-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1914265005438867454946313298300', 'a10': [0.0, 1.7320508075688772], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [1.7320508075688772, 0.0], 'a6': [0.0, 0.0], 'a7': [2.0, -1.7320508075688772], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-2.0, 1.7320508075688772]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.377', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1883470420657243282750087928046', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [5.0, 0]], [[1.0, 0], [-2.0, 1.7320508075688772]], [[1.0, 0], [0, -3.0], [-11.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-13.0, 0]], [[1.0, 0], [-6.928203230275509, 0], [17.0, 0]], [[1.0, 0], [0, 1.7320508075688772], [-19.0, 0]], [[1.0, 0], [0, -3.0], [-23.0, 0]], [[1.0, 0], [0, -6.0], [-29.0, 0]], [[1.0, 0], [0, -5.196152422706632], [-31.0, 0]], [[1.0, 0], [-7.0, 0], [37.0, 0]], [[1.0, 0], [12.12435565298214, 0], [41.0, 0]], [[1.0, 0], [2.0, 0], [43.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [47.0, 0]], [[1.0, 0], [0, 12.0], [-53.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [59.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-61.0, 0]], [[1.0, 0], [-2.0, 0], [67.0, 0]], [[1.0, 0], [0, 3.0], [-71.0, 0]], [[1.0, 0], [0, -3.4641016151377544], [-73.0, 0]], [[1.0, 0], [10.0, 0], [79.0, 0]], [[1.0, 0], [17.320508075688775, 0], [83.0, 0]], [[1.0, 0], [5.196152422706632, 0], [89.0, 0]], [[1.0, 0], [0, 13.856406460551018], [-97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [0, -19.05255888325765], [-103.0, 0]], [[1.0, 0], [0, 0], [-107.0, 0]], [[1.0, 0], [-13.0, 0], [109.0, 0]], [[1.0, 0], [0, 12.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-378-21.20-c1-0-5', '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/378/2/d/b/377/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.5853945723255247, 1.5567366657926982, 1.525488266399929, 1.4871388836165196, 1.4353570017803328, 1.3631700247737641, 1.2641081145141417, 1.1332036973367492, 0.9678189145946319, 0.7683001340595821, 0.5384472152613529, 0.28576212374022, 0.021424782337760656, -0.24005850043279486, -0.4815754827114521, -0.6845110992041857, -0.8302075683205734, -0.9017085189240949, -0.88566402520621, -0.7742266732856992, -0.5667323633378685, -0.27094061327438207, 0.09638591133589719, 0.50974940943111, 0.9361553817992924, 1.3373520158806953, 1.6729864199754187, 1.9044673385109059, 1.9992005107637534, 1.934759213138009, 1.7024864833073696, 1.3100130623145056, 0.7822277972055629, 0.1603597319584938, -0.5009810318530724, -1.1387179163464904, -1.6878269262030534, -2.088850041949434, -2.295576810523768, -2.2819323847212685, -2.047086670419603, -1.6179080316544983, -1.0481303128447599, -0.41396838429048083, 0.1936306763899176, 0.6794299848279363, 0.9559188415052746, 0.9554379729053363, 0.6407744430736376, 0.012627731308570233, -0.8873737999013002, -1.9789258645900525, -3.1507158831883566, -4.272885001882119, -5.21291450457351, -5.852949409357501, -6.1061963269126736, -5.929981079848469, -5.333363828474263, -4.377870819373922, -3.170839638879007, -1.8519640313819117, -0.5747030573342486, 0.5148877213663984, 1.2987986891022016, 1.7039942770777468, 1.712866897695428, 1.3653628645581282, 0.7521917556233891, -3.4483029841518533e-05, -0.7495159515665493, -1.3625502681324306, -1.735549956751553, -1.8120335481530614, -1.5915742072377432, -1.1289985893458117, -0.5238007594868587, 0.09851223569429095, 0.6099118307626981, 0.9039600549460802, 0.9160819721350901, 0.6361196056551207, 0.11062744100781743, -0.5657516125369093, -1.2684073640107651, -1.8670646479532742, -2.251628060915713, -2.35446820843705, -2.164582197347362, -1.7305337937613257, -1.1512405612791092, -0.5561219684708207, -0.07836782742993131, 0.1733422316282665, 0.13880067821768627, -0.17928878883973506, -0.7138115398298077, -1.3455040871922732, -1.926906056350912, -2.313336407048705, -2.394506367617137, -2.119949306374786, -1.5124692815359013, -0.6661439583400791, 0.27137148588982984, 1.1290580413551674, 1.7491653405437957, 2.0224361095225296, 1.9140066646520355, 1.4737308518303396, 0.8278215684098142, 0.15271847584302722, -0.3638737314284287, -0.5666769177602905, -0.37164469036958725, 0.2091786877891551, 1.063182755666922, 1.9953198533918135, 2.7661110626391086, 3.142194839960767, 