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lfunc_lfunctions • Show schema
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{'Lhash': '5791102070762442892224478751270', 'a10': [9.0, -15.588457268119896], 'a2': [-1.0, -1.7320508075688772], 'a3': [2.5, -4.330127018922194], 'a4': [-2.0, 3.4641016151377544], 'a5': [4.5, 7.794228634059948], 'a6': [-10.0, -3.111507638930571e-61], 'a7': [-14.0, 12.12435565298214], 'a8': [8.0, 0.0], 'a9': [1.0, 1.7320508075688772], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.826026740080369, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.7320508075688772]]], [7, [[1.0, 0], [14.0, -12.12435565298214]]]], 'bad_primes': [2, 7], 'central_character': '14.11', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '3363443588430400426233428741450', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.7320508075688772]], [[1.0, 0], [-2.5, 4.330127018922194], [-13.5, -23.382685902179844]], [[1.0, 0], [-4.5, -7.794228634059948], [-62.5, 108.25317547305482]], [[1.0, 0], [14.0, 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'sign_arg': {'__RealLiteral__': 0, 'data': '0.146493713613', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.56837402176893666395382714770', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.08174257950588709211683065132', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '9.368781952174122019062954225025', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.826026740080369, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/4/c/a/11/1'], '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': '2-14-7.4-c3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-14-7.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '4.56837402176893666395382714770', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5791102070762442892224478751270', 'Lhash_array': ['5791102070762442892224478751270'], 'factors': ['2-14-7.4-c3-0-1'], 'label': '2-14-7.4-c3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/4/c/a/11/1'}