-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '681969983291630954225992776203', 'a10': [0.8940363159270277, 4.067456348164178e-61], 'a2': [0.7742581614986561, -0.44701815796351385], 'a3': [-0.5132741945635516, 1.6542519763310357], 'a4': [-0.6003495329018139, 1.039835893286185], 'a5': [0.8660254037844386, 0.5], 'a6': [0.3420739370395229, 1.5102609788335912], 'a7': [-1.7695403369357823, 1.021644589871775], 'a8': [0.0, 2.861541201182155], 'a9': [-2.4730992023902747, -1.6981697015129515], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.671248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.5132741945635516, -1.6542519763310357]]], [5, [[1.0, 0], [-0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-2.224920091568663, 2.837204713469596]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.571', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '3172355899008580294807357589828', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.7742581614986561, 0.44701815796351385], [1.0, -1.7320508075688772]], [[1.0, 0], [0.5132741945635516, -1.6542519763310357]], [[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [1.7695403369357823, -1.021644589871775], [3.5, -6.06217782649107]], [[1.0, 0], [0.6597901114708034, -0.38092999846632153], [5.5, -9.526279441628825]], [[1.0, 0], [-2.224920091568663, 2.837204713469596]], [[1.0, 0], [2.677832231845946, 0], [17.0, 0]], [[1.0, 0], [0, -7.380786046950973], [-19.0, 0]], [[1.0, 0], [1.7291733078072031, -2.9950160242140127], [-11.5, -19.91858428704209]], [[1.0, 0], [4.28618610947119, 7.42389211230008], [-14.5, 25.11473670974872]], [[1.0, 0], [7.284966606469806, 4.2059774312827765], [15.5, 26.846787517317598]], [[1.0, 0], [0, -3.2452232121957407], [-37.0, 0]], [[1.0, 0], [-5.2528445277576905, -3.032731202112155], [20.5, 35.50704155516198]], [[1.0, 0], [-5.422690659673024, -9.392375736282869], [-21.5, 37.239092362730865]], [[1.0, 0], [0.7196892501432237, -0.41551278230307015], [23.5, -40.703193977868615]], [[1.0, 0], [-12.959648504630287, 0], [53.0, 0]], [[1.0, 0], [-8.577212748648096, -4.952056089328669], [29.5, 51.09549882328188]], [[1.0, 0], [-1.1195845777869273, -1.9391773720975078], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.8741530914162197, -0.504692522642098], [33.5, 58.023702053557386]], [[1.0, 0], [0, -16.282899995788313], [-71.0, 0]], [[1.0, 0], [0, -8.994470446929897], [-73.0, 0]], [[1.0, 0], [7.117381065592208, 12.327665622434422], [-39.5, 68.41600689897065]], [[1.0, 0], [-7.5252144840641435, 4.344684608084104], [41.5, -71.88010851410841]], [[1.0, 0], [0, 6.843285116104544], [-89.0, 0]], [[1.0, 0], [0.07885396897526636, -0.045526360214540436], [48.5, -84.00446416709055]], [[1.0, 0], [1.0198248951799458, 1.766388533275271], [-50.5, 87.4685657822283]], [[1.0, 0], [-3.809152335777352, 6.597645379336037], [-51.5, -89.20061658979718]], [[1.0, 0], [-5.464649299709073, 0], [107.0, 0]], [[1.0, 0], [0, -14.061791084606083], [-109.0, 0]], [[1.0, 0], [-1.5604948733923814, 2.702856405666367], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-585-117.103-c1-0-12', '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/585/2/bt/b/571/35', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.130185713680817, 0.8714590458059187, 0.6146188274931504, 0.35336972144384, 0.08373758228502085, -0.19452402925943135, -0.47713199426283137, -0.7550637786430993, -1.0148737061449438, -1.2394818464483977, -1.4094041771465773, -1.5043924508841768, -1.5054234388397845, -1.3969276294885358, -1.1690891757119648, -0.8199944769530785, -0.35736804532920824, 0.20037835781211588, 0.8240357343645095, 1.4746187961406825, 2.1056098332324242, 2.666384091534165, 3.106619945684293, 3.3813374090328683, 3.4560661602894953, 3.3115430687359098, 2.94730162631111, 2.3835590946183034, 1.6609400080653471, 0.8377933874491472, -0.014851753864017521, -0.8203233458993388, -1.5046465772993378, -2.005232472671439, -2.278795912978784, -2.3073633004911995, -2.101375884352685, -1.6992084099322802, -1.1628782628635848, -0.5702646495502581, -0.004715229432313814, 0.4565993987132686, 0.7539031283670395, 0.8538397286653647, 0.7547372265643305, 0.48701666957129797, 0.10835670711755761, -0.30593085779014767, -0.6760081534482324, -0.9320834939061753, -1.028001319221634, -0.9513609120576314, -0.7280722937066139, -0.4200699237987271, -0.11602923254193749, 0.08380467834178579, 0.08638067481697778, -0.1749776920449561, -0.724526717433545, -1.5344958189092317, -2.5243304192403913, -3.5697618167405194, -4.520924727049441, -5.226966126679209, -5.563130000943413, -5.455473046623128, -4.898386651289502, -3.9610466975946848, -2.78068682346726, -1.5429222122824915, -0.4518337630036273, 0.3053167763230872, 0.5924833199029216, 0.3518103977304271, -0.38236809133281546, -1.4859249183510765, -2.764193779664953, -3.9853020135037673, -4.921901350725583, -5.393665763283501, -5.302381966804803, -4.65252083303966, -3.552727499691949, -2.1972683737422765, -0.830441779459059, 0.29950575767513116, 0.9880708220337927, 1.1142986763353269, 