-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2029321063418643162363631532180', 'a10': [-0.6691306063588582, 0.7431448254773942], 'a2': [0.9781476007338057, 0.20791169081775934], 'a3': [0.6691306063588582, -0.7431448254773942], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [-0.5, 0.8660254037844386], 'a6': [0.8090169943749475, -0.5877852522924731], 'a7': [0.0, 0.0], 'a8': [0.8090169943749475, 0.5877852522924731], 'a9': [-0.10452846326765347, -0.9945218953682733], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9781476007338057, -0.20791169081775934]]], [3, [[1.0, 0], [-0.6691306063588582, 0.7431448254773942]]], [5, [[1.0, 0], [0.5, -0.8660254037844386]]], [31, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1319', 'coefficient_field': 'CDF', 'conductor': 1860, 'conductor_radical': 930, 'conjugate': '2209638383933003766272779724237', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 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, 0], [0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [-0.7044885311072939, 1.5823071476607464], [-0.6691306063588582, -0.7431448254773942]], [[1.0, 0], [-0.30901699437494745, -1.4538106560769117], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [1.3090169943749475, -0.9510565162951535], [0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0, 0], [-0.9135454576426009, 0.4067366430758002]], [[1.0, 0], [0.7736590696265117, -0.2513770698908791], [0.8090169943749475, -0.5877852522924731]], [[1.0, 0], [1.8916930583764064, -0.19882495225804087], [0.9781476007338057, -0.20791169081775934]], [[1.0, 0], [0, 0], [-0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0, 0.4158233816355187], [-1.0, 0]], [[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], [1.2225624520175484, 0.5443198732193534], [0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [1.2225624520175484, 1.3577931593709538], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0, 0], [0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0], [-0.30901699437494745, 0.9510565162951535]], [[1.0, 0], [0, 0], [-0.10452846326765347, 0.9945218953682733]], [[1.0, 0], [0.47814760073380563, -1.073937094602198], [-0.6691306063588582, -0.7431448254773942]], [[1.0, 0], [0.19098300562505258, 0.5877852522924731], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.9135454576426009, -0.4067366430758002], [0.6691306063588582, -0.7431448254773942]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-1860-1860.1319-c0-0-2', 'leading_term': '2.42087412731289169397212453179', '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/b/1319/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.4208741273128918, 2.425981483198375, 2.455598632916273, 2.5066914907562343, 2.5748744760039495, 2.654924820744716, 2.7412574130840017, 2.8282841727245995, 2.9106464362109876, 2.9833466487128626, 3.041815982898806, 3.081949180036038, 3.100127730555602, 3.0932431633315702, 3.0587254548199683, 2.9945772895975877, 2.899412442084271, 2.77249526691278, 2.6137777227035968, 2.4239302222187997, 2.2043627345085506, 1.9572328713815352, 1.6854381243071053, 1.3925899541592734, 1.0829680605727579, 0.7614538585795478, 0.4334429551383127, 0.1047372316697338, -0.21858201858568896, -0.5302976010186824, -0.8242134531259718, -1.0943212998171035, -1.3349723357013916, -1.5410487609348045, -1.7081295652631625, -1.8326446987652132, -1.912011712731689, -1.9447491198721616, -1.9305611224062682, -1.8703889940759901, -1.7664252728732237, -1.6220880103818696, -1.4419536056989732, -1.231648191154336, -0.9976990878914439, -0.7473494574287893, -0.48834087899909456, -0.22867011500054238, 0.023672281172661336, 0.260972678645217, 0.4760646616453727, 0.6625885884883633, 0.8152299193654242, 0.9299260529347656, 1.0040320932369795, 1.03643709741693, 1.0276239150117163, 0.9796676845138731, 0.8961703453284028, 0.7821310762619048, 0.6437552907610244, 0.48820759494451527, 0.32331682686993884, 0.15724381813730345, -0.0018752751423515319, -0.1462954575724014, -0.2690233629462121, -0.3641552963403366, -0.42717657496315653, -0.45520678040666757, -0.4471771839799715, -0.4039289907576352, -0.32822410350148634, -0.22466373491977065, -0.09951426171879678, 0.03955594782619762, 0.18382057842121077, 0.32390782904713605, 0.45026487038197366, 0.553654460688559, 0.6256612136985367, 0.6591832683874972, 0.6488844354759559, 0.5915823894157007, 0.48655018695481844, 0.3357113165690973, 0.14371254905632147, -0.08213606083160427, -0.3320587667710002, -0.5941475731154322, -0.8548229955429149, -1.0994068422983678, -1.3127853110545558, -1.4801349896733051, -1.5876796700002824, -1.6234425276882367, -1.5779564344300452, -1.4448951337554057, -1.2215898314949987, -0.9093994426493368, -0.5139082186777015, -0.044931577854461544, 0.4836805919832258, 1.05444444724922, 1.6468377955469813, 2.2380719671042106, 2.8040114336084363, 3.3202039019782705, 