Formats: - HTML - YAML - JSON - 2026-10-24T10:31:24.752263
  • lfunc_lfunctions • Show schema
    {'Lhash': '1877598190078679039528818377094', 'a10': [336.76320340690165, -583.2909784204061], 'a2': [4.694933459514875, 8.131863290034882], 'a3': [-4.5, 7.794228634059948], 'a4': [-28.084800378544625, 48.64430117606893], 'a5': [-35.86453421660413, -62.119195452950805], 'a6': [-84.50880227126775, 0], 'a7': [0, 0], 'a8': [-226.94933459514874, 0], 'a9': [-40.5, -70.14805770653953], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [4.5, -7.794228634059948]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.67', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'conjugate': '575356190372141120733274971622', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.694933459514875, -8.131863290034882], [-16.0, 27.712812921102035]], [[1.0, 0], [4.5, -7.794228634059948]], [[1.0, 0], [35.86453421660413, 62.119195452950805], [-1562.5, 2706.329386826371]], [[1.0, 0], [0, 0]], [[1.0, 0], [-280.30506654048514, 485.5026168670951], [-80525.5, -139474.25730488764]], [[1.0, 0], [533.5088022712678, 0], [371293.0, 0]], [[1.0, 0], [-502.8501520082015, 870.9620118719381], [-709928.5, -1229632.2317411618]], [[1.0, 0], [-684.2632034069017, -1185.178634050591], [-1238049.5, 2144364.636285245]], [[1.0, 0], [1614.0395055305814, 2795.5984290023152], [-3218171.5, 5574036.5454701455]], [[1.0, 0], [753.4559886436613, 0], [20511149.0, 0]], [[1.0, 0], [-4103.208896907424, 7106.966283512306], [-14314575.5, -24793572.054780666]], [[1.0, 0], [-1404.3318921147818, -2432.3741878321375], [-34671978.5, 60053628.36093575]], [[1.0, 0], [245.82741349916853, 0], [115856201.0, 0]], [[1.0, 0], [17504.49811557778, 0], [147008443.0, 0]], [[1.0, 0], [8172.739809546984, 14155.600587176166], [-114672503.5, 198618602.2931199]], [[1.0, 0], [-14820.828487610546, 25670.427950805668], [-209097746.5, -362167920.6861574]], [[1.0, 0], [5178.054360919766, -8968.653237466626], [-357462149.5, -619142604.7167817]], [[1.0, 0], [-477.08927899415795, -826.3428709642848], [-422298150.5, 731441852.6083683]], [[1.0, 0], [-9907.598162895858, 17160.463399111693], [-675062553.5, -1169242640.9491835]], [[1.0, 0], [-62125.37315431777, 0], [1804229351.0, 0]], [[1.0, 0], [-13554.815862074549, 23477.62976035365], [-1036535796.5, -1795332663.4018745]], [[1.0, 0], [22343.675262324658, 38700.38078216617], [-1538528199.5, 2664809010.4114656]], [[1.0, 0], [15606.642720762504, 0], [3939040643.0, 0]], [[1.0, 0], [-6817.658650263066, -11808.531170917086], [-2792029724.5, 4835937339.076535]], [[1.0, 0], [-12919.494656653256, 0], [8587340257.0, 0]], [[1.0, 0], [-12571.461285871022, 21774.40967251378], [-5255050250.5, -9102014030.193556]], [[1.0, 0], [80376.56138760938, 139216.28806101828], [-5796370371.5, 10039607982.924889]], [[1.0, 0], [-47187.761109604435, -81731.59973725762], [-7012758653.5, 12146454289.080307]], [[1.0, 0], [-41696.7367965931, 72220.866641526], [-7693119774.5, -13324874318.146824]], [[1.0, 0], [179253.57341221478, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-147-7.4-c5-0-18', 'leading_term': '1.619999331117107171747623037965841495674331366572944620', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/147/6/e/l/67/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.07421875', 'prec': 24}, 'plot_values': [1.6199993311171073, 1.7704990394371742, 1.8876302343085882, 1.9716932442487674, 2.0233037617395326, 2.0433856825344545, 2.0331632790855627, 1.9941523966067551, 1.9281502777038193, 1.8372235590069073, 1.7236939439574117, 1.5901210423060672, 1.4392818807436356, 1.2741466314172911, 1.097850176085303, 0.913659222691262, 0.7249348166974918, 0.5350902392343166, 0.3475444547550124, 0.16567145833553282, -0.007253927904223874, -0.16811305426055584, -0.31400227849855605, -0.4422924781607256, -0.5506878984824535, -0.6372828334885999, -0.7006145075198369, -0.7397104323611216, -0.7541284687385094, -0.7439878269714347, -0.7099893058036693, -0.653423195391912, -0.5761634630141712, -0.48064709928297805, -0.3698378273572163, -0.24717376429413013, -0.11649906616183077, 0.018019921921351822, 0.1519929644670216, 0.28091708982909297, 0.40029845464210445, 0.5057822341828241, 0.5932873484967067, 0.6591423824901684, 0.7002186822340362, 0.7140563305607904, 0.6989785425805081, 0.6541899938179003, 0.5798547151243675, 0.4771494702940768, 0.3482889806229056, 0.19651997620736444, 0.026081831175532342, -0.1578675327190954, -0.3493607314449731, -0.541764086635799, -0.7279527329412238, -0.9005142497310675, -1.0519761384940223, -1.175051259150218, -1.262894235569169, -1.3093608933397596, -1.3092620506274728, -1.2586024919179086, -1.1547957553676107, -0.9968454906383928, -0.7854846191909475, -0.5232643653389514, -0.21458642319037485, 0.1343269329962145, 0.5155281293751283, 0.9195061693737816, 1.335413971987362, 1.7513575581759422, 2.154740940111508, 2.53265807671512, 2.872320908517611, 3.161510378277261, 3.3890355824807448, 3.5451848785659177, 3.6221519789286174, 3.6144198663414904, 3.5190858183123717, 3.336111959573159, 3.0684875761258446, 2.722291897062988, 2.306649128707116, 1.8335711274538902, 