-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4818660800468690872904183286682', 'a10': [0.0, 0.0], 'a2': [0.0, -2.414213562373095], 'a3': [0.0, -2.8284271247461903], 'a4': [-3.8284271247461903, 0.0], 'a5': [0.0, 0.0], 'a6': [-6.82842712474619, 0.0], 'a7': [0.0, 2.0], 'a8': [0.0, 4.414213562373095], 'a9': [-5.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11], 'central_character': '275.199', 'coefficient_field': 'CDF', 'conductor': 275, 'conductor_radical': 55, 'conjugate': '1045460681076024833317833732389', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.414213562373095], [-2.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.17157287525381], [-13.0, 0]], [[1.0, 0], [0, 6.82842712474619], [-17.0, 0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-23.0, 0]], [[1.0, 0], [-3.65685424949238, 0], [29.0, 0]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [0, -7.656854249492381], [-37.0, 0]], [[1.0, 0], [-6.0, 0], [41.0, 0]], [[1.0, 0], [0, 6.0], [-43.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-47.0, 0]], [[1.0, 0], [0, -11.65685424949238], [-53.0, 0]], [[1.0, 0], [1.6568542494923801, 0], [59.0, 0]], [[1.0, 0], [9.313708498984761, 0], [61.0, 0]], [[1.0, 0], [0, 12.48528137423857], [-67.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [71.0, 0]], [[1.0, 0], [0, 1.17157287525381], [-73.0, 0]], [[1.0, 0], [4.0, 0], [79.0, 0]], [[1.0, 0], [0, 6.0], [-83.0, 0]], [[1.0, 0], [-13.313708498984761, 0], [89.0, 0]], [[1.0, 0], [0, 3.65685424949238], [-97.0, 0]], [[1.0, 0], [-9.313708498984761, 0], [101.0, 0]], [[1.0, 0], [0, -6.82842712474619], [-103.0, 0]], [[1.0, 0], [0, 7.656854249492381], [-107.0, 0]], [[1.0, 0], [-7.656854249492381, 0], [109.0, 0]], [[1.0, 0], [0, -19.65685424949238], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-275-5.4-c1-0-15', '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/275/2/b/d/199/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.0222938725453434, 1.2390219410543828, 1.4918262561942215, 1.7880776246730152, 2.133476575770707, 2.531413016654928, 2.982498610814763, 3.4842059293542063, 4.0305759823728895, 4.612001551697884, 5.215129155245579, 5.822939014207253, 6.415062340784571, 6.968383004104475, 7.457949467300747, 7.858195002503609, 8.144431456944618, 8.294546496765198, 8.290799209504007, 8.121577807682975, 7.782960019400306, 7.279905722603721, 6.626916171276985, 5.848017428404583, 4.975968393966208, 4.050655007870612, 3.116708284852238, 2.2204687564506016, 1.40650535393724, 0.7139728234395003, 0.17314780110356554, -0.1974903513965993, -0.39327998296100314, -0.42419973420758766, -0.31429161866222544, -0.09961751236806755, 0.17515769633695108, 0.46129336120320863, 0.7111890226240531, 0.8837413482674991, 0.9492219753731032, 0.8930539420026797, 0.7179418009641337, 0.4439673913206112, 0.10648842764504984, -0.24805167293707556, -0.5680086698921436, -0.8034609415132062, -0.913316293317061, -0.8716463577959604, -0.6723162946572673, -0.3311356171503108, 0.11495931979043367, 0.6117972081573413, 1.0946079859633198, 1.4966439403462137, 1.7586690781289838, 1.8379768070849987, 1.7155546790300167, 1.4001808452061015, 0.9286053972627193, 0.36150378682727663, -0.22447853214396418, -0.7476318419786087, -1.1335349397276386, -1.3269981723067974, -1.3016542647088138, -1.0654768715626355, -0.66103086719357, -0.16002695779016798, 0.34733776125870414, 0.7668605217367759, 1.01648173300657, 1.0414822304505806, 0.8260438053192609, 0.39887344159842586, -0.16859452259559504, -0.7717606915422588, -1.2892220163159442, -1.6037047673088256, -1.6243471574501858, -1.3065800688210147, -0.665923972063693, 0.217268581011685, 1.2038085417560256, 2.112397816299506, 2.745248392431894, 2.919081365323959, 2.4967888335032393, 1.4145496559666892, -0.30044759835246326, -2.5253032633534347, -5.051431904090458, -7.608675979937826, -9.900486300513654, -11.645137959688912, -12.616687280358368, -12.679121781760621, -11.80800908112076, -10.095816454968938, -7.739667807472702, -5.013200618326043, -2.226879351053409, 0.3168736706344681, 2.366434283071826, 3.7546563708037466, 4.418081521719455, 4.39882711223815, 3.8293654116731215, 2.9034288273413633, 1.8386904207604287, 0.8382131293141141, 0.057674273602518256, -0.41595053345123434, -0.5709580461283246, -0.4624520031739407, -0.19153975051812694, 0.1227375034329104, 0.3723968554866266, 0.48417270607062446, 0.4330089129750274, 