-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '935987049608051240186089957031', 'a10': [-0.36602540378443865, 0.6339745962155614], 'a2': [-1.0, 1.0], 'a3': [-0.8660254037844386, -0.5], 'a4': [0.0, -2.0], 'a5': [0.5, -0.13397459621556135], 'a6': [1.3660254037844386, -0.36602540378443865], 'a7': [2.366025403784439, 1.3660254037844386], 'a8': [2.0, 2.0], 'a9': [0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.0]]], [3, [[1.0, 0], [0.8660254037844386, 0.5]]], [37, [[1.0, 0], [5.5, -2.598076211353316]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.547', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '1524451410566688770410112954476', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.0]], [[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, 0.13397459621556135], [4.330127018922194, -2.5]], [[1.0, 0], [-2.366025403784439, -1.3660254037844386], [3.5, 6.06217782649107]], [[1.0, 0], [0, 1.2679491924311228], [-11.0, 0]], [[1.0, 0], [5.098076211353316, -1.3660254037844386], [11.258330249197702, -6.5]], [[1.0, 0], [-5.964101615137754, -1.598076211353316], [14.722431864335457, 8.5]], [[1.0, 0], [-1.098076211353316, -4.098076211353316], [-16.454482671904334, 9.5]], [[1.0, 0], [0.7320508075688773, 0.7320508075688773], [0, 23.0]], [[1.0, 0], [-4.830127018922194, 4.830127018922194], [0, -29.0]], [[1.0, 0], [-3.196152422706632, 3.196152422706632], [0, -31.0]], [[1.0, 0], [5.5, -2.598076211353316]], [[1.0, 0], [-9.86602540378444, -5.696152422706632], [20.5, 35.50704155516198]], [[1.0, 0], [-1.0, 1.0], [0, -43.0]], [[1.0, 0], [0, -2.196152422706632], [-47.0, 0]], [[1.0, 0], [11.196152422706632, -6.464101615137754], [26.5, -45.89934640057525]], [[1.0, 0], [-13.660254037844387, -3.6602540378443864], [51.09549882328188, 29.5]], [[1.0, 0], [-2.133974596215561, -7.964101615137754], [-52.827549630850754, 30.5]], [[1.0, 0], [-11.36602540378444, -6.56217782649107], [33.5, 58.023702053557386]], [[1.0, 0], [-10.098076211353316, -5.830127018922194], [35.5, 61.48780366869514]], [[1.0, 0], [0, 0], [-73.0, 0]], [[1.0, 0], [3.366025403784439, -0.9019237886466841], [68.41600689897065, -39.5]], [[1.0, 0], [-1.4641016151377546, -2.5358983848622456], [-41.5, 71.88010851410841]], [[1.0, 0], [0.6961524227066319, -2.598076211353316], [-77.07626093681505, -44.5]], [[1.0, 0], [12.758330249197702, -12.758330249197702], [0, -97.0]], [[1.0, 0], [14.856406460551018, 0], [101.0, 0]], [[1.0, 0], [-4.464101615137754, 4.464101615137754], [0, -103.0]], [[1.0, 0], [-5.830127018922194, 10.098076211353316], [-53.5, -92.66471820493493]], [[1.0, 0], [-1.8397459621556136, 6.866025403784438], [-94.39676901250381, -54.5]], [[1.0, 0], [0.4378221735089295, -1.6339745962155614], [-97.86087062764156, -56.5]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 21, 'label': '2-888-296.251-c1-0-21', '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/888/2/bu/a/547/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9661805213111447, 0.8661058624533803, 0.7427393500944106, 0.5934910006864412, 0.41592638396239895, 0.20958060900849737, -0.022529218902541483, -0.27290365304426184, -0.5291756658393663, -0.7743927897738925, -0.987993350569862, -1.147468862814352, -1.2306448517592123, -1.2184285175622287, -1.0977755717316926, -0.8645376006195293, -0.5257850159081838, -0.1011780952393912, 0.37700453204720275, 0.8654651530893458, 1.313225385389563, 1.6665847723177771, 1.8753178175343124, 1.8994677141053633, 1.7158805641125134, 1.323499591173237, 0.7464438281882263, 0.03405552388158051, -0.7425804740231036, -1.4976856553105937, -2.140901238074846, -2.5894047224359773, -2.780488466796989, -2.68275105493436, -2.3039971563168202, -1.6941908828533407, -0.9423680442460524, -0.1672372275730191, 0.49781310849502036, 0.9235807424345845, 1.0052202643737251, 0.6806269739105175, -0.05611780510944604, -1.1489191927350177, -2.4831473936731348, -3.898714243676082, -5.211438481516451, -6.239850335039065, -6.8333927163227255, -6.897385500518039, -6.410302787325519, -5.429915243934164, -4.086564113232162, -2.564006144359198, -1.0705313401084247, 0.19501382874870168, 1.0764632951359643, 1.4868112219007543, 1.4228681305919073, 0.9650081230203129, 0.2616166056193917, -0.4992317819090665, -1.1257604636557093, -1.4593520083334053, -1.4050902438135686, -0.9498315544565907, -0.16400004584066374, 0.8134692769607406, 1.8041411753164784, 2.6271581568905047, 3.1366640151608887, 3.251621615041574, 2.971571498475721, 2.3748451217971542, 1.5995794298849981, 0.8117453431714585, 0.16741822932935338, -0.22204761831501868, -0.3138239064513971, -0.14075099883353884, 0.19993153288190255, 0.5735869630576669, 0.8443243596044819, 0.9112778407526151, 0.7357671388423499, 0.35215630839609546, -0.14079296424347895, -0.6063096258256602, -0.9072482007582099, -0.9452156998814699, -0.6905765310754661, -0.19462614661994468, 0.42044226898343795, 0.9923852853828166, 1.3634130153979611, 1.4269654427423368, 1.1639258334824525, 