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lfunc_lfunctions • Show schema
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{'Lhash': '2408431657561573317720001712419', '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': '1437300143899126439027412254238', '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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'5.46574611784435309914614765564948', '5.98948727477099169452092171609354', '7.27916820149496197138447423522660', '7.981958361200105561781584318346052', '9.176036876797502361463801934899358', '10.22725342752357392760793905013983', '11.33415209979723446586040572134523', '12.22609197447092347763668712708032'], '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': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89991757754696464948889841600', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.11542342142085977188427012875', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.46574611784435309914614765565', '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': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/c/c/64/3'], '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-c1-0-8', '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': '2-273-13.12-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': '1.89991757754696464948889841600', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2408431657561573317720001712419', 'Lhash_array': ['2408431657561573317720001712419'], 'label': '2-273-13.12-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/c/c/64/3'}