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lfunc_lfunctions • Show schema
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{'Lhash': '2218235256961832470876349167760', 'a10': [0, 0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [0, -1.0], 'a5': [0, 0], 'a6': [0, 1.0], 'a7': [-0.189468690981506, 2.6389584337646843], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.189468690981506, -2.6389584337646843]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.643', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '206218811651657941436021232551', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 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0.747884305026376837412817001238097195475917562299499045*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36553488688538294', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.74987907280007489240298717788', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.85554319197831453240911812308', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.03132427745053649826209954858', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.13', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/m/c/643/2'], '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': '2-1050-35.13-c1-0-16', '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': '2-1050-35.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.36553488688538294, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74987907280007489240298717788', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2218235256961832470876349167760', 'Lhash_array': ['2218235256961832470876349167760'], 'label': '2-1050-35.13-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/m/c/643/2'}