-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1764169528326216623760250408595', 'a10': [0.10452846326765347, 0.9945218953682733], 'a2': [0.9135454576426009, 0.4067366430758002], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [0.6691306063588582, 0.7431448254773942], 'a5': [0.5, 0.8660254037844386], 'a6': [-0.30901699437494745, 0.9510565162951535], 'a7': [0.0, 0.0], 'a8': [0.30901699437494745, 0.9510565162951535], 'a9': [-0.9781476007338057, 0.20791169081775934], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9135454576426009, -0.4067366430758002]]], [3, [[1.0, 0], [-0.10452846326765347, -0.9945218953682733]]], [5, [[1.0, 0], [-0.5, -0.8660254037844386]]], [31, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1199', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '3104788974952824795334447493249', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9135454576426009, -0.4067366430758002]], [[1.0, 0], [-0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [0, 0], [0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0, 0], [0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [-1.2871645951087531, 1.1589682071129128], [0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0.8090169943749475, 1.8170819200795922], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [-0.19098300562505258, 0.5877852522924731], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9781476007338057, 0.20791169081775934]], [[1.0, 0], [0, 0], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [-0.8736191374661522, -1.2024335861860327], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0.24441485128374268, 1.1498814685531944], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [0, 0], [-0.9781476007338057, 0.20791169081775934]], [[1.0, 0], [0, -0.8134732861516004], [-1.0, 0]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.9135454576426009, -0.4067366430758002]], [[1.0, 0], [0, 0], [-0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [-0.1398863880160892, -0.1553595731849211], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0.1398863880160892, -1.3309300777698674], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [1.413545457642601, -1.2727620468602387], [0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [1.3090169943749475, -0.9510565162951535], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [-0.6691306063588582, 0.7431448254773942], [-0.10452846326765347, -0.9945218953682733]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1860-1860.1199-c0-0-2', 'leading_term': '2.16007458806377284041260907280', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1860/1/df/c/1199/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.160074588063773, 2.081223475264082, 2.0244042493788053, 1.984495075210273, 1.9558512997946, 1.932843299802811, 1.9102714880320317, 1.8836231421852596, 1.8491922364292988, 1.8041064490930656, 1.746303407172304, 1.6744857355769127, 1.588071515163446, 1.487147190716417, 1.3724241494072746, 1.2451971932722847, 1.107301927986582, 0.9610679172364364, 0.8092648236898317, 0.6550393975486472, 0.5018419336008093, 0.3533416205731532, 0.2133310117526983, 0.08562062921241159, -0.026074542359733364, -0.11825422902672211, -0.1877546518598502, -0.23186934572359422, -0.24846502897841743, -0.2360882657249162, -0.19405853829723096, -0.12254339044611788, -0.022611522961716063, 0.10373986978589331, 0.25358664109476464, 0.4231104571613534, 0.6076641943578591, 0.8018702949780243, 0.9997512128146743, 1.1948898091593851, 1.3806162578278125, 1.5502167347152112, 1.6971579572914923, 1.8153205585446146, 1.899233384203045, 1.9443001450150672, 1.947009485617002, 1.9051194884259828, 1.817807945023103, 1.6857804159614822, 1.5113291655406977, 1.2983374874557525, 1.052225700030509, 0.7798371385399804, 0.4892647429544088, 0.18962125324586346, -0.1092415107169785, -0.3970563933982673, -0.6634975247412812, -0.8985576827892302, -1.0929326478953965, -1.2383976557291039, -1.3281604691078144, -1.3571756229114458, -1.322405094575995, -1.2230120306612522, -1.0604762037576236, -0.8386225381590723, -0.5635572501997892, -0.24350979233641032, 0.1114172663984096, 0.4895842058433213, 0.8782256981351796, 1.2639238329485454, 1.6331251115431866, 1.972681074171372, 2.2703901646070346, 2.5155172787811284, 2.6992673005644185, 2.8151898643018862, 2.8594946211555494, 2.8312593935160844, 2.7325176940631652, 2.5682170259145276, 2.346044980434675, 2.076126178681481, 1.7705992950201654, 1.4430894668130263, 1.1080970307292035, 0.7803284356653938, 0.47399908439357963, 0.20214050430619038, -0.024054556390897514, -0.1958159041910474, -0.3072773929126719, -0.3558286674407877, -0.34231492333676866, -0.27106903799291354, -0.1497681186780864, 0.010885030876560344, 0.19764619055187296, 0.39536163639058397, 