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lfunc_lfunctions • Show schema
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{'Lhash': '1437300143899126439027412254238', 'a10': [1.722285323750082, 0.0], 'a2': [0.0, 1.2905143063074807], 'a3': [-1.0, 0.0], 'a4': [0.33457282521572174, 0.0], 'a5': [0.0, -1.3345728252157216], 'a6': [0.0, -1.2905143063074807], 'a7': [0.0, 1.0], 'a8': [0.0, 3.012799630057563], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [-3.593828242672524, 0.29051430630748076]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.64', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2408431657561573317720001712419', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.2905143063074807], [-2.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.3345728252157216], [-5.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -4.884342548980005], [-11.0, 0]], [[1.0, 0], 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'3.00273709224930792780520742132479', '3.90085870543605897686305727419441', '5.72958120324261592209655112441406', '6.54465153365751015014753326542012', '7.65957611228186134236810493365004', '9.017971186718983760595319926923770', '10.31226187478168377812048716304190', '10.79891655490311148453729235955358', '11.46166985465251710283019630049907'], 'prelabel': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.5256753882018733, 'root_number': '-0.08057417135749827 - 0.9967486157051098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.262837694101', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13382989259055541112227494903', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00273709224930792780520742132', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90085870543605897686305727419', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '13.12', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/c/64/6'], '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': '2-273-13.12-c1-0-2', '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': '2-273-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.26283769410093666, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13382989259055541112227494903', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1437300143899126439027412254238', 'Lhash_array': ['1437300143899126439027412254238'], 'label': '2-273-13.12-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/c/64/6'}