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lfunc_lfunctions • Show schema
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{'Lhash': '398328479494005305550766763460', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.5369599235874976, 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], [2.5369599235874976, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.912385594185021, 0], [11.0, 0]], [[1.0, 0], [0.1654965778497174, 0], [13.0, 0]], [[1.0, 0], [6.847683286033719, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.1654965778497175, 0], [23.0, 0]], [[1.0, 0], 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'group': 'GL2', 'index': 3, 'label': '2-9576-1.1-c1-0-3', 'leading_term': '0.48801240892727445925588296654141', '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/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [0.48801240892727443, 0.4770247448599394, 0.44408834078536524, 0.3892893222438448, 0.312791964601091, 0.21486818628003743, 0.09593577421636093, -0.043397404783287206, -0.2022863377285975, -0.3796022416333737, -0.5738896461616527, -0.7833302464643844, -1.005716262567411, -1.2384356255241442, -1.4784708378430895, -1.7224128504042007, -1.966490776124669, -2.206617731656953, -2.4384525680943487, -2.6574767241205044, -2.859084914682212, -3.038687861123526, -3.191824783136264, -3.3142829196603576, -3.4022209380040245, -3.4522927425727925, 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'5.45272280538112849703193518582388', '6.40945460484058457153849874702433', '7.30529304155128337310313550832453', '7.56574373467446865642442213231452'], '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': '0.31422576490895026381145820510', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86314391387657025371408245253', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.56399640259234639467548118934', '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': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/2'], '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-c1-0-3', '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': '0.31422576490895026381145820510', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '398328479494005305550766763460', 'Lhash_array': ['398328479494005305550766763460'], 'label': '2-9576-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/co/1/2'}