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lfunc_lfunctions • Show schema
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{'Lhash': '868954425222363717049857020071', 'a10': [-19.79898987322333, -34.292856398964496], 'a2': [-1.0, 1.7320508075688772], 'a3': [0, 0], 'a4': [-2.0, -3.4641016151377544], 'a5': [-9.899494936611665, 17.146428199482248], 'a6': [0, 0], 'a7': [0, 0], 'a8': [8.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 52.039684625063245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.7320508075688772]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '882.667', 'coefficient_field': 'CDF', 'conductor': 882, 'conductor_radical': 42, 'conjugate': '941701432019317384381218251060', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.7320508075688772]], [[1.0, 0], [0, 0]], [[1.0, 0], [9.899494936611665, -17.146428199482248], [-62.5, -108.25317547305482]], [[1.0, 0], [0, 0]], [[1.0, 0], [7.0, 12.12435565298214], [-665.5, 1152.6798124370878]], [[1.0, 0], 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[{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/882/4/g/ba/667/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3711507380669676, 1.313631266817243, 1.2372962051845382, 1.1441810641488626, 1.0365016295151104, 0.9166379945493315, 0.7871177510147891, 0.6505976626739377, 0.509843144946262, 0.3677049168887101, 0.2270922757029274, 0.09094256668039422, -0.037813421428655854, -0.1562902196831743, -0.2616904765275567, -0.35135144169252075, -0.4227945572030956, -0.473777345482143, -0.5023465623668117, -0.5068913775037063, -0.4861951641188654, -0.43948433234867246, -0.36647253249738343, -0.26739849345737315, -0.14305575296244907, 0.005187414829669475, 0.17537945915866804, 0.36498981185538437, 0.5709271217994627, 0.7895723427536744, 1.0168271969163363, 1.248178128693874, 1.478775411483989, 1.7035265851248262, 1.9172028957062621, 2.1145568972122595, 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'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.4768821436017044, 'root_number': '0.072563057582222932578567522876046274224033485589134161 - 0.997363826632146810272721562873300903683311227235026732*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.2384410718008522', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68548417447671785441001962924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.46293490880201235149352338711', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.09464924440503464844772903846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 52.039684625063245, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 882, 'conductor_radical': 42, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/882/4/g/ba/667/1'], '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': '2-882-7.2-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-882-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.213853659803701, 'root_angle': -0.2384410718008522, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68548417447671785441001962924', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '868954425222363717049857020071', 'Lhash_array': ['868954425222363717049857020071'], 'label': '2-882-7.2-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/882/4/g/ba/667/1'}