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lfunc_lfunctions • Show schema
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{'Lhash': '239399269882359535859543987823', 'a10': [2.35284277561327, 0], 'a2': [0, -2.35284277561327], 'a3': [0, 0], 'a4': [-3.5358691267555558, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, 3.6027366378155983], 'a8': [0, 3.613658579174271], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.013745554734713, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [-2.430632228031985, -2.6630859866050645]]]], 'bad_primes': [3, 5, 13], 'central_character': '1755.1351', 'coefficient_field': 'CDF', 'conductor': 1755, 'conductor_radical': 195, 'conjugate': '1867769748916048441353007453771', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.35284277561327], [-2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -3.6027366378155983], [-7.0, 0]], [[1.0, 0], [0, 4.888711902368826], [-11.0, 0]], [[1.0, 0], [-2.430632228031985, -2.6630859866050645]], 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['0.18885272474864745184448975971905', '1.89076090986937723222988975241314', '3.97673978909626124685469695815980', '4.29948790648030398409709026575501', '5.26812596716759203756084309864835', '6.20226453875947257862717168701476', '6.83999013884511628128041631297806', '7.68444019344812069477308746020582', '7.999763086675098780429242019013503', '8.979217047169985395401980145581523'], 'prelabel': '2-1755-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7434937631489, 'root_angle': -0.2354838793130198, 'root_number': '0.738607159667243541275254268302407771593223034443867916 - 0.674136086920353942410750203549048134875599654940633490*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1177419396565099', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18885272474864745184448975972', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89076090986937723222988975241', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97673978909626124685469695816', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.013745554734713, 'bad_primes': [3, 5, 13], 'central_character': '13.12', 'conductor': 1755, 'conductor_radical': 195, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1755/2/b/c/1351/2'], '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': '2-1755-13.12-c1-0-3', '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': '2-1755-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7434937631489, 'root_angle': -0.1177419396565099, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18885272474864745184448975972', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '239399269882359535859543987823', 'Lhash_array': ['239399269882359535859543987823'], 'label': '2-1755-13.12-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1755/2/b/c/1351/2'}