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lfunc_lfunctions • Show schema
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{'Lhash': '824132397067812055286829767485', 'a10': [0.14688341237176727, 2.3942042544308335], 'a2': [0.6307832576219068, -1.2657458204173124], 'a3': [-0.5, 0.8660254037844386], 'a4': [-1.2042249638077904, -1.5968225438482906], 'a5': [-1.468901215462345, 0.8480705121601534], 'a6': [0.7807764064044151, 1.1791472355911317], 'a7': [0.0, 0.0], 'a8': [-2.780776406404415, 0.5169937887291752], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6307832576219068, 1.2657458204173124]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '588.31', 'coefficient_field': 'CDF', 'conductor': 588, 'conductor_radical': 42, 'conjugate': '2011540174070796352150636533820', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6307832576219068, 1.2657458204173124]], [[1.0, 0], 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'2-588-28.3-c1-0-7', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/588/2/o/a/31/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1924741040884579, 1.0409461924068657, 0.8623006117564531, 0.6475055663962722, 0.3866363542334765, 0.07075144051110928, -0.30635341284794476, -0.7466503181023499, -1.246698702851868, -1.7968218539355674, -2.3807077869315663, -2.9755252113613277, -3.552646815632225, -4.079044730994278, -4.519368392508755, -4.838638951663426, -5.005405587370424, -4.995118541543927, -4.7933943603556886, -4.398794412320465, -3.8247213641736244, -3.1000703653212924, -2.268357896846372, -1.3851905750739548, -0.5141196532695356, 0.27886282322451683, 0.9317180840471443, 1.3929926002848232, 1.6279108178678174, 1.6231143738105351, 1.389304067470005, 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'9.486906061658635448457490984725864', '10.76412319063662641434438981433611'], 'prelabel': '2-588-28.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.18550117643622266, 'root_number': '0.8349418935815154 - 0.5503381091134009*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0927505882181', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65012582877287655327773126415', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07896598928470252315693370359', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07844195589967697979503407375', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6952036388512886, 'bad_primes': [2, 3, 7], 'central_character': '28.3', 'conductor': 588, 'conductor_radical': 42, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/588/2/o/a/31/3'], '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': '2-588-28.3-c1-0-7', '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': '2-588-28.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.166841858293145, 'root_angle': -0.09275058821811133, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65012582877287655327773126415', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '824132397067812055286829767485', 'Lhash_array': ['824132397067812055286829767485'], 'label': '2-588-28.3-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/588/2/o/a/31/3'}