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lfunc_lfunctions • Show schema
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{'Lhash': '1966581675456652307294978712485', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.3625081376117922, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.053355524960888, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [8.306460975505523, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.21230790698127, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 17], 'central_character': '6664.1', 'coefficient_field': 'CDF', 'conductor': 6664, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.3625081376117922, 0], [3.0, 0]], [[1.0, 0], [4.053355524960888, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.808371374309763, 0], [11.0, 0]], [[1.0, 0], [-1.8478995501123732, 0], [13.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.44473407623487154, 0], [19.0, 0]], [[1.0, 0], [7.7089992251550425, 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'6.62201892530563714808813104313417', '7.38395191183082180169362719620068', '7.78001882306337083225805990921369'], 'prelabel': '2-6664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.294676682827093, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55135940069178879398535178653', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49042893688228498850525978960', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40105722446238217165584068037', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.21230790698127, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 6664, 'conductor_radical': 238, 'degree': 2, 'index': 142, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6664/2/a/t/1/6'], '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': '2-6664-1.1-c1-0-142', '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': '2-6664-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.294676682827093, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55135940069178879398535178653', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1966581675456652307294978712485', 'Lhash_array': ['1966581675456652307294978712485'], 'factors': ['2-6664-1.1-c1-0-142'], 'label': '2-6664-1.1-c1-0-142', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6664/2/a/t/1/6'}