-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '595578194740376854174808358167', 'a10': [0.0, 0.0], 'a2': [0.0, -2.778457118258389], 'a3': [0.0, -1.0], 'a4': [-5.71982395800071, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.778457118258389, 0.0], 'a7': [0.0, 2.7198239580007098], 'a8': [0.0, 10.335371354775166], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.785414197074841, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.274', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '1566959657752590721805287501540', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.778457118258389], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.7198239580007098], [-7.0, 0]], [[1.0, 0], [2.7198239580007098, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, -2.8370902785160674], [-17.0, 0]], [[1.0, 0], [-3.5569142365167776, 0], [19.0, 0]], [[1.0, 0], [0, 4.837090278516068], [-23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [-7.556914236516778, 0], [31.0, 0]], [[1.0, 0], [0, -4.276738194517487], [-37.0, 0]], [[1.0, 0], [-2.8370902785160674, 0], [41.0, 0]], [[1.0, 0], [0, -11.113828473033555], [-43.0, 0]], [[1.0, 0], [0, -11.556914236516777], [-47.0, 0]], [[1.0, 0], [0, -1.1629097214839326], [-53.0, 0]], [[1.0, 0], [-2.1172663205153577, 0], [59.0, 0]], [[1.0, 0], [-6.6025576374853525, 0], [61.0, 0]], [[1.0, 0], [0, 1.8827336794846423], [-67.0, 0]], [[1.0, 0], [6.71982395800071, 0], [71.0, 0]], [[1.0, 0], [0, -9.113828473033555], [-73.0, 0]], [[1.0, 0], [10.276738194517488, 0], [79.0, 0]], [[1.0, 0], [0, -2.1172663205153577], [-83.0, 0]], [[1.0, 0], [1.1629097214839326, 0], [89.0, 0]], [[1.0, 0], [0, -10.837090278516067], [-97.0, 0]], [[1.0, 0], [-7.674180557032135, 0], [101.0, 0]], [[1.0, 0], [0, -3.7654673589692846], [-103.0, 0]], [[1.0, 0], [0, -12.602557637485353], [-107.0, 0]], [[1.0, 0], [11.43964791600142, 0], [109.0, 0]], [[1.0, 0], [0, 13.113828473033555], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-975-5.4-c1-0-4', '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/975/2/c/i/274/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8740652875890864, 0.7393527526701713, 0.5434261569385532, 0.2702364567555764, -0.09893457054741805, -0.5830540989428423, -1.1985283517885703, -1.9562842311376245, -2.8589546592455286, -3.8983750290625077, -5.053638231445688, -6.289997788297811, -7.558917897213913, -8.79952629078343, -9.941624361506996, -10.910252968301492, -11.631614892276872, -12.039937820321692, -12.084654098039346, -11.737109061622744, -10.995922759809842, -9.890149625603778, -8.47952565243726, -6.8513651307797145, -5.11405120421939, -3.3875174003639, -1.7915830361744192, -0.4334135155943629, 0.6043463516666416, 1.273135907264195, 1.564264195640749, 1.5098438271637011, 1.1784149907504313, 0.6655582025919219, 0.08058432250622803, -0.46891536474813855, -0.8924070204524278, -1.1292502505437476, -1.156896080882081, -0.992952416556975, -0.6905769770156625, -0.32778309191289506, 0.0076499687682557715, 0.23509060802065848, 0.2967537647071859, 0.16921767110778177, -0.13156577454637713, -0.5529532739210529, -1.0157220177925634, -1.4298525892275864, -1.7129825633905313, -1.8078192333608707, -1.6948110643983993, -1.3971684780430287, -0.9767915597699671, -0.5215456783321835, -0.12625085599839464, 0.12870263305623708, 0.19640725262100228, 0.07565875268321676, -0.1869143801156241, -0.5059813716688331, -0.7765344787175272, -0.89901193772488, -0.8049668247878902, -0.47712874142657585, 0.04149056726570821, 0.6526405847598888, 1.2220895355730774, 1.6097123528880095, 1.7040507161135734, 1.453250895922764, 0.8843352482149349, 0.10477370596358711, -0.7159879382036455, -1.3827320591209553, -1.7215019888241088, -1.6271470486768203, -1.0997798168262733, -0.25992490909856536, 0.6638750801076867, 1.37532847587124, 1.5722743412035125, 1.0181292216362172, -0.3926494790310539, -2.5908181743563654, -5.3225702663345515, -8.179326689429269, -10.664175086383029, -12.28350831479468, -12.645870322099737, -11.54713834412399, -9.022875676620357, -5.354868686259085, -1.028331885662622, 3.353011080978481, 7.17723049222738, 9.937078470611656, 11.321627666243565, 11.26722188864111, 9.957236067703922, 7.7716026017020825, 5.198357473521273, 2.7278832678586857, 0.7540233919203712, -0.49605219961516916, -0.9888638345278519, -0.8650018204079039, -0.3807851121686418, 0.1717570303477231, 0.5450135121099972, 0.5956314142660704, 