0.6645487822373076, -0.26484768143448195, -1.4868569131969538, -2.761208578302442, -3.8424509745408555, -4.52864340365087, -4.700486354004179, -4.342657806017808, -3.5429344484837237, -2.469527976877625, -1.3318917327394582, -0.33395337079626347, 0.3695710369349558, 0.7038666452927459, 0.6848608485265018, 0.40807608152254876, 0.01863124832019576, -0.3298888935153163, -0.5172191388504552, -0.48816602661238584, -0.26609530081948796, 0.055490732469828566, 0.3413051308527689, 0.45530328363832906, 0.3035687421968252, -0.13262982862166156, -0.7831472468890034, -1.4994289881999956, -2.0877126445546903, -2.3574016183591837, -2.1725984548230812, -1.4932695359175445, -0.39447657624914234, 0.9427836790251017, 2.2685187580832515, 3.3205614322707673, 3.887775553260723, 3.863788476245551, 3.2770490955462113, 2.2884495486950316, 1.1557249319151628, 0.17238522401913456, -0.404179397136813, -0.41742745913644613, 0.14754577235444732, 1.1582833118131832, 2.3666553338880294, 3.470625924725796, 4.190697120333895, 4.341391940588951, 3.8789904924960195, 2.912616377917131, 1.6752644671661514, 0.4620157117931812, -0.44835228353019924, -0.8673688217861855, -0.746328220414214, -0.18742131909955131, 0.5869114511843322, 1.2983219890617637, 1.6929387849348185, 1.6152678461421528, 1.054415407093185, 0.14878901420857873, -0.8530792391847507, -1.6654383873759655, -2.051795279836523, -1.9002207156164703, -1.2650755164093266, -0.36156975848286677, 0.4874074813657863, 0.9390925252073035, 0.7297706858000086, -0.24279697013708615, -1.8774630496750533, -3.8817983812067043, -5.837041586046573, -7.2999487972759844, -7.914905623006034, -7.506184748873171, -6.125115792669282, -4.038960723921544, -1.66416961244943, 0.538025641823506, 2.175388439675384, 3.017132939717208, 3.0406197643637958, 2.420984926693461, 1.4686107872659377, 0.5339388570114674, -0.09215231815268828, -0.25383594153477296, 0.03882577304421966, 0.6302659605946569, 1.282011481641423, 1.756029400871026, 1.8917935192520057, 1.653012000276021, 1.1304318256634163, 0.5017347509297516, -0.03642617909795385, -0.3402509066315704, -0.3695204869942762, -0.19964339253938548, 0.009242645797708268, 0.07546955070929101, -0.13082294186583288, -0.6305436486672275, -1.3162501325443114, -1.9796368114478948, -2.3789643879668154, -2.3250266382702183, -1.7564127458478629, -0.7765868554380271, 0.3634275679977708, 1.3354855873665787, 1.838425999333056, 1.703549227211351, 0.9662576392374667, -0.1227991176632674, -1.155858872236511, -1.6823706441053048, -1.3474306442599806, -0.012458153728854152, 2.180739179830495, 4.825859953291278, 7.347697265478415, 9.152571104121357, 9.790939455092344, 9.08433217835751, 7.178222360399399, 4.504020799178314, 1.6605786676692524, -0.7500022926826495, -2.2835284765231174, -2.764192828102115, -2.312597650078757, -1.2852956356053395, -0.14731445911611057, 0.6803899571269372, 0.9496815631515866, 0.650135426404007, -0.008367381587556812, -0.6864720904200043, -1.0467311550933867, -0.879845747857998, -0.18265482356267387, 0.8382255416208757, 1.8375338513273003, 2.452047867922739, 2.4286947993426167, 1.7155256849247065, 0.48386328215268704, -0.9262913783671037, -2.118982036544167, -2.7743967558125116, -2.7548138379877005, -2.1478478934009093, -1.2321432913929615, -0.37757941187860344, 0.08516061257040781, -0.019875296276789124, -0.6535807075489927, -1.5776077604744678, -2.44047985451257, -2.9033560980048283, -2.76077566635243, -2.0134848740219438, -0.8674951455201656], 'positive_zeros': ['0.53797945835299429072061995733291', '2.08213550634002877026332299074269', '3.74779599827455488760940751650097', '5.00112327687537456945565855373948', '5.78274270947612113503959819990776', '6.81059174270818740434159463468001', '7.05826978092624943395413086611834', '8.816040991691338914847785352778599', '9.194254625346483042916920968651537', '10.58763229492687339669661243010295'], 'prelabel': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.8190053463717173, 'root_number': '-0.842649456361658 - 0.5384625276594485*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.409502673186', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53797945835299429072061995733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.08213550634002877026332299074', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74779599827455488760940751650', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.671248518244905, 'bad_primes': [3, 5, 13], 'central_character': '117.103', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/35'], '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': '2-585-117.103-c1-0-12', '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': '2-585-117.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.161307131863703, 'root_angle': -0.40950267318585865, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53797945835299429072061995733', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '681969983291630954225992776203', 'Lhash_array': ['681969983291630954225992776203'], 'label': '2-585-117.103-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/2/bt/b/571/35'}