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lfunc_lfunctions • Show schema
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{'Lhash': '1716309586089578765240654192613', 'a10': [1.629683664318002, -2.822694906863802], 'a2': [1.0, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [1.629683664318002, -2.822694906863802], 'a6': [0, 0], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.2125', 'coefficient_field': 'CDF', 'conductor': 2646, 'conductor_radical': 42, 'conjugate': '1349928030272210938830462575884', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.629683664318002, 2.822694906863802], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.8117376914898995, -4.870072539216931], [-5.5, 9.526279441628825]], [[1.0, 0], [0.6136160175714132, 1.0628141187717646], [-6.5, 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'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.11927972996430325, 'root_number': '0.73205913147779643790423860940694760080881308061595229732 + 0.68124109390139872016282358643377355819256019352520341720*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.11927972996430324', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35392953372212519608363938723', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47041748646888862525483567180', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.41685446740096527117448335716', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '63.25', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2646/2/e/s/2125/4'], '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': '2-2646-63.25-c1-0-32', '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': '2-2646-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.11927972996430325, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35392953372212519608363938723', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1716309586089578765240654192613', 'Lhash_array': ['1716309586089578765240654192613'], 'factors': ['2-2646-63.25-c1-0-32'], 'label': '2-2646-63.25-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/e/s/2125/4'}