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lfunc_lfunctions • Show schema
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{'Lhash': '3809571754067814484716628738019', 'a10': [10.11096689992496, 134.92147676916673], 'a2': [-3.608725166059531, -4.525198227763907], 'a3': [-0.052505031288765595, -0.007913860127927417], 'a4': [-0.3338517898041502, 1.4627002620608454], 'a5': [-19.314269214551874, -13.16824578270965], 'a6': [0.15366444193084292, 0.2661546207409373], 'a7': [53.22022725516338, -92.1801375963049], 'a8': [-159.04849856264346, 76.59372006721479], 'a9': [-232.20149765690368, -71.62467634690246], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.896504251958168, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [8519.037341644298, -8627.539960595375]]]], 'bad_primes': [43], 'central_character': '43.9', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '214510648332439317044880119956', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.608725166059531, 4.525198227763907], [-7.120669886602061, 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-0.7300489813903798, 'root_number': '-0.6614272842671022 - 0.750009298360391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.365024490695', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.00522222241833389699772169914', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.47716690325731668623113360800', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.91443342886322350321897267649', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.896504251958168, 'bad_primes': [43], 'central_character': '43.9', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/6/g/a/9/5'], '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': '2-43-43.9-c5-0-14', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-43-43.9-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6261196187451494, 'root_angle': -0.3650244906951899, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '3.00522222241833389699772169914', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3809571754067814484716628738019', 'Lhash_array': ['3809571754067814484716628738019'], 'label': '2-43-43.9-c5-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/6/g/a/9/5'}