-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '596524369996075980269309845024', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-0.8090169943749475, 0.5877852522924731], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.30901699437494745, 0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]]], 'bad_primes': [2, 5], 'central_character': '3200.2879', 'coefficient_field': 'CDF', 'conductor': 3200, 'conductor_radical': 10, 'conjugate': '2102838563230367864010603503557', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.5, -1.5388417685876268], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.118033988749895, 1.5388417685876268], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.118033988749895, -1.5388417685876268], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [-0.19098300562505258, -0.5877852522924731], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [-0.5, -1.5388417685876268], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [1.3090169943749475, 0.9510565162951535], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [1.118033988749895, 0.36327126400268045], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-1.118033988749895, -0.36327126400268045], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.19098300562505258, -0.5877852522924731], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.118033988749895, -1.5388417685876268], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, -1.902113032590307], [-1.0, 0]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.118033988749895, 0.36327126400268045], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-1.8090169943749475, 0.5877852522924731], [0.8090169943749475, -0.5877852522924731]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-3200-200.179-c0-0-0', 'leading_term': '0.78054464351150989132711559287757', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3200/1/bi/a/2879/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.7805446435115099, 0.7061454817488638, 0.6344258873007349, 0.5630863794519919, 0.48979332045913954, 0.4123703072433255, 0.3289481573066788, 0.23806552388431604, 0.13872498999192792, 0.03041566391146036, -0.0868862037722753, -0.2127295908256576, -0.34620836135662164, -0.4859853339497578, -0.6303198486908806, -0.7770990812388489, -0.9238739038921182, -1.0679002389530676, -1.2061867431112807, -1.335549407476623, -1.452673322304199, -1.5541814790525017, -1.6367100907521046, -1.6969895219421496, -1.7319295446467968, -1.7387072880976804, -1.7148559374983907, -1.658351971125818, -1.5676985152869216, -1.4420022524825273, -1.2810412481914635, -1.0853210734271836, -0.8561166994780477, -0.5954978318291188, -0.3063356335495756, 0.007710836994489543, 0.342229687842105, 0.69211342777107, 1.0516384378430246, 1.4145660822604744, 1.774264161669634, 2.1238466967142657, 2.456329320401643, 2.7647968788697237, 3.042579216670611, 3.283430580166578, 3.4817076358676666, 3.6325407927100577, 3.731993358981468, 3.777203072889575, 3.766500733213893, 3.6995010303455933, 3.577161239555015, 3.4018041822301455, 3.177102774904115, 2.908024550936303, 2.6007357296760496, 2.262465690331966, 1.901334044369327, 1.526143848077447, 1.1461458094741617, 0.7707795723696916, 0.4093992562198194, 0.07099134578462939, -0.23610628470630968, -0.5044750012783763, -0.7278663511301972, -0.9014241600343599, -1.0218691515684142, -1.087638307180448, -1.0989723625412655, -1.0579463113113665, -0.9684395260761872, -0.8360440593253881, -0.6679117954088515, -0.472543318295019, -0.259523563112993, -0.039211450328073875, 0.17760732368186904, 0.38009342955043773, 0.5577406518059916, 0.7007628782402313, 0.8004673855470692, 0.8496003831862861, 0.8426512076096118, 0.7761025215248658, 0.6486153578283876, 0.46113982420434313, 0.21694470013147002, -0.07843805903344385, -0.4173548366727337, -0.790255584129023, -1.1859971788457337, -1.5922161192008084, -1.9957587624985214, -2.383154644977106, -2.741116210173792, -3.0570466235028877, -3.319536357787571, -3.5188289657908274, -3.647236954260078, -3.699489952954757, -3.6729994134235535, -3.5680268255169683, -3.3877458225791446, -3.1381924469170586, -2.8281021268668933, -2.4686364149391427, -2.073007076264552, -1.6560095115449922, -1.2334815606282996, -0.8217072793579535, -0.43678814526805426, -0.09400618073433067, 0.19279543165587906, 0.4117886088741912, 0.5536688807819268, 0.6120736118295425, 0.5838904780104988, 0.46944075824576703, 0.27252679280778724, 