-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '865891973028780518658825164471', 'a10': [-0.5, 0.8660254037844386], 'a2': [-1.0, 0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0.5, -0.8660254037844386], 'a6': [0, 0], 'a7': [0, 0], 'a8': [3.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.5642081874154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '1323.802', 'coefficient_field': 'CDF', 'conductor': 1323, 'conductor_radical': 21, 'conjugate': '1242766495891803034366939500857', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-2.5, -4.330127018922194]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5, -4.330127018922194], [-5.5, 9.526279441628825]], [[1.0, 0], [2.5, 4.330127018922194], [-6.5, 11.258330249197702]], [[1.0, 0], [1.5, -2.598076211353316], [-8.5, -14.722431864335457]], [[1.0, 0], [-0.5, -0.8660254037844386], [-9.5, 16.454482671904334]], [[1.0, 0], [-1.5, 2.598076211353316], [-11.5, -19.91858428704209]], [[1.0, 0], [0.5, -0.8660254037844386], [-14.5, -25.11473670974872]], [[1.0, 0], [0, 0], [31.0, 0]], [[1.0, 0], [1.5, 2.598076211353316], [-18.5, 32.04293994002423]], [[1.0, 0], [-2.5, -4.330127018922194], [-20.5, 35.50704155516198]], [[1.0, 0], [-0.5, 0.8660254037844386], [-21.5, -37.239092362730865]], [[1.0, 0], [0, 0], [47.0, 0]], [[1.0, 0], [4.5, -7.794228634059948], [-26.5, -45.89934640057525]], [[1.0, 0], [0, 0], [59.0, 0]], [[1.0, 0], [-14.0, 0], [61.0, 0]], [[1.0, 0], [-4.0, 0], [67.0, 0]], [[1.0, 0], [-12.0, 0], [71.0, 0]], [[1.0, 0], [-1.5, 2.598076211353316], [-36.5, -63.21985447626402]], [[1.0, 0], [-8.0, 0], [79.0, 0]], [[1.0, 0], [-4.5, 7.794228634059948], [-41.5, -71.88010851410841]], [[1.0, 0], [-6.5, -11.258330249197702], [-44.5, 77.07626093681505]], [[1.0, 0], [4.5, -7.794228634059948], [-48.5, -84.00446416709055]], [[1.0, 0], [-8.5, -14.722431864335457], [-50.5, 87.4685657822283]], [[1.0, 0], [0.5, -0.8660254037844386], [-51.5, -89.20061658979718]], [[1.0, 0], [-8.5, -14.722431864335457], [-53.5, 92.66471820493493]], [[1.0, 0], [-4.5, 7.794228634059948], [-54.5, -94.39676901250381]], [[1.0, 0], [0.5, 0.8660254037844386], [-56.5, 97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-1323-63.25-c1-0-13', 'leading_term': '0.9498928835141494397746716623330403671943764166674679479', '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/1323/2/h/a/802/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.9498928835141495, 0.9170437663711446, 0.8758883125555529, 0.8262221417652167, 0.7677429118870331, 0.7000935539707462, 0.6229129531985321, 0.5358909546264647, 0.438824644130886, 0.33167315095597133, 0.21460862974868755, 0.08806150963269922, -0.0472415206927401, -0.19024802014134437, -0.3395597994001697, -0.4934232630220621, -0.6497307986750627, -0.806033794607005, -0.9595677178880017, -1.1072895000809588, -1.24592724381937, -1.3720419801777435, -1.4821008752402447, -1.5725609121160085, -1.639961672763823, -1.6810254262661084, -1.692762312778441, -1.672578013050709, -1.6183809309629424, -1.528685610129143, -1.402708874210388, -1.2404550420780998, -1.0427865395868656, -0.8114763231655178, -0.5492387571663799, -0.2597359533827154, 0.052442910848911985, 0.3818311334250051, 0.722163949426679, 1.0664880872801263, 1.4073006096769884, 1.7367151807047978, 2.0466528167975673, 2.3290530969808665, 2.57610076748889, 2.7804617195756087, 2.9355214905506215, 3.035618779350348, 3.0762660194261655, 3.0543488491746893, 2.968296393139725, 2.8182146373917183, 2.605975861846494, 2.3352580818390374, 2.011529739989001, 1.641976453544056, 1.2353684253315573, 0.8018691189953744, 0.35278792048553254, -0.0997183132511002, -0.5429877599815738, -0.964231082814078, -1.3509328589500258, -1.6912644428570243, -1.9744945057951406, -2.191382715734988, -2.3345417422283026, -2.39875303616139, -2.3812226722905137, -2.2817649594783416, -2.102903502865193, -1.8498819027943445, -1.5305792317893954, -1.1553287544877415, -0.7366419360750107, -0.2888434941736565, 0.17237305493947738, 0.6304563736028853, 1.0685586087606316, 1.4701280887036239, 1.819512339208367, 2.102548947590753, 2.307121236248346, 2.4236560440202055, 2.4455421902533296, 2.3694504107358356, 2.1955386640276116, 1.9275306274183426, 1.5726598100242568, 1.141476845757011, 0.6475229984861345, 0.1068784979018039, -0.46240020727591835, -1.040935083907313, -1.6087493324222184, -2.1460309970532325, -2.6339073124061962, -3.0551982508124778, -3.395117558341543, -3.641890758737066, -3.787262169851553, -3.8268668601317137, -3.7604485542679487, -3.59191059773648, -3.32919397503959, -2.983983764644551, -2.571252987840254, -2.108660229427881, -1.6158243284245817, -1.1135055187184717, -0.6227273302550668, -0.16387706990114376, 0.24417542671362907, 