-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4040663893800817676677287071579', 'a10': [2.5304826124660975, -2.1926756654163295], 'a2': [-0.5406408174555976, 0.8412535328311812], 'a3': [0.07009140410724245, -1.7306320218551012], 'a4': [-0.41541501300188644, -0.9096319953545183], 'a5': [-3.2126783380452952, -0.9433274733393006], 'a6': [1.4180060284032237, 0.9946149523368911], 'a7': [-1.8075819759620975, -1.5662786981470935], 'a8': [0.9898214418809327, 0.14231483827328514], 'a9': [-2.9901743901405506, -0.24260485680955987], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5406408174555976, -0.8412535328311812]]], [3, [[1.0, 0], [-0.07009140410724245, 1.7306320218551012]]], [23, [[1.0, 0], [-2.566779514360804, 4.051128598879294]]]], 'bad_primes': [2, 3, 23], 'central_character': '138.113', 'coefficient_field': 'CDF', 'conductor': 138, 'conductor_radical': 138, 'conjugate': '761893892291284893589670199440', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [-0.07009140410724245, 1.7306320218551012]], [[1.0, 0], [3.2126783380452952, 0.9433274733393006], [4.206267664155906, 2.703204087277988]], [[1.0, 0], [1.8075819759620975, 1.5662786981470935], [0.996203867912996, 6.92875009316653]], [[1.0, 0], [-0.14674564535399845, 0.09430769983839801], [4.569565143020751, -10.005951948899702]], [[1.0, 0], [-0.435504362122145, -0.5025988263494411], [-1.850092897552707, 12.867678744452126]], [[1.0, 0], [-1.460114699621929, 3.1972052191034495], [-11.132632477069846, -12.84774276402239]], [[1.0, 0], [-6.0897705025211595, 2.781105002245858], [12.442353944960416, -14.359241912730907]], [[1.0, 0], [-2.566779514360804, 4.051128598879294]], [[1.0, 0], [5.549682504236147, 2.534455077907731], [18.990961284413267, 21.91673765627349]], [[1.0, 0], [1.229881922116839, -8.554016659565022], [-29.744282182049417, -8.73370926208432]], [[1.0, 0], [2.5975230328675836, 8.84635104575803], [-31.126380714753704, 20.00371024585711]], [[1.0, 0], [0.7919080140015041, -2.696991017659052], [-34.49139484607843, -22.1662735156795]], [[1.0, 0], [5.734819067154977, -0.8245425018453869], [41.25819786542339, -12.114499944181476]], [[1.0, 0], [0, -7.880483503364087], [-47.0, 0]], [[1.0, 0], [-7.739023928555921, 8.93130972243059], [-7.542686428484113, -52.46053641968943]], [[1.0, 0], [-7.683444490328161, 6.6577425497901705], [8.396575458123824, -58.39946507097503]], [[1.0, 0], [0.6197327605825461, 0.08910411904935372], [58.52907139048434, 17.185685967327213]], [[1.0, 0], [-4.043983738342327, 6.292561524679431], [-27.83280587112639, -60.94534368875273]], [[1.0, 0], [2.1283838184711033, -3.3118298668904855], [-29.494465923133937, -64.58387167017081]], [[1.0, 0], [2.526438912599615, 5.53212955064494], [-47.80483357800581, 55.169718927860856]], [[1.0, 0], [3.9330631537215934, -3.4080186227031355], [11.242872223589526, -78.19589390859369]], [[1.0, 0], [-11.407123944908086, 3.3494337984566283], [69.82404322498803, -44.8731878488146]], [[1.0, 0], [-2.1602668909657012, -15.02498625447056], [-85.39487465169027, 25.074197558887242]], [[1.0, 0], [1.1045892285913925, -3.7618854400282262], [-81.60159268462458, -52.442159293192965]], [[1.0, 0], [3.774130101799561, 12.853506725606552], [-84.9666068159493, 54.60472256301536]], [[1.0, 0], [0.7097862324607991, 1.1044489360288106], [-42.7877463391943, 93.6920955215154]], [[1.0, 0], [0.2957393252126522, -2.056912187475195], [-102.66574817675122, -30.145383582032977]], [[1.0, 0], [-2.64482709043018, -1.2078520608002459], [71.37982000003608, 82.37670360461415]], [[1.0, 0], [8.755232196420415, 5.626646078687179], [46.94189646921317, 