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lfunc_lfunctions • Show schema
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{'Lhash': '467187102841240636198223514651', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [2.083176578068721, 1.6310657082367634], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.305753273406665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.083176578068721, -1.6310657082367634]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '6300.4049', 'coefficient_field': 'CDF', 'conductor': 6300, 'conductor_radical': 210, 'conjugate': '1252457594821193301859995606315', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.083176578068721, -1.6310657082367634]], [[1.0, 0], [5.108167674352498, 2.9492019818531596], [5.5, 9.526279441628825]], [[1.0, 0], [4.657255312331254, 0], [13.0, 0]], [[1.0, 0], [-1.8207053944829203, 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7.092654881876508, 'root_angle': -0.48540515406035656, 'root_number': '0.045834996874293281275630785274199173346433745798552786 - 0.998949024255759271391013256314462960908525579473207641*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2427025770301783', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36854564085492302465812385818', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.64799790075879068463947362890', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54503109117055617279874395561', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.305753273406665, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.59', 'conductor': 6300, 'conductor_radical': 210, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6300/2/dd/b/4049/11'], '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': '2-6300-105.59-c1-0-13', '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': '2-6300-105.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.092654881876508, 'root_angle': -0.24270257703017828, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.36854564085492302465812385818', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '467187102841240636198223514651', 'Lhash_array': ['467187102841240636198223514651'], 'label': '2-6300-105.59-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6300/2/dd/b/4049/11'}