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lfunc_lfunctions • Show schema
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{'Lhash': '1996570945303428108497819200334', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -2.540916257645335], 'a4': [0.0, 0.0], 'a5': [-1.307438291767609, 1.8140025119111043], 'a6': [0.0, 0.0], 'a7': [0.0, 0.7805730423605425], 'a8': [0.0, 0.0], 'a9': [-3.4562554283663744, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.346236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.307438291767609, -1.8140025119111043]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '920.369', 'coefficient_field': 'CDF', 'conductor': 920, 'conductor_radical': 230, 'conjugate': '767603138789134643382426274162', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.540916257645335], [-3.0, 0]], [[1.0, 0], [1.307438291767609, -1.8140025119111043]], [[1.0, 0], [0, -0.7805730423605425], [-7.0, 0]], [[1.0, 0], [-5.162868144837034, 0], [11.0, 0]], [[1.0, 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'4.16389947476425594091212152774833', '4.64589034915056079061429949060215', '5.97917812305238099603429422023240', '6.84146407768621400905324645360675', '8.293480799818272274258981187484877', '8.802825339056164590740239014398506', '9.471610173602630030023751223995562', '10.33245867760254836648453376656506'], 'prelabel': '2-920-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.6987894132709974, 'root_number': '-0.5847041793557156 + 0.8112465855977202*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.349394706635', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57501676325003354652614005464', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.63088755850380672814281006515', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16389947476425594091212152775', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.346236985957799, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 920, 'conductor_radical': 230, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/920/2/e/c/369/3'], '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': '2-920-5.4-c1-0-22', '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': '2-920-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.710394249174426, 'root_angle': 0.3493947066354987, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57501676325003354652614005464', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1996570945303428108497819200334', 'Lhash_array': ['1996570945303428108497819200334'], 'label': '2-920-5.4-c1-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/920/2/e/c/369/3'}