1.3176871132947012, 0.7758641204207628, 0.22672629840703243, -0.30991445502874193, -0.8136999129088579, -1.2644186534281194, -1.6427274505939968, -1.9308751007303968, -2.113401410326404, -2.177783638491215, -2.1150033555988372, -1.9200084846819485, -1.5920482229686221, -1.1348625373476584, -0.5567128791771472, 0.12975348787685237, 0.9078068111449996, 1.7571003921213033, 2.6542861391860786, 3.5737613454245882, 4.4885218328743886, 5.371091318867457, 6.194492631458094, 6.933223464012977, 7.5641979021919195, 8.067615110269998, 8.42771839148646, 8.633411328647714, 8.678702779280869, 8.562958979977234, 8.290948669797165, 7.872675669830003, 7.32300239804926, 6.6610769585616625, 5.909585302829166, 5.093858094876578, 4.240868917607604, 3.3781659658272547, 2.532783073888154, 1.7301775882340715, 0.9932420743954588, 0.34143410290385046, -0.20993654388243166, -0.6502307854273367, -0.9737894011891856, -1.1800144625611262, -1.2732198391035354, -1.2622587010943653, -1.1599468612378248, -0.9823109598321655, -0.7476993623220896, -0.4758007187519488, -0.18662002197052346, 0.10053561101368255, 0.3680095059615723, 0.6006374434824222, 0.7864358694129768, 0.9171011001292737, 0.9882943695505729, 0.9996991198431243, 0.9548493990222492, 0.8607409286857389, 0.7272486437530762, 0.5663855880474588, 0.3914473238884114, 0.21609291242847828, 0.053417594294748294, -0.08492675461223631, -0.18950963046066108, -0.25375012812207237, -0.2743556238207465, -0.2515421708245665, -0.1890208394037786, -0.09374844016364112, 0.024544305581510488, 0.1540199123699616, 0.2815565088447672, 0.393674657269539, 0.4775099823879013, 0.52176857097863, 0.5176015136577182, 0.45933835023245884, 0.3450264737198348, 0.17673442748562695, -0.03940905694350112, -0.29345224759561067, -0.5721282631797003, -0.8596102061806776, -1.1384731970913982, -1.3908078538743625, -1.5994176388463504, -1.7490242124980506, -1.8274011721276413, -1.8263577388207182, -1.742500222197454, -1.577710257102397, -1.3392943720770527, -1.0397786189839702, -0.696343707479526, -0.32991908129613884, 0.036022756459666294, 0.37690907014568015, 0.6686659783741973, 0.8893789061082163, 1.0209108740206423, 1.0503726189914293, 0.9713426486844727, 0.7847460640209641, 0.49931795410871166, 0.1315995864454143, -0.2945576892345446, -0.7489764223682169, -1.196589986388028, -1.5992677751193967, -1.9179369753469415, -2.114886706649476, -2.156123909609493, -2.0136413306794445, -1.6674571566398475, -1.1072936696976634, -0.33377857471133604, 0.6409232962031604, 1.793109572876672, 3.0881973688399693, 4.482025462509914, 5.9227503558082155, 7.353247721268285, 8.713897710523984, 9.945605910421495, 10.992893251004944, 11.806879286664975, 12.347984819448158, 12.588192009837893, 12.51272245724161, 12.121025106014075, 11.427004516176401, 10.458463794984384, 9.25578270087654, 7.869897269155515, 6.359689890043014, 4.788935357935567, 3.2229765928877705, 1.7253215871908933, 0.35435935250620554, -0.8396133379416882, -1.816880598241104, -2.550166651006151, -3.0257590941840222, -3.2438349243664866, -3.217977369725805, -2.9739218811932493, -2.5476176223840046, -1.9827333405196332, -1.3277707690339886, -0.6329724031253653, 0.05277801993761285, 0.6848655330478437, 1.225482139758917, 1.6456374376603322, 1.926522722940064, 2.060154270728189, 2.049270907632743, 1.9065118216410584, 1.6529492913351764, 1.316094285254115, 0.9275276688606537, 0.5203336246870593, 0.12652316148491255, -0.22536653444467003], 'positive_zeros': ['1.48116380786680013415431719405559', '2.73618795758857292681513818732521', '3.87018363236734616704635388603435', '5.09342162660238438750609300708956', '6.71067307135083434897238490374748', '7.63128611379144953824655800406176', '9.618444116989085715666313718934391', '10.43850107268601620212683452794511', '11.45654325351979223473409307323100', '12.00884119019060135401276668598813'], 'prelabel': '2-147-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': -0.020172953053946126, 'root_number': '0.99197791640852265169404803750682485961305798168199772605 - 0.1264112865127400184730959576238026966982488495928982352*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.020172953053946122', 'prec': 57}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48116380786680013415431719406', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.73618795758857292681513818733', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.87018363236734616704635388603', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '7.4', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/e/l/67/2'], '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': '2-147-7.4-c5-0-18', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-147-7.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': -0.020172953053946126, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48116380786680013415431719406', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1877598190078679039528818377094', 'Lhash_array': ['1877598190078679039528818377094'], 'factors': ['2-147-7.4-c5-0-18'], 'label': '2-147-7.4-c5-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/e/l/67/2'}