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lfunc_lfunctions • Show schema
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{'Lhash': '1091764933321042439259531322861', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7653668647301796, 0.0], 'a4': [0.0, 0.0], 'a5': [2.9301512653149673, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.4142135623730951, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.414213562373095, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.70672466791646, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '4096.1', 'coefficient_field': 'CDF', 'conductor': 4096, 'conductor_radical': 2, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7653668647301796, 0], [3.0, 0]], [[1.0, 0], [-2.9301512653149673, 0], [5.0, 0]], [[1.0, 0], [1.4142135623730951, 0], [7.0, 0]], [[1.0, 0], [-4.460884994775326, 0], [11.0, 0]], [[1.0, 0], [-0.7653668647301796, 0], [13.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [17.0, 0]], [[1.0, 0], [-4.0125434656073615, 0], [19.0, 0]], [[1.0, 0], 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'4.94928562724744873809332586146023', '5.52484016574616715552493761348472', '6.30583384465341812978344227872346', '6.63179091674743259614464418007150', '7.53414710337617039749418878705435', '8.856313051979487730953540238595799'], 'prelabel': '2-2e12-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.718979337951525, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.861250673588195133176180452833', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90088098073121330925499240519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.92815817530618094709578774489', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.70672466791646, 'bad_primes': [2], 'central_character': '1.1', 'conductor': 4096, 'conductor_radical': 2, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4096/2/a/f/1/2'], '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': '2-2e12-1.1-c1-0-39', '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': '2-2e12-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.718979337951525, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.861250673588195133176180452833', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1091764933321042439259531322861', 'Lhash_array': ['1091764933321042439259531322861'], 'label': '2-2e12-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4096/2/a/f/1/2'}