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lfunc_lfunctions • Show schema
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{'Lhash': '1964418697727999541051908264379', 'a10': [-0.7071067811865476, -2.1213203435596424], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [0.6180339887498949, 0.6180339887498949], 'a4': [0.0, 1.0], 'a5': [2.0, 1.0], 'a6': [0.0, -0.8740320488976422], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, -2.23606797749979], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.148480955638592, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-2.0, -1.0]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [11, [[1.0, 0], [1.0, 3.1622776601683795]]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '770.43', 'coefficient_field': 'CDF', 'conductor': 770, 'conductor_radical': 770, 'conjugate': '1325159762242544682804399797852', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.113150347152', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54965311212279088476321487505', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23754584438027759947358721070', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.31152480589164532733961860849', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.148480955638592, 'bad_primes': [2, 5, 7, 11], 'central_character': '55.43', 'conductor': 770, 'conductor_radical': 770, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/770/2/m/d/43/2'], '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': '2-770-55.43-c1-0-27', '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': '2-770-55.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4796130657097675, 'root_angle': 0.11315034715207414, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54965311212279088476321487505', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1964418697727999541051908264379', 'Lhash_array': ['1964418697727999541051908264379'], 'label': '2-770-55.43-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/770/2/m/d/43/2'}