-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2030717986691511223831160098547', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.5, -2.598076211353316], 'a4': [0.0, 0.0], 'a5': [-9.479009157039513, 16.418125465403072], 'a6': [0.0, 0.0], 'a7': [12.80327939264716, -13.381929486954283], 'a8': [0.0, 0.0], 'a9': [-4.5, 7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.912320880964428, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.5, 2.598076211353316]]], [7, [[1.0, 0], [-12.80327939264716, 13.381929486954283]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.121', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': '610360351754039717419799954556', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.5, 2.598076211353316]], [[1.0, 0], [9.479009157039513, -16.418125465403072], [-62.5, -108.25317547305482]], [[1.0, 0], [-12.80327939264716, 13.381929486954283]], [[1.0, 0], [27.365404481703926, 47.39827093198426], [-665.5, 1152.6798124370878]], [[1.0, 0], [-62.017300921066315, 0], [2197.0, 0]], [[1.0, 0], [61.21954450484112, 106.03536149860888], [-2456.5, 4254.782808792947]], [[1.0, 0], [-6.252875730228934, 10.830298458170859], [-3429.5, -5940.068244557465]], [[1.0, 0], [-37.21954450484112, 64.46614211695582], [-6083.5, -10536.931087845265]], [[1.0, 0], [232.5722332929185, 0], [24389.0, 0]], [[1.0, 0], [5.183866738847896, 8.97872057135094], [-14895.5, 25799.76280414221]], [[1.0, 0], [-122.99332076887303, 213.03068056330451], [-25326.5, -43866.78477789317]], [[1.0, 0], [-238.6526435917165, 0], [68921.0, 0]], [[1.0, 0], [92.97176616210137, 0], [79507.0, 0]], [[1.0, 0], [-242.82225656276486, 420.580485575234], [-51911.5, -89913.35549711177]], [[1.0, 0], [-189.2784518006292, -327.8398952966666], [-74438.5, 128931.26403921588]], [[1.0, 0], [-91.39177147392307, -158.29519158655873], [-102689.5, 177863.43140384424]], [[1.0, 0], [198.23497858022796, -343.35305473828294], [-113490.5, -196571.31217639567]], [[1.0, 0], [-130.61950428898496, -226.23961788798283], [-150381.5, 260468.39851841913]], [[1.0, 0], [874.5226911448942, 0], [357911.0, 0]], [[1.0, 0], [76.2032291984779, 131.9878646725799], [-194508.5, 336898.604504011]], [[1.0, 0], [286.67868528247345, -496.5420483562922], [-246519.5, -426984.29905647587]], [[1.0, 0], [-317.7536991171713, 0], [571787.0, 0]], [[1.0, 0], [-47.50799638756448, 82.28626350906036], [-352484.5, -610521.062880512]], [[1.0, 0], [1608.7762843325816, 0], [912673.0, 0]], [[1.0, 0], [-391.521377458501, -678.1349180074759], [-515150.5, 892266.8395445109]], [[1.0, 0], [-744.8045513354201, 1290.0393246214899], [-546363.5, -946329.3414011582]], [[1.0, 0], [356.38457224844973, -617.2761861680162], [-612521.5, -1060918.3587283]], [[1.0, 0], [520.9239364662928, 902.2667248384009], [-647514.5, 1121528.0126375577]], [[1.0, 0], [-352.092709351726, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-168-7.2-c3-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/168/4/q/f/121/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9670388931962701, 1.158293292505759, 1.3176371261713122, 1.4411774830819004, 1.5247770751561267, 1.5641118032192463, 1.5548415261943145, 1.4928887221697706, 1.3748100917962802, 1.1982374104320055, 0.9623562437131168, 0.6683846213864673, 0.3200086593448615, -0.07627112083098994, -0.5109297605050057, -0.9713885960221906, -1.4422047765721715, -1.9055066990931084, -2.341687017328631, -2.730345157653241, -3.0514481943895513, -3.286653992070615, -3.420715764295515, -3.4428651385210114, -3.3480542379681686, -3.1379289996736675, -2.821408450260985, -2.414759822520714, -1.9410880866067026, -1.429200258205358, -0.911857780918436, -0.4234908065047609, 0.002488752034231957, 0.3365792297801412, 0.5560415976033956, 0.6474368434927856, 0.6085663473516071, 0.44955532280162147, 0.19287225997233798, -0.12784014806038124, -0.47013958987073656, -0.7862571044906506, -1.0274322188234748, -1.148753987208179, -1.1140557005145197, -0.9003535525115243, -0.5013124337926598, 0.07072724406507117, 0.7845177026259494, 1.5916590357199774, 2.4303288360247235, 3.230747485634392, 3.921918016522046, 4.438988315280616, 4.730450639074957, 4.764341920903643, 4.532653534507, 4.053305796514216, 3.369282652876223, 2.5448347869633183, 1.6590119944297905, 0.7971364464790835, 0.041131536081179386, -0.5401679447783123, -0.8995160089331563, -1.0174265060424434, -0.9050998058667242, -0.6035533642942649, -0.17886939215414638, 0.2860157304011372, 0.7020645725721528, 0.9861178444221184, 1.0725362281789002, 0.9228952180560449, 0.5323000687781091, -0.06872067579606406, -0.8172189157164405, -1.6255331033025664, -2.3928165202733616, -3.0189074755048924, -3.418641390640619, -3.5345403999725273, -3.345949384072513, -2.873118214172373, -2.1754126082763494, -1.3436822956980907, -0.48770519819351416, 0.27957534073924095, 0.8587271762591545, 1.1788774226834133, 1.208726694290714, 0.9616497414485329, 