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lfunc_lfunctions • Show schema
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{'Lhash': '664156410033561881561223016780', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-0.5155591823700209, -0.8929746981735448], 'a6': [0, 0], 'a7': [-2.631177265995623, -0.27731966195673474], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.1100711784264, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.631177265995623, 0.27731966195673474]]]], 'bad_primes': [2, 3, 7], 'central_character': '2268.2053', 'coefficient_field': 'CDF', 'conductor': 2268, 'conductor_radical': 42, 'conjugate': '1148741863948188778773254382594', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5155591823700209, 0.8929746981735448], [-2.5, 4.330127018922194]], [[1.0, 0], [2.631177265995623, 0.27731966195673474]], [[1.0, 0], [-0.7928788443267556, 1.3733064426204353], [-5.5, -9.526279441628825]], [[1.0, 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'8.928766265224725342090256563036379'], 'prelabel': '2-2268-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.2089694969738431, 'root_number': '0.7921351061531610260865860446320649540555191134013638507 - 0.6103457819955179412611951236128006904189635644055796852*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10448474848692156', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.52392702682741311351917898977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.29418575830759712962846517191', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06118579724547976904613150538', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.1100711784264, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 2268, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2268/2/i/n/2053/3'], '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': '2-2268-63.58-c1-0-7', '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': '2-2268-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.255592929125905, 'root_angle': -0.10448474848692155, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.52392702682741311351917898977', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '664156410033561881561223016780', 'Lhash_array': ['664156410033561881561223016780'], 'label': '2-2268-63.58-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2268/2/i/n/2053/3'}