0.5877212972377612, 0.7580994479437687, 0.890443292226509, 0.9701656045211275, 0.9849954764223798, 0.9257413626241536, 0.7869231487343701, 0.56723485476924, 0.26980670409259827, -0.09775563597183419, -0.523566180000674, -0.9918879047268852, -1.483783694156531, -1.9779642793914765, -2.4517970694116946, -2.882429725106122, -3.2479742743804314, -3.5286920236736385, -3.7081169034085932, -3.774055466761273, -3.719405657973313, -3.542743619636505, -3.2486379800055083, -2.8476638384226103, -2.3561034754294377, -1.7953369430661494, -1.1909423247415472, -0.5715417130584414, 0.032556060451244526, 0.5908520659244928, 1.074219494844194, 1.456451345618585, 1.7157112229863736, 1.8358070299513138, 1.8072138882609, 1.6277834211643116, 1.3030911412383854, 0.8463914482382809, 0.2781697973106216, -0.3746970749249217, -1.0801405118000356, -1.8024061064624652, -2.5037956877419427, -3.146559214486844, -3.694839995066242, -4.11657094790966, -4.385219373599666, -4.481283107607142, -4.393451840261134, -4.119363384464634, -3.6659049962881003, -3.049033492492319, -2.293113624704882, -1.429800567997335, -0.49651798651160717, 0.4653935227603598, 1.4127631201490496, 2.3028022378499404, 3.095324618038646, 3.754853066242557, 4.252496381348672, 4.567490876724971, 4.688318056965086, 4.613332500655267, 4.3508606267138, 3.918760324548364, 3.343461750250898, 2.6585391798905484, 1.9028909209871896, 1.1186272807674102, 0.3487840544076199, -0.36501018811161734, -0.984781309243451, -1.478243861712871, -1.820506755851564, -1.995353422774058, -1.9960241676283292, -1.8254574758232796, -1.495978850653735, -1.0284584159299894, -0.4509900270336786, 0.20282694185086464, 0.8958984004062256, 1.5898169835997562, 2.2470824225530213, 2.833227489593603, 3.3187227758861595, 3.680548058257269, 3.9033395134700566, 3.9800492057421475, 3.912084393058317, 3.7089272862491534, 3.3872688242882436, 2.9697206656720563, 2.483195938736914, 1.9570696105843095, 1.421242278032976, 0.9042358880910382, 0.43144603731024145, 0.023663328757514326, -0.3040434058858701, -0.5430150577146717, -0.6912246698257999, -0.7530302641123455, -0.7384867042654549, -0.6622757866045917, -0.5423400016641606, -0.39832550739577716, -0.24995236479597635, -0.11543409734651491, -0.010063829852212113, 0.054929052045060094, 0.07316868364169077, 0.043512923998968, -0.030000839819792288, -0.13863598049334747, -0.2698220763875584, -0.4083348732080416, -0.5376955666958638, -0.6416767064891277, -0.7057929612311591, -0.7186551644094739, -0.6730755995670661, -0.5668308065527399, -0.40301405365485776, -0.18994119038583707, 0.059391427310336004, 0.3282624686614977, 0.5975262879023154, 0.8471610876051272, 1.057944584331774, 1.2131236104754894, 1.2999406041690007, 1.3108870794436298, 1.244571678389746, 1.1061172377755533, 0.9070356679510113, 0.6645689306546366, 0.40052614222259286, 0.13968768926725195, -0.09211593497237193, -0.27011303613536164, -0.3727295070018322, -0.3835907014276261, -0.2932231173702715, -0.10030875899724727, 0.18762696056068248, 0.5541747788046731, 0.9746838521653763, 1.4175717824974947, 1.8462364357104208, 2.221455556656229, 2.5041188482167462, 2.6581058703765557, 2.6531045183106308], 'positive_zeros': ['1.39168437107874467355329039400249', '1.88641005498357129818911909852419', '3.25968842984587021400459646163421', '4.08366887893652301688017258527053', '5.38369649213999038657207478647857', '5.79714236523696041186868227552552', '6.48927764254152569556837746293035', '7.61394041385909770071204389597207', '8.228865174339714994616084457886565', '9.170922571533276151383834201758273'], 'prelabel': '2-1860-1860.1199-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.33380050491790897, 'root_number': '-0.50253990888620993198399413692930 - 0.86455401218006028049428848741001*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.33380050491790897', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39168437107874467355329039400', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88641005498357129818911909852', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.25968842984587021400459646163', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1199', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/df/c/1199/1'], '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': '2-1860-1860.1199-c0-0-2', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1860-1860.1199-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.33380050491790897, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39168437107874467355329039400', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1764169528326216623760250408595', 'Lhash_array': ['1764169528326216623760250408595'], 'factors': ['2-1860-1860.1199-c0-0-2'], 'label': '2-1860-1860.1199-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/df/c/1199/1'}