-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1829949747253839143272552852290', 'a10': [0.0, 0.0], 'a2': [2.2336547411570957, 0.0], 'a3': [1.0, 0.0], 'a4': [2.9892135026935716, 0.0], 'a5': [0.0, 0.0], 'a6': [2.2336547411570957, 0.0], 'a7': [-1.031426839143289, 0.0], 'a8': [2.209561430308114, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.2336547411570957, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.031426839143289, 0], [7.0, 0]], [[1.0, 0], [-6.176434338136656, 0], [11.0, 0]], [[1.0, 0], [-0.9377628814750312, 0], [13.0, 0]], [[1.0, 0], [6.5632902527722266, 0], [17.0, 0]], [[1.0, 0], [-5.674526459579955, 0], [19.0, 0]], [[1.0, 0], [-1.6465958621372452, 0], [23.0, 0]], [[1.0, 0], [-8.358193780375816, 0], [29.0, 0]], [[1.0, 0], [-5.533708338993852, 0], [31.0, 0]], [[1.0, 0], [1.2954795652902198, 0], [37.0, 0]], [[1.0, 0], [4.981055618655969, 0], [41.0, 0]], [[1.0, 0], [-7.756188660636248, 0], [43.0, 0]], [[1.0, 0], [7.672876753129552, 0], [47.0, 0]], [[1.0, 0], [-0.5005464026926549, 0], [53.0, 0]], [[1.0, 0], [1.1933993070101623, 0], [59.0, 0]], [[1.0, 0], [12.363684611087004, 0], [61.0, 0]], [[1.0, 0], [7.588510524200062, 0], [67.0, 0]], [[1.0, 0], [-10.612545618860896, 0], [71.0, 0]], [[1.0, 0], [7.986377548658911, 0], [73.0, 0]], [[1.0, 0], [13.921286971655446, 0], [79.0, 0]], [[1.0, 0], [-1.4622253549780238, 0], [83.0, 0]], [[1.0, 0], [8.511611603545637, 0], [89.0, 0]], [[1.0, 0], [-3.7562258678758518, 0], [97.0, 0]], [[1.0, 0], [2.6056571453332604, 0], [101.0, 0]], [[1.0, 0], [-17.218176252894725, 0], [103.0, 0]], [[1.0, 0], [-5.542962177147628, 0], [107.0, 0]], [[1.0, 0], [5.984583099859623, 0], [109.0, 0]], [[1.0, 0], [-0.32363628466551325, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 52, 'label': '2-1875-1.1-c1-0-52', 'leading_term': '5.44715149573137875115492822269', '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/1875/2/a/o/1/7', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [5.4471514957313785, 5.4427107360944404, 5.429103477514524, 5.4054922070075495, 5.370537715010634, 5.322479268259586, 5.259238085280056, 5.178537030258564, 5.078029300985752, 4.955429468769871, 4.808641244994138, 4.63587751053581, 4.435769227652268, 4.207460731440448, 3.9506895312127757, 3.6658491672402413, 3.354033926628999, 3.01706439557685, 2.6574929801149665, 2.278588715650109, 1.88430094216556, 1.4792017654868401, 1.0684076602055452, 0.6574810899875593, 0.25231361060110163, -0.14100744197370024, -0.5163459183811219, -0.8676740695709305, -1.189235992510932, -1.4757127603318907, -1.7223842622578545, -1.9252824871881744, -2.0813308554026104, -2.188464257499112, -2.2457247144488828, -2.2533280366846657, -2.2126975345767557, -2.1264617099201035, -1.9984139213778158, -1.8334332400926838, -1.6373670597055525, -1.4168774542237332, -1.179254736689548, -0.932203104780894, -0.6836046058940561, -0.44126885196263077, -0.2126769023750787, -0.004728454836131436, 0.17649811144484986, 0.32596324904718094, 0.4398520604496646, 0.5157199092580332, 0.5525904509745637, 0.5510002261000126, 0.5129858148107203, 0.44201169284371905, 0.34283927948282317, 0.22134014265593024, 0.08425882301061327, -0.0610668501371336, -0.20701786554673987, -0.3460265718358958, -0.4709161804678282, -0.5752327801439413, -0.6535550243774804, -0.7017669086727369, -0.7172799809287753, -0.6991929284825132, -0.6483787260570208, -0.5674923468231785, -0.4608953381425358, -0.33449721927258674, -0.19551751987512744, -0.052176175126874405, 0.0866762578876182, 0.21197368544686318, 0.31487709566141064, 0.3872247423157779, 0.4219685672671618, 0.41357513255097644, 0.3583699651292259, 0.2548059133947109, 0.10363885470920721, -0.09200219638844168, -0.3266589761658536, -0.5927050335060039, -0.8806214803393485, -1.1793790974930745, -1.4769127135076217, -1.760668419999609, -2.018199523104841, -2.237783433875147, -2.409029216020096, -2.523444434393454, -2.574930418651745, -2.5601771382995024, -2.4789325628970373, -2.334126555580204, -2.1318358362149503, -1.8810840898029462, -1.5934795527345278, -1.282700993226827, -0.9638514815621405, -0.6527072694743737, -0.36489601809736644, -0.11504410921609765, 0.08406352472504872, 