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lfunc_lfunctions • Show schema
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{'Lhash': '1650963551963899547889216180100', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.805830250144402, 0.805830250144402], 'a4': [0, 0], 'a5': [0, -0.2513322496523631], 'a6': [0, 0], 'a7': [0.7071067811865476, 0.7071067811865476], 'a8': [0, 0], 'a9': [0, -1.701275215904421], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.166826152042992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]]], [41, [[1.0, 0], [6.165286805461699, -1.7289414699173224]]]], 'bad_primes': [2, 7, 41], 'central_character': '1148.337', 'coefficient_field': 'CDF', 'conductor': 1148, 'conductor_radical': 574, 'conjugate': '1242944481651174921544366531770', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.805830250144402, -0.805830250144402], [0, 3.0]], [[1.0, 0], [0, 0.2513322496523631], [-5.0, 0]], [[1.0, 0], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], 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0.17373272497735374338944579702983362981350266662001817486*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.027791441585972815', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.30238060208913875996547950408', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47382259211329319473806232143', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43238921356898905469411423634', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.166826152042992, 'bad_primes': [2, 7, 41], 'central_character': '41.9', 'conductor': 1148, 'conductor_radical': 574, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1148/2/k/b/337/12'], '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': '2-1148-41.9-c1-0-14', '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': '2-1148-41.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.0276766921259926, 'root_angle': 0.027791441585972815, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30238060208913875996547950408', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1650963551963899547889216180100', 'Lhash_array': ['1650963551963899547889216180100'], 'label': '2-1148-41.9-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1148/2/k/b/337/12'}