.1190', 'conductor': 1191, 'conductor_radical': 1191, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1191/1/d/f/1190/3'], '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': '2-1191-1191.1190-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1191-1191.1190-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7709646101124914, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.791120237111673491467288084319', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1002864043427312066690529789136', 'Lhash_array': ['1002864043427312066690529789136'], 'label': '2-1191-1191.1190-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1191/1/d/f/1190/3'}