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lfunc_lfunctions • Show schema
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{'Lhash': '768203143539243307523400177735', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.414213562373095, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.8284271247461901, 0.0], 'a8': [0.0, 0.0], 'a9': [2.8284271247461903, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.552128646809734, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.1', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.414213562373095, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8284271247461901, 0], [7.0, 0]], [[1.0, 0], [-5.242640687119285, 0], [11.0, 0]], [[1.0, 0], [5.656854249492381, 0], [13.0, 0]], [[1.0, 0], [-0.1715728752538099, 0], [17.0, 0]], [[1.0, 0], [-1.5857864376269049, 0], [19.0, 0]], [[1.0, 0], [-4.82842712474619, 0], [23.0, 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'6.41030030655787428061247477009553', '7.03676014516620699102890183706324', '7.56887103064768595205763100330053', '9.004226813107531565084218041728691'], 'prelabel': '2-3200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60600542720599434226467620275', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.80009446496141328112468694990', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15978815668361773663467847378', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 25.552128646809734, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/a/bh/1/1'], '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': '2-3200-1.1-c1-0-9', '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': '2-3200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60600542720599434226467620275', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '768203143539243307523400177735', 'Lhash_array': ['768203143539243307523400177735'], 'label': '2-3200-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/a/bh/1/1'}