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lfunc_lfunctions • Show schema
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{'Lhash': '857616461485884666343794792238', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.7915867879778797, 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], [-1.7915867879778797, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7366195081353232, 0], [11.0, 0]], [[1.0, 0], [5.068836960846233, 0], [13.0, 0]], [[1.0, 0], [-3.333587459545685, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.068836960846233, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 33, 'label': '2-9576-1.1-c1-0-33', 'leading_term': '2.14053237183881606841096985896', '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/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.140532371838816, 2.1297101504585765, 2.0972366089463983, 2.043098309661966, 1.9672963206786283, 1.8698796496742909, 1.750988693879906, 1.6109057105467595, 1.45010890889631, 1.2693266046949396, 1.069587939253876, 0.8522669054291804, 0.6191167970272875, 0.3722926599724607, 0.11435983657284775, -0.1517127686562068, -0.42257552896356787, -0.6945373266069759, -0.963620925825311, -1.2256337122822873, -1.476252509978253, -1.711120689212446, -1.9259553050006728, -2.1166615640521367, -2.2794515220884923, -2.410963575920418, -2.5083790513176787, 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'5.11704527273308374420525792952140', '5.61510946919811668310432851035542', '6.14511356796167422456840516026853', '7.16651290043403391744809839586010', '7.69483541606010408088783795773259'], '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': '0.67654009814019598512140254832', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.07004711388864479692031643526', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.23198625118616367925005824542', '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': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/4'], '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-c1-0-33', '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': '0.67654009814019598512140254832', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '857616461485884666343794792238', 'Lhash_array': ['857616461485884666343794792238'], 'label': '2-9576-1.1-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/4'}