-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1629345563588560413608222014709', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': -1, 'a7': -1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '462.1', 'coefficient_field': '1.1.1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 0, 5], [1, 1], [1, 1], [1, -6, 13], [1, -4, 17], [1, -6, 19], [1, 4, 23], [1, -6, 29], [1, 2, 31], [1, -10, 37], [1, 4, 41], [1, -8, 43], [1, 6, 47], [1, 10, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, -16, 71], [1, -12, 73], [1, 16, 79], [1, 2, 83], [1, 6, 89], [1, 6, 97], [1, 14, 101], [1, 14, 103], [1, -8, 107], [1, 14, 109], [1, 2, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, -1], 1]], [[[1, 0, 5], 1]], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, -6, 13], 1]], [[[1, -4, 17], 1]], [[[1, -6, 19], 1]], [[[1, 4, 23], 1]], [[[1, -6, 29], 1]], [[[1, 2, 31], 1]], [[[1, -10, 37], 1]], [[[1, 4, 41], 1]], [[[1, -8, 43], 1]], [[[1, 6, 47], 1]], [[[1, 10, 53], 1]], [[[1, 0, 59], 1]], [[[1, 2, 61], 1]], [[[1, 4, 67], 1]], [[[1, -16, 71], 1]], [[[1, -12, 73], 1]], [[[1, 16, 79], 1]], [[[1, 2, 83], 1]], [[[1, 6, 89], 1]], [[[1, 6, 97], 1]], [[[1, 14, 101], 1]], [[[1, 14, 103], 1]], [[[1, -8, 107], 1]], [[[1, 14, 109], 1]], [[[1, 2, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-462-1.1-c1-0-2', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/462/2/a/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.291728636980333, 1.2872799120137903, 1.2723184148194004, 1.2423108549484143, 1.1906478300343315, 1.1097925048711352, 0.9925168200715313, 0.8330863937758847, 0.6283290443768254, 0.37854992855324143, 0.08824701403108096, -0.23344190479817364, -0.5726460967444446, -0.9111089352400408, -1.2270426870043276, -1.4965206324978304, -1.695381244492027, -1.8015521182683465, -1.7976289735909368, -1.6734761556924476, -1.4285598999929778, -1.0736948798370474, -0.6318879806445654, -0.13800804528461366, 0.3629004624539831, 0.8187108942638139, 1.1746021499969572, 1.3784469236781072, 1.386729869820718, 1.1703775262567797, 0.7197893554658674, 0.04834482918931316, -0.806258914471718, -1.7833053526672227, -2.8031892028388907, -3.774237534173884, -4.601710041362848, -5.19811420885244, -5.493687693000671, -5.445737434752593, -5.045523594017103, -4.321558941027999, -3.338558793652302, -2.1917928293818996, -0.9972005238414655, 0.12174332592368581, 1.0488800995494947, 1.6900268499745303, 1.9854054688390994, 1.9179671676616117, 1.5162000989904048, 0.8507256814311973, 0.024873602843438095, -0.8396491810700997, -1.6200594772011767, -2.210259926779828, -2.536343256043893, -2.567338191287141, -2.3193410967418027, -1.8521725064265213, -1.2588999042593634, -0.6497849398567667, -0.13323317918937427, 0.20304675222189955, 0.30736996119941523, 0.17307103958383033, -0.16062355095294156, -0.6162291116599768, -1.0929661278692093, -1.486451519706601, -1.7095020687914746, -1.7100540645641575, -1.4825722173434879, -1.0704180304472604, -0.5583074516415157, -0.055920279245591245, 0.3244363698749656, 0.4918363665024268, 0.39754605388451425, 0.04812875910413461, -0.49236193538306144, -1.1122511603849934, -1.6728936679045605, -2.036492908551219, -2.09573082249981, -1.7991034456292145, -1.1663349948806956, -0.28993431391402574, 0.6784056851479754, 1.5547708543054124, 2.1586262583859286, 2.350196172532164, 2.0619372139156353, 1.3171609925848282, 0.23112479734552646, -1.0066916196906923, -2.1665213064329225, -3.022289365607289, -3.397005683500247, -3.200179476602498, -2.4490694690020574, -1.2686082522120532, 0.13087086196644754, 1.4942858502743204, 2.572929463836293, 3.1755949514399235, 3.2088371563989, 2.69745880082378, 1.780297685876369, 0.6816105558022466, -0.33630685824382234, -1.0293463494468678, -1.2245332618338416, -0.8579987961528164, 0.01064064112326046, 1.2110105896067824, 2.4992883545119544, 3.6119598042539565, 4.324009399986681, 4.498335726939231, 4.115028610032781, 3.2736753348194196, 2.1680846656073394, 1.039296767845437, 0.11794750943319797, -0.43029909403325706, -0.5431425876363776, -0.27453859920835083, 0.22111906834891074, 0.7297430450791567, 1.0332638644874002, 0.966535841466576, 0.46121321639711327, -0.4345350620095593, -1.5656690847799044, -2.7071384627118205, -3.618904215546979, -4.1053462232254185, -4.0640033280205765, -3.5111558497851902, -2.5775772521026292, -1.475409155918109, -0.4446012433198931, 0.3072561985958608, 0.6560499291035751, 0.5898325974400306, 0.20756282661762107, -0.3116786305244556, -0.7606327756319465, -0.9628115261826399, -0.8222702531807582, -0.350392017673127, 0.3379124782958057, 1.0577480381250561, 1.6083055468599705, 1.83226778695841, 1.6635199772493225, 1.1490739266856804, 0.43815182967643557, -0.25934782350139013, -0.733823703554802, -0.8391373476016547, -0.5393918040672696, 0.07527492038627787, 0.810098699907411, 1.4199463266370385, 1.6822406029721424, 1.4681501816302842, 