-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1996110786438343353304778571350', 'a10': [0.0, 0.0], 'a2': [-4.0, 0.0], 'a3': [14.300297616411443, 0.0], 'a4': [16.0, 0.0], 'a5': [0.0, 0.0], 'a6': [-57.20119046564577, 0.0], 'a7': [-49.0, 0.0], 'a8': [-64.0, 0.0], 'a9': [-38.501488082057215, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.134336934543235, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [49.0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '350.1', 'coefficient_field': 'CDF', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 0]], [[1.0, 0], [-14.300297616411443, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [49.0, 0]], [[1.0, 0], [-425.90386901334875, 0], [161051.0, 0]], [[1.0, 0], [399.30327378052584, 0], [371293.0, 0]], [[1.0, 0], [1751.5193450667439, 0], [1419857.0, 0]], [[1.0, 0], [-2874.2339282709045, 0], [2476099.0, 0]], [[1.0, 0], [-2313.429166408321, 0], [6436343.0, 0]], [[1.0, 0], [2127.927678326264, 0], [20511149.0, 0]], [[1.0, 0], [10262.533332152327, 0], [28629151.0, 0]], [[1.0, 0], [-7266.047618625831, 0], [69343957.0, 0]], [[1.0, 0], [5893.43511873655, 0], [115856201.0, 0]], [[1.0, 0], [20157.738687476223, 0], [147008443.0, 0]], [[1.0, 0], [20056.530650947356, 0], [229345007.0, 0]], [[1.0, 0], [-33954.898211644264, 0], [418195493.0, 0]], [[1.0, 0], [4319.338094014909, 0], [714924299.0, 0]], [[1.0, 0], [12253.617263523374, 0], [844596301.0, 0]], [[1.0, 0], [-17533.827382481362, 0], [1350125107.0, 0]], [[1.0, 0], [-1658.180947235136, 0], [1804229351.0, 0]], [[1.0, 0], [-8246.908328830745, 0], [2073071593.0, 0]], [[1.0, 0], [9168.612196072581, 0], [3077056399.0, 0]], [[1.0, 0], [95203.20714279388, 0], [3939040643.0, 0]], [[1.0, 0], [14441.824397459695, 0], [5584059449.0, 0]], [[1.0, 0], [62132.422919120945, 0], [8587340257.0, 0]], [[1.0, 0], [108137.63213548639, 0], [10510100501.0, 0]], [[1.0, 0], [138033.5723261025, 0], [11592740743.0, 0]], [[1.0, 0], [6189.610131358563, 0], [14025517307.0, 0]], [[1.0, 0], [68652.91279750569, 0], [15386239549.0, 0]], [[1.0, 0], [-62835.85237163086, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 37, 'label': '2-350-1.1-c5-0-37', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/350/6/a/p/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [-1.5557538194652854e-60, 0.21955989074423146, 0.43617428052975105, 0.6469329996380411, 0.8489963455112244, 1.039629820987635, 1.2162382587361111, 1.376399095984886, 1.5178945387972533, 1.6387423265104086, 1.737224776037472, 1.8119157542517468, 1.8617051964982168, 1.885820762382721, 1.883846198389779, 1.8557359625735184, 1.801825661470514, 1.72283785527418, 1.6198828057595984, 1.494453773764472, 1.34841652020688, 1.1839927272747601, 1.0037371347618578, 0.8105082803037466, 0.6074328407563199, 0.39786369392622006, 0.18533195356436974, -0.026506626282517785, -0.2339303315477491, -0.43321455358645505, -0.6206983869769159, -0.7928537576191456, -0.9463559381750309, -1.0781541798322754, -1.1855410787059217, -1.2662192064563365, -1.3183634722930118, -1.3406776515588497, -1.3324435182373062, -1.2935610581192774, -1.224578318429669, -1.1267095700312064, -1.001840620522969, -0.8525203201959689, -0.6819375463082006, -0.49388323169311593, -0.29269731726702425, -0.08320084925344041, 0.12938619561505754, 0.3395403976726563, 0.5415423545743031, 0.7295943979423615, 0.8979464888157764, 1.0410278785424525, 1.1535818223517775, 1.230800380516879, 1.2684561470403417, 1.2630276176800057, 1.2118148562747144, 1.1130421476957266, 0.9659444425415874, 0.7708346060644868, 0.5291487826086166, 0.24346757538460634, -0.08248878463608285, -0.4438925546249745, -0.834868533704436, -1.2485820309268185, -1.6773540058104863, -2.112801898112611, -2.546003917095046, -2.967683829958155, -3.3684125958799327, -3.7388225580677155, -4.069829352997876, -4.352856244229224, -4.580055256832299, -4.744519294250456, -4.840479375968437, -4.863481251754244, -4.810535932328498, -4.680239128335916, -4.472855205704294, -4.190362036953549, -3.8364540406016214, -3.416501735220951, -2.9374672668041777, -2.4077765693947657, -1.8371500571733053, -1.2363949861564927, -0.6171638281477562, 0.008315869577825687, 0.6275336460899554, 1.2280029460955622, 1.7975745431727383, 2.3247480354078176, 2.7989726399815376, 3.210928525742372, 3.5527802008144738, 3.8183940189530086, 4.003512678313609, 4.105880645393861, 4.125315722202979, 4.063723454817579, 3.9250527171230645, 3.7151925485160566, 3.441812126714586, 3.1141475603913493, 