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lfunc_lfunctions • Show schema
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{'Lhash': '1674399483690973208479156913909', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.618033988749895], 'a4': [0, 0], 'a5': [0, 0.38196601125010515], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [-3.8541019662496847, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.606153953490637, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [3.4641016151377544, -2.23606797749979]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2549', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '756255765095357103362081802932', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.618033988749895], [-3.0, 0]], [[1.0, 0], [0, -0.38196601125010515], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-11.0, 0]], [[1.0, 0], [-5.605034153776294, 0], [13.0, 0]], [[1.0, 0], [3.4641016151377544, 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'3.67043224649599321921372115004387', '4.23748265203578384865544958956397', '5.06493583889182356400676604394910', '5.58294461599859872533555127500521', '6.73440119696524537083701368100740', '7.36761549484760061862415102719826', '8.669605116930259278263584191341667', '8.907726294747932747935762122715012'], 'prelabel': '2-3332-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.8175437199199347, 'root_number': '-0.84016805041680588211757644839614885632543190116502750979 + 0.5423261445466404300001337812801643033674591205130861182*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.40877185995996734', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32086829240605591844262954489', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71849793775440241749226796441', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67043224649599321921372115004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.606153953490637, 'bad_primes': [2, 7, 17], 'central_character': '17.16', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 47, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/2/b/c/2549/1'], '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': '2-3332-17.16-c1-0-47', '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': '2-3332-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.158115348990427, 'root_angle': 0.40877185995996734, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32086829240605591844262954489', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1674399483690973208479156913909', 'Lhash_array': ['1674399483690973208479156913909'], 'label': '2-3332-17.16-c1-0-47', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/2/b/c/2549/1'}