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lfunc_lfunctions • Show schema
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{'Lhash': '1188749780992921200665169325805', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-6.656854249492381, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [0.0, 0.0], 'a9': [17.31370849898476, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.16427841285903, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '2240.1', 'coefficient_field': 'CDF', 'conductor': 2240, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [6.656854249492381, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [38.254833995939045, 0], [1331.0, 0]], [[1.0, 0], [19.34314575050762, 0], [2197.0, 0]], [[1.0, 0], [87.22539674441619, 0], [4913.0, 0]], [[1.0, 0], [-44.22539674441618, 0], [6859.0, 0]], [[1.0, 0], [-218.16652224137047, 0], 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'5.85985201329594277154502253863004', '6.76950186469420237058774765478481', '7.12448867655729755119902880627915', '8.394276931229722136317906976252059'], 'prelabel': '2-2240-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.496272370332004, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.937758228315355352230454524923', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.33319207470437124870764521727', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21178269050764190163728250258', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.16427841285903, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 2240, 'conductor_radical': 70, 'degree': 2, 'index': 79, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2240/4/a/bn/1/1'], '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': '2-2240-1.1-c3-0-79', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2240-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.496272370332004, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.937758228315355352230454524923', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1188749780992921200665169325805', 'Lhash_array': ['1188749780992921200665169325805'], 'label': '2-2240-1.1-c3-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2240/4/a/bn/1/1'}