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lfunc_lfunctions • Show schema
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{'Lhash': '1708780494259771133989081864216', 'a10': [-2.0274795125008787, 2.426793527762343], 'a2': [0.5785729831454004, 1.290446939309878], 'a3': [0.9876883405951378, 0.15643446504023087], 'a4': [-1.3305066063484643, 1.4932354705347353], 'a5': [0.9793017052120611, 2.010215951127826], 'a6': [0.3695794130223151, 1.365068151218129], 'a7': [0.0808032911737541, -0.0808032911737541], 'a8': [-2.696736318950189, -0.853002477168141], 'a9': [0.9510565162951535, 0.30901699437494745], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5785729831454004, -1.290446939309878]]], [3, [[1.0, 0], [-0.9876883405951378, -0.15643446504023087]]], [5, [[1.0, 0], [-0.9793017052120611, -2.010215951127826]]]], 'bad_primes': [2, 3, 5], 'central_character': '300.67', 'coefficient_field': 'CDF', 'conductor': 300, 'conductor_radical': 30, 'conjugate': 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0.9215554776300119*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.31345957775', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.34799012752577102394020127802', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70738493797472134879516342665', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13041916539875376124362702129', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.3955120606384126, 'bad_primes': [2, 3, 5], 'central_character': '100.67', 'conductor': 300, 'conductor_radical': 30, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/300/2/w/a/67/19'], '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': '2-300-100.67-c1-0-11', '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': '2-300-100.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5477441844951034, 'root_angle': -0.3134595777499867, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34799012752577102394020127802', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1708780494259771133989081864216', 'Lhash_array': ['1708780494259771133989081864216'], 'label': '2-300-100.67-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/300/2/w/a/67/19'}