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lfunc_lfunctions • Show schema
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{'Lhash': '2128552629573793763733537306242', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -1.0], 'a4': [0, 0], 'a5': [0, -3.7979326519318133], 'a6': [0, 0], 'a7': [2.1589416510366775, 0], 'a8': [0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.530043500937346, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3], 'central_character': '3072.1537', 'coefficient_field': 'CDF', 'conductor': 3072, 'conductor_radical': 6, 'conjugate': '497845839385656886020822850732', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 3.7979326519318133], [-5.0, 0]], [[1.0, 0], [-2.1589416510366775, 0], [7.0, 0]], [[1.0, 0], [0, -2.542660740595396], [-11.0, 0]], [[1.0, 0], [0, 1.9568743029684907], [-13.0, 0]], [[1.0, 0], [-0.22477743852204093, 0], [17.0, 0]], [[1.0, 0], [0, -0.22477743852204093], [-19.0, 0]], [[1.0, 0], 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[-109.0, 0]], [[1.0, 0], [18.848584857219635, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-3072-8.5-c1-0-57', 'leading_term': '1.3086674405086590339728135170975778932370315888277470551', '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/3072/2/d/i/1537/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3086674405086591, 1.5151463443155528, 1.7224407937966495, 1.9295813212393387, 2.1353028799977385, 2.3379789643959046, 2.5355797260829163, 2.7256571765046287, 2.9053585669313153, 3.071467328417812, 3.2204696434697038, 3.348643805295971, 3.4521689214380213, 3.5272491298632875, 3.570249218875994, 3.57783730784334, 3.5471300192919206, 3.4758353514911864, 3.362388264584889, 3.2060738570454306, 3.0071329729048233, 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'4.33693633064703629021155670864254', '5.24234261776260177001516539176963', '6.22354838497288595376339731031611', '6.67011802317632519784179953800002', '7.69376601574364777251167385239503', '8.185384706701491511704366747146104', '9.177730645240211616917209939174395'], 'prelabel': '2-3072-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.952781390384331, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67913195417614797231818087898', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80644089449937185565487791420', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42082400333398484311204239755', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.530043500937346, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 3072, 'conductor_radical': 6, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3072/2/d/i/1537/1'], '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': '2-3072-8.5-c1-0-57', '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': '2-3072-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.952781390384331, 'root_angle': 0.5, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67913195417614797231818087898', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2128552629573793763733537306242', 'Lhash_array': ['2128552629573793763733537306242'], 'label': '2-3072-8.5-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3072/2/d/i/1537/1'}