0.7909828806577536, -0.18390587291722937, -1.1732079761530199, -1.8469747752961312, -1.9193197080935234, -1.234111353202627, 0.17876325408776023, 2.0941262288697753, 4.134657638227287, 5.857661713324873, 6.864208794753166, 6.9023251441837, 5.936359635242841, 4.1628107501846685, 1.9667479648149155, -0.1711582034728661, -1.7934238201280497, -2.579369092473559, -2.423510032873162, -1.457855529540798, -0.012269711570969746, 1.476174769642651, 2.5800858557369133, 2.9931004651725353, 2.605727040115129, 1.5258846172366407, 0.039984584518365285, -1.4729374030758757, -2.6486206528205174, -3.235621125917205, -3.156606018040967, -2.5168828088610766, -1.5599765478019112, -0.5856401031336409, 0.14363730181561615, 0.47891443107427695, 0.421270158748084, 0.10875953665027348, -0.2401750408875687, -0.40728870462681055, -0.2523041134623651, 0.23763808015211016, 0.9429082971589077, 1.6521726582642506, 2.1354336603896935, 2.2250031604085128, 1.8772115530025457, 1.193658109194351, 0.3938576584743121, -0.25289611289785663, -0.5149070588404426, -0.2762016598266332, 0.4208288995626269, 1.3835469632551713, 2.3269357550524714, 2.96377388991763, 3.0984839139605027, 2.693893231638993, 1.8880518503447103, 0.9539107586226796, 0.21318935869090966, -0.0688279061786838, 0.2263252937015432, 1.0249072188381914, 2.0770231783935658, 3.0310212046059024, 3.543943832195735, 3.393236011550476, 2.5533658274646807, 1.2112968104570871, -0.2861325811247474, -1.5378920687005715, -2.214740502474734, -2.1651730687918884, -1.4663815316625726, -0.4022185799774117, 0.6265408442403747, 1.2321309373058684, 1.168573619644877, 0.4172594627316413, -0.7997001675879344, -2.0845575996776238, -2.988246418662455, -3.154981043033944, -2.4406987445220265, -0.9664026159790259, 0.9121812339579936, 2.7104053671786725, 3.963114776759734], 'positive_zeros': ['1.28532701621031142017445445957356', '2.90909027996993607554406630510099', '3.88277706681863956744577131696282', '5.61053425475447892671224791396931', '6.50358738357793944503631024402546', '7.79089756844307556875120056781847', '8.197346169778720895812897743278528', '9.390494128648731058380768364756289', '9.887801410706601661642293806047558', '10.91263470896410358926772918246843'], 'prelabel': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 2047086587960306487, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28532701621031142017445445957', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90909027996993607554406630510', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88277706681863956744577131696', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.6890885733831555, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 462, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, -1, -1, 1, 0, -1, 1, 6, 1, 0, 1, 4, -1, 6, 0, -1, 1, -4, -1, -5, -6, 1, -1, 6, 0, -2, -1, -1, -4, 0, 1, 10, -6, 6, 0, -4, 1, 8, -1, 0, 4, -6, 1, 1, 5, 4, 6, -10, -1, 0, 1, 6, -6, 0, 0, -2, 2, -1, 1, 0, 1, -4, 4, -4, 0, 16, -1, 12, -10, -5, 6, 1, -6, -16, 0, 1, 4, -2, -1, 0, -8, 6, 1, -6, 0, -6, -4, -2, 6, 0, -1, -6, -1, -1, -5], 'euler11': [1, 1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -4, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -10, 37], 'euler41': [1, 4, 41], 'euler43': [1, -8, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 10, 53], 'euler59': [1, 0, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -16, 71], 'euler73': [1, -12, 73], 'euler79': [1, 16, 79], 'euler83': [1, 2, 83], 'euler89': [1, 6, 89], 'euler97': [1, 6, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 0, 5], [1, 1, 0], [1, 1, 0], [1, -6, 13], [1, -4, 17], [1, -6, 19], [1, 4, 23], [1, -6, 29], [1, 2, 31], [1, -10, 37], [1, 4, 41], [1, -8, 43], [1, 6, 47], [1, 10, 53], [1, 0, 59], [1, 2, 61], [1, 4, 67], [1, -16, 71], [1, -12, 73], [1, 16, 79], [1, 2, 83], [1, 6, 89], [1, 6, 97]], 'index': 2, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/462/d', 'ModularForm/GL2/Q/holomorphic/462/2/a/d/1/1', 'ModularForm/GL2/Q/holomorphic/462/2/a/d'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-462-1.1-c1-0-2', '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': '2-462-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.9207000217064496, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2047086587960306487, 'z1': {'__RealLiteral__': 0, 'data': '1.28532701621031142017445445957', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 10913660
{'Lhash': '1629345563588560413608222014709', 'Lhash_array': ['1629345563588560413608222014709'], 'label': '2-462-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/d'}
-
id: 24549429
{'Lhash': '1629345563588560413608222014709', 'Lhash_array': ['1629345563588560413608222014709'], 'label': '2-462-1.1-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/462/2/a/d/1/1'}
-
id: 41117
{'Lhash': '2047086587960306487', 'Lhash_array': ['2047086587960306487'], 'label': '2-462-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/462/d'}