-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1179464751160881430101541712151', 'a10': -2, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 77.47086004104627, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '9702.1', 'coefficient_field': '1.1.1.1', 'conductor': 9702, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -2, 5], [1], [1, -1], [1, -7, 13], [1, -2, 17], [1, 0, 19], [1, -8, 23], [1, -5, 29], [1, 4, 31], [1, -4, 37], [1, -4, 41], [1, 8, 43], [1, -2, 47], [1, -6, 53], [1, -3, 59], [1, 1, 61], [1, -9, 67], [1, -2, 71], [1, 4, 73], [1, -9, 79], [1, -6, 83], [1, -6, 89], [1, 7, 97], [1, 9, 101], [1, 18, 103], [1, 2, 107], [1, 2, 109], [1, 5, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, -2, 5], 1]], [1], [[[1, -1], 1]], [[[1, -7, 13], 1]], [[[1, -2, 17], 1]], [[[1, 0, 19], 1]], [[[1, -8, 23], 1]], [[[1, -5, 29], 1]], [[[1, 4, 31], 1]], [[[1, -4, 37], 1]], [[[1, -4, 41], 1]], [[[1, 8, 43], 1]], [[[1, -2, 47], 1]], [[[1, -6, 53], 1]], [[[1, -3, 59], 1]], [[[1, 1, 61], 1]], [[[1, -9, 67], 1]], [[[1, -2, 71], 1]], [[[1, 4, 73], 1]], [[[1, -9, 79], 1]], [[[1, -6, 83], 1]], [[[1, -6, 89], 1]], [[[1, 7, 97], 1]], [[[1, 9, 101], 1]], [[[1, 18, 103], 1]], [[[1, 2, 107], 1]], [[[1, 2, 109], 1]], [[[1, 5, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 81, 'label': '2-9702-1.1-c1-0-81', 'leading_term': '2.38581764115166078144562245515000000000000000000000000000000000000000000000000000000000000', '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/9702/2/a/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.385817641151661, 2.3780491912986363, 2.3547486353247473, 2.3159362810027444, 2.2616652753473576, 2.192049002912654, 2.1072964860881562, 2.007753151392667, 1.8939439747676086, 1.7666158854023417, 1.6267763718965762, 1.4757254615407502, 1.3150785920218773, 1.1467783253811017, 0.9730933335920049, 0.7966035893812078, 0.6201712088804746, 0.44689690486625394, 0.2800625152098934, 0.12306056685000828, -0.020687683080704327, -0.14782382617386186, -0.2551511659245095, -0.3397381349657236, -0.3990231927077935, -0.4309178510957046, -0.433904276840052, -0.4071238126015447, -0.35045276024140354, -0.26456188732260233, -0.15095636155319409, -0.011993191095527078, 0.1491262484250414, 0.32839039167717765, 0.5210394151669615, 0.721655129743635, 0.9242781205632872, 1.1225504469788565, 1.3098812173426095, 1.4796313663177605, 1.6253130212421578, 1.7407979871520476, 1.8205291452600947, 1.8597279837624143, 1.8545910968398212, 1.8024683273213538, 1.7020153145618635, 1.5533135582617317, 1.3579517293225742, 1.11906284894213, 0.8413131052791316, 0.5308394607702931, 0.19513478949486684, -0.15711897044404735, -0.5162673123892042, -0.871945069290513, -1.2133776225439725, -1.5297135150268495, -1.8103789526906315, -2.0454432971288736, -2.2259835747876457, -2.344435318032181, -2.3949167604344135, -2.3735135721918876, -2.2785119653723642, -2.110569129600209, -1.8728115653614599, -1.5708539335956593, -1.2127334866581523, -0.8087579184666323, -0.37126748497739187, 0.0856846004427998, 0.5467263109208121, 0.9956252145524787, 1.4157980001335366, 1.7908554392523337, 2.10516502593231, 2.344412018147118, 2.496138738924518, 2.55024184683373, 2.4994079000513527, 2.3394689305454817, 2.069661900564072, 1.69277878653691, 1.2151975484236135, 0.6467882883847319, 