-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '217322745080634706464994480498', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-29.20876640972224, 0.0], 'a4': [0.0, 0.0], 'a5': [-98.5052309660039, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [610.1520351777182, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 125.74091473337684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '784.1', 'coefficient_field': 'CDF', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [29.20876640972224, 0], [243.0, 0]], [[1.0, 0], [98.5052309660039, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [129.1520351777182, 0], [161051.0, 0]], [[1.0, 0], [126.13971524103134, 0], [371293.0, 0]], [[1.0, 0], [-1614.0381824051276, 0], [1419857.0, 0]], [[1.0, 0], [1399.467068731747, 0], [2476099.0, 0]], [[1.0, 0], [2773.2162814217454, 0], [6436343.0, 0]], [[1.0, 0], [-3499.9357537559727, 0], [20511149.0, 0]], [[1.0, 0], [710.4560866415026, 0], [28629151.0, 0]], [[1.0, 0], [3051.1049497983913, 0], [69343957.0, 0]], [[1.0, 0], [15263.7316184132, 0], [115856201.0, 0]], [[1.0, 0], [7880.578216196247, 0], [147008443.0, 0]], [[1.0, 0], [16787.656371436275, 0], [229345007.0, 0]], [[1.0, 0], [3230.1284924880547, 0], [418195493.0, 0]], [[1.0, 0], [-12163.328090945693, 0], [714924299.0, 0]], [[1.0, 0], [51007.39029323975, 0], [844596301.0, 0]], [[1.0, 0], [27232.316834005363, 0], [1350125107.0, 0]], [[1.0, 0], [-13313.85874386202, 0], [1804229351.0, 0]], [[1.0, 0], [49712.91748471692, 0], [2073071593.0, 0]], [[1.0, 0], [21105.927387320822, 0], [3077056399.0, 0]], [[1.0, 0], [79860.15161106776, 0], [3939040643.0, 0]], [[1.0, 0], [36846.53335256766, 0], [5584059449.0, 0]], [[1.0, 0], [27968.45782102714, 0], [8587340257.0, 0]], [[1.0, 0], [-93531.54339735195, 0], [10510100501.0, 0]], [[1.0, 0], [-179413.76978854003, 0], [11592740743.0, 0]], [[1.0, 0], [188902.92979992542, 0], [14025517307.0, 0]], [[1.0, 0], [-104679.52474899196, 0], [15386239549.0, 0]], [[1.0, 0], [-25226.646859655048, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-28e2-1.1-c5-0-3', 'leading_term': '0.098072744402237869689900167941818', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/784/6/a/bi/1/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [0.09807274440223787, 0.08478920585218137, 0.04539761370509939, -0.01873437773460244, -0.10535863362356011, -0.2113931247770412, -0.3329864429771538, -0.4655995158474356, -0.6041035511899021, -0.7428929801420396, -0.8760118878813107, -0.9972921220438817, -1.1005009571025741, -1.1794958746646673, -1.2283837043245467, -1.2416810687556523, -1.2144728033146732, -1.1425647890119375, -1.0226274634626809, -0.8523261726579314, -0.6304345117622517, -0.3569268889999538, -0.03304674428338539, 0.3386528280062557, 0.7542988598404781, 1.208720933026255, 1.695507793706145, 2.2070989023901997, 2.7349107611452967, 3.2694968769734905, 3.800739182522322, 4.318067671165762, 4.81070394629467, 5.267923370669808, 5.679329569351346, 6.035134228323014, 6.326434479214675, 6.54547970512907, 6.685919376411948, 6.743023555835026, 6.713868020725295, 6.59747654732468, 6.394913792707703, 6.10932338388656, 5.74590726295578, 5.311844010366261, 4.816145733375217, 4.269455110367918, 3.683786261490532, 3.07221520135676, 2.4485276441962673, 1.8268337961780448, 1.2211614039411778, 0.6450396556565926, 0.11108748051027008, -0.36937969678076155, -0.786710666211544, -1.1332330232640768, -1.4035090856164811, -1.594522138170815, -1.705784065172897, -1.7393579339453094, -1.699791978167756, -1.5939645978056303, -1.430843337992713, -1.2211642062725496, -0.9770410022821405, -0.7115174267690496, -0.43807746880936543, -0.1701318087999247, 0.07950039950362814, 0.29909409291066935, 0.478484812482558, 0.6094794872217427, 0.6861933758054091, 0.7052974511153584, 0.6661636779669513, 0.5708994718587269, 0.42426700338252954, 0.23348776535821167, 0.00793775803896706, -0.24125643679415207, -0.5017057485736027, -0.7603117221331404, -1.0038619405393887, -1.2196424021311947, -1.3960398442085997, -1.5231065152699153, -1.5930606370673677, -1.6006977913000486, -1.5436916804741412, -1.4227670563395516, -1.2417329324130164, -1.007370295419238, -0.729175152721867, -0.4189646098361847, -0.09036044881460527, 0.24182895253618852, 0.5623018830715762, 0.8560006637524896, 1.1088587427329306, 1.3085213777412268, 1.4450036759732732, 1.5112514366629595, 1.5035736768125005, 1.4219208271467223, 1.2699891869016158, 1.0551400633890728, 0.7881307620882257, 