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lfunc_lfunctions • Show schema
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{'Lhash': '1857515055054606607870690269111', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.224744871391589, -0.7071067811865476], 'a6': [0, 0], 'a7': [3.449489742783178, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [4.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1889', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'conjugate': '53026695814279489603422621748', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [2.5, 4.330127018922194]], [[1.0, 0], [-3.449489742783178, 0], [7.0, 0]], [[1.0, 0], [0, -6.292528739883945], [-11.0, 0]], [[1.0, 0], [2.1742346141747673, -1.255294939775204], [6.5, -11.258330249197702]], 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'root_number': '-0.95392674726814142789883715837678966477458854186505879951 + 0.3000395987972644767200427619198776157797344807097368081*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4515000512945431', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46532100779203454900093783724', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.60255352649336640045602417744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62940711054893405007587423713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '57.8', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/dc/a/1889/1'], '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': '2-2736-57.8-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': '2-2736-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.4515000512945431, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46532100779203454900093783724', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1857515055054606607870690269111', 'Lhash_array': ['1857515055054606607870690269111'], 'label': '2-2736-57.8-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/dc/a/1889/1'}