0.0006933473290084449, -0.7070152256176125, -1.4577926420194924, -2.231179957856663, -3.0054471225684596, -3.758299513440083, -4.467623815344028, -5.112246771832431, -5.672678954133439, -6.1318153646307465, -6.475565466499261, -6.693387123429975, -6.778701908869036, -6.729173222292828, -6.546833504760242, -6.238052409365227, -5.813343849691969, -5.287016187006537, -4.67667617022876, -4.002603346870181, -3.2870172539530116, -2.553264523529675, -1.8249568696232996, -1.1250935686969514, -0.47520335515601264, 0.10545946926760492, 0.6006315051922895, 0.9976391323391044, 1.2878540097513307, 1.466985005135976, 1.5351929388404846, 1.4970218376551827, 1.3611481318417988, 1.1399570659453584, 0.8489631861382878, 0.5060987709848668, 0.1309001620150309, -0.25637316924359527, -0.635648558169649, -0.9879390512403533, -1.2961912283116102, -1.5460436865786846, -1.7264614867989823, -1.830217059806377, -1.8541947062384168, -1.799503619610444, -1.6713929860074102, -1.4789717791615904, -1.2347449636290473, -0.9539865157140343, -0.6539775546781567, -0.35314455716056414, -0.0701377651864256, 0.1771067820917431, 0.3722768547133002, 0.5015213434799413, 0.5541742649353231, 0.5233293842091697, 0.4062361314659332, 0.20449576077314896, -0.07595387893239368, -0.4250664608611246, -0.82911932858378, -1.2713307394265054, -1.7326339666736479, -2.192571975849322, -2.6302700147096565, -3.02543909959416, -3.3593612944660225, -3.615808006488177, -3.7818452879002407, -3.84848524026569, -3.8111498454385666, -3.6699225674618625, -3.4295734530612396, -3.099354699615907, -2.692575199115019, -2.225973819418327, -1.7189215687427084, -1.1924917583634043, -0.6684443479757438, -0.16817543377629904, 0.2883149607872823, 0.6833841598659307, 1.0025878124267034, 1.2353570858037686, 1.3754768040862162, 1.4213394121161957, 1.3759612266382566, 1.2467598514628482, 1.0451042347696327, 0.7856609642592379, 0.48557137470848893, 0.16350327769641296, -0.16137190620152267, -0.47042153390072666, -0.7465572087049243, -0.975148592664324, -1.1447955242953425, -1.2479158914459558, -1.2811166108555483, -1.24532686924901, -1.1456858595980275, -0.9911908931907787, -0.7941252324683911, -0.5692975176050463, -0.3331355372081756, -0.10268568599922642, 0.10542475719865756, 0.27600277787470706, 0.3962231939834997, 0.4564257595164415, 0.45072823503524845, 0.37741799899228207, 0.23909720739496815, 0.04257055871842054, -0.2015203951280318, -0.47929757631914416, -0.774448525727965, -1.0691852321555393, -1.345304641890857, -1.585289029873971, -1.7733811098763592, -1.8965692263315774, -1.9454222492063014, -1.9147217086596944, -1.8038498651788106, -1.6169062223098312, -1.3625406938529159, -1.0535083487075152, -0.7059674090926306, -0.33855798242346413, 0.02868709183609284, 0.3755367664266832, 0.6827915248242687, 0.9334745556520273, 1.1139112904851443, 1.2146293230305332, 1.2310200012966894, 1.163715986870679, 1.0186551202792031, 0.8068191348447686, 0.5436550899137628, 0.248206722133238, -0.057998912721399856, -0.352248228099167, -0.6120474119038821, -0.8165558097336267, -0.9479601419404765, -0.9927045709856004, -0.942498014601006, -0.7950313461854189, -0.5543526886080299, -0.2308680717683813, 0.15904376083883362, 0.5937908668595854, 1.0476677625128257, 1.4922398431899586, 1.897938734456787, 2.2357802031341314, 2.4791065994408883, 2.6052517171125738, 2.5970278291042166, 2.443942516035951, 