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lfunc_lfunctions • Show schema
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{'Lhash': '1071031270242257732861816233929', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.600285364484913, -2.537535566689734], 'a4': [0, 0], 'a5': [0, 1.5623728031530835], 'a6': [0, 0], 'a7': [-4.5959394346820535, 7.9604006093787], 'a8': [0, 0], 'a9': [-3.878173504430778, 8.121562058467022], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.63765008224431, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.600285364484913, 2.537535566689734]]], [19, [[1.0, 0], [-8.518623770262092, 16.98331678620892]]]], 'bad_primes': [2, 3, 19], 'central_character': '684.353', 'coefficient_field': 'CDF', 'conductor': 684, 'conductor_radical': 114, 'conjugate': '747018636039374623777937633611', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.600285364484913, 2.537535566689734]], [[1.0, 0], [0, -1.5623728031530835], [-25.0, 0]], [[1.0, 0], [4.5959394346820535, -7.9604006093787], [-24.5, 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'2-684-171.11-c2-0-18', 'leading_term': '1.073146842607675715391243200146403348230322126899795181', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/684/3/m/a/353/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.0731468426076758, 1.1117497951498854, 1.133474243686069, 1.1377161570023289, 1.1238674829980357, 1.0913269424378662, 1.0395182892470358, 0.9679154700678495, 0.8760738032416302, 0.7636660338612529, 0.6305219125454913, 0.47666979143140514, 0.30237862820537187, 0.10819873255323213, -0.10500042625972994, -0.3359970113071503, -0.583189815768041, -0.8445789858187418, -1.1177558672629284, -1.3999032183888347, -1.687806837722749, -1.9778794219372136, -2.2661971952747684, -2.5485495381037433, -2.8205014912098565, -3.077468628920299, -3.3148033852427212, 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'7.57687279291024632556005304977117', '8.863340805355106629555900028930329', '9.957174164258719087943582068540787', '10.21961589987268443644750471298737'], 'prelabel': '2-684-171.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': 0.2775966612872116, 'root_number': '0.6432233804831639927491557647292598152586066950933415597 + 0.7656785766885546385404089846075972218657345109764254717*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1387983306436058', 'prec': 60}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.844894697363317559077278931326', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.95787339552109557210216496056', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.92042329026696509075591273083', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.63765008224431, 'bad_primes': [2, 3, 19], 'central_character': '171.11', 'conductor': 684, 'conductor_radical': 114, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/684/3/m/a/353/14'], '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': '2-684-171.11-c2-0-18', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-684-171.11-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.317134475811972, 'root_angle': 0.1387983306436058, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.844894697363317559077278931326', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1071031270242257732861816233929', 'Lhash_array': ['1071031270242257732861816233929'], 'label': '2-684-171.11-c2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/684/3/m/a/353/14'}