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lfunc_lfunctions • Show schema
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{'Lhash': '2498605219051568603338623259253', 'a10': [-2.4761233110063663, -4.4834648193160435e-61], 'a2': [-1.5667333618157795, -0.4198049390534361], 'a3': [0.0, 0.5139263762209899], 'a4': [0.5463664326040375, 0.31544480694011656], 'a5': [1.4745677579386374, -0.3951092399246291], 'a6': [0.21574883104740591, -0.8051855991425125], 'a7': [1.2765702483654628, -2.31740553226839], 'a8': [1.570271615739887, 1.570271615739887], 'a9': [2.7358796798243614, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-1.2765702483654628, 2.31740553226839]]], [13, [[1.0, 0], [-2.944667582987378, 2.080608763247736]]]], 'bad_primes': [7, 13], 'central_character': '91.19', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '1940185196063308477439615969947', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5667333618157795, 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'4.71079133922441173577319243247457', '6.47988469027670881603100599059434', '7.53537197876985461209202556004681', '8.744575055620273928503921917586778', '9.608229075990084718517360948524279', '10.60458522776038280977122265110091', '12.02696652539369362440880940298672', '13.21031976382428187667547263439291', '14.08928965066931106915399758000191'], 'prelabel': '2-91-91.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.18377523979383445, 'root_number': '0.837913643007965 + 0.5458028278244081*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0918876198969', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97105197489096490057304707290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.71079133922441173577319243247', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.47988469027670881603100599059', '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': '91.19', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/w/a/19/2'], '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': '2-91-91.19-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': '2-91-91.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.09188761989691722, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97105197489096490057304707290', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2498605219051568603338623259253', 'Lhash_array': ['2498605219051568603338623259253'], 'label': '2-91-91.19-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/w/a/19/2'}