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lfunc_lfunctions • Show schema
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{'Lhash': '1268985934327505582551015817856', 'a10': [5.22298214754408, 0.0], 'a2': [-1.276564082537673, 0.0], 'a3': [-2.576033921831658, 0.0], 'a4': [-0.3703841431747494, 0.0], 'a5': [-4.091437491458596, 0.0], 'a6': [3.2884723800089537, 0.0], 'a7': [-1.0, 0.0], 'a8': [3.025947258993722, 0.0], 'a9': [3.635950766427391, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.763329051202452, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [7, 11], 'central_character': '847.1', 'coefficient_field': 'CDF', 'conductor': 847, 'conductor_radical': 77, 'conjugate': '1268985934327505582551015817856', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.276564082537673, 0], [2.0, 0]], [[1.0, 0], [2.576033921831658, 0], [3.0, 0]], [[1.0, 0], [4.091437491458596, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.39090733075258, 0], [13.0, 0]], [[1.0, 0], 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'5.22218825339016560749926027054368', '6.63443509371981719485893390110034', '7.10567662592236911419728729202186', '8.270244025647070504285398411942977', '8.707822811923367019229510178177254', '9.898026122445404779941929924126809'], 'prelabel': '2-847-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00105339286632749263155777480', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53265249391648651910892017062', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42407652456914028532917430642', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.763329051202452, 'bad_primes': [7, 11], 'central_character': '1.1', 'conductor': 847, 'conductor_radical': 77, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/847/2/a/m/1/3'], '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': '2-847-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-847-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6006401233547196, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00105339286632749263155777480', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1268985934327505582551015817856', 'Lhash_array': ['1268985934327505582551015817856'], 'label': '2-847-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/847/2/a/m/1/3'}