0.5849009901291383, 0.844838231911214, 1.0141901331529144, 1.0872609559171003, 1.0627111399605615, 0.9436158987666261, 0.7373221695683431, 0.45510799563398124, 0.11165788121161932, -0.2756233018271112, -0.6874271185144766, -1.1034515006469936, -1.5033610545336193, -1.8677518300835882, -2.179073672790282, -2.4224646350362646, -2.586455589606147, -2.663509042465444, -2.6503639432285393, -2.548167691447397, -2.3623870920797847, -2.102501207357627, -1.781490318480075, -1.4151459616643878, -1.021236661026385, -0.6185720080165389, -0.22601366697208836, 0.13851464964357965, 0.4589654413597154, 0.7220031891440233, 0.9176917553497628, 1.0399949663365156, 1.0870616033083491, 1.061277468170063, 0.9690798145475115, 0.8205425712049806, 0.6287537194584693, 0.40901819164913367, 0.17793003876959598, -0.047634252851199724, -0.25154404973634464, -0.41940499301677775, -0.5394532062636577, -0.6032994383538635, -0.6064769909624149, -0.5487578279053185, -0.43421412647339175, -0.27101702771957564, -0.07097967671828238, 0.1511330545324787, 0.37849139415546756, 0.5932347002378595, 0.7775933516687068, 0.9150324117469553, 0.9913479711967962, 0.9956481015149213, 0.9211554626177909, 0.7657776297888725, 0.5324037156242494, 0.22890122389740516, -0.13219554548277668, -0.5342957948941223, -0.9576330859334113, -1.3803713421295816, -1.779875521176984, -2.1340745970021513, -2.422836605427753, -2.6292722206980463, -2.740884989607185, -2.7504930144335935, -2.6568583040559335, -2.464975667308421, -2.1859920931671866, -1.8367490045085226, -1.4389623636270552, -1.0180780163439, -0.6018605228632268, -0.21879172268924182, 0.10363076545945411, 0.3405959749236447, 0.47158060820993086, 0.4817491784274477, 0.3630628067350754, 0.11502095124589475, -0.2550198842537771, -0.7319826627954418, -1.2936673478962355, -1.9117877369627678, -2.553398876195791, -3.182641528488581, -3.762709118792721, -4.2579266891173555, -4.635821772188222, -4.869064498922453, -4.937159038368477, -4.827780532007248, -4.537670477147027, -4.073028055131726, -3.4493638254759427, -2.690813845203957, -1.828944740049912, -0.9011115673971415, 0.0515414916766573, 0.986324308185341, 1.8613577644355979, 2.637905299660031, 3.2825391335038474, 3.7690091703855484, 4.0796988079602485, 4.206575556990508, 4.151574193621188, 3.9263843575878203, 3.551651015499309, 3.0556327705896438, 2.4723973118161853, 1.8396631439600633, 1.1964201539205133, 0.5804769455269282, 0.02608909728543144, -0.4381809890145679, -0.791235116581315, -1.0207257698844618, -1.1237724085222176, -1.1070576488681036, -0.9862927983781047, -0.7850828090687475, -0.5332599153301005, -0.26479045244997323, -0.015388265699916618, 0.18001126235526582, 0.28975168511600674, 0.2877653484288118, 0.1555380643411521, -0.11640516142536347, -0.5275972788388485, -1.0673761221814864, -1.7153061365781823, -2.4422558782823525, -3.212068943047094, -3.9837262515245886, -4.71386416870026, -5.359488053268571, -5.880706280026658, -6.243306644851767], 'positive_zeros': ['0.68306832566709173924618476460401', '2.09978212722409360862569811087612', '3.44407408799182771456716684405007', '4.43129392912592130279411663121692', '5.34319958937089259603435096709968', '6.52643661197486758932776076302036', '7.10730281059877771206481189488336', '8.180150274112877491943119789698524', '8.893537615000344072015385619257649', '9.452751642132007660349974921531767'], 'prelabel': '2-1323-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.15145701721900337, 'root_number': '0.8889191217005998862406421276894234741749644438419081703 - 0.4580641822660161762428872949230161411327298952261922774*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.07572850860950167', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68306832566709173924618476460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09978212722409360862569811088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44407408799182771456716684405', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 10.5642081874154, 'bad_primes': [3, 7], 'central_character': '63.25', 'conductor': 1323, 'conductor_radical': 21, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/h/a/802/1'], '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': '2-1323-63.25-c1-0-13', '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': '2-1323-63.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.250262787439717, 'root_angle': -0.07572850860950169, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68306832566709173924618476460', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '865891973028780518658825164471', 'Lhash_array': ['865891973028780518658825164471'], 'label': '2-1323-63.25-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/h/a/802/1'}