3.7629762848687225, 4.110546503102499, 4.344097883891181, 4.448762261535599, 4.414459925769516, 4.2365493261863065, 3.9162468173652987, 3.460786463839272, 2.8833016257077686, 2.202423200349814, 1.4416033873436005, 0.6281879823266614, -0.20772623967460457, -1.0346002542673716, -1.8208686138173147, -2.5363957720241834, -3.1539018789599136, -3.650286102974918, -4.007778327262489, -4.214856568628191, -4.266877475819804, -4.166380388423777, -3.9230410936147124, -3.5532688645313075, -3.0794587309966084, -2.5289292661915717, -1.932593481701667, -1.3234257359942538, -0.7347999785047404, -0.1987833996244242, 0.25552596334607575, 0.6035292874909487, 0.8264412824298816, 0.9123149925690625, 0.8567172326655123, 0.6630123722622917, 0.3422325292282395, -0.08746569543979374, -0.601735193021437, -1.1713183748467835, -1.7636086432013023, -2.344411880818805, -2.8798138903359245, -3.3380520696156766, -3.6912875268241536, -3.917177581413526, -4.000158095622291, -3.9323599322467433, -3.7141033125360194, -3.353936937893794, -2.868214186966756, -2.280225080518649, -1.618928503018548, -0.9173528603428729, -0.21075350165273538, 0.4653694211076224, 1.0772794472431286, 1.5949224050087707, 1.9936426285908448, 2.255594792896428, 2.3707660696496307, 2.3375453531214427, 2.162802463346166, 1.8614690069937634, 1.455642267685436, 0.9732623227914571, 0.4464387726484483, -0.09047462380935577, -0.6029428998415216, -1.0583264829738213, -1.4278455615367616, -1.6883120931338718, -1.8235225757738431, -1.8252247154737773, -1.6935967600398092, -1.4372080058327168, -1.0724610149401832, -0.6225484195659308, -0.11598779979920446, 0.41517496327614345, 0.9373819956438875, 1.4176729693742045, 1.8257547915534569, 2.1359001545406637, 2.32855388470722, 2.391544128872102, 2.3208203182090976, 2.12067001075303, 1.8034002306897832, 1.3885036417660872, 0.9013635490581804, 0.37158209097808853, -0.1689589792819541, -0.6881775324958456, -1.1558732572659491, -1.5456751177082622, -1.836724941302463, -2.0149852642760417, -2.074084452209258, -2.0156430283987485, -1.8490600468837017, -1.590774907401277, -1.263055748655362, -0.8923980208291706, -0.507643768047252, -0.13795163851719214, 0.18924173368756242, 0.45012738763172067, 0.6261640456141955, 0.7053379982567484, 0.6829547332792297, 0.5619068820362632, 0.35239988247756576, 0.07115513958674763, -0.2598523006097473, -0.6150311188143334, -0.9670684882605967, -1.2889456351336044, -1.5559283163102358, -1.7473875186459553, -1.848317347360472, -1.8504384851592515, -1.7528053204046956, -1.5618707897198127, -1.2910026018971827, -0.9594849444195002, -0.5910780583904026, -0.21224135351480686, 0.1498485010645943, 0.4693368372843601, 0.7236345478839051, 0.895118915946217, 0.9724618133157887, 0.9514824701069504, 0.8354571984060722, 0.6348591761394601, 0.36654466505089983, 0.05244460791405427, -0.28214082316341194, -0.6105154815927816, -0.9066768740772638, -1.1473598984966005, -1.3138739809252458, -1.393586942781795, -1.3809346115425993, -1.2778707494902546, -1.0937147543491486, -0.8444016021911203, -0.5511860838735785], 'positive_zeros': ['1.60085205107249715092043955546644', '2.80687947084866682571113686745760', '3.74928230218081610832258352816120', '4.37824861667948162738485138869158', '5.07719892886026270354526938511269', '5.92319162693235298190935485092476', '7.01671682434634101823033726430613', '8.051508531909118500601151671906525', '8.485152551394022483689732373390747', '9.510032821812701749201237547937747'], 'prelabel': '2-1860-1860.1319-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.01984676550544969, 'root_number': '0.99223491238613613050415204504255 - 0.12437796686743499309531955756122*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.019846765505449688', 'prec': 70}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60085205107249715092043955547', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.80687947084866682571113686746', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.74928230218081610832258352816', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9282609234973845, 'bad_primes': [2, 3, 5, 31], 'central_character': '1860.1319', 'conductor': 1860, 'conductor_radical': 930, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1860/1/df/b/1319/1'], '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': '2-1860-1860.1319-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': '2-1860-1860.1319-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9634629850167491, 'root_angle': -0.01984676550544969, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60085205107249715092043955547', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2029321063418643162363631532180', 'Lhash_array': ['2029321063418643162363631532180'], 'factors': ['2-1860-1860.1319-c0-0-2'], 'label': '2-1860-1860.1319-c0-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1860/1/df/b/1319/1'}