-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1418592794985686995314860700773', 'a10': 0, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': -1, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.1304369398954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [31, [1, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '4650.1', 'coefficient_field': '1.1.1.1', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 1, 7], [1, 5, 11], [1, -4, 13], [1, 0, 17], [1, 5, 19], [1, -9, 23], [1, 2, 29], [1, -1], [1, 8, 37], [1, -6, 41], [1, 1, 43], [1, -12, 47], [1, -13, 53], [1, -10, 59], [1, 14, 61], [1, 14, 67], [1, 9, 71], [1, -9, 73], [1, -5, 79], [1, 6, 83], [1, -3, 89], [1, -18, 97], [1, 7, 101], [1, 8, 103], [1, 11, 107], [1, 2, 109], [1, 13, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [1], [[[1, 1, 7], 1]], [[[1, 5, 11], 1]], [[[1, -4, 13], 1]], [[[1, 0, 17], 1]], [[[1, 5, 19], 1]], [[[1, -9, 23], 1]], [[[1, 2, 29], 1]], [[[1, -1], 1]], [[[1, 8, 37], 1]], [[[1, -6, 41], 1]], [[[1, 1, 43], 1]], [[[1, -12, 47], 1]], [[[1, -13, 53], 1]], [[[1, -10, 59], 1]], [[[1, 14, 61], 1]], [[[1, 14, 67], 1]], [[[1, 9, 71], 1]], [[[1, -9, 73], 1]], [[[1, -5, 79], 1]], [[[1, 6, 83], 1]], [[[1, -3, 89], 1]], [[[1, -18, 97], 1]], [[[1, 7, 101], 1]], [[[1, 8, 103], 1]], [[[1, 11, 107], 1]], [[[1, 2, 109], 1]], [[[1, 13, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 50, 'label': '2-4650-1.1-c1-0-50', '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/4650/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.710414857349677e-61, 0.10175576150227636, 0.20263052652526312, 0.30172014763854166, 0.39807603677490505, 0.4906874692495539, 0.5784689723666943, 0.6602539638737681, 0.734795431123385, 0.800774053919512, 0.8568138024091464, 0.9015047068983835, 0.9334322102633124, 0.9512122783429994, 0.9535312559731995, 0.939189309566361, 0.9071461840627987, 0.8565679164278119, 0.7868730854686062, 0.697777136786165, 0.5893333025460764, 0.46196864054742126, 0.3165137489911273, 0.15422477607451193, -0.023203559357257462, -0.2136350854032006, -0.41450040840584496, -0.6228170194978461, -0.8352217847037083, -1.048016036777366, -1.2572231640490048, -1.4586582416820824, -1.6480088813570692, -1.82092609546858, -1.973123591744174, -2.100483545152533, -2.19916654824716, -2.2657231313211046, -2.297203982623839, -2.291265798750773, -2.246269567692655, -2.161368042199216, -2.0365792076261124, -1.8728426927012736, -1.6720563175157839, -1.4370903214582977, -1.1717772625226643, -0.8808761227865378, -0.5700097837502153, -0.2455757370181194, 0.0853693454832602, 0.41524976102172906, 0.7361334120481943, 1.0399138909228522, 1.3185082048959078, 1.5640656223867824, 1.76918249802437, 1.9271174230237016, 2.032000673344041, 2.079031712085255, 2.064658462522636, 1.9867322173836544, 1.8446323965238645, 1.6393559112617555, 1.3735666350910196, 1.0516014064059362, 0.6794300815453727, 0.2645683914950738, -0.18405629771540535, -0.6562847989255528, -1.1409485140889337, -1.6261300178593017, -2.099456004929933, -2.548415511793735, -2.960695198518315, -3.324522551242181, -3.629007182886193, -3.8644700038177637, -4.022749934378816, -4.097478057027002, -4.084309667125082, -3.981105577041249, -3.7880552456034, -3.50773581978262, -3.1451029519407685, -2.707411247326094, -2.204064346132626, -1.6463968873403467, -1.0473928661576244, -0.42134710727409186, 0.21652134549225144, 0.8504932531814823, 1.4647983622875622, 2.0440762471171947, 2.573834488165306, 3.04088948272203, 3.433775290684075, 3.743106526180293, 3.9618824130125954, 4.085720709947311, 4.11301224332345, 4.044989204422387, 3.8857031063286396, 3.6419112638710467, 3.322873762978064, 2.940066015875865, 2.5068150442207044, 2.037870480422785, 1.548923817939619, 1.0560915712420391, 0.5753796339302877, 0.12214717288817867, -0.2894111899312839, -0.646746414013472, -0.9393817412128128, -1.159269116150191, -1.3010616188694055, -1.3622910039066582, -1.343442715897086, -1.2479243922039212, -1.0819277398948095, -0.8541876464549605, -0.5756463013959198, -0.2590338171963016, 0.08161980614754413, 0.43152366794560265, 0.7756959588738317, 1.0995434944745563, 1.3894286104492555, 1.6332013748454115, 1.8206760739050076, 1.9440327790092569, 1.9981274492822474, 1.9806973818507114, 1.8924527721613704, 1.7370495454202537, 1.520943300131371, 1.253128982749437, 0.9447755964463166, 0.6087696433827009, 0.25918492177526015, -0.08930042580809032, -0.4220162380870793, -0.7249170988778103, -0.9851780454142753, -1.1917442183915483, -1.335810993361948, -1.4112136856037056, -1.414709397850955, -1.3461378556371335, -1.208452984623774, -1.0076223331653988, -0.7523970128666573, -0.45396038653788723, -0.12546903811794405, 0.21849562075413778, 0.5625426359614956, 0.891127995602596, 1.1892244556117295, 1.4429758522175322, 1.6403072898686957, 1.7714640890295317, 1.8294550870317752, 1.8103797124315728, 1.713623052837885, 1.5419087152224555, 1.3012054044841295, 1.000489559025882, 0.6513728011225021, 