-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1962473698830372688192206434619', 'a10': [0.8330221869309979, 1.634476288623914], 'a2': [1.4044282237797436, 0.1660763807736491], 'a3': [-1.6272246012817684, 0.5934139339309362], 'a4': [1.9448372714982518, 0.4664847129234088], 'a5': [0.7206838884178125, 1.0785796604662705], 'a6': [-2.383872194916759, 0.5631637047100546], 'a7': [-0.7670301619128943, 1.8517746196393405], 'a8': [2.6539122619423785, 0.9781358320355551], 'a9': [2.2957198060332207, -1.931235504071627], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.4044282237797436, -0.1660763807736491]]], [3, [[1.0, 0], [1.6272246012817684, -0.5934139339309362]]]], 'bad_primes': [2, 3], 'central_character': '192.107', 'coefficient_field': 'CDF', 'conductor': 192, 'conductor_radical': 6, 'conjugate': '3180073212835835304603608031800', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4044282237797436, -0.1660763807736491]], [[1.0, 0], [1.6272246012817684, -0.5934139339309362]], [[1.0, 0], [-0.7206838884178125, -1.0785796604662705], [-1.913417161825449, 4.619397662556434]], [[1.0, 0], [0.7670301619128943, -1.8517746196393405], [-4.949747468305833, -4.949747468305833]], [[1.0, 0], [0.9679979864072354, 0.1925467710950052], [10.162674857624154, 4.2095177560159875]], [[1.0, 0], [-2.7677539885580207, -1.849354090170405], [4.974884620746167, 12.010433922646728]], [[1.0, 0], [4.2020145585470186, 4.2020145585470186], [0, 17.0]], [[1.0, 0], [-1.3159258157712226, -0.8792735191848577], [7.270985214936705, 17.55371111771445]], [[1.0, 0], [3.4194796006763046, 8.25535402821087], [-16.263455967290593, 16.263455967290593]], [[1.0, 0], [-0.3031949529469136, -1.524263960763257], [-26.792506442827317, 11.097819538587604]], [[1.0, 0], [-1.8572172846650856, 0], [31.0, 0]], [[1.0, 0], [3.5397351759476354, 5.29758806263297], [-14.159286997508321, 34.18354270291761]], [[1.0, 0], [0.6060155085891948, -0.2510198426660734], [28.991378028648448, -28.991378028648448]], [[1.0, 0], [7.79176130759671, 1.5498776877512812], [39.72681989798533, 16.45538759169886]], [[1.0, 0], [-3.5698824609593984, 3.5698824609593984], [0, -47.0]], [[1.0, 0], [-0.6055185177155366, 3.0441471573248218], [-48.9656152230982, -20.28222191534976]], [[1.0, 0], [6.010656471202029, -4.016192253928592], [22.578322509540296, -54.50889241816592]], [[1.0, 0], [-2.314395250972551, -11.635250645602818], [-56.35665148318849, 23.343689374270475]], [[1.0, 0], [-12.258011747450634, 2.438270136053064], [61.89992867825621, -25.639789968461013]], [[1.0, 0], [-10.230200779982875, -4.237487908868722], [50.204581464244875, 50.204581464244875]], [[1.0, 0], [8.22378172375727, -3.406401923976251], [51.61879502661797, -51.61879502661797]], [[1.0, 0], [-4.224032948697322, 4.224032948697322], [0, -79.0]], [[1.0, 0], [8.63709572744257, -12.926327238384024], [-31.76272488630245, -76.6820011984368]], [[1.0, 0], [10.447575265918058, 4.327527369056955], [62.932503525602726, 62.932503525602726]], [[1.0, 0], [0, -4.0244044256907845], [-97.0, 0]], [[1.0, 0], [-13.909806670276913, 9.294235674666407], [38.65102666887407, -93.31183278363996]], [[1.0, 0], [3.570719456378393, 1.4790404262614156], [72.8319984622144, 72.8319984622144]], [[1.0, 0], [-0.46910136927010704, 2.35833183954192], [-98.85510997870769, -40.94712726306461]], [[1.0, 0], [6.703094904433315, -10.031890461668574], [-41.712494127794784, -100.70286904373026]], [[1.0, 0], [14.173491473614643, -14.173491473614643], [0, -113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-192-192.107-c1-0-9', '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/192/2/s/a/107/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6623926262471702, 