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lfunc_lfunctions • Show schema
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{'Lhash': '1082213256499688825348420580457', 'a10': [22.29691395973168, 0.0], 'a2': [-4.459382791946336, 0.0], 'a3': [0.0, 0.0], 'a4': [11.886094885107095, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [5.081234416107328, 0.0], 'a8': [-17.329584658517255, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.965257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '135.1', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '1082213256499688825348420580457', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.459382791946336, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-5.081234416107328, 0], [343.0, 0]], [[1.0, 0], [58.300676292106395, 0], [1331.0, 0]], [[1.0, 0], [-21.21191721124963, 0], [2197.0, 0]], [[1.0, 0], [-68.84505583253478, 0], [4913.0, 0]], 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'4.90389355221207762736139942573401', '6.63608848599958390522406247067268', '7.975669044862759349257491451064150', '8.253434029612455221632646646446265', '9.665427418684236906183210959972073', '10.55181642592999060164628626276758', '11.26970250011170405448771694660784', '12.53097571097461536359890796373743'], 'prelabel': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.853715729164523564642244320077', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.75516325646685517928478298989', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.90389355221207762736139942573', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.965257850774987, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/4/a/g/1/1'], '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': '2-135-1.1-c3-0-0', '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': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.853715729164523564642244320077', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1082213256499688825348420580457', 'Lhash_array': ['1082213256499688825348420580457'], 'label': '2-135-1.1-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/4/a/g/1/1'}