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lfunc_lfunctions • Show schema
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{'Lhash': '742326210440931110513710725731', 'a10': [-2496.0, 0], 'a2': [-4.0, 6.928203230275509], 'a3': [0, 0], 'a4': [-32.0, -55.42562584220407], 'a5': [156.0, 270.19992598074487], 'a6': [0, 0], 'a7': [-161.5, 279.7262054223737], 'a8': [512.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.606374128427746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, -6.928203230275509]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '162.55', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '1664849820767132121906458550337', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, -6.928203230275509]], [[1.0, 0], [0, 0]], [[1.0, 0], [-156.0, -270.19992598074487], [-39062.5, 67658.23467065927]], [[1.0, 0], [161.5, -279.7262054223737], [-411771.5, -713209.159108848]], [[1.0, 0], [-1860.0, 3221.614502078112], [-9743585.5, -16876385.133891404]], [[1.0, 0], 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'rational': False, 'root_analytic_conductor': 7.113815722130265, 'root_angle': -0.7777777777777778, 'root_number': '-0.7660444431189780352023926505554166739358324570803952459 - 0.6427876096865393263226434099072634329075598842056817903*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.3888888888888889', 'prec': 64}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58559212633771622085649779422', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.50676143875448754014717157756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.04798904711665549597888295593', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 50.606374128427746, 'bad_primes': [2, 3], 'central_character': '9.7', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/8/c/f/55/1'], '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': '2-162-9.7-c7-0-8', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-162-9.7-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.113815722130265, 'root_angle': -0.3888888888888889, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58559212633771622085649779422', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '742326210440931110513710725731', 'Lhash_array': ['742326210440931110513710725731'], 'label': '2-162-9.7-c7-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/8/c/f/55/1'}