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lfunc_lfunctions • Show schema
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{'Lhash': '1288362985036818971130902991011', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.7319155945964555, 0.02164193137421862], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-2.6439590373416433, 0.09736841818295669], 'a8': [0, 0], 'a9': [2.9990632536127872, 0.07496399688839105], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.768584424468887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.7319155945964555, -0.02164193137421862]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.6439590373416433, -0.09736841818295669]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '2100.101', 'coefficient_field': 'CDF', 'conductor': 2100, 'conductor_radical': 210, 'conjugate': '1395141335791653867482363565548', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7319155945964555, -0.02164193137421862]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.6439590373416433, -0.09736841818295669]], [[1.0, 0], 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'8.510225522918374641370993747688918', '9.148800814329543455763316552721724'], 'prelabel': '2-2100-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': -0.04808555213608199, 'root_number': '0.98861133290372608152157113081656825541644392613571444280 - 0.15049130358368912989684235931994713494035791316025352307*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.024042776068040995', 'prec': 70}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01633919062938990123612420262', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35650959257809695266322488909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30255786593561683399087942537', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.768584424468887, 'bad_primes': [2, 3, 5, 7], 'central_character': '21.17', 'conductor': 2100, 'conductor_radical': 210, 'degree': 2, 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2100/2/bi/n/101/16'], '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': '2-2100-21.17-c1-0-25', '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': '2-2100-21.17-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.0949462053205155, 'root_angle': -0.024042776068040995, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01633919062938990123612420262', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1288362985036818971130902991011', 'Lhash_array': ['1288362985036818971130902991011'], 'label': '2-2100-21.17-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2100/2/bi/n/101/16'}