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lfunc_lfunctions • Show schema
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{'Lhash': '2081162598508541438662902989305', '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': [-2.6389584337646843, 0.189468690981506], '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], [2.6389584337646843, -0.189468690981506]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.643', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '415475245143426683647294940009', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-0.7071067811865476, 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0.9282108210906265476490474632461455745976863650856693727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3106733042894005', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64174781137156115278535678415', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95796146022287404728338367227', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71511074113471462979507680920', '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': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/m/c/643/1'], '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-c1-0-15', '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': 0.3106733042894005, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.64174781137156115278535678415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2081162598508541438662902989305', 'Lhash_array': ['2081162598508541438662902989305'], 'label': '2-1050-35.13-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/m/c/643/1'}