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lfunc_lfunctions • Show schema
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{'Lhash': '2668315314119594596096487171014', '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': '18.11', 'coefficient_field': 'CDF', 'conductor': 18, 'conductor_radical': 6, 'conjugate': '3674832782707915162904736983749', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.898979485566356, -2.8284271247461903]], 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['2.10492963411147185629111956060307', '4.13649598353590919107784415859912', '6.65161925255404150004090982820046', '8.547007156034662046228693818676664', '10.20234104803373087620740184412131', '12.07530547442694177273090832266204', '13.25550783972698840405812192849968', '14.43893579050471927713847743808396', '15.39803937252827189608268853608973', '17.24658019521784782259658905517394'], 'prelabel': '2-18-9.2-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': 50}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.10492963411147185629111956060', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.13649598353590919107784415860', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.65161925255404150004090982820', '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': '9.2', 'conductor': 18, 'conductor_radical': 6, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/18/7/d/a/11/6'], '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': '2-18-9.2-c6-0-3', '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': '2-18-9.2-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': '2.10492963411147185629111956060', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2668315314119594596096487171014', 'Lhash_array': ['2668315314119594596096487171014'], 'label': '2-18-9.2-c6-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/18/7/d/a/11/6'}