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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '497959167552129752', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 695.656702409395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '87120.1', 'coefficient_field': '1.1.1.1', 'conductor': 87120, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, 0, 7], [1], [1, 0, 13], [1, -2, 17], [1, -2, 19], [1, -6, 23], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, -2, 41], [1, 2, 43], [1, 2, 47], [1, 2, 53], [1, -8, 59], [1, 4, 61], [1, -4, 67], [1, 2, 71], [1, -10, 73], [1, -4, 79], [1, 12, 83], [1, 0, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 117, 'label': '2-87120-1.1-c1-0-117', 'leading_term': '6.4351840287', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/87120/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.446532059432562, 1.983591309722302, 1.149286295150592, -0.4682921332830017, -1.30493981815741, -0.1707528029275511, 2.204241897248527, 3.446352359260865, 1.992803418893101, -0.8530886402881932, -2.146131260275165, -0.8642392723334199, 0.6993152738918244, 0.02345979818952656, -1.962153142154028, -2.035525766208964, 0.499783783464618, 2.430435172556754, 1.298524494314645, -0.7121287164374925, -0.1076164320561639, 2.123219280852601, 1.741475557686013, -1.794797169059795, -3.907053635196661, -1.955502963131861, 0.5488343236220552, -0.1554113639061068, -1.867261020624583, -0.6306864201374677, 2.003746452601852, 1.756894269719686, -0.4129213874835101, 0.07508410627792125, 2.758618271643303, 2.620212848614576, -0.5281979492799485, -1.279877403679047, 1.386874292635001, 1.966852763958934, -1.287904409008995, -2.89523468069775, -0.3715786173327436, 1.261377734629818, -0.65497226070435, -1.514503243104994, 0.9372193186190708, 1.917826170636531, -0.5472538609459447, -1.3961868122454, 0.9828710384740608, 1.054833641145494, -2.414352836937395, -3.10912862470453, 0.3216222633474144, 1.251616291056404, -1.751614993903028, -2.322142188415826, 0.4515093709738279, 0.4918457048920238, -2.197371361961789, -1.739019709489531, 0.8115538539629501, -0.1168718086006825, -2.219436779841947, -0.2796889667012927, 2.066615535599064, 0.01942068559931934, -1.531169392847116, 1.62993168448136, 3.444024606581216, 0.272162575654437, -1.195555864456116, 1.784815381013303, 2.464632330014372, -0.5529262374765341, -1.08365127669839, 0.2127918263705653, -2.010716229679344, -4.321283584471947, -1.485659118589271, 1.327724166701699, -0.4753644380175758, -1.142502631479861, 1.562007249158219, 0.7622704169238148, -3.240950368877815, -2.219185118309166, 2.193600756456232, 2.031605767413229, -0.1606243037879688, 1.201436739669062, 1.74613407785445, -1.232608351411732, -1.32024511101107, 1.821723954808639, 1.064348731549521, -1.482577432745154, 0.6313337586273934, 2.675959398096577, -0.2169229718758365, -1.129638516838466, 2.575120959976438, 2.770535639875133, -0.5918801888836931, 0.446427221693168, 3.280312916673045, 1.471908588268467, -0.3551871452094997, 1.078455792145656, -0.3523281231673677, -3.847378785788596, -2.173956607815359, 0.782320080039645, -1.256434050891022, -2.099706382893092, 1.500315163536076, 1.441428433715008, -2.099426729100663, -0.7108270123474262], 'positive_zeros': ['0.9273012256259188', '1.520117029609025', '2.422170530367224', '3.111765051234592', '3.503208349644700', '4.207737267941194', '4.890365431657997', '5.262773659159644', '5.884356157093315', '6.668479466048576', '6.980378823231359', '7.555093606625250', '8.191347038913660', '8.491719587937563', '9.206746214918916', '9.632349046284574', '10.16325420990684', '10.78033232567414', '11.18407198350395', '11.66856904005622', '12.20118618857810', '12.65532903764547', '13.08657335456314', '13.72678963514116', '14.11678616051947', '14.70633882581212', '15.04875225562640', '15.65229418660528', '15.98894572861677', '16.52023854308121', '17.00151913427730', '17.39820602281843', '18.01864750609806', '18.36933799279530', '18.95273288246898', '19.41600961625330', '19.57104156579499'], 'prelabel': '2-87120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.375304783251227, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 497959167552129752, 'z1': {'__RealLiteral__': 0, 'data': '0.9273012256259188', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.520117029609025', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.422170530367224', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 695.656702409395, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 87120, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 2, 0, -2, 0, 0, 0, -2, 0, -7, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 0, -12, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -18, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 0, 13], 'euler17': [1, -2, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 6, 37], 'euler41': [1, -2, 41], 'euler43': [1, 2, 43], 'euler47': [1, 2, 47], 'euler5': [1, 1, 0], 'euler53': [1, 2, 53], 'euler59': [1, -8, 59], 'euler61': [1, 4, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 2, 71], 'euler73': [1, -10, 73], 'euler79': [1, -4, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, 0, 7], [1, 0, 0], [1, 0, 13], [1, -2, 17], [1, -2, 19], [1, -6, 23], [1, -2, 29], [1, 0, 31], [1, 6, 37], [1, -2, 41], [1, 2, 43], [1, 2, 47], [1, 2, 53], [1, -8, 59], [1, 4, 61], [1, -4, 67], [1, 2, 71], [1, -10, 73], [1, -4, 79], [1, 12, 83], [1, 0, 89], [1, 18, 97]], 'index': 117, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/87120/bm'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-87120-1.1-c1-0-117', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-87120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 26.375304783251227, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 497959167552129752, 'z1': {'__RealLiteral__': 0, 'data': '0.9273012256259188', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '497959167552129752', 'Lhash_array': ['497959167552129752'], 'label': '2-87120-1.1-c1-0-117', 'type': 'ECQ', 'url': 'EllipticCurve/Q/87120/bm'}