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  • lfunc_lfunctions • Show schema
    {'Lhash': '2543945369199346587529201526841,3974129954609225866422749172715', 'a10': -20, 'a2': 2, 'a3': -8, 'a4': -1, 'a5': -10, 'a6': -16, 'a7': 8, 'a8': 4, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50.968620851909904, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 7}, 'bad_lfactors': [[11, [1]]], 'bad_primes': [11], 'central_character': '121.1', 'coefficient_field': '1.1.1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'euler_factors': [[1, -2, 5, -16, 64], [1, 8, 58, 216, 729], [1, 10, 263, 1250, 15625], [1, -8, 114, -2744, 117649], [1], [1, 130, 8607, 285610, 4826809], [1, -14, 5987, -68782, 24137569], [1, -48, 13322, -329232, 47045881], [1, 128, 15362, 1557376, 148035889], [1, -30, 32575, -731670, 594823321], [1, 184, 41538, 5481544, 887503681], [1, -126, 30383, -6382278, 2565726409], [1, 370, 172019, 25500770, 4750104241], [1, -264, 170630, -20989848, 6321363049], [1, -256, 76178, -26578688, 10779215329], [1, 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['2.00681904677939763336250160153983', '3.13503575345897247454467492782534', '4.39845555320542357281520624522807', '4.47231568123055483752832949685717', '5.46878470524807813214073256177559', '5.47917828216595279784852420200910', '6.42345903594017074979024138692218', '7.41852144421451785192015086387015', '7.48234883765916247769608028512041', '8.151027611245406041490546202910296', '9.159887904830082668646101406963767', '9.681570485516770586160890005603456', '10.28111825555725124204274080062210', '10.90719447861233799602214177927985', '11.34914709297063317340334113431509', '11.94850120732507187867012432319821', '12.11001168689768623227759337808497', '12.31812303298236229662790663132598'], 'prelabel': '4-11e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.671933964508595, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1526052392886456549, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.00681904677939763336250160154', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.13503575345897247454467492783', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.39845555320542357281520624523', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 50.968620851909904, 'bad_primes': [11], 'central_character': '1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'dirichlet_coefficients': [1, 2, -8, -1, -10, -16, 8, 4, 6, -20, 0, 8, -130, 16, 80, -19, 14, 12, 48, 10, -64, 0, -128, -32, -163, -260, 200, -8, 30, 160, -184, -202, 0, 28, -80, -6, 126, 96, 1040, -40, -370, -128, 264, 0, -60, -256, 256, 152, -50, -326, -112, 130, -162, 400, 0, 32, -384, 60, -1304, -80, 300, -368, 48, -181, 1300, 0, -656, -14, 1024, -160, -1176, 24, 668, 252, 1304, -48, 0, 2080, -416, 190, -949, -740, 960, 64, -140, 528, -240, 0, -1074, -120, -1040, 128, 1472, 512, -480, 1616, -338, -100, 0, 163], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 130, 8607, 285610, 4826809], 'euler17': [1, -14, 5987, -68782, 24137569], 'euler19': [1, -48, 13322, -329232, 47045881], 'euler2': [1, -2, 5, -16, 64], 'euler23': [1, 128, 15362, 1557376, 148035889], 'euler29': [1, -30, 32575, -731670, 594823321], 'euler3': [1, 8, 58, 216, 729], 'euler31': [1, 184, 41538, 5481544, 887503681], 'euler37': [1, -126, 30383, -6382278, 2565726409], 'euler41': [1, 370, 172019, 25500770, 4750104241], 'euler43': [1, -264, 170630, -20989848, 6321363049], 'euler47': [1, -256, 76178, -26578688, 10779215329], 'euler5': [1, 10, 263, 1250, 15625], 'euler53': [1, 162, 217615, 24118074, 22164361129], 'euler59': [1, 1304, 814694, 267814216, 42180533641], 'euler61': [1, -300, 374894, -68094300, 51520374361], 'euler67': [1, 656, 707658, 197300528, 90458382169], 'euler7': [1, -8, 114, -2744, 117649], 'euler71': [1, 1176, 1023934, 420903336, 128100283921], 'euler73': [1, -668, 500790, -259863356, 151334226289], 'euler79': [1, 416, 886770, 205104224, 243087455521], 'euler83': [1, -960, 1342762, -548915520, 326940373369], 'euler89': [1, 1074, 1326595, 757136706, 496981290961], 'euler97': [1, 338, 1196835, 308483474, 832972004929], 'euler_factors': [[1, -2, 5, -16, 64], [1, 8, 58, 216, 729], [1, 10, 263, 1250, 15625], [1, -8, 114, -2744, 117649], [1, 0, 0, 0, 0], [1, 130, 8607, 285610, 4826809], [1, -14, 5987, -68782, 24137569], [1, -48, 13322, -329232, 47045881], [1, 128, 15362, 1557376, 148035889], [1, -30, 32575, -731670, 594823321], [1, 184, 41538, 5481544, 887503681], [1, -126, 30383, -6382278, 2565726409], [1, 370, 172019, 25500770, 4750104241], [1, -264, 170630, -20989848, 6321363049], [1, -256, 76178, -26578688, 10779215329], [1, 162, 217615, 24118074, 22164361129], [1, 1304, 814694, 267814216, 42180533641], [1, -300, 374894, -68094300, 51520374361], [1, 656, 707658, 197300528, 90458382169], [1, 1176, 1023934, 420903336, 128100283921], [1, -668, 500790, -259863356, 151334226289], [1, 416, 886770, 205104224, 243087455521], [1, -960, 1342762, -548915520, 326940373369], [1, 1074, 1326595, 757136706, 496981290961], [1, 338, 1196835, 308483474, 832972004929]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/4/a/e'], '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': '4-11e4-1.1-c3e2-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 2, 'prelabel': '4-11e4-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.671933964508595, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1526052392886456549, 'z1': {'__RealLiteral__': 0, 'data': '2.00681904677939763336250160154', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2543945369199346587529201526841,3974129954609225866422749172715', 'Lhash_array': ['2543945369199346587529201526841', '3974129954609225866422749172715'], 'factors': ['2-11e2-1.1-c3-0-12', '2-11e2-1.1-c3-0-22'], 'label': '4-11e4-1.1-c3e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/4/a/e'}