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lfunc_lfunctions • Show schema
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{'Lhash': '1009669622363690435824475076682', 'a10': [-0.1526658669020623, 0.0], 'a2': [-0.12417463958032422, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.9845806588850965, 0.0], 'a5': [1.229444815930455, 0.0], 'a6': [0.0, 0.0], 'a7': [2.667026902723409, 0.0], 'a8': [0.4947838671957877, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 69.06261270820544, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 31], 'central_character': '8649.1', 'coefficient_field': 'CDF', 'conductor': 8649, 'conductor_radical': 93, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.12417463958032422, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.229444815930455, 0], [5.0, 0]], [[1.0, 0], [-2.667026902723409, 0], [7.0, 0]], [[1.0, 0], [-5.631919355769495, 0], [11.0, 0]], [[1.0, 0], [0.013465393163935562, 0], [13.0, 0]], [[1.0, 0], [3.544850873743809, 0], [17.0, 0]], [[1.0, 0], 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'4.37652629585445695994476818625437', '4.73266102168970595199306083566099', '5.78619949023977449587576404665696', '6.27888857598783163278969331119447', '7.07309197254017743562461697498878', '7.934529035521204323592134497752482'], 'prelabel': '2-93e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.310391850460809, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.796488892271977982452317244850', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.62005889590599354771321830846', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.48030832966797027759744736568', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 69.06261270820544, 'bad_primes': [3, 31], 'central_character': '1.1', 'conductor': 8649, 'conductor_radical': 93, 'degree': 2, 'index': 140, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8649/2/a/bs/1/6'], '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': '2-93e2-1.1-c1-0-140', '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': '2-93e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.310391850460809, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.796488892271977982452317244850', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1009669622363690435824475076682', 'Lhash_array': ['1009669622363690435824475076682'], 'factors': ['2-93e2-1.1-c1-0-140'], 'label': '2-93e2-1.1-c1-0-140', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8649/2/a/bs/1/6'}