Formats: - HTML - YAML - JSON - 2026-10-11T09:24:26.286416
  • lfunc_lfunctions • Show schema
    {'Lhash': '781724074317241890809442153375', 'a10': [-35142.878582435886, -60869.25122900308], 'a2': [16.0, -27.712812921102035], 'a3': [0, 0], 'a4': [-512.0, -886.8100134752651], 'a5': [1098.2149557011214, -1902.1641009063462], 'a6': [0, 0], 'a7': [39703.51887539704, 20023.918994816944], 'a8': [-32768.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 96.81124075050822, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-16.0, 27.712812921102035]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-39703.51887539704, -20023.918994816944]]]], 'bad_primes': [2, 3, 7], 'central_character': '126.37', 'coefficient_field': 'CDF', 'conductor': 126, 'conductor_radical': 42, 'conjugate': '1471655343912110876569985318400', 'degree': 2, 'euler_factors': [[[1.0, 0], [-16.0, 27.712812921102035]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1098.2149557011214, 1902.1641009063462], [-24414062.5, -42286396.66916204]], [[1.0, 0], [-39703.51887539704, -20023.918994816944]], [[1.0, 0], [-206568.75789536256, -357787.5839311626], [-142655835305.5, 247087154745.30405]], [[1.0, 0], [-1895688.9634437358, 0], [1792160394037.0, 0]], [[1.0, 0], [4554166.087291388, 7888047.049295843], [-17135948153816.5, 29680332838276.28]], [[1.0, 0], [1243401.7483364113, -2153635.002338635], [-58245129449109.5, -100883523499283.9]], [[1.0, 0], [29546741.79115117, -51176457.98039248], [-476404878956963.5, -825157455327161.9]], [[1.0, 0], [-79256427.8868489, 0], [12200509765705828, 0]], [[1.0, 0], [-54655097.56110384, -94665405.86846569], [-12704238448202416, 22004386463756576]], [[1.0, 0], [338291691.322815, -585938397.1495231], [-88958810889730200, -154081180241924220]], [[1.0, 0], [252468396.75985032, 0], [550329031716248450, 0]], [[1.0, 0], [1752009517.44228, 0], [929293739471222700, 0]], [[1.0, 0], [-1291881740.6042671, 2237604812.097108], [-1236079607542006300, -2140952682462552600]], [[1.0, 0], [-2446969329.6471176, -4238275203.5115647], [-4634517964686095000, 8027220583427022000]], [[1.0, 0], [1465295808.829959, 2537966789.011222], [-15077944222368922000, 26115765466832577000]], [[1.0, 0], [572842715.5188164, -992192688.0243145], [-21756958805717918000, -37684158069686520000]], [[1.0, 0], [-5820607619.06118, -10081588127.136477], [-61065066452484006000, 105767797663272090000]], [[1.0, 0], [5249571471.5222225, 0], [231122292121701580000, 0]], [[1.0, 0], [-8751109171.019876, -15157365706.788385], [-156863342784179860000, 271695279547292350000]], [[1.0, 0], [-21203962677.123566, 36726340678.572205], [-373996905263760500000, -647781641790357200000]], [[1.0, 0], [-8466841242.693178, 0], [1287831418538085800000, 0]], [[1.0, 0], [9362691288.301247, -16216657006.920267], [-1387586536883495000000, -2403370381780759600000]], [[1.0, 0], [-103324072894.46906, 0], [7153014030880804000000, 0]], [[1.0, 0], [31322116029.310436, 54251496363.33322], [-5578341733326583000000, 9661971304103478000000]], [[1.0, 0], [27136841744.88471, -47002388659.09638], [-6921169353622228000000, -11987816968262345000000]], [[1.0, 0], [38243776126.60021, -66240163324.56125], [-10524259761499174000000, -18228552618969286000000]], [[1.0, 0], [-82599080968.71646, -143065804896.31244], [-12902132026527038000000, 22347148195906435000000]], [[1.0, 0], [-120454917815.97859, 0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-126-7.2-c11-0-15', 'leading_term': '2.964381060790771448953474144242954411535835415253192580', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/126/12/g/b/37/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 