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lfunc_lfunctions • Show schema
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{'Lhash': '3085733397549463728007391516722', 'a10': [0.0, 0.0], 'a2': [1.3955847598499216, 1.3955847598499216], 'a3': [4.935076395006043, -1.626352045362307], 'a4': [0.0, -4.104686356149273], 'a5': [0.0, 0.0], 'a6': [9.15702953422391, 4.617605276907142], 'a7': [3.8024486919732627, -3.8024486919732627], 'a8': [16.893115801405205, -16.893115801405205], 'a9': [21.709958049091682, -16.052343178074636], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.425143250430549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-4.935076395006043, 1.626352045362307]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '75.68', 'coefficient_field': 'CDF', 'conductor': 75, 'conductor_radical': 15, 'conjugate': '2300824292858826560672804492160', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3955847598499216, -1.3955847598499216], [0, 8.0]], [[1.0, 0], [-4.935076395006043, 1.626352045362307]], [[1.0, 0], [0, 0]], 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.0214149557142', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43421444126157824795225885850', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63836623840192012017307902618', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.03386215011262935759672110049', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.425143250430549, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 75, 'conductor_radical': 15, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/75/4/e/d/68/6'], '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': '2-75-15.8-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-75-15.8-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.103602445908102, 'root_angle': 0.021414955714178074, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43421444126157824795225885850', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3085733397549463728007391516722', 'Lhash_array': ['3085733397549463728007391516722'], 'label': '2-75-15.8-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/75/4/e/d/68/6'}