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lfunc_lfunctions • Show schema
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{'Lhash': '1128383159064542919769462910739', 'a10': [-17.617381357407044, 0], 'a2': [1.7617381357407045, 3.0514199607345756], 'a3': [0, 0], 'a4': [-2.2074425178462653, 3.8234025956974995], 'a5': [-2.5, 4.330127018922194], 'a6': [0, 0], 'a7': [-12.716232639464431, -22.02516101241808], 'a8': [12.632067507270287, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.89577355232496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.5, -4.330127018922194]]]], 'bad_primes': [3, 5], 'central_character': '405.271', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '1641255026708062783625970689369', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7617381357407045, -3.0514199607345756], [-4.0, 6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, -4.330127018922194]], [[1.0, 0], [12.716232639464431, 22.02516101241808], [-171.5, 297.04671349806245]], 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'9.009985588308919498185416661887997', '9.629971972259437566259853266890981', '11.05896072684238651553853932524171'], 'prelabel': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': -0.5555555555555556, 'root_number': '-0.1736481776669303488517166267693147960003756771840693873 - 0.9848077530122080593667430245895230136706432517198424188*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2777777777777778', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.890137360295800280281725224499', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.38022650239251822366217767131', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42564324526607843813127527420', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.89577355232496, 'bad_primes': [3, 5], 'central_character': '9.4', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/u/271/3'], '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': '2-405-9.4-c3-0-20', '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': '2-405-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': -0.2777777777777778, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.890137360295800280281725224499', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1128383159064542919769462910739', 'Lhash_array': ['1128383159064542919769462910739'], 'label': '2-405-9.4-c3-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/u/271/3'}