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lfunc_lfunctions • Show schema
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{'Lhash': '914092402475900993305923559828', 'a10': [-17.872874638453347, 0], 'a2': [1.7872874638453347, -3.0956726951110425], 'a3': [0, 0], 'a4': [-2.388792956837377, -4.137510770005025], 'a5': [-2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-7.079870597486294, 12.262695585859285], 'a8': [11.518760599615462, 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': '405.136', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '1762179109841826530406027904061', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7872874638453347, 3.0956726951110425], [-4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [7.079870597486294, -12.262695585859285], [-171.5, -297.04671349806245]], 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'7.08320573699232518674654685562162', '7.76030876716268352398465606203573', '8.640920214108262785598153011902093', '10.28094815694178581238589876322419', '10.61655494417001296880557520999052'], 'prelabel': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.055555555555555566, 'root_number': '0.9848077530122080593667430245895230136706432517198424188 + 0.173648177666930348851716626769314796000375677184069388*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.027777777777777776', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72109176007278871045405310221', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.01053959519038441884542041925', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99754730565636156907249938209', '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': '9.7', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/4/e/w/136/5'], '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': '2-405-9.7-c3-0-17', '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': '2-405-9.7-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.8883303440259604, 'root_angle': 0.027777777777777783, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72109176007278871045405310221', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '914092402475900993305923559828', 'Lhash_array': ['914092402475900993305923559828'], 'label': '2-405-9.7-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/4/e/w/136/5'}