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lfunc_lfunctions • Show schema
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{'Lhash': '3009157620229262883864232914677', 'a10': [-1.8018126144298574, -4.950439472234531], 'a2': [1.30760618253834, -1.097211865493052], 'a3': [0.38785979455188635, 1.688065395584593], 'a4': [0.15866369549988618, -0.8998265317218647], 'a5': [1.0555689926046978, -2.9001519718578703], 'a6': [2.359333247077735, 1.7817603790654153], 'a7': [-0.4215535487201126, -0.7301521644941971], 'a8': [0.9271279239508445, 1.605832669398717], 'a9': [-2.699129559540337, 1.309465395043178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.38785979455188635, -1.688065395584593]]], [19, [[1.0, 0], [3.910697537052695, -1.9252129164562513]]]], 'bad_primes': [3, 19], 'central_character': '171.110', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '2886837924755590293496630406065', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.0689111698497', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37380680424676198446337872767', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.84940659555384118565077710424', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.87511383702001386205943559588', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3654418745638952, 'bad_primes': [3, 19], 'central_character': '171.110', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/2/x/a/110/15'], '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': '2-171-171.110-c1-0-13', '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': '2-171-171.110-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1685212341091176, 'root_angle': 0.06891116984973347, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37380680424676198446337872767', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3009157620229262883864232914677', 'Lhash_array': ['3009157620229262883864232914677'], 'label': '2-171-171.110-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/2/x/a/110/15'}