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lfunc_lfunctions • Show schema
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{'Lhash': '1578154606694355640209210702255', 'a10': [2.23606797749979, 0.7265425280053609], 'a2': [1.3449970239279148, 0.4370160244488211], 'a3': [0.0, 0.0], 'a4': [1.618033988749895, 1.1755705045849463], 'a5': [1.6625077511098136, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 3.572664554992563], 'a8': [1.6625077511098136, 2.288245611270737], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.473997629191848, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.3449970239279148, -0.4370160244488211]]], [3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [1.87826090972485, 3.0776835371752536]]]], 'bad_primes': [2, 3, 13], 'central_character': '936.181', 'coefficient_field': 'CDF', 'conductor': 936, 'conductor_radical': 78, 'conjugate': '2516893834161363301148257917079', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3449970239279148, -0.4370160244488211]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.6625077511098136, 0], [5.0, 0]], 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'positive_zeros': ['1.24494447161561924757164829927982', '2.37972371560328035167213193800907', '3.78951878150467678515650876660193', '4.35244830006680637660784180482327', '5.53017424152506196396004677532060', '6.32922016060331245974635352045839', '7.14833222372990245013581069917521', '7.961985262251116094918513146186881', '9.533216816461733886970206725524729', '10.04692609644976326271259446519721'], 'prelabel': '2-936-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7338613039420725, 'root_angle': -0.37441692922699704, 'root_number': '0.3843751249968628 - 0.9231769945593564*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.187208464613', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24494447161561924757164829928', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37972371560328035167213193801', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.78951878150467678515650876660', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.473997629191848, 'bad_primes': [2, 3, 13], 'central_character': '104.77', 'conductor': 936, 'conductor_radical': 78, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/936/2/m/h/181/16'], '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': '2-936-104.77-c1-0-40', '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': '2-936-104.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7338613039420725, 'root_angle': -0.18720846461349852, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24494447161561924757164829928', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1578154606694355640209210702255', 'Lhash_array': ['1578154606694355640209210702255'], 'label': '2-936-104.77-c1-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/936/2/m/h/181/16'}