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lfunc_lfunctions • Show schema
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{'Lhash': '1802635885895772298920031664403', 'a10': [0.0, 0.0], 'a2': [-2.9378126156712296, 0.0], 'a3': [3.0, 0.0], 'a4': [0.6307429647970323, 0.0], 'a5': [0.0, 0.0], 'a6': [-8.81343784701369, 0.0], 'a7': [18.91152333081604, 0.0], 'a8': [21.649496286143243, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 110.62858126076371, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.9378126156712296, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-18.91152333081604, 0], [343.0, 0]], [[1.0, 0], [6.0678041208877795, 0], [1331.0, 0]], [[1.0, 0], [-78.24988897676612, 0], [2197.0, 0]], [[1.0, 0], [-38.40097105433083, 0], [4913.0, 0]], [[1.0, 0], [92.95604856499412, 0], [6859.0, 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'5.17173263570908966620922184695484', '6.24817942923156069020841561334478', '7.28512774116924520580698225083487', '8.036344299624704961188254129486106', '8.552524288402296319920664915729530'], 'prelabel': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42202897673161948304178206609', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86023140571303293097269545125', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43790659197265624820137947886', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 110.62858126076371, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 210, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/4/a/g/1/4'], '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': '2-1875-1.1-c3-0-210', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1875-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.51801222954051, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42202897673161948304178206609', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1802635885895772298920031664403', 'Lhash_array': ['1802635885895772298920031664403'], 'label': '2-1875-1.1-c3-0-210', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/4/a/g/1/4'}