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lfunc_lfunctions • Show schema
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{'Lhash': '750159560511647377297112532690', 'a10': [1.4884836371729186, 1.4884836371729186], 'a2': [-1.4884836371729186, -1.4884836371729186], 'a3': [-1.3642197302591443, -1.0671946999360835], 'a4': [0.0, 2.431167076263042], 'a5': [-1.0, 0.0], 'a6': [0.44211689746666616, 3.6191205945317124], 'a7': [-1.310132275057406, 0.0], 'a8': [0.6417851379052258, -0.6417851379052258], 'a9': [0.7221909448566654, 2.911776131361585], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.3642197302591443, 1.0671946999360835]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [-0.16855714853990955, -5.382526218020317]]]], 'bad_primes': [3, 5, 29], 'central_character': '435.191', 'coefficient_field': 'CDF', 'conductor': 435, 'conductor_radical': 435, 'conjugate': '1223602919576963768221975340761', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.4884836371729186, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.130950594338', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59177154996541453191102467639', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42207333922996409433069980393', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70003408437216877628501510838', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.4734924879256983, 'bad_primes': [3, 5, 29], 'central_character': '87.17', 'conductor': 435, 'conductor_radical': 435, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/435/2/q/c/191/3'], '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': '2-435-87.17-c1-0-3', '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': '2-435-87.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8637307981373539, 'root_angle': 0.13095059433842912, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59177154996541453191102467639', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '750159560511647377297112532690', 'Lhash_array': ['750159560511647377297112532690'], 'label': '2-435-87.17-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/435/2/q/c/191/3'}