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lfunc_lfunctions • Show schema
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{'Lhash': '1863946107010013636171185535392', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-3.271187325527613, 0.0], 'a4': [0.0, 0.0], 'a5': [3.8214143379542276, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.1006323760151262, 0.0], 'a8': [0.0, 0.0], 'a9': [7.700666518692497, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.035981290937706, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [59, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 17, 59], 'central_character': '4012.1', 'coefficient_field': 'CDF', 'conductor': 4012, 'conductor_radical': 2006, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [3.271187325527613, 0], [3.0, 0]], [[1.0, 0], [-3.8214143379542276, 0], [5.0, 0]], [[1.0, 0], [1.1006323760151262, 0], [7.0, 0]], [[1.0, 0], [-4.055970855118781, 0], [11.0, 0]], [[1.0, 0], [-2.22527043636623, 0], [13.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [5.587246596206177, 0], 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0], [7.7690763152128985, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-4012-1.1-c1-0-57', '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/4012/2/a/g/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-5.979928743569691e-61, 0.1427581272500501, 0.28471091790923786, 0.4250137010091533, 0.5627463948794597, 0.6968836853543542, 0.8262739710062538, 0.9496289497764009, 1.065525009947938, 1.1724168797793941, 1.268663342527798, 1.3525642713191999, 1.4224077924851166, 1.4765260401271616, 1.513357702351839, 1.531515361507538, 1.52985547989814, 1.5075487672023296, 1.464148580800816, 1.3996549557584554, 1.3145718421238557, 1.2099551511355477, 1.087449287758271, 0.9493099834782724, 0.798411447956995, 0.6382361363273731, 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'6.65177269654539609537899435459286', '8.036853089570065392119885470304032'], 'prelabel': '2-4012-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.660033682844803, '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': '1.47039421325910029539278827958', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.93279542512458449066619225962', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66422431408558999955487766107', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.035981290937706, 'bad_primes': [2, 17, 59], 'central_character': '1.1', 'conductor': 4012, 'conductor_radical': 2006, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4012/2/a/g/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': '2-4012-1.1-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': 1, 'prelabel': '2-4012-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.660033682844803, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47039421325910029539278827958', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1863946107010013636171185535392', 'Lhash_array': ['1863946107010013636171185535392'], 'label': '2-4012-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4012/2/a/g/1/1'}