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lfunc_lfunctions • Show schema
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{'Lhash': '631554438675367222216322911739', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.2570684646676455, -1.191544743238007], 'a4': [0.0, 0.0], 'a5': [-0.5, -0.8660254037844386], 'a6': [0.0, 0.0], 'a7': [-0.25706846466764555, 0.44525564182808686], 'a8': [0.0, 0.0], 'a9': [0.16044224972374319, 2.995706641930011], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.749228945532191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.2570684646676455, 1.191544743238007]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.241', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': '1694408069885060289517407696843', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.2570684646676455, 1.191544743238007]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.25706846466764555, -0.44525564182808686], [-3.5, 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'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.2948093547092259, 'root_number': '0.6008990726153001 - 0.7993249054859184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.147404677355', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49820860618979817483233831968', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75750824543165746762763474346', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83624502821156579531255766328', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.749228945532191, 'bad_primes': [2, 3, 5], 'central_character': '9.7', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/2/q/i/241/1'], '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': '2-720-9.7-c1-0-3', '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': '2-720-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.14740467735461296, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.49820860618979817483233831968', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '631554438675367222216322911739', 'Lhash_array': ['631554438675367222216322911739'], 'label': '2-720-9.7-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/2/q/i/241/1'}