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lfunc_lfunctions • Show schema
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{'Lhash': '1638142978623546360682706071532', 'a10': [0.45880389985380304, -0.45880389985380304], 'a2': [0, -1.0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [-1.0, 0], 'a5': [0.45880389985380304, 0.45880389985380304], 'a6': [-0.7071067811865476, 0.7071067811865476], 'a7': [0.41421356237309503, -0.41421356237309503], 'a8': [0, 1.0], 'a9': [0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.846059710490024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 17], 'central_character': '1734.829', 'coefficient_field': 'CDF', 'conductor': 1734, 'conductor_radical': 102, 'conjugate': '514530153867771830784864943881', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [-0.45880389985380304, -0.45880389985380304], [0, 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0.405504071799804455994443321337791058427776046176828691*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.43354800353266193', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.29226695299841537362575258443', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00808381652038882853036335698', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94911595267418191847131473961', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.846059710490024, 'bad_primes': [2, 3, 17], 'central_character': '17.13', 'conductor': 1734, 'conductor_radical': 102, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1734/2/f/m/829/1'], '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': '2-1734-17.13-c1-0-36', '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': '2-1734-17.13-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.721029388555004, 'root_angle': 0.43354800353266193, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.29226695299841537362575258443', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1638142978623546360682706071532', 'Lhash_array': ['1638142978623546360682706071532'], 'label': '2-1734-17.13-c1-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1734/2/f/m/829/1'}