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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': 0, 'A4': -1, 'A5': -2, 'A6': 0, 'A7': 1, 'A8': 3, 'A9': 0, 'Lhash': '1131198675785912680', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 935.1839533526299, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, -1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [3, 7, 11, 13], 'central_character': '117117.1', 'coefficient_field': '1.1.1.1', 'conductor': 117117, 'conductor_radical': 3003, 'degree': 2, 'euler_factors': [[1, 1, 2], [1], [1, 2, 5], [1, -1], [1, -1], [1], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, 6, 37], [1, -6, 41], [1, -12, 43], [1, -4, 47], [1, -10, 53], [1, 0, 59], [1, -10, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, 0, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-117117-1.1-c1-0-17', 'leading_term': '1.16602019837', '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': 0, 'origin': 'EllipticCurve/Q/117117/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.16602019837038, 0.7571556936362268, -0.1430174162375096, -0.6836153056718584, -0.1442777104150608, 1.050391062470441, 1.262296160779862, -0.6494338350136782, -3.382590676487921, -3.853881160130075, -0.7132337187637056, 3.305343757203348, 3.989844194496655, 0.8033190648611115, -2.25432731702155, -1.938648355850629, -0.09066168841358316, -0.4262979421894696, -2.365001460982696, -1.790381121229534, 1.862949430154238, 3.817542979107301, 1.524183986010097, -0.3147361191969642, 3.337325198356891, 9.140274012837923, 9.517595111021478, 3.915708139221686, -0.7598397305007306, -0.8324748460508087, 0.147446933507995, -0.6953750062393756, -1.047044025616462, 0.5849336720728999, 1.384348456475735, 0.1175002396390763, -0.1378364558007398, 1.524290786527019, 1.569614976092159, -0.6005105384274552, -0.7381470758936949, 1.68712676509287, 1.752100806968312, -1.085424950531621, -1.33423637793674, 1.546701749446086, 1.757289557313211, -0.8761247385992355, -0.3242045369258116, 2.505396109203423, 0.565190476354494, -4.343621591045403, -3.517432645378701, 1.576355978239653, 1.605170213834803, -2.509245180264225, -2.233779385919472, 0.9173460683025982, -0.4987952863470376, -3.282833845284117, -0.2882133216281563, 3.825883527555062, 1.715062927257598, -1.88807208161029, -0.7402104956646685, 0.4859486822029373, -2.183540670979631, -3.236934942688918, -0.3556568570347457, 0.7672482233265531, -0.6318671994427525, 0.2917222283037129, 2.094567340760269, 0.7248941867390082, -0.6864002984450905, 0.7038288309278316, 0.96406618636988, -0.7180731540292687, -0.441885740047268, -0.3256054212619591, -3.666059690808236, -4.724011157205082, -0.6093780485626538, 0.3784056447718886, -3.007553091151242, -0.2852989006285485, 7.301359849447987, 6.708903485390811, -0.4554250194640908, -1.954658693798431, 0.3474328566546982, -1.119335447850156, -1.640322893566436, 1.708787983655304, 1.029712940827322, -3.239814004484699, -2.333908725513336, 0.00590102294244646, -3.607188055433009, -5.691383798886426, -0.7763264685690857, 1.154048251933988, -3.289545803240321, -4.059952921077403, -0.2411867475395739, 0.2905350686888889, -0.9272766706219503, 0.2830608127125374, 0.3949540707337929, -1.162569991286206, -0.6032124083110733, 0.1391585121444668, -0.3223757879772866, 1.24165808439311, 1.520105968536516, -3.223143140697673, -4.79612971995477, -0.161805199867237, -0.3781814033488706, -5.311098535358333, -2.662700799874124], 'positive_zeros': ['0.4606856354816626', '1.032372683482642', '1.688033911276760', '2.540564126887465', '3.301488885883444', '4.021695148205644', '4.171186559096408', '4.882380289254931', '5.637425901786496', '5.807227939354293', '6.935655066299235', '7.416995918147194', '7.594856664576335', '8.173437792138120', '8.772516110922545', '9.028679152082999', '9.680120652508632', '10.08424082103391', '10.65543244752087', '11.12063871191774', '11.66040070430642', '12.02734231117142', '12.52802014571226', '13.16475455354092', '13.59638442028590', '14.15754942980666', '14.46439150566050', '15.01350459656519', '15.59431557619094', '16.07640107908901', '16.32193732344458', '17.03151671852445', '17.38285701223709', '17.71689976406942', '18.32981957554485', '18.65177472729496', '19.13733265051003', '19.61709089397969', '19.67815900967121'], 'prelabel': '2-117117-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.58077751386694, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1131198675785912680, 'z1': {'__RealLiteral__': 0, 'data': '0.4606856354816626', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.032372683482642', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.688033911276760', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 935.1839533526299, 'bad_primes': [3, 7, 11, 13], 'central_character': '1.1', 'conductor': 117117, 'conductor_radical': 3003, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, -1, -2, 0, 1, 3, 0, 2, 1, 0, 0, -1, 0, -1, 2, 0, 4, 2, 0, -1, 0, 0, -1, 0, 0, -1, -6, 0, 4, -5, 0, -2, -2, 0, -6, -4, 0, -6, 6, 0, 12, -1, 0, 0, 4, 0, 1, 1, 0, 0, 10, 0, -2, 3, 0, 6, 0, 0, 10, -4, 0, 7, 0, 0, -12, -2, 0, 2, 0, 0, -14, 6, 0, -4, 1, 0, 0, 2, 0, -6, -4, 0, -4, -12, 0, 3, -14, 0, 0, 0, 0, -4, -8, 0, 14, -1, 0, 1], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 2], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -6, 41], 'euler43': [1, -12, 43], 'euler47': [1, -4, 47], 'euler5': [1, 2, 5], 'euler53': [1, -10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 0, 79], 'euler83': [1, 4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 2], [1, 0, 0], [1, 2, 5], [1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -2, 17], [1, -4, 19], [1, 0, 23], [1, 6, 29], [1, -4, 31], [1, 6, 37], [1, -6, 41], [1, -12, 43], [1, -4, 47], [1, -10, 53], [1, 0, 59], [1, -10, 61], [1, 12, 67], [1, 0, 71], [1, 14, 73], [1, 0, 79], [1, 4, 83], [1, 14, 89], [1, -14, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/117117/o'], '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': '2-117117-1.1-c1-0-17', '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': '2-117117-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 30.58077751386694, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1131198675785912680, 'z1': {'__RealLiteral__': 0, 'data': '0.4606856354816626', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1131198675785912680', 'Lhash_array': ['1131198675785912680'], 'label': '2-117117-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/117117/o'}