1.5990998801322829, 1.54628149341451, 1.4977875419356845, 1.446203344115839, 1.3835964700699601, 1.302176135339972, 1.1948320696736825, 1.0555811500449985, 0.879964122711803, 0.6654185887969668, 0.4116293422464503, 0.12083532371664618, -0.20194208206089967, -0.5487917278410619, -0.9089690137450382, -1.2691527373102036, -1.6139280509125793, -1.926504628419168, -2.1896583310785434, -2.3868607510456186, -2.5035358030172636, -2.528358369903216, -2.4544896398597604, -2.2806301450189506, -2.01176746252058, -1.6595034287444015, -1.2418670494255695, -0.7825543330333424, -0.3095837769669861, 0.14658675642270144, 0.5553741658018444, 0.8886470039074373, 1.1233446397105005, 1.2438817441598313, 1.244067448001038, 1.1282829936263543, 0.9117073458568913, 0.6194567529314162, 0.28460753665479477, -0.054806682316396994, -0.3596033425145473, -0.593723861942006, -0.7285327718871624, -0.7466466314431577, -0.6447904398102927, -0.4352339807686101, -0.14547764741232452, 0.183969145340873, 0.5036580062107162, 0.7608247263688142, 0.9060408413101461, 0.9001770991394125, 0.7208379832816767, 0.36739450881475016, -0.13618095012146036, -0.7412854045359132, -1.3777794092792195, -1.960157662728272, -2.3963487440252296, -2.5983101257492094, -2.4932652068083727, -2.0342274169638044, -1.2084126560393802, -0.04227838872369404, 1.3977540089608183, 3.0093624385393425, 4.663060065523999, 6.214872551375663, 7.52165082194853, 8.4572678630454, 8.927704027700356, 8.883034511814463, 8.324614593734482, 7.306294770648714, 5.929232285015924, 4.330707283099991, 2.668187475868782, 1.1005932433253425, -0.23081594027954605, -1.2193669243098229, -1.8053613106598454, -1.9821484617934764, -1.7949611417057059, -1.3326197121819223, -0.7132615947829614, -0.06616544165303469, 0.4876344088754385, 0.8530193786773109, 0.9740433427993509, 0.8407316883764783, 0.48838354113930144, -0.010462773572419017, -0.560036592489343, -1.058940998350193, -1.418349671189282, -1.5776464924394138, -1.5147591315426572, -1.249327339223049, -0.8380895735734096, -0.3632619218970064, 0.08402129745850037, 0.4221726827403232, 0.5960482493134792, 0.5889841886725881, 0.4274857156173505, 0.17738227182777394, -0.06815384766997809, -0.20674843218098324, -0.14786979402548145, 0.16719980742389856, 0.7504378724738838, 1.5604055953498137, 2.505603139599065, 3.4577939538396283, 4.273304760835122, 4.818656934943447, 4.995849090926641, 4.762424822872259, 4.142206947705688, 3.224166482101477, 2.1490576178800476, 1.0857979080957514, 0.2016558928023795, -0.3682966422433673, -0.5466147453744444, -0.3286736956389296, 0.21571563932591134, 0.9550879646986986, 1.721514864235118, 2.343677565152173, 2.681533688707101, 2.6557064023647428, 2.2654901122798057, 1.5913942596206565, 0.7810881056887793, 0.020913944242639048, -0.5018480715621766, -0.6386788912437741, -0.31348129672459424, 0.45692354297663096, 1.5602267134773282, 2.8053190651564828, 3.955716687471128, 4.773711487259902, 5.066825034274447, 4.727357366753673, 3.756882902039833, 2.2703040581701734, 0.47802289924889424, -1.3508410324841666, -2.937360336669021, -4.044402167086606, -4.520747786953323, -4.3288839868168285, -3.550797653095844, -2.370507099772623, -1.0367960849626432, 0.186309014828602, 1.0712320184138033, 1.4701671946884736, 1.3412445909227277, 0.7523841919463652, -0.1375849740194065, -1.1161382221945364, -1.964325224804734, -2.503752193972293, -2.6331310091535247, -2.3466813959265815, -1.7308005490072569, -0.9403177378692456, -0.16022342668152487, 