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lfunc_lfunctions • Show schema
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{'Lhash': '1145896301456526631488656621821', 'a10': [0.6548607339452851, -0.7557495743542583], 'a2': [0.14231483827328514, -0.9898214418809327], 'a3': [-0.3335954222567045, -0.38498964025242377], 'a4': [-0.9594929736144974, -0.28173255684142967], 'a5': [0.8412535328311812, 0.5406408174555976], 'a6': [-0.42854657939104684, 0.2754101634735959], 'a7': [-0.6173618970881405, 4.2938463097199095], 'a8': [-0.41541501300188644, 0.9096319953545183], 'a9': [0.3900133974687937, -2.71260276243387], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.349976935425788, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.14231483827328514, 0.9898214418809327]]], [5, [[1.0, 0], [-0.8412535328311812, -0.5406408174555976]]], [67, [[1.0, 0], [3.402103817357597, 7.4448431558979715]]]], 'bad_primes': [2, 5, 67], 'central_character': '670.461', 'coefficient_field': 'CDF', 'conductor': 670, 'conductor_radical': 670, 'conjugate': 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0.11915868779014267*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0190098626698', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.903952793656405027072272479941', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.98544217860313491980823804062', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34111619047705514153182919494', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.349976935425788, 'bad_primes': [2, 5, 67], 'central_character': '67.59', 'conductor': 670, 'conductor_radical': 670, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/670/2/k/c/461/3'], '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': '2-670-67.59-c1-0-7', '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': '2-670-67.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3130017153962052, 'root_angle': 0.019009862669761575, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.903952793656405027072272479941', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1145896301456526631488656621821', 'Lhash_array': ['1145896301456526631488656621821'], 'label': '2-670-67.59-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/670/2/k/c/461/3'}