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lfunc_lfunctions • Show schema
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{'Lhash': '1145958950856759578817656325494', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.2968417846343463, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.5633069050624013, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.9118849548950965, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.1', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.2968417846343463, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.5633069050624013, 0], [7.0, 0]], [[1.0, 0], [5.563306905062402, 0], [11.0, 0]], [[1.0, 0], [-5.266465120428055, 0], [13.0, 0]], [[1.0, 0], [-1.4063164307313074, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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[[1.0, 0], [-1.8601486896967476, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-1520-1.1-c1-0-7', 'leading_term': '1.53212838241386839180768730499', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1520/2/a/t/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.5321283824138683, 1.5268649821886597, 1.5109588280756399, 1.4840714819095657, 1.445669559676958, 1.395068321395381, 1.3314882249135171, 1.254120764007924, 1.1621997523611067, 1.0550744061396298, 0.9322809879854762, 0.7936102709553655, 0.6391685587723879, 0.46943039870281916, 0.2852814269321081, 0.08805000543071922, -0.12047352704302759, -0.3380310244367112, -0.5619050040650218, -0.7889421083866771, -1.0155920031609393, -1.2379618497218925, -1.4518861173759456, 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'5.31219731892161718757037795716134', '5.99499942851479253306723669855969', '7.24363724972524303487633719576454', '8.140745889908473752209333767609943', '8.332480922053630567729612998642034', '9.296682033672329674018181599719819'], 'prelabel': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.904002215318984343370097964583', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.39338449353553854301783853164', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.37776397168955146406808504636', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/a/t/1/3'], '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': '2-1520-1.1-c1-0-7', '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': '2-1520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.904002215318984343370097964583', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1145958950856759578817656325494', 'Lhash_array': ['1145958950856759578817656325494'], 'label': '2-1520-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/a/t/1/3'}