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lfunc_lfunctions • Show schema
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{'Lhash': '4127288147308251379361550908350', 'a10': [-0.4580330854770482, -0.7933365755937859], 'a2': [0.355143321653864, 0.6151262770732687], 'a3': [-1.2039411548998784, -2.085287249609741], 'a4': [0.7477464421693202, -1.2951348290161258], 'a5': [-1.289713356692272, 0.0], 'a6': [0.855143321653864, -1.4811516808577074], 'a7': [0.5, -0.8660254037844386], 'a8': [2.482801907522941, 0.0], 'a9': [-1.3989486089233059, 2.4230500678329694], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [-1.2540919305771698, -3.380422078625867]]]], 'bad_primes': [7, 13], 'central_character': '91.29', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '1954108233545873136505239485933', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.355143321653864, -0.6151262770732687], [-1.0, 1.7320508075688772]], 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'11.81817518642034313736296876105300', '12.88587816488495172105977744887246', '14.34682488027570077772998314398649'], 'prelabel': '2-91-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.3015468907460063, 'root_number': '0.5838467466343812 + 0.8118638903439718*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.150773445373', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.25585626399353990198167632791', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.38592304884536978046225303563', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.75126890898905878344211176071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.3', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/f/c/29/3'], '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': '2-91-13.3-c1-0-5', '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': '2-91-13.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.15077344537300316, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.25585626399353990198167632791', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4127288147308251379361550908350', 'Lhash_array': ['4127288147308251379361550908350'], 'label': '2-91-13.3-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/f/c/29/3'}