-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1630597413126287896714079781253', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.2360679774997898, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 76.46474497557813, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '9576.1', 'coefficient_field': 'CDF', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.2360679774997898, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.0, 0], [11.0, 0]], [[1.0, 0], [4.47213595499958, 0], [13.0, 0]], [[1.0, 0], [1.2360679774997898, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.0, 0], [23.0, 0]], [[1.0, 0], [-5.708203932499369, 0], [29.0, 0]], [[1.0, 0], [1.5278640450004206, 0], [31.0, 0]], [[1.0, 0], [-8.47213595499958, 0], [37.0, 0]], [[1.0, 0], [8.47213595499958, 0], [41.0, 0]], [[1.0, 0], [-8.0, 0], [43.0, 0]], [[1.0, 0], [-1.7082039324993692, 0], [47.0, 0]], [[1.0, 0], [-11.23606797749979, 0], [53.0, 0]], [[1.0, 0], [8.94427190999916, 0], [59.0, 0]], [[1.0, 0], [13.416407864998739, 0], [61.0, 0]], [[1.0, 0], [1.5278640450004206, 0], [67.0, 0]], [[1.0, 0], [-7.708203932499369, 0], [71.0, 0]], [[1.0, 0], [-12.47213595499958, 0], [73.0, 0]], [[1.0, 0], [-4.0, 0], [79.0, 0]], [[1.0, 0], [13.70820393249937, 0], [83.0, 0]], [[1.0, 0], [-4.47213595499958, 0], [89.0, 0]], [[1.0, 0], [17.41640786499874, 0], [97.0, 0]], [[1.0, 0], [10.76393202250021, 0], [101.0, 0]], [[1.0, 0], [-4.0, 0], [103.0, 0]], [[1.0, 0], [18.18033988749895, 0], [107.0, 0]], [[1.0, 0], [-10.0, 0], [109.0, 0]], [[1.0, 0], [7.23606797749979, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 103, 'label': '2-9576-1.1-c1-0-103', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bi/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-8.70249792763394e-61, 0.22069407419527476, 0.4397691102403862, 0.6555649626094384, 0.8663430700300582, 1.0702564587130736, 1.2653300323705556, 1.449453399038682, 1.620387650024106, 1.775786641016212, 1.9132324971567705, 2.0302843215301043, 2.1245384583054476, 2.1936981574983005, 2.235650104649161, 2.2485450048604316, 2.2308792335210597, 2.181574473998355, 2.1000522472726093, 1.9863002955285651, 1.840927910104239, 1.6652074952361782, 1.4610999349748228, 1.2312616833080439, 0.9790319271656444, 0.7083986762920365, 0.42394320748271525, 0.13076292430940284, -0.16562662558776184, -0.4594091217063463, -0.7446020534271844, -1.0152056256939768, -1.265362423437611, -1.4895236570410841, -1.6826172860855806, -1.840212907767615, -1.9586780237444368, -2.0353201859237062, -2.0685095851100916, -2.0577768987506873, -2.003881661710409, -1.9088470668551343, -1.77595793282489, -1.6097195798140007, -1.4157765079201545, -1.2007910467982683, -0.9722835032538552, -0.7384367323607868, -0.5078694502058756, -0.2893839415966627, -0.09169504149519332, 0.07685166774161366, 0.20856365006538755, 0.2966778137846048, 0.3356198310319186, 0.3212367271514105, 0.2509934681292033, 0.12412501061859839, -0.05826363206451246, -0.29315533155456297, -0.575641092163619, -0.89900492204598, -1.2548734665956998, -1.6334282371637319, -2.023675914830442, -2.413769894352103, -2.7913740477344375, -3.1440577208762406, -3.4597093179597063, -3.726954557498689, -3.935564671438776, -4.076839520682982, -4.143950856010679, -4.132231781922141, -4.039399880101332, -3.865703393643947, -3.6139823144078784, -3.289639082674487, -2.9005168086572986, -2.456686348791779, -1.9701470908880854, -1.4544497853697242, -0.9242530638033191, -0.39482826979231145, 0.11847024379819612, 0.6007502461826574, 1.0381218149994973, 1.4182117000072383, 1.7306313005895861, 1.9673788480866647, 2.1231583671240695, 2.1956007546958785, 2.185375779571824, 2.096187852217183, 1.934652901541156, 1.7100584490938338, 1.434013804623509, 1.120002018455996, 0.782849611891045, 0.4381339680537235, 0.10155141805354558, -0.21172866037675278, -0.48769713244089874, -0.7140989944946268, -0.8809620207909926, -0.9810364173095492, -1.0101249086608908, -0.9672868497308892, -0.8549049594863748, -0.6786089290819662, -0.44705623280782636, -0.1715767138385313, 0.1343063444522025, 0.45546019362672846, 0.7758080680622927, 1.0790483279014167, 1.3493964355743246, 1.5723171159463072, 1.735213679445483, 1.8280425964045555, 1.8438239954204514, 