102.78841547506057]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-138-69.44-c1-0-6', '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/138/2/f/a/113/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5149301107212507, 0.6142104374542762, 0.7210519161435124, 0.8381764325873812, 0.9669002182402896, 1.1070953864383049, 1.2572428781656333, 1.414522944339146, 1.5749173879750442, 1.7333253616386284, 1.883709923538097, 2.0192961720375866, 2.132837949349302, 2.2169624908976626, 2.264593033060317, 2.269439234248908, 2.22653485148737, 2.132791973566569, 1.9875319254185442, 1.7929455890648045, 1.554431320539702, 1.2807578891900941, 0.9840038324596858, 0.6792339697326909, 0.3838888334160853, 0.11688322325026948, -0.1025648691199761, -0.2563255833664822, -0.32889029603826925, -0.3089407119651039, -0.1908256495281902, 0.024197222555214296, 0.32710083418634095, 0.7007453864154531, 1.1201632094123877, 1.5535425441545845, 1.9639270303794447, 2.3115831441804735, 2.556917562210464, 2.6637567697544395, 2.6027395425742235, 2.3545269642625475, 1.9125117053800933, 1.2847143579348033, 0.4945934037061735, -0.4194324441233179, -1.4058482201956894, -2.403265561190391, -3.344837772524991, -4.163561642159642, -4.798037486851428, -5.198167261342201, -5.330224419218578, -5.1807392730852015, -4.7587153528514765, -4.095824628375448, -3.244414060604701, -2.2733771548151545, -1.2621801641303847, -0.2935571931338918, 0.5544260066528477, 1.2161192114518053, 1.6449906743284421, 1.8184936876039195, 1.7404667109233378, 1.4406870010781556, 0.9715120389381302, 0.4018877694472735, -0.19066339308307304, -0.7291822291960814, -1.1464625337726133, -1.3931546692806527, -1.4437308356313092, -1.2994871896412135, -0.9881078244253803, -0.5597497123484713, -0.08007270526612062, 0.378927382783699, 0.7490842773907261, 0.9758345845869651, 1.0262011303531908, 0.8937803479878466, 0.5999044925653788, 0.19066877262602264, -0.2698911275928227, -0.709597095273649, -1.0595346182998426, -1.265381322851677, -1.2968905169858402, -1.153944934324599, -0.8680338175464435, -0.4986501845856637, -0.1248695010957617, 0.166854236017381, 0.29697403473332107, 0.2070729734783558, -0.12825510004017768, -0.6939323744137319, -1.4328403765944036, -2.250855443407808, -3.028154726466467, -3.6354574521935508, -3.952997046512958, -3.889444115094819, -3.397830087903649, -2.4858105402340493, -1.218338743009244, 0.2880963989363684, 1.8792319100383577, 3.3830714976049867, 4.633407531423439, 5.493342754737368, 5.875174467993254, 5.7534297959912735, 5.168808189239437, 4.222163722962014, 3.059236335983586, 1.8483643231855105, 0.7546224475097044, -0.08548690976914647, -0.5846464030079315, -0.7171791018556017, -0.5211770692700062, -0.08983664782154477, 0.44663006011110734, 0.9454832477297846, 1.2781410563396254, 1.354384618075986, 1.139738622545976, 0.6627976603829437, 0.010990711827455195, -0.6846818184403114, -1.2733994258019772, -1.6126190641253781, -1.5954803979739374, -1.1724773555234567, -0.3632747282261622, 0.7437483812825492, 2.004450893505668, 3.242304859774597, 4.278149409297278, 4.961011638476677, 5.19437581040854, 4.953021349217801, 4.2872234525542785, 3.3134240766268745, 2.19300998737823, 1.1030986845861002, 0.20478960365920923, -0.3851307340639207, -0.6136613810931673, -0.49854491378668697, -0.12144170962385492, 0.3912412828402505, 0.895971781303963, 1.2625579344779985, 1.4012506699260132, 1.2809249942594896, 0.9345795035257753, 0.4509927271661177, -0.04574220242326359, -0.4245090211175956, -0.5772703050077426, -0.44448068750968694, -0.03019919500940088, 