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lfunc_lfunctions • Show schema
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{'Lhash': '2407575483854638850322308122559', 'a10': [0.0, 0.0], 'a2': [1.885864517124154, 0.0], 'a3': [1.8894236767123984, 0.0], 'a4': [1.5564849769479183, 0.0], 'a5': [0.0, 0.0], 'a6': [3.563197069726171, 0.0], 'a7': [0.3353288669242418, 0.0], 'a8': [-0.836409244785422, 0.0], 'a9': [0.5699218301213979, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.69191546037511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '7225.1', 'coefficient_field': 'CDF', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.885864517124154, 0], [2.0, 0]], [[1.0, 0], [-1.8894236767123984, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.3353288669242418, 0], [7.0, 0]], [[1.0, 0], [3.8072992744735155, 0], [11.0, 0]], [[1.0, 0], [-0.5588017375941223, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[[1.0, 0], [2.5607868232845568, 0], [109.0, 0]], [[1.0, 0], [-7.082353038582274, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 393, 'label': '2-85e2-1.1-c1-0-393', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7225/2/a/bx/1/22', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.208617939821461e-59, 0.45007562892842745, 0.8992701179334538, 1.3466205793619426, 1.7910054886255353, 2.2310771592685543, 2.665207429777389, 3.0914495297757916, 3.507518094730912, 3.9107882830629626, 4.298314002263863, 4.666864428838134, 5.012977338784215, 5.333027253717144, 5.623306037491257, 5.880113324801345, 6.099854000197012, 6.279139849951038, 6.41489246311659, 6.504444451717123, 6.545636089585318, 6.536904536184567, 6.477362920405274, 6.366866716034101, 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'5.44748645496610974723677577734896', '5.86644428194017450752063374725946', '6.81324709434217771930770458624354', '7.64027052650438020094685611538080'], 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89924217558148589626514521696', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.57422302469991083216391374153', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21615478631743197588691421302', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.69191546037511, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'index': 393, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7225/2/a/bx/1/22'], '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': '2-85e2-1.1-c1-0-393', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89924217558148589626514521696', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2407575483854638850322308122559', 'Lhash_array': ['2407575483854638850322308122559'], 'label': '2-85e2-1.1-c1-0-393', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7225/2/a/bx/1/22'}