20}, 'plot_values': [2.9643810607907715, 2.787491573960582, 2.5566533939967964, 2.2757524819963066, 1.949933097274963, 1.5854911319808827, 1.1897389633065627, 0.7708447412382693, 0.33764963491771527, -0.10053290488088606, -0.5341313577047768, -0.9535389513289088, -1.3493399599555638, -1.7125342089061364, -2.034754478181218, -2.3084715809640963, -2.527182095339109, -2.685574046819473, -2.779666271924815, -2.806917732728542, -2.7663036902313083, -2.6583563693837093, -2.485168547002503, -2.2503593499263377, -1.9590024467824774, -1.6175177332218078, -1.2335285265926597, -0.8156871799601171, -0.373472874812483, 0.08303386561098856, 0.5433947065038127, 0.9970692547661262, 1.4336767588064472, 1.843257167338515, 2.2165248077437174, 2.5451079622526764, 2.821767814076689, 3.040590607990133, 3.1971474183774293, 3.288616635182091, 3.313865152313713, 3.2734852567073145, 3.16978534743237, 3.006733836607913, 2.789856867019834, 2.526091791553186, 2.223599660599379, 1.891541217604768, 1.5398220714315964, 1.1788137592763457, 0.819058299325581, 0.4709645248504537, 0.14450496191194348, -0.1510777625721436, -0.40754603444399784, -0.6179152520187831, -0.7766666643931099, -0.8799178582184749, -0.9255448141426125, -0.9132507951960298, -0.8445788673668344, -0.7228665465720798, -0.5531428681567753, -0.34197003093630074, -0.09723361916836261, 0.17211280853564423, 0.456341316534095, 0.7452724596911615, 1.028617281923238, 1.2963273811932627, 1.5389413929417104, 1.7479160368140014, 1.9159300637113732, 2.037150041758189, 2.10744792690645, 2.1245617581896776, 2.0881925660063176, 2.0000326368861407, 1.863722579272645, 1.6847371094210015, 1.4702020422630577, 1.2286475394686887, 0.9697051420644338, 0.7037584029521072, 0.44155894307702764, 0.1938213975006216, -0.029188082400150882, -0.21805441047139157, -0.36459173035098247, -0.4621821035182655, -0.5060606915895559, -0.49353500818056906, -0.42412795663820907, -0.2996369869364867, -0.12410471624386055, 0.09630033792496086, 0.3534907826957773, 0.6377494769582038, 0.938091668941296, 1.2426878480086048, 1.539332178294743, 1.8159390428228797, 2.061048499520598, 2.2643204301576154, 2.41699692034695, 2.5123129855801984, 2.545837165385269, 2.515725722073518, 2.4228771448665105, 2.270977283575478, 2.0664295961654022, 1.8181695413973937, 1.5373669084178296, 1.2370246601422206, 0.9314874776630494, 0.6358774283896419, 0.3654778479572376, 0.13508944751226207, -0.04161531984505252, -0.1527125988512, -0.1885952475556666, -0.14246304664958573, -0.01071170642972536, 0.20679915938994295, 0.5066144847413838, 0.8816987589979003, 1.3216018375855503, 1.8127735200643622, 2.339018440282756, 2.8820765281782954, 3.4223084316361296, 3.9394601014189163, 4.413476495081606, 4.825331268044176, 5.157837569971428, 5.396404778140366, 5.529707242019242, 5.550233884448553, 5.4546917356681215, 5.244242029819977, 4.924554167568392, 4.5056703830661915, 4.0016820400413415, 3.4302267753255524, 2.811823841846965, 2.1690726042824524, 1.525745847711197, 0.9058150395971374, 0.33244865005069424, -0.1729731435730452, -0.591783719298671, -0.9088532405781775, -1.1132714566112665, -1.1988571236829122, -1.1644681927730052, -1.01409536755324, -0.7567311046956998, -0.4060161910520895, 0.020323765332191056, 0.5012297267772505, 1.013217239514005, 1.5314020105094195, 2.0305978517085785, 2.48643765351437, 2.8764661490738317, 3.1811537184903935, 3.3847833913495435, 3.476168453875015, 3.449165454079344, 3.302956614715289, 3.0420863018083315, 2.676247767406363, 