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lfunc_lfunctions • Show schema
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{'Lhash': '753154027622550239353964572659', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-47923.97079176394, 0], 'a4': [0, 0], 'a5': [-9765625.0, 0], 'a6': [0, 0], 'a7': [-667863034.2833368, 0], 'a8': [0, 0], 'a9': [-8163646226.550157, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 223.5818754296497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [9765625.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '80.1', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [47923.97079176394, 0], [10460353203.0, 0]], [[1.0, 0], [9765625.0, 0]], [[1.0, 0], [667863034.2833368, 0], [558545864083284030, 0]], [[1.0, 0], [-126792936569.12602, 0], [7400249944258161000000, 0]], [[1.0, 0], [-912749797432.6476, 0], [247064529073450400000000, 0]], [[1.0, 0], [-8604062242294.3125, 0], [69091933913008730000000000, 0]], [[1.0, 0], 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'label': '2-80-1.1-c21-0-11', 'leading_term': '1.6887829965715060347584323749839557244150377702565658130', 'load_key': 'CMFs-workshop', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/80/22/a/d/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.688782996571506, 1.6647663897202116, 1.5934947519899627, 1.47727994782912, 1.3199001127636594, 1.1264894230975167, 0.903388164998504, 0.6579573479291798, 0.39836311535106766, 0.13333706764501693, -0.12808069587880305, -0.37680850665381477, -0.6039924205256239, -0.8012701819036915, -0.9610222946026536, -1.076602977826974, -1.1425443316470092, -1.1547277713323605, -1.1105176942565358, -1.0088533922213252, -0.8502963873234878, -0.6370316189151033, -0.37282220832615076, -0.06291884080691006, 0.2860739059798956, 0.6663707267917515, 1.0692135498549802, 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'8.644865390586306989862122776662110', '9.286662644454206807728707160481752', '10.78864462770805101729053899041360'], 'prelabel': '2-80-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.952654460986173, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59413376800117591162270982246', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.44926322757208746880444991362', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35006483537657709078053752191', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 223.5818754296497, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/22/a/d/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': '2-80-1.1-c21-0-11', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-80-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.952654460986173, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.59413376800117591162270982246', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '753154027622550239353964572659', 'Lhash_array': ['753154027622550239353964572659'], 'factors': ['2-80-1.1-c21-0-11'], 'label': '2-80-1.1-c21-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/22/a/d/1/1'}