-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1265197546112075986370856636690', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.506100370238147, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.623031520731018, 0.0], 'a8': [0.0, 0.0], 'a9': [3.280539065707776, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 74.10117307574824, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 29], 'central_character': '9280.1', 'coefficient_field': 'CDF', 'conductor': 9280, 'conductor_radical': 290, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.506100370238147, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.623031520731018, 0], [7.0, 0]], [[1.0, 0], [-4.891369845962501, 0], [11.0, 0]], [[1.0, 0], [3.577480009271255, 0], [13.0, 0]], [[1.0, 0], [3.3519187047408843, 0], [17.0, 0]], [[1.0, 0], [-5.342492455023242, 0], [19.0, 0]], [[1.0, 0], [0.6861101633087541, 0], [23.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.610830780254725, 0], [31.0, 0]], [[1.0, 0], [-9.723560793368186, 0], [37.0, 0]], [[1.0, 0], [-9.246063041462037, 0], [41.0, 0]], [[1.0, 0], [1.351918704740884, 0], [43.0, 0]], [[1.0, 0], [9.30524194001885, 0], [47.0, 0]], [[1.0, 0], [-6.8744209528347335, 0], [53.0, 0]], [[1.0, 0], [-8.205259682653747, 0], [59.0, 0]], [[1.0, 0], [3.1263574002105132, 0], [61.0, 0]], [[1.0, 0], [8.137432887424536, 0], [67.0, 0]], [[1.0, 0], [-10.024401480952587, 0], [71.0, 0]], [[1.0, 0], [-8.455222468136704, 0], [73.0, 0]], [[1.0, 0], [-13.714912896695791, 0], [79.0, 0]], [[1.0, 0], [0.44024723690175926, 0], [83.0, 0]], [[1.0, 0], [2.1099555223548108, 0], [89.0, 0]], [[1.0, 0], [17.8949226897664, 0], [97.0, 0]], [[1.0, 0], [-7.368019189238099, 0], [101.0, 0]], [[1.0, 0], [10.354693195499536, 0], [103.0, 0]], [[1.0, 0], [-10.464648717854345, 0], [107.0, 0]], [[1.0, 0], [-17.41322380048084, 0], [109.0, 0]], [[1.0, 0], [10.630007148869078, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 120, 'label': '2-9280-1.1-c1-0-120', 'leading_term': '4.43028578969238124813054238660', '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/9280/2/a/cl/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [4.430285789692381, 4.419376299649218, 4.386596711138787, 4.331802347763674, 4.254780419714906, 4.155290516964858, 4.033117470933194, 3.8881331821521057, 3.720363569539354, 3.5300566364767874, 3.3177477390792713, 3.0843184317835983, 2.831045696437031, 2.5596388787596958, 2.272262216237585, 1.9715414132676239, 1.6605532844398057, 1.342798036814246, 1.0221542948641396, 0.7028174881946133, 0.3892227230527705, 0.0859537429969767, -0.2023599520286656, -0.4711553227061602, -0.7160544394127818, -0.9329863110500164, -1.118308357381959, -1.2689237836673908, -1.3823910046858916, -1.4570212598042842, -1.4919606721944605, -1.48725324129995, -1.4438816219574546, -1.3637830356291478, -1.249838273601803, -1.105832478311037, -0.9363872115869855, -0.7468642170535715, -0.5432422329954633, -0.33196918254112806, -0.11979302754127787, 0.0864245136943811, 0.27990635248900875, 0.45416477263136945, 0.6032062196728223, 0.7217294460449156, 0.8053101506271403, 0.8505653113212315, 0.8552907137071213, 0.8185657337371326, 0.7408202344174861, 0.6238594726908879, 0.4708441606184757, 0.28622425214534153, 0.07562659178272428, -0.1543017851531229, -0.3960912259572582, -0.6416827773274784, -0.8826905539268355, -1.110685065142031, -1.3174882271600008, -1.495469889647212, -1.6378351415595143, -1.7388914708139696, -1.794285067517981, -1.8011961958837632, -1.7584846159000382, -1.666777495624369, -1.5284940848077408, -1.3478035698062003, -1.1305149318139582, -0.8839002046114874, -0.6164551817088461, -0.3376042546852683, -0.05735856826553773, 0.21406105423626984, 0.46662303317865905, 0.6908909284339573, 0.8784204625700313, 1.0221314405473072, 1.116638585136276, 1.1585262154755227, 1.1465532602664867, 1.0817772874131668, 0.9675889912030696, 0.8096518223244535, 0.6157450662792501, 0.3955125416643149, 0.1601230536908684, -0.07814735940361443, -0.3063976741165464, -0.5116316268519646, -0.681315223792225, -0.8039402359705596, -0.8695706616853002, -0.8703487994383304, -0.8009381923099815, -0.6588822984866174, -0.4448602912439396, -0.16282483194627254, 0.1799891127484624, 0.5731904662909786, 1.0034939680936952, 1.4551129474720175, 1.9102724283288999, 2.349826615754566, 2.753959827940841, 3.102945624448404, 3.377935457529982, 3.561745820201517, 3.639611727644967, 3.5998745450675305, 3.434573709863606, 3.139914775856734, 2.716590360177874, 