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lfunc_lfunctions • Show schema
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{'Lhash': '4038656066552331713134475431253', 'a10': [5.577740988850534, -8.299928039525202], 'a2': [1.994969851442857, -0.1417578633941163], 'a3': [-2.174770681662762, -2.06648795839223], 'a4': [3.9598094163318702, -0.5656053273524341], 'a5': [3.0760012942804735, -3.9418543907131895], 'a6': [-4.631542861430393, -3.8142903301575206], 'a7': [-5.187662554240727, 5.187662554240727], 'a8': [7.819521400311807, -1.6896996981906824], 'a9': [0.459255035639828, 8.988274851841117], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.994969851442857, 0.1417578633941163]]], [3, [[1.0, 0], [2.174770681662762, 2.06648795839223]]], [5, [[1.0, 0], [-3.0760012942804735, 3.9418543907131895]]]], 'bad_primes': [2, 3, 5], 'central_character': '60.47', 'coefficient_field': 'CDF', 'conductor': 60, 'conductor_radical': 30, 'conjugate': '2614377084774328873331463049153', 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'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': 0.11571546040347462, 'root_number': '0.7471306586857748 + 0.664677198985914*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.115715460403', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18593788053680329378922370223', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.72581375215691755531891321956', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.25339269530633731171869977223', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6348815861617816, 'bad_primes': [2, 3, 5], 'central_character': '60.47', 'conductor': 60, 'conductor_radical': 30, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/60/3/l/a/47/20'], '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': '2-60-60.47-c2-0-15', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-60-60.47-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2786248809411545, 'root_angle': 0.11571546040347462, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18593788053680329378922370223', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4038656066552331713134475431253', 'Lhash_array': ['4038656066552331713134475431253'], 'factors': ['2-60-60.47-c2-0-15'], 'label': '2-60-60.47-c2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/60/3/l/a/47/20'}