-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1631545552849430626387025126900', 'a10': [0.0, 0.0], 'a2': [2.349084651375157, 0.0], 'a3': [0.0, 0.0], 'a4': [3.518198699326341, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.8595233886152185, 0.0], 'a8': [3.566377262325235, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.13604686409738, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 5, 19], 'central_character': '4275.1', 'coefficient_field': 'CDF', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.349084651375157, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.8595233886152185, 0], [7.0, 0]], [[1.0, 0], [1.933592629168975, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [-2.4345852219001567, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [4.368177851069131, 0], [23.0, 0]], [[1.0, 0], [-8.264546565075548, 0], [29.0, 0]], [[1.0, 0], [1.176874010037464, 0], [31.0, 0]], [[1.0, 0], [-7.036397398652682, 0], [37.0, 0]], [[1.0, 0], [-7.934555113394366, 0], [41.0, 0]], [[1.0, 0], [3.719046777230438, 0], [43.0, 0]], [[1.0, 0], [13.263523863838577, 0], [47.0, 0]], [[1.0, 0], [-1.1317920404250783, 0], [53.0, 0]], [[1.0, 0], [3.236385810644053, 0], [59.0, 0]], [[1.0, 0], [-4.36529875715551, 0], [61.0, 0]], [[1.0, 0], [2.542172767192974, 0], [67.0, 0]], [[1.0, 0], [6.501955076956573, 0], [71.0, 0]], [[1.0, 0], [2.719046777230438, 0], [73.0, 0]], [[1.0, 0], [-8.213271408690147, 0], [79.0, 0]], [[1.0, 0], [6.802763072969288, 0], [83.0, 0]], [[1.0, 0], [-1.1317920404250783, 0], [89.0, 0]], [[1.0, 0], [-16.401696155808192, 0], [97.0, 0]], [[1.0, 0], [7.9637385690628335, 0], [101.0, 0]], [[1.0, 0], [-6.823125989962536, 0], [103.0, 0]], [[1.0, 0], [8.76553915780673, 0], [107.0, 0]], [[1.0, 0], [18.12074293303863, 0], [109.0, 0]], [[1.0, 0], [-18.46268575932007, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 100, 'label': '2-4275-1.1-c1-0-100', 'leading_term': '6.64377693518012410977006668331', '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/4275/2/a/bu/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [6.643776935180124, 6.636272890615598, 6.613626738186468, 6.575444388139823, 6.521095124839326, 6.449749215437835, 6.360427639685707, 6.252061366564529, 6.123557295286183, 5.973867888290787, 5.802061619449676, 5.607391592731183, 5.389360001704026, 5.147776450328574, 4.882808503780668, 4.595023161406379, 4.285418231892319, 3.955442842951838, 3.60700654047684, 3.2424766347270464, 2.864663643949447, 2.476794877897218, 2.082476401831914, 1.685643829752762, 1.2905026149661751, 0.9014587352134025, 0.5230409046624388, 0.1598156805420595, -0.1837029389467575, -0.5031476145162377, -0.7943934613082315, -1.0536533783001245, -1.2775706303136527, -1.4633063295893545, -1.60861944676206, -1.7119370241562977, -1.7724123716830802, -1.7899691995678277, -1.7653298830170416, -1.7000263599680485, -1.596392530280929, -1.4575374469018378, -1.2872990582246848, -1.0901787655819069, -0.8712575880758965, -0.6360952647470972, -0.39061415598115573, -0.1409703158004261, 0.10658542245998945, 0.3458530892744609, 0.5708323492767802, 0.7758705399104731, 0.9558059615610092, 1.1061023546792403, 1.2229705698750681, 1.3034736302099632, 1.3456117019244518, 1.3483839276433578, 1.3118246276511714, 1.237012028937524, 1.1260484231740802, 0.982011464631367, 0.8088771749495026, 0.6114160985010575, 0.39506492255875414, 0.16577671200987595, -0.0701463200778543, -0.30623290560916955, -0.5360305181201032, -0.7532952965979322, -0.9521782683504838, -1.12740197159614, -1.2744216986042558, -1.389565896526635, -1.4701507737406432, -1.5145648559228129, -1.5223201025952489, -1.4940672091731075, -1.4315738528887574, -1.3376658590260664, -1.2161325276034862, -1.0715986273877562, -0.9093667891104271, -0.73523516754981, -0.5552962482642143, -0.375723507424429, -0.2025532549619127, -0.04146937067270372, 0.10240124399081636, 0.2246748441851943, 0.3218714512561659, 0.3915434324311464, 0.4323665931564987, 0.44418956794570413, 0.4280387416414095, 0.3860775354356086, 0.32152059644116043, 0.2385051752604084, 0.1419236976723678, 0.03722316701213647, -0.06982149375399663, -0.1733518005681698, -0.2676784367999314, -0.3475323796150573, -0.40830417908147515, -0.4462612667672568, -0.45873369925584817, -0.44425967385851195, -0.402683469036434, -0.3352001246571685, -0.24434313566226815, -0.1339136212424565, -0.008851772149654017, 0.12494621646463086, 