-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1578683612837239741425194372459', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.114907541476756, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [-2.114907541476756, 0.0], 'a7': [-3.5877414504720115, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.4728339089952556, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.11987282308817, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [73, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 11, 73], 'central_character': '8030.1', 'coefficient_field': 'CDF', 'conductor': 8030, 'conductor_radical': 8030, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.114907541476756, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.5877414504720115, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-5.7026489919487675, 0], [13.0, 0]], [[1.0, 0], [1.3579263675184998, 0], [17.0, 0]], [[1.0, 0], [0.24301882604174396, 0], [19.0, 0]], [[1.0, 0], [-6.229815082953512, 0], [23.0, 0]], [[1.0, 0], [9.101703798388524, 0], [29.0, 0]], [[1.0, 0], [-5.587741450472011, 0], [31.0, 0]], [[1.0, 0], [5.587741450472011, 0], [37.0, 0]], [[1.0, 0], [-3.054332182009489, 0], [41.0, 0]], [[1.0, 0], [-1.6009451935602437, 0], [43.0, 0]], [[1.0, 0], [-3.6009451935602437, 0], [47.0, 0]], [[1.0, 0], [-0.07377910255549924, 0], [53.0, 0]], [[1.0, 0], [-5.325275703884257, 0], [59.0, 0]], [[1.0, 0], [13.290390442420778, 0], [61.0, 0]], [[1.0, 0], [14.16227915785579, 0], [67.0, 0]], [[1.0, 0], [-10.702648991948767, 0], [71.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [10.0, 0], [79.0, 0]], [[1.0, 0], [16.418501726985767, 0], [83.0, 0]], [[1.0, 0], [2.2235719054957337, 0], [89.0, 0]], [[1.0, 0], [-16.580780884841555, 0], [97.0, 0]], [[1.0, 0], [-10.798109612879513, 0], [101.0, 0]], [[1.0, 0], [9.743777430870024, 0], [103.0, 0]], [[1.0, 0], [7.492280829541266, 0], [107.0, 0]], [[1.0, 0], [-7.431705470073999, 0], [109.0, 0]], [[1.0, 0], [-15.344722624430267, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 175, 'label': '2-8030-1.1-c1-0-175', '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/8030/2/a/s/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-9.431757530508293e-61, 0.18003999925123107, 0.3587300452397405, 0.5346850009319264, 0.7064524747217396, 0.8724867454407415, 1.031131134317236, 1.18061069268543, 1.319036404232986, 1.444421406276383, 1.5547090700445105, 1.6478121840623825, 1.7216619794555608, 1.7742653285158552, 1.8037681346881205, 1.8085227038663778, 1.7871567324409752, 1.7386414571378523, 1.6623564785028728, 1.5581487904803477, 1.4263836225009283, 1.2679848295373242, 1.0844627524355062, 0.8779277181321005, 0.6510876587150446, 0.40722869941475154, 0.1501779958374888, -0.11575141542172382, -0.3858334596973101, -0.6550187049891139, -0.9180394427761183, -1.1695281465070735, -1.404146716890924, -1.6167233911163972, -1.8023937187226085, -1.9567416111694018, -2.0759361755870693, -2.1568598644492214, -2.197223428227099, -2.1956632603041677, -2.1518169812569554, -2.0663735268838765, -1.9410945794939434, -1.7788049075013717, -1.583350040772236, -1.359520688792775, -1.11294438004381, -0.8499459330124706, -0.577379526373439, -0.30243627858402805, -0.03243233342978634, 0.22541656531155754, 0.46422718286416736, 0.6776800983360536, 0.8602422779250083, 1.0073728016901156, 1.115703719351654, 1.1831883945160175, 1.209210380871291, 1.1946468539800301, 1.1418818825931292, 1.0547663365269841, 0.9385229552023471, 0.7995969922252649, 0.6454548474922117, 0.4843351317250334, 0.3249586055368232, 0.17620531892473207, 0.046768969433079656, -0.055200077810379986, -0.12245057813522998, -0.14897178705016406, -0.13030698044969352, -0.06382591779736578, 0.05105618659637234, 0.21272434544461843, 0.41728352767566385, 0.6585596064252678, 0.928186076821432, 1.2157781530972083, 1.50919268610365, 1.794869055250667, 2.0582429027410667, 2.284221419090682, 2.4577059860706747, 2.5641454624019016, 2.590101376917007, 2.5238048785362728, 2.355684569272512, 2.0788443800007257, 1.6894714768689905, 1.187155817516421, 0.5751053878325187, -0.1397557132008035, -0.9468153976968328, -1.8319326818154205, -2.777727830931904, -3.763998750583761, -4.768253895074083, -5.766347203898833, -6.733196168744611, -7.643560269715783, -8.472853874427054, -9.197965422197095, -9.79805344381631, -10.255289786189206, -10.555521371101714, -10.68882392464948, -10.649924328174079, -10.438472475726218, -10.059148644739022, -9.521598221826821, -8.840191964535398, -8.033616583973709, -7.124307044392173, -6.137738326237566, -5.101600222744748, -4.044883783254604, -2.9969120497754607, -1.9863505621683317, -1.0402345813833214, -0.1830500013776394, 