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lfunc_lfunctions • Show schema
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{'Lhash': '1144355121791042434897167273324', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, -1.4142135623730951], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '3200.1857', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '944957397795855574454169752995', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, 1.4142135623730951], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 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1.2637278347910232, 'root_angle': 0.42620819117478337, 'root_number': '0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.21310409558739168', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.902737017270382947585579771008', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.74304594496652906932792203210', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.94058827844325653207229184536', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '40.37', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/m/d/1857/1'], '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': '2-3200-40.37-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-40.37-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': 0.21310409558739168, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.902737017270382947585579771008', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1144355121791042434897167273324', 'Lhash_array': ['1144355121791042434897167273324'], 'label': '2-3200-40.37-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/m/d/1857/1'}