0.24299210758866033, -0.023743023472489008, -0.28685236235064304, -0.4711181081758016, -0.5273151132894385, -0.4453409791363012, -0.2563148251779906, -0.023145576152406717, 0.17796405075230187, 0.28019337054754895, 0.24681549589581808, 0.08405844634600061, -0.1579908091792633, -0.39760727510003363, -0.544512764757278, -0.5284718088100725, -0.3260882685288067, 0.021759006783252634, 0.40775439389220813, 0.6738784836167744, 0.6433980463666266, 0.16321277484002833, -0.8525692578284297, -2.3882790284535678, -4.310946861175546, -6.379169917336249, -8.277461009081733, -9.671171470666621, -10.271936146878685, -9.900323553196923, -8.531881141728373, -6.315353629079419, -3.5571381405955287, -0.6729939344060102, 1.8848281107671083, 3.711133188262485, 4.525142321906172, 4.225413361344323, 2.9102843186769807, 0.8588103271439996, -1.5244972551101903, -3.789986523248704, -5.5315381663927115, -6.464935249522004, -6.479418552036536, -5.651767591279832, -4.220523912317492, -2.5268112373866947, -0.9355804663653804, 0.24469692293936585, 0.825833392090368, 0.7733232093607794, 0.20277892986332224, -0.6583470484795237, -1.5333635083528243, -2.167336867427828, -2.3889573447142536, -2.148449887485857, -1.523008530173066, -0.6895487051086072, 0.1271928343071354, 0.7170982109770219, 0.9411326747372365, 0.7671808510302578, 0.2762301987492907, -0.3622073762822639, -0.9384098976393885, -1.261244963554689, -1.2115217927728987, -0.7755268545563441, -0.049766054220703, 0.784282206114977, 1.508510725502418, 1.9265120827207973, 1.9161123450468258, 1.4619451895052666, 0.6593708684897813, -0.3111165305090779, -1.2317860678806651, -1.9045976573595826, -2.201506245672915, -2.0944688787699035, -1.6572851679844014, -1.0394102904645905, -0.4198323185724777, 0.04526992534770243, 0.2657131148029794, 0.23879050962216697, 0.04303899672981274, -0.1933323561695347, -0.339202645336083, -0.30751408933449215, -0.08714547314408855, 0.25124241346904147, 0.5783530768555701, 0.752100250164356, 0.6720872397679248, 0.3248298760738129, -0.1966262760745522, -0.7082572840961134, -0.985011791577577, -0.833388140780029, -0.16645535960330002, 0.9419507906960959, 2.243536468864364, 3.352281306375082, 3.8279095273254318, 3.2885825114386082, 1.5251542732963788, -1.4139653486423394, -5.193316121299131, -9.229772696012922, -12.797283795775366, -15.176171025633648, -15.813330465629479, -14.454891871625593, -11.217826705526374, -6.580757821213224, -1.2935137563493564, 3.7750860044851824, 7.8163081248994155, 10.245724748940653, 10.814513725734853, 9.643017866766437, 7.171123180083599, 4.040467478091963, 0.9396753196543555, -1.548417007999841, -3.0610700255437555, -3.506793151122809, -3.046284445967787, -2.014630651193638, -0.8106150915136138, 0.21452496688871955, 0.8393248466564351, 1.006497828353055], 'positive_zeros': ['3.80125312101073682934274451958679', '4.42235240349404129175085364338856', '5.53736346430189683680820110308926', '6.46973436054866681085470473147591', '7.70147510800215435011818007093346', '8.663498480924810325294990729435105', '9.464759372223001050603872617831448', '10.34637056010627434359659982229379', '11.23081722949860818297754489194528', '12.85825471891489269932012584455432'], 'prelabel': '2-275-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579 - 0.8944271909999159*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.323791808825', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.80125312101073682934274451959', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.42235240349404129175085364339', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.53736346430189683680820110309', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.1958860555852118, 'bad_primes': [5, 11], 'central_character': '5.4', 'conductor': 275, 'conductor_radical': 55, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/275/2/b/d/199/1'], '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': '2-275-5.4-c1-0-15', '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': '2-275-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4818522381078392, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.80125312101073682934274451959', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4818660800468690872904183286682', 'Lhash_array': ['4818660800468690872904183286682'], 'label': '2-275-5.4-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/275/2/b/d/199/1'}