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lfunc_lfunctions • Show schema
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{'Lhash': '2731684003942280368672017148297', 'a10': [-0.8219703436330604, 2.0795107006668054], 'a2': [-0.9659258262890683, 0.25881904510252074], 'a3': [-0.681137815350185, -1.5924984384607657], 'a4': [0.8660254037844386, -0.5], 'a5': [1.3321793571859297, -1.7959115123768439], 'a6': [1.070097532278529, 1.3619439310821142], 'a7': [1.2255413760106033, -4.573782682049445], 'a8': [-0.7071067811865476, 0.7071067811865476], 'a9': [-2.0721025529999544, 2.1694218146434943], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, -0.25881904510252074]]], [3, [[1.0, 0], [0.681137815350185, 1.5924984384607657]]], [5, [[1.0, 0], [-1.3321793571859297, 1.7959115123768439]]], [13, [[1.0, 0], [-3.590701544132348, -0.32689818134331905]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '390.59', 'coefficient_field': 'CDF', 'conductor': 390, 'conductor_radical': 390, 'conjugate': '1083863348680213545421063473186', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, -0.25881904510252074]], [[1.0, 0], [0.681137815350185, 1.5924984384607657]], [[1.0, 0], [-1.3321793571859297, 1.7959115123768439]], [[1.0, 0], [-1.2255413760106033, 4.573782682049445], [-6.06217782649107, -3.5]], [[1.0, 0], [-0.9572840528304618, 0.2565034888831144], [9.526279441628825, -5.5]], [[1.0, 0], [-3.590701544132348, -0.32689818134331905]], [[1.0, 0], [6.315389267744614, -3.6461916937696266], [8.5, -14.722431864335457]], [[1.0, 0], [-0.5039413931363197, 1.8807348832217867], [-16.454482671904334, -9.5]], [[1.0, 0], [-3.1403266916719073, -1.8130684607801426], [11.5, 19.91858428704209]], [[1.0, 0], [2.9602844052763078, 1.7091209982641276], [14.5, 25.11473670974872]], [[1.0, 0], [-2.8904253531582516, -2.8904253531582516], [0, 31.0]], [[1.0, 0], [4.310986846073565, -1.1551254439866043], [32.04293994002423, -18.5]], [[1.0, 0], [1.429119660612822, 5.333547183502642], [-35.50704155516198, 20.5]], [[1.0, 0], [3.678029739029073, 6.370534379747653], [-21.5, 37.239092362730865]], [[1.0, 0], [0.710336867437197, -0.710336867437197], [0, -47.0]], [[1.0, 0], [-9.899480040911637, 0], [53.0, 0]], [[1.0, 0], [0.3584895230572339, -1.3379011140307315], [-51.09549882328188, -29.5]], [[1.0, 0], [-3.4780286881408773, -6.024122398042129], [-30.5, 52.827549630850754]], [[1.0, 0], [-2.6799428163019012, -10.001682751817922], [-58.023702053557386, 33.5]], [[1.0, 0], [0.3448221855503621, 0.09239482615055426], [61.48780366869514, 35.5]], [[1.0, 0], [-8.412338685737147, -8.412338685737147], [0, 73.0]], [[1.0, 0], [-0.6261897750948483, 0], [79.0, 0]], [[1.0, 0], [-2.202477000602853, -2.202477000602853], [0, 83.0]], [[1.0, 0], [-1.9154727014501038, 0.5132493634774163], [77.07626093681505, -44.5]], [[1.0, 0], [10.68512750980571, 2.8630712872760133], [84.00446416709055, 48.5]], [[1.0, 0], [1.8182795054318424, -3.1493524857691613], [-50.5, 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'positive_zeros': ['2.15491871612766527291996393162645', '3.25611067674030808425475969264019', '4.92556408275378892466621542889838', '5.97083481100886438179901362753196', '6.67731102263723830846352156288863', '8.362656149632517939913497593011827', '9.090446531739165461924411584835851', '9.655323966590673779076869023770097', '10.85444728115713559960250338178311', '11.29648854101890110180531901748352'], 'prelabel': '2-390-195.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.6785248608284983, 'root_number': '-0.5319081977145045 + 0.8468020247992488*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.339262430414', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.15491871612766527291996393163', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25611067674030808425475969264', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.92556408275378892466621542890', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1141656788299366, 'bad_primes': [2, 3, 5, 13], 'central_character': '195.59', 'conductor': 390, 'conductor_radical': 390, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/390/2/bj/a/59/6'], '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': '2-390-195.59-c1-0-21', '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': '2-390-195.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7646998835014231, 'root_angle': 0.33926243041424914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.15491871612766527291996393163', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2731684003942280368672017148297', 'Lhash_array': ['2731684003942280368672017148297'], 'label': '2-390-195.59-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/390/2/bj/a/59/6'}