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  • lfunc_lfunctions • Show schema
    {'Lhash': '912393031548995617474882299867', 'a10': [1.4235397293892482, -2.918139772504993], 'a2': [-1.2710407569911464, -0.6200446710257042], 'a3': [1.5040144872550814, 0.8590345872704047], 'a4': [1.2310892118652526, 1.5762040960576746], 'a5': [0.0, 2.295866404325947], 'a6': [-1.37902389434257, -2.024424140053722], 'a7': [0.0, -1.336917568840005], 'a8': [-0.5874476135633959, -2.766749952799976], 'a9': [1.524119155746331, 2.5840009286157564], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.2710407569911464, 0.6200446710257042]]], [3, [[1.0, 0], [-1.5040144872550814, -0.8590345872704047]]], [37, [[1.0, 0], [5.7350740307241335, -2.0270485593871808]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.443', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '2274131972437535775741844865047', 'degree': 2, 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5.473226260157309, 5.309124675211334, 4.148985690926548, 2.5044800642674416, 0.9745278451194141, 0.031085890653211108, -0.13893502523290713, 0.3207107850361664], 'positive_zeros': ['0.71975119278508386578999320705046', '1.97486961015438687801719679185143', '3.13193775121581739952775311040945', '4.75639525120464302118801199101148', '5.72679321286967005653422981797482', '6.70905277001227809594013979505578', '7.60352336371006160841937658199764', '8.454615985656412597193465702906598', '8.868248473007159252437147658545808', '9.482345045177750263211216998588327'], 'prelabel': '2-888-888.443-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.2547771191013043, 'root_number': '-0.03001101776131978 - 0.9995495679619544*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.254777119101', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71975119278508386578999320705', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.97486961015438687801719679185', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.13193775121581739952775311041', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.090715699489701, 'bad_primes': [2, 3, 37], 'central_character': '888.443', 'conductor': 888, 'conductor_radical': 222, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/888/2/c/d/443/14'], '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': '2-888-888.443-c1-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-888-888.443-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.2547771191013043, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71975119278508386578999320705', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '912393031548995617474882299867', 'Lhash_array': ['912393031548995617474882299867'], 'factors': ['2-888-888.443-c1-0-33'], 'label': '2-888-888.443-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/888/2/c/d/443/14'}