0.6573438332133869, 0.07974177761680894, -0.34593982670911644, -0.40346044136824954, 0.055415814527516524, 1.061604580495089, 2.5057034156641134, 4.1498261917941495, 5.674253490139337, 6.74970216114766, 7.1185756812982515, 6.664949801584435, 5.454495926502828, 3.732007454429868, 1.874297224626002, 0.30754881160070213, -0.5921685139806555, -0.5911948389154709, 0.34001905148019995, 2.0125047555592412, 4.0570456969880855, 6.007331470269745, 7.40855751293587, 7.925025734448792, 7.419944066610182, 5.987213686719968, 3.926982118935933, 1.67108057422515, -0.32261204495903306, -1.6798062738022614, -2.195458707895201, -1.8740034346257586, -0.9149852693085812, 0.3503913015928316, 1.553213438078054, 2.384897542420705, 2.6724911672870455, 2.4115265184183325, 1.7492893276017838, 0.9257767604634433, 0.19167832247895975, -0.27109078787588803, -0.40224684364302493, -0.274002472148537, -0.05780674016932342, 0.041370759132155675, -0.13858388152130874, -0.654999434188478, -1.4334638660724655, -2.2852554017826363, -2.964340642613091, -3.2462193199968707, -3.0034405163155764, -2.2530829507119656, -1.1599001343425204, 0.007328063868629346, 0.9537250729012026, 1.4466887148770924, 1.3869109351645763, 0.8391366325658506, 0.01212772254705862, -0.8066336406102558, -1.3413115404141, -1.4145058461217406, -1.002476795474445, -0.2406135363501148, 0.6230743365579743, 1.3116010528620887, 1.6123867647444101, 1.4492139043551049, 0.9081309710579745, 0.2076518966730032, -0.37773125560504406, -0.6154908778872062, -0.4010296975436103, 0.19887086674832477, 0.9622121237850083, 1.5847562820029135, 1.7871822708924414, 1.4207276268029603, 0.5341349051379487, -0.624122710225461, -1.6736998089813429, -2.2220230641320677, -1.998605971783349, -0.9595499059146079, 0.6750852628781431, 2.4682887216655196, 3.8877928328973037, 4.467567450944324, 3.9592168541315753, 2.4239956552698403, 0.23290368934262393, -2.029611020306867, -3.7321464382902043, -4.383489746279785, -3.7826722227519882, -2.0843030343313877, 0.24282400549281988, 2.552634346801226, 4.21275144713753, 4.790730846669657, 4.17798525653712, 2.613511194987629, 0.6013592291252218, -1.2505310176781834, -2.41795621402206, -2.6149203399755914, -1.8673312704815925, -0.48558892615030363, 1.0509114909052217, 2.256089715436833, 2.791241628269375, 2.560795659066827, 1.7213941055092523, 0.6064941857267353, -0.4026028260817006, -1.0114238217489275, -1.1052261039038465, -0.7698077033579791, -0.23725386077469138, 0.21888815089402958, 0.3968968348315043, 0.24497755896806397, -0.12468256813631697, -0.489425518279284, -0.614482306761085, -0.35626570811256436, 0.2709871745846225, 1.0923283926757332, 1.8349928128823676, 2.2330439223085135, 2.1328227054123152, 1.5571703498644534, 0.7018434403614194, -0.13619702667263128, -0.6719092984622721, -0.7427861258346644, -0.37270759375523177, 0.23801571757697731, 0.7948885963125674, 1.033164691794669, 0.8347330841386653, 0.28966912008343726, -0.32613843707867757, -0.6537493547727784, -0.3982560180002653, 0.5360631074396106, 1.9780257927799603, 3.5221929839643797, 4.657916284467979, 4.953046113037672, 4.226385119705664, 2.64243302688703, 0.6866133867651373, -0.9789350385266852, -1.7346233887924905, -1.223107591295547, 0.5094806356728251, 3.005200436611934], 'positive_zeros': ['0.73836359122895138429544384409929', '2.15229137424105223579925658079693', '3.38060627064021495013109666427258', '4.65368437821963455248805605088172', '5.24236028948356383276878098289195', '6.85338089396733834053705062810973', '7.54241441450711061265993030037698', '8.272146796916316202574478220073170', '9.543268447283632471150469208624014', '9.931474636563045276139988517322030'], 'prelabel': '2-888-296.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.40069723848160216, 'root_number': '0.3069330231437937 - 0.9517311171249007*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.200348619241', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.73836359122895138429544384410', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15229137424105223579925658080', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38060627064021495013109666427', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.090715699489701, 'bad_primes': [2, 3, 37], 'central_character': '296.251', 'conductor': 888, 'conductor_radical': 222, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/888/2/bu/a/547/1'], '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': '2-888-296.251-c1-0-21', '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': '2-888-296.251-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': -0.20034861924080108, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.73836359122895138429544384410', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '935987049608051240186089957031', 'Lhash_array': ['935987049608051240186089957031'], 'label': '2-888-296.251-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/888/2/bu/a/547/1'}