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lfunc_lfunctions • Show schema
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{'Lhash': '999329218657288101495175614434', 'a10': [-0.2860159190457856, -0.49539410356080754], 'a2': [-1.7205627779275454, -1.7205627779275454], 'a3': [-1.7068887504684156, 0.9854726795596837], 'a4': [0.0, 3.9206725455795044], 'a5': [0.2270797766379144, 0.06084584276756889], 'a6': [4.632376861234126, 1.2412416390043028], 'a7': [1.2734234778426494, 2.319136185323995], 'a8': [3.3046376905114427, -3.3046376905114427], 'a9': [0.4423128043170859, -0.7661082499154636], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.2734234778426494, -2.319136185323995]]], [13, [[1.0, 0], [2.0319676611298383, -2.978440434879055]]]], 'bad_primes': [7, 13], 'central_character': '91.59', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '2625187272223164030306885469007', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7205627779275454, 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'4.98337545971446518303935498451016', '6.39934366158846451560198160682433', '7.01062520053824977929776872288025', '8.181390557251988753400356424975224', '9.400206096345534907622019295858017', '10.63783978898472541581038859233140', '11.52667541946837131279775239281620', '13.01980813747962515749924033078102', '14.33122606386237934966196879479358'], 'prelabel': '2-91-91.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.18448913214094206, 'root_number': '0.8366874325170145 - 0.5476806918890662*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0922445660705', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.78833175204379473140735539350', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.98337545971446518303935498451', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.39934366158846451560198160682', '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': '91.59', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/ba/a/59/1'], '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': '2-91-91.59-c1-0-0', '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': '2-91-91.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': -0.09224456607047103, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.78833175204379473140735539350', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '999329218657288101495175614434', 'Lhash_array': ['999329218657288101495175614434'], 'label': '2-91-91.59-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/ba/a/59/1'}