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lfunc_lfunctions • Show schema
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{'Lhash': '1229133562206659089697555939006', 'a10': [2.719050498756433, 0.0], 'a2': [-1.0, 0.0], 'a3': [-2.239974552438622, 0.0], 'a4': [1.0, 0.0], 'a5': [-2.719050498756433, 0.0], 'a6': [2.239974552438622, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [2.017485995572606, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.693484254447895, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 7, 29], 'central_character': '2842.1', 'coefficient_field': 'CDF', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [2.239974552438622, 0], [3.0, 0]], [[1.0, 0], [2.719050498756433, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.7365364943290387, 0], [11.0, 0]], [[1.0, 0], [3.0623513782978655, 0], [13.0, 0]], [[1.0, 0], [5.823249984418677, 0], [17.0, 0]], [[1.0, 0], 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'5.36210402769674996931154809618259', '6.36519085276343438738576655538092', '6.90264231436436918320433287676953', '7.53769906585950459688224368594921', '8.405924405856592046082525680458719'], 'prelabel': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, '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': '0.969615414519871914200733060874', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43606853080874667852167528849', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.77773793262733775569761663638', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.693484254447895, 'bad_primes': [2, 7, 29], 'central_character': '1.1', 'conductor': 2842, 'conductor_radical': 406, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2842/2/a/t/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': '2-2842-1.1-c1-0-29', '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': '2-2842-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.763767863199035, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.969615414519871914200733060874', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1229133562206659089697555939006', 'Lhash_array': ['1229133562206659089697555939006'], 'label': '2-2842-1.1-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2842/2/a/t/1/2'}