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lfunc_lfunctions • Show schema
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{'Lhash': '2106100966307860039903565612446', 'a10': [-2.172767648824529, 0.0], 'a2': [-1.0, 0.0], 'a3': [0.6550213345375226, 0.0], 'a4': [1.0, 0.0], 'a5': [2.172767648824529, 0.0], 'a6': [-0.6550213345375226, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [-2.5709470513006827, 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], [-0.6550213345375226, 0], [3.0, 0]], [[1.0, 0], [-2.172767648824529, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.1826738827151162, 0], [11.0, 0]], [[1.0, 0], [1.4955075021268471, 0], [13.0, 0]], [[1.0, 0], [4.618215625957687, 0], [17.0, 0]], [[1.0, 0], 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'6.28111997588082548695294831054627', '6.83409154245527559922193731304361', '7.911534438062839068159022948145368', '8.497905948193227281787631604880239'], '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': '1.66142071476846615663474914407', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.42643309435168845272111350240', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.23039172578527183245737146903', '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': 79, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2842/2/a/s/1/4'], '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-c1-0-79', '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': '1.66142071476846615663474914407', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2106100966307860039903565612446', 'Lhash_array': ['2106100966307860039903565612446'], 'label': '2-2842-1.1-c1-0-79', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2842/2/a/s/1/4'}