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lfunc_lfunctions • Show schema
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{'Lhash': '3081905784138827048550869713702', 'a10': [0.3722655305979846, -2.7764901723370454], 'a2': [1.4016708737833188, 0.18793286457537872], 'a3': [-1.6458837551350565, -0.5395059449000775], 'a4': [1.9293624768249846, 0.5268400450039464], 'a5': [0.0, -1.9808431667292081], 'a6': [-2.2055964235254066, -1.0655254180599991], 'a7': [2.425161263024641, -1.4001675080355291], 'a8': [2.6053206299054112, 1.1010469632986917], 'a9': [2.417866670834949, 1.775928141019653], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.2456662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4016708737833188, -0.18793286457537872]]], [3, [[1.0, 0], [1.6458837551350565, 0.5395059449000775]]], [13, [[1.0, 0], [-0.23535033181861234, 3.597861895808797]]]], 'bad_primes': [2, 3, 13], 'central_character': '156.35', 'coefficient_field': 'CDF', 'conductor': 156, 'conductor_radical': 78, 'conjugate': '2296489336780018774930374966108', 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'7.23268331817566379192075003933510', '9.018044962284188906185727494235352', '10.68841794308105218105222962559478', '11.17588248165114776467294242286841', '11.67852754353718570423739722150592', '13.02304380088179986637477516563347'], 'prelabel': '2-156-156.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1160942036996584, 'root_angle': 0.1251764082661416, 'root_number': '0.9236673063686142 + 0.38319539029814625*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0625882041331', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.43119498668162731261968920431', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.20121808469175137726327348737', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.26219912382360758983068934303', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.2456662715319746, 'bad_primes': [2, 3, 13], 'central_character': '156.35', 'conductor': 156, 'conductor_radical': 78, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/156/2/p/b/35/20'], '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': '2-156-156.35-c1-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-156-156.35-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1160942036996584, 'root_angle': 0.0625882041330708, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43119498668162731261968920431', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3081905784138827048550869713702', 'Lhash_array': ['3081905784138827048550869713702'], 'label': '2-156-156.35-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/156/2/p/b/35/20'}