2.7427409323559915, 2.3391386530365046, 1.9155576379531334, 1.4845290470482668, 1.0585302688981997, 0.6496164571809231, 0.26906319773761483, -0.07296821961957699, -0.367731939427553, -0.6081549744908273, -0.7890420563285613, -0.9072205932503965, -0.9616202889277504, -0.9532840725860835, -0.8853092610654653, -0.7627202387445075, -0.592276323179499, -0.3822207981496076, -0.1419792568133558, 0.11818267652421699, 0.3875305637994023, 0.6552483940246764, 0.9108281353182437, 1.1444475688036053, 1.3473225636982749, 1.5120206555669116, 1.6327239956939696, 1.705431418806203, 1.7280914799526088, 1.7006607723936678, 1.6250845740511006, 1.5051997842022449, 1.346563098240409, 1.1562103135674517, 0.9423554488276827, 0.7140408786338545, 0.4807518302160229, 0.25201026167709023, 0.036964263697530135, -0.15601036340505245, -0.3196798461612308, -0.44827778269804164, -0.5377718493090666, -0.5860596956301908, -0.5930844780773638, -0.5608635645196833, -0.493427375953009, -0.3966689841705769, -0.2781088155904521, -0.14658246985246345, -0.011863094650995986, 0.11576718338789334, 0.22597972677371447, 0.3088767992946417, 0.3554637929430349, 0.35809577430083855, 0.31087833920269486, 0.21000410646899892, 0.054008353265637916, -0.15606976770601153, -0.4166303838721529, -0.721566243458216, -1.062427530738519, -1.428694721786262, -1.8081513157656885, -2.1873437396413347, -2.552111580474603, -2.8881677391959575, -3.181705294552286, -3.4200059611712565, -3.592024133148042, -3.6889206964466092, -3.7045220977759077, -3.6356825555526058, -3.482530723365805, -3.248586454626964, -2.9407384120298476, -2.569078922144252, -2.146598468022735, -1.6887482929931816, -1.2128854965712135, -0.7376204772033768, -0.2820913651338348, 0.1348060375108221, 0.49520153042201276, 0.7830142284620112, 0.9846638165153208, 1.089697742301645, 1.0913054435632565, 0.9866947357599404, 0.7773107093791343, 0.4688837088010374, 0.07129994383509698, -0.4017042638219409, -0.9330159877348122, -1.5027709089549002, -2.0891072522503666, -2.6690193568655944, -3.219276800198558, -3.7173713675789926, -4.142452099695573, -4.476208283283935, -4.703661640176796, -4.81383209723141, -4.800246288810372, -4.661264181656085, -4.400206675546605, -4.0252754166726055, -3.5492650093310742, -2.989076935752729, -2.365053386414543, -1.700157457307357, -1.0190333988664064, -0.3469864538106974, 0.29107399704781994, 0.871681976024305, 1.3738068847961569, 1.7797455077837316, 2.075873526823021, 2.253221832026915, 2.3078503924037053, 2.2410012925197345, 2.059022364087441, 1.773063205797966, 1.3985558185182985, 0.9545021007566905, 0.462599575496676, -0.053755488841827924, -0.57054233195614, -1.0642180671818195, -1.512797126189464, -1.8968573608080854, -2.2004253802247815, -2.4116989859911113, -2.5235719181129554, -2.533935222443673, -2.445739982130212, -2.2668174416374494, -2.009464158760257, -1.689811191064433, -1.3270069033405536, -0.9422522460445971, -0.5577348310480285, -0.19551342984886644, 0.1235926491661043, 0.38105465678078765, 0.5615738194420064, 0.6538620169046616, 0.6512241369212736], 'positive_zeros': ['1.57465376191117731310130598058916', '2.77685717157013274585504820013401', '3.73579329572425449819983081827507', '5.33125099248837841779382226464897', '6.72512503625368285468796041640733', '7.41519047390506433311844203792882', '8.565342975898545369161051037890437', '9.263055503283541779605107291392060', '9.743125265180136967832348672775292'], 'prelabel': '2-350-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57465376191117731310130598059', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77685717157013274585504820013', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73579329572425449819983081828', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 56.134336934543235, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 350, 'conductor_radical': 70, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/350/6/a/p/1/2'], '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': '2-350-1.1-c5-0-37', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-350-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.492285161053551, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57465376191117731310130598059', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1996110786438343353304778571350', 'Lhash_array': ['1996110786438343353304778571350'], 'factors': ['2-350-1.1-c5-0-37'], 'label': '2-350-1.1-c5-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/350/6/a/p/1/2'}