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lfunc_lfunctions • Show schema
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{'Lhash': '525344900298801456323308713840', 'a10': [1.1862472434977568e-60, 6.295525636213601], 'a2': [1.0797175123888436, -1.2867572243762877], 'a3': [0.0, 0.0], 'a4': [-0.14265789259155479, -0.8090531126794606], 'a5': [-2.871066915508858, 2.409111189888774], 'a6': [0.0, 0.0], 'a7': [-1.863345294830217, -1.8782822770377439], 'a8': [1.714313775907256, 0.989759519995538], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [1.863345294830217, 1.8782822770377439]]]], 'bad_primes': [3, 7], 'central_character': '567.143', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '2857816649464567318712627835590', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0797175123888436, 1.2867572243762877], [-0.3472963553338607, -1.969615506024416]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.871066915508858, 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0.7432848528171744, 0.529815634671682, 0.17251684743373885, -0.1361565721671296, -0.26225416050517414], 'positive_zeros': ['0.41442405360295471212940593587151', '2.96641929751821270332784904749177', '4.15783564122414425887994130452163', '5.06718910550030061210316907902415', '5.77698558221475375399543257980402', '6.79831005984977339625521777071509', '8.021790033171305647341828323438509', '8.304468029503531300851012174586676', '9.481601498044164997718303546375606', '10.67083748271718615543723931311520'], 'prelabel': '2-567-189.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.226905750990982, 'root_number': '0.14459676840003138 - 0.9894906642148109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.226905750991', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41442405360295471212940593587', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '189.101', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/17'], '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': '2-567-189.101-c1-0-2', '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': '2-567-189.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': -0.226905750990982, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41442405360295471212940593587', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '525344900298801456323308713840', 'Lhash_array': ['525344900298801456323308713840'], 'factors': ['2-567-189.101-c1-0-2'], 'label': '2-567-189.101-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/17'}