-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1830209885788809573412768752640', 'a10': [-0.5, 0.8660254037844386], 'a2': [1.0, 0.0], 'a3': [-0.5, -0.8660254037844386], 'a4': [1.0, 0.0], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.5, -0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.426087387979079, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [31, [[1.0, 0], [-2.0, -5.196152422706632]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '930.211', 'coefficient_field': 'CDF', 'conductor': 930, 'conductor_radical': 930, 'conjugate': '1265197727538988863411458442132', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-3.5, 6.06217782649107]], [[1.0, 0], [-0.5, 0.8660254037844386], [-5.5, -9.526279441628825]], [[1.0, 0], [-3.0, 5.196152422706632], [-6.5, -11.258330249197702]], [[1.0, 0], [-0.5, -0.8660254037844386], [-8.5, 14.722431864335457]], [[1.0, 0], [2.0, 3.4641016151377544], [-9.5, 16.454482671904334]], [[1.0, 0], [-7.0, 0], [23.0, 0]], [[1.0, 0], [-6.0, 0], [29.0, 0]], [[1.0, 0], [-2.0, -5.196152422706632]], [[1.0, 0], [3.5, 6.06217782649107], [-18.5, 32.04293994002423]], [[1.0, 0], [-1.0, 1.7320508075688772], [-20.5, -35.50704155516198]], [[1.0, 0], [-3.5, -6.06217782649107], [-21.5, 37.239092362730865]], [[1.0, 0], [-3.0, 0], [47.0, 0]], [[1.0, 0], [-2.0, 3.4641016151377544], [-26.5, -45.89934640057525]], [[1.0, 0], [6.0, 10.392304845413264], [-29.5, 51.09549882328188]], [[1.0, 0], [14.0, 0], [61.0, 0]], [[1.0, 0], [2.5, -4.330127018922194], [-33.5, -58.023702053557386]], [[1.0, 0], [3.0, -5.196152422706632], [-35.5, -61.48780366869514]], [[1.0, 0], [1.0, -1.7320508075688772], [-36.5, -63.21985447626402]], [[1.0, 0], [1.5, 2.598076211353316], [-39.5, 68.41600689897065]], [[1.0, 0], [8.0, -13.856406460551018], [-41.5, -71.88010851410841]], [[1.0, 0], [-4.0, 0], [89.0, 0]], [[1.0, 0], [6.0, 0], [97.0, 0]], [[1.0, 0], [-15.0, 0], [101.0, 0]], [[1.0, 0], [-1.0, 1.7320508075688772], [-51.5, -89.20061658979718]], [[1.0, 0], [-2.0, -3.4641016151377544], [-53.5, 92.66471820493493]], [[1.0, 0], [12.0, 0], [109.0, 0]], [[1.0, 0], [9.5, -16.454482671904334], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 15, 'label': '2-930-31.25-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/930/2/i/e/211/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.214732427414843, 2.3254400124370966, 2.4121185002216965, 2.4675567765772537, 2.4796578382916765, 2.4333802974016714, 2.313197132503316, 2.105691245020282, 1.8020337687672416, 1.4001622267942004, 0.9064822976504157, 0.3368972962395672, -0.28303697334094235, -0.9190035176378853, -1.5299563836540662, -2.0712688942618525, -2.4988222138634035, -2.773695905716765, -2.8669721572762903, -2.764055457259312, -2.467866245930629, -2.0003115703707257, -1.401579074809162, -0.7270395358152281, -0.04185766461361581, 0.586235728118899, 1.0952155230823144, 1.4370119616210653, 1.5845282363622144, 1.5362454495833286, 1.3174608166043902, 0.9776217167218116, 0.5837836030682109, 0.21085870988862923, -0.07006585501661872, -0.20358983325701555, -0.16006227403132875, 0.05804282038772604, 0.41488566709435826, 0.8458477082982595, 1.267665752537337, 1.5927923484899182, 1.7457414918192884, 1.6785688791940898, 1.3824924109005305, 0.89306832475729, 0.28729134455019484, -0.3276347522609672, -0.832524775898226, -1.1186021966362776, -1.1100999766996074, -0.7826613992531187, -0.1734962765718123, 0.6195396776685199, 1.4508652779755244, 2.15072099642839, 2.555712403934551, 2.540966911675754, 2.0476857242448157, 1.1002219197535452, -0.1916042909701972, -1.646637637909522, -3.0414670936030577, -4.14979883857253, -4.785011246796699, -4.8375963459089775, -4.299641660686771, -3.270629130536452, -1.9423058000640816, -0.5645750874054142, 0.6015800758453257, 1.3350864565138616, 1.4993306330159741, 1.070770490119996, 0.14505866163796258, -1.0813445574450076, -2.350897692359731, -3.398132226924695, -4.005122014844926, -4.047295945476599, -3.5194134310667193, -2.5356802955029463, -1.303656824377184, -0.0775507100964878, 0.8986798734077628, 1.4454434662656959, 1.4863163359752387, 1.0624070367885925, 0.31884742931962584, -0.5333762445934382, -1.2710124750394816, -1.7144161540734664, -1.7718309913253938, -1.460924495959618, -0.9020041203620496, -0.28447583608443555, 0.1849894609289703, 0.3392253013970597, 0.09737257399094276, -0.510875037120689, -1.3504863953594217, -2.2149975920069567, -2.8806440386143897, -3.1666044960919586, -2.985212227424791, -2.3682566138609285, -1.4616004049482845, -0.48874800462346446, 0.3074980436551151, 0.7298921700622414, 0.6804936796404828, 