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lfunc_lfunctions • Show schema
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{'Lhash': '2240079720412327073564069238439', 'a10': [-8927.152090221944, 0], 'a2': [9.797958971132712, 5.656854249492381], 'a3': [0, 0], 'a4': [64.0, 110.85125168440814], 'a5': [-683.3427336645019, 394.5281112299749], 'a6': [0, 0], 'a7': [89.71317181703344, -155.3877716952582], 'a8': [0, 1448.1546878700494], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.99844494330088, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-9.797958971132712, -5.656854249492381]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '54.35', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '145560686149100410737968169523', 'degree': 2, 'euler_factors': [[[1.0, 0], [-9.797958971132712, -5.656854249492381]], [[1.0, 0], [0, 0]], [[1.0, 0], [683.3427336645019, -394.5281112299749], [195312.5, -338291.17335329636]], [[1.0, 0], [-89.71317181703344, 155.3877716952582], 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'4.69451969799484402523051889626637', '6.44966111440585644953492886414310', '7.966782824740716459030607404207773', '9.269066972807591501461075940282362', '10.84096040887647941342448063654215', '12.01715640666761170797571782029416', '12.50731264305958403241673528423913', '14.05679738856145286702793780478471'], 'prelabel': '2-54-9.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.690249987292882, 'root_angle': 0.6464709649475684, 'root_number': '-0.4440843980838834 + 0.8959849593483559*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.32323548247378425', 'prec': 64}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.76711131601169937168228179510085', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.78390187354681791564859734198090', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.69451969799484402523051889626637', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.99844494330088, 'bad_primes': [2, 3], 'central_character': '9.2', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/9/d/a/35/5'], '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': '2-54-9.2-c8-0-6', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-54-9.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.690249987292882, 'root_angle': 0.3232354824737842, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '1.76711131601169937168228179510085', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2240079720412327073564069238439', 'Lhash_array': ['2240079720412327073564069238439'], 'label': '2-54-9.2-c8-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/9/d/a/35/5'}