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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '820343999773261530', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 86.23843418298286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '10800.1', 'coefficient_field': '1.1.1.1', 'conductor': 10800, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 4, 7], [1, -6, 11], [1, -4, 13], [1, 3, 17], [1, -7, 19], [1, -9, 23], [1, 0, 29], [1, -7, 31], [1, 2, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -9, 53], [1, 12, 59], [1, 7, 61], [1, -2, 67], [1, -6, 71], [1, 2, 73], [1, -1, 79], [1, 9, 83], [1, -6, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 31, 'label': '2-10800-1.1-c1-0-31', 'leading_term': '2.32786527689', '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/10800/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.327865276887251, 2.051187880632357, 1.259229325527728, 0.163598478427307, -0.7367715606218977, -0.8027611952809754, 0.3145728335466156, 2.255571469282917, 3.964636867583064, 4.313630993493322, 2.986042955211589, 0.8762404065323465, -0.5163416749785712, -0.3618277549786665, 0.6770141238393569, 1.009312241036031, -0.2565178966477604, -2.181905933218277, -2.710606076351256, -0.7750552591163989, 2.326969855957275, 3.960846848039932, 2.772306574039499, 0.1223634505007988, -1.390062778881511, -0.7875880640422835, 0.3640081445498276, 0.1643112910392424, -0.9517208333357355, -0.5834042242013964, 2.401110299594522, 5.821957962807412, 6.296884525380957, 3.235925095462944, -0.3141296331897461, -1.273649697900254, -0.07411033634920908, 0.4641916565096217, -0.6706525771838227, -1.285183459281829, 0.5642277030476301, 3.203907797376293, 3.206910519078167, 0.2139269944477658, -2.210795941172178, -1.304013392309971, 1.122601974425668, 1.380512039268404, -0.7117082298866121, -1.659800858523214, 0.3547252562624224, 2.637966616646664, 2.028225486359844, -0.3416570589836928, -0.9865619744833612, 0.2671144735516466, -0.04884346992583567, -3.219640602490415, -5.589024906820919, -3.722990213842691, 0.2330351797112463, 1.542045526745807, -0.2059323369395633, -1.003824165718043, 0.8850479158997191, 2.358675400036154, 1.041952540624047, -0.5463045798157597, 0.5700771867614567, 2.2823925990889, 0.5872154120459809, -3.343087489846046, -4.277740359417027, -1.055950480911329, 1.495531980433756, 0.1673992417423806, -1.987595156590747, -1.374402322090961, 0.2012394806451048, -0.5389190354752149, -2.003613476020804, -0.6856251895924679, 1.74890763008442, 0.5049421099957654, -3.829173322658915, -5.260595611624762, -1.792278616855764, 1.441331872847095, 0.6064035378200126, -1.301012564757577, -0.7035533875303008, 0.5324413294463158, -0.008789869573996504, 0.4730681152941591, 4.837665555864052, 9.090929473612723, 7.542807782158682, 2.175908850992636, -0.3535823016809841, 0.7701629898598471, 0.6697695702752509, -1.579530190011547, -1.772599034409049, 0.6416476736887324, 1.069367330362901, -1.38734565463585, -1.882333498653555, 0.9773538627472359, 2.133635313991313, -0.4518360620665715, -1.564564251145317, 1.765857877055171, 4.539964257171713, 2.690126341679025, 0.06304875078499536, 0.7359685660105447, 1.761845217134254, -0.01116632580939573, -1.070692555907749, 1.750262781367663, 4.231927336590472], 'positive_zeros': ['0.7876065460097878', '1.449701929719029', '2.876348027843199', '3.342831635639116', '3.965216657212247', '4.813324027085895', '5.762583830952507', '6.401966853674812', '6.789005133119176', '7.317814906424539', '8.470906990903180', '9.014282567655022', '9.379165502155909', '9.947747959284723', '10.76564578145262', '11.37713582480028', '11.92267839621329', '12.46861478402799', '13.20973801330491', '13.69643306058531', '13.99374616772559', '14.98257610766646', '15.47479735174780', '15.90695253684528', '16.62680347662897', '16.92906999220843', '17.53895084540246', '18.32202025842936', '18.76589834448775', '19.44680239712066', '19.66306175767087'], 'prelabel': '2-10800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.28646510697062, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 820343999773261530, 'z1': {'__RealLiteral__': 0, 'data': '0.7876065460097878', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.449701929719029', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.876348027843199', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 86.23843418298286, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 10800, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 6, 0, 4, 0, 0, 0, -3, 0, 7, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -2, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 0, 0, -12, 0, -7, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, -2, 0, 0, 0, -24, 0, 1, 0, 0, 0, -9, 0, 0, 0, 0, 0, 6, 0, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0], 'euler11': [1, -6, 11], 'euler13': [1, -4, 13], 'euler17': [1, 3, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -9, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -7, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, 12, 59], 'euler61': [1, 7, 61], 'euler67': [1, -2, 67], 'euler7': [1, 4, 7], 'euler71': [1, -6, 71], 'euler73': [1, 2, 73], 'euler79': [1, -1, 79], 'euler83': [1, 9, 83], 'euler89': [1, -6, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 4, 7], [1, -6, 11], [1, -4, 13], [1, 3, 17], [1, -7, 19], [1, -9, 23], [1, 0, 29], [1, -7, 31], [1, 2, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -9, 53], [1, 12, 59], [1, 7, 61], [1, -2, 67], [1, -6, 71], [1, 2, 73], [1, -1, 79], [1, 9, 83], [1, -6, 89], [1, 8, 97]], 'index': 31, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10800/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': '2-10800-1.1-c1-0-31', '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': '2-10800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.28646510697062, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 820343999773261530, 'z1': {'__RealLiteral__': 0, 'data': '0.7876065460097878', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '820343999773261530', 'Lhash_array': ['820343999773261530'], 'factors': ['2-10800-1.1-c1-0-31'], 'label': '2-10800-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10800/o'}