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lfunc_lfunctions • Show schema
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{'Lhash': '1337578817733667700870980292158', 'a10': [5.2609661206902185, 4.414474731507328], 'a2': [-0.998593861420135, -1.1900778218899704], 'a3': [0.17364817766693036, 0.984807753012208], 'a4': [-0.07179916675453989, 0.4071933090787223], 'a5': [-4.353530608412013, 0.7676449076031768], 'a6': [0.998593861420135, -1.1900778218899704], 'a7': [2.6103363100213444, -0.4314444907333398], 'a8': [-2.134513806367489, 1.2323621206952424], 'a9': [-0.9396926207859084, 0.3420201433256687], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.186031040649089, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [7, [[1.0, 0], [-2.6103363100213444, 0.4314444907333398]]], [19, [[1.0, 0], [3.6041762773026056, 2.4515124642002397]]]], 'bad_primes': [3, 7, 19], 'central_character': '399.10', 'coefficient_field': 'CDF', 'conductor': 399, 'conductor_radical': 399, 'conjugate': 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[[1.0, 0], [-6.101171276593582, -3.522512878913317], [41.5, 71.88010851410841]], [[1.0, 0], [0.5055026779119047, -2.8668481470098524], [-83.63264324994584, -30.439792755984517]], [[1.0, 0], [-1.0315748474503945, -5.850351677920335], [-91.15018421623311, 33.17595390258987]], [[1.0, 0], [0.8915206260691121, 2.4494327891029335], [-77.37048875501678, 64.92154857834048]], [[1.0, 0], [-1.0628659158578548, 1.840937767899032], [-51.5, -89.20061658979718]], [[1.0, 0], [0, -15.807380934803366], [-107.0, 0]], [[1.0, 0], [-5.600277389070179, -6.674150697948508], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [0, 10.088283840636098], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-399-133.10-c1-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/399/2/ck/b/10/5', 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{'__RealLiteral__': 0, 'data': '0.128467170062', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05516363696183186086615411693', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49599738030402495793693068961', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36519512283155404206033454211', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.186031040649089, 'bad_primes': [3, 7, 19], 'central_character': '133.10', 'conductor': 399, 'conductor_radical': 399, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/399/2/ck/b/10/5'], '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': '2-399-133.10-c1-0-8', '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': '2-399-133.10-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7849456688227485, 'root_angle': 0.1284671700616991, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05516363696183186086615411693', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1337578817733667700870980292158', 'Lhash_array': ['1337578817733667700870980292158'], 'factors': ['2-399-133.10-c1-0-8'], 'label': '2-399-133.10-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/399/2/ck/b/10/5'}