2.1430664305304132, 1.699491664806627, 1.126342929032362, 0.4443290589580448, -0.31915098613523574, -1.131307052198858, -1.9555964358431752], 'positive_zeros': ['0.930433631277048359621158016997499', '1.45683528128934257946421228553580', '2.46365880421015085487796170448669', '3.31941568253155764991923042646466', '4.03129780667914228339613638582190', '5.19411244710029851212503471851425', '5.73463467816586580011825936375313', '6.48124991250803522400862921820409', '6.83219647419296523001917030474300', '7.84477951969434096310577982884198'], 'prelabel': '2-9702-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.801753236773129, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1671573157118953136, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.930433631277048359621158016997', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.45683528128934257946421228554', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.46365880421015085487796170449', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 77.47086004104627, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 9702, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 2, 0, 0, -1, 0, -2, 1, 0, 7, 0, 0, 1, 2, 0, 0, 2, 0, -1, 8, 0, -1, -7, 0, 0, 5, 0, -4, -1, 0, -2, 0, 0, 4, 0, 0, -2, 4, 0, -8, 1, 0, -8, 2, 0, 0, 1, 0, 7, 6, 0, 2, 0, 0, -5, 3, 0, -1, 4, 0, 1, 14, 0, 9, 2, 0, 0, 2, 0, -4, -4, 0, 0, 0, 0, 9, 2, 0, -4, 6, 0, 4, 8, 0, -1, 6, 0, 0, 8, 0, -2, 0, 0, -7, 0, 0, -1], 'euler11': [1, -1, 0], 'euler13': [1, -7, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, -8, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -4, 41], 'euler43': [1, 8, 43], 'euler47': [1, -2, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -3, 59], 'euler61': [1, 1, 61], 'euler67': [1, -9, 67], 'euler7': [1, 0, 0], 'euler71': [1, -2, 71], 'euler73': [1, 4, 73], 'euler79': [1, -9, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -2, 5], [1, 0, 0], [1, -1, 0], [1, -7, 13], [1, -2, 17], [1, 0, 19], [1, -8, 23], [1, -5, 29], [1, 4, 31], [1, -4, 37], [1, -4, 41], [1, 8, 43], [1, -2, 47], [1, -6, 53], [1, -3, 59], [1, 1, 61], [1, -9, 67], [1, -2, 71], [1, 4, 73], [1, -9, 79], [1, -6, 83], [1, -6, 89], [1, 7, 97]], 'index': 81, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/9702/y', 'ModularForm/GL2/Q/holomorphic/9702/2/a/y/1/1', 'ModularForm/GL2/Q/holomorphic/9702/2/a/y'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-9702-1.1-c1-0-81', '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': '2-9702-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 8.801753236773129, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1671573157118953136, 'z1': {'__RealLiteral__': 0, 'data': '0.930433631277048359621158016997', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
-
id: 22868386
{'Lhash': '1179464751160881430101541712151', 'Lhash_array': ['1179464751160881430101541712151'], 'label': '2-9702-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9702/2/a/y'}
-
id: 24589779
{'Lhash': '1179464751160881430101541712151', 'Lhash_array': ['1179464751160881430101541712151'], 'label': '2-9702-1.1-c1-0-81', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9702/2/a/y/1/1'}
-
id: 38242
{'Lhash': '1671573157118953136', 'Lhash_array': ['1671573157118953136'], 'label': '2-9702-1.1-c1-0-81', 'type': 'ECQ', 'url': 'EllipticCurve/Q/9702/y'}