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lfunc_lfunctions • Show schema
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{'Lhash': '1538854388834810249038947949397', 'a10': [8.0046302534938, 0.0], 'a2': [-2.5887228148311308, 0.0], 'a3': [0.2851329729716339, 0.0], 'a4': [4.701485812027213, 0.0], 'a5': [-3.092115620735534, 0.0], 'a6': [-0.7381302323922969, 0.0], 'a7': [5.202215777417976, 0.0], 'a8': [-6.993397955537451, 0.0], 'a9': [-2.9186991877243575, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.012026170331325, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[19, [[1.0, 0], [1.0, 0]]], [211, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [19, 211], 'central_character': '4009.1', 'coefficient_field': 'CDF', 'conductor': 4009, 'conductor_radical': 4009, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.5887228148311308, 0], [2.0, 0]], [[1.0, 0], [-0.2851329729716339, 0], [3.0, 0]], [[1.0, 0], [3.092115620735534, 0], [5.0, 0]], [[1.0, 0], [-5.202215777417976, 0], [7.0, 0]], [[1.0, 0], [-2.2823197217223834, 0], [11.0, 0]], [[1.0, 0], 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'8.197551129566521205220836704614276'], 'prelabel': '2-4009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.657917122964186, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21394206617955529530228342928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01835462742641236870487251934', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.14693061735681974816943192872', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.012026170331325, 'bad_primes': [19, 211], 'central_character': '1.1', 'conductor': 4009, 'conductor_radical': 4009, 'degree': 2, 'index': 188, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4009/2/a/d/1/6'], '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': '2-4009-1.1-c1-0-188', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4009-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.657917122964186, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21394206617955529530228342928', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1538854388834810249038947949397', 'Lhash_array': ['1538854388834810249038947949397'], 'label': '2-4009-1.1-c1-0-188', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4009/2/a/d/1/6'}