0.18827196734622134, -0.5976290749715303, -1.4478321385245008, -2.1154361047606702, -2.4044066163447546, -2.2245335952100818, -1.6171769381418257, -0.7439553625660853, 0.15904610453161847, 0.8489795922294342, 1.146616223952866, 0.9889022916723499, 0.44787578907575015, -0.2903704896206702, -0.9812979131938995, -1.3962082938161224, -1.3931571870000048, -0.9626696715329008, -0.23325391219100045, 0.5666290145491114, 1.1802627640796546, 1.4073107605802695, 1.17557234954788, 0.5765631692537555, -0.14861520507228118, -0.6722166863819696, -0.675713557544726, 0.04835110538533783, 1.5189987956291615, 3.5389902369689348, 5.728345885226648, 7.6135180856152935, 8.749783311283098, 8.843480434264903, 7.839101461892628, 5.94483796098993, 3.5868743549602184, 1.3028693563178027, -0.3971583991098316, -1.1642563681831792, -0.9008297879118415, 0.21787126007501656, 1.7972701257536066, 3.3366535439259013, 4.369469037211697, 4.59042756903769, 3.9332650877296826, 2.5778916514205457, 0.8867997836363115, -0.7083915434816789, -1.8349190847832983, -2.2825389376563647, -2.0524972398528045, -1.339160877546369, -0.4530136716284542, 0.28807414023321404, 0.663106044755509, 0.6140694524507316, 0.25361469899820477, -0.1861644126237264, -0.44464949218604816, -0.3311124248162009, 0.20361187192876987, 1.0468475430657895, 1.9618984579388605, 2.6704622107702187, 2.950578930179212, 2.715542285861011, 2.0457142750247557, 1.1615864248097163, 0.3471142935221178, -0.1498699382737957, -0.20479800384484692, 0.1404549854901064, 0.6946879601244597, 1.189742279455928, 1.3829439853503984, 1.1527869304511655, 0.5522767650744206, -0.20150106964052888, -0.8006080408186588, -0.9583341774817478, -0.5209149236345495, 0.46214065214278405, 1.7372428244849287, 2.91995544491908, 3.620421937707339, 3.5792917727067834, 2.766502736059101, 1.4059517827452468, -0.08664430651958276, -1.2355204280222587, -1.6639032574796562, -1.2265278161155029, -0.06874510026914925, 1.4111217449250046, 2.686949541612011, 3.2777627276036565, 2.9109391677457506, 1.6197655866531868, -0.25955714209118824, -2.1927199486085946, -3.620300000776207, -4.141311521681581, -3.6451498664419035, -2.3466788835716637, -0.7120464426145993, 0.6996556314518927, 1.4246177146306465, 1.2477072089483903, 0.26843757664757756, -1.1424670415266673, -2.479472427419818, -3.2825213905664774, -3.296913834912255, -2.556204456386974, -1.359510348911487, -0.15284016382886287, 0.6412434425717758, 0.7827218231036083, 0.30339547721472987, -0.5065072626849777, -1.209414201859341, -1.3881404794087253, -0.808162299431113, 0.4858987933561234, 2.175865957326967, 3.776428417973641, 4.803974654956794, 4.94636197797652, 4.171793597993245, 2.7374859461698726, 1.095821248069359, -0.26660835069861133, -0.9973296699514567, -0.992069750100217, -0.41413314586739647, 0.3852710783795644, 1.0128004334644842, 1.1875897666738346, 0.8453128716041006, 0.1530032369151365, -0.5686817059488448, -0.9828313856336616, -0.8774051220568391, -0.25348215769044286], 'positive_zeros': ['1.44378102724780495009563903982675', '3.00785757185597485027405220046088', '4.21290607583222055117696661273154', '4.59919520368904898218184099729587', '5.80717677167120521784200319954860', '6.52919672020546172684816452614821', '7.48284618114923384848553218494342', '8.681136048549815276933184667396563', '9.265983887851629742557743782328496', '10.38358508955195293006385249304299'], 'prelabel': '2-930-31.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.2553639835726929, 'root_number': '0.6950911729069698 + 0.7189215961054537*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.127681991786', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44378102724780495009563903983', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00785757185597485027405220046', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21290607583222055117696661273', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.426087387979079, 'bad_primes': [2, 3, 5, 31], 'central_character': '31.25', 'conductor': 930, 'conductor_radical': 930, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/930/2/i/e/211/1'], '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': '2-930-31.25-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': '2-930-31.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.7250848405103056, 'root_angle': 0.12768199178634645, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44378102724780495009563903983', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1830209885788809573412768752640', 'Lhash_array': ['1830209885788809573412768752640'], 'label': '2-930-31.25-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/930/2/i/e/211/1'}