1.7790227469052937, 1.6337800460643799, 1.4119817249589623, 1.1211566426609945, 0.7722061213093809, 0.37897317624982346, -0.042332126197741196, -0.47382781855953876, -0.8967461924450165, -1.2922765519881354, -1.642426701833077, -1.9308635528255735, -2.1436932848628207, -2.270143426056513, -2.303112952018026, -2.239561951747084, -2.0807193350612523, -1.8320951806565022, -1.503293287311567, -1.1076288858347045, -0.661565855518258, -0.18399671300803744, 0.30460334024387975, 0.7831103259355907, 1.230730344828145, 1.6279773181382475, 1.957602662978953, 2.2054313262062784, 2.3610622313124376, 2.4183969558258367, 2.375968121107906, 2.2370482108757614, 2.0095299205764077, 1.7055801896395726, 1.3410812492821331, 0.9348827759919778, 0.5078990279394842, 0.0820931458617834, -0.32060282944840945, -0.6793795987092255, -0.9755997641046635, -1.1937515407814863, -1.3222579178148977, -1.3540985859999244, -1.287210653830388, -1.1246447680745892, -0.8744652414875168, -0.5493955840639508, -0.16622379711971844, 0.2550057409936935, 0.6919756448156285, 1.1212064241541404, 1.5192399093644477, 1.8638356114777888, 2.135118850509975, 2.3166210482406417, 2.396157266564965, 2.3664936951418665, 2.225768009930357, 1.9776378505800292, 1.6311464910212412, 1.2003094032077248, 0.7034400809227013, 0.16224742302438644, -0.39925057925194857, -0.9559418370468649, -1.4829013198209486, -1.956671556999083, -2.356474874009289, -2.66529255818327, -2.870752470783516, -2.9657761759419925, -2.948948984562025, -2.8245907908034296, -2.6025214611659377, -2.297530981134793, -1.928580684902139, -1.5177768039101938, -1.0891704337541863, -0.6674480971369893, -0.2765837736515783, 0.061473848423144795, 0.3280062880674308, 0.5085549205803447, 0.593716908868983, 0.579661319367708, 0.4683344133585057, 0.26734012915043426, -0.010500190000183124, -0.34788670825457785, -0.7240394711198853, -1.1159019679811697, -1.499483368976354, -1.8512642705085465, -2.149586268886217, -2.3759456253040647, -2.516115761919979, -2.5610321558011413, -2.507385941450299, -2.357888528640552, -2.121187927857494, -1.8114372362144249, -1.447535761029065, -1.052082400466793, -0.650098045622341, -0.26758789661085847, 0.06997516651995618, 0.33915930294439967, 0.5199868877676695, 0.5971687971459178, 0.5610856291969281, 0.4084553030044353, 0.14264381064500145, -0.22640400199505883, -0.6826150077965849, -1.204598965130183, -1.7667782646583707, -2.340775129491493, -2.896979322286324, -3.406207862717638, -3.8413617198261223, -4.178983375046371, -4.4006236974893485, -4.493936548785178, -4.45343443246162, -4.280857515457773, -3.9851304137953, -3.581904990152944, -3.0927116719471277, -2.543765033154216, -1.9644901995988533, -1.3858537670807114, -0.8385952969295449, -0.35146227507155053, 0.050447790303679275, 0.3471398252464045], 'positive_zeros': ['1.28631455136984362766715061694419', '2.36809958452679431388331325288780', '2.70520558057069912964138036902930', '3.92647562332410808656653822711862', '4.70221612849787860038625425424364', '5.22984499420197939245598446605293', '5.94849896135790945206059990783793', '6.67391760073726690808913027879464', '7.41551329369254784495455900499613'], 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28631455136984362766715061694', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.36809958452679431388331325289', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70520558057069912964138036903', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 76.46474497557813, 'bad_primes': [2, 3, 7, 19], 'central_character': '1.1', 'conductor': 9576, 'conductor_radical': 798, 'degree': 2, 'index': 103, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9576/2/a/bi/1/2'], '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': '2-9576-1.1-c1-0-103', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9576-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.744412214413163, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28631455136984362766715061694', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1630597413126287896714079781253', 'Lhash_array': ['1630597413126287896714079781253'], 'label': '2-9576-1.1-c1-0-103', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9576/2/a/bi/1/2'}