0.22226600609448102, 0.29270718876883034, 0.2923731057074978, 0.2224503017429479, 0.08847677203198312, -0.09973326172549718, -0.32839849224868023, -0.5803093330994993, -0.8355797276569676, -1.0725831254480844, -1.269032522942577, -1.4031547556608115, -1.4549016792853924, -1.407136008129505, -1.2467277905171685, -0.9654990466935947, -0.5609590618740209, -0.03678111904454543, 0.5970172090974147, 1.3242141749272522, 2.1228524757212823, 2.9660274218568503, 3.8229683224731854, 4.660369992307484, 5.443916066416298, 6.139923040101118, 6.717024436546062, 7.147808909701592, 7.410324894457013, 7.489367878593506, 7.377474503869976, 7.075560261295945, 6.593154026587547, 5.948202345003346, 5.166438270902412, 4.28033258315497, 3.3276681113870428, 2.3497994544939806, 1.3896793123212363, 0.4897478414654095, -0.31020808966198105, -0.9751138813784949, -1.4764735065772971, -1.7939392724976682, -1.916494129275097, -1.8431739487687928, -1.5832800628453114, -1.1560586122365921, -0.5898515501898159, 0.07924705544041413, 0.8091680742592721, 1.5539913532643892, 2.266309528118501, 2.899708996576421, 3.4112365226457135, 3.7637181574542318, 3.9278027958636095, 3.883615591673712, 3.6219260592077567, 3.144761022356992, 2.4654223040057652, 1.607901561301286, 0.6057181478050192, -0.4997615925374195, -1.661435522636583, -2.82889427551106, -3.951035168572651, -4.978717922450975, -5.867315249941362, -6.579016450797858, -7.084755490946632, -7.365655976133592, -7.4139127988741755, -7.233062486934452, -6.837629536579155, -6.2521721911012245, -5.5097860575696025, -4.650155523985787, -3.717269207826074, -2.756935002399153, -1.8142414677237497, -0.9311146094821954, -0.14411232112787833, 0.5174166862702722, 1.0327058427731648, 1.3904014670512959, 1.588811211223442, 1.6355664689078888, 1.5467314188740233, 1.3454255163750206, 1.0600559343512923, 0.7222797914265939, 0.3648314814943783, 0.019357045971070647, -0.2856051133069762, -0.5263696031249818, -0.6854679164246322, -0.7525501841846973, -0.7247762260074107, -0.6066823361061617, -0.4095458368515037, -0.15030319431383757, 0.14989287778717425, 0.46736841702759774, 0.7777506731132394, 1.0577864745269825, 1.2870273030389028, 1.4492633176318097, 1.533608259199397, 1.53516369078897, 1.4552224785938264, 1.3010055315402849, 1.0849601279970047, 0.823680178498774, 0.5365361700276771, 0.2441233022494283, -0.03335107451685804, -0.27761611852036056, -0.4737035450472581, -0.611027216321984, -0.6840951640116877, -0.6928018673391979, -0.642281568846567, -0.5423379065186452, -0.40649854418620507, -0.25077321535147407, -0.09221733225395078, 0.05258084434123333, 0.16896484381943216, 0.24550499924943298, 0.2750153052432329, 0.2552053171537125, 0.18890925802379038, 0.08386853542705289, -0.047919640048981756, -0.19123875568469947, -0.32899303676060987, -0.4437426184544733, -0.519306865952893, -0.5423002142864379, -0.5034671214296114, -0.398695916648477, -0.22961471391300528, -0.00370455037853858, 0.2660968225915643, 0.5622854151725875, 0.8641188695009692, 1.1492862822308867, 1.3957923973233757, 1.5839056829892686], 'positive_zeros': ['1.44357581412762530873971807092856', '2.75532563651551502475747797245564', '3.43261770948563942196773415410948', '4.29893795253070812661075414764230', '4.83728188170894312480323240784646', '6.18413473174725498223878955835343', '6.53332033579277077894156467202192', '7.26931127012519355969430526229455', '8.589502753416992573644026753879640', '9.134023466243786244989036656346964'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44357581412762530873971807093', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.75532563651551502475747797246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43261770948563942196773415411', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/7'], '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': '2-1875-1.1-c1-0-52', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44357581412762530873971807093', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1829949747253839143272552852290', 'Lhash_array': ['1829949747253839143272552852290'], 'label': '2-1875-1.1-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/o/1/7'}