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lfunc_lfunctions • Show schema
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{'Lhash': '356912462402626647318637817175', 'a10': [-121.42265014083705, 210.31019923359008], 'a2': [-5.111926281448734, -8.854116044015848], 'a3': [-4.5, 7.794228634059948], 'a4': [-36.26358061393256, 62.810364087700975], 'a5': [-11.876408564564192, -20.57054304527134], 'a6': [92.01467306607721, -2.8042959816823314e-60], 'a7': [30.684045850480313, 125.95828408741373], 'a8': [414.3437211864677, 0.0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.368060216072594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [4.5, -7.794228634059948]]], [7, [[1.0, 0], [-30.684045850480313, -125.95828408741373]]]], 'bad_primes': [3, 7], 'central_character': '21.4', 'coefficient_field': 'CDF', 'conductor': 21, 'conductor_radical': 21, 'conjugate': '2995447559913337723247080209048', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.111926281448734, 8.854116044015848], [-16.0, 27.712812921102035]], 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['0.28155428817559639907044665996547', '5.35191017856911452163792293594186', '7.11009184049610254783570598158177', '7.76346036288667338088240328212934', '9.610485331536739691646612393950857', '11.13318506035209393954303444478808', '13.50314498711475112594532765746071', '14.56434737488541730233843468879054', '15.89678226819538714757303367299735', '16.99024184990649280752339102823374'], 'prelabel': '2-21-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8352275652007284, 'root_angle': -0.3892207433766759, 'root_number': '0.3410402795649946 - 0.9400486836936852*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.194610371688', 'prec': 50}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28155428817559639907044665997', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.35191017856911452163792293594', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.11009184049610254783570598158', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.368060216072594, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 21, 'conductor_radical': 21, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/21/6/e/c/4/1'], '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': '2-21-7.4-c5-0-0', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-21-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8352275652007284, 'root_angle': -0.19461037168833795, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28155428817559639907044665997', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '356912462402626647318637817175', 'Lhash_array': ['356912462402626647318637817175'], 'label': '2-21-7.4-c5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/21/6/e/c/4/1'}