0.5966045223623899, 1.3151430353825058, 1.9777779224532817, 2.44167516164335, 2.6003500869506917, 2.40812005068026, 1.8918205549949387, 1.1467623535717146, 0.31728859241784696, -0.4342780144650952, -0.9637778130928054, -1.17852526744723, -1.0601588761333662, -0.6713941276404194, -0.14437559593800056, 0.3476790555624604, 0.6300384037248148, 0.5689350308809059, 0.10758765320133647, -0.7126865487448557, -1.7519024038556192, -2.7928196580012017, -3.581065024734537, -3.8764610754018194, -3.5052553145571457, -2.4022324857336734, -0.63331730804885, 1.607024688146487, 4.024223017572533, 6.273134838481089, 8.019386568742243, 9.000517362980547, 9.074660740331858, 8.246824324979466, 6.667291124769569, 4.602352668808048, 2.383292303315246, 0.3440364211198887, -1.2398029588648425, -2.198176683691581, -2.490864103046546, -2.204505219207215, -1.5240479357394625, -0.6857274591064777, 0.07748382227104915, 0.5856922732444737, 0.7463548672547607, 0.566077727714234, 0.1384075839773703, -0.3882716843885281, -0.8540525800964129, -1.1309156321571552, -1.1554103931912125, -0.9426889273367074, -0.5788007636726125, -0.19371579769578717, 0.07753795310495847, 0.13517571873594172, -0.054469400969275425, -0.4460116640579708, -0.9239607827483525, -1.3318278199441569, -1.5143142182017053, -1.3618451143415906, -0.8457038074034309, -0.03400799277240846, 0.9166772891064666, 1.7932486111985062, 2.3746021566647735, 2.485384569310297, 2.041740080283744, 1.0773049109994977, -0.25782642329125327, -1.7259864382935448, -3.052623475367898, -3.987166728934207, -4.359593172775304, -4.118901696992259, -3.343836087851307, -2.222848265819997, -1.0078525330202266, 0.04708777808425595, 0.7470628096440376, 1.0023047271169647, 0.8471930544583615, 0.4272704864814462, -0.04266627249832166, -0.338879142373153, -0.29195782904962136, 0.1634748054699697, 0.9659934778056913, 1.9382427374781432], 'positive_zeros': ['3.18752177695757134439454584521353', '3.86322877543449006011483223900531', '5.56931850114443235561850754952182', '7.41580006776251228937541864170499', '8.459291322958385232547885293685450', '9.520884035685781149649475977734002', '10.42733427454645250899990829289534', '11.54739184938148497717780157647520', '11.96186287828523588380400763763552', '13.35203103242392038750577068279705'], 'prelabel': '2-138-69.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.6226064635165419, 'root_number': '-0.37572555131382573 + 0.9267309804306327*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.311303231758', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18752177695757134439454584521', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.86322877543449006011483223901', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.56931850114443235561850754952', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.1019355478936699, 'bad_primes': [2, 3, 23], 'central_character': '69.44', 'conductor': 138, 'conductor_radical': 138, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/138/2/f/a/113/2'], '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': '2-138-69.44-c1-0-6', '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': '2-138-69.44-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0497311788708907, 'root_angle': 0.31130323175827096, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18752177695757134439454584521', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4040663893800817676677287071579', 'Lhash_array': ['4040663893800817676677287071579'], 'label': '2-138-69.44-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/138/2/f/a/113/2'}