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lfunc_lfunctions • Show schema
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{'Lhash': '856948753009835984836250568139', 'a10': [0, 31.11269837220809], 'a2': [0, -3.3166247903554], 'a3': [0, 0], 'a4': [-7.0, 0], 'a5': [-9.38083151964686, 0], 'a6': [0, 0], 'a7': [0, 9.899494936611665], 'a8': [0, 9.9498743710662], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.673100788836337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.604', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '374661559586987726508740340860', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 3.3166247903554], [-4.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [9.38083151964686, 0], [25.0, 0]], [[1.0, 0], [0, -9.899494936611665], [-49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -12.727922061357855], [-169.0, 0]], [[1.0, 0], [0, 0], [-289.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-361.0, 0]], [[1.0, 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'5.99868530817628027886733231835091', '6.99675131041694832433716493231159', '7.63107037348670199349080715256508', '7.895409914747986776663892539744235', '8.677881388159523526484937303098636', '9.886506370766587891483509298712797'], 'prelabel': '2-33e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.8597811009962283, 'root_number': '-0.90453403373329086794043620091018727743466051243346007193 + 0.4264014327112208685968754648676787527807480321283397413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42989055049811414', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67601336902735647994752421435', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.41393027928313446351803696745', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13745357914872663926915114863', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.673100788836337, 'bad_primes': [3, 11], 'central_character': '11.10', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/3/c/b/604/1'], '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': '2-33e2-11.10-c2-0-29', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-33e2-11.10-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.447302156924686, 'root_angle': 0.42989055049811414, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67601336902735647994752421435', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '856948753009835984836250568139', 'Lhash_array': ['856948753009835984836250568139'], 'label': '2-33e2-11.10-c2-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/3/c/b/604/1'}