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lfunc_lfunctions • Show schema
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{'Lhash': '896638474090616006245705374590', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-4.303076028446016, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': 'CDF', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.303076028446016, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.566268406554797, 0], [11.0, 0]], [[1.0, 0], [-2.8142907986428, 0], [13.0, 0]], [[1.0, 0], [-7.965364886052722, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.8142907986427999, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 40, 'label': '2-9576-1.1-c1-0-40', 'leading_term': '1.7464836259872872173661355895300', '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/9576/2/a/co/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [1.7464836259872871, 1.7376618260181147, 1.7112214271480999, 1.6672438071347881, 1.6058853632931445, 1.5274070245595752, 1.4322124415601218, 1.320892057941326, 1.1942698807833219, 1.053449607042522, 0.8998568070886094, 0.7352740802897364, 0.561866439702938, 0.38219461321274306, 0.1992144335523045, 0.016261004958659724, -0.162983136327621, -0.33453611635371633, -0.4941807876358081, -0.6375439490578081, -0.7601893862873892, -0.8577228903953561, -0.9259069272363174, -0.9607821776333565, -0.9587927614115185, -0.9169116114438679, 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'6.52504118779308284189520414993109', '7.11646391828886085916920668897466', '7.79353157073495250244653670466300'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.70732303832711008265485724378', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.41525172964452349384319530777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.91902880629184358501316294680', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/1'], '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': '2-9576-1.1-c1-0-40', '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': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.70732303832711008265485724378', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '896638474090616006245705374590', 'Lhash_array': ['896638474090616006245705374590'], 'label': '2-9576-1.1-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/1'}