2.219828341488133, 1.6912330092026726, 1.1120172903565213, 0.5058699773929634, -0.1025059213715401, -0.6885601713691251, -1.2290534544878402, -1.703149762163263, -2.0933888682740696, -2.386490214050277, -2.5739475822636937, -2.6523841608598198, -2.62364951173524, -2.494652984761443, -2.276941595918166, -1.986043628857759, -1.640611526004959, -1.2614083469927007, -0.8701905973185128, -0.48854608017268825, -0.13674824282609188, 0.1673119266345414, 0.4090590795300424, 0.5779812001445576, 0.6681508708193442, 0.6784911292151609, 0.6127706320136775, 0.47932754748118855, 0.2905365345697524, 0.06204751198842835, -0.18816212452622633, -0.4408693563106757, -0.6767609363866802, -0.8775970136760569, -1.0273164929671472, -1.1130201832459432, -1.125773988484137, -1.0611839694468346, -0.9197075736422621, -0.7066800396153915, -0.43205113590170063, -0.10984409845035814, 0.2426350639993604, 0.6057947650514001, 0.9589056764009452, 1.2813336313375043, 1.5537859510250054, 1.7594975463367173, 1.8852854183322505, 1.922406682038054, 1.867165681861587, 1.7212296261192412, 1.4916287033482558, 1.1904349398170675, 0.8341330755460183, 0.44271536681838, 0.03854935382275695, -0.3549177887943381, -0.714543599426608, -1.018881775523277, -1.2494969692127487, -1.392122006552322, -1.4375843500257577, -1.3824409468704433, -1.2292768777705931, -0.9866425599812052, -0.6686255775952001, -0.29407527373765247, 0.11448026759914556, 0.5321656109882198, 0.9332619943812878, 1.2927959481590887, 1.5881172049946954, 1.8003689459714556, 1.915757631102168, 1.9265396125378276, 1.8316569677910413, 1.6369747258840468, 1.3550948045360176, 1.004747208151605, 0.6097848694632573, 0.19783339182119503, -0.2013306779996211, -0.5575809742732178, -0.8423164756692031], 'positive_zeros': ['0.61667156089895694408651362413161', '2.02636455583095651333419134114253', '3.68958251172123835977012851837349', '4.52599971386766965079465445872177', '6.03709150896260449397271881702319', '6.65055064588992988445902497079240', '8.277929180335006627563420922855437', '8.582368168015786127136005733590352', '10.45123693198746189625826735393921', '11.10624215654867304991535880021687'], 'prelabel': '2-126-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.839270336285523, 'root_angle': -0.019076866139287392, 'root_number': '0.99282496911063717587568258975647487909758445531885445989 - 0.1195766729360803781755554747808106968532377366253317332*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.019076866139287392', 'prec': 57}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61667156089895694408651362413', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.02636455583095651333419134114', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.68958251172123835977012851837', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 96.81124075050822, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 126, 'conductor_radical': 42, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/126/12/g/b/37/3'], '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': '2-126-7.2-c11-0-15', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-126-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.839270336285523, 'root_angle': -0.019076866139287392, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61667156089895694408651362413', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '781724074317241890809442153375', 'Lhash_array': ['781724074317241890809442153375'], 'factors': ['2-126-7.2-c11-0-15'], 'label': '2-126-7.2-c11-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/126/12/g/b/37/3'}