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lfunc_lfunctions • Show schema
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{'Lhash': '2253474916065349090121428912439', 'a10': [7.5706377253761366, 1.7651209773790632e-60], 'a2': [1.228894728748758, -2.128508107346423], 'a3': [0.0, 0.0], 'a4': [-2.020364508692967, -3.499373978865152], 'a5': [1.5401314588362758, 2.6675859370396044], 'a6': [0.0, 0.0], 'a7': [1.3293335667991255, -2.302473277902841], 'a8': [-5.015682264540414, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.487', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1645799548771669971758165037704', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.228894728748758, 2.128508107346423], [-1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5401314588362758, -2.6675859370396044], [-2.5, 4.330127018922194]], [[1.0, 0], [-1.3293335667991255, 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'10.58650866800508500260504889480858'], 'prelabel': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.6666666666666667, 'root_number': '-0.5000000000000002 + 0.8660254037844385*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.333333333333', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.77767826218015488202376326621', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.64124594652811815031499594295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.83087425018707118182114387834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/c/a/487/6'], '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': '2-3e6-9.7-c1-0-21', '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': '2-3e6-9.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.33333333333333337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.77767826218015488202376326621', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2253474916065349090121428912439', 'Lhash_array': ['2253474916065349090121428912439'], 'label': '2-3e6-9.7-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/c/a/487/6'}