0.4380370813604189, 0.7355213262619626, 0.6910816070654379, 0.34741054625289924, -0.1831130023588281, -0.748903195466344, -1.1982176748458895, -1.417029444022489, -1.356351357520684, -1.0423270135958242, -0.5667485510926837, -0.0606166364679794, 0.34230468395947306, 0.542362793329641, 0.5015313324438037, 0.25407699288231317, -0.10281635395012395, -0.43641914164976814, -0.6169044391343281, -0.5567226881111583, -0.24005975184124723, 0.26633306788139816, 0.8251181812422276, 1.2614722443407773, 1.4098651473260722, 1.1629272863977185, 0.5094336843767483, -0.4496700902446562, -1.5133975918429412, -2.420414891320805, -2.908616474464288, -2.7812869461993643, -1.9639083360558007, -0.5368334875375553, 1.2660639747275892, 3.095040257902458, 4.552106971266485, 5.27477193473667, 5.017459699084543, 3.7118034190398856, 1.4910955282466416, -1.3280677193585961, -4.3042507446385185, -6.957739943748193, -8.866466245771031, -9.750096905452905, -9.523591713719862, -8.308436584056007, -6.399512652963421, -4.195812824067059, -2.111507399448005, -0.4881712392488945, 0.471732157524727, 0.7355689362527055, 0.4299135987394133, -0.20676619179470676, -0.8946484445686151, -1.3875884305219792, -1.53350184120502, -1.3054368254233197, -0.7968174454963223, -0.183985834326639, 0.33223281174434743, 0.5889277141738851, 0.5098352514253173, 0.12696353436912516, -0.4305248276989423, -0.9765186617314595, -1.3253874465543114, -1.3498938082300844, -1.0226682487420067, -0.42890717642473736, 0.2539471170149072, 0.8044075430300274, 1.0198430810906876, 0.7764620239644564, 0.0692282045834387, -0.9801253914608767, -2.1500793199590835, -3.174633131781415, -3.812198422948147, -3.9092860964760754, -3.441349661207542, -2.5192758642849866, -1.359469164875682], 'positive_zeros': ['1.54811877853175509554612031902506', '3.70880129500629187579853141200032', '4.97931698797219112214821618700109', '5.93099687173723650305129885509489', '6.84410689260906250679827416247740', '8.003998255621574504767296000787551', '9.851092067198715640923864564087239', '10.76347830799372217109012397325190', '11.49758145867779592028254966527428', '12.59971552982382744731560708388458'], 'prelabel': '2-192-192.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': -0.1463797605786072, 'root_number': '0.6060340235431007 - 0.795438723163614*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.146379760579', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54811877853175509554612031903', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.70880129500629187579853141200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.97931698797219112214821618700', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5331277188085841, 'bad_primes': [2, 3], 'central_character': '192.107', 'conductor': 192, 'conductor_radical': 6, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/192/2/s/a/107/30'], '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': '2-192-192.107-c1-0-9', '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': '2-192-192.107-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2381953475960827, 'root_angle': -0.1463797605786072, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54811877853175509554612031903', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1962473698830372688192206434619', 'Lhash_array': ['1962473698830372688192206434619'], 'factors': ['2-192-192.107-c1-0-9'], 'label': '2-192-192.107-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/192/2/s/a/107/30'}