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lfunc_lfunctions • Show schema
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{'Lhash': '4695332391707879906425245155924', 'a10': [-123.73679659309838, 214.31841846506194], 'a2': [-3.194933459514875, -5.533787078681566], 'a3': [4.5, -7.794228634059948], 'a4': [-4.415199621455375, 7.647350069919583], 'a5': [-19.364534216604124, -33.54035712806433], 'a6': [-57.50880227126775, 5.48568260085501e-61], 'a7': [-87.5, 95.65955258101513], 'a8': [-148.05066540485126, 0.0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.368060216072594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-4.5, 7.794228634059948]]], [7, [[1.0, 0], [87.5, -95.65955258101513]]]], 'bad_primes': [3, 7], 'central_character': '21.4', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '1073782582287085393379894598584', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.194933459514875, 5.533787078681566], [-16.0, 27.712812921102035]], [[1.0, 0], [-4.5, 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'9.245271005216166249143835702643790', '10.58961778243552219371916689167335', '12.50507141260342186601110567731130', '14.45488707215421780811473907422939', '15.28091175938255730592532770559124', '16.46621334729973753839585077465655', '17.32457896799792680685549169209191'], 'prelabel': '2-21-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8352275652007284, 'root_angle': 0.9226686410332108, 'root_number': '-0.9706340591692696 + 0.24056085130500113*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.461334320517', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.70396416083621652751346224856', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.47103772572418322098874192107', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.65268311827782394120043657193', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.368060216072594, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/6/e/b/4/1'], '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': '2-21-7.4-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-21-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8352275652007284, 'root_angle': 0.4613343205166054, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '3.70396416083621652751346224856', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4695332391707879906425245155924', 'Lhash_array': ['4695332391707879906425245155924'], 'label': '2-21-7.4-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/6/e/b/4/1'}