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lfunc_lfunctions • Show schema
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{'Lhash': '1032629199814077939821980643344', 'a10': [-1.5, -2.598076211353316], 'a2': [-0.5, 0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-1.5, 2.598076211353316], 'a6': [0, 0], 'a7': [-1.0, 0], 'a8': [1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.116186243894532, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0.5, -4.330127018922194]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '2394.505', 'coefficient_field': 'CDF', 'conductor': 2394, 'conductor_radical': 798, 'conjugate': '277191431036738248098790164925', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5, -2.598076211353316], [-2.5, -4.330127018922194]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.0, 0], [11.0, 0]], [[1.0, 0], [1.5, 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'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.814600805322982599120281158000', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.23421797727027978624717093921', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.10850891205835588942920262761', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.116186243894532, 'bad_primes': [2, 3, 7, 19], 'central_character': '19.11', 'conductor': 2394, 'conductor_radical': 798, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2394/2/o/a/505/1'], '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': '2-2394-19.11-c1-0-22', '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': '2-2394-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.372206107206582, 'root_angle': 0.06775328806227679, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.814600805322982599120281158000', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1032629199814077939821980643344', 'Lhash_array': ['1032629199814077939821980643344'], 'label': '2-2394-19.11-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2394/2/o/a/505/1'}