0.4826638408620174, 0.1547703590422875, -0.17794822448704528, -0.49718678550723816, -0.7848724199833803, -1.024124937998221, -1.2001943919243758, -1.3013273059212904, -1.3195149246480116, -1.2510808793191444, -1.0970720750628362, -0.8634251069176885, -0.5608907664781243, -0.20471075523378193, 0.18594696485024712, 0.5887752796446607, 0.979306589730583, 1.3320412537310105, 1.6216748653410964, 1.8243665234282702, 1.9189860648412036, 1.8882770692494546, 1.7198744892409865, 1.4071210198699808, 0.949634643292617, 0.35359084145422637, -0.3683037190449107, -1.1971542806605937, -2.10853026864877, -3.0734031973299905, -4.059331451266027, -5.031839540829915, -5.955928128502056, -6.797642831420579, -7.525625059357827, -8.11256730273682, -8.536498499262855, -8.781832320652702, -8.840122152782984, -8.7104807009726, -8.39963885265946, -7.921636827928397, -7.297159781747025, -6.5525488603277635, -5.7185362161020485, -4.828767656688655, -3.9181885531700136, -3.0213766308923593, -2.170908786022424, -1.3958478287229836, -0.720429029206725, -0.1630157895358198, 0.2646207984931691, 0.5576615577676065, 0.7182211276595608, 0.7549565406994622, 0.682328035517751, 0.5195575560330997, 0.2893477935860937, 0.016438489357039475, -0.27391384606598224, -0.5574422490926022, -0.812272105706493, -1.0201372934506086, -1.1673380160406068, -1.2453846543811007, -1.251291485554805, -1.1875060550358314, -1.0614830026710982, -0.884933820420559, -0.6728049307479268, -0.44205427000867786, -0.21031005875398606, 0.005496296657615387, 0.19042882573356804, 0.33268652140875626, 0.42450289529159235, 0.46273992659278823, 0.4491306471766264, 0.39014792030992684, 0.2965022779351352, 0.18229736710465433, 0.06389593947625194, -0.04142924333695442, -0.11696821618228434, -0.1480676425243305, -0.1235382684674272, -0.03687097642507294, 0.11283405015167638, 0.32030426986670524, 0.5739549187351268, 0.856202706797975, 1.1442337731881556, 1.4111958382583856, 1.6277546453795113, 1.7639278534490308, 1.7910873968803622, 1.6840055896018502, 1.4228121596819676, 0.994729744016578, 0.39546440076551836, -0.36985489899099383, -1.2862689288530584, -2.3291631144352936, -3.465039476480615, -4.652862962162553, -5.84592233411401, -6.994111276988324, -8.046505861283805, -8.954092028569475, -9.672482981324633, -10.1644623997945, -10.402195779720614, -10.368968737234939, -10.060337038591943, -9.484606927305105, -8.662604031389197, -7.626732297405448, -6.41936829313977, -5.090678017415726, -3.695980303232612, -2.29281051282601, -0.937858450044346, 0.3160362114034309, 1.4226499411428142, 2.344735665859819, 3.0558350328021104, 3.541434455330136, 3.799398202672409, 3.83965780988909, 3.6831846738824257, 3.360318712833918, 2.9085673118754816, 2.3700226479904356, 1.7885695486376414, 1.2070686012938538, 0.6646993743151174, 0.19463625668651266, -0.17779463986247054, -0.43636324496986606, -0.5745156478049646, -0.5952611183031845, -0.5103890895876804, -0.3390859185930908, -0.10606294718016405, 0.16065893527166064, 0.4321398011518117, 0.6809067662068964], 'positive_zeros': ['0.17143741740942468476368882576250', '1.38089144553797206850479095209312', '3.38880418197122650482583575836715', '4.35440155718264946677635244194086', '5.00206936414679590518825903066099', '6.01694760039519927622429990959415', '6.90397827040638328380575199146082', '7.65822089888836814729028686967382', '8.406883644039174738615422256232234', '10.02162197526838363969264304108118'], 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17143741740942468476368882576', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.38089144553797206850479095209', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38880418197122650482583575837', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 125.74091473337684, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 784, 'conductor_radical': 14, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/784/6/a/bi/1/1'], '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': '2-28e2-1.1-c5-0-3', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-28e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.213425646669123, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17143741740942468476368882576', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '217322745080634706464994480498', 'Lhash_array': ['217322745080634706464994480498'], 'factors': ['2-28e2-1.1-c5-0-3'], 'label': '2-28e2-1.1-c5-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/784/6/a/bi/1/1'}