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  • lfunc_lfunctions • Show schema
    {'Lhash': '1387426510076316302435059390023,2768027710751907346377040182789', 'a10': -3760, 'a2': 8, 'a3': -6, 'a4': -148, 'a5': -470, 'a6': -48, 'a7': 1228, 'a8': -1856, 'a9': -2187, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1428.7332611120612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', '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, -8, 212, -1024, 16384], [1, 6, 2223, 13122, 4782969], [1, 470, 187475, 36718750, 6103515625], [1, -1228, 1620642, -1011310804, 678223072849], [1], [1, 344, 109427178, 21585489848, 3937376385699289], [1, -8468, 32230742, -3474747882964, 168377826559400929], [1, -35280, 1565373638, -31535794951920, 799006685782884121], [1, 61486, 6650536943, 209349097434242, 11592836324538749809], [1, 179040, 34622681578, 3088417854363360, 297558232675799463481], [1, 57166, 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'rational': True, 'root_analytic_conductor': 6.1480556343919615, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c7e2-0', 'trace_hash': 2088632515631569440, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09448653266643213527323513432', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.18358884558059466152211341764', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.44684350157786579715326917153', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1428.7332611120612, 'bad_primes': [11], 'central_character': '1.1', 'conductor': 14641, 'conductor_radical': 11, 'degree': 4, 'dirichlet_coefficients': [1, 8, -6, -148, -470, -48, 1228, -1856, -2187, -3760, 0, 888, -344, 9824, 2820, 8336, 8468, -17496, 35280, 69560, -7368, 0, -61486, 11136, 33425, -2752, 13338, -181744, -179040, 22560, -57166, 177536, 0, 67744, -577160, 323676, -877698, 282240, 2064, 872320, 283616, -58944, -275484, 0, 1027890, -491888, 1662512, -50016, -112658, 267400, -50808, 50912, 1616484, 106704, 0, -2279168, -211680, -1432320, -2454130, -417360, 6019176, -457328, -2685636, 177344, 161680, 0, -174698, -1253264, 368916, -4617280, -1151466, 4059072, -885944, -7021584, -200550, -5221440, 0, 16512, -3801460, -3917920, 77436, 2268928, 2282916, 1090464, -3979960, -2203872, 1074240, 0, -13481970, 8223120, -422432, 9099928, 342996, 13300096, -16581600, -1065216, -68078, -901264, 0, -4946900], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, 344, 109427178, 21585489848, 3937376385699289], 'euler17': [1, -8468, 32230742, -3474747882964, 168377826559400929], 'euler19': [1, -35280, 1565373638, -31535794951920, 799006685782884121], 'euler2': [1, -8, 212, -1024, 16384], 'euler23': [1, 61486, 6650536943, 209349097434242, 11592836324538749809], 'euler29': [1, 179040, 34622681578, 3088417854363360, 297558232675799463481], 'euler3': [1, 6, 2223, 13122, 4782969], 'euler31': [1, 57166, 31335570111, 1572786098269426, 756943935220796320321], 'euler37': [1, 877698, 381609348827, 83321518695879834, 9012061295995008299689], 'euler41': [1, -283616, 125033442626, -55235428141033696, 37929227194915558802161], 'euler43': [1, 275484, 552841024778, 74881678262200788, 73885357344138503765449], 'euler47': [1, -1662512, 1690275368222, -842267017247183056, 256666986187667409334369], 'euler5': [1, 470, 187475, 36718750, 6103515625], 'euler53': [1, -1616484, 2738235417598, -1898901762168273108, 1379946262057143768386569], 'euler59': [1, 2454130, 5185075198823, 6107474268438852470, 6193386212891813387462761], 'euler61': [1, -6019176, 15292993001786, -18916722252749538696, 9876832533361318095112441], 'euler67': [1, 174698, 2881438572447, 1058794196026717454, 36732225162896895721934329], 'euler7': [1, -1228, 1620642, -1011310804, 678223072849], 'euler71': [1, 1151466, 6215147678071, 10472721628301851206, 82721210695570328927708881], 'euler73': [1, 885944, 20004042345618, 9787376433602872568, 122045014039746588673695409], 'euler79': [1, 3801460, 35726075376258, 73002891854523992140, 368790120348678391253573281], 'euler83': [1, -2282916, 53736100067578, -61949324981035312332, 736365263311636486061599129], 'euler89': [1, 13481970, 131461606905283, 596325530121475112130, 1956410986640441413344189841], 'euler97': [1, 68078, 159761571363987, 5500585610700976814, 6528362774606076144776040769], 'euler_factors': [[1, -8, 212, -1024, 16384], [1, 6, 2223, 13122, 4782969], [1, 470, 187475, 36718750, 6103515625], [1, -1228, 1620642, -1011310804, 678223072849], [1, 0, 0, 0, 0], [1, 344, 109427178, 21585489848, 3937376385699289], [1, -8468, 32230742, -3474747882964, 168377826559400929], [1, -35280, 1565373638, -31535794951920, 799006685782884121], [1, 61486, 6650536943, 209349097434242, 11592836324538749809], [1, 179040, 34622681578, 3088417854363360, 297558232675799463481], [1, 57166, 31335570111, 1572786098269426, 756943935220796320321], [1, 877698, 381609348827, 83321518695879834, 9012061295995008299689], [1, -283616, 125033442626, -55235428141033696, 37929227194915558802161], [1, 275484, 552841024778, 74881678262200788, 73885357344138503765449], [1, -1662512, 1690275368222, -842267017247183056, 256666986187667409334369], [1, -1616484, 2738235417598, -1898901762168273108, 1379946262057143768386569], [1, 2454130, 5185075198823, 6107474268438852470, 6193386212891813387462761], [1, -6019176, 15292993001786, -18916722252749538696, 9876832533361318095112441], [1, 174698, 2881438572447, 1058794196026717454, 36732225162896895721934329], [1, 1151466, 6215147678071, 10472721628301851206, 82721210695570328927708881], [1, 885944, 20004042345618, 9787376433602872568, 122045014039746588673695409], [1, 3801460, 35726075376258, 73002891854523992140, 368790120348678391253573281], [1, -2282916, 53736100067578, -61949324981035312332, 736365263311636486061599129], [1, 13481970, 131461606905283, 596325530121475112130, 1956410986640441413344189841], [1, 68078, 159761571363987, 5500585610700976814, 6528362774606076144776040769]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/121/8/a/b'], '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-c7e2-0-0', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [7, 7], 'order_of_vanishing': 2, 'prelabel': '4-11e4-1.1-c7e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.1480556343919615, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7e2-0', 'trace_hash': 2088632515631569440, 'z1': {'__RealLiteral__': 0, 'data': '1.09448653266643213527323513432', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1387426510076316302435059390023,2768027710751907346377040182789', 'Lhash_array': ['1387426510076316302435059390023', '2768027710751907346377040182789'], 'factors': ['2-11e2-1.1-c7-0-25', '2-11e2-1.1-c7-0-52'], 'label': '4-11e4-1.1-c7e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/121/8/a/b'}