0.5640965509751049, 1.1841858701625996, 1.6648443488439708, 1.9987295094172997, 2.183726820146754, 2.2229491029836383, 2.1245377030175248, 1.9012726148516574, 1.5700066109552484, 1.1509457523175897, 0.6668051579120325, 0.1418742710999234, -0.39897016418207576, -0.9312628135612089, -1.4319188682836086, -1.8801333821364954, -2.2581734908347, -2.5520306738468332, -2.751906192868408, -2.8525100452622096, -2.8531618983787186, -2.7576911676589786, -2.5741422813670636, -2.314299836144799, -1.9930563920691688, -1.6276527072862783, -1.2368259345352368, -0.8399054157738056, -0.4558980087495224, -0.10260523538215507, 0.20418707890738644, 0.4514095447730905, 0.6292685034014784, 0.7316388869063668, 0.7562737044295638, 0.7048220975531951, 0.5826572032559959, 0.398524317927418, 0.16402861770192717, -0.10701047721763134, -0.3993046989356478, -0.6969036453131495, -0.9840214337399041, -1.2458410634187782, -1.4692555373905298, -1.6435081689925888, -1.7606998064976962, -1.8161376983405584, -1.8085090438552922, -1.7398715115041432, -1.6154626857015937, -1.4433400224663464, -1.2338719472578126, -0.9991087319175226, -0.7520683063376264, -0.5059768311023132, -0.27350640931954245, -0.06605258735979974, 0.10690775711866221, 0.23834183397536615, 0.3240396902095305, 0.3628243642354443, 0.3565808722973305, 0.31010161743699055, 0.23075623595013356, 0.12800401017897406, 0.012776213713163658, -0.10323641327971492, -0.2083498967122977, -0.29166207874865957, -0.34379035383861484, -0.35752732426015427, -0.3283735571289339, -0.2549129881145438, -0.13900498851859897, 0.01422274005437935, 0.19658499165934798, 0.39724633648453134, 0.6033059064426848, 0.8005298512871971, 0.974192182575964, 1.1099772863937334, 1.1948924371469933, 1.2181365323212199, 1.1718721893652515, 1.0518523322935869, 0.8578593061828056, 0.5939240821701063, 0.26830478692101806, -0.10678299283002918, -0.5156776244514306, -0.9400039356237887, -1.359592800840016, -1.7535419287184737, -2.1013623392818745, -2.3841482390263544, -2.5857045409574533, -2.693566433669079, -2.6998492792577826, -2.601874608652057, -2.4025287719696253, -2.1103243825202083, -1.7391503853321724, -1.307713564864337, -0.8386916653593882, -0.35763506675107687, 0.10833081999549504, 0.5319375014315393, 0.8872652205074906, 1.1512144995243077, 1.3048758811216532, 1.3347194540533354, 1.2335333086312201, 1.001051772092733, 0.6442295877353411, 0.17713636741956953, -0.3795342712378883, -0.9993255422959108, -1.6512123294606722, -2.30107486938421, -2.9133795002880163, -3.4529816156381195, -3.886957240435096, -4.186365872376221, -4.327848726869019, -4.294973330522498, -4.079247262038608, -3.6807401927322694, -3.1082734166998605, -2.3791587436808537, -1.5184927458413644, -0.5580365870486709, 0.4652653298210215, 1.5110541924995555, 2.5375226383136598], 'positive_zeros': ['1.24536178388036227556971348787795', '2.34950108898838854547891654277776', '3.20725645543578603701505639300219', '3.45025494663409000223677597294543', '4.35069113155604112144780290699880', '5.68270281930637856168444003569344', '6.24671709116291276527045072237524', '7.09293067572053562514158832581046', '7.52894998124220174089741300222258'], 'prelabel': '2-8030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.007488546547425, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24536178388036227556971348788', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34950108898838854547891654278', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20725645543578603701505639300', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 64.11987282308817, 'bad_primes': [2, 5, 11, 73], 'central_character': '1.1', 'conductor': 8030, 'conductor_radical': 8030, 'degree': 2, 'index': 175, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8030/2/a/s/1/3'], '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': '2-8030-1.1-c1-0-175', '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': '2-8030-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.007488546547425, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24536178388036227556971348788', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1578683612837239741425194372459', 'Lhash_array': ['1578683612837239741425194372459'], 'label': '2-8030-1.1-c1-0-175', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8030/2/a/s/1/3'}