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lfunc_lfunctions • Show schema
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{'Lhash': '540206657865640635331810171993', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.9238795325112867, -0.3826834323650898], 'a4': [0.0, 0.0], 'a5': [-0.3826834323650898, -0.9238795325112867], 'a6': [0.0, 0.0], 'a7': [-0.7071067811865476, -0.7071067811865476], 'a8': [0.0, 0.0], 'a9': [0.7071067811865476, 0.7071067811865476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]], [5, [[1.0, 0], [0.3826834323650898, 0.9238795325112867]]], [7, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '3360.2897', 'coefficient_field': 'CDF', 'conductor': 3360, 'conductor_radical': 210, 'conjugate': '1280220936067950438326057070769', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.9238795325112867, 0.3826834323650898]], 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'3.05530646386958373743540368207591', '4.11205462903971628560263862571021', '5.11441074311235905104273159082813', '5.60782853870331109566493749939991', '6.65812395965823788660405176833653', '6.93312311874782241439005281964438', '7.86100885711562542914360694184638', '8.838073353409543104981287376247609'], 'prelabel': '2-3360-840.797-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': -0.1762081911747834, 'root_number': '0.85065080835203993218154049706283 - 0.52573111211913360602566908484825*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.08810409558739168', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42614791313030668874294794406', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.52621335711375944197659963931', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.05530646386958373743540368208', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6768584424468882, 'bad_primes': [2, 3, 5, 7], 'central_character': '840.797', 'conductor': 3360, 'conductor_radical': 210, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3360/1/cv/d/2897/1'], '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': '2-3360-840.797-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3360-840.797-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2949356904676341, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.42614791313030668874294794406', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '540206657865640635331810171993', 'Lhash_array': ['540206657865640635331810171993'], 'label': '2-3360-840.797-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3360/1/cv/d/2897/1'}