0.2676090981741635, -0.13549789194883455, -0.5417620637887917, -0.9348277659069401, -1.2988969699232484, -1.6194382291132525, -1.8838453128004962, -2.082015228539606, -2.2068185758085983, -2.254439691301434, -2.224569664006789, -2.120441780543246, -1.9487060252789177, -1.7191465903653784, -1.4442536138329165, -1.138667221454477, -0.8185180742937284, -0.5006937203448056, -0.20206385926672712, 0.061300047057463156, 0.27487468357311795, 0.4263691574176454, 0.5063111334798156, 0.5085065406574397, 0.43035017240310836, 0.2729712718293985, 0.0412058092239003, -0.2566047210106871, -0.6089799163711008, -1.0018164588855318, -1.4190301389904, -1.8432942792825489, -2.256839984574978, -2.642280307902377, -2.983418879225781, -3.266003899088058, -3.478390667011529, -3.61207991414324, -3.6621049700989783, -3.627247958596812, -3.5100734545235808, -3.3167769563065517, -3.0568547002667845, -2.7426103156263726, -2.3885221389649196, -2.0105022479909183, -1.625084055115964, -1.2485793060091583, -0.896247324781863, -0.5815192001382848, -0.3153172858218773, -0.10550597358307665, 0.043496624847800744, 0.13092439048103377, 0.15967379029609213, 0.13611681324331834, 0.06972398463070428, -0.02748475821009937, -0.14163424714803227, -0.25779818374113955, -0.36087164997315574, -0.4364661970427664, -0.4717796708635128, -0.4563933896774144, -0.3829522392299572, -0.24768859293776818, -0.050758470513606, 0.20363232697395753, 0.5073236727173014, 0.8485181919862208, 1.212308203136427, 1.58138932988986, 1.936927125754384, 2.259534121685965, 2.5303078204379976, 2.731875725040537, 2.849391795202672, 2.8714299278545417, 2.790724161886368, 2.604712165462858, 2.3158478818578927, 1.9316605549073398, 1.4645501791725597, 0.9313230828950236, 0.35248515427746674, -0.24867656029801044, -0.8471812344554107, -1.4175579964118834], 'positive_zeros': ['1.11907239639241425993466858056024', '2.33168793702765242932465964579897', '3.16862760216165321198410729321516', '4.20286458843937323543842719075930', '5.21648710926090040275192227103336', '5.80145992300714357198572964663421', '6.59723825959542964745887016379718', '7.23598419140195569877606113214745', '7.953128662222385189458196963311568'], 'prelabel': '2-4650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.093474947835217, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 402132723424937070, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11907239639241425993466858056', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33168793702765242932465964580', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16862760216165321198410729322', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 37.1304369398954, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -5, -1, 4, 1, 0, 1, 0, -1, -5, 0, 1, 5, 9, 1, 0, -4, -1, -1, -2, 0, 1, -1, 5, 0, 0, 1, -8, 5, -4, 0, 6, -1, -1, -5, 0, -9, 12, -1, -6, 0, 0, 4, 13, 1, 0, 1, 5, 2, 10, 0, -14, -1, -1, 1, 0, -5, -14, 0, -9, 0, -9, -1, 9, 8, 0, -5, 5, 4, 5, 0, 1, -6, -6, 1, 0, 1, 2, 5, 3, 0, -4, 9, -1, -12, 0, 1, 18, 6, -5, 0], 'euler11': [1, 5, 11], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 5, 19], 'euler2': [1, 1, 0], 'euler23': [1, -9, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, -1, 0], 'euler37': [1, 8, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -13, 53], 'euler59': [1, -10, 59], 'euler61': [1, 14, 61], 'euler67': [1, 14, 67], 'euler7': [1, 1, 7], 'euler71': [1, 9, 71], 'euler73': [1, -9, 73], 'euler79': [1, -5, 79], 'euler83': [1, 6, 83], 'euler89': [1, -3, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 1, 7], [1, 5, 11], [1, -4, 13], [1, 0, 17], [1, 5, 19], [1, -9, 23], [1, 2, 29], [1, -1, 0], [1, 8, 37], [1, -6, 41], [1, 1, 43], [1, -12, 47], [1, -13, 53], [1, -10, 59], [1, 14, 61], [1, 14, 67], [1, 9, 71], [1, -9, 73], [1, -5, 79], [1, 6, 83], [1, -3, 89], [1, -18, 97]], 'index': 50, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/4650/f', 'ModularForm/GL2/Q/holomorphic/4650/2/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/4650/2/a/f'], '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': '2-4650-1.1-c1-0-50', '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': '2-4650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.093474947835217, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 402132723424937070, 'z1': {'__RealLiteral__': 0, 'data': '1.11907239639241425993466858056', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
-
id: 19977874
{'Lhash': '1418592794985686995314860700773', 'Lhash_array': ['1418592794985686995314860700773'], 'label': '2-4650-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/a/f'}
-
id: 24566830
{'Lhash': '1418592794985686995314860700773', 'Lhash_array': ['1418592794985686995314860700773'], 'label': '2-4650-1.1-c1-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/a/f/1/1'}
-
id: 100444
{'Lhash': '402132723424937070', 'Lhash_array': ['402132723424937070'], 'label': '2-4650-1.1-c1-0-50', 'type': 'ECQ', 'url': 'EllipticCurve/Q/4650/f'}