-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1915540023100082254002465795942', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.6180339887498949, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.618033988749895, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.065546335746074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.1', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.6180339887498949, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.4721359549995796, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.381966011250105, 0], [17.0, 0]], [[1.0, 0], [0.38196601125010515, 0], [19.0, 0]], [[1.0, 0], [8.47213595499958, 0], [23.0, 0]], [[1.0, 0], [4.618033988749895, 0], [29.0, 0]], [[1.0, 0], [3.090169943749474, 0], [31.0, 0]], [[1.0, 0], [-7.0901699437494745, 0], [37.0, 0]], [[1.0, 0], [6.381966011250105, 0], [41.0, 0]], [[1.0, 0], [5.23606797749979, 0], [43.0, 0]], [[1.0, 0], [4.47213595499958, 0], [47.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [53.0, 0]], [[1.0, 0], [-13.562305898749054, 0], [59.0, 0]], [[1.0, 0], [12.47213595499958, 0], [61.0, 0]], [[1.0, 0], [0.38196601125010515, 0], [67.0, 0]], [[1.0, 0], [15.70820393249937, 0], [71.0, 0]], [[1.0, 0], [6.47213595499958, 0], [73.0, 0]], [[1.0, 0], [-16.562305898749052, 0], [79.0, 0]], [[1.0, 0], [6.0, 0], [83.0, 0]], [[1.0, 0], [8.326237921249264, 0], [89.0, 0]], [[1.0, 0], [2.291796067500631, 0], [97.0, 0]], [[1.0, 0], [0, 0], [101.0, 0]], [[1.0, 0], [-11.618033988749895, 0], [103.0, 0]], [[1.0, 0], [-14.652475842498529, 0], [107.0, 0]], [[1.0, 0], [10.94427190999916, 0], [109.0, 0]], [[1.0, 0], [11.23606797749979, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 57, 'label': '2-3640-1.1-c1-0-57', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3640/2/a/n/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.204170532336466e-61, 0.17405818171893395, 0.34743604248538945, 0.5194046501252806, 0.6891412422909122, 0.8556905197724155, 1.0179350696629896, 1.1745768767582156, 1.32413115209296, 1.4649329887043105, 1.5951567077064224, 1.7128472174187073, 1.815962284147603, 1.902424295736548, 1.9701798678390674, 2.0172654747086187, 2.041877160529386, 2.042442289258416, 2.0176912128825375, 1.966726678613836, 1.8890887586170928, 1.7848130785274858, 1.6544801521673687, 1.499253708718558, 1.320906033538279, 1.121828541510426, 0.905026066648253, 0.6740936851757372, 0.43317529000952054, 0.18690359771941073, -0.05967821330773858, -0.30121247377288557, -0.5321392534531768, -0.7468228975380704, -0.9396903203344877, -1.1053779383401767, -1.2388836046800615, -1.335719458075009, -1.3920612435984534, -1.404889419929785, -1.3721172569389422, -1.2927011635134615, -1.1667286799816439, -0.9954799290723528, -0.7814588455617366, -0.5283911932431027, -0.24118721809593074, 0.07413223832148554, 0.4105462542606855, 0.7601798911668843, 1.1144835059957006, 1.4644417854715535, 1.8008077799642026, 2.114356096286571, 2.396148412283614, 2.6378036455456715, 2.8317644851357238, 2.971551615529769, 3.0519968564223148, 3.069446633129361, 3.0219276931567887, 2.9092677976640418, 2.733165233178765, 2.497202388216172, 2.206800288645169, 1.8691128403561854, 1.492861532971277, 1.0881134496439102, 0.6660075336312969, 0.2384361053414779, -0.18230947547804777, -0.5839184278200255, -0.9544534896946745, -1.2827442041063828, -1.5587669795283683, -1.7739982284637443, -1.9217272621989316, -1.9973165066228307, -1.9983979962174372, -1.9249969740210489, -1.7795757271690005, -1.5669934535131915, -1.2943808996820896, -0.9709316339209534, -0.6076150047791529, -0.21681896720969, 0.18806609516213896, 0.593108784183191, 0.9843273593428657, 1.3481920141372128, 1.6721200542871915, 1.9449449242042975, 2.157340419197516, 2.3021825711153987, 2.374833590559917, 2.3733348440488538, 2.298499062804588, 2.1538957148457527, 1.9457275907974207, 1.6826010011133923, 1.3751963863211927, 1.0358504204265466, 0.6780646559431649, 0.3159592374205869, -0.03630696777759601, -0.36512645295512386, -0.6580189010205402, -0.9041681916834761, -1.0948969657172014, -1.224057114255049, -1.288317546506179, -1.2873344784184155, -1.2237941415839588, -1.1033230605460151, -0.9342666787657371, -0.7273428945776018, -0.4951827482398847, -0.25177582402742527, -0.011842647508282254, 