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lfunc_lfunctions • Show schema
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{'Lhash': '578223105512552592732509053915', 'a10': [2.0, 0], 'a2': [0, -1.4142135623730951], 'a3': [0, 0], 'a4': [-2.0, 0], 'a5': [0, 1.4142135623730951], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 2.8284271247461903], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03275931657819, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.4142135623730951]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.197', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '1488235378289360218339417958185', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.4142135623730951]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-25.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 7.0710678118654755], [-121.0, 0]], [[1.0, 0], [15.0, 0], [169.0, 0]], [[1.0, 0], [0, -11.313708498984761], [-289.0, 0]], [[1.0, 0], [-13.0, 0], [361.0, 0]], 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'5.11559708713634202278128079984086', '6.70763316536792190446646403702347', '7.12313120230937540786521166770001', '8.117301664371589118834300451147991', '8.958656233103028161858077082397187', '9.743405561536101881666670195893029'], 'prelabel': '2-882-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.19591327601530362, 'root_number': '0.8164965809277260327324280249019637973219824935522233761 - 0.5773502691896257645091487805019574556476017512701268760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09795663800765182', 'prec': 67}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.45613760243433685964316918352', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.20227081949867521130733780516', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57271242295702705018898993639', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 24.03275931657819, 'bad_primes': [2, 3, 7], 'central_character': '3.2', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/3/b/d/197/1'], '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': '2-882-3.2-c2-0-6', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-882-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.902321829151794, 'root_angle': -0.09795663800765181, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.45613760243433685964316918352', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '578223105512552592732509053915', 'Lhash_array': ['578223105512552592732509053915'], 'label': '2-882-3.2-c2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/3/b/d/197/1'}