2.9488771642147897, 2.1131330468907885, 0.6870403477962773, -1.154519386424554, -3.142639134066083, -4.964556854016656, -6.3251865611118125, -7.007080969480184, -6.915789037530347, -6.10038815101767, -4.744178371347257, -3.127020127103269, -1.5671330451141143, -0.3548933460813531, 0.30686208592275527, 0.34282244979424786, -0.1833642980958165, -1.0885966357365746, -2.1160528921453614, -2.9963762779689023, -3.5099485815542675, -3.535676880975314, -3.0749782951901734, -2.2456424053195176, -1.2475595404462945, -0.309156586951994, 0.3719096250471687, 0.6788774698014993, 0.6042413061878973, 0.24927735843022603, -0.20500384732573804, -0.5479019126989016, -0.5970579736800892, -0.2493287480493434, 0.48888208879375, 1.4999684971847558, 2.5828458375705434, 3.5030570120657267, 4.052310307888578, 4.101886841694821, 3.6358314319711504, 2.7550789405956335, 1.6513334616730309, 0.5575964591275229, -0.31143683843762066, -0.8130688901326271, -0.9098429731058716, -0.6733143081995053, -0.2574104857138616, 0.1510765665352375, 0.3907922424241531, 0.3761253278389251, 0.12469515031365005, -0.24657609201361952, -0.5565393071127295, -0.6167011915752534, -0.29385245897342843, 0.4399852924120291, 1.4858887177057065, 2.6327956280670346, 3.606739561339445, 4.14255317037047, 4.058933285624224, 3.315741964418033, 2.0362887989970835, 0.4862739791337983, -0.9872231093676068, -2.042021474205153, -2.4299869409419688, -2.0648609651887053, -1.0494434210533268, 0.3467689038934973, 1.7550948573659473, 2.8033907041218926, 3.2147623789596187, 2.8824969516395456, 1.900261276206275, 0.5384046461936527, -0.828161618995598, -1.8215654951090428, -2.1646092364287757, -1.7579488963051488, -0.7092073247043573, 0.6945611224445055, 2.0640023199641298, 3.0132582906583103, 3.265311560549642, 2.727670518048011, 1.5173183085161985, -0.07201495668070669, -1.6510151904006753, -2.8415127130521265, -3.37874578630763, -3.180524693383579, -2.364245767136566, -1.2077319551146173, -0.06600082344022003, 0.7314063837714074, 0.9726153897546053, 0.6187064651836084, -0.1931011590652998, -1.1979696325810687, -2.0879536759218116, -2.606334590723373, -2.6231352157182424, -2.1693888210498637, -1.4207081236506127, -0.636437051734332, -0.0743198927066583, 0.09202363304970611, -0.17325419026447594, -0.7601308792297724, -1.4522034926331793, -2.0005493140271278, -2.207700882662819, -1.9941973200988719, -1.4257578025853603, -0.6918596728137806, -0.04236508030607049, 0.29726565616256234, 0.2042487750111041, -0.29604785280124946, -1.0334141647855937, -1.7450899420128754, -2.161005368091819, -2.0945646244184752, -1.5089128734182378, -0.5358038165863689, 0.5608751038880566, 1.4668272239612505, 1.9189190524091606, 1.7937284440109684, 1.1532776300774203, 0.23114309889335433, -0.6388901504263674, -1.1304945719044917, -1.0348939965229593], 'positive_zeros': ['1.51008882502341006757253193254430', '2.71904355305484860998769327283996', '4.15556038138719123885405847201694', '5.45834006401551436258061214975056', '6.12703243987095352421551891843842', '7.81229356765347982834276473698585', '8.624994435318074747412456594025339', '9.604336155420799240544733645748364', '10.27185399734461277503975208608065', '11.52773240506220881516800536628555'], 'prelabel': '2-378-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.227185525828505, 'root_number': '0.7559289460184545 - 0.6546536707079771*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.113592762914', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51008882502341006757253193254', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.71904355305484860998769327284', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15556038138719123885405847202', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '21.20', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/d/b/377/4'], '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': '2-378-21.20-c1-0-5', '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': '2-378-21.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': -0.1135927629142525, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51008882502341006757253193254', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1914265005438867454946313298300', 'Lhash_array': ['1914265005438867454946313298300'], 'label': '2-378-21.20-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/d/b/377/4'}