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lfunc_lfunctions • Show schema
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{'Lhash': '1494710670162248709596572561725', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [1.0547104178477718, -1.826812030984541], 'a6': [0, 0], 'a7': [-1.4391413194866753, -2.4926658846226357], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.596298938554515, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '3456.2305', 'coefficient_field': 'CDF', 'conductor': 3456, 'conductor_radical': 6, 'conjugate': '1131511365185918177242785321804', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0547104178477718, 1.826812030984541], [-2.5, -4.330127018922194]], [[1.0, 0], [1.4391413194866753, 2.4926658846226357], [-3.5, 6.06217782649107]], [[1.0, 0], [-1.2132478260817119, -2.101406876946014], [-5.5, 9.526279441628825]], [[1.0, 0], [-3.300076662762063, 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5.253217960312947, 'root_angle': 0.3765061919430523, 'root_number': '0.37830751293091433150625188510570768412092055702535241509 + 0.92567998015514307970384236138334498886837602619369083857*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.18825309597152615', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.17911881230769671766816772585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33127462883853417175066959254', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19540187531946204595804472771', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.596298938554515, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 3456, 'conductor_radical': 6, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3456/2/i/l/2305/4'], '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': '2-3456-9.4-c1-0-35', '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': '2-3456-9.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.253217960312947, 'root_angle': 0.18825309597152615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.17911881230769671766816772585', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1494710670162248709596572561725', 'Lhash_array': ['1494710670162248709596572561725'], 'label': '2-3456-9.4-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3456/2/i/l/2305/4'}