0.20983976449940586, 0.3991302086619119, 0.5432028331117303, 0.6311829804048241, 0.6547094822907966, 0.6083960093713543, 0.4901678520897942, 0.30145547320875016, 0.047232139786809166, -0.26411032469375423, -0.6210464134143353, -1.0093538006130118, -1.412686353928978, -1.813260750953382, -2.1926282924342666, -2.5324987773137706, -2.81557997121014, -3.026394460690392, -3.1520356731076395, -3.1828266112776493, -3.1128483767358155, -2.94031072345158, -2.667743502486136, -2.3019956584066423, -1.8540370862503317, -1.3385677678959664, -0.7734477586121239, -0.178970352563889, 0.4229913104647974, 1.0099272303324218, 1.5596810389179858, 2.051442674807091, 2.466696762928978, 2.79008127053431, 3.010114270755159, 3.11975201780498, 3.1167488189470745, 3.003798073148756, 2.7884439424454848, 2.482763965972269, 2.1028340046949894, 1.667997677340365, 1.1999723752939824, 0.7218325139750705, 0.2569174319023222, -0.1722840936233625, -0.545218663491602, -0.8442689125778247, -1.0556197401379106, -1.1699456527441205, -1.1828828993929323, -1.0952602018996387, -0.9130735213990211, -0.6472028972407753, -0.3128823286595823, 0.07105370929926007, 0.48311186729447303, 0.9002243170250172, 1.2989226732087849, 1.6565428161087787, 1.9523995436470554, 2.168870636876834, 2.292333705214175, 2.313905953980905, 2.229946492413317, 2.0422925331412, 1.758214253621667, 1.390087524184328, 0.9547984161695499, 0.4729076167188525, -0.03238416629907672, -0.5364177345054938, -1.014343383565115, -1.442409534384387, -1.7992042947340199, -2.0667839073302607, -2.2316272663534393, -2.2853642445908777, -2.2252370637151526, -2.054267789656803, -1.7811205332236644, -1.4196632690592703, -0.9882504784361319, -0.5087631834048253, -0.005456515719888977, 0.4963240199884684, 0.9714886203253311, 1.3965385062221305, 1.750817262855576, 2.0176088678091504, 2.185020877449857, 2.2466025626132513, 2.20166205223443, 2.055263005807928, 1.8178991038562573, 1.504862741630116, 1.1353417205038998, 0.7312934598449683, 0.3161593826096276, -0.08650812549314095, -0.4544280285108634, -0.7679026976772182, -1.0109833459489082, -1.1724200531034719, -1.246339234313111, -1.2326064989152639, -1.1368505806619422, -0.9701434154657558, -0.748351403336587, -0.49119227101576657, -0.22104961685267402, 0.03838788516188405, 0.2635844325170377, 0.4326271875294173, 0.5266215655807805, 0.5309278846237145, 0.4361636265706358, 0.2389082214139621, -0.05793616511902788, -0.44515478812373016, -0.9076069005051629, -1.4249720883864971, -1.9728181930675543, -2.523933047457807, -3.0498457557231355, -3.5224508757146795, -3.91564142696276, -4.206854666280581, -4.378438256756655, -4.418753678871173, -4.322948036870978, -4.093344030166795, -3.7394197479304396, -3.277373850901726, -2.7292962307020483, -2.1219879254757044, -1.48549548862135, -0.8514428341470401], 'positive_zeros': ['1.51109463660980875131059846007666', '2.37512246164586866441784118169881', '3.53248685223367240810849843416406', '4.34370917078153160969723114031258', '5.27588964375858326568990371452121', '5.99477111280608324298256454865932', '6.45751529802274101618450950947180', '7.42914088619605982098954106374257', '8.307065685524497764506402086081029'], 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51109463660980875131059846008', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37512246164586866441784118170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53248685223367240810849843416', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 29.065546335746074, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/2/a/n/1/1'], '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': '2-3640-1.1-c1-0-57', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.51109463660980875131059846008', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1915540023100082254002465795942', 'Lhash_array': ['1915540023100082254002465795942'], 'label': '2-3640-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/2/a/n/1/1'}