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lfunc_lfunctions • Show schema
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{'Lhash': '3674832782707915162904736983749', 'a10': [10.436190803195055, -1.3234599517621057e-60], 'a2': [4.898979485566356, -2.8284271247461903], 'a3': [25.648496522731385, -8.435320155360795], 'a4': [16.0, -27.712812921102035], 'a5': [1.5977088953846514, 0.9224376608369882], 'a6': [101.79276996714036, -113.86936366914873], 'a7': [6.344105093808247, 10.988312351032402], 'a8': [0.0, -181.01933598375618], 'a9': [586.6907477531279, -432.7065593457947], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.140973505157318, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-4.898979485566356, 2.8284271247461903]]], [3, [[1.0, 0], [-25.648496522731385, 8.435320155360795]]]], 'bad_primes': [2, 3], 'central_character': '18.5', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '2668315314119594596096487171014', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, 2.8284271247461903]], 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['2.89893191550281573396473599300613', '4.86317093346278517272727683692132', '7.21167299158374884369317297291090', '8.729480083695416397887817718888801', '10.47225791968756840191232791848006', '12.51116138468688426295457208306780', '13.72753207912969945392100949253287', '14.88453984207508013941199817084103', '15.80532557520805129867838457093323', '17.29392126391587615726051532914517'], 'prelabel': '2-18-9.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.24216569694432916, 'root_number': '0.7242943122419137 + 0.689490934859925*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.121082848472', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.89893191550281573396473599301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.86317093346278517272727683692', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.21167299158374884369317297291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.140973505157318, 'bad_primes': [2, 3], 'central_character': '9.5', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/7/d/a/5/6'], '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': '2-18-9.5-c6-0-4', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-18-9.5-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0349382067171766, 'root_angle': 0.12108284847216458, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '2.89893191550281573396473599301', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3674832782707915162904736983749', 'Lhash_array': ['3674832782707915162904736983749'], 'label': '2-18-9.5-c6-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/7/d/a/5/6'}