0.493855929364315, -0.1043537227354093, -0.7230826439806924, -1.2509522051898334, -1.5940084510554153, -1.6923371934963505, -1.5315373559703462, -1.1469220163448604, -0.619428195699971, -0.06355551329742071, 0.39099273766539666, 0.6211531028405578, 0.5322969779318372, 0.0762886599298174, -0.7374161935473477, -1.8398151332798232, -3.1102675277583325, -4.393334834139798, -5.522054102517565, -6.343945330812617, -6.745445193321719, -6.670578682179517, -6.1305377551373, -5.202311972173079, -4.016373135922225, -2.735336849851952, -1.5271650693349683, -0.53752690568201, 0.13381409999425822, 0.44834516221430126, 0.43306261704781884, 0.17280567837681132, -0.20798061191555947, -0.570701424885614, -0.7905146739781395, -0.7813538637122137, -0.5131942237013016, -0.018085643108218447, 0.6164093534125578, 1.2652909699143875, 1.7923225726944658, 2.0792556748152373, 2.052220686181436, 1.6998063242667834, 1.0788397900353541, 0.3062222787147922, -0.46206528427445814, -1.0610306761020536, -1.3500723179440832, -1.2430711383649466, -0.7289336586056586, 0.12196953394768459, 1.1673555142423657, 2.217302474491839, 3.06896134085063, 3.5451653571733313, 3.5293879564946447, 2.98998858643137, 1.9886272032148933, 0.6707725506590065, -0.7602121849868808, -2.0805671541332478, -3.0879249290342385, -3.639083851404484, -3.676134012268924, -3.2355757000983494, -2.438504322447994, -1.4638402739032375, -0.5101440038387189, 0.24598831284614495, 0.6861540023138032, 0.773270015270419, 0.5566133281633933, 0.15766197059035308, -0.2601992460524157, -0.5314623462811009, -0.5289360524062925, -0.19573038047560065, 0.4385885222017275, 1.261632405449744, 2.101198904162338, 2.762859741541418, 3.07393343129274, 2.924011660214641, 2.292754671092613, 1.25833169968686, -0.015889788021592636, -1.3139269357206012, -2.4121273447600995, -3.126607028353525, -3.352531672515619, -3.086233467197205, -2.4249009740172465, -1.5436197929457576, -0.6547458291328575, 0.04124041975986692, 0.4021147551101304, 0.3766858796033961, 0.01611365908414746, -0.5391930781904845, -1.094362555544271, -1.4486077598286207, -1.446177604949424, -1.0175238435392935, -0.20053756040110837, 0.8637874738096262, 1.960947183811746, 2.851420649854682, 3.327031354187492, 3.2619733794426575, 2.646220992315778, 1.5929096048073157, 0.31724138158593645, -0.908847080084185, -1.8161978124017746, -2.198525630175879, -1.959125026303032, -1.1331765782254735, 0.11973218438472125, 1.551267104144525, 2.8799018113054267, 3.8533267252776215, 4.303031419715886, 4.178285442214746, 3.5517683554689166, 2.5960390130781454, 1.5371883282752896, 0.5976116303764273, -0.057546851072015945, -0.35677036532410755, -0.33234023247372146, -0.10208755773595261, 0.172054471022501, 0.33732954794821407, 0.30064464693334153, 0.06217370915023273, -0.27775186160761, -0.5413404415233525, -0.5206014099899346, -0.03734863595998492, 0.9997633823089828, 2.5567571269854885, 4.465768294300181, 6.450422740706202, 8.180528933288109, 9.343716111102582, 9.716840880919678, 9.219442291448297, 7.935504298106435, 6.0973759548068935, 4.035035897991222, 2.1026049909465243, 0.5998538332666261, -0.2921364122484687, -0.5454567785775264, -0.28179421456708603, 0.26775057155832865, 0.8286689888222357, 1.1575223775270465, 1.105470804286377, 0.6544411403052587, -0.08314667509014735, -0.9004363648241347, -1.5577421939036742, -1.8526251523344999], 'positive_zeros': ['1.60195402923005614836986799945080', '3.99919149971048796991793690535095', '4.82713014809901132334423929790908', '5.86122206868806473572176012404292', '7.75763791523220469491928184499653', '8.548069614648120679031211198382332', '9.362366581762346604689184795692048', '10.82662729537695756453911667809631', '11.60413890179999848695336035557222', '12.64026365794903157314141766086633'], 'prelabel': '2-168-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': 0.5561273994468576, 'root_number': '-0.17541710418561307 + 0.9844942049393353*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.278063699723', 'prec': 47}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60195402923005614836986799945', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.99919149971048796991793690535', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82713014809901132334423929791', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.912320880964428, 'bad_primes': [2, 3, 7], 'central_character': '7.2', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/4/q/f/121/1'], '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': '2-168-7.2-c3-0-8', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-168-7.2-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.148383852227112, 'root_angle': 0.2780636997234288, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60195402923005614836986799945', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2030717986691511223831160098547', 'Lhash_array': ['2030717986691511223831160098547'], 'label': '2-168-7.2-c3-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/4/q/f/121/1'}