0.26086014475163155, 0.391818911748384, 0.5106048722163269, 0.6101778912218802, 0.6840062368292762, 0.7263906191700222, 0.7327673793183989, 0.6999770900813378, 0.6264856678197089, 0.5125465014993701, 0.36029405022003375, 0.17376178771154, -0.041179796562855815, -0.2769662936297961, -0.5245613966539227, -0.7737522899854425, -1.0135095388100361, -1.2323995220212038, -1.4190347168599302, -1.5625448962086657, -1.653050653862919, -1.6821197255687588, -1.6431863953545427, -1.5319149101126694, -1.3464892809506426, -1.0878141040828082, -0.7596140290379232, -0.36842314612238636, 0.07654026454221025, 0.5636136340649329, 1.079039919017817, 1.6074178302593867, 2.1322384013213327, 2.6364896296242497, 3.103307308942429, 3.516647309906878, 3.8619526093340686, 4.126787439758045, 4.3014111107299815, 4.379265383101633, 4.357351749796997, 4.236478536243525, 4.021362277266483, 3.7205732056167204, 3.3463207097582885, 2.9140810593944715, 2.442076303854327, 1.950619751016545, 1.4613495565361276, 0.9963774233927705, 0.5773839755983774, 0.22469580097514316, -0.0436187310076983, -0.2125971179507072, -0.27113696999098674, -0.21262243204165224, -0.03539232888794144, 0.2569750492784287, 0.655579000660542, 1.146326183626811, 1.7102756686143785, 2.3241931238881484, 2.9612992395791466, 3.5921890690459466, 4.185891228402149, 4.711029190126454, 5.137041548507583, 5.435414389604305, 5.580876972607013, 5.552511958217718, 5.334733459171544, 4.918090210698509, 4.299857051751398, 3.4843854755079717, 2.4831929774541432, 1.3147809614743096, 0.004181664589946788, -1.4177545037655268, -2.9153090959201338, -4.449051080619821, -5.977156537599896, -7.45684409798052, -8.845872081839655, -10.104039861347921, -11.194634873184574, -12.085768008244003, -12.751543808336274, -13.173017883197447, -13.338902010103835, -13.245987182564479, -12.899266041986694, -12.311748198858842, -11.50397442286617, -10.50324802402135, -9.342613426662648, -8.05962244382935, -6.694937624530036, -5.290828870551269, -3.8896239878108436, -2.5321757357210575, -1.256407164376044, -0.09599359948179294, 0.9207663163780797, 1.7718463411474596, 2.4421210667108677, 2.9237046437188456, 3.215989953896237, 3.32539136873522, 3.2648070361085715, 3.0528286812189767, 2.712737649535204, 2.271334868432356, 1.7576591533085106, 1.2016525256013109, 0.6328327526609082, 0.07903209670353754, -0.43474266450551785, -0.8872803181844463, -1.2619254079181088, -1.5470989684258418, -1.7365619448382257, -1.8294158694142169, -1.829847926116451, -1.7466396128702304, -1.59246923207072, -1.3830478730425082, -1.1361359445957744, -0.8704923208188546, -0.6048105461220707, -0.3566962036608862, -0.1417365175646122, 0.027292298789635253, 0.14104222514998407, 0.19400703804192965, 0.18471516772504207, 0.11569634493972093, -0.006771561205729263, -0.17311769781827993, -0.37110718017350086, -0.586606836051583, -0.8044439472033201, -1.0093097675172207, -1.1866577591946836], 'positive_zeros': ['1.28706250173011800091311498749236', '2.22969354577418503571933055176750', '3.07987431289750515395022940578116', '4.09101191376281501310767810946347', '4.65691050375251754103758767408698', '5.25317284637200083988533642359364', '5.89766282549838383912421669310272', '6.64852776202110500439357182449797', '7.77236816506646628459913158568091', '7.975543871811192703983321623335155'], 'prelabel': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28706250173011800091311498749', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22969354577418503571933055177', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.07987431289750515395022940578', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 34.13604686409738, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 4275, 'conductor_radical': 285, 'degree': 2, 'index': 100, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4275/2/a/bu/1/6'], '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': '2-4275-1.1-c1-0-100', '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': '2-4275-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.842606170545588, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28706250173011800091311498749', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1631545552849430626387025126900', 'Lhash_array': ['1631545552849430626387025126900'], 'factors': ['2-4275-1.1-c1-0-100'], 'label': '2-4275-1.1-c1-0-100', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4275/2/a/bu/1/6'}