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lfunc_lfunctions • Show schema
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{'Lhash': '3204049887242304887946480145768', 'a10': [0.0, -1.4142135623730951], 'a2': [1.0, 0.0], 'a3': [1.0, 1.4142135623730951], 'a4': [1.0, 0.0], 'a5': [0.0, -1.4142135623730951], 'a6': [1.0, 1.4142135623730951], 'a7': [-4.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-1.0, 2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [-1.0, -1.4142135623730951]]], [19, [[1.0, 0], [-1.0, 4.242640687119285]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.113', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': '3809158365960652287870385123431', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, -1.4142135623730951]], [[1.0, 0], [0, 1.4142135623730951], [-5.0, 0]], [[1.0, 0], [4.0, 0], [7.0, 0]], [[1.0, 0], [0, 5.656854249492381], [-11.0, 0]], [[1.0, 0], [0, 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'10.28203756050024740552854529558501', '11.93527617100321057580621015372438', '12.78992616265785395876288403105994', '13.25092394538342122552329217173691'], 'prelabel': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.12223174263583228, 'root_number': '0.9271726499455306 - 0.3746343246326776*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0611158713179', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.52754969442324543840005105817', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64773973712878028607102946935', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.77270130908789855328915338266', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.56', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/b/d/113/2'], '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': '2-114-57.56-c1-0-4', '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': '2-114-57.56-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.06111587131791614, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.52754969442324543840005105817', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3204049887242304887946480145768', 'Lhash_array': ['3204049887242304887946480145768'], 'label': '2-114-57.56-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/d/113/2'}