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lfunc_lfunctions • Show schema
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{'Lhash': '1159413488600334683068533917584', 'a10': [6.898522423275195, 0], 'a2': [0, -1.3514086223051631], 'a3': [0, 0], 'a4': [2.1736947355592613, 0], 'a5': [0, 5.104690253868627], 'a6': [0, 0], 'a7': [-13.167915426530296, 0], 'a8': [0, -8.34318429711478], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.485', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '889022633887085504038962992977', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.3514086223051631], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -5.104690253868627], [-25.0, 0]], [[1.0, 0], [13.167915426530296, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.670269063127289, 0], [169.0, 0]], [[1.0, 0], [0, 17.216095252422523], [-289.0, 0]], [[1.0, 0], 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'2.54447959345324781670723812276372', '3.52412379590895416101403928093711', '4.79463147612271146939839516080974', '5.84293138949568250851089533578955', '6.32526904456281792403383718407482', '7.22864289315838725218769592529278', '8.049315136469241306478403937500719', '8.971744462273135296379155301467916', '9.647817971484157047152863712200360'], 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.3040867239846964, 'root_number': '0.577350269189625764509148780501957455647601751270126876 + 0.816496580927726032732428024901963797321982493552223376*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1520433619923482', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.914615974142711269722602387389', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.54447959345324781670723812276', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.52412379590895416101403928094', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/b/i/485/6'], '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': '2-33e2-3.2-c2-0-34', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.1520433619923482, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.914615974142711269722602387389', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1159413488600334683068533917584', 'Lhash_array': ['1159413488600334683068533917584'], 'label': '2-33e2-3.2-c2-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/b/i/485/6'}