0.0003383575806695108, -0.33678150957996666, -0.7257047519628091, -1.151008283541907, -1.5955679121011421, -2.041233499245141, -2.4695586161165477, -2.8625549531402132, -3.2034399510669997, -3.4773456563473863, -3.671957728522764, -3.778055842805685, -3.789930376736608, -3.7056551230751404, -3.527201650457829, -3.2603876047737432, -2.9146584298540623, -2.50270937558989, -2.0399619252773364, -1.5439155773724813, -1.0334019360635043, -0.5277730023417663, -0.04605915566285014, 0.3938656267747348, 0.7760733875821215, 1.0872900805182668, 1.3174882589536563, 1.460335796322, 1.513478031749658, 1.478638087155705, 1.3615283339123943, 1.171574730578901, 0.9214646062052557, 0.6265370074209033, 0.30404254606178166, -0.02769361533577195, -0.35016677013088515, -0.6456033200282603, -0.8978432189583024, -1.0931509353825966, -1.2209143540898129, -1.2741957656375988, -1.2501056702427185, -1.1499782757381578, -0.979336933765009, -0.7476479026177805, -0.4678712669146778, -0.1558280737022548, 0.17058775105958646, 0.492315852635962, 0.7901107798721628, 1.04555011251318, 1.242019000735865, 1.3656209159512662, 1.4059671205355575, 1.3568025226637983, 1.2164329880017553, 0.9879285106696156, 0.6790874736415711, 0.3021590385686982, -0.12666708114293174, -0.5879822054412545, -1.0600591944181121, -1.5198896795941892, -1.9443080112407454, -2.3111464961529578, -2.6003638093218924, -2.7950886972693256, -2.8825243028597254, -2.8546645304548277, -2.708782583762239, -2.447662751602644, -2.0795591686525725, -1.6178790173728126, -1.0806017711192275, -0.48945987783966416, 0.13108097898445906, 0.7549929184339935, 1.3559504496389474, 1.9086250938002443, 2.3899439804633347, 2.780247228251373, 3.0642832256343175, 3.2319885042498138, 3.279009404809201, 3.2069356693062754, 3.023230808707979, 2.7408598397580324, 2.377630935002296, 1.9552828364543478, 1.498363713492246, 1.0329587314067186, 0.5853322771928671, 0.180556047558802, -0.15880429901584867, -0.41387363007647604, -0.5704589096716369, -0.6197935860422067, -0.5589933952851701, -0.39119745887507407, -0.12538544467481968, 0.22412083987343426, 0.6384457075003676, 1.0951958583488757, 1.5696888059630998, 2.03630654605038, 2.4699000794020507, 2.847166990879358, 3.1479251886349324, 3.356211132169924, 3.461140191562582, 3.4574797156562913, 3.345901263894069, 3.1328964164813233, 2.830359629679316, 2.4548606776624187, 2.0266472308372205, 1.568434016994295, 1.1040478538933869, 0.657006847219215, 0.24911664122398233, -0.10083353968293285, -0.3781972738870787, -0.5733515094397972, -0.6822767241484595, -0.7067991135519514, -0.6544767030194818, -0.5381320808749634, -0.37505539519903486, -0.18592112477193667, 0.00652025661633569, 0.17890032284095816, 0.30875498611381413, 0.3760203989213375, 0.36441191953778945, 0.2626010313296103], 'positive_zeros': ['0.47057475450149827222893662640221', '1.77613831638991402525053912138374', '3.21046568866023685678916216702432', '3.91920670958254897482281886613807', '4.50680658835662007852365179416912', '5.75377103737526064573708768653891', '6.14458728011958769585507479191745', '7.26678644220347364704891937832824', '7.917620232005015055231186763683814', '8.555591596230864262933126751341913'], 'prelabel': '2-3200-200.179-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': -0.6799999999999999, 'root_number': '-0.53582679497899661827130876786751 - 0.84432792550201507854855806396698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.34', 'prec': 17}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47057475450149827222893662640', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.77613831638991402525053912138', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.21046568866023685678916216702', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5970080404256077, 'bad_primes': [2, 5], 'central_character': '200.179', 'conductor': 3200, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/1/bi/a/2879/1'], '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': '2-3200-200.179-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3200-200.179-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2637278347910232, 'root_angle': -0.33999999999999997, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47057475450149827222893662640', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '596524369996075980269309845024', 'Lhash_array': ['596524369996075980269309845024'], 'label': '2-3200-200.179-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/1/bi/a/2879/1'}