2.169935867918573, 1.5099081197459419, 0.7508819775974181, -0.08873252290076775, -0.9870424737609887, -1.9193764055338935, -2.859116332288135, -3.778627233119105, -4.650248769921862, -5.4473105079253, -6.145129939076825, -6.72195234248388, -7.159793012437717, -7.445145627390903, -7.569525427667775, -7.529822243084419, -7.328446019233151, -6.973256024844707, -6.477274023216831, -5.8581909630266615, -5.137685774037093, -4.340583227397152, -3.4938851439516267, -2.625715151228821, -1.7642214009398303, -0.93648393638375, -0.16747360050313426, 0.5208925481173955, 1.1105583419845146, 1.5879630879383027, 1.9444761850099743, 2.1766132914427057, 2.2860254633817627, 2.279263092782375, 2.167326886709216, 1.9650280568325733, 1.6901888430337522, 1.3627220332250831, 1.003633878365239, 0.6339984342151438, 0.2739526849417802, -0.05823927575083199, -0.34700818883348117, -0.5801485769386596, -0.7493032444070955, -0.850241170054506, -0.8829170885549862, -0.8513121629233259, -0.7630663491693247, -0.6289237724009415, -0.46202211423503026, -0.2770651413966467, -0.08942364376407366, 0.08578614790449109, 0.23459635711782004, 0.34500458735600825, 0.40766954235127095, 0.41644679191305184, 0.3687349483779286, 0.2656128275563168, 0.11175964050165307, -0.08483770473395423, -0.313374163718437, -0.5608857393185954, -0.8130411993403134, -1.0550213144467355, -1.2724350728580012, -1.4522195414524526, -1.5834702039004154, -1.658151762611201, -1.6716454257931255, -1.6230973355557807, -1.515543599413392, -1.3557998073945927, -1.154116289426897, -0.9236139635508335, -0.6795286859404625, -0.4383037914392694, -0.21658031461388652, -0.030141605865993803, 0.10712676612415804, 0.18420011759764865, 0.19374172551713573, 0.13274094889398821, 0.0029187506311065515, -0.18913100686517104, -0.4320819697165328, -0.7102993420879613, -1.0045334237940602, -1.2928527315605538, -1.551772285105358, -1.7575202122481743, -1.8873762438417856, -1.9210095457782712, -1.8417411098335668, -1.6376578282876215, -1.302511413662342, -0.8363452668520612, -0.2458057911318856, 0.4558891631293054, 1.249333890986439, 2.109660488289938, 3.007577503499089, 3.9106745466864528, 4.784929995571745, 5.596346206727833, 6.312627784121794, 6.904814064419713, 7.348777399463708, 7.626504138873414, 7.727085253815598, 7.647357840814415, 7.392156595978693, 6.974154833166848, 6.413296643804378, 5.735844160320877, 4.973085343901178, 4.159767050147061, 3.3323342083065173, 2.5270678173283807, 1.7782213712341164, 1.116256799942705, 0.5662768718592726, 0.1467413888411654, -0.13146013603093812, -0.26552554677156603, -0.2608152841085918, -0.13047848874581416, 0.10535234603147416, 0.4207561752696275, 0.7855434217636587, 1.1670181092449787, 1.5318846241574728, 1.8481926095502499, 2.087210436253776, 2.2251208401137896, 2.2444415542263125, 2.1350886426596114, 1.8950199655013322, 1.5304196915449166, 1.055410709745605, 0.4913087004759468], 'positive_zeros': ['0.998064881509375087906000248549535', '1.90196469821586092146825128608007', '2.54703519251766838038129431982356', '3.47847245290467345890884156009295', '4.15640892835786435670425711881836', '4.66384901152172158286527482845538', '5.52646817500137101309425705981609', '6.62024079209216770963103334854828', '7.30388138786923804645060753758284', '7.85139049954278322225278325178706'], 'prelabel': '2-9280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.60820382401278, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.998064881509375087906000248550', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.90196469821586092146825128608', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.54703519251766838038129431982', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 74.10117307574824, 'bad_primes': [2, 5, 29], 'central_character': '1.1', 'conductor': 9280, 'conductor_radical': 290, 'degree': 2, 'index': 120, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9280/2/a/cl/1/4'], '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': '2-9280-1.1-c1-0-120', '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': '2-9280-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.60820382401278, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.998064881509375087906000248550', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1265197546112075986370856636690', 'Lhash_array': ['1265197546112075986370856636690'], 'factors': ['2-9280-1.1-c1-0-120'], 'label': '2-9280-1.1-c1-0-120', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9280/2/a/cl/1/4'}