0.3101061188444192, -0.2079590885075769, -0.7824187209746257, -1.226084215540019, -1.4003434966463888, -1.2556259690982723, -0.8418726850613814, -0.2875424903829236, 0.24480383942024575, 0.6114669119211874, 0.7321011867153782, 0.6118604392684159, 0.33473980164925915, 0.03103032191828641, -0.16981954273781738, -0.18492253685680551, -0.006727037956638408, 0.29506582946872095, 0.5993557737581973, 0.7786720748898669, 0.7479024055205635, 0.49938859895474896, 0.11105549841069332, -0.27697069652528244, -0.5109324398527941, -0.481497998331435, -0.17099632581022609, 0.32841251172548064, 0.8353257446836794, 1.1354865890809944, 1.0581852517815182, 0.5481813442480212, -0.2926290130051334, -1.212327246732313, -1.869196737664373, -1.932246037487458, -1.1944443130379963, 0.3363183871460841, 2.400487789135629, 4.522770737671814, 6.1185645736162675, 6.646820473370911, 5.7687807926118975, 3.466485202258044, 0.08288185338198627, -3.73463035147839, -7.1785934873988815, -9.47919041883982, -10.103284653749828, -8.89976988293272, -6.14901084779201, -2.4997257511992617, 1.192094189531944, 4.07974689661586, 5.539164129383035, 5.320813853043279, 3.599224056726211, 0.9083651102980325, -2.016384489703744, -4.442802714590714, -5.833960797036844, -5.9744718184953385, -4.998561368961002, -3.3178254952609536, -1.4762976264715701, 0.01931575507250162, 0.8416340479546186, 0.9159839326755604, 0.40826566681771176, -0.3614995228284787, -1.0457034069886295, -1.3908293322723337, -1.314004210218966, -0.9120172668419289, -0.4049350800449186, -0.03905033769973285, 0.01312298021539039, -0.2810678210841531, -0.8052124225192098, -1.342787802546601, -1.6640298585659297, -1.6169286712045443, -1.1876976416227054, -0.5080467859889592, 0.19315702234128515, 0.6752959654802239, 0.7760427211311453, 0.47196096743607285, -0.11321168316435905, -0.7556228180820964, -1.215693926878907, -1.327579373656036, -1.0594645886741956, -0.5216570194520752, 0.0803747458620889, 0.5293212485462958, 0.6825096662315745, 0.5266946655160715, 0.17853060547567634, -0.17025491151670763, -0.3411675869447609, -0.2540615182362234, 0.02815079484345004, 0.31763189768020655, 0.37997615467392515, 0.044271639546487065, -0.699973854991377, -1.6632667876337919, -2.4993665769241096, -2.8256678016631693, -2.382783125508377, -1.174488823970533, 0.47105932395920114, 1.9553876113370052, 2.5765603675996176, 1.7638900462105072, -0.6948806843180441, -4.515460829630342, -8.927001048043206, -12.843794810519139, -15.158249686274202, -15.070404345923508, -12.35078626451772, -7.448615627079333, -1.4028071351394946, 4.425180651389968, 8.720042109232418, 10.572206214112944, 9.719023854100074, 6.595192034784222, 2.180488190503803, -2.30322320782588, -5.747693428084017, -7.455568773015537, -7.291658618041437, -5.651937174489378, -3.2749376098938243, -0.9696827665222528, 0.6440138548800157, 1.2992179590865136, 1.105816459871742, 0.4431343540746106, -0.22534979980752604, -0.5395016131537975, -0.36358005531165344], 'positive_zeros': ['0.46982835383278973730882110018075', '3.42225285713798905431475253851856', '4.26732705592754898469084346295652', '5.24675698141683186756169204555817', '5.70269919139442202744505731647607', '7.05177773414504190564659540935841', '7.41683285203310310313027527155075', '8.241082687892807732523634138988254', '9.140699322993607204497120372422953', '9.909704695376116867404801418199377'], 'prelabel': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.35241638234956674, 'root_number': '0.44721359549995804 + 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176208191175', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46982835383278973730882110018', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.42225285713798905431475253852', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26732705592754898469084346296', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.785414197074841, 'bad_primes': [3, 5, 13], 'central_character': '5.4', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/2/c/i/274/1'], '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': '2-975-5.4-c1-0-4', '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': '2-975-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.790235509249146, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46982835383278973730882110018', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '595578194740376854174808358167', 'Lhash_array': ['595578194740376854174808